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13200	https://www.studocu.com/ph/document/davao-medical-school-foundation/dentistry-1-2/wheelers-dental-anatomy-part-2-incisors-canines/61168543	Wheeler's Dental Anatomy - Part 2: Maxillary & Mandibular Incisors - Studocu Skip to document Teachers University High School Discovery Sign in Welcome to Studocu Sign in to access study resources Sign in Register Guest user Add your university or school 0 followers 0 Uploads 0 upvotes New Home My Library AI Notes Ask AI AI Quiz Chats Recent You don't have any recent items yet. My Library Courses You don't have any courses yet. Add Courses Books You don't have any books yet. Studylists You don't have any Studylists yet. Create a Studylist Home My Library Discovery Discovery Universities High Schools Teaching resources Lesson plan generator Test generator Live quiz generator Ask AI Wheeler's Dental Anatomy - Part 2: Maxillary & Mandibular Incisors This document contains a summary of Wheeler's Dental Anatomy for chapter of...Maxillary and Mandibular central incisors, lateral incisors and Canines View more Original title: Wheeler's Dental Anatomy - Part 2 ( Incisors - Canines) Course Dentistry 1-2 153 documents University Davao Medical School Foundation Academic year:2022/2023 Uploaded by: Anonymous Student Davao Medical School Foundation Comments Please sign in or register to post comments. Report Document Students also viewed Dental Materials Review: Instruments and Properties Overview IHS-Reviewer (BONE - Midterm Review on Skeletal System & Joints) ### ANTH 101 - The Impact of Globalization on Contemporary Society Science, Technology, and Society: A Historical Overview Pur Com-Reviewer: Key Concepts in Purposive Communication RPH 101: Module 1 - Introduction to History in Purposive Communication Related documents Snell's Anatomy - Lower Limb Osteology and Thigh Overview Snell's Anatomy - Thorax Overview and Osteology (Chapter 3) Orban's Oral Histology: Mucous Membranes Overview - Finals S.Y. 2022-2023 Wheeler's Dental Anatomy - Part 3 (Premolars and Molars Overview) GENANA Final Exam Notes on Head and Neck Anatomy DMD Final Exam: Synthesis on Cancer Genetics and Gene Mutations Related Studylists Dental Notes Dentistry 1-2 - 05/03/2025 DENT 205 Preview text Maxillary Central Incisor maxillary central incisor is the widest mesiodistally of any of the anterior teeth labial face is less convex than that of the maxillary lateral incisor or canine, which gives the central incisor a squared or rectangular appearance crown nearly always looks symmetrical and regularly formed mesial incisal angle is relatively sharp, the distal incisal angle rounded enamel surface is relatively smooth. Tooth Numbering system Universal Notation system 8, Zsigmondy/Palmer Notation System 1, Federation Dentaire Internationale (FDI) system 11, First Evidence of Calcification 3-4 months Crown Completion 4-5 years Eruption 7-8 years Root Completion 10 years Labial Aspect o crown of the average central incisor will be 10 to 11 mm long from the highest point on the cervical line to the lowest point on the incisal edge CROWN Mesial outline: - slightly convex Distal outline : is more convex than the mesial outline, with the crest of curvature higher toward the cervical line. Incisal outline: regular and straight in a mesiodistal direction after the tooth has been in function long enough to obliterate the mamelons. Cervical outline: Semicircular direction with the curvature rootwise, from the point at which the root outline joins the crown mesially to the point at which the root outline joins the crown distally. ROOT labial aspect: cone-shaped, in most instances with a relatively blunt apex outline mesially and distally is regular Lingual Aspect lingual outline: - of the maxillary central incisor is the reverse of that found on the labial aspect Cervical outline: below the cervical line a smooth convexity is to be found; this is called the cingulum o Mesially and distally confluent with the cingulum are the marginal ridges. Between the marginal ridges, below the cingulum, a shallow concavity is present called the lingual fossa o Crown calibration at the two labial line angles is greater than the calibration at the two lingual line angles o Lingual portion of the root is narrower than the labial portion. o mesial side of this triangle is slightly longer than the distal side Mesial Aspect o crown is wedge-shaped, or triangular, with the base of the triangle at the cervix and the apex at the incisal ridge CROWN labial outline: from the crest of curvature to the incisal ridge is very slightly convex lingual outline: convex at the point where it joins the crest of curvature at the cingulum; it then becomes concave at the mesial marginal ridge and slightly convex again at the linguoincisal ridge and the incisal edge o Cervical curvature is greater on the mesial surface of this tooth than on and surface of any other tooth in the mouth. ROOT o mesial aspect is cone shaped o apex of the root is usually bluntly rounded. ORAL ANATOMY MODULE 1: PERMANENT MAXILLARY INCISORS Distal Aspect o crown gives the impression of being somewhat thicker toward the incisal third. Because of the slope of the labial surface distolingually, more of that surface is seen from the distal aspect; this creates the illusion of greater thickness o curvature of the cervical line outlining the CEJ is less in extent on the distal than on the mesial surfaces Incisal Aspect o labial face of the crown is relatively o broad and flat in comparison with the lingual surface, especially toward the incisal third. o outline of the lingual portion tapers lingually toward the cingulum o mesiolabial and distolabial line angles are prominent o The mesiodistal calibration of the crown at the labial line angles is greater than the same calibration at the lingual line angles. o crown conforms to a triangular outline reflected by the outline of the root cross section at the cervix mentioned earlier. Maxillary Lateral Incisor supplements the central incisor in function, the crowns bear a close resemblance. smaller in all dimensions except root length vary in form more than any other tooth in the mouth except the third molar If the variation is too great, it is considered a developmental anomaly. o common situation is to find maxillary lateral incisors with a nondescript, pointed form; such teeth are called peg- shaped laterals o lateral incisors are missing entirely 7 ; in these cases, the maxillary central incisor may be in contact distally with the canine. o Presence of a palatogingival groove in maxillary incisors may be a predisposing factor in localized periodontal disease. This groove is also referred to as the palatoradicular groove. enamel surface is relatively smooth. Tooth Numbering system Universal Notation system 7, Zsigmondy/Palmer Notation System 2, Federation Dentaire Internationale (FDI) system - 12, 22 First Evidence of Calcification 10-12 months Crown Completion 4-5 years Eruption 8-9 years Root Completion 11 years Labial Aspect o more curvature, with a rounded incisal ridge and rounded incisal angles mesially and distally o relatively narrow mesiodistally, usually about 2 mm narrower than the central incisor. CROWN mesial outline: more rounded mesioincisal angle. crest of contour mesially is usually at the point of junction of the middle and incisal thirds so-called square forms, the mesioincisal angle is almost as sharp as that found on most maxillary central incisors more rounded mesioincisal angle distal outline: always more rounded crest of contour is more cervical, usually in the center of the middle third. Labial surface: more convex than that of the central incisor except in some square and flat-faced forms. ROOT o root length is greater in proportion to its crown length than that of the central incisor o The root is often about 1 times the length of the crown. o root tapers evenly from the cervical line to a point approximately two thirds of its length apically. o Most cases, it curves sharply from this location in a distal direction and ends in a pointed apex. Lingual Aspect o mesial and distal marginal ridges o are marked o cingulum is usually prominent, with a tendency toward deep developmental grooves within the lingual fossa, where it joins the cingulum o linguoincisal ridge is well developed o lingual fossa is more concave and circumscribed than that found on the central incisor. Mesial Aspect Mandibular Central Incisor smallest tooth in the dental arches crown has little more than half the mesiodistal diameter of the maxillary central incisor; however, the labiolingual diameter is only about 1 mm less. single root is very narrow mesiodistally and corresponds to the narrowness of the crown, although the root and crown are wide labiolingually. The length of the root is as great as, if not greater than, that of the maxillary central incisor. Tooth Numbering system Universal Notation system 24, Zsigmondy/Palmer Notation System 1, Federation Dentaire Internationale (FDI) system 31, First Evidence of Calcification 3-4 months Crown Completion 4-5 years Eruption 6-7 years Root Completion 9 years Labial Aspect o Bilaterally symmetrical o Incisal ridge – straight and approx.. at right angles o Narrowest tooth mesiodistally of all permanent teeth o root outlines are straight with the o mesial and distal outlines of the crown down to the apical o portion. o The apical third of the root terminates in a small, o pointed taper, in most cases curving distally Lingual Aspect o lingual surface of the crown is smooth, with very o slight concavity at the incisal third between the inconspicuous marginal ridges o marginal ridges – more prominent near the incisal ridges o no developmental lines mark the cingulum o becomes flat and then convex o shallow lingual fossa o smooth cingulum Mesial Aspect o wedge-shaped or triangular o incisal ridge is rounded or worn flat o center is usually lingual to the center of the root Labial Surface: o Inclined lingually outline – almost straight o Near cervical third – convex o Cervical line – convex incisally Lingual surface: o Lingual margin – “S” shaped Distal Aspect o Cervical line curves less incisally o developmental depression on the distal surface of the root may be more marked, with a deeper, more well-defined developmental groove at its center Incisal Aspect o Bilateral symmetry o Incisal edge – right angles to a line bisecting the crown labiolingually o Labiolingual diameter greater than mesiodistal diameter TRAITS Maxillary Central Incisor Crown wider mesiodistally than labiolingually Pronounced lingual fossa often with lingual pit More prominent cingulum and marginal ridges Mandibular Central Incisor Crown wider labiolingually than mesiodistally Shallow lingual fossa without grooves or pits Not Prominent ORAL ANATOMY MODULE 2 : PERMANENT MANDIBULAR INCISORS 1 ST SEMESTER  MIDTERMS  S. 2022 – 2023 TRANS : KYLLAH KRISTIANNE ONES Mandibular Lateral Incisor resembles the mandibular central incisor so closely that only a brief description of each aspect of the lateral incisor is necessary supplements CI in function mandibular lateral incisor is somewhat larger than the mandibular central incisor (compare measurements), but generally speaking, its form closely resembles that of the mandibular central incisor Tooth Numbering system Universal Notation system 23, Zsigmondy/Palmer Notation System 2, Federation Dentaire Internationale (FDI) system 32, 42 First Evidence of Calcification 3-4 months Crown Completion 4-5 years Eruption 7-8 years Root Completion 10 years Labial Aspect o Incisal ridge (usually straight) slopes downward in a distal direction o Crown tilts distally (distolingual twist) o More rounded Lingual Aspects o Incisal ridge (usually straight) slopes downward in a distal direction o Cingulum is distal to center o Longer mesial marginal ridges o Shorter distal marginal ridges Mesial and Distal Aspects Mesial o Mesial side is longer than the distal side Distal surface: o deep concavity immediately above cervical line Incisal Aspect o Best view to identify the tooth (esp. if its right or left ) o Incisal edge follows the curvature of mandibular arch (distolingual twist) MANDIBULAR CENTRAL VS MANDIBULAR LATERAL INCISOR CROWN CENTRAL INCISOR LATERAL INCISOR Labial Aspect Symmetry Bilaterally symmetrical Asymmetrical Mesio-incisal angle Right angle ( degrees) Round Disto-incisal angle Right angle ( degrees) Round Mesial contact Incisal 3rd Incisal 3rd Distal contact Incisal 3rd Incisal 3rd Incisal Aspect Incisal ridge form right angle with labio- lingual bisecting line Incisal ridge twisted n crown Incisal Aspect labiolingual dimension is greater than the mesiodistal. Tip of cusp is labial to center of crown labiolingually and mesial to the center The crown of this tooth gives the impression of having the entire distal portion stretched to make contact with the first premolar. line bisecting the cusp and cusp ridges drawn in the mesiodistal direction is almost always straight distal slope is longer than mesial slope Mandibular Canine Tooth Numbering system Universal Notation system - 27, 22 Zsigmondy/Palmer Notation System - 3, Federation Dentaire Internationale (FDI) system - 43, First Evidence of Calcification 4-5 months Crown Completion 6-7 years Eruption 9-10 years Root Completion 12 – 14 years mandibular canine crown is narrower mesiodistally than that of the maxillary canine, just as long in most instances and in many instances is longer by 0 to 1 mm Function: cut, pierce or shear food Root Variation – Bifurcated roots Labial Aspect The essential differences between mandibular and maxillary canines viewed from the labial aspect may be described as follows: The crowns of the mandibular canines appear longer. Sometimes they are longer, but the effect of greater length is emphasized by the narrowness of the crown mesiodistally and the height of the contact areas above the cervix. The mesial outline of the crown of the mandibular canine is nearly straight with the mesial outline of the root, with the mesial contact area being near the mesioincisal angle. When the cusp ridges have not been affected by wear, the cusp angle is on a line with the center of the root, as on the maxillary canine. The mesial cusp ridge is shorter. The distal contact area of the mandibular canine is more toward the incisal aspect than that of the area. The cervical line labially has a semicircular curvature apically. Many mandibular canines give the impression from this aspect of being bent distally on the root base. The maxillary canine crowns are more likely to be in line with the root. The mandibular canine root is shorter by l or 2 mm on average than that of the maxillary canine, and its apical end is more sharply pointed. Root curvatures are infrequent. When curvature of root ends is present, it is often in a mesial direction Lingual Aspect The lingual surface of the crown of the mandibular canine is flatter, simulating the lingual surfaces of mandibular incisors cingulum is smooth and poorly developed. The marginal ridges are less distinct. This is true of the lingual ridge except toward the cusp tip, where it is raised. Generally speaking, the lingual surface of the crown is smooth and regular. Mesial : longs, almost straight Distal: short, curved, elevated Mesial Aspect & Distal Aspect The mandibular canine has less curvature labially on the crown, with very little curvature directly above the cervical line. The curvature at the cervical portion as a rule is less than 0. mm. The lingual outline of the crown is curved in the same manner as that of the maxillary canine, but it differs in degree The tip of the cusp is more nearly centered over the root The cervical line curves more toward the incisal portion than does the cervical line on the maxillary canine more pointed root tip on the mandibular canine. Developmental depression mesially on the root of the mandibular canine is more pronounced and sometimes quite deep Incisal Aspect The mesiodistal dimension of the mandibular canine is less than the labiolingual dimension. A similarity is evident in this, but the outlines of the mesial surface are less curved. The cusp tip and mesial cusp ridge are more likely to be inclined in a lingual direction in the mandibular canine, with the distal cusp ridge and the contact area extension distinctly so. Note that the cusp ridges of the maxillary canine with the contact area extensions are more nearly in a straight line mesiodistally from the incisal aspect. Wheeler's Dental Anatomy - Part 2: Maxillary & Mandibular Incisors Download Download AI Tools Ask AI Multiple Choice Flashcards Quiz Video Audio Lesson 12 0 Save Wheeler's Dental Anatomy - Part 2: Maxillary & Mandibular Incisors Course: Dentistry 1-2 153 documents University: Davao Medical School Foundation Info More info Download Download AI Tools Ask AI Multiple Choice Flashcards Quiz Video Audio Lesson 12 0 Save Maxill ary Central Incisor •maxillary central incisor is the widest mesiodistally of any of the anterior teeth •labial face is less convex than that of the maxillary lateral incisor or canine, which gives the central incisor a squared or rectangular appearance •crown nearly always looks symmetrical and regularly formed •mesial incisal angle is relativel y sharp, the distal incisal angle rounded •enamel surface is relatively smooth. Tooth Numbering system Universal Notation system -8,9 Zsigmondy/Palmer Notation System -1,1 Federation Dentaire Inte rnationale (FDI) system -11,21 First Evidence of Calcification 3-4 months Crown Completion 4-5 years Eruption 7-8 years Root Completion 10 years Labial Aspect o crown of the average ce ntral inciso r will be 10 to 11 mm long from the highest point on the cervical line to the lowest point on the incisal edge CROWN Mesial outline: slightly convex Distal outline : is more convex than the mesial outline, with the crest of curvature higher toward the cervical line. Incisal outline: -regular and straight in a mesiodistal direction after the tooth has been in function long enough to obliterate the mamelons. Cervical outline: -Semicircular direction with the curvature rootwise, from the point at which the root outline joins the crown mesially to the point at which the root outline joins the crown distally. ROOT labial aspect: -cone-sh aped, in most instances with a relatively blunt apex -outline mesially and distally is regular Lingual Aspect lingual outline: of the maxillary central incisor is the reve rse of that found on the labial aspect Cervical outline: -below the cervical line a smooth convexity is to be found; this is called the cingulum o Mesially and distally confluent with the cingulum are the marginal ridges. Between the marginal ridges, below the cingulum, a shallow concavity is present called the lingual fossa o Crown calibration at the two labial line angles is greater than the calibration at the two lingual line angles o Lingual portion of the root is n arro wer than the labial portion. o mesial side of this triangle is slightly longer than the distal side Mesial Aspect o crown is wedge-shaped, or triangular, with the base of the triangle at the cervix a nd the apex at the incisal ridge CROWN labial outline: -from the crest of curvature to the incisal ridge is very slightly convex lingual outline: -convex at the point where it joins the crest of curvature at the cingulum; -it then becomes concave at the mesial marginal ridge and slightly convex again a t the linguoincisal ridge and the incisal edge o Cervical curvature is greater on the mesial surface of this tooth than on and surface of any other tooth in the m outh. ROOT o mesial aspect is cone shaped o apex of the root is usually bluntly round ed. ORAL ANATOMY MODULE 1: PERMANENT M AXILLARY INCI SORS Distal Aspect o crown gives the impression of being somewhat thicker tow ard the incisal thir d. Because of the slope of the labial surface distolingually, more of that sur face is seen from the distal asp ect; this creates the illusion of greater t hickn ess o curvature of the cervical line outlining the CEJ is less in extent on the distal than on the mesial surfaces Incisal Aspect o labial face of the crow n is relatively o broad and flat in comparison with the lingual surface, e specially toward the incisal third. o outline of the lingual portion tapers lingually toward the cingulum o mesiolabial and distolabial line angles are prominent o The mesiodistal calibration of the crown at the labial line angles is greater t han the same calibration at the lingual line angles. o crown conforms to a triangular outline reflected by the outline of the root cross section at the cervix mentioned earlier. Maxill ary Later al Inci sor •supplements the central incisor in function, the crowns bear a close resemblance. •smaller in all dimensions except root length •vary in form more than any other tooth in the mouth except the third mo lar •If the varia tion is too great, it is considered a developmental anomaly. o common situation is to find maxillary lateral incisors with a nondescript, pointed form; such teeth are called peg- shaped laterals o lateral incisors are missing entirely 7; in these cases, the maxillary central incisor may be in contact distally with the canine. o Presence of a pa latoging ival groove in maxillary incisors may be a predisposing factor in localized periodontal disease. This groove is also referred to as the palatoradicula r groove. •enamel surface is relatively smooth. Tooth Numbering system Universal Notation system -7,10 Zsigmondy/Palmer Notation System -2,2 Federation Dentaire Inte rnationale (FDI) system -12, 22 First Evidence of Calcification 10-12 months Crown Completion 4-5 years Eruption 8-9 years Root Completion 11 years Labial Aspect o more curvature, with a rounded incisal ridge and rounded incisal angles mesially and distally o relatively narrow mesiodistally, usually about 2 mm narrower than the central incisor. CROWN mesial outline: -more rounded mesioincisal angle. -crest of contour mesially is usually at the point of junction of the middle and incisal thirds -so-called square for ms, the mesioincisal angle is almost as sharp as that found on most maxillary central incisors -more rounded mesioincisal angl e distal outline: -always more rounded -crest of contour is more cervical, usually in the center of the middle third. Labial surface: -more convex than that of the central incisor except in some square and flat-faced forms. ROOT o root length is gr eater in pr oportion to its crown length than that of the central incisor o The root is often about 1.5 times the length of the crown. o root tapers evenly from the cervical line to a point approximately two thirds of its length apically. o Most cases, it curves sharply fr om this location in a distal direction and ends in a pointed apex. Lingual Aspect o mesial and distal marginal ridges o are marked o cingulum is usually prominent, with a tendency toward deep developmental grooves within the lingual fossa, whe re it joins the cingulum o linguoincisal ridge is well developed o lingual fossa is more concave and circumscribed than that found on the central incisor. Mesial Aspect o mesial aspect of the maxillary lateral incisor is similar to that of a small central incisor except that the root appears longer o The crown is shorter, the root is relatively longer o labiolingual measurement of the crown and root is a millimeter or so less than that of the maxillary central incisor of the same mouth. Distal Aspect o width of the crown distally appears thicker than it does on the mesial aspect from marginal ridge to labial face o curvature of the cervical line is usually a millimeter or so less in depth than on the mesial side. Incisal Aspect o sometimes resembles that of th e central incisor, or it may resemble that of a small canine o labiolingual dimension may be greater than usu al in compa rison with the mesiodistal dimension. o All maxill ary lateral incisors exhibit more convexity labially and lingually from the incisal aspect than do the maxill ary central incisors Too long to read on your phone? Save to read later on your computer Save to a Studylist Mandibu lar Central Incisor •smallest tooth in the dental arches •crown has little more than half the mesiodistal diameter of the maxillary central incisor; howeve r, the labiolingual diameter is only about 1 mm less. •single root is very narrow mesiodistally and corresponds to the narrowness of the crown, although the root and crown are wide labiolingually. •The length of the root is as great as, if not greate r than, that of the maxillary central incisor. Tooth Numbering system Universal Notation system -24,25 Zsigmondy/Palmer Notation System -1,1 Federation Dentaire Inte rnationale (FDI) system -31,41 First Evidence of Calcification 3-4 months Crown Completion 4-5 years Eruption 6-7 years Root Completion 9 years Labial Aspect o Bilaterally symmetrical o Incisal ridge – straigh t and approx.. a t right angles o Narrowest tooth mesiodistally of all permanent teeth o root outlines are straight with the o mesial and distal outlines of the crown down to the apical o portion. o The apical third of the root terminates in a small, o pointed taper, in most cases curving distall y Lingual Aspect o lingual surface of the crown is smooth, with very o slight concavity at the incisal third between the inconspicuous marginal ridges o marginal ridges – more prominent near the incisal ridges o no developmental lines mark the cingulum o becomes flat and then convex o shallow lingual fossa o smooth cingulum Mesial Aspect o wedge-shaped or triangular o incisal ridge is rounded or worn flat o center is usually lingual to the center of the root Labial Surface: o Inclined lingually outline – almos t straight o Near cervica l third– convex o Cervical line – convex incisally Lingual surface: o Lingual margin –“S” shaped Distal Aspect o Cervical line curves less incisally o developmental depression on the distal surface of the root may be more marked, with a deepe r, more well-d efined deve lopm ental groove at its center Incisal Aspect o Bilateral symmetry o Incisal edge – right angles to a line bisecting the crown labiolingually o Labiolingual diameter greater than mesiodistal diameter TRAITS Maxillary Central Incisor Crown wider mesiodistally than labiolingually Pronounced lingual fossa often with lin gual pit More prominent cingulum and marginal ridge s Mandibular Central Incisor Crown wider labiolingually than mesiodistally Shallow lingual fossa without grooves or pits Not Prominent ORAL ANATOMY MODULE 2: P ERMANENT MANDIBULAR INCISORS 1 ST SEMESTER  MIDTERMS  S.Y. 2022– 2023 TRANS : KYLLAH K RISTIANNE ONES Mandibu lar Lateral Incisor •resembles the mandibular central incisor so closely that only a brief description of each aspect of the lateral incisor is necessary •supplements CI in function •mandibular lateral incisor is somewhat larger than the mandibular central incisor (compare measurements), but g enerally speaking, its form closely resembles that of the mandibular central incisor Tooth Numbering system Universal Notation system -23,26 Zsigmondy/Palmer Notation System -2,2 Federation Dentaire Inte rnationale (FDI) system -32, 42 First Evidence of Calcification 3-4 months Crown Completion 4-5 years Eruption 7-8 years Root Completion 10 years Labial Aspect o Incisal ridge (usually straight) slopes downward in a distal direction o Crown tilts distally (distolingual twist) o More rounded Lingual Aspects o Incisal ridge (usually straight) slopes downward in a distal direction o Cingulum is distal to center o Longer mesial marginal ridges o Shorter distal marginal ridges Mesial and Distal Aspects Mesial o Mesial side is longer than the distal side Distal surface: o deep concavity immediately above cervica l line Incisal Aspect o Best view to identify the tooth (esp. if its right or left ) o Incisal edge follows the curvature of mandibular arch (distolingual twist) MANDIBULAR CENTRAL VS MANDIBULAR LATERAL INCISOR CROWN CENTRAL INCISOR LATERAL INCISOR Labial Aspect Symmetry Bilaterally symmetrical Asymmetrical Mesio-incisal angle Right angle (90 degrees) Round Disto-incisal angle Right angle (90 degrees) Round Mesial contact Incisal 3 rd Incisal 3 rd Distal contact Incisal 3 rd Incisal 3 rd Incisal Aspect Incisal ridge form right angle with l abio- lingual bisecting line Incisal ridge twisted n crown CANINE •commonly referred to as the cornerstone of the dental arches, •longest teeth in the mouth •crowns are u sually a s long as those of the maxillary central incisors •resemblance to th e prehensile teeth of the carnivore gives rise to the term canine. •Crown portions o f the canines are sh aped in a manner that promotes cleanliness. •self-cleansing quality, along with the efficient anchorage in the jaws, tends to preserve these teeth throughout life. o last ones to go Function •support the incisors and premolars, since t hey are located between these groups •canine guidance •canine eminence •tear or crush food •crowns are shaped in a manner th at promo tes cleanliness Maxill ary Canine Tooth Numbering system Universal Notation system -6,11 Zsigmondy/Palmer Notation System -3,3 Federation Dentaire Inte rnationale (FDI) system -13,23 First Evidence of Calcification 4-5 months Crown Completion 6-7 years Eruption 11-12 years Root Completion 13-15 years Labial Aspect •crown a nd root are narrower mesiodis tally than thos e of the maxillary central incisor •difference is about 1 mm •cervical line: is convex toward the root portion Mesial outline: o convex from the cervix to the center of the mesial contact area o slight concavity above the contact area Distal Outline: o Concave between the c ervical l ine and the distal contact area. o contact area is usually at the center of the middle third of the crown •cusp tip is on a line with the center of the root •labial surface is smooth, with no deve lopm e ntal lines •root of the m axillary canine appears slender from the l abial aspect when comp ared with the bulk of the crown •sharp curve in the vicinity of the apical third. Lingual Aspect •crown and r oot are narrower lingually than labially •CEJ s hows a more even curvatur e, maybe straight for a short interval •cingulum is lar ge a nd, in some instances, is pointed like a small cusp •Developmental depress ions mesially and distally may be see n on mo st of these roots Mesial Aspect • shows greater bulk and greater labiolingual m easurement th an any of the other anterior teeth • The o utline of th e ro ot from this aspect is conical, with a tapered or bluntly pointed apex. • Developmental depressions o n the heavy roots help anchor the te eth in the alve oli and help prevent rotation and displacement. Distal Aspect •less curvature toward the cusp ridge •the distal margin al ridge is heavier a nd more •irregular in outline surface dis plays mo re concavity, usually above the contact area; •and th e developmental d epression on th e distal side of the root is more pronounced ORAL ANATOMY MODULE 3: PERMANENT CANINES Document continues below Discover more from: Dentistry 1-2Davao Medical School Foundation 153 documents Go to course 14 Wheeler's Dental Anatomy - Part 3 (Premolars and Molars Overview)Dentistry 1-2 Lecture notes 100% (9) 174 Understanding Jose Rizal: Life, Works, and the Rizal Law (HIST 101)Dentistry 1-2 Practice materials 100% (7) 40 RPH 101: Module 1 - Introduction to History in Purposive Communication Dentistry 1-2 Lecture notes 100% (6) 27 Muscular System Overview and Structure Notes (Course Code: BIO101)Dentistry 1-2 Summaries 100% (6) 7 Understanding the Self: Key Concepts & Insights (Course Code: CS)Dentistry 1-2 Lecture notes 100% (6) 10 IHS-Reviewer (BONE - Midterm Review on Skeletal System & Joints)Dentistry 1-2 Lecture notes 100% (6) Discover more from: Dentistry 1-2Davao Medical School Foundation153 documents Go to course 14 Wheeler's Dental Anatomy - Part 3 (Premolars and Molars Overview) Dentistry 1-2 100% (9) 174 Understanding Jose Rizal: Life, Works, and the Rizal Law (HIST 101) Dentistry 1-2 100% (7) 40 RPH 101: Module 1 - Introduction to History in Purposive Communication Dentistry 1-2 100% (6) 27 Muscular System Overview and Structure Notes (Course Code: BIO101) Dentistry 1-2 100% (6) 7 Understanding the Self: Key Concepts & Insights (Course Code: CS) Dentistry 1-2 100% (6) 10 IHS-Reviewer (BONE - Midterm Review on Skeletal System & Joints) Dentistry 1-2 100% (6) Incisal Aspect •labiolingual dim ension is greater th an the mesiodistal. •Tip of cusp is l abial to center of crown labiolingually and m esial to the center •The crown of this tooth gives the impression of h aving t he entire distal p ortion stretched to make contact with th e first premolar. •line bisecting t h e cusp and cu sp ridges drawn in the mesiodistal direction is almost always straight •distal slope is longer than mesial slope Mandibu lar Canine Tooth Numbering system Universal Notation system -27, 22 Zsigmondy/Palmer Notation System -3,3 Federation Dentaire Inte rnationale (FDI) system -43,33 First Evidence of Calcification 4-5 months Crown Completion 6-7 years Eruption 9-10 years Root Completion 12 – 14 years •mandibular canine cro w n is narro wer mesiodistally than that of th e maxil l ary canine, j ust as lo ng in most ins tances and in many in stance s is longer by 0.5 to 1 mm •Function: cut, pierce or shear food •Root Variation – Bifurcated roots Labial Aspect The essential differences between mandibular and maxillary canines viewed fro m the labial aspect may be described as follows: • The crowns of th e mandibular canines appear longer. Sometimes they are longer, but the effect of greater length is emphasized by the narrowness of the crown mesiodistally and the height o f the contact areas ab ove the cervix. • The mesial outl ine of th e crown of th e mandibular ca nine is nea r ly s traight with the mesial outlin e of the roo t, with t he mesial c ont act area being ne ar the mesioincisal angle. • When the cusp rid ges have not been affected by wear, the cusp angle is on a l ine with the center of the root, as o n the maxillary canine. The mesial cusp ridge is shorte r. • The distal contact area o f the mandibular canine is more toward the incisal aspect than that of the area. • Th e cervical line labially has a semicircula r cu rvature apically. • Many mandibular canines give th e impression from t his aspect of being bent distally on the root ba s e. Th e maxillary canine crowns are more likely to be in lin e with th e root. • The mandibular ca nine root is shorter by l or 2 m m on average than that of the maxil lary canine, and it s apical end is more s harply pointed. Root curvatures a re infrequent. When curvature of r oot ends is present, it is o ften in a mesial direction Lingual Aspect •The lingual surface of th e crown of the mandibular canine is flatter, simulating the lingual surfaces of mandibular incisors •cingulum is smooth and po orly developed. •The margin al ridges are less distinct. Th is is true of th e l ingual r idge except toward th e cusp t ip, where it is raised. Generally speaking, the l ingu al surface of th e crown is smoo th and regular. •Mesial : longs, almost straight •Distal: short, curved, eleva ted 1 out of 8 Share Download Download More from:Dentistry 1-2 More from: Dentistry 1-2Davao Medical School Foundation 153 documents Go to course 14 Wheeler's Dental Anatomy - Part 3 (Premolars and Molars Overview)Dentistry 1-2 Lecture notes 100% (9) 174 Understanding Jose Rizal: Life, Works, and the Rizal Law (HIST 101)Dentistry 1-2 Practice materials 100% (7) 40 RPH 101: Module 1 - Introduction to History in Purposive Communication Dentistry 1-2 Lecture notes 100% (6) 27 Muscular System Overview and Structure Notes (Course Code: BIO101)Dentistry 1-2 Summaries 100% (6) More from: Dentistry 1-2Davao Medical School Foundation153 documents Go to course 14 Wheeler's Dental Anatomy - Part 3 (Premolars and Molars Overview) Dentistry 1-2 100% (9) 174 Understanding Jose Rizal: Life, Works, and the Rizal Law (HIST 101) Dentistry 1-2 100% (7) 40 RPH 101: Module 1 - Introduction to History in Purposive Communication Dentistry 1-2 100% (6) 27 Muscular System Overview and Structure Notes (Course Code: BIO101) Dentistry 1-2 100% (6) 7 Understanding the Self: Key Concepts & Insights (Course Code: CS) Dentistry 1-2 100% (6) 10 IHS-Reviewer (BONE - Midterm Review on Skeletal System & Joints) Dentistry 1-2 100% (6) More from:Dental NotesbyMaria Mercedes M. 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Lynum24 documents Go to Studylist 4 Nerve Block - Anesthesiology Dentistry 100% (18) 8 Wheeler's Dental Anatomy - Part 2: Maxillary & Mandibular Incisors Dentistry 1-2 100% (12) 108 GENERAL ANATOMY TOPICS Dentistry 100% (11) 18 DDM3101 - Final Exam Notes on Dental Materials Science Doctor of Dental Medicine 100% (10) 14 Wheeler's Dental Anatomy - Part 3 (Premolars and Molars Overview) Dentistry 1-2 100% (9) 25 Complete Denture Notes FROM DIFFERENT SOURCES Dentistry 100% (5) Students also viewed Dental Materials Review: Instruments and Properties Overview IHS-Reviewer (BONE - Midterm Review on Skeletal System & Joints) ### ANTH 101 - The Impact of Globalization on Contemporary Society Science, Technology, and Society: A Historical Overview Pur Com-Reviewer: Key Concepts in Purposive Communication RPH 101: Module 1 - Introduction to History in Purposive Communication Related documents Snell's Anatomy - Lower Limb Osteology and Thigh Overview Snell's Anatomy - Thorax Overview and Osteology (Chapter 3) Orban's Oral Histology: Mucous Membranes Overview - Finals S.Y. 2022-2023 Wheeler's Dental Anatomy - Part 3 (Premolars and Molars Overview) GENANA Final Exam Notes on Head and Neck Anatomy DMD Final Exam: Synthesis on Cancer Genetics and Gene Mutations Get homework AI help with the Studocu App Open the App English Philippines Company About us Studocu Premium Academic Integrity Jobs Blog Dutch Website Study Tools All Tools Ask AI AI Notes AI Quiz Generator Notes to Quiz Videos Notes to Audio Infographic Generator Contact & Help F.A.Q. 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13201	https://www.quora.com/What-is-the-interpretation-for-the-colonies-growing-inside-the-zone-of-inhibition	What is the interpretation for the colonies growing inside the zone of inhibition? - Quora Something went wrong. Wait a moment and try again. Try again Skip to content Skip to search Sign In Microbiology Zones of Inhibition Laboratory Experiment Antibiotics Cellular Growth Scientific Technique Antibiotic Sensitivity Antibiosis Antibiotic Therapy 5 What is the interpretation for the colonies growing inside the zone of inhibition? All related (34) Sort Recommended Assistant Bot · 1y The presence of colonies growing inside the zone of inhibition in an antimicrobial susceptibility test (such as a disk diffusion test) can indicate several important points: Resistance: The bacteria that are growing within the zone of inhibition may have developed or possess intrinsic resistance to the antibiotic being tested. This suggests that the antibiotic is ineffective against these particular strains. Incomplete Inhibition: The antibiotic may not fully inhibit the growth of all bacterial cells. This can happen if the concentration of the antibiotic decreases as it diffuses away from the d Continue Reading The presence of colonies growing inside the zone of inhibition in an antimicrobial susceptibility test (such as a disk diffusion test) can indicate several important points: Resistance: The bacteria that are growing within the zone of inhibition may have developed or possess intrinsic resistance to the antibiotic being tested. This suggests that the antibiotic is ineffective against these particular strains. Incomplete Inhibition: The antibiotic may not fully inhibit the growth of all bacterial cells. This can happen if the concentration of the antibiotic decreases as it diffuses away from the disk, allowing some bacteria to survive and grow. Mutant Selection: Sometimes, a few bacterial cells may carry mutations that confer resistance. These resistant variants can survive in the presence of the antibiotic and proliferate, leading to visible colonies. Environmental Factors: Conditions such as nutrient availability, pH, or temperature in the agar can also affect bacterial growth. If the conditions favor the growth of certain bacteria, they may thrive even in the presence of an antibiotic. Testing Errors: Contamination or errors in the procedure could also lead to unexpected growth patterns. It's essential to ensure that the test is conducted under controlled conditions to avoid misleading results. In summary, colonies growing within the zone of inhibition typically indicate some form of resistance or adaptation of the bacteria to the antibiotic being tested. Further investigation, such as conducting additional susceptibility tests or molecular analysis, may be necessary to understand the underlying mechanisms. Upvote · Pejhman Keshvardoust PhD in Microbiology, University of New South Wales (Graduated 2016) · Author has 78 answers and 182.4K answer views ·7y The zone of inhibition is a parameter measured in the Calibrated Disk Sensititvity test, to determine if bacteria are resistant or susceptible to antibiotics at set concentrations. The zone of inhibition refers to an area on an agar plate around a disc of an antibiotic in which bacteria should not grow if they are susceptible to the antibiotic. This is because the antibiotic interferes with one or more components that the cells need to survive. So while colonies (or a lawn) of bacteria grow elsewhere on the plate, there is a circle around that disc where the concentration of antibiotics is hig Continue Reading The zone of inhibition is a parameter measured in the Calibrated Disk Sensititvity test, to determine if bacteria are resistant or susceptible to antibiotics at set concentrations. The zone of inhibition refers to an area on an agar plate around a disc of an antibiotic in which bacteria should not grow if they are susceptible to the antibiotic. This is because the antibiotic interferes with one or more components that the cells need to survive. So while colonies (or a lawn) of bacteria grow elsewhere on the plate, there is a circle around that disc where the concentration of antibiotics is high enough that these organisms can’t grow. If something is growing within that zone of inhibition, it means that it has resistance to that antibiotic (at least, at the concentration being tested). There are many reasons that bacteria can be resistant to various antibiotics. Importantly, just because something is susceptible on one of these assays doesn’t mean that the drug can be safely used - you also have to factor in the safe dosage that can be given to the patient, and any allergies. Upvote · 9 3 Sponsored by Grammarly 92% of professionals who use Grammarly say it has saved them time Work faster with AI, while ensuring your writing always makes the right impression. Download 999 207 Catherine Schneider A.S in Pre-Med&Microbiology, Tulsa Community College (Graduated 2019) · Author has 394 answers and 659.3K answer views ·7y That they have mutated their DNA to resist the antibiotic, or that they have some form of virulence factor protection (I.e a capsule, slime-layer, or endospores) that protect against the antibiotic. Upvote · Related questions More answers below Why do colonies sometimes appear in the inhibiting zone? What are zones of inhibition? Are bacteria alive in the zone of inhibition? Why is the shape of a zone of inhibition different? Why is a partial inhibition zone of bacteria considered as inhibition? Susan Cook Ph.D. in Microbiology&Virology, Baylor College of Medicine (Graduated 1984) · Author has 1.3K answers and 941.4K answer views ·7y They are exhibiting resistance. Upvote · 9 1 Christopher Belica B.S. in Biology&Chemistry, Hope College · Author has 71 answers and 34.6K answer views ·5y Related Are bacteria alive in the zone of inhibition? This depends entirely upon the bacteria and compound being tested. They may be completely dead or their growth may simply be inhibited to the point where they are not forming visible colonies. You can test what is happening in a very simple way, all you need to do is take a streak from the zone of inhibition (a sterile toothpick works well), and streak it onto a fresh plate. If colonies appear, you know the growth was only inhibited, if nothing appears, you know they bacteria were killed by the substance. Upvote · Related questions More answers below Why is a partial inhibition zone of bacteria considered as inhibition? What does it mean if there is no zone of inhibition? In what ways do antibiotics inhibit the growth of bacteria? Did you notice any colonies (isolated mounds of cells) growing within any of the zones of inhibition? If so, which plate(s) and which drug(s)? What is a good zone of inhibition? Lois Cronholm Ph.D. in Biology; Post Doctoral in Microbiology/Immunology · Author has 10.2K answers and 2.4M answer views ·3y Related What is the zone of inhibition in bacterial cultures? A standard test for determining what antibiotics are effective for specific bacteria is to plate the bacterial culture on a medium on which it can grown, and placing discs with antibiotics in areas around the plate, incubating the plate in an environment in which the bacteria can grow, and looking for areas around colonies where no growth has occurred. The clear area is known as the zone of inhibition because it is the area where no bacteria grew. The gradient of concentration of the antibiotics is used to determine the resistance of the bacteria and the MIC (minimum inhibitory concentration) Continue Reading A standard test for determining what antibiotics are effective for specific bacteria is to plate the bacterial culture on a medium on which it can grown, and placing discs with antibiotics in areas around the plate, incubating the plate in an environment in which the bacteria can grow, and looking for areas around colonies where no growth has occurred. The clear area is known as the zone of inhibition because it is the area where no bacteria grew. The gradient of concentration of the antibiotics is used to determine the resistance of the bacteria and the MIC (minimum inhibitory concentration) required to kill/inhibit the bacteria, an important clinical consideration. Upvote · 9 1 Sponsored by Amazon Web Services (AWS) Get AI certified. Invest an hour a week in your future with our free AWS Certified AI Practitioner Exam Prep Plan. Learn More 99 97 Dejian Huang Studied at United States Medical Licensing Examination ·Updated 9y Related How do transduction, transformation, and conjugation work in bacteria? that is a very good question, daily lives of bacteria high depend on these activities, including virulence, exotoxin, drug resistance and even fertility. Let’s start with the simplest one transformation: this activity is described as the bacteria takeing up genetic material directly from the environment henceforth getting its new feature. A famous experiment perfectly manifest this procedure, in which, a scientist inoculate 2 strains of Strep. pneumonia, one is with rough capsule (Strep.R) while the other with smooth capsule (Strep.S). Firstly, the scientist inject these 2 kinds of bacteria into Continue Reading that is a very good question, daily lives of bacteria high depend on these activities, including virulence, exotoxin, drug resistance and even fertility. Let’s start with the simplest one transformation: this activity is described as the bacteria takeing up genetic material directly from the environment henceforth getting its new feature. A famous experiment perfectly manifest this procedure, in which, a scientist inoculate 2 strains of Strep. pneumonia, one is with rough capsule (Strep.R) while the other with smooth capsule (Strep.S). Firstly, the scientist inject these 2 kinds of bacteria into 2 rats respectively, and later on only the rat receiving Strep.S is dead, so we assume the Strep.S is toxic to its host and Strep.R is rather safe. Then the scientist centrifuge the Strep.S strain to broke down its cell membrane so that the genetic material (DNA) release outside and float in the upper layer of fluid after the centrifuge. Now the scientist pick up 2 new mice, one is injected with the genetic material of Strep.S (upper layer) solely, the other is injected with a combination of genetic material of Strep.S and living Strep.R. This time something interesting happened, the rat getting only DNA of Strep.S lives, while the one receiving Strep.R and DNA of Strep.S is dead. The Strep.R strain is considered achieving the toxic smooth capsule feature by “eating the corpse” of Strep.S. More precisely, it absorb the DNA fragments of the dead Strep.S and incorporate on its very own chromosome. The capsule of bacteria plays an important role in infecting and surviving inside human body, therefore, many bacteria use their transformation ability to get their brand new capsule and become virulent. Classic example include the story of Hemophilea. influenzae, which nontypeable or wild type stain do not have capsule (while they can cause disease anyway), once they get a capsule they are capable of cause epiglottitis, pneumonia, meningitis, etc. Conjugation: F+ plasmid contains genes required for sex pilus and conjugation. Bacteria without this plasmid is termed F-. Sex pilus on F+ bacteria contacts F- bacteria. A single strand of plasmid DNA is transferred across the conjugal bridge. F+ plasmid can become incorporated into the bacterial chromosome, termed Hfr. Replication of incorporated plasmid DNA may include some flanking chromosomal DNA. Now we have a really nasty bug with multiple drug resistance gene along its chromosome, with OriT operon as a start, we have resistance gene in the order of vancomycin, neomycin, erythromycin and amoxicillin down the way, then tra operon. Then we culture this strain with a perfect strain of bacteria that is sensitive to all antibiotics mentioned above. After a period of time, we separate new strains of bacteria with different drug resistance: 5% is resistant to all four antibiotics, 10% is resistant to vancomycin, neomycin and erythromycin, 25% is resistant to vancomycin and neomycin, 60% is resistant only to vancomycin. The replication of donating piece is from OriT operon to tra operon. During this procedure, some chromosomal gene downstream may be covered and transfer to the recipient bacteria, but we do not sure how long it will go along the circle chromosome of donating bacteria, and hence do not sure how many genes is taken along with the Hfr. But what we can confirm is the closer a gene is to the OriT operon, the higher chance it is to be conjugated to the recipient bacteria. Upvote · 9 4 9 1 Lois Cronholm Ph.D. in Biology; Post Doctoral in Microbiology/Immunology · Author has 10.2K answers and 2.4M answer views ·4y Related Why do bacterial colonies stop growing? For pretty much the same reason that a lot of things stop growing — bacterial cultures accumulate waste products and use up nutrients and their genomes provide aging response to cell life. Upvote · 9 3 Sponsored by Stake.com Join Stake's $75,000 weekly raffle. Just one ticket could see you sharing in $75k every single week. Winners are drawn on every week! Play Now 99 35 WEDGYVEGGI Science nerd · Author has 618 answers and 132.1K answer views ·3y Related What is the zone of inhibition in bacterial cultures? The area around the antibiotic disk that has no bacterial growth is known as the zone of inhibition. The larger this zone is, the more sensitive the bacteria is to that antibiotic. Hope this helps. Source: Upvote · James Anderson Former Business Manager (2015–2020) · Author has 309 answers and 344.7K answer views ·4y Related How do you know what type of inhibition is? the inhibitors in your brain serve to filter what your senses are transmitting to your bran in raw data. The receptors put together the information the eyes get, or sound from ears, touch or pain received-call called stimuli. Then the processor gets to work analysing it. At this point inhibitors should discard much of the raw data to allow the processing part of the brain to send efficiently streamlined thoughts on which you act- a smile or frown -it is all worked through the brain. So fewer inhibitors means more data, so more thoughts and more assessments have to be made constantly on the data Continue Reading the inhibitors in your brain serve to filter what your senses are transmitting to your bran in raw data. The receptors put together the information the eyes get, or sound from ears, touch or pain received-call called stimuli. Then the processor gets to work analysing it. At this point inhibitors should discard much of the raw data to allow the processing part of the brain to send efficiently streamlined thoughts on which you act- a smile or frown -it is all worked through the brain. So fewer inhibitors means more data, so more thoughts and more assessments have to be made constantly on the data given as it is raw-but this gives an active inquiring mind some huge advantages- dont lie to one they know before you do you will lie. sometimes for brain’s not ready to work at 110 percent all day this is too much and autism is the brain’s coping mechanism. On thre opposite spectrum too manty will slow your mind-cacting on limited filtered info-or stimuli Emotions are also exaggerated. Upvote · Sponsored by All Out Kill Dengue, Malaria and Chikungunya with New 30% Faster All Out. Chance Mat Lo, Naya All Out Lo - Recommended by Indian Medical Association. Shop Now 999 621 Fernando Jose Isart Infante Lab guy ·9y Related What is the difference between noncompetitive and uncompetitive inhibition? Non-competitive inhibition is a type of enzyme inhibition where the inhibitor reduces the activity of the enzyme and binds equally well to the enzyme whether or not it has already bound the substrate. 1[] The inhibitor may bind to the enzyme whether or not the substrate has already been bound, but if it has a higher affinity for binding the enzyme in one state or the other, it is called a mixed inhibitor. Uncompetitive inhibition, also known as anti-competitive inhibition, takes place when an enzyme inhibitor binds only to the complex formed between the enzyme and thesubstrate (the E-S complex). Continue Reading Non-competitive inhibition is a type of enzyme inhibition where the inhibitor reduces the activity of the enzyme and binds equally well to the enzyme whether or not it has already bound the substrate. [1[] The inhibitor may bind to the enzyme whether or not the substrate has already been bound, but if it has a higher affinity for binding the enzyme in one state or the other, it is called a mixed inhibitor. [ Uncompetitive inhibition, also known as anti-competitive inhibition, takes place when an enzyme inhibitor binds only to the complex formed between the enzyme and thesubstrate (the E-S complex). While uncompetitive inhibition requires that an enzyme-substrate complex must be formed, non-competitive inhibition can occur with or without the substrate present. Your response is private Was this worth your time? This helps us sort answers on the page. Absolutely not Definitely yes Upvote · 9 5 Uldis Sprogis Talent etc. defined in Logical English Dictionary · Author has 2.8K answers and 2.9M answer views ·8y Related What is an inhibition? Inhibition: n. sensing selfrestraint primarily because of some (doubt and/or anxiety) and/or absence of selfconfidence An inhibited human frequently selfrestrains him or herself because there is frequently much doubt and anxiety over saying something and/or doing something which may cause much embarrassment or be considered offensive by some. Absence of enough selfconfidence can also be a reason for inhibition in saying or doing something and if it extends to many things then you can actually say that the human has an inhibited personality. Social inhibition is sometimes present in humans who do Continue Reading Inhibition: n. sensing selfrestraint primarily because of some (doubt and/or anxiety) and/or absence of selfconfidence An inhibited human frequently selfrestrains him or herself because there is frequently much doubt and anxiety over saying something and/or doing something which may cause much embarrassment or be considered offensive by some. Absence of enough selfconfidence can also be a reason for inhibition in saying or doing something and if it extends to many things then you can actually say that the human has an inhibited personality. Social inhibition is sometimes present in humans who do not have well developed social skills and are not only inhibited but may actually be timid and shy too when interacting with humans in small and/or large groups. Upvote · 9 1 Jasse Li Biologist · Author has 79 answers and 484.9K answer views ·7y Related What is the relationship between the concentration of a plant extract and the inhibition of a bacteria? Well it depends. If there is a bacteriostatic (bacteria-stopping) or bacteriocidal (bacteria-killing) compound within the extract, then you can expect a dose-response curve as follows: Where the x axis is the concentration of the extract while the y axis is the relative bacterial growth, for example. In general, the higher the concentration of extract, the lower the bacterial growth. Of course, if there’s no active compound within the extract, you can expect a straight line. remember that an extract is a mixture of active and inactive compounds. Continue Reading Well it depends. If there is a bacteriostatic (bacteria-stopping) or bacteriocidal (bacteria-killing) compound within the extract, then you can expect a dose-response curve as follows: Where the x axis is the concentration of the extract while the y axis is the relative bacterial growth, for example. In general, the higher the concentration of extract, the lower the bacterial growth. Of course, if there’s no active compound within the extract, you can expect a straight line. remember that an extract is a mixture of active and inactive compounds. Upvote · Related questions Why do colonies sometimes appear in the inhibiting zone? What are zones of inhibition? Are bacteria alive in the zone of inhibition? Why is the shape of a zone of inhibition different? Why is a partial inhibition zone of bacteria considered as inhibition? Did you notice any colonies (isolated mounds of cells) growing within any of the zones of inhibition? If so, which plate(s) and which drug(s)? What is the zone of inhibition? What are its functions? How is the zone of inhibition measured? What does it mean if there is no zone of inhibition? How is a zone of inhibition produced? What is the zone of inhibition in bacterial cultures? Why is the zone of inhibition circular? In what ways do antibiotics inhibit the growth of bacteria? What are some pictures for zone of inhibition? What does a large zone of inhibition mean? Related questions Why do colonies sometimes appear in the inhibiting zone? What are zones of inhibition? Are bacteria alive in the zone of inhibition? Why is the shape of a zone of inhibition different? Why is a partial inhibition zone of bacteria considered as inhibition? Did you notice any colonies (isolated mounds of cells) growing within any of the zones of inhibition? If so, which plate(s) and which drug(s)? Advertisement About · Careers · Privacy · Terms · Contact · Languages · Your Ad Choices · Press · © Quora, Inc. 2025
13202	https://artofproblemsolving.com/wiki/index.php/Function?srsltid=AfmBOoou9HYLYR_Rf0ZyEpsN1iKjJiKElGThO4pLRYMhTLniludUBf5S	Art of Problem Solving Function - AoPS Wiki Art of Problem Solving AoPS Online Math texts, online classes, and more for students in grades 5-12. Visit AoPS Online ‚ Books for Grades 5-12Online Courses Beast Academy Engaging math books and online learning for students ages 6-13. Visit Beast Academy ‚ Books for Ages 6-13Beast Academy Online AoPS Academy Small live classes for advanced math and language arts learners in grades 2-12. Visit AoPS Academy ‚ Find a Physical CampusVisit the Virtual Campus Sign In Register online school Class ScheduleRecommendationsOlympiad CoursesFree Sessions books tore AoPS CurriculumBeast AcademyOnline BooksRecommendationsOther Books & GearAll ProductsGift Certificates community ForumsContestsSearchHelp resources math training & toolsAlcumusVideosFor the Win!MATHCOUNTS TrainerAoPS Practice ContestsAoPS WikiLaTeX TeXeRMIT PRIMES/CrowdMathKeep LearningAll Ten contests on aopsPractice Math ContestsUSABO newsAoPS BlogWebinars view all 0 Sign In Register AoPS Wiki ResourcesAops Wiki Function Page ArticleDiscussionView sourceHistory Toolbox Recent changesRandom pageHelpWhat links hereSpecial pages Search Function A function is a rule that maps one set of values to another set of values, assigning to each value in the first set exactly one value in the second. For instance, one function may map 1 to 1, 2 to 4, 3 to 9, 4 to 16, and so on. This function has the rule that it takes its input value, and squares it to get an output value. One can call this function . Contents [hide] 1 Rigorous Definition 2 Introductory Topics 2.1 Domain and Range 2.2 Real Functions 2.3 Graphs 2.4 Inverses 3 Intermediate Topics 3.1 Injections, Surjections, Bijections 3.1.1 Examples 3.2 Monotonic functions 4 Advanced Topics 4.1 Functions of Real Variables 4.2 Continuity 4.2.1 Epsilon-Delta Definition 4.2.2 Heine Definition 4.2.3 Properties of Continuous Functions 4.3 Differentiability 4.4 Integrability 4.5 Convexity 5 Notation 6 History of Functions 7 Problems 7.1 Introductory 7.2 Intermediate 7.3 Olympiad 7.4 Advanced 8 See Also Rigorous Definition Let , be sets and let be a subset of , which denotes the Cartesian product of and . (That is, is a relation between and .) We say that is a function from to (written ) if and only if For every there is some such that , and if and then . (Here is an ordered pair.) Introductory Topics Domain and Range The domain of a function is the set of input values for the argument of a function. The range of a function is the set of output values for that function. For an example, consider the function: . The domain of the function is the set , where is a real number, because the square root is only defined when its argument is nonnegative. The range is the set of all non-negative real numbers, because the square root can never return a negative value. Real Functions A real function is a function whose range is in the real numbers. Usually we speak about functions whose domain is also a subset of the real numbers. Graphs Functions are often graphed. A graph corresponds to a function only if it stands up to the vertical line test. Inverses The inverse of a function is a function that "undoes" a function. For an example, consider the function: . The function has the property that . Therefore, is called the (right) inverse function. (Similarly, a function that satisfies is called the left inverse function. Typically the right and left inverses coincide on a suitable domain, and in this case we simply call the right and left inverse function the inverse function.) Often the inverse of a function is denoted by . Intermediate Topics Injections, Surjections, Bijections An injection (or one-to-one function) is a function which always gives distinct values for distinct arguments within a given domain. By definition, is injective if , or equivalently, Injectivity of a function implies that has an inverse. Furthermore, if and are finite sets, injectivity implies . A surjection (or onto function) maps at least one element from its domain, onto every element of its range, A bijection (or one-to-one correspondence, which must be one-to-one and onto) is a function, that is both injective and surjective. If is an injection from and is an injection from then there exists a bijection, between and . This is the Schroeder-Bernstein Theorem. Examples is injective and surjective (and therefore bijective) from . is injective from . is surjective from . is neither injective from (since ) nor surjective from (since does not map any value to , which is an element of ). Monotonic functions A function is called monotonically increasing if holds whenever . If the inequality holds strictly , then the function is called strictly increasing. Similarly, a function is called monotonically decreasing if holds whenever . If the inequality holds strictly , then the function is called strictly decreasing. Advanced Topics Functions of Real Variables A real function is a function whose range is in the real numbers. Usually we speak about function whose domain is also a subset of the real numbers. Continuity Intuitively, a continuous function has the propriety that its graph can be drawn without taking the pencil off the paper. To rigorously define continuous functions, more complex mathematics is necessary. Epsilon-Delta Definition A function is called continuous at some point in its domain if, for all , there exists such that, for any , the condition implies that . Heine Definition The previous definition of continuity at is equivalent with the following: for every sequence such that , we have that . It is easy to see that a function is continuous in isolated points, and is continuous in large groups of points if the limit of the function in those points equals the value of the function. A function is continuous on a set if it is continuous in every point of the set. Properties of Continuous Functions The sum and product of two continuous functions are continuous functions. The composition of two continuous functions is a continuous function. In any closed interval , there exist real numbers and such that has a maximum value at and has a minimum value at . If a function is continuous, then it has the Intermediate Value Theorem. The converse is not always true. Differentiability Differentiability is a smoothness condition on functions. For functions of one variable, differentiability is simply the question of whether or not a derivative exists. For functions of more than one variable, the notion of differentiability is significantly more complicated. In the case of both one and multivariable functions, differentiability implies continuity. A single-variable function is differentiable at if . The derivative is the value of this limit. Integrability All continuous functions are integrable, as well as many non-continuous functions. Convexity A twice-differentiable function is concave up (or convex) in the interval if in the interval and concave down (or concave) if . The points of inflection, when the concavity switches, of the function occur at the roots of . Notation A common notation to define is: (where the , of course, is merely an example). This tells us that is a function that squares its argument (its input value). Note that this "rule" can be arbitrarily complicated and doesn't need to be given by a simple formula or description. The only requirement is that should be uniquely determined by . The following are examples of functions: for , otherwise History of Functions Without being used explicitly, the notion of function first appears with the ancient Greeks and Egyptians. The rigorous definition was stated in the 19th century and is the result of the works of some famous mathematicians: A.L. Cauchy, Leonhard Euler, and Bernhard Riemann. With the development of set theory, a new branch of mathematics appeared, mathematical analysis, in which the notion of function has a central role. The current notation used is attributed to Leonhard Euler. Problems Introductory Define . What is ? (Source) Intermediate The function f is defined on the set of integers and satisfies Find . (Source) Olympiad Let be a function with the following properties: is defined for every positive integer ; is an integer; ; for all and ; whenever . Prove that . (Source) Advanced Describe all polynomials such that for all . See Also Odd function Even function Algebra Functional equation Polynomials Calculus Limit Derivative Integral Retrieved from " Categories: Algebra Definition Functions Art of Problem Solving is an ACS WASC Accredited School aops programs AoPS Online Beast Academy AoPS Academy About About AoPS Our Team Our History Jobs AoPS Blog Site Info Terms Privacy Contact Us follow us Subscribe for news and updates © 2025 AoPS Incorporated © 2025 Art of Problem Solving About Us•Contact Us•Terms•Privacy Copyright © 2025 Art of Problem Solving Something appears to not have loaded correctly. Click to refresh.
13203	https://brainly.in/question/14480955	The acidity of formic acid is more than acetic acid. Explain. - Brainly.in Skip to main content Ask Question Log in Join for free For parents For teachers Honor code Textbook Solutions Brainly App janajaivid6197 04.01.2020 Chemistry Secondary School answered The acidity of formic acid is more than acetic acid. Explain. 1 See answer See what the community says and unlock a badge. Add answer+13 pts 0:00 / 0:15 Read More janajaivid6197 is waiting for your help. Add your answer and earn points. Add answer +13 pts Answer No one rated this answer yet — why not be the first? 😎 boniiii boniiii Explanation: Acetic acid contains an electron donating methyl group. It Destabilise the conjugate base of acetic acid. Formic acid has no such electron donating group and is stronger acid than acetic acid. Therefore formic acid is more powerful than acetic acid. Hope it helps! :) Explore all similar answers Thanks 0 rating answer section Answer rating 5.0 (1 vote) Find Chemistry textbook solutions? See all Class 12 Class 11 Class 10 Class 9 Class 8 Class 7 Class 6 Preeti Gupta - All In One Chemistry 11 3080 solutions Selina - Concise Chemistry - Class 9 1071 solutions 1500 Selected Problems In Chemistry for JEE Main & Advanced 2928 solutions Lakhmir Singh, Manjit Kaur - Chemistry 10 1797 solutions Lakhmir Singh, Manjit Kaur - Chemistry 9 1137 solutions NCERT Class 11 Chemistry Part 1 431 solutions NEET Exam - Chemistry 360 solutions Chemistry 643 solutions Selina - Concise Chemistry - Class 8 487 solutions Selina - Chemistry - Class 7 394 solutions SEE ALL Advertisement Still have questions? Find more answers Ask your question New questions in Chemistry Write the structural formula of 3- ethyl-2, 5-dimethyl hexan-3-ol Anti iron gel how to prepare for neede rotation 90 degree Copper Sulphate give the valency 1. Re write the correct functions of the given table Sl.No. 1 23 Forms of water Character Solid Liquid Gaseous When water is heated it convert into 1. Re write the correct functions of the given table Forms of water Sl.No. 1 Solid 2 Liquid Gaseous 23 Character When water is heated it convert into PreviousNext Advertisement Ask your question Free help with homework Why join Brainly? ask questions about your assignment get answers with explanations find similar questions I want a free account Company Careers Advertise with us Terms of Use Copyright Policy Privacy Policy Cookie Preferences Help Signup Help Center Safety Center Responsible Disclosure Agreement Get the Brainly App ⬈(opens in a new tab)⬈(opens in a new tab) Brainly.in We're in the know (opens in a new tab)(opens in a new tab)(opens in a new tab)(opens in a new tab)
13204	https://pages.ucsd.edu/~mboyle/COGS107a/pdf-files/Neuroscience.pdf	NEUROSCIENCE Third Edition Edited by DALE PURVES GEORGE J. AUGUSTINE DAVID FITZPATRICK WILLIAM C. HALL ANTHONY-SAMUEL LAMANTIA JAMES O. MCNAMARA S. MARK WILLIAMS NEUROSCIENCE THIRD EDITION Sinauer Associates, Inc. • Publishers Sunderland, Massachusetts U.S.A. NEUROSCIENCE: Third Edition Copyright © 2004 by Sinauer Associates, Inc. All rights reserved. This book may not be reproduced in whole or in part without permission. Address inquiries and orders to Sinauer Associates, Inc. 23 Plumtree Road Sunderland, MA 01375 U.S.A. www.sinauer.com FAX: 413-549-1118 orders@sinauer.com publish@sinauer.com Library of Congress Cataloging-in-Publication Data Neuroscience / edited by Dale Purves ... [et al.].— 3rd ed. p. ; cm. Includes bibliographical references and index. ISBN 0-87893-725-0 (casebound : alk. paper) 1. Neurosciences. [DNLM: 1. Nervous System Physiology. 2. Neurochemistry. WL 102 N50588 2004] I. Purves, Dale. QP355.2.N487 2004 612.8—dc22 2004003973 Printed in U.S.A. 5 4 3 2 1 THE COVER Dorsal view of the human brain. (Courtesy of S. Mark Williams.) George J. Augustine, Ph.D. Dona M. Chikaraishi, Ph.D. Michael D. Ehlers, M.D., Ph.D. Gillian Einstein, Ph.D. David Fitzpatrick, Ph.D. William C. Hall, Ph.D. Erich Jarvis, Ph.D. Lawrence C. Katz, Ph.D. Julie Kauer, Ph.D. Anthony-Samuel LaMantia, Ph.D. James O. McNamara, M.D. Richard D. Mooney, Ph.D. Miguel A. L. Nicolelis, M.D., Ph.D. Dale Purves, M.D. Peter H. Reinhart, Ph.D. Sidney A. Simon, Ph.D. J. H. Pate Skene, Ph.D. James Voyvodic, Ph.D. Leonard E. White, Ph.D. S. Mark Williams, Ph.D. UNIT EDITORS UNIT I: George J. Augustine UNIT II: David Fitzpatrick UNIT III: William C. Hall UNIT IV: Anthony-Samuel LaMantia UNIT V: Dale Purves Contributors 1. Studying the Nervous Systems of Humans and Other Animals 1 UNIT I NEURAL SIGNALING 2. Electrical Signals of Nerve Cells 31 3. Voltage-Dependent Membrane Permeability 47 4. Channels and Transporters 69 5. Synaptic Transmission 93 6. Neurotransmitters, Receptors, and Their Effects 129 7. Molecular Signaling within Neurons 165 UNIT II SENSATION AND SENSORY PROCESSING 8. The Somatic Sensory System 189 9. Pain 209 10. Vision: The Eye 229 11. Central Visual Pathways 259 12. The Auditory System 283 13. The Vestibular System 315 14. The Chemical Senses 337 UNIT III MOVEMENT AND ITS CENTRAL CONTROL 15. Lower Motor Neuron Circuits and Motor Control 371 16. Upper Motor Neuron Control of the Brainstem and Spinal Cord 393 17. Modulation of Movement by the Basal Ganglia 417 18. Modulation of Movement by the Cerebellum 435 19. Eye Movements and Sensory Motor Integration 453 20. The Visceral Motor System 469 UNIT IV THE CHANGING BRAIN 21. Early Brain Development 501 22. Construction of Neural Circuits 521 23. Modification of Brain Circuits as a Result of Experience 557 24. Plasticity of Mature Synapses and Circuits 575 UNIT V COMPLEX BRAIN FUNCTIONS 25. The Association Cortices 613 26. Language and Speech 637 27. Sleep and Wakefulness 659 28. Emotions 687 29. Sex, Sexuality, and the Brain 711 30. Memory 733 APPENDIX A THE BRAINSTEM AND CRANIAL NERVES 755 APPENDIX B VASCULAR SUPPLY, THE MENINGES, AND THE VENTRICULAR SYSTEM 763 Contents in Brief Chapter 1 Studying the Nervous Systems of Humans and Other Animals 1 Overview 1 Genetics, Genomics, and the Brain 1 The Cellular Components of the Nervous System 2 Neurons 4 Neuroglial Cells 8 Cellular Diversity in the Nervous System 9 Neural Circuits 11 Overall Organization of the Human Nervous System 14 Neuroanatomical Terminology 16 The Subdivisions of the Central Nervous System 18 Organizational Principles of Neural Systems 20 Functional Analysis of Neural Systems 23 Analyzing Complex Behavior 24 BOX A Brain Imaging Techniques 25 Summary 26 Contents Unit I NEURAL SIGNALING Chapter 2 Electrical Signals of Nerve Cells 31 Overview 31 Electrical Potentials across Nerve Cell Membranes 31 How Ionic Movements Produce Electrical Signals 34 The Forces That Create Membrane Potentials 36 Electrochemical Equilibrium in an Environment with More Than One Permeant Ion 38 The Ionic Basis of the Resting Membrane Potential 40 BOX A The Remarkable Giant Nerve Cells of Squid 41 The Ionic Basis of Action Potentials 43 BOX B Action Potential Form and Nomenclature 44 Summary 45 Chapter 3 Voltage-Dependent Membrane Permeability 47 Overview 47 Ionic Currents Across Nerve Cell Membranes 47 BOX A The Voltage Clamp Method 48 Two Types of Voltage-Dependent Ionic Current 49 Two Voltage-Dependent Membrane Conductances 52 Reconstruction of the Action Potential 54 Long-Distance Signaling by Means of Action Potentials 56 BOX B Threshold 57 BOX C Passive Membrane Properties 60 The Refractory Period 61 Increased Conduction Velocity as a Result of Myelination 63 Summary 65 BOX D Multiple Sclerosis 66 Preface xvi Acknowledgments xvii Supplements to Accompany NEUROSCIENCE xviii Chapter 4 Channels and Transporters 69 Overview 69 Ion Channels Underlying Action Potentials 69 BOX A The Patch Clamp Method 70 The Diversity of Ion Channels 73 BOX B Expression of Ion Channels in Xenopus Oocytes 75 Voltage-Gated Ion Channels 76 Ligand-Gated Ion Channels 78 Stretch- and Heat-Activated Channels 78 The Molecular Structure of Ion Channels 79 BOX C Toxins That Poison Ion Channels 82 BOX D Diseases Caused by Altered Ion Channels 84 Active Transporters Create and Maintain Ion Gradients 86 Functional Properties of the Na+/K+ Pump 87 The Molecular Structure of the Na+/K+ Pump 89 Summary 90 Chapter 5 Synaptic Transmission 93 Overview 93 Electrical Synapses 93 Signal Transmission at Chemical Synapses 96 Properties of Neurotransmitters 96 BOX A Criteria That Define a Neurotransmitter 99 Quantal Release of Neurotransmitters 102 Release of Transmitters from Synaptic Vesicles 103 Local Recycling of Synaptic Vesicles 105 The Role of Calcium in Transmitter Secretion 107 BOX B Diseases That Affect the Presynaptic Terminal 108 Molecular Mechanisms of Transmitter Secretion 110 Neurotransmitter Receptors 113 BOX C Toxins That Affect Transmitter Release 115 Postsynaptic Membrane Permeability Changes during Synaptic Transmission 116 Excitatory and Inhibitory Postsynaptic Potentials 121 Summation of Synaptic Potentials 123 Two Families of Postsynaptic Receptors 124 Summary 126 Chapter 6 Neurotransmitters and Their Receptors 129 Overview 129 Categories of Neurotransmitters 129 Acetylcholine 129 BOX A Addiction 134 BOX B Neurotoxins that Act on Postsynaptic Receptors 136 Glutamate 137 BOX C Myasthenia Gravis: An Autoimmune Disease of Neuromuscular Synapses 140 GABA and Glycine 143 BOX D Excitotoxicity Following Acute Brain Injury 145 The Biogenic Amines 147 BOX E Biogenic Amine Neurotransmitters and Psychiatric Disorders 148 ATP and Other Purines 152 Peptide Neurotransmitters 153 Unconventional Neurotransmitters 157 BOX F Marijuana and the Brain 160 Summary 161 Chapter 7 Molecular Signaling within Neurons 165 Overview 165 Strategies of Molecular Signaling 165 The Activation of Signaling Pathways 167 Receptor Types 168 G-Proteins and Their Molecular Targets 170 Second Messengers 172 Second Messenger Targets: Protein Kinases and Phosphatases 175 Nuclear Signaling 178 Examples of Neuronal Signal Transduction 181 Summary 184 Contents ix x Contents Chapter 8 The Somatic Sensory System 189 Overview 189 Cutaneous and Subcutaneous Somatic Sensory Receptors 189 Mechanoreceptors Specialized to Receive Tactile Information 192 Differences in Mechanosensory Discrimination across the Body Surface 193 BOX A Receptive Fields and Sensory Maps in the Cricket 195 BOX B Dynamic Aspects of Somatic Sensory Receptive Fields 196 Mechanoreceptors Specialized for Proprioception 197 Active Tactile Exploration 199 The Major Afferent Pathway for Mechanosensory Information: The Dorsal Column–Medial Lemniscus System 199 The Trigeminal Portion of the Mechanosensory System 202 BOX C Dermatomes 202 The Somatic Sensory Components of the Thalamus 203 The Somatic Sensory Cortex 203 Higher-Order Cortical Representations 206 BOX D Patterns of Organization within the Sensory Cortices: Brain Modules 207 Summary 208 Chapter 9 Pain 209 Overview 209 Nociceptors 209 Transduction of Nociceptive Signals 211 BOX A Capsaicin 212 Central Pain Pathways 213 BOX B Referred Pain 215 BOX C A Dorsal Column Pathway for Visceral Pain 218 Sensitization 220 BOX D Phantom Limbs and Phantom Pain 222 Descending Control of Pain Perception 224 The Placebo Effect 224 The Physiological Basis of Pain Modulation 225 Summary 227 Chapter 10 Vision:The Eye 229 Overview 229 Anatomy of the Eye 229 The Formation of Images on the Retina 231 BOX A Myopia and Other Refractive Errors 232 The Retina 234 Phototransduction 236 BOX B Retinitis Pigmentosa 239 Functional Specialization of the Rod and Cone Systems 240 BOX C Macular Degeneration 243 Anatomical Distribution of Rods and Cones 244 Cones and Color Vision 245 BOX D The Importance of Context in Color Perception 247 Retinal Circuits for Detecting Luminance Change 249 BOX E The Perception of Light Intensity 250 Contribution of Retinal Circuits to Light Adaptation 254 Summary 257 Chapter 11 Central Visual Pathways 259 Overview 259 Central Projections of Retinal Ganglion Cells 259 BOX A The Blind Spot 262 The Retinotopic Representation of the Visual Field 263 Visual Field Deficits 267 The Functional Organization of the Striate Cortex 269 The Columnar Organization of the Striate Cortex 271 BOX B Random Dot Stereograms and Related Amusements 272 Division of Labor within the Primary Visual Pathway 275 BOX C Optical Imaging of Functional Domains in the Visual Cortex 276 The Functional Organization of Extrastriate Visual Areas 278 Summary 281 Chapter 12 The Auditory System 283 Overview 283 Sound 283 The Audible Spectrum 284 Unit II SENSATION AND SENSORY PROCESSING Chapter 15 Lower Motor Neuron Circuits and Motor Control 371 Overview 371 Neural Centers Responsible for Movement 371 Motor Neuron–Muscle Relationships 373 The Motor Unit 375 The Regulation of Muscle Force 377 The Spinal Cord Circuitry Underlying Muscle Stretch Reflexes 379 A Synopsis of Auditory Function 285 BOX A Four Causes of Acquired Hearing Loss 285 BOX B Music 286 The External Ear 287 The Middle Ear 289 The Inner Ear 289 BOX C Sensorineural Hearing Loss and Cochlear Implants 290 BOX D The Sweet Sound of Distortion 295 Hair Cells and the Mechanoelectrical Transduction of Sound Waves 294 Two Kinds of Hair Cells in the Cochlea 300 Tuning and Timing in the Auditory Nerve 301 How Information from the Cochlea Reaches Targets in the Brainstem 303 Integrating Information from the Two Ears 303 Monaural Pathways from the Cochlear Nucleus to the Lateral Lemniscus 307 Integration in the Inferior Colliculus 307 The Auditory Thalamus 308 The Auditory Cortex 309 BOX E Representing Complex Sounds in the Brains of Bats and Humans 310 Summary 313 Chapter 13 The Vestibular System 315 Overview 315 The Vestibular Labyrinth 315 Vestibular Hair Cells 316 The Otolith Organs: The Utricle and Saccule 317 BOX A A Primer on Vestibular Navigation 318 BOX B Adaptation and Tuning of Vestibular Hair Cells 320 How Otolith Neurons Sense Linear Forces 322 The Semicircular Canals 324 How Semicircular Canal Neurons Sense Angular Accelerations 325 BOX C Throwing Cold Water on the Vestibular System 326 Central Pathways for Stabilizing Gaze, Head, and Posture 328 Vestibular Pathways to the Thalamus and Cortex 331 BOX D Mauthner Cells in Fish 332 Summary 333 Chapter 14 The Chemical Senses 337 Overview 337 The Organization of the Olfactory System 337 Olfactory Perception in Humans 339 Physiological and Behavioral Responses to Odorants 341 The Olfactory Epithelium and Olfactory Receptor Neurons 342 BOX A Olfaction, Pheromones, and Behavior in the Hawk Moth 344 The Transduction of Olfactory Signals 345 Odorant Receptors 346 Olfactory Coding 348 The Olfactory Bulb 350 BOX B Temporal “Coding”of Olfactory Information in Insects 350 Central Projections of the Olfactory Bulb 353 The Organization of the Taste System 354 Taste Perception in Humans 356 Idiosyncratic Responses to Tastants 357 The Organization of the Peripheral Taste System 359 Taste Receptors and the Transduction of Taste Signals 360 Neural Coding in the Taste System 362 Trigeminal Chemoreception 363 Summary 366 Contents xi Unit III MOVEMENT AND ITS CENTRAL CONTROL xii Contents The Influence of Sensory Activity on Motor Behavior 381 Other Sensory Feedback That Affects Motor Performance 382 BOX A Locomotion in the Leech and the Lamprey 384 Flexion Reflex Pathways 387 Spinal Cord Circuitry and Locomotion 387 BOX B The Autonomy of Central Pattern Generators: Evidence from the Lobster Stomatogastric Ganglion 388 The Lower Motor Neuron Syndrome 389 BOX C Amyotrophic Lateral Sclerosis 391 Summary 391 Chapter 16 Upper Motor Neuron Control of the Brainstem and Spinal Cord 393 Overview 393 Descending Control of Spinal Cord Circuitry: General Information 393 Motor Control Centers in the Brainstem: Upper Motor Neurons That Maintain Balance and Posture 397 BOX A The Reticular Formation 398 The Corticospinal and Corticobulbar Pathways: Upper Motor Neurons That Initiate Complex Voluntary Movements 402 BOX B Descending Projections to Cranial Nerve Motor Nuclei and Their Importance in Diagnosing the Cause of Motor Deficits 404 Functional Organization of the Primary Motor Cortex 405 BOX C What Do Motor Maps Represent? 408 The Premotor Cortex 411 BOX D Sensory Motor Talents and Cortical Space 410 Damage to Descending Motor Pathways: The Upper Motor Neuron Syndrome 412 BOX E Muscle Tone 414 Summary 415 Chapter 17 Modulation of Movement by the Basal Ganglia 417 Overview 417 Projections to the Basal Ganglia 417 Projections from the Basal Ganglia to Other Brain Regions 422 Evidence from Studies of Eye Movements 423 Circuits within the Basal Ganglia System 424 BOX A Huntington’s Disease 426 BOX B Parkinson’s Disease: An Opportunity for Novel Therapeutic Approaches 429 BOX C Basal Ganglia Loops and Non-Motor Brain Functions 432 Summary 433 Chapter 18 Modulation of Movement by the Cerebellum 435 Overview 435 Organization of the Cerebellum 435 Projections to the Cerebellum 438 Projections from the Cerebellum 440 Circuits within the Cerebellum 441 BOX A Prion Diseases 444 Cerebellar Circuitry and the Coordination of Ongoing Movement 445 Futher Consequences of Cerebellar Lesions 448 Summary 449 BOX B Genetic Analysis of Cerebellar Function 450 Chapter 19 Eye Movements and Sensory Motor Integration 453 Overview 453 What Eye Movements Accomplish 453 The Actions and Innervation of Extraocular Muscles 454 BOX A The Perception of Stabilized Retinal Images 456 Types of Eye Movements and Their Functions 457 Neural Control of Saccadic Eye Movements 458 BOX B Sensory Motor Integration in the Superior Colliculus 462 Neural Control of Smooth Pursuit Movements 466 Neural Control of Vergence Movements 466 Summary 467 Chapter 20 The Visceral Motor System 469 Overview 469 Early Studies of the Visceral Motor System 469 Distinctive Features of the Visceral Motor System 470 The Sympathetic Division of the Visceral Motor System 471 The Parasympathetic Division of the Visceral Motor System 476 The Enteric Nervous System 479 Sensory Components of the Visceral Motor System 480 Chapter 21 Early Brain Development 501 Overview 501 The Initial Formation of the Nervous System: Gastrulation and Neurulation 501 The Molecular Basis of Neural Induction 503 BOX A Stem Cells: Promise and Perils 504 BOX B Retinoic Acid:Teratogen and Inductive Signal 506 Formation of the Major Brain Subdivisions 510 BOX C Homeotic Genes and Human Brain Development 513 BOX D Rhombomeres 514 Genetic Abnormalities and Altered Human Brain Development 515 The Initial Differentiation of Neurons and Glia 516 BOX E Neurogenesis and Neuronal Birthdating 517 The Generation of Neuronal Diversity 518 Neuronal Migration 520 BOX F Mixing It Up: Long-Distance Neuronal Migration 524 Summary 525 Chapter 22 Construction of Neural Circuits 527 Overview 527 The Axonal Growth Cone 527 Non-Diffusible Signals for Axon Guidance 528 BOX A Choosing Sides: Axon Guidance at the Optic Chiasm 530 Diffusible Signals for Axon Guidance: Chemoattraction and Repulsion 534 The Formation of Topographic Maps 537 Selective Synapse Formation 539 BOX B Molecular Signals That Promote Synapse Formation 542 Trophic Interactions and the Ultimate Size of Neuronal Populations 543 Further Competitive Interactions in the Formation of Neuronal Connections 545 Molecular Basis of Trophic Interactions 547 BOX C Why Do Neurons Have Dendrites? 548 BOX D The Discovery of BDNF and the Neurotrophin Family 552 Neurotrophin Signaling 553 Summary 554 Chapter 23 Modification of Brain Circuits as a Result of Experience 557 Overview 557 Critical Periods 557 BOX A Built-In Behaviors 558 The Development of Language: Example of a Human Critical Period 559 BOX B Birdsong 560 Critical Periods in Visual System Development 562 Effects of Visual Deprivation on Ocular Dominance 563 BOX C Transneuronal Labeling with Radioactive Amino Acids 564 Visual Deprivation and Amblyopia in Humans 568 Mechanisms by which Neuronal Activity Affects the Development of Neural Circuits 569 Cellular and Molecular Correlates of Activity-Dependent Plasticity during Critical Periods 572 Evidence for Critical Periods in Other Sensory Systems 572 Summary 573 Contents xiii Unit IV THE CHANGING BRAIN Central Control of Visceral Motor Functions 483 BOX A The Hypothalamus 484 Neurotransmission in the Visceral Motor System 487 BOX B Horner’s Syndrome 488 BOX C Obesity and the Brain 490 Visceral Motor Reflex Functions 491 Autonomic Regulation of Cardiovascular Function 491 Autonomic Regulation of the Bladder 493 Autonomic Regulation of Sexual Function 496 Summary 498 xiv Contents Chapter 25 The Association Cortices 613 Overview 613 The Association Cortices 613 An Overview of Cortical Structure 614 Specific Features of the Association Cortices 615 BOX A A More Detailed Look at Cortical Lamination 617 Lesions of the Parietal Association Cortex: Deficits of Attention 619 Lesions of the Temporal Association Cortex: Deficits of Recognition 622 Lesions of the Frontal Association Cortex: Deficits of Planning 623 BOX B Psychosurgery 625 “Attention Neurons” in the Monkey Parietal Cortex 626 “Recognition Neurons” in the Monkey Temporal Cortex 627 “Planning Neurons” in the Monkey Frontal Cortex 630 BOX C Neuropsychological Testing 632 BOX D Brain Size and Intelligence 634 Summary 635 Chapter 26 Language and Speech 637 Overview 637 Language Is Both Localized and Lateralized 637 Aphasias 638 BOX A Speech 640 BOX B Do Other Animals Have Language? 642 BOX C Words and Meaning 645 A Dramatic Confirmation of Language Lateralization 646 Anatomical Differences between the Right and Left Hemispheres 648 Mapping Language Functions 649 BOX D Language and Handedness 650 The Role of the Right Hemisphere in Language 654 Sign Language 655 Summary 656 Chapter 27 Sleep and Wakefulness 659 Overview 659 Why Do Humans (and Many Other Animals) Sleep? 659 BOX A Styles of Sleep in Different Species 661 Unit V COMPLEX BRAIN FUNCTIONS Chapter 24 Plasticity of Mature Synapses and Circuits 575 Overview 575 Synaptic Plasticity Underlies Behavioral Modification in Invertebrates 575 BOX A Genetics of Learning and Memory in the Fruit Fly 581 Short-Term Synaptic Plasticity in the Mammalian Nervous System 582 Long-Term Synaptic Plasticity in the Mammalian Nervous System 583 Long-Term Potentiation of Hippocampal Synapses 584 Molecular Mechanisms Underlying LTP 587 BOX B Dendritic Spines 590 Long-Term Synaptic Depression 592 BOX C Silent Synapses 594 Changes in Gene Expression Cause Enduring Changes in Synaptic Function during LTP and LTD 597 Plasticity in the Adult Cerebral Cortex 599 BOX D Epilepsy:The Effect of Pathological Activity on Neural Circuitry 600 Recovery from Neural Injury 602 Generation of Neurons in the Adult Brain 605 BOX E Why Aren’t We More Like Fish and Frogs? 606 Summary 609 The Circadian Cycle of Sleep and Wakefulness 662 Stages of Sleep 665 BOX B Molecular Mechanisms of Biological Clocks 666 BOX C Electroencephalography 668 Physiological Changes in Sleep States 671 The Possible Functions of REM Sleep and Dreaming 671 Neural Circuits Governing Sleep 674 BOX D Consciousness 675 Thalamocortical Interactions 679 Sleep Disorders 681 BOX E Drugs and Sleep 682 Summary 684 Chapter 28 Emotions 687 Overview 687 Physiological Changes Associated with Emotion 687 The Integration of Emotional Behavior 688 BOX A Facial Expressions: Pyramidal and Extrapyramidal Contributions 690 The Limbic System 693 BOX B The Anatomy of the Amygdala 696 The Importance of the Amygdala 697 BOX C The Reasoning Behind an Important Discovery 698 The Relationship between Neocortex and Amygdala 701 BOX D Fear and the Human Amygdala: A Case Study 702 BOX E Affective Disorders 704 Cortical Lateralization of Emotional Functions 705 Emotion, Reason, and Social Behavior 707 Summary 708 Chapter 29 Sex,Sexuality,and the Brain 711 Overview 711 Sexually Dimorphic Behavior 711 What Is Sex? 712 BOX A The Development of Male and Female Phenotypes 714 Hormonal Influences on Sexual Dimorphism 715 BOX B The Case of Bruce/Brenda 716 The Effect of Sex Hormones on Neural Circuitry 718 BOX C The Actions of Sex Hormones 718 Other Central Nervous System Dimorphisms Specifically Related to Reproductive Behaviors 720 Brain Dimorphisms Related to Cognitive Function 728 Hormone-Sensitive Brain Circuits in Adult Animals 729 Summary 731 Chapter 30 Memory 733 Overview 733 Qualitative Categories of Human Memory 733 Temporal Categories of Memory 734 BOX A Phylogenetic Memory 735 The Importance of Association in Information Storage 736 Forgetting 738 BOX B Savant Syndrome 739 Brain Systems Underlying Declarative Memory Formation 741 BOX C Clinical Cases That Reveal the Anatomical Substrate for Declarative Memories 742 Brain Systems Underlying Long-Term Storage of Declarative Memory 746 Brain Systems Underlying Nondeclarative Learning and Memory 748 Memory and Aging 749 BOX D Alzheimer’s Disease 750 Summary 753 Appendix A The Brainstem and Cranial Nerves 755 Appendix B Vascular Supply,the Meninges, and the Ventricular System 763 The Blood Supply of the Brain and Spinal Cord 763 The Blood-Brain Barrier 766 BOX A Stroke 767 The Meninges 768 The Ventricular System 770 Glossary Illustration Source References Index Contents xv Whether judged in molecular, cellular, systemic, behavioral, or cogni-tive terms, the human nervous system is a stupendous piece of bio-logical machinery. Given its accomplishments—all the artifacts of human culture, for instance—there is good reason for wanting to understand how the brain and the rest of the nervous system works. The debilitating and costly effects of neurological and psychiatric dis-ease add a further sense of urgency to this quest. The aim of this book is to highlight the intellectual challenges and excitement—as well as the uncertainties—of what many see as the last great frontier of bio-logical science. The information presented should serve as a starting point for undergraduates, medical students, graduate students in the neurosciences, and others who want to understand how the human nervous system operates. Like any other great challenge, neuro-science should be, and is, full of debate, dissension, and considerable fun. All these ingredients have gone into the construction of the third edition of this book; we hope they will be conveyed in equal measure to readers at all levels. Preface We are grateful to numerous colleagues who provided helpful contri-butions, criticisms and suggestions to this and previous editions. We particularly wish to thank Ralph Adolphs, David Amaral, Eva Anton, Gary Banker, Bob Barlow, Marlene Behrmann, Ursula Bellugi, Dan Blazer, Bob Burke, Roberto Cabeza, Nell Cant, Jim Cavanaugh, John Chapin, Milt Charlton, Michael Davis, Rob Deaner, Bob Desimone, Allison Doupe, Sasha du Lac, Jen Eilers, Anne Fausto-Sterling, Howard Fields, Elizabeth Finch, Nancy Forger, Jannon Fuchs, Michela Gallagher, Dana Garcia, Steve George, the late Patricia Gold-man-Rakic, Mike Haglund, Zach Hall, Kristen Harris, Bill Henson, John Heuser, Jonathan Horton, Ron Hoy, Alan Humphrey, Jon Kaas, Jagmeet Kanwal, Herb Killackey, Len Kitzes, Arthur Lander, Story Landis, Simon LeVay, Darrell Lewis, Jeff Lichtman, Alan Light, Steve Lisberger, Donald Lo, Arthur Loewy, Ron Mangun, Eve Marder, Robert McCarley, Greg McCarthy, Jim McIlwain, Chris Muly, Vic Nadler, Ron Oppenheim, Larysa Pevny, Michael Platt, Franck Polleux, Scott Pomeroy, Rodney Radtke, Louis Reichardt, Marnie Rid-dle, Jamie Roitman, Steve Roper, John Rubenstein, Ben Rubin, David Rubin, Josh Sanes, Cliff Saper, Lynn Selemon, Carla Shatz, Bill Snider, Larry Squire, John Staddon, Peter Strick, Warren Strittmatter, Joe Takahashi, Richard Weinberg, Jonathan Weiner, Christina Williams, Joel Winston, and Fulton Wong. It is understood, of course, that any errors are in no way attributable to our critics and advisors. We also thank the students at Duke University Medical School as well as many other students and colleagues who provided sugges-tions for improvement of the last edition. Finally, we owe special thanks to Robert Reynolds and Nate O’Keefe, who labored long and hard to put the third edition together, and to Andy Sinauer, Graig Donini, Carol Wigg, Christopher Small, Janice Holabird, and the rest of the staff at Sinauer Associates for their outstanding work and high standards. Acknowledgments For the Student Sylvius for Neuroscience: A Visual Glossary of Human Neuroanatomy (CD-ROM) S. Mark Williams, Leonard E. White, and Andrew C. Mace Sylvius for Neuroscience: A Visual Glossary of Human Neuroanatomy, included in every copy of the textbook, is an interactive CD reference guide to the structure of the human nervous system. By entering a corresponding page number from the textbook, students can quickly search the CD for any neuroanatomical structure or term and view corresponding images and animations. Descriptive information is provided with all images and animations. Additionally, students can take notes on the content and share these with other Sylvius users. Sylvius is an essential study aid for learning basic human neuro-anatomy. Sylvius for Neuroscience features: • Over 400 neuroanatomical structures and terms. • High-resolution images. • Animations of pathways and 3-D reconstructions. • Definitions and descriptions. • Audio pronunciations. • A searchable glossary. • Categories of anatomical structures and terms (e.g., cranial nerves, spinal cord tracts, lobes, cortical areas, etc.), that can be easily browsed. In addition, structures can be browsed by text-book chapter. Supplements to Accompany NEUROSCIENCE Third Edition • Images and text relevant to the textbook: Icons in the textbook indicate specific content on the CD. By entering a textbook page number, students can automatically load the relevant images and text. • A history feature that allows the student to quickly reload recently viewed structures. • A bookmark feature that adds bookmarks to structures of in-terest; bookmarks are automatically stored on the student’s computer. • A notes feature that allows students to type notes for any selected structure; notes are automatically saved on the stu-dent’s computer and can be shared among students and instructors (i.e., imported and exported). • A self-quiz mode that allows for testing on structure identifica-tion and functional information. • A print feature that formats images and text for printed output. • An image zoom tool. For the Instructor Instructor’s Resource CD (ISBN 0-87893-750-1) This expanded resource includes all the figures and tables from the textbook in JPEG format, reformatted and relabeled for optimal read-ability. Also included are ready-to-use PowerPoint® presentations of all figures and tables. In addition, new for the Third Edition, the Instructor’s Resource CD includes a set of short-answer study ques-tions for each chapter in Microsoft® Word® format. Overhead Transparencies (ISBN 0-87893-751-X) This set includes 100 illustrations (approximately 150 transparencies), selected from throughout the textbook for teaching purposes. These are relabeled and optimized for projection in classrooms. Supplements xix Overview Neuroscience encompasses a broad range of questions about how nervous systems are organized, and how they function to generate behavior. These questions can be explored using the analytical tools of genetics, molecular and cell biology, systems anatomy and physiology, behavioral biology, and psychology. The major challenge for a student of neuroscience is to integrate the diverse knowledge derived from these various levels of analysis into a more or less coherent understanding of brain structure and function (one has to qualify this statement because so many questions remain unan-swered). Many of the issues that have been explored successfully concern how the principal cells of any nervous system—neurons and glia—perform their basic functions in anatomical, electrophysiological, and molecular terms. The varieties of neurons and supporting glial cells that have been identified are assembled into ensembles called neural circuits, and these cir-cuits are the primary components of neural systems that process specific types of information. Neural systems comprise neurons and circuits in a number of discrete anatomical locations in the brain. These systems subserve one of three general functions. Sensory systems represent information about the state of the organism and its environment, motor systems organize and generate actions; and associational systems link the sensory and motor sides of the nervous system, providing the basis for “higher-order” functions such as perception, attention, cognition, emotions, rational thinking, and other complex brain functions that lie at the core of understanding human beings, their history and their future. Genetics, Genomics, and the Brain The recently completed sequencing of the genome in humans, mice, the fruit fly Drosophila melanogaster, and the nematode worm Caenorhabditis elegans is perhaps the logical starting point for studying the brain and the rest of the nervous system; after all, this inherited information is also the starting point of each individual organism. The relative ease of obtaining, analyzing, and correlating gene sequences with neurobiological observations has facilitated a wealth of new insights into the basic biology of the nervous system. In par-allel with studies of normal nervous systems, the genetic analysis of human pedigrees with various brain diseases has led to a widespread sense that it will soon be possible to understand and treat disorders long considered beyond the reach of science and medicine. A gene consists of DNA sequences called exons that are transcribed into a messenger RNA and subsequently a protein. The set of exons that defines Chapter 1 1 Studying the Nervous Systems of Humans and Other Animals 2 Chapter One Figure 1.1 Estimates of the number of genes in the human genome, as well as in the genomes of the mouse, the fruit fly Drosophila melanogaster, and the nematode worm Caenorhabditis elegans. the transcript of any gene is flanked by upstream (or 5′) and downstream (or 3′) regulatory sequences that control gene expression. In addition, sequences between exons—called introns—further influence transcription. Of the approximately 35,000 genes in the human genome, a majority are expressed in the developing and adult brain; the same is true in mice, flies, and worms—the species commonly used in modern genetics (and increasingly in neuroscience) (Figure 1.1). Nevertheless, very few genes are uniquely ex-pressed in neurons, indicating that nerve cells share most of the basic struc-tural and functional properties of other cells. Accordingly, most “brain-specific” genetic information must reside in the remainder of nucleic acid sequences—regulatory sequences and introns—that control the timing, quantity, variability and cellular specificity of gene expression. One of the most promising dividends of sequencing the human genome has been the realization that one or a few genes, when altered (mutated), can begin to explain some aspects of neurological and psychiatric diseases. Before the “postgenomic era” (which began following completion of the sequencing of the human genome), many of the most devastating brain dis-eases remained largely mysterious because there was little sense of how or why the normal biology of the nervous system was compromised. The iden-tification of genes correlated with disorders such as Huntington’s disease, Parkinson’s disease, Alzheimer’s disease, major depression, and schizophre-nia has provided a promising start to understanding these pathological processes in a much deeper way (and thus devising rational therapies). Genetic and genomic information alone do not completely explain how the brain normally works or how disease processes disrupt its function. To achieve these goals it is equally essential to understand the cell biology, anatomy, and physiology of the brain in health as well as disease. The Cellular Components of the Nervous System Early in the nineteenth century, the cell was recognized as the fundamental unit of all living organisms. It was not until well into the twentieth century, however, that neuroscientists agreed that nervous tissue, like all other organs, is made up of these fundamental units. The major reason was that the first generation of “modern” neurobiologists in the nineteenth century had difficulty resolving the unitary nature of nerve cells with the micro-scopes and cell staining techniques that were then available. This inade-Number of genes 0 50,000 40,000 30,000 20,000 10,000 Human Mouse D. melanogaster C. elegans quacy was exacerbated by the extraordinarily complex shapes and extensive branches of individual nerve cells, which further obscured their resemblance to the geometrically simpler cells of other tissues (Figures 1.2–1.4). As a result, some biologists of that era concluded that each nerve cell was con-nected to its neighbors by protoplasmic links, forming a continuous nerve cell network, or reticulum. The “reticular theory” of nerve cell communica-tion, which was championed by the Italian neuropathologist Camillo Golgi (for whom the Golgi apparatus in cells is named), eventually fell from favor and was replaced by what came to be known as the “neuron doctrine.” The major proponents of this new perspective were the Spanish neuroanatomist Santiago Ramón y Cajal and the British physiologist Charles Sherrington. The contrasting views represented by Golgi and Cajal occasioned a spir-ited debate in the early twentieth century that set the course of modern neu-roscience. Based on light microscopic examination of nervous tissue stained with silver salts according to a method pioneered by Golgi, Cajal argued persuasively that nerve cells are discrete entities, and that they communicate Studying the Nervous Systems of Humans and Other Animals 3 Axon Cell body Dendrites Dendrites (C) Retinal ganglion cell (F) Cerebellar Purkinje cells Axon Cell body (A) Neurons in mesencephalic nucleus of cranial nerve V Axons Cell bodies (B) Retinal bipolar cell Dendrites Dendrites Cell body Axon Cell body Axon Cell body Dendrites (D) Retinal amacrine cell (E) Cortical pyramidal cell Figure 1.2 Examples of the rich variety of nerve cell morphologies found in the human nervous system. Tracings are from actual nerve cells stained by impregnation with silver salts (the so-called Golgi technique, the method used in the classical studies of Golgi and Cajal). Asterisks indicate that the axon runs on much farther than shown. Note that some cells, like the retinal bipolar cell, have a very short axon, and that others, like the retinal amacrine cell, have no axon at all. The drawings are not all at the same scale. 4 Chapter One with one another by means of specialized contacts that Sherrington called “synapses.” The work that framed this debate was recognized by the award of the Nobel Prize for Physiology or Medicine in 1906 to both Golgi and Cajal ( the joint award suggests some ongoing concern about just who was correct, despite Cajal’s overwhelming evidence). The subsequent work of Sherrington and others demonstrating the transfer of electrical signals at synaptic junctions between nerve cells provided strong support of the “neu-ron doctrine,” but challenges to the autonomy of individual neurons remained. It was not until the advent of electron microscopy in the 1950s that any lingering doubts about the discreteness of neurons were resolved. The high-magnification, high-resolution pictures that could be obtained with the electron microscope clearly established that nerve cells are functionally independent units; such pictures also identified the specialized cellular junc-tions that Sherrington had named synapses (see Figures 1.3 and 1.4). The histological studies of Cajal, Golgi, and a host of successors led to the further consensus that the cells of the nervous system can be divided into two broad categories: nerve cells (or neurons), and supporting cells called neuroglia (or simply glia; see Figure 1.5). Nerve cells are specialized for elec-trical signaling over long distances, and understanding this process repre-sents one of the more dramatic success stories in modern biology (and the subject of Unit I of this book). Supporting cells, in contrast, are not capable of electrical signaling; nevertheless, they have several essential functions in the developing and adult brain. Neurons Neurons and glia share the complement of organelles found in all cells, including the endoplasmic reticulum and Golgi apparatus, mitochondria, and a variety of vesicular structures. In neurons, however, these organelles are often more prominent in distinct regions of the cell. In addition to the distribution of organelles and subcellular components, neurons and glia are in some measure different from other cells in the specialized fibrillar or tubular proteins that constitute the cytoskeleton (Figures 1.3 and 1.4). Although many of these proteins—isoforms of actin, tubulin, and myosin, as well as several others—are found in other cells, their distinctive organization in neurons is critical for the stability and function of neuronal processes and synaptic junctions. The filaments, tubules, vesicular motors, and scaffolding proteins of neurons orchestrate the growth of axons and dendrites; the traf-ficking and appropiate positioning of membrane components, organelles, and vesicles; and the active processes of exocytosis and endocytosis that underlie synaptic communication. Understanding the ways in which these molecular components are used to insure the proper development and func-tion of neurons and glia remains a primary focus of modern neurobiology. The basic cellular organization of neurons resembles that of other cells; however, they are clearly distinguished by specialization for intercellular communication. This attribute is apparent in their overall morphology, in the specific organization of their membrane components for electrical signaling, and in the structural and functional intricacies of the synaptic contacts between neurons (see Figures 1.3 and 1.4). The most obvious sign of neu-ronal specialization for communication via electrical signaling is the exten-sive branching of neurons. The most salient aspect of this branching for typ-ical nerve cells is the elaborate arborization of dendrites that arise from the neuronal cell body (also called dendritic branches or dendritic processes). Den-drites are the primary target for synaptic input from other neurons and are Studying the Nervous Systems of Humans and Other Animals 5 Mitochondrion Endoplasmic reticulum Axons Ribosomes Golgi apparatus Nucleus Dendrite Soma (A) (B) Axon (C) Synaptic endings (terminal boutons) (D) Myelinated axons (G) Myelinated axon and node of Ranvier (F) Neuronal cell body (soma) (E) Dendrites F E B D G C Figure 1.3 The major light and electron microscopical features of neurons. (A) Dia-gram of nerve cells and their component parts. (B) Axon initial segment (blue) entering a myelin sheath (gold). (C) Terminal boutons (blue) loaded with synaptic vesicles (arrowheads) forming synapses (arrows) with a dendrite (purple). (D) Transverse section of axons (blue) ensheathed by the processes of oligodendro-cytes (gold). (E) Apical dendrites (purple) of cortical pyramidal cells. (F) Nerve cell bodies (purple) occupied by large round nuclei. (G) Portion of a myelinated axon (blue) illustrating the intervals between adjacent segments of myelin (gold) referred to as nodes of Ranvier (arrows). (Micrographs from Peters et al., 1991.) 6 Chapter One Figure 1.4 Distinctive arrangement of cytoskeletal elements in neurons. (A) The cell body, axons, and dendrites are distinguished by the distribution of tubulin (green throughout cell) versus other cytoskeletal elements—in this case, Tau (red), a microtubule-binding protein found only in axons. (B) The strikingly distinct localization of actin (red) to the growing tips of axonal and dendritic processes is shown here in cultured neuron taken from the hip-pocampus. (C) In contrast, in a cultured epithelial cell, actin (red) is distributed in fibrils that occupy most of the cell body. (D) In astroglial cells in culture, actin (red) is also seen in fibrillar bun-dles. (E) Tubulin (green) is seen throughout the cell body and dendrites of neurons. (F) Although tubulin is a major component of dendrites, extend-ing into spines, the head of the spine is enriched in actin (red). (G) The tubulin component of the cytoskeleton in non-neuronal cells is arrayed in filamentous networks. (H–K) Synapses have a dis-tinct arrangement of cytoskeletal ele-ments, receptors, and scaffold proteins. (H) Two axons (green; tubulin) from motor neurons are seen issuing two branches each to four muscle fibers. The red shows the clustering of postsynaptic receptors (in this case for the neuro-transmitter acetylcholine). (I) A higher power view of a single motor neuron synapse shows the relationship between the axon (green) and the postsynaptic receptors (red). (J) The extracellular space between the axon and its target muscle is shown in green. (K) The clus-tering of scaffolding proteins (in this case, dystrophin) that localize receptors and link them to other cytoskeletal ele-ments is shown in green. (A courtesy of Y. N. Jan; B courtesy of E. Dent and F. Gertler; C courtesy of D. Arneman and C. Otey; D courtesy of A. Gonzales and R. Cheney; E from Sheng, 2003; F from Matus, 2000; G courtesy of T. Salmon et al.; H–K courtesy of R. Sealock.) (A) (B) (C) (D) (E) (G) (F) (H) (I) (J) (K) also distinguished by their high content of ribosomes as well as specific cytoskeletal proteins that reflect their function in receiving and integrating information from other neurons. The spectrum of neuronal geometries ranges from a small minority of cells that lack dendrites altogether to neu-rons with dendritic arborizations that rival the complexity of a mature tree (see Figure 1.2). The number of inputs that a particular neuron receives depends on the complexity of its dendritic arbor: nerve cells that lack den-drites are innervated by (thus, receive electrical signals from) just one or a few other nerve cells, whereas those with increasingly elaborate dendrites are innervated by a commensurately larger number of other neurons. The synaptic contacts made on dendrites (and, less frequently, on neu-ronal cell bodies) comprise a special elaboration of the secretory apparatus found in most polarized epithelial cells. Typically, the presynaptic terminal is immediately adjacent to a postsynaptic specialization of the target cell (see Figure 1.3). For the majority of synapses, there is no physical continuity between these pre- and postsynaptic elements. Instead, pre- and postsynap-tic components communicate via secretion of molecules from the presynap-tic terminal that bind to receptors in the postsynaptic specialization. These molecules must traverse an interval of extracellular space between pre- and postsynaptic elements called the synaptic cleft. The synaptic cleft, however, is not simply a space to be traversed; rather, it is the site of extracellular pro-teins that influence the diffusion, binding, and degradation of molecules secreted by the presynaptic terminal (see Figure 1.4). The number of synap-tic inputs received by each nerve cell in the human nervous system varies from 1 to about 100,000. This range reflects a fundamental purpose of nerve cells, namely to integrate information from other neurons. The number of synaptic contacts from different presynaptic neurons onto any particular cell is therefore an especially important determinant of neuronal function. The information conveyed by synapses on the neuronal dendrites is inte-grated and “read out” at the origin of the axon, the portion of the nerve cell specialized for signal conduction to the next site of synaptic interaction (see Figures 1.2 and 1.3). The axon is a unique extension from the neuronal cell body that may travel a few hundred micrometers (µm; usually called microns) or much farther, depending on the type of neuron and the size of the species. Moreover, the axon also has a distinct cytoskeleton whose ele-ments are central for its functional integrity (see Figure 1.4). Many nerve cells in the human brain (as well as that of other species) have axons no more than a few millimeters long, and a few have no axons at all. Relatively short axons are a feature of local circuit neurons or interneu-rons throughout the brain. The axons of projection neurons, however, extend to distant targets. For example, the axons that run from the human spinal cord to the foot are about a meter long. The electrical event that carries sig-nals over such distances is called the action potential, which is a self-regen-erating wave of electrical activity that propagates from its point of initiation at the cell body (called the axon hillock) to the terminus of the axon where synaptic contacts are made. The target cells of neurons include other nerve cells in the brain, spinal cord, and autonomic ganglia, and the cells of mus-cles and glands throughout the body. The chemical and electrical process by which the information encoded by action potentials is passed on at synaptic contacts to the next cell in a path-way is called synaptic transmission. Presynaptic terminals (also called syn-aptic endings, axon terminals, or terminal boutons) and their postsynaptic spe-cializations are typically chemical synapses, the most abundant type of Studying the Nervous Systems of Humans and Other Animals 7 8 Chapter One synapse in the nervous system. Another type, the electrical synapse, is far more rare (see Chapter 5). The secretory organelles in the presynaptic termi-nal of chemical synapses are synaptic vesicles (see Figure 1.3), which are generally spherical structures filled with neurotransmitter molecules. The positioning of synaptic vesicles at the presynaptic membrane and their fusion to initiate neurotransmitter release is regulated by a number of pro-teins either within or associated with the vesicle. The neurotransmitters released from synaptic vesicles modify the electrical properties of the target cell by binding to neurotransmitter receptors (Figure 1.4), which are local-ized primarily at the postsynaptic specialization. The intricate and concerted activity of neurotransmitters, receptors, related cytoskeletal elements, and signal transduction molecules are thus the basis for nerve cells communicating with one another, and with effector cells in muscles and glands. Neuroglial Cells Neuroglial cells—also referred to as glial cells or simply glia—are quite dif-ferent from nerve cells. Glia are more numerous than neurons in the brain, outnumbering them by a ratio of perhaps 3 to 1. The major distinction is that glia do not participate directly in synaptic interactions and electrical signal-ing, although their supportive functions help define synaptic contacts and maintain the signaling abilities of neurons. Although glial cells also have complex processes extending from their cell bodies, these are generally less prominent than neuronal branches, and do not serve the same purposes as axons and dendrites (Figure 1.5). (B) Oligodendrocyte (A) Astrocyte Cell body Glial processes (D) (E) (F) (G) (C) Microglial cell Figure 1.5 Varieties of neuroglial cells. Tracings of an astrocyte (A), an oligodendrocyte (B), and a microglial cell (C) visualized using the Golgi method. The images are at approxi-mately the same scale. (D) Astrocytes in tissue culture, labeled (red) with an antibody against an astrocyte-specific protein. (E) Oligodendroglial cells in tissue culture labeled with an antibody against an oligodendroglial-specific protein. (F) Peripheral axon are en-sheathed by myelin (labeled red) except at a distinct region called the node of Ranvier. The green label indicates ion channels concentrated in the node; the blue label indicates a molecularly dis-tinct region called the paranode. (G) Microglial cells from the spinal cord, labeled with a cell type-specific anti-body. Inset: Higher-magnification image of a single microglial cell labeled with a macrophage-selective marker. (A–C after Jones and Cowan, 1983; D, E courtesy of A.-S. LaMantia; F courtesy of M. Bhat; G courtesy of A. Light; inset courtesy of G. Matsushima.) The term glia (from the Greek word meaning “glue”) reflects the nine-teenth-century presumption that these cells held the nervous system together in some way. The word has survived, despite the lack of any evi-dence that binding nerve cells together is among the many functions of glial cells. Glial roles that are well-established include maintaining the ionic milieu of nerve cells, modulating the rate of nerve signal propagation, mod-ulating synaptic action by controlling the uptake of neurotransmitters at or near the synaptic cleft, providing a scaffold for some aspects of neural devel-opment, and aiding in (or impeding, in some instances) recovery from neural injury. There are three types of glial cells in the mature central nervous system: astrocytes, oligodendrocytes, and microglial cells (see Figure 1.5). Astro-cytes, which are restricted to the brain and spinal cord, have elaborate local processes that give these cells a starlike appearance (hence the prefix “astro”). A major function of astrocytes is to maintain, in a variety of ways, an appropriate chemical environment for neuronal signaling. Oligodendro-cytes, which are also restricted to the central nervous system, lay down a laminated, lipid-rich wrapping called myelin around some, but not all, axons. Myelin has important effects on the speed of the transmission of elec-trical signals (see Chapter 3). In the peripheral nervous system, the cells that elaborate myelin are called Schwann cells. Finally, microglial cells are derived primarily from hematopoietic precur-sor cells (although some may be derived directly from neural precursor cells). They share many properties with macrophages found in other tissues, and are primarily scavenger cells that remove cellular debris from sites of injury or normal cell turnover. In addition, microglia, like their macrophage counterparts, secrete signaling molecules—particularly a wide range of cytokines that are also produced by cells of the immune system—that can modulate local inflammation and influence cell survival or death. Indeed, some neurobiologists prefer to categorize microglia as a type of macrophage. Following brain damage, the number of microglia at the site of injury increases dramatically. Some of these cells proliferate from microglia resident in the brain, while others come from macrophages that migrate to the injured area and enter the brain via local disruptions in the cerebral vasculature. Cellular Diversity in the Nervous System Although the cellular constituents of the human nervous system are in many ways similar to those of other organs, they are unusual in their extraordi-nary numbers: the human brain is estimated to contain 100 billion neurons and several times as many supporting cells. More importantly, the nervous system has a greater range of distinct cell types—whether categorized by morphology, molecular identity, or physiological activity—than any other organ system (a fact that presumably explains why so many different genes are expressed in the nervous system; see above). The cellular diversity of any nervous system—including our own—undoubtedly underlies the the capac-ity of the system to form increasingly complicated networks to mediate increasingly sophisticated behaviors. For much of the twentieth century, neuroscientists relied on the same set of techniques developed by Cajal and Golgi to describe and categorize the diversity of cell types in the nervous system. From the late 1970s onward, however, new technologies made possible by the advances in cell and mole-cular biology provided investigators with many additional tools to discern the properties of neurons (Figure 1.6). Whereas general cell staining methods Studying the Nervous Systems of Humans and Other Animals 9 10 Chapter One showed mainly differences in cell size and distribution, antibody stains and probes for messenger RNA added greatly to the appreciation of distinctive types of neurons and glia in various regions of the nervous system. At the same time, new tract tracing methods using a wide variety of tracing sub-stances allowed the interconnections among specific groups of neurons to be (A) (B) (C) (D) (E) (F) (G) (H) (I) (J) (K) (L) (M) (N) (O) (P) explored much more fully. Tracers can be introduced into either living or fixed tissue, and are transported along nerve cell processes to reveal their origin and termination. More recently, genetic and neuroanatomical meth-ods have been combined to visualize the expression of fluorescent or other tracer molecules under the control of regulatory sequences of neural genes. This approach, which shows individual cells in fixed or living tissue in remarkable detail, allows nerve cells to be identified by both their transcrip-tional state and their structure. Finally, ways of determining the molecular identity and morphology of nerve cells can be combined with measurements of their physiological activity, thus illuminating structure–function relation-ships. Examples of these various approaches are shown in Figure 1.6. Neural Circuits Neurons never function in isolation; they are organized into ensembles or neural circuits that process specific kinds of information and provide the foundation of sensation, perception and behavior. The synaptic connections that define such circuits are typically made in a dense tangle of dendrites, axons terminals, and glial cell processes that together constitute what is called neuropil (the suffix -pil comes from the Greek word pilos, meaning “felt”; see Figure 1.3). The neuropil is thus the region between nerve cell bodies where most synaptic connectivity occurs. Although the arrangement of neural circuits varies greatly according to the function being served, some features are characteristic of all such ensem-bles. Preeminent is the direction of information flow in any particular circuit, which is obviously essential to understanding its purpose. Nerve cells that Studying the Nervous Systems of Humans and Other Animals 11 Figure 1.6 Structural diversity in the nervous system demonstrated with cellular and molecular markers. First row: Cellular organization of different brain regions demonstrated with Nissl stains, which label nerve and glial cell bodies. (A) The cerebral cortex at the boundary between the primary and secondary visual areas. (B) The olfactory bulbs. (C) Differences in cell density in cerebral cortical layers. (D) Individual Nissl-stained neurons and glia at higher magnification. Second row: Clas-sical and modern approaches to seeing individual neurons and their processes. (E) Golgi-labeled cortical pyramidal cells. (F) Golgi-labeled cerebellar Purkinje cells. (G) Cortical interneuron labeled by intracellular injection of a fluorescent dye. (H) Reti-nal neurons labeled by intracellular injection of fluorescent dye. Third row: Cellular and molecular approaches to seeing neural connections and systems. (I) At top, an antibody that detects synaptic proteins in the olfactory bulb; at bottom, a fluorescent label shows the location of cell bodies. (J) Synaptic zones and the location of Purk-inje cell bodies in the cerebellar cortex labeled with synapse-specific antibodies (green) and a cell body marker (blue). (K) The projection from one eye to the lateral geniculate nucleus in the thalamus, traced with radioactive amino acids (the bright label shows the axon terminals from the eye in distinct layers of the nucleus). (L) The map of the body surface of a rat in the somatic sensory cortex, shown with a marker that distinguishes zones of higher synapse density and metabolic activity. Fourth row: Peripheral neurons and their projections. (M) An autonomic neuron labeled by intracellular injection of an enzyme marker. (N) Motor axons (green) and neuromuscular synapses (orange) in transgenic mice genetically engineered to express fluorescent proteins. (O) The projection of dorsal root ganglia to the spinal cord, demonstrated by an enzymatic tracer. (P) Axons of olfactory receptor neurons from the nose labeled in the olfactory bulb with a vital fluorescent dye. (G courtesy of L. C. Katz; H courtesy of C. J. Shatz; N,O courtesy of W. Snider and J. Lichtman; all others courtesy of A.-S. LaMantia and D. Purves.) ▲ 12 Chapter One carry information toward the brain or spinal cord (or farther centrally within the spinal cord and brain) are called afferent neurons; nerve cells that carry information away from the brain or spinal cord (or away from the circuit in question) are called efferent neurons. Interneurons or local circuit neurons only participate in the local aspects of a circuit, based on the short distances over which their axons extend. These three functional classes—afferent neu-rons, efferent neurons, and interneurons—are the basic constituents of all neural circuits. A simple example of a neural circuit is the ensemble of cells that subserves the myotatic spinal reflex (the “knee-jerk” reflex; Figure 1.7). The afferent neurons of the reflex are sensory neurons whose cell bodies lie the dorsal root ganglia and whose peripheral axons terminate in sensory endings in skeletal muscles (the ganglia that serve this same of function for much of the head and neck are called cranial nerve ganglia; see Appendix A). The central axons of these afferent sensory neurons enter the the spinal cord where they terminate on a variety of central neurons concerned with the regualtion of muscle tone, most obviously the motor neurons that determine the activity of the related muscles. These neurons constitute the efferent neurons as well as interneurons of the circuit. One group of these efferent neurons in the ventral horn of the spinal cord projects to the flexor muscles in the limb, and the other to extensor muscles. Spinal cord interneurons are the third element of this circuit. The interneurons receive synaptic contacts from sensory afferent neurons and make synapses on the efferent motor neurons that project to the Sensory (afferent) axon Interneuron Motor (efferent) axons Muscle sensory receptor Flexor muscle Extensor muscle 2C 2B 2A 1 3A 3B 4 Hammer tap stretches tendon, which, in turn, stretches sensory receptors in leg extensor muscle Leg extends (C) Interneuron synapse inhibits motor neuron to flexor muscles (B) Sensory neuron also excites spinal interneuron (A) Sensory neuron synapses with and excites motor neuron in the spinal cord (B) Flexor muscle relaxes because the activity of its motor neurons has been inhibited (A) Motor neuron conducts action potential to synapses on extensor muscle fibers, causing contraction 1 2 3 4 Figure 1.7 A simple reflex circuit, the knee-jerk response (more formally, the myotatic reflex), illustrates several points about the functional organization of neural circuits. Stimulation of periph-eral sensors (a muscle stretch receptor in this case) initiates receptor potentials that trigger action potentials that travel centrally along the afferent axons of the sensory neurons. This information stim-ulates spinal motor neurons by means of synaptic contacts. The action poten-tials triggered by the synaptic potential in motor neurons travel peripherally in efferent axons, giving rise to muscle con-traction and a behavioral response. One of the purposes of this particular reflex is to help maintain an upright posture in the face of unexpected changes. flexor muscles; therefore they are capable of modulating the input–output linkage. The excitatory synaptic connections between the sensory afferents and the extensor efferent motor neurons cause the extensor muscles to con-tract; at the same time, the interneurons activated by the afferents are inhibitory, and their activation diminishes electrical activity in flexor efferent motor neurons and causes the flexor muscles to become less active (Figure 1.8). The result is a complementary activation and inactivation of the syner-gist and antagonist muscles that control the position of the leg. A more detailed picture of the events underlying the myotatic or any other circuit can be obtained by electrophysiological recording (Figure 1.9). There are two basic approaches to measuring the electrical activity of a nerve cell: extracellular recording (also referred to as single-unit recording), where an electrode is placed near the nerve cell of interest to detect its activity; and intracellular recording, where the electrode is placed inside the cell. Extracel-lular recordings primarily detect action potentials, the all-or-nothing changes in the potential across nerve cell membranes that convey information from one point to another in the nervous system. This sort of recording is particu-larly useful for detecting temporal patterns of action potential activity and relating those patterns to stimulation by other inputs, or to specific behavioral events. Intracellular recordings can detect the smaller, graded potential changes that trigger action potentials, and thus allow a more detailed analy-sis of communication between neurons within a circuit. These graded trig-gering potentials can arise at either sensory receptors or synapses and are called receptor potentials or synaptic potentials, respectively. For the myotatic circuit, electrical activity can be measured both extracellu-larly and intracellularly, thus defining the functional relationships between neurons in the circuit. The pattern of action potential activity can be measured for each element of the circuit (afferents, efferents, and interneurons) before, during, and after a stimulus (see Figure 1.8). By comparing the onset, dura-tion, and frequency of action potential activity in each cell, a functional picture of the circuit emerges. As a result of the stimulus, the sensory neuron is trig-gered to fire at higher frequency (i.e., more action potentials per unit time). This increase triggers a higher frequency of action potentials in both the exten-sor motor neurons and the interneurons. Concurrently, the inhibitory synapses made by the interneurons onto the flexor motor neurons cause the frequency of action potentials in these cells to decline. Using intracellular recording, it is possible to observe directly the potential changes underlying the synaptic con-nections of the myotatic reflex circuit (see Figure 1.9). Studying the Nervous Systems of Humans and Other Animals 13 Sensory (afferent) axon Interneuron Motor (efferent) axons Motor neuron (extensor) Interneuron Sensory neuron Hammer tap Leg extends Motor neuron (flexor) Figure 1.8 Relative frequency of action potentials (indicated by individual verti-cal lines) in different components of the myotatic reflex as the reflex pathway is activated. Notice the modulatory effect of the interneuron. 14 Chapter One Overall Organization of the Human Nervous System When considered together, circuits that process similar types of information comprise neural systems that serve broader behavioral purposes. The most general functional distinction divides such collections into sensory systems that acquire and process information from the environment (e.g., the visual system or the auditory system, see Unit II), and motor systems that respond to such information by generating movements and other behavior (see Unit III). There are, however, large numbers of cells and circuits that lie between these relatively well-defined input and output systems. These are collec-tively referred to as associational systems, and they mediate the most com-plex and least well-characterized brain functions (see Unit V). In addition to these broad functional distinctions, neuroscientists and neurologists have conventionally divided the vertebrate nervous system anatomically into central and peripheral components (Figure 1.10). The cen-tral nervous system, typically referred to as the CNS, comprises the brain (cerebral hemispheres, diencephalon, cerebellum, and brainstem) and the spinal cord (see Appendix A for more information about the gross anatomi-cal features of the CNS). The peripheral nervous system (PNS) includes the sensory neurons that link sensory receptors on the body surface or deeper within it with relevant processing circuits in the central nervous system. The motor portion of the peripheral nervous system in turn consists of two com-ponents. The motor axons that connect the brain and spinal cord to skeletal (C) Interneuron Interneuron Sensory neuron (A) Sensory neuron Motor neuron (flexor) (D) Motor neuron (flexor) Motor neuron (extensor) (B) Motor neuron (extensor) Microelectrode to measure membrane potential Record Record Record Record Membrane potential (mV) Membrane potential (mV) Membrane potential (mV) Membrane potential (mV) Time (ms) Activate excitatory synapse Activate excitatory synapse Activate inhibitory synapse Action potential Action potential Synaptic potential Action potential Synaptic potential Figure 1.9 Intracellularly recorded responses underlying the myotatic reflex. (A) Action potential measured in a sensory neuron. (B) Postsynaptic trig-gering potential recorded in an extensor motor neuron. (C) Postsynaptic trigger-ing potential in an interneuron. (D) Postsynaptic inhibitory potential in a flexor motor neuron. Such intracellular recordings are the basis for understand-ing the cellular mechanisms of action potential generation, and the sensory receptor and synaptic potentials that trigger these conducted signals. muscles make up the somatic motor division of the peripheral nervous sys-tem, whereas the cells and axons that innervate smooth muscles, cardiac muscle, and glands make up the visceral or autonomic motor division. Those nerve cell bodies that reside in the peripheral nervous system are located in ganglia, which are simply local accumulations of nerve cell bodies (and supporting cells). Peripheral axons are gathered into bundles called nerves, many of which are enveloped by the glial cells of the peripheral ner-vous system called Schwann cells. In the central nervous system, nerve cells are arranged in two different ways. Nuclei are local accumulations of neu-rons having roughly similar connections and functions; such collections are found throughout the cerebrum, brainstem and spinal cord. In contrast, cor-tex (plural, cortices) describes sheet-like arrays of nerve cells (again, consult Appendix A for additional information and illustrations). The cortices of the cerebral hemispheres and of the cerebellum provide the clearest example of this organizational principle. Axons in the central nervous system are gathered into tracts that are more or less analogous to nerves in the periphery. Tracts that cross the midline of the brain are referred to as commissures. Two gross histological terms dis-tinguish regions rich in neuronal cell bodies versus regions rich in axons. Gray matter refers to any accumulation of cell bodies and neuropil in the brain and spinal cord (e.g., nuclei or cortices), whereas white matter, named for its relatively light appearance resulting from the lipid content of myelin, refers to axon tracts and commissures. Studying the Nervous Systems of Humans and Other Animals 15 SENSORY COMPONENTS Cerebral hemispheres, diencephalon, cerebellum, brainstem, and spinal cord (analysis and integration of sensory and motor information) (B) (A) MOTOR COMPONENTS INTERNAL AND EXTERNAL ENVIRONMENT Sensory ganglia and nerves (sympathetic, parasympathetic, and enteric divisions) VISCERAL MOTOR SYSTEM SOMATIC MOTOR SYSTEM Sensory receptors (at surface and within the body) Autonomic ganglia and nerves Motor nerves Smooth muscles, cardiac muscles, and glands Skeletal (striated) muscles EFFECTORS Central nervous system Peripheral nervous system Central nervous system Peripheral nervous system Cranial nerves Spinal nerves Brain Spinal cord Figure 1.10 The major components of the nervous system and their functional relationships. (A) The CNS (brain and spinal cord) and PNS (spinal and cranial nerves). (B) Diagram of the major com-ponents of the central and peripheral nervous systems and their functional relationships. Stimuli from the environ-ment convey information to processing circuits within the brain and spinal cord, which in turn interpret their significance and send signals to peripheral effectors that move the body and adjust the workings of its internal organs. 16 Chapter One The organization of the visceral motor division of the peripheral nervous system is a bit more complicated (see Chapter 20). Visceral motor neurons in the brainstem and spinal cord, the so-called preganglionic neurons, form synapses with peripheral motor neurons that lie in the autonomic ganglia. The motor neurons in autonomic ganglia innervate smooth muscle, glands, and cardiac muscle, thus controlling most involuntary (visceral) behavior. In the sympathetic division of the autonomic motor system, the ganglia lie along or in front of the vertebral column and send their axons to a variety of peripheral targets. In the parasympathetic division, the ganglia are found within the organs they innervate. Another component of the visceral motor system, called the enteric system, is made up of small ganglia as well as individual neurons scattered throughout the wall of the gut. These neurons influence gastric motility and secretion. Neuroanatomical Terminology Describing the organization of any neural system requires a rudimentary understanding of anatomical terminology. The terms used to specify location in the central nervous system are the same as those used for the gross anatomical description of the rest of the body (Figure 1.11). Thus, anterior and posterior indicate front and back (head and tail); rostral and caudal, toward the head and tail; dorsal and ventral, top and bottom (back and belly); and medial and lateral, at the midline or to the side. Nevertheless, the com-parison between these coordinates in the body versus the brain can be con-fusing. For the entire body these anatomical terms refer to the long axis, which is straight. The long axis of the central nervous system, however, has a bend in it. In humans and other bipeds, a compensatory tilting of the ros-tral–caudal axis for the brain is necessary to properly compare body axes to brain axes. Once this adjustment has been made, the other axes for the brain can be easily assigned. The proper assignment of the anatomical axes then dictates the standard planes for histological sections or live images (see Box A) used to study the internal anatomy of the brain (see Figure 1.11B). Horizontal sections (also referred to as axial or transverse sections) are taken parallel to the rostral– caudal axis of the brain; thus, in an individual standing upright, such sections are parallel to the ground. Sections taken in the plane dividing the two hemi-spheres are sagittal, and can be further categorized as midsagittal and parasagittal, according to whether the section is near the midline (midsagittal) Figure 1.11 A flexure in the long axis of the nervous system arose as humans evolved upright posture, leading to an approximately 120° angle between the long axis of the brainstem and that of the forebrain The consequences of this flexure for anatomical terminology are indicated in (A). The terms anterior, posterior, superior, and inferior refer to the long axis of the body, which is straight. Therefore, these terms indicate the same direction for both the forebrain and the brainstem. In contrast, the terms dorsal, ventral, rostral, and caudal refer to the long axis of the central nervous system. The dorsal direction is toward the back for the brainstem and spinal cord, but toward the top of the head for the forebrain. The opposite direction is ventral. The rostral direction is toward the top of the head for the brainstem and spinal cord, but toward the face for the forebrain. The opposite direction is caudal. (B) The major planes of section used in cutting or imaging the brain. (C) The subdivisions and com-ponents of the central nervous system. (Note that the position of the brackets on the left side of the figure refers to the vertebrae, not the spinal segments.) ▲ or more lateral (parasagittal). Sections in the plane of the face are called coro-nal or frontal. Different terms are usually used to refer to sections of the spinal cord. The plane of section orthogonal to the long axis of the cord is called transverse, whereas sections parallel to the long axis of the cord are called longitudinal. In a transverse section through the human spinal cord, the dorsal and ventral axes and the anterior and posterior axes indicate the same directions (see Figure 1.11). Tedious though this terminology may be, it Studying the Nervous Systems of Humans and Other Animals 17 (B) Posterior (behind) Superior (above) Anterior (in front of) Inferior (below) Caudal Longitudinal axis of the forebrain Longitudinal axis of the brainstem and spinal cord (A) Rostral Caudal Horizontal Coronal Sagittal Dorsal Ventral Dorsal Ventral Dorsal Ventral Dorsal Ventral Spinal cord Cervical enlargement Lumbar enlargement Cauda equina C 1 2 3 4 5 6 7 8 T 1 T 1 Cervical nerves Thoracic nerves Lumbar nerves (C) Sacral nerves Coccygeal nerve T 1 2 3 4 5 6 7 8 9 10 11 12 L 1 2 3 4 5 S 1 3 4 5 Coc 1 2 Medulla Pons Midbrain Diencephalon Cerebrum Cerebellum 18 Chapter One is essential for understanding the basic subdivisions of the nervous system (Figure 1.11C). The Subdivisions of the Central Nervous System The central nervous system (defined as the brain and spinal cord) is usually considered to have seven basic parts: the spinal cord, the medulla, the pons, the cerebellum, the midbrain, the diencephalon, and the cerebral hemi-spheres (see Figures 1.10 and 1.11C). Running through all of these subdivi-sons are fluid-filled spaces called ventricles (a detailed account of the ven-tricular system can be found in Appendix B). These ventricles are the remnants of the continuous lumen initially enclosed by the neural plate as it rounded to become the neural tube during early development (see Chapter 21). Variations in the shape and size of the mature ventricular space are char-acteristic of each adult brain region. The medulla, pons, and midbrain are collectively called the brainstem and they surround the 4th ventricle (medulla and pons) and cerebral aqueduct (midbrain). The diencephalon and cerebral hemispheres are collectively called the forebrain, and they enclose the 3rd and lateral ventricles, respectively. Within the brainstem are the cranial nerve nuclei that either receive input from the cranial sensory ganglia mentioned earlier via the cranial sensory nerves, or give rise to axons that constitute the cranial motor nerves (see Appendix A). The brainstem is also a conduit for several major tracts in the central ner-vous system that relay sensory information from the spinal cord and brain-stem to the forebrain, or relay motor commands from forebrain back to motor neurons in the brainstem and spinal cord. Accordingly, detailed knowledge of the consequences of damage to the brainstem provides neu-rologists and other clinicians an essential tool in the localization and diagno-sis of brain injury. The brainstem contains numerous additional nuclei that are involved in a myriad of important functions including the control of heart rate, respiration, blood pressure, and level of consciousness. Finally, one of the most prominent features of the brainstem is the cerebellum, which extends over much of its dorsal aspect. The cerebellum is essential for the coordination and planning of movements (see Chapter 18) as well as learning motor tasks and storing that information (see Chapter 30). There are several anatomical subdivisions of the forebrain. The most obvi-ous anatomical structures are the prominent cerebral hemispheres (Figure 1.12). In humans, the cerebral hemispheres (the outermost portions of which are continuous, highly folded sheets of cortex) are proportionally larger than in any other mammal, and are characterized by the gyri (singular, gyrus) or crests of folded cortical tissue, and sulci (singular, sulcus) the grooves that divide gyri from one another (as pictured on the cover of this book, for example). Although gyral and sulcal patterns vary from individual to indi-vidual, there are some fairly consistent landmarks that help divide the hemi-spheres into four lobes. The names of the lobes are derived from the cranial bones that overlie them: occipital, temporal, parietal, and frontal. A key fea-ture of the surface anatomy of the cerebrum is the central sulcus located Figure 1.12 Gross anatomy of the forebrain (A) Cerebral hemisphere surface anatomy, showing the four lobes of the brain and the major sulci and gyri. The ven-tricular system and basal ganglia can also be seen in this phantom view. (B) Mid-sagittal view showing the location of the hippocampus, amygdala, thalamus and hypothalamus. Studying the Nervous Systems of Humans and Other Animals 19 Precentral gyrus (A) (B) (E) (D) (F) (C) Postcentral gyrus Central sulcus Parieto-occipital sulcus Preoccipital notch Lateral (Sylvian) fissure Cerebral hemisphere Cerebellum Brainstem Spinal cord Cerebellum Cingulate gyrus Parieto-occipital sulcus Spinal cord Cingulate sulcus Diencephalon Corpus callosum Anterior commissure Brainstem Midbrain Pons Medulla Calcarine sulcus Central sulcus Corpus callosum Caudate Putamen Internal capsule White matter Optic chiasm Basal forebrain nuclei Anterior commissure Temporal lobe Cerebral cortex (gray matter) Amygdala Corpus callosum Lateral ventricle Fornix Third ventricle Hippocampus Mammillary body Lateral ventricle (temporal horn) Thalamus Caudate Putamen Globus pallidus Tail of caudate nucleus Basal ganglia Internal capsule Frontal lobe Temporal lobe Parietal lobe Occipital lobe Frontal lobe Temporal lobe Parietal lobe Occipital lobe Level of section shown in (E) Level of section shown in (F) 20 Chapter One roughly halfway between the rostral and caudal poles of the hemispheres (Figure 1.12A). This prominent sulcus divides the frontal lobe at the rostral end of the hemisphere from the more caudal parietal lobe. Prominent on either side of the central sulcus are the pre- and postcentral gyri. These gyri are also functionally significant in that the precentral gyrus contains the pri-mary motor cortex important for the control of movement, and the postcen-tral gyrus contains the primary somatic sensory cortex which is important for the bodily senses (see below). The remaining subdivisions of the forebrain lie deeper in the cerebral hemispheres (Figure 1.12B). The most prominent of these is the collection of deep structures involved in motor and cognitive processes collectively referred to as the basal ganglia. Other particularly important structures are the hippocampus and amygdala in the temporal lobes (these are vital sub-strates for memory and emotional behavior, respectively), and the olfactory bulbs (the central stations for processing chemosensory information arising from receptor neurons in the nasal cavity) on the anterior–inferior aspect of the frontal lobes. Finally, the thalamus lies in the diencephalon and is a crit-ical relay for sensory information (although it has many other functions as well); the hypothalamus, which as the name implies lies below the thala-mus, is the central organizing structure for the regulation of the body’s many homeostatic functions (e.g., feeding, drinking, thermoregulation). This rudimentary description of some prominent anatomical landmarks provides a framework for understanding how neurons resident in a number of widely distributed and distinct brain structures communicate with one another to define neural systems dedicated to encoding, processing and relaying specific sorts of information about aspects of the organism’s envi-ronment, and then initiating and coordinating appropriate behavioral responses. Organizational Principles of Neural Systems These complex perceptual and motor capacities of the brain reflect the inte-grated function of various neural systems. The processing of somatic sensory information (arising from receptors in the skin, subcutaneous tissues, and the musculoskeletal system that respond to physical deformation at the body surface or displacement of muscles and joints) provides a convenient example. These widely distributed structures that participate in generating somatic sensations are referred to as the somatic sensory system (Figure 1.13). The components in the peripheral nervous system include the recep-tors distributed throughout the skin as well as in muscles and tendons, the related neurons in dorsal root ganglia, and neurons in some cranial ganglia. The central nervous system components include neurons in the spinal cord, as well as the long tracts of their axons that originate in the spinal cord, travel through the brainstem, and ultimately terminate in distinct relay nuclei in the thalamus in the diencephalon. The still-higher targets of the thalamic neurons are the cortical areas around the postcentral gyrus that are collectively referred to as the somatic sensory cortex. Thus, the somatic sen-sory system includes specific populations of neurons in practically every subdivision of the nervous system. Two further principles of neural system organization are evident in the somatic sensory system: topographic organization and the prevalence of parallel pathways (see Figure 1.13). As the name implies, topography refers to a mapping function—in this case a map of the body surface that can be discerned within the various structures that constitute the somatic sensory system. Thus, adjacent areas on the body surface are mapped to adjacent regions in nuclei, in white matter tracts, and in the thal-amic and cortical targets of the system. Beginning in the periph-ery, the cells in each dorsal root ganglion define a discrete der-matome (the area of the skin innervated by the processes of cells from a single dorsal root). In the spinal cord, from caudal to ros-tral, the dermatomes are represented in corresponding regions of the spinal cord from sacral (back) to lumbar (legs) to thoracic (chest) and cervical (arms and shoulders) (see Figures 1.13 and 1.11C). This so-called somatotopy is maintained in the somatic sensory tracts in spinal cord and brainstem that convey infor-mation to the relevant forebrain structures of the somatic sen-sory system (Figure 1.14). Parallel pathways refer to the segregation of nerve cell axons that process the distinct stimulus attributes that comprise a par-ticular sensory, motor, or cognitive modality. For somatic sensa-tion, the stimulus attributes relayed via parallel pathways are pain, temperature, touch, pressure, and proprioception (the sense of joint or limb position). From the dorsal root ganglia, through Studying the Nervous Systems of Humans and Other Animals 21 Central nervous system Peripheral nervous system Sensory receptors for body Sensory receptors for face Sensory receptor Thalamus Cerebral cortex Somatic sensory cortex (A) (B) Brainstem Spinal cord Thalamus Cerebral cortex Somatic sensory cortex Brainstem Spinal cord Dorsal root ganglia Dorsal root ganglia (DRG) Mechanical sensation Trigeminal ganglia Trigeminal ganglion Trigeminal ganglia Pain and temperature Mechanical sensation Pain and temperature Cervical Thoracic Lumbar Sacral Figure 1.13 The anatomical and functional organi-zation of the somatic sensory system. Central ner-vous system components of the somatic sensory sys-tem are found in the spinal cord, brainstem, thalamus, and cerebral cortex. (A) Somatosensory information from the body surface is mapped onto dorsal root ganglia (DRG), schematically depicted here as attachments to the spinal cord. The various shades of purple indicate correspondence between regions of the body and the DRG that relay informa-tion from the body surface to the central nervous system. Information from the head and neck is relayed to the CNS via the trigeminal ganglia. (B) Somatosensory information travels from the peri-pheral sensory receptors via parallel pathways for mechanical sensation and for the sensation of pain and temperature. These parallel pathways relay through the spinal cord and brainstem, ultimately sending sensory information to the thalamus, from which it is relayed to the somatic sensory cortex in the postcentral gyrus (indicated in blue in the image of the whole brain; MRI courtesy of L. E. White, J. Vovoydic, and S. M. Williams). 22 Chapter One the spinal cord and brainstem, and on to the somatic sensory cortex, these submodalities are kept largely segregated. Thus anatomically, biochemically, and physiologically distinct neurons transduce, encode, and relay pain, tem-perature, and mechanical information. Although this information is subse-quently integrated to provide unitary perception of the relevant stimuli, neu-rons and circuits in the somatic sensory system are clearly specialized to process discrete aspects of somatic sensation. This basic outline of the organization of the somatic system is representa-tive of the principles pertinent to understanding any neural system. It will in every case be pertinent to consider the anatomical distribution of neural cir-cuits dedicated to a particular function, how the function is represented or “mapped” onto the neural elements within the system, and how distinct stimulus attributes are segregated within subsets of neurons that comprise the system. Such details provide a framework for understanding how activ-ity within the system provides a representation of relevant stimulus, the required motor response, and higher order cognitive correlates. Somatic sensory cortex Shoulder Neck Head Neck Arm Hand Digits Thumb Eyes Nose Face Lips Jaw Tongue Throat Toes Genitalia Feet Leg Trunk Lateral Medial Figure 1.14 Somatotopic organization of sensory information. (Top) The locations of primary and secondary somatosensory cortical areas on the lateral surface of the brain. (Bottom) Cortical representation of different regions of skin. Functional Analysis of Neural Systems A wide range of physiological methods is now available to evaluate the elec-trical (and metabolic) activity of the neuronal circuits that make up a neural system. Two approaches, however, have been particularly useful in defining how neural systems represent information. The most widely used method is single-cell, or single-unit electrophysiological recording with microelec-trodes (see above; this method often records from several nearby cells in addition to the one selected, providing further useful information). The use of microelectrodes to record action potential activity provides a cell-by-cell analysis of the organization topographic maps (Figure 1.15), and can give specific insight into the type of stimulus to which the neuron is “tuned” (i.e., the stimulus that elicits a maximal change in action potential activity from the baseline state). Single-unit analysis is often used to define a neuron’s receptive field—the region in sensory space (e.g., the body surface, or a spe-cialized structure such as the retina) within which a specific stimulus elicits the greatest action potential response. This approach to understanding neural systems was introduced by Stephen Kuffler and Vernon Mountcastle in the early 1950s and has now been used by several generations of neuro-scientists to evaluate the relationship between stimuli and neuronal re-sponses in both sensory and motor systems. Electrical recording techniques Studying the Nervous Systems of Humans and Other Animals 23 (A) (B) Somatic sensory cortex Receptive field (surround) Activity of cortical neuron Period of stimulation Central sulcus Postcentral gyrus Record Receptive field (center) Touch in the surround of receptive field decreases cell firing Touch outside of receptive field has no effect Touch in the center of receptive field increases cell firing Figure 1.15 Single-unit electrophysiological recording from cortical pyramidal neuron, showing the firing pattern in response to a specific peripheral stimulus. (A) Typical experimental set-up. (B) Defining neuronal receptive fields. 24 Chapter One at the single-cell level have now been extended and refined to include single and simultaneous multiple cell analysis in animals performing complex cog-nitive tasks, intracellular recordings in intact animals, and the use of patch electrodes to detect and monitor the activity of the individual membrane molecules that ultimately underlie neural signaling (see Unit I). The second major area in which remarkable technical advances have been made is functional brain imaging in human subjects (and to a lesser extent animals), which has revolutionized the functional understanding of neural systems over the last two decades (Box A). Unlike electrical methods of recording neural activity, which are invasive in the sense of having to expose the brain and insert electrodes into it, functional imaging is noninvasive and thus applicable to both patients and normal human subjects. Moreover, func-tional imaging allows the simultaneous evaluation of multiple brain struc-tures (which is possible but obviously difficult with electrical recording methods). The tasks that can be evaluated with functional imaging permit a far more ambitious and integrative approach to studying the operations of a neural system. Over the last 20 years, these noninvasive methods have allowed neurosci-entists to evaluate the representation of an enormous number of complex human behaviors, and at the same time have provided diagnostic tools that are used more and more routinely. Many of the resulting observations have confirmed inferences about functional localization and the organization of neural systems that were originally based on the study of neurological patients who exhibited altered behavior after stroke or other forms of brain injury. Others findings, however, have given new insights into the way neural systems function in the human brain. Analyzing Complex Behavior Many of the most widely heralded advances in modern neuroscience have involved reducing the complexity of the brain to more readily analyzed components—i.e., genes, molecules, or cells. Nevertheless, the brain func-tions as a whole, and the study of more complex (and, some might argue, more interesting) brain functions such as perception, language, emotion, memory, and consciousness remain a central challenge for contemporary neuroscientists. In recognition of this challenge, over the last 20 years or so a field called cognitive neuroscience has emerged that is specifically devoted to understanding these issues (see Unit V). This evolution has also rejuve-nated the field of neuroethology (which is devoted to observing complex behaviors of animals in their native environments—for example, social com-munication in birds and non-human primates), and has encouraged the development of tasks to better evaluate the genesis of complex behaviors in human subjects. When used in combination with functional imaging, well designed behavioral tasks can facilitate identification of brain networks devoted to specific complex functions, including language skills, mathemat-ical and musical ability, emotional responses, aesthetic judgments, and abstract thinking. Carefully constructed behavioral tasks can also be used to study the pathology of complex brain diseases that compromise cognition, such Alzheimer’s disease, schizophrenia, and depression. In short, new or revitalized efforts to study higher brain functions with increasingly powerful techniques offer ways of beginning to understand even the most complex aspects of human behavior. Studying the Nervous Systems of Humans and Other Animals 25 Box A Brain Imaging Techniques In the 1970s, computerized tomography, or CT, opened a new era in noninvasive imaging by introducing the use of com-puter processing technology to help probe the living brain. Prior to CT, the only brain imaging technique available was standard X-ray film, which has poor soft tissue contrast and involves rela-tively high radiation exposure. The CT approach uses a narrow X-ray beam and a row of very sensitive detec-tors placed on opposite sides of the head to probe just a small portion of tissue at a time with limited radiation exposure (see Figure A). In order to make an image, the X-ray tube and detectors rotate around the head to collect radiodensity informa-tion from every orientation around a nar-row slice. Computer processing tech-niques then calculate the radiodensity of each point within the slice plane, produc-ing a tomographic image (tomo means “cut” or “slice”). If the patient is slowly moved through the scanner while the X-ray tube rotates in this way, a three-dimensional radiodensity matrix can be created, allowing images to be computed for any plane through the brain. CT scans can readily distinguish gray matter and white matter, differentiate the ventricles quite well, and show many other brain structures with a spatial resolution of sev-eral millimeters. Brain imaging took another large step forward in the 1980s with the develop-ment of magnetic resonance imaging (MRI). MRI is based on the fact that the nuclei of some atoms act as spinning magnets, and that if they are placed in a strong magnetic field they will line up with the field and spin at a frequency that is dependent on the field strength. If they then receive a brief radiofrequency pulse tuned to their spinning frequency they are knocked out of alignment with the field, and subsequently emit energy in an oscillatory fashion as they gradu-ally realign themselves with the field. The strength of the emitted signal depends on how many nuclei are involved in this process. To get spatial information in MRI, the magnetic field is distorted slightly by imposing magnetic gradients along three different spatial axes so that only nuclei at certain locations are tuned to the detector’s frequency at any given time. Almost all MRI scanners use detec-tors tuned to the radio frequencies of spinning hydrogen nuclei in water mole-cules, and thus create images based on the distribution of water in different tis-sues. Careful manipulation of magnetic field gradients and radiofrequency pulses make it possible to construct extraordi-narily detailed images of the brain at any location and orientation with sub-mil-limeter resolution. The strong magnetic field and radio-frequency pulses used in MRI scanning are harmless, making this technique completely noninvasive (although metal objects in or near a scanner are a safety concern) (see Figure B). MRI is also extremely versatile because, by changing the scanning parameters, images based on a wide variety of different contrast mechanisms can be generated. For exam-ple, conventional MR images take advan-tage of the fact that hydrogen in different types of tissue (e.g., gray matter, white matter, cerebrospinal fluid) have slightly different realignment rates, meaning that soft tissue contrast can be manipulated simply by adjusting when the realigning hydrogen signal is measured. Different parameter settings can also be used to generate images in which gray and white matter are invisible but in which the brain vasculature stands out in sharp detail. Safety and versatility have made MRI the technique of choice for imaging brain structure in most applications. Imaging functional variations in the living brain has also become possible with the recent development of tech-niques for detecting small, localized X-ray source X-ray detector (A) In computerized tomography, the X-ray source and detectors are moved around the patient’s head. The inset shows a horizontal CT section of a normal adult brain. (continued) 26 Chapter One Summary The brain can be studied by methods that range from genetics and molecu-lar biology to behavioral testing of normal human subjects. In addition to an ever-increasing store of knowledge about the anatomical organization of the nervous system, many of the brightest successes of modern neuroscience have come from understanding nerve cells as the basic structural and func-tional unit of the nervous system. Studies of the distinct cellular architecture and molecular components of neurons and glia have revealed much about Box A (continued) Brain Imaging Techniques changes in metabolism or cerebral blood flow. To conserve energy, the brain regu-lates its blood flow such that active neu-rons with relatively high metabolic demands receive more blood than rela-tively inactive neurons. Detecting and mapping these local changes in cerebral blood flow forms the basis for three widely used functional brain imaging techniques: positron emission tomogra-phy (PET), single-photon emission computerized tomography (SPECT), and functional magnetic resonance imaging (fMRI). In PET scanning, unstable positron-emitting isotopes are incorporated into different reagents (including water, pre-cursor molecules of specific neurotrans-mitters, or glucose) and injected into the bloodstream. Labeled oxygen and glu-cose quickly accumulate in more meta-bolically active areas, and labeled trans-mitter probes are taken up selectively by appropriate regions. As the unstable iso-tope decays, it results in the emission of two positrons moving in opposite direc-tions. Gamma ray detectors placed around the head register a “hit” only when two detectors 180° apart react simultaneously. Images of tissue isotope density can then be generated (much the way CT images are calculated) showing the location of active regions with a spa-tial resolution of about 4 mm. Depending on the probe injected, PET imaging can be used to visualize activity-dependent changes in blood flow, tissue metabolism, or biochemical activity. SPECT imaging is similar to PET in that it involves injection or inhalation of a radiolabeled compound (for example, 133Xe or 123I-labeled iodoamphetamine), which produce pho-tons that are detected by a gamma cam-era moving rapidly around the head. Functional MRI, a variant of MRI, currently offers the best approach for visualizing brain function based on local metabolism. fMRI is predicated on the fact that hemoglobin in blood slightly distorts the magnetic resonance proper-ties of hydrogen nuclei in its vicinity, and (B) In MRI scanning, the head is placed in the center of a large magnet. A radiofrequency antenna coil is placed around the head for exciting and recording the magnetic resonance sig-nal. For fMRI, stimuli can be presented using virtual reality video goggles and stereo head-phones while inside the scanner. their individual functions, as well as providing a basis for understanding how nerve cells are organized into circuits, and circuits into systems that process specific types of information pertinent to perception and action. Goals that remain include understanding how basic molecular genetic phe-nomena are linked to cellular, circuit, and system functions; understanding how these processes go awry in neurological and psychiatric diseases; and beginning to understand the especially complex functions of the brain that make us human. Studying the Nervous Systems of Humans and Other Animals 27 the amount of magnetic distortion changes depending on whether the hemoglobin has oxygen bound to it. When a brain area is activated by a spe-cific task it begins to use more oxygen and within seconds the brain microvas-culature responds by increasing the flow of oxygen-rich blood to the active area. These changes in the concentration of oxygen and blood flow lead to localized blood oxygenation level-dependent (BOLD) changes in the magnetic reso-nance signal. Such fluctuations are detected using statistical image process-ing techniques to produce maps of task-dependent brain function (see Figure C). Because fMRI uses signals intrinsic to the brain without any radioactivity, repeated observations can be made on the same individual—a major advantage over imaging methods such as PET. The spa-tial resolution (2–3 mm) and temporal resolution (a few seconds) of fMRI are also superior to other functional imaging techniques. MRI has thus emerged as the technology of choice for probing both the structure and function of the living human brain. References HUETTEL, S. A., A. W. SONG AND G. MCCARTHY (2004) Functional Magnetic Resonance Imaging. Sunderland, MA: Sinauer Associates. OLDENDORF, W. AND W. OLDENDORF JR. (1988) Basics of Magnetic Resonance Imaging. Boston: Kluwer Academic Publishers. RAICHLE, M. E. (1994) Images of the mind: Studies with modern imaging techniques. Ann. Rev. Psychol. 45: 333–356. SCHILD, H. (1990) MRI Made Easy (…Well, Almost). Berlin: H. Heineman. in progress Right Left Tumor (C) MRI images of an adult patient with a brain tumor, with fMRI activity during a hand motion task superimposed (left hand activity is shown in yellow, right hand activity in green). At right is a three-dimensional surface reconstructed view of the same data. 28 Chapter One Additional Reading BRODAL, P. (1992) The Central Nervous System: Structure and Function. New York: Oxford Uni-versity Press. CARPENTER, M. B. AND J. SUTIN (1983) Human Neuroanatomy, 8th Ed. Baltimore, MD: Wil-liams and Wilkins. ENGLAND, M. A. AND J. WAKELY (1991) Color Atlas of the Brain and Spinal Cord: An Introduc-tion to Normal Neuroanatomy. St. Louis: Mosby Yearbook. GIBSON, G. AND S. MUSE (2001) A Primer of Genome Science. Sunderland, MA: Sinauer Associates. HAINES, D. E. (1995) Neuroanatomy: An Atlas of Structures, Sections, and Systems, 2nd Ed. Balti-more: Urban and Schwarzenberg. MARTIN, J. H. (1996) Neuroanatomy: Text and Atlas, 2nd Ed. Stamford, CT: Appleton and Lange. NATURE VOL. 409, NO. 6822 (2001) Issue of February 16. Special issue on the human genome. NETTER, F. H. (1983) The CIBA Collection of Medical Illustrations, Vols. I and II. A. Brass and R. V. Dingle (eds.). Summit, NJ: CIBA Pharmaceutical Co. PETERS, A., S. L. PALAY AND H. DE F. WEBSTER (1991) The Fine Structure of the Nervous System: Neurons and Their Supporting Cells, 3rd Ed. New York: Oxford University Press. POSNER, M. I. AND M. E. RAICHLE (1997) Images of Mind, 2nd Ed. New York: W. H. Freeman & Co. RAMÓN Y CAJAL, S. (1984) The Neuron and the Glial Cell. (Transl. by J. de la Torre and W. C. Gibson.) Springfield, IL: Charles C. Thomas. RAMÓN Y CAJAL, S. (1990) New Ideas on the Structure of the Nervous System in Man and Ver-tebrates. (Transl. by N. Swanson and L. W. Swanson.) Cambridge, MA: MIT Press. SCIENCE VOL. 291, NO. 5507 (2001) Issue of February 16. Special issue on the human genome. SHEPHERD, G. M. (1991) Foundations of the Neu-ron Doctrine. History of Neuroscience Series, No. 6. Oxford: Oxford University Press. WAXMAN, S. G. AND J. DEGROOT (1995) Correla-tive Neuroanatomy, 22nd Ed. Norwalk, CT: Appleton and Lange. Neural Signaling I Calcium signaling in a cerebel-lar Purkinje neuron. An elec-trode was used to fill the neu-ron with a fluorescent calcium indicator dye. This dye revealed the release of intra-cellular calcium ions (color) produced by the actions of the second messenger IP3. (Cour-tesy of Elizabeth A. Finch and George J. Augustine.) UNIT I NEURAL SIGNALING 2 Electrical Signals of Nerve Cells 3 Voltage-Dependent Membrane Permeability 4 Channels and Transporters 5 Synaptic Transmission 6 Neurotransmitters, Receptors, and Their Effects 7 Molecular Signaling within Neurons The brain is remarkably adept at acquiring, coordinating, and dis-seminating information about the body and its environment. Such information must be processed within milliseconds, yet it also can be stored away as memories that endure for years. Neurons within the central and peripheral nervous systems perform these functions by generating sophisticated electrical and chemical signals. This unit describes these signals and how they are produced. It explains how one type of electrical signal, the action potential, allows information to travel along the length of a nerve cell. It also explains how other types of signals—both electrical and chemical—are generated at syn-aptic connections between nerve cells. Synapses permit information transfer by interconnecting neurons to form the circuitry on which neural processing depends. Finally, it describes the intricate bio-chemical signaling events that take place within neurons. Appreciat-ing these fundamental forms of neuronal signaling provides a foun-dation for appreciating the higher-level functions considered in the rest of the book. The cellular and molecular mechanisms that give neurons their unique signaling abilities are also targets for disease processes that compromise the function of the nervous system. A working knowl-edge of the cellular and molecular biology of neurons is therefore fundamental to understanding a variety of brain pathologies, and for developing novel approaches to diagnosing and treating these all too prevalent problems. Overview Nerve cells generate electrical signals that transmit information. Although neurons are not intrinsically good conductors of electricity, they have evolved elaborate mechanisms for generating these signals based on the flow of ions across their plasma membranes. Ordinarily, neurons generate a negative potential, called the resting membrane potential, that can be mea-sured by recording the voltage between the inside and outside of nerve cells. The action potential transiently abolishes the negative resting potential and makes the transmembrane potential positive. Action potentials are propa-gated along the length of axons and are the fundamental signal that carries information from one place to another in the nervous system. Still other types of electrical signals are produced by the activation of synaptic contacts between neurons or by the actions of external forms of energy on sensory neurons. All of these electrical signals arise from ion fluxes brought about by nerve cell membranes being selectively permeable to different ions, and from the non-uniform distribution of these ions across the membrane. Electrical Potentials across Nerve Cell Membranes Neurons employ several different types of electrical signal to encode and transfer information. The best way to observe these signals is to use an intra-cellular microelectrode to measure the electrical potential across the neu-ronal plasma membrane. A typical microelectrode is a piece of glass tubing pulled to a very fine point (with an opening of less than 1 µm diameter) and filled with a good electrical conductor, such as a concentrated salt solution. This conductive core can then be connected to a voltmeter, such as an oscil-loscope, to record the transmembrane voltage of the nerve cell. The first type of electrical phenomenon can be observed as soon as a microelectrode is inserted through the membrane of the neuron. Upon enter-ing the cell, the microelectrode reports a negative potential, indicating that neurons have a means of generating a constant voltage across their mem-branes when at rest. This voltage, called the resting membrane potential, depends on the type of neuron being examined, but it is always a fraction of a volt (typically –40 to –90 mV). The electrical signals produced by neurons are caused by responses to stimuli, which then change the resting membrane potential. Receptor poten-tials are due to the activation of sensory neurons by external stimuli, such as light, sound, or heat. For example, touching the skin activates Pacinian cor-puscles, receptor neurons that sense mechanical disturbances of the skin. These neurons respond to touch with a receptor potential that changes the resting potential for a fraction of a second (Figure 2.1A). These transient Chapter 2 31 Electrical Signals of Nerve Cells 32 Chapter Two changes in potential are the first step in generating the sensation of vibra-tions (or “tickles”) of the skin in the somatic sensory system (Chapter 8). Similar sorts of receptor potentials are observed in all other sensory neurons during transduction of sensory signals (Unit II). Another type of electrical signal is associated with communication between neurons at synaptic contacts. Activation of these synapses generates synaptic potentials, which allow transmission of information from one neu-ron to another. An example of such a signal is shown in Figure 2.1B. In this case, activation of a synaptic terminal innervating a hippocampal pyramidal neuron causes a very brief change in the resting membrane potential in the pyramidal neuron. Synaptic potentials serve as the means of exchanging information in complex neural circuits in both the central and peripheral nervous systems (Chapter 5). The use of electrical signals—as in sending electricity over wires to pro-vide power or information—presents a series of problems in electrical engi-neering. A fundamental problem for neurons is that their axons, which can be quite long (remember that a spinal motor neuron can extend for a meter or more), are not good electrical conductors. Although neurons and wires –60 −70 –50 −60 Membrane potential (mV) Membrane potential (mV) 40 −60 Membrane potential (mV) Activate synapse Touch skin Activate motor neuron Record Stimulate Record Stimulate (A) Receptor potential (B) Synaptic potential Time (ms) Time (ms) Time (ms) (C) Action potential Record Figure 2.1 Types of neuronal electrical signals. In all cases, microelectrodes are used to measure changes in the resting membrane potential during the indi-cated signals. (A) A brief touch causes a receptor potential in a Pacinian corpus-cle in the skin. (B) Activation of a synap-tic contact onto a hippocampal pyrami-dal neuron elicits a synaptic potential. (C) Stimulation of a spinal reflex pro-duces an action potential in a spinal motor neuron. are both capable of passively conducting electricity, the electrical properties of neurons compare poorly to an ordinary wire. To compensate for this defi-ciency, neurons have evolved a “booster system” that allows them to con-duct electrical signals over great distances despite their intrinsically poor electrical characteristics. The electrical signals produced by this booster sys-tem are called action potentials (which are also referred to as “spikes” or “impulses”). An example of an action potential recorded from the axon of a spinal motor neuron is shown in Figure 2.1C. One way to elicit an action potential is to pass electrical current across the membrane of the neuron. In normal circumstances, this current would be generated by receptor potentials or by synaptic potentials. In the laboratory, however, electrical current suitable for initiating an action potential can be readily produced by inserting a second microelectrode into the same neuron and then connecting the electrode to a battery (Figure 2.2A). If the current delivered in this way makes the membrane potential more negative (hyper-polarization), nothing very dramatic happens. The membrane potential sim-ply changes in proportion to the magnitude of the injected current (central part of Figure 2.2B). Such hyperpolarizing responses do not require any unique property of neurons and are therefore called passive electrical responses. A much more interesting phenomenon is seen if current of the opposite polarity is delivered, so that the membrane potential of the nerve cell becomes more positive than the resting potential (depolarization). In this case, at a certain level of membrane potential, called the threshold potential, an action potential occurs (see right side of Figure 2.2B). The action potential, which is an active response generated by the neuron, is a brief (about 1 ms) change from negative to positive in the transmem-Electrical Signals of Nerve Cells 33 Neuron (A) Microelectrode to measure membrane potential Microelectrode to inject current Record Stimulate −50 Time Current (nA) Membrane potential (mV) −65 −100 0 +40 0 −2 +2 Threshold Depolarization Hyperpolarization Resting potential Action potentials Insert microelectrode Passive responses (B) Figure 2.2 Recording passive and active electrical signals in a nerve cell. (A) Two microelectrodes are inserted into a neuron; one of these measures membrane potential while the other injects current into the neuron. (B) In-serting the voltage-measuring micro-electrode into the neuron reveals a nega-tive potential, the resting membrane potential. Injecting current through the current-passing microelectrode alters the neuronal membrane potential. Hyperpolarizing current pulses produce only passive changes in the membrane potential. While small depolarizing cur-rents also elict only passive responses, depolarizations that cause the mem-brane potential to meet or exceed threshold additionally evoke action potentials. Action potentials are active responses in the sense that they are gen-erated by changes in the permeability of the neuronal membrane. 34 Chapter Two Figure 2.3 Ion transporters and ion channels are responsible for ionic move-ments across neuronal membranes. Transporters create ion concentration differences by actively transporting ions against their chemical gradients. Chan-nels take advantage of these concentra-tion gradients, allowing selected ions to move, via diffusion, down their chemi-cal gradients. brane potential. Importantly, the amplitude of the action potential is inde-pendent of the magnitude of the current used to evoke it; that is, larger cur-rents do not elicit larger action potentials. The action potentials of a given neuron are therefore said to be all-or-none, because they occur fully or not at all. If the amplitude or duration of the stimulus current is increased suffi-ciently, multiple action potentials occur, as can be seen in the responses to the three different current intensities shown in Figure 2.2B (right side). It fol-lows, therefore, that the intensity of a stimulus is encoded in the frequency of action potentials rather than in their amplitude. This arrangement differs dramatically from receptor potentials, whose amplitudes are graded in pro-portion to the magnitude of the sensory stimulus, or synaptic potentials, whose amplitude varies according to the number of synapses activated and the previous amount of synaptic activity. Because electrical signals are the basis of information transfer in the ner-vous system, it is essential to understand how these signals arise. Remarkably, all of the neuronal electrical signals described above are produced by similar mechanisms that rely upon the movement of ions across the neuronal mem-brane. The remainder of this chapter addresses the question of how nerve cells use ions to generate electrical potentials. Chapter 3 explores more specifically the means by which action potentials are produced and how these signals solve the problem of long-distance electrical conduction within nerve cells. Chapter 4 examines the properties of membrane molecules responsible for electrical signaling. Finally, Chapters 5–7 consider how electrical signals are transmitted from one nerve cell to another at synaptic contacts. How Ionic Movements Produce Electrical Signals Electrical potentials are generated across the membranes of neurons—and, indeed, all cells—because (1) there are differences in the concentrations of spe-cific ions across nerve cell membranes, and (2) the membranes are selectively permeable to some of these ions. These two facts depend in turn on two dif-ferent kinds of proteins in the cell membrane (Figure 2.3). The ion concentra-tion gradients are established by proteins known as active transporters, which, as their name suggests, actively move ions into or out of cells against their concentration gradients. The selective permeability of membranes is ION TRANSPORTERS ION CHANNELS 1 Ion binds Ions Ion transporters −Actively move ions against concentration gradient −Create ion concentration gradients 2 Ion transported across membrane Inside Outside Ion channels −Allow ions to diffuse down concentration gradient −Cause selective permeability to certain ions Ion diffuses through channel Neuronal Neuronal membrane membrane Neuronal membrane due largely to ion channels, proteins that allow only certain kinds of ions to cross the membrane in the direction of their concentration gradients. Thus, channels and transporters basically work against each other, and in so doing they generate the resting membrane potential, action potentials, and the syn-aptic potentials and receptor potentials that trigger action potentials. The structure and function of these channels and transporters are described in Chapter 4. To appreciate the role of ion gradients and selective permeability in gener-ating a membrane potential, consider a simple system in which an artificial membrane separates two compartments containing solutions of ions. In such a system, it is possible to determine the composition of the two solutions and, thereby, control the ion gradients across the membrane. For example, take the case of a membrane that is permeable only to potassium ions (K+). If the con-centration of K+ on each side of this membrane is equal, then no electrical potential will be measured across it (Figure 2.4A). However, if the concentra-tion of K+ is not the same on the two sides, then an electrical potential will be generated. For instance, if the concentration of K+ on one side of the mem-brane (compartment 1) is 10 times higher than the K+ concentration on the other side (compartment 2), then the electrical potential of compartment 1 will be negative relative to compartment 2 (Figure 2.4B). This difference in electrical potential is generated because the potassium ions flow down their concentration gradient and take their electrical charge (one positive charge per ion) with them as they go. Because neuronal membranes contain pumps that accumulate K+ in the cell cytoplasm, and because potassium-permeable channels in the plasma membrane allow a transmembrane flow of K+, an analogous situation exists in living nerve cells. A continual resting efflux of K+ is therefore responsible for the resting membrane potential. In the hypothetical case just described, an equilibrium will quickly be reached. As K+ moves from compartment 1 to compartment 2 (the initial conditions on the left of Figure 2.4B), a potential is generated that tends to impede further flow of K+. This impediment results from the fact that the Electrical Signals of Nerve Cells 35 Voltmeter V = 0 Initially V = 0 V1−2=−58 mV + + + + + – – – – – log [K+]2 [K+]1 (mM) −116 −58 0 Membrane potential V1−2 (mV) −2 −1 0 100 10 1 [K+]1 1 1 mM KCl No net flux of K+ Net flux of K+ from 1 to 2 Flux of K+ from 1 to 2 balanced by opposing membrane potential Initial conditions At equilibrium 2 1 mM KCl (A) (B) (C) 1 10 mM KCl 2 1 mM KCl 1 10 mM KCl 2 1 mM KCl Slope = 58 mV per tenfold change in K+ gradient Permeable to K+ Figure 2.4 Electrochemical equilib-rium. (A) A membrane permeable only to K+ (yellow spheres) separates com-partments 1 and 2, which contain the indicated concentrations of KCl. (B) Increasing the KCl concentration in com-partment 1 to 10 mM initially causes a small movement of K+ into compartment 2 (initial conditions) until the electromo-tive force acting on K+ balances the concentration gradient, and the net movement of K+ becomes zero (at equi-librium). (C) The relationship between the transmembrane concentration gradi-ent ([K+]2/[K+]1) and the membrane potential. As predicted by the Nernst equation, this relationship is linear when plotted on semi-logarithmic coordinates, with a slope of 58 mV per tenfold differ-ence in the concentration gradient. 36 Chapter Two potential gradient across the membrane tends to repel the positive potas-sium ions that would otherwise move across the membrane. Thus, as com-partment 2 becomes positive relative to compartment 1, the increasing posi-tivity makes compartment 2 less attractive to the positively charged K+. The net movement (or flux) of K+ will stop at the point (at equilibrium on the right of Figure 2.4B) where the potential change across the membrane (the relative positivity of compartment 2) exactly offsets the concentration gradi-ent (the tenfold excess of K+ in compartment 1). At this electrochemical equilibrium, there is an exact balance between two opposing forces: (1) the concentration gradient that causes K+ to move from compartment 1 to com-partment 2, taking along positive charge, and (2) an opposing electrical gra-dient that increasingly tends to stop K+ from moving across the membrane (Figure 2.4B). The number of ions that needs to flow to generate this electri-cal potential is very small (approximately 10–12 moles of K+ per cm2 of mem-brane, or 1012 K+ ions). This last fact is significant in two ways. First, it means that the concentrations of permeant ions on each side of the mem-brane remain essentially constant, even after the flow of ions has generated the potential. Second, the tiny fluxes of ions required to establish the mem-brane potential do not disrupt chemical electroneutrality because each ion has an oppositely charged counter-ion (chloride ions in the example shown in Figure 2.4) to maintain the neutrality of the solutions on each side of the membrane. The concentration of K+ remains equal to the concentration of Cl– in the solutions in compartments 1 and 2, meaning that the separation of charge that creates the potential difference is restricted to the immediate vicinity of the membrane. The Forces That Create Membrane Potentials The electrical potential generated across the membrane at electrochemical equilibrium, the equilibrium potential, can be predicted by a simple for-mula called the Nernst equation. This relationship is generally expressed as where EX is the equilibrium potential for any ion X, R is the gas constant, T is the absolute temperature (in degrees on the Kelvin scale), z is the valence (electrical charge) of the permeant ion, and F is the Faraday constant (the amount of electrical charge contained in one mole of a univalent ion). The brackets indicate the concentrations of ion X on each side of the membrane and the symbol ln indicates the natural logarithm of the concentration gradi-ent. Because it is easier to perform calculations using base 10 logarithms and to perform experiments at room temperature, this relationship is usually simplified to where log indicates the base 10 logarithm of the concentration ratio. Thus, for the example in Figure 2.4B, the potential across the membrane at electro-chemical equilibrium is The equilibrium potential is conventionally defined in terms of the potential difference between the reference compartment, side 2 in Figure 2.4, and the other side. This approach is also applied to biological systems. In this case, E K 2 1 58 log K K 58 log 1 10 58 mV = [ ] [ ] = = − z E X 2 1 58 log X X = [ ] [ ] z E RT zF X 2 1 ln X X = [ ] [ ] the outside of the cell is the conventional reference point (defined as zero potential). Thus, when the concentration of K+ is higher inside than out, an inside-negative potential is measured across the K+-permeable neuronal membrane. For a simple hypothetical system with only one permeant ion species, the Nernst equation allows the electrical potential across the membrane at equi-librium to be predicted exactly. For example, if the concentration of K+ on side 1 is increased to 100 mM, the membrane potential will be –116 mV. More generally, if the membrane potential is plotted against the logarithm of the K+ concentration gradient ([K]2/[K]1), the Nernst equation predicts a lin-ear relationship with a slope of 58 mV (actually 58/z) per tenfold change in the K+ gradient (Figure 2.4C). To reinforce and extend the concept of electrochemical equilibrium, con-sider some additional experiments on the influence of ionic species and ionic permeability that could be performed on the simple model system in Figure 2.4. What would happen to the electrical potential across the membrane (the potential of side 1 relative to side 2) if the potassium on side 2 were replaced with 10 mM sodium (Na+) and the K+ in compartment 1 were replaced by 1 mM Na+? No potential would be generated, because no Na+ could flow across the membrane (which was defined as being permeable only to K+). However, if under these ionic conditions (10 times more Na+ in compartment 2) the K+-permeable membrane were to be magically replaced by a mem-brane permeable only to Na+, a potential of +58 mV would be measured at equilibrium. If 10 mM calcium (Ca2+) were present in compartment 2 and 1 mM Ca2+ in compartment 1, and a Ca2+-selective membrane separated the two sides, what would happen to the membrane potential? A potential of +29 mV would develop, because the valence of calcium is +2. Finally, what would happen to the membrane potential if 10 mM Cl– were present in com-partment 1 and 1 mM Cl– were present in compartment 2, with the two sides separated by a Cl–-permeable membrane? Because the valence of this anion is –1, the potential would again be +58 mV. The balance of chemical and electrical forces at equilibrium means that the electrical potential can determine ionic fluxes across the membrane, just as the ionic gradient can determine the membrane potential. To examine the influence of membrane potential on ionic flux, imagine connecting a battery across the two sides of the membrane to control the electrical potential across the membrane without changing the distribution of ions on the two sides (Figure 2.5). As long as the battery is off, things will be just as in Figure 2.4, with the flow of K+ from compartment 1 to compartment 2 causing a nega-tive membrane potential (Figure 2.5A, left). However, if the battery is used to make compartment 1 initially more negative relative to compartment 2, there will be less K+ flux, because the negative potential will tend to keep K+ in compartment 1. How negative will side 1 need to be before there is no net flux of K+? The answer is –58 mV, the voltage needed to counter the tenfold difference in K+ concentrations on the two sides of the membrane (Figure 2.5A, center). If compartment 1 is initially made more negative than –58 mV, then K+ will actually flow from compartment 2 into compartment 1, because the positive ions will be attracted to the more negative potential of compart-ment 1 (Figure 2.5A, right). This example demonstrates that both the direc-tion and magnitude of ion flux depend on the membrane potential. Thus, in some circumstances the electrical potential can overcome an ionic concentra-tion gradient. The ability to alter ion flux experimentally by changing either the poten-tial imposed on the membrane (Figure 2.5B) or the transmembrane concen-Electrical Signals of Nerve Cells 37 38 Chapter Two tration gradient for an ion (see Figure 2.4C) provides convenient tools for studying ion fluxes across the plasma membranes of neurons, as will be evi-dent in many of the experiments described in the following chapters. Electrochemical Equilibrium in an Environment with More Than One Permeant Ion Now consider a somewhat more complex situation in which Na+ and K+ are unequally distributed across the membrane, as in Figure 2.6A. What would happen if 10 mM K+ and 1 mM Na+ were present in compartment 1, and 1 mM K+ and 10 mM Na+ in compartment 2? If the membrane were perme-able only to K+, the membrane potential would be –58 mV; if the membrane were permeable only to Na+, the potential would be +58 mV. But what would the potential be if the membrane were permeable to both K+ and Na+? In this case, the potential would depend on the relative permeability of the membrane to K+ and Na+. If it were more permeable to K+, the potential would approach –58 mV, and if it were more permeable to Na+, the potential would be closer to +58 mV. Because there is no permeability term in the Nernst equation, which only considers the simple case of a single permeant ion species, a more elaborate equation is needed that takes into account both the concentration gradients of the permeant ions and the relative permeabil-ity of the membrane to each permeant species. Such an equation was developed by David Goldman in 1943. For the case most relevant to neurons, in which K+, Na+, and Cl– are the primary perme-ant ions, the Goldman equation is written where V is the voltage across the membrane (again, compartment 1 relative to the reference compartment 2) and P indicates the permeability of the V P P P P P P = [ ] + [ ] + [ ] [ ] + [ ] + [ ] 58 log K Na Cl K Na Cl K 2 Na 2 Cl 1 K 1 Na 1 Cl 2 V1−2= −58 mV V1−2= 0 mV V1−2= −116 mV + + + + + + + − − − − − − − Net flux of K+ from 1 to 2 No net flux of K+ Battery off Battery on Battery on (A) (B) 1 10 mM KCl 2 1 mM KCl 1 10 mM KCl 2 1 mM KCl Membrane potential V1−2 (mV) Net flux of K+ No net flux of K+ −58 0 0 −116 1 2 2 1 Net flux of K+ from 1 to 2 Net flux of K+ from 2 to 1 1 10 mM KCl 2 1 mM KCl Net flux of K+ from 2 to 1 Battery Battery Battery Figure 2.5 Membrane potential influ-ences ion fluxes. (A) Connecting a bat-tery across the K+-permeable membrane allows direct control of membrane potential. When the battery is turned off (left), K+ ions (yellow) flow simply according to their concentration gradi-ent. Setting the initial membrane poten-tial (V1–2) at the equilibrium potential for K+ (center) yields no net flux of K+, while making the membrane potential more negative than the K+ equilibrium potential (right) causes K+ to flow against its concentration gradient. (B) Relationship between membrane poten-tial and direction of K+ flux. Figure 2.6 Resting and action poten-tials entail permeabilities to different ions. (A) Hypothetical situation in which a membrane variably permeable to Na+ (red) and K+ (yellow) separates two compartments that contain both ions. For simplicity, Cl– ions are not shown in the diagram. (B) Schematic representation of the membrane ionic permeabilities associated with resting and action potentials. At rest, neuronal membranes are more permeable to K+ (yellow) than to Na+ (red); accordingly, the resting membrane potential is nega-tive and approaches the equilibrium potential for K+, EK. During an action potential, the membrane becomes very permeable to Na+ (red); thus the mem-brane potential becomes positive and approaches the equilibrium potential for Na+, ENa. The rise in Na+ permeability is transient, however, so that the mem-brane again becomes primarily perme-able to K+ (yellow), causing the poten-tial to return to its negative resting value. Notice that at the equilibrium potential for a given ion, there is no net flux of that ion across the membrane. membrane to each ion of interest. The Goldman equation is thus an extended version of the Nernst equation that takes into account the relative permeabilities of each of the ions involved. The relationship between the two equations becomes obvious in the situation where the membrane is perme-able only to one ion, say, K+; in this case, the Goldman expression collapses back to the simpler Nernst equation. In this context, it is important to note that the valence factor (z) in the Nernst equation has been eliminated; this is why the concentrations of negatively charged chloride ions, Cl–, have been inverted relative to the concentrations of the positively charged ions [remem-ber that –log (A/B) = log (B/A)]. If the membrane in Figure 2.6A is permeable to K+ and Na+ only, the terms involving Cl– drop out because PCl is 0. In this case, solution of the Goldman equation yields a potential of –58 mV when only K+ is permeant, +58 mV when only Na+ is permeant, and some intermediate value if both ions are permeant. For example, if K+ and Na+ were equally permeant, then the potential would be 0 mV. With respect to neural signaling, it is particularly pertinent to ask what would happen if the membrane started out being permeable to K+, and then temporarily switched to become most permeable to Na+. In this circum-stance, the membrane potential would start out at a negative level, become positive while the Na+ permeability remained high, and then fall back to a negative level as the Na+ permeability decreased again. As it turns out, this last case essentially describes what goes on in a neuron during the genera-tion of an action potential. In the resting state, PK of the neuronal plasma membrane is much higher than PNa; since, as a result of the action of ion transporters, there is always more K+ inside the cell than outside (Table 2.1), the resting potential is negative (Figure 2.6B). As the membrane potential is depolarized (by synaptic action, for example), PNa increases. The transient increase in Na+ permeability causes the membrane potential to become even more positive (red region in Figure 2.6B), because Na+ rushes in (there is much more Na+ outside a neuron than inside, again as a result of ion pumps). Because of this positive feedback loop, an action potential occurs. The rise in Na+ permeability during the action potential is transient, how-ever; as the membrane permeability to K+ is restored, the membrane poten-tial quickly returns to its resting level. Electrical Signals of Nerve Cells 39 Resting potential Repolarization Action potential 0 Membrane potential Time PNa>> PK PNa PNa PK>>PNa PK>>PNa EK ENa Voltmeter 10 mM KCl 1 mM NaCl Variable permeability to Na+ and K+ 1 mM KCl 10 mM NaCl (A) (B) Na+ permeable K+ permeable 1 2 40 Chapter Two Armed with an appreciation of these simple electrochemical principles, it will be much easier to understand the following, more detailed account of how neurons generate resting and action potentials. The Ionic Basis of the Resting Membrane Potential The action of ion transporters creates substantial transmembrane gradients for most ions. Table 2.1 summarizes the ion concentrations measured directly in an exceptionally large nerve cell found in the nervous system of the squid (Box A). Such measurements are the basis for stating that there is much more K+ inside the neuron than out, and much more Na+ outside than in. Similar concentration gradients occur in the neurons of most animals, including humans. However, because the ionic strength of mammalian blood is lower than that of sea-dwelling animals such as squid, in mammals the concentrations of each ion are several times lower. These transporter-dependent concentration gradients are, indirectly, the source of the resting neuronal membrane potential and the action potential. Once the ion concentration gradients across various neuronal membranes are known, the Nernst equation can be used to calculate the equilibrium potential for K+ and other major ions. Since the resting membrane potential of the squid neuron is approximately –65 mV, K+ is the ion that is closest to being in electrochemical equilibrium when the cell is at rest. This fact implies that the resting membrane is more permeable to K+ than to the other ions listed in Table 2.1, and that this permeability is the source of resting potentials. It is possible to test this guess, as Alan Hodgkin and Bernard Katz did in 1949, by asking what happens to the resting membrane potential if the con-centration of K+ outside the neuron is altered. If the resting membrane were permeable only to K+, then the Goldman equation (or even the simpler Nernst equation) predicts that the membrane potential will vary in propor-tion to the logarithm of the K+ concentration gradient across the membrane. Assuming that the internal K+ concentration is unchanged during the exper-iment, a plot of membrane potential against the logarithm of the external K+ concentration should yield a straight line with a slope of 58 mV per tenfold change in external K+ concentration at room temperature (see Figure 2.4C). (The slope becomes about 61 mV at mammalian body temperatures.) TABLE 2.1 Extracellular and Intracellular Ion Concentrations Concentration (mM) Ion Intracellular Extracellular Squid neuron Potassium (K+) 400 20 Sodium (Na+) 50 440 Chloride (Cl–) 40–150 560 Calcium (Ca2+) 0.0001 10 Mammalian neuron Potassium (K+) 140 5 Sodium (Na+) 5–15 145 Chloride (Cl–) 4–30 110 Calcium (Ca2+) 0.0001 1–2 Electrical Signals of Nerve Cells 41 Box A The Remarkable Giant Nerve Cells of Squid Many of the initial insights into how ion concentration gradients and changes in membrane permeability produce electri-cal signals came from experiments per-formed on the extraordinarily large nerve cells of the squid. The axons of these nerve cells can be up to 1 mm in diameter—100 to 1000 times larger than mammalian axons. Thus, squid axons are large enough to allow experiments that would be impossible on most other nerve cells. For example, it is not difficult to insert simple wire electrodes inside these giant axons and make reliable elec-trical measurements. The relative ease of this approach yielded the first intracellu-lar recordings of action potentials from nerve cells and, as discussed in the next chapter, the first experimental measure-ments of the ion currents that produce action potentials. It also is practical to extrude the cytoplasm from giant axons and measure its ionic composition (see Table 2.1). In addition, some giant nerve cells form synaptic contacts with other giant nerve cells, producing very large synapses that have been extraordinarily valuable in understanding the funda-mental mechanisms of synaptic trans-mission (see Chapter 5). Giant neurons evidently evolved in squid because they enhanced survival. These neurons participate in a simple neural circuit that activates the contrac-tion of the mantle muscle, producing a jet propulsion effect that allows the squid to move away from predators at a remarkably fast speed. As discussed in Chapter 3, larger axonal diameter allows faster conduction of action potentials. Thus, presumably these huge nerve cells help squid escape more successfully from their numerous enemies. Today—nearly 70 years after their dis-covery by John Z. Young at University College London—the giant nerve cells of squid remain useful experimental sys-tems for probing basic neuronal functions. References LLINÁS, R. (1999) The Squid Synapse: A Model for Chemical Transmission. Oxford: Oxford University Press. YOUNG, J. Z. (1939) Fused neurons and syn-aptic contacts in the giant nerve fibres of cephalopods. Phil. Trans. R. Soc. Lond. 229(B): 465–503. Brain 1st-level neuron 2nd-level neuron Squid giant axon = 800 µm diameter Mammalian axon = 2 µm diameter 3rd-level neuron (A) (B) (C) Stellate ganglion Presynaptic (2nd level) Postsynaptic (3rd level) Stellate nerve Giant axon Smaller axons Cross section 1 mm Stellate nerve with giant axon 1 mm (A) Diagram of a squid, showing the location of its giant nerve cells. Different colors indi-cate the neuronal components of the escape circuitry. The first- and second-level neurons originate in the brain, while the third-level neurons are in the stellate ganglion and inner-vate muscle cells of the mantle. (B) Giant synapses within the stellate ganglion. The sec-ond-level neuron forms a series of fingerlike processes, each of which makes an extraordi-narily large synapse with a single third-level neuron. (C) Structure of a giant axon of a third-level neuron lying within its nerve. The enormous difference in the diameters of a squid giant axon and a mammalian axon are shown below. 42 Chapter Two When Hodgkin and Katz carried out this experiment on a living squid neuron, they found that the resting membrane potential did indeed change when the external K+ concentration was modified, becoming less negative as external K+ concentration was raised (Figure 2.7A). When the external K+ concentration was raised high enough to equal the concentration of K+ inside the neuron, thus making the K+ equilibrium potential 0 mV, the rest-ing membrane potential was also approximately 0 mV. In short, the resting membrane potential varied as predicted with the logarithm of the K+ con-centration, with a slope that approached 58 mV per tenfold change in K+ concentration (Figure 2.7B). The value obtained was not exactly 58 mV because other ions, such as Cl– and Na+, are also slightly permeable, and thus influence the resting potential to a small degree. The contribution of these other ions is particularly evident at low external K+ levels, again as predicted by the Goldman equation. In general, however, manipulation of the external concentrations of these other ions has only a small effect, emphasizing that K+ permeability is indeed the primary source of the resting membrane potential. In summary, Hodgkin and Katz showed that the inside-negative resting potential arises because (1) the membrane of the resting neuron is more per-meable to K+ than to any of the other ions present, and (2) there is more K+ inside the neuron than outside. The selective permeability to K+ is caused by K+-permeable membrane channels that are open in resting neurons, and the (A) (B) 0 −20 −60 −40 −80 0 −20 −60 −40 −80 Resting membrane potential (mV) Resting membrane potential (mV) 2 5 10 20 50 100 200 500 [K+]out (mM) 3.5 mM K+ 10 mM K+ 20 mM K+ 50 mM K+ 200 mM K+ 450 mM K+ Time (min) 10 5 0 Slope = 58 mV per tenfold change in K+ gradient Figure 2.7 Experimental evidence that the resting membrane potential of a squid giant axon is determined by the K+ concentration gradient across the membrane. (A) Increasing the external K+ concentration makes the resting membrane potential more positive. (B) Relationship between resting membrane potential and external K+ concentration, plotted on a semi-logarithmic scale. The straight line represents a slope of 58 mV per tenfold change in concentration, as given by the Nernst equa-tion. (After Hodgkin and Katz, 1949.) Figure 2.8 The role of sodium in the generation of an action potential in a squid giant axon. (A) An action poten-tial evoked with the normal ion concen-trations inside and outside the cell. (B) The amplitude and rate of rise of the action potential diminish when external sodium concentration is reduced to one-third of normal, but (C) recover when the Na+ is replaced. (D) While the amplitude of the action potential is quite sensitive to the external concentra-tion of Na+, the resting membrane potential (E) is little affected by chang-ing the concentration of this ion. (After Hodgkin and Katz, 1949.) large K+ concentration gradient is, as noted, produced by membrane trans-porters that selectively accumulate K+ within neurons. Many subsequent studies have confirmed the general validity of these principles. The Ionic Basis of Action Potentials What causes the membrane potential of a neuron to depolarize during an action potential? Although a general answer to this question has been given (increased permeability to Na+), it is well worth examining some of the experimental support for this concept. Given the data presented in Table 2.1, one can use the Nernst equation to calculate that the equilibrium potential for Na+ (ENa) in neurons, and indeed in most cells, is positive. Thus, if the membrane were to become highly permeable to Na+, the membrane poten-tial would approach ENa. Based on these considerations, Hodgkin and Katz hypothesized that the action potential arises because the neuronal mem-brane becomes temporarily permeable to Na+. Taking advantage of the same style of ion substitution experiment they used to assess the resting potential, Hodgkin and Katz tested the role of Na+ in generating the action potential by asking what happens to the action potential when Na+ is removed from the external medium. They found that lowering the external Na+ concentration reduces both the rate of rise of the action potential and its peak amplitude (Figure 2.8A–C). Indeed, when they examined this Na+ dependence quantitatively, they found a more-or-less lin-ear relationship between the amplitude of the action potential and the loga-rithm of the external Na+ concentration (Figure 2.8D). The slope of this rela-Electrical Signals of Nerve Cells 43 (D) (A) (B) (C) 100 +40 Membrane potential (mV) Membrane potential (mV) Membrane potential (mV) −40 −80 0 +40 Time (ms) −40 −80 0 +40 −40 −80 0 0 1 2 3 Time (ms) 0 1 2 3 Time (ms) 0 1 2 3 Action potential amplitude (mV) Resting membrane potential (mV) 80 40 60 20 50 100 200 500 1000 0 −40 −20 −60 −80 50 100 200 [Na+]out (mM) [Na+]out (mM) 500 1000 Control Low [Na+] Recovery Slope = 58 mV per tenfold change in Na+ gradient (E) 44 Chapter Two Box B Action Potential Form and Nomenclature The action potential of the squid giant axon has a characteristic shape, or wave-form, with a number of different phases (Figure A). During the rising phase, the membrane potential rapidly depolarizes. In fact, action potentials cause the mem-brane potential to depolarize so much that the membrane potential transiently becomes positive with respect to the external medium, producing an over-shoot. The overshoot of the action poten-tial gives way to a falling phase in which the membrane potential rapidly repolar-izes. Repolarization takes the membrane potential to levels even more negative than the resting membrane potential for a short time; this brief period of hyper-polarization is called the undershoot. Although the waveform of the squid action potential is typical, the details of the action potential form vary widely from neuron to neuron in different ani-mals. In myelinated axons of vertebrate motor neurons (Figure B), the action potential is virtually indistinguishable from that of the squid axon. However, the action potential recorded in the cell body of this same motor neuron (Figure C) looks rather different. Thus, the action potential waveform can vary even within the same neuron. More complex action potentials are seen in other central neu-rons. For example, action potentials recorded from the cell bodies of neurons in the mammalian inferior olive (a region of the brainstem involved in motor con-trol) last tens of milliseconds (Figure D). These action potentials exhibit a pro-nounced plateau during their falling phase, and their undershoot lasts even longer than that of the motor neuron. One of the most dramatic types of action potentials occurs in the cell bodies of cerebellar Purkinje neurons (Figure E). These potentials have several complex phases that result from the summation of multiple, discrete action potentials. The variety of action potential wave-forms could mean that each type of neu-ron has a different mechanism of action potential production. Fortunately, how-ever, these diverse waveforms all result from relatively minor variations in the scheme used by the squid giant axon. For example, plateaus in the repolariza-tion phase result from the presence of ion channels that are permeable to Ca2+, and long-lasting undershoots result from the presence of additional types of mem-brane K+ channels. The complex action potential of the Purkinje cell results from these extra features plus the fact that dif-ferent types of action potentials are gen-erated in various parts of the Purkinje neuron—cell body, dendrites, and axons—and are summed together in recordings from the cell body. Thus, the lessons learned from the squid axon are applicable to, and indeed essential for, understanding action potential genera-tion in all neurons. References BARRETT, E. F. AND J. N. BARRETT (1976) Sepa-ration of two voltage-sensitive potassium currents, and demonstration of a tetro-dotoxin-resistant calcium current in frog motoneurones. J. Physiol. (Lond.) 255: 737–774. DODGE, F. A. AND B. FRANKENHAEUSER (1958) Membrane currents in isolated frog nerve fibre under voltage clamp conditions. J. Physiol. (Lond.) 143: 76–90. HODGKIN, A. L. AND A. F. HUXLEY (1939) Action potentials recorded from inside a nerve fibre. Nature 144: 710–711. LLINÁS, R. AND M. SUGIMORI (1980) Electro-physiological properties of in vitro Purkinje cell dendrites in mammalian cerebellar slices. J. Physiol. (Lond.) 305: 197–213. LLINÁS, R. AND Y. YAROM (1981) Electrophysi-ology of mammalian inferior olivary neu-rones in vitro. Different types of voltage-dependent ionic conductances. J. Physiol. (Lond.) 315: 549–567. (A) (B) (C) (D) (E) 0 −40 0 2 4 6 8 4 4 6 8 3 2 2 20 10 30 40 1 0 0 0 0 50 100 150 +40 Membrane potential (mV) Time (ms) Overshoot phase Falling phase Undershoot phase Rising phase (A) The phases of an action potential of the squid giant axon. (B) Action potential recorded from a myelinated axon of a frog motor neuron. (C) Action potential recorded from the cell body of a frog motor neuron. The action potential is smaller and the undershoot prolonged in comparison to the action potential recorded from the axon of this same neuron (B). (D) Action potential recorded from the cell body of a neuron from the inferior olive of a guinea pig. This action potential has a pronounced plateau during its falling phase. (E) Action potential recorded from the cell body of a Purkinje neuron in the cerebellum of a guinea pig. (A after Hodgkin and Huxley, 1939; B after Dodge and Frankenhaeuser, 1958; C after Barrett and Bar-rett, 1976; D after Llinás and Yarom, 1981; E after Llinás and Sugimori, 1980.) tionship approached a value of 58 mV per tenfold change in Na+ concentra-tion, as expected for a membrane selectively permeable to Na+. In contrast, lowering Na+ concentration had very little effect on the resting membrane potential (Figure 2.8E). Thus, while the resting neuronal membrane is only slightly permeable to Na+, the membrane becomes extraordinarily perme-able to Na+ during the rising phase and overshoot phase of the action potential (see Box B for an explanation of action potential nomenclature). This temporary increase in Na+ permeability results from the opening of Na+-selective channels that are essentially closed in the resting state. Mem-brane pumps maintain a large electrochemical gradient for Na+, which is in much higher concentration outside the neuron than inside. When the Na+ channels open, Na+ flows into the neuron, causing the membrane potential to depolarize and approach ENa. The time that the membrane potential lingers near ENa (about +58 mV) during the overshoot phase of an action potential is brief because the increased membrane permeability to Na+ itself is short-lived. The membrane potential rapidly repolarizes to resting levels and is actually followed by a transient undershoot. As will be described in Chapter 3, these latter events in the action potential are due to an inactivation of the Na+ permeability and an increase in the K+ permeability of the membrane. During the undershoot, the membrane potential is transiently hyperpolarized because K+ permeabil-ity becomes even greater than it is at rest. The action potential ends when this phase of enhanced K+ permeability subsides, and the membrane poten-tial thus returns to its normal resting level. The ion substitution experiments carried out by Hodgkin and Katz pro-vided convincing evidence that the resting membrane potential results from a high resting membrane permeability to K+, and that depolarization during an action potential results from a transient rise in membrane Na+ permeabil-ity. Although these experiments identified the ions that flow during an action potential, they did not establish how the neuronal membrane is able to change its ionic permeability to generate the action potential, or what mech-anisms trigger this critical change. The next chapter addresses these issues, documenting the surprising conclusion that the neuronal membrane poten-tial itself affects membrane permeability. Summary Nerve cells generate electrical signals to convey information over substantial distances and to transmit it to other cells by means of synaptic connections. These signals ultimately depend on changes in the resting electrical potential across the neuronal membrane. A resting potential occurs because nerve cell membranes are permeable to one or more ion species subject to an electro-chemical gradient. More specifically, a negative membrane potential at rest results from a net efflux of K+ across neuronal membranes that are predomi-nantly permeable to K+. In contrast, an action potential occurs when a tran-sient rise in Na+ permeability allows a net flow of Na+ in the opposite direc-tion across the membrane that is now predominantly permeable to Na+. The brief rise in membrane Na+ permeability is followed by a secondary, tran-sient rise in membrane K+ permeability that repolarizes the neuronal mem-brane and produces a brief undershoot of the action potential. As a result of these processes, the membrane is depolarized in an all-or-none fashion dur-ing an action potential. When these active permeability changes subside, the membrane potential returns to its resting level because of the high resting membrane permeability to K+. Electrical Signals of Nerve Cells 45 46 Chapter Two Additional Reading Reviews HODGKIN, A. L. (1951) The ionic basis of elec-trical activity in nerve and muscle. Biol. Rev. 26: 339–409. HODGKIN, A. L. (1958) The Croonian Lecture: Ionic movements and electrical activity in giant nerve fibres. Proc. R. Soc. Lond. (B) 148: 1–37. Important Original Papers BAKER, P. F., A. L. HODGKIN AND T. I. SHAW (1962) Replacement of the axoplasm of giant nerve fibres with artificial solutions. J. Phys-iol. (London) 164: 330–354. COLE, K. S. AND H. J. CURTIS (1939) Electric impedence of the squid giant axon during activity. J. Gen. Physiol. 22: 649–670. GOLDMAN, D. E. (1943) Potential, impedence, and rectification in membranes. J. Gen. Phys-iol. 27: 37–60. HODGKIN, A. L. AND P. HOROWICZ (1959) The influence of potassium and chloride ions on the membrane potential of single muscle fibres. J. Physiol. (London) 148: 127–160. HODGKIN, A. L. AND B. KATZ (1949) The effect of sodium ions on the electrical activity of the giant axon of the squid. J. Physiol. (London) 108: 37–77. HODGKIN, A. L. AND R. D. KEYNES (1953) The mobility and diffusion coefficient of potas-sium in giant axons from Sepia. J. Physiol. (London) 119: 513–528. KEYNES, R. D. (1951) The ionic movements during nervous activity. J. Physiol. (London) 114: 119–150. Books HODGKIN, A. L. (1967) The Conduction of the Nervous Impulse. Springfield, IL: Charles C. Thomas. HODGKIN, A. L. (1992) Chance and Design. Cambridge: Cambridge University Press. JUNGE, D. (1992) Nerve and Muscle Excitation, 3rd Ed. Sunderland, MA: Sinauer Associates. KATZ, B. (1966) Nerve, Muscle, and Synapse. New York: McGraw-Hill. Overview The action potential, the primary electrical signal generated by nerve cells, reflects changes in membrane permeability to specific ions. Present under-standing of these changes in ionic permeability is based on evidence obtained by the voltage clamp technique, which permits detailed characteri-zation of permeability changes as a function of membrane potential and time. For most types of axons, these changes consist of a rapid and transient rise in sodium (Na+) permeability, followed by a slower but more prolonged rise in potassium (K+) permeability. Both permeabilities are voltage-depen-dent, increasing as the membrane potential depolarizes. The kinetics and voltage dependence of Na+ and K+ permeabilities provide a complete expla-nation of action potential generation. Depolarizing the membrane potential to the threshold level causes a rapid, self-sustaining increase in Na+ perme-ability that produces the rising phase of the action potential; however, the Na+ permeability increase is short-lived and is followed by a slower increase in K+ permeability that restores the membrane potential to its usual negative resting level. A mathematical model that describes the behavior of these ionic permeabilities predicts virtually all of the observed properties of action potentials. Importantly, this same ionic mechanism permits action potentials to be propagated along the length of neuronal axons, explaining how electri-cal signals are conveyed throughout the nervous system. Ionic Currents Across Nerve Cell Membranes The previous chapter introduced the idea that nerve cells generate electrical signals by virtue of a membrane that is differentially permeable to various ion species. In particular, a transient increase in the permeability of the neu-ronal membrane to Na+ initiates the action potential. This chapter considers exactly how this increase in Na+ permeability occurs. A key to understand-ing this phenomenon is the observation that action potentials are initiated only when the neuronal membrane potential becomes more positive than a threshold level. This observation suggests that the mechanism responsible for the increase in Na+ permeability is sensitive to the membrane potential. Therefore, if one could understand how a change in membrane potential activates Na+ permeability, it should be possible to explain how action potentials are generated. The fact that the Na+ permeability that generates the membrane potential change is itself sensitive to the membrane potential presents both conceptual and practical obstacles to studying the mechanism of the action potential. A practical problem is the difficulty of systematically varying the membrane Chapter 3 47 Voltage-Dependent Membrane Permeability 48 Chapter Three potential to study the permeability change, because such changes in mem-brane potential will produce an action potential, which causes further, uncontrolled changes in the membrane potential. Historically, then, it was not really possible to understand action potentials until a technique was developed that allowed experimenters to control membrane potential and simultaneously measure the underlying permeability changes. This tech-Box A The Voltage Clamp Method Breakthroughs in scientific research often rely on the development of new tech-nologies. In the case of the action poten-tial, detailed understanding came only after of the invention of the voltage clamp technique by Kenneth Cole in the 1940s. This device is called a voltage clamp because it controls, or clamps, membrane potential (or voltage) at any level desired by the experimenter. The method measures the membrane poten-tial with a microelectrode (or other type of electrode) placed inside the cell (1), and electronically compares this voltage to the voltage to be maintained (called the command voltage) (2). The clamp cir-cuitry then passes a current back into the cell though another intracellular elec-trode (3). This electronic feedback circuit holds the membrane potential at the de-sired level, even in the face of permeabil-ity changes that would normally alter the membrane potential (such as those gen-erated during the action potential). Most importantly, the device permits the simultaneous measurement of the cur-rent needed to keep the cell at a given voltage (4). This current is exactly equal to the amount of current flowing across the neuronal membrane, allowing direct measurement of these membrane cur-rents. Therefore, the voltage clamp tech-nique can indicate how membrane potential influences ionic current flow across the membrane. This information gave Hodgkin and Huxley the key insights that led to their model for action potential generation. Today, the voltage clamp method remains widely used to study ionic cur-rents in neurons and other cells. The most popular contemporary version of this approach is the patch clamp tech-nique, a method that can be applied to virtually any cell and has a resolution high enough to measure the minute elec-trical currents flowing through single ion channels (see Box A in Chapter 4). References COLE, K. S. (1968) Membranes, Ions and Impulses: A Chapter of Classical Biophysics. Berkeley, CA: University of California Press. Command voltage Current-passing electrode Voltage clamp amplifier Measure current Measure Vm Recording electrode 4 The current flowing back into the axon, and thus across its membrane, can be measured here Squid axon Saline solution 2 Voltage clamp amplifier compares membrane potential to the desired (command) potential 3 When Vm is different from the command potential, the clamp amplifier injects current into the axon through a second electrode. This feedback arrangement causes the membrane potential to become the same as the command potential 1 One internal electrode measures membrane potential (Vm) and is connected to the voltage clamp amplifier + − Reference electrode Voltage clamp technique for studying mem-brane currents of a squid axon. nique, the voltage clamp method (Box A), provides the information needed to define the ionic permeability of the membrane at any level of membrane potential. In the late 1940s, Alan Hodgkin and Andrew Huxley working at the Uni-versity of Cambridge used the voltage clamp technique to work out the per-meability changes underlying the action potential. They again chose to use the giant neuron of the squid because its large size (up to 1 mm in diameter; see Box A in Chapter 2) allowed insertion of the electrodes necessary for voltage clamping. They were the first investigators to test directly the hypothesis that potential-sensitive Na+ and K+ permeability changes are both necessary and sufficient for the production of action potentials. Hodgkin and Huxley’s first goal was to determine whether neuronal membranes do, in fact, have voltage-dependent permeabilities. To address this issue, they asked whether ionic currents flow across the membrane when its potential is changed. The result of one such experiment is shown in Figure 3.1. Figure 3.1A illustrates the currents produced by a squid axon when its membrane potential, V m, is hyperpolarized from the resting level of –65 mV to –130 mV. The initial response of the axon results from the redistri-bution of charge across the axonal membrane. This capacitive current is nearly instantaneous, ending within a fraction of a millisecond. Aside from this brief event, very little current flows when the membrane is hyperpolar-ized. However, when the membrane potential is depolarized from –65 mV to 0 mV, the response is quite different (Figure 3.1B). Following the capacitive current, the axon produces a rapidly rising inward ionic current (inward refers to a positive charge entering the cell—that is, cations in or anions out), which gives way to a more slowly rising, delayed outward current. The fact that membrane depolarization elicits these ionic currents establishes that the membrane permeability of axons is indeed voltage-dependent. Two Types of Voltage-Dependent Ionic Current The results shown in Figure 3.1 demonstrate that the ionic permeability of neuronal membranes is voltage-sensitive, but the experiments do not iden-tify how many types of permeability exist, or which ions are involved. As discussed in Chapter 2 (see Figure 2.5), varying the potential across a mem-brane makes it possible to deduce the equilibrium potential for the ionic fluxes through the membrane, and thus to identify the ions that are flowing. Voltage-Dependent Membrane Permeability 49 (A) (B) −65 −130 −130 Membrane current (mA/cm2) Membrane potential (mV) 0 0 1 2 3 Time (ms) Capacitive current Transient inward current Delayed outward current 4 0 2 Time (ms) 4 +1 0 −1 +1 −1 0 −65 0 1 3 65 mV Hyperpolarization Capacitive current 65 mV Depolarization Outward Inward Outward Inward Figure 3.1 Current flow across a squid axon membrane during a voltage clamp experiment. (A) A 65 mV hyperpolariza-tion of the membrane potential pro-duces only a very brief capacitive cur-rent. (B) A 65 mV depolarization of the membrane potential also produces a brief capacitive current, which is fol-lowed by a longer lasting but transient phase of inward current and a delayed but sustained outward current. (After Hodgkin et al., 1952.) 50 Chapter Three Because the voltage clamp method allows the membrane potential to be changed while ionic currents are being measured, it was a straightforward matter for Hodgkin and Huxley to determine ionic permeability by examin-ing how the properties of the early inward and late outward currents changed as the membrane potential was varied (Figure 3.2). As already noted, no appreciable ionic currents flow at membrane potentials more neg-ative than the resting potential. At more positive potentials, however, the currents not only flow but change in magnitude. The early current has a U-shaped dependence on membrane potential, increasing over a range of depolarizations up to approximately 0 mV but decreasing as the potential is depolarized further. In contrast, the late current increases monotonically with increasingly positive membrane potentials. These different responses to membrane potential can be seen more clearly when the magnitudes of the two current components are plotted as a function of membrane potential, as in Figure 3.3. The voltage sensitivity of the early inward current gives an important clue about the nature of the ions carrying the current, namely, that no cur-rent flows when the membrane potential is clamped at +52 mV. For the squid neurons studied by Hodgkin and Huxley, the external Na+ concentra-tion is 440 mM, and the internal Na+ concentration is 50 mM. For this con-centration gradient, the Nernst equation predicts that the equilibrium poten- Time (ms) 0 −2 2 4 6 7 Membrane current (mA/cm2) 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 8 8 0 2 4 6 0 2 4 6 −50 −25 −26 0 25 50 75 Membrane potential (mV) +26 0 +52 +65 Figure 3.2 Current produced by membrane depolarizations to several different potentials. The early current first increases, then decreases in magnitude as the depolarization increases; note that this current is actually reversed in polarity at potentials more positive than about +55 mV. In contrast, the late current increases monotonically with increasing depolarization. (After Hodgkin et al., 1952.) Membrane current (mA/cm2) Late 0 0 1.0 2.0 3.0 50 Membrane potential (mV) −50 −100 Early Figure 3.3 Relationship between current amplitude and membrane potential, taken from experiments such as the one shown in Figure 3.2. Whereas the late out-ward current increases steeply with increasing depolarization, the early inward cur-rent first increases in magnitude, but then decreases and reverses to outward cur-rent at about +55 mV (the sodium equilibrium potential). (After Hodgkin et al., 1952.) tial for Na+ should be +55 mV. Recall further from Chapter 2 that at the Na+ equilibrium potential there is no net flux of Na+ across the membrane, even if the membrane is highly permeable to Na+. Thus, the experimental obser-vation that no current flows at the membrane potential where Na+ cannot flow is a strong indication that the early inward current is carried by entry of Na+ into the axon. An even more demanding way to test whether Na+ carries the early inward current is to examine the behavior of this current after removing external Na+ . Removing the Na+ outside the axon makes ENa negative; if the permeability to Na+ is increased under these conditions, current should flow outward as Na+ leaves the neuron, due to the reversed electrochemical gra-dient. When Hodgkin and Huxley performed this experiment, they obtained the result shown in Figure 3.4. Removing external Na+ caused the early inward current to reverse its polarity and become an outward current at a membrane potential that gave rise to an inward current when external Na+ was present. This result demonstrates convincingly that the early inward current measured when Na+ is present in the external medium must be due to Na+ entering the neuron. Notice that removal of external Na+ in the experiment shown in Figure 3.4 has little effect on the outward current that flows after the neuron has been kept at a depolarized membrane voltage for several milliseconds. This fur-ther result shows that the late outward current must be due to the flow of an ion other than Na+. Several lines of evidence presented by Hodgkin, Huxley, and others showed that this late outward current is caused by K+ exiting the neuron. Perhaps the most compelling demonstration of K+ involvement is that the amount of K+ efflux from the neuron, measured by loading the neu-ron with radioactive K+, is closely correlated with the magnitude of the late outward current. Taken together, these experiments using the voltage clamp show that changing the membrane potential to a level more positive than the resting potential produces two effects: an early influx of Na+ into the neuron, fol-lowed by a delayed efflux of K+. The early influx of Na+ produces a transient inward current, whereas the delayed efflux of K+ produces a sustained out-ward current. The differences in the time course and ionic selectivity of the two fluxes suggest that two different ionic permeability mechanisms are acti-vated by changes in membrane potential. Confirmation that there are indeed two distinct mechanisms has come from pharmacological studies of drugs that specifically affect these two currents (Figure 3.5). Tetrodotoxin, an alka-loid neurotoxin found in certain puffer fish, tropical frogs, and salamanders, blocks the Na+ current without affecting the K+ current. Conversely, tetra-ethylammonium ions block K+ currents without affecting Na+ currents. The differential sensitivity of Na+ and K+ currents to these drugs provides strong additional evidence that Na+ and K+ flow through independent permeability pathways. As discussed in Chapter 4, it is now known that these pathways are ion channels that are selectively permeable to either Na+ or K+. In fact, tetrodotoxin, tetraethylammonium, and other drugs that interact with spe-Voltage-Dependent Membrane Permeability 51 Membrane potential (mV) Membrane current (mA/cm2) Early current is inward 0 0 2 4 Time (ms) 6 8 −1 +1 0 −1 +1 0 −1 +1 25 0 −25 −50 −75 460 mM Na+ 460 mM Na+ Early current is outward Early current is inward again Na+-free Figure 3.4 Dependence of the early inward current on sodium. In the presence of normal external concentrations of Na+, depolarization of a squid axon to 0 mV pro-duces an inward initial current. However, removal of external Na+ causes the initial inward current to become outward, an effect that is reversed by restoration of exter-nal Na+. (After Hodgkin and Huxley, 1952a.) 52 Chapter Three Figure 3.5 Pharmacological separation of Na+ and K+ currents into sodium and potassium components. Panel (1) shows the current that flows when the mem-brane potential of a squid axon is depo-larized to 0 mV in control conditions. (2) Treatment with tetrodotoxin causes the early Na+ currents to disappear but spares the late K+ currents. (3) Addition of tetraethylammonium blocks the K+ currents without affecting the Na+ cur-rents. (After Moore et al., 1967 and Arm-strong and Binstock, 1965.) cific types of ion channels have been extraordinarily useful tools in charac-terizing these channel molecules (see Chapter 4). Two Voltage-Dependent Membrane Conductances The next goal Hodgkin and Huxley set for themselves was to describe Na+ and K+ permeability changes mathematically. To do this, they assumed that the ionic currents are due to a change in membrane conductance, defined as the reciprocal of the membrane resistance. Membrane conductance is thus closely related, although not identical, to membrane permeability. When evaluating ionic movements from an electrical standpoint, it is convenient to describe them in terms of ionic conductances rather than ionic permeabili-ties. For present purposes, permeability and conductance can be considered synonymous. If membrane conductance (g) obeys Ohm’s Law (which states that voltage is equal to the product of current and resistance), then the ionic current that flows during an increase in membrane conductance is given by Iion = gion (Vm – Eion) where Iion is the ionic current, V m is the membrane potential, and Eion is the equilibrium potential for the ion flowing through the conductance, gion. The difference between V m and Eion is the electrochemical driving force acting on the ion. Hodgkin and Huxley used this simple relationship to calculate the depen-dence of Na+ and K+ conductances on time and membrane potential. They knew V m, which was set by their voltage clamp device (Figure 3.6A), and could determine ENa and EK from the ionic concentrations on the two sides 0 −75 −50 −25 25 0 −1 +1 (1) (2) (3) 0 −1 +1 Membrane current (mA/cm2 ) 0 0 5 Time (ms) Time (ms) 10 0 Time (ms) 5 10 5 10 Membrane potential (mV) Add tetrodotoxin Add tetraethyl-ammonium Na+ current blocked K+ current blocked of the axonal membrane (see Table 2.1). The currents carried by Na+ and K+—INa and IK—could be determined separately from recordings of the membrane currents resulting from depolarization (Figure 3.6B) by measur-ing the difference between currents recorded in the presence and absence of external Na+ (as shown in Figure 3.4). From these measurements, Hodgkin and Huxley were able to calculate gNa and gK (Figure 3.6C,D), from which they drew two fundamental conclusions. The first conclusion is that the Na+ and K+ conductances change over time. For example, both Na+ and K+ con-ductances require some time to activate, or turn on. In particular, the K+ con-ductance has a pronounced delay, requiring several milliseconds to reach its maximum (Figure 3.6D), whereas the Na+ conductance reaches its maximum more rapidly (Figure 3.6C). The more rapid activation of the Na+ conduc-tance allows the resulting inward Na+ current to precede the delayed out-ward K+ current (see Figure 3.6B). Although the Na+ conductance rises rapidly, it quickly declines, even though the membrane potential is kept at a depolarized level. This fact shows that depolarization not only causes the Na+ conductance to activate, but also causes it to decrease over time, or inac-tivate. The K+ conductance of the squid axon does not inactivate in this way; thus, while the Na+ and K+ conductances share the property of time-depen-dent activation, only the Na+ conductance inactivates. (Inactivating K+ conductances have since been discovered in other types of nerve cells; see Chapter 4.) The time courses of the Na+ and K+ conductances are voltage-Voltage-Dependent Membrane Permeability 53 Membrane potential (mV) 0 2 −2 4 6 Membrane current mA/cm2 30 20 10 0 60 40 20 0 Na+ conductance mSiemens/cm2 K+ conductance mSiemens/cm2 44 −2 −27 23 Time (ms) 0 2 4 6 0 2 4 6 0 2 4 6 0 2 4 6 0 2 4 6 (A) (B) (C) (D) 8 8 8 8 8 −50 −75 −25 0 25 50 −39 + + Figure 3.6 Membrane conductance changes underlying the action potential are time- and voltage-dependent. Depo-larizations to various membrane poten-tials (A) elicit different membrane cur-rents (B). Below are shown the Na+ (C) and K+ (D) conductances calculated from these currents. Both peak Na+ con-ductance and steady-state K+ conduc-tance increase as the membrane poten-tial becomes more positive. In addition, the activation of both conductances, as well as the rate of inactivation of the Na+ conductance, occur more rapidly with larger depolarizations. (After Hodgkin and Huxley, 1952b.) 54 Chapter Three Figure 3.7 Depolarization increases Na+ and K+ conductances of the squid giant axon. The peak magnitude of Na+ conductance and steady-state value of K+ conductance both increase steeply as the membrane potential is depolarized. (After Hodgkin and Huxley, 1952b.) dependent, with the speed of both activation and inactivation increasing at more depolarized potentials. This finding accounts for more rapid time courses of membrane currents measured at more depolarized potentials. The second conclusion derived from Hodgkin and Huxley’s calculations is that both the Na+ and K+ conductances are voltage-dependent—that is, both conductances increase progressively as the neuron is depolarized. Fig-ure 3.7 illustrates this by plotting the relationship between peak value of the conductances (from Figure 3.6C,D) against the membrane potential. Note the similar voltage dependence for each conductance; both conductances are quite small at negative potentials, maximal at very positive potentials, and exquisitely dependent on membrane voltage at intermediate potentials. The observation that these conductances are sensitive to changes in membrane potential shows that the mechanism underlying the conductances somehow “senses” the voltage across the membrane. All told, the voltage clamp experiments carried out by Hodgkin and Hux-ley showed that the ionic currents that flow when the neuronal membrane is depolarized are due to three different voltage-sensitive processes: (1) activa-tion of Na+ conductance, (2) activation of K+ conductance, and (3) inactiva-tion of Na+ conductance. Reconstruction of the Action Potential From their experimental measurements, Hodgkin and Huxley were able to construct a detailed mathematical model of the Na+ and K+ conductance changes. The goal of these modeling efforts was to determine whether the Na+ and K+ conductances alone are sufficient to produce an action potential. Using this information, they could in fact generate the form and time course of the action potential with remarkable accuracy (Figure 3.8A). Further, the Hodgkin-Huxley model predicted other features of action potential behavior in the squid axon, such as how the delay before action potential generation changes in response to stimulating currents of different intensities (Figure 3.8B,C). The model also predicted that the axon membrane would become refractory to further excitation for a brief period following an action poten-tial, as was experimentally observed. The Hodgkin-Huxley model also provided many insights into how action potentials are generated. Figure 3.8A shows a reconstructed action potential, together with the time courses of the underlying Na+ and K+ conductances. The coincidence of the initial increase in Na+ conductance with the rapid ris-ing phase of the action potential demonstrates that a selective increase in Membrane potential (mV) 0 5 10 15 20 Conductance (mSiemens/cm2 ) −60 −80 −40 −20 0 20 40 Na+ Membrane potential (mV) 0 10 20 30 40 Conductance (mSiemens/cm2 ) −60 −80 −40 −20 0 20 40 K+ Na+ conductance is responsible for action potential initiation. The increase in Na+ conductance causes Na+ to enter the neuron, thus depolarizing the membrane potential, which approaches ENa. The rate of depolarization sub-sequently falls both because the electrochemical driving force on Na+ decreases and because the Na+ conductance inactivates. At the same time, depolarization slowly activates the voltage-dependent K+ conductance, caus-ing K+ to leave the cell and repolarizing the membrane potential toward EK. Because the K+ conductance becomes temporarily higher than it is in the resting condition, the membrane potential actually becomes briefly more negative than the normal resting potential (the undershoot). The hyperpo-larization of the membrane potential causes the voltage-dependent K+ con-ductance (and any Na+ conductance not inactivated) to turn off, allowing the membrane potential to return to its resting level. Voltage-Dependent Membrane Permeability 55 K+ Na+ (B) Time (ms) 0 10 20 30 0 50 75 25 0 +20 −20 −60 −40 −80 +40 (A) Membrane potential (mV) Membrane potential (mV) Conductance mSiemens/cm2 ACTION POTENTIALS OF SQUID AXON 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 Time (ms) 0 −25 −50 −75 50 25 Stimulus current Membrane potential (mV) 2 3 4 (C) Time (ms) 0 −25 −50 −75 50 25 MATHEMATICAL MODEL BASED ON Na+ AND K+ CONDUCTANCES 0 1 0 0 1 2 3 4 1 2 3 4 Figure 3.8 Mathematical reconstruction of the action potential. (A) Reconstruction of an action potential (black curve) together with the underlying changes in Na+ (red curve) and K+ (yellow curve) conductance. The size and time course of the action potential were calculated using only the properties of gNa and gK measured in voltage clamp experiments. Real action potentials evoked by brief current pulses of different intensities (B) are remarkably similar to those generated by the mathemati-cal model (C). The reconstructed action potentials shown in (A) and (C) differ in duration because (A) simulates an action potential at 19°C, whereas (C) simulates an action potential at 6°C. (After Hodgkin and Huxley, 1952d.) 56 Chapter Three This mechanism of action potential generation represents a positive feed-back loop: Activating the voltage-dependent Na+ conductance increases Na+ entry into the neuron, which makes the membrane potential depolarize, which leads to the activation of still more Na+ conductance, more Na+ entry, and still further depolarization (Figure 3.9). Positive feedback continues unabated until Na+ conductance inactivation and K+ conductance activation restore the membrane potential to the resting level. Because this positive feedback loop, once initiated, is sustained by the intrinsic properties of the neuron—namely, the voltage dependence of the ionic conductances—the action potential is self-supporting, or regenerative. This regenerative quality explains why action potentials exhibit all-or-none behavior (see Figure 2.1), and why they have a threshold (Box B). The delayed activation of the K+ con-ductance represents a negative feedback loop that eventually restores the membrane to its resting state. Hodgkin and Huxley’s reconstruction of the action potential and all its features shows that the properties of the voltage-sensitive Na+ and K+ con-ductances, together with the electrochemical driving forces created by ion transporters, are sufficient to explain action potentials. Their use of both empirical and theoretical methods brought an unprecedented level of rigor to a long-standing problem, setting a standard of proof that is achieved only rarely in biological research. Long-Distance Signaling by Means of Action Potentials The voltage-dependent mechanisms of action potential generation also explain the long-distance transmission of these electrical signals. Recall from Chapter 2 that neurons are relatively poor conductors of electricity, at least compared to a wire. Current conduction by wires, and by neurons in the absence of action potentials, is called passive current flow (Box C). The pas-sive electrical properties of a nerve cell axon can be determined by measur-ing the voltage change resulting from a current pulse passed across the axonal membrane (Figure 3.10A). If this current pulse is not large enough to generate action potentials, the magnitude of the resulting potential change decays exponentially with increasing distance from the site of current injec-tion (Figure 3.10B). Typically, the potential falls to a small fraction of its ini-tial value at a distance of no more than a couple of millimeters away from the site of injection (Figure 3.10C). The progressive decrease in the amplitude of the induced potential change occurs because the injected current leaks out across the axonal membrane; accordingly, less current is available to change the membrane potential farther along the axon. Thus, the leakiness of the axonal membrane prevents effective passive transmission of electrical signals in all but the shortest axons (those 1 mm or less in length). Likewise, the leakiness of the membrane slows the time course of the responses measured at increasing distances from the site where current was injected (Figure 3.10D). FAST POSITIVE CYCLE Increase Na+ current Open Na+ channels SLOW NEGATIVE CYCLE Increase K+ current Open K+ channels Depolarize membrane potential H y p e r p o l a r i z e s D e p o l a r i z e s m o r e Figure 3.9 Feedback cycles responsible for membrane potential changes during an action potential. Membrane depolarization rapidly activates a positive feedback cycle fueled by the voltage-dependent activation of Na+ conductance. This phe-nomenon is followed by the slower activation of a negative feedback loop as depo-larization activates a K+ conductance, which helps to repolarize the membrane potential and terminate the action potential. Voltage-Dependent Membrane Permeability 57 Box B Threshold An important—and potentially puz-zling—property of the action potential is its initiation at a particular membrane potential, called threshold. Indeed, action potentials never occur without a depolarizing stimulus that brings the membrane to this level. The depolarizing “trigger” can be one of several events: a synaptic input, a receptor potential gen-erated by specialized receptor organs, the endogenous pacemaker activity of cells that generate action potentials spon-taneously, or the local current that medi-ates the spread of the action potential down the axon. Why the action potential “takes off” at a particular level of depolarization can be understood by comparing the under-lying events to a chemical explosion (Figure A). Exogenous heat (analogous to the initial depolarization of the mem-brane potential) stimulates an exother-mic chemical reaction, which produces more heat, which further enhances the reaction (Figure B). As a result of this positive feedback loop, the rate of the reaction builds up exponentially—the definition of an explosion. In any such process, however, there is a threshold, that is, a point up to which heat can be supplied without resulting in an explo-sion. The threshold for the chemical explosion diagrammed here is the point at which the amount of heat supplied exogenously is just equal to the amount of heat that can be dissipated by the cir-cumstances of the reaction (such as escape of heat from the beaker). The threshold of action potential initi-ation is, in principle, similar (Figure C). There is a range of “subthreshold” depo-larization, within which the rate of increased sodium entry is less than the rate of potassium exit (remember that the membrane at rest is highly permeable to K+, which therefore flows out as the membrane is depolarized). The point at which Na+ inflow just equals K+ outflow represents an unstable equilibrium anal-ogous to the ignition point of an explo-sive mixture. The behavior of the mem-brane at threshold reflects this instability: The membrane potential may linger at the threshold level for a variable period before either returning to the resting level or flaring up into a full-blown action potential. In theory at least, if there is a net internal gain of a single Na+ ion, an action potential occurs; con-versely, the net loss of a single K+ ion leads to repolarization. A more precise definition of threshold, therefore, is that value of membrane potential, in depolar-izing from the resting potential, at which the current carried by Na+ entering the neuron is exactly equal to the K+ current that is flowing out. Once the triggering event depolarizes the membrane beyond this point, the positive feedback loop of Na+ entry on membrane potential closes and the action potential “fires.” Because the Na+ and K+ conductances change dynamically over time, the threshold potential for producing an action potential also varies as a conse-quence of the previous activity of the neuron. For example, following an action potential, the membrane becomes tem-porarily refractory to further excitation because the threshold for firing an action potential transiently rises. There is, there-fore, no specific value of membrane potential that defines the threshold for a given nerve cell in all circumstances. (A) (C) (B) Some heat escapes Additional heat produced Heat source K+ loss repolarizes membrane potential Increase in Na+ permeability Na+ entry ACTION POTENTIAL Depolarization of membrane Heat escape slows reaction Exothermic reaction Increase in reaction rate CHEMICAL EXPLOSION Heat A positive feedback loop underlying the action potential explains the phenomenon of threshold. 58 Chapter Three If the experiment shown in Figure 3.10 is repeated with a depolarizing current pulse large enough to produce an action potential, the result is dra-matically different (Figure 3.11A). In this case, an action potential occurs without decrement along the entire length of the axon, which in humans −50 −65 −65 −62 −59 −60 −55 Membrane potential (mV) Membrane potential (mV) Threshold Current injection electrode 0 10 10 20 30 40 0 10 20 30 40 Time (ms) 0 10 20 30 40 0 10 20 30 40 0 10 20 30 40 0 10 20 30 40 0 −0.5 0 0.5 1.0 1.5 2.0 2.5 20 30 40 Distance along axon (mm) (A) (B) (C) Resting potential Potential recording electrodes Record Record Record Record Record Record Record Stimulate Axon 10 0 20 30 40 −65 −60 Membrane potential (mV) Time (ms) 0.5 1.0 1.5 2.0 2.5 0 Distance from current injection (mm) (D) −0 −1 Current (nA) +1 1 mm Figure 3.10 Passive current flow in an axon. (A) Experimental arrangement for examining the local flow of electrical current in an axon. A current-passing electrode produces a subthreshold change in membrane potential, which spreads passively along the axon. (B) Potential responses recorded at the posi-tions indicated by microelectrodes. With increasing distance from the site of cur-rent injection, the amplitude of the potential change is attenuated. (C) Rela-tionship between the amplitude of potential responses and distance. (D) Superimposed responses (from B) to current pulse, measured at indicated distances along axon. Note that the responses develop more slowly at greater distances from the site of current injection, for reasons explained in Box C. (After Hodgkin and Rushton, 1938.) may be a distance of a meter or more (Figure 3.11B). Thus, action potentials somehow circumvent the inherent leakiness of neurons. How, then, do action potentials traverse great distances along such a poor passive conductor? The answer is in part provided by the observation that the amplitude of the action potentials recorded at different distances is con-stant. This all-or-none behavior indicates that more than simple passive flow of current must be involved in action potential propagation. A second clue comes from examination of the time of occurrence of the action potentials recorded at different distances from the site of stimulation: Action potentials occur later and later at greater distances along the axon (Figure 3.11B). Thus, the action potential has a measurable rate of transmission, called the con-duction velocity. The delay in the arrival of the action potential at succes-sively more distant points along the axon differs from the case shown in Fig-ure 3.10, in which the electrical changes produced by passive current flow occur at more or less the same time at successive points. The mechanism of action potential propagation is easy to grasp once one understands how action potentials are generated and how current passively flows along an axon (Figure 3.12). A depolarizing stimulus—a synaptic potential or a receptor potential in an intact neuron, or an injected current pulse in an experiment—locally depolarizes the axon, thus opening the volt-age-sensitive Na+ channels in that region. The opening of Na+ channels causes inward movement of Na+, and the resultant depolarization of the membrane potential generates an action potential at that site. Some of the local current generated by the action potential will then flow passively down Voltage-Dependent Membrane Permeability 59 ms −65 −65 −50 −50 −25 25 0 0 Potential recording electrodes Current injection electrode Axon ms ms ms ms ms 0 2 6 8 4 ms 0 2 6 8 4 0 2 6 8 4 0 2 6 8 4 0 2 6 8 4 0 2 6 8 4 0 2 6 8 4 Membrane potential (mV) Record Record Record Record Record Record Record Stimulate Membrane potential (mV) −0.5 0 0.5 1.0 1.5 2.0 2.5 Distance along axon (mm) (C) (B) (A) Threshold Resting potential 1 mm Figure 3.11 Propagation of an action potential. (A) In this experimental arrangement, an electrode evokes an action potential by injecting a supra-threshold current. (B) Potential responses recorded at the positions indi-cated by microelectrodes. The amplitude of the action potential is constant along the length of the axon, although the time of appearance of the action poten-tial is delayed with increasing distance. (C) The constant amplitude of an action potential (solid black line) measured at different distances. 60 Chapter Three the axon, in the same way that subthreshold currents spread along the axon (see Figure 3.10). Note that this passive current flow does not require the movement of Na+ along the axon but, instead, occurs by a shuttling of charge, somewhat similar to what happens when wires passively conduct electricity by transmission of electron charge. This passive current flow depolarizes the membrane potential in the adjacent region of the axon, thus opening the Na+ channels in the neighboring membrane. The local depolar-ization triggers an action potential in this region, which then spreads again in a continuing cycle until the end of the axon is reached. Thus, action poten-tial propagation requires the coordinated action of two forms of current Box C Passive Membrane Properties The passive flow of electrical current plays a central role in action potential propagation, synaptic transmission, and all other forms of electrical signaling in nerve cells. Therefore, it is worthwhile understanding in quantitative terms how passive current flow varies with distance along a neuron. For the case of a cylindri-cal axon, such as the one depicted in Fig-ure 3.10, subthreshold current injected into one part of the axon spreads pas-sively along the axon until the current is dissipated by leakage out across the axon membrane. The decrement in the current flow with distance (Figure A) is described by a simple exponential function: Vx = V0 e–x/λ where V x is the voltage response at any distance x along the axon, V 0 is the volt-age change at the point where current is injected into the axon, e is the base of natural logarithms (approximately 2.7), and λ is the length constant of the axon. As evident in this relationship, the length constant is the distance where the initial voltage response (V 0) decays to 1/e (or 37%) of its value. The length constant is thus a way to characterize how far pas-sive current flow spreads before it leaks out of the axon, with leakier axons hav-ing shorter length constants. The length constant depends upon the physical properties of the axon, in particular the relative resistances of the plasma membrane (r m), the intracellular axoplasm (r i), and the extracellular medium (r 0). The relationship between these parameters is: Hence, to improve the passive flow of current along an axon, the resistance of the plasma membrane should be as high as possible and the resistances of the axoplasm and extracellular medium should be low. Another important consequence of the passive properties of neurons is that currents flowing across a membrane do not immediately change the membrane potential. For example, when a rectangu-lar current pulse is injected into the axon shown in the experiment illustrated in Figure 3.10A, the membrane potential depolarizes slowly over a few millisec-onds and then repolarizes over a similar time course when the current pulse ends (see Figure 3.10D). These delays in changing the membrane potential are due to the fact that the plasma mem-λ = + r r r m 0 i 1.0 0.4 0.6 0.8 0.2 0.0 0 1 2 3 4 5 −5 −4 −3 −2 −1 Distance from current injection (mm) 37% VX = V0e−x/λ VX/V0 λ λ (A) Spatial decay of membrane potential along a cylindrical axon. A current pulse injected at one point in the axon (0 mm) produces voltage responses (V x) that decay exponentially with distance. The distance where the voltage response is 1/e of its initial value (V0) is the length constant, λ. flow—the passive flow of current as well as active currents flowing through voltage-dependent ion channels. The regenerative properties of Na+ channel opening allow action potentials to propagate in an all-or-none fashion by acting as a booster at each point along the axon, thus ensuring the long-dis-tance transmission of electrical signals. The Refractory Period Recall that the depolarization that produces Na+ channel opening also causes delayed activation of K+ channels and Na+ channel inactivation, lead-Voltage-Dependent Membrane Permeability 61 brane behaves as a capacitor, storing the initial charge that flows at the beginning and end of the current pulse. For the case of a cell whose membrane potential is spatially uniform, the change in the membrane potential at any time, V t, after beginning the current pulse (Figure B) can also be described by an exponential relationship: Vt = V∞(1 − e−t/τ) where V ∞is the steady-state value of the membrane potential change, t is the time after the current pulse begins, and τ is the membrane time constant. The time constant is thus defined as the time when the voltage response (V t) rises to 1 − (1/e) (or 63%) of V ∞. After the current pulse ends, the membrane potential change also declines exponentially according to the relationship Vt = V∞ e−t/τ During this decay, the membrane poten-tial returns to 1/e of V ∞at a time equal to t. For cells with more complex geome-tries than the axon in Figure 3.10, the time courses of the changes in mem-brane potential are not simple exponen-tials, but nonetheless depend on the membrane time constant. Thus, the time constant characterizes how rapidly cur-rent flow changes the membrane poten-tial. The membrane time constant also depends on the physical properties of the nerve cell, specifically on the resistance (rm) and capacitance (cm) of the plasma membrane such that: τ = rmcm The values of rm and cm depend, in part, on the size of the neuron, with larger cells having lower resistances and larger capacitances. In general, small nerve cells tend to have long time constants and large cells brief time constants. References HODGKIN, A. L. AND W. A. H. RUSHTON (1938) The electrical constants of a crustacean nerve fibre. Proc. R. Soc. Lond. 133: 444–479. JOHNSTON, D. AND S. M.-S. WU (1995) Founda-tions of Cellular Neurophysiology. Cambridge, MA: MIT Press. RALL, W. (1977) Core conductor theory and cable properties of neurons. In Handbook of Physiology, Section 1: The Nervous System, Vol. 1: Cellular Biology of Neurons. E. R. Kan-del (ed.). Bethesda, MD: American Physio-logical Society, pp. 39–98. 1.0 0.40 0.60 0.80 0.20 0.00 0 5 10 15 20 25 30 35 40 Time (ms) 37% 63% Vt = V∞e−t/τ Vt = V∞(1 – e−t/τ) V∞/Vτ −0 −1 Current (nA) +1 τ τ (B) Time course of potential changes produced in a spatially uniform cell by a current pulse. The rise and fall of the membrane potential (V t) can be described as exponential functions, with the time constant τ defining the time required for the response to rise to 1 – (1/e) of the steady-state value (V ∞), or to decline to 1/e of V ∞. 62 Chapter Three Axon Point A Point B Point C Point A Point B Point C Point A Point B Point C Na+ Na+ Na+ Na+ Na+ channel K+ channel Membrane 1 Na+ channels locally open in response to stimulus, generating an action potential here 2 Some depolarizing current passively flows down axon K+ K+ K+ Na+ Na+ Na+ K+ K+ K+ Na+ 3 Local depolarization causes neighboring Na+ channels to open and generates an action potential here 4 Upstream Na+ channels inactivate, while K+ channels open. Membrane potential repolarizes and axon is refractory here 5 The process is repeated, propagating the action potential along the axon Na+ t = 2 t = 3 t = 3 t = 2 t = 1 Point A Point B Point C t = 1 Stimulate 0 mV −65 Resting potential Threshold 0 −65 Resting potential Threshold 0 −65 Resting potential Threshold Purves Neuroscience 3E Pyramis Studios P3_312 Figure 3.12 Action potential conduction requires both active and passive current flow. Depolarization opens Na+ channels locally and produces an action potential at point A of the axon (time t = 1). The resulting inward current flows passively along the axon, depolarizing the adjacent region (point B) of the axon. At a later time (t = 2), the depolarization of the adja-cent membrane has opened Na+ channels at point B, resulting in the initia-tion of the action potential at this site and additional inward current that again spreads passively to an adjacent point (point C) farther along the axon. At a still later time (t = 3), the action potential has propagated even farther. This cycle continues along the full length of the axon. Note that as the action potential spreads, the membrane potential repolarizes due to K+ channel opening and Na+ channel inactivation, leaving a “wake” of refrac-toriness behind the action potential that prevents its backward propaga-tion (panel 4). The panel to the left of this figure legend shows the time course of membrane potential changes at the points indicated. ing to repolarization of the membrane potential as the action potential sweeps along the length of an axon (see Figure 3.12). In its wake, the action potential leaves the Na+ channels inactivated and K+ channels activated for a brief time. These transitory changes make it harder for the axon to produce subsequent action potentials during this interval, which is called the refrac-tory period. Thus, the refractory period limits the number of action poten-tials that a given nerve cell can produce per unit time. As might be expected, different types of neurons have different maximum rates of action potential firing due to different types and densities of ion channels. The refractoriness of the membrane in the wake of the action potential also explains why action potentials do not propagate back toward the point of their initiation as they travel along an axon. Increased Conduction Velocity as a Result of Myelination The rate of action potential conduction limits the flow of information within the nervous system. It is not surprising, then, that various mechanisms have evolved to optimize the propagation of action potentials along axons. Because action potential conduction requires passive and active flow of cur-rent (see Figure 3.12), the rate of action potential propagation is determined by both of these phenomena. One way of improving passive current flow is to increase the diameter of an axon, which effectively decreases the internal resistance to passive current flow (see Box C). The consequent increase in action potential conduction velocity presumably explains why giant axons evolved in invertebrates such as squid, and why rapidly conducting axons in all animals tend to be larger than slowly conducting ones. Another strategy to improve the passive flow of electrical current is to insulate the axonal membrane, reducing the ability of current to leak out of the axon and thus increasing the distance along the axon that a given local current can flow passively (see Box C). This strategy is evident in the myeli-nation of axons, a process by which oligodendrocytes in the central nervous system (and Schwann cells in the peripheral nervous system) wrap the axon in myelin, which consists of multiple layers of closely opposed glial mem-branes (Figure 3.13; see also Chapter 1). By acting as an electrical insulator, myelin greatly speeds up action potential conduction (Figure 3.14). For example, whereas unmyelinated axon conduction velocities range from about 0.5 to 10 m/s, myelinated axons can conduct at velocities of up to 150 m/s. The major reason underlying this marked increase in speed is that the time-consuming process of action potential generation occurs only at spe-cific points along the axon, called nodes of Ranvier, where there is a gap in the myelin wrapping (see Figure 1.4F). If the entire surface of an axon were insulated, there would be no place for current to flow out of the axon and action potentials could not be generated. As it happens, an action potential generated at one node of Ranvier elicits current that flows passively within the myelinated segment until the next node is reached. This local current flow then generates an action potential in the neighboring segment, and the cycle is repeated along the length of the axon. Because current flows across the neuronal membrane only at the nodes (see Figure 3.13), this type of propagation is called saltatory, meaning that the action potential jumps from node to node. Not surprisingly, loss of myelin, as occurs in diseases such as multiple sclerosis, causes a variety of serious neurological problems (Box D). Voltage-Dependent Membrane Permeability 63 Axon Myelin sheath Node of Ranvier (A) Myelinated axon Na+ Na Na+ Na+ Na Na+ Na+ Na+ Na+ K+ K+ K+ K+ K+ (B) Action potential propagation t = 1 Na+ Na+ t = 1.5 t = 2 Oligodendrocyte Point A Point B Point C Point A Point B Point C Point A Point B Point C t = 2 t = 1.5 t = 1 Point A Point B Point C 0 mV −65 Resting potential Threshold 0 −65 Resting potential Threshold 0 −65 Resting potential Threshold Purves Neuroscience 3E Pyramis Studios P3_313 120103 Figure 3.13 Saltatory action potential conduction along a myeli-nated axon. (A) Diagram of a myelinated axon. (B) Local current in response to action potential initiation at a particular site flows locally, as described in Figure 3.12. However, the presence of myelin prevents the local current from leaking across the internodal mem-brane; it therefore flows farther along the axon than it would in the absence of myelin. Moreover, voltage-gated Na+ channels are present only at the nodes of Ranvier (K+ channels are present at the nodes of some neurons, but not others). This arrangement means that the generation of active, voltage-gated Na+ currents need only occur at these unmyelinated regions. The result is a greatly enhanced velocity of action potential conduction. The panel to the left of this figure leg-end shows the time course of membrane potential changes at the points indicated. Summary The action potential and all its complex properties can be explained by time-and voltage-dependent changes in the Na+ and K+ permeabilities of neu-ronal membranes. This conclusion derives primarily from evidence obtained by a device called the voltage clamp. The voltage clamp technique is an elec-tronic feedback method that allows control of neuronal membrane potential Voltage-Dependent Membrane Permeability 65 Myelinated axon Unmyelinated axon t = 2 t = 1 t = 3 Figure 3.14 Comparison of speed of action potential conduction in unmyeli-nated (upper) and myelinated (lower) axons. 66 Chapter Three Box D Multiple Sclerosis Multiple sclerosis (MS) is a disease of the central nervous system characterized by a variety of clinical problems arising from multiple regions of demyelination and inflammation along axonal path-ways. The disorder commonly begins between ages 20 and 40, characterized by the abrupt onset of neurological deficits that typically persist for days or weeks and then remit. The clinical course ranges from patients with no persistent neurological loss, some of whom experi-ence only occasional later exacerbations, to others who progressively deteriorate as a result of extensive and relentless central nervous system involvement. The signs and symptoms of MS are determined by the location of the affected regions. Particularly common are monocular blindness (due to lesions of the optic nerve), motor weakness or paralysis (due to lesions of the corti-cospinal tracts), abnormal somatic sensa-tions (due to lesions of somatic sensory pathways, often in the posterior columns), double vision (due to lesions of medial longitudinal fasciculus), and dizziness (due to lesions of vestibular pathways). Abnormalities are often apparent in the cerebrospinal fluid, which usually contains an abnormal number of cells associated with inflam-mation and an increased content of anti-bodies (a sign of an altered immune response). The diagnosis of MS generally relies on the presence of a neurological problem that remits and then returns at an unrelated site. Confirmation can sometimes be obtained from magnetic resonance imaging (MRI), or functional evidence of lesions in a particular path-way by abnormal evoked potentials. The histological hallmark of MS at post-mortem exam is multiple lesions at dif-ferent sites showing loss of myelin asso-ciated with infiltration of inflammatory cells and, in some instances, loss of axons themselves. The concept of MS as a demyelinating disease is deeply embedded in the clini-cal literature, although precisely how the demyelination translates into functional deficits is poorly understood. The loss of the myelin sheath surrounding many axons clearly compromises action poten-tial conduction, and the abnormal pat-terns of nerve conduction that result pre-sumably produce most of the clinical deficits in the disease. However, MS may have effects that extend beyond loss of the myelin sheath. It is clear that some axons are actually destroyed, probably as a result of inflammatory processes in the overlying myelin and/or loss of trophic support of the axon by oligodendrocytes. Thus, axon loss also contributes to the functional deficits in MS, especially in the chronic, progressive forms of the disease. The ultimate cause of MS remains unclear. The immune system undoubt-edly contributes to the damage and new immunoregulatory therapies provide substantial benefits to many patients. Precisely how the immune system is acti-vated to cause the injury is not known. The most popular hypothesis is that MS is an autoimmune disease (i.e., a disease in which the immune system attacks the body’s proper constituents). The fact that immunization of experimental animals with any one of several molecular con-stituents of the myelin sheath can induce a demyelinating disease (called experi-mental allergic encephalomyelitis) shows that an autoimmune attack on the myelin membrane is sufficient to pro-duce a picture similar to MS. A possible explanation of the human disease is that a genetically susceptible individual becomes transiently infected (by a minor viral illness, for example) with a microor-ganism that expresses a molecule struc-turally similar to a component of myelin. An immune response to this antigen is mounted to attack the invader, but the failure of the immune system to discrim-inate between the foreign protein and self results in destruction of otherwise normal myelin, a scenario occurring in mice infected with Theiler’s virus. An alternative hypothesis is that MS is caused by a persistent infection by a virus or other microorganism. In this interpretation, the immune system’s ongoing efforts to get rid of the pathogen cause the damage to myelin. Tropical spastic paraparesis (TSP) provides a precedent for this idea. TSP is a disease characterized by the gradual progression of weakness of the legs and impaired control of bladder function associated with increased deep tendon reflexes and a positive Babinski sign (see Chapter 16). This clinical picture is similar to that of rapidly advancing MS. TSP is known to be caused by persistent infection with a retrovirus (human T lymphotropic virus-1). This precedent notwithstand-ing, proving the persistent viral infection hypothesis for MS requires unambigu-ous demonstration of the presence of a virus. Despite periodic reports of a virus associated with MS, convincing evidence has not been forthcoming. In sum, MS remains a daunting clinical challenge. References ADAMS, R. D. AND M. VICTOR (2001) Principles of Neurology, 7th Ed. New York: McGraw-Hill, pp. 954–982. MILLER, D. H. AND 9 OTHERS. (2003) A con-trolled trial of natalizumab for relapsing mul-tiple sclerosis. N. Engl. J. Med. 348: 15–23. ZANVIL, S. S. AND L. STEINMAN (2003) Diverse targets for intervention during inflammatory and neurodegenerative phases of multiple sclerosis. Neuron 38: 685–688. and, simultaneously, direct measurement of the voltage-dependent fluxes of Na+ and K+ that produce the action potential. Voltage clamp experiments show that a transient rise in Na+ conductance activates rapidly and then inactivates during a sustained depolarization of the membrane potential. Such experiments also demonstrate a rise in K+ conductance that activates in a delayed fashion and, in contrast to the Na+ conductance, does not inacti-vate. Mathematical modeling of the properties of these conductances indi-cates that they, and they alone, are responsible for the production of all-or-none action potentials in the squid axon. Action potentials propagate along the nerve cell axons initiated by the voltage gradient between the active and inactive regions of the axon by virtue of the local current flow. In this way, action potentials compensate for the relatively poor passive electrical prop-erties of nerve cells and enable neural signaling over long distances. These classical electrophysiological findings provide a solid basis for considering the functional and ultimately molecular variations on neural signaling taken up in the next chapter. Voltage-Dependent Membrane Permeability 67 Additional Reading Reviews ARMSTRONG, C. M. AND B. HILLE (1998) Volt-age-gated ion channels and electrical excitability. Neuron 20: 371–80. NEHER, E. (1992) Ion channels for communica-tion between and within cells. Science 256: 498–502. Important Original Papers ARMSTRONG, C. M. AND L. BINSTOCK (1965) Anomalous rectification in the squid giant axon injected with tetraethylammonium chlo-ride. J. Gen. Physiol. 48: 859–872. HODGKIN, A. L. AND A. F. HUXLEY (1952a) Cur-rents carried by sodium and potassium ions through the membrane of the giant axon of Loligo. J. Physiol. 116: 449–472. HODGKIN, A. L. AND A. F. HUXLEY (1952b) The components of membrane conductance in the giant axon of Loligo. J. Physiol. 116: 473–496. HODGKIN, A. L. AND A. F. HUXLEY (1952c) The-dual effect of membrane potential on sodium conductance in the giant axon of Loligo. J. Physiol. 116: 497–506. HODGKIN, A. L. AND A. F. HUXLEY (1952d) A quantitative description of membrane current and its application to conduction and excita-tion in nerve. J. Physiol. 116: 507–544. HODGKIN, A. L. AND W. A. H. RUSHTON (1938) The electrical constants of a crustacean nerve fibre. Proc. R. Soc. Lond. 133: 444–479. HODGKIN, A. L., A. F. HUXLEY AND B. KATZ (1952) Measurements of current–voltage rela-tions in the membrane of the giant axon of Loligo. J. Physiol. 116: 424–448. MOORE, J. W., M. P. BLAUSTEIN, N. C. ANDER-SON AND T. NARAHASHI (1967) Basis of tetrodotoxin’s selectivity in blockage of squid axons. J. Gen. Physiol. 50: 1401–1411. Books AIDLEY, D. J. AND P. R. STANFIELD (1996) Ion Channels: Molecules in Action. Cambridge: Cambridge University Press. HILLE, B. (2001) Ion Channels of Excitable Mem-branes, 3rd Ed. Sunderland, MA: Sinauer Associates. JOHNSTON, D. AND S. M.-S. WU (1995) Founda-tions of Cellular Neurophysiology. Cambridge, MA: MIT Press. JUNGE, D. (1992) Nerve and Muscle Excitation, 3rd Ed. Sunderland, MA: Sinauer Associates. Overview The generation of electrical signals in neurons requires that plasma mem-branes establish concentration gradients for specific ions and that these membranes undergo rapid and selective changes in the membrane perme-ability to these ions. The membrane proteins that create and maintain ion gradients are called active transporters, whereas other proteins called ion channels give rise to selective ion permeability changes. As their name implies, ion channels are transmembrane proteins that contain a specialized structure, called a pore, that permits particular ions to cross the neuronal membrane. Some of these channels also contain other structures that are able to sense the electrical potential across the membrane. Such voltage-gated channels open or close in response to the magnitude of the membrane poten-tial, allowing the membrane permeability to be regulated by changes in this potential. Other types of ion channels are gated by extracellular chemical signals such as neurotransmitters, and some by intracellular signals such as second messengers. Still others respond to mechanical stimuli, temperature changes, or a combination of such effects. Many types of ion channels have now been characterized at both the gene and protein level, resulting in the identification of a large number of ion channel subtypes that are expressed differentially in neuronal and non-neuronal cells. The specific expression pattern of ion channels in each cell type can generate a wide spectrum of electrical characteristics. In contrast to ion channels, active transporters are membrane proteins that produce and maintain ion concentration gradients. The most important of these is the Na+ pump, which hydrolyzes ATP to reg-ulate the intracellular concentrations of both Na+ and K+. Other active trans-porters produce concentration gradients for the full range of physiologically important ions, including Cl–, Ca2+, and H+. From the perspective of electri-cal signaling, active transporters and ion channels are complementary: Transporters create the concentration gradients that help drive ion fluxes through open ion channels, thus generating electrical signals. Ion Channels Underlying Action Potentials Although Hodgkin and Huxley had no knowledge of the physical nature of the conductance mechanisms underlying action potentials, they nonetheless proposed that nerve cell membranes have channels that allow ions to pass selectively from one side of the membrane to the other (see Chapter 3). Based on the ionic conductances and currents measured in voltage clamp experiments, the postulated channels had to have several properties. First, because the ionic currents are quite large, the channels had to be capable of allowing ions to move across the membrane at high rates. Second, because Chapter 4 69 Channels and Transporters 70 Chapter Four A wealth of new information about ion channels resulted from the invention of the patch clamp method in the 1970s. This technique is based on a very simple idea. A glass pipette with a very small opening is used to make tight contact with a tiny area, or patch, of neuronal membrane. After the application of a small amount of suction to the back of the pipette, the seal between pipette and membrane becomes so tight that no ions can flow between the pipette and the membrane. Thus, all the ions that flow when a single ion channel opens must flow into the pipette. The resulting elec-trical current, though small, can be mea-sured with an ultrasensitive electronic amplifier connected to the pipette. Based on the geometry involved, this arrange-ment usually is called the cell-attached patch clamp recording method. As with the conventional voltage clamp method, the patch clamp method allows experimen-tal control of the membrane potential to characterize the voltage dependence of membrane currents. Although the ability to record cur-rents flowing through single ion chan-nels is an important advantage of the cell-attached patch clamp method, minor technical modifications yield still other advantages. For example, if the mem-brane patch within the pipette is dis-rupted by briefly applying strong suc-tion, the interior of the pipette becomes continuous with the cytoplasm of the cell. This arrangement allows measure-ments of electrical potentials and cur-rents from the entire cell and is therefore called the whole-cell recording method. The whole-cell configuration also allows dif-fusional exchange between the pipette and the cytoplasm, producing a conve-nient way to inject substances into the interior of a “patched” cell. Two other variants of the patch clamp method originate from the finding that once a tight seal has formed between the membrane and the glass pipette, small pieces of membrane can be pulled away from the cell without disrupting the seal; this yields a preparation that is free of the complications imposed by the rest of the cell. Simply retracting a pipette that is in the cell-attached configuration causes a small vesicle of membrane to remain attached to the pipette. By expos-ing the tip of the pipette to air, the vesicle opens to yield a small patch of mem-brane with its (former) intracellular sur-Retract pipette Strong pulse of suction Cytoplasm is continuous with pipette interior Mild suction Tight contact between pipette and membrane Expose to air Cytoplasmic domain accessible Ends of membrane anneal Extracellular domain accessible Whole-cell recording Outside-out recording Inside-out recording Recording pipette Cell-attached recording Four configurations in patch clamp measurements of ionic currents. Box A The Patch Clamp Method the ionic currents depend on the electrochemical gradient across the mem-brane, the channels had to make use of these gradients. Third, because Na+ and K+ flow across the membrane independently of each other, different channel types had to be capable of discriminating between Na+ and K+, allowing only one of these ions to flow across the membrane under the rele-vant conditions. Finally, given that the conductances are voltage-dependent, the channels had to be able to sense the voltage drop across the membrane, opening only when the voltage reached appropriate levels. While this con-cept of channels was highly speculative in the 1950s, later experimental work established beyond any doubt that transmembrane proteins called voltage-sensitive ion channels indeed exist and are responsible for all of the ionic conductance phenomena described in Chapter 3. The first direct evidence for the presence of voltage-sensitive, ion-selective channels in nerve cell membranes came from measurements of the ionic cur-rents flowing through individual ion channels. The voltage-clamp apparatus used by Hodgkin and Huxley could only resolve the aggregate current result-ing from the flow of ions through many thousands of channels. A technique capable of measuring the currents flowing through single channels was devised in 1976 by Erwin Neher and Bert Sakmann at the Max Planck Insti-tute in Goettingen. This remarkable approach, called patch clamping (Box A), revolutionized the study of membrane currents. In particular, the patch clamp method provided the means to test directly Hodgkin and Huxley’s proposals about the characteristics of ion channels. Currents flowing through Na+ channels are best examined in experimental circumstances that prevent the flow of current through other types of chan-nels that are present in the membrane (e.g., K+ channels). Under such condi-tions, depolarizing a patch of membrane from a squid giant axon causes tiny inward currents to flow, but only occasionally (Figure 4.1). The size of these currents is minuscule—approximately l–2 pA (i.e., 10–12 ampere), which is orders of magnitude smaller than the Na+ currents measured by voltage clamping the entire axon. The currents flowing through single channels are called microscopic currents to distinguish them from the macroscopic cur-rents flowing through a large number of channels distributed over a much more extensive region of surface membrane. Although microscopic currents are certainly small, a current of 1 pA nonetheless reflects the flow of thou-sands of ions per millisecond. Thus, as predicted, a single channel can let many ions pass through the membrane in a very short time. Channels and Transporters 71 face exposed. This arrangement, called the inside-out patch recording configura-tion, allows the measurement of single-channel currents with the added benefit of making it possible to change the medium to which the intracellular sur-face of the membrane is exposed. Thus, the inside-out configuration is particu-larly valuable when studying the influ-ence of intracellular molecules on ion channel function. Alternatively, if the pipette is retracted while it is in the whole-cell configuration, a membrane patch is produced that has its extracellu-lar surface exposed. This arrangement, called the outside-out recording configu-ration, is optimal for studying how chan-nel activity is influenced by extracellular chemical signals, such as neurotransmit-ters (see Chapter 5). This range of possi-ble configurations makes the patch clamp method an unusually versatile technique for studies of ion channel function. References HAMILL, O. P., A. MARTY, E. NEHER, B. SAK-MANN AND F. J. SIGWORTH (1981) Improved patch-clamp techniques for high-resolution current recording from cells and cell-free membrane patches. Pflügers Arch. 391: 85–100. LEOIS, R. A. AND J. L. RAE (1998) Low-noise patch-clamp techniques. Meth. Enzym. 293: 218–266. SIGWORTH, F. J. (1986) The patch clamp is more useful than anyone had expected. Fed. Proc. 45: 2673–2677. 72 Chapter Four Several observations further proved that the microscopic currents in Fig-ure 4.1B are due to the opening of single, voltage-activated Na+ channels. First, the currents are carried by Na+; thus, they are directed inward when the membrane potential is more negative than ENa, reverse their polarity at ENa, are outward at more positive potentials, and are reduced in size when the Na+ concentration of the external medium is decreased. This behavior exactly parallels that of the macroscopic Na+ currents described in Chapter 3. Second, the channels have a time course of opening, closing, and inactivating that matches the kinetics of macroscopic Na+ currents. This correspondence is difficult to appreciate in the measurement of microscopic currents flowing through a single open channel, because individual channels open and close in a stochastic (random) manner, as can be seen by examining the individual traces in Figure 4.1B. However, repeated depolarization of the membrane potential causes each Na+ channel to open and close many times. When the current responses to a large number of such stimuli are averaged together, the collective response has a time course that looks much like the macro-scopic Na+ current (Figure 4.1C). In particular, the channels open mostly at the beginning of a prolonged depolarization, showing that they subse-quently inactivate, as predicted from the macroscopic Na+ current (compare Figures 4.1C and 4.1D). Third, both the opening and closing of the channels are voltage-dependent; thus, the channels are closed at –80 mV but open when the membrane potential is depolarized. In fact, the probability that any given channel will be open varies with membrane potential (Figure 4.1E), again as predicted from the macroscopic Na+ conductance (see Figure 3.7). Finally, tetrodotoxin, which blocks the macroscopic Na+ current (see Box C), also blocks microscopic Na+ currents. Taken together, these results show that the macroscopic Na+ current measured by Hodgkin and Huxley does indeed arise from the aggregate effect of many thousands of micro-scopic Na+ currents, each representing the opening of a single voltage-sensi-tive Na+ channel. Patch clamp experiments have also revealed the properties of the channels responsible for the macroscopic K+ currents associated with action poten-tials. When the membrane potential is depolarized (Figure 4.2A), micro-scopic outward currents (Figure 4.2B) can be observed under conditions that block Na+ channels. The microscopic outward currents exhibit all the fea-tures expected for currents flowing through action-potential-related K+ channels. Thus, the microscopic currents (Figure 4.2C), like their macro-scopic counterparts (Figure 4.2D), fail to inactivate during brief depolariza-tions. Moreover, these single-channel currents are sensitive to ionic manipu-Figure 4.1 Patch clamp measurements of ionic currents flowing through single Na+ channels in a squid giant axon. In these experiments, Cs+ was applied to the axon to block voltage-gated K+ channels. Depolarizing voltage pulses (A) applied to a patch of membrane containing a single Na+ channel result in brief currents (B, downward deflections) in the seven successive recordings of membrane current (INa). (C) The sum of many such current records shows that most channels open in the initial 1–2 ms following depolarization of the membrane, after which the proba-bility of channel openings diminishes because of channel inactivation. (D) A macro-scopic current measured from another axon shows the close correlation between the time courses of microscopic and macroscopic Na+ currents. (E) The probability of an Na+ channel opening depends on the membrane potential, increasing as the mem-brane is depolarized. (B,C after Bezanilla and Correa, 1995; D after Vandenburg and Bezanilla, 1991; E after Correa and Bezanilla, 1994.) Closed Open 0 0 5 10 15 200 −600 −800 −400 −200 Macroscopic INa (pA) (B) (A) (D) −80 0 −40 Membrane potential (mV) Microscopic INa Membrane potential (mV) Time (ms) 0 5 10 15 Time (ms) 0 5 10 15 Time (ms) 0 5 10 15 Time (ms) 0 0.2 0.4 −60 −80 −40 –20 0 20 40 60 (E) 0.6 0.8 Probability of Na+ channel opening 0 −0.8 −0.4 0.4 Summed microscopic INa (pA) (C) 2 pA lations and drugs that affect the macroscopic K+ currents and, like the macroscopic K+ currents, are voltage-dependent (Figure 4.2E). This and other evidence shows that macroscopic K+ currents associated with action potentials arise from the opening of many voltage-sensitive K+ channels. In summary, patch clamping has allowed direct observation of micro-scopic ionic currents flowing through single ion channels, confirming that voltage sensitive Na+ and K+ channels are responsible for the macroscopic conductances and currents that underlie the action potential. Measurements of the behavior of single ion channels has also provided some insight into the molecular attributes of these channels. For example, single channel stud-ies show that the membrane of the squid axon contains at least two types of channels—one selectively permeable to Na+ and a second selectively perme-able to K+. Both channel types are voltage-gated, meaning that their opening is influenced by membrane potential (Figure 4.3). For each channel, depolar-ization increases the probability of channel opening, whereas hyperpolariza-tion closes them (see Figures 4.1E and 4.2E). Thus, both channel types must have a voltage sensor that detects the potential across the membrane (Figure 4.3). However, these channels differ in important respects. In addition to their different ion selectivities, depolarization also inactivates the Na+ chan-nel but not the K+ channel, causing Na+ channels to pass into a nonconduct-ing state. The Na+ channel must therefore have an additional molecular mechanism responsible for inactivation. And, as expected from the macro-scopic behavior of the Na+ and K+ currents described in Chapter 3, the kinetic properties of the gating of the two channels differs. This information about the physiology of single channels set the stage for subsequent studies of the molecular diversity of ion channels in various cell types, and of their detailed functional characteristics. The Diversity of Ion Channels Molecular genetic studies, in conjunction with the patch clamp method and other techniques, have led to many additional advances in understanding ion channels. Genes encoding Na+ and K+ channels, as well as many other channel types, have now been identified and cloned. A surprising fact that has emerged from these molecular studies is the diversity of genes that code for ion channels. Well over 100 ion channel genes have now been discovered, a number that could not have been anticipated from early studies of ion channel function. To understand the functional significance of this multitude of ion channel genes, the channels can be selectively expressed in well-Channels and Transporters 73 Figure 4.2 Patch clamp measurements of ionic currents flowing through single K+ channels in a squid giant axon. In these experiments, tetrodotoxin was applied to the axon to block voltage-gated Na+ channels. Depolarizing voltage pulses (A) applied to a patch of membrane containing a single K+ channel results in brief cur-rents (B, upward deflections) whenever the channel opens. (C) The sum of such cur-rent records shows that most channels open with a delay, but remain open for the duration of the depolarization. (D) A macroscopic current measured from another axon shows the correlation between the time courses of microscopic and macro-scopic K+ currents. (E) The probability of a K+ channel opening depends on the membrane potential, increasing as the membrane is depolarized. (B and C after Augustine and Bezanilla, in Hille 1992; D after Augustine and Bezanilla, 1990; E after Perozo et al., 1991.) (A) (B) (C) −100 50 0 −50 Membrane potential (mV) Microscopic IK Summed microscopic IK (pA) Macroscopic IK (mA/cm2) Membrane potential (mV) 0 −60 −80 −40 −20 0 20 40 60 (E) (D) Probability of K+ channel opening 0.6 0.4 0.2 0 10 20 30 40 Time (ms) 0 10 20 30 40 Time (ms) 0 10 20 30 40 Time (ms) 0 10 20 30 40 Time (ms) 0 1 2 3 1 0 Open Closed 2 pA 74 Chapter Four Figure 4.3 Functional states of voltage-gated Na+ and K+ channels. The gates of both channels are closed when the membrane potential is hyperpolarized. When the potential is depolarized, volt-age sensors (indicated by +) allow the channel gates to open—first the Na+ channels and then the K+ channels. Na+ channels also inactivate during pro-longed depolarization, whereas many types of K+ channels do not. defined experimental systems, such as in cultured cells or frog oocytes (Box B), and then studied with patch clamping and other physiological tech-niques. Such studies have found many voltage-gated channels that respond to membrane potential in much the same way as the Na+ and K+ channels that underlie the action potential. Other channels, however, are gated by chemical signals that bind to extracellular or intracellular domains on these proteins and are insensitive to membrane voltage. Still others are sensitive to mechanical displacement, or to changes in temperature. Further magnifying this diversity of ion channels are a number of mecha-nisms that can produce functionally different types of ion channels from a single gene. Ion channel genes contain a large number of coding regions that can be spliced together in different ways, giving rise to channel proteins that can have dramatically different functional properties. RNAs encoding ion channels also can be edited, modifying their base composition after tran-scription from the gene. For example, editing the RNA encoding of some receptors for the neurotransmitter glutamate (Chapter 6) changes a single amino acid within the receptor, which in turn gives rise to channels that dif-fer in their selectivity for cations and in their conductance. Channel proteins can also undergo posttranslational modifications, such as phosphorylation by protein kinases (see Chapter 7), which can further change their functional characteristics. Thus, although the basic electrical signals of the nervous sys-tem are relatively stereotyped, the proteins responsible for generating these signals are remarkably diverse, conferring specialized signaling properties to many of the neuronal cell types that populate the nervous system. These channels also are involved in a broad range of neurological diseases. + + + + + + + + + + Na+ CHANNEL Closed Inactivated Closed Open Inactivating Na+ Na+ K+ CHANNEL K+ K+ Closed Closed Closed Open Open −100 50 0 −50 Membrane potential (mV) 0 5 10 15 Time (ms) Channels and Transporters 75 Box B Expression of Ion Channels in Xenopus Oocytes Bridging the gap between the sequence of an ion channel gene and understand-ing channel function is a challenge. To meet this challenge, it is essential to have an experimental system in which the gene product can be expressed effi-ciently, and in which the function of the resulting channel can be studied with methods such as the patch clamp tech-nique. Ideally, the vehicle for expression should be readily available, have few endogenous channels, and be large enough to permit mRNA and DNA to be microinjected with ease. Oocytes (imma-ture eggs) from the clawed African frog, Xenopus laevis (Figure A), fulfill all these demands. These huge cells (approxi-mately 1 mm in diameter; Figure B) are easily harvested from the female Xenopus. Work performed in the 1970s by John Gurdon, a developmental biologist, showed that injection of exogenous mRNA into frog oocytes causes them to synthesize foreign protein in prodigious quantities. In the early 1980s, Ricardo Miledi, Eric Barnard, and other neurobi-ologists demonstrated that Xenopus oocytes could express exogenous ion channels, and that physiological meth-ods could be used to study the ionic cur-rents generated by the newly-synthe-sized channels (Figure C). As a result of these pioneering stud-ies, heterologous expression experiments have now become a standard way of studying ion channels. The approach has been especially valuable in deciphering the relationship between channel struc-ture and function. In such experiments, defined mutations (often affecting a sin-gle nucleotide) are made in the part of the channel gene that encodes a struc-ture of interest; the resulting channel proteins are then expressed in oocytes to assess the functional consequences of the mutation. The ability to combine molecular and physiological methods in a single cell system has made Xenopus oocytes a powerful experimental tool. Indeed, this system has been as valuable to contem-porary studies of voltage-gated ion channels as the squid axon was to such studies in the 1950s and 1960s. References GUNDERSEN, C. B., R. MILEDI AND I. PARKER (1984) Slowly inactivating potassium chan-nels induced in Xenopus oocytes by messen-ger ribonucleic acid from Torpedo brain. J. Physiol. (Lond.) 353: 231–248. GURDON, J. B., C. D. LANE, H. R. WOODLAND AND G. MARBAIX (1971) Use of frog eggs and oocytes for the study of messenger RNA and its translation in living cells. Nature 233: 177–182. STÜHMER, W. (1998) Electrophysiological recordings from Xenopus oocytes. Meth. Enzym. 293: 280–300. SUMIKAWA, K., M. HOUGHTON, J. S. EMTAGE, B. M. RICHARDS AND E. A. BARNARD (1981) Active multi-subunit ACh receptor assem-bled by translation of heterologous mRNA in Xenopus oocytes. Nature 292: 862– 864. (A) (B) (C) PHOTO: PU04BXCB.tif as in 2/e Time (s) −100 −50 0 Membrane potential (mV) K+ current (µA) 0 0 0.2 0.4 0.6 0.8 1.0 50 1 2 3 4 (A) The clawed African frog, Xenopus laevis. (B) Several oocytes from Xenopus highlight-ing the dark coloration of the original pole and the lighter coloration of the vegetal pole. (Courtesy of P. Reinhart.) (C) Results of a voltage clamp experiment showing K+ cur-rents produced following injection of K+ channel mRNA into an oocyte. (After Gun-dersen et al., 1984.) 76 Chapter Four Voltage-Gated Ion Channels Voltage-gated ion channels that are selectively permeable to each of the major physiological ions—Na+, K+, Ca2+, and Cl–—have now been discov-ered (Figure 4.4 A–D). Indeed, many different genes have been discovered for each type of voltage-gated ion channel. An example is the identification of 10 human Na+ channel genes. This finding was unexpected because Na+ channels from many different cell types have similar functional properties, consistent with their origin from a single gene. It is now clear, however, that all of these Na+ channel genes (called SCN genes) produce proteins that dif-fer in their structure, function, and distribution in specific tissues. For instance, in addition to the rapidly inactivating Na+ channels discovered by Hodgkin and Huxley in squid axon, a voltage-sensitive Na+ channel that does not inactivate has been identified in mammalian axons. As might be expected, this channel gives rise to action potentials of long duration and is a target of local anesthetics such as benzocaine and lidocaine. Other electrical responses in neurons entail the activation of voltage-gated Ca2+ channels (Figure 4.4B). In some neurons, voltage-gated Ca2+ channels give rise to action potentials in much the same way as voltage-sensitive Na+ channels. In other neurons, Ca2+ channels control the shape of action poten-tials generated primarily by Na+ conductance changes. More generally, by affecting intracellular Ca2+ concentrations, the activity of Ca2+ channels reg-ulates an enormous range of biochemical processes within cells (see Chapter 7). Perhaps the most important of the processes regulated by voltage-sensi-tive Ca2+ channels is the release of neurotransmitters at synapses (see Chap-ter 5). Given these crucial functions, it is perhaps not surprising that 16 dif-ferent Ca2+ channel genes (called CACNA genes) have been identified. Like Na+ channels, Ca2+ channels differ in their activation and inactivation prop-erties, allowing subtle variations in both electrical and chemical signaling processes mediated by Ca2+. As a result, drugs that block voltage-gated Ca2+ channels are especially valuable in treating a variety of conditions ranging from heart disease to anxiety disorders. By far the largest and most diverse class of voltage-gated ion channels are the K+ channels (Figure 4.4C). Nearly 100 K+ channel genes are now known, and these fall into several distinct groups that differ substantially in their activation, gating, and inactivation properties. Some take minutes to inacti-vate, as in the case of squid axon K+ channels studied by Hodgkin and Hux-ley (Figure 4.5A). Others inactivate within milliseconds, as is typical of most voltage-gated Na+ channels (Figure 4.5B). These properties influence the (A) Na+ channel (B) Ca2+ channel (C) K+ channel (D) Cl− channel (E) Neurotransmitter receptor (F) Ca2+-activated K+ channel (G) Cyclic nucleotide gated channel Outside Inside Na+ Glutamate Ca2+ K+ K+ Na+ K+ VOLTAGE-GATED CHANNELS LIGAND-GATED CHANNELS cAMP cAMP cGMP Na+ + Ca2+ + K+ + Cl− + Voltage sensor Figure 4.4 Types of voltage-gated ion channels. Examples of voltage-gated channels include those selectively per-meable to Na+ (A), Ca2+ (B), K+ (C), and Cl– (D). Ligand-gated ion channels include those activated by the extracel-lular presence of neurotransmitters, such as glutamate (E). Other ligand-gated channels are activated by intracel-lular second messengers, such as Ca2+ (F) or the cyclic nucleotides, cAMP and cGMP (G). Figure 4.5 Diverse properties of K+ channels. Different types of K+ channels were expressed in Xenopus oocytes (see Box B), and the voltage clamp method was used to change the membrane potential (top) and measure the result-ing currents flowing through each type of channel. These K+ channels vary markedly in their gating properties, as evident in their currents (left) and con-ductances (right). (A) KV2.1 channels show little inactivation and are closely related to the delayed rectifier K+ chan-nels involved in action potential repolar-ization. (B) KV4.1 channels inactivate during a depolarization. (C) HERG channels inactivate so rapidly that cur-rent flows only when inactivation is rapidly removed at the end of a depolar-ization. (D) Inward rectifying K+ chan-nels allow more K+ current to flow at hyperpolarized potentials than at depo-larized potentials. (E) Ca2+-activated K+ channels open in response to intracellu-lar Ca2+ ions and, in some cases, mem-brane depolarization. (F) K+ channels with two pores usually respond to chemical signals, such as pH, rather than changes in membrane potential. Channels and Transporters 77 Membrane potential (mV) − 60 − 30 0 30 50 − 90 − 120 Time (ms) 0 100 200 300 −100 0 100 Membrane potential (mV) 1 0 −100 0 100 Membrane potential (mV) 1 0 −100 0 100 Membrane potential (mV) 1 0 −100 0 100 Membrane potential (mV) 1 0 −100 0 100 Membrane potential (mV) 1 0 6 7 8 pH 1 0 (A) KV2.1 (B) KV4.1 (C) HERG (D) Inward rectifier (E) Ca2+- activated (F) 2-pore K+ current (µA) K+ current (µA) K+ current (µA) K+ current (µA) K+ conductance K+ conductance K+ conductance K+ conductance K+ conductance K+ conductance Shaw K+ current (µA) K+ current (µA) Time (ms) 0 100 200 300 pH 8 pH 6 10 µM Ca2+ 1 µM Ca2+ +50 mV +50 mV +50 mV −120 mV −120 mV −120 mV −120 mV +50 mV −120 mV 10µM Ca2+ 1µM Ca2+ +50 mV +50 mV 78 Chapter Four duration and rate of action potential firing, with important consequences for axonal conduction and synaptic transmission. Perhaps the most important function of K+ channels is the role they play in generating the resting mem-brane potential (see Chapter 2). At least two families of K+ channels that are open at substantially negative membrane voltage levels contribute to setting the resting membrane potential (Figure 4.5D). Finally, several types of voltage-gated Cl– channel have been identified (see Figure 4.4D). These channels are present in every type of neuron, where they control excitability, contribute to the resting membrane potential, and help regulate cell volume. Ligand-Gated Ion Channels Many types of ion channels respond to chemical signals (ligands) rather than to changes in the membrane potential (Figure 4.4E–G). The most important of these ligand-gated ion channels in the nervous system is the class activated by binding neurotransmitters (Figure 4.4E). These channels are essential for synaptic transmission and other forms of cell-cell signaling phenomena discussed in Chapters 5–7. Whereas the voltage-gated ion chan-nels underlying the action potential typically allow only one type of ion to permeate, channels activated by extracellular ligands are usually less selec-tive, allowing two or more types of ions to pass through the channel pore. Other ligand-gated channels are sensitive to chemical signals arising within the cytoplasm of neurons (see Chapter 7), and can be selective for specific ions such as K+ or Cl–, or permeable to all physiological cations. Such channels are distinguised by ligand-binding domains on their intracel-lular surfaces that interact with second messengers such as Ca2+, the cyclic nucleotides cAMP and cGMP, or protons. Examples of channels that respond to intracellular cues include Ca2+-activated K+ channels (Figure 4.4.F), the cyclic nucleotide gated cation channel (Figure 4.4G), or acid-sensing ion channels (ASICs). The main function of these channels is to convert intracel-lular chemical signals into electrical information. This process is particularly important in sensory transduction, where channels gated by cyclic nucleotides convert odors and light, for example, into electrical signals. Although many of these ligand-gated ion channels are located in the cell surface membrane, others are in membranes of intracellular organelles such as mitochondria or the endoplasmic reticulum . Some of these latter chan-nels are selectively permeable to Ca2+ and regulate the release of Ca2+ from the lumen of the endoplasmic reticulum into the cytoplasm, where this sec-ond messenger can then trigger a spectrum of cellular responses such as described in Chapter 7. Stretch- and Heat-Activated Channels Still other ion channels respond to heat or membrane deformation. Heat-activated ion channels, such as some members of the transient receptor potential (TRP) gene family, contribute to the sensations of pain and temper-ature and help mediate inflammation (see Chapter 9). These channels are often specialized to detect specific temperature ranges, and some are even activated by cold. Other ion channels respond to mechanical distortion of the plasma membrane and are the basis of stretch receptors and neuromus-cular stretch reflexes (see Chapters 8, 15 and 16). A specialized form of these channels enables hearing by allowing auditory hair cells to respond to sound waves (see Chapter 12). In summary, this tremendous variety of ion channels allows neurons to generate electrical signals in response to changes in membrane potential, synaptic input, intracellular second messengers, light, odors, heat, sound, touch, and many other stimuli. The Molecular Structure of Ion Channels Understanding the physical structure of ion channels is obviously the key to sorting out how they actually work. Until recently, most information about channel structure was derived indirectly from studies of the amino acid composition and physiological properties of these proteins. For example, a great deal has been learned by exploring the functions of particular amino acids within the proteins using mutagenesis and the expression of such channels in Xenopus oocytes (see Box B). Such studies have discovered a gen-eral transmembrane architecture common to all the major ion channel fami-lies. Thus, these molecules are all integral membrane proteins that span the plasma membrane repeatedly. Na+ (and Ca2+) channel proteins, consist of repeating motifs of 6 membrane-spanning regions that are repeated 4 times, for a total of 24 transmembrane regions (Figure 4.6A,B). Na+ (or Ca2+) chan-nels can be produced by just one of these proteins, although other accessory proteins, called β subunits, can regulate the function of these channels. K+ channel proteins typically span the membrane six times (Figure 4.6C), Channels and Transporters 79 N N N N N N N N N N C C C C C C C C C C I II III IV I II III IV (A) Na+ CHANNEL β subunit β subunit (B) Ca2+ CHANNEL (F) 2-pore (C) Kv and HERG K+ CHANNELS (D) Inward rectifier (E) Ca2+-activated (G) Cl− CHANNEL β subunit Figure 4.6 Topology of the principal subunits of voltage-gated Na+, Ca2+, K+, and Cl– channels. Repeating motifs of Na+ (A) and Ca2+ (B) channels are labeled I, II, III, and IV; (C–F) K+ chan-nels are more diverse. In all cases, four subunits combine to form a functional channel. (G) Chloride channels are structurally distinct from all other voltage-gated channels. 80 Chapter Four though there are some K+ channels, such as a bacterial channel and some mammalian channels, that span the membrane only twice (Figure 4.6D), and others that span the membrane four times (Figure 4.6F) or seven times (Fig-ure 4.6E). Each of these K+ channel proteins serves as a channel subunit, with 4 of these subunits typically aggregating to form a single functional ion channel. Other imaginative mutagenesis experiments have provided information about how these proteins function. Two membrane-spanning domains of all ion channels appear to form a central pore through which ions can diffuse, and one of these domains contains a protein loop that confers an ability to selectivity allow certain ions to diffuse through the channel pore (Figure 4.7). As might be expected, the amino acid composition of the pore loop differs among channels that conduct different ions. These distinct structural fea-tures of channel proteins also provide unique binding sites for drugs and for various neurotoxins known to block specific subclasses of ion channels (Box C). Furthermore, many voltage gated ion channels contain a distinct type of transmembrane helix containing a number of positively charged amino acids along one face of the helix (Figures 4.6 and 4.7). This structure evidently serves as a sensor that detects changes in the electrical potential across the membrane. Membrane depolarization influences the charged amino acids such that the helix undergoes a conformational change, which in turn allows the channel pore to open. One suggestion is that the helix rotates to cause the pore to open (Figure 4.7). Other types of mutagenesis experiments have demonstrated that one end of certain K+ channels plays a key role in channel inactivation. This intracellular structure (labeled “N” in Figure 4.6C) can plug the channel pore during prolonged depolarization. More recently, very direct information about the structural underpinnings of ion channel function has come from X-ray crystallography studies of bac-terial K+ channels (Figure 4.8). This molecule was chosen for analysis because the large quantity of channel protein needed for crystallography could be obtained by growing large numbers of bacteria expressing this mol-ecule. The results of such studies showed that the channel is formed by sub-units that each cross the plasma membrane twice; between these two mem-brane-spanning structures is a loop that inserts into the plasma membrane (Figure 4.8A). Four of these subunits are assembled together to form a chan-Membrane depolarization causes charged helix to rotate Pore closed Pore open Depolarize Hyperpolarize Ion flux Figure 4.7 A charged voltage sensor permits voltage-dependent gating of ion channels. The process of voltage activa-tion may involve the rotation of a posi-tively charged transmembrane domain. This movement causes a change in the conformation of the pore loop, enabling the channel to conduct specific ions. nel (Figure 4.8B). In the center of the assembled channel is a narrow opening through the protein that allows K+ to flow across the membrane. This open-ing is the channel pore and is formed by the protein loop, as well as by the membrane-spanning domains. The structure of the pore is well suited for conducting K+ ions (Figure 4.8C). The narrowest part is near the outside mouth of the channel and is so constricted that only a non-hydrated K+ ion can fit through the bottleneck. Larger cations, such as Cs+, cannot traverse this region of the pore, and smaller cations such as Na+ cannot enter the pore because the “walls” of the pore are too far apart to stabilize a dehydrated Na+ ion. This part of the channel complex is responsible for the selective per-meability to K+ and is therefore called the selectivity filter. The sequence of amino acids making up part of this selectivity filter is often referred to as the K+ channel “signature sequence”. Deeper within the channel is a water-filled cavity that connects to the interior of the cell. This cavity evidently collects K+ from the cytoplasm and, utilizing negative charges from the protein, Channels and Transporters 81 (A) (C) (B) Pore helix Outer helix Inner helix Outer helix Inner helix Selectivity filter Pore loop SIDE VIEW TOP VIEW K+ ion in pore K+ ions Pore Selectivity filter Water-filled cavity Negatively charged pore helix Figure 4.8 Structure of a simple bacterial K+ channel determined by crystallography. (A) Structure of one subunit of the channel, which con-sists of two membrane-spanning domains and a pore loop that inserts into the membrane. (B) Three-dimensional arrangement of four subunits (each in a different color) to form a K+ channel. The top view illustrates a K+ ion (green) within the channel pore. (C) The permeation pathway of the K+ channel consists of a large aqueous cavity connected to a narrow selectivity filter. Helical domains of the channel point negative charges (red) toward this cavity, allowing K+ ions (green) to become dehydrated and then move through the selectivity filter. (A, B from Doyle et al., 1998; C after Doyle et al., 1998.) 82 Chapter Four Box C Toxins That Poison Ion Channels Given the importance of Na+ and K+ channels for neuronal excitation, it is not surprising that a number of organisms have evolved channel-specific toxins as mechanisms for self-defense or for cap-turing prey. A rich collection of natural toxins selectively target the ion channels of neurons and other cells. These toxins are valuable not only for survival, but for studying the function of cellular ion channels. The best-known channel toxin is tetrodotoxin, which is produced by cer-tain puffer fish and other animals. Tetrodotoxin produces a potent and spe-cific obstruction of the Na+ channels responsible for action potential genera-tion, thereby paralyzing the animals unfortunate enough to ingest it. Saxitoxin, a chemical homologue of tetrodotoxin produced by dinoflagel-lates, has a similar action on Na+ chan-nels. The potentially lethal effects of eat-ing shellfish that have ingested these “red tide” dinoflagellates are due to the potent neuronal actions of saxitoxin. Scorpions paralyze their prey by injecting a potent mix of peptide toxins that also affect ion channels. Among these are the a-toxins, which slow the inactivation of Na+ channels (Figure A1); exposure of neurons to these toxins pro-longs the action potential (Figure A2), thereby scrambling information flow within the nervous system of the soon-to-be-devoured victim. Other peptides in scorpion venom, called b-toxins, shift the voltage dependence of Na+ channel acti-vation (Figure B). These toxins cause Na+ channels to open at potentials much more negative than normal, disrupting action potential generation. Some alka-loid toxins combine these actions, both removing inactivation and shifting activa-tion of Na+ channels. One such toxin is batrachotoxin, produced by a species of frog; some tribes of South American Indians use this poison on their arrow tips. A number of plants produce similar toxins, including aconitine, from butter-cups; veratridine, from lilies; and a num-ber of insecticidal toxins produced by plants such as chrysanthemums and rhododendrons. Potassium channels have also been targeted by toxin-producing organisms. Peptide toxins affecting K+ channels include dendrotoxin, from wasps; apamin, from bees; and charybdotoxin, yet another toxin produced by scorpions. All of these toxins block K+ channels as their primary action; no toxin is known to affect the activation or inactivation of these chan-nels, although such agents may simply be awaiting discovery. References CAHALAN, M. (1975) Modification of sodium channel gating in frog myelinated nerve fibers by Centruroides sculpturatus scorpion venom. J. Physiol. (Lond.) 244: 511–534. NARAHASHI, T. (2000) Neuroreceptors and ion channels as the basis for drug action: Present and future. J. Pharmacol. Exptl. Therapeutics 294: 1–26. SCHMIDT, O. AND H. SCHMIDT (1972) Influence of calcium ions on the ionic currents of nodes of Ranvier treated with scorpion venom. Pflügers Arch. 333: 51–61. (A) (1) (B) Membrane potential (mV) Membrane potential (mV) Membrane potential (mV) Na+ current (nA/cm2 ) Time (ms) Time (ms) Time (s) +50 0 −40 −80 +40 0 −40 −80 −120 0 0 0 20 40 60 80 0 20 40 60 80 0 8 10 4 2 4 6 −75 Control Treated with scorpion toxin Treated with scorpion toxin Control −25 −50 +25 Normalized Na+ conductance Control Treated with scorpion toxin (2) (A) Effects of toxin treatment on frog axons. (1) α-Toxin from the scorpion Leiurus quinquestriatus prolongs Na+ currents recorded with the voltage clamp method. (2) As a result of the increased Na+ current, α-toxin greatly prolongs the duration of the axonal action potential. Note the change in timescale after treating with toxin. (B) Treat-ment of a frog axon with β-toxin from another scorpion, Centruroides sculpturatus, shifts the activation of Na+ channels, so that Na+ conductance begins to increase at poten-tials much more negative than usual. (A after Schmidt and Schmidt, 1972; B after Cahalan, 1975.) Figure 4.9 Structural features of K+ channel gating. (A) Voltage sensing may involve paddle-like structures of the channel. These paddles reside within the lipid bilayer of the plasma mem-brane and may respond to changes in membrane potential by moving through the membrane. The gating charges that sense membrane potential are indicated by red “plus” signs. (B) Structure of K+ channels in closed (left) and open (right) conformations. Three of the four channel subunits are shown. Opening of the pore of the channel involves kink-ing of a transmembrane domain at the point indicated in red, which then dilates the pore. (A after Jiang et al., 2003; B after MacKinnon, 2003). allows K+ ions to become dehydrated so they can enter the selectivity filter. These “naked” ions are then able to move through four K+ binding sites within the selectivity filter to eventually reach the extracellular space (recall that the normal concentration gradient drives K+ out of cells). On average, two K+ ions reside within the selectivity filter at any moment, with electro-static repulsion between the two ions helping to speed their transit through the selectivity filter, thereby permitting rapid ion flux through the channel. Crystallographic studies have also determined the structure of the voltage sensor in another type of bacterial K+ channel. Such studies indicate that the sensor is at the interface between proteins and lipid on the cytoplasmic sur-face of the channel, leading to the suggestion that the sensor is a paddle-like structure that moves through the membrane to gate the opening of the chan-nel pore (Figure 4.9A), rather than being a rotating helix buried within the ion channel protein (as in Figure 4.7). Crystallographic work has also revealed the molecular basis of the rapid transitions between the closed and the open state of the channel during channel gating. By comparing data from K+ channels crystallized in what is believed to be closed and open con-formations (Figure 4.9B), it appears that channels gate by a conformational change in one of the transmembrane helices lining the channel pore. Pro-ducing a “kink” in one of these helices increases the opening from the cen-tral water-filled pore to the intracellular space, thereby permitting ion fluxes. Channels and Transporters 83 (A) (B) (A) Closed Open Closed Depolarize Hyperpolarize Open 84 Chapter Four Several genetic diseases, collectively called channelopathies, result from small but critical alterations in ion channel genes. The best-characterized of these dis-eases are those that affect skeletal muscle cells. In these disorders, alterations in ion channel proteins produce either myotonia (muscle stiffness due to excessive electri-cal excitability) or paralysis (due to insuf-ficient muscle excitability). Other disor-ders arise from ion channel defects in heart, kidney, and the inner ear. Channelopathies associated with ion channels localized in brain are much more difficult to study. Nonetheless, voltage-gated Ca2+ channels have re-cently been implicated in a range of neu-rological diseases. These include episodic ataxia, spinocerebellar degeneration, night blindness, and migraine head-aches. Familial hemiplegic migraine (FHM) is characterized by migraine attacks that typically last one to three days. During such episodes, patients experience severe headaches and vomiting. Several muta-tions in a human Ca2+ channel have been identified in families with FHM, each having different clinical symptoms. For example, a mutation in the pore-forming region of the channel produces hemi-plegic migraine with progressive cerebel-lar ataxia, whereas other mutations cause only the usual FHM symptoms. How these altered Ca2+ channel properties lead to migraine attacks is not known. Episodic ataxia type 2 (EA2) is a neuro-logical disorder in which affected indi-viduals suffer recurrent attacks of abnor-mal limb movements and severe ataxia. These problems are sometimes accompa-N N N C C C (B) Na+ CHANNEL N C (A) Ca2+ CHANNEL (C) K+ CHANNEL (D) Cl− CHANNEL C N C FHM EA2 CSNB GEFS Myotonia Paralysis EA1 BFNC Myotonia Paralysis β subunit I II III IV I II III IV Box D Diseases Caused by Altered Ion Channels Genetic mutations in (A) Ca2+ channels, (B) Na+ channels, (C) K+ channels, and (D) Cl– channels that result in diseases. Red regions indicate the sites of these mutations; the red circles indicate mutations. (After Lehmann-Horn and Jurkat-Kott, 1999.) In short, ion channels are integral membrane proteins with characteristic features that allow them to assemble into multimolecular aggregates. Collec-tively, these structures allow channels to conduct ions, sense the transmem-brane potential, to inactivate, and to bind to various neurotoxins. A combi-nation of physiological, molecular biological and crystallographic studies has begun to provide a detailed physical picture of K+ channels. This work has now provided considerable insight into how ions are conducted from one side of the plasma membrane to the other, how a channel can be selec-tively permeable to a single type of ion, how they are able to sense changes in membrane voltage, and how they gate the opening of their pores. It is likely that other types of ion channels will be similar in their functional architecture. Finally, this sort of work has illuminated how mutations in ion channel genes can lead to a variety of neurological disorders (Box D). Channels and Transporters 85 nied by vertigo, nausea, and headache. Usually, attacks are precipitated by emo-tional stress, exercise, or alcohol and last for a few hours. The mutations in EA2 cause Ca2+ channels to be truncated at various sites, which may cause the clini-cal manifestations of the disease by pre-venting the normal assembly of Ca2+ channels in the membrane. X-linked congenital stationary night blindness (CSNB) is a recessive retinal dis-order that causes night blindness, decreased visual acuity, myopia, nystag-mus, and strabismus. Complete CSNB causes retinal rod photoreceptors to be nonfunctional. Incomplete CSNB causes subnormal (but measurable) functioning of both rod and cone photoreceptors. Like EA2, the incomplete type of CSNB is caused by mutations producing trun-cated Ca2+ channels. Abnormal retinal function may arise from decreased Ca2+ currents and neurotransmitter release from photoreceptors (see Chapter 11). A defect in brain Na+ channels causes generalized epilepsy with febrile seizures (GEFS) that begins in infancy and usu-ally continues through early puberty. This defect has been mapped to two mutations: one on chromosome 2 that encodes an α subunit for a voltage-gated Na+ channel, and the other on chromo-some 19 that encodes a Na+ channel β subunit. These mutations cause a slow-ing of Na+ channel inactivation (see fig-ure above), which may explain the neu-ronal hyperexcitability underlying GEFS. Another type of seizure, benign famil-ial neonatal convulsion (BFNC), is due to K+ channel mutations. This disease is characterized by frequent brief seizures commencing within the first week of life and disappearing spontaneously within a few months. The mutation has been mapped to at least two voltage-gated K+ channel genes. A reduction in K+ current flow through the mutated channels prob-ably accounts for the hyperexcitability associated with this defect. A related dis-ease, episodic ataxia type 1 (EA1), has been linked to a defect in another type of voltage-gated K+ channel. EA1 is charac-terized by brief episodes of ataxia. Mu-tant channels inhibit the function of other, non-mutant K+ channels and may produce clinical symptoms by impairing action potential repolarization. Muta-tions in the K+ channels of cardiac mus-cle are responsible for the irregular heart-beat of patients with long Q-T syndrome. Numerous genetic disorders affect the voltage-gated channels of skeletal mus-cle and are responsible for a host of mus-cle diseases that either cause muscle weakness (paralysis) or muscle contrac-tion (myotonia). References BARCHI, R. L. (1995) Molecular pathology of the skeletal muscle sodium channel. Ann. Rev. Physiol. 57: 355–385. BERKOVIC, S. F. AND I. E. SCHEFFER (1997) Epi-lepsies with single gene inheritance. Brain Develop. 19 :13–28. COOPER, E. C. AND L. Y. JAN (1999) Ion chan-nel genes and human neurological disease: Recent progress, prospects, and challenges. Proc. Natl. Acad. Sci. USA 96: 4759–4766. DAVIES, N. P. AND M. G. HANNA (1999) Neuro-logical channelopathies: Diagnosis and ther-apy in the new millennium. Ann. Med. 31: 406–420. JEN, J. (1999) Calcium channelopathies in the central nervous system. Curr. Op. Neurobiol. 9: 274–280. LEHMANN-HORN, F. AND K. JURKAT-ROTT (1999) Voltage-gated ion channels and hered-itary disease. Physiol. Rev. 79: 1317–1372. OPHOFF, R. A., G. M. TERWINDT, R. R. FRANTS AND M. D. FERRARI (1998) P/Q-type Ca2+ channel defects in migraine, ataxia and epilepsy. Trends Pharm. Sci. 19: 121–127. Mutations in Na+ channels slow the rate of inactivation of Na+ currents. (After Barchi, 1995.) Na+ current (nA) Wild type Na+ channel mutants 0 5 10 Time (ms) −80 −40 0 40 Membrane potential (mV) 86 Chapter Four Active Transporters Create and Maintain Ion Gradients Up to this point, the discussion of the molecular basis of electrical signaling has taken for granted the fact that nerve cells maintain ion concentration gradients across their surface membranes. However, none of the ions of physiological importance (Na+, K+, Cl–, and Ca2+) are in electrochemical equilibrium. Because channels produce electrical effects by allowing one or more of these ions to diffuse down their electrochemical gradients, there would be a gradual dissipation of these concentration gradients unless nerve cells could restore ions displaced during the current flow that occurs as a result of both neural signaling and the continual ionic leakage that occurs at rest. The work of generating and maintaining ionic concentration gradients for particular ions is carried out by a group of plasma membrane proteins known as active transporters. Active transporters carry out this task by forming complexes with the ions that they are translocating. The process of ion binding and unbinding for transport typically requires several milliseconds. As a result, ion translo-cation by active transporters is much slower than ion movement through channels: Recall that ion channels can conduct thousands of ions across a membrane each millisecond. In short, active transporters gradually store energy in the form of ion concentration gradients, whereas the opening of ion channels rapidly dissipates this stored energy during relatively brief electrical signaling events. Several types of active transporter have now been identified (Figure 4.10). Although the specific jobs of these transporters differ, all must translocate ions against their electrochemical gradients. Moving ions uphill requires the consumption of energy, and neuronal transporters fall into two classes based on their energy sources. Some transporters acquire energy directly from the hydrolysis of ATP and are called ATPase pumps (Figure 4.10, left). The most prominent example of an ATPase pump is the Na+ pump (or, more properly, the Na+/K+ ATPase pump), which is responsible for maintaining transmem-brane concentration gradients for both Na+ and K+ (Figure 4.10A). Another is the Ca2+ pump, which provides one of the main mechanisms for removing Ca2+ from cells (Figure 4.10B). The second class of active transporter does not use ATP directly, but depends instead on the electrochemical gradients of other ions as an energy source. This type of transporter carries one or more ions up its electrochemical gradient while simultaneously taking another ion (most often Na+) down its gradient. Because at least two species of ions are ATPase PUMPS ION EXCHANGERS (A) Na+/K+ pump Inside Outside (B) Ca2+ pump (C) Na+/Ca2+ exchanger (E) Na+/H+ exchanger (D) Cl−/HCO3 − exchanger ATP ADP Cl− Na+ Na+ Ca2+ HCO3 − H+ Na+ K+ ATP ADP (F) Na+/neurotransmitter transporter Na+ H+ Ca2+ GABA, Dopamine Figure 4.10 Examples of ion trans-porters found in cell membranes. (A,B) Some transporters are powered by the hydrolysis of ATP (ATPase pumps), whereas others (C–F) use the electro-chemical gradients of co-transported ions as a source of energy (ion ex-changers). involved in such transactions, these transporters are usually called ion exchangers (Figure 4.10, right). An example of such a transporter is the Na+/Ca2+ exchanger, which shares with the Ca2+ pump the important job of keeping intracellular Ca2+ concentrations low (Figure 4.10C). Another exchanger in this category regulates both intracellular Cl– concentration and pH by swapping intracellular Cl– for another extracellular anion, bicarbon-ate (Figure 4.10D). Other ion exchangers, such as the Na+/H+ exchanger (Figure 4.10E), also regulate intracellular pH, in this case by acting directly on the concentration of H+. Yet other ion exchangers are involved in trans-porting neurotransmitters into synaptic terminals (Figure 4.10F), as described in Chapter 6. Although the electrochemical gradient of Na+ (or other counter ions) is the proximate source of energy for ion exchangers, these gradients ultimately depend on the hydrolysis of ATP by ATPase pumps, such as the Na+/K+ ATPase pump. Functional Properties of the Na+/K+ Pump Of these various transporters, the best understood is the Na+/K+ pump. The activity of this pump is estimated to account for 20–40% of the brain’s energy consumption, indicating its importance for brain function. The Na+ pump was first discovered in neurons in the 1950s, when Richard Keynes at Cambridge University used radioactive Na+ to demonstrate the energy-dependent efflux of Na+ from squid giant axons. Keynes and his collabora-tors found that this efflux ceased when the supply of ATP in the axon was interrupted by treatment with metabolic poisons (Figure 4.11A, point 4). Other conditions that lower intracellular ATP also prevent Na+ efflux. These experiments showed that removing intracellular Na+ requires cellular metabolism. Further studies with radioactive K+ demonstrated that Na+ efflux is associated with simultaneous, ATP-dependent influx of K+. These opposing fluxes of Na+ and K+ are operationally inseparable: Removal of external K+ greatly reduces Na+ efflux (Figure 4.11, point 2), and vice versa. These energy-dependent movements of Na+ and K+ implicated an ATP-hydrolyzing Na+/K+ pump in the generation of the transmembrane gradi-ents of both Na+ and K+. The exact mechanism responsible for these fluxes of Na+ and K+ is still not entirely clear, but the pump is thought to alter-nately shuttle these ions across the membranes in a cycle fueled by the trans-fer of a phosphate group from ATP to the pump protein (Figure 4.11B). Additional quantitative studies of the movements of Na+ and K+ indicate that the two ions are not pumped at identical rates: The K+ influx is only about two-thirds the Na+ efflux. Thus, the pump apparently transports two K+ into the cell for every three Na+ that are removed (see Figure 4.11B). This stoichiometry causes a net loss of one positively charged ion from inside of the cell during each round of pumping, meaning that the pump generates an electrical current that can hyperpolarize the membrane potential. For this reason, the Na+/K+ pump is said to be electrogenic. Because pumps act much more slowly than ion channels, the current produced by the Na+/K+ pump is quite small. For example, in the squid axon, the net current gener-ated by the pump is less than 1% of the current flowing through voltage-gated Na+ channels and affects the resting membrane potential by only a millivolt or less. Although the electrical current generated by the activity of the Na+/K+ pump is small, under special circumstances the pump can significantly influence the membrane potential. For instance, prolonged stimulation of Channels and Transporters 87 88 Chapter Four 0 50 100 Time (min) Na+ efflux (logarithmic scale) (A) (B) 150 200 250 300 ATP ADP Dephosphorylation-induced conformational change leads to K+ release Conformational change causes Na+ release and K+ binding 2. Phosphorylation 3. 1. Na+ binding 1 Efflux of Na+ 3 Recovery when K+ is restored 5 Recovery when ATP is restored 2 Na+ efflux reduced by removal of external K+ 4 Efflux decreased by metabolic inhibitors, such as dinitrophenol, which block ATP synthesis 4. Outside Inside Na+ K+ K+ Na+ Pi Pi Pi Figure 4.11 Ionic movements due to the Na+/K+ pump. (A) Measurement of radioactive Na+ efflux from a squid giant axon. This efflux depends on external K+ and intracellular ATP. (B) A model for the movement of ions by the Na+/K+ pump. Uphill movements of Na+ and K+ are driven by ATP, which phosphorylates the pump. These fluxes are asymmetrical, with three Na+ car-ried out for every two K+ brought in. (A after Hodgkin and Keynes, 1955; B after Lingrel et al., 1994.) small unmyelinated axons produces a substantial hyperpolarization (Figure 4.12). During the period of stimulation, Na+ enters through voltage-gated channels and accumulates within the axons. As the pump removes this extra Na+, the resulting current generates a long-lasting hyperpolarization. Sup-port for this interpretation comes from the observation that conditions that block the Na+/K+ pump—for example, treatment with ouabain, a plant gly-coside that specifically inhibits the pump—prevent the hyperpolarization. The electrical contribution of the Na+/K+ pump is particularly significant in these small-diameter axons because their large surface-to-volume ratio causes intracellular Na+ concentration to rise to higher levels than it would in other cells. Nonetheless, it is important to emphasize that, in most cir-cumstances, the Na+/K+ pump plays no part in generating the action poten-tial and has very little direct effect on the resting potential. The Molecular Structure of the Na+/K+ Pump These observations imply that the Na+ and K+ pump must exhibit several molecular properties: (1) It must bind both Na+ and K+; (2) it must possess sites that bind ATP and receive a phosphate group from this ATP; and (3) it must bind ouabain, the toxin that blocks this pump (Figure 4.13A). A variety of studies have now identified the aspects of the protein that account for these properties of the Na+/K+ pump. This pump is a large, integral mem-brane protein made up of at least two subunits, called α and β. The primary sequence shows that the α subunit spans the membrane 10 times, with most of the molecule found on the cytoplasmic side, whereas the β subunit spans the membrane once and is predominantly extracellular. Although a detailed account of the functional domains of the Na+/K+ pump is not yet available, some parts of the amino acid sequence have identified functions (Figure 4.13B). One intracellular domain of the protein is required for ATP binding Channels and Transporters 89 10 Time (min) 20 0 5 mV Membrane potential (mV) − 60 − 80 − 20 − 40 − 60 − 80 0 Individual action potentials Trains of action potentials Time (s) Ouabain Poststimulus hyperpolarization blocked Ouabain binding site N N C C Phosphorylation site ATP ADP + Pi Membrane Membrane Ouabain binding site Outside 2 K+ 3 Na+ Inside Outside (A) (B) Inside Membrane ATP binding site Membrane Membrane Membrane Na+ and K+ binding β subunit α subunit Figure 4.12 The electrogenic transport of ions by the Na+/K+ pump can influence membrane potential. Measurements of the membrane potential of a small unmyeli-nated axon show that a train of action potentials is followed by a long-lasting hyperpolarization. This hyperpolarization is blocked by ouabain, indicating that it results from the activity of the Na+/K+ pump. (After Rang and Ritchie, 1968.) Figure 4.13 Molecular structure of the Na+/K+ pump. (A) General features of the pump. (B) The molecule spans the membrane 10 times. Amino acid residues thought to be important for binding of ATP, K+, and ouabain are highlighted. (After Lingrel et al., 1994.) 90 Chapter Four and hydrolysis, and the amino acid phosphorylated by ATP has been identi-fied. Another extracellular domain may represent the binding site for ouabain. However, the sites involved in the most critical function of the pump—the movement of Na+ and K+—have not yet been defined. Nonethe-less, altering certain membrane-spanning domains (red in Figure 4.13B) impairs ion translocation; moreover, kinetic studies indicate that both ions bind to the pump at the same site. Because these ions move across the mem-brane, it is likely that this site traverses the plasma membrane; it is also likely that the site has a negative charge, since both Na+ and K+ are posi-tively charged. The observation that removing negatively charged residues in a membrane-spanning domain of the protein (pale yellow in Figure 4.13B) greatly reduces Na+ and K+ binding provides at least a hint about the ion-translocating domain of the transporter molecule. Summary Ion transporters and channels have complementary functions. The primary purpose of transporters is to generate transmembrane concentration gradi-ents, which are then exploited by ion channels to generate electrical signals. Ion channels are responsible for the voltage-dependent conductances of nerve cell membranes. The channels underlying the action potential are inte-gral membrane proteins that open or close ion-selective pores in response to the membrane potential, allowing specific ions to diffuse across the mem-brane. The flow of ions through single open channels can be detected as tiny electrical currents, and the synchronous opening of many such channels generates the macroscopic currents that produce action potentials. Molecular studies show that such voltage-gated channels have highly conserved struc-tures that are responsible for features such as ion permeation and voltage sensing, as well as the features that specify ion selectivity and toxin sensitiv-ity. Other types of channels are sensitive to chemical signals, such as neuro-transmitters or second messengers, or to heat or membrane deformation. A large number of ion channel genes create channels with a correspondingly wide range of functional characteristics, thus allowing different types of neu-rons to have a remarkable spectrum of electrical properties. Ion transporter proteins are quite different in both structure and function. The energy needed for ion movement against a concentration gradient (e.g., in main-taining the resting potential) is provided either by the hydrolysis of ATP or by the electrochemical gradient of co-transported ions. The Na+/K+ pump produces and maintains the transmembrane gradients of Na+ and K+, while other transporters are responsible for the electrochemical gradients for other physiologically important ions, such as Cl–, Ca2+, and H+. Together, trans-porters and channels provide a reasonably comprehensive molecular expla-nation for the ability of neurons to generate electrical signals. Additional Reading Reviews ARMSTRONG, C. M. AND B. HILLE (1998) Volt-age-gated ion channels and electrical excit-ability. Neuron 20: 371–380. BEZANILLA, F. AND A. M. CORREA (1995) Single-channel properties and gating of Na+ and K+ channels in the squid giant axon. In Cephalo-pod Neurobiology, N. J. Abbott, R. Williamson and L. Maddock (eds.). New York: Oxford University Press, pp. 131–151. CATTERALL, W. A. (1988) Structure and func-tion of voltage-sensitive ion channels. Science 242: 50–61. ISOM, L. L., K. S. DE JONGH AND W. A. CATTER-ALL (1994) Auxiliary subunits of voltage-gated ion channels. Neuron 12: 1183–1194. JAN, L. Y. AND Y. N. JAN (1997) Voltage-gated and inwardly rectifying potassium channels. J. Physiol. 505: 267–282. JENTSCH, T. J., T. FRIEDRICH, A. SCHRIEVER AND H. YAMADA (1999) The CLC chloride channel family. Pflügers Archiv. 437: 783–795. KAPLAN, J. H. (2002) Biochemistry of Na,K-ATPase. Annu. Rev. Biochem. 71: 511–535. KRISHTAL, O. (2003). The ASICs: Signaling molecules? Modulators? Trends Neurosci, 26: 477–483. LINGREL, J. B., J. VAN HUYSSE, W. O’BRIEN, E. JEWELL-MOTZ, R. ASKEW AND P. SCHULTHEIS (1994) Structure-function studies of the Na, K-ATPase. Kidney Internat. 45: S32–S39. MACKINNON, R. (2003) Potassium channels. FEBS Lett. 555: 62–65. NEHER, E. (1992) Nobel lecture: Ion channels for communication between and within cells. Neuron 8: 605–612. PATAPOUTIAN, A., A. M. PEIER, G. M. STORY AND V. VISWANATH (2003). ThermoTRP channels and beyond: Mechanisms of temperature sen-sation. Nat. Rev. Neurosci. 4: 529–539. SEEBURG, P. H. (2002). A-to-I editing: New and old sites, functions and speculations. Neuron 35: 17–20. SKOU, J. C. (1988) Overview: The Na,K pump. Meth. Enzymol. 156: 1–25. Important Original Papers ANTZ, C. AND 7 OTHERS (1997) NMR structure of inactivation gates from mammalian volt-age-dependent potassium channels. Nature 385: 272–275. BEZANILLA, F., E. PEROZO, D. M. PAPAZIAN AND E. STEFANI (1991) Molecular basis of gating charge immobilization in Shaker potassium channels. Science 254: 679–683. BOULTER, J. AND 6 OTHERS (1990) Molecular cloning and functional expression of gluta-mate receptor subunit genes. Science 249: 1033–1037. CATERINA, M. J., M. A. SCHUMACHER, M. TOMI-NAGA, T. A. ROSEN, J. D. LEVINE AND D. JULIUS (1997) The capsaicin receptor: A heat-activated ion channel in the pain pathway. Nature 389: 816–824. CHA, A., G. E. SNYDER, P. R. SELVIN AND F. BEZANILLA (1999) Atomic scale movement of the voltage-sensing region in a potassium channel measured via spectroscopy. Nature 402: 809–813. DOYLE, D. A. AND 7 OTHERS (1998) The struc-ture of the potassium channel: Molecular basis of K+ conduction and selectivity. Science 280: 69–77. FAHLKE, C., H. T. YU, C. L. BECK, T. H. RHODES AND A. L. GEORGE JR. (1997) Pore-forming seg-ments in voltage-gated chloride channels. Nature 390: 529–532. HO, K. AND 6 OTHERS (1993) Cloning and expression of an inwardly rectifying ATP-reg-ulated potassium channel. Nature 362: 31–38. HODGKIN, A. L. AND R. D. KEYNES (1955) Active transport of cations in giant axons from Sepia and Loligo. J. Physiol. 128: 28–60. HOSHI, T., W. N. ZAGOTTA AND R. W. ALDRICH (1990) Biophysical and molecular mechanisms of Shaker potassium channel inactivation. Sci-ence 250: 533–538. JIANG, Y. AND 6 OTHERS (2003) X-ray structure of a voltage-dependent K+ channel. Nature 423: 33–41. LLANO, I., C. K. WEBB AND F. BEZANILLA (1988) Potassium conductance of squid giant axon. Single-channel studies. J. Gen. Physiol. 92: 179–196. MIKAMI, A. AND 7 OTHERS (1989) Primary struc-ture and functional expression of the cardiac dihydropyridine-sensitive calcium channel. Nature 340: 230–233. NODA, M. AND 6 OTHERS (1986) Expression of functional sodium channels from cloned cDNA. Nature 322: 826–828. NOWYCKY, M. C., A. P. FOX AND R. W. TSIEN (1985) Three types of neuronal calcium chan-nel with different calcium agonist sensitivity. Nature 316: 440–443. PAPAZIAN, D. M., T. L. SCHWARZ, B. L. TEMPEL, Y. N. JAN AND L. Y. JAN (1987) Cloning of genomic and complementary DNA from Shaker, a putative potassium channel gene from Drosophila. Science 237: 749–753. RANG, H. P. AND J. M. RITCHIE (1968) On the electrogenic sodium pump in mammalian non-myelinated nerve fibres and its activation by various external cations. J. Physiol. 196: 183–221. SIGWORTH, F. J. AND E. NEHER (1980) Single Na+ channel currents observed in cultured rat muscle cells. Nature 287: 447–449. THOMAS, R. C. (1969) Membrane current and intracellular sodium changes in a snail neu-rone during extrusion of injected sodium. J. Physiol. 201: 495–514. TOYOSHIMA, C., M. NAKASAKO, H. NOMURA AND H. OGAWA (2000) Crystal structure of the calcium pump of sarcoplasmic reticulum at 2.6 Å resolution. Nature 405: 647–655. VANDERBERG, C. A. AND F. BEZANILLA (1991) A sodium channel model based on single chan-nel, macroscopic ionic, and gating currents in the squid giant axon. Biophys. J. 60: 1511–1533. WALDMANN, R., G. CHAMPIGNY, F. BASSILANA, C. HEURTEAUX AND M. LAZDUNSKI (1997) A proton-gated cation channel involved in acid-sensing. Nature 386: 173–177. WEI, A. M., A. COVARRUBIAS, A. BUTLER, K. BAKER, M. PAK AND L. SALKOFF (1990) K+ cur-rent diversity is produced by an extended gene family conserved in Drosophila and mouse. Science 248: 599–603. YANG, N., A. L. GEORGE JR. AND R. HORN (1996) Molecular basis of charge movement in volt-age-gated sodium channels. Neuron 16: 113–22. Books AIDLEY, D. J. AND P. R. STANFIELD (1996) Ion Channels: Molecules in Action. Cambridge: Cambridge University Press. ASHCROFT, F. M. (2000) Ion Channels and Dis-ease. Boston: Academic Press. HILLE, B. (2001) Ion Channels of Excitable Mem-branes, 3rd Ed. Sunderland, MA: Sinauer Associates. JUNGE, D. (1992) Nerve and Muscle Excitation, 3rd Ed. Sunderland, MA: Sinauer Associates. NICHOLLS, D. G. (1994) Proteins, Transmitters and Synapses. Oxford: Blackwell Scientific SIEGEL, G. J., B. W. AGRANOFF, R. W. ALBERS, S. K. FISHER AND M. D. UHLER (1999) Basic Neuro-chemistry. Philadelphia: Lippincott-Raven. Channels and Transporters 91 Overview The human brain contains at least 100 billion neurons, each with the ability to influence many other cells. Clearly, sophisticated and highly efficient mechanisms are needed to enable communication among this astronomical number of elements. Such communication is made possible by synapses, the functional contacts between neurons. Two different types of synapse—elec-trical and chemical—can be distinguished on the basis of their mechanism of transmission. At electrical synapses, current flows through gap junctions, which are specialized membrane channels that connect two cells. In contrast, chemical synapses enable cell-to-cell communication via the secretion of neurotransmitters; these chemical agents released by the presynaptic neu-rons produce secondary current flow in postsynaptic neurons by activating specific receptor molecules. The total number of neurotransmitters is not known, but is well over 100. Virtually all neurotransmitters undergo a simi-lar cycle of use: synthesis and packaging into synaptic vesicles; release from the presynaptic cell; binding to postsynaptic receptors; and, finally, rapid removal and/or degradation. The secretion of neurotransmitters is triggered by the influx of Ca2+ through voltage-gated channels, which gives rise to a transient increase in Ca2+ concentration within the presynaptic terminal. The rise in Ca2+ concentration causes synaptic vesicles to fuse with the presynap-tic plasma membrane and release their contents into the space between the pre- and postsynaptic cells. Although it is not yet understood exactly how Ca2+ triggers exocytosis, specific proteins on the surface of the synaptic vesi-cle and elsewhere in the presynaptic terminal mediate this process. Neuro-transmitters evoke postsynaptic electrical responses by binding to members of a diverse group of neurotransmitter receptors. There are two major classes of receptors: those in which the receptor molecule is also an ion channel, and those in which the receptor and ion channel are separate molecules. These receptors give rise to electrical signals by transmitter-induced opening or closing of the ion channels. Whether the postsynaptic actions of a particular neurotransmitter are excitatory or inhibitory is determined by the ionic per-meability of the ion channel affected by the transmitter, and by the concen-tration of permeant ions inside and outside the cell. Electrical Synapses Although there are many kinds of synapses within the human brain, they can be divided into two general classes: electrical synapses and chemical synapses. Although they are a distinct minority, electrical synapses are found in all nervous systems, permitting direct, passive flow of electrical current from one neuron to another. Chapter 5 93 Synaptic Transmission 94 Chapter Five The structure of an electrical synapse is shown schematically in Figure 5.1A. The “upstream” neuron, which is the source of current, is called the presynaptic element, and the “downstream” neuron into which this current flows is termed postsynaptic. The membranes of the two communicating neurons come extremely close at the synapse and are actually linked together by an intercellular specialization called a gap junction. Gap junc-tions contain precisely aligned, paired channels in the membrane of the pre-and postsynaptic neurons, such that each channel pair forms a pore (see Fig-ure 5.2A). The pore of a gap junction channel is much larger than the pores of the voltage-gated ion channels described in the previous chapter. As a result, a variety of substances can simply diffuse between the cytoplasm of the pre- and postsynaptic neurons. In addition to ions, substances that dif-fuse through gap junction pores include molecules with molecular weights as great as several hundred daltons. This permits ATP and other important intracellular metabolites, such as second messengers (see Chapter 7), to be transferred between neurons. Electrical synapses thus work by allowing ionic current to flow passively through the gap junction pores from one neuron to another. The usual source of this current is the potential difference generated locally by the action potential (see Chapter 3). This arrangement has a number of interest-ing consequences. One is that transmission can be bidirectional; that is, cur-rent can flow in either direction across the gap junction, depending on which member of the coupled pair is invaded by an action potential (although Cytoplasm Mitochondrion Microtubule Presynaptic neuron Presynaptic neuron Postsynaptic neurotransmitter receptor Gap junction channels Gap junction Presynaptic membrane Postsynaptic membrane Synaptic vesicle Presynaptic membrane Postsynaptic membrane Synaptic cleft Synaptic vesicle fusing Postsynaptic neuron Postsynaptic neuron Ions flow through gap junction channels Neurotransmitter released Ions flow through postsynaptic channels P N i 3E (A) ELECTRONIC SYNAPSE (B) CHEMICAL SYNAPSE Figure 5.1 Electrical and chemical syn-apses differ fundamentally in their transmission mechanisms. (A) At electri-cal synapses, gap junctions between pre-and postsynaptic membranes permit current to flow passively through inter-cellular channels (blowup). This current flow changes the postsynaptic mem-brane potential, initiating (or in some instances inhibiting) the generation of postsynaptic action potentials. (B) At chemical synapses, there is no intercel-lular continuity, and thus no direct flow of current from pre- to postsynaptic cell. Synaptic current flows across the post-synaptic membrane only in response to the secretion of neurotransmitters, which open or close postsynaptic ion channels after binding to receptor mole-cules (blowup). some types of gap junctions have special features that render their transmis-sion unidirectional). Another important feature of the electrical synapse is that transmission is extraordinarily fast: because passive current flow across the gap junction is virtually instantaneous, communication can occur with-out the delay that is characteristic of chemical synapses. These features are apparent in the operation of the first electrical synapse to be discovered, which resides in the crayfish nervous system. A postsynap-tic electrical signal is observed at this synapse within a fraction of a millisec-ond after the generation of a presynaptic action potential (Figure 5.2). In fact, at least part of this brief synaptic delay is caused by propagation of the action potential into the presynaptic terminal, so that there may be essen-tially no delay at all in the transmission of electrical signals across the syn-apse. Such synapses interconnect many of the neurons within the circuit that allows the crayfish to escape from its predators, thus minimizing the time between the presence of a threatening stimulus and a potentially life-saving motor response. A more general purpose of electrical synapses is to synchronize electrical activity among populations of neurons. For example, the brainstem neurons that generate rhythmic electrical activity underlying breathing are synchro-nized by electrical synapses, as are populations of interneurons in the cere-bral cortex, thalamus, cerebellum, and other brain regions. Electrical trans-mission between certain hormone-secreting neurons within the mammalian hypothalamus ensures that all cells fire action potentials at about the same time, thus facilitating a burst of hormone secretion into the circulation. The fact that gap junction pores are large enough to allow molecules such as ATP and second messengers to diffuse intercellularly also permits electrical syn-apses to coordinate the intracellular signaling and metabolism of coupled cells. This property may be particularly important for glial cells, which form large intracellular signaling networks via their gap junctions. Synaptic Transmission 95 (A) (B) Membrane potential (mV) 0 1 Time (ms) 3 2 4 Postsynaptic neuron Presynaptic neuron Connexons Presynaptic cell membrane Pores connecting cytoplasm of two neurons Postsynaptic cell membrane 20 nm 20 nm 20 nm 3.5 nm 3.5 nm 3.5 nm 0 −25 25 −50 0 25 −50 −25 Brief (~0.1 ms) synaptic delay Figure 5.2 Structure and function of gap junctions at electrical synapses. (A) Gap junctions consist of hexameric com-plexes formed by the coming together of subunits called connexons, which are present in both the pre- and postsynap-tic membranes. The pores of the chan-nels connect to one another, creating electrical continuity between the two cells. (B) Rapid transmission of signals at an electrical synapse in the crayfish. An action potential in the presynaptic neuron causes the postsynaptic neuron to be depolarized within a fraction of a millisecond. (B after Furshpan and Pot-ter, 1959.) 96 Chapter Five Signal Transmission at Chemical Synapses The general structure of a chemical synapse is shown schematically in Figure 5.1B. The space between the pre- and postsynaptic neurons is substantially greater at chemical synapses than at electrical synapses and is called the syn-aptic cleft. However, the key feature of all chemical synapses is the presence of small, membrane-bounded organelles called synaptic vesicles within the presynaptic terminal. These spherical organelles are filled with one or more neurotransmitters, the chemical signals secreted from the presynaptic neu-ron, and it is these chemical agents acting as messengers between the com-municating neurons that gives this type of synapse its name. Transmission at chemical synapses is based on the elaborate sequence of events depicted in Figure 5.3. The process is initiated when an action poten-tial invades the terminal of the presynaptic neuron. The change in mem-brane potential caused by the arrival of the action potential leads to the opening of voltage-gated calcium channels in the presynaptic membrane. Because of the steep concentration gradient of Ca2+ across the presynaptic membrane (the external Ca2+ concentration is approximately 10–3 M, where-as the internal Ca2+ concentration is approximately 10–7 M), the opening of these channels causes a rapid influx of Ca2+ into the presynaptic terminal, with the result that the Ca2+ concentration of the cytoplasm in the terminal transiently rises to a much higher value. Elevation of the presynaptic Ca2+ concentration, in turn, allows synaptic vesicles to fuse with the plasma mem-brane of the presynaptic neuron. The Ca2+-dependent fusion of synaptic vesicles with the terminal membrane causes their contents, most importantly neurotransmitters, to be released into the synaptic cleft. Following exocytosis, transmitters diffuse across the synaptic cleft and bind to specific receptors on the membrane of the postsynaptic neuron. The binding of neurotransmitter to the receptors causes channels in the postsyn-aptic membrane to open (or sometimes to close), thus changing the ability of ions to flow into (or out of) the postsynaptic cells. The resulting neurotrans-mitter-induced current flow alters the conductance and (usually) the mem-brane potential of the postsynaptic neuron, increasing or decreasing the probability that the neuron will fire an action potential. In this way, informa-tion is transmitted from one neuron to another. Properties of Neurotransmitters The notion that electrical information can be transferred from one neuron to the next by means of chemical signaling was the subject of intense debate through the first half of the twentieth century. A key experiment that sup-ported this idea was performed in 1926 by German physiologist Otto Loewi. Acting on an idea that allegedly came to him in the middle of the night, Loewi proved that electrical stimulation of the vagus nerve slows the heart-beat by releasing a chemical signal. He isolated and perfused the hearts of two frogs, monitoring the rates at which they were beating (Figure 5.4). His experiment collected the perfusate flowing through the stimulated heart and transferred this solution to the second heart. When the vagus nerve to the first heart was stimulated, the beat of this heart slowed. Remarkably, even though the vagus nerve of the second heart had not been stimulated, its beat also slowed when exposed to the perfusate from the first heart. This result showed that the vagus nerve regulates the heart rate by releasing a chemical that accumulates in the perfusate. Originally referred to as “vagus sub-stance,” the agent was later shown to be acetylcholine (ACh). ACh is now known to be a neurotransmitter that acts not only in the heart but at a vari-ety of postsynaptic targets in the central and peripheral nervous systems, preeminently at the neuromuscular junction of striated muscles and in the visceral motor system (see Chapters 6 and 20). Over the years, a number of formal criteria have emerged that definitively identify a substance as a neurotransmitter (Box A). These have led to the identification of more than 100 different neurotransmitters, which can be Synaptic Transmission 97 Across dendrite Myelin Transmitter receptor Ions Postsynaptic current flow Synaptic vesicle 9 2 Transmitter molecules Ca2+ Opening or closing of postsynaptic channels 8 Transmitter binds to receptor molecules in postsynaptic membrane 7 Influx of Ca2+ through channels 4 6 Transmitter is synthesized and then stored in vesicles 1 Transmitter is released into synaptic cleft via exocytosis Retrieval of vesicular membrane from plasma membrane 10 Ca2+ causes vesicles to fuse with presynaptic membrane 5 Postsynaptic current causes excitatory or inhibitory postsynaptic potential that changes the excitability of the postsynaptic cell Depolarization of presynaptic terminal causes opening of voltage-gated Ca2+ channels 3 An action potential invades the presynaptic terminal Transmitter molecules Figure 5.3 Sequence of events involved in transmission at a typical chemical synapse. 98 Chapter Five classified into two broad categories: small-molecule neurotransmitters and neuropeptides (Chapter 6). Having more than one transmitter diversifies the physiological repertoire of synapses. Multiple neurotransmitters can pro-duce different types of responses on individual postsynaptic cells. For exam-ple, a neuron can be excited by one type of neurotransmitter and inhibited by another type of neurotransmitter. The speed of postsynaptic responses produced by different transmitters also differs, allowing control of electrical signaling over different time scales. In general, small-molecule neurotrans-mitters mediate rapid synaptic actions, whereas neuropeptides tend to mod-ulate slower, ongoing synaptic functions. Until relatively recently, it was believed that a given neuron produced only a single type of neurotransmitter. It is now clear, however, that many types of neurons synthesize and release two or more different neurotrans-mitters. When more than one transmitter is present within a nerve terminal, the molecules are called co-transmitters. Because different types of transmit-ters can be packaged in different populations of synaptic vesicles, co-trans-mitters need not be released simultaneously. When peptide and small-mole-cule neurotransmitters act as co-transmitters at the same synapse, they are differentially released according to the pattern of synaptic activity: low-fre-quency activity often releases only small neurotransmitters, whereas high-frequency activity is required to release neuropeptides from the same pre-synaptic terminals. As a result, the chemical signaling properties of such synapses change according to the rate of activity. Effective synaptic transmission requires close control of the concentration of neurotransmitters within the synaptic cleft. Neurons have therefore devel-oped a sophisticated ability to regulate the synthesis, packaging, release, and Heart 1 Heart 2 Vagus nerve Stimulate vagus nerve of heart 1 (A) (B) Contraction force Contraction force Inhibitory effect of vagus transferred Heartbeat slowed Heart 1 Heart 2 Time (s) Time (s) Stimulate Solution transferred to heart 2 Figure 5.4 Loewi’s experiment demonstrating chemical neurotransmission. (A) Diagram of experimental setup. (B) Where the vagus nerve of an isolated frog’s heart was stimulated, the heart rate decreased (upper panel). If the perfusion fluid from the stimulated heart was transferred to a second heart, its rate decreased as well (lower panel). Synaptic Transmission 99 Box A Criteria That Define a Neurotransmitter Three primary criteria have been used to confirm that a molecule acts as a neuro-transmitter at a given chemical synapse. 1. The substance must be present within the presynaptic neuron. Clearly, a chemical cannot be secreted from a presynaptic neuron unless it is present there. Because elaborate biochemical pathways are required to produce neurotransmitters, showing that the enzymes and precur-sors required to synthesize the substance are present in presynaptic neurons pro-vides additional evidence that the sub-stance is used as a transmitter. Note, however, that since the transmitters glu-tamate, glycine, and aspartate are also needed for protein synthesis and other metabolic reactions in all neurons, their presence is not sufficient evidence to establish them as neurotransmitters. 2. The substance must be released in response to presynaptic depolarization, and the release must be Ca2+-dependent. Another essential criterion for identify-ing a neurotransmitter is to demonstrate that it is released from the presynaptic neuron in response to presynaptic elec-trical activity, and that this release requires Ca2+ influx into the presynaptic terminal. Meeting this criterion is techni-cally challenging, not only because it may be difficult to selectively stimulate the presynaptic neurons, but also because enzymes and transporters effi-ciently remove the secreted neurotrans-mitters. 3. Specific receptors for the substance must be present on the postsynaptic cell. A neurotransmitter cannot act on its target unless specific receptors for the trans-mitter are present in the postsynaptic membrane. One way to demonstrate receptors is to show that application of exogenous transmitter mimics the post-synaptic effect of presynaptic stimula-tion. A more rigorous demonstration is to show that agonists and antagonists that alter the normal postsynaptic response have the same effect when the substance in question is applied exoge-nously. High-resolution histological methods can also be used to show that specific receptors are present in the post-synaptic membrane (by detection of radioactively labeled receptor antibod-ies, for example). Fulfilling these criteria establishes unambiguously that a substance is used as a transmitter at a given synapse. Prac-tical difficulties, however, have pre-vented these standards from being applied at many types of synapses. It is for this reason that so many substances must be referred to as “putative” neurotransmitters. (1) (2) (3) Postsynaptic cell 2 Neurotransmitter released Ca2+ Ca2+ 3 Neurotransmitter receptors activated Application of transmitter, agonists, or antagonists Action potential Presynaptic terminal 1 Neuro-transmitter present Demonstrating the identity of a neurotransmitter at a synapse requires showing (1) its pres-ence, (2) its release, and (3) the postsynaptic presence of specific receptors. 100 Chapter Five degradation (or removal) of neurotransmitters to achieve the desired levels of transmitter molecules. The synthesis of small-molecule neurotransmitters occurs locally within presynaptic terminals (Figure 5.5A). The enzymes needed to synthesize these transmitters are produced in the neuronal cell body and transported to the nerve terminal cytoplasm at 0.5–5 millimeters a day by a mechanism called slow axonal transport. The precursor molecules required to make new molecules of neurotransmitter are usually taken into the nerve terminal by transporters found in the plasma membrane of the ter-minal. The enzymes synthesize neurotransmitters in the cytoplasm of the presynaptic terminal and the transmitters are then loaded into synaptic vesi-cles via transporters in the vesicular membrane (see Chapter 4). For some small-molecule neurotransmitters, the final steps of synthesis occur inside the synaptic vesicles. Most small-molecule neurotransmitters are packaged in vesicles 40 to 60 nm in diameter, the centers of which appear clear in elec-tron micrographs; accordingly, these vesicles are referred to as small clear-core vesicles (Figure 5.5B). Neuropeptides are synthesized in the cell body of a neuron, meaning that the peptide is produced a long distance away from its site of secretion (Figure 5.5C). To solve this problem, peptide-filled vesi-cles are transported along an axon and down to the synaptic terminal via fast axonal transport. This process carries vesicles at rates up to 400 mm/day along cytoskeletal elements called microtubules (in contrast to the slow axonal transport of the enzymes that synthesize small-molecule trans-mitters). Microtubules are long, cylindrical filaments, 25 nm in diameter, pre-sent throughout neurons and other cells. Peptide-containing vesicles are moved along these microtubule “tracks” by ATP-requiring “motor” proteins such as kinesin. Neuropeptides are packaged into synaptic vesicles that range from 90 to 250 nm in diameter. These vesicles are electron-dense in electron micrographs—hence they are referred to as large dense-core vesi-cles (Figure 5.5D). After a neurotransmitter has been secreted into the synaptic cleft, it must be removed to enable the postsynaptic cell to engage in another cycle of syn-Figure 5.5 Metabolism of small-molecule and peptide transmitters. (A) Small-mol-ecule neurotransmitters are synthesized at nerve terminals. The enzymes necessary for neurotransmitter synthesis are made in the cell body of the presynaptic cell (1) and are transported down the axon by slow axonal transport (2). Precursors are taken up into the terminals by specific transporters, and neurotransmitter synthesis and packaging take place within the nerve endings (3). After vesicle fusion and release (4), the neurotransmitter may be enzymatically degraded. The reuptake of the neurotransmitter (or its metabolites) starts another cycle of synthesis, packaging, release, and removal (5). (B) Small clear-core vesicles at a synapse between an axon terminal (AT) and a dendritic spine (Den) in the central nervous system. Such vesi-cles typically contain small-molecule neurotransmitters. (C) Peptide neurotransmit-ters, as well as the enzymes that modify their precursors, are synthesized in the cell body (1). Enzymes and propeptides are packaged into vesicles in the Golgi appara-tus. During fast axonal transport of these vesicles to the nerve terminals (2), the enzymes modify the propeptides to produce one or more neurotransmitter peptides (3). After vesicle fusion and exocytosis, the peptides diffuse away and are degraded by proteolytic enzymes (4). (D) Large dense-core vesicles in a central axon terminal (AT) synapsing onto a dendrite (Den). Such vesicles typically contain neuropeptides or, in some cases, biogenic amines. (B and D from Peters, Palay, and Webster, 1991.) ▲ Enzymes (A) RER Nucleus Golgi apparatus Microtubules Terminal Axon Transport of precursors into terminal 1 Synthesis of enzymes in cell body 2 Slow axonal transport of enzymes 4 Release and diffusion of neuro– transmitter Neuro-transmitter Neuro-transmitter Diffusion and Diffusion and degradation degradation Diffusion and degradation (C) 1 Synthesis of neurotransmitter precursors and enzymes 2 Transport of enzymes and peptide precursors down microtubule tracks 3 Enzymes modify precursors to produce peptide neurotransmitter 4 Neurotransmitter diffuses away and is degraded by proteolytic enzymes (B) (D) 5 3 Synthesis and packaging of neurotransmitter Precursor AT AT Den Den AT AT Den Den AT Den AT Den 0.5 mm 102 Chapter Five aptic transmission. The removal of neurotransmitters involves diffusion away from the postsynaptic receptors, in combination with reuptake into nerve terminals or surrounding glial cells, degradation by specific enzymes, or a combination of these mechanisms. Specific transporter proteins remove most small-molecule neurotransmitters (or their metabolites) from the syn-aptic cleft, ultimately delivering them back to the presynaptic terminal for reuse. Quantal Release of Neurotransmitters Much of the evidence leading to the present understanding of chemical syn-aptic transmission was obtained from experiments examining the release of ACh at neuromuscular junctions. These synapses between spinal motor neu-rons and skeletal muscle cells are simple, large, and peripherally located, making them particularly amenable to experimental analysis. Such synapses occur at specializations called end plates because of the saucer-like appear-ance of the site on the muscle fiber where the presynaptic axon elaborates its terminals (Figure 5.6A). Most of the pioneering work on neuromuscular transmission was performed by Bernard Katz and his collaborators at Uni-versity College London during the 1950s and 1960s, and Katz has been widely recognized for his remarkable contributions to understanding synap-tic transmission. Though he worked primarily on the frog neuromuscular junction, numerous subsequent experiments have confirmed the applicabil-ity of his observations to transmission at chemical synapses throughout the nervous system. When an intracellular microelectrode is used to record the membrane potential of a muscle cell, an action potential in the presynaptic motor neu-ron can be seen to elicit a transient depolarization of the postsynaptic muscle fiber. This change in membrane potential, called an end plate potential (EPP), is normally large enough to bring the membrane potential of the mus-cle cell well above the threshold for producing a postsynaptic action poten-tial (Figure 5.6B). The postsynaptic action potential triggered by the EPP causes the muscle fiber to contract. Unlike the case for electrical synapses, there is a pronounced delay between the time that the presynaptic motor neuron is stimulated and when the EPP occurs in the postsynaptic muscle cell. Such a delay is characteristic of all chemical synapses. One of Katz’s seminal findings, in studies carried out with Paul Fatt in 1951, was that spontaneous changes in muscle cell membrane potential occur even in the absence of stimulation of the presynaptic motor neuron (Figure 5.6C). These changes have the same shape as EPPs but are much +50 0 −50 −100 Postsynaptic membrane potential (mV) (B) Stimulate motor axon Time (ms) 2 0 4 6 End plate potential (EPP) Action potential Postsynaptic membrane potential (mV) (C) Time (ms) 1 mV 0 200 400 MEPP Postsynaptic membrane potential (mV) 1 mV (D) Stimulate motor axon Time (ms) 0 20 40 60 80 100 Spontaneous MEPP Subthreshold EPP (A) Stimulate axon Record postsynaptic membrane potential Muscle cell Record Stimulate Axon Threshold Figure 5.6 Synaptic transmission at the neuromuscular junction. (A) Experimental arrangement, typically using the muscle of a frog or rat. The axon of the motor neu-ron innervating the muscle fiber is stimulated with an extracellular electrode, while an intracellular microelectrode is inserted into the postsynaptic muscle cell to record its electrical responses. (B) End plate potentials (EPPs) evoked by stimulation of a motor neuron are normally above threshold and therefore produce an action poten-tial in the postsynaptic muscle cell. (C) Spontaneous miniature EPPs (MEPPs) occur in the absence of presynaptic stimulation. (D) When the neuromuscular junction is bathed in a solution that has a low concentration of Ca2+, stimulating the motor neuron evokes EPPs whose amplitudes are reduced to about the size of MEPPs. (After Fatt and Katz, 1952.) smaller (typically less than 1 mV in amplitude, compared to an EPP of per-haps 40 or 50 mV). Both EPPs and these small, spontaneous events are sensi-tive to pharmacological agents that block postsynaptic acetylcholine recep-tors, such as curare (see Box B in Chapter 6). These and other parallels between EPPs and the spontaneously occurring depolarizations led Katz and his colleagues to call these spontaneous events miniature end plate potentials, or MEPPs. The relationship between the full-blown end plate potential and MEPPs was clarified by careful analysis of the EPPs. The magnitude of the EPP pro-vides a convenient electrical assay of neurotransmitter secretion from a motor neuron terminal; however, measuring it is complicated by the need to prevent muscle contraction from dislodging the microelectrode. The usual means of eliminating muscle contractions is either to lower Ca2+ concentra-tion in the extracellular medium or to partially block the postsynaptic ACh receptors with the drug curare. As expected from the scheme illustrated in Figure 5.3, lowering the Ca2+ concentration reduces neurotransmitter secre-tion, thus reducing the magnitude of the EPP below the threshold for post-synaptic action potential production and allowing it to be measured more precisely. Under such conditions, stimulation of the motor neuron produces very small EPPs that fluctuate in amplitude from trial to trial (Figure 5.6D). These fluctuations give considerable insight into the mechanisms responsi-ble for neurotransmitter release. In particular, the variable evoked response in low Ca2+ is now known to result from the release of unit amounts of ACh by the presynaptic nerve terminal. Indeed, the amplitude of the smallest evoked response is strikingly similar to the size of single MEPPs (compare Figure 5.6C and D). Further supporting this similarity, increments in the EPP response (Figure 5.7A) occur in units about the size of single MEPPs (Figure 5.7B). These “quantal” fluctuations in the amplitude of EPPs indicated to Katz and colleagues that EPPs are made up of individual units, each equiva-lent to a MEPP. The idea that EPPs represent the simultaneous release of many MEPP-like units can be tested statistically. A method of statistical analysis based on the independent occurrence of unitary events (called Poisson statistics) predicts what the distribution of EPP amplitudes would look like during a large number of trials of motor neuron stimulation, under the assumption that EPPs are built up from unitary events like MEPPs (see Figure 5.7B). The dis-tribution of EPP amplitudes determined experimentally was found to be just that expected if transmitter release from the motor neuron is indeed quantal (the red curve in Figure 5.7A). Such analyses confirmed the idea that release of acetylcholine does indeed occur in discrete packets, each equivalent to a MEPP. In short, a presynaptic action potential causes a postsynaptic EPP because it synchronizes the release of many transmitter quanta. Release of Transmitters from Synaptic Vesicles The discovery of the quantal release of packets of neurotransmitter immedi-ately raised the question of how such quanta are formed and discharged into the synaptic cleft. At about the time Katz and his colleagues were using physiological methods to discover quantal release of neurotransmitter, elec-tron microscopy revealed, for the first time, the presence of synaptic vesicles in presynaptic terminals. Putting these two discoveries together, Katz and others proposed that synaptic vesicles loaded with transmitter are the source of the quanta. Subsequent biochemical studies confirmed that synaptic vesi-Synaptic Transmission 103 104 Chapter Five (B) (A) MEPP amplitude (mV) EPP amplitude (mV) Number of MEPPs Number of EPPs 0 0 10 20 30 0 5 10 15 20 0.4 0.8 0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 Prediction of statistical model No EPP in response to stimulation Figure 5.7 Quantized distribution of EPP ampli-tudes evoked in a low Ca2+ solution. Peaks of EPP amplitudes (A) tend to occur in integer multiples of the mean amplitude of MEPPs, whose ampli-tude distribution is shown in (B). The leftmost bar in the EPP amplitude distribution shows trials in which presynaptic stimulation failed to elicit an EPP in the muscle cell. The red curve indicates the prediction of a statistical model based on the assumption that the EPPs result from the indepen-dent release of multiple MEPP-like quanta. The observed match, including the predicted number of failures, supports this interpretation. (After Boyd and Martin, 1955.) cles are the repositories of transmitters. These studies have shown that ACh is highly concentrated in the synaptic vesicles of motor neurons, where it is present at a concentration of about 100 mM. Given the diameter of a small, clear-core synaptic vesicle (∼50 nm), approximately 10,000 molecules of neu-rotransmitter are contained in a single vesicle. This number corresponds quite nicely to the amount of ACh that must be applied to a neuromuscular junction to mimic a MEPP, providing further support for the idea that quanta arise from discharge of the contents of single synaptic vesicles. To prove that quanta are caused by the fusion of individual synaptic vesi-cles with the plasma membrane, it is necessary to show that each fused vesicle causes a single quantal event to be recorded postsynaptically. This challenge was met in the late 1970s, when John Heuser, Tom Reese, and col-leagues correlated measurements of vesicle fusion with the quantal content of EPPs at the neuromuscular junction. In their experiments, the number of vesicles that fused with the presynaptic plasma membrane was measured by electron microscopy in terminals that had been treated with a drug (4-aminopyridine, or 4-AP) that enhances the number of vesicle fusion events produced by single action potentials (Figure 5.8A). Parallel electrical mea-surements were made of the quantal content of the EPPs elicited in this way. A comparison of the number of synaptic vesicle fusions observed with the electron microscope and the number of quanta released at the synapse showed a good correlation between these two measures (Figure 5.8B). These results remain one of the strongest lines of support for the idea that a quantum of transmitter release is due to a synaptic vesicle fusing with the presynaptic membrane. Subsequent evidence, based on other means of measuring vesicle fusion, has left no doubt about the validity of this general interpretation of chemical synaptic transmission. Very recent work has identified structures within the presynaptic terminal that connect vesicles to the plasma membrane and may be involved in membrane fusion (Figure 5.8C). Local Recycling of Synaptic Vesicles The fusion of synaptic vesicles causes new membrane to be added to the plasma membrane of the presynaptic terminal, but the addition is not per-manent. Although a bout of exocytosis can dramatically increase the surface area of presynaptic terminals, this extra membrane is removed within a few minutes. Heuser and Reese performed another important set of experi-ments showing that the fused vesicle membrane is actually retrieved and taken back into the cytoplasm of the nerve terminal (a process called endo-cytosis). The experiments, again carried out at the frog neuromuscular junc-tion, were based on filling the synaptic cleft with horseradish peroxidase (HRP), an enzyme that can be made to produce a dense reaction product that is visible in an electron microscope. Under appropriate experimental conditions, endocytosis could then be visualized by the uptake of HRP into the nerve terminal (Figure 5.9). To activate endocytosis, the presynaptic ter-minal was stimulated with a train of action potentials, and the subsequent fate of the HRP was followed by electron microscopy. Immediately follow-Synaptic Transmission 105 0 (B) (A) (C) 4-AP concentration: 10−3M 10−4M 10−5M Number of quanta released Number of vesicles fusing 1000 0 1000 2000 3000 4000 5000 6000 2000 3000 4000 5000 6000 Figure 5.8 Relationship of synaptic vesicle exocytosis and quantal transmit-ter release. (A) A special electron micro-scopical technique called freeze-fracture microscopy was used to visualize the fusion of synaptic vesicles in presynap-tic terminals of frog motor neurons. Left: Image of the plasma membrane of an unstimulated presynaptic terminal. Right: Image of the plasma membrane of a terminal stimulated by an action potential. Stimulation causes the appearance of dimple-like structures that represent the fusion of synaptic vesicles with the presynaptic membrane. The view is as if looking down on the release sites from outside the presynap-tic terminal. (B) Comparison of the number of observed vesicle fusions to the number of quanta released by a pre-synaptic action potential. Transmitter release was varied by using a drug (4-AP) that affects the duration of the pre-synaptic action potential, thus changing the amount of calcium that enters dur-ing the action potential. The diagonal line is the 1:1 relationship expected if each vesicle that opened released a sin-gle quantum of transmitter. (C) Fine structure of vesicle fusion sites of frog presynaptic terminals. Synaptic vesicles are arranged in rows and are connected to each other and to the plasma mem-brane by a variety of proteinaceous structures (yellow). Green structures in the presynaptic membrane, correspond-ing to the rows of particles seen in (A), are thought to be Ca2+ channels. (A and B from Heuser et al., 1979; C after Har-low et al., 2001) 106 Chapter Five ing stimulation, the HRP was found within special endocytotic organelles called coated vesicles (Figure 5.9A,B). A few minutes later, however, the coated vesicles had disappeared and the HRP was found in a different organelle, the endosome (Figure 5.9C). Finally, within an hour after stimu-lating the terminal, the HRP reaction product appeared inside synaptic vesi-cles (Figure 5.9D). These observations indicate that synaptic vesicle membrane is recycled within the presynaptic terminal via the sequence summarized in Figure 5.9E. In this process, called the synaptic vesicle cycle, the retrieved vesicular mem-brane passes through a number of intracellular compartments—such as coated vesicles and endosomes—and is eventually used to make new synap-tic vesicles. After synaptic vesicles are re-formed, they are stored in a reserve pool within the cytoplasm until they need to participate again in neurotrans-mitter release. These vesicles are mobilized from the reserve pool, docked at the presynaptic plasma membrane, and primed to participate in exocytosis once again. More recent experiments, employing a fluorescent label rather than HRP, have determined the time course of synaptic vesicle recycling. These studies indicate that the entire vesicle cycle requires approximately 1 minute, with membrane budding during endocytosis requiring 10–20 sec-Endosome Docking Budding Priming Fusion 1 msec Ca2+ (A) (E) Horseradish peroxidase (HRP) Briefly stimulate presynaptic terminal Wash away extracellular HRP; wait 5 minutes 1 hour later (B) (C) (D) Coated pits and coated vesicles contain HRP Endosome contains HRP Synaptic vesicles contain HRP 1 2 3 4 Synaptic vesicles fuse Budding Endocytosis Exocytosis 10–20 sec 1 min Figure 5.9 Local recycling of synaptic vesicles in presynaptic terminals. (A) Horseradish peroxidase (HRP) introduced into the synaptic cleft is used to follow the fate of membrane retrieved from the pre-synaptic plasma membrane. Stimulation of endocy-tosis by presynaptic action potentials causes HRP to be taken up into the presynaptic terminals via a pathway that includes (B) coated vesicles and (C) endosomes. (D) Eventually, the HRP is found in newly formed synaptic vesicles. (E) Interpretation of the results shown in A–D. Calcium-regulated fusion of vesicles with the presynaptic membrane is fol-lowed by endocytotic retrieval of vesicular mem-brane via coated vesicles and endosomes, and sub-sequent re-formation of new synaptic vesicles. (After Heuser and Reese, 1973.) onds of this time. As can be seen from the 1-millisecond delay in transmission following excitation of the presynaptic terminal (see Figure 5.6B), membrane fusion during exocytosis is much more rapid than budding during endocyto-sis. Thus, all of the recycling steps interspersed between membrane budding and subsequent refusion of a vesicle are completed in less than a minute. The precursors to synaptic vesicles originally are produced in the endo-plasmic reticulum and Golgi apparatus in the neuronal cell body. Because of the long distance between the cell body and the presynaptic terminal in most neurons, transport of vesicles from the soma would not permit rapid replen-ishment of synaptic vesicles during continuous neural activity. Thus, local recycling is well suited to the peculiar anatomy of neurons, giving nerve ter-minals the means to provide a continual supply of synaptic vesicles. As might be expected, defects in synaptic vesicle recycling can cause severe neurological disorders, some of which are described in Box B. The Role of Calcium in Transmitter Secretion As was apparent in the experiments of Katz and others described in the pre-ceding sections, lowering the concentration of Ca2+ outside a presynaptic motor nerve terminal reduces the size of the EPP (compare Figure 5.6B and D). Moreover, measurement of the number of transmitter quanta released under such conditions shows that the reason the EPP gets smaller is that lowering Ca2+ concentration decreases the number of vesicles that fuse with the plasma membrane of the terminal. An important insight into how Ca2+ regulates the fusion of synaptic vesicles was the discovery that presynaptic terminals have voltage-sensitive Ca2+ channels in their plasma membranes (see Chapter 4). The first indication of presynaptic Ca2+ channels was provided by Katz and Ricardo Miledi. They observed that presynaptic terminals treated with tetrodotoxin (which blocks Na+ channels; see Chapter 3) could still produce a peculiarly prolonged type of action potential. The explanation for this sur-prising finding was that current was still flowing through Ca2+ channels, substituting for the current ordinarily carried by the blocked Na+ channels. Subsequent voltage clamp experiments, performed by Rodolfo Llinás and others at a giant presynaptic terminal of the squid (Figure 5.10A), confirmed Synaptic Transmission 107 (A) CONTROL (B) Postsynaptic membrane potential (mV) Presynaptic calcium current (µA/cm2) Presynaptic membrane potential (mV) –75 –50 –25 0 200 –75 0 –25 –50 0 Time (ms) 0 3 CADMIUM ADDED 9 6 12 –3 –3 0 3 9 6 12 Presynaptic neuron Vpre Ipre Postsynaptic neuron Postsynaptic membrane potential Record Voltage clamp Figure 5.10 The entry of Ca2+ through the specific voltage-dependent calcium channels in the presynaptic terminals causes transmitter release. (A) Experi-mental setup using an extraordinarily large synapse in the squid. The voltage clamp method detects currents flowing across the presynaptic membrane when the membrane potential is depolarized. (B) Pharmacological agents that block currents flowing through Na+ and K+ channels reveal a remaining inward cur-rent flowing through Ca2+ channels. This influx of calcium triggers transmit-ter secretion, as indicated by a change in the postsynaptic membrane potential. Treatment of the same presynaptic ter-minal with cadmium, a calcium channel blocker, eliminates both the presynaptic calcium current and the postsynaptic response. (After Augustine and Eckert, 1984.) 108 Chapter Five Box B Diseases That Affect the Presynaptic Terminal Various steps in the exocytosis and endo-cytosis of synaptic vesicles are targets of a number of rare but debilitating neuro-logical diseases. Many of these are myas-thenic syndromes, in which abnormal transmission at neuromuscular synapses leads to weakness and fatigability of skeletal muscles (see Box B in Chapter 7). One of the best-understood examples of such disorders is the Lambert-Eaton myasthenic syndrome (LEMS), an occa-sional complication in patients with cer-tain kinds of cancers. Biopsies of muscle tissue removed from LEMS patients allow intracellular recordings identical to those shown in Figure 5.6. Such record-ings have shown that when a motor neu-ron is stimulated, the number of quanta contained in individual EPPs is greatly reduced, although the amplitude of spontaneous MEPPs is normal. Thus, LEMS impairs evoked neurotransmitter release, but does not affect the size of individual quanta. Several lines of evidence indicate that this reduction in neurotransmitter release is due to a loss of voltage-gated Ca2+ channels in the presynaptic terminal of motor neurons (see figure). Thus, the defect in neuromuscular transmission can be overcome by increasing the extra-cellular concentration of Ca2+, and anatomical studies indicate a lower den-sity of Ca2+ channel proteins in the pre-synaptic plasma membrane. The loss of presynaptic Ca2+ channels in LEMS apparently arises from a defect in the immune system. The blood of LEMS patients has a very high concentration of antibodies that bind to Ca2+ channels, and it seems likely that these antibodies are the primary cause of LEMS. For example, removal of Ca2+ channel anti-bodies from the blood of LEMS patients by plasma exchange reduces muscle weakness. Similarly, immunosuppres-sant drugs also can alleviate LEMS symptoms. Perhaps most telling, inject-ing these antibodies into experimental animals elicits muscle weakness and abnormal neuromuscular transmission. Why the immune system generates anti-bodies against Ca2+ channels is not clear. Most LEMS patients have small-cell car-cinoma, a form of lung cancer that may somehow initiate the immune response to Ca2+ channels. Whatever the origin, the binding of antibodies to Ca2+ chan-nels causes a reduction in Ca2+ channel currents. It is this antibody-induced defect in presynaptic Ca2+ entry that accounts for the muscle weakness associ-ated with LEMS. Congenital myasthenic syndromes are genetic disorders that also cause muscle weakness by affecting neuromus-cular transmission. Some of these syn-dromes affect the acetylcholinesterase that degrades acetylcholine in the synap-tic cleft, whereas others arise from autoimmune attack of acetylcholine receptors (see Box C in Chapter 6). How-ever, a number of congenital myasthenic syndromes arise from defects in acetyl-choline release due to altered synaptic vesicle traffic within the motor neuron terminal. Neuromuscular synapses in some of these patients have EPPs with reduced quantal content, a deficit that is especially prominent when the synapse is activated repeatedly. Electron microscopy shows that presynaptic motor nerve terminals have a greatly reduced number of synaptic vesicles. The defect in neurotransmitter release evi-dently results from an inadequate num-ber of synaptic vesicles available for release during sustained presynaptic activity. The origins of this shortage of synaptic vesicles is not clear, but could result either from an impairment in endocytosis in the nerve terminal (see figure) or from a reduced supply of vesi-cles from the motor neuron cell body. Still other patients suffering from familial infantile myasthenia appear to have neuromuscular weakness that arises from reductions in the size of indi-vidual quanta, rather than the number of quanta released. Motor nerve terminals from these patients have synaptic vesi-cles that are normal in number, but smaller in diameter. This finding sug-gests a different type of genetic lesion that somehow alters formation of new synaptic vesicles following endocytosis, thereby leading to less acetylcholine in each vesicle. Another disorder of synaptic trans-mitter release results from poisoning by anaerobic Clostridium bacteria. This genus of microorganisms produces some Endosome Docking Budding Priming Fusion Ca2+ Budding Impaired endocytosis in congenital myasthenic syndromes Botulinum and tetanus toxins affect SNARE proteins involved in vesicle fusion LEMS attacks presynaptic Ca2+ channels Presynaptic targets of several neurological disorders. the presence of voltage-gated Ca2+ channels in the presynaptic terminal (Fig-ure 5.10B). Such experiments showed that the amount of neurotransmitter released is very sensitive to the exact amount of Ca2+ that enters. Further, blockade of these Ca2+ channels with drugs also inhibits transmitter release (Figure 5.10B, right). These observations all confirm that the voltage-gated Ca2+ channels are directly involved in neurotransmission. Thus, presynaptic action potentials open voltage-gated Ca2+ channels, with a resulting influx of Ca2+. That Ca2+ entry into presynaptic terminals causes a rise in the concentra-tion of Ca2+ within the terminal has been documented by microscopic imag-ing of terminals filled with Ca2+-sensitive fluorescent dyes (Figure 5.11A). The consequences of the rise in presynaptic Ca2+ concentration for neuro-transmitter release has been directly shown in two ways. First, microinjec-tion of Ca2+ into presynaptic terminals triggers transmitter release in the absence of presynaptic action potentials (Figure 5.11B). Second, presynaptic microinjection of calcium chelators (chemicals that bind Ca2+ and keep its concentration buffered at low levels) prevents presynaptic action potentials from causing transmitter secretion (Figure 5.11C). These results prove beyond any doubt that a rise in presynaptic Ca2+ concentration is both nec-essary and sufficient for neurotransmitter release. Thus, as is the case for many other forms of neuronal signaling (see Chapter 7), Ca2+ serves as a sec-ond messenger during transmitter release. While Ca2+ is a universal trigger for transmitter release, not all transmit-ters are released with the same speed. For example, while secretion of ACh Synaptic Transmission 109 of the most potent toxins known, includ-ing several botulinum toxins and tetanus toxin. Both botulism and tetanus are potentially deadly disorders. Botulism can occur by consuming food containing Clostridium bacteria or by infection of wounds with the spores of these ubiquitous organisms. In either case, the presence of the toxin can cause paralysis of peripheral neuromuscular synapses due to abolition of neurotrans-mitter release. This interference with neuromuscular transmission causes skeletal muscle weakness, in extreme cases producing respiratory failure due to paralysis of the diaphragm and other muscles required for breathing. Botu-linum toxins also block synapses inner-vating the smooth muscles of several organs, giving rise to visceral motor dys-function. Tetanus typically results from the con-tamination of puncture wounds by Clostridium bacteria that produce tetanus toxin. In contrast to botulism, tetanus poisoning blocks the release of inhibitory transmitters from interneurons in the spinal cord. This effect causes a loss of synaptic inhibition on spinal motor neu-rons, producing hyperexcitation of skele-tal muscle and tetanic contractions in affected muscles (hence the name of the disease). Although their clinical consequences are dramatically different, clostridial tox-ins have a common mechanism of action (see figure). Tetanus toxin and botulinum toxins work by cleaving the SNARE pro-teins involved in fusion of synaptic vesi-cles with the presynaptic plasma mem-brane (see Box C). This proteolytic action presumably accounts for the block of transmitter release at the afflicted syn-apses. The different actions of these tox-ins on synaptic transmission at excitatory motor versus inhibitory synapses appar-ently results from the fact that these tox-ins are taken up by different types of neurons: Whereas the botulinum toxins are taken up by motor neurons, tetanus toxin is preferentially targeted to interneurons. The basis for this differen-tial uptake of toxins is not known, but presumably arises from the presence of different types of toxin receptors on the two types of neurons. References ENGEL, A. G. (1991) Review of evidence for loss of motor nerve terminal calcium chan-nels in Lambert-Eaton myasthenic syndrome. Ann. N.Y. Acad. Sci. 635: 246–258. ENGEL, A. G. (1994) Congenital myasthenic syndromes. Neurol. Clin. 12: 401–437. LANG, B. AND A. VINCENT (2003) Autoantibod-ies to ion channels at the neuromuscular junction. Autoimmun. Rev. 2: 94–100. MASELLI, R. A. (1998) Pathogenesis of human botulism. Ann. N.Y. Acad. Sci. 841: 122–139. 110 Chapter Five Figure 5.11 Evidence that a rise in pre-synaptic Ca2+ concentration triggers transmitter release from presynaptic ter-minals. (A) Fluorescence microscopy measurements of presynaptic Ca2+ con-centration at the squid giant synapse (see Figure 5.8A). A train of presynaptic action potentials causes a rise in Ca2+ concentration, as revealed by a dye (called fura-2) that fluoresces more strongly when the Ca2+ concentration increases. (B) Microinjection of Ca2+ into a squid giant presynaptic terminal trig-gers transmitter release, measured as a depolarization of the postsynaptic mem-brane potential. (C) Microinjection of BAPTA, a Ca2+ chelator, into a squid giant presynaptic terminal prevents transmitter release. (A from Smith et al., 1993; B after Miledi, 1971; C after Adler et al., 1991.) from motor neurons requires only a fraction of a millisecond (see Figure 5.6), release of neuropeptides require high-frequency bursts of action potentials for many seconds. These differences in the rate of release probably arise from differences in the spatial arrangement of vesicles relative to presynaptic Ca2+ channels. This perhaps is most evident in cases where small molecules and peptides serve as co-transmitters (Figure 5.12). Whereas the small, clear-core vesicles containing small-molecule transmitters are typically docked at the plasma membrane in advance of Ca2+ entry, large dense core vesicles containing peptide transmitters are farther away from the plasma membrane (see Figure 5.5D). At low firing frequencies, the concentration of Ca2+ may increase only locally at the presynaptic plasma membrane, in the vicinity of open Ca2+ channels, limiting release to small-molecule transmitters from the docked small, clear-core vesicles. Prolonged high-frequency stimulation increases the Ca2+ concentration throughout the presynaptic terminal, thereby inducing the slower release of neuropeptides. Molecular Mechanisms of Transmitter Secretion Precisely how an increase in presynaptic Ca2+ concentration goes on to trig-ger vesicle fusion and neurotransmitter release is not understood. However, many important clues have come from molecular studies that have identified and characterized the proteins found on synaptic vesicles and their binding −75 −50 −25 0 25 CONTROL (C) (B) (A) INJECT Ca2+ BUFFER PHOTO with line overlay Time (s) − 65 − 64 0 1 2 3 Postsynaptic membrane potential (mV) Presynaptic membrane potential (mV) Postsynaptic membrane potential (mV) 0 −75 −50 −25 0 25 1 2 3 4 5 Time (ms) 0 1 2 3 4 5 Ca2+ injection 4 250µm Ca2+ partners on the presynaptic plasma membrane and cytoplasm (Figure 5.13). Most, if not all, of these proteins act at one or more steps in the synaptic vesi-cle cycle. Although a complete molecular picture of neurotransmitter release is still lacking, the roles of several proteins involved in vesicle fusion have been deduced. Several of the proteins important for neurotransmitter release are also involved in other types of membrane fusion events common to all cells. For example, two proteins originally found to be important for the fusion of vesicles with membranes of the Golgi apparatus, the ATPase NSF (NEM-sen-sitive fusion protein) and SNAPs (soluble NSF-attachment proteins), are also involved in priming synaptic vesicles for fusion. These two proteins work by regulating the assembly of other proteins that are called SNAREs (SNAP receptors). One of these SNARE proteins, synaptobrevin, is in the mem-brane of synaptic vesicles, while two other SNARE proteins called syntaxin and SNAP-25 are found primarily on the plasma membrane. These SNARE proteins can form a macromolecular complex that spans the two mem-branes, thus bringing them into close apposition (Figure 5.14A). Such an arrangement is well suited to promote the fusion of the two membranes, and several lines of evidence suggest that this is what actually occurs. One important observation is that toxins that cleave the SNARE proteins block neurotransmitter release (Box C). In addition, putting SNARE proteins into artificial lipid membranes and allowing these proteins to form complexes with each other causes the membranes to fuse. Many other proteins, such as Synaptic Transmission 111 Localized increase in Ca2+ concentration Small-molecule neurotransmitter in small clear-core vesicles Low-frequency stimulation More diffuse increase in Ca2+ concentration High-frequency stimulation Release of both types of transmitter Preferential release of small-molecule neurotransmitter Neuropeptide in large dense-core vesicles Figure 5.12 Differential release of neu-ropeptide and small-molecule co-trans-mitters. Low-frequency stimulation preferentially raises the Ca2+ concentra-tion close to the membrane, favoring the release of transmitter from small clear-core vesicles docked at presynaptic spe-cializations. High-frequency stimulation leads to a more general increase in Ca2+, causing the release of peptide neuro-transmitters from large dense-core vesi-cles, as well as small-molecule neuro-transmitters from small clear-core vesicles. 112 Chapter Five Synaptic vesicle Synaptic vesicle membrane Synaptic cleft Cytoplasm Plasma membrane of presynaptic terminal SV2 Rab 3 Rabphilin Synaptophysin Cysteine string protein GTP-binding proteins Miscellaneous important proteins Proteins that form channels, transporters, or receptors Ca2+-binding proteins SNARE-associated proteins Proteins involved in endocytosis Ca2+ channel Neurexin I CLI Ca2+/CaM dependent protein kinase II Synapsin DOC2 RIM Synaptotagmin Syndapin Dynamin Clathrin AP–2 AP180 Amphiphysin Auxilin Synaptojanin Hsc70 Snapin Tomosyn SNAP Synaptobrevin Syntaxin SNAP–25 Syntaphilin Complexin NSF nSec1 Figure 5.13 Presynaptic proteins implicated in neurotransmitter release. Structures adapted from Brunger (2001) and Brodsky et al. (2001). complexin, nSec-1, snapin, syntaphilin, and tomosyn, bind to the SNAREs and presumably regulate the formation or disassembly of this complex. Because the SNARE proteins do not bind Ca2+, still other molecules must be responsible for Ca2+ regulation of neurotransmitter release. Several pre-synaptic proteins, including calmodulin, CAPS, and munc-13, are capable of binding Ca2+. However, the leading candidate for Ca2+ regulation of neuro-transmitter release is synaptotagmin, a protein found in the membrane of synaptic vesicles. Synaptotagmin binds Ca2+ at concentrations similar to those required to trigger vesicle fusion within the presynaptic terminal. It may act as a Ca2+ sensor, signaling the elevation of Ca2+ within the terminal and thus triggering vesicle fusion. In support of this idea, alterations of the properties of synaptotagmin in the presynaptic terminals of mice, fruit flies, squid, and other experimental animals impair Ca2+-dependent neurotrans-mitter release. In fact, deletion of only one of the 19 synaptotagmin genes of mice is a lethal mutation, causing the mice to die soon after birth. How Ca2+ binding to synaptotagmin could lead to exocytosis is not yet clear. It is known that Ca2+ changes the chemical properties of synaptotagmin, allow-ing it to insert into membranes and to bind to other proteins, including the SNAREs. A plausible model is that the SNARE proteins bring the two mem-branes close together, and that Ca2+-induced changes in synaptotagmin then produce the final fusion of these membranes (Figure 5.14B). Still other proteins appear to be involved at subsequent steps of the syn-aptic vesicle cycle (Figure 5.14C). For example, the protein clathrin is involved in endocytotic budding of vesicles from the plasma membrane. Clathrin forms structures that resemble geodesic domes (Figure 5.14D); these structures form coated pits that initiate membrane budding. Assembly of individual clathrin triskelia (so named because of their 3-legged appear-ance) into coats is aided by several other accessory proteins, such as AP2, AP180 and amphiphysin. The coats increase the curvature of the budding membrane until it forms a coated vesicle-like structure. Another protein, called dynamin, is at least partly responsible for the final pinching-off of membrane to convert the coated pits into coated vesicles. The coats are then removed by an ATPase, Hsc70, with another protein called auxilin serving as a co-factor. Other proteins, such as synaptojanin, are also important for vesicle uncoating. Several lines of evidence indicate that the protein synapsin, which reversibly binds to synaptic vesicles, may cross-link newly formed vesicles to the cytoskeleton to keep the vesicles tethered within the reserve pool. Mobilization of these reserve pool vesicles is caused by phos-phorylation of synapsin by proteins kinases (Chapter 7), which allows synapsin to dissociate from the vesicles, thus freeing the vesicles to make their way to the plasma membrane. In summary, a complex cascade of proteins, acting in a defined temporal and spatial order, allows neurons to secrete transmitters. Although the detailed mechanisms responsible for transmitter secretion are not completely clear, rapid progress is being made toward this goal. Neurotransmitter Receptors The generation of postsynaptic electrical signals is also understood in con-siderable depth. Such studies began in 1907, when the British physiologist John N. Langley introduced the concept of receptor molecules to explain the specific and potent actions of certain chemicals on muscle and nerve cells. Much subsequent work has shown that receptor molecules do indeed account for the ability of neurotransmitters, hormones, and drugs to alter the Synaptic Transmission 113 114 Chapter Five Endosome Docking Budding Uncoating Synapsin Dynamin Hsc 70 Auxilin Synaptojanin Priming Fusion Ca2+ Budding SNAREs NSF SNAPs (C) (D) Synaptotagmin Clathrin triskelion Clathrin (1) Vesicle docks (2) SNARE complexes form to pull membranes together (3) Entering Ca2+ binds to synaptotagmin (4) Ca2+-bound synaptotagmin catalyzes membrane fusion Syntaxin Synaptobrevin SNAP-25 Vesicle Ca2+ channel Synaptotagmin Ca2+ Presynaptic plasma membrane Synaptic vesicle membrane Syntaxin Synaptobrevin SNAP-25 (A) Clathrin coat (B) Synaptotagmin Figure 5.14 Molecular mechanisms of neurotransmitter release. (A) Struc-ture of the SNARE complex. The vesicular SNARE, synaptobrevin (blue), forms a helical complex with the plasma membrane SNAREs syntaxin (red) and SNAP-25 (green). Also shown is the structure of synaptotagmin, a vesic-ular Ca2+-binding protein. (B) A model for Ca2+-triggered vesicle fusion. SNARE proteins on the synaptic vesicle and plasma membranes form a com-plex (as in A) that brings together the two membranes. Ca2+ then binds to synaptotagmin, causing the cytoplasmic region of this protein to insert into the plasma membrane, bind to SNAREs and catalyze membrane fusion. (C) Roles of presynaptic proteins in synaptic vesicle cycling. (D) Individual clathrin triskelia (left) assemble together to form membrane coats (right) involved in membrane budding during endocytosis. (A after Sutton et al., 1998; C after Sudhof, 1995; D after Marsh and McMahon, 2001.) Synaptic Transmission 115 Box C Toxins That Affect Transmitter Release Several important insights about the molecular basis of neurotransmitter secretion have come from analyzing the actions of a series of biological toxins produced by a fascinating variety of organisms. One family of such agents is the clostridial toxins responsible for bot-ulism and tetanus (see Box B). Clever and patient biochemical work has shown that these toxins are highly specific pro-teases that cleave presynaptic SNARE proteins (see figure). Tetanus toxin and botulinum toxin (types B, D, F, and G) specifically cleave the vesicle SNARE protein, synaptobrevin. Other botulinum toxins are proteases that cleave syntaxin (type C) and SNAP-25 (types A and E), SNARE proteins found on the presynap-tic plasma membrane. Destruction of these presynaptic proteins is the basis for the actions of the toxins on neurotrans-mitter release. The evidence described in the text also implies that these three syn-aptic SNARE proteins are somehow important in the process of vesicle–plasma membrane fusion. Another toxin that targets neurotrans-mitter release is α-latrotoxin, a protein found in the venom of the female black widow spider. Application of this mole-cule to neuromuscular synapses causes a massive discharge of synaptic vesicles, even when Ca2+ is absent from the extra-cellular medium. While it is not yet clear how this toxin triggers Ca2+-independent exocytosis, α-latrotoxin binds to two dif-ferent types of presynaptic proteins that may mediate its actions. One group of binding partners for α-latrotoxin is the neurexins, a group of integral membrane proteins found in presynaptic terminals (see Figure 5.13). Several lines of evi-dence implicate binding to neurexins in at least some of the actions of α-latro-toxin. Because the neurexins bind to synaptotagmin, a vesicular Ca2+-binding protein that is known to be important in exocytosis, this interaction may allow α-latrotoxin to bypass the usual Ca2+ requirement for triggering vesicle fusion. Another type of presynaptic protein that can bind to α-latrotoxin is called CL1 (based on its previous names, Ca2+-inde-pendent receptor for latrotoxin and lat-rophilin-1). CL1 is a relative of the G-pro-tein-coupled receptors that mediate the actions of neurotransmitters and other extracellular chemical signals (see Chap-ter 7). Thus, the binding of α-latrotoxin to CL1 is thought to activate an intracel-lular signal transduction cascade that may be involved in the Ca2+-indepen-dent actions of α-latrotoxin. While more work is needed to establish the roles of neurexins and CL1 in the actions of α-latrotoxin definitively, effects on these two proteins probably account for the potent presynaptic actions of this toxin. Still other toxins produced by snakes, snails, spiders, and other predatory ani-mals are known to affect transmitter release, but their sites of action have yet to be identified. Based on the precedents described here, it is likely that these bio-logical poisons will continue to provide valuable tools for elucidating the molec-ular basis of neurotransmitter release, just as they will continue to enable the predators to feast on their prey. References KRASNOPEROV, V. G. AND 10 OTHERS (1997) α-Latrotoxin stimulates exocytosis by the inter-action with a neuronal G-protein-coupled receptor. Neuron 18: 925–937. MONTECUCCO, C. AND G. SCHIAVO (1994) Mechanism of action of tetanus and botu-linum neurotoxins. Mol. Microbiol. 13: 1–8. SCHIAVO, G., M. MATTEOLI AND C. MONTE-CUCCO (2000) Neurotoxins affecting neuro-exocytosis. Physiol. Rev. 80: 717–766. SUGITA, S., M. KHVOCHTEV AND T. C. SUDHOF (1999) Neurexins are functional α-latrotoxin receptors. Neuron 22: 489–496. BoTX−G BoTX−D BoTX−F BoTX−A BoTX−C BoTX−E BoTX−B TeTX Syntaxin Synaptobrevin SNAP-25 Presynaptic plasma membrane Synaptic vesicle membrane Cleavage of SNARE proteins by clostridial toxins. Indicated are the sites of proteolysis by tetanus toxin (TeTX) and various types of botulinum toxin (BoTX). (After Sutton et al., 1998.) 116 Chapter Five functional properties of neurons. While it has been clear since Langley’s day that receptors are important for synaptic transmission, their identity and detailed mechanism of action remained a mystery until quite recently. It is now known that neurotransmitter receptors are proteins embedded in the plasma membrane of postsynaptic cells. Domains of receptor molecules that extend into the synaptic cleft bind neurotransmitters that are released into this space by the presynaptic neuron. The binding of neurotransmitters, either directly or indirectly, causes ion channels in the postsynaptic mem-brane to open or close. Typically, the resulting ion fluxes change the mem-brane potential of the postsynaptic cell, thus mediating the transfer of infor-mation across the synapse. Postsynaptic Membrane Permeability Changes during Synaptic Transmission Just as studies of the neuromuscular synapse paved the way for understand-ing neurotransmitter release mechanisms, this peripheral synapse has been equally valuable for understanding the mechanisms that allow neurotrans-mitter receptors to generate postsynaptic signals. The binding of ACh to post-synaptic receptors opens ion channels in the muscle fiber membrane. This effect can be demonstrated directly by using the patch clamp method (see Box A in Chapter 4) to measure the minute postsynaptic currents that flow when two molecules of individual ACh bind to receptors, as Erwin Neher and Bert Sakmann first did in 1976. Exposure of the extracellular surface of a patch of postsynaptic membrane to ACh causes single-channel currents to flow for a few milliseconds (Figure 5.15A). This shows that ACh binding to its receptors opens ligand-gated ion channels, much in the way that changes in membrane potential open voltage-gated ion channels (Chapter 4). The electrical actions of ACh are greatly multiplied when an action poten-tial in a presynaptic motor neuron causes the release of millions of molecules of ACh into the synaptic cleft. In this more physiological case, the transmit-ter molecules bind to many thousands of ACh receptors packed in a dense array on the postsynaptic membrane, transiently opening a very large num-ber of postsynaptic ion channels. Although individual ACh receptors only open briefly, (Figure 5.15B1), the opening of a large number of channels is synchronized by the brief duration during which ACh is secreted from pre-synaptic terminals (Figure 5.15B2,3). The macroscopic current resulting from the summed opening of many ion channels is called the end plate current, or EPC. Because the current flowing during the EPC is normally inward, it causes the postsynaptic membrane potential to depolarize. This depolarizing change in potential is the EPP (Figure 5.15C), which typically triggers a post-synaptic action potential by opening voltage-gated Na+ and K+ channels (see Figure 5.6B). The identity of the ions that flow during the EPC can be determined via the same approaches used to identify the roles of Na+ and K+ fluxes in the currents underlying action potentials (Chapter 3). Key to such an analysis is identifying the membrane potential at which no current flows during trans-mitter action. When the potential of the postsynaptic muscle cell is controlled by the voltage clamp method (Figure 5.16A), the magnitude of the membrane potential clearly affects the amplitude and polarity of EPCs (Figure 5.16B). Thus, when the postsynaptic membrane potential is made more negative than the resting potential, the amplitude of the EPC becomes larger, whereas this current is reduced when the membrane potential is made more positive. At approximately 0 mV, no EPC is detected, and at even more positive poten-tials, the current reverses its polarity, becoming outward rather than inward (Figure 5.16C). The potential where the EPC reverses, about 0 mV in the case of the neuromuscular junction, is called the reversal potential. As was the case for currents flowing through voltage-gated ion channels (see Chapter 3), the magnitude of the EPC at any membrane potential is given by the product of the ionic conductance activated by ACh (gACh) and the electrochemical driving force on the ions flowing through ligand-gated channels. Thus, the value of the EPC is given by the relationship EPC = gACh(Vm – Erev) where Erev is the reversal potential for the EPC. This relationship predicts that the EPC will be an inward current at potentials more negative than Erev because the electrochemical driving force, Vm – Erev, is a negative number. Further, the EPC will become smaller at potentials approaching Erev because the driving force is reduced. At potentials more positive than Erev, the EPC is outward because the driving force is reversed in direction (that is, positive). Because the channels opened by ACh are largely insensitive to membrane voltage, gACh will depend only on the number of channels opened by ACh, which depends in turn on the concentration of ACh in the synaptic cleft. Synaptic Transmission 117 2 µM Acetylcholine (ACh) I (pA) 0 2 4 6 8 10 Time (ms) 12 2 0 Channel closed Channel closed Channel open Channel open Channel open 0 0 0 0 600,000 0 20 0 2 4 200,000 10 300,000 Micropipette (A) Patch clamp measurement of single ACh receptor current (1) SINGLE OPEN CHANNEL (B) Currents produced by: Outside-out membrane patch ACh receptor ACh Na+ 0 2 –2 4 6 8 10 12 14 Time (ms) (3) ALL CHANNELS OPEN 1 Number of open channels Number of open channels Number of open channels (2) FEW OPEN CHANNELS Membranre current (pA) −90 −70 −100 −80 0 2 4 6 8 10 12 14 –2 (C) Postsynaptic potential change (EPP) produced by EPC Time (ms) Membrane potential (mV) ACh release by stimulating motor neuron Channel closed 2 Figure 5.15 Activation of ACh receptors at neuromuscular syn-apses. (A) Outside-out patch clamp measurement of single ACh receptor currents from a patch of membrane removed from the postsynaptic muscle cell. When ACh is applied to the extracellu-lar surface of the membrane clamped at negative voltages, the repeated brief opening of a single channel can be seen as down-ward deflections corresponding to inward current (i.e., positive ions flowing into the cell). (B) Synchronized opening of many ACh-activated channels at a synapse being voltage-clamped at negative voltages. (1) If a single channel is examined during the release of ACh from the presynaptic terminal, the channel opens transiently. (2) If a number of channels are examined together, ACh release opens the channels almost synchronously. (3) The opening of a very large number of post-synaptic channels produces a macroscopic EPC. (C) In a normal muscle cell (i.e., not being voltage-clamped), the inward EPC depolarizes the postsynaptic muscle cell, giving rise to an EPP. Typically, this depolarization generates an action poten-tial (not shown). 118 Chapter Five Thus, the magnitude and polarity of the postsynaptic membrane potential determines the direction and amplitude of the EPC solely by altering the dri-ving force on ions flowing through the receptor channels opened by ACh. When Vm is at the reversal potential, Vm – Erev is equal to 0 and there is no net driving force on the ions that can permeate the receptor-activated chan-nel. As a result, the identity of the ions that flow during the EPC can be deduced by observing how the reversal potential of the EPC compares to the equilibrium potential for various ion species (Figure 5.17). For example, if ACh were to open an ion channel permeable only to K+, then the reversal (B) Effect of membrane voltage on postsynaptic end plate currents 4 2 0 0 200 100 −100 −200 −300 6 (C) Postsynaptic membrane potential (mV) 100 200 −100 0 −200 −300 −110 −60 +70 0 EPC amplitude (nA) EPC (nA) Time (ms) 4 2 0 6 4 2 0 6 4 2 0 6 EK ECl ENa (A) Scheme for voltage clamping postsynaptic muscle fiber Postsynaptic muscle fiber Presynaptic terminals Axon of presynaptic motor neuron Voltage clamp amplifier Voltage-measuring electrode Current-passing electrode −110 mV Stimulate −110 −60 +70 0 −110 −60 +70 0 Reversal potential −60 mV 0 mV +70 mV Stimulate presynaptic axon Stimulate presynaptic axon Stimulate presynaptic axon Stimulate presynaptic axon (D) Lower external [Na+] shifts reversal potential to left (E) Higher external [K+] shifts reversal potential to right Figure 5.16 The influence of the postsynaptic membrane potential on end plate currents. (A) A postsynaptic muscle fiber is voltage clamped using two electrodes, while the presynaptic neuron is electri-cally stimulated to cause the release of ACh from presynaptic termi-nals. This experimental arrangement allows the recording of macro-scopic EPCs produced by ACh. (B) Amplitude and time course of EPCs generated by stimulating the presynaptic motor neuron while the postsynaptic cell is voltage clamped at four different membrane potentials. (C) The relationship between the peak amplitude of EPCs and postsynaptic membrane potential is nearly linear, with a reversal potential (the voltage at which the direction of the current changes from inward to outward) close to 0 mV. Also indicated on this graph are the equilibrium potentials of Na+, K+, and Cl– ions. (D) Lowering the external Na+ concentration causes EPCs to reverse at more nega-tive potentials. (E) Raising the external K+ concentration makes the reversal potential more positive. (After Takeuchi and Takeuchi, 1960.) potential of the EPC would be at the equilibrium potential for K+, which for a muscle cell is close to –100 mV (Figure 5.17A). If the ACh-activated chan-nels were permeable only to Na+, then the reversal potential of the current would be approximately +70 mV, the Na+ equilibrium potential of muscle cells (Figure 5.17B); if these channels were permeable only to Cl–, then the reversal potential would be approximately –50 mV (Figure 5.17C). By this reasoning, ACh-activated channels cannot be permeable to only one of these ions, because the reversal potential of the EPC is not near the equilibrium potential for any of them (see Figure 5.16C). However, if these channels were permeable to both Na+ and K+, then the reversal potential of the EPC would be between +70 mV and –100 mV (Figure 5.17D). The fact that EPCs reverse at approximately 0 mV is therefore consistent with the idea that ACh-activated ion channels are almost equally permeable to both Na+ and K+. This was tested in 1960, by the husband and wife team of Akira and Noriko Takeuchi, by altering the extracellular concentration of these two ions. As predicted, the magnitude and reversal potential of the EPC was changed by altering the concentration gradient of each ion. Lower-ing the external Na+ concentration, which makes ENa more negative, pro-duces a negative shift in Erev (Figure 5.16D), whereas elevating external K+ concentration, which makes EK more positive, causes Erev to shift to a more positive potential (Figure 5.16E). Such experiments confirm that the ACh-activated ion channels are in fact permeable to both Na+ and K+. Even though the channels opened by the binding of ACh to its receptors are permeable to both Na+ and K+, at the resting membrane potential the EPC is generated primarily by Na+ influx (Figure 5.18). If the membrane potential is kept at EK, the EPC arises entirely from an influx of Na+ because at this potential there is no driving force on K+ (Figure 5.18A). At the usual muscle fiber resting membrane potential of –90 mV, there is a small driving force on K+, but a much greater one on Na+. Thus, during the EPC, much more Na+ flows into the muscle cell than K+ flows out (Figure 5.18B); it is the net influx of positively charged Na+ that constitutes the inward current mea-sured as the EPC. At the reversal potential of about 0 mV, Na+ influx and K+ efflux are exactly balanced, so no current flows during the opening of chan-nels by ACh binding (Figure 5.18C). At potentials more positive than Erev the balance reverses; for example, at ENa there is no influx of Na+ and a large efflux of K+ because of the large driving force on Na+ (Figure 5.18D). Even more positive potentials cause efflux of both Na+ and K+ and produce an even larger outward EPC. Were it possible to measure the EPP at the same time as the EPC (of course, the voltage clamp technique prevents this by keeping membrane potential constant), the EPP would be seen to vary in parallel with the ampli-tude and polarity of the EPC (Figures 5.18E,F). At the usual postsynaptic resting membrane potential of –90 mV, the large inward EPC causes the postsynaptic membrane potential to become more depolarized (see Figure Synaptic Transmission 119 Figure 5.17 The effect of ion channel selectivity on the reversal potential. Voltage clamping a postsynaptic cell while activating presynaptic neurotransmitter release reveals the identity of the ions permeating the postsynaptic receptors being acti-vated. (A) The activation of postsynaptic channels permeable only to K+ results in currents reversing at EK, near –100 mV. (B) The activation of postsynaptic Na+ chan-nels results in currents reversing at ENa, near +70 mV. (C) Cl–-selective currents reverse at ECl, near –50 mV. (D) Ligand-gated channels that are about equally per-meable to both K+ and Na+ show a reversal potential near 0 mV. (A) −150 −100 100 −50 50 0 Membrane potential Only K+ selective channel open 100 200 300 −100 0 0 0 0 −200 −300 EPC amplitude (nA) (B) Only Na+ selective channel open −150 −100 100 −50 50 0 Membrane potential 100 200 300 −100 −200 −300 EPC amplitude (nA) Only Cl− selective channel open (C) −150 −100 100 −50 50 0 Membrane potential 100 200 300 −100 −200 −300 EPC amplitude (nA) (D) Cation non-selective channel open −150 −100 100 −50 50 0 Membrane potential 100 200 300 −100 −200 −300 EPC amplitude (nA) K+ efflux K+ influx Erev = EK Erev = ENa Erev = ECl Erev = 0 Na+ efflux Na+ influx Cl− influx Cl− efflux Cation efflux Cation influx 120 Chapter Five Figure 5.18 Na+ and K+ movements during EPCs and EPPs. (A–D) Each of the postsynaptic potentials (Vpost) indi-cated at the left results in different rela-tive fluxes of net Na+ and K+ (ion fluxes). These ion fluxes determine the amplitude and polarity of the EPCs, which in turn determine the EPPs. Note that at about 0 mV the Na+ flux is exactly balanced by an opposite K+ flux, resulting in no net current flow, and hence no change in the membrane potential. (E) EPCs are inward currents at potentials more negative than Erev and outward currents at potentials more positive than Erev. (F) EPPs depo-larize the postsynaptic cell at potentials more negative than Erev. At potentials more positive than Erev, EPPs hyperpo-larize the cell. 5.18F). However, at 0 mV, the EPP reverses its polarity, and at more positive potentials, the EPP is hyperpolarizing. Thus, the polarity and magnitude of the EPC depend on the electrochemical driving force, which in turn deter-mines the polarity and magnitude of the EPP. EPPs will depolarize when the membrane potential is more negative than Erev, and hyperpolarize when the membrane potential is more positive than Erev. The general rule, then, is that EPPs EPCs NET ION FLUXES Postsynaptic membrane potential −100 −90 +70 0 Postsynaptic membrane potential EPC peak amplitude (nA) EPP peak amplitude (mV) 0 Postsynaptic membrane potential −100 −90 +70 Na+ Outside cell −90 mV Na+ 0 mV (Erev) +70 mV (ENa) K+ ACh- activated channel ACh Inside cell EK ENa EK ENa Na+ K+ K+ −100 mV (EK) (A) (B) (C) (D) (E) (F) Outward Inward Depolarizing Hyper− polarizing the action of a transmitter drives the postsynaptic membrane potential toward Erev for the particular ion channels being activated. Although this discussion has focused on the neuromuscular junction, sim-ilar mechanisms generate postsynaptic responses at all chemical synapses. The general principle is that transmitter binding to postsynaptic receptors produces a postsynaptic conductance change as ion channels are opened (or sometimes closed). The postsynaptic conductance is increased if—as at the neuromuscular junction—channels are opened, and decreased if channels are closed. This conductance change typically generates an electrical current, the postsynaptic current (PSC), which in turn changes the postsynaptic mem-brane potential to produce a postsynaptic potential (PSP). As in the specific case of the EPP at the neuromuscular junction, PSPs are depolarizing if their reversal potential is more positive than the postsynaptic membrane potential and hyperpolarizing if their reversal potential is more negative. The conductance changes and the PSPs that typically accompany them are the ultimate outcome of most chemical synaptic transmission, conclud-ing a sequence of electrical and chemical events that begins with the inva-sion of an action potential into the terminals of a presynaptic neuron. In many ways, the events that produce PSPs at synapses are similar to those that generate action potentials in axons; in both cases, conductance changes produced by ion channels lead to ionic current flow that changes the mem-brane potential (see Figure 5.18). Excitatory and Inhibitory Postsynaptic Potentials PSPs ultimately alter the probability that an action potential will be produced in the postsynaptic cell. At the neuromuscular junction, synaptic action increases the probability that an action potential will occur in the postsynap-tic muscle cell; indeed, the large amplitude of the EPP ensures that an action potential always is triggered. At many other synapses, PSPs similarly increase the probability of firing a postsynaptic action potential. However, still other synapses actually decrease the probability that the postsynaptic cell will generate an action potential. PSPs are called excitatory (or EPSPs) if they increase the likelihood of a postsynaptic action potential occurring, and inhibitory (or IPSPs) if they decrease this likelihood. Given that most neu-rons receive inputs from both excitatory and inhibitory synapses, it is impor-tant to understand more precisely the mechanisms that determine whether a particular synapse excites or inhibits its postsynaptic partner. The principles of excitation just described for the neuromuscular junction are pertinent to all excitatory synapses. The principles of postsynaptic inhi-bition are much the same as for excitation, and are also quite general. In both cases, neurotransmitters binding to receptors open or close ion channels in the postsynaptic cell. Whether a postsynaptic response is an EPSP or an IPSP depends on the type of channel that is coupled to the receptor, and on the concentration of permeant ions inside and outside the cell. In fact, the only distinction between postsynaptic excitation and inhibition is the reversal potential of the PSP in relation to the threshold voltage for generating action potentials in the postsynaptic cell. Consider, for example, a neuronal synapse that uses glutamate as the transmitter. Many such synapses have receptors that, like the ACh receptors at neuromuscular synapses, open ion channels that are nonselectively per-meable to cations (see Chapter 6). When these glutamate receptors are acti-vated, both Na+ and K+ flow across the postsynaptic membrane, yielding an Erev of approximately 0 mV for the resulting postsynaptic current. If the rest-Synaptic Transmission 121 122 Chapter Five ing potential of the postsynaptic neuron is –60 mV, the resulting EPSP will depolarize by bringing the postsynaptic membrane potential toward 0 mV. For the hypothetical neuron shown in Figure 5.19A, the action potential threshold voltage is –40 mV. Thus, a glutamate-induced EPSP will increase the probability that this neuron produces an action potential, defining the synapse as excitatory. As an example of inhibitory postsynaptic action, consider a neuronal syn-apse that uses GABA as its transmitter. At such synapses, the GABA recep-tors typically open channels that are selectively permeable to Cl– and the action of GABA causes Cl– to flow across the postsynaptic membrane. Con-sider a case where ECl is –70 mV, as is typical for many neurons, so that the postsynaptic resting potential of –60 mV is less negative than ECl. The result-ing positive electrochemical driving force (Vm – Erev) will cause negatively charged Cl– to flow into the cell and produce a hyperpolarizing IPSP (Figure 5.19B). This hyperpolarizing IPSP will take the postsynaptic membrane away from the action potential threshold of –40 mV, clearly inhibiting the postsynaptic cell. Surprisingly, inhibitory synapses need not produce hyperpolarizing IPSPs. For instance, if ECl were –50 mV instead of –70 mV, then the negative electrochemical driving force would cause Cl– to flow out of the cell and pro-duce a depolarizing IPSP (Figure 5.19C). However, the synapse would still be inhibitory: Given that the reversal potential of the IPSP still is more nega-tive than the action potential threshold (–40 mV), the depolarizing IPSP would inhibit because the postsynaptic membrane potential would be kept more negative than the threshold for action potential initiation. Another way to think about this peculiar situation is that if another excitatory input onto this neuron brought the cell’s membrane potential to –41 mV, just below threshold for firing an action potential, the IPSP would then hyperpolarize the membrane potential toward –50 mV, bringing the potential away from the action potential threshold. Thus, while EPSPs depolarize the postsynap-tic cell, IPSPs can hyperpolarize or depolarize; indeed, an inhibitory conduc-tance change may produce no potential change at all and still exert an inhibitory effect by making it more difficult for an EPSP to evoke an action potential in the postsynaptic cell. Although the particulars of postsynaptic action can be complex, a simple rule distinguishes postsynaptic excitation from inhibition: An EPSP has a reversal potential more positive than the action potential threshold, whereas Threshold mV Time (ms) −60 −40 −50 −70 −110 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 +50 0 Activate GABA synapse Activate GABA synapse Erev Erev Erev Vrest ENa (A) (B) (C) (D) EK Activate glutamate synapse Action potential EPSP IPSP IPSP Erev > threshold = excitatory Erev < threshold = inhibitory Figure 5.19 Reversal potentials and threshold potentials determine postsyn-aptic excitation and inhibition. (A) If the reversal potential for a PSP (0 mV) is more positive than the action potential threshold (–40 mV), the effect of a trans-mitter is excitatory, and it generates EPSPs. (B) If the reversal potential for a PSP is more negative than the action potential threshold, the transmitter is inhibitory and generate IPSPs. (C) IPSPs can nonetheless depolarize the postsyn-aptic cell if their reversal potential is between the resting potential and the action potential threshold. (D) The gen-eral rule of postsynaptic action is: If the reversal potential is more positive than threshold, excitation results; inhibition occurs if the reversal potential is more negative than threshold. Figure 5.20 Summation of postsynap-tic potentials. (A) A microelectrode records the postsynaptic potentials pro-duced by the activity of two excitatory synapses (E1 and E2) and an inhibitory synapse (I). (B) Electrical responses to synaptic activation. Stimulating either excitatory synapse (E1 or E2) produces a subthreshold EPSP, whereas stimulating both synapses at the same time (E1 + E2) produces a suprathreshold EPSP that evokes a postsynaptic action poten-tial (shown in blue). Activation of the inhibitory synapse alone (I) results in a hyperpolarizing IPSP. Summing this IPSP (dashed red line) with the EPSP (dashed yellow line) produced by one excitatory synapse (E1 + I) reduces the amplitude of the EPSP (orange line), while summing it with the suprathresh-old EPSP produced by activating syn-apses E1 and E2 keeps the postsynaptic neuron below threshold, so that no action potential is evoked. an IPSP has a reversal potential more negative than threshold (Figure 5.19D). Intuitively, this rule can be understood by realizing that an EPSP will tend to depolarize the membrane potential so that it exceeds threshold, whereas an IPSP will always act to keep the membrane potential more negative than the threshold potential. Summation of Synaptic Potentials The PSPs produced at most synapses in the brain are much smaller than those at the neuromuscular junction; indeed, EPSPs produced by individual excitatory synapses may be only a fraction of a millivolt and are usually well below the threshold for generating postsynaptic action potentials. How, then, can such synapses transmit information if their PSPs are subthreshold? The answer is that neurons in the central nervous system are typically inner-vated by thousands of synapses, and the PSPs produced by each active syn-apse can sum together—in space and in time—to determine the behavior of the postsynaptic neuron. Consider the highly simplified case of a neuron that is innervated by two excitatory synapses, each generating a subthreshold EPSP, and an inhibitory synapse that produces an IPSP (Figure 5.20A). While activation of either one of the excitatory synapses alone (E1 or E2 in Figure 5.20B) produces a sub-Synaptic Transmission 123 Record Excitatory (E1) Inhibitory (I) Excitatory (E2) Cell body Dendrites (A) (B) Vrest Time (ms) −40 −60 −20 +20 0 EPSP (Synapse E1 or E2) Summed EPSPs (Synapses E1 + E2) IPSP (Synapse I) Threshold Postsynaptic membrane potential (mV) Summed EPSP + IPSP (Synapses E1 + I) Summed EPSPs + IPSP (Synapses E1 + I +E2) Postsynaptic membrane potential Axon 124 Chapter Five Figure 5.21 Events from neurotrans-mitter release to postsynaptic excitation or inhibition. Neurotransmitter release at all presynaptic terminals on a cell results in receptor binding, which causes the opening or closing of specific ion channels. The resulting conductance change causes current to flow, which may change the membrane potential. The postsynaptic cell sums (or inte-grates) all of the EPSPs and IPSPs, resulting in moment-to-moment control of action potential generation. threshold EPSP, activation of both excitatory synapses at about the same time causes the two EPSPs to sum together. If the sum of the two EPSPs (E1 + E2) depolarizes the postsynaptic neuron sufficiently to reach the threshold potential, a postsynaptic action potential results. Summation thus allows subthreshold EPSPs to influence action potential production. Likewise, an IPSP generated by an inhibitory synapse (I) can sum (algebraically speaking) with a subthreshold EPSP to reduce its amplitude (E1 + I) or can sum with suprathreshold EPSPs to prevent the postsynaptic neuron from reaching threshold (E1 + I + E2). In short, the summation of EPSPs and IPSPs by a postsynaptic neuron permits a neuron to integrate the electrical information provided by all the inhibitory and excitatory synapses acting on it at any moment. Whether the sum of active synaptic inputs results in the production of an action potential depends on the balance between excitation and inhibition. If the sum of all EPSPs and IPSPs results in a depolarization of sufficient amplitude to raise the membrane potential above threshold, then the postsynaptic cell will pro-duce an action potential. Conversely, if inhibition prevails, then the postsyn-aptic cell will remain silent. Normally, the balance between EPSPs and IPSPs changes continually over time, depending on the number of excitatory and inhibitory synapses active at a given moment and the magnitude of the cur-rent at each active synapse. Summation is therefore a neurotransmitter-induced tug-of-war between all excitatory and inhibitory postsynaptic cur-rents; the outcome of the contest determines whether or not a postsynaptic neuron fires an action potential and, thereby, becomes an active element in the neural circuits to which it belongs (Figure 5.21). Two Families of Postsynaptic Receptors The opening or closing of postsynaptic ion channels is accomplished in dif-ferent ways by two broad families of receptor proteins. The receptors in one family—called ionotropic receptors—are linked directly to ion channels (the Greek tropos means to move in response to a stimulus). These receptors con-tain two functional domains: an extracellular site that binds neurotransmit-ters, and a membrane-spanning domain that forms an ion channel (Figure 5.22A). Thus ionotropic receptors combine transmitter-binding and channel functions into a single molecular entity (they are also called ligand-gated ion channels to reflect this concatenation). Such receptors are multimers made up of at least four or five individual protein subunits, each of which contributes to the pore of the ion channel. The second family of neurotransmitter receptors are the metabotropic receptors, so called because the eventual movement of ions through a chan-nel depends on one or more metabolic steps. These receptors do not have ion channels as part of their structure; instead, they affect channels by the activa-tion of intermediate molecules called G-proteins (Figure 5.22B). For this rea-son, metabotropic receptors are also called G-protein-coupled receptors. Metabotropic receptors are monomeric proteins with an extracellular domain that contains a neurotransmitter binding site and an intracellular domain that binds to G-proteins. Neurotransmitter binding to metabotropic receptors acti-vates G-proteins, which then dissociate from the receptor and interact directly with ion channels or bind to other effector proteins, such as enzymes, that make intracellular messengers that open or close ion channels. Thus, G-pro-teins can be thought of as transducers that couple neurotransmitter binding to the regulation of postsynaptic ion channels. The postsynaptic signaling events initiated by metabotropic receptors are taken up in detail in Chapter 7. Postsynaptic cells excited or inhibited Postsynaptic potential changes Conductance change causes current flow Ion channels open or close Receptor binding Neurotransmitter release Summation determines whether or not an action potential occurs These two families of postsynaptic receptors give rise to PSPs with very different time courses, producing postsynaptic actions that range from less than a millisecond to minutes, hours, or even days. Ionotropic receptors gen-erally mediate rapid postsynaptic effects. Examples are the EPP produced at neuromuscular synapses by ACh (see Figure 5.15), EPSPs produced at cer-tain glutamatergic synapses (Figure 5.19A), and IPSPs produced at certain GABAergic synapses (Figure 5.19B). In all three cases, the PSPs arise within a millisecond or two of an action potential invading the presynaptic terminal and last for only a few tens of milliseconds or less. In contrast, the activation of metabotropic receptors typically produces much slower responses, rang-ing from hundreds of milliseconds to minutes or even longer. The compara-tive slowness of metabotropic receptor actions reflects the fact that multiple proteins need to bind to each other sequentially in order to produce the final physiological response. Importantly, a given transmitter may activate both ionotropic and metabotropic receptors to produce both fast and slow PSPs at the same synapse. Perhaps the most important principle to keep in mind is that the response elicited at a given synapse depends upon the neurotransmitter released and the postsynaptic complement of receptors and associated channels. The mol-ecular mechanisms that allow neurotransmitters and their receptors to gen-erate synaptic responses are considered in the next chapter. Synaptic Transmission 125 Neurotransmitter binds Neurotransmitter Outside cell Inside cell Ions (A) Ligand-gated ion channels (B) G-protein-coupled receptors 1 Neurotransmitter binds Neurotrans-mitter Ions Ions flow across membrane G-protein is activated G-protein Receptor G-protein subunits or intracellular messengers modulate ion channels I n t r a c e l l u l a r m e s s e n g e r s β γ Effector protein α 3 3 1 2 α Channel opens 2 Ions flow across membrane 5 Ion channel opens 4 Figure 5.22 A neurotransmitter can affect the activity of a postsynaptic cell via two different types of receptor proteins: ionotropic or ligand-gated ion channels, and metabotropic or G-protein-coupled receptors. (A) Ligand-gated ion channels com-bine receptor and channel functions in a single protein complex. (B) Metabotropic receptors usually activate G-proteins, which modulate ion channels directly or indi-rectly through intracellular effector enzymes and second messengers. 126 Chapter Five Summary Synapses communicate the information carried by action potentials from one neuron to the next in neural circuits. The cellular mechanisms that underlie synaptic transmission are closely related to the mechanisms that generate other types of neuronal electrical signals, namely ion flow through membrane channels. In the case of electrical synapses, these channels are gap junctions; direct but passive flow of current through the gap junctions is the basis for transmission. In the case of chemical synapses, channels with smaller and more selective pores are activated by the binding of neurotrans-mitters to postsynaptic receptors after release from the presynaptic terminal. The large number of neurotransmitters in the nervous system can be divided into two broad classes: small-molecule transmitters and neuropeptides. Neu-rotransmitters are synthesized from defined precursors by regulated enzy-matic pathways, packaged into one of several types of synaptic vesicle, and released into the synaptic cleft in a Ca2+-dependent manner. Many synapses release more than one type of neurotransmitter, and multiple transmitters can even be packaged within the same synaptic vesicle. Transmitter agents are released presynaptically in units or quanta, reflecting their storage within synaptic vesicles. Vesicles discharge their contents into the synaptic cleft when the presynaptic depolarization generated by the invasion of an action potential opens voltage-gated calcium channels, allowing Ca2+ to enter the presynaptic terminal. How calcium triggers neurotransmitter release is not yet established, but synaptotagmin, SNAREs, and a number of other proteins found within the presynaptic terminal are clearly involved. Postsynaptic receptors are a diverse group of proteins that transduce bind-ing of neurotransmitters into electrical signals by opening or closing post-synaptic ion channels. The postsynaptic currents produced by the synchro-nous opening or closing of ion channels changes the conductance of the postsynaptic cell, thus increasing or decreasing its excitability. Conductance changes that increase the probability of firing an action potential are excita-tory, whereas those that decrease the probability of generating an action potential are inhibitory. Because postsynaptic neurons are usually innervated by many different inputs, the integrated effect of the conductance changes underlying all EPSPs and IPSPs produced in a postsynaptic cell at any moment determines whether or not the cell fires an action potential. Two broadly different families of neurotransmitter receptors have evolved to carry out the postsynaptic signaling actions of neurotransmitters. The post-synaptic effects of neurotransmitters are terminated by the degradation of the transmitter in the synaptic cleft, by transport of the transmitter back into cells, or by diffusion out of the synaptic cleft. Additional Reading Reviews AUGUSTINE, G. J. (2001) How does calcium trigger neurotransmitter release? Curr. Opin. Neurobiol. 11: 320–326. BENNETT, M. V. L. (2000) Electrical synapses, a personal perspective (or history). Brain Res. Rev. 32: 16–28. BRODSKY, F. M., C. Y. CHEN, C. KNUEHL, M. C. TOWLER AND D. E. WAKEHAM (2001) Biological basket weaving: Formation and function of clathrin-coated vesicles. Annu. Rev. Cell. Dev. Biol. 17: 517–568. BRUNGER, A. T. (2001) Structure of proteins involved in synaptic vesicle fusion in neurons. Annu. Rev. Biophys. Biomol. Struct. 30: 157–171. CARLSSON, A. (1987) Perspectives on the dis-covery of central monoaminergic neurotrans-mission. Annu. Rev. Neurosci. 10: 19–40. CHANGEUX, J.-P. (1993) Chemical signaling in the brain. Sci. Am. 269 (May): 58–62. EMSON, P. C. (1979) Peptides as neurotransmit-ter candidates in the CNS. Prog. Neurobiol. 13: 61–116. GALARRETA, M. AND S. HESTRIN (2001) Electri-cal synapses between GABA-releasing interneurons. Nature Rev. Neurosci. 2: 425–433. JAHN, R., T. LANG AND T. C. SÜDHOF (2003) Membrane fusion. Cell 112: 519–533. KUPFERMANN, I. (1991) Functional studies of cotransmission. Physiol. Rev. 71: 683–732. MARSH, M. AND H. T. MCMAHON (1999) The structural era of endocytosis. Science 285: 215–220. MURTHY, V. N. AND P. DE CAMILLI (2003) Cell biology of the presynaptic terminal. Annu. Rev. Neurosci. 26: 701–728. ROTHMAN, J. E. (1994) Mechanisms of intracel-lular protein transport. Nature 372: 55–63. SÜDHOF, T. C. (1995) The synaptic vesicle cycle: A cascade of protein-protein interactions. Nature 375: 645–653. TUCKER, W. C. AND E. R. CHAPMAN (2002) Role of synaptotagmin in Ca2+ triggered exocyto-sis. Biochem. J. 366: 1–13. Important Original Papers ADLER, E., M. ADLER, G. J. AUGUSTINE, M. P. CHARLTON AND S. N. DUFFY (1991) Alien intra-cellular calcium chelators attenuate neuro-transmitter release at the squid giant synapse. J. Neurosci. 11: 1496–1507. AUGUSTINE, G. J. AND R. ECKERT (1984) Diva-lent cations differentially support transmitter release at the squid giant synapse. J. Physiol. (Lond.) 346: 257–271. BOYD, I. A. AND A. R. MARTIN (1955) The end-plate potential in mammalian muscle. J. Phys-iol. (Lond.) 132: 74–91. CURTIS, D. R., J. W. PHILLIS AND J. C. WATKINS (1959) Chemical excitation of spinal neurons. Nature 183: 611–612. DALE, H. H., W. FELDBERG AND M. VOGT (1936) Release of acetylcholine at voluntary motor nerve endings. J. Physiol. 86: 353–380. DEL CASTILLO, J. AND B. KATZ (1954) Quantal components of the end plate potential. J. Physiol. (Lond.) 124: 560–573. FATT, P. AND B. KATZ (1951) An analysis of the end plate potential recorded with an intracel-lular electrode. J. Physiol. (Lond.) 115: 320–370. FATT, P. AND B. KATZ (1952) Spontaneous sub-threshold activity at motor nerve endings. J. Physiol. (Lond.) 117: 109–128. FURSHPAN, E. J. AND D. D. POTTER (1959) Trans-mission at the giant motor synapses of the crayfish. J. Physiol. (Lond.) 145: 289–325. GEPPERT, M. AND 6 OTHERS (1994) Synaptotag-min I: A major Ca2+ sensor for transmitter release at a central synapse. Cell 79: 717–727. GIBSON, J. R., M. BEIERLEIN AND B. W. CONNORS. (1999) Two networks of electrically coupled inhibtory neurons in neocortex. Nature 402: 75–79. HARRIS, B. A., J. D. ROBISHAW, S. M. MUMBY AND A. G. GILMAN (1985) Molecular cloning of complementary DNA for the alpha subunit of the G protein that stimulates adenylate cyclase. Science 229: 1274–1277. HEUSER, J. E. AND 5 OTHERS (1979) Synaptic vesicle exocytosis captured by quick freezing and correlated with quantal transmitter release. J. Cell Biol. 81: 275–300. HEUSER, J. E. AND T. S. REESE (1973) Evidence for recycling of synaptic vesicle membrane during transmitter release at the frog neuro-muscular junction. J. Cell Biol. 57: 315–344. HÖKFELT, T., O. JOHANSSON, A. LJUNGDAHL, J. M. LUNDBERG AND M. SCHULTZBERG (1980) Pep-tidergic neurons. Nature 284: 515–521. JONAS, P., J. BISCHOFBERGER AND J. SANDKUHLER (1998) Corelease of two fast neurotransmitters at a central synapse. Science 281: 419–424. LOEWI, O. (1921) Über humorale übertrag-barheit der herznervenwirkung. Pflügers Arch. 189: 239–242. MILEDI, R. (1973) Transmitter release induced by injection of calcium ions into nerve termi-nals. Proc. R. Soc. Lond. B 183: 421–425. NEHER, E. AND B. SAKMANN (1976) Single-channel currents recorded from membrane of denervated frog muscle fibres. Nature 260:799-802. REKLING, J. C., X. M. SHAO AND J. L. FELDMAN (2000) Electrical coupling and excitatory syn-aptic transmission between rhythmogenic res-piratory neurons in the preBotzinger complex. J. Neurosci. 20: RC113: 1–5. SMITH, S. J., J. BUCHANAN, L. R. OSSES, M. P. CHARLTON AND G. J. AUGUSTINE (1993) The spatial distribution of calcium signals in squid presynaptic terminals. J. Physiol. (Lond.) 472: 573–593. SOSSIN, W. S., A. SWEET-CORDERO AND R. H. SCHELLER (1990) Dale’s hypothesis revisited: Different neuropeptides derived from a com-mon prohormone are targeted to different processes. Proc. Natl. Acad. Sci. U.S.A. 87: 4845–4548. SUTTON, R. B., D. FASSHAUER, R. JAHN AND A. T. BRÜNGER (1998) Crystal structure of a SNARE complex involved in synaptic exocytosis at 2.4 Å resolution. Nature 395: 347–353. TAKEUCHI, A. AND N. TAKEUCHI (1960) One the permeability of end-plate membrane during the action of transmitter. J. Physiol. (Lond.) 154: 52–67. WICKMAN, K. AND 7 OTHERS (1994) Recombi-nant Gβγ activates the muscarinic-gated atrial potassium channel IKACh. Nature 368: 255– 257. Books BRADFORD, H. F. (1986) Chemical Neurobiology. New York: W. H. Freeman. COOPER, J. R., F. E. BLOOM AND R. H. ROTH (1991) The Biochemical Basis of Neuropharmacol-ogy. New York: Oxford University Press. HALL, Z. (1992) An Introduction to Molecular Neurobiology. Sunderland, MA: Sinauer Asso-ciates. KATZ, B. (1966) Nerve, Muscle, and Synapse. New York: McGraw-Hill. KATZ, B. (1969) The Release of Neural Transmit-ter Substances. Liverpool: Liverpool University Press. LLINÁS, R. R. (1999) The Squid Giant Synapse: A Model for Chemical Synaptic Transmission. Oxford: Oxford University Press. NICHOLLS, D. G. (1994) Proteins, Transmitters, and Synapses. Oxford: Blackwell. PETERS, A., S. L. PALAY AND H. DEF. WEBSTER (1991) The Fine Structure of the Nervous System: Neurons and their Supporting Cells. 3rd edition. Oxford: Oxford University Press. Synaptic Transmission 127 Overview For the most part, neurons in the human brain communicate with one another by releasing chemical messengers called neurotransmitters. A large number of neurotransmitters are now known and more remain to be discov-ered. Neurotransmitters evoke postsynaptic electrical responses by binding to members of a diverse group of proteins called neurotransmitter receptors. There are two major classes of receptors: those in which the receptor mole-cule is also an ion channel, and those in which the receptor and ion channel are separate molecules. The former are called ionotropic receptors or ligand-gated ion channels, and give rise to fast postsynaptic responses that typically last only a few milliseconds. The latter are called metabotropic receptors, and they produce slower postsynaptic effects that may endure much longer. Abnormalities in the function of neurotransmitter systems contribute to a wide range of neurological and psychiatric disorders. As a result, many neu-ropharmacological therapies are based on drugs that affect neurotransmitter release, binding, and/or removal. Categories of Neurotransmitters More than 100 different agents are known to serve as neurotransmitters. This large number of transmitters allows for tremendous diversity in chemical signaling between neurons. It is useful to separate this panoply of transmit-ters into two broad categories based simply on size (Figure 6.1). Neuropep-tides are relatively large transmitter molecules composed of 3 to 36 amino acids. Individual amino acids, such as glutamate and GABA, as well as the transmitters acetylcholine, serotonin, and histamine, are much smaller than neuropeptides and have therefore come to be called small-molecule neuro-transmitters. Within the category of small-molecule neurotransmitters, the biogenic amines (dopamine, norepinephrine, epinephrine, serotonin, and histamine) are often discussed separately because of their similar chemical properties and postsynaptic actions. The particulars of synthesis, packaging, release, and removal differ for each neurotransmitter (Table 6.1). This chap-ter will describe some of the main features of these transmitters and their postsynaptic receptors. Acetylcholine As mentioned in the previous chapter, acetylcholine (ACh) was the first sub-stance identified as a neurotransmitter. In addition to the action of ACh as the neurotransmitter at skeletal neuromuscular junctions (see Chapter 5), as well as the neuromuscular synapse between the vagus nerve and cardiac Chapter 6 129 Neurotransmitters and Their Receptors 130 Chapter Six Acetylcholine SMALL-MOLECULE NEUROTRANSMITTERS AMINO ACIDS PURINES PEPTIDE NEUROTRANSMITTERS (more than 100 peptides, usually 3−30 amino acids long) Example: Methionine enkephalin (Tyr–Gly–Gly–Phe–Met) Tyr Gly Gly Phe Met INDOLEAMINE IMIDAZOLEAMINE CH3 C O O CH2 CH2 (CH3)3N Glutamate OH HO CH2 Dopamine CH2 Aspartate GABA ATP NH3 OH OH HO CH2 Norepinephrine CH2 NH3 OH O− OH HO CH2 Epinephrine CH2 CH2 CH2 H C CH3 OH NH2 N HO CH2 Serotonin (5-HT) Histamine CH2 NH3 CH2 CH2 NH3 Glycine C H O H N H C C H O H N H C C O H N H C CH2 CH2 S CH3 C O H N H C C O HN N CH2 H3N + + + + + + + H3N + H C COO− COOH CH2 CH2 H3N + H C COO− COOH H H3N + H C COO− H3N + COO− CH2 CH2 CH2 CATECHOLAMINES BIOGENIC AMINES CH2 P O− O− O O P O− O O OH OH P O− O O H H NH2 O N N N N muscle fibers, ACh serves as a transmitter at synapses in the ganglia of the visceral motor system, and at a variety of sites within the central nervous system. Whereas a great deal is known about the function of cholinergic transmission at neuromuscular junctions and ganglionic synapses, the actions of ACh in the central nervous system are not as well understood. Acetylcholine is synthesized in nerve terminals from the precursors acetyl coenzyme A (acetyl CoA, which is synthesized from glucose) and choline, in a reaction catalyzed by choline acetyltransferase (CAT; Figure 6.2). Choline is present in plasma at a high concentration (about 10 mM) and is taken up into cholinergic neurons by a high-affinity Na+/choline transporter. After synthesis in the cytoplasm of the neuron, a vesicular ACh Neurotransmitters and Their Receptors 131 Figure 6.1 Examples of small-molecule and peptide neurotransmitters. Small-mol-ecule transmitters can be subdivided into acetylcholine, the amino acids, purines, and biogenic amines. The catcholamines, so named because they all share the cate-chol moiety (i.e., a hydroxylated benzene ring), make up a distinctive subgroup within the biogenic amines. Serotonin and histamine contain an indole ring and an imidazole ring, respectively. Size differences between the small-molecule neuro-transmitters and the peptide neurotransmitters are indicated by the space-filling models for glycine, norepinephrine, and methionine enkephalin. (Carbon atoms are black, nitrogen atoms blue, and oxygen atoms red.) ▲ TABLE 6.1 Functional Features of the Major Neurotransmitters Postsynaptic Rate-limiting Removal Type of Neurotransmitter effecta Precursor(s) step in synthesis mechanism vesicle ACh Excitatory Choline + CAT AChEase Small, clear acetyl CoA Glutamate Excitatory Glutamine Glutaminase Transporters Small, clear GABA Inhibitory Glutamate GAD Transporters Small, clear Glycine Inhibitory Serine Phosphoserine Transporters Small, clear Catecholamines Excitatory Tyrosine Tyrosine Transporters, Small dense-(epinephrine, hydroxylase MAO, COMT core, norepinephrine, or large dopamine) irregular dense-core Serotonin (5-HT) Excitatory Tryptophan Tryptophan Transporters, Large, hydroxylase MAO dense-core Histamine Excitatory Histidine Histidine Transporters Large, decarboxylase dense-core ATP Excitatory ADP Mitochondrial Hydrolysis to Small, clear oxidative phosphor-AMP and ylation; glycolysis adenosine Neuropeptides Excitatory Amino acids Synthesis and Proteases Large, and inhibitory (protein synthesis) transport dense-core Endocannabinoids Inhibits Membrane lipids Enzymatic Hydrolasis None inhibition modification of lipids by FAAH Nitric oxide Excitatory and Arginine Nitric oxide synthase Spontaneous None inhibitory oxidation aThe most common postsynaptic effect is indicated; the same transmitter can elicit postsynaptic excitation or inhibition depending on the nature of the ion channels affected by transmitter binding (see Chapter 7). 132 Chapter Six transporter loads approximately 10,000 molecules of ACh into each cholin-ergic vesicle. In contrast to most other small-molecule neurotransmitters, the postsynap-tic actions of ACh at many cholinergic synapses (the neuromuscular junction in particular) is not terminated by reuptake but by a powerful hydrolytic enzyme, acetylcholinesterase (AChE). This enzyme is concentrated in the synaptic cleft, ensuring a rapid decrease in ACh concentration after its release from the presynaptic terminal. AChE has a very high catalytic activity (about 5000 molecules of ACh per AChE molecule per second) and hydrolyzes ACh into acetate and choline. The choline produced by ACh hydrolysis is trans-ported back into nerve terminals and used to resynthesize ACh. Among the many interesting drugs that interact with cholinergic enzymes are the organophosphates. This group includes some potent chemical warfare agents. One such compound is the nerve gas “Sarin,” which was made notori-ous after a group of terrorists released this gas in Tokyo’s underground rail sys-tem. Organophosphates can be lethal because they inhibit AChE, causing ACh to accumulate at cholinergic synapses. This build-up of ACh depolarizes the postsynaptic cell and renders it refractory to subsequent ACh release, causing neuromuscular paralysis and other effects. The high sensitivity of insects to these AChE inhibitors has made organophosphates popular insecticides. Many of the postsynaptic actions of ACh are mediated by the nicotinic ACh receptor (nAChR), so named because the CNS stimulant, nicotine, also Acetyl CoA Acetylcholine Acetylcholine Acetylcholine receptors Na+/choline transporter Choline acetyl-transferase O + O + Choline + + Acetate Choline Choline Acetylcholinesterase Presynaptic terminal Postsynaptic cell CoA (CH3)3 N CH2 CH2 HO CH3 C S + (CH3)3 N CH2 CH2 CH3 O C (CH3)3 N CH2 CH2 HO Glucose Pyruvate CH3 OO− C Vesicular ACh transporter Figure 6.2 Acetylcholine metabolism in cholinergic nerve terminals. The syn-thesis of acetylcholine from choline and acetyl CoA requires choline acetyltrans-ferase. Acetyl CoA is derived from pyru-vate generated by glycolysis, while choline is transported into the terminals via a Na+-dependent transporter. Acetylcholine is loaded into synaptic vesicles via a vesicular transporter. After release, acetylcholine is rapidly metabo-lized by acetylcholinesterase, and choline is transported back into the terminal. Neurotransmitters and Their Receptors 133 Receptor Membrane 2 nm 3 nm 6.5 nm α α γ δ (A) (B) (C) (D) N C Outside cell Inside cell 3 nm ACh ACh α β γ α δ Figure 6.3 The structure of the nACh receptor/channel. (A) Each receptor sub-unit crosses the membrane four times. The membrane-spanning domain that lines the pore is shown in blue. (B) Five such subunits come together to form a complex structure containing 20 transmembrane domains that surround a central pore. (C) The openings at either end of the channel are very large—approximately 3 nm in diameter; even the narrowest region of the pore is approximately 0.6 nm in diame-ter. By comparison, the diameter of Na+ or K+ is less than 0.3 nm. (D) An electron micrograph of the nACh receptor, showing the actual position and size of the pro-tein with respect to the membrane. (D from Toyoshima and Unwin, 1990.) binds to these receptors. Nicotine consumption produces some degree of euphoria, relaxation, and eventually addiction (Box A), effects believed to be mediated in this case by nAChRs. Nicotinic receptors are the best-studied type of ionotropic neurotransmitter receptor. As described in Chapter 5, nAChRs are nonselective cation channels that generate exci-tatory postsynaptic responses. A number of biological toxins specifically bind to and block nicotinic receptors (Box B). The availability of these highly specific ligands—particularly a component of snake venom called α-bungarotoxin—has provided a valuable way to isolate and purify nAChRs. This pioneering work paved the way to cloning and sequenc-ing the genes encoding the various subunits of the nAChR. Based on these molecular studies, the nAChR is now known to be a large protein complex consisting of five subunits arranged around a cen-tral membrane-spanning pore (Figure 6.3). In the case of skeletal muscle AChRs, the receptor pentamer contains two α subunits, each of which binds one molecule of ACh. Because both ACh binding sites must be occupied for the channel to open, only relatively high concentrations of this neurotransmitter lead to channel activation. These subunits also bind other ligands, such as nicotine and α-bungarotoxin. At the neuromuscu-lar junction, the two α subunits are combined with up to four other types of subunit—β, γ, δ, ε—in the ratio 2α:β:ε:δ. Neuronal nAChRs typically differ from those of muscle in that they lack sensitivity to α-bungaro-134 Chapter Six toxin, and comprise only two receptor subunit types (α and β), which are present in a ratio of 3α:2β. In all cases, however, five individual subunits assemble to form a functional, cation-selective nACh receptor. Each subunit of the nAChR molecule contains four transmembrane domains that make up the ion channel portion of the receptor, and a long extracellular region that makes up the ACh-binding domain (Figure 6.3A). Unraveling the molecular structure of this region of the nACh receptor has provided insight into the mechanisms that allow ligand-gated ion channels to respond rapidly to neurotransmitters: The intimate association of the ACh binding sites with the pore of the channel presumably accounts for the rapid response to ACh (Figure 6.3B–D). Indeed, this general arrange-ment is characteristic of all of the ligand-gated ion channels at fast-acting synapses, as summarized in Figure 6.4. Thus, the nicotinic receptor has served as a paradigm for studies of other ligand-gated ion channels, at the same time leading to a much deeper appreciation of several neuromuscular diseases (Box C). Box A Addiction Drug addiction is a chronic, relapsing disease with obvious medical, social, and political consequences. Addiction (also called substance dependence) is a persistent disorder of brain function in which compulsive drug use occurs despite serious negative consequences for the afflicted individual. The diag-nostic manual of the American Psychi-atric Association defines addiction in terms of both physical dependence and psychological dependence (in which an individual continues the drug-taking behavior despite obviously maladaptive consequences). The range of substances that can generate this sort of dependence is wide; the primary agents of abuse at present are opioids, cocaine, ampheta-mines, marijuana, alcohol, and nicotine. Addiction to more “socially acceptable” agents such as alcohol and nicotine are sometimes regarded as less problem-atic, but in fact involve medical and behavioral consequences that are at least as great as for drugs of abuse that are considered more dangerous. Impor-tantly, the phenomenon of addiction is not limited to human behavior, but is demonstrable in laboratory animals. Most of these same agents are self-administered if primates, rodents, or other species are provided with the opportunity to do so. In addition to a compulsion to take the agent of abuse, a major feature of addiction for many drugs is a constella-tion of negative physiological and emo-tional features, loosely referred to as “withdrawal syndrome,” that occur when the drug is not taken. The signs and symptoms of withdrawal are differ-ent for each agent of abuse, but in gen-eral are characterized by effects oppo-site those of the positive experience induced by the drug itself. Consider, as an example, cocaine, a drug that was estimated to be in regular use by 5 to 6 million Americans during the decade of the 1990s, with about 600,000 regular users either addicted or at high risk for addiction. The positive effects of the drug smoked or inhaled as a powder in the form of the alkaloidal free base is a “high” that is nearly immediate but generally lasts only a few minutes, typi-cally leading to a desire for additional drug in as little as 10 minutes to half an hour. The “high” is described as a feel-ing of well-being, self-confidence, and satisfaction. Conversely, when the drug is not available, frequent users experi-ence depression, sleepiness, fatigue, drug-craving, and a general sense of malaise. Another aspect of addiction to cocaine or other agents is tolerance, defined as a reduction in the response to the drug upon repeated administra-tion. Tolerance occurs as a consequence of persistent use of a number of drugs but is particularly significant in drug addiction, since it progressively increases the dose needed to experience the desired effects. Although it is fair to say that the neu-robiology of addiction is incompletely understood, for cocaine and many other agents of abuse the addictive effects involve activation of dopamine receptors in critical brain regions involved in moti-vation and emotional reinforcement (see Chapter 28). The most important of these areas is the midbrain dopamine system, A second class of ACh receptors is activated by muscarine, a poisonous alkaloid found in some mushrooms (see Box B), and thus they are referred to as muscarinic ACh receptors (mAChRs). mAChRs are metabotropic and mediate most of the effects of ACh in brain. Several subtypes of mAChR are known (Figure 6.5). Muscarinic ACh receptors are highly expressed in the striatum and various other forebrain regions, where they exert an inhibitory influence on dopamine-mediated motor effects. These receptors are also found in the ganglia of the peripheral nervous system. Finally, they mediate peripheral cholinergic responses of autonomic effector organs—such as heart, smooth muscle, and exocrine glands—and are responsible for the inhibition of heart rate by the vagus nerve. Numerous drugs act as mACh receptor agonists or antagonists, but most of these do not discriminate between different types of muscarinic receptors and often produce side effects. Nevertheless, mACh blockers that are therapeutically useful include atropine (used to dilate the pupil), scopolamine (effective in preventing motion sickness), and ipratropium (useful in the treatment of asthma). Neurotransmitters and Their Receptors 135 especially its projections from the ven-tral-tegmental area to the nucleus acum-bens. Agents such as cocaine appear to act by raising dopamine levels in these areas, making this transmitter more available to receptors by interfering with re-uptake of synaptically released dopamine by the dopamine transporter. The reinforcement and motivation of drug-taking behaviors is thought to be related to the projections to the nucleus acumbens. The most common opioid drug of abuse is heroin. Heroin is a derivative of the opium poppy and is not legally available for clinical purposes in the United States. The number of heroin addicts in the United States is estimated to be between 750,000 and a million individuals. The positive feelings pro-duced by heroin, generally described as the “rush,” are often compared to the feeling of sexual orgasm and begin in less than a minute after intravenous injection. There is then a feeling of gen-eral well-being (referred to as “on the nod”) that lasts about an hour. The symptoms of withdrawal can be intense; these are restlessness, irritabil-ity, nausea, muscle pain, depression, sleeplessness, and a sense of anxiety and malaise. The reinforcing aspects of the drug entail the same dopaminergic circuitry in the ventral tegmental area and nucleus acumbens as does cocaine, although additional areas are certainly involved, particularly the sites of opioid receptors described in Chapter 9. Interestingly, addiction to heroin or any other agent is not an inevitable con-sequence of drug use, but depends criti-cally on the environment. For instance, returning veterans who were heroin addicts in Vietnam typically lost their addiction upon returning to the United States. Likewise, patients given other opioids (e.g., morphine) for painful con-ditions rarely become addicts. The treatment of any form of addic-tion is difficult and must be tailored to the circumstances of the individual. In addition to treating acute problems of withdrawal and “detoxification,” pat-terns of behavior must be changed that may take months or years. Addiction is thus a chronic disease state that requires continual monitoring during the life-time of susceptible individuals. References AMERICAN PSYCHIATRIC ASSOCIATION (1994) Diagnostic and Statistical Manual of Mental Disorders, 4thEdition (DSM IV). Washington, D.C. HYMAN, S. E. AND R. C. MALENKA (2001) Addiction and the brain: The neurobiology of compulsion and its persistence. Nature Rev. Neurosci. 2: 695–703. LAAKSO, A., A. R. MOHN, R. R. GAINETDINOV AND M. G. CARON (2002) Experimental genetic approaches to addiction. Neuron 36: 213–228. O’BRIEN, C. P. (2001) Goodman and Gilman’s The Pharmaceutical Basis of Therapeutics, 10th Edition. New York: McGraw-Hill, Chapter 24, pp. 621–642.. 136 Chapter Six Box B Neurotoxins that Act on Postsynaptic Receptors Poisonous plants and venomous animals are widespread in nature. The toxins they produce have been used for a vari-ety of purposes, including hunting, heal-ing, mind-altering, and, more recently, research. Many of these toxins have potent actions on the nervous system, often interfering with synaptic transmis-sion by targeting neurotransmitter recep-tors. The poisons found in some organ-isms contain a single type of toxin, whereas others contain a mixture of tens or even hundreds of toxins. Given the central role of ACh recep-tors in mediating muscle contraction at neuromuscular junctions in numerous species, it is not surprising that a large number of natural toxins interfere with transmission at this synapse. In fact, the classification of nicotinic and muscarinic ACh receptors is based on the sensitivity of these receptors to the toxic plant alka-loids nicotine and muscarine, which acti-vate nicotinic and muscarinic ACh recep-tors, respectively. Nicotine is derived from the dried leaves of the tobacco plant Nicotinia tabacum, and muscarine is from the poisonous red mushroom Amanita muscaria. Both toxins are stimulants that produce nausea, vomiting, mental confu-sion, and convulsions. Muscarine poi-soning can also lead to circulatory col-lapse, coma, and death. The poison α-bungarotoxin, one of many peptides that together make up the venom of the banded krait, Bungarus multicinctus (Figure A), blocks transmis-sion at neuromuscular junctions and is used by the snake to paralyze its prey. This 74-amino-acid toxin blocks neuro-muscular transmission by irreversibly binding to nicotinic ACh receptors, thus preventing ACh from opening postsyn-aptic ion channels. Paralysis ensues because skeletal muscles can no longer be activated by motor neurons. As a result of its specificity and its high affin-ity for nicotinic ACh receptors, α-bun-garotoxin has contributed greatly to understanding the ACh receptor mole-cule. Other snake toxins that block nico-tinic ACh receptors are cobra α-neuro-toxin and the sea snake peptide erabu-toxin. The same strategy used by these snakes to paralyze prey was adopted by South American Indians who used curare, a mixture of plant toxins from Chondodendron tomentosum, as an arrow-head poison to immobilize their quarry. Curare also blocks nicotinic ACh recep-tors; the active agent is the alkaloid δ-tubocurarine. Another interesting class of animal toxins that selectively block nicotinic ACh and other receptors includes the peptides produced by fish-hunting marine cone snails (Figure B). These col-orful snails kill small fish by “shooting” venomous darts into them. The venom contains hundreds of peptides, known as the conotoxins, many of which target proteins that are important in synaptic transmission. There are conotoxin pep-tides that block Ca2+ channels, Na+ chan-nels, glutamate receptors, and ACh (B) (C) (A) (A) The banded krait Bungarus multicinctus. (B) A marine cone snail (Conus sp.) uses ven-omous darts to kill a small fish. (C) Betel nuts, Areca catechu, growing in Malaysia. (A, Robert Zappalorti/Photo Researchers, Inc.; B, Zoya Maslak and Baldomera Olivera, Uni-versity of Utah; C, Fletcher Baylis/Photo Researchers, Inc.) Neurotransmitters and Their Receptors 137 Glutamate Glutamate is the most important transmitter in normal brain function. Nearly all excitatory neurons in the central nervous system are glutamater-gic, and it is estimated that over half of all brain synapses release this agent. Glutamate plays an especially important role in clinical neurology because elevated concentrations of extracellular glutamate, released as a result of neural injury, are toxic to neurons (Box D). Glutamate is a nonessential amino acid that does not cross the blood-brain barrier and therefore must be synthesized in neurons from local precursors. The most prevalent precursor for glutamate synthesis is glutamine, which is released by glial cells. Once released, glutamine is taken up into presynaptic receptors. The array of physiological responses produced by these peptides all serve to immobilize any prey unfortu-nate enough to encounter the cone snail. Many other organisms, including other mollusks, corals, worms and frogs, also utilize toxins containing specific blockers of ACh receptors. Other natural toxins have mind- or behavior-altering effects and in some cases have been used for thousands of years by shamans and, more recently, physicians. Two examples are plant alka-loid toxins that block muscarinic ACh receptors: atropine from deadly night-shade (belladonna), and scopolamine from henbane. Because these plants grow wild in many parts of the world, exposure is not unusual, and poisoning by either toxin can also be fatal. Another postsynaptic neurotoxin that, like nicotine, is used as a social drug is found in the seeds from the betel nut, Areca catechu (Figure C). Betel nut chew-ing, although unknown in the United States, is practiced by up to 25% of the population in India, Bangladesh, Ceylon, Malaysia, and the Philippines. Chewing these nuts produces a euphoria caused by arecoline, an alkaloid agonist of nico-tinic ACh receptors. Like nicotine, arecol-ine is an addictive central nervous sys-tem stimulant. Many other neurotoxins alter trans-mission at noncholinergic synapses. For example, amino acids found in certain mushrooms, algae, and seeds are potent glutamate receptor agonists. The excito-toxic amino acids kainate, from the red alga Digenea simplex, and quisqualate, from the seed of Quisqualis indica, are used to distinguish two families of non-NMDA glutamate receptors (see text). Other neurotoxic amino acid activators of glutamate receptors include ibotenic acid and acromelic acid, both found in mushrooms, and domoate, which occurs in algae, seaweed, and mussels. Another large group of peptide neurotoxins blocks glutamate receptors. These include the α-agatoxins from the funnel web spider, NSTX-3 from the orb weaver spider, jorotoxin from the Joro spider, and β-philanthotoxin from wasp venom, as well as many cone snail toxins. All the toxins discussed so far target excitatory synapses. The inhibitory GABA and glycine receptors, however, have not been overlooked by the exigen-cies of survival. Strychnine, an alkaloid extracted from the seeds of Strychnos nux-vomica, is the only drug known to have specific actions on transmission at glycinergic synapses. Because the toxin blocks glycine receptors, strychnine poi-soning causes overactivity in the spinal cord and brainstem, leading to seizures. Strychnine has long been used commer-cially as a poison for rodents, although alternatives such as the anticoagulant coumadin are now more popular because they are safer for humans. Neu-rotoxins that block GABAA receptors include plant alkaloids such as bicu-culline from Dutchman’s breeches and picrotoxin from Anamerta cocculus. Dield-rin, a commercial insecticide, also blocks these receptors. These agents are, like strychnine, powerful central nervous system stimulants. Muscimol, a mush-room toxin that is a powerful depressant as well as a hallucinogen, activates GABAA receptors. A synthetic analogue of GABA, baclofen, is a GABAB agonist that reduces EPSPs in some brainstem neurons and is used clinically to reduce the frequency and severity of muscle spasms. Chemical warfare between species has thus given rise to a staggering array of molecules that target synapses throughout the nervous system. Although these toxins are designed to defeat normal synaptic transmission, they have also provided a set of power-ful tools to understand postsynaptic mechanisms. References ADAMS, M. E. AND B. M. OLIVERA (1994) Neu-rotoxins: Overview of an emerging research technology. TINS 17: 151–155. HUCHO, F. AND Y. OVCHINNIKOV (1990) Toxins as Tools in Neurochemistry. Berlin: Walter de Gruyer. MYERS, R. A., L. J. CRUZ, J. E. RIVIER AND B. M. OLIVERA (1993) Conus peptides as chemical probes for receptors and ion channels. Chem. Rev. 93: 1923–1926. 138 Chapter Six terminals and metabolized to glutamate by the mitochondrial enzyme gluta-minase (Figure 6.6). Glutamate can also be synthesized by transamination of 2-oxoglutarate, an intermediate of the tricarboxylic acid cycle. Hence, some of the glucose metabolized by neurons can also be used for glutamate synthesis. The glutamate synthesized in the presynaptic cytoplasm is packaged into synaptic vesicles by transporters, termed VGLUT. At least three different VGLUT genes have been identified. Once released, glutamate is removed from the synaptic cleft by the excitatory amino acid transporters (EAATs). There are five different types of high-affinity glutamate transporters exist, some of which are present in glial cells and others in presynaptic terminals. Glutamate taken up by glial cells is converted into glutamine by the enzyme (A) N C N Pore loop Outside Inside C Four transmembrane helices Three transmembrane helices plus pore loop Assembled subunits (B) Transmitter binding site Transmitter Subunits (combi-nation of 4 or 5 required for each receptor type) AMPA (C) Receptor Glu R1 Glu R2 Glu R3 Glu R4 NMDA NR1 NR2A NR2B NR2C NR2D GABA Glycine α1−7 β1−4 γ1−4 ε ρ1−3 δ α1 α2 α3 α4 β nACh Kainate Glu R5 Glu R6 Glu R7 KA1 KA2 α2−9 β1−4 γ δ Purines P2X1 P2X2 P2X3 P2X4 P2X5 P2X6 P2X7 Serotonin 5-HT3 Figure 6.4 The general architecture of ligand-gated receptors. (A) One of the sub-units of a complete receptor. The long N-terminal region forms the ligand-binding site, while the remainder of the protein spans the membrane either four times (left) or three times (right). (B) Assembly of either four or five subunits into a complete receptor. (C) A diversity of subunits come together to form functional ionotropic neurotransmitter receptors. Neurotransmitters and Their Receptors 139 glutamine synthetase; glutamine is then transported out of the glial cells and into nerve terminals. In this way, synaptic terminals cooperate with glial cells to maintain an adequate supply of the neurotransmitter. This overall sequence of events is referred to as the glutamate-glutamine cycle (see Fig-ure 6.6). Several types of glutamate receptors have been identified. Three of these are ionotropic receptors called, respectively, NMDA receptors, AMPA recep-tors, and kainate receptors (Figure 6.4C). These glutamate receptors are named after the agonists that activate them: NMDA (N-methyl-D-aspartate), AMPA (α-amino-3-hydroxyl-5-methyl-4-isoxazole-propionate), and kainic acid. All of the ionotropic glutamate receptors are nonselective cation chan-nels similar to the nAChR, allowing the passage of Na+ and K+, and in some cases small amounts of Ca2+. Hence AMPA, kainate, and NMDA receptor activation always produces excitatory postsynaptic responses. Like other ionotropic receptors, AMPA/kainate and NMDA receptors are also formed (A) N C G-protein binding site I IV VII II III Neuro-transmitter binding site V VI Receptor subtype Receptor class mGlu R1 mGlu R5 mGlu R2 mGlu R3 Glutamate Class I Class II mGlu R4 mGlu R6 mGlu R7 mGlu R8 Class III Dopamine NE, Epi Histamine Serotonin Purines Muscarinic GABAB GABAB R1 GABAB R2 D1A D1B D2 H1 5-HT 1 A type P type A1 A2a A2b A3 P2x P2y P2z P2t P2u 5-HT 3 5-HT 2 5-HT 4 5-HT 5 5-HT 6 5-HT 7 H2 H3 M1 M2 M3 M4 M5 β1 β2 β3 α2 α1 D3 D4 (B) Figure 6.5 Structure and function of metabotropic receptors. (A) The transmembrane architecture of metabotropic receptors. These mono-meric proteins contain seven transmembrane domains. Portions of domains II, III, VI, and VII make up the neurotransmitter-binding region. G-proteins bind to both the loop between domains V and VI and to portions of the C-terminal region. (B) Varieties of metabotropic neurotransmitter receptors. 140 Chapter Six Box C Myasthenia Gravis: An Autoimmune Disease of Neuromuscular Synapses Myasthenia gravis is a disease that interferes with transmission between motor neurons and skeletal muscle fibers and afflicts approximately 1 of every 200,000 people. Originally described by the British physician Thomas Willis in 1685, the hallmark of the disorder is muscle weakness, partic-ularly during sustained activity. Although the course is variable, myas-thenia commonly affects muscles con-trolling the eyelids (resulting in droop-ing of the eyelids, or ptosis) and eye movements (resulting in double vision, or diplopia). Muscles controlling facial expression, chewing, swallowing, and speaking are other common targets. An important indication of the cause of myasthenia gravis came from the clinical observation that the muscle weakness improves following treatment with inhibitors of acetylcholinesterase, the enzyme that normally degrades acetylcholine at the neuromuscular junction. Studies of muscle obtained by biopsy from myasthenic patients showed that both end plate potentials (EPPs) and miniature end plate poten-tials (MEPPs) are much smaller than normal (see figure; also see Chapter 5). Because both the frequency of MEPPs and the quantal content of EPPs are nor-mal, it seemed likely that myasthenia gravis entails a disorder of the postsyn-aptic muscle cells. Indeed, electron microscopy shows that the structure of neuromuscular junctions is altered, obvious changes being a widening of the synaptic cleft and an apparent reduction in the number of acetyl-choline receptors in the postsynaptic membrane. A chance observation in the early 1970s led to the discovery of the under-lying cause of these changes. Jim Patrick and Jon Lindstrom, then working at the Salk Institute, were attempting to raise antibodies to nicotinic acetylcholine receptors by immunizing rabbits with the receptors. Unexpectedly, the immu-nized rabbits developed muscle weak-ness that improved after treatment with acetylcholinesterase inhibitors. Subse-quent work showed that the blood of myasthenic patients contains antibodies directed against the acetylcholine recep-tor, and that these antibodies are pre-sent at neuromuscular synapses. Removal of antibodies by plasma exchange improves the weakness. Finally, injecting the serum of myas-thenic patients into mice produces myasthenic effects (because the serum carries circulating antibodies). These findings indicate that myas-thenia gravis is an autoimmune disease that targets nicotinic acetylcholine receptors. The immune response reduces the number of functional recep-tors at the neuromuscular junction and can eventually destroys them altogether, diminishing the efficiency of synaptic transmission; muscle weakness thus occurs because motor neurons are less capable of exciting the postsynaptic muscle cells. This causal sequence also explains why cholinesterase inhibitors alleviate the signs and symptoms of myasthenia: The inhibitors increase the concentration of acetylcholine in the synaptic cleft, allowing more effective activation of those postsynaptic recep-tors not yet destroyed by the immune system. Despite all these insights, it is still not clear what triggers the immune sys-tem to produce an autoimmune (A) (B) –4 5 10 15 0 4 8 0 20 0.05 0.10 0.20 0.50 1 2 3 40 60 80 0 20 40 60 80 0 20 40 60 80 Normal EMG recording of muscle action potentials (mV) Number of MEPPs Time (ms) MEPP amplitude (mV) Myasthenia gravis after neostigmine treatment Myasthenia gravis Normal Myasthenia gravis (A) Myasthenia gravis reduces the efficiency of neuromuscular transmission. Electromyographs show muscle responses elicited by stimulating motor nerves. In normal individuals, each stimu-lus in a train evokes the same contractile response. In contrast, transmission rapidly fatigues in myasthenic patients, although it can be partially restored by administration of acetyl-cholinesterase inhibitors such as neostigmine. (B) Distribution of MEPP amplitudes in muscle fibers from myasthenic patients (solid line) and controls (dashed line). The smaller size of MEPPs in myasthenics is due to a diminished number of postsynaptic receptors. (A after Harvey et al., 1941; B after Elmqvist et al., 1964.) from the association of several protein subunits that can combine in many ways to produce a large number of receptor isoforms (see Figure 6.4C). NMDA receptors have especially interesting properties (Figure 6.7A). Per-haps most significant is the fact that NMDA receptor ion channels allow the entry of Ca2+ in addition to monovalent cations such as Na+ and K+. As a result, EPSPs produced by NMDA receptors can increase the concentration of Ca2+ within the postsynaptic neuron; the Ca2+ concentration change can then act as a second messenger to activate intracellular signaling cascades (see Chapter 7). Another key property is that they bind extracellular Mg2+. At hyperpolarized membrane potentials, this ion blocks the pore of the NMDA receptor channel. Depolarization, however, pushes Mg2+ out of the pore, allowing other cations to flow. This property provides the basis for a voltage-dependence to current flow through the receptor (dashed line in Fig-ure 6.7B) and means that NMDA receptors pass cations (most notably Ca2+) Neurotransmitters and Their Receptors 141 response to acetylcholine receptors. Sur-gical removal of the thymus is beneficial in young patients with hyperplasia of the thymus, though precisely how the thymus contributes to myasthenia gravis is incompletely understood. Many patients are treated with combi-nations of immunosuppression and cholinesterase inhibitors. References ELMQVIST, D., W. W. HOFMANN, J. KUGELBERG AND D. M. J. QUASTEL (1964) An electrophysi-ological investigation of neuromuscular transmission in myasthenia gravis. J. Physiol. (Lond.) 174: 417–434. PATRICK, J. AND J. LINDSTROM (1973) Autoim-mune response to acetylcholine receptor. Sci-ence 180: 871–872. VINCENT, A. (2002) Unravelling the pathogen-esis of myasthenia gravis. Nature Rev. Immunol. 2: 797–804. Postsynaptic cell + H3N COO− O + Glutamate Glutamine Glutaminase Glutamate receptors VGLUT EATT Presynaptic terminal Glutamate Glutamine Glutamine synthetase Glial cell NH2 C CH2 CH2 CH COO− + Glutamate NH3 COO− CH2 CH2 CH EATT Figure 6.6 Glutamate synthesis and cycling between neurons and glia. The action of glutamate released into the synaptic cleft is terminated by uptake into neurons and surrounding glial cells via specific transporters. Within the nerve terminal, the glutamine released by glial cells and taken up by neurons is converted back to glutamate. Glutamate is transported into cells via excitatory amino acid transporters (EATTs) and loaded into synaptic vesicles via vesicu-lar glutamate transporters (VGLUT). 142 Chapter Six only during depolarization of the postsynaptic cell, due to either activation of a large number of excitatory inputs and/or by repetitive firing of action potentials in the presynaptic cell. These properties are widely thought to be the basis for some forms of information storage at synapses, such as mem-ory, as described in Chapter 24. Another unusual property of NMRA recep-tors is that opening the channel of this receptor requires the presence of a co-agonist, the amino acid glycine (Figure 6.7A,B). There are at least five forms of NMDA receptor subunits (NMDA-R1, and NMDA-R2A through NMDA-R2D); different synapses have distinct combinations of these subunits, pro-ducing a variety of NMDA receptor-mediated postsynaptic responses. Whereas some glutamatergic synapses have only AMPA or NMDA recep-tors, most possess both AMPA and NMDA receptors. An antagonist of Membrane potential (mV) EPSC (pA) (B) EPSC (pA) 50 50 75 100 25 25 −25 0 50 75 100 25 0 50 75 100 25 0 0 EPSC (pA) 50 25 −25 0 EPSC (pA) 50 25 −25 0 0 0 −50 −50 50 50 −100 −100 −150 150 100 100 (C) (A) AMPA only NMDA only AMPA and NMDA Time (ms) Time (ms) Time (ms) Mg2+, glycine Glycine, no Mg2+ No glycine, no Mg2+ Glutamate Glycine Mg2+ binding site Mg2+ Channel pore K+ Na+ Ca2+ Figure 6.7 NMDA and AMPA/kainate receptors. (A) NMDA receptors contain binding sites for glutamate and the co-activator glycine, as well as an Mg2+-binding site in the pore of the channel. At hyperpolarized poten-tials, the electrical driving force on Mg2+ drives this ion into the pore of the receptor and blocks it. (B) Current flow across NMDA receptors at a range of postsynaptic voltages, showing the requirement for glycine, and Mg2+ block at hyperpolarized potentials (dotted line). (C) The differential effects of glu-tamate receptor antagonists indicate that activation of AMPA or kainate receptors produces very fast EPSCs (top panel) and activation of NMDA receptors causes slower EPSCs (middle panel), so that EPSCs recorded in the absence of antagonists have two kinetic components due to the contribution of both types of response (bottom panel). NMDA receptors, APV (2-amino-5-phosphono-valerate), is often used to dif-ferentiate between the two receptor types. The use of this drug has also revealed differences between the EPSPs produced by NMDA and those pro-duced by AMPA/kainate receptors, such as the fact that the synaptic cur-rents produced by NMDA receptors are slower and longer-lasting than the those produced by AMPA/kainate receptors (see Figure 6.7C). In addition to these ionotropic glutamate receptors, there are three types of metabotropic glutamate receptor (mGluRs) (Figure 6.5). These receptors, which modulate postsynaptic ion channels indirectly, differ in their coupling to intracellular signal transduction pathways (see Chapter 7) and in their sensitivity to pharmacological agents. Activation of many of these receptors leads to inhibition of postsynaptic Ca2+ and Na+ channels. Unlike the excita-tory ionotropic glutamate receptors, mGluRs cause slower postsynaptic re-sponses that can either increase or decrease the excitability of postsynaptic cells. As a result the physiological roles of mGluRs are quite varied. GABA and Glycine Most inhibitory synapses in the brain and spinal cord use either γ-aminobu-tyric acid (GABA) or glycine as neurotransmitters. Like glutamate, GABA was identified in brain tissue during the 1950s. The details of its synthesis and degradation were worked out shortly thereafter by the work of Ernst Florey and Eugene Roberts. During this era, David Curtis and Jeffrey Watkins first showed that GABA can inhibit action potential firing in mam-malian neurons. Subsequent studies by Edward Kravitz and colleagues established that GABA serves as an inhibitory transmitter at lobster neuro-muscular synapses. It is now known that as many as a third of the synapses in the brain use GABA as their inhibitory neurotransmitter. GABA is most commonly found in local circuit interneurons, although cerebellar Purkinje cells provide an example of a GABAergic projection neuron (see Chapter 18). The predominant precursor for GABA synthesis is glucose, which is metabolized to glutamate by the tricarboxylic acid cycle enzymes (pyruvate and glutamine can also act as precursors). The enzyme glutamic acid decar-boxylase (GAD), which is found almost exclusively in GABAergic neurons, catalyzes the conversion of glutamate to GABA (Figure 6.8A). GAD requires a cofactor, pyridoxal phosphate, for activity. Because pyridoxal phosphate is derived from vitamin B6, a B6 deficiency can lead to diminished GABA syn-thesis. The significance of this became clear after a disastrous series of infant deaths was linked to the omission of vitamin B6 from infant formula. This lack of B6 resulted in a large reduction in the GABA content of the brain, and the subsequent loss of synaptic inhibition caused seizures that in some cases were fatal. Once GABA is synthesized, it is transported into synaptic vesicles via a vesicular inhibitory amino acid transporter (VIATT). The mechanism of GABA removal is similar to that for glutamate: Both neurons and glia contain high-affinity transporters for GABA, termed GATs (several forms of GAT have been identified). Most GABA is eventually con-verted to succinate, which is metabolized further in the tricarboxylic acid cycle that mediates cellular ATP synthesis. The enzymes required for this degradation, GABA transaminase and succinic semialdehyde dehydroge-nase, are mitochondrial enzymes. Inhibition of GABA breakdown causes a rise in tissue GABA content and an increase in the activity of inhibitory neurons. There are also other pathways for degradation of GABA. The most noteworthy of these results in the production of γ-hydroxybutyrate, a GABA derivitive that has been abused as a “date rape” drug. Oral adminis-Neurotransmitters and Their Receptors 143 144 Chapter Six Glucose Glycine receptors GABA receptors GABA Postsynaptic cell Presynaptic terminal Presynaptic terminal (A) Glycine H3N — C — COO– + H H Serine H3N — C — COO– + COOH H + GABA Glutamic acid decarboxylase + pyridoxal phosphate Glutamate Glucose NH3 COO− + Postsynaptic cell CH CH2 CH2 COO− H3N CH2 CH2 CH2 COO− Glial cell Glial cell Glucose Glycine Glycine H3N + H H Serine H3N + COOH H Serine transhydroxy- methylase C COO− COO− C GABA breakdown GAT VIATT VIATT Glycine transporter (B) Figure 6.8 Synthesis, release, and reuptake of the inhibitory neurotrans-mitters GABA and glycine. (A) GABA is synthesized from glutamate by the enzyme glutamic acid decarboxylase, which requires pyridoxal phosphate. (B) Glycine can be synthesized by a number of metabolic pathways; in the brain, the major precursor is serine. High-affinity transporters terminate the actions of these transmitters and return GABA or glycine to the synaptic terminals for reuse, with both transmitters being loaded into synaptic vesicles via the vesicular inhibitory amino acid trans-porter (VIATT). tration of γ-hydroxybutyrate can cause euphoria, memory deficits, and unconsciousness. Presumably these effects arise from actions on GABAergic synapses in the CNS. Inhibitory synapses employing GABA as their transmitter can exhibit three types of postsynaptic receptors, called GABAA, GABAB, and GABAC. GABAA and GABAC receptors are ionotropic receptors, while GABAB receptors are metabotropic. The ionotropic GABA receptors are usually Neurotransmitters and Their Receptors 145 Box D Excitotoxicity Following Acute Brain Injury Excitotoxicity refers to the ability of glu-tamate and related compounds to destroy neurons by prolonged excitatory synaptic transmission. Normally, the concentration of glutamate released into the synaptic cleft rises to high levels (approximately 1 mM), but it remains at this concentration for only a few millisec-onds. If abnormally high levels of gluta-mate accumulate in the cleft, the exces-sive activation of neuronal glutamate receptors can literally excite neurons to death. The phenomenon of excitotoxicity was discovered in 1957 when D. R. Lucas and J. P. Newhouse serendipitously found that feeding sodium glutamate to infant mice destroys neurons in the retina. Roughly a decade later, John Olney at Washington University extended this discovery by showing that regions of glutamate-induced neuronal loss can occur throughout the brain. The damage was evidently restricted to the postsynaptic cells—the dendrites of the target neurons were grossly swollen— while the presynaptic terminals were spared. Olney also examined the relative potency of glutamate analogs and found that their neurotoxic actions paralleled their ability to activate postsynaptic glu-tamate receptors. Furthermore, gluta-mate receptor antagonists were effective in blocking the neurotoxic effects of glu-tamate. In light of this evidence, Olney postulated that glutamate destroys neu-rons by a mechanism similar to transmis-sion at excitatory glutamatergic syn-apses, and coined the term excitotoxic to refer to this pathological effect. Evidence that excitotoxicity is an important cause of neuronal damage after brain injury has come primarily from studying the consequences of reduced blood flow. The most common cause of reduced blood flow to the brain (ischemia) is the occlusion of a cerebral blood vessel (i.e., a stroke; see Appendix 3). The idea that excessive synaptic activ-ity contributes to ischemic injury emerged from the observation that con-centrations of glutamate and aspartate in the extracellular space around neurons increase during ischemia. Moreover, microinjection of glutamate receptor antagonists in experimental animals pro-tects neurons from ischemia-induced damage. Together, these findings imply that extracellular accumulation of gluta-mate during ischemia activates gluta-mate receptors excessively, and that this somehow triggers a chain of events that leads to neuronal death. The reduced supply of oxygen and glucose presum-ably elevates extracellular glutamate lev-els by slowing the energy-dependent removal of glutamate at synapses. Excitotoxic mechanisms have now been shown to be involved in other acute forms of neuronal insult, including hypoglycemia, trauma, and repeated intense seizures (called status epilepti-cus). Understanding excitotoxicity there-fore has important implications for treat-ing a variety of neurological disorders. For instance, a blockade of glutamate receptors could, in principle, protect neu-rons from injury due to stroke, trauma, or other causes. Unfortunately, clinical trials of glutamate receptor antagonists have not led to much improvement in the outcome of stroke. The ineffective-ness of this quite logical treatment is probably due to several factors, one of which is that substantial excitotoxic injury occurs quite soon after ischemia, prior to the typical initiation of treat-ment. It is also likely that excitotoxicity is only one of several mechanisms by which ischemia damages neurons, other candidates including damage secondary to inflammation. Pharmacological inter-ventions that target all these mechanisms nonetheless hold considerable promise for minimizing brain injury after stroke and other causes. References LUCAS, D. R. AND J. P. NEWHOUSE (1957) The toxic effects of sodium L-glutamate on the inner layers of the retina. Arch. Opthalmol. 58: 193–201. OLNEY, J. W. (1969) Brain lesions, obesity and other disturbances in mice treated with monosodium glutamate. Science 164: 719–721. OLNEY, J. W. (1971) Glutamate-induced neu-ronal necrosis in the infant mouse hypothala-mus: An electron microscopic study. J. Neu-ropathol. Exp. Neurol. 30: 75–90. ROTHMAN, S. M. (1983) Synaptic activity medi-ates death of hypoxic neurons. Science 220: 536–537. SYNTICHAKI, P. AND N. TAVERNARAKIS (2003) The biochemistry of neuronal necrosis: Rogue biology? Nature Neurosci. Rev. 4: 672–684. 146 Chapter Six inhibitory because their associated channels are permeable to Cl– (Figure 6.9A); the flow of the negatively charged chloride ions inhibits postsynaptic cells since the reversal potential for Cl– is more negative than the threshold for neuronal firing (see Figure 5.19B). Like other ionotropic receptors, GABA receptors are pentamers assembled from a combination of five types of subunits (α, β, γ, δ, and ρ; see Figure 6.4C). As a result of this subunit diversity, as well as variable stoichiometry of subunits, the function of GABAA receptors differs widely among neuronal types. Drugs that act as agonists or modulators of postsynaptic GABA receptors, such as benzodi-azepines and barbiturates, are used clinically to treat epilepsy and are effec-tive sedatives and anesthetics. Binding sites for GABA, barbiturates, steroids, and picrotoxin are all located within the pore domain of the chan-nel (Figure 6.9B). Another site, called the benzodiazepine binding site, lies outside the pore and modulates channel activity. Benzodiazepines, such as diazepam (Valium®) and chlordiazepoxide (Librium®), are tranquilizing (anxiety reducing) drugs that enhance GABAergic transmission by binding to the α and δ subunits of GABAA receptors. Barbiturates, such as pheno-barbital and pentobarbital, are hypnotics that bind to the α and β subunits of some GABA receptors and are used therapeutically for anesthesia and to control epilepsy. Another drug that can alter the activity of GABA-mediated inhibitory circuits is alcohol; at least some aspects of drunken behavior are caused by the alcohol-mediated alterations in ionotropic GABA receptors. Metabotropic GABA receptors (GABAB) are also widely distributed in brain. Like the ionotropic GABAA receptors, GABAB receptors are inhibitory. Rather than activating Cl−selective channels, however, GABAB-mediated inhibition is due to the activation of K+ channels. A second mechanism for 0 50 100 150 200 250 300 350 400 Time (ms) Stimulate presynaptic neuron Membrane potential (mV) 0 –50 (B) (A) Benzodiazepine GABA Barbiturates Picrotoxin Steroids a Subunit Channel pore Chloride ions b b a g Figure 6.9 Ionotropic GABA receptors. (A) Stimulation of a presynaptic GABAergic interneuron, at the time indicated by the arrow, causes a transient inhibition of action potential firing in its postynaptic target. This inhibitory response is caused by activation of postsynaptic GABAA receptors. (B) Ionotropic GABA receptors contain two binding sites for GABA and numerous sites at which drugs bind to and modulate these receptors. (A after Chavas and Marty, 2003). GABAB-mediated inhibition is by blocking Ca2+ channels, which tends to hyperpolarize postsynaptic cells. Unlike most metabotropic receptors, GABAB receptors appear to assemble as heterodimers of GABAB R1 and R2 subunits. The distribution of the neutral amino acid glycine in the central nervous system is more localized than that of GABA. About half of the inhibitory synapses in the spinal cord use glycine; most other inhibitory synapses use GABA. Glycine is synthesized from serine by the mitochondrial isoform of serine hydroxymethyltransferase (Figure 6.8B), and is transported into syn-aptic vesicles via the same vesicular inhibitory amino acid transporter that loads GABA into vesicles. Once released from the presynaptic cell, glycine is rapidly removed from the synaptic cleft by the plasma membrane glycine transporters. Mutations in the genes coding for some of these enzymes result in hyperglycinemia, a devastating neonatal disease characterized by lethargy, seizures, and mental retardation. The receptors for glycine are also ligand-gated Cl– channels, their general structure mirroring that of the GABAA receptors. Glycine receptors are pen-tamers consisting of mixtures of the 4 gene products encoding glycine-bind-ing α subunits, along with the accessory β subunit. Glycine receptors are potently blocked by strychnine, which may account for the toxic properties of this plant alkaloid (see Box B). The Biogenic Amines Biogenic amine transmitters regulate many brain functions and are also active in the peripheral nervous system. Because biogenic amines are impli-cated in such a wide range of behaviors (ranging from central homeostatic functions to cognitive phenomena such as attention), it is not surprising that defects in biogenic amines function are implicated in most psychiatric disorders. The pharmacology of amine synapses is critically important in psychotherapy, with drugs affecting the synthesis, receptor binding, or catabolism of these neurotransmitters being among the most important agents in the armamentarium of modern pharmacology (Box E). Many drugs of abuse also act on biogenic amine pathways. There are five well-established biogenic amine neurotransmitters: the three catecholamines—dopamine, norepinephrine (noradrenaline), and epineph-rine (adrenaline)—and histamine and serotonin (see Figure 6.1). All the cat-echolamines (so named because they share the catechol moiety) are derived from a common precursor, the amino acid tyrosine (Figure 6.10). The first step in catecholamine synthesis is catalyzed by tyrosine hydroxylase in a reaction requiring oxygen as a co-substrate and tetrahydrobiopterin as a cofactor to synthesize dihydroxyphenylalanine (DOPA). Histamine and sero-tonin are synthesized via other routes, as described below. • Dopamine is present in several brain regions (Figure 6.11A), although the major dopamine-containing area of the brain is the corpus striatum, which receives major input from the substantia nigra and plays an essential role in the coordination of body movements. In Parkinson’s disease, for instance, the dopaminergic neurons of the substantia nigra degenerate, leading to a characteristic motor dysfunction (see Box B in Chapter 17). Dopamine is also believed to be involved in motivation, reward, and reinforcement, and many drugs of abuse work by affecting dopaminergic synapses in the CNS (see Box A). In addition to these roles in the CNS, dopamine also plays a poorly understood role in some sympathetic ganglia. Neurotransmitters and Their Receptors 147 Tyrosine Dihydroxyphenylalanine (DOPA) Dopamine Norepinephrine Epinephrine Tyrosine hydroxylase DOPA decarboxylase Phenylethanol-amine N-methyl-transferase Dopamine-β hydroxylase HO CH2 H CH COO− O2 HO OH CH2 CH COO− NH3 HO OH CH OH NH3 HO OH CH2 CH3 CH H CH NH3 O2 HO OH CH OH NH2 H CH RCH3 R CO2 + NH3 + + + + Figure 6.10 The biosynthetic pathway for the catecholamine neurotransmitters. The amino acid tyrosine is the precursor for all three catecholamines. The first step in this reaction pathway, catalyzed by tyrosine hydroxylase, is rate-limiting. 148 Chapter Six Box E Biogenic Amine Neurotransmitters and Psychiatric Disorders The regulation of the biogenic amine neurotransmitters is altered in a variety of psychiatric disorders. Indeed, most psychotropic drugs (defined as drugs that alter behavior, mood, or percep-tion) selectively affect one or more steps in the synthesis, packaging, or degrada-tion of biogenic amines. Sorting out how these drugs work has been extremely useful in beginning to under-stand the molecular mechanisms underlying some of these diseases. Based on their effects on humans, psychotherapeutic drugs can be divided into several broad categories: antipsy-chotics, antianxiety drugs, antidepres-sants, and stimulants. The first antipsy-chotic drug used to ameliorate disorders such as schizophrenia was reserpine. Reserpine was developed in the 1950s and initially used as an antihyperten-sive agent; it blocks the uptake of norep-inephrine into synaptic vesicles and therefore depletes the transmitter at aminergic terminals, diminishing the ability of the sympathetic division of the visceral motor system to cause vasocon-striction (see Chapter 20). A major side effect in hypertensive patients treated with reserpine—behavioral depres-sion—suggested the possibility of using it as an antipsychotic agent in patients suffering from agitation and pathologi-cal anxiety. (Its ability to cause depres-sion in mentally healthy individuals also suggested that aminergic transmit-ters are involved in mood disorders; see Box E in Chapter 28.) Although reserpine is no longer used as an antipsychotic agent, its ini-tial success stimulated the development of antipsychotic drugs such as chlor-promazine, haloperidol, and benperi-dol, which over the last several decades have radically changed the approach to treating psychotic disorders. Prior to the discovery of these drugs, psychotic patients were typically hospitalized for long periods, sometimes indefinitely, and in the 1940s were subjected to des-perate measures such as frontal lobot-omy (see Box B in Chapter 25). Modern antipsychotic drugs now allow most patients to be treated on an outpatient basis after a brief hospital stay. Impor-tantly, the clinical effectiveness of these drugs is correlated with their ability to block brain dopamine receptors, imply-ing that activation of dopamine recep-tors contributes to some types of psy-chotic illness. A great deal of effort continues to be expended on develop-ing more effective antipsychotic drugs with fewer side effects, and on discov-ering the mechanism and site of action of these medications. The second category of psychothera-peutic drugs is the antianxiety agents. Anxiety disorders are estimated to afflict 10–35% of the population, mak-ing them the most common psychiatric problem. The two major forms of pathological anxiety—panic attacks and generalized anxiety disorder—both respond to drugs that affect aminergic transmission. The agents used to treat panic disorders include inhibitors of the enzyme monoamine oxidase (MAO inhibitors) required for the catabolism of the amine neurotransmitters, and blockers of serotonin receptors. The most effective drugs in treating general-ized anxiety disorder have been benzo-diazepines, such as chlordiazepoxide (Librium®), and diazepam (Valium®). In contrast to most other psychotherapeu-tic drugs, these agents increase the effi-cacy of transmission at GABAAsyn-apses rather than acting at aminergic synapses. Antidepressants and stimulants also affect aminergic transmission. A large number of drugs are used clinically to treat depressive disorders. The three major classes of antidepressants—MAO inhibitors, tricyclic antidepressants, and serotonin uptake blockers such as flu-oxetine (Prozac®) and trazodone—all influence various aspects of aminergic transmission. MAO inhibitors such as phenelzine block the breakdown of amines, whereas the tricyclic antide-pressants such as desipramine block the reuptake of norepinephrine and other amines. The extraordinarily popular antidepressant fluoxetine (Prozac®) selectively blocks the reuptake of sero-tonin without affecting the reuptake of catecholamines. Stimulants such as amphetamine are also used to treat some depressive disorders. Ampheta-mine stimulates the release of norepi-nephrine from nerve terminals; the transient “high” resulting from taking amphetamine may reflect the emotional opposite of the depression that some-times follows reserpine-induced norepi-nephrine depletion. Despite the relatively small number of aminergic neurons in the brain, this litany of pharmacological actions emphasizes that these neurons are criti-cally important in the maintenance of mental health. References FRANKLE, W. G., J. LERMA AND M. LARUELLE (2003) The synaptic hypothesis of schizo-phrenia. Neuron 39: 205–216. FREEDMAN, R. (2003) Schizophrenia. N. Engl. J. Med. 349: 1738–1749. LEWIS, D. A. AND P. LEVITT (2002) Schizophre-nia as a disorder of neurodevelopment. Annu. Rev. Neurosci. 25: 409–432. NESTLER, E. J., M. BARROT, R. J. DILEONE, A. J. EISCH, S. J. GOLD AND L. M. MONTEGGIA (2002) Neurobiology of depression. Neuron 34: 13–25. Dopamine is produced by the action of DOPA decarboxylase on DOPA (see Figure 6.10). Following its synthesis in the cytoplasm of presynaptic ter-minals, dopamine is loaded into synaptic vesicles via a vesicular monoamine transporter (VMAT). Dopamine action in the synaptic cleft is terminated by reuptake of dopamine into nerve terminals or surrounding glial cells by a Na+-dependent dopamine transporter, termed DAT. Cocaine apparently pro-duces its psychotropic effects by binding to and inhibiting DAT, yielding a net increase in dopamine release from specific brain areas. Amphetamine, another addictive drug, also inhibits DAT as well as the transporter for nor-epinepherine (see below). The two major enzymes involved in the catabo-lism of dopamine are monoamine oxidase (MAO) and catechol O-methyl-transferase (COMT). Both neurons and glia contain mitochondrial MAO and cytoplasmic COMT. Inhibitors of these enzymes, such as phenelzine and tranylcypromine, are used clinically as antidepressants (see Box E). Once released, dopamine acts exclusively by activating G-protein-coupled receptors. These are mainly dopamine-specific receptors, although β-adren-ergic receptors also serve as important targets of norepinepherine and epi-nepherine (see below). Most dopamine receptor subtypes (see Figure 6.5B) Neurotransmitters and Their Receptors 149 (B) Norepinephrine (A) Dopamine Pons Medulla Cerebellum Corpus callosum Cerebral cortex To striatum Thalamus Pons Medulla Cerebellum Corpus callosum Cerebral cortex Thalamus Locus coeruleus To spinal cord Substantia nigra and ventral tegmental area To spinal cord (C) Epinephrine Pons Medulla Cerebellum Corpus callosum Cerebral cortex Thalamus To spinal cord Hypothalamus Medullary epinephrine neurons Figure 6.11 The distribution in the human brain of neurons and their projections (arrows) containing catecholamine neurotransmitters. Curved arrows along the perimeter of the cortex indicate the inner-vation of lateral cortical regions not shown in this midsagittal plane of section. 150 Chapter Six act by either activating or inhibiting adenylyl cyclase (see Chapter 7). Acti-vation of these receptors generally contribute to complex behaviors; for example, administration of dopamine receptor agonists elicits hyperactivity and repetitive, stereotyped behavior in laboratory animals. Activation of another type of dopamine receptor in the medulla inhibits vomiting. Thus, antagonists of these receptors are used as emetics to induce vomiting after poisoning or a drug overdose. Dopamine receptor antagonists can also elicit catalepsy, a state in which it is difficult to initiate voluntary motor move-ment, suggesting a basis for this aspect of some psychoses. • Norepinephrine (also called noradrenaline) is used as a neurotransmitter in the locus coeruleus, a brainstem nucleus that projects diffusely to a variety of forebrain targets (Figure 6.11B) and influences sleep and wakefulness, attention, and feeding behavior. Perhaps the most prominent noradrenergic neurons are sympathetic ganglion cells, which employ norepinephrine as the major peripheral transmitter in this division of the visceral motor system (see Chapter 20). Norepinephrine synthesis requires dopamine β-hydroxylase, which cat-alyzes the production of norepinephrine from dopamine (see Figure 6.10). Norepinephrine is then loaded into synaptic vesicles via the same VMAT involved in vesicular dopamine transport. Norepinepherine is cleared from the synaptic cleft by the norepinepherine transporter (NET), which also is capable of taking up dopamine. As mentioned, NET serves as a molecular target of amphetamine, which acts as a stimulant by producing a net increase in the release of norepinepherine and dopamine. A mutation in the NET gene is a cause of orthostatic intolerance, a disorder that produces lightheadedness while standing up. Like dopamine, norepinepherine is degraded by MAO and COMT. Norepinepherine, as well as epinephrine, acts on α- and β-adrenergic receptors (Figure 6.5B). Both types of receptor are G-protein-coupled; in fact, the β-adrenergic receptor was the first identified metabotropic neurotrans-mitter receptor. Two subclasses of α-adrenergic receptors are now known. Activation of α1 receptors usually results in a slow depolarization linked to the inhibition of K+ channels, while activation of α2 receptors produces a slow hyperpolarization due to the activation of a different type of K+ chan-nel. There are three subtypes of β-adrenergic receptor, two of which are expressed in many types of neurons. Agonists and antagonists of adrenergic receptors, such as the β blocker propanolol (Inderol®), are used clinically for a variety of conditions ranging from cardiac arrhythmias to migraine headaches. However, most of the actions of these drugs are on smooth mus-cle receptors, particularly in the cardiovascular and respiratory systems (see Chapter 20). • Epinephrine (also called adrenaline) is found in the brain at lower levels than the other catecholamines and also is present in fewer brain neurons than other catecholamines. Epinephrine-containing neurons in the central nervous system are primarily in the lateral tegmental system and in the medulla and project to the hypothalamus and thalamus (Figure 6.11C). The function of these epinepherine-secreting neurons is not known. The enzyme that synthesizes epinephrine, phenylethanolamine-N-methyltransferase (see Figure 6.10), is present only in epinephrine-secreting neurons. Otherwise, the metabolism of epinepherine is very similar to that of norepinepherine. Epinepherine is loaded into vesicles via the VMAT. No plasma membrane transporter specific for epinepherine has been identified, though the NET is capable of transporting epinepherine. As already noted, epinepherine acts on both α- and β-adrenergic receptors. • Histamine is found in neurons in the hypothalamus that send sparse but widespread projections to almost all regions of the brain and spinal cord (Figure 6.12A). The central histamine projections mediate arousal and atten-tion, similar to central ACh and norepinephrine projections. Histamine also controls the reactivity of the vestibular system. Allergic reactions or tissue damage cause release of histamine from mast cells in the bloodstream. The close proximity of mast cells to blood vessels, together with the potent actions of histamine on blood vessels, also raises the possibility that hista-mine may influence brain blood flow. Histamine is produced from the amino acid histidine by a histidine decar-boxylase (Figure 6.13A) and is transported into vesicles via the same VMAT as the catecholamines. No plasma membrane histamine transporter has been identified yet. Histamine is degraded by the combined actions of histamine methyltransferase and MAO. There are three known types of histamine receptors, all of which are G-protein-coupled receptors (Figure 6.5B). Because of the importance of hista-mine receptors in the mediation of allergic responses, many histamine recep-tor antagonists have been developed as antihistamine agents. Antihistamines that cross the blood-brain barrier, such as diphenhydramine (Benadryl®), act as sedatives by interfering with the roles of histamine in CNS arousal. Antagonists of the H1 receptor also are used to prevent motion sickness, per-haps because of the role of histamine in controling vestibular function. H2 receptors control the secretion of gastric acid in the digestive system, allow-ing H2 receptor antagonists to be used in the treatment of a variety of upper gastrointestinal disorders (e.g., peptic ulcers). • Serotonin, or 5-hydroxytryptamine (5-HT), was initially thought to increase vascular tone by virtue of its presence in serum (hence the name serotonin). Serotonin is found primarily in groups of neurons in the raphe region of the pons and upper brainstem, which have widespread projections to the forebrain (see Figure 6.12B) and regulate sleep and wakefulness (see Chapter 27). 5-HT occupies a place of prominence in neuropharmacology because a large number of antipsychotic drugs that are valuable in the treat-ment of depression and anxiety act on serotonergic pathways (see Box E). 5-HT is synthesized from the amino acid tryptophan, which is an essential dietary requirement. Tryptophan is taken up into neurons by a plasma mem-Neurotransmitters and Their Receptors 151 (B) Serotonin (A) Histamine Pons Medulla Cerebellum Corpus callosum Cerebral cortex Thalamus Pons Medulla Cerebellum Corpus callosum Cerebral cortex Thalamus To spinal cord To spinal cord Tuberomammillary nucleus of hypothalamus Raphe nuclei Figure 6.12 The distribution in the human brain of neurons and their pro-jections (arrows) containing histamine (A) or serotonin (B). Curved arrows along the perimeter of the cortex indi-cate the innervation of lateral cortical regions not shown in this midsagittal plane of section. 152 Chapter Six brane transporter and hydroxylated in a reaction catalyzed by the enzyme tryptophan-5-hydroxylase (Figure 6.13B), the rate-limiting step for 5-HT syn-thesis. Loading of 5-HT into synaptic vesicles is done by the VMAT that is also responsible for loading of other monoamines into synaptic vesicles. The synaptic effects of serotonin are terminated by transport back into nerve ter-minals via a specific serotonin transporter (SERT). Many antidepressant drugs are selective serotonin reuptake inhibitors (SSRIs) that inhibit transport of 5-HT by SERT. Perhaps the best known example of an SSRI is Prozac (see Box E). The primary catabolic pathway for 5-HT is mediated by MAO. A large number of 5-HT receptors have been identified. Most 5-HT recep-tors are metabotropic (see Figure 6.5B). These have been implicated in behaviors, including the emotions, circadian rhythms, motor behaviors, and state of mental arousal. Impairments in the function of these receptors have been implicated in numerous psychiatric disorders, such as depression, anx-iety disorders, and schizophrenia (see Chapter 28), and drugs acting on sero-tonin receptors are effective treatments for a number of these conditions. Activation of 5-HT receptors also mediates satiety and decreased food con-sumption, which is why serotonergic drugs are sometimes useful in treating eating disorders. Only one group of serotonin receptors, called the 5-HT3 receptors, are lig-and-gated ion channels (see Figure 6.4C). These are non-selective cation channels and therefore mediate excitatory postsynaptic responses. Their general structure, with functional channels formed by assembly of multiple subunits, is similar to the other ionotropic receptors described in the chapter. Two types of 5-HT3 subunit are known, and form functional channels by assembling as a heteromultimer. 5-HT receptors are targets for a wide vari-ety of therapeutic drugs including ondansetron (Zofran®) and granisetron (Kytril®), which are used to prevent postoperative nausea and chemother-apy-induced emesis. ATP and Other Purines Interestingly, all synaptic vesicles contain ATP, which is co-released with one or more “classical” neurotransmitters. This observation raises the possibility that ATP acts as a co-transmitter. It has been known since the 1920s that the extracellular application of ATP (or its breakdown products AMP and adenosine) can elicit electrical responses in neurons. The idea that some purines (so named because all these compounds contain a purine ring; see Figure 6.1) are also neurotransmitters has now received considerable experi-mental support. ATP acts as an excitatory neurotransmitter in motor neurons of the spinal cord, as well as sensory and autonomic ganglia. Postsynaptic actions of ATP have also been demonstrated in the central nervous system, specifically for dorsal horn neurons and in a subset of hippocampal neurons. Adenosine, however, cannot be considered a classical neurotransmitter because it is not stored in synaptic vesicles or released in a Ca2+-dependent manner. Rather, it is generated from ATP by the action of extracellular enzymes. A number of enzymes, such as apyrase and ecto-5′ nucleotidase, as well as nucleoside transporters are involved in the rapid catabolism and removal of purines from extracellular locations. Despite the relative novelty of this evidence, it suggests that excitatory transmission via purinergic syn-apses is widespread in the mammalian brain. In accord with this evidence, receptors for both ATP and adenosine are widely distributed in the nervous system, as well as many other tissues. COO− Tryptophan (B) (A) Serotonin (5-HT) Histidine Histamine 5-Hydroxytryptophan N CH2 CH NH3 COO− COO− CO2 CH NH3 N HO CH2 CH CH H HO CH2 Tryptophan-5-hydroxylase Aromatic L-amino acid decarboxylase Histidine decarboxylase O2 CO2 N CH CH2 CH2 HN N HN N H + + NH3 + NH3 + NH3 + Figure 6.13 Synthesis of histamine and serotonin. (A) Histamine is synthe-sized from the amino acid histidine. (B) Serotonin is derived from the amino acid tryptophan by a two-step process that requires the enzymes tryptophan-5-hydroxylase and a decarboxylase. Three classes of these purinergic receptors are now known. One of these classes consists of ligand-gated ion channels (see Figure 6.4C); the other two are G-protein-coupled metabotropic receptors (see Figure 6.5B). Like many ionotropic transmitter receptors, the ligand-gated channels are nonselective cation channels that mediate excitatory postsynaptic responses. The genes encoding these channels, however, are unique in that they appear to have only two transmembrane domains. Ionotropic purinergic receptors are widely distributed in central and peripheral neurons. In sensory nerves they evidently play a role in mechanosensation and pain; their function in most other cells, however, is not known. The two types of metabotropic receptors activated by purines differ in their sensitivity to agonists: One type is preferentially stimulated by ade-nosine, whereas the other is preferentially activated by ATP. Both receptor types are found throughout the brain, as well as in peripheral tissues such as the heart, adipose tissue, and the kidney. Xanthines such as caffeine and theophylline block adenosine receptors, and this activity is thought to be responsible for the stimulant effects of these agents. Peptide Neurotransmitters Many peptides known to be hormones also act as neurotransmitters. Some peptide transmitters have been implicated in modulating emotions (see Chapter 28). Others, such as substance P and the opioid peptides, are involved in the perception of pain (see Chapter 9). Still other peptides, such as melanocyte-stimulating hormone, adrenocorticotropin, and β-endorphin, regulate complex responses to stress. The mechanisms responsible for the synthesis and packaging of peptide transmitters are fundamentally different from those used for the small-molecule neurotransmitters and are much like the synthesis of proteins that are secreted from non-neuronal cells (pancreatic enzymes, for instance). Peptide-secreting neurons generally synthesize polypeptides in their cell bodies that are much larger than the final, “mature” peptide. Processing these polypeptides in their cell bodies, which are called pre-propeptides (or pre-proproteins), takes place by a sequence of reactions in several intracel-lular organelles. Pre-propeptides are synthesized in the rough endoplasmic reticulum, where the signal sequence of amino acids—that is, the sequence indicating that the peptide is to be secreted—is removed. The remaining polypeptide, called a propeptide (or proprotein), then traverses the Golgi apparatus and is packaged into vesicles in the trans-Golgi network. The final stages of peptide neurotransmitter processing occur after packaging into vesicles and involve proteolytic cleavage, modification of the ends of the peptide, glycosylation, phosphorylation, and disulfide bond formation. Propeptide precursors are typically larger than their active peptide prod-ucts and can give rise to more than one species of neuropeptide (Figure 6.14). The means that multiple neuroactive peptides can be released from a single vesicle. In addition, neuropeptides often are co-released with small-molecule neurotransmitters. Thus, peptidergic synapses often elicit complex postsyn-aptic responses. Peptides are catabolized into inactive amino acid fragments by enzymes called peptidases, usually located on the extracellular surface of the plasma membrane. The biological activity of the peptide neurotransmitters depends on their amino acid sequence (Figure 6.15). Based on their amino acid sequences, neuropeptide transmitters have been loosely grouped into five categories: Neurotransmitters and Their Receptors 153 154 Chapter Six the brain/gut peptides, opioid peptides, pituitary peptides, hypothalamic releasing hormones, and a catch-all category containing other peptides that are not easily classified. Substance P is an example of the first of these categories (Figure 6.15A). The study of neuropeptides actually began more than 60 years ago with the accidental discovery of substance P, a powerful hypotensive agent. (The peculiar name derives from the fact that this molecule was an unidentified component of powder extracts from brain and intestine.) This 11-amino-acid peptide (see Figure 6.15) is present in high concentrations in the human hip-pocampus, neocortex, and also in the gastrointestinal tract; hence its classifi-cation as a brain/gut peptide. It is also released from C fibers, the small-diameter afferents in peripheral nerves that convey information about pain and temperature (as well as postganglionic autonomic signals). Substance P is a sensory neurotransmitter in the spinal cord, where its release can be inhibited by opioid peptides released from spinal cord interneurons, result-ing in the suppression of pain (see Chapter 9). The diversity of neuropep-tides is highlighted by the finding that the gene coding for substance P encodes a number of other neuroactive peptides including neurokinin A, neuropeptide K, and neuropeptide γ. An especially important category of peptide neurotransmitters is the fam-ily of opioids (Figure 6.15B). These peptides are so named because they bind (A) (B) Signal peptide Pre-propeptide Signal peptide Pre-propeptide Propeptide Propeptide Active peptides Met-enkephalin Met-enkephalin Leu-enkephalin Active peptide ACTH β-lipotropin γ-lipotropin β-endorphin Proenkephalin A Pre-proenkephalin A Proopiomelanocortin Pre-proopiomelanocortin Active peptides Figure 6.14 Proteolytic processing of the pre-propeptides pre-proopiome-lanocortin (A) and pre-proenkephalin A (B). For each pre-propeptide, the signal sequence is indicated in orange at the left; the locations of active peptide prod-ucts are indicated by different colors. The maturation of the pre-propeptides involves cleaving the signal sequence and other proteolytic processing. Such processing can result in a number of dif-ferent neuroactive peptides such as ACTH, γ-lipotropin, and β-endorphin (A), or multiple copies of the same pep-tide, such as met-enkephalin (B). to the same postsynaptic receptors activated by opium. The opium poppy has been cultivated for at least 5000 years, and its derivatives have been used as an analgesic since at least the Renaissance. The active ingredients in opium are a variety of plant alkaloids, predominantly morphine. Morphine, named for Morpheus, the Greek god of dreams, is still one of the most effec-tive analgesics in use today, despite its addictive potential (see Box A). Syn-thetic opiates such as meperidine and methadone are also used as anal-gesics, and fentanyl, a drug with 80 times the analgesic potency of morphine, is widely used in clinical anesthesiology. The opioid peptides were discovered in the 1970s during a search for endorphins, endogenous compounds that mimicked the actions of morphine. It was hoped that such compounds would be analgesics, and that under-standing them would shed light on drug addiction. The endogenous lig-ands of the opioid receptors have now been identified as a family of more than 20 opioid peptides that fall into three classes: the endorphins, the enkephalins, and the dynorphins (Table 6.2). Each of these classes are liber-ated from an inactive pre-propeptide (pre-proopiomelanocortin, pre-proenkephalin A, and pre-prodynorphin), derived from distinct genes (see Figure 6.14). Opioid precursor processing is carried out by tissue-specific processing enzymes that are packaged into vesicles, along with the precur-sor peptide, in the Golgi apparatus. Neurotransmitters and Their Receptors 155 Hydrophobic Polar, uncharged Acidic Basic Neurotensin Leu Leu Pro Pro Ile Glu Glu Asn Lys Arg Arg Tyr Neuropeptide-γ Leu Leu Leu Pro Pro Pro Pro Ala Ala Ala Ala Ile Ile Gly Ser Ser Asp Asp Asp Glu Glu Asn Asn Gln Thr His Lys Arg Arg Arg Arg Tyr Tyr Tyr Tyr Tyr Angiotensin-II Pro Val Phe Ile Asp His Arg Tyr Thyrotropin releasing hormone (TRH) Pro Glu His Leutinizing hormone-releasing hormone (LHRH) Leu Pro Trp Gly Gly Ser Glu His Arg Tyr Somatostatin-14 Ala Phe Phe Phe Trp Gly Ser Asn Thr Thr Lys Lys Cys Cys Vasoactive intestinal peptide (VIP) Leu Leu Leu Ala Ala Val Val Met Phe Ile Ser Asp Asp Asn Asn Asn Gln Thr Thr His Lys Lys Lys Arg Arg Tyr Tyr Cholecystokinin octapeptide (CCK-8) Met Met Phe Trp Gly Asp Asp Tyr Substance P Leu Pro Pro Met Phe Phe Gly Gln Lys Arg Gln Dynorphin A Asn Leu Arg Gly Gln Lys Lys Ile Gly Asp Pro Leu Trp Arg Arg Phe Tyr Leucine enkephalin Leu Phe Gly Gly Tyr α-Endorphin Leu Pro Val Ser Ser Glu Gln Thr Thr Thr Lys Met Phe Gly Gly Tyr Adrenocorticotropic hormone (ACTH) Pro Arg Val Arg Glu Tyr Tyr Arg Gly Pro Trp Val Ser Lys Lys His Lys Gly Phe Met Pro Lys Val Ser Vasopressin Leu Pro Phe Gly Gln Arg Tyr Cys Cys Oxytocin Pro Ile Gly Gln Arg/ Lys Arg Cys Tyr Cys Amino acid properties (A) Brain–gut peptides (B) Opioid peptides (C) Pituitary peptides (D) Hypothalamic–releasing peptides (E) Miscellaneous peptides Figure 6.15 Neuropeptides vary in length, but usually contain between 3 and 36 amino acids. The sequence of amino acids determines the biological activity of each peptide. 156 Chapter Six Opioid peptides are widely distributed throughout the brain and are often co-localized with other small-molecule neurotransmitters, such as GABA and 5-HT. In general, these peptides tend to be depressants. When injected intracerebrally in experimental animals, they act as analgesics; on the basis of this and other evidence, opioids are likely to be involved in the mechanisms underlying acupuncture-induced analgesia. Opioids are also involved in complex behaviors such as sexual attraction and aggressive/sub-missive behaviors. They have also been implicated in psychiatric disorders such as schizophrenia and autism, although the evidence for this is debated. Unfortunately, the repeated administration of opioids leads to tolerance and addiction. Virtually all neuropeptides initiate their effects by activating G-protein-coupled receptors. The study of these metabotropic peptide receptors in the brain has been difficult because few specific agonists and antagonists are known. Peptides activate their receptors at low (nM to µM) concentrations compared to the concentrations required to activate receptors for small-mol-ecule neurotransmitters. These properties allow the postsynaptic targets of peptides to be quite far removed from presynaptic terminals and to modu-late the electrical properties of neurons that are simply in the vicinity of the site of peptide release. Neuropeptide receptor activation is especially impor-tant in regulating the postganglionic output from sympathetic ganglia and the activity of the gut (see Chapter 20). Peptide receptors, particularly the neuropeptide Y receptor, are also implicated in the initiation and mainte-nance of feeding behavior leading to satiety or obesity. Other behaviors ascribed to peptide receptor activation include anxiety and panic attacks, and antagonists of cholecystokinin receptors are clinically useful in the treatment of these afflictions. Other useful drugs have been developed by targeting the opiate receptors. Three well-defined opioid receptor subtypes (µ, δ, and κ) play a role in reward mechanisms as well as addiction. The µ-opiate receptor has been specifically identified as the pri-mary site for drug reward mediated by opiate drugs TABLE 6.2 Endogenous Opioid Peptides Name Amino acid sequencea Endorphins α-Endorphin Tyr-Gly-Gly-Phe-Met-Thr-Ser-Glu-Lys-Ser-Gln-Thr-Pro-Leu-Val-Thr α-Neoendorphin Tyr-Gly-Gly-Phe-Leu-Arg-Lys-Tyr-Pro-Lys β-Endorphin Tyr-Gly-Gly-Phe-Met-Thr-Ser-Glu-Lys-Ser-Gln-Thr-Pro-Leu-Val-Thr-Leu-Phe-Lys-Asn-Ala-Ile-Val-Lys-Asn-Ala-His-Lys-Gly-Gln γ-Endorphin Tyr-Gly-Gly-Phe-Met-Thr-Ser-Glu-Lys-Ser-Gln-Thr-Pro-Leu-Val-Thr-Leu Enkephalins Leu-enkephalin Tyr-Gly-Gly-Phe-Leu Met-enkephalin Tyr-Gly-Gly-Phe-Met Dynorphins Dynorphin A Tyr-Gly-Gly-Phe-Leu-Arg-Arg-Ile-Arg-Pro-Lys-Leu-Lys-Trp-Asp-Asn-Gln Dynorphin B Tyr-Gly-Gly-Phe-Leu-Arg-Arg-Gln-Phe-Lys-Val-Val-Thr a Note the initial homology, indicated by italics. Unconventional Neurotransmitters In addition to the conventional neurotransmitters already described, some unusual molecules are also used for signaling between neurons and their targets. These chemical signals can be considered as neurotransmitters because of their roles in interneuronal signaling and because their release from neurons is regulated by Ca2+. However, they are unconventional, in comparison to other neurotransmitters, because they are not stored in syn-aptic vesicles and are not released from presynaptic terminals via exocytotic mechanisms. In fact, these unconventional neurotransmitters need not be released from presynaptic terminals at all and are often associated with “ret-rograde” signaling from postsynaptic cells back to presynaptic terminals. • Endocannabinoids are a family of related endogenous signals that inter-act with cannabinoid receptors. These receptors are the molecular targets of ∆9-tetrahydrocannabinol, the psychoactive component of the marijuana plant, Cannabis (Box F). While some members of this emerging group of chemical signals remain to be determined, anandamide and 2-arachidonyl-glycerol (2-AG) have been established as endocannabinoids. These signals are unsaturated fatty acid with polar head groups and are produced by enzymatic degradation of membrane lipids (Figure 6.16A,B). Production of endocannabinoids is stimulated by a second messenger signal within post-synaptic neurons, typically a rise in postsynaptic Ca2+ concentration. Although the mechanism of endocannabinoid release is not entirely clear, it is likely that these hyrophobic signals diffuse through the postsynaptic membrane to reach cannabinoid receptors on other nearby cells. Endo-cannabinoid action is terminated by carrier-mediated transport of these sig-nals back into the postsynaptic neuron. There they are hydrolyzed by the enzyme fatty acid hydrolase (FAAH). At least two types of cannabinoid receptor have been identified, with most actions of endocannabinoids in the CNS mediated by the type termed CB1. CB1 is a G-protein-coupled receptor that is related to the metabotropic receptors for ACh, glutamate, and the other conventional neurotransmitters. Several compounds that are structurally related to endocannabinoids and that bind to the CB1 receptor have been synthesized (see Figure 6.16C). These compounds act as agonists or antagonists of the CB1 receptor and serve as both tools for elucidating the physiological functions of endo-cannabinoids and as targets for developing therapeutically useful drugs. Endocannabinoids participate in several forms of synaptic regulation. The best-documented action of these agents is to inhibit communication between postsynaptic target cells and their presynaptic inputs. In both the hippocampus and the cerebellum, among other regions, endocannabinoids serve as retrograde signals to regulate GABA release at certain inhibitory terminals. At such synapses, depolarization of the postsynaptic neuron causes a transient reduction in inhibitory postsynaptic responses (Figure 6.17). Depolarization reduces synaptic transmission by elevating the con-centration of Ca2+ within the postsynaptic neuron. This rise in Ca2+ triggers synthesis and release of endocannabinoids from the postsynaptic cells. The endocannabinoids then make their way to the presynaptic terminals and bind to CB1 receptors on these terminals. Activation of the CB1 receptors inhibits the amount of GABA released in response to presynaptic action potentials, thereby reducing inhibitory transmission. These mechanisms responsible for the reduction in GABA release are not entirely clear, but probably involve effects on voltage-gated Ca2+ channels and/or K+ channels in the presynaptic neurons. Neurotransmitters and Their Receptors 157 N N O O O CH3 WIN 55,212–2 Cl Cl Cl N N N O N Rimonabant O O O –O O CH2 C CH CH2 P O OH OH OH OH HO O O C Phosphatidylinositol 1,2-Diacylglycerol (1,2-DAG) Arachidonyl Inositol Acyl 1,2-Diacylglycerol lipase O OH O CH2 C CH CH2 O O C Lysophosphatidylinositol O O O –O O CH2 C CH P O OH OH OH OH HO HO CH2 2-Arachidonylglycerol (2-AG) HO O OH O CH2 C CH CH2 Phospholipase C Lysophospholipase C Phospholipase A1 N-Acyltransferase Phospholipase D Acyl O O O –O O CH2 C CH CH2 P O O O C Phosphatidylethanolamine Alkyl NH3 Anandamide O NH2 + HO O O O –O O CH2 C CH CH2 P O O O C N-Archidonoyl phosphatidylethanolamine NH O (A) (B) (C) Figure 6.16 Endocannabinoid signals involved in synaptic transmission. Possible mechanism of production of the endocannabinoids (A) anan-damide and (B) 2-AG. (C) Structures of the endo-cannabinoid receptor agonist WIN 55,212-2 and the antagonist rimonabant. (A,B after Freund et al., 2003; C after Iversen, 2003.) •Nitric oxide (NO) is an unusual but especially interesting chemical signal. NO is a gas that is produced by the action of nitric oxide synthase, an enzyme that converts the amino acid arginine into a metabolite (citrulline) and simultaneously generates NO (Figure 6.18). NO is produced by an enzyme, nitric oxide synthase. Neuronal NO synthase is regulated by Ca2+ binding to the Ca2+ sensor protein calmodulin (see Chapter 7). Once pro-duced, NO can permeate the plasma membrane, meaning that NO gener-ated inside one cell can travel through the extracellular medium and act within nearby cells. Thus, this gaseous signal has a range of influence that extends well beyond the cell of origin, diffusing a few tens of micrometers from its site of production before it is degraded. This property makes NO a Neurotransmitters and Their Receptors 159 (A) (B) IPSC (pA) Time (ms) 0 50 100 150 200 0 –300 –200 –100 100 (C) Time (s) 0 –20 0 20 40 60 IPSC amplitude (%) 100 75 50 25 Control After depolarizing Vpost Control Rimonabant–treated Record Stimulate Pyramidal neuron Inhibitory interneuron Depolarize Vpost Figure 6.17 Endocannabinoid-mediated retrograde control of GABA release. (A) Experimental arrangement. Stimulation of a presynaptic interneuron causes release of GABA onto a postsynaptic pyramidal neuron. (B) IPSCs elicited by the inhibitory synapse (control) are reduced in amplitude following a brief depolarization of the postsynaptic neuron. This reduction in the IPSC is due to less GABA being released from the presynaptic interneuron. (C) The reduction in IPSC amplitude produced by postsynaptic depolarization lasts a few seconds and is mediated by endo-cannabinoids, because it is prevented by the endocannabinoid receptor antagonist rimonabant. (B,C after Ohno-Shosaku et al., 2001.) Protein kinase G Guanylyl cyclase cGMP GTP NO synthase + Other target cells Citrulline COO− + NH3 CH2 CH2 CH2 CH O NH2 C NH Nitric oxide Arginine COO− + NH3 CH2 CH2 CH2 CH NH2 C NH NH Nitric oxide O2 Various nitrogen oxides Figure 6.18 Synthesis, release, and termination of NO. 160 Chapter Six Box F Marijuana and the Brain Medicinal use of the marijuana plant, Cannabis sativa (Figure A), dates back thousands of years. Ancient civiliza-tions—including both Greek and Roman societies in Europe, as well as Indian and Chinese cultures in Asia—appreciated that this plant was capable of producing relaxation, euphoria, and a number of other psychopharmacological actions. In more recent times, medicinal use of mari-juana has largely subsided (although it remains useful in relieving the symptoms of terminal cancer patients); the recre-ational use of marijuana (Figure B) has become so popular that some societies have decriminalized its use. Understanding the brain mecha-nisms underlying the actions of mari-juana was advanced by the discovery that a cannabinoid, ∆9-tetrahydro-cannabinol (THC; Figure C), is the active component of marijuana. This finding led to the development of syn-thetic derivatives, such as WIN 55,212-2 and rimonabant (see Figure 6.16), that have served as valuable tools for prob-ing the brain actions of THC. Of particu-lar interest is that receptors for these cannabinoids exist in the brain and exhibit marked regional variations in distribution, being especially enriched in the brain areas—such as substantia nigra and caudate putamen—that have been implicated in drug abuse (Figure D). The presence of these brain receptors for cannabinoids led in turn to a search for endogenous cannabinoid com-pounds in the brain, culiminating in the discovery of endocannabinoids such as 2-AG and anandamide (see Figure 6.16). This path of discovery closely parallels the identification of endogenous opioid peptides, which resulted from the search for endogenous morphine-like compounds in the brain (see text and Table 6.2). Given that THC interacts with brain endocannabinoid receptors, particularly (A) Leaf of Cannabis sativa, the marijuana plant. (B) Smoking ground-up Cannabis leaves is a popular method of achieving the euphoric effects of marijuana. (C) Structure of THC (∆9-tetrahydrocannabinol), the active ingredient of marijuana. (D) Distribution of brain CB1 receptors, visualized by examining the binding of CP-55,940, a CB1 receptor ligand. (B photo © Henry Diltz/Corbis; C after Iversen, 2003; D courtesy of M. Herkenham, NIMH.) (C) (D) Cannabis sativa CH3 CH3 CH2 CH2 CH2 CH2 CH3 OH H3C O Hippocampus Caudate putamen Substantia nigra Cerebellum ∆9-Tetrahydrocannabinol (THC) (A) (B) Neurotransmitters and Their Receptors 161 potentially useful agent for coordinating the activities of multiple cells in a very localized region and may mediate certain forms of synaptic plasticity that spread within small networks of neurons. All of the known actions of NO are mediated within its cellular targets; for this reason, NO often is considered a second messenger rather than a neurotransmitter. Some of these actions of NO are due to the activation of the enzyme guanylyl cyclase, which then produces the second messenger cGMP within target cells (see Chapter 7). Other actions of NO are the result of covalent modification of target proteins via nitrosylation, the addition of a nitryl group to selected amino acids within the proteins. NO decays sponta-neously by reacting with oxygen to produce inactive nitrogen oxides. As a result, NO signals last for only a short time, on the order of seconds or less. NO signaling evidently regulates a variety of synapses that also employ con-ventional neurotransmitters; so far, presynaptic terminals that release gluta-mate are the best-studied target of NO in the central nervous system. NO may also be involved in some neurological diseases. For example, it has been proposed that an imbalance between nitric oxide and superoxide generation underlies some neurodegenerative diseases. Summary The complex synaptic computations occurring at neural circuits throughout the brain arise from the actions of a large number of neurotransmitters, which act on an even larger number of postsynaptic neurotransmitter recep-tors. Glutamate is the major excitatory neurotransmitter in the brain, whereas GABA and glycine are the major inhibitory neurotransmitters. The actions of these small-molecule neurotransmitters are typically faster than those of the neuropeptides. Thus, most small-molecule transmitters mediate synaptic transmission when a rapid response is essential, whereas the neu-ropeptide transmitters, as well as the biogenic amines and some small-mole-cule neurotransmitters, tend to modulate ongoing activity in the brain or in peripheral target tissues in a more gradual and ongoing way. Two broadly different families of neurotransmitter receptors have evolved to carry out the postsynaptic signaling actions of neurotransmitters. Ionotropic or ligand-the CB1 receptor, it is likely that such actions are responsible for the behav-ioral consequences of marijuana use. Indeed, many of the well-documented effects of marijuana are consistent with the distribution and actions of brain CB1 receptors. 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F. STEVENS (1998) The tetrameric structure of a glutamate receptor channel. Science: 280: 1596–1599. THOMAS, S. A. AND R. D. PALMITER (1995) Tar-geted disruption of the tyrosine hydroxylase gene reveals that catecholamines are required for mouse fetal development. Nature 374: 640–643. UNWIN, N. (1995) Acetylcholine receptor chan-nels imaged in the open state. Nature 373: 37–43. WANG, Y.M. AND 8 OTHERS (1997) Knockout of the vesicular monoamine transporter 2 gene results in neonatal death and supersensitivity to cocaine and amphetamine. Neuron 19: 1285–1296. Books BRADFORD, H. F. (1986) Chemical Neurobiology. New York: W. H. Freeman. COOPER, J. R., F. E. BLOOM AND R. H. ROTH (2003) The Biochemical Basis of Neuropharmacol-ogy. New York: Oxford University Press. FELDMAN, R. S., J. S. MEYER AND L. F. QUENZER (1997) Principles of Neuropharmacology, 2nd Edition. Sunderland, MA: Sinauer Associates. HALL, Z. (1992) An Introduction to Molecular Neurobiology. Sunderland, MA: Sinauer Asso-ciates. HILLE, B. (2002) Ion Channels of Excitable Mem-branes, 3rd Edition. Sunderland, MA: Sinauer Associates. MYCEK, M. J., R. A. HARVEY AND P. C. CHAMPE (2000) Pharmacology, 2nd Edition. Philadel-phia, New York: Lippincott/Williams and Wilkins Publishers. NICHOLLS, D. G. (1994) Proteins, Transmitters, and Synapses. Boston: Blackwell Scientific. SIEGEL, G.J., B. W. AGRANOFF, R. W. ALBERS, S. K. FISHER AND M. D. UHLER (1999) Basic Neuro-chemistry. Philadelphia: Lippincott-Raven. Overview As is apparent in the preceding chapters, electrical and chemical signaling mechanisms allow one nerve cell to receive and transmit information to another. This chapter focuses on the related events within neurons and other cells that are triggered by the interaction of a chemical signal with its recep-tor. This intracellular processing typically begins when extracellular chemi-cal signals, such as neurotransmitters, hormones, and trophic factors, bind to specific receptors located either on the surface or within the cytoplasm or nucleus of the target cells. Such binding activates the receptors and in so doing stimulates cascades of intracellular reactions involving GTP-binding proteins, second messenger molecules, protein kinases, ion channels, and many other effector proteins whose modulation temporarily changes the physiological state of the target cell. These same intracellular signal trans-duction pathways can also cause longer-lasting changes by altering the tran-scription of genes, thus affecting the protein composition of the target cells on a more permanent basis. The large number of components involved in intracellular signaling pathways allows precise temporal and spatial control over the function of individual neurons, thereby allowing the coordination of electrical and chemical activity in the related populations of neurons that comprise neural circuits and systems. Strategies of Molecular Signaling Chemical communication coordinates the behavior of individual nerve and glial cells in physiological processes that range from neural differentiation to learning and memory. Indeed, molecular signaling ultimately mediates and modulates all brain functions. To carry out such communication, a series of extraordinarily diverse and complex chemical signaling pathways has evolved. The preceding chapters have described in some detail the electrical signaling mechanisms that allow neurons to generate action potentials for conduction of information. These chapters also described synaptic transmis-sion, a special form of chemical signaling that transfers information from one neuron to another. Chemical signaling is not, however, limited to syn-apses (Figure 7.1A). Other well-characterized forms of chemical communica-tion include paracrine signaling, which acts over a longer range than synap-tic transmission and involves the secretion of chemical signals onto a group of nearby target cells, and endocrine signaling, which refers to the secretion of hormones into the bloodstream where they can affect targets throughout the body. Chemical signaling of any sort requires three components: a molecular signal that transmits information from one cell to another, a receptor molecule Chapter 7 165 Molecular Signaling within Neurons 166 Chapter Seven that transduces the information provided by the signal, and a target mole-cule that mediates the cellular response (Figure 7.1B). The part of this process that take place within the confines of the target cell is called intra-cellular signal transduction. A good example of transduction in the context of intercellular communication is the sequence of events triggered by chemi-cal synaptic transmission (see Chapter 5): Neurotransmitters serve as the sig-nal, neurotransmitter receptors serve as the transducing receptor, and the target molecule is an ion channel that is altered to cause the electrical response of the postsynaptic cell. In many cases, however, synaptic transmis-sion activates additional intracellular pathways that have a variety of func-tional consequences. For example, the binding of the neurotransmitter nor-epinephrine to its receptor activates GTP-binding proteins, which produces second messengers within the postsynaptic target, activates enzyme cas-cades, and eventually changes the chemical properties of numerous target molecules within the affected cell. A general advantage of chemical signaling in both intercellular and intra-cellular contexts is signal amplification. Amplification occurs because indi-vidual signaling reactions can generate a much larger number of molecular products than the number of molecules that initiate the reaction. In the case of norepinephrine signaling, for example, a single norepinephrine molecule binding to its receptor can generate many thousands of second messenger molecules (such as cyclic AMP), yielding an amplification of tens of thou-sands of phosphates transferred to target proteins (Figure 7.2). Similar amplification occurs in all signal transduction pathways. Because the trans-duction processes often are mediated by a sequential set of enzymatic reac-tions, each with its own amplification factor, a small number of signal mole-cules ultimately can activate a very large number of target molecules. Such amplification guarantees that a physiological response is evoked in the face of other, potentially countervailing, influences. Another rationale for these complex signal transduction schemes is to permit precise control of cell behavior over a wide range of times. Some mol-ecular interactions allow information to be transferred rapidly, while others are slower and longer lasting. For example, the signaling cascades associated with synaptic transmission at neuromuscular junctions allow a person to respond to rapidly changing cues, such as the trajectory of a pitched ball, while the slower responses triggered by adrenal medullary hormones (epi-nephrine and norepinephrine) secreted during a challenging game produce slower (and longer lasting) effects on muscle metabolism (see Chapter 20) and emotional state (see Chapter 29). To encode information that varies so Signaling cell Signal Receptor Target molecule Response (A) (B) Target molecules Target molecules Target molecules in distant cells Activated receptors Synaptic Paracrine Endocrine Capillary Blood flow Figure 7.1 Chemical signaling mecha-nisms. (A) Forms of chemical communi-cation include synaptic transmission, paracrine signaling, and endocrine sig-naling. (B) The essential components of chemical signaling are: cells that initiate the process by releasing signaling mole-cules; specific receptors on target cells; second messenger target molecules; and subsequent cellular responses. widely over time, the concentration of the relevant signaling molecules must be carefully controlled. On one hand, the concentration of every signaling molecule within the signaling cascade must return to subthreshold values before the arrival of another stimulus. On the other hand, keeping the inter-mediates in a signaling pathway activated is critical for a sustained response. Having multiple levels of molecular interactions facilitates the intricate tim-ing of these events. The Activation of Signaling Pathways The molecular components of these signal transduction pathways are always activated by a chemical signaling molecule. Such signaling molecules can be grouped into three classes: cell-impermeant, cell-permeant, and cell-associated signaling molecules (Figure 7.3). The first two classes are secreted molecules and thus can act on target cells removed from the site of signal synthesis or release. Cell-impermeant signaling molecules typically bind to receptors associated with cell membranes. Hundreds of secreted molecules have now been identified, including the neurotransmitters dis-cussed in Chapter 6, as well as proteins such as neurotrophic factors (see Chapter 22), and peptide hormones such as glucagon, insulin, and various reproductive hormones. These signaling molecules are typically short-lived, either because they are rapidly metabolized or because they are internalized by endocytosis once bound to their receptors. Molecular Signaling within Neurons 167 Amplification Amplification Amplification No amplification No amplification G-proteins Cyclic AMP Protein kinases Phosphates transferred to target proteins Adenylyl cyclase Receptor Figure 7.2 Amplification in signal transduction pathways. The activation of a single receptor by a signaling mole-cule, such as the neurotransmitter nor-epinephrine, can lead to the activation of numerous G-proteins inside cells. These activated proteins can bind to other signaling molecules, such as the enzyme adenylyl cyclase. Each activated enzyme molecule generates a large number of cAMP molecules. cAMP binds to and activates another family of enzymes, protein kinases. These enzymes can then phosphorylate many target proteins. While not every step in this signaling pathway involves amplifi-cation, overall the cascade results in a tremendous increase in the potency of the initial signal. 168 Chapter Seven Figure 7.3 Three classes of cell signal-ing molecules. (A) Cell-impermeant molecules, such as neurotransmitters, cannot readily traverse the plasma membrane of the target cell and must bind to the extracellular portion of transmembrane receptor proteins. (B) Cell-permeant molecules are able to cross the plasma membrane and bind to receptors in the cytoplasm or nucleus of target cells. (C) Cell-associated mole-cules are presented on the extracellular surface of the plasma membrane. These signals activate receptors on target cells only if they are directly adjacent to the signaling cell. Cell-permeant signaling molecules can cross the plasma membrane to act directly on receptors that are inside the cell. Examples include numerous steroid (glucocorticoids, estradiol, and testosterone) and thyroid (thyroxin) hormones, and retinoids. These signaling molecules are relatively insoluble in aqueous solutions and are often transported in blood and other extracel-lular fluids by binding to specific carrier proteins. In this form, they may persist in the bloodstream for hours or even days. The third group of chemical signaling molecules, cell-associated signal-ing molecules, are arrayed on the extracellular surface of the plasma mem-brane. As a result, these molecules act only on other cells that are physically in contact with the cell that carries such signals. Examples include proteins such as the integrins and neural cell adhesion molecules (NCAMs) that influence axonal growth (see Chapter 22). Membrane-bound signaling mol-ecules are more difficult to study, but are clearly important in neuronal development and other circumstances where physical contact between cells provides information about cellular identities. Receptor Types Regardless of the nature of the initiating signal, cellular responses are determined by the presence of receptors that specifically bind the signaling molecules. Binding of signal molecules causes a conformational change in the receptor, which then triggers the subsequent signaling cascade within the affected cell. Given that chemical signals can act either at the plasma membrane or within the cytoplasm (or nucleus) of the target cell, it is not surprising that receptors are actually found on both sides of the plasma membrane. The receptors for impermeant signal molecules are membrane-spanning proteins. The extracellular domain of such receptors includes the binding site for the signal, while the intracellular domain activates intra-cellular signaling cascades after the signal binds. A large number of these receptors have been identified and are grouped into families defined by the mechanism used to transduce signal binding into a cellular response (Figure 7.4). (A) Cell-impermeant molecules (B) Cell-permeant molecules (C) Cell-associated molecules Transmembrane receptors Nucleus Signaling molecules Signaling molecules Signaling molecules Receptor Intracellular receptor Figure 7.4 Categories of cellular recep-tors. Membrane-impermeant signaling molecules can bind to and activate either channel-linked receptors (A), enzyme-linked receptors (B), or G-pro-tein-coupled receptors (C). Membrane permeant signaling molecules activate intracellular receptors (D). Channel-linked receptors (also called ligand-gated ion channels) have the receptor and transducing functions as part of the same protein mole-cule. Interaction of the chemical signal with the binding site of the receptor causes the opening or closing of an ion channel pore in another part of the same molecule. The resulting ion flux changes the membrane potential of the target cell and, in some cases, can also lead to entry of Ca2+ ions that serve as a second messenger signal within the cell. Good examples of such receptors are the ionotropic neurotransmitter receptors described in Chap-ters 5 and 6. Enzyme-linked receptors also have an extracellular binding site for chemical signals. The intracellular domain of such receptors is an enzyme whose catalytic activity is regulated by the binding of an extracellular signal. The great majority of these receptors are protein kinases, often tyrosine kinases, that phosphorylate intracellular target proteins, thereby changing the physiological function of the target cells. Noteworthy members of this Molecular Signaling within Neurons 169 (C) G-protein-coupled receptors (B) Enzyme-linked receptors (D) Intracellular receptors Receptor Signaling molecule Receptor G-protein γ β α γ β α Enzyme inactive Substrate Product Ions (A) Channel-linked receptors Channel closed Signal binds 1 Signal binds 1 1 Signal binds 1 Ions flow across membrane 3 Enzyme generates product 3 Channel opens 2 3 2 Enzyme activated 2 G-protein activated G-protein binds 2 Signal binds Activated receptor regulates transcription 170 Chapter Seven group of receptors are the Trk family of neurotrophin receptors (see Chapter 22) and other receptors for growth factors. G-protein-coupled receptors regulate intracellular reactions by an indi-rect mechanism involving an intermediate transducing molecule, called the GTP-binding proteins (or G-proteins). Because these receptors all share the structural feature of crossing the plasma membrane seven times, they are also referred to as 7-transmembrane receptors (or metabotropic receptors; see Chapter 5). Hundreds of different G-protein-linked receptors have been identified. Well-known examples include the β-adrenergic receptor, the mus-carinic type of acetylcholine receptor, metabotropic glutamate receptors, receptors for odorants in the olfactory system, and many types of receptors for peptide hormones. Rhodopsin, a light-sensitive, 7-transmembrane pro-tein in retinal photoreceptors, is another form of G-protein-linked receptor (see Chapter 10). Intracellular receptors are activated by cell-permeant or lipophilic signal-ing molecules (Figure 7.4D). Many of these receptors lead to the activation of signaling cascades that produce new mRNA and protein within the target cell. Often such receptors comprise a receptor protein bound to an inhibitory protein complex. When the signaling molecule binds to the receptor, the inhibitory complex dissociates to expose a DNA-binding domain on the receptor. This activated form of the receptor can then move into the nucleus and directly interact with nuclear DNA, resulting in altered transcription. Some intracellular receptors are located primarily in the cytoplasm, while others are in the nucleus. In either case, once these receptors are activated they can affect gene expression by altering DNA transcription. G-Proteins and Their Molecular Targets Both G-protein-linked receptors and enzyme-linked receptors can activate biochemical reaction cascades that ultimately modify the function of target proteins. For both these receptor types, the coupling between receptor acti-vation and their subsequent effects are the GTP-binding proteins. There are two general classes of GTP-binding protein (Figure 7.5). Heterotrimeric G-proteins are composed of three distinct subunits (α, β, and γ). There are many different α, β, and γ subunits, allowing a bewildering number of G-protein permutations. Regardless of the specific composition of the het-erotrimeric G-protein, its α subunit binds to guanine nucleotides, either GTP or GDP. Binding of GDP then allows the α subunit to bind to the β and γ subunits to form an inactive trimer. Binding of an extracellular signal to a G-protein-coupled receptor in turn allows the G-protein to bind to the receptor and causes GDP to be replaced with GTP (Figure 7.5A). When GTP is bound to the G-protein, the α subunit dissociates from the βγ complex and activates the G-protein. Following activation, both the GTP-bound α subunit and the free βγ complex can bind to downstream effector molecules that mediate a variety of responses in the target cell. The second class of GTP-binding proteins are monomeric G-proteins (also called small G-proteins). These monomeric GTPases also relay signals from activated cell surface receptors to intracellular targets such as the cytoskeleton and the vesicle trafficking apparatus of the cell. The first small G-protein was discovered in a virus that causes rat sarcoma tumors and was therefore called ras. Ras is a molecule that helps regulate cell differentiation and proliferation by relaying signals from receptor kinases to the nucleus; the viral form of ras is defective, which accounts for the ability of the virus to cause the uncontrolled cell proliferation that leads to tumors. Since then, a large number of small GTPases have been identified and can be sorted into five different subfamilies with different functions. For instance, some are involved in vesicle trafficking in the presynaptic terminal or elsewhere in the neuron, while others play a central role in protein and RNA trafficking in and out of the nucleus. Termination of signaling by both heterotrimeric and monomeric G-pro-teins is determined by hydrolysis of GTP to GDP. The rate of GTP hydrolysis is an important property of a particular G-protein that can be regulated by other proteins, termed GTPase-activating proteins (GAPs). By replacing GTP with GDP, GAPs return G-proteins to their inactive form. GAPs were first recognized as regulators of small G-proteins, but recently similar proteins have been found to regulate the α subunits of heterotrimeric G-proteins. Hence, monomeric and trimeric G-proteins function as molecular timers that are active in their GTP-bound state, and become inactive when they have hydrolized the bound GTP to GDP (Figure 7.5B). Activated G-proteins alter the function of many downstream effectors. Most of these effectors are enzymes that produce intracellular second mes-sengers. Effector enzymes include adenylyl cyclase, guanylyl cyclase, phos-pholipase C, and others (Figure 7.6). The second messengers produced by these enzymes trigger the complex biochemical signaling cascades discussed in the next section. Because each of these cascades is activated by specific G-protein subunits, the pathways activated by a particular receptor are deter-mined by the specific identity of the G-protein subunits associated with it. As well as activating effector molecules, G-proteins can also directly bind to and activate ion channels. For example, some neurons, as well as heart muscle cells, have G-protein-coupled receptors that bind acetylcholine. Because these receptors are also activated by the agonist muscarine, they are usually called muscarinic receptors (see Chapters 6 and 20). Activation of muscarinic receptors can open K+ channels, thereby inhibiting the rate at which the neuron fires action potentials, or slowing the heartbeat of muscle Molecular Signaling within Neurons 171 G-protein Effector protein GDP GTP γ α β γ β GDP Receptor α α GTP Chemical signaling molecule Chemical signaling molecule Receptor GDP GTP GTP GDP GDP Inactive Active GAP GAP Ras Ras Pi Pi (B) Monomeric G-proteins (A) Heterotrimeric G-proteins Figure 7.5 Types of GTP-binding pro-tein. (A) Heterotrimeric G-proteins are composed of three distinct subunits (α, β, and γ). Receptor activation causes the binding of the G-protein and the α sub-unit to exchange GDP for GTP, leading to a dissociation of the α and βγ sub-units. The biological actions of these G-proteins are terminated by hydrolysis of GTP, which is enhanced by GTPase-acti-vating (GAP) proteins. (B) Monomeric G-proteins use similar mechanisms to relay signals from activated cell surface receptors to intracellular targets. Bind-ing of GTP stimulates the biological actions of these G-proteins, and their activity is terminated by hydrolysis of GTP, which is also regulated by GAP proteins. 172 Chapter Seven cells. These inhibitory responses are believed to be the result of βγ subunits of G-proteins binding to the K+ channels. The activation of α subunits can also lead to the rapid closing of voltage-gated Ca2+ and Na+ channels. Because these channels carry inward currents involved in generating action potentials, closing them makes it more difficult for target cells to fire (see Chapters 3 and 4). In summary, the binding of chemical signals to their receptors activates cascades of signal transduction events in the cytosol of target cells. Within such cascades, G-proteins serve a pivotal function as the molecular trans-ducing elements that couple membrane receptors to their molecular effectors within the cell. The diversity of G-proteins and their downstream targets leads to many types of physiological responses. By directly regulating the gating of ion channels, G-proteins can influence the membrane potential of target cells. Second Messengers Neurons use many different second messengers as intracellular signals. These messengers differ in the mechanism by which they are produced and removed, as well as their downstream targets and effects (Figure 7.7A). This section summarizes the attributes of some of the principal second messen-gers. • Calcium. The calcium ion (Ca2+) is perhaps the most common intracellu-lar messenger in neurons. Indeed, few neuronal functions are immune to the influence—direct or indirect—of Ca2+. In all cases, information is transmit-ted by a transient rise in the cytoplasmic calcium concentration, which Gs Gq Norepinephrine Glutamate Dopamine Adenylyl cyclase Protein kinase A b- adrenergic mGluR Dopamine D2 Neuro-transmitter Receptor G-protein Effector protein Later effectors Target action cAMP Second messengers Phospholipase C Diacylglycerol IP3 Protein kinase C Ca2+ release Increase protein phosphorylation and activate calcium-binding proteins Decrease protein phosphorylation Increase protein phosphorylation Gi Adenylyl cyclase Protein kinase A cAMP Figure 7.6 Effector pathways associ-ated with G-protein-coupled receptors. In all three examples shown here, bind-ing of a neurotransmitter to such a receptor leads to activation of a G-pro-tein and subsequent recruitment of sec-ond messenger pathways. Gs, Gq, and Gi refer to three different types of heterotrimeric G-protein. Molecular Signaling within Neurons 173 PKC cGMP GMP GTP cAMP phosphodiesterase Cyclic nucleotide- gated channel Cyclic nucleotide- gated channel cAMP AMP ATP PKA cGMP phosphodiesterase PKG Adenylyl cyclase Guanylyl cyclase Second messenger Sources Ca2+ Cyclic AMP Cyclic GMP IP3 Diacylglycerol Plasma membrane: Voltage-gated Ca2+ channels Various ligand-gated channels Endoplasmic reticulum: IP3 receptors Ryanodine receptors Phospholipase C acts on PIP2 Phospholipase C acts on PIP2 Intracellular targets Protein kinase A Cyclic nucleotide- gated channels Protein kinase G Cyclic nucleotide- gated channels IP3 receptors on endoplasmic reticulum Protein kinase C Removal mechanisms Plasma membrane: Na+/Ca2+ exchanger Ca2+ pump Endoplasmic reticulum: Ca2+ pump Mitochondria cAMP phosphodiesterase cGMP phosphodiesterase Various enzymes Adenylyl cyclase acts on ATP acts on GTP Guanylyl cyclase Phosphatases Calmodulin Protein kinases Ion channels Synaptotagmin Many other Ca2+- binding proteins Protein phosphatases Phosphatidylinositol biphosphate (PIP2) Diacylglycerol Phospholipase C Inositol Phosphatases IP3 IP3 receptors ATP ADP ATP ADP (A) (C) (D) Voltage-gated Ca2+channel Ligand-gated Ca2+channel Ca2+ pump Ca2+ pump Ca2+ Na+/Ca2+ exchanger Na+ H+ Mitochondrion Endoplasmic reticulum Endoplasmic reticulum IP3 receptor Ryanodine receptor Ca2+- binding buffer proteins Ca2+-binding effector proteins [Ca2+]i [Ca2+]i (B) Figure 7.7 Neuronal second messen-gers. (A) Mechanisms responsible for producing and removing second mes-sengers, as well as the downstream tar-gets of these messengers. (B) Proteins involved in delivering calcium to the cytoplasm and in removing calcium from the cytoplasm. (C) Mechanisms of production and degradation of cyclic nucleotides. (D) Pathways involved in production and removal of diacylglyc-erol (DAG) and IP3. 174 Chapter Seven allows Ca2+ to bind to a large number of Ca2+-binding proteins that serve as molecular targets. One of the most thoroughly studied targets of Ca2+ is calmodulin, a Ca2+-binding protein abundant in the cytosol of all cells. Bind-ing of Ca2+ to calmodulin activates this protein, which then initiates its effects by binding to still other downstream targets, such as protein kinases. Ordinarily the concentration of Ca2+ ions in the cytosol is extremely low, typically 50–100 nanomolar (10–9 M). The concentration of Ca2+ ions outside neurons—in the bloodstream or cerebrospinal fluid, for instance—is several orders of magnitude higher, typically several millimolar (10–3 M). This steep Ca2+ gradient is maintained by a number of mechanisms (Figure 7.7B). Most important in this maintenance are two proteins that translocate Ca2+ from the cytosol to the extracellular medium: an ATPase called the calcium pump, and an Na+/Ca2+ exchanger, which is a protein that replaces intracel-lular Ca2+ with extracellular sodium ions (see Chapter 4). In addition to these plasma membrane mechanisms, Ca2+ is also pumped into the endo-plasmic reticulum and mitochondria. These organelles can thus serve as storage depots of Ca2+ ions that are later released to participate in signaling events. Finally, nerve cells contain other Ca2+-binding proteins—such as cal-bindin—that serve as Ca2+ buffers. Such buffers reversibly bind Ca2+ and thus blunt the magnitude and kinetics of Ca2+ signals within neurons. The Ca2+ ions that act as intracellular signals enter cytosol by means of one or more types of Ca2+-permeable ion channels (see Chapter 4). These can be voltage-gated Ca2+ channels or ligand-gated channels in the plasma membrane, both of which allow Ca2+ to flow down the Ca2+ gradient and into the cell from the extracellular medium. In addition, other channels allow Ca2+ to be released from the interior of the endoplasmic reticulum into the cytosol. These intracellular Ca2+-releasing channels are gated, so they can be opened or closed in response to various intracellular signals. One such channel is the inositol trisphosphate (IP3) receptor. As the name implies, these channels are regulated by IP3, a second messenger described in more detail below. A second type of intracellular Ca2+-releasing channel is the ryanodine receptor, named after a drug that binds to and partially opens these receptors. Among the biological signals that activate ryanodine recep-tors are cytoplasmic Ca2+ and, at least in muscle cells, depolarization of the plasma membrane. These various mechanisms for elevating and removing Ca2+ ions allow precise control of both the timing and location of Ca2+ signaling within neu-rons, which in turn permit Ca2+ to control many different signaling events. For example, voltage-gated Ca2+ channels allow Ca2+ concentrations to rise very rapidly and locally within presynaptic terminals to trigger neurotrans-mitter release, as already described in Chapter 5. Slower and more wide-spread rises in Ca2+ concentration regulate a wide variety of other responses, including gene expression in the cell nucleus. • Cyclic nucleotides. Another important group of second messengers are the cyclic nucleotides, specifically cyclic adenosine monophosphate (cAMP) and cyclic guanosine monophosphate (cGMP) (Figure 7.7C). Cyclic AMP is a derivative of the common cellular energy storage molecule, ATP. Cyclic AMP is produced when G-proteins activate adenylyl cyclase in the plasma mem-brane. This enzyme converts ATP into cAMP by removing two phosphate groups from the ATP. Cyclic GMP is similarly produced from GTP by the action of guanylyl cyclase. Once the intracellular concentration of cAMP or cGMP is elevated, these nucleotides can bind to two different classes of tar-gets. The most common targets of cyclic nucleotide action are protein kinases, either the cAMP-dependent protein kinase (PKA) or the cGMP-dependent Figure 7.8 Regulation of cellular pro-teins by phosphorylation. Protein kinases transfer phosphate groups (Pi) from ATP to serine, threonine, or tyro-sine residues on substrate proteins. This phosphorylation reversibly alters the structure and function of cellular pro-teins. Removal of the phosphate groups is catalyzed by protein phosphatases. Both kinases and phosphatases are reg-ulated by a variety of intracellular sec-ond messengers. protein kinase (PKG). These enzymes mediate many physiological responses by phosphorylating target proteins, as described in the following section. In addition, cAMP and cGMP can bind to certain ligand-gated ion channels, thereby influencing neuronal signaling. These cyclic nucleotide-gated chan-nels are particularly important in phototransduction and other sensory trans-duction processes, such as olfaction. Cyclic nucleotide signals are degraded by phosphodiesterases, enzymes that cleave phosphodiester bonds and con-vert cAMP into AMP or cGMP into GMP. • Diacylglycerol and IP3. Remarkably, membrane lipids can also be con-verted into intracellular second messengers (Figure 7.7D). The two most important messengers of this type are produced from phosphatidylinositol bisphosphate (PIP2). This lipid component is cleaved by phospholipase C, an enzyme activated by certain G-proteins and by calcium ions. Phospholipase C splits the PIP2 into two smaller molecules that each act as second messen-gers. One of these messengers is diacylglycerol (DAG), a molecule that remains within the membrane and activates protein kinase C, which phos-phorylates substrate proteins in both the plasma membrane and elsewhere. The other messenger is inositol trisphosphate (IP3), a molecule that leaves the cell membrane and diffuses within the cytosol. IP3 binds to IP3 receptors, channels that release calcium from the endoplasmic reticulum. Thus, the action of IP3 is to produce yet another second messenger (perhaps a third messenger, in this case!) that triggers a whole spectrum of reactions in the cytosol. The actions of DAG and IP3 are terminated by enzymes that convert these two molecules into inert forms that can be recycled to produce new molecules of PIP2. Second Messenger Targets: Protein Kinases and Phosphatases As already mentioned, second messengers typically regulate neuronal func-tions by modulating the phosphorylation state of intracellular proteins (Fig-ure 7.8). Phosphorylation (the addition of phosphate groups) rapidly and reversibly changes protein function. Proteins are phosphorylated by a wide variety of protein kinases; phosphate groups are removed by other enzymes called protein phosphatases. The degree of phosphorylation of a target pro-tein thus reflects a balance between the competing actions of protein kinases and phosphatases, thus integrating a host of cellular signaling pathways. The substrates of protein kinases and phosphatases include enzymes, neuro-transmitter receptors, ion channels, and structural proteins. Molecular Signaling within Neurons 175 ATP ADP Pi P i Protein Phosphoprotein Second messengers Second messengers Protein kinase Protein phosphatase 176 Chapter Seven Protein kinases and phosphatases typically act either on the serine and threonine residues (Ser/Thr kinases or phosphatases) or the tyrosine residues (Tyr kinases or phosphatases) of their substrates. Some of these enzymes act specifically on only one or a handful of protein targets, while others are multifunctional and have a broad range of substrate proteins. The activity of protein kinases and phosphatases can be regulated either by sec-ond messengers, such as cAMP or Ca2+, or by extracellular chemical signals, such as growth factors (see Chapter 22). Typically, second messengers acti-vate Ser/Thr kinases, whereas extracellular signals activate Tyr kinases. Although thousands of protein kinases are expressed in the brain, a rela-tively small number function as regulators of neuronal signaling. • cAMP-dependent protein kinase (PKA). The primary effector of cAMP is the cAMP-dependent protein kinase (PKA). PKA is a tetrameric complex of two catalytic subunits and two inhibitory (regulatory) subunits. cAMP acti-vates PKA by binding to the regulatory subunits and causing them to release active catalytic subunits. Such displacement of inhibitory domains is a gen-eral mechanism for activation of several protein kinases by second messen-gers (Figure 7.9A). The catalytic subunit of PKA phosphorylates serine and threonine residues of many different target proteins. Although this subunit is similar to the catalytic domains of other protein kinases, distinct amino acids allow the PKA to bind to specific target proteins, thus allowing only those targets to be phosphorylated in response to intracellular cAMP signals. • Ca2+/calmodulin-dependent protein kinase type II (CaMKII). Ca2+ ions bind-ing to calmodulin can regulate protein phosphorylation/dephosphorylation. In neurons, the most abundant Ca2+/calmodulin-dependent protein kinase is CaMKII, a multifunctional Ser/Thr protein kinase. CaMKII is composed of approximately 14 subunits, which in the brain are the α and β types. Each subunit contains a catalytic domain and a regulatory domain, as well as other domains that allow the enzyme to oligomerize and target to the proper region within the cell. Ca2+/calmodulin activates CaMKII by displac-ing the inhibitory domain from the catalytic site (Figure 7.9B). CaMKII phosphorylates a large number of substrates, including ion channels and other proteins involved in intracellular signal transduction. • Protein kinase C (PKC). Another important group of Ser/Thr protein kinases is protein kinase C (PKC). PKCs are diverse monomeric kinases acti-vated by the second messengers DAG and Ca2+. DAG causes PKC to move from the cytosol to the plasma membrane, where it also binds Ca2+ and phosphatidylserine, a membrane phospholipid (Figure 7.9C). These events relieve autoinhibition and cause PKC to phosphorylate various protein sub-strates. PKC also diffuses to sites other than the plasma membrane—such as the cytoskeleton, perinuclear sites, and the nucleus—where it phosphory-lates still other substrate proteins. Prolonged activation of PKC can be accomplished with phorbol esters, tumor-promoting compounds that acti-vate PKC by mimicking DAG. • Protein tyrosine kinases. Two classes of protein kinases transfer phosphate groups to tyrosine residues on substrate proteins. Receptor tyrosine kinases are transmembrane proteins with an extracellular domain that binds to pro-tein ligands (growth factors, neurotrophic factors, or cytokines) and an intra-cellular catalytic domain that phosphorylates the relevant substrate proteins. Non-receptor tyrosine kinases are cytoplasmic or membrane-associated enzymes that are indirectly activated by extracellular signals. Tyrosine phos-phorylation is less common than Ser/Thr phosphorylation, and it often serves to recruit signaling molecules to the phosphorylated protein. Tyrosine Figure 7.9 Mechanism of activation of protein kinases. Protein kinases contain several specialized domains with spe-cific functions. Each of the kinases has homologous catalytic domains responsi-ble for transferring phosphate groups to substrate proteins. These catalytic domains are kept inactive by the pres-ence of an autoinhibitory domain that occupies the catalytic site. Binding of second messengers, such as cAMP, DAG, and Ca2+, to the appropriate regu-latory domain of the kinase removes the autoinhibitory domain and allows the catalytic domain to be activated. For some kinases, such as PKC and CaMKII, the autoinhibitory and catalytic domains are part of the same molecule. For other kinases, such as PKA, the autoinhibitory domain is a separate sub-unit. kinases are particularly important for cell growth and differentiation (see Chapters 21 and 22). • Mitogen-activated protein kinase (MAPK). In addition to protein kinases that are directly activated by second messengers, some of these molecules can be activated by other signals, such as phosphorylation by another pro-tein kinase. Important examples of such protein kinases are the mitogen-acti-vated protein kinases (MAPKs), also called extracellular signal-regulated kinases (ERKs). MAPKs were first identified as participants in the control of cell growth and are now known to have many other signaling functions. Molecular Signaling within Neurons 177 Inactive Inactive Inactive Active Active Active cAMP DAG Ca2+ PS (A) PKA (C) PKC (B) CaMKII Ca2+/CaM Catalytic domains Regulatory domain Catalytic domain Regulatory domain Phosphorylates substrates Phosphorylates substrates Catalytic domain Regulatory domain Phosphorylates substrates 178 Chapter Seven MAPKs are normally inactive in neurons but become activated when they are phosphorylated by other kinases. In fact, MAPKs are part of a kinase cas-cade in which one protein kinase phosphorylates and activates the next pro-tein kinase in the cascade. The extracellular signals that trigger these kinase cascades are often extracellular growth factors that bind to receptor tyrosine kinases that, in turn, activate monomeric G-proteins such as ras. Once acti-vated, MAPKs can phosphorylate transcription factors, proteins that regu-late gene expression. Among the wide variety of other MAPK substrates are various enzymes, including other protein kinases, and cytoskeletal proteins. The best-characterized protein phosphatases are the Ser/Thr phos-phatases PP1, PP2A, and PP2B (also called calcineurin). In general, protein phosphatases display less substrate specificity than protein kinases. Their limited specificity may arise from the fact that the catalytic subunits of the three major protein phosphatases are highly homologous, though each still associates with specific targeting or regulatory subunits. PP1 dephosphory-lates a wide array of substrate proteins and is probably the most prevalent Ser/Thr protein phosphatase in mammalian cells. PP1 activity is regulated by several inhibitory proteins expressed in neurons. PP2A is a multisubunit enzyme with a broad range of substrates that overlap with PP1. PP2B, or cal-cineurin, is present at high levels in neurons. A distinctive feature of this phosphatase is its activation by Ca2+/calmodulin. PP2B is composed of a cat-alytic and a regulatory subunit. Ca2+/calmodulin activates PP2B primarily by binding to the catalytic subunit and displacing the inhibitory regulatory domain. PP2B generally does not have the same molecular targets as CaMKII, even though both enzymes are activated by Ca2+/calmodulin. In summary, activation of membrane receptors can elicit complex cas-cades of enzyme activation, resulting in second messenger production and protein phosphorylation or dephosphorylation. These cytoplasmic signals produce a variety of rapid physiological responses by transiently regulating enzyme activity, ion channels, cytoskeletal proteins, and many other cellular processes. In addition, such signals can propagate to the nucleus to cause long-lasting changes in gene expression. Nuclear Signaling Second messengers elicit prolonged changes in neuronal function by pro-moting the synthesis of new RNA and protein. The resulting accumulation of new proteins requires at least 30–60 minutes, a time frame that is orders of magnitude slower than the responses mediated by ion fluxes or phosphory-lation. Likewise, the reversal of such events requires hours to days. In some cases, genetic “switches” can be thrown to permanently alter a neuron, as in neuronal differentiation (see Chapter 21). The amount of protein present in cells is determined primarily by the rate of transcription of DNA into RNA (Figure 7.10). The first step in RNA syn-thesis is the decondensation of the structure of chromatin to provide binding sites for the RNA polymerase complex and for transcriptional activator pro-teins, also called transcription factors. Transcriptional activator proteins attach to binding sites that are present on the DNA molecule near the start of the target gene sequence; they also bind to other proteins that promote unwrapping of DNA. The net result of these actions is to allow RNA poly-merase, an enzyme complex, to assemble on the promoter region of the DNA and begin transcription. In addition to clearing the promoter for RNA polymerase, activator proteins can stimulate transcription by interacting Figure 7.10 Steps involved in tran-scription of DNA into RNA. Condensed chromatin (A) is decondensed into a beads-on-a-DNA-string array (B) in which an upstream activator site (UAS) is free of proteins and is bound by a sequence-specific transcriptional activa-tor protein (transcription factor). The transcriptional activator protein then binds co-activator complexes that enable the RNA polymerase with its associated factors to bind at the start site of tran-scription and initiate RNA synthesis. with the RNA polymerase complex or by interacting with other activator proteins that influence the polymerase. Intracellular signal transduction cascades regulate gene expression by converting transcriptional activator proteins from an inactive state to an active state in which they are able to bind to DNA. This conversion comes about in several ways. The key activator proteins and the mechanisms that allow them to regulate gene expression in response to signaling events are briefly summarized in the following sections. • CREB. The cAMP response element binding protein, usually abbreviated CREB, is a ubiquitous transcriptional activator (Figure 7.11). CREB is nor-mally bound to its binding site on DNA (called the cAMP response element, or CRE), either as a homodimer or bound to another, closely related tran-scription factor. In unstimulated cells, CREB is not phosphorylated and has little or no transcriptional activity. However, phosphorylation of CREB greatly potentiates transcription. Several signaling pathways are capable of causing CREB to be phosphorylated. Both PKA and the ras pathway, for example, can phosphorylate CREB. CREB can also be phosphorylated in response to increased intracellular calcium, in which case the CRE site is also called the CaRE (calcium response element) site. The calcium-dependent phosphorylation of CREB is primarily caused by Ca2+/calmodulin kinase IV (a relative of CaMKII) and by MAP kinase, which leads to prolonged CREB phosphorylation. CREB phosphorylation must be maintained long enough for transcription to ensue, even though neuronal electrical activity only tran-Molecular Signaling within Neurons 179 UAS UAS UAS UAS Beads-on-a-string chromatin Chromosome Binding of transcriptional activator protein Transcriptional activator protein Binding of co-activator complex Co-activator complex RNA polymerase and associated factors Binding of RNA polymerase Transcription begins Start site of RNA (A) (B) Condensed chromatin 180 Chapter Seven Figure 7.11 Transcriptional regulation by CREB. Multiple signaling pathways converge by activating kinases that phosphorylate CREB. These include PKA, Ca2+/calmodulin kinase IV, and MAP kinase. Phosphorylation of CREB allows it to bind co-activators (not shown in the figure), which then stimu-late RNA polymerase to begin synthesis of RNA. RNA is then processed and exported to the cytoplasm, where it serves as mRNA for translation into protein. siently raises intracellular calcium concentration. Such signaling cascades can potentiate CREB-mediated transcription by inhibiting a protein phosphatase that dephosphorylates CREB. CREB is thus an example of the convergence of multiple signaling pathways onto a single transcriptional activator. Many genes whose transcription is regulated by CREB have been identi-fied. CREB-sensitive genes include the immediate early gene, c-fos (see below), the neurotrophin BDNF (see Chapter 22), the enzyme tyrosine hydroxylase (which is important for synthesis of catecholamine neurotransmitters; see Chapter 6), and many neuropeptides (including somatostatin, enkephalin, and corticotropin releasing hormone). CREB also is thought to mediate long-last-ing changes in brain function. For example, CREB has been implicated in spa-tial learning, behavioral sensitization, long-term memory of odorant-condi-tioned behavior, and long-term synaptic plasticity (see Chapters 23 and 24). γ α β DNA CRE/CaRE RNA polymerase Target genes mRNA Transcription G-protein-coupled receptor Ca2+ channel Ca2+ Ca2+ ras Receptor tyrosine kinase Adenylate cyclase Protein kinase A Nucleus Ca2+/calmodulin kinase IV MAP kinase Inside cell Outside cell Newly synthesized protein, e.g., enzyme, structural protein, channels mRNA Translation cAMP Heterotrimeric G-protein Electrical signal CREB Pi Pi • Nuclear receptors. Nuclear receptors for membrane-permeant ligands also are transcriptional activators. The receptor for glucocorticoid hormones illustrates one mode of action of such receptors. In the absence of glucocorti-coid hormones, the receptors are located in the cytoplasm. Binding of gluco-corticoids causes the receptor to unfold and move to the nucleus, where it binds a specific recognition site on the DNA. This DNA binding activates the relevant RNA polymerase complex to initiate transcription and subsequent gene expression. Thus, a critical regulatory event for steroid receptors is their translocation to the nucleus to allow DNA binding. The receptors for thyroid hormone (TH) and other non-steroid nuclear receptors illustrate a second mode of regulation. In the absence of TH, the receptor is bound to DNA and serves as a potent repressor of transcription. Upon binding TH, the receptor undergoes a conformational change that ulti-mately opens the promoter for polymerase binding. Hence, TH binding switches the receptor from being a repressor to being an activator of tran-scription. • c-fos. A different strategy of gene regulation is apparent in the function of the transcriptional activator protein, c-fos. In resting cells, c-fos is present at a very low concentration. However, stimulation of the target cell causes c-fos to be synthesized, and the amount of this protein rises dramatically over 30–60 minutes. Therefore, c-fos is considered to be an immediate early gene because its synthesis is directly triggered by the stimulus. Once synthesized, c-fos protein can act as a transcriptional activator to induce synthesis of sec-ond-order genes. These are termed delayed response genes because their activity is delayed by the fact that an immediate early gene—c-fos in this case—needs to be activated first. Multiple signals converge on c-fos, activating different transcription fac-tors that bind to at least three distinct sites in the promoter region of the gene. The regulatory region of the c-fos gene contains a binding site that mediates transcriptional induction by cytokines and ciliary neurotropic fac-tor. Another site is targeted by growth factors such as neurotrophins through ras and protein kinase C, and a CRE/CaRE that can bind to CREB and thereby respond to cAMP or calcium entry resulting from electrical activity. In addition to synergistic interactions among these c-fos sites, transcriptional signals can be integrated by converging on the same activator, such as CREB. Nuclear signaling events typically result in the generation of a large and relatively stable complex composed of a functional transcriptional activator protein, additional proteins that bind to the activator protein, and the RNA polymerase and associated proteins bound at the start site of transcription. Most of the relevant signaling events act to “seed” this complex by generat-ing an active transcriptional activator protein by phosphorylation, by induc-ing a conformational change in the activator upon ligand binding, by foster-ing nuclear localization, by removing an inhibitor, or simply by making more activator protein. Examples of Neuronal Signal Transduction Understanding the general properties of signal transduction processes at the plasma membrane, in the cytosol, and within the nucleus make it possi-ble to consider how these processes work in concert to mediate specific functions in the brain. Three important signal transduction pathways illus-trate some of the roles of intracellular signal transduction processes in the nervous system. Molecular Signaling within Neurons 181 182 Chapter Seven Figure 7.12 Mechanism of action of NGF. NGF binds to a high-affinity tyro-sine kinase receptor, TrkA, on the plasma membrane to induce phosphor-ylation of TrkA at two different tyrosine residues. These phosphorylated tyrosines serve to tether various adapter proteins or phospholipase C (PLC), which, in turn, activate three major sig-naling pathways: the PI 3 kinase path-way leading to activation of Akt kinase, the ras pathway leading to MAP kinases, and the PLC pathway leading to release of intracellular Ca2+ and acti-vation of PKC. The ras and PLC path-ways primarily stimulate processes responsible for neuronal differentiation, while the PI 3 kinase pathway is primar-ily involved in cell survival. • NGF/TrkA. The first of these is signaling by the nerve growth factor (NGF). This protein is a member of the neurotrophin growth factor family and is required for the differentiation, survival, and synaptic connectivity of sympathetic and sensory neurons (see Chapter 22). NGF works by binding to a high-affinity tyrosine kinase receptor, TrkA, found on the plasma mem-brane of these target cells (Figure 7.12). NGF binding causes TrkA receptors to dimerize, and the intrinsic tyrosine kinase activity of each receptor then phosphorylates its partner receptor. Phosphorylated TrkA receptors trigger the ras cascade, resulting in the activation of multiple protein kinases. Some of these kinases translocate to the nucleus to activate transcriptional activa-tors, such as CREB. This ras-based component of the NGF pathway is pri-marily responsible for inducing and maintaining differentiation of NGF-sen-sitive neurons. Phosphorylation of TrkA also causes this receptor to stimulate the activity of phospholipase C, which increases production of IP3 and DAG. IP3 induces release of Ca2+ from the endoplasmic reticulum, and diacylglycerol activates PKC. These two second messengers appear to target many of the same downstream effectors as ras. Finally, activation of TrkA receptors also causes activation of other protein kinases (such as Akt kinase) that inhibit cell death. This pathway, therefore, primarily mediates the NGF-dependent survival of sympathetic and sensory neurons described in Chap-ter 22. • Long-term depression (LTD). The interplay between several intracellular signals can be observed at the excitatory synapses that innervate Purkinje Pi Pi Pi Pi Ca2+ release from ER ras pathway TrkA MAP Kinase Inside cell Outside cell NGF dimer PI 3 kinase pathway PLC pathway Adapter proteins PI 3 kinase Akt kinase Cell survival GEF ras Kinases Neurite outgrowth and neuronal differentiation PLC DAG PKC IP3 Figure 7.13 Signaling at cerebellar par-allel fiber synapses. Glutamate released by parallel fibers activates both AMPA-type and metabotropic receptors. The latter produces IP3 and DAG within the Purkinje cell. When paired with a rise in Ca2+ associated with activity of climbing fiber synapses, the IP3 causes Ca2+ to be released from the endoplasmic reticu-lum, while Ca2+ and DAG together acti-vate protein kinase C. These signals together change the properties of AMPA receptors to produce LTD. cells in the cerebellum. These synapses are central to information flow through the cerebellar cortex, which in turn helps coordinate motor move-ments (see Chapter 18). One of the synapses is between the parallel fibers (PFs) and their Purkinje cell targets. LTD is a form of synaptic plasticity that causes the PF synapses to become less effective (see Chapter 24). When PFs are active, they release the neurotransmitter glutamate onto the dendrites of Purkinje cells. This activates AMPA-type receptors, which are ligand-gated ion channels (see Chapter 6), and causes a small EPSP that briefly depolar-izes the Purkinje cell. In addition to this electrical signal, PF synaptic trans-mission also generates two second messengers within the Purkinje cell (Fig-ure 7.13). The glutamate released by PFs activates metabotropic glutamate receptors, which stimulates phospholipase C to produce IP3 and DAG. When the PF synapses alone are active, these intracellular signals are insuffi-cient to open IP3 receptors or to stimulate PKC. LTD is induced when PF synapses are activated at the same time as the glutamatergic climbing fiber synapses that also innervate Purkinje cells. The climbing fiber synapses produce large EPSPs that strongly depolarize the membrane potential of the Purkinje cell. This depolarization allows Ca2+ to Molecular Signaling within Neurons 183 Na+ AMPA receptor mGluR Glutamate Na+ Presynaptic terminal of parallel fiber Dendritic spine Phospholipase C PIP2 IP3 DAG PKC Release Ca2+ Ca2+ Ca2+ Climbing fiber depolarizes VM Endoplasmic reticulum Long-term depression 184 Chapter Seven enter the Purkinje cell via voltage-gated Ca2+ channels. When both synapses are simultaneously activated, the rise in intracellular Ca2+ concentration caused by the climbing fiber synapse enhances the sensitivity of IP3 recep-tors to the IP3 produced by PF synapses and allows the IP3 receptors within the Purkinje cell to open. This releases Ca2+ from the endoplasmic reticulum and further elevates Ca2+ concentration locally near the PF synapses. This larger rise in Ca2+, in conjunction with the DAG produced by the PF syn-apses, activates PKC. PKC in turn phosphorylates a number of substrate pro-teins. Ultimately, these signaling processes change AMPA-type receptors at the PF synapse, so that these receptors produce smaller electrical signals in response to the glutamate released from the PFs. This weakening of the PF synapse is the final cause of LTD. In short, transmission at Purkinje cell synapses produces brief electrical signals and chemical signals that last much longer. The temporal interplay between these signals allows LTD to occur only when both PF and climbing fiber synapses are active. The actions of IP3, DAG and Ca2+ also are restricted to small parts of the Purkinje cell dendrite, which is a more limited spatial range than the EPSPs, which spread throughout the entire dendrite and cell body of the Purkinje cell. Thus, in contrast to the electrical signals, the sec-ond messenger signals can impart precise information about the location of active synapses and allow LTD to occur only in the vicinity of active PFs. • Phosphorylation of tyrosine hydroxylase. A third example of intracellular signaling in the nervous system is the regulation of the enzyme tyrosine hydroxylase. Tyrosine hydroxylase governs the synthesis of the catechol-amine neurotransmitters: dopamine, norepinephrine, and epinephrine (see Chapter 6). A number of signals, including electrical activity, other neuro-transmitters, and NGF, increase the rate of catecholamine synthesis by increasing the catalytic activity of tyrosine hydroxylase (Figure 7.14). The rapid increase of tyrosine hydroxylase activity is largely due to phosphory-lation of this enzyme. Tyrosine hydroxylase is a substrate for several protein kinases, including PKA, CaMKII, MAP kinase, and PKC. Phosphorylation causes conforma-tional changes that increase the catalytic activity of tyrosine hydroxylase. Stimuli that elevate cAMP, Ca2+, or DAG can all increase tyrosine hydroxy-lase activity and thus increase the rate of catecholamine biosynthesis. This regulation by several different signals allows for close control of tyrosine hydroxylase activity, and illustrates how several different pathways can con-verge to influence a key enzyme involved in synaptic transmission. Summary A diversity of signal transduction pathways exist within all neurons. Activa-tion of these pathways typically is initiated by chemical signals such as neu-rotransmitters and hormones. These molecules bind to receptors that include ligand-gated ion channels, G-protein-coupled receptors and tyrosine kinase receptors. Many of these receptors activate either heterotrimeric or monomeric G-proteins that regulate intracellular enzyme cascades and/or ion channels. A common outcome of the activation of these receptors is the production of second messengers, such as cAMP, Ca2+, and IP3, that bind to effector enzymes. Particularly important effectors are protein kinases and phosphatases that regulate the phosphorylation state of their substrates, and thus their function. These substrates can be metabolic enzymes or other sig-nal transduction molecules, such as ion channels, protein kinases, or tran-scription factors that regulate gene expression. Examples of transcription Figure 7.14 Regulation of tyrosine hydroxylase by protein phosphoryla-tion. This enzyme governs the synthesis of the catecholamine neurotransmitters and is stimulated by a number of intra-cellular signals. In the example shown here, neuronal electrical activity (1) causes influx of Ca2+ (2). The resultant rise in intracellular Ca2+ concentration (3) activates protein kinases (4), which phosphorylates tyrosine hydroxylase (5) to stimulate catecholamine synthesis (6). This, in turn, increases release of catecholamines (7) and enhances the postsynaptic response produced by the synapse (8). factors include CREB, steroid hormone receptors, and c-fos. This plethora of molecular components allows intracellular signal transduction pathways to generate responses over a wide range of times and distances, greatly aug-menting and refining the information-processing ability of neuronal circuits and ultimately systems. Molecular Signaling within Neurons 185 P i Tyrosine hydroxylase Protein kinase Ca2+ Ca2+ Calcium channel 2 Calcium influx 1 Activation of second messengers 3 Activation of protein kinases 4 Tyrosine hydroxlyase phosphorylated 5 Increase in catecholamine synthesis 6 Increase in transmitter release 7 Increase in postsynaptic response 8 Action potential Additional Reading Reviews AUGUSTINE, G. J., F. SANTAMARIA AND K. TANAKA (2003) Local calcium signaling in neu-rons. Neuron 40: 331–346. DEISSEROTH, K., P. G. MERMELSTEIN, H. XIA AND R. W. 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New York: Oxford Univer-sity Press. 186 Chapter Seven Sensation and Sensory Processing II Surface view of the primary visual cortex illustrating pat-terns of neural activity visual-ized with intrinsic signal opti-cal imaging techniques (see Box C in Chapter 11). Each panel illustrates the activity evoked by viewing a single thin vertical line. The smooth progression of the activated region from the upper left to the lower right panel illustrates the orderly mapping of visual space. The patchy appearance of the activated region in each panel reflects the columnar mapping of orientation prefer-ence. Red regions are the most active, black the least. (Cour-tesy of Bill Bosking, Justin Crowley, Tom Tucker, and David Fitzpatrick.) UNIT II SENSATION AND SENSORY PROCESSING 8 The Somatic Sensory System 9 Pain 10 Vision: The Eye 11 Central Visual Pathways 12 The Auditory System 13 The Vestibular System 14 The Chemical Senses Sensation entails the ability to transduce, encode, and ultimately perceive information generated by stimuli arising from both the external and internal environments. Much of the brain is devoted to these tasks. Although the basic senses—somatic sensation, vision, audition, vestibular sensation, and the chemical senses—are very different from one another, a few fundamental rules govern the way the nervous system deals with each of these diverse modalities. Highly specialized nerve cells called receptors convert the energy associated with mechanical forces, light, sound waves, odorant mol-ecules, or ingested chemicals into neural signals—afferent sensory signals—that convey information about the stimulus to the brain. Afferent sensory signals activate central neurons capable of repre-senting both the qualitative and quantitative aspects of the stimulus (what it is and how strong it is) and, in some modalities (somatic sensation, vision, and audition) the location of the stimulus in space (where it is). The clinical evaluation of patients routinely requires an assess-ment of the sensory systems to infer the nature and location of potential neurological problems. Knowledge of where and how the different sensory modalities are transduced, relayed, represented, and further processed to generate appropriate behavioral responses is therefore essential to understanding and treating a wide variety of diseases. Accordingly, these chapters on the neurobiology of sensa-tion also introduce some of the major structure/function relation-ships in the sensory components of the nervous system. Overview The somatic sensory system has two major components: a subsystem for the detection of mechanical stimuli (e.g., light touch, vibration, pressure, and cutaneous tension), and a subsystem for the detection of painful stimuli and temperature. Together, these two subsystems give humans and other ani-mals the ability to identify the shapes and textures of objects, to monitor the internal and external forces acting on the body at any moment, and to detect potentially harmful circumstances. This chapter focuses on the mechanosen-sory subsystem; the pain and temperature subsystem is taken up in the fol-lowing chapter. Mechanosensory processing of external stimuli is initiated by the activa-tion of a diverse population of cutaneous and subcutaneous mechanorecep-tors at the body surface that relays information to the central nervous system for interpretation and ultimately action. Additional receptors located in mus-cles, joints, and other deep structures monitor mechanical forces generated by the musculoskeletal system and are called proprioceptors. Mechanosen-sory information is carried to the brain by several ascending pathways that run in parallel through the spinal cord, brainstem, and thalamus to reach the primary somatic sensory cortex in the postcentral gyrus of the parietal lobe. The primary somatic sensory cortex projects in turn to higher-order associa-tion cortices in the parietal lobe, and back to the subcortical structures involved in mechanosensory information processing. Cutaneous and Subcutaneous Somatic Sensory Receptors The specialized sensory receptors in the cutaneous and subcutaneous tissues are dauntingly diverse (Table 8.1). They include free nerve endings in the skin, nerve endings associated with specializations that act as amplifiers or filters, and sensory terminals associated with specialized transducing cells that influ-ence the ending by virtue of synapse-like contacts. Based on function, this vari-ety of receptors can be divided into three groups: mechanoreceptors, nocicep-tors, and thermoceptors. On the basis of their morphology, the receptors near the body surface can also be divided into free and encapsulated types. Noci-ceptor and thermoceptor specializations are referred to as free nerve endings because the unmyelinated terminal branches of these neurons ramify widely in the upper regions of the dermis and epidermis (as well as in some deeper tis-sues); their role in pain and temperature sensation is discussed in Chapter 9. Most other cutaneous receptors show some degree of encapsulation, which helps determine the nature of the stimuli to which they respond. Despite their variety, all somatic sensory receptors work in fundamentally the same way: Stimuli applied to the skin deform or otherwise change the Chapter 8 189 The Somatic Sensory System 190 Chapter Eight nerve endings, which in turn affects the ionic permeability of the receptor cell membrane. Changes in permeability generate a depolarizing current in the nerve ending, thus producing a receptor (or generator) potential that triggers action potentials, as described in Chapters 2 and 3. This overall process, in which the energy of a stimulus is converted into an electrical sig-nal in the sensory neuron, is called sensory transduction and is the critical first step in all sensory processing. The quality of a mechanosensory (or any other) stimulus (i.e., what it rep-resents and where it is) is determined by the properties of the relevant recep-tors and the location of their central targets (Figure 8.1). The quantity or strength of the stimulus is conveyed by the rate of action potential discharge triggered by the receptor potential (although this relationship is nonlinear and often quite complex). Some receptors fire rapidly when a stimulus is first presented and then fall silent in the presence of continued stimulation (which is to say they “adapt” to the stimulus), whereas others generate a sustained discharge in the presence of an ongoing stimulus (Figure 8.2). The usefulness of having some receptors that adapt quickly and others that do not is to provide information about both the dynamic and static qualities of a stimulus. Receptors that initially fire in the presence of a stimulus and then TABLE 8.1 The Major Classes of Somatic Sensory Receptors Associated Axonal Receptor Anatomical axonsa (and conduction Rate of Threshold type characteristics diameters) velocities Location Function adaptation of activation Free nerve Minimally C, Aδ 2–20 m/s All skin Pain, Slow High endings specialized temperature, nerve endings crude touch Meissner’s Encapsulated; Aβ Principally Touch, Rapid Low corpuscles between dermal 6–12 µm glabrous pressure papillae skin (dynamic) Pacinian Encapsulated; Aβ Subcutaneous Deep pressure, Rapid Low corpuscles onionlike 6–12 µm tissue, vibration covering interosseous (dynamic) membranes, viscera Merkel’s Encapsulated; Aβ All skin, hair Touch, Slow Low disks associated follicles pressure with peptide-(static) releasing cells Ruffini’s Encapsulated; Aβ All skin Stretching Slow Low corpuscles oriented along 6–12 µm of skin stretch lines Muscle Highly Ia and II Muscles Muscle Both slow Low spindles specialized length and rapid (see Figure 8.5 and Chapter 15) Golgi tendon Highly Ib Tendons Muscle Slow Low organs specialized tension (see Chapter 15) Joint Minimally — Joints Joint position Rapid Low receptors specialized aIn the 1920s and 1930s, there was a virtual cottage industry classifying axons according to their conduction velocity. Three main categories were discerned, called A, B, and C. A comprises the largest and fastest axons, C the smallest and slowest. Mechanoreceptor axons generally fall into category A. The A group is further broken down into subgroups designated a (the fastest), b, and d (the slowest). To make matters even more confusing, muscle afferent axons are usually classified into four additional groups—I (the fastest), II, III, and IV (the slowest)—with subgroups designated by lowercase roman letters! Figure 8.1 General organization of the somatic sensory system. (A) Mecha-nosensory information about the body reaches the brain by way of a three-neu-ron relay (shown in red). The first syn-apse is made by the terminals of the centrally projecting axons of dorsal root ganglion cells onto neurons in the brain-stem nuclei (the local branches involved in segmental spinal reflexes are not shown here). The axons of these second-order neurons synapse on third-order neurons of the ventral posterior nuclear complex of the thalamus, which in turn send their axons to the primary somatic sensory cortex (red). Information about pain and temperature takes a different course (shown in blue; the anterolateral system), and is discussed in the follow-ing chapter. (B) Lateral and midsagittal views of the human brain, illustrating the approximate location of the primary somatic sensory cortex in the anterior parietal lobe, just posterior to the central sulcus. The Somatic Sensory System 191 Central sulcus Primary somatic sensory cortex Medulla Midbrain Gracile nucleus Cuneate nucleus Spinal cord Ventral posterior nuclear complex of thalamus Cerebrum Receptor endings Mechanosensory afferent fiber Pain and temperature afferent fiber Dorsal root ganglion cells (A) (B) Medial leminiscus Somatic sensory cortex 192 Chapter Eight Figure 8.2 Slowly adapting mechano-receptors continue responding to a stim-ulus, whereas rapidly adapting receptors respond only at the onset (and often the offset) of stimulation. These functional differences allow the mechanoreceptors to provide information about both the static (via slowly adapting receptors) and dynamic (via rapidly adapting receptors) qualities of a stimulus. become quiescent are particularly effective in conveying information about changes in the information the receptor reports; conversely, receptors that continue to fire convey information about the persistence of a stimulus. Accordingly, somatic sensory receptors and the neurons that give rise to them are usually classified into rapidly or slowly adapting types (see Table 8.1). Rapidly adapting, or phasic, receptors respond maximally but briefly to stimuli; their response decreases if the stimulus is maintained. Con-versely, slowly adapting, or tonic, receptors keep firing as long as the stim-ulus is present. Mechanoreceptors Specialized to Receive Tactile Information Four major types of encapsulated mechanoreceptors are specialized to pro-vide information to the central nervous system about touch, pressure, vibra-tion, and cutaneous tension: Meissner’s corpuscles, Pacinian corpuscles, Merkel’s disks, and Ruffini’s corpuscles (Figure 8.3 and Table 8.1). These receptors are referred to collectively as low-threshold (or high-sensitivity) mechanoreceptors because even weak mechanical stimulation of the skin induces them to produce action potentials. All low-threshold mechanorecep-tors are innervated by relatively large myelinated axons (type Aβ; see Table 8.1), ensuring the rapid central transmission of tactile information. Meissner’s corpuscles, which lie between the dermal papillae just beneath the epidermis of the fingers, palms, and soles, are elongated recep-tors formed by a connective tissue capsule that comprises several lamellae of Schwann cells. The center of the capsule contains one or more afferent nerve fibers that generate rapidly adapting action potentials following minimal skin depression. Meissner’s corpuscles are the most common mechanore-ceptors of “glabrous” (smooth, hairless) skin (the fingertips, for instance), and their afferent fibers account for about 40% of the sensory innervation of the human hand. These corpuscles are particularly efficient in transducing information about the relatively low-frequency vibrations (30–50 Hz) that occur when textured objects are moved across the skin. Pacinian corpuscles are large encapsulated endings located in the subcu-taneous tissue (and more deeply in interosseous membranes and mesenter-ies of the gut). These receptors differ from Meissner’s corpuscles in their morphology, distribution, and response threshold. The Pacinian corpuscle has an onion-like capsule in which the inner core of membrane lamellae is separated from an outer lamella by a fluid-filled space. One or more rapidly adapting afferent axons lie at the center of this structure. The capsule again acts as a filter, in this case allowing only transient disturbances at high fre-quencies (250–350 Hz) to activate the nerve endings. Pacinian corpuscles adapt more rapidly than Meissner’s corpuscles and have a lower response threshold. These attributes suggest that Pacinian corpuscles are involved in the discrimination of fine surface textures or other moving stimuli that pro-duce high-frequency vibration of the skin. In corroboration of this supposi-tion, stimulation of Pacinian corpuscle afferent fibers in humans induces a sensation of vibration or tickle. They make up 10–15% of the cutaneous receptors in the hand. Pacinian corpuscles located in interosseous mem-branes probably detect vibrations transmitted to the skeleton. Structurally similar endings found in the bills of ducks and geese and in the legs of cranes and herons detect vibrations in water; such endings in the wings of soaring birds detect vibrations produced by air currents. Because they are rapidly adapting, Pacinian corpuscles, like Meissner’s corpuscles, provide information primarily about the dynamic qualities of mechanical stimuli. Rapidly adapting 0 1 2 Time (s) 3 4 Slowly adapting Stimulus Slowly adapting cutaneous mechanoreceptors include Merkel’s disks and Ruffini’s corpuscles (see Figure 8.3 and Table 8.1). Merkel’s disks are located in the epidermis, where they are precisely aligned with the papillae that lie beneath the dermal ridges. They account for about 25% of the mechanoreceptors of the hand and are particularly dense in the fingertips, lips, and external genitalia. The slowly adapting nerve fiber associated with each Merkel’s disk enlarges into a saucer-shaped ending that is closely applied to another specialized cell containing vesicles that apparently release peptides that modulate the nerve terminal. Selective stimulation of these receptors in humans produces a sensation of light pressure. These several properties have led to the supposition that Merkel’s disks play a major role in the static discrimination of shapes, edges, and rough textures. Ruffini’s corpuscles, although structurally similar to other tactile recep-tors, are not well understood. These elongated, spindle-shaped capsular spe-cializations are located deep in the skin, as well as in ligaments and tendons. The long axis of the corpuscle is usually oriented parallel to the stretch lines in skin; thus, Ruffini’s corpuscles are particularly sensitive to the cutaneous stretching produced by digit or limb movements. They account for about 20% of the receptors in the human hand and do not elicit any particular tac-tile sensation when stimulated electrically. Although there is still some ques-tion as to their function, they probably respond primarily to internally gen-erated stimuli (see the section on proprioception, below). Differences in Mechanosensory Discrimination across the Body Surface The accuracy with which tactile stimuli can be sensed varies from one region of the body to another, a phenomenon that illustrates some further principles The Somatic Sensory System 193 Meissner corpuscle Ruffini's corpuscles Merkel's disks Free nerve endings Epidermis Dermis Sweat gland Pacinian corpuscle Figure 8.3 The skin harbors a variety of morphologically distinct mechanore-ceptors. This diagram represents the smooth, hairless (also called glabrous) skin of the fingertip. The major charac-teristics of the various receptor types are summarized in Table 8.1. (After Darian-Smith, 1984.) 194 Chapter Eight Figure 8.4 Variation in the sensitivity of tactile discrimination as a function of location on the body surface, measured here by two-point discrimination. (After Weinstein, 1968.) of somatic sensation. Figure 8.4 shows the results of an experiment in which variation in tactile ability across the body surface was measured by two-point discrimination. This technique measures the minimal interstimulus distance required to perceive two simultaneously applied stimuli as distinct (the indentations of the points of a pair of calipers, for example). When applied to the skin, such stimuli of the fingertips are discretely perceived if they are only 2 mm apart. In contrast, the same stimuli applied to the forearm are not per-ceived as distinct until they are at least 40 mm apart! This marked regional difference in tactile ability is explained by the fact that the encapsulated mechanoreceptors that respond to the stimuli are three to four times more numerous in the fingertips than in other areas of the hand, and many times more dense than in the forearm. Equally important in this regional difference are the sizes of the neuronal receptive fields. The receptive field of a somatic sensory neuron is the region of the skin within which a tactile stimulus evokes a sensory response in the cell or its axon (Boxes A and B). Analysis of the human hand shows that the receptive fields of mechanosensory neurons are 1–2 mm in diameter on the fingertips but 5–10 mm on the palms. The receptive fields on the arm are larger still. The importance of receptive field size is easy to envision. If, for instance, the receptive fields of all cutaneous receptor neurons covered the entire digital pad, it would be impossible to dis-criminate two spatially separate stimuli applied to the fingertip (since all the receptive fields would be returning the same spatial information). 0 5 10 15 20 25 30 35 40 45 50 1 4 3 2 Fingers Thumb Palm Forearm Upper arm Shoulder Forehead Back Breast Belly Thigh Calf Two-point discrimination threshold (mm) Sole Toe Upper lip Nose Cheek The Somatic Sensory System 195 Box A Receptive Fields and Sensory Maps in the Cricket Two principles of somatiosensory organi-zation have emerged from studies of the mammalian brain: (1) individual neu-rons are tuned to particular aspects of complex stimuli; and (2) these stimulus qualities are represented in an orderly fashion in relevant regions of the ner-vous system. These principles apply equally well to invertebrates, including the equivalent of the somatic sensory system in insects such as crickets, grass-hoppers, and cockroaches. In the cricket, the salient tactile stimu-lation for the animal comes from air cur-rents that displace sensory hairs of bilat-erally symmetric sensory structures called cerci (sing. cercus). The location and structure of specific cercal hairs allow them to be displaced by air cur-rents having different directions and speeds (Figure A). Accordingly, the peripheral sensory neurons associated with the hairs represent the full range of air current directions and velocities impinging on the animal. This informa-tion is carried centrally and is systemati-cally represented in a region of the cricket central nervous system called the termi-nal ganglion. Individual neurons in this ganglion correspond to the cercal hairs, and have receptive fields and response properties that represent a full range of directions and speeds for extrinsic mechanical forces, including air currents (Figure B). For the cricket, the significance of this information is, among other things, detecting the direction and speed of oncoming objects to then execute motor programs for escape. (This is also the likely significance of this representation for cockroaches, which can therefore escape the consequences of a descending human foot.) Much like the somatic sensory system in mammals, the primary sensory affer-ents project to the terminal ganglion in an orderly fashion, such that there is a somatotopic map of air current direc-tions. And, like mammals, individual neurons within this representation are tuned to specific aspects of the mechani-cal forces acting on the cricket. These facts about insects’ mecha-nosensory system emphasize that somatic sensory functions are basically similar across a wide range of animals. Indeed, regardless of sensory modality, nervous system organization, or the identity of the organism, it is likely that stimulus specificity will be reflected in receptive fields of individual neurons and there will be orderly mapping of those receptive fields into either a topo-graphic or computational map in the ani-mal’s brain. References JACOBS, G. A. AND F. E. THEUNISSEN (1996) Functional organization of a neural map in the cricket cercal sensory system. J. Neurosci. 16: 769–784. MILLER, J. P., G. A. JACOBS AND F. E. THEUNIS-SEN (1991) Representation of sensory infor-mation in the cricket cercal sensory system. I. Response properties of the primary inter-neurons. J. Neurophys. 66: 1680–1688. MURPHEY, R. K. (1981) The structure and development of somatotopic map in crickets: The cercal afferent projection. Dev. Biol. 88: 236–246. MURPHEY, R. K. AND H. V. B. HIRSCH (1982) From cat to cricket: The genesis of response selectivity of interneurons. Curr. Topics Dev. Biol. 17: 241–256. (A) 0° 90° 135° 315° Front Front Right Rear Left Air current stimulus orientation % Maximal i response response 0 50 100 % Maximal % response response 0 50 100 0° 0° 360/0° 90° 90° 180° 180° 270° 270° Time (ms) Membrane potential (mV) 0 100 200 (B) Speaker velocity (A) Intracellular recording of action potential activity of an individual sensory neuron’s responses to different directions of wind current. (B) The plots indicate this neuron’s receptive field for wind direction (top) and the tuning curve for the neuron’s selective firing to its pre-ferred direction. (After Miller et al., 1991.) 196 Chapter Eight Receptor density and receptive field sizes in different regions are not the only factors determining somatic sensation. Psychophysical analysis of tac-tile performance suggests that something more than the cutaneous periph-ery is needed to explain variations in tactile perception. For instance, sensory thresholds in two-point discrimination tests vary with practice, fatigue, and stress. The contextual significance of stimuli is also important in determin-ing what we actually feel; even though we spend most of the day wearing clothes, we usually ignore the tactile stimulation that they produce. Some aspect of the mechanosensory system allows us to filter out this information and pay attention to it only when necessary. The fascinating phenomenon of “phantom limb” sensations after amputation (see Box C in Chapter 9) pro-vides further evidence that tactile perception is not fully explained by the Box B Dynamic Aspects of Somatic Sensory Receptive Fields When humans explore objects with their hands, multiple contacts between the skin and the object surface generate extraordinarily complex patterns of tac-tile stimuli. As a consequence, the somatic sensory system must process signals that change continuously in time. Nonetheless, we routinely discriminate the size, texture and shape of objects with great accuracy. Until recently, the temporal structure of such stimuli was not considered a major variable in char-acterizing the physiological properties of somatic sensory neurons. For instance, the classical definition of the receptive field of a somatic sensory neuron takes into account only the overall area of the body surface that elicits significant varia-tion in the neuron’s firing rate. By the same token, the topographic maps in the somatic sensory system have been inter-preted as evidence that tactile informa-tion processing involves primarily spatial criteria. The advent of multiple electrode recording to simultaneously monitor the activity of large populations of single neurons has begun to change this “stat-ic” view of the somatic sensory system. In both primates and rodents, this approach has shown that the receptive fields of cortical and subcortical neurons SI VPM (A) SpV PrV (A) Simultaneous electrode recordings in behaving rats allow monitoring of the spatiotempo-ral spread of neuronal activation across several levels of the somatic sensory system following stimulation (of a single facial whisker, in this example). These 3-D graphs represent patterns of neuronal ensemble activity at each level of the pathway. The x axis represents the poststim-ulus time in ms, the y axis the number of neurons recorded at each level; the color-coded gra-dient in the z axis shows the response of the neurons, with red the highest firing and green the lowest. SI, somatic sensory cortex; VPM, ventral posterior medial nucleus of the thalamus; SpV, spinal nucleus of the trigeminal brainstem complex; PrV, principal nucleus of the brain-stem trigeminal complex. (From Nicholelis et al., 1997.) peripheral information that travels centrally. The central nervous system clearly plays an active role in determining the perception of the mechanical forces that act on us. Mechanoreceptors Specialized for Proprioception Whereas cutaneous mechanoreceptors provide information derived from external stimuli, another major class of receptors provides information about mechanical forces arising from the body itself, the musculoskeletal system in particular. These are called proprioceptors, roughly meaning “receptors for self.” The purpose of proprioceptors is primarily to give detailed and contin-uous information about the position of the limbs and other body parts in The Somatic Sensory System 197 vary as a function of time: The neuron responds differently to a spatially defined stimulus as the period of stimu-lation proceeds (see Figures A and B). This coupling of space and time can also be demonstrated at level of somato-topic maps. By recording the activity of single neurons located in different regions of the map simultaneously, it is apparent that the stimulation of a small area of the skin tends to excite more and more neurons as time goes by. Thus, many more neurons than those located in the area of the map directly represent-ing the stimulated skin actually respond to the stimulus, albeit at longer latencies. The end result of these more complex neuronal responses is the emergence of spatiotemporal representations at all lev-els of the somatic sensory system. Thus, contrary to the classical notion of recep-tive fields, the somatic sensory system processes information in a dynamic way. Such processing is not only relevant for the normal operation of the system, but may also account for some aspects of adult plasticity (see Chapter 24). References GHAZANFAR, A. A. AND M. A. L. NICOLELIS (1999) Spatiotemporal properties of layer V neurons of the rat primary somatosensory cortex. Cereb. Cortex 4: 348–361. NICOLELIS, M. A. L., A. A. GHAZANFAR, B. FAG-GIN, S. VOTAW AND L. M. O. OLIVEIRA (1997) Reconstructing the engram: Simultaneous, multiple site, many single neuron recordings. Neuron 18: 529–537. NICOLELIS, M. A. L. AND 7 OTHERS (1998) Simultaneous encoding of tactile information by three primate cortical areas. Nature Neu-rosci. 1: 621–630. (B) Receptive fields of two cortical neurons from two different animals. Each panel represents the matrix of whiskers on the animals’ snout (whisker columns are on the x axis and whisker rows on the y axis) for a 4-ms epoch of poststimulus time. Within a particular time period, the center of the receptive field is defined as the whisker eliciting the greatest response magnitude (yellow). Note that the receptive field centers shift as a function of time. (From Ghazanfar and Nicholelis, 1998.) (B) Whisker rows Whisker rows Whisker columns A B C D E A B C D E 0 2 1 3 4 0 2 1 3 4 0 2 1 3 4 0 2 1 3 4 0 2 1 3 4 Whisker columns 0 2 1 3 4 0 2 1 3 4 0 2 1 3 4 0 2 1 3 4 0 2 1 3 4 8−12 ms 12−16 ms 16−20 ms 20−24 ms 24−28 ms 8−12 ms 12−16 ms 16−20 ms 20−24 ms 24−28 ms 198 Chapter Eight Figure 8.5 A muscle spindle and sev-eral extrafusal muscle fibers. See text for description. (After Matthews, 1964.) space (specialized mechanoreceptors also exist in the heart and major vessels to provide information about blood pressure, but these neurons are consid-ered to be part of the visceral motor system; see Chapter 20). Low-threshold mechanoreceptors, including muscle spindles, Golgi tendon organs, and joint receptors, provide this kind of sensory information, which is essential to the accurate performance of complex movements. Information about the position and motion of the head is particularly important; in this case, pro-prioceptors are integrated with the highly specialized vestibular system, which is considered separately in Chapter 13. The most detailed knowledge about proprioception derives from studies of muscle spindles, which are found in all but a few striated (skeletal) mus-cles. Muscle spindles consist of four to eight specialized intrafusal muscle fibers surrounded by a capsule of connective tissue. The intrafusal fibers are distributed among the ordinary (extrafusal) fibers of skeletal muscle in a parallel arrangement (Figure 8.5). In the largest of the several intrafusal fibers, the nuclei are collected in an expanded region in the center of the fiber called a bag; hence the name nuclear bag fibers. The nuclei in the remain-ing two to six smaller intrafusal fibers are lined up single file, with the result that these fibers are called nuclear chain fibers. Myelinated sensory axons belonging to group Ia innervate muscle spindles by encircling the middle portion of both types of intrafusal fibers (see Figure 8.5 and Table 8.1). The Ia axon terminal is known as the primary sensory ending of the spindle. Sec-ondary innervation is provided by group II axons that innervate the nuclear chain fibers and give off a minor branch to the nuclear bag fibers. The intra-fusal muscle fibers contract when commanded to do so by motor axons derived from a pool of specialized motor neurons in the spinal cord (called g motor neurons). The major function of muscle spindles is to provide infor-mation about muscle length (that is, the degree to which they are being stretched). A detailed account of how these important receptors function during movement is given in Chapters 15 and 16. The density of spindles in human muscles varies. Large muscles that gen-erate coarse movements have relatively few spindles; in contrast, extraocular muscles and the intrinsic muscles of the hand and neck are richly supplied with spindles, reflecting the importance of accurate eye movements, the need to manipulate objects with great finesse, and the continuous demand for precise positioning of the head. This relationship between receptor den-Extrafusal muscle fibers Intrafusal muscle fibers Nuclear chain fiber Subcapsular space Capsule surrounding spindle Nuclear bag fiber Axons of g motor neurons Group I and II afferent axons Axon of a motor neuron sity and muscle size is consistent with the generalization that the sensory motor apparatus at all levels of the nervous system is much richer for the hands, head, speech organs, and other parts of the body that are used to per-form especially important and demanding tasks. Spindles are lacking alto-gether in a few muscles, such as those of the middle ear, which do not require the kind of feedback that these receptors provide. Whereas muscle spindles are specialized to signal changes in muscle length, low-threshold mechanoreceptors in tendons inform the central ner-vous system about changes in muscle tension. These mechanoreceptors, called Golgi tendon organs, are innervated by branches of group Ib afferents and are distributed among the collagen fibers that form the tendons (see Chapter 15). Finally, rapidly adapting mechanoreceptors in and around joints gather dynamic information about limb position and joint movement. The function of these joint receptors is not well understood. Active Tactile Exploration Tactile discrimination—that is, perceiving the detailed shape or texture of an object—normally entails active exploration. In humans, this is typically accomplished by using the hands to grasp and manipulate objects, or by moving the fingers across a surface so that a sequence of contacts between the skin and the object of interest is established. Psychophysical evidence indicates that relative movement between the skin and a surface is the single most important requirement for accurate discrimination of texture. Animal experiments confirm the dependence of tactile discrimination on active exploration. Rats, for instance, discriminate the details of texture by rhyth-mically brushing their facial whiskers across surfaces. Active touching, which is called haptics, involves the interpretation of complex spatiotempo-ral patterns of stimuli that are likely to activate many classes of mechanore-ceptors. Haptics also requires dynamic interactions between motor and sen-sory signals, which presumably induce sensory responses in central neurons that differ from the responses of the same cells during passive stimulation of the skin (see Box B). The Major Afferent Pathway for Mechanosensory Information: The Dorsal Column–Medial Lemniscus System The action potentials generated by tactile and other mechanosensory stimuli are transmitted to the spinal cord by afferent sensory axons traveling in the peripheral nerves. The neuronal cell bodies that give rise to these first-order axons are located in the dorsal root (or sensory) ganglia associated with each segmental spinal nerve (see Figure 8.1 and Box C). Dorsal root ganglion cells are also known as first-order neurons because they initiate the sensory process. The ganglion cells thus give rise to long peripheral axons that end in the somatic receptor specializations already described, and shorter central axons that reach the dorsolateral region of the spinal cord via the dorsal (sensory) roots of each spinal cord segment. The large myelinated fibers that innervate low-threshold mechanoreceptors are derived from the largest neu-rons in these ganglia, whereas the smaller ganglion cells give rise to smaller afferent nerve fibers that end in the high-threshold nociceptors and thermo-ceptors (see Table 8.1). Depending on whether they belong to the mechanosensory system or to the pain and temperature system, the first-order axons carrying information The Somatic Sensory System 199 200 Chapter Eight from somatic receptors have different patterns of termination in the spinal cord and define distinct somatic sensory pathways within the central ner-vous system (see Figure 8.1). The dorsal column–medial lemniscus path-way carries the majority of information from the mechanoreceptors that mediate tactile discrimination and proprioception (Figure 8.6); the spino-thalamic (anterolateral) pathway mediates pain and temperature sensation and is described in Chapter 9. This difference in the afferent pathways of these modalities is one of the reasons that pain and temperature sensation is treated separately here. Upon entering the spinal cord, the first-order axons carrying information from peripheral mechanoreceptors bifurcate into ascending and descending branches, which in turn send collateral branches to several spinal segments. Some collateral branches penetrate the dorsal horn of the cord and synapse on neurons located mainly in a region called Rexed’s laminae III–V. These synapses mediate, among other things, segmental reflexes such as the “knee-jerk” or myotatic reflex described in Chapter 1, and are further considered in Chapters 15 and 16. The major branch of the incoming axons, however, ascends ipsilaterally through the dorsal columns (also called the posterior funiculi) of the cord, all the way to the lower medulla, where it terminates by contacting second-order neurons in the gracile and cuneate nuclei (together referred to as the dorsal column nuclei; see Figures 8.1 and 8.6A). Axons in the dorsal columns are topographically organized such that the fibers that convey information from lower limbs are in the medial subdivision of the dorsal columns, called the gracile tract, a fact of some significance in the clinical localization of neural injury. The lateral subdivision, called the cuneate tract, contains axons conveying information from the upper limbs, trunk, and neck. At the level of the upper thorax, the dorsal columns account for more than a third of the cross-sectional area of the human spinal cord. Despite their size, lesions limited to the dorsal columns of the spinal cord in both humans and monkeys have only a modest effect on the performance of simple tactile tasks. Such lesions, however, do impede the ability to detect the direction and speed of tactile stimuli, as well as degrading the ability to sense the position of the limbs in space. Dorsal column lesions may also reduce a patient’s ability to initiate active movements related to tactile explo-ration. For instance, such individuals have difficulty recognizing numbers and letters drawn on their skin. The relatively mild deficit that follows dor-sal column lesions is presumably explained by the fact that some axons responsible for cutaneous mechanoreception also run in the spinothalamic (pain and temperature) pathway, as described in Chapter 9. The second-order relay neurons in the dorsal column nuclei send their axons to the somatic sensory portion of the thalamus (see Figure 8.6A). The axons from dorsal column nuclei project in the dorsal portion of each side of the lower brainstem, where they form the internal arcuate tract. The internal arcuate axons subsequently cross the midline to form another named tract that is elongated dorsoventrally, the medial lemniscus. (The crossing of these fibers is called the decussation of the medial lemniscus, from the roman numeral “X,” or decem; the word lemniscus means “ribbon.”) In a cross-section through the medulla, such as the one shown in Figure 8.6A, the medial lemniscal axons carrying information from the lower limbs are located ventrally, whereas the axons related to the upper limbs are located dorsally (again, a fact of some clinical importance). As the medial lemniscus ascends through the pons and midbrain, it rotates 90° laterally, so that the upper body is eventually represented in the medial portion of the tract, and the lower body in the lateral portion. The axons of the medial lem-The Somatic Sensory System 201 Mid-pons Midbrain Rostral medulla Caudal medulla Cervical spinal cord Lumbar spinal cord Ventral posterior lateral nucleus of the thalamus Cerebrum Primary somatic sensory cortex (A) (B) Internal arcuate fibers Medial leminiscus Medial lemniscus Medial lemniscus Gracile tract Ventral posterior medial nucleus of thalamus Trigeminothalamic tract (trigeminal lemniscus) Cuneate tract Mechanosensory receptors from upper body Mechanosensory receptors from lower body Cuneate nucleus (pathways from upper body) Gracile nucleus (pathways from lower body) Trigeminal ganglion Mechano-sensory receptors from face Principal nucleus of trigeminal complex Figure 8.6 Schematic representation of the main mechanosensory pathways. (A) The dorsal column–medial lemnis-cus pathway carries mechanosensory information from the posterior third of the head and the rest of the body. (B) The trigeminal portion of the mechano-sensory system carries similar informa-tion from the face. 202 Chapter Eight niscus thus reach the ventral posterior lateral (VPL) nucleus of the thalamus, whose cells are the third-order neurons of the dorsal column–medial lem-niscus system (see Figure 8.7). The Trigeminal Portion of the Mechanosensory System As noted, the dorsal column–medial lemniscus pathway described in the preceding section carries somatic information from only the upper and lower body and from the posterior third of the head. Tactile and propriocep-Each dorsal root (or sensory) ganglion and associated spinal nerve arises from an iterated series of embryonic tissue masses called somites. This fact of devel-opment explains the overall segmental arrangement of somatic nerves (and the targets they innervate) in the adult (see figure). The territory innervated by each spinal nerve is called a dermatome. In humans, the cutaneous area of each der-matome has been defined in patients in whom specific dorsal roots were affected (as in herpes zoster, or “shingles”) or after surgical interruption (for relief of pain or other reasons). Such studies show that dermatomal maps vary among individuals. Moreover, dermatomes overlap substantially, so that injury to an individual dorsal root does not lead to complete loss of sensation in the relevant skin region, the overlap being more extensive for touch, pressure, and vibra-tion than for pain and temperature. Thus, testing for pain sensation provides a more precise assessment of a segmental nerve injury than does testing for responses to touch, pressure, or vibra-tion. Finally, the segmental distribution of proprioceptors does not follow the dermatomal map but is more closely allied with the pattern of muscle inner-vation. Despite these limitations, knowl-edge of dermatomes is essential in the clinical evaluation of neurological patients, particularly in determining the level of a spinal lesion. Cervical Trigeminal nerve branches Thoracic Lumbar Sacral S1 S2−S4 L5 L4 L3 L2 L1 T12 T11 T10 T9 T8 T6 T5 T4 C5 C4 C3 C2 C8 C7 C6 C5 T7 T1 T2 T3 Sacral Lumbar Thoracic Cervical The innervation arising from a single dorsal root ganglion and its spinal nerve is called a der-matome. The full set of sen-sory dermatomes is shown here for a typical adult. Knowledge of this arrange-ment is particularly impor-tant in defining the location of suspected spinal (and other) lesions. The numbers refer to the spinal segments by which each nerve is named. (After Rosenzweig et al., 2002.) Box C Dermatomes tive information from the face is conveyed from the periphery to the thala-mus by a different route. Information derived from the face is transmitted to the central nervous system via the trigeminal somatic sensory system (Fig-ure 8.6B). Low-threshold mechanoreception in the face is mediated by first-order neurons in the trigeminal (cranial nerve V) ganglion. The peripheral processes of these neurons form the three main subdivisions of the trigemi-nal nerve (the ophthalmic, maxillary, and mandibular branches), each of which innervates a well-defined territory on the face and head, including the teeth and the mucosa of the oral and nasal cavities. The central processes of trigeminal ganglion cells form the sensory roots of the trigeminal nerve; they enter the brainstem at the level of the pons to terminate on neurons in the subdivisions of the trigeminal brainstem complex. The trigeminal complex has two major components: the principal nucleus (responsible for processing mechanosensory stimuli), and the spinal nucleus (responsible for processing painful and thermal stimuli). Thus, most of the axons carrying information from low-threshold cutaneous mechanore-ceptors in the face terminate in the principal nucleus. In effect, this nucleus corresponds to the dorsal column nuclei that relay mechanosensory infor-mation from the rest of the body. The spinal nucleus corresponds to a por-tion of the spinal cord that contains the second-order neurons in the pain and temperature system for the rest of the body (see Chapter 9). The second-order neurons of the trigeminal brainstem nuclei give off axons that cross the midline and ascend to the ventral posterior medial (VPM) nucleus of the thalamus by way of the trigeminothalamic tract (also called the trigeminal lemniscus). The Somatic Sensory Components of the Thalamus Each of the several ascending somatic sensory pathways originating in the spinal cord and brainstem converge on the thalamus (Figure 8.7). The ven-tral posterior complex of the thalamus, which comprises a lateral and a medial nucleus, is the main target of these ascending pathways. As already mentioned, the more laterally located ventral posterior lateral (VPL) nucleus receives projections from the medial lemniscus carrying all somatosensory information from the body and posterior head, whereas the more medially located ventral posterior medial (VPM) nucleus receives axons from the trigeminal lemniscus (that is, mechanosensory and nocicep-tive information from the face). Accordingly, the ventral posterior complex of the thalamus contains a complete representation of the somatic sensory periphery. The Somatic Sensory Cortex The axons arising from neurons in the ventral posterior complex of the thal-amus project to cortical neurons located primarily in layer IV of the somatic sensory cortex (see Figure 8.7; also see Box A in Chapter 25 for a more detailed description of cortical lamination). The primary somatic sensory cortex in humans (also called SI), which is located in the postcentral gyrus of the parietal lobe, comprises four distinct regions, or fields, known as Brod-mann’s areas 3a, 3b, 1, and 2. Experiments carried out in nonhuman pri-mates indicate that neurons in areas 3b and 1 respond primarily to cuta-neous stimuli, whereas neurons in 3a respond mainly to stimulation of proprioceptors; area 2 neurons process both tactile and proprioceptive stim-uli. Mapping studies in humans and other primates show further that each The Somatic Sensory System 203 204 Chapter Eight of these four cortical areas contains a separate and complete representation of the body. In these somatotopic maps, the foot, leg, trunk, forelimbs, and face are represented in a medial to lateral arrangement, as shown in Figures 8.8A,B and 8.9. Although the topographic organization of the several somatic sensory areas is similar, the functional properties of the neurons in each region and their organization are distinct (Box D). For instance, the neuronal receptive fields are relatively simple in area 3b; the responses elicited in this region are generally to stimulation of a single finger. In areas 1 and 2, however, the majority of the receptive fields respond to stimulation of multiple fingers. Furthermore, neurons in area 1 respond preferentially to particular direc-tions of skin stimulation, whereas many area 2 neurons require complex stimuli to activate them (such as a particular shape). Lesions restricted to area 3b produce a severe deficit in both texture and shape discrimination. In contrast, damage confined to area 1 affects the ability of monkeys to perform accurate texture discrimination. Area 2 lesions tend to produce deficits in finger coordination, and in shape and size discrimination. A salient feature of cortical maps, recognized soon after their discovery, is their failure to represent the body in actual proportion. When neurosurgeons determined the representation of the human body in the primary sensory (and motor) cortex, the homunculus (literally, “little man”) defined by such mapping procedures had a grossly enlarged face and hands compared to the torso and proximal limbs (Figure 8.8C). These anomalies arise because Central sulcus Primary somatic sensory cortex (SI) Somatic sensory cortex Secondary somatic sensory cortex (SII) Thalamus Posterior parietal cortex Postcentral gyrus 4 3a 3b 1 2 5 7 Ventral posterior lateral nucleus (VPL) VP complex Ventral posterior medial nucleus (VPM) Figure 8.7 Diagram of the somatic sensory portions of the thalamus and their cor-tical targets in the postcentral gyrus. The ventral posterior nuclear complex com-prises the VPM, which relays somatic sensory information carried by the trigeminal system from the face, and the VPL, which relays somatic sensory information from the rest of the body. Inset above shows organization of the primary somatosensory cortex in the postcentral gyrus, shown here in a section cutting across the gyrus from anterior to posterior. (After Brodal, 1992, and Jones et al., 1982.) manipulation, facial expression, and speaking are extraordinarily important for humans, requiring more central (and peripheral) circuitry to govern them. Thus, in humans, the cervical spinal cord is enlarged to accommodate the extra circuitry related to the hand and upper limb, and as stated earlier, the density of receptors is greater in regions such as the hands and lips. Such distortions are also apparent when topographical maps are compared across species. In the rat brain, for example, an inordinate amount of the somatic sensory cortex is devoted to representing the large facial whiskers that pro-The Somatic Sensory System 205 (B) (C) Central sulcus Shoulder Neck Head Neck Arm Hand Digits Thumb Eyes Nose Face Lips Jaw Tongue Throat Toes Genitalia Feet Leg Trunk (A) Somatic sensory cortex Lateral Medial Figure 8.8 Somatotopic order in the human primary somatic sensory cortex. (A) Diagram showing the region of the human cortex from which electrical activity is recorded following mechanosensory stimulation of different parts of the body. The patients in the study were undergoing neurosurgical procedures for which such mapping was required. Although modern imaging methods are now refining these classical data, the human somatotopic map first defined in the 1930s has remained generally valid. (B) Diagram along the plane in (A) showing the somatotopic repre-sentation of body parts from medial to lateral. (C) Cartoon of the homunculus con-structed on the basis of such mapping. Note that the amount of somatic sensory cor-tex devoted to the hands and face is much larger than the relative amount of body surface in these regions. A similar disproportion is apparent in the primary motor cortex, for much the same reasons (see Chapter 17). (After Penfield and Rasmussen, 1950, and Corsi, 1991.) 206 Chapter Eight Figure 8.9 The primary somatic sensory map in the owl monkey based, as in Fig-ure 8.8, on the electrical responsiveness of the cortex to peripheral stimulation. Much more detailed mapping is possible in experimental animals than in neuro-surgical patients. The enlargement on the right shows areas 3b and 1, which process most cutaneous mechanosensory infor-mation. The arrangement is generally similar to that determined in humans. (After Kaas, 1983.) vide a key component of the somatic sensory input for rats and mice (see Boxes B and D), while raccoons overrepresent their paws and the platypus its bill. In short, the sensory input (or motor output) that is particularly sig-nificant to a given species gets relatively more cortical representation. Higher-Order Cortical Representations Somatic sensory information is distributed from the primary somatic sensory cortex to “higher-order” cortical fields (as well as to subcortical structures). One of these higher-order cortical centers, the secondary somatosensory cor-tex (sometimes called SII and adjacent to the primary cortex; see Figure 8.7), receives convergent projections from the primary somatic sensory cortex and sends projections in turn to limbic structures such as the amygdala and hip-pocampus (see Chapters 28 and 30). This latter pathway is believed to play an important role in tactile learning and memory. Neurons in motor cortical areas in the frontal lobe also receive tactile information from the anterior pari-etal cortex and, in turn, provide feedback projections to several cortical somatic sensory regions. Such integration of sensory and motor information is considered in Chapters 19 and 25, where the role of these “association” regions of the cerebral cortex are discussed in more detail. Finally, a fundamental but often neglected feature of the somatic sensory system is the presence of massive descending projections. These pathways originate in sensory cortical fields and run to the thalamus, brainstem, and spinal cord. Indeed, descending projections from the somatic sensory cortex outnumber ascending somatic sensory pathways! Although their physiolog-ical role is not well understood, it is generally assumed (with some experi-mental support) that descending projections modulate the ascending flow of sensory information at the level of the thalamus and brainstem. 3b 1 Chin Chin DV V DI I L. lip U. lip Oral U. lip L. lip Foot IV III II DV DI DII DIII DIV DV IV III II I Foot F P. leg A. leg Foot pads Trunk Arm Arm Hand pads Hand H 3b 3b 1 1 The Somatic Sensory System 207 Box D Patterns of Organization within the Sensory Cortices: Brain Modules Observations over the last 40 years have made it clear that there is an iterated sub-structure within the somatic sensory (and many other) cortical maps. This substruc-ture takes the form of units called modules, each involving hundreds or thousands of nerve cells in repeating pat-terns. The advantages of these iterated patterns for brain function remain largely mysterious; for the neurobiologist, how-ever, such iterated arrangements have provided important clues about cortical connectivity and the mechanisms by which neural activity influences brain development (see Chapters 22 and 23). The observation that the somatic sen-sory cortex comprises elementary units of vertically linked cells was first noted in the 1920s by the Spanish neu-roanatomist Rafael Lorente de Nó, based on his studies in the rat. The potential importance of cortical modularity remained largely unexplored until the 1950s, however, when electrophysiologi-cal experiments indicated an arrange-ment of repeating units in the brains of cats and, later, monkeys. Vernon Mount-castle, a neurophysiologist at Johns Hop-kins, found that vertical microelectrode penetrations in the primary somatosen-sory cortex of these animals encountered cells that responded to the same sort of mechanical stimulus presented at the same location on the body surface. Soon after Mountcastle’s pioneering work, David Hubel and Torsten Wiesel discov-ered a similar arrangement in the cat pri-mary visual cortex. These and other observations led Mountcastle to the gen-eral view that “the elementary pattern of organization of the cerebral cortex is a vertically oriented column or cylinder of cells capable of input-output functions of considerable complexity.” Since these discoveries in the late 1950s and early 1960s, the view that modular circuits represent a fundamental feature of the mammalian cerebral cortex has gained wide acceptance, and many such entities have now been described in various cor-tical regions (see figure). This wealth of evidence for such pat-terned circuits has led many neuroscien-tists to conclude, like Mountcastle, that modules are a fundamental feature of the cerebral cortex, essential for perception, cognition, and perhaps even conscious-ness. Despite the prevalence of iterated modules, there are some problems with the view that modular units are univer-sally important in cortical function. First, although modular circuits of a given class are readily seen in the brains of some species, they have not been found in the same brain regions of other, sometimes closely related, animals. Second, not all regions of the mammalian cortex are organized in a modular fashion. And third, no clear function of such modules has been discerned, much effort and speculation notwithstanding. This salient feature of the organization of the somatic sensory cortex and other cortical (and some subcortical) regions therefore remains a tantalizing puzzle. References HUBEL, D. H. (1988) Eye, Brain, and Vision. Sci-entific American Library. New York: W. H. Freeman. LORENTE DE NÓ, R. (1949) The structure of the cerebral cortex. Physiology of the Nervous Sys-tem, 3rd Ed. New York: Oxford University Press. MOUNTCASTLE, V. B. (1957) Modality and topographic properties of single neurons of cat’s somatic sensory cortex. J. Neurophysiol. 20: 408–434. MOUNTCASTLE, V. B. (1998) Perceptual Neuro-science: The Cerebral Cortex. Cambridge: Har-vard University Press. PURVES, D., D. RIDDLE AND A. LAMANTIA (1992) Iterated patterns of brain circuitry (or how the cortex gets its spots). Trends Neu-rosci. 15: 362–368. WOOLSEY, T. A. AND H. VAN DER LOOS (1970) The structural organization of layer IV in the somatosensory region (SI) of mouse cerebral cortex. The description of a cortical field composed of discrete cytoarchitectonic units. Brain Res. 17: 205–242. (A) (B) (C) (D) (E) (F) Examples of iterated, modular substructures in the mammalian brain. (A) Ocular domi-nance columns in layer IV in the primary visual cortex (V1) of a rhesus monkey. (B) Re-peating units called “blobs” in layers II and III in V1 of a squirrel monkey. (C) Stripes in layers II and III in V2 of a squirrel monkey. (D) Barrels in layer IV in primary somatic sensory cortex of a rat. (E) Glomeruli in the olfactory bulb of a mouse. (F) Iterated units called “barreloids” in the thalamus of a rat. These and other examples indicate that mod-ular organization is commonplace in the brain. These units are on the order of one hundred to several hundred microns across. (From Purves et al., 1992.) Additional Reading Reviews CHAPIN, J. K. (1987) Modulation of cutaneous sensory transmission during movement: Pos-sible mechanisms and biological significance. In Higher Brain Function: Recent Explorations of the Brain’s Emergent Properties. S. P. Wise (ed.). New York: John Wiley and Sons, pp. 181–208. DARIAN-SMITH, I. (1982) Touch in primates. Annu. Rev. Psychol. 33: 155–194. JOHANSSON, R. S. AND A. B. VALLBO (1983) Tac-tile sensory coding in the glabrous skin of the human. Trends Neurosci. 6: 27–32. KAAS, J. H. (1990) Somatosensory system. In The Human Nervous System. G Paxinos (ed.). San Diego: Academic Press, pp. 813–844. KAAS, J. H. (1993) The functional organization of somatosensory cortex in primates. Ann. Anat. 175: 509–518. KAAS, J. H. AND C. E. COLLINS (2003) The orga-nization of somatosensory cortex in anthro-poid primates. Adv. Neurol. 2003: 93: 57–67. MOUNTCASTLE, V. B. (1975) The view from within: Pathways to the study of perception. Johns Hopkins Med. J. 136: 109–131. NICOLELIS, M. A. AND E. E. FANSELOW (2002) Thalamocortical optimization of tactile pro-cessing according to behavioral state. Nat. Neurosci. 5(6): 517–523. PETERSEN, R. S., S. PANZERI AND M. E. DIAMOND (2002) Population coding in somatosensory cortex. Curr. Opin. Neurobiol. 12(4): 441–447. WOOLSEY, C. (1958) Organization of somatic sensory and motor areas of the cerebral cor-tex. In Biological and Biochemical Bases of Behav-ior. H. F. Harlow and C. N. Woolsey (eds.). Madison, WI: University of Wisconsin Press, pp. 63–82. Important Original Papers ADRIAN, E. D. AND Y. ZOTTERMAN (1926) The impulses produced by sensory nerve endings. II. The response of a single end organ. J. Phys-iol. 61: 151–171. JOHANSSON, R. S. (1978) Tactile sensibility of the human hand: Receptive field characteris-tics of mechanoreceptive units in the glabrous skin. J. Physiol. (Lond.) 281: 101–123. JOHNSON, K. O. AND G. D. LAMB (1981) Neural mechanisms of spatial tactile discrimination: Neural patterns evoked by Braille-like dot patterns in the monkey. J. Physiol. (London) 310: 117–144. JONES, E. G. AND D. P. FRIEDMAN (1982) Projec-tion pattern of functional components of thala-mic ventrobasal complex on monkey somato-sensory cortex. J. Neurophysiol. 48: 521–544. JONES, E. G. AND T. P. S. POWELL (1969) Con-nexions of the somatic sensory cortex of the rhesus monkey. I. Ipsilateral connexions. Brain 92: 477–502. LAMOTTE, R. H. AND M. A. SRINIVASAN (1987) Tactile discrimination of shape: Responses of rapidly adapting mechanoreceptive afferents to a step stroked across the monkey finger-pad. J. Neurosci. 7: 1672–1681. LAUBACH, M., J. WESSBER AND M. A. L. NICOLELIS (2000) Cortical ensemble activity increasingly predicts behavior outcomes dur-ing learning of a motor task. Nature 405: 567–571. MOORE, C. I. AND S. B. NELSON (1998) Spatio-temporal subthreshold receptive fields in the vibrissa representation of rat primary somato-sensory cortex. J. Neurophysiol. 80: 2882– 2892. MOORE, C. I., S. B. NELSON AND M. SUR (1999) Dynamics of neuronal processing in rat somatosensory cortex. TINS 22: 513–520. NICOLELIS, M. A. L., L. A. BACCALA, R. C. S. LIN AND J. K. CHAPIN (1995) Sensorimotor encod-ing by synchronous neural ensemble activity at multiple levels of the somatosensory sys-tem. Science 268: 1353–1358. SUR, M. (1980) Receptive fields of neurons in areas 3b and 1 of somatosensory cortex in monkeys. Brain Res. 198: 465–471. WALL, P. D. AND W. NOORDENHOS (1977) Sen-sory functions which remain in man after complete transection of dorsal columns. Brain 100: 641–653. ZHU, J. J. AND B. CONNORS (1999) Intrinsic fir-ing patterns and whisker-evoked synaptic responses of neurons in the rat barrel cortex. J. Neurophysiol. 81: 1171–1183. 208 Chapter Eight Summary The components of the somatic sensory system considered in this chapter process information conveyed by mechanical stimuli that impinge upon the body surface or that are generated within the body itself (proprioception). This processing is performed by neurons distributed across several brain structures that are connected by both ascending and descending pathways. Transmission of afferent mechanosensory information from the periphery to the brain begins with a variety of receptor types that initiate action poten-tials. This activity is conveyed centrally via a chain of neurons, referred to as the first-, second-, and third-order cells. First-order neurons are located in the dorsal root and cranial nerve ganglia. Second-order neurons are located in brainstem nuclei. Third-order neurons are found in the thalamus, from whence they project to the cerebral cortex. These pathways are topographi-cally arranged throughout the system, the amount of cortical and subcortical space allocated to various body parts being proportional to the density of peripheral receptors. Studies of non-human primates show that specific cor-tical regions correspond to each functional submodality; area 3b, for exam-ple, processes information from low-threshold cutaneous receptors, and area 3a from proprioceptors. Thus, at least two broad criteria operate in the orga-nization of the somatic sensory system: modality and somatotopy. The end result of this complex interaction is the unified perceptual representation of the body and its ongoing interaction with the environment. Overview A natural assumption is that the sensation of pain arises from excessive stim-ulation of the same receptors that generate other somatic sensations (i.e., those discussed in Chapter 8). This is not the case. Although similar in some ways to the sensory processing of ordinary mechanical stimulation, the per-ception of pain, called nociception, depends on specifically dedicated recep-tors and pathways. Since alerting the brain to the dangers implied by nox-ious stimuli differs substantially from informing it about innocuous somatic sensory stimuli, it makes good sense that a special subsystem be devoted to the perception of potentially threatening circumstances. The overriding importance of pain in clinical practice, as well as the many aspects of pain physiology and pharmacology that remain imperfectly understood, continue to make nociception an extremely active area of research. Nociceptors The relatively unspecialized nerve cell endings that initiate the sensation of pain are called nociceptors (noci is derived from the Latin nocere, “to hurt”). Like other cutaneous and subcutaneous receptors, they transduce a variety of stimuli into receptor potentials, which in turn trigger afferent action potentials (see Figure 8.2). Moreover, nociceptors, like other somatic sensory receptors, arise from cell bodies in dorsal root ganglia (or in the trigeminal ganglion) that send one axonal process to the periphery and the other into the spinal cord or brainstem (see Figure 8.1). Because peripheral nociceptive axons terminate in unspecialized “free endings,” it is conventional to categorize nociceptors according to the prop-erties of the axons associated with them (see Table 8.1). As described in the previous chapter, the somatic sensory receptors responsible for the percep-tion of innocuous mechanical stimuli are associated with myelinated axons that have relatively rapid conduction velocities. The axons associated with nociceptors, in contrast, conduct relatively slowly, being only lightly myeli-nated or, more commonly, unmyelinated. Accordingly, axons conveying information about pain fall into either the Aδ group of myelinated axons, which conduct at about 20 m/s, or into the C fiber group of unmyelinated axons, which conduct at velocities generally less than 2 m/s. Thus, even though the conduction of all nociceptive information is relatively slow, there are fast and slow pain pathways. In general, the faster-conducting Aδ nociceptors respond either to danger-ously intense mechanical or to mechanothermal stimuli, and have receptive fields that consist of clusters of sensitive spots. Other unmyelinated nocicep-tors tend to respond to thermal, mechanical, and chemical stimuli, and are Chapter 9 209 Pain 210 Chapter Nine therefore said to be polymodal. In short, there are three major classes of noci-ceptors in the skin: Aδ mechanosensitive nociceptors; Aδ mechanothermal nociceptors; and polymodal nociceptors, the latter being specifically associ-ated with C fibers. The receptive fields of all pain-sensitive neurons are rela-tively large, particularly at the level of the thalamus and cortex, presumably because the detection of pain is more important than its precise localization. Studies carried out in both humans and experimental animals demon-strated some time ago that the rapidly conducting axons that subserve somatic sensory sensation are not involved in the transmission of pain. A typical experiment of this sort is illustrated in Figure 9.1. The peripheral axons responsive to nonpainful mechanical or thermal stimuli do not dis-charge at a greater rate when painful stimuli are delivered to the same region of the skin surface. The nociceptive axons, on the other hand, begin to discharge only when the strength of the stimulus (a thermal stimulus in the example in Figure 9.1) reaches high levels; at this same stimulus intensity, other thermoreceptors discharge at a rate no different from the maximum rate already achieved within the nonpainful temperature range, indicating that there are both nociceptive and nonnociceptive thermoreceptors. Equally important, direct stimulation of the large-diameter somatic sensory afferents at any frequency in humans does not produce sensations that are described as painful. In contrast, the smaller-diameter, more slowly conducting Aδ and C fibers are active when painful stimuli are delivered; and when stimulated electrically in human subjects, they produce pain. How, then, do these different classes of nociceptors lead to the perception of pain? As mentioned, one way of determining the answer has been to stimulate different nociceptors in human volunteers while noting the sensa-tions reported. In general, two categories of pain perception have been described: a sharp first pain and a more delayed, diffuse, and longer-lasting sensation that is generally called second pain (Figure 9.2A). Stimulation of the large, rapidly conducting Aα and Aβ axons in peripheral nerves does not elicit the sensation of pain. When the stimulus intensity is raised to a level that activates a subset of Aδ fibers, however, a tingling sensation or, if the stimulation is intense enough, a feeling of sharp pain is reported. If the stim-ulus intensity is increased still further, so that the small-diameter, slowly conducting C fiber axons are brought into play, then a duller, longer-lasting (C) (B) (A) Heat stimulus Nociceptor Nonnociceptive thermoreceptor Stimulus Temperature (°C) 45° 0 Magnitude of afferent response (action potentials per second) 40 45 50 Nociceptor Thermoreceptor Record Figure 9.1 Experimental demonstra-tion that nociception involves special-ized neurons, not simply greater dis-charge of the neurons that respond to normal stimulus intensities. (A) Ar-rangement for transcutaneous nerve recording. (B) In the painful stimulus range, the axons of thermoreceptors fire action potentials at the same rate as at lower temperatures; the number and frequency of action potential discharge in the nociceptive axon, however, con-tinues to increase. (Note that 45°C is the approximate threshold for pain.) (C) Summary of results. (After Fields, 1987.) sensation of pain is experienced. It is also possible to selectively anesthetize C fibers and Aδ fibers; in general, these selective blocking experiments con-firm that the Aδ fibers are responsible for first pain, and that C fibers are responsible for the duller, longer-lasting second pain (Figure 9.2B,C). Transduction of Nociceptive Signals Given the variety of stimuli (mechanical, thermal, and chemical) that can give rise to painful sensations, the transduction of nociceptive signals is a complex task. While many puzzles remain, some insights have come from the identifi-cation of specific receptors associated with nociceptive afferent endings. These receptors are sensitive to both heat and to capsaicin, the ingredient in chili peppers that is responsible for the familiar tingling or burning sensation produced by spicy foods (Box A). The so-called vanilloid receptor (VR-1 or TRPV1) is found in C and Aδ fibers and is activated by moderate heat (45°C—a temperature that is perceived as uncomfortable) as well as by cap-saicin. Another type of receptor (vanilloid-like receptor, VRL-1 or TRPV2) has a higher threshold response to heat (52°C), is not sensitive to capsaicin, and is found in Aδ fibers. Both are members of the larger family of transient receptor potential (TRP) channels, first identified in studies of the phototransduction pathway in fruit flies and now known to comprise a large number of recep-tors sensitive to different ranges of heat and cold. Structurally, TRP channels resemble voltage-gated potassium or cyclic nucleotide-gated channels, hav-ing six transmembrane domains with a pore between domains 5 and 6. Under resting conditions the pore of the channel is closed. In the open, acti-vated state, these receptors allow an influx of sodium and calcium that initi-ates the generation of action potentials in the nociceptive fibers. Since the same receptor is responsive to heat as well as capsaicin, it is not surprising that chili peppers seem “hot.” A puzzle, however, is why the ner-vous system has evolved receptors that are sensitive to a chemical in chili peppers. As with the case of other plant compounds that selectively activate neural receptors (see the discussion of opiates below), it seems likely that TRPV1 receptors detect endogenous substances whose chemical structure resembles that of capsaicin. In fact, there is now some evidence that ‘endovanilloids’ that are produced by peripheral tissues in response to injury, Pain 211 Time C fiber (A) (B) (C) First pain Second pain Aδ fiber Subjective pain intensity X X Figure 9.2 Pain can be separated into an early perception of sharp pain and a later sensation that is described as hav-ing a duller, burning quality. (A) First and second pain, as these sensations are called, are carried by different axons, as can be shown by (B) the selective block-ade of the more rapidly conducting myelinated axons that carry the sensa-tion of first pain, or (C) blockade of the more slowly conducting C fibers that carry the sensation of second pain. (After Fields, 1990.) 212 Chapter Nine Box A Capsaicin Capsaicin, the principle ingredient responsible for the pungency of hot pep-pers, is eaten daily by over a third of the world’s population. Capsaicin activates responses in a subset of nociceptive C fibers (polymodal nociceptors; see Chap-ter 9) by opening ligand-gated ion chan-nels that permit the entry of Na+ and Ca2+. One of these channels (VR-1) has been cloned and has been found to be activated by capsaicin, acid, and anan-damide (an endogeneous compound that also activates cannabanoid recep-tors), and by heating the tissue to about 43°C. It follows that anandamide and temperature are probably the endoge-nous activators of these channels. Mice whose VR-1 receptors have been knocked out drink capsaicin solutions as if they were water. Receptors for cap-saicin have been found in polymodal nociceptors of all mammals, but are not present in birds (leading to the produc-tion of squirrel-proof birdseed laced with capsaicin!). When applied to the mucus mem-branes of the oral cavity, capsaicin acts as an irritant, producing protective reac-tions. When injected into skin, it pro-duces a burning pain and elicits hyperal-gesia to thermal and mechanical stimuli. Repeated applications of capsaicin also desensitize pain fibers and prevent neu-romodulators such as substance P, VIP, and somatostatin from being released by peripheral and central nerve terminals. Consequently, capsaicin is used clinically as an analgesic and anti-inflammatory agent; it is usually applied topically in a cream (0.075%) to relieve the pain associ-ated with arthritis, postherpetic neural-gia, mastectomy, and trigeminal neural-gia. Thus, this remarkable chemical irritant not only gives gustatory pleasure on an enormous scale, but is also a use-ful pain reliever! References CATERINA, M. J., M. A. SCHUMACHER, M. TOMI-NAGA, T. A ROSEN, J. D. LEVINE AND D. JULIUS (1997) The capsaicin receptor: A heat-acti-vated ion channel in the pain pathway. Nature 389: 816–766. CATERINA, M. J. AND 8 OTHERS (2000) Impaired nociception and pain sensation in mice lack-ing the capsaicin receptor. Science 288: 306–313. SZALLASI, A. AND P. M. BLUMBERG (1999) Vanilloid (capsaicin) receptors and mecha-nisms. Pharm. Reviews 51: 159–212. TOMINAGA, M. AND 8 OTHERS (1998) The cloned capsaicin receptor integrates multiple pain-producing stimuli. Neuron 21: 531–543. ZYGMUNT, P. M. AND 7 OTHERS (1999) Vanilloid receptors on sensory nerves mediate the vasodilator action of anandamide. Nature 400: 452–457. (B) Capsaicin CH3O HO O N H (C) (A) Habañero Jalapeño Red chile (D) Outside Inside Ca2+ Na+ VR-1 receptor H+ Heat Capsaicin (A) Some popular peppers that contain capsaicin. (B) The chemical structure of capsaicin. (C) The capsaicin molecule. (D) Schematic of the VR-1/capsaicin recep-tor channel. This channel can be activated by capsaicin intercellularly, or by heat or protons (H+) at the cell surface. and that these substances, along with other factors, contribute to the nocieceptive response to injury. Central Pain Pathways The pathways that carry information about noxious stimuli to the brain, as might be expected for such an important and multifaceted system, are also complex (see Boxes B and C). It helps in understanding this complexity to dis-tinguish two components of pain: the sensory discriminative component, which signals the location, intensity, and quality of the noxious stimululation, and the affective-motivational component of pain—which signals the unpleas-ant quality of the experience, and enables the autonomic activation that fol-lows a noxious stimulus (the classic fight-or-flight reaction; see Chapter 20). The discriminative component is thought to depend on pathways that target the traditional somatosensory areas of cortex, while the affective- motivational component is thought to depend on additional cortical and brainstem path-ways. The major pathways are summarized in Figure 9.3. Pathways responsible for the discriminative component of pain originate with other sensory neurons, in dorsal root ganglia and, like other sensory nerve cells the central axons of nociceptive nerve cells enter the spinal cord via the dorsal roots (Figure 9.3A). When these centrally projecting axons reach the dorsal horn of the spinal cord, they branch into ascending and descending collaterals, forming the dorsolateral tract of Lissauer (named after the German neurologist who first described this pathway in the late nineteenth century). Axons in Lissauer’s tract typically run up and down for one or two spinal cord segments before they penetrate the gray matter of the dorsal horn. Once within the dorsal horn, the axons give off branches that contact neurons located in several of Rexed’s laminae (these laminae are the descriptive divisions of the spinal gray matter in cross section, again named after the neuroanatomist who described these details in the 1950s). The axons of these second-order neurons in the dorsal horn of the spinal cord cross the midline and ascend all the way to the brainstem and thalamus in the anterolateral (also called ventrolateral) quadrant of the contralateral half of the spinal cord. These fibers form the spinothalamic tract, the major ascending pathway for information about pain and temperature. This overall pathway is also referred to as the anterolateral system, much as the mechanosensory pathway is referred to as the dorsal column–medial lemnis-cus system. The location of the spinothalamic tract is particularly important clinically because of the characteristic sensory deficits that follow certain spinal cord injuries. Since the mechanosensory pathway ascends ipsilaterally in the cord, a unilateral spinal lesion will produce sensory loss of touch, pressure, vibration, and proprioception below the lesion on the same side. The path-ways for pain and temperature, however, cross the midline to ascend on the opposite side of the cord. Therefore, diminished sensation of pain below the lesion will be observed on the side opposite the mechanosensory loss (and the lesion). This pattern is referred to as a dissociated sensory loss and (together with local dermatomal signs; see Box C in Chapter 8) helps define the level of the lesion (Figure 9.4). As is the case of the mechanosensory pathway, information about noxious and thermal stimulation of the face follows a separate route to the thalamus (see Figure 9.3B). First-order axons originating from the trigeminal ganglion cells and from ganglia associated with nerves VII, IX, and X carry informa-tion from facial nociceptors and thermoreceptors into the brainstem. After Pain 213 214 Chapter Nine Mid-pons Mid-pons Midbrain Midbrain Middle medulla Middle medulla Caudal medulla Caudal medulla Cervical spinal cord Lumbar spinal cord Ventral posterior lateral nucleus of the thalamus Cerebrum Primary somatic sensory cortex (A) (B) Spinothalamic tract Anterolateral system Pain and temperature information from lower body Pain and temperature information from upper body (excluding the face) Ventral posterior medial nucleus of thalamus Trigemino-thalamic tract Pain and temperature information from face Spinal nucleus of the trigeminal complex Spinal trigeminal tract (afferent axons) Cerebrum Figure 9.3 Major pathways for the discrimina-tive aspects of pain and temperature sensation. (A) The spinothalamic system. (B) The trigeminal pain and temperature system, which carries information about these sensations from the face. Pain 215 Box B Referred Pain Surprisingly, there are few, if any, neu-rons in the dorsal horn of the spinal cord that are specialized solely for the trans-mission of visceral pain. Obviously, we recognize such pain, but it is conveyed centrally via dorsal horn neurons that are also concerned with cutaneous pain. As a result of this economical arrange-ment, the disorder of an internal organ is sometimes perceived as cutaneous pain. A patient may therefore present to the physician with the complaint of pain at a site other than its actual source, a potentially confusing phenomenon called referred pain. The most common clinical example is anginal pain (pain arising from heart muscle that is not being adequately perfused with blood) referred to the upper chest wall, with radiation into the left arm and hand. Other important examples are gallblad-der pain referred to the scapular region, esophogeal pain referred to the chest wall, ureteral pain (e.g., from passing a kidney stone) referred to the lower abdominal wall, bladder pain referred to the perineum, and the pain from an inflamed appendix referred to the ante-rior abdominal wall around the umbili-cus. Understanding referred pain can lead to an astute diagnosis that might otherwise be missed. References CAPPS, J. A. AND G. H. COLEMAN (1932) An Experimental and Clinical Study of Pain in the Pleura, Pericardium, and Peritoneum. New York: Macmillan. HEAD, H. (1893) On disturbances of sensation with special reference to the pain of visceral disease. Brain 16: 1–32. KELLGREW, J. H. (1939–1942) On the distribu-tion of pain arising from deep somatic struc-tures with charts of segmental pain areas. Clin. Sci. 4: 35–46. Esophagus Left ureter Urinary/bladder Right prostate Heart Examples of pain arising from a visceral disorder referred to a cutaneous region (color). 216 Chapter Nine entering the pons, these small myelinated and unmyelinated trigeminal fibers descend to the medulla, forming the spinal trigeminal tract (or spinal tract of cranial nerve V), and terminate in two subdivisions of the spinal trigeminal complex: the pars interpolaris and pars caudalis. Axons from the second-order neurons in these two trigeminal nuclei, like their counterparts in the spinal cord, cross the midline and ascend to the contralateral thalamus in the trigeminothalamic tract. The principal target of the spinothalamic and trigeminothalamic pathway is the ventral posterior nucleus of the thalamus. Similar to the organization of the mechanosensory pathways, information from the body terminates in the VPL, while information from the face terminate in the VPM. These nuclei send their axons to primary and secondary somatosensory cortex. The noci-ceptive information transmitted to these cortical areas is thought to be responsible for the discriminative component of pain: identifying the loca-tion, the intensity, and quality of the stimulation. Consistent with this inter-pretation, electrophysiological recordings from nociceptive neurons in S1, show that these neurons have small localized receptive fields, properties commensurate with behavioral measures of pain localization. The affective–motivational aspect of pain is evidently mediated by sepa-rate projections of the anterolateral system to the reticular formation of the midbrain (in particular the parabrachial nucleus), and to thalamic nuclei that lie medial to the ventral posterior nucleus (including the so-called intralami-nar nuclei; see Figure 9.5). Studies in rodents show that neurons in the parabrachial nucleus respond to most types of noxious stimuli, and have large receptive fields that can include the whole surface of the body. Neu-rons in the parabrachial nucleus project in turn to the hypothalamus and the amygdala, thus providing nociceptive information to circuits known to be concerned with motivation and affect (see Chapter 28). These parabrachial targets are also the source of projections to the periaqueductal grey of the midbrain, a structure that plays an important role in the descending control of activity in the pain pathway. Nociceptive inputs to the parabrachial nucleus and to the ventral posterior nucleus arise from separate populations of neurons in the dorsal horn of the spinal cord. Parabrachial inputs arise from neurons in the most superficial part of the dorsal horn (lamina I), while ventral posterior inputs arise from deeper parts of the dorsal horn (e.g., lam-ina V). By taking advantage of the unique molecular signature of these two sets of neurons, it has been possible to selectively eliminate the nociceptive inputs to the parabrachial nucleus in rodents. In these animals, the behav-ioral responses to the presentation of noxious stimulation (capsaicin, for example) are substantially attenuated. Projections from the anterolateral system to the medial thalamic nuclei pro-vide nociceptive signals to areas in the frontal lobe, the insula and the cingu-late cortex (Figure 9.5). In accord with this anatomy, functional imaging stud-ies in humans have shown a strong correlation between activity in the anterior cingulate cortex and the experience of a painful stimulus. Moreover, experi-ments using hypnosis have been able to tease apart the neural response to changes in the intensity of a painful stimulus from changes in its unpleasant-ness. Changes in intensity are accompanied by changes in the activity of neu-rons in somatosensory cortex, with little change in the activity of cingulate cortex, whereas changes in unpleasantness are correlated with changes in the activity of neurons in cingulate cortex. From this description, it should be evident that the full experience of pain involves the cooperative action of an extensive network of brain regions whose properties are only beginning to be understood (Box C). The cortical Zone of complete loss of sensation Reduced sensation of temperature and pain Reduced sensation of two-point discrimination, vibration, and proprioception Normal sensation Figure 9.4 Pattern of “dissociated” sensory loss following a spinal cord hemisection at the 10th thoracic level on the left side. This pattern, together with motor weakness on the same side as the lesion, is sometimes referred to as Brown-Séquard syndrome. Pain 217 Superior cerebellar peduncle Parabrachial nucleus Mid-pons Middle medulla Caudal medulla Cervical spinal cord Lumbar spinal cord Intralaminar nuclei of the thalamus Cerebrum Cingulate cortex Insula Anterolateral system Information from lower body Information from upper body (excluding the face) Projections to the amygdala and hypothalamus Reticular formation Figure 9.5 Affective–motivational pain pathways. Nociceptive information critical for signaling the unpleasant quality of pain is mediated by projections to the reticular formation (including the parabrachial nucleus) and to the intralaminar nuclei of the thalamus. 218 Chapter Nine Box C A Dorsal Column Pathway for Visceral Pain Chapters 8 and 9 present a framework for considering the central neural pathways that convey innocuous mechanosensory signals and painful signals from cuta-neous and deep somatic sources. Consid-ering just the signals derived from the body below the head, discriminitive mechanosensory and proprioceptive information travels to the ventral poste-rior thalamus via the dorsal-column medial lemniscal system (see Figure 8.6A), while nociceptive information trav-els to the same (and additional) thalamic relays via the anterolateral systems (see Figure 9.3A). But how do painful signals that arise in the visceral organs of the pelvis, abdomen, and thorax enter the central nervous system and ultimately reach consciousness? The answer is via a newly discovered component of the dorsal column medial lemniscal pathway that conveys visceral nociception. Although Chapter 20 will present more information on the sys-tems that receive and process visceral sensory information, at this juncture it is worth considering this component of the pain pathways and how this particular pathway has begun to impact clinical medicine. Primary visceral afferents from the pelvic and abdominal viscera enter the spinal cord and synapse on second-order neurons in the dorsal horn of the lum-bar-sacral spinal cord. As discussed in Box A and Chapter 20, some of these sec-ond-order neurons are cells that give rise to the anterolateral systems and con-tribute to referred visceral pain patterns. However, other neurons—perhaps pri-marily those that give rise to nociceptive signals—synapse upon neurons in the intermediate gray region of the spinal cord near the central canal. These neu-rons, in turn, send their axons not through the anterolateral white matter of the spinal cord (as might be expected for a pain pathway) but through the dorsal columns in a position very near the mid-line (see Figure A). Similarly, second-order neurons in the thoracic spinal cord that convey nociceptive signals from tho-racic viscera send their axons rostrally through the dorsal columns along the dorsal intermediate septum, near the division of the gracile and cuneate fasci-culi. These second order axons then syn-apse in the dorsal column nuclei of the caudal medulla, where neurons give rise to arcuate fibers that form the contralat-eral medial lemniscus and eventually synapse on thalamocortical projection neurons in the ventral-posterior thala-mus. This dorsal column visceral sensory projection now appears to be the princi-pal pathway by which painful sensations arising in the viscera are detected and discriminated. Several observations sup-port this conclusion: (1) neurons in the ventral posterior lateral nucleus, nucleus gracilis and near the central canal of the spinal cord all respond to noxious vis-ceral stimulation; (2) responses of neu-rons in the ventral posterior lateral nucleus and nucleus gracilis to such stimulation are greatly reduced by spinal lesions of the dorsal columns (see Figure B), but not lesions of the anterolateral white matter; and (3) infusion of drugs that block nociceptive synaptic transmis-sion into the intermediate gray region of the sacral spinal cord blocks the responses of neurons in the nucleus gra-cilis to noxious visceral stimulation, but not to innocuous cutaneous stimulation. The discovery of this visceral sensory component in the dorsal-column medial lemniscal system has helped to explain why surgical transection of the axons that run in the medial part of the dorsal columns (a procedure termed midline myelotomy) generates significant relief from the debilitating pain that can result from visceral cancers in the abdomen and pelvis. Although the initial develop-ment of this surgical procedure preceded the elucidation of this visceral pain path-way, these new discoveries have renewed interest in midline myelotomy as a pal-liative neurosurgical intervention for cancer patients whose pain is otherwise unmanageable. Indeed, precise knowl-edge of the visceral sensory pathway in the dorsal columns has led to further refinements that permit a minimally invasive (“punctate”) surgical procedure that attempts to interupt the second-order axons of this pathway within just a single spinal segment (typically, a mid-or lower-thoracic level; see Figure C). In so doing, this procedure offers some hope to patients who struggle to main-tain a reasonable quality of life in extra-ordinarily difficult circumstances. References AL-CHAER, E. D., N. B. LAWAND, K. N. WEST-LUND AND W. D. WILLIS (1996) Visceral nocicep-tive input into the ventral posterolateral nucleus of the thalamus: a new function for the dorsal column pathway. J. Neurophys. 76: 2661–2674. AL-CHAER, E. D., N. B. LAWAND, K. N. WEST-LUND AND W. D. WILLIS (1996) Pelvic visceral input into the nucleus gracilis is largely medi-ated by the postsynaptic dorsal column path-way. J. Neurophys. 76: 2675–2690. BECKER, R., S. GATSCHER, U. SURE AND H. BERTA-LANFFY (2001) The punctate midline myelo-tomy concept for visceral cancer pain control – case reort and review of the literature. Acta Neurochir. [Suppl.] 79: 77–78. HITCHCOCK, E. R. (1970) Stereotactic cervical myelotomy. J. Neurol. Neurosurg. Psychiatry 33: 224–230. KIM, Y. S. AND S. J. KWON (2000) High thoracic midline dorsal column myelotomy for severe visceral pain due to advanced stomach cancer. Neurosurg. 46:85-90. NAUTA, H. AND 8 OTHERS (2000) Punctate mid-line myelotomy for the relief of visceral cancer pain. J. Neurosurg. (Spine 2) 92: 125–130. WILLIS, W. D., E. D. AL-CHAER, M. J. QUAST AND K. N. WESTLUND (1999) A visceral pain path-way in the dorsal column of the spinal cord. Proc. Natl. Acad. Sci. USA 96: 7675–7679. Pain 219 Medulla Midbrain Gracile nucleus Cuneate nucleus Spinal cord Ventral posterior nuclear complex of thalamus Cerebrum Dorsal root ganglion cells (A) Medial leminiscus Insular cortex (B) Sham lesion Dorsal column lesion Before surgery 4 months after surgery Dorsal columns Needle Dorsal horn (C) Gastrointestinal tract (A) A visceral pain pathway in the dorsal-column medial lemniscal system. For simplicity, only the pathways that mediate visceral pain from the pelvis and lower abdomen are illustrated. The mechanosen-sory component of this system for the discrimination of tactile stimuli and the anterolateral system for the detection of painful and thermal cutaneous stimuli are also shown for comparison (see also Figures 8.6A and 9.3A). (B) Empirical evidence supporting the existence of the visceral pain pathway shown in (A). Increased neural activity was observed with functional MRI techniques in the thalamus of monkeys that were subjected to noxious distention of the colon and rectum, indicating the processing of visceral pain. This activity was abolished by lesion of the dorsal columns at T10, but not by “sham” surgery. (From Willis et al., 1999.) (C) Top, one method of punctate midline myelotomy for the relief of severe visceral pain. Bottom, myelin-stained section of the thoracic spinal cord (T10) from a patient who underwent midline myelotomy for the treatment of colon cancer pain that was not controlled by analgesics. After surgery, the patient expe-rienced relief from pain during the remaining three months of his life. (From Hirshberg et al., 1996; drawing after Nauta et al., 1997.) 220 Chapter Nine representation of pain is the least well documented aspect of the central pathways for nociception, and further studies will be needed to elucidate the contribution of regions outside the somatosensory areas of the parietal lobe. Nevertheless, a prominent role for these areas in the perception of pain is suggested by the fact that ablations of the relevant regions of the parietal cortex do not generally alleviate chronic pain (although they impair con-tralateral mechanosensory perception, as expected). Sensitization Following a painful stimulus associated with tissue damage (e.g., cuts, scrapes, and bruises), , stimuli in the area of the injury and the surrounding region that would ordinarily be perceived as slightly painful are perceived as significantly more so, a phenomenon referred to as hyperalgesia. A good example of hyperalgesia is the increased sensitivity to temperature that occurs after a sunburn. This effect is due to changes in neuronal sensitivity that occur at the level of peripheral receptors as well as their central targets. Peripheral sensitization results from the interaction of nociceptors with the “inflammatory soup” (Figure 9.6) of substances released when tissue is damaged. These products of tissue damage include extracellular protons, arachidonic acid and other lipid metabolites, bradykinin, histamine, sero-tonin, prostaglandins, nucleotides, and nerve growth factor (NGF), all of which can interact with receptors or ion channels of nociceptive fibers, aug-menting their response. For example, the responses of the TRPV1 receptor to heat can be potentiated by direct interaction of the channel with extracellu-lar protons or lipid metabolites. NGF and bradykinin also potentiate the Spinal cord Mast cell or neutrophil Substance P Substance P Blood vessel CGRP Dorsal root ganglion cell body Anterolateral system Histamine Bradykinin 5–HT Prostaglandin ATP H+ Tissue injury Figure 9.6 Inflammatory response to tissue damage. Substances released by damaged tissues augment the response of nociceptive fibers. In addition, elec-trical activation of nociceptors causes the release of peptides and neurotrans-mitters that further contribute to the inflammatory response. activity of the TRPV1 receptors, but do so indirectly through the actions of separate cell-surface receptors (TrkA and bradykinin receptors respectively) and their associated intracellular signalling pathways. The prostaglandins are thought to contribute to peripheral sensitization by binding to G-protein-coupled receptors that increase levels of cyclic AMP within nociceptors. Prostaglandins also reduce the threshold depolarization required for gener-ating action potentials via phosphorylation of a specific class of TTX-resis-tant Na channels that are expressed in nociceptors. In addition, electrical activity in the nociceptors causes them to release peptides and neurotrans-mitters such as substance P, calcitonin-gene–related peptide (CGRP) and ATP which further contribute to the inflammatory response, causing vasodi-lation, swelling, and the release of histamine from mast cells. The presumed purpose of the complex chemical signaling arising from local damage is not only to protect the injured area (as a result of the painful perceptions pro-duced by ordinary stimuli close to the site of damage), but also to promote healing and guard against infection by means of local effects such as increased blood flow and the migration of white blood cells to the site. Obvi-ously the identification of the components of the inflammatory soup and their mechanisms of action is a fertile area to explore for potential analgesics (i.e., compounds that reduce pain intensity). For example, so-called nons-teroidal anti-inflammatory drugs (NSAIDs), which include aspirin and ibuprofen, act by inhibiting cyclooxygenase (COX), an enzyme important in the biosynthesis of prostaglandins. Central sensitization refers to an immediate onset, activity dependent increase in the excitability of neurons in the dorsal horn of the spinal cord following high levels of activity in the nociceptive afferents. As a result, activity levels in nociceptive afferents that were subthreshold prior to the sensitizing event, become sufficient to generate action potentials in dorsal horn neurons, contributing to an increase in pain sensitivity. Although cen-tral sensitization is triggered in dorsal horn neurons by activity in nocicep-tors, the effects generalize to other inputs that arise from low threshold mechanoreceptors. Thus, stimuli that under normal conditions would be innocuous (such as brushing the surface of the skin) activate second-order neurons in the dorsal horn that receive nociceptive inputs, and give rise to a sensation of pain. The induction of pain by what is normally an innocuous stimulus is referred to as allodynia. This phenomenon typically occurs immediately after the painful event and can outlast the stimulus by several hours. Like its peripheral counterpart, a number of different mechanisms con-tribute to central sensitization, and these can be divided broadly into tran-scription independent and dependent processes. One form of transcription independent central sensitization called “windup” involves a progressive increase in the discharge rate of dorsal horn neurons in response to repeated low frequency activation of nociceptive afferents. A behavioral correlate of the windup phenomenon has been studied by examining the perceived intensity of pain in response to multiple presentations of a noxious stimulus. Although the intensity of the stimulation is constant, the perceived intensity increases with each stimulus presentation. Windup lasts only during the period of stimulation and arises from the summation of the slow synaptic potentials that are evoked in dorsal horn neurons by nociceptive inputs. The sustained depolarization of the dorsal horn neurons results in part from the activation of voltage dependent L-type calcium channels, and from the removal of the Mg block of NMDA receptors, increasing the sensitivity of the Pain 221 222 Chapter Nine the dorsal horn neuron to glutamate, the transmitter in nociceptive afferents. Other forms of central sensitization that last longer than the period of sen-sory stimulation (such as allodynia) are thought to involve an LTP-like enhancement of postsynaptic potentials (see Chapter 24). The longest lasting forms, resulting from transcription dependent processes, can be elicited by changes in neuronal activity or by humoral signals. Those elicited by neu-ronal activity are localized to the site of the injury, while humoral activation can lead to more widespread changes. For example, cytokines released from microglia and from other sources promote the widespread transcription of COX-2 and the production of prostaglandins in dorsal horn neurons. As described for nociceptive afferents, increased levels of prostaglandins in CNS neurons augments neuronal excitability. Thus the analgesic effects of drugs that inhibit COX are due to actions in both the periphery and within the dorsal horn. As injured tissue heals, the sensitization induced by peripheral and cen-tral mechanisms typically declines and the theshold for pain returns to Following the amputation of an extrem-ity, nearly all patients have an illusion that the missing limb is still present. Although this illusion usually dimin-ishes over time, it persists in some degree throughout the amputee’s life and can often be reactivated by injury to the stump or other perturbations. Such phantom sensations are not limited to amputated limbs; phantom breasts fol-lowing mastectomy, phantom genitalia following castration, and phantoms of the entire lower body following spinal cord transection have all been reported. Phantoms are also common after local nerve block for surgery. During recovery from brachial plexus anesthesia, for example, it is not unusual for the patient to experience a phantom arm, perceived as whole and intact, but displaced from the real arm. When the real arm is viewed, the phantom appears to “jump into” the arm and may emerge and reen-ter intermittently as the anesthesia wears off. These sensory phantoms demon-strate that the central machinery for pro-cessing somatic sensory information is not idle in the absence of peripheral stimuli; apparently, the central sensory processing apparatus continues to oper-ate independently of the periphery, giv-ing rise to these bizarre sensations. Interestingly, considerable functional reorganization of somatotopic maps in the primary somatosensory cortex occurs in amputees (see Chapter 24). This reor-ganization starts immediately after the amputation and tends to evolve for sev-eral years. One of the effects of this process is that neurons that have lost their original inputs (i.e., from the removed limb) respond to tactile stimula-tion of other body parts. A surprising consequence is that stimulation of the face, for example, can be experienced as if the missing limb had been touched. Further evidence that the phenome-non of phantom limb is the result of a central representation is the experience of children born without limbs. Such individuals have rich phantom sensa-tions, despite the fact that a limb never developed. This observation suggests that a full represenation of the body exists independently of the peripheral elements that are mapped. Based on these results, Ronald Melzack proposed that the loss of a limb generates an inter-nal mismatch between the brain’s repre-sentation of the body and the pattern of peripheral tactile input that reaches the neocortex. The consequence would be an illusory sensation that the missing body part is still present and functional. With time, the brain may adapt to this loss and alter its intrinsic somatic representation to better accord with the new configura-tion of the body. This change could explain why the phantom sensation appears almost immediately after limb loss, but usually decreases in intensity over time. Phantoms might simply be a curios-ity—or a provocative clue about higher-order somatic sensory processing—were it not for the fact that a substantial num-ber of amputees also develop phantom pain. This common problem is usually described as a tingling or burning sensa-tion in the missing part. Sometimes, how-ever, the sensation becomes a more seri-Box D Phantom Limbs and Phantom Pain preinjury levels. However, when the afferent fibers or central pathways themselves are damaged—a frequent complication in pathological condi-tions that include diabetes, shingles, AIDs, multiple sclerosis, and stroke— these processes can persist. The resulting condition is refered to as neuro-pathic pain, a chronic, intensely painful experience that is difficult to treat with conventional analgesic medications. (See Box D for a description of neuropathic pain associated with amputation of an extremity.) The pain can arise spontaneously (without a stimulus) or can be produced by mild forms of stimulation that are common to everyday experience, such as the gentle touch and pressure of clothing, or warm and cool temperatures. Patients often describe their experience as a constant burning sensation interrupted by episodes of shooting, stabbing, or electric shocklike jolts. Because the dis-ability and psychological stress associated with chronic neuropathic pain can be severe, much present research is being devoted to better understanding of the mechanisms of peripheral and central sensitization with the hope of more effective therapies for this debilitating syndrome. Pain 223 ous pain that patients find increasingly debilitating. Phantom pain is, in fact, one of the more common causes of chronic pain syndromes and is extraordinarily difficult to treat. Because of the wide-spread nature of central pain processing, ablation of the spinothalamic tract, por-tions of the thalamus, or even primary sensory cortex does not generally relieve the discomfort felt by these patients. References MELZACK, R. (1989) Phantom limbs, the self, and the brain. The D.O. Hebb Memorial Lec-ture. Canad. Psychol. 30: 1–14. MELZACK, R. (1990) Phantom limbs and the concept of a neuromatrix. TINS 13: 88–92. NASHOLD, B. S., JR. (1991) Paraplegia and pain. In Deafferentation Pain Syndromes: Patho-physiology and Treatment, B. S. Nashold, Jr. and J. Ovelmen-Levitt (eds.). New York: Raven Press, pp. 301–319. RAMACHANDRAN, V. S. AND S. BLAKESLEE (1998) Phantoms in the Brain. New York: William Morrow & Co. SOLONEN, K. A. (1962) The phantom phenom-enon in amputated Finnish war veterans. Acta. Orthop. Scand. Suppl. 54: 1–37. Drawings of phantom arms and legs, based on patients’ reports. The phantom is indicated by a dashed line, with the colored regions showing the most vividly experienced parts. Note that some phantoms are telescoped into the stump. (After Solonen, 1962.) 224 Chapter Nine Descending Control of Pain Perception With respect to the interpretation of pain, observers have long commented on the difference between the objective reality of a painful stimulus and the subjective response to it. Modern studies of this discrepancy have provided considerable insight into how circumstances affect pain perception and, ulti-mately, into the anatomy and pharmacology of the pain system. During World War II, Henry Beecher and his colleagues at Harvard Med-ical School made a fundamental observation. In the first systematic study of its kind, they found that soldiers suffering from severe battle wounds often experienced little or no pain. Indeed, many of the wounded expressed sur-prise at this odd dissociation. Beecher, an anesthesiologist, concluded that the perception of pain depends on its context. For instance, the pain of an injured soldier on the battlefield would presumably be mitigated by the imagined benefits of being removed from danger, whereas a similar injury in a domestic setting would present quite a different set of circumstances that could exacerbate the pain (loss of work, financial liability, and so on). Such observations, together with the well-known placebo effect (discussed in the next section), make clear that the perception of pain is subject to cen-tral modulation (all sensations are subject to at least some degree of this kind of modification). This statement, incidentally, should not be taken as a vague acknowledgment about the importance of psychological or “top-down” influences on sensory experience. On the contrary, there has been a gradual realization among neuroscientists and neurologists that such “psy-chological” effects are as real and important as any other neural phenome-non. This appreciation has provided a much more rational view of psycho-somatic problems in general, and pain in particular. The Placebo Effect The placebo effect is defined as a physiological response following the administration of a pharmacologically inert “remedy.” The word placebo means “I will please,” and the placebo effect has a long history of use (and abuse) in medicine. The reality of the effect is undisputed. In one classic study, medical students were given one of two different pills, one said to be a sedative and the other a stimulant. In fact, both pills contained only inert ingredients. Of the students who received the “sedative,” more than two-thirds reported that they felt drowsy, and students who took two such pills felt sleepier than those who had taken only one. Conversely, a large fraction of the students who took the “stimulant” reported that they felt less tired. Moreover, about a third of the entire group reported side effects ranging from headaches and dizziness to tingling extremities and a staggering gait! Only 3 of the 56 students studied reported that the pills they took had no appreciable effect. In another study of this general sort, 75% of patients suffering from post-operative wound pain reported satisfactory relief after an injection of sterile saline. The researchers who carried out this work noted that the responders were indistinguishable from the nonresponders, both in the apparent sever-ity of their pain and psychological makeup. Most tellingly, this placebo effect in postoperative patients could be blocked by naloxone, a competitive antagonist of opiate receptors, indicating a substantial pharmacological basis for the pain relief experienced (see the next section). A common mis-understanding about the placebo effect is the view that patients who respond to a therapeutically meaningless reagent are not suffering real pain, but only “imagining” it; this is certainly not the case. Among other things, the placebo effect probably explains the efficacy of acupuncture anesthesia and the analgesia that can sometimes be achieved by hypnosis. In China, surgery has often been carried out under the effect of a needle (often carrying a small electrical current) inserted at locations dic-tated by ancient acupuncture charts. Before the advent of modern anesthetic techniques, operations such as thyroidectomies for goiter were commonly done without extraordinary discomfort, particularly among populations where stoicism was the cultural norm. The mechanisms of pain amelioration on the battlefield, in acupuncture anesthesia, and with hypnosis are presumably related. Although the mecha-nisms by which the brain affects the perception of pain are only beginning to be understood, the effect is neither magical nor a sign of a suggestible intel-lect. In short, the placebo effect is quite real. The Physiological Basis of Pain Modulation Understanding the central modulation of pain perception (on which the placebo effect is presumably based) was greatly advanced by the finding that electrical or pharmacological stimulation of certain regions of the mid-brain produces relief of pain. This analgesic effect arises from activation of descending pain-modulating pathways that project to the dorsal horn of the spinal cord (as well as to the spinal trigeminal nucleus) and regulate the transmission of information to higher centers (Figure 9.7A). One of the major brainstem regions that produce this effect is located in the periaque-ductal gray of the midbrain. Electrical stimulation at this site in experimen-tal animals not only produces analgesia by behavioral criteria, but also demonstrably inhibits the activity of nociceptive projection neurons in the dorsal horn of the spinal cord. Further studies of descending pathways to the spinal cord that regulate the transmission of nociceptive information have shown that they arise from a number of brainstem sites, including the parabrachial nucleus, the dorsal raphe, and locus coeruleus and the medullary reticular formation (see Figure 9.7A). The analgesic effects of stimulating the periaqueductal gray are medi-ated through these brainstem sites. These centers employ a wealth of differ-ent neurotransmitters (noradrenaline, serotonin, dopamine, histamine, acetylcholine) and can exert both facilitatory and inhibitory effects on the the activity of neurons in the dorsal horn. The complexity of these interactions is made even greater by the fact that descending projections can exert their effects on a variety of sites within the dorsal horn including the synaptic ter-minals of nociceptive afferents, excitatory and inhibitory interneurons, the synaptic terminals of the other descending pathways, as well as by contact-ing the projection neurons themselves. Although these descending projec-tions were originally viewed as a mechanism that served primarily to inhibit the transmission of nociceptive signals, it is now evident that these projec-tions provide a balance of facilitatory and inhibitory influences that ulti-mately determines the efficacy of nociceptive transmission. In addition to descending projections, local interactions between mech-anoreceptive afferents and neural circuits within the dorsal horn can modu-late the transmission of nociceptive information to higher centers (Figure 9.7B). These interactions are thought to explain the ability to reduce the sen-sation of sharp pain by activating low-threshold mechanoreceptors: If you crack your shin or stub a toe, a natural (and effective) reaction is to vigor-Pain 225 226 Chapter Nine ously rub the site of injury for a minute or two. Such observations, but-tressed by experiments in animals, led Ronald Melzack and Patrick Wall to propose that the flow of nociceptive information through the spinal cord is modulated by concomitant activation of the large myelinated fibers associ-ated with low-threshold mechanoreceptors. Even though further investiga-tion led to modification of some of the original propositions in Melzack and Wall’s gate theory of pain, the idea stimulated a great deal of work on pain modulation and has emphasized the importance of synaptic interactions within the dorsal horn for modulating the perception of pain intensity. The most exciting advance in this long-standing effort to understand cen-tral mechanisms of pain regulation has been the discovery of endogenous opioids. For centuries it had been apparent that opium derivatives such as morphine are powerful analgesics—indeed, they remain a mainstay of anal-gesic therapy today. Modern animal studies have shown that a variety of brain regions are susceptible to the action of opiate drugs, particularly—and significantly—the periaqueductal gray matter and other sources of descend-Dorsal horn of spinal cord Anterolateral system Medullary reticular formation Parabrachial nucleus Raphe nuclei Locus coeruleus (A) Hypothalamus Amygdala Midbrain periaqueductal gray Somatic sensory cortex (B) Axon terminal of enkephalin-containing local circuit neuron Dorsal horn projection neuron C fiber (nociceptor) − + + Descending inputs, e.g. raphe nuclei C fiber (nociceptor) Dorsal horn projection neuron Inhibitory local circuit neuron To anterolateral system To dorsal columns Aβ fiber (mechanoreceptor) − − + + + (C) Figure 9.7 The descending systems that modulate the transmission of ascending pain signals. (A) These mod-ulatory systems originate in the somatic sensory cortex, the hypothalamus, the periaqueductal gray matter of the midbrain, the raphe nuclei, and other nuclei of the ros-tral ventral medulla. Complex modulatory effects occur at each of these sites, as well as in the dorsal horn. (B) Gate theory of pain. Activation of mechanoreceptors modulates the transmission of nociceptive information to higher centers. (C) The role of enkephalin-containing local circuit neurons in the descending control of noci-ceptive signal transmission. ing projections. There are, in addition, opiate-sensitive neurons within the dorsal horn of the spinal cord. In other words, the areas that produce anal-gesia when stimulated are also responsive to exogenously administered opi-ates. It seems likely, then, that opiate drugs act at most or all of the sites shown in Figure 9.7 in producing their dramatic pain-relieving effects. The analgesic action of opiates implied the existence of specific brain and spinal cord receptors for these drugs long before the receptors were actually found during the 1960s and 1970s. Since such receptors are unlikely to exist for the purpose of responding to the administration of opium and its deriva-tives, the conviction grew that there must be endogenous compounds for which these receptors had evolved (see Chapter 6). Several categories of endogenous opioids have now been isolated from the brain and intensively studied. These agents are found in the same regions that are involved in the modulation of nociceptive afferents, although each of the families of endoge-nous opioid peptides has a somewhat different distribution. All three of the major groups (enkephalins, endorphins, and dynorphins; see Table 6.2) are present in the periaqueductal gray matter. The enkephalins and dynorphins have also been found in the rostral ventral medulla and in the spinal cord regions involved in the modulation of pain. One of the most compelling examples of the mechanism by which endogenous opiates modulate transmission of nociceptive information occurs at the first synapse in the pain pathway between nociceptive affer-ents and projection neurons in the dorsal horn of the spinal cord (see Figure 9.7B). A class of enkephalin-containing local circuit neurons within the dor-sal horn synapses with the axon terminals of nociceptive afferents, which synapse in turn with dorsal horn projection neurons. The release of enkephalin onto the nociceptive terminals inhibits their release of neuro-transmitter onto the projection neuron, reducing the level of activity that is passed on to higher centers. Enkephalin-containing local circuit neurons are themselves the targets of descending projections, thus providing a powerful mechanism by which higher centers can decrease the activity relayed by nociceptive afferents. A particularly impressive aspect of this story is the wedding of physiology, pharmacology, and clinical research to yield a much richer understanding of the intrinsic modulation of pain. This information has finally begun to explain the subjective variability of painful stimuli and the striking depen-dence of pain perception on the context of the experience. Precisely how pain is modulated is being explored in many laboratories at present, motivated by the tremendous clinical (and economic) benefits that would accrue from still deeper knowledge of the pain system and its molecular underpinnings. Summary Whether from a structural or functional perspective, pain is an extraordinarily complex sensory modality. Because of the importance of warning an animal about dangerous circumstances, the mechanisms and pathways that subserve nociception are widespread and redundant. A distinct set of pain afferents with membrane receptors known as nociceptors transduces noxious stimula-tion and conveys this information to neurons in the dorsal horn of the spinal cord. The major central pathway responsible for transmitting the discrimina-tive aspects of pain (location, intensity and quality) differs from the mechano-sensory pathway primarily in that the central axons of dorsal root ganglion cells synapse on second-order neurons in the dorsal horn; the axons of the sec-ond-order neurons then cross the midline in the spinal cord and ascend to Pain 227 228 Chapter Nine Additional Reading Reviews CATERINA, M. J. AND D. JULIUS (1999) Sense and specificity: A molecular identity for nocicep-tors. Curr. Opin. Neurobiol. 9: 525–530. DI MARZO, V., P. M. BLUMBERG AND A. SZALLASI (2002) Endovanilloid signaling in pain. Curr. Opin. Neurobiol. 12: 372–379. DUBNER, R. AND M. S. GOLD (1999) The neuro-biology of pain. Proc. Natl. Acad. Sci. USA 96: 7627–7630. FIELDS, H. L. AND A. I. BASBAUM (1978) Brain-stem control of spinal pain transmission neu-rons. Annu. Rev. Physiol. 40: 217–248. HUNT, S. P. AND P. W. MANTYH (2001) The mol-ecular dynamics of pain control. Nat. Rev. Neurosci. 2: 83–91. JI, R. R., T. KOHNO, K. A. MOORE AND C. J. WOOLF (2003) Central sensitization and LTP: Do pain and memory share similar mecha-nisms? TINS 26: 696–705. JULIUS, D. AND A. I. BASBAUM (2001) Molecular mechanisms of nociception. Nature 413: 203–209. MILLAN, M. J. (2002) Descending control of pain. Prog. Neurobiol. 66: 355–474. PATAPOUTIAN, A., A. M. PEIER, G. M. STORY AND V. VISWANATH (2003) ThermoTRP channels and beyond: Mechanisms of temperature sen-sation. Nat. Rev. Neurosci. 4: 529–539. RAINVILLE, P. (2002) Brain mechanisms of pain affect and pain modulation. Curr. Opin. Neu-robiol. 12: 195–204. SCHOLZ, J. AND C. J. WOOLF (2002) Can we con-quer pain? Nat. Rev. Neurosci. 5 (Suppl): 1062–1067. TREEDE, R. D., D. R. KENSHALO, R. H. GRACELY AND A. K. JONES (1999) The cortical representa-tion of pain. Pain 79: 105–111. Important Original Papers BASBAUM, A. I. AND H. L. FIELDS (1979) The ori-gin of descending pathways in the dorsolat-eral funiculus of the spinal cord of the cat and rat: Further studies on the anatomy of pain modulation. J. Comp. Neurol. 187: 513–522. BEECHER, H. K. (1946) Pain in men wounded in battle. Ann. Surg. 123: 96. BLACKWELL, B., S. S. BLOOMFIELD AND C. R. BUNCHER (1972) Demonstration to medical students of placebo response and non-drug factors. Lancet 1: 1279–1282. CATERINA, M. J. AND 8 OTHERS (2000) Impaired nociception and pain sensation in mice lack-ing the capsaicin receptor. Science 288: 306–313. CRAIG, A. D., M. C. BUSHNELL, E.-T. ZHANG AND A. BLOMQVIST (1994) A thalamic nucleus specific for pain and temperature sensation. Nature 372: 770–773. CRAIG, A. D., E. M. REIMAN, A. EVANS AND M. C. BUSHNELL (1996) Functional imaging of an illusion of pain. Nature 384: 258–260. LEVINE, J. D., H. L. FIELDS AND A. I. BASBAUM (1993) Peptides and the primary afferent noci-ceptor. J. Neurosci. 13: 2273–2286. MOGIL, J. S. AND J. E. GRISEL (1998) Transgenic studies of pain. Pain 77: 107–128. Books FIELDS, H. L. (1987) Pain. New York: McGraw-Hill. FIELDS, H. L. (ed.) (1990) Pain Syndromes in Neurology. London: Butterworths. KOLB, L. C. (1954) The Painful Phantom. Spring-field, IL: Charles C. Thomas. SKRABANEK, P. AND J. MCCORMICK (1990) Follies and Fallacies in Medicine. New York: Prometh-eus Books. WALL, P. D. AND R. MELZACK (1989) Textbook of Pain. New York: Churchill Livingstone. thalamic nuclei that relay information to the somatic sensory cortex of the postcentral gyrus. Additional pathways involving a number of centers in the brainstem, thalamus, and cortex mediate the affective and motivational responses to painful stimuli. Descending pathways interact with local circuits in the spinal cord to regulate the transmission of nociceptive signals to higher centers. Tremendous progress in understanding pain has been made in the last 25 years, and much more seems likely, given the importance of the prob-lem. No patients are more distressed—or more difficult to treat—than those with chronic pain. Indeed, some aspects of pain seem much more destructive to the sufferer than required by any physiological purposes. Perhaps such seemingly excessive effects are a necessary but unfortunate by-product of the protective benefits of this vital sensory modality. Overview The human visual system is extraordinary in the quantity and quality of information it supplies about the world. A glance is sufficient to describe the location, size, shape, color, and texture of objects and, if the objects are mov-ing, their direction and speed. Equally remarkable is the fact that visual information can be discerned over a wide range of stimulus intensities, from the faint light of stars at night to bright sunlight. The next two chapters describe the molecular, cellular, and higher-order mechanisms that allow us to see. The first steps in the process of seeing involve transmission and refraction of light by the optics of the eye, the transduction of light energy into electrical signals by photoreceptors, and the refinement of these signals by synaptic interactions within the neural circuits of the retina. Anatomy of the Eye The eye is a fluid-filled sphere enclosed by three layers of tissue (Figure 10.1). Only the innermost layer of the eye, the retina, contains neurons that are sensitive to light and are capable of transmitting visual signals to central targets. The immediately adjacent layer of tissue includes three distinct but continuous structures collectively referred to as the uveal tract. The largest component of the uveal tract is the choroid, which is composed of a rich cap-illary bed (important for nourishing the photoreceptors of the retina) as well as a high concentration of the light absorbing pigment melanin. Extending from the choroid near the front of the eye is the ciliary body, a ring of tissue that encircles the lens and consists of a muscular component that is impor-tant for adjusting the refractive power of the lens, and a vascular component (the so-called ciliary processes) that produces the fluid that fills the front of the eye. The most anterior component of the uveal tract is the iris, the col-ored portion of the eye that can be seen through the cornea. It contains two sets of muscles with opposing actions, which allow the size of the pupil (the opening in its center) to be adjusted under neural control. The sclera forms the outermost tissue layer of the eye and is composed of a tough white fibrous tissue. At the front of the eye, however, this opaque outer layer is transformed into the cornea, a specialized transparent tissue that permits light rays to enter the eye. Beyond the cornea, light rays pass through two distinct fluid environ-ments before striking the retina. In the anterior chamber, just behind the cornea and in front of the lens, lies aqueous humor, a clear, watery liquid that supplies nutrients to both of these structures. Aqueous humor is pro-duced by the ciliary processes in the posterior chamber (the region between Chapter 10 229 Vision:The Eye 230 Chapter Ten the lens and the iris) and flows into the anterior chamber through the pupil. The amount of fluid produced by the ciliary processes is substantial: it is estimated that the entire volume of fluid in the anterior chamber is replaced 12 times a day. Thus the rates of a aqueous humor production must be bal-anced by comparable rates of drainage from the anterior chamber in order to ensure a constant intraocular pressure. A specialized meshwork of cells that lies at the junction of the iris and the cornea (a region called the lim-bus) is responsible for aqueous drainage. Failure of adequate drainage results in a disorder known as glaucoma, in which high levels of intraocular pressure can reduce the blood supply to the eye and eventually damage retinal neurons. The space between the back of the lens and the surface of the retina is filled with a thick, gelatinous substance called the vitreous humor, which accounts for about 80% of the volume of the eye. In addition to maintaining the shape of the eye, the vitreous humor contains phagocytic cells that remove blood and other debris that might otherwise interfere with light transmission. The housekeeping abilities of the vitreous humor are limited, however, as a large number of middle-aged and elderly individuals with vit-real “floaters” will attest. Floaters are collections of debris too large for phagocytic consumption that therefore remain to cast annoying shadows on the retina; they typically arise when the aging vitreous membrane pulls away from the overly long eyeball of myopic individuals (Box A). Ciliary muscle Aqueous humor in anterior chamber Posterior chamber Cornea Pupil Iris Retina Optic disk Optic nerve and retinal vessels Zonule fibers Sclera Fovea Vitreous humor Lens Choroid Figure 10.1 Anatomy of the human eye. The Formation of Images on the Retina Normal vision requires that the optical media of the eye be transparent, and both the cornea and the lens are remarkable examples of tissue specializa-tions that achieve a level of transparency that rivals that found in inorganic materials such as glass. Not surprisingly, alterations in the composition of the cornea or the lens can significantly reduce their transparency and have serious consequences for visual perception. Indeed, cataracts (opacities in the lens) account for roughly half the cases of blindness in the world, and almost everyone over the age of 70 will experience some loss of transparency in the lens that ultimately degrades the quality of visual experience. Fortu-nately, there are successful surgical treatments for cataracts that can restore vision in most cases. Furthermore, the recognition that a major factor in the production of cataracts is exposure to ultraviolet (UV) solar radiation has heightened public awareness of the need to protect the lens (and the retina) by reducing UV exposure through the use of sunglasses. Beyond efficiently transmitting light energy, the primary function of the optical components of the eye is to achieve a focused image on the surface of the retina. The cornea and the lens are primarily responsible for the refrac-tion (bending) of light that is necessary for formation of focused images on the photoreceptors of the retina (Figure 10.2). The cornea contributes most of the necessary refraction, as can be appreciated by considering the hazy, out-of-focus images experienced when swimming underwater. Water, unlike air, has a refractive index close to that of the cornea; as a result, immersion in water virtually eliminates the refraction that normally occurs at the air/cornea interface; thus the image is no longer focused on the retina. The lens has considerably less refractive power than the cornea; however, the refraction supplied by the lens is adjustable, allowing objects at various dis-tances from the observer to be brought into sharp focus. Dynamic changes in the refractive power of the lens are referred to as accommodation. When viewing distant objects, the lens is made relatively thin and flat and has the least refractive power. For near vision, the lens becomes thicker and rounder and has the most refractive power (see Figure 10.2). These changes result from the activity of the ciliary muscle that sur-rounds the lens. The lens is held in place by radially arranged connective tis-sue bands (called zonule fibers) that are attached to the ciliary muscle. The shape of the lens is thus determined by two opposing forces: the elasticity of the lens, which tends to keep it rounded up (removed from the eye, the lens Vision: The Eye 231 Unaccommodated Cornea Iris Lens Accommodated Aqueous humor Vitreous humor Zonule fibers Ciliary muscle Figure 10.2 Diagram showing the anterior part of the human eye in the unaccommodated (left) and accommo-dated (right) state. Accommodation for focusing on near objects involves the contraction of the ciliary muscle, which reduces the tension in the zonule fibers and allows the elasticity of the lens to increase its curvature. 232 Chapter Ten becomes spheroidal), and the tension exerted by the zonule fibers, which tends to flatten it. When viewing distant objects, the force from the zonule fibers is greater than the elasticity of the lens, and the lens assumes the flat-ter shape appropriate for distance viewing. Focusing on closer objects requires relaxing the tension in the zonule fibers, allowing the inherent elas-ticity of the lens to increase its curvature. This relaxation is accomplished by the sphincter-like contraction of the ciliary muscle. Because the ciliary mus-cle forms a ring around the lens, when the muscle contracts, the attachment points of the zonule fibers move toward the central axis of the eye, thus Box A Myopia and Other Refractive Errors Optical discrepancies among the various components of the eye cause a majority of the human population to have some form of refractive error, called ametropia. People who are unable to bring distant objects into clear focus are said to be nearsighted, or myopic (Figures A and B). Myopia can be caused by the corneal surface being too curved, or by the eye-ball being too long. In either case, with the lens as flat as it can be, the image of distant objects focuses in front of, rather than on, the retina. People who are un-able to focus on near objects are said to be farsighted, or hyperopic. Hyperopia can be caused by the eyeball being too short or the refracting system too weak (Figure C). Even with the lens in its most rounded-up state, the image is out of focus on the retinal surface (focusing at some point behind it). Both myopia and hyperopia are correctable by appropriate lenses—concave (minus) and convex (plus), respectively—or by the increas-ingly popular technique of corneal surgery. Myopia, or nearsightedness, is by far the most common ametropia; an esti-mated 50% of the population in the United States is affected. Given the large number of people who need glasses, con-tact lenses, or surgery to correct this refractive error, one naturally wonders how nearsighted people coped before spectacles were invented only a few cen-turies ago. From what is now known about myopia, most people’s vision may have been considerably better in ancient times. The basis for this assertion is the surprising finding that the growth of the eyeball is strongly influenced by focused light falling on the retina. This phenome-non was first described in 1977 by Torsten Wiesel and Elio Raviola at Har-vard Medical School, who studied mon-keys reared with their lids sutured (the same approach used to demonstrate the effects of visual deprivation on cortical connections in the visual system; see Chapter 23), a procedure that deprives the eye of focused retinal images. They found that animals growing to maturity under these conditions show an elonga-tion of the eyeball. The effect of focused light deprivation appears to be a local one, since the abnormal growth of the eye occurs in experimental animals even if the optic nerve is cut. Indeed, if only a portion of the retinal surface is deprived of focused light, then only that region of the eyeball grows abnormally. Although the mechanism of light-mediated control of eye growth is not fully understood, many experts now believe that the prevalence of myopia is due to some aspect of modern civiliza-tion—perhaps learning to read and write at an early age—that interferes with the normal feedback control of vision on eye development, leading to abnormal elon-gation of the eyeball. A corollary of this hypothesis is that if children (or, more likely, their parents) wanted to improve their vision, they might be able to do so by practicing far vision to counterbalance the near work “overload.” Practically, of (A) Emmetropia (normal) (B) Myopia (nearsighted) (C) Hyperopia (farsighted) Refractive errors. (A) In the normal eye, with ciliary muscles relaxed, an image of a distant object is focused on the retina. (B) In myopia, light rays are focused in front of the retina. (C) In hyperopia, images are focused at a point beyond the retina. reducing the tension on the lens. Unfortunately, changes in the shape of the lens are not always able to produce a focused image on the retina, in which case a sharp image can be focused only with the help of additional corrective lenses (see Box A). Adjustments in the size of the pupil also contribute to the clarity of images formed on the retina. Like the images formed by other optical instru-ments, those generated by the eye are affected by spherical and chromatic aberrations, which tend to blur the retinal image. Since these aberrations are greatest for light rays that pass farthest from the center of the lens, narrow-Vision: The Eye 233 course, most people would probably choose wearing glasses or contacts or having corneal surgery rather than indulging in the onerous daily practice that would presumably be required. Not everyone agrees, however, that such a remedy would be effective, and a number of investigators (and drug companies) are exploring the possibility of pharmacologi-cal intervention during the period of childhood when abnormal eye growth is presumed to occur. In any event, it is a remarkable fact that deprivation of focused light on the retina causes a com-pensatory growth of the eye and that this feedback loop is so easily perturbed. Even people with normal (em-metropic) vision as young adults eventu-ally experience difficulty focusing on near objects. One of the many conse-quences of aging is that the lens loses its elasticity; as a result, the maximum cur-vature the lens can achieve when the cil-iary muscle contracts is gradually reduced. The near point (the closest point that can be brought into clear focus) thus recedes, and objects (such as this book) must be farther and farther away from the eye in order to focus them on the retina. At some point, usually during early middle age, the accommodative ability of the eye is so reduced that near vision tasks like reading become difficult or impossible (Figure D). This condition is referred to as presbyopia, and can be corrected by convex lenses for near-vision tasks, or by bifocal lenses if myopia is also present (which requires a negative correction). Bifocal correction presents a particular problem for those who prefer contact lenses. Because contact lenses float on the surface of the cornea, having the distance correction above and the near correction below (as in conventional bifocal glasses) doesn’t work (although “omnifocal” contact lenses have recently been used with some success). A surpris-ingly effective solution to this problem for some contact lens wearers has been to put a near correcting lens in one eye and a distance correcting lens in the other! The success of this approach is another testament to the remarkable ability of the visual system to adjust to a wide variety of unusual demands. References BOCK, G. AND K. WIDDOWS (1990) Myopia and the Control of Eye Growth. Ciba Foundation Symposium 155. Chichester: Wiley. COSTER, D. J. (1994) Physics for Ophthalmolo-gists. Edinburgh: Churchill Livingston. KAUFMAN, P. L. AND A. ALM (EDS.) (2002) Adler’s Physiology of the Eye: Clinical Applica-tion, 10th Ed. St. Louis, MO: Mosby Year Book. SHERMAN, S. M., T. T. NORTON AND V. A. CASAGRANDE (1977) Myopia in the lid-sutured tree shrew. Brain Res. 124: 154–157. WALLMAN, J., J. TURKEL AND J. TRACTMAN (1978) Extreme myopia produced by modest changes in early visual experience. Science 201: 1249–1251. WIESEL, T. N. AND E. RAVIOLA (1977) Myopia and eye enlargement after neonatal lid fusion in monkeys. Nature 266: 66–68. (D) Changes in the ability of the lens to round up (accommodate) with age. The graph also shows how the near point (the closest point to the eye that can be brought into focus) changes. Accommodation, which is an optical measurement of the refractive power of the lens, is given in diopters. (After Westheimer, 1974.) 14 0.07 0.1 0.2 1.0 0.5 15 20 Age (years) Amplitude of accommodation (diopters) Near point (m) 25 30 35 40 45 50 55 60 65 70 13 12 11 10 9 8 7 6 5 4 3 2 1 0 Accommodation range (D) Accommodation range 234 Chapter Ten ing the pupil reduces both spherical and chromatic aberration, just as closing the iris diaphragm on a camera lens improves the sharpness of a photo-graphic image. Reducing the size of the pupil also increases the depth of field—that is, the distance within which objects are seen without blurring. However, a small pupil also limits the amount of light that reaches the retina, and, under conditions of dim illumination, visual acuity becomes lim-ited by the number of available photons rather than by optical aberrations. An adjustable pupil thus provides an effective means of reducing optical aberrations, while maximizing depth of field to the extent that different lev-els of illumination permit. The size of the pupil is controlled by innervation from both sympathetic and parasympathetic divisions of the visceral motor system, which are in turn modulated by several brainstem centers (see Chapters 19 and 20). The Retina Despite its peripheral location, the retina or neural portion of the eye, is actually part of the central nervous system. During development, the retina forms as an outpocketing of the diencephalon, called the optic vesicle, which undergoes invagination to form the optic cup (Figure 10.3; see also Chapter 21). The inner wall of the optic cup gives rise to the retina, while the outer wall gives rise to the retinal pigment epithelium. This epithelium is a thin melanin-containing structure that reduces backscattering of light that enters the eye; it also plays a critical role in the maintenance of photoreceptors, renewing photopigments and phagocytosing the photoreceptor disks, whose turnover at a high rate is essential to vision. Consistent with its status as a full-fledged part of the central nervous sys-tem, the retina comprises complex neural circuitry that converts the graded electrical activity of photoreceptors into action potentials that travel to the brain via axons in the optic nerve. Although it has the same types of func-tional elements and neurotransmitters found in other parts of the central nervous system, the retina comprises fewer classes of neurons, and these are arranged in a manner that has been less difficult to unravel than the circuits in other areas of the brain. There are five types of neurons in the retina: pho-toreceptors, bipolar cells, ganglion cells, horizontal cells, and amacrine cells. The cell bodies and processes of these neurons are stacked in alternat-ing layers, with the cell bodies located in the inner nuclear, outer nuclear, and ganglion cell layers, and the processes and synaptic contacts located in the inner plexiform and outer plexiform layers (Figure 10.4). A direct three-Optic vesicle Optic cup Ventricle (B) 4.5-mm embryo (A) 4-mm embryo Lens Lens forming (D) 7-mm embryo (C) 5-mm embryo Pigment epithelium Retina Figure 10.3 Development of the human eye. (A) The retina develops as an outpocketing from the neural tube, called the optic vesicle. (B) The optic vesicle invaginates to form the optic cup. (C, D) The inner wall of the optic cup becomes the neural retina, while the outer wall becomes the pigment epithelium. (A–C from Hilfer and Yang, 1980; D courtesy of K. Tosney.) neuron chain—photoreceptor cell to bipolar cell to ganglion cell—is the major route of information flow from photoreceptors to the optic nerve. There are two types of photoreceptors in the retina: rods and cones. Both types have an outer segment composed of membranous disks that contain light-sensitive photopigment and lies adjacent to the pigment epithelium, and an inner segment that contains the cell nucleus and gives rise to synap-tic terminals that contact bipolar or horizontal cells (see also Figure 10.8). Absorption of light by the photopigment in the outer segment of the pho-toreceptors initiates a cascade of events that changes the membrane potential of the receptor, and therefore the amount of neurotransmitter released by the photoreceptor synapses onto the cells they contact. The synapses between photoreceptor terminals and bipolar cells (and horizontal cells) occur in the outer plexiform layer; more specifically, the cell bodies of photoreceptors make up the outer nuclear layer, whereas the cell bodies of bipolar cells lie in the inner nuclear layer. The short axonal processes of bipolar cells make syn-aptic contacts in turn on the dendritic processes of ganglion cells in the inner plexiform layer. The much larger axons of the ganglion cells form the optic Vision: The Eye 235 Ganglion Ganglion cell cell Horizontal Horizontal cell cell Amacrine Amacrine cell cell Amacrine cell Horizontal cell Rod Rod Ganglion cell Rod Rod Rod Rod Light Light Ganglion cell layer Distal Virtical information flow Virtical information flow To optic nerve To optic nerve Inner plexiform layer Outer plexiform layer Inner nuclear layer Outer nuclear layer Nerve fiber layer Photo-receptor outer segments Pigment epithelium Vertical information flow To optic nerve Proximal Lateral Lateral information information flow flow Lateral information flow Bipolar Bipolar cell cell Bipolar cell Cone Cone Cone Cone Cone Cone Cone Cone Cone Rod Rod Rod (A) Section of retina (B) Figure 10.4 Structure of the retina. (A) Section of the retina showing overall arrangement of retinal layers. (B) Dia-gram of the basic circuitry of the retina. A three-neuron chain—photoreceptor, bipolar cell, and ganglion cell—provides the most direct route for transmitting visual information to the brain. Hori-zontal cells and amacrine cells mediate lateral interactions in the outer and inner plexiform layers, respectively. The terms inner and outer designate relative distances from the center of the eye (inner, near the center of the eye; outer, away from the center, or toward the pig-ment epithelium). 236 Chapter Ten nerve and carry information about retinal stimulation to the rest of the cen-tral nervous system. The two other types of neurons in the retina, horizontal cells and amacrine cells, have their cell bodies in the inner nuclear layer and have processes that are limited to the outer and inner plexiform layers respec-tively (see Figure 10.4). The processes of horizontal cells enable lateral inter-actions between photoreceptors and bipolar cells that maintain the visual system’s sensitivity to luminance contrast over a wide range of light intensi-ties. The processes of amacrine cells are postsynaptic to bipolar cell terminals and presynaptic to the dendrites of ganglion cells. Different subclasses of amacrine cells are thought to make distinct contributions to visual function. One class of amacrine cells, for example, plays an important role in trans-forming the sustained responses of bipolar cells to step changes in light intensity into transient onset or offset responses exhibited by some types of ganglion cells. Another type serves as an obligatory step in the pathway that transmits information from rod photoreceptors to retinal ganglion cells. The variety of amacrine cell subtypes illustrates the more general rule that although there are only five basic retinal cell types, there can be considerable diversity within a given cell type. This diversity is also a hallmark of retinal ganglion cells and the basis for pathways that convey different sorts of infor-mation to central targets in a parallel manner (see Chapter 11). At first glance, the spatial arrangement of retinal layers seems counterin-tuitive, since light rays must pass through various non-light-sensitive ele-ments of the retina as well as the retinal vasculature (which branches exten-sively on the inner surface of the retina—see Figure 11.1) before reaching the outer segments of the photoreceptors, where photons are absorbed (Figure 10.4). The reason for this curious feature of retinal organization lies in the special relationship that exists among the outer segments of the photorecep-tors, the pigment epithelium, and the underlying choroid. Recall that the outer segments contain membranous disks that house the light-sensitive pho-topigment and other proteins involved in the transduction process. These disks are formed near the inner segment of the photoreceptor and move toward the tip of the outer segment, where they are shed. The pigment epithelium plays an essential role in removing the expended receptor disks; this is no small task, since all the disks in the outer segments are replaced every 12 days. In addition, the pigment epithelium contains the biochemical machinery that is required to regenerate photopigment molecules after they have been exposed to light. Finally, the capillaries in the choroid underlying the pigment epithelium are the primary source of nourishment for retinal photoreceptors. These functional considerations presumably explain why rods and cones are found in the outermost rather than the innermost layer of the retina. They also explain why disruptions in the normal relationships between the pigment epithelium and retinal photoreceptors such as those that occur in retinitis pigmentosa have severe consequences for vision (Box B). Phototransduction In most sensory systems, activation of a receptor by the appropriate stimulus causes the cell membrane to depolarize, ultimately stimulating an action potential and transmitter release onto the neurons it contacts. In the retina, however, photoreceptors do not exhibit action potentials; rather, light activa-tion causes a graded change in membrane potential and a corresponding change in the rate of transmitter release onto postsynaptic neurons. Indeed, much of the processing within the retina is mediated by graded potentials, largely because action potentials are not required to transmit information over the relatively short distances involved. Perhaps even more surprising is that shining light on a photoreceptor, either a rod or a cone, leads to membrane hyperpolarization rather than depo-larization (Figure 10.5). In the dark, the receptor is in a depolarized state, with a membrane potential of roughly –40 mV (including those portions of the cell that release transmitters). Progressive increases in the intensity of illumination cause the potential across the receptor membrane to become more negative, a response that saturates when the membrane potential reaches about –65 mV. Although the sign of the potential change may seem odd, the only logical requirement for subsequent visual processing is a con-sistent relationship between luminance changes and the rate of transmitter release from the photoreceptor terminals. As in other nerve cells, transmitter release from the synaptic terminals of the photoreceptor is dependent on voltage-sensitive Ca2+ channels in the terminal membrane. Thus, in the dark, when photoreceptors are relatively depolarized, the number of open Ca2+ channels in the synaptic terminal is high, and the rate of transmitter release is correspondingly great; in the light, when receptors are hyperpolarized, the number of open Ca2+ channels is reduced, and the rate of transmitter release is also reduced. The reason for this unusual arrangement compared to other sensory receptor cells is not known. The relatively depolarized state of photoreceptors in the dark depends on the presence of ion channels in the outer segment membrane that permit Na+ and Ca2+ ions to flow into the cell, thus reducing the degree of inside negativity (Figure 10.6). The probability of these channels in the outer seg-ment being open or closed is regulated in turn by the levels of the nucleotide cyclic guanosine monophosphate (cGMP) (as in many other second messen-ger systems; see Chapter 7). In darkness, high levels of cGMP in the outer segment keep the channels open. In the light, however, cGMP levels drop and some of the channels close, leading to hyperpolarization of the outer segment membrane, and ultimately the reduction of transmitter release at the photoreceptor synapse. The series of biochemical changes that ultimately leads to a reduction in cGMP levels begins when a photon is absorbed by the photopigment in the receptor disks. The photopigment contains a light-absorbing chromophore (retinal, an aldehyde of vitamin A) coupled to one of several possible pro-teins called opsins that tune the molecule’s absorption of light to a particu-lar region of the spectrum. Indeed, it is the different protein component of Vision: The Eye 237 −40 −45 −50 −55 −60 −65 0 100 Time (ms) Membrane potential (mV) 200 300 400 500 600 Most intense flash response Least intense flash response Light flash Figure 10.5 An intracellular recording from a sin-gle cone stimulated with different amounts of light (the cone has been taken from the turtle retina, which accounts for the relatively long time course of the response). Each trace represents the response to a brief flash that was varied in intensity. At the highest light levels, the response amplitude satu-rates (at about –65 mV). The hyperpolarizing response is characteristic of vertebrate photorecep-tors; interestingly, some invertebrate photorecep-tors depolarize in response to light. (After Schnapf and Baylor, 1987.) 238 Chapter Ten the photopigment in rods and cones that contributes to the functional spe-cialization of these two receptor types. Most of what is known about the molecular events of phototransduction has been gleaned from experiments in rods, in which the photopigment is rhodopsin (Figure 10.7A). When the retinal moiety in the rhodopsin molecule absorbs a photon, its configuration changes from the 11-cis isomer to all-trans retinal; this change then triggers a series of alterations in the protein component of the molecule (Figure 10.7B). The changes lead, in turn, to the activation of an intracellular messenger called transducin, which activates a phosphodiesterase that hydrolyzes Na+ Ca2+ cGMP cGMP Out-side In-side Rod outer segment Rod inner segment Rod outer segment Rod inner segment 0 Light Na+ Rod cGMP Dark + − 0 + − cGMP Na+ Ca2+ Figure 10.6 Cyclic GMP-gated chan-nels in the outer segment membrane are responsible for the light-induced changes in the electrical activity of pho-toreceptors (a rod is shown here, but the same scheme applies to cones). In the dark, cGMP levels in the outer segment are high; this molecule binds to the Na+-permeable channels in the membrane, keeping them open and allowing sodium (and other cations) to enter, thus depolarizing the cell. Exposure to light leads to a decrease in cGMP levels, a closing of the channels, and receptor hyperpolarization. Open Na+ channel Rhodopsin PDE Light Disk Disk membrane Na+ Na+ Outside of cell Inside of cell Closed Na+ channel α α β γ α GTP GTP GMP GMP GMP GDP cGMP cGMP cGMP 2 Activated G-protein activates cGMP phosphodiesterase (PDE) Outer segment membrane 3 PDE hydrolyzes cGMP, reducing its concentration 4 This leads to closure of Na+ channels β γ 1 Light stimulation of rhodopsin leads to activation of a G-protein, transducin Transducin (B) (A) N C 11-cis retinal Opsin Figure 10.7 Details of phototransduc-tion in rod photoreceptors. (A) The mol-ecular structure of rhodopsin, the pig-ment in rods. (B) The second messenger cascade of phototransduction. Light stimulation of rhodopsin in the receptor disks leads to the activation of a G-pro-tein (transducin), which in turn activates a phosphodiesterase (PDE). The phos-phodiesterase hydrolyzes cGMP, reduc-ing its concentration in the outer seg-ment and leading to the closure of sodium channels in the outer segment membrane. Vision: The Eye 239 Box B Retinitis Pigmentosa Retinitis pigmentosa (RP) refers to a heterogeneous group of hereditary eye disorders characterized by progressive vision loss due to a gradual degeneration of photoreceptors. An estimated 100,000 people in the United States have RP. In spite of the name, inflammation is not a prominent part of the disease process; instead the photoreceptor cells appear to die by apoptosis (determined by the presence of DNA fragmentation). Classification of this group of disor-ders under one rubric is based on the clinical features commonly observed in these patients. The hallmarks of RP are night blindness, a reduction of peripheral vision, narrowing of the retinal vessels, and the migration of pigment from dis-rupted retinal pigment epithelium into the retina, forming clumps of various sizes, often next to retinal blood vessels (see figure). Typically, patients first notice diffi-culty seeing at night due to the loss of rod photoreceptors; the remaining cone photoreceptors then become the main-stay of visual function. Over many years, the cones also degenerate, leading to a progressive loss of vision. In most RP patients, visual field defects begin in the midperiphery, between 30° and 50° from the point of foveal fixation. The defective regions gradually enlarge, leaving islands of vision in the periphery and a constricted central field—a condition known as tunnel vision. When the visual field contracts to 20° or less and/or cen-tral vision is 20/200 or worse, the patient is categorized as legally blind. Inheritance patterns indicate that RP can be transmitted in an X-linked (XLRP), autosomal dominant (ADRP), or recessive (ARRP) manner. In the United States, the percentage of these genetic types is estimated to be 9%, 16%, and 41%, respectively. When only one mem-ber of a pedigree has RP, the case is clas-sified as “simplex,” which accounts for about a third of all cases. Among the three genetic types of RP, ADRP is the mildest. These patients often retain good central vision until 60 years of age or older. In contrast, patients with the XLRP form of the disease are usually legally blind by 30 to 40 years of age. However, the severity and age of onset of the symptoms varies greatly among patients with the same type of RP, and even within the same family (when, presumably, all the affected members have the same genetic mutation). To date, RP-inducing mutations of 30 genes have been identified. Many of these genes encode photoreceptor-spe-cific proteins, several being associated with phototransduction in the rods. Among the latter are genes for rhodopsin, subunits of the cGMP phos-phodiesterase, and the cGMP-gated channel. Multiple mutations have been found in each of these cloned genes. For example, in the case of the rhodopsin gene, 90 different mutations have been identified among ADRP patients. The heterogeneity of RP at all levels, from genetic mutations to clinical symp-toms, has important implications for understanding the pathogenesis of the disease and designing therapies. Given the complex molecular etiology of RP, it is unlikely that a single cellular mecha-nism will explain the disease in all cases. Regardless of the specific mutation or causal sequence, the vision loss that is most critical to RP patients is due to the gradual degeneration of cones. In many cases, the protein that the RP-causing mutation affects is not even expressed in the cones; the prime example is rhodopsin—the rod-specific visual pig-ment. Therefore, the loss of cones may be an indirect result of a rod-specific muta-tion. In consequence, understanding and treating this disease presents a particu-larly difficult challenge. References WELEBER, R. G. AND K. GREGORY-EVANS (2001) Retinitis pigmentosa and allied disorders. In Retina, 3rd Ed., Vol. 1: Basic Science and Inher-ited Retinal Diseases. S. J. Ryan (ed. in chief). St. Louis, MO: Mosby Year Book, pp. 362–460. RATTNER, A., A. SUN AND J. NATHANS (1999) Molecular genetics of human retinal disease. Annu. Rev. Genet. 33: 89–131. THE FOUNDATION FIGHTING BLINDNESS of Hunt Valley, MD, maintains a web site that pro-vides updated information about many forms of retinal degeneration: www.blind-ness.org RETNET provides updated information, including references to original articles, on genes and mutations associated with retinal diseases: www.sph.uth.tmc.edu/RetNet Characteristic appearance of the retina in patients with retinitis pigmentosa. Note the dark clumps of pigment that are the hall-mark of this disorder. 240 Chapter Ten cGMP. All of these events take place within the disk membrane. The hydrol-ysis by phosphodiesterase at the disk membrane lowers the concentration of cGMP throughout the outer segment, and thus reduces the number of cGMP molecules that are available for binding to the channels in the surface of the outer segment membrane, leading to channel closure. One of the important features of this complex biochemical cascade initi-ated by photon capture is that it provides enormous signal amplification. It has been estimated that a single light-activated rhodopsin molecule can acti-vate 800 transducin molecules, roughly eight percent of the transducin mol-ecules on the disk surface. Although each transducin molecule activates only one phosphodiesterase molecule, each of these is in turn capable of catalyz-ing the breakdown of as many as six cGMP molecules. As a result, the absorption of a single photon by a rhodopsin molecule results in the closure of approximately 200 ion channels, or about 2% of the number of channels in each rod that are open in the dark. This number of channel closures causes a net change in the membrane potential of about 1 mV. Equally important is the fact that the magnitude of this amplification varies with the prevailing levels of illumination, a phenomenon known as light adaptation. At low levels of illumination, photoreceptors are the most sensitive to light. As levels of illumination increase, sensitivity decreases, preventing the receptors from saturating and thereby greatly extending the range of light intensities over which they operate. The concentration of Ca2+ in the outer segment appears to play a key role in the light-induced modula-tion of photoreceptor sensitivity. The cGMP-gated channels in the outer seg-ment are permeable to both Na+ and Ca2+; thus, light-induced closure of these channels leads to a net decrease in the internal Ca2+ concentration. This decrease triggers a number of changes in the phototransduction cascade, all of which tend to reduce the sensitivity of the receptor to light. For example, the decrease in Ca2+ increases the activity of quanylate cyclase, the cGMP synthesizing enzyme, leading to an increase in cGMP levels. Likewise, the decrease in Ca2+ increases the affinity of the cGMP-gated channels for cGMP, reducing the impact of the light-induced reduction of cGMP levels. The reg-ulatory effects of Ca2+ on the phototransduction cascade are only one part of the mechanism that adapts retinal sensitivity to background levels of illumi-nation; another important contribution comes from neural interactions between horizontal cells and photoreceptor terminals (see below). Once initiated, additional mechanisms limit the duration of this amplify-ing cascade and restore the various molecules to their inactivated states. The protein arrestin, for instance, blocks the ability of activated rhodopsin to activate transducin, and facilitates the breakdown of activated rhodopsin. The all-trans retinal then dissociates from the opsin, diffuses into the cytosol of the outer segment, is converted to all-trans retinol and is transported out of the outer segment and into the pigment epithelium, where appropriate enzymes ultimately convert it to 11-cis retinal. After it is transported back into the outer segment, the 11-cis retinal recombines with opsin in the recep-tor disks. The recycling of rhodopsin is critically important for maintaining the light sensitivity of photoreceptors. Even under intense levels of illumina-tion, the rate of regeneration is sufficient to maintain a significant number of active photopigment molecules. Functional Specialization of the Rod and Cone Systems The two types of photoreceptors, rods and cones, are distinguished by shape (from which they derive their names), the type of photopigment they con-tain, distribution across the retina, and pattern of synaptic connections (Fig-ure 10.8). These properties reflect the fact that the rod and cone systems (the receptors and their connections within the retina) are specialized for differ-ent aspects of vision. The rod system has very low spatial resolution but is extremely sensitive to light; it is therefore specialized for sensitivity at the expense of resolution. Conversely, the cone system has very high spatial res-olution but is relatively insensitive to light; it is therefore specialized for acu-ity at the expense of sensitivity. The properties of the cone system also allow humans and many other animals to see color. The range of illumination over which the rods and cones operate is shown in Figure 10.9. At the lowest levels of light, only the rods are activated. Such rod-mediated perception is called scotopic vision. The difficulty of making fine visual discriminations under very low light conditions where only the rod system is active is a common experience. The problem is primarily the poor resolution of the rod system (and, to a lesser degree, the fact that there is no perception of color in dim light because the cones are not involved to a significant degree). Although cones begin to contribute to visual perception at about the level of starlight, spatial discrimination at this light level is still very poor. As illumination increases, cones become more and more domi-nant in determining what is seen, and they are the major determinant of per-ception under relatively bright conditions such as normal indoor lighting or sunlight. The contributions of rods to vision drops out nearly entirely in so-called photopic vision because their response to light saturates—that is, the membrane potential of individual rods no longer varies as a function of illu-mination because all of the membrane channels are closed (see Figure 10.5). Mesopic vision occurs in levels of light at which both rods and cones con-tribute—at twilight, for example. From these considerations it should be clear that most of what we think of as normal “seeing” is mediated by the cone system, and that loss of cone function is devastating, as occurs in Vision: The Eye 241 (A) Rod Outer segment Outer segment Disks Cytoplasmic space Plasma membrane Cilium Mitochondria Nucleus Synaptic vesicles Inner segment Inner segment Synaptic terminal Synaptic terminal (B) Cone Figure 10.8 Structural differences between rods and cones. Although generally similar in structure, rods (A) and cones (B) differ in their size and shape, as well as in the arrangement of the membranous disks in their outer segments. 242 Chapter Ten elderly individuals suffering from macular degeneration (Box C). People who have lost cone function are legally blind, whereas those who have lost rod function only experience difficulty seeing at low levels of illumination (night blindness; see Box B). Differences in the transduction mechanisms utilized by the two receptor types is a major factor in the ability of rods and cones to respond to different ranges of light intensity. For example, rods produce a reliable response to a single photon of light, whereas more than 100 photons are required to pro-duce a comparable response in a cone. It is not, however, that cones fail to effectively capture photons. Rather, the change in current produced by single photon capture in cones is comparatively small and difficult to distinguish from noise. Another difference is that the response of an individual cone does not saturate at high levels of steady illumination, as does the rod response. Although both rods and cones adapt to operate over a range of luminance values, the adaptation mechanisms of the cones are more effective. This dif-ference in adaptation is apparent in the time course of the response of rods and cones to light flashes. The response of a cone, even to a bright light flash that produces the maximum change in photoreceptor current, recovers in about 200 milliseconds, more than four times faster than rod recovery. The arrangement of the circuits that transmit rod and cone information to retinal ganglion cells also contributes to the different characteristics of sco-topic and photopic vision. In most parts of the retina, rod and cone signals converge on the same ganglion cells; i.e., individual ganglion cells respond to both rod and cone inputs, depending on the level of illumination. The early stages of the pathways that link rods and cones to ganglion cells, how-ever, are largely independent. For example, the pathway from rods to gan-glion cells involves a distinct class of bipolar cell (called rod bipolar) that, unlike cone bipolar cells, does not contact retinal ganglion cells. Instead, rod bipolar cells synapse with the dendritic processes of a specific class of amacrine cell that makes gap junctions and chemical synapses with the ter-minals of cone bipolars; these processes, in turn, make synaptic contacts on the dendrites of ganglion cells in the inner plexiform layer. As a conse-quence, the circuits linking the rods and cones to retinal ganglion cells differ dramatically in their degree of convergence. Each rod bipolar cell is con-tacted by a number of rods, and many rod bipolar cells contact a given amacrine cell. In contrast, the cone system is much less convergent. Thus, each retinal ganglion cell that dominates central vision (called midget gan-Luminance of white paper in: Visual function −6 −4 −2 0 Luminance (log cd/m−2) 2 4 6 8 Sunlight Best acuity Scotopic Mesopic Photopic Absolute threshold Cone threshold Rod saturation begins Indirect ophthalmo-scope Damage possible Good color vision Best acuity No color vision Poor acuity Starlight Moonlight Indoor lighting 50% bleach Figure 10.9 The range of luminance values over which the visual system operates. At the lowest levels of illumi-nation, only rods are activated. Cones begin to contribute to perception at about the level of starlight and are the only receptors that function under rela-tively bright conditions. Vision: The Eye 243 Box C Macular Degeneration An estimated six million people in the United States suffer from a condition known as age-related macular degenera-tion (AMD), which causes a progressive loss of central vision. Since central vision is critical for sight, diseases that affect the macula (see Figure 11.1) severely limit the ability to perform visual tasks. Indeed, AMD is the most common cause of vision loss in people over age 55, and its incidence is rising with the increasing percentage of elderly individuals in the population. The underlying problem, which remains poorly understood, is degenera-tion of the photoreceptors. Usually, patients first notice a blurring of central vision when performing tasks such as reading. Images may also appear dis-torted. A graph paper-like chart known as the Amsler grid is used as a simple test for early signs of AMD. By focusing on a marked spot in the middle of the grid, the patient can assess whether the parallel and perpendicular lines on the grid appear blurred or distorted. Blurred central vision often progresses to having blind spots within central vision, and in most cases both eyes are eventually involved. Although the risk of developing AMD clearly increases with age, the causes of the disease are not known. Various stud-ies have implicated hereditary factors, cardiovascular disease, environmental factors such as smoking and light expo-sure, and nutritional causes. Indeed, it may be that all these contribute to the risk of developing AMD. In descriptive terms, macular degen-eration is broadly divided into two types. In the exudative-neovascular form, or “wet” AMD, which accounts for 10% of all cases, abnormal blood vessel growth occurs under the macula. These blood vessels leak fluid and blood into the retina and cause damage to the photore-ceptors. Wet AMD tends to progress rapidly and can cause severe damage; rapid loss of central vision may occur over just a few months. The treatment for this form of the disease is laser therapy. By transferring thermal energy, the laser beam destroys the leaky blood vessels under the macula, thus slowing the rate of vision loss. A disadvantage of this approach is that the high thermal energy delivered by the beam also destroys nearby healthy tissue. An improvement in the laser treatment of AMD involves a light-activated drug to target abnormal blood vessels. Once the drug is adminis-tered, relatively low energy laser pulses aimed at the abnormal blood vessels are delivered to stimulate the drug, which in turn destroys the abnormal blood vessels with minimal damage to the surround-ing tissue. The remaining 90% of AMD cases are the nonexudative, or “dry” form. In these patients there is a gradual disappearance of the retinal pigment epithelium, result-ing in circumscribed areas of atrophy. Since photoreceptor loss follows the dis-appearance of the pigment epithelium, the affected retinal areas have little or no visual function. Vision loss from dry AMD occurs more gradually, typically over the course of many years. These patients usually retain some central vision, although the loss can be severe enough to compromise performance of tasks that require seeing details. Unfortu-nately, at the present time there is no treatment for dry AMD. A radical and quite fascinating new approach that offers some promise entails surgically repositioning the retina away from the abnormal area. Occasionally, macular degeneration occurs in much younger individuals. Many of these cases are caused by vari-ous mutations, each with its own clinical manifestations and genetic cause. The most common form of juvenile macular degeneration is known as Stargardt dis-ease, which is inherited as an autosomal recessive. Patients are usually diagnosed before they reach the age of 20. Although the progression of vision loss is variable, most of these patients are legally blind by age 50. Mutations that cause Stargardt disease have been identified in the ABCR gene, which codes for a protein that transports retinoids across the photore-ceptor membrane. Thus, the visual cycle of photopigment regeneration may be disrupted in this form of macular degen-eration, presumably by dysfunctional proteins encoded by the abnormal gene. Interestingly, the ABCR gene is expressed only in rods, suggesting that the cones may have their own visual cycle enzymes. References FINE, S. L., J. W. BERGER, M. G. MAGUIRE AND A. C. HO (2000) Drug therapy: Age-related macular degeneration. NEJM 342: 483–492. SARKS, S. H. AND J. P. SARKS (2001) Age-related macular degeneration—atrophic form. In Retina, 3rd Ed., Vol. 2: Medical Retina. S. J. Ryan (ed.-in-chief). St. Louis, MO: Mosby Year Book, pp. 1071–1102. ELMAN, M. J. AND S. L. FINE (2001) Exudative age-related macular degeneration. In Retina, 3rd Ed., Vol. 2: Medical Retina. S. J. Ryan (ed.-in-chief). St. Louis, MO: Mosby Year Book, pp. 1103–114. DEUTMAN, A. F. (2001) Macular dystrophies. In Retina, 3rd Ed., Vol. 2: Medical Retina. S. J. Ryan (ed.-in-chief). St. Louis, MO: Mosby Year Book, pp. 1186–1240. THE FOUNDATION FIGHTING BLINDNESS of Hunt Valley, MD, maintains a web site that pro-vides updated information about many forms of retinal degeneration: www.blind-ness.org RETNET provides updated information, including references to original articles, on genes and mutations associated with retinal diseases: www.sph.uth.tmc.edu/RetNet 244 Chapter Ten Figure 10.10 Distribution of rods and cones in the human retina. Graph illus-trates that cones are present at a low density throughout the retina, with a sharp peak in the center of the fovea. Conversely, rods are present at high density throughout most of the retina, with a sharp decline in the fovea. Boxes at top illustrate the appearance of face on sections through the outer segments of the photoreceptors at different eccen-tricities. The increased density of cones in the fovea is accompanied by a strik-ing reduction in the diameter of their outer segments. glion cells) receives input from only one cone bipolar cell, which, in turn, is contacted by a single cone. Convergence makes the rod system a better detector of light, because small signals from many rods are pooled to gener-ate a large response in the bipolar cell. At the same time, convergence reduces the spatial resolution of the rod system, since the source of a signal in a rod bipolar cell or retinal ganglion cell could have come from anywhere within a relatively large area of the retinal surface. The one-to-one relation-ship of cones to bipolar and ganglion cells is, of course, just what is required to maximize acuity. Anatomical Distribution of Rods and Cones The distribution of rods and cones across the surface of the retina also has important consequences for vision (Figure 10.10). Despite the fact that per-ception in typical daytime light levels is dominated by cone-mediated vision, the total number of rods in the human retina (about 90 million) far exceeds the number of cones (roughly 4.5 million). As a result, the density of rods is much greater than cones throughout most of the retina. However, this relationship changes dramatically in the fovea, a highly specialized region of the central retina that measures about 1.2 millimeters in diameter (Figure 10.11). In the fovea, cone density increases almost 200-fold, reaching, at its center, the highest receptor packing density anywhere in the retina. This high density is achieved by decreasing the diameter of the cone outer seg-ments such that foveal cones resemble rods in their appearance. The increased density of cones in the fovea is accompanied by a sharp decline in the density of rods. In fact, the central 300 µm of the fovea, called the fove-ola, is totally rod-free. The extremely high density of cone receptors in the fovea, and the one-to-one relationship with bipolar cells and retinal ganglion cells (see earlier), endows this component of the cone system with the capacity to mediate high visual acuity. As cone density declines with eccentricity and the degree of convergence onto retinal ganglion cells increases, acuity is markedly reduced. Just 6° eccentric to the line of sight, acuity is reduced by 75%, a fact Temporal Eccentricity (degrees) Nasal 0 20 40 60 80 100 120 140 160 Receptor density (mm−2 × 103) 80 80 60 60 40 40 20 20 0 Cones Cones Rods Rods Optic disk that can be readily appreciated by trying to read the words on any line of this page beyond the word being fixated on. The restriction of highest acuity vision to such a small region of the retina is the main reason humans spend so much time moving their eyes (and heads) around—in effect directing the foveas of the two eyes to objects of interest (see Chapter 19). It is also the rea-son why disorders that affect the functioning of the fovea have such devas-tating effects on sight (see Box C). Conversely, the exclusion of rods from the fovea, and their presence in high density away from the fovea, explain why the threshold for detecting a light stimulus is lower outside the region of central vision. It is easier to see a dim object (such as a faint star) by looking slightly away from it, so that the stimulus falls on the region of the retina that is richest in rods (see Figure 10.10). Another anatomical feature of the fovea (which literally means “pit”) that contributes to the superior acuity of the cone system is that the layers of cell bodies and processes that overlie the photoreceptors in other areas of the retina are displaced around the fovea, and especially the foveola (see Figure 10.11). As a result, photons are subjected to a minimum of scattering before they strike the photoreceptors. Finally, another potential source of optical distortion that lies in the light path to the receptors—the retinal blood ves-sels—are diverted away from the foveola. This central region of the fovea is therefore dependent on the underlying choroid and pigment epithelium for oxygenation and metabolic sustenance. Cones and Color Vision A special property of the cone system is color vision. Perceiving color allows humans (and many other animals) to discriminate objects on the basis of the distribution of the wavelengths of light that they reflect to the eye. While dif-ferences in luminance (i.e., overall light intensity) are often sufficient to dis-tinguish objects, color adds another perceptual dimension that is especially useful when differences in luminance are subtle or nonexistent. Color obvi-ously gives us a quite different way of perceiving and describing the world we live in. Vision: The Eye 245 Ganglion cell layer Inner nuclear layer Outer nuclear layer Pigment epithelium Cones Rods Bipolar cells Ganglion cells Capillaries Choroid Avascular zone Foveola Fovea Figure 10.11 Diagrammatic cross section through the human fovea. The overlying cellular layers and blood vessels are displaced so that light is subjected to a mini-mum of scattering before photons strike the outer segments of the cones in the cen-ter of the fovea, called the foveola. 246 Chapter Ten Figure 10.12 Color vision. The light absorption spectra of the four photopig-ments in the normal human retina. (Recall that light is defined as electro-magnetic radiation having wavelengths between ~400 and 700 nm.) The solid curves indicate the three kinds of cone opsins; the dashed curve shows rod rhodopsin for comparison. Absorbance is defined as the log value of the inten-sity of incident light divided by inten-sity of transmitted light. Unlike rods, which contain a single photopigment, there are three types of cones that differ in the photopigment they contain. Each of these photopig-ments has a different sensitivity to light of different wavelengths, and for this reason are referred to as “blue,” “green,” and “red” or, more appropri-ately, short (S), medium (M), and long (L) wavelength cones—terms that more or less describe their spectral sensitivities (Figure 10.12). This nomen-clature implies that individual cones provide color information for the wave-length of light that excites them best. In fact, individual cones, like rods, are entirely color blind in that their response is simply a reflection of the number of photons they capture, regardless of the wavelength of the photon (or, more properly, its vibrational energy). It is impossible, therefore, to deter-mine whether the change in the membrane potential of a particular cone has arisen from exposure to many photons at wavelengths to which the receptor is relatively insensitive, or fewer photons at wavelengths to which it is most sensitive. This ambiguity can only be resolved by comparing the activity in different classes of cones. Based on the responses of individual ganglion cells, and cells at higher levels in the visual pathway (see Chapter 11), com-parisons of this type are clearly involved in how the visual system extracts color information from spectral stimuli. Despite these insights, a full under-standing of the neural mechanisms that underlie color perception has been elusive (Box D). Much additional information about color vision has come from studies of individuals with abnormal color detecting abilities. Color vision deficiencies result either from the inherited failure to make one or more of the cone pig-ments or from an alteration in the absorption spectra of cone pigments (or, rarely, from lesions in the central stations that process color information; see Chapter 11). Under normal conditions, most people can match any color in a test stimulus by adjusting the intensity of three superimposed light sources generating long, medium, and short wavelengths. The fact that only three such sources are needed to match (nearly) all the perceived colors is strong 100 Short Medium Long 50 0 Wavelength (nm) 400 450 500 550 600 650 Relative spectral absorbance Rods Vision: The Eye 247 Box D The Importance of Context in Color Perception Seeing color logically demands that reti-nal responses to different wavelengths in some way be compared. The discovery of the three human cone types and their different absorption spectra is correctly regarded, therefore, as the basis for human color vision. Nevertheless, how these human cone types and the higher-order neurons they contact (see Chapter 11) produce the sensations of color is still unclear. Indeed, this issue has been debated by some of the greatest minds in science (Hering, Helmholtz, Maxwell, Schroedinger, and Mach, to name only a few) since Thomas Young first proposed that humans must have three different receptive “particles”—i.e., the three cone types. A fundamental problem has been that, although the relative activities of three cone types can more or less explain the colors perceived in color-matching experiments performed in the laboratory, the perception of color is strongly influ-enced by context. For example, a patch returning the exact same spectrum of wavelengths to the eye can appear quite different depending on its surround, a phenomenon called color contrast (Figure A). Moreover, test patches returning dif-ferent spectra to the eye can appear to be the same color, an effect called color con-stancy (Figure B). Although these phe-nomena were well known in the nine-teenth century, they were not accorded a central place in color vision theory until Edwin Land’s work in the 1950s. In his most famous demonstration, Land (who among other achievements founded the Polaroid company and became a billion-aire) used a collage of colored papers that have been referred to as “the Land Mon-drians” because of their similarity to the work of the Dutch artist Piet Mondrian. Using a telemetric photometer and three adjustable illuminators generating short, middle, and long wavelength light, Land showed that two patches that in white light appeared quite different in color (e. g., green and brown) continued to look their respective colors even when the three illuminators were adjusted so that the light being returned from the “green” surfaces produced exactly the same readings on the three telephotome-ters as had previously come from the “brown” surface—a striking demonstra-tion of color constancy. The phenomena of color contrast and color constancy have led to a heated modern debate about how color percepts are generated that now spans several decades. For Land, the answer lay in a series of ratiometric equations that could integrate the spectral returns of different regions over the entire scene. It was rec-ognized even before Land’s death in 1991, however, that his so-called retinex theory did not work in all circumstances and was in any event a description rather than an explanation. An alternative expla-nation of these contextual aspects of color vision is that color, like brightness, is gen-erated empirically according to what spectral stimuli have typically signified in past experience (see Box E). References LAND, E. (1986) Recent advances in Retinex theory. Vis. Res. 26: 7–21. PURVES, D. AND R. B. LOTTO (2003) Why We See What We Do: An Empirical Theory of Vision, Chapters 5 and 6. Sunderland MA: Sinauer Associates, pp. 89–138. The genesis of contrast and constancy effects by exactly the same context. The two panels demonstrate the effects on apparent color when two similarly reflective target surfaces (A) or two differently reflective target surfaces (B) are presented in the same context in which all the information provided is consistent with illumination that differs only in intensity. The appear-ances of the relevant target surfaces in a neutral context are shown in the insets below. (From Purves and Lotto, 2003) (A) (B) 248 Chapter Ten Figure 10.13 Many deficiencies of color vision are the result of genetic alterations in the red or green cone pig-ments due to the crossing over of chro-mosomes during meiosis. This recombi-nation can lead to the loss of a gene, the duplication of a gene, or the formation of a hybrid with characteristics distinct from those of normal genes. confirmation of the fact that color sensation is based on the relative levels of activity in three sets of cones with different absorption spectra. That color vision is trichromatic was first recognized by Thomas Young at the begin-ning of the nineteenth century (thus, people with normal color vision are called trichromats). For about 5–6% of the male population in the United States and a much smaller percentage of the female population, however, color vision is more limited. Only two bandwidths of light are needed to match all the colors that these individuals can perceive; the third color cate-gory is simply not seen. Such dichromacy, or “color blindness” as it is com-monly called, is inherited as a recessive, sex-linked characteristic and exists in two forms: protanopia, in which all color matches can be achieved by using only green and blue light, and deuteranopia, in which all matches can be achieved by using only blue and red light. In another major class of color deficiencies, all three light sources (i.e., short, medium, and long wave-lengths) are needed to make all possible color matches, but the matches are made using values that are significantly different from those used by most individuals. Some of these anomalous trichromats require more red than nor-mal to match other colors (protanomalous trichromats); others require more green than normal (deuteranomalous trichromats). Jeremy Nathans and his colleagues at Johns Hopkins University have pro-vided a deeper understanding of these color vision deficiencies by identify-ing and sequencing the genes that encode the three human cone pigments (Figure 10.13). The genes that encode the red and green pigments show a high degree of sequence homology and lie adjacent to each other on the X chromosome, thus explaining the prevalence of color blindness in males. In contrast, the blue-sensitive pigment gene is found on chromosome 7 and is quite different in its amino acid sequence. These facts suggest that the red and green pigment genes evolved relatively recently, perhaps as a result of the duplication of a single ancestral gene; they also explain why most color vision abnormalities involve the red and green cone pigments. Human dichromats lack one of the three cone pigments, either because the corresponding gene is missing or because it exists as a hybrid of the red and green pigment genes (see Figure 10.13). For example, some dichromats lack the green pigment gene altogether, while others have a hybrid gene that is thought to produce a red-like pigment in the “green” cones. Anomalous trichromats also possess hybrid genes, but these genes elaborate pigments Red pigment gene (1) Hybrid gene (2) Loss of gene Patterns in color-blind men (3) Duplication of gene (does not affect color vision) Green pigment gene Crossover event Different crossover events can lead to: whose spectral properties lie between those of the normal red and green pig-ments. Thus, although most anomalous trichromats have distinct sets of medium and long-wavelength cones, there is more overlap in their absorp-tion spectra than in normal trichromats, and thus less difference in how the two sets of cones respond to a given wavelength (with resulting anomalies in color perception). Retinal Circuits for Detecting Luminance Change Despite the esthetically pleasing nature of color vision, most of the informa-tion in visual scenes consists of spatial variations in light intensity (a black and white movie, for example, has most of the information a color version has, although it is deficient in some respects and usually is less fun to watch). How the spatial patterns of light and dark that fall on the photoreceptors are deciphered by central targets has been a vexing problem (Box E). To under-stand what is accomplished by the complex neural circuits within the retina during this process, it is useful to start by considering the responses of indi-vidual retinal ganglion cells to small spots of light. Stephen Kuffler, working at Johns Hopkins University in the 1950s, pioneered this approach by charac-terizing the responses of single ganglion cells in the cat retina. He found that each ganglion cell responds to stimulation of a small circular patch of the retina, which defines the cell’s receptive field (see Chapter 8 for discussion of receptive fields). Based on these responses, Kuffler distinguished two classes of ganglion cells, “on”-center and “off”-center (Figure 10.14). Turning on a spot of light in the receptive field center of an on-center gan-glion cell produces a burst of action potentials. The same stimulus applied to the receptive field center of an off-center ganglion cell reduces the rate of Vision: The Eye 249 Off-center ganglion cell + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + ++ + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + On-center ganglion cell (A) Time t0 t1 t2 Light spot in center t0 t1 t2 (B) Time t0 t1 t2 Dark spot in center t0 t1 t2 (C) Time t0 t1 t2 t3 t3 t0 t1 t2 Center only Center plus surround Figure 10.14 The responses of on-cen-ter and off-center retinal ganglion cells to stimulation of different regions of their receptive fields. Upper panels indi-cate the time sequence of stimulus changes. (A) Effects of light spot in the receptive field center. (B) Effects of dark spot in the receptive field center. (C) Effects of light spot in the center fol-lowed by the addition of light in the surround. 250 Chapter Ten Box E The Perception of Light Intensity Understanding the link between retinal stimulation and what we see (percep-tion) is arguably the central problem in vision, and the relation of luminance (a physical measurement of light intensity) and brightness (the sensation elicited by light intensity) is probably the simplest place to consider this challenge. As indicated in the text, how we see the brightness differences (i.e., contrast) between adjacent territories with distinct luminances depends in the first instance on the relative firing rate of retinal gan-glion cells, modified by lateral interac-tions. However, there is a problem with the assumption that the central nervous system simply “reads out” these relative rates of ganglion cell activity to sense brightness. The difficulty, as in perceiv-ing color, is that the brightness of a given target is markedly affected by its context in ways that are difficult or impossible to explain in terms of the retinal output as such. The accompanying figures, which illustrate two simultaneous brightness contrast illusions, help make this point. In Figure A, two photometrically identi-cal (equiluminant) gray squares appear differently bright as a function of the background in which they are presented. A conventional interpretation of this phenomenon is that the receptive field properties illustrated in Figures 10.14 through 10.17 cause ganglion cells to fire differently depending on whether the surround of the equiluminant target is dark or light. The demonstration in Fig-ure B, however, undermines this expla-nation, since in this case the target sur-rounded by more dark area actually looks darker than the same target sur-rounded by more light area. An alternative interpretation of lumi-nance perception that can account for these puzzling phenomena is that bright-ness percepts are generated on a statisti-cal basis as a means of contending with the inherent ambiguity of luminance (i.e., the fact that a given value of lumi-nance can be generated by many differ-ent combinations of illumination and surface reflectance properties). Since to be successful an observer has to respond to the real-world sources of luminance and not to light intensity as such, this ambiguity of the retinal stimulus pre-sents a quandary. A plausible solution to (B) (A) (C) (A) Standard illusion of simultaneous brightness contrast. (B) Another illusion of simultane-ous brightness contrast that is difficult to explain in conventional terms. (C) Cartoons of some possible sources of the standard simultaneous brightness contrast illusion in (A). (Courtesy of R. Beau Lotto and Dale Purves.) discharge, and when the spot of light is turned off, the cell responds with a burst of action potentials (Figure 10.14A). Complementary patterns of activ-ity are found for each cell type when a dark spot is placed in the receptive field center (Figure 10.14B). Thus, on-center cells increase their discharge rate to luminance increments in the receptive field center, whereas off-center cells increase their discharge rate to luminance decrements in the receptive field center. On- and off-center ganglion cells are present in roughly equal numbers. The receptive fields have overlapping distributions, so that every point on the retinal surface (that is, every part of visual space) is analyzed by several on-center and several off-center ganglion cells. A rationale for having these two distinct types of retinal ganglion cells was suggested by Peter Schiller and his colleagues at the Massachusetts Institute of Technology, who exam-ined the effects of pharmacologically inactivating on-center ganglion cells on a monkey’s ability to detect a variety of visual stimuli. After silencing on-center ganglion cells, the animals showed a deficit in their ability to detect stimuli that were brighter than the background; however, they could still see objects that were darker than the background. These observations imply that information about increases or decreases in luminance is carried separately to the brain by the axons of these two differ-ent types of retinal ganglion cells. Having separate luminance “channels” means that changes in light intensity, whether increases or decreases, are always conveyed to the brain by an increased number of action potentials. Because ganglion cells rapidly adapt to changes in luminance, their “resting” discharge rate in constant illumination is relatively low. Although an increase in discharge rate above resting level serves as a reliable signal, a decrease in firing rate from an initially low rate of discharge might not. Thus, having luminance changes signaled by two classes of adaptable cells provides unam-biguous information about both luminance increments and decrements. The functional differences between these two ganglion cell types can be understood in terms of both their anatomy and their physiological proper-Vision: The Eye 251 the inherent uncertainty of the relation-ship between luminance values and their actual sources would be to generate the sensation of brightness elicited by a given luminance (e.g., in the brightness of the identical test patches in the figure) on the basis of what the luminance of the test patches had typically turned out to be in the past experience of human observers. To get the gist of this explana-tion consider Figure C, which illustrates the point that the two equiluminant tar-get patches in Figure A could have been generated by two differently painted sur-faces in different illuminants, as in a comparison of the target patches on the left and middle cubes, or two similarly reflecting surfaces in similar amounts of light, as in a comparison of the target patches on the middle and right cubes. An expedient—and perhaps the only— way the visual system can cope with this ambiguity is to generate the perception of the stimulus in Figure A (and in Fig-ure B) empirically, i.e., based on what the target patches typically turned out to sig-nify in the past. Since the equiluminant targets will have arisen from a variety of possible sources, it makes sense to have the brightness elicited by the patches determined statistically by the relative frequency of occurrence of that lumi-nance in the particular context in which it is presented. The advantage of seeing luminance according to the relative prob-abilities of the possible sources of the stimulus is that percepts generated in this way give the observer the best chance of making appropriate behavioral responses to profoundly ambiguous stimuli. References ADELSON, E. H. (1999) Light perception and lightness illusions. In The Cognitive Neuro-sciences, 2nd Ed. M. Gazzaniga (ed.). Cam-bridge, MA: MIT Press, pp. 339–351. PURVES, D. AND R. B. LOTTO (2003) Why We See What We Do: An Empirical Theory of Vision, Chapters 3 and 4. Sunderland MA: Sinauer Associates, pp. 41–87. 252 Chapter Ten ties and relationships (Figure 10.15). On- and off-center ganglion cells have dendrites that arborize in separate strata of the inner plexiform layer, form-ing synapses selectively with the terminals of on- and off-center bipolar cells that respond to luminance increases and decreases, respectively (Figure 10.15A). As mentioned previously, the principal difference between ganglion cells and bipolar cells lies in the nature of their electrical response. Like most other cells in the retina, bipolar cells have graded potentials rather than action potentials. Graded depolarization of bipolar cells leads to an increase in transmitter release (glutamate) at their synapses and consequent depolar-ization of the on-center ganglion cells that they contact via AMPA, kainate, and NMDA receptors. The selective response of on- and off-center bipolar cells to light incre-ments and decrements is explained by the fact that they express different types of glutamate receptors (Figure 10.15A). Off-center bipolar cells have ionotropic receptors (AMPA and kainate) that cause the cells to depolarize in response to glutamate released from photoreceptor terminals. In contrast, on-center bipolar cells express a G-protein-coupled metabotropic glutamate receptor (mGluR6). When bound to glutamate, these receptors activate an intracellular cascade that closes cGMP-gated Na+ channels, reducing inward Glutamate mGluR6 AMPA kainate Glutamate AMPA, kainate, NMDA – + + + On-center ganglion cell Off-center ganglion cell Center Surround Surround On-center bipolar cell Off-center bipolar cell (A) Center cone On-center ganglion cell Off-center ganglion cell On-center bipolar cell Off-center bipolar cell (B) On-center ganglion cell Off-center ganglion cell Center cone On-center bipolar cell Off-center bipolar cell (C) Center cone Time t0 t1 t2 Time t0 t1 t2 t1 t2 t1 t2 t1 t2 t1 t2 t1 t2 t1 t2 t1 t2 t1 t2 Light spot in center t0 t1 t2 Dark spot in center t0 t1 t2 Figure 10.15 Circuitry responsible for generating receptive field center responses of retinal ganglion cells. (A) Functional anatomy of cone inputs to the center of a ganglion cell receptive field. A plus indicates a sign-conserving synapse; a minus represents a sign-inverting synapse. (B) Responses of vari-ous cell types to the presentation of a light spot in the center of the ganglion cell receptive field. (C) Responses of var-ious cell types to the presentation of a dark spot in the center of the ganglion cell receptive field. current and hyperpolarizing the cell. Thus, glutamate has opposite effects on these two classes of cells, depolarizing off-center bipolar cells and hyperpo-larizing on-center cells. Photoreceptor synapses with off-center bipolar cells are called sign-conserving, since the sign of the change in membrane poten-tial of the bipolar cell (depolarization or hyperpolarization) is the same as that in the photoreceptor (Figure 10.15B,C). Photoreceptor synapses with on-center bipolar cells are called sign-inverting because the change in the mem-brane potential of the bipolar cell is the opposite of that in the photoreceptor. In order to understand the response of on- and off-center bipolar cells to changes in light intensity, recall that photoreceptors hyperpolarize in response to light increments, decreasing their release of neurotransmitter (Figure 10.15B). Under these conditions, on-center bipolar cells contacted by the photoreceptors are freed from the hyperpolarizing influence of the pho-toreceptor’s transmitter, and they depolarize. In contrast, for off-center cells, the reduction in glutamate represents the withdrawal of a depolarizing influence, and these cells hyperpolarize. Decrements in light intensity natu-rally have the opposite effect on these two classes of bipolar cells, hyperpo-larizing on-center cells and depolarizing off-center ones (Figure 10.15C). Kuffler’s work also called attention to the fact that retinal ganglion cells do not act as simple photodetectors. Indeed, most ganglion cells are rela-tively poor at signaling differences in the level of diffuse illumination. Instead, they are sensitive to differences between the level of illumination that falls on the receptive field center and the level of illumination that falls on the surround—that is, to luminance contrast. The center of a ganglion cell receptive field is surrounded by a concentric region that, when stimulated, antagonizes the response to stimulation of the receptive field center (see Fig-ure 10.14C). For example, as a spot of light is moved from the center of the receptive field of an on-center cell toward its periphery, the response of the cell to the spot of light decreases (Figure 10.16). When the spot falls com-pletely outside the center (that is, in the surround), the response of the cell falls below its resting level; the cell is effectively inhibited until the distance from the center is so great that the spot no longer falls on the receptive field at all, in which case the cell returns to its resting level of firing. Off-center Vision: The Eye 253 Figure 10.16 Rate of discharge of an on-center ganglion cell to a spot of light as a function of the distance of the spot from the receptive field center. Zero on the x axis corresponds to the center; at a distance of 5°, the spot falls outside the receptive field. 100 80 60 40 20 0 1 2 3 4 5 Response rate (impulses/s) Spontaneous level of activity Distance (degrees) from center of receptive field + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Light + + 254 Chapter Ten cells exhibit a similar surround antagonism. Stimulation of the surround by light opposes the decrease in firing rate that occurs when the center is stim-ulated alone, and reduces the response to light decrements in the center (compare Figures 10.14A and 10.14C). Because of their antagonistic surrounds, ganglion cells respond much more vigorously to small spots of light confined to their receptive field cen-ters than to large spots, or to uniform illumination of the visual field (see Figure 10.14C). To appreciate how center-surround antagonism makes the ganglion cell sensitive to luminance contrast, consider the activity levels in a hypothetical population of on-center ganglion cells whose receptive fields are distributed across a retinal image of a light-dark edge (Figure 10.17). The neurons whose firing rates are most affected by this stimulus—either increased (neuron D) or decreased (neuron B)—are those with receptive fields that lie along the light-dark border; those with receptive fields completely illuminated (or completely darkened) are less affected (neurons A and E). Thus, the infor-mation supplied by the retina to central visual stations for further processing does not give equal weight to all regions of the visual scene; rather, it emphasizes the regions where there are differences in luminance. Contribution of Retinal Circuits to Light Adaptation In addition to making ganglion cells especially sensitive to light-dark bor-ders in the visual scene, center-surround mechanisms make a significant contribution to the process of light adaptation. As illustrated for an on-cen-ter cell in Figure 10.18, the response rate of a ganglion cell to a small spot of light turned on in its receptive field center varies as a function of the spot’s intensity. In fact, response rate is proportional to the spot’s intensity over a range of about one log unit. However, the intensity of spot illumination required to evoke a given discharge rate is dependent on the background level of illumination. Increases in background level of illumination are accompanied by adaptive shifts in the cell’s operating range such that Figure 10.17 Responses of a hypothet-ical population of on-center ganglion cells whose receptive fields (A–E) are distributed across a light-dark edge. Those cells whose activity is most affected have receptive fields that lie along the light-dark edge. A B Position Spontaneous level of activity On-center ganglion cells Response rate Light C D E A B C D E Dark Edge + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + greater stimulus intensities are required to achieve the same discharge rate. Thus, firing rate is not an absolute measure of light intensity, but rather sig-nals the difference from background level of illumination. Because the range of light intensities over which we can see is enormous compared to the narrow range of ganglion cell discharge rates (see Figure 10.9), adaptational mechanisms are essential. By scaling the ganglion cell’s response to ambient levels of illumination, the entire dynamic range of a neuron’s firing rate is used to encode information about intensity differences over the range of luminance values that are relevant for a given visual scene. Due to the antagonistic center-surround organization of retinal ganglion cells, the signal sent to the brain from the retina downplays the background level of illumination (see Figure 10.14). This arrangement presumably ex-plains why the relative brightness of objects remains much the same over a wide range of lighting conditions. In bright sunlight, for example, the print on this page reflects considerably more light to the eye than it does in room light. In fact, the print reflects more light in sunlight than the paper reflects in room light; yet it continues to look black and the page white, indoors or out. Like the mechanism responsible for generating the on- and off-center response, the antagonistic surround of ganglion cells is a product of interac-tions that occur at the early stages of retinal processing (Figure 10.19). Much of the antagonism is thought to arise via lateral connections established by horizontal cells and receptor terminals. Horizontal cells receive synaptic inputs from photoreceptor terminals and are linked via gap junctions with a vast network of other horizontal cells distributed over a wide area of the reti-nal surface. As a result, the activity in horizontal cells reflects levels of illu-mination over a broad area of the retina. Although the details of their actions are not entirely clear, horizontal cells are thought to exert their influence via the release of neurotransmitter directly onto photoreceptor terminals, regu-lating the amount of transmitter that the photoreceptors release onto bipolar cell dendrites. Glutamate release from photoreceptor terminals has a depolarizing effect on horizontal cells (sign-conserving synapse), while the transmitter released from horizontal cells (GABA) has a hyperpolarizing influence on photore-ceptor terminals (sign-inverting synapse) (Figure 10.19A). As a result, the net effect of inputs from the horizontal cell network is to oppose changes in the Vision: The Eye 255 Figure 10.18 A series of curves illus-trating the discharge rate of a single on-center ganglion cell to the onset of a small test spot of light in the center of its receptive field. Each curve represents the discharge rate evoked by spots of varying intensity at a constant back-ground level of illumination, which is given by the red numbers at the top of each curve (the highest background level is 0, the lowest –5). The response rate is proportional to stimulus intensity over a range of 1 log unit, but the oper-ating range shifts to the right as the background level of illumination increases. Discharge rate (spikes/s) 400 −5 −4 −3 −2 −1 0 300 200 100 0 Test spot luminance (cd/m2) 9 x 10−5 9 x 10−4 9 x 10−3 9 x 10−2 9 x 10−1 9 256 Chapter Ten (B) Horizontal cell Horizontal cell t1 t2 Horizontal cell t1 t2 On-center bipolar cell t1 t2 On-center ganglion cell t1 t2 On-center ganglion cell On-center bipolar cell Center cone Surround cone Surround cone Time t0 t1 t2 Transduction-mediated hyperpolarization Horizontal cell mediated depolarization Center cone Surround Center t0 t1 t2 Center only Center plus surround (A) – – – – – + + + + + Figure 10.19 Circuitry responsible for generating the receptive field surround of an on-center retinal ganglion cell. (A) Functional anatomy of horizontal cell inputs responsible for surround antagonism. A plus indicates a sign-conserving synapse; a minus represents a sign-inverting synapse. (B) Responses of various cell types to the presentation of a light spot in the center of the receptive field (t1) followed by the addition of light stimulation in the surround (t2). Light stimulation of the sur-round leads to hyperpolarization of the horizontal cells and a decrease in the release of inhibitory transmitter (GABA) onto the photoreceptor terminals. The net effect is to depolarize the center cone terminal, offsetting much of the hyperpolar-ization induced by the transduction cascade in the center cone’s outer segment. Vision: The Eye 257 membrane potential of the photoreceptor that are induced by phototrans-duction events in the outer segment. How these events lead to surround suppression in an on-center ganglion cell is illustrated in Figure 10.19. A small spot of light centered on a photoreceptor supplying input to the center of the ganglion cell’s receptive field produces a strong hyperpolarizing response in the photoreceptor. Under these conditions, changes in the mem-brane potential of the horizontal cells that synapse with the photoreceptor terminal are relatively small, and the response of the photoreceptor to light is largely determined by its phototransduction cascade (Figure10.19B). With the addition of light to the surround, however, the impact of the horizontal network becomes significantly greater; the light-induced reduction in the release of glutamate from the photoreceptors in the surround leads to a strong hyperpolarization of the horizontal cells whose processes converge on the terminal of the photoreceptor in the receptive field center. The reduc-tion in GABA release from the horizontal cells has a depolarizing effect on the membrane potential of the central photoreceptor, reducing the light-evoked response and ultimately reducing the firing rate of the on-center ganglion cell. Thus, even at the earliest stages in visual processing, neural signals do not represent the absolute numbers of photons that are captured by recep-tors, but rather the relative intensity of stimulation—how much the current level of stimulation differs from ambient levels. While it may seem that the actions of horizontal cells decrease the sensitivity of the retina, they play a critical role in allowing the full range of the photoreceptor’s electrical response (about 30 mV) to be applied to the limited range of stimulus inten-sities that are present at any given moment. The network mechanisms of adaptation described here function in conjunction with cellular mechanisms in the receptor outer segments that regulate the sensitivity of the photo-transduction cascade at different light levels. Together, they allow retinal cir-cuits to convey the most salient aspects of luminance changes to the central stages of the visual system described in the following chapter. Summary The light that falls on photoreceptors is transformed by retinal circuitry into a pattern of action potentials that ganglion cell axons convey to the visual centers in the brain. This process begins with phototransduction, a bio-chemical cascade that ultimately regulates the opening and closing of ion channels in the membrane of the photoreceptor’s outer segment, and thereby the amount of neurotransmitter the photoreceptor releases. Two sys-tems of photoreceptors—rods and cones—allow the visual system to meet the conflicting demands of sensitivity and acuity, respectively. Retinal gan-glion cells operate quite differently from the photoreceptor cells. The center-surround arrangement of ganglion cell receptive fields makes these neurons particularly sensitive to luminance contrast and relatively insensitive to the overall level of illumination. It also allows the retina to adapt, such that it can respond effectively over the enormous range of illuminant intensities in the world. The underlying organization is generated by the synaptic inter-actions between photoreceptors, horizontal cells, and bipolar cells in the outer plexiform layer. As a result, the signal sent to the visual centers in the brain is already highly processed when it leaves the retina, emphasizing those aspects of the visual scene that convey the most information. Additional Reading Reviews ARSHAVSKY, V. Y., T. D. LAMB AND E. N. PUGH JR. (2002) G proteins and phototransduction. Annu. Rev. Physiol. 64: 153–187. BURNS, M. E. AND D. A. BAYLOR (2001) Activa-tion, deactivation, and adaptation in verte-brate photoreceptor cells. Annu. Rev. Neu-rosci. 24: 779–805. NATHANS, J. (1987) Molecular biology of visual pigments. Annu. Rev. Neurosci. 10: 163–194. SCHNAPF, J. L. AND D. A. BAYLOR (1987) How photoreceptor cells respond to light. Sci. Amer. 256 (April): 40–47. STERLING, P. (1990) Retina. In The Synaptic Organization of the Brain, G. M. Shepherd (ed.). New York: Oxford University Press, pp. 170–213. STRYER, L. (1986) Cyclic GMP cascade of vision. Annu. Rev. Neurosci. 9: 87–119. Important Original Papers BAYLOR, D. A., M. G. F. FUORTES AND P. M. O’BRYAN (1971) Receptive fields of cones in the retina of the turtle. J. Physiol. (Lond.) 214: 265–294. DOWLING, J. E. AND F. S. WERBLIN (1969) Orga-nization of the retina of the mud puppy, Nec-turus maculosus. I. Synaptic structure. J. Neu-rophysiol. 32: 315–338. ENROTH-CUGELL, C. AND R. M. SHAPLEY (1973) Adaptation and dynamics of cat retinal gan-glion cells. J. Physiol. 233: 271–309. FASENKO, E. E., S. S. KOLESNIKOV AND A. L. LYUBARSKY (1985) Induction by cyclic GMP of cationic conductance in plasma membrane of retinal rod outer segment. Nature 313: 310–313. KUFFLER, S. W. (1953) Discharge patterns and functional organization of mammalian retina. J. Neurophysiol. 16: 37–68. NATHANS, J., D. THOMAS AND D. S. HOGNESS (1986) Molecular genetics of human color vision: The genes encoding blue, green and red pigments. Science 232: 193–202. NATHANS, J., T. P. PIANTANIDA, R. EDDY, T. B. SHOWS AND D. S. HOGNESS (1986) Molecular genetics of inherited variation in human color vision. Science 232: 203–210. SCHILLER, P. H., J. H. SANDELL AND J. H. R. MAUNSELL (1986) Functions of the “on” and “off” channels of the visual system. Nature 322: 824–825. WERBLIN, F. S. AND J. E. DOWLING (1969) Orga-nization of the retina of the mud puppy, Nec-turus maculosus. II. Intracellular recording. J. Neurophysiol. 32: 339–354. Books BARLOW, H. B. AND J. D. MOLLON (1982) The Senses. London: Cambridge University Press. DOWLING, J. E. (1987) The Retina: An Approach-able Part of the Brain. Cambridge, MA: Belknap Press. FAIN, G. L. (2003) Sensory Transduction. Sun-derland, MA: Sinauer Associates. HART, W. M. J. (ed.) (1992) Adler’s Physiology of the Eye: Clinical Application, 9th Ed. St. Louis, MO: Mosby Year Book. HELMHOLTZ, H. L. F. VON (1924) Helmholtz’s Treatise on Physiological Optics, Vol. I–III. Transl. from the Third German Edition by J. P. C. Southall. Menasha, WI: George Banta Pub-lishing Company. HOGAN, M. J., J. A. ALVARADO AND J. E. WED-DELL (1971) Histology of the Human Eye: An Atlas and Textbook. Philadelphia: Saunders. HUBEL, D. H. (1988) Eye, Brain, and Vision, Sci-entific American Library Series. New York: W. H. Freeman. HURVICH, L. (1981) Color Vision. Sunderland, MA: Sinauer Associates, pp. 180–194. OGLE, K. N. (1964) Researches in Binocular Vision. Hafner: New York. OYSTER, C. (1999) The Human Eye: Structure and Function. Sunderland, MA: Sinauer Asso-ciates. POLYAK, S. (1957) The Vertebrate Visual System. Chicago: The University of Chicago Press. RODIECK, R. W. (1973) The Vertebrate Retina. San Francisco: W. H. Freeman. RODIECK, R. W. (1998) First Steps in Seeing. Sunderland, MA: Sinauer Associates. WANDELL, B. A. (1995) Foundations of Vision. Sunderland, MA: Sinauer Associates. Overview Information supplied by the retina initiates interactions between multiple subdivisions of the brain that eventually lead to conscious perception of the visual scene, at the same time stimulating more conventional reflexes such as adjusting the size of the pupil, directing the eyes to targets of interest, and regulating homeostatic behaviors that are tied to the day/night cycle. The pathways and structures that mediate this broad range of functions are nec-essarily diverse. Of these, the primary visual pathway from the retina to the dorsal lateral geniculate nucleus in the thalamus and on to the primary visual cortex is the most important and certainly the most thoroughly stud-ied component of the visual system. Different classes of neurons within this pathway encode the varieties of visual information—luminance, spectral dif-ferences, orientation, and motion—that we ultimately see. The parallel pro-cessing of different categories of visual information continues in cortical pathways that extend beyond primary visual cortex, supplying a variety of visual areas in the occipital, parietal, and temporal lobes. Visual areas in the temporal lobe are primarily involved in object recognition, whereas those in the parietal lobe are concerned with motion. Normal vision depends on the integration of information in all these cortical areas. The processes underly-ing visual perception are not understood and remain one of the central chal-lenges of modern neuroscience. Central Projections of Retinal Ganglion Cells Ganglion cell axons exit the retina through a circular region in its nasal part called the optic disk (or optic papilla), where they bundle together to form the optic nerve. This region of the retina contains no photoreceptors and, because it is insensitive to light, produces the perceptual phenomenon known as the blind spot (Box A). The optic disk is easily identified as a whitish circular area when the retina is examined with an ophthalmoscope; it also is recognized as the site from which the ophthalmic artery and veins enter (or leave) the eye (Figure 11.1). In addition to being a conspicuous reti-nal landmark, the appearance of the optic disk is a useful gauge of intracra-nial pressure. The subarachnoid space surrounding the optic nerve is contin-uous with that of the brain; as a result, increases in intracranial pressure—a sign of serious neurological problems such as a space-occupying lesion—can be detected as papilledema, a swelling of the optic disk. Axons in the optic nerve run a straight course to the optic chiasm at the base of the diencephalon. In humans, about 60% of these fibers cross in the chiasm, while the other 40% continue toward the thalamus and midbrain tar-gets on the same side. Once past the chiasm, the ganglion cell axons on each Chapter 11 259 Central Visual Pathways 260 Chapter Eleven side form the optic tract. Thus, the optic tract, unlike the optic nerve, contains fibers from both eyes. The partial crossing (or decussation) of ganglion cell axons at the optic chiasm allows information from corresponding points on the two retinas to be processed by approximately the same cortical site in each hemisphere, an important issue that is considered in the next section. The ganglion cell axons in the optic tract reach a number of structures in the diencephalon and midbrain (Figure 11.2). The major target in the dien-cephalon is the dorsal lateral geniculate nucleus of the thalamus. Neurons in the lateral geniculate nucleus, like their counterparts in the thalamic relays of other sensory systems, send their axons to the cerebral cortex via the internal capsule. These axons pass through a portion of the internal cap-sule called the optic radiation and terminate in the primary visual cortex, or striate cortex (also referred to as Brodmann’s area 17 or V1), which lies largely along and within the calcarine fissure in the occipital lobe. The retinogeniculostriate pathway, or primary visual pathway, conveys infor-mation that is essential for most of what is thought of as seeing. Thus, dam-age anywhere along this route results in serious visual impairment. A second major target of the ganglion cell axons is a collection of neurons that lies between the thalamus and the midbrain in a region known as the pretectum. Although small in size compared to the lateral geniculate nucleus, the pretectum is particularly important as the coordinating center for the pupillary light reflex (i.e., the reduction in the diameter of the pupil that occurs when sufficient light falls on the retina) (Figure 11.3). The initial com-ponent of the pupillary light reflex pathway is a bilateral projection from the retina to the pretectum. Pretectal neurons, in turn, project to the Edinger-Westphal nucleus, a small group of nerve cells that lies close to the nucleus of the oculomotor nerve (cranial nerve III) in the midbrain. The Edinger-West-phal nucleus contains the preganglionic parasympathetic neurons that send their axons via the oculomotor nerve to terminate on neurons in the ciliary Fovea Optic disk (papilla) Macula lutea Branch of ophthalmic artery Branch of ophthalmic vein Figure 11.1 The retinal surface of the left eye, viewed with an ophthalmoscope. The optic disk is the region where the ganglion cell axons leave the retina to form the optic nerve; it is also characterized by the entrance and exit, respectively, of the ophthalmic arteries and veins that supply the retina. The macula lutea can be seen as a distinct area at the center of the optical axis (the optic disk lies nasally); the macula is the region of the retina that has the highest visual acuity. The fovea is a depression or pit about 1.5 mm in diameter that lies at the center of the macula (see Chapter 10). Figure 11.2 Central projections of reti-nal ganglion cells. Ganglion cell axons terminate in the lateral geniculate nucleus of the thalamus, the superior colliculus, the pretectum, and the hypo-thalamus. For clarity, only the crossing axons of the right eye are shown (view is looking up at the inferior surface of the brain). ganglion (see Chapter 19). Neurons in the ciliary ganglion innervate the con-strictor muscle in the iris, which decreases the diameter of the pupil when activated. Shining light in the eye thus leads to an increase in the activity of pretectal neurons, which stimulates the Edinger-Westphal neurons and the ciliary ganglion neurons they innervate, thus constricting the pupil. In addition to its normal role in regulating the amount of light that enters the eye, the pupillary reflex provides an important diagnostic tool that allows the physician to test the integrity of the visual sensory apparatus, the motor outflow to the pupillary muscles, and the central pathways that medi-Central Visual Pathways 261 Optic tract Superior colliculus: orienting the movements of head and eyes Pretectum: reflex control of pupil and lens Hypothalamus: regulation of circadian rhythms Optic nerve Optic chiasm Lateral geniculate nucleus Optic radiation Striate cortex Iris Postganglionic parasympathetic fiber Lens Retina Vitreous humor Aqueous humor Cornea Optic nerve Ciliary ganglion Preganglionic parasympathetic fiber in cranial nerve III Pretectum Superior colliculus Edinger-Westphal nucleus Pupillary constrictor muscle Figure 11.3 The circuitry responsible for the pupillary light reflex. This path-way includes bilateral projections from the retina to the pretectum and projec-tions from the pretectum to the Edinger-Westphal nucleus. Neurons in the Edinger-Westphal nucleus termi-nate in the ciliary ganglion, and neu-rons in the ciliary ganglion innervate the pupillary constrictor muscles. Notice that the afferent axons activate both Edinger-Westphal nuclei via the neurons in the pretectum. 262 Chapter Eleven Box A The Blind Spot It is logical to suppose that a visual field defect (called a scotoma) arising from damage to the retina or central visual pathways would be obvious to the indi-vidual suffering from such pathology. When the deficit involves a peripheral region of the visual field, however, a sco-toma often goes unnoticed until a car accident or some other mishap all too dramatically reveals the sensory loss. In fact, all of us have a physiological sco-toma of which we are quite unaware, the so-called “blind spot.” The blind spot is the substantial gap in each monocular visual field that corresponds to the loca-tion of the optic disk, the receptor-free region of the retina where the optic nerve leaves the eye (see Figure 11.1). To find the “blind spot” of the right eye, close the left eye and fixate on the X shown in the figure here, holding the book about 30–40 centimeters away. Now take a pencil in your right hand and, without breaking fixation, move the tip slowly toward the X from the right side of the page. At some point, the tip of the pencil (indeed the whole end of the pencil) will disappear; mark this point and continue to move the pencil to the left until it reappears; then make another mark. The borders of the blind spot along the vertical axis can be determined in the same way by moving the pencil up and down so that its path falls between the two horizontal marks. To prove that information from the region of visual space bounded by the marks is really not perceived, put a penny inside the demarcated area. When you fixate the X with both eyes and then close the left eye, the penny will disappear, a seemingly magical event that amazed the French royal court when it was first reported by the natural philosopher Edmé Mariotte in 1668. How can we be unaware of such a large defect in the visual field (typically about 5°–8°)? The optic disk is located in the nasal retina of each eye. With both eyes open, information about the corre-sponding region of visual space is, of course, available from the temporal retina of the other eye. But this fact does not explain why the blind spot remains undetected with one eye closed. When the world is viewed monocularly, the visual system appears to “fill-in” the missing part of the scene based on the information supplied by the regions sur-rounding the optic disk. To observe this phenomenon, notice what happens when a pencil or some other object lies across the optic disk representation. Remarkably, the pencil looks complete! Although electrophysiological recordings have shown that neurons in the visual cortex whose receptive fields lie in the optic disk representation can be activated by stimulating the regions that surround the optic disk of the contralateral eye, suggesting that “filling-in” the blind spot is based on cortical mechanisms that integrate information from different points in the visual field, the mechanism of this striking phenomenon is not clear. Herman von Helmholtz pointed out in the nineteenth century that it may just be that this part of the visual world is ignored, the pencil being completed across the blind spot because the rest of the scene simply “collapses” around it. References FIORANI, M., M. G. P. ROSA, R. GATTASS AND C. E. ROCHA-MIRANDA (1992) Dynamic sur-rounds of receptive fields in striate cortex: A physiological basis for perceptual comple-tion? Proc. Natl. Acad. Sci. USA 89: 8547–8551. GILBERT, C. D. (1992) Horizontal integration and cortical dynamics. Neuron 9: 1–13. RAMACHANDRAN, V. S. AND T. L. GREGORY (1991) Perceptual filling in of artificially induced scotomas in human vision. Nature 350: 699–702. VON HELMHOLTZ, H. (1968). Helmholtz’s Trea-tise on Physiological Optics, Vols. I–III (Trans-lated from the Third German Ed. published in 1910). J. P. C. Southall (ed.). New York: Dover Publications. See pp. 204ff in Vol. III. X ate the reflex. Under normal conditions, the pupils of both eyes respond identically, regardless of which eye is stimulated; that is, light in one eye produces constriction of both the stimulated eye (the direct response) and the unstimulated eye (the consensual response; see Figure 11.3). Comparing the response in the two eyes is often helpful in localizing a lesion. For exam-ple, a direct response in the left eye without a consensual response in the right eye suggests a problem with the visceral motor outflow to the right eye, possibly as a result of damage to the oculomotor nerve or Edinger-West-phal nucleus in the brainstem. Failure to elicit a response (either direct or indirect) to stimulation of the left eye if both eyes respond normally to stim-ulation of the right eye suggests damage to the sensory input from the left eye, possibly to the left retina or optic nerve. There are several other important targets of retinal ganglion cell axons. One is the suprachiasmatic nucleus of the hypothalamus, a small group of neu-rons at the base of the diencephalon (see Box A in Chapter 20). The retino-hypothalamic pathway is the route by which variation in light levels influ-ences the broad spectrum of visceral functions that are entrained to the day/night cycle (see Chapters 20 and 27). Another target is the superior col-liculus, a prominent structure visible on the dorsal surface of the midbrain (see Figure 1.14). The superior colliculus coordinates head and eye movements to visual (as well as other) targets; its functions are considered in Chapter 19. The type of visual information required to perform the functions of these different retinal targets is quite different. Reading the text on this page, for example, requires a high-resolution sampling of the retinal image, whereas regulating circadian rhythms and adjusting the pupil accordingly require only a measure of overall changes in light levels, and little or no information about the features of the image. It should come as no surprise, then, that there is a diversity of ganglion cell types that provide information appropri-ate to the functions of these different targets. Projections to the lateral geniculate nucleus (which are described in more detail later) arise from at least three broad classes of ganglion cells, whose tuning properties are appropriate for mediating the richness of visual per-ception (high acuity, color, motion). In contrast, projections to the hypothala-mus and the pretectum arise from ganglion cells that lack these properties and are highly suited for detecting luminance flux. The retinal specializa-tions responsible for constructing these distinct classes of retinal ganglion cells are only beginning to be identified; they include not only differences in ganglion cell synaptic connections, but in the locus of the phototransduction event itself. Unlike the majority of ganglion cells, which depend on rods and cones for their sensitivity to light, the ganglion cells that project to the hypo-thalamus and pretectum express their own light-sensitive photopigment (melanopsin) and are capable of modulating their response to changes in light levels in the absence of signals from rods and cones. The presence of light sensitivity within this class of ganglion cells presumably explains why nor-mal circadian rhythms are maintained in animals that have completely lost form vision due to degeneration of rod and cone photoreceptors. The Retinotopic Representation of the Visual Field The spatial relationships among the ganglion cells in the retina are main-tained in most of their central targets as orderly representations or “maps” of visual space. Most of these structures receive information from both eyes, requiring that these inputs be integrated to form a coherent map of individ-Central Visual Pathways 263 264 Chapter Eleven Figure 11.4 Projection of the visual fields onto the left and right retinas. (A) Projection of an image onto the surface of the retina. The passage of light rays through the pupil of the eye results in images that are inverted and left–right reversed on the retinal surface. (B) Reti-nal quadrants and their relation to the organization of monocular and binocu-lar visual fields, as viewed from the back surface of the eyes. Vertical and horizontal lines drawn through the cen-ter of the fovea define retinal quadrants (bottom). Comparable lines drawn through the point of fixation define visual field quadrants (center). Color coding illustrates corresponding retinal and visual field quadrants. The overlap of the two monocular visual fields is shown at the top. ual points in space. As a general rule, information from the left half of the visual world, whether it originates from the left or right eye, is represented in the right half of the brain, and vice versa. Understanding the neural basis for the appropriate arrangement of inputs from the two eyes requires considering how images are projected onto the two retinas, and the central destination of the ganglion cells located in dif-ferent parts of the retina. Each eye sees a part of visual space that defines its visual field (Figure 11.4A). For descriptive purposes, each retina and its cor-responding visual field are divided into quadrants. In this scheme, the sur-face of the retina is subdivided by vertical and horizontal lines that intersect at the center of the fovea (Figure 11.4B). The vertical line divides the retina into nasal and temporal divisions and the horizontal line divides the retina Binocular visual field Left monocular visual field Right monocular visual field Right visual field Monocular portion of visual field Left visual field Left retina I S I S T N Inferior (I) Superior (S) S I Temporal (T) T T Right retina Fixation point Eye Lens (A) (B) F F F F F Fovea F Nasal (N) Monocular portion of visual field Figure 11.5 Projection of the binocular field of view onto the two retinas and its relation to the crossing of fibers in the optic chiasm. Points in the binocular portion of the left visual field (B) fall on the nasal retina of the left eye and the temporal retina of the right eye. Points in the binocular portion of the right visual field (C) fall on the nasal retina of the right eye and the temporal retina of the left eye. Points that lie in the mono-cular portions of the left and right visual fields (A and D) fall on the left and right nasal retinas, respectively. The axons of ganglion cells in the nasal retina cross in the optic chiasm, whereas those from the temporal retina do not. As a result, in-formation from the left visual field is carried in the right optic tract, and infor-mation from the right visual field is car-ried in the left optic tract. into superior and inferior divisions. Corresponding vertical and horizontal lines in visual space (also called meridians) intersect at the point of fixation (the point in visual space that falls on the fovea) and define the quadrants of the visual field. The crossing of light rays diverging from different points on an object at the pupil causes the images of objects in the visual field to be inverted and left-right reversed on the retinal surface. As a result, objects in the temporal part of the visual field are seen by the nasal part of the retina, and objects in the superior part of the visual field are seen by the inferior part of the retina. (It may help in understanding Figure 11.4B to imagine that you are looking at the back surfaces of the retinas, with the corresponding visual fields projected onto them.) With both eyes open, the two foveas are normally aligned on a single tar-get in visual space, causing the visual fields of both eyes to overlap exten-sively (see Figure 11.4B and Figure 11.5). This binocular field of view consists of two symmetrical visual hemifields (left and right). The left binocular hemi-field includes the nasal visual field of the right eye and the temporal visual field of the left eye; the right hemifield includes the temporal visual field of Central Visual Pathways 265 Binocular visual field Right visual field Left visual field Temporal retina Temporal retina Nasal retina Optic chiasm Left optic tract Left visual field Right visual field C A B FP Right optic tract D Fixation point B C A D 266 Chapter Eleven the right eye and the nasal visual field of the left eye. The temporal visual fields are more extensive than the nasal visual fields, reflecting the size of the nasal and temporal retinas respectively. As a result, vision in the periphery of the field of view is strictly monocular, mediated by the most medial portion of the nasal retina. Most of the rest of the field of view can be seen by both eyes; i.e., individual points in visual space lie in the nasal visual field of one eye and the temporal visual field of the other. It is worth noting, however, that the shape of the face and nose impact the extent of this region of binocu-lar vision. In particular, the inferior nasal visual fields are less extensive than the superior nasal fields, and consequently the binocular field of view is smaller in the lower visual field than in the upper (see Figure 11.4B). Ganglion cells that lie in the nasal division of each retina give rise to axons that cross in the chiasm, while those that lie in the temporal retina give rise to axons that remain on the same side (see Figure 11.5). The bound-ary (or line of decussation) between contralaterally and ipsilaterally project-ing ganglion cells runs through the center of the fovea and defines the bor-der between the nasal and temporal hemiretinas. Images of objects in the left visual hemifield (such as point B in Figure 11.5) fall on the nasal retina of the left eye and the temporal retina of the right eye, and the axons from gan-glion cells in these regions of the two retinas project through the right optic tract. Objects in the right visual hemifield (such as point C in Figure 11.5) fall on the nasal retina of the right eye and the temporal retina of the left eye; the axons from ganglion cells in these regions project through the left optic tract. As mentioned previously, objects in the monocular portions of the visual hemifields (points A and D in Figure 11.5) are seen only by the most periph-eral nasal retina of each eye; the axons of ganglion cells in these regions (like the rest of the nasal retina) run in the contralateral optic tract. Thus, unlike the optic nerve, the optic tract contains the axons of ganglion cells that orig-inate in both eyes and represent the contralateral field of view. Optic tract axons terminate in an orderly fashion within their target struc-tures thus generating well ordered maps of the contralateral hemifield. For the primary visual pathway, the map of the contralateral hemifield that is established in the lateral geniculate nucleus is maintained in the projections of the lateral geniculate nucleus to the striate cortex (Figure 11.6). Thus the Parieto-occipital sulcus Binocular portion Left visual field Monocular portion Macula Calcarine sulcus Right occipital lobe (A) (B) Medial surface Myelinated stria Myelinated stria Figure 11.6 Visuotopic organization of the striate cortex in the right occipital lobe, as seen in mid-sagittal view. (A) The primary visual cortex occupies a large part of the occipital lobe. The area of central vision (the fovea) is repre-sented over a disproportionately large part of the caudal portion of the lobe, whereas peripheral vision is represented more anteriorly. The upper visual field is represented below the calcarine sul-cus, the lower field above the calcarine sulcus. (B) Photomicrograph of a coro-nal section of the human striate cortex, showing the characteristic myelinated band, or stria, that gives this region of the cortex its name. The calcarine sulcus on the medial surface of the occipital lobe is indicated. (B courtesy of T. Andrews and D. Purves.) Figure 11.7 Course of the optic radia-tion to the striate cortex. Axons carrying information about the superior portion of the visual field sweep around the lat-eral horn of the ventricle in the tempo-ral lobe (Meyer’s loop) before reaching the occipital lobe. Those carrying infor-mation about the inferior portion of the visual field travel in the parietal lobe. fovea is represented in the posterior part of the striate cortex, whereas the more peripheral regions of the retina are represented in progressively more anterior parts of the striate cortex. The upper visual field is mapped below the calcarine sulcus, and the lower visual field above it. As in the somatic sen-sory system, the amount of cortical area devoted to each unit area of the sen-sory surface is not uniform, but reflects the density of receptors and sensory axons that supply the peripheral region. Like the representation of the hand region in the somatic sensory cortex, the representation of the macula is therefore disproportionately large, occupying most of the caudal pole of the occipital lobe. Visual Field Deficits A variety of retinal or more central pathologies that involve the primary visual pathway can cause visual field deficits that are limited to particular regions of visual space. Because the spatial relationships in the retinas are maintained in central visual structures, a careful analysis of the visual fields can often indicate the site of neurological damage. Relatively large visual field deficits are called anopsias and smaller ones are called scotomas (see Box A). The former term is combined with various prefixes to indicate the specific region of the visual field from which sight has been lost (Figures 11.7 and 11.8). Damage to the retina or one of the optic nerves before it reaches the chi-asm results in a loss of vision that is limited to the eye of origin. In contrast, damage in the region of the optic chiasm—or more centrally—results in spe-cific types of deficits that involve the visual fields of both eyes (Figure 11.8). Damage to structures that are central to the optic chiasm, including the optic tract, lateral geniculate nucleus, optic radiation, and visual cortex, results in deficits that are limited to the contralateral visual hemifield. For example, interruption of the optic tract on the right results in a loss of sight in the left visual field (that is, blindness in the temporal visual field of the left eye and the nasal visual field of the right eye). Because such damage affects corre-sponding parts of the visual field in each eye, there is a complete loss of vision in the affected region of the binocular visual field, and the deficit is referred to as a homonymous hemianopsia (in this case, a left homonymous hemianopsia). Central Visual Pathways 267 Lateral ventricles Lateral geniculate nucleus Fibers representing inferior retinal quadrants (superior visual ﬁeld) Fibers representing superior retinal quadrants (inferior visual ﬁeld) Meyer’s loop 268 Chapter Eleven In contrast, damage to the optic chiasm results in visual field deficits that involve noncorresponding parts of the visual field of each eye. For example, damage to the middle portion of the optic chiasm (which is often the result of pituitary tumors) can affect the fibers that are crossing from the nasal retina of each eye, leaving the uncrossed fibers from the temporal retinas intact. The resulting loss of vision is confined to the temporal visual field of each eye and is known as bitemporal hemianopsia. It is also called het-eronomous hemianopsia to emphasize that the parts of the visual field that are lost in each eye do not overlap. Individuals with this condition are able to see in both left and right visual fields, provided both eyes are open. How-ever, all information from the most peripheral parts of visual fields (which are seen only by the nasal retinas) is lost. Damage to central visual structures is rarely complete. As a result, the deficits associated with damage to the chiasm, optic tract, optic radiation, or visual cortex are typically more limited than those shown in Figure 11.8. This is especially true for damage along the optic radiation, which fans out under the temporal and parietal lobes in its course from the lateral geniculate nucleus to the striate cortex. Some of the optic radiation axons run out into the temporal lobe on their route to the striate cortex, a branch called Meyer’s loop (see Figure 11.7). Meyer’s loop carries information from the superior portion of the contralateral visual field. More medial parts of the optic radiation, which pass under the cortex of the parietal lobe, carry information from the inferior portion of the contralateral visual field. Damage to parts of the tempo-ral lobe with involvement of Meyer’s loop can thus result in a superior Optic nerve Optic chiasm Lateral geniculate nucleus Optic radiation Striate cortex Left eye visual field Right eye visual field Left Right (A) (B) (C) (D) (E) A B C D E Optic tract Figure 11.8 Visual field deficits result-ing from damage at different points along the primary visual pathway. The diagram on the left illustrates the basic organization of the primary visual path-way and indicates the location of vari-ous lesions. The right panels illustrate the visual field deficits associated with each lesion. (A) Loss of vision in right eye. (B) Bitemporal (heteronomous) hemianopsia. (C) Left homonymous hemianopsia. (D) Left superior quadran-tanopsia. (E) Left homonymous hemi-anopsia with macular sparing. Figure 11.9 Neurons in the primary visual cortex respond selectively to ori-ented edges. (A) An anesthetized ani-mal is fitted with contact lenses to focus the eyes on a screen, where images can be projected; an extracellular electrode records the neuronal responses. (B) Neurons in the primary visual cortex typically respond vigorously to a bar of light oriented at a particular angle and weakly—or not at all—to other orientations. homonymous quadrantanopsia; damage to the optic radiation underlying the parietal cortex results in an inferior homonymous quadrantanopsia. Injury to central visual structures can also lead to a phenomenon called macular sparing, i.e., the loss of vision throughout wide areas of the visual field, with the exception of foveal vision. Macular sparing is commonly found with damage to the cortex, but can be a feature of damage anywhere along the length of the visual pathway. Although several explanations for macular sparing have been offered, including overlap in the pattern of crossed and uncrossed ganglion cells supplying central vision, the basis for this selective preservation is not clear. The Functional Organization of the Striate Cortex Much in the same way that Stephen Kuffler explored the response properties of individual retinal ganglion cells (see Chapter 10), David Hubel and Torsten Wiesel used microelectrode recordings to examine the properties of neurons in more central visual structures. The responses of neurons in the lateral geniculate nucleus were found to be remarkably similar to those in the retina, with a center-surround receptive field organization and selectivity for luminance increases or decreases. How-ever, the small spots of light that were so effective at stimulating neurons in the retina and lateral geniculate nucleus were largely ineffective in visual cortex. Instead, most cortical neurons in cats and monkeys responded vigor-ously to light–dark bars or edges, and only if the bars were presented at a particular range of orientations within the cell’s receptive field (Figure 11.9). The responses of cortical neurons are thus tuned to the orientation of edges, much like cone receptors are tuned to the wavelength of light; the peak in the tuning curve (the orientation to which a cell is most responsive) is referred to as the neuron’s preferred orientation. By sampling the responses of a large number of single cells, Hubel and Weisel demonstrated that all edge orientations were roughly equally represented in visual cortex. As a Central Visual Pathways 269 Recording from visual cortex (A) Experimental setup (B) Light bar stimulus projected on screen Time (s) Stimulus presented Stimulus orientation 0 1 2 3 Record 270 Chapter Eleven result, a given orientation in a visual scene appears to be “encoded” in the activity of a distinct population of orientation-selective neurons. Hubel and Wiesel also found that there are subtly different subtypes within a class of neurons that preferred the same orientation. For example, the receptive fields of some cortical cells, which they called simple cells, were composed of spatially separate “on” and “off” response zones, as if the “on” and “off” centers of lateral geniculate cells that supplied these neurons were arrayed in separate parallel bands. Other neurons, referred to as complex cells, exhibited mixed “on” and “off” responses throughout their receptive field, as if they received their inputs from a number of simple cells. Further analysis uncovered cortical neurons sensitive to the length of the bar of light that was moved across their receptive field, decreasing their rate of response when the bar exceeded a certain length. Still other cells responded selectively to the direction in which an edge moved across their receptive field. Although the mechanisms responsible for generating these selective responses are still not well understood, there is little doubt that the specificity of the receptive field properties of neurons in the striate cortex (and beyond) plays an impor-tant role in determining the basic attributes of visual scenes. Another feature that distinguishes the responses of neurons in the striate cortex from those at earlier stages in the primary visual pathway is binocu-larity. Although the lateral geniculate nucleus receives inputs from both eyes, the axons terminate in separate layers, so that individual geniculate I II III IV Layer (A) Lateral geniculate nucleus Striate cortex V VI 1 2 3 4 5 6 (B) Parieto- occipital sulcus Calcarine sulcus Posterior pole of occipital lobe Figure 11.10 Mixing of the pathways from the two eyes first occurs in the striate cortex. (A) Although the lateral geniculate nucleus receives inputs from both eyes, these are segregated in separate layers (see also Figure 11.14). In many species, includ-ing most primates, the inputs from the two eyes remain segre-gated in the ocular dominance columns of layer IV, the primary cortical target of lateral geniculate axons. Layer IV neurons send their axons to other cortical layers; it is at this stage that the information from the two eyes converges onto individual neurons. (B) Pattern of ocular dominance columns in human striate cortex. The alternating left and right eye columns in layer IV have been reconstructed from tissue sections and pro-jected onto a photograph of the medial wall of the occipital lobe. (B from Horton and Hedley-Whyte, 1984.) Figure 11.11 Binocular disparities are generally thought to be the basis of stereopsis. When the eyes are fixated on point b, points that lie beyond the plane of fixation (point c) or in front of the point of fixation (point a) project to non-corresponding points on the two retinas. When these disparities are small, the images are fused and the disparity is interpreted by the brain as small differ-ences in depth. When the disparities are greater, double vision occurs (although this normal phenomenon is generally unnoticed). neurons are monocular, driven by either the left or right eye but not by both (Figure 11.10; see also Figure 11.14). In some species, including most (but not all) primates, inputs from the left and right eyes remain segregated to some degree even beyond the geniculate because the axons of geniculate neurons terminate in alternating eye-specific columns within cortical layer IV—the so-called ocular dominance columns (see the next section). Beyond this point, the signals from the two eyes are combined at the cellular level. Thus, most cortical neurons have binocular receptive fields, and these fields are almost identical, having the same size, shape, preferred orientation, and roughly the same position in the visual field of each eye. Bringing together the inputs from the two eyes at the level of the striate cortex provides a basis for stereopsis, the special sensation of depth that arises from viewing nearby objects with two eyes instead of one. Because the two eyes look at the world from slightly different angles, objects that lie in front of or behind the plane of fixation project to noncorresponding points on the two retinas. To convince yourself of this fact, hold your hand at arm’s length and fixate on the tip of one finger. Maintain fixation on the finger as you hold a pencil in your other hand about half as far away. At this distance, the image of the pencil falls on noncorresponding points on the two retinas and will therefore be perceived as two separate pencils (a phenomenon called double vision, or diplopia). If the pencil is now moved toward the fin-ger (the point of fixation), the two images of the pencil fuse and a single pen-cil is seen in front of the finger. Thus, for a small distance on either side of the plane of fixation, where the disparity between the two views of the world remains modest, a single image is perceived; the disparity between the two eye views of objects nearer or farther than the point of fixation is interpreted as depth (Figure 11.11). Although the neurophysiological basis of stereopsis is not understood, some neurons in the striate cortex and in other visual cortical areas have receptive field properties that make them good candidates for extracting information about binocular disparity. Unlike many binocular cells whose monocular receptive fields sample the same region of visual space, these neurons have monocular fields that are slightly displaced (or perhaps differ in their internal organization) so that the cell is maximally activated by stim-uli that fall on noncorresponding parts of the retinas. Some of these neurons (so-called far cells) discharge to disparities beyond the plane of fixation, while others (near cells) respond to disparities in front of the plane of fixa-tion. The pattern of activity in these different classes of neurons seems likely to contribute to sensations of stereoscopic depth (Box B). Interestingly, the preservation of the binocular responses of cortical neu-rons is contingent on the normal activity from the two eyes during early postnatal life. Anything that creates an imbalance in the activity of the two eyes—for example, the clouding of one lens or the abnormal alignment of the eyes during infancy (strabismus)—can permanently reduce the effective-ness of one eye in driving cortical neurons, and thus impair the ability to use binocular information as a cue for depth. Early detection and correction of visual problems is therefore essential for normal visual function in maturity (see Chapter 23). The Columnar Organization of the Striate Cortex The variety of response properties exhibited by cortical neurons raises the question of how neurons with different receptive fields are arranged within striate cortex. For the most part, the responses of neurons are qualitatively Central Visual Pathways 271 Right b c Left Fixation point Far disparities Images of fixation point Near disparities a 272 Chapter Eleven Box B Random Dot Stereograms and Related Amusements An important advance in studies of stereopsis was made in 1959 when Bela Julesz, then working at the Bell Laborato-ries in Murray Hill, New Jersey, discov-ered an ingenious way of showing that stereoscopy depends on matching infor-mation seen by the two eyes without any prior recognition of what object(s) such matching might generate. Julesz, a Hun-garian whose background was in engi-neering and physics, was working on the problem of how to “break” camouflage. He surmised that the brain’s ability to fuse the slightly different views of the two eyes to bring out new information would be an aid in overcoming military camouflage. Julesz also realized that, if his hypothesis was correct, a hidden fig-ure in a random pattern presented to the two eyes should emerge when a portion of the otherwise identical pattern was shifted horizontally in the view of one eye or the other. A horizontal shift in one direction would cause the hidden object to appear in front of the plane of the background, whereas a shift in the other direction would cause the hidden object to appear in back of the plane. Such a fig-ure, called a random dot stereogram, and the method of its creation are shown in Figures A and B. The two images can be easily fused in a stereoscope (like the familiar Viewmaster® toy) but can also be fused simply by allowing the eyes to diverge. Most people find it easiest to do this by imagining that they are looking “through” the figure; after some seconds, during which the brain tries to make sense of what it is presented with, the two images merge and the hidden figure appears (in this case, a square that occu-pies the middle portion of the figure). The random dot stereogram has been widely used in stereoscopic research for about 40 years, although how such stim-uli elicit depth remains very much a mat-ter of dispute. An impressive—and extraordinarily popular—derivative of the random dot stereogram is the autostereogram (Figure C). The possibility of autostereograms was first discerned by the nineteenth-century British physicist David Brewster. While staring at a Victorian wallpaper with an iterated but offset pattern, he noticed that when the patterns were fused, he perceived two different planes. The plethora of autostereograms that can be seen today in posters, books, and newspapers are close cousins of the ran-dom dot stereogram in that computers are used to shift patterns of iterated (A) (B) Binocular fusion pro- duces sensation that the shifted square is in front of the background plane. Random dot stereograms and autostere-ograms. (A) to construct a random dot stere-ogram, a random dot pattern is created to be observed by one eye. The stimulus for the other eye is created by copying the first image, displacing a particular region hori-zontally, and then filling in the gap with a random sample of dots. (B) When the right and left images are viewed simultaneously but independently by the two eyes (by using a stereoscope or fusing the images by con-verging or diverging the eyes), the shifted region (a square) appears to be in a different plane from the other dots. (A after Wandell, 1995.) similar at any one point in primary visual cortex, but tend to shift smoothly across its surface. With respect to orientation, for example, all the neurons encountered in an electrode penetration perpendicular to the surface at a particular point will very likely have the same orientation preference, form-ing a “column” of cells with similar response properties. Adjacent columns, however, usually have slightly different orientation preferences; the se-quence of orientation preferences encountered along a tangential electrode penetration gradually shifts as the electrode advances (Figure 11.12). Thus, orientation preference is mapped in the cortex, much like receptive field Central Visual Pathways 273 information with respect to each other. The result is that different planes emerge from what appears to be a meaningless array of visual information (or, depend-ing on the taste of the creator, an appar-ently “normal” scene in which the iter-ated and displaced information is hidden). Some autostereograms are designed to reveal the hidden figure when the eyes diverge, and others when they converge. (Looking at a plane more distant than the plane of the surface causes divergence; looking at a plane in front of the picture causes the eyes to converge; see Figure 11.11.) The elevation of the autostereogram to a popular art form should probably be attributed to Chris W. Tyler, a student of Julesz’s and a visual psychophysicist, who was among the first to create com-mercial autostereograms. Numerous graphic artists—preeminently in Japan, where the popularity of the autostere-ogram has been enormous—have gener-ated many of such images. As with the random dot stereogram, the task in viewing the autostereogram is not clear to the observer. Nonetheless, the hidden figure emerges, often after minutes of effort in which the brain automatically tries to make sense of the occult infor-mation. References JULESZ, B. (1971) Foundations of Cyclopean Per-ception. Chicago: The University of Chicago Press. JULESZ, B. (1995) Dialogues on Perception. Cam-bridge, MA: MIT Press. N. E. THING ENTERPRISES (1993) Magic Eye: A New Way of Looking at the World. Kansas City: Andrews and McMeel. (C) (C) An autostereogram. The hidden figure (three geometrical forms) emerges by diverg-ing the eyes in this case. (C courtesy of Jun Oi.) 274 Chapter Eleven location (Box C). Unlike the map of visual space, however, the map of orien-tation preference is iterated many times, such that the same orientation pref-erence is repeated at approximately 1-mm intervals across the striate cortex. This iteration presumably ensures that there are neurons for each region of visual space that represent the full range of orientation values. The orderly progression of orientation preference (as well as other properties that are mapped in this systematic way) is accommodated within the orderly map of visual space by the fact that the mapping is relatively coarse. Each small region of visual space is represented by a set of neurons whose receptive fields cover the full range of orientation preferences, the set being distrib-uted over several millimeters of the cortical surface The columnar organization of the striate cortex is equally apparent in the binocular responses of cortical neurons. Although most neurons in the stri-ate cortex respond to stimulation of both eyes, the relative strength of the inputs from the two eyes varies from neuron to neuron. At the extremes of this continuum are neurons that respond almost exclusively to the left or right eye; in the middle are those that respond equally well to both eyes. As in the case of orientation preference, vertical electrode penetrations tend to encounter neurons with similar ocular preference (or ocular dominance, as it is usually called), whereas tangential penetrations show gradual shifts in ocular dominance. And, like the arrangement of orientation preference, a movement of about a millimeter across the surface is required to sample the full complement of ocular dominance values (Figure 11.13). These shifts in ocular dominance result from the ocular segregation of the inputs from lat-eral geniculate nucleus within cortical layer IV (see Figure 11.10). Although the modular arrangement of the visual cortex was first recog-nized on the basis of these orientation and ocular dominance columns, fur-ther work has shown that other stimulus features such as color, direction of motion, and spatial frequency also tend to be distributed in iterated patterns that are systematically related to each other (for example, orientation columns tend to intersect ocular dominance columns at right angles). In short, the striate cortex is composed of repeating units, or modules, that con-tain all the neuronal machinery necessary to analyze a small region of visual space for a variety of different stimulus attributes. As described in Box D in Chapter 8, a number of other cortical regions show a similar columnar arrangement of their processing circuitry. Vertical electrode penetration IV V VI II−III I Oblique electrode penetration Figure 11.12 Columnar organization of orientation selectivity in the monkey striate cortex. Vertical electrode penetra-tions encounter neurons with the same preferred orientations, whereas oblique penetrations show a systematic change in orientation across the cortical surface. The circles denote the lack of orienta-tion-selective cells in layer IV. Figure 11.13 Columnar organization of ocular dominance. (A) Cortical neu-rons in all layers vary in the strength of their response to the inputs from the two eyes, from complete domination by one eye to equal influence of the two eyes. (B) Tangential electrode penetra-tion across the superficial cortical layers reveals a gradual shift in the ocular dominance of the recorded neurons from one eye to the other. In contrast, all neurons encountered in a vertical elec-trode penetration (other than those neu-rons that lie in layer IV) tend to have the same ocular dominance. Division of Labor within the Primary Visual Pathway In addition to being specific for input from one eye or the other, the layers in the lateral geniculate are also distinguished on the basis of cell size: Two ventral layers are composed of large neurons and are referred to as the mag-nocellular layers, while more dorsal layers are composed of small neurons and are referred to as the parvocellular layers. The magno- and parvocellu-lar layers receive inputs from distinct populations of ganglion cells that exhibit corresponding differences in cell size. M ganglion cells that terminate in the magnocellular layers have larger cell bodies, more extensive dendritic fields, and larger-diameter axons than the P ganglion cells that terminate in the parvocellular layers (Figure 11.14A). Moreover, the axons of relay cells in the magno- and parvocellular layers of the lateral geniculate nucleus termi-nate on distinct populations of neurons located in separate strata within layer 4 of striate cortex. Thus the retinogeniculate pathway is composed of parallel magnocellular and parvocellular streams that convey distinct types of information to the initial stages of cortical processing. The response properties of the M and P ganglion cells provide important clues about the contributions of the magno- and parvocellular streams to visual perception. M ganglion cells have larger receptive fields than P cells, and their axons have faster conduction velocities. M and P ganglion cells also differ in ways that are not so obviously related to their morphology. M cells respond transiently to the presentation of visual stimuli, while P cells respond in a sustained fashion. Moreover, P ganglion cells can transmit information about color, whereas M cells cannot. P cells convey color infor-mation because their receptive field centers and surrounds are driven by dif-ferent classes of cones (i.e., cones responding with greatest sensitivity to Central Visual Pathways 275 Left Right 1 2 3 4 5 6 7 (A) Cortical cell Ocular dominance groups Distance along electrode track 1 2 3 4 5 6 7 Layer IV (B) Left eye Left eye Left eye Right eye Right eye Right eye Electrode Electrode track Recording site 276 Chapter Eleven Box C Optical Imaging of Functional Domains in the Visual Cortex The recent availability of optical imaging techniques has made it possible to visu-alize how response properties, such as the selectivity for edge orientation or ocular dominance, are mapped across the cortical surface. These methods gen-erally rely on intrinsic signals (changes in the amount of light reflected from the cortical surface) that correlate with levels of neural activity. Such signals are thought to arise at least in part from local changes in the ratio of oxyhemoglobin and deoxyhemoglobin that accompany such activity, more active areas having a higher deoxyhemoglobin/oxyhemoglo-bin ratio (see also Box A in Chapter 1). This change can be detected when the cortical surface is illuminated with red light (605–700 nm). Under these condi-tions, active cortical regions absorb more light than less active ones. With the use of a sensitive video camera, and averag-ing over a number of trials (the changes are small, 1 or 2 parts per thousand), it is possible to visualize these differences and use them to map cortical patterns of activity (Figure A). This approach has now been success-fully applied to both striate and extrastri-ate areas in both experimental animals and human patients undergoing neuro-surgery. The results emphasize that maps of stimulus features are a general princi-ple of cortical organization. For example, orientation preference is mapped in a con-tinuous fashion such that adjacent posi-tions on the cortical surface tend to have only slightly shifted orientation prefer-ences. However, there are points where continuity breaks down. Around these points, orientation preference is repre-sented in a radial pattern resembling a pinwheel, covering the whole 180° of pos-sible orientation values (Figure B). This powerful technique can also be used to determine how maps for differ-ent stimulus properties are arranged rel-ative to one another, and to detect addi-tional maps such as that for direction of motion. A comparison of ocular domi-nance bands and orientation preference maps, for example, shows that pinwheel centers are generally located in the center of ocular dominance bands, and that the iso-orientation contours that emanate from the pinwheel centers run orthogo-nal to the borders of ocular dominance bands (Figure C). An orderly relation-ship between maps of orientation selec-tivity and direction selectivity has also been demonstrated. These systematic relationships between the functional maps that coexist within primary visual cortex are thought to ensure that all com-binations of stimulus features (orienta-tion, direction, ocular dominance, and spatial frequency) are analyzed for all regions of visual space. References BLASDEL, G. G. AND G. SALAMA (1986) Voltage-sensitive dyes reveal a modular organization in monkey striate cortex. Nature 321: 579–585. BONHOEFFER, T. AND A. GRINVALD (1993) The layout of iso-orientation domains in area 18 of the cat visual cortex: Optical imaging reveals a pinwheel-like organization. J. Neu-rosci 13: 4157–4180. BONHOEFFER, T. AND A. GRINVALD (1996) Opti-cal imaging based on intrinsic signals: The methodology. In Brain Mapping: The Methods, A. Toge (ed.). New York: Academic Press. OBERMAYER, K. AND G. G. BLASDEL (1993) Geometry of orientation and ocular domi-nance columns in monkey striate cortex. J. Neurosci. 13: 4114–4129. WELIKY, M., W. H. BOSKING AND D. FITZ-PATRICK (1996) A systematic map of direction preference in primary visual cortex. Nature 379: 725–728. 1 mm (A) (B) P ganglion cell M ganglion cell Koniocellular layers K ganglion cell 6 5 4 3 2 1 Parvo-cellular layers Magno-cellular layers short-, medium-, or long-wavelength light). For example, some P ganglion cells have centers that receive inputs from long-wavelength (“red”) sensitive cones and surrounds that receive inputs from medium-wavelength (“green”) cones. Others have centers that receive inputs from “green cones” and sur-rounds from “red cones” (see Chapter 10). As a result, P cells are sensitive to differences in the wavelengths of light striking their receptive field center Central Visual Pathways 277 (A) (B) Visual stimulation computer Imaging computer Monitor Data display Illuminator Video camera Macro lens Optical chamber Purves Neuroscience 3E Pyramis Studios P3_12BXC 121503 (C) (A) The technique of optical imaging. A sensitive video camera is used to record changes in light absorption that occur as the animal views various stimuli presented on a video monitor. Images are digitized and stored in a computer in order to construct maps that compare patterns of activity associated with different stimuli. (B) Maps of orientation preference in the visual cortex visualized with optical imaging. Each color represents the angle of an edge that was most effective in activating the neurons at a given site. Orienta-tion preference changes in a continuous fashion, rotating around pinwheel centers. (Note that this image shows only a small region of the overall map of orientation) (C) Compari-son of optical image maps of orientation preference and ocular dominance in monkey visual cortex. The thick black lines represent the borders between ocular dominance columns. The thin gray lines represent the iso-orientation contours, which converge at orientation pinwheel centers (arrow). Iso-orientation contour lines generally intersect the borders of ocular dominance bands at right angles. (B from Bonhoeffer and Grinvald, 1993; C from Obermeyer and Blasdel, 1993.) Figure 11.14 Magno- and parvocellular streams. (A) Tracings of M and P gan-glion cells as seen in flat mounts of the retina after staining by the Golgi method. M cells have large-diameter cell bodies and large dendritic fields. They supply the magnocellular layers of the lateral geniculate nucleus. P cells have smaller cell bod-ies and dendritic fields. They supply the parvocellular layers of the lateral genicu-late nucleus. (B) Photomicrograph of the human lateral geniculate nucleus showing the magnocellular and parvocellular layers. (A after Watanabe and Rodieck, 1989; B courtesy of T. Andrews and D. Purves.) ▲ 278 Chapter Eleven and surround. Although M ganglion cells also receive inputs from cones, there is no difference in the type of cone input to the receptive field center and surround; the center and surround of each M cell receptive field is dri-ven by all cone types. The absence of cone specificity to center-surround antagonism makes M cells largely insensitive to differences in the wave-lengths of light that strike their receptive field centers and surrounds, and they are thus unable to transmit color information to their central targets. The contribution of the magno- and parvocellular streams to visual per-ception has been tested experimentally by examining the visual capabilities of monkeys after selectively damaging either the magno- or parvocellular layers of the lateral geniculate nucleus. Damage to the magnocellular layers has little effect on visual acuity or color vision, but sharply reduces the abil-ity to perceive rapidly changing stimuli. In contrast, damage to the parvocel-lular layers has no effect on motion perception but severely impairs visual acuity and color perception. These observations suggest that the visual infor-mation conveyed by the parvocellular stream is particularly important for high spatial resolution vision—the detailed analysis of the shape, size, and color of objects. The magnocellular stream, on the other hand, appears criti-cal for tasks that require high temporal resolution, such as evaluating the location, speed and direction of a rapidly moving object. In addition to the magno- and parvocellular streams, a third distinct anatomical pathway—the koniocellular, or K-cell pathway—has been iden-tified within the lateral geniculate nucleus. Neurons contributing to the K-cell pathway reside in the interlaminar zones that separate lateral geniculate layers; these neurons receive inputs from fine-caliber retinal axons and pro-ject in a patchy fashion to the superficial layers (layers II and III) of striate cortex. Although the contribution of the K-cell pathway to perception is not understood, it appears that some aspects of color vision, especially informa-tion derived from short-wavelength-sensitive cones, may be transmitted via the K-cell rather than the P-cell pathway. Why short-wavelength-sensitive cone signals should be processed differently from middle- and long-wave-length information is not clear, but the distinction may reflect the earlier evo-lutionary origin of the K-cell pathway (see Chapter 10). The Functional Organization of Extrastriate Visual Areas Anatomical and electrophysiological studies in monkeys have led to the dis-covery of a multitude of areas in the occipital, parietal, and temporal lobes that are involved in processing visual information (Figure 11.15). Each of these areas contains a map of visual space, and each is largely dependent on the primary visual cortex for its activation. The response properties of the neurons in some of these regions suggest that they are specialized for differ-ent aspects of the visual scene. For example, the middle temporal area (MT) contains neurons that respond selectively to the direction of a moving edge without regard to its color. In contrast, neurons in another cortical area called V4 respond selectively to the color of a visual stimulus without regard to its direction of movement. These physiological findings are supported by behavioral evidence; thus, damage to area MT leads to a specific impairment in a monkey’s ability to perceive the direction of motion in a stimulus pat-tern, while other aspects of visual perception remain intact. Recent functional imaging studies have indicated a similar arrangement of visual areas within human extrastriate cortex. Using retinotopically restricted stimuli, it has been possible to localize at least 10 separate repre-sentations of the visual field (Figure 11.16). One of these areas exhibits a large motion-selective signal, suggesting that it is the homologue of the motion-selective middle temporal area described in monkeys. Another area exhibits color-selective responses, suggesting that it may be similar to V4 in non-human primates. A role for these areas in the perception of motion and color, respectively, is further supported by evidence for increases in activity not only during the presentation of the relevant stimulus, but also during periods when subjects experience motion or color afterimages. The clinical description of selective visual deficits after localized damage to various regions of extrastriate cortex also supports functional specializa-tion of extrastriate visual areas in humans. For example, a well-studied patient who suffered a stroke that damaged the extrastriate region thought to be comparable to area MT in the monkey was unable to appreciate the motion of objects. The neurologist who treated her noted that she had diffi-culty in pouring tea into a cup because the fluid seemed to be “frozen.” In addition, she could not stop pouring at the right time because she was unable to perceive when the fluid level had risen to the brim. The patient also had trouble following a dialogue because she could not follow the movements of the speaker’s mouth. Crossing the street was potentially terri-fying because she couldn’t judge the movement of approaching cars. As the patient related, “When I’m looking at the car first, it seems far away. But Central Visual Pathways 279 (A) (B) V1 V2 V2 V3 V4 MT Visual areas MT V3 V4 V2 V1 V2 V1 V2 V4 (A) (B) Motor Somatic sensory Auditory Figure 11.15 Subdivisions of the extrastriate cortex in the macaque mon-key. (A) Each of the subdivisions indi-cated in color contains neurons that respond to visual stimulation. Many are buried in sulci, and the overlying cortex must be removed in order to expose them. Some of the more extensively studied extrastriate areas are specifically identified (V2, V3, V4, and MT). V1 is the primary visual cortex; MT is the middle temporal area. (B) The arrange-ment of extrastriate and other areas of neocortex in a flattened view of the monkey neocortex. There are at least 25 areas that are predominantly or exclu-sively visual in function, plus 7 other areas suspected to play a role in visual processing. (A after Maunsell and New-some, 1987; B after Felleman and Van Essen, 1991.) 280 Chapter Eleven then, when I want to cross the road, suddenly the car is very near.” Her abil-ity to perceive other features of the visual scene, such as color and form, was intact. Another example of a specific visual deficit as a result of damage to extras-triate cortex is cerebral achromatopsia. These patients lose the ability to see the world in color, although other aspects of vision remain in good working order. The normal colors of a visual scene are described as being replaced by “dirty” shades of gray, much like looking at a poor quality black-and-white movie. Achromatopsic individuals know the normal colors of objects—that a school bus is yellow, an apple red—but can no longer see them. Thus, when asked to draw objects from memory, they have no difficulty with shapes but are unable to appropriately color the objects they have represented. It is important to distinguish this condition from the color blindness that arises from the congenital absence of one or more cone pigments in the retina (see Chapter 10). In achromatopsia, the three types of cones are functioning nor-mally; it is damage to specific extrastriate cortical areas that renders the patient unable to use the information supplied by the retina. V1 V1 V2 V2 V3 V3a V4 V4 VP VP VP MT MST MT V3a V3a V3 V1 V2 V2 (B) Medial (A) Lateral (C) Brain “inflated” to reveal buried cortex Flattened occipital lobe Sulci Gyri Calcarine sulcus Figure 11.16 Localization of multiple visual areas in the human brain using fMRI. (A,B) Lateral and medial views (respectively) of the human brain, illus-trating the location of primary visual cortex (V1) and additional visual areas V2, V3, VP (ventral posterior area), V4, MT (middle temporal area), and MST (medial superior temporal area). (C) Un-folded and flattened view of retinotopi-cally defined visual areas in the occipital lobe. Dark grey areas correspond to cor-tical regions that were buried in sulci; light regions correspond to regions that were located on the surface of gyri. Visual areas in humans show a close resemblance to visual areas originally defined in monkeys (compare with Fig-ure 11.15). (After Sereno et al., 1995.) Figure 11.17 The visual areas beyond the striate cortex are broadly organized into two pathways: a ventral pathway that leads to the temporal lobe, and a dorsal pathway that leads to the parietal lobe. The ventral pathway plays an important role in object recognition, the dorsal pathway in spatial vision. Based on the anatomical connections between visual areas, differences in electrophysiological response properties, and the effects of cortical lesions, a consensus has emerged that extrastriate cortical areas are organized into two largely separate systems that eventually feed information into cortical asso-ciation areas in the temporal and parietal lobes (see Chapter 25). One system, called the ventral stream, includes area V4 and leads from the striate cortex into the inferior part of the temporal lobe. This system is thought to be responsible for high-resolution form vision and object recognition. The dor-sal stream, which includes the middle temporal area, leads from striate cor-tex into the parietal lobe. This system is thought to be responsible for spatial aspects of vision, such as the analysis of motion, and positional relationships between objects in the visual scene (Figure 11.17). The functional dichotomy between these two streams is supported by observations on the response properties of neurons and the effects of selec-tive cortical lesions. Neurons in the ventral stream exhibit properties that are important for object recognition, such as selectivity for shape, color, and tex-ture. At the highest levels in this pathway, neurons exhibit even greater selectivity, responding preferentially to faces and objects (see Chapter 25). In contrast, those in the dorsal stream are not tuned to these properties, but show selectivity for direction and speed of movement. Consistent with this interpretation, lesions of the parietal cortex severely impair an animal’s abil-ity to distinguish objects on the basis of their position, while having little effect on its ability to perform object recognition tasks. In contrast, lesions of the inferotemporal cortex produce profound impairments in the ability to perform recognition tasks but no impairment in spatial tasks. These effects are remarkably similar to the syndromes associated with damage to the pari-etal and temporal lobe in humans (see Chapters 25 and 26). What, then, is the relationship between these “higher-order” extrastriate visual pathways and the magno- and parvocellular pathways that supply the primary visual cortex? Not long ago, it seemed that these intracortical path-ways were simply a continuation of the geniculostriate pathways—that is, the magnocellular pathway provided input to the dorsal stream and the parvo-cellular pathway provided input to the ventral stream. However, more recent work has indicated that the situation is more complicated. The temporal path-way clearly has access to the information conveyed by both the magno- and parvocellular streams; and the parietal pathway, while dominated by inputs from the magnocellular stream, also receives inputs from the parvocellular stream. Thus, interaction and cooperation between the magno- and parvocel-lular streams appear to be the rule in complex visual perceptions. Summary Distinct populations of retinal ganglion cells send their axons to a number of central visual structures that serve different functions. The most important projections are to the pretectum for mediating the pupillary light reflex, to the hypothalamus for the regulation of circadian rhythms, to the superior colliculus for the regulation of eye and head movements, and—most impor-tant of all—to the lateral geniculate nucleus for mediating vision and visual perception. The retinogeniculostriate projection (the primary visual path-way) is arranged topographically such that central visual structures contain an organized map of the contralateral visual field. Damage anywhere along the primary visual pathway, which includes the optic nerve, optic tract, lat-eral geniculate nucleus, optic radiation, and striate cortex, results in a loss of vision confined to a predictable region of visual space. Compared to retinal Central Visual Pathways 281 Dorsal (spatial vision) pathway V2 V2 V1 Ventral (object recognition) pathway MT V4 Parietal lobe Temporal lobe 282 Chapter Eleven ganglion cells, neurons at higher levels of the visual pathway become increasingly selective in their stimulus requirements. Thus, most neurons in the striate cortex respond to light–dark edges only if they are presented at a certain orientation; some are selective for the length of the edge, and others to movement of the edge in a specific direction. Indeed, a point in visual space is related to a set of cortical neurons, each of which is specialized for processing a limited set of the attributes in the visual stimulus. The neural circuitry in the striate cortex also brings together information from the two eyes; most cortical neurons (other than those in layer IV, which are segre-gated into eye-specific columns) have binocular responses. Binocular con-vergence is presumably essential for the detection of binocular disparity, an important component of depth perception. The primary visual pathway is composed of separate functional streams that convey information from dif-ferent types of retinal ganglion cells to the initial stages of cortical process-ing. The magnocellular stream conveys information that is critical for the detection of rapidly changing stimuli, the parvocellular stream mediates high acuity vision and appears to share responsibility for color vision with the koniocellular stream. Finally, beyond striate cortex, parcellation of func-tion continues in the ventral and dorsal streams that lead to the extrastriate and association areas in the temporal and parietal lobes, respectively. Areas in the inferotemporal cortex are especially important in object recognition, whereas areas in the parietal lobe are critical for understanding the spatial relations between objects in the visual field. Additional Reading Reviews BERSON, D. M. (2003) Strange vision: Ganglion cells as circadian photoreceptors. Trends Neu-rosci. 26: 314–320. COURTNEY, S. M. AND L. G. UNGERLEIDER (1997) What fMRI has taught us about human vision. Curr. Op. Neurobiol. 7: 554–561. FELLEMAN, D. J. AND D. C. VAN ESSEN (1991) Distributed hierarchical processing in primate cerebral cortex. Cerebral Cortex 1: 1–47. HORTON, J. C. (1992) The central visual path-ways. In Alder’s Physiology of the Eye. W. M. Hart (ed.). St. Louis: Mosby Yearbook. HENDRY, S. H. AND R. C. REID (2000) The koniocellular pathway in primate vision. Annu. Rev. Neurosci. 23: 127–153. HUBEL, D. H. AND T. N. WIESEL (1977) Func-tional architecture of macaque monkey visual cortex. Proc. R. Soc. (Lond.) 198: 1–59. MAUNSELL, J. H. R. (1992) Functional visual streams. Curr. Opin. Neurobiol. 2: 506–510. SCHILLER, P. H. AND N. K. LOGOTHETIS (1990) The color-opponent and broad-band channels of the primate visual system. Trends Neu-rosci. 13: 392–398. TOOTELL, R.B., A. M. DALE, M. I. SERENO AND R. MALACH (1996) New images from human visual cortex. Trends Neurosci. 19: 481–489. UNGERLEIDER, J. G. AND M. MISHKIN (1982) Two cortical visual systems. In Analysis of Visual Behavior. D. J. Ingle, M. A. Goodale and R. J. W. Mansfield (eds.). Cambridge, MA: MIT Press, pp. 549–586. Important Original Papers HATTAR, S., H. W. LIAO, M. TAKAO, D. M. BERSON AND K. W. YAU (2002) Melanopsin-containing retinal ganglion cells: Architecture, projections, and intrinsic photosensitivity. Sci-ence 295: 1065–1070. HUBEL, D. H. AND T. N. WIESEL (1962) Recep-tive fields, binocular interaction and func-tional architecture in the cat’s visual cortex. J. Physiol. (Lond.) 160: 106–154. HUBEL, D. H. AND T. N. WIESEL (1968) Recep-tive fields and functional architecture of mon-key striate cortex. J. Physiol. (Lond.) 195: 215–243. SERENO, M. I. AND 7 OTHERS (1995) Borders of multiple visual areas in humans revealed by functional magnetic resonance imaging. Sci-ence 268: 889–893. ZIHL, J., D. VON CRAMON AND N. MAI (1983) Selective disturbance of movement vision after bilateral brain damage. Brain 106: 313–340. Books CHALUPA, L. M. AND J. S. WERNER (EDS.) (2004) The Visual Neurosciences. Cambridge, MA: MIT Press. HUBEL, D. H. (1988) Eye, Brain, and Vision. New York: Scientific American Library. RODIECK, R. W. (1998) The First Steps in Seeing. Sunderland, MA: Sinauer Associates. ZEKI, S. (1993) A Vision of the Brain. Oxford: Blackwell Scientific Publications. Overview The auditory system is one of the engineering masterpieces of the human body. At the heart of the system is an array of miniature acoustical detectors packed into a space no larger than a pea. These detectors can faithfully transduce vibrations as small as the diameter of an atom, and they can respond a thousand times faster than visual photoreceptors. Such rapid auditory responses to acoustical cues facilitate the initial orientation of the head and body to novel stimuli, especially those that are not initially within the field of view. Although humans are highly visual creatures, much human communication is mediated by the auditory system; indeed, loss of hearing can be more socially debilitating than blindness. From a cultural perspective, the auditory system is essential not only to understanding speech, but also to music, one of the most aesthetically sophisticated forms of human expression. For these and other reasons, audition represents a fas-cinating and especially important mode of sensation. Sound In physical terms, sound refers to pressure waves generated by vibrating air molecules (somewhat confusingly, sound is used more casually to refer to an auditory percept). Sound waves are much like the ripples that radiate out-ward when a rock is thrown in a pool of water. However, instead of occur-ring across a two-dimensional surface, sound waves propagate in three dimensions, creating spherical shells of alternating compression and rarefac-tion. Like all wave phenomena, sound waves have four major features: waveform, phase, amplitude (usually expressed in log units known as deci-bels, abbreviated dB), and frequency (expressed in cycles per second or Hertz, abbreviated Hz). For human listeners, the amplitude and frequency of a sound pressure change at the ear roughly correspond to loudness and pitch, respectively. The waveform of a sound stimulus is its amplitude plotted against time. It helps to begin by visualizing an acoustical waveform as a sine wave. At the same time, it must be kept in mind that sounds composed of single sine waves (i.e., pure tones) are extremely rare in nature; most sounds in speech, for example, consist of acoustically complex waveforms. Interestingly, such complex waveforms can often be modeled as the sum of sinusoidal waves of varying amplitudes, frequencies, and phases. In engineering applications, an algorithm called the Fourier transform decomposes a complex signal into its sinusoidal components. In the auditory system, as will be apparent later in the chapter, the inner ear acts as a sort of acoustical prism, decomposing complex sounds into a myriad of constituent tones. Chapter 12 283 The Auditory System 284 Chapter Twelve Figure 12.1 Diagram of the periodic condensation and rarefaction of air mol-ecules produced by the vibrating tines of a tuning fork. The molecular distur-bance of the air is pictured as if frozen at the instant the constituent molecules responded to the resultant pressure wave. Shown below is a plot of the air pressure versus distance from the fork. Note its sinusoidal quality. Figure 12.1 diagrams the behavior of air molecules near a tuning fork that vibrates sinusoidally when struck. The vibrating tines of the tuning fork pro-duce local displacements of the surrounding molecules, such that when the tine moves in one direction, there is molecular condensation; when it moves in the other direction, there is rarefaction. These changes in density of the air molecules are equivalent to local changes in air pressure. Such regular, sinusoidal cycles of compression and rarefaction can be thought of as a form of circular motion, with one complete cycle equivalent to one full revolution (360°). This point can be illustrated with two sinusoids of the same frequency projected onto a circle, a strategy that also makes it easier to understand the concept of phase (Figure 12.2). Imagine that two tuning forks, both of which resonate at the same frequency, are struck at slightly different times. At a given time t = 0, one wave is at position P and the other at position Q. By projecting P and Q onto the circle, their respective phase angles, θ1 and θ2, are apparent. The sine wave that starts at P reaches a particular point on the circle, say 180°, at time t1, whereas the wave that starts at Q reaches 180° at time t2. Thus, phase differences have correspond-ing time differences, a concept that is important in appreciating how the auditory system locates sounds in space. The human ear is extraordinarily sensitive to sound pressure. At the threshold of hearing, air molecules are displaced an average of only 10 picometers (10–11 m), and the intensity of such a sound is about one-trillionth of a watt per square meter! This means a listener on an otherwise noiseless planet could hear a 1-watt, 3-kHz sound source located over 450 km away (consider that even a very dim light bulb consumes more than 1 watt of power). Even dangerously high sound pressure levels (>100 dB) have power at the eardrum that is only in the milliwatt range (Box A). The Audible Spectrum Humans can detect sounds in a frequency range from about 20 Hz to 20 kHz. Human infants can actually hear frequencies slightly higher than 20 kHz, but lose some high-frequency sensitivity as they mature; the upper limit in average adults is closer to 15–17 kHz. Not all mammalian species are sensitive to the same range of frequencies. Most small mammals are sensi-tive to very high frequencies, but not to low frequencies. For instance, some species of bats are sensitive to tones as high as 200 kHz, but their lower limit is around 20 kHz—the upper limit for young people with normal hearing. One reason for these differences is that small objects, including the audi-tory structures of these small mammals, resonate at high frequencies, whereas large objects tend to resonate at low frequencies—which explains why the violin has a higher pitch than the cello. Different animal species tend to emphasize frequency bandwidths in both their vocalizations and their range of hearing. In general, vocalizations by virtue of their periodicity can be distinguished from the noise “barrier” created by environmental sounds, such as wind and rustling leaves. Animals that echolocate, such as bats and dolphins, rely on very high-frequency vocal sounds to maximally resolve spatial features of the target, while animals intent on avoiding pre-dation have auditory systems “tuned” to the low frequency vibrations that approaching predators transmit through the substrate. These behavioral dif-ferences are mirrored by a wealth of anatomical and functional specializa-tions throughout the auditory system. Air pressure Tuning fork Distance Sinusoidal wave Normal atmospheric pressure Concentric waves + − Time Q O θ1 θ2 t1 t2 P Figure 12.2 A sine wave and its pro-jection as circular motion. The two sinu-soids shown are at different phases, such that point P corresponds to phase angle θ1 and point Q corresponds to phase angle θ2. A Synopsis of Auditory Function The auditory system transforms sound waves into distinct patterns of neural activity, which are then integrated with information from other sensory sys-tems to guide behavior, including orienting movements to acoustical stimuli and intraspecies communication. The first stage of this transformation occurs at the external and middle ears, which collect sound waves and amplify their pressure, so that the sound energy in the air can be success-fully transmitted to the fluid-filled cochlea of the inner ear. In the inner ear, a series of biomechanical processes occur that break up the signal into sim-pler, sinusoidal components, with the result that the frequency, amplitude, and phase of the original signal are all faithfully transduced by the sensory hair cells and encoded by the electrical activity of the auditory nerve fibers. One product of this process of acoustical decomposition is the systematic representation of sound frequency along the length of the cochlea, referred to as tonotopy, which is an important organizational feature preserved The Auditory System 285 Box A Four Causes of Acquired Hearing Loss Acquired hearing loss is an increasingly common sensory deficit that can often lead to impaired oral communication and social isolation. Four major causes of acquired hearing loss are acoustical trauma, infection of the inner ear, oto-toxic drugs, and presbyacusis (literally, the hearing of the old). The exquisite sensitivity of the audi-tory periphery, combined with the direct mechanical linkage between the acousti-cal stimulus and the receptor cells, make the ear especially susceptible to acute or chronic acoustical trauma. Extremely loud, percussive sounds, such as those generated by explosives or gunfire, can rupture the eardrum and so severely dis-tort the inner ear that the organ of Corti is torn. The resultant loss of hearing is abrupt and often quite severe. Less well appreciated is the fact that repeated exposure to less dramatic but nonethe-less loud sounds, including those pro-duced by industrial or household machinery or by amplified musical instruments, can also damage the inner ear. Although these sounds leave the eardrum intact, specific damage is done to the hair bundle itself; the stereocilia of cochlear hair cells of animals exposed to loud sounds shear off at their pivot points with the hair cell body, or fuse together in a platelike fashion that impedes movement. In humans, the mechanical resonance of the ear to stim-ulus frequencies centered about 3 kHz means that exposure to loud, broadband noises (such as those generated by jet engines) results in especially pronounced deficits near this resonant frequency. Ototoxic drugs include aminoglyco-side antibiotics (such as gentamycin and kanamycin), which directly affect hair cells, and ethacrynic acid, which poisons the potassium-extruding cells of the stria vascularis that generate the endocochlear potential. In the absence of these ion pumping cells, the endocochlear poten-tial, which supplies the energy to drive the transduction process, is lost. Although still a matter of some debate, the relatively nonselective transduction channel apparently affords a means of entry for aminoglycoside antibiotics, which then poison hair cells by disrupt-ing phosphoinositide metabolism. In par-ticular, outer hair cells and those inner hair cells that transduce high-frequency stimuli are more affected, simply because of their greater energy requirements. Finally, presbyacusis, the hearing loss associated with aging, may in part stem from atherosclerotic damage to the espe-cially fine microvasculature of the inner ear, as well as from genetic predisposi-tions to hair cell damage. Recent advances in understanding the genetic transmission of acquired hearing loss in both humans and mice point to muta-tions in myosin isoforms unique to hair cells as a likely culprit. References HOLT, J. R. AND D. P. COREY (1999) Ion chan-nel defects in hereditary hearing loss. Neu-ron 22: 217–219. KEATS, B. J. AND D. P. COREY (1999) The usher syndromes. Amer. J. Med. Gen. 89: 158–166. PRIUSKA, E. M. AND J. SCHACT (1997) Mecha-nism and prevention of aminoglycoside oto-toxicity: Outer hair cells as targets and tools. Ear, Nose, Throat J. 76: 164–171. 286 Chapter Twelve throughout the central auditory pathways. The earliest stage of central pro-cessing occurs at the cochlear nucleus, where the peripheral auditory infor-mation diverges into a number of parallel central pathways. Accordingly, the output of the cochlear nucleus has several targets. One of these is the supe-rior olivary complex, the first place that information from the two ears inter-acts and the site of the initial processing of the cues that allow listeners to localize sound in space. The cochlear nucleus also projects to the inferior col-liculus of the midbrain, a major integrative center and the first place where auditory information can interact with the motor system. The inferior col-liculus is an obligatory relay for information traveling to the thalamus and cortex, where additional integrative aspects (such as harmonic and temporal combinations) of sound especially germane to speech and music are processed (Box B). The large number of stations between the auditory periphery and the cortex far exceeds those in other sensory systems, provid-ing a hint that the perception of communication and environmental sounds Box B Music Even though we all recognize it when we hear it, the concept of music is vague. The Oxford English Dictionary defines it as “The art or science of combining vocal or instrumental sounds with a view toward beauty or coherence of form and expression of emotion.” In terms of the present chapter, music chiefly concerns the aspect of human audition that is experienced as tones. The stimuli that give rise to tonal percepts are periodic, meaning that they repeat systematically over time, as in the sine wave in Figure 12.1. Periodic stimuli, which do not occur naturally as sine waves but rather as complex repetitions involving a num-ber of different frequencies, give rise to a sense of harmony when sounded together in appropriate combinations, and a sense of melody when they occur sequentially. Although we usually take the way tone-evoking stimuli are heard for granted, this aspect of audition presents some profoundly puzzling qualities. The most obvious of these is that humans perceive periodic stimuli whose funda-mental frequencies have a 2:1 ratio as highly similar, and, for the most part, musically interchangeable. Thus in West-ern musical terminology, any two tones related by an interval of one or more octaves are given the same name (i.e., A, B, C…G), and are distinguished only by a qualifier that denotes relative ordinal position (e.g., C1, C2, C3, etc.). As a result, music is framed in repeating intervals (called octaves) defined by these more or less interchangeable tones. A key ques-tion, then, is why periodic sound stimuli whose fundamentals have a 2:1 ratio are perceived as similar when there is no obvious physical or physiological basis for this phenomenon. A second puzzling feature is that most if not all musical traditions subdi-vide octaves into a relatively small set of intervals for composition and perfor-mance, each interval being defined by its relationship to the lowest tone of the set. Such sets are called musical scales. The scales predominantly employed in all cultures over the centuries have used some (or occasionally all) of the 12 tonal intervals that in Western musical termi-nology are referred to as the chromatic scale (see figure). Moreover, some inter-vals of the chromatic scale, such as the fifth, the fourth, the major third, and the major sixth, are more often used in com-position and performance than others. These form the majority of the intervals employed in the pentatonic and diatonic major scales, the two most frequently used scales in music world-wide. Again, Illustration of 10 of the 12 tones in the chro-matic scale, related to a piano keyboard. The function above the keyboard indicates that these tones correspond statistically to peaks of power in normalized human speech. (After Schwartz et al., 2003.) is an especially intensive neural process. Furthermore, both the peripheral and central auditory system are “tuned” to conspecific communication vocalizations, pointing to the interdependent evolution of neural systems used for generating and perceiving these signals. The External Ear The external ear, which consists of the pinna, concha, and auditory meatus, gathers sound energy and focuses it on the eardrum, or tympanic mem-brane (Figure 12.3). One consequence of the configuration of the human auditory meatus is that it selectively boosts the sound pressure 30- to 100-fold for frequencies around 3 kHz via passive resonance effects. This ampli-fication makes humans especially sensitive to frequencies in the range of 2–5 kHz—and also explains why they are particularly prone to hearing loss near this frequency following exposure to loud broadband noises, such as those The Auditory System 287 there is no principled explanation of these preferences among all the possible intervals within the octave. Perhaps the most fundamental ques-tion in music—and arguably the com-mon denominator of all musical tonal-ity—is why certain combinations of tones are perceived as relatively consonant or ‘harmonious’ and others relatively disso-nant or ‘inharmonious’. These perceived differences among the possible combina-tions of tones making up the chromatic scale are the basis for polytonal music, in which the perception of relative harmo-niousness guides the composition of chords and melodic lines. The more com-patible of these combinations are typi-cally used to convey ‘resolution’ at the end of a musical phrase or piece, whereas less compatible combinations are used to indicate a transition, a lack of resolution, or to introduce a sense of tension in a chord or melodic sequence. Like octaves and scales, the reason for this phenome-nology remains a mystery. The classical approaches to rationaliz-ing octaves, scales and consonance have been based on the fact that the musical intervals corresponding to octaves, fifths, and fourths (in modern musical terminol-ogy) are produced by physical sources whose relative proportions (e.g., the rela-tive lengths of two plucked strings or their fundamental frequencies) have ratios of 2:1, 3:2, or 4:3, respectively (these relationships were first described by Pythagoras). This coincidence of numeri-cal simplicity and perceptual effect has been so impressive over the centuries that attempts to rationalize phenomena such as consonance and scale structure in terms of mathematical relationships have tended to dominate the thinking about these issues. This conceptual framework, however, fails to account for many of the perceptual observations that have been made over the last century. Another way to consider the problem is in terms of the biological rationale for evolving a sense of tonality in the first place. A pertinent fact in this regard is that only a small minority of naturally occurring sound stimuli are periodic. Since the auditory system evolved in the world of natural sounds, this point is presumably critical for thinking about the biological purposes of tonality and music. Indeed, the majority of periodic sounds that humans would have been exposed to during evolution are those made by the human vocal tract in the process of communication, initially pre-linguistic but more recently speech sounds (see Chapter 26). Thus develop-ing a sense of tonality would enable lis-teners to respond not only the distinc-tions among the different speech sounds that are important for understanding spoken language, but to information about the probable sex, age, and emo-tional state of the speaker. It may thus be that music reflects the advantage of facil-itating a listener’s ability to glean the lin-guistic intent and biological state of fel-low humans through vocal utterances. References BURNS, E. M. (1999) Intervals, scales, and tun-ing. In The Psychology of Music, D. Deutsch (ed.). New York: Academic Press, pp. 215–264. CARTERETTE, E. C. AND R. A. KENDALL (1999) Comparative music perception and cogni-tion. In The Psychology of Music, D. Deutsch (ed.). New York: Academic Press. LEWICKI, M. S. (2002) Efficient coding of nat-ural sounds. Nature Neurosci. 5: 356–363. PIERCE, J. R. (1983, 1992) The Science of Musical Sound. New York: W.H. Freeman and Co., Chapters 4–6. PLOMP, R. AND W. J. LEVELT (1965) Tonal con-sonance and critical bandwidth. J. Acoust. Soc. Amer. 28: 548–560. RASCH, R. AND R. PLOMP (1999) The percep-tion of musical tones. In The Psychology of Music, D. Deutsch (ed.). New York: Academic Press, pp. 89–112. SCHWARTZ, D. A., C. Q. HOWE AND D. PURVES (2003) The statistical structure of human speech sounds predicts musical universals. J. Neurosci. 23: 7160–7168. TERHARDT, E. (1974) Pitch, consonance, and harmony. J. Acoust. Soc. Amer. 55: 1061–1069. 288 Chapter Twelve generated by heavy machinery or high explosives (see Box A). The sensitiv-ity to this frequency range in the human auditory system appears to be directly related to speech perception: although human speech is a broad-band signal, the energy of the plosive consonants (e.g., ba and pa) that distin-guish different phonemes (the elementary human speech sounds) is concen-trated around 3 kHz (see Box A in Chapter 26). Therefore, selective hearing loss in the 2–5 kHz range disproportionately degrades speech recognition. Most vocal communication occurs in the low-kHz range to overcome envi-ronmental noise; as already noted, generation of higher frequencies is diffi-cult for animals the size of humans. A second important function of the pinna and concha is to selectively fil-ter different sound frequencies in order to provide cues about the elevation of the sound source. The vertically asymmetrical convolutions of the pinna are shaped so that the external ear transmits more high-frequency compo-nents from an elevated source than from the same source at ear level. This effect can be demonstrated by recording sounds from different elevations after they have passed through an “artificial” external ear; when the recorded sounds are played back via earphones, so that the whole series is at the same elevation relative to the listener, the recordings from higher eleva-tions are perceived as coming from positions higher in space than the record-ings from lower elevations. Outer ear Pinna Bone Semicircular canals Stapes Incus Malleus Stapes Incus Malleus Tympanic membrane Tympanic membrane Base of stapes in oval window Round window Vestibule Cochlea Eustachian tube Oval window Vestibular nerve Cochlear nerve Concha External auditory meatus Middle ear Inner ear Figure 12.3 The human ear. Note the large surface area of the tympanic mem-brane (eardrum) relative to the oval win-dow, a feature that facilitates transmis-sion of airborne sounds to the fluid-filled cochlea. The Middle Ear Sounds impinging on the external ear are airborne; however, the environ-ment within the inner ear, where the sound-induced vibrations are con-verted to neural impulses, is aqueous. The major function of the middle ear is to match relatively low-impedance airborne sounds to the higher-imped-ance fluid of the inner ear. The term “impedance” in this context describes a medium’s resistance to movement. Normally, when sound waves travel from a low-impedance medium like air to a much higher-impedance medium like water, almost all (more than 99.9%) of the acoustical energy is reflected. The middle ear (see Figure 12.3) overcomes this problem and ensures transmis-sion of the sound energy across the air–fluid boundary by boosting the pres-sure measured at the tympanic membrane almost 200-fold by the time it reaches the inner ear. Two mechanical processes occur within the middle ear to achieve this large pressure gain. The first and major boost is achieved by focusing the force impinging on the relatively large-diameter tympanic membrane on to the much smaller-diameter oval window, the site where the bones of the middle ear contact the inner ear. A second and related process relies on the mechanical advantage gained by the lever action of the three small intercon-nected middle ear bones, or ossicles (i.e., the malleus, incus, and stapes; see Figure 12.3), which connect the tympanic membrane to the oval window. Conductive hearing losses, which involve damage to the external or middle ear, lower the efficiency at which sound energy is transferred to the inner ear and can be partially overcome by artificially boosting sound pressure levels with an external hearing aid (Box C). In normal hearing, the efficiency of sound transmission to the inner ear also is regulated by two small muscles in the middle ear, the tensor tympani, innervated by cranial nerve V, and the stapedius, innervated by cranial nerve VII (see Appendix A). Flexion of these muscles, which is triggered automatically by loud noises or during self-gen-erated vocalization, stiffens the ossicles and reduces the amount of sound energy transmitted to the cochlea, serving to protect the inner ear. Con-versely, conditions that lead to flaccid paralysis of either of these muscles, such as Bell’s palsy (nerve VII), can trigger a painful sensitivity to moderate or even low intensity sounds known as hyperacusis. Bony and soft tissues, including those surrounding the inner ear, have impedances close to that of water. Therefore, even without an intact tym-panic membrane or middle ear ossicles, acoustical vibrations can still be transferred directly through the bones and tissues of the head to the inner ear. In the clinic, bone conduction can be exploited using a simple test involving a tuning fork to determine whether hearing loss is due to conduc-tive problems or is due to damage to the hair cells of the inner ear or to the auditory nerve itself (sensorineural hearing loss; see Boxes A and C) The Inner Ear The cochlea of the inner ear is arguably the most critical structure in the auditory pathway, for it is there that the energy from sonically generated pressure waves is transformed into neural impulses. The cochlea not only amplifies sound waves and converts them into neural signals, but it also acts as a mechanical frequency analyzer, decomposing complex acoustical wave-forms into simpler elements. Many features of auditory perception derive from aspects of the physical properties of the cochlea; hence, it is important to consider this structure in some detail. The Auditory System 289 290 Chapter Twelve The cochlea (from the Latin for “snail”) is a small (about 10 mm wide) coiled structure, which, were it uncoiled, would form a tube about 35 mm long (Figures 12.4 and 12.5). Both the oval window and, the round window, another region where the bone is absent surrounding the cochlea, are at the basal end of this tube. The cochlea is bisected from its basal almost to its api-cal end by the cochlear partition, which is a flexible structure that supports the basilar membrane and the tectorial membrane. There are fluid-filled chambers on each side of the cochlear partition, named the scala vestibuli and the scala tympani; a distinct channel, the scala media, runs within the Box C Sensorineural Hearing Loss and Cochlear Implants The same features that make the audi-tory periphery exquisitely sensitive to detecting airborne sounds also make it highly vulnerable to damage. By far the most common forms of hearing loss involve the peripheral auditory system, namely to those structures that transmit and transduce sounds into neural impulses. Monaural hearing deficits are the defining symptom of a peripheral hearing loss, because unilateral damage at or above the auditory brainstem results in a binaural deficit (due to the extensive bilateral organization of the central auditory system). Peripheral hearing insults can be further divided into conductive hearing losses, which involve damage to the outer or middle ear, and sensorineural hearing losses, which stem from damage to the inner ear, most typically the cochlear hair cells or the VIIIth nerve itself. Although both forms of peripheral hearing loss manifest themselves as a raised threshold for hearing on the affected side, their diag-noses and treatments differ. Conductive hearing loss can be due to occlusion of the ear canal by wax or for-eign objects, rupture of the tympanic membrane itself, or arthritic ossification of the middle ear bones. In contrast, sen-sorineural hearing loss usually is due to congenital or environmental insults that lead to hair cell death (see Box A) or damage to the eighth nerve. As hair cells are relatively few in number and do not regenerate in humans, their depletion leads to a diminished ability to detect sounds. The Weber test, a simple test involving a tuning fork, can be used to distinguish between these two forms of hearing loss. If a resonating tuning fork (∼256 Hz) is placed on the vertex, a patient with conductive hearing loss will report that the sound is louder in the affected ear. In the “plugged” state, sounds propagating through the skull do not dissipate so freely back out through the auditory meatus, and thus a greater amount of sound energy is transmitted to the cochlea on the blocked side. In contrast, a patient with a monaural sen-sorineural hearing loss will report that a Weber test sounds louder on the intact side, because even though the inner ear may vibrate equally on the two sides, the damaged side cannot transduce this vibration into a neural signal. Treatment also differs for these two types of deafness. An external hearing aid is used to boost sounds to compen-sate for the reduced efficiency of the con-ductive apparatus in conductive hearing losses. These miniature devices are inserted in the ear canal, and contain a microphone and speaker, as well as an amplifier. One limitation of hearing aids is that they often provide rather flat amplification curves, which can interfere with listening in noisy environments; moreover, they do not achieve a high degree of directionality. The use of digi-tal signal processing strategies partly overcomes these problems, and hearing aids obviously provide significant bene-fits to many people. The treatment of sensorineural hear-ing loss is more complicated and inva-sive; conventional hearing aids are use-less, because no amount of mechanical amplification can compensate for the inability to generate or convey a neural impulse from the cochlea. However, if the VIIIth nerve is intact, cochlear implants can be used to partially restore hearing. The cochlear implant consists of a peripherally mounted microphone and digital signal processor that transforms a sound into its spectral components, and additional electronics that use this infor-mation to activate different combinations of contacts on a threadlike multi-site stimulating electrode array. The electrode is inserted into the cochlea through the round window (see figure) and posi-tioned along the length of the tonotopi-cally organized basilar membrane and VIIIth nerve endings. This placement enables electrical stimulation of the nerve in a manner that mimics some aspects of the spectral decomposition naturally performed by the cochlea. Cochlear implants can be remarkably effective in restoring hearing to people with hair cell damage, permitting them to engage in spoken communication. Despite such success in treating those who have lost their hearing after having cochlear partition. The cochlear partition does not extend all the way to the apical end of the cochlea; instead there is an opening, known as the heli-cotrema, that joins the scala vestibuli to the scala tympani, allowing their fluid, known as perilymph, to mix. One consequence of this structural arrangement is that inward movement of the oval window displaces the fluid of the inner ear, causing the round window to bulge out slightly and deforming the cochlear partition. The manner in which the basilar membrane vibrates in response to sound is the key to understanding cochlear function. Measurements of the vibra-The Auditory System 291 Cable to speech processor Electrode array Round window Round window Cochlea Auditory nerve Implantable cochlear stimulator Microphone Headpiece Acoronal section at the level of the auditory meatus shows the components of the cochlear implant, including the filamentous stimulatory electrode inserted into the cochlea through the round window. learned to speak, whether cochlear implants can enable development of spo-ken language in the congenitally deaf is still a matter of debate. Although cochlear implants cannot help patients with VIIIth nerve damage, brainstem implants are being developed that use a conceptually similar approach to stimu-late the cochlear nuclei directly, bypass-ing the auditory periphery altogether. References RAMSDEN, R. T. (2002) Cochlear implants and brain stem implants. Brit. Med. Bull. 63: 183–193. RAUSCHECKER, J. P. AND R. V. SHANNON (2002) Sending sound to the brain. Science. 295: 1025–1029. 292 Chapter Twelve tion of different parts of the basilar membrane, as well as the discharge rates of individual auditory nerve fibers that terminate along its length, show that both these features are highly tuned; that is, they respond most intensely to a sound of a specific frequency. Frequency tuning within the inner ear is attributable in part to the geometry of the basilar membrane, which is wider and more flexible at the apical end and narrower and stiffer at the basal end. One feature of such a system is that regardless of where energy is supplied to it, movement always begins at the stiff end (i.e., the base), and then prop-agates to the more flexible end (i.e., the apex). Georg von Békésy, working at Harvard University, showed that a membrane that varies systematically in its width and flexibility vibrates maximally at different positions as a func-tion of the stimulus frequency (Figure 12.5). Using tubular models and human cochleas taken from cadavers, he found that an acoustical stimulus initiates a traveling wave of the same frequency in the cochlea, which prop-agates from the base toward the apex of the basilar membrane, growing in Inner hair cells Outer hair cells Cochlea Cross section of cochlea Auditory nerve Vestibular nerve Spiral ganglion Scala media Scala vestibuli Basilar membrane Scala tympani Round window Oval window Cochlea Auditory nerve Stereocilia Organ of Corti Inner hair cells Afferent axons Tectorial membrane Basilar membrane Tunnel of Corti Outer hair cells Stereocilia of outer hair cells Stereocilia of inner hair cells Efferent axons Tectorial membrane Figure 12.4 The cochlea, viewed face-on (upper left) and in cross sec-tion (subsequent panels). The stapes transfers force from the tympanic membrane to the oval window. The cross section of the cochlea shows the scala media between the scalae vestibuli and tympani. Blowup of the organ of Corti shows that the hair cells are located between the basilar and tectorial membranes; the latter is rendered transparent in the line drawing and removed in the scanning electron micrograph. The hair cells are named for their tufts of stereocilia; inner hair cells receive afferent inputs from cranial nerve VIII, whereas outer hair cells receive mostly efferent input. (Micrograph from Kessel and Kardon, 1979.) amplitude and slowing in velocity until a point of maximum displacement is reached. This point of maximal displacement is determined by the sound frequency. The points responding to high frequencies are at the base of the basilar membrane where it is stiffer, and the points responding to low fre-quencies are at the apex, giving rise to a topographical mapping of frequency (that is, to tonotopy). An important feature is that complex sounds cause a pattern of vibration equivalent to the superposition of the vibrations gener-ated by the individual tones making up that complex sound, thus account-ing for the decompositional aspects of cochlear function mentioned earlier. This process of spectral decomposition appears to be an important strategy for detecting the various harmonic combinations that distinguish different natural sounds. Indeed, tonotopy is conserved throughout much of the audi-tory system, including the auditory cortex, suggesting that it is important to speech processing. Von Békésy’s model of cochlear mechanics was a passive one, resting on the premise that the basilar membrane acts like a series of linked resonators, much as a concatenated set of tuning forks. Each point on the basilar mem-brane was postulated to have a characteristic frequency at which it vibrated most efficiently; because it was physically linked to adjacent areas of the membrane, each point also vibrated (if somewhat less readily) at other fre-quencies, thus permitting propagation of the traveling wave. It is now clear, however, that the tuning of the auditory periphery, whether measured at the basilar membrane or recorded as the electrical activity of auditory nerve fibers, is too sharp to be explained by passive mechanics alone. At very low sound intensities, the basilar membrane vibrates one hundred-fold more than would be predicted by linear extrapolation from the motion measured at high intensities. Therefore, the ear’s sensitivity arises from an active bio-mechanical process, as well as from its passive resonant properties (Box D). The outer hair cells, which together with the inner hair cells comprise the The Auditory System 293 Relative amplitude 10 0 20 30 Distance from stapes (mm) 200 Hz 100 Hz 50 Hz 25 Hz 1600 Hz 800 Hz 400 Hz Cochlea Round window Stapes on oval window “Uncoiled” cochlea Scala tympani Traveling wave Cochlear base Scala vestibuli Basilar membrane Cochlear apex Apex is “tuned” for low frequencies Base of basilar membrane is “tuned” for high frequencies Helicotrema 1 2 3 4 5 6 7 1 2 3 4 5 6 7 Figure 12.5 Traveling waves along the cochlea. A traveling wave is shown at a given instant along the cochlea, which has been uncoiled for clarity. The graphs on the right profile the amplitude of the traveling wave along the basilar mem-brane for different frequencies and show that the position (i.e., 1–7) where the traveling wave reaches its maximum amplitude varies directly with the fre-quency of stimulation. (Drawing after Dallos, 1992; graphs after von Békésy, 1960.) 294 Chapter Twelve sensory cells of the inner ear, are the most likely candidates for driving this active process. The motion of the traveling wave initiates sensory transduction by dis-placing the hair cells that sit atop the basilar membrane. Because these struc-tures are anchored at different positions, the vertical component of the trav-eling wave is translated into a shearing motion between the basilar membrane and the overlying tectorial membrane (Figure 12.6). This motion bends the tiny processes, called stereocilia, that protrude from the apical ends of the hair cells, leading to voltage changes across the hair cell mem-brane. How the bending of stereocilia leads to receptor potentials in hair cells is considered in the following section. Hair Cells and the Mechanoelectrical Transduction of Sound Waves The hair cell is an evolutionary triumph that solves the problem of trans-forming vibrational energy into an electrical signal. The scale at which the Box D The Sweet Sound of Distortion As early as the first half of the eighteenth century, musical composers such as G. Tartini and W. A. Sorge discovered that upon playing pairs of tones, other tones not present in the original stimulus are also heard. These combination tones, fc, are mathematically related to the played tones f1 and f2 (f2 > f1) by the formula fc = mf1 ± nf2 where m and n are positive integers. Combination tones have been used for a variety of compositional effects, as they can strengthen the harmonic texture of a chord. Furthermore, organ builders sometimes use the difference tone (f2 – f1) created by two smaller organ pipes to produce the extremely low tones that would otherwise require building one especially large pipe. Modern experiments suggest that this distortion product is due at least in part to the nonlinear properties of the inner ear. M. Ruggero and his colleagues placed small glass beads (10–30 mm in diameter) on the basilar membrane of an anesthetized animal and then deter-mined the velocity of the basilar mem-brane in response to different combina-tions of tones by measuring the Doppler shift of laser light reflected from the beads. When two tones were played into the ear, the basilar membrane vibrated not only at those two frequencies, but also at other frequencies predicted by the above formula. Related experiments on hair cells studied in vitro suggest that these non-linearities result from the properties of the mechanical linkage of the transduc-tion apparatus. By moving the hair bun-dle sinusoidally with a metal-coated glass fiber, A. J. Hudspeth and his co-workers found that the hair bundle exerts a force at the same frequency. However, when two sinusoids were applied simultaneously, the forces exerted by the hair bundle occurred not only at the primary frequencies, but at several combination frequencies as well. These distortion products are due to the transduction apparatus, since blocking the transduction channels causes the forces exerted at the combination fre-quencies to disappear, even though the forces at the primary frequencies remain unaffected. It seems that the tip links add a certain extra springiness to the hair bundle in the small range of motions over which the transduction channels are changing between closed and open states. If nonlinear distortions of basilar membrane vibrations arise from the properties of the hair bundle, then it is likely that hair cells can indeed influence basilar membrane motion, thereby accounting for the cochlea’s extreme sen-sitivity. When we hear difference tones, we may be paying the price in distortion for an exquisitely fast and sensitive transduction mechanism. References JARAMILLO, F., V. S. MARKIN AND A. J. HUD-SPETH (1993) Auditory illusions and the single hair cell. Nature 364: 527–529. PLANCHART, A. E. (1960) A study of the theo-ries of Giuseppe Tartini. J. Music Theory 4: 32–61. ROBLES, L., M. A. RUGGERO AND N. C. RICH (1991) Two-tone distortion in the basilar membrane of the cochlea. Nature 439: 413–414. The Auditory System 295 Figure 12.6 Movement of the basilar membrane creates a shearing force that bends the stereocilia of the hair cells. The pivot point of the basilar membrane is off-set from the pivot point of the tectorial membrane, so that when the basilar mem-brane is displaced, the tectorial membrane moves across the tops of the hair cells, bending the stereocilia. (A) Resting position Downward phase Upward phase Shear force Shear force (B) Sound-induced vibration Basilar membrane Inner hair cell Tectorial membrane Outer hair cells Pivot points for tectorial and basilar membranes are offset 296 Chapter Twelve hair cell operates is truly amazing: At the limits of human hearing, hair cells can faithfully detect movements of atomic dimensions and respond in the tens of microseconds! Furthermore, hair cells can adapt rapidly to constant stimuli, thus allowing the listener to extract signals from a noisy back-ground. The hair cell is a flask-shaped epithelial cell named for the bundle of hair-like processes that protrude from its apical end into the scala media. Each hair bundle contains anywhere from 30 to a few hundred hexagonally arranged stereocilia, with one taller kinocilium (Figure 12.7A). Despite their names, only the kinocilium is a true ciliary structure, with the characteristic two central tubules surrounded by nine doublet tubules that define cilia (Fig-ure 12.7B). The function of the kinocilium is unclear, and in the cochlea of humans and other mammals it actually disappears shortly after birth (Figure 12.7C). The stereocilia are simpler, containing only an actin cytoskeleton. Each stereocilium tapers where it inserts into the apical membrane, forming a hinge about which each stereocilium pivots (Figure 12.7D). The stereocilia are graded in height and are arranged in a bilaterally symmetric fashion (in vestibular hair cells, this plane runs through the kinocilium). Displacement of the hair bundle parallel to this plane toward the tallest stereocilia depolarizes the hair cell, while movements parallel to this plane toward the shortest stere-ocilia cause hyperpolarization. In contrast, displacements perpendicular to the plane of symmetry do not alter the hair cell’s membrane potential. The hair bundle movements at the threshold of hearing are approximately 0.3 nm, about the diameter of an atom of gold. Hair cells can convert the displace-ment of the stereociliary bundle into an electrical potential in as little as 10 microseconds; as described below, such speed is required for the accurate localization of the source of the sound. The need for microsecond resolution places certain constraints on the transduction mechanism, ruling out the rela-(C) (B) (D) (A) Figure 12.7 The structure and function of the hair bundle in vestibular and cochlear hair cells. The vestibular hair bundles shown here resemble those of cochlear hair cells, except for the pres-ence of the kinocilium, which disap-pears in the mammalian cochlea shortly after birth. (A) The hair bundle of a guinea pig vestibular hair cell. This view shows the increasing height lead-ing to the kinocilium (arrow). (B) Cross section through the vestibular hair bun-dle shows the 9 + 2 array of micro-tubules in the kinocilium (top), which contrasts with the simpler actin filament structure of the stereocilia. (C) Scanning electron micrograph of a guinea pig cochlear outer hair cell bundle viewed along the plane of mirror symmetry. Note the graded lengths of the stere-ocilia, and the absence of a kinocilium. (D) Tip links that connect adjacent stere-ocilia are believed to be the mechanical linkage that opens and closes the trans-duction channel. (A from Lindeman, 1973; B from Hudspeth, 1983; C from Pickles, 1988; D from Fain, 2003.) Figure 12.8 Mechanoelectrical trans-duction mediated by hair cells. (A,B) When the hair bundle is deflected toward the tallest stereocilium, cation-selective channels open near the tips of the stereocilia, allowing K+ ions to flow into the hair cell down their electro-chemical gradient (see text on next page for the explanation of this peculiar situ-ation). The resulting depolarization of the hair cell opens voltage-gated Ca2+ channels in the cell soma, allowing cal-cium entry and release of neurotrans-mitter onto the nerve endings of the auditory nerve. (After Lewis and Hud-speth, 1983) tively slow second messenger pathways used in visual and olfactory trans-duction (see Chapters 7, 10, and 14); a direct, mechanically gated transduc-tion channel is needed to operate this quickly. Evidently the filamentous structures that connect the tips of adjacent stereocilia, known as tip links, directly open cation-selective transduction channels when stretched, allowing K+ ions to flow into the cell (see Figure 12.7D). As the linked stereocilia pivot from side to side, the tension on the tip link varies, modulating the ionic flow and resulting in a graded receptor potential that follows the movements of the stereocilia (Figures 12.8 and 12.9). The tip link model also explains why only deflections along the axis of the hair bundle activate transduction chan-nels, since tip links join adjacent stereocilia along the axis directed toward the tallest stereocilia (see also Box B in Chapter 13). The exquisite mechanical sen-sitivity of the stereocilia also presents substantial risks: high intensity sounds can shear off the hair bundle, resulting in profound hearing deficits. Because human stereocilia, unlike those in fishes and birds, do not regenerate such damage is irreversible. The small number of hair cells (a total of about 30,000 in a human, or 15,000 per ear) further compounds the sensitivity of the inner The Auditory System 297 (B) (A) K+ Depolarization Ca2+ Ca2+ K+ Transmitter To brain Afferent nerve Vesicles Depolarization Nucleus K+ Ca2+ channel K+ Transmitter To brain Afferent nerve Vesicles Nucleus Hyperpolarization 298 Chapter Twelve ear to environmental and genetic insults. An important goal of current research is to identify the stem cells and factors that could contribute to the regeneration of human hair cells, thus affording a possible therapy for some forms of sensorineural hearing loss. Understanding the ionic basis of hair cell transduction has been greatly advanced by intracellular recordings made from these tiny structures. The hair cell has a resting potential between –45 and –60 mV relative to the fluid that bathes the basal end of the cell. At the resting potential, only a small frac-tion of the transduction channels are open. When the hair bundle is displaced in the direction of the tallest stereocilium, more transduction channels open, causing depolarization as K+ enters the cell. Depolarization in turn opens voltage-gated calcium channels in the hair cell membrane, and the resultant Ca2+ influx causes transmitter release from the basal end of the cell onto the auditory nerve endings (Figure 12.8A,B). Such calcium-dependent exocytosis is similar to chemical neurotransmission elsewhere in the central and periph-eral nervous system (see Chapters 5 and 6); thus the hair cell has become a useful model for studying calcium-dependent transmitter release. Because some transduction channels are open at rest, the receptor potential is bipha-sic: Movement toward the tallest stereocilia depolarizes the cell, while move-0 10 20 30 40 Time (ms) 50 60 70 (C) (A) 25 mV a.c. component d.c. component 2000 1000 900 700 500 300 3000 4000 5000 (B) 10 5 0 0 –5 –1 1 2 –2 –10 15 Membrane potential Displacement Receptor potentials (mV) Hair bundle displacement (µm) 0° 0° 0° 0° 90° 90° 90° Time Figure 12.9 Mechanoelectrical trans-duction mediated by vestibular hair cells. (A) Vestibular hair cell receptor potentials (bottom three traces; blue) measured in response to symmetrical displacement (top trace; yellow) of the hair bundle about the resting position, either parallel (0°) or orthogonal (90°) to the plane of bilateral symmetry. (B) The asymmetrical stimulus/response (x-axis/y-axis) function of the hair cell. Equivalent displacements of the hair bundle generate larger depolarizing responses than hyperpolarizing responses because most transduction channels are closed “at rest” (i.e., 0 µm). (C) Receptor potentials generated by an individual hair cell in the cochlea in response to pure tones (indicated in Hz, right). Note that the hair cell potential faithfully follows the waveform of the stimulating sinusoids for low frequen-cies (< 3kHz), but still responds with a DC offset to higher frequencies. (A after Shotwell et al., 1981; B after Hudspeth and Corey, 1977; C after Palmer and Russell, 1986.) ment in the opposite direction leads to hyperpolarization. This situation allows the hair cell to generate a sinusoidal receptor potential in response to a sinusoidal stimulus, thus preserving the temporal information present in the original signal up to frequencies of around 3 kHz (Figure 12.9). Hair cells still can signal at frequencies above 3 kHz, although without preserving the exact temporal structure of the stimulus: the asymmetric displacement-receptor current function of the hair cell bundle is filtered by the cell’s membrane time constant to produce a tonic depolarization of the soma, augmenting transmit-ter release and thus exciting VIIIth nerve terminals. The high-speed demands of mechanoelectrical transduction have resulted in some impressive ionic specializations within the inner ear. An unusual adaptation of the hair cell in this regard is that K+ serves both to depolarize and repolarize the cell, enabling the hair cell’s K+ gradient to be largely main-tained by passive ion movement alone. As with other epithelial cells, the basal and apical surfaces of the hair cell are separated by tight junctions, allowing separate extracellular ionic environments at these two surfaces. The apical end (including the stereocilia) protrudes into the scala media and is exposed to the K+-rich, Na+-poor endolymph, which is produced by dedi-cated ion pumping cells in the stria vascularis (Figure 12.10). The basal end of the hair cell body is bathed in the same fluid that fills the scala tympani, the perilymph, which resembles other extracellular fluids in that it is K+-poor and Na+-rich. In addition, the compartment containing endolymph is about 80 mV more positive than the perilymph compartment (this difference is known as the endocochlear potential), while the inside of the hair cell is about 45 mV more negative than the perilymph (and 125 mV more negative than the endolymph). The resulting electrical gradient across the membrane of the stereocilia (about 125 mV; the difference between the hair cell resting potential and the endocochlear potential) drives K+ through open transduc-The Auditory System 299 Outer hair cells Spiral ganglion Perilymph Low K+ 0 mV Inner hair cells –45 mV Scala vestibuli Scala tympani Basilar membrane Stria vascularis Tectorial membrane Endolymph High K+ 80 mV Scala media Tunnel of Corti Figure 12.10 The stereocilia of the hair cells protrude into the endolymph, which is high in K+ and has an electrical potential of +80 mV relative to the perilymph. 300 Chapter Twelve tion channels into the hair cell, even though these cells already have a high internal K+ concentration. K+ entry via the transduction channels electroton-ically depolarizes the hair cell, opening voltage-gated Ca2+ and K+ channels located in the membrane of the hair cell soma (see Box B in Chapter 13). The opening of somatic K+ channels favors K+ efflux, and thus repolarization; the efflux occurs because the perilymph surrounding the basal end is low in K+ relative to the cytosol, and because the equilibrium potential for K+ is more negative than the hair cell’s resting potential (EKBasal ≈ –85 mV). Repolariza-tion of the hair cell via K+ efflux is also facilitated by Ca2+ entry. In addition to modulating the release of neurotransmitter, Ca2+ entry opens Ca2+-depen-dent K+ channels, which provide another avenue for K+ to enter the peri-lymph. Indeed, the interaction of Ca2+ influx and Ca2+-dependent K+ efflux can lead to electrical resonances that enhance the tuning of response proper-ties within the inner ear (also explained in Box B in Chapter 13). In essence, the hair cell operates as two distinct compartments, each dominated by its own Nernst equilibrium potential for K+; this arrangement ensures that the hair cell’s ionic gradient does not run down, even during prolonged stimula-tion. At the same time, rupture of Reissner’s membrane, which normally separates the scalae media and vestibuli, or compounds such as ethacrynic acid (see Box A), which selectively poison the ion-pumping cells of the stria vascularis, can cause the endocochlear potential to dissipate, resulting in a sensorineural hearing deficit. In short, the hair cell exploits the different ionic milieus of its apical and basal surfaces to provide extremely fast and energy-efficient repolarization. Two Kinds of Hair Cells in the Cochlea The cochlear hair cells in humans consist of one row of inner hair cells and three rows of outer hair cells (see Figure 12.4). The inner hair cells are the actual sensory receptors, and 95% of the fibers of the auditory nerve that project to the brain arise from this subpopulation. The terminations on the outer hair cells are almost all from efferent axons that arise from cells in the superior olivary complex. A clue to the significance of this efferent pathway was provided by the discovery that an active process within the cochlea, as mentioned, influences basilar membrane motion. First, it was found that the cochlea actually emits sound under certain conditions. These otoacoustical emissions can be detected by placing a sensitive microphone at the eardrum and monitoring the response after briefly presenting a tone or click, and provide a useful means to assess cochlear function in the newborn (this test is now done rou-tinely to rule out congenital deafness). Such emissions can also occur spon-taneously, especially in certain pathological states, and are thus one potential source of tinnitus (ringing in the ears). These observations clearly indicate that a process within the cochlea is capable of producing sound. Second, stimulation of the crossed olivocochlear bundle, which supplies efferent input to the outer hair cells, can broaden VIIIth nerve tuning curves. Third, the high sensitivity notch of VIIIth nerve tuning curves is lost when the outer hair cells are selectively inactivated. Finally, isolated outer hair cells contract and expand in response to small electrical currents, thus providing a potential source of energy to drive an active process within the cochlea. Thus, it seems likely that the outer hair cells sharpen the frequency-resolv-ing power of the cochlea by actively contracting and relaxing, thus changing the stiffness of the tectorial membrane at particular locations. This active process explains the nonlinear vibration of the basilar membrane at low sound intensities (see Box D). Tuning and Timing in the Auditory Nerve The rapid response time of the transduction apparatus allows the membrane potential of the hair cell to follow deflections of the hair bundle up to mod-erately high frequencies of oscillation. In humans, the receptor potentials of certain hair cells and the action potentials of their associated auditory nerve fiber can follow stimuli of up to about 3 kHz in a one-to-one fashion. Such real-time encoding of stimulus frequency by the pattern of action potentials in the auditory nerve is known as the “volley theory” of auditory informa-tion transfer. Even these extraordinarily rapid processes, however, fail to fol-low frequencies above 3 kHz (see Figure 12.9). Accordingly, some other mechanism must be used to transmit auditory information at higher fre-quencies. The tonotopically organized basilar membrane provides an alter-native to temporal coding, namely a “labeled-line” coding mechanism. In this case, frequency information is specified by preserving the tonotopy of the cochlea at higher levels in the auditory pathway. Because the auditory nerve fibers associate with the inner hair cells in approximately a one-to-one ratio (although several or more VIIIth nerve fibers synapse on a single hair cell), each auditory nerve fiber transmits information about only a small part of the audible frequency spectrum. As a result, auditory nerve fibers related to the apical end of the cochlea respond to low frequencies, and fibers that are related to the basal end respond to high frequencies (see Figure 12.5). The limitations of specific fibers can be seen in electrophysiological record-ings of responses to sound (Figure 12.11). These threshold functions are called tuning curves, and the lowest threshold of the tuning curve is called the characteristic frequency. Since the topographical order of the character-istic frequency of neurons is retained throughout the system, information about frequency is also preserved. Cochlear implants (see Box C) exploit the tonotopic organization of the cochlea, and particularly its eighth nerve affer-ents, to roughly recreate the patterns of VIIIth nerve activity elicited by sounds. In patients with damaged hair cells, such implants can effectively bypass the impaired transduction apparatus, and thus restore some degree of auditory function. The other prominent feature of hair cells—their ability to follow the wave-form of low-frequency sounds—is also important in other more subtle aspects of auditory coding. As mentioned earlier, hair cells have biphasic response properties. Because hair cells release transmitter only when depo-larized, auditory nerve fibers fire only during the positive phases of low-fre-quency sounds (see Figure 12.11). The resultant “phase locking” that results provides temporal information from the two ears to neural centers that com-pare interaural time differences. The evaluation of interaural time differences provides a critical cue for sound localization and the perception of auditory “space.” That auditory space can be perceived is remarkable, given that the cochlea, unlike the retina, cannot represent space directly. A final point is that VIIIth nerve activity patterns are not simply faithful neural replicas of the auditory stimulus itself. Indeed, William Bialek and his colleagues at Princeton University have shown that the VIIIth nerve in the bullfrog encodes conspecific mating calls more efficiently than artificial sounds with similar frequency and amplitude characteristics. Thus both animal and human studies support the idea that the auditory periphery is optimized to The Auditory System 301 302 Chapter Twelve −20 −80 −20 −80 −20 −80 −20 −80 −20 −80 −20 −80 0.1 Frequency (kHz) 1.0 10.0 Threshold intensity (relative dB) required to stimulate unit above spontaneous firing rate (A) (B) (C) Spikes/second −80 −60 −40 0.1 Frequency (kHz) 1.0 10.0 Cochlea Basilar membrane Cranial nerve VIII Apex: Low frequencies Base: High frequencies Figure 12.11 Response properties of auditory nerve fibers. (A) Frequency tuning curves of six different fibers in the auditory nerve. Each graph plots, across all fre-quencies to which the fiber responds, the minimum sound level required to increase the fiber’s firing rate above its spontaneous firing level. The lowest point in the plot is the weakest sound intensity to which the neuron will respond. The frequency at this point is called the neuron’s characteristic frequency. (B) The frequency tuning curves of auditory nerve fibers superimposed and aligned with their approximate relative points of innervation along the basilar membrane. (In the side view schematic, the basilar membrane is represented as a black line within the unrolled cochlea.) (C) Temporal response patterns of a low-frequency axon in the auditory nerve. The stimulus waveform is indicated beneath the histograms, which show the phase-locked responses to a 50-ms tone pulse of 260 Hz. Note that the spikes are all timed to the same phase of the sinusoidal stimulus. (A after Kiang and Moxon, 1972; C after Kiang, 1984.) transmit species-typical vocal sounds, rather than simply transmitting all sounds equally well to central auditory areas. How Information from the Cochlea Reaches Targets in the Brainstem A hallmark of the ascending auditory system is its parallel organization. This arrangement becomes evident as soon as the auditory nerve enters the brainstem, where it branches to innervate the three divisions of the cochlear nucleus. The auditory nerve (the major component of cranial nerve VIII) comprises the central processes of the bipolar spiral ganglion cells in the cochlea (see Figure 12.4); each of these cells sends a peripheral process to contact one inner hair cell and a central process to innervate the cochlear nucleus. Within the cochlear nucleus, each auditory nerve fiber branches, sending an ascending branch to the anteroventral cochlear nucleus and a descending branch to the posteroventral cochlear nucleus and the dorsal cochlear nucleus (Figure 12.12). The tonotopic organization of the cochlea is maintained in the three parts of the cochlear nucleus, each of which contains different populations of cells with quite different properties. In addition, the patterns of termination of the auditory nerve axons differ in density and type; thus, there are several opportunities at this level for transformation of the information from the hair cells. Integrating Information from the Two Ears Just as the auditory nerve branches to innervate several different targets in the cochlear nuclei, the neurons in these nuclei give rise to several different pathways (see Figure 12.12). One clinically relevant feature of the ascending projections of the auditory brainstem is a high degree of bilateral connectiv-ity, which means that damage to central auditory structures is almost never manifested as a monaural hearing loss. Indeed, monaural hearing loss strongly implicates unilateral peripheral damage, either to the middle or inner ear, or to the VIIIth nerve itself (see Box C). Given the relatively byzan-tine organization already present at the level of the auditory brainstem, it is useful to consider these pathways in the context of their functions. The best-understood function mediated by the auditory brainstem nuclei, and certainly the one most intensively studied, is sound localization. Humans use at least two different strategies to localize the horizontal posi-tion of sound sources, depending on the frequencies in the stimulus. For fre-quencies below 3 kHz (which can be followed in a phase-locked manner), interaural time differences are used to localize the source; above these fre-quencies, interaural intensity differences are used as cues. Parallel pathways originating from the cochlear nucleus serve each of these strategies for sound localization. The human ability to detect interaural time differences is remarkable. The longest interaural time differences, which are produced by sounds arising directly lateral to one ear, are on the order of only 700 microseconds (a value given by the width of the head divided by the speed of sound in air, about 340 m/s). Psychophysical experiments show that humans can actually detect interaural time differences as small as 10 microseconds; two sounds presented through earphones separated by such small interaural time differ-ences are perceived as arising from the side of the leading ear. This sensitiv-ity translates into accuracy for sound localization of about 1 degree. The Auditory System 303 304 Chapter Twelve Mid-pons Rostral midbrain Caudal midbrain Pons- midbrain junction Rostral medulla Cerebrum Primary auditory cortex Nucleus of lateral leminiscus Posteroventral Anteroventral Inferior colliculus Superior olive Medial geniculate complex of the thalamus Cochlea Auditory nerve Spiral ganglion Cochlear nuclei Dorsal Figure 12.12 Diagram of the major auditory pathways. Although many details are missing from this diagram, two important points are evident: (1) the auditory system entails several parallel pathways, and (2) information from each ear reaches both sides of the sys-tem, even at the level of the brainstem. How is timing in the 10 microseconds range accomplished by neural com-ponents that operate in the millisecond range? The neural circuitry that com-putes such tiny interaural time differences consists of binaural inputs to the medial superior olive (MSO) that arise from the right and left anteroventral cochlear nuclei (Figure 12.13; see also Figure 12.12). The medial superior olive contains cells with bipolar dendrites that extend both medially and laterally. The lateral dendrites receive input from the ipsilateral anteroventral cochlear nucleus, and the medial dendrites receive input from the contralateral anteroventral cochlear nucleus (both inputs are excitatory). As might be expected, the MSO cells work as coincidence detectors, responding when both excitatory signals arrive at the same time. For a coincidence mechanism to be useful in localizing sound, different neurons must be maximally sensi-tive to different interaural time delays. The axons that project from the anteroventral cochlear nucleus evidently vary systematically in length to cre-ate delay lines. (Remember that the length of an axon divided by its conduc-tion velocity equals the conduction time.) These anatomical differences com-pensate for sounds arriving at slightly different times at the two ears, so that the resultant neural impulses arrive at a particular MSO neuron simultane-ously, making each cell especially sensitive to sound sources in a particular place. The mechanisms enabling MSO neurons to function as coincidence detectors at the microsecond level are still poorly understood, but certainly reflect one of the more impressive biophysical specializations in the nervous system. Sound localization perceived on the basis of interaural time differences requires phase-locked information from the periphery, which, as already The Auditory System 305 Loudspeaker 2 1 Action potential begins traveling toward MSO Sound reaches left ear first 3 Sound reaches right ear a little later 4 Action potential from right ear begins traveling toward MSO A 1 1 2 3 4 5 2 3 4 B C Longer path to neuron E Shorter path to neuron E MSO Right ear leading neuron Left ear leading neuron Left ear Cochlea and cochlear nucleus Right ear D E 5 5 Action potentials converge on an MSO neuron that responds most strongly if their arrival is coincident Cochlea and cochlear nucleus Figure 12.13 Diagram illustrating how the MSO computes the location of a sound by interaural time differences. A given MSO neuron responds most strongly when the two inputs arrive simultaneously, as occurs when the con-tralateral and ipsilateral inputs precisely compensate (via their different lengths) for differences in the time of arrival of a sound at the two ears. The systematic (and inverse) variation in the delay lengths of the two inputs creates a map of sound location: In this model, E would be most sensitive to sounds located to the left, and A to sounds from the right; C would respond best to sounds coming from directly in front of the listener. (After Jeffress, 1948.) 306 Chapter Twelve emphasized, is available to humans only for frequencies below 3 kHz. (In barn owls, the reigning champions of sound localization, phase locking occurs at up to 9 kHz.) Therefore, a second mechanism must come into play at higher frequencies. At frequencies higher than about 2 kHz, the human head begins to act as an acoustical obstacle because the wavelengths of the sounds are too short to bend around it. As a result, when high-frequency sounds are directed toward one side of the head, an acoustical “shadow” of lower intensity is created at the far ear. These intensity differences provide a second cue about the location of a sound. The circuits that compute the posi-tion of a sound source on this basis are found in the lateral superior olive (LSO) and the medial nucleus of the trapezoid body (MNTB) (Figure 12.14). Excitatory axons project directly from the ipsilateral anteroventral cochlear nucleus to the LSO (as well as to the MSO; see Figure 12.13). Note that the LSO also receives inhibitory input from the contralateral ear, via an inhibitory neuron in the MNTB. This excitatory/inhibitory interaction (A) (B) 70 Right > left Left > right Relative loudness 40 20 0 −20 −40 −70 Speaker Section from pons Net excitation to higher centers MNTB LSO Net inhibition 2 This stimulus also inhibits right LSO via MNTB interneuron Output of LSO Left LSO output Right LSO output 3 Excitation from left side is greater than inhibition from right side, resulting in net excitation to higher centers 4 Inhibition from left side is greater than excitation from right side, resulting in net inhibition on right and no signal to higher centers 1 Stronger stimulus to left ear excites left LSO Figure 12.14 Lateral superior olive neurons encode sound location through inter-aural intensity differences. (A) LSO neurons receive direct excitation from the ipsi-lateral cochlear nucleus; input from the contralateral cochlear nucleus is relayed via inhibitory interneurons in the MNTB. (B) This arrangement of excitation–inhibition makes LSO neurons fire most strongly in response to sounds arising directly lateral to the listener on the same side as the LSO, because excitation from the ipsilateral input will be great and inhibition from the contralateral input will be small. In con-trast, sounds arising from in front of the listener, or from the opposite side, will silence the LSO output, because excitation from the ipsilateral input will be mini-mal, but inhibition driven by the contralateral input will be great. Note that LSOs are paired and bilaterally symmetrical; each LSO only encodes the location of sounds arising on the same side of the body as its location. results in a net excitation of the LSO on the same side of the body as the sound source. For sounds arising directly lateral to the listener, firing rates will be highest in the LSO on that side; in this circumstance, the excitation via the ipsilateral anteroventral cochlear nucleus will be maximal, and inhi-bition from the contralateral MNTB minimal. In contrast, sounds arising closer to the listener’s midline will elicit lower firing rates in the ipsilateral LSO because of increased inhibition arising from the contralateral MNTB. For sounds arising at the midline, or from the other side, the increased inhi-bition arising from the MNTB is powerful enough to completely silence LSO activity. Note that each LSO only encodes sounds arising in the ipsilateral hemifield; it therefore takes both LSOs to represent the full range of horizon-tal positions. In summary, there are two separate pathways—and two separate mecha-nisms—for localizing sound. Interaural time differences are processed in the medial superior olive, and interaural intensity differences are processed in the lateral superior olive. These two pathways are eventually merged in the midbrain auditory centers. Monaural Pathways from the Cochlear Nucleus to the Lateral Lemniscus The binaural pathways for sound localization are only part of the output of the cochlear nucleus. This fact is hardly surprising, given that auditory per-ception involves much more than locating the position of the sound source. A second major set of pathways from the cochlear nucleus bypasses the superior olive and terminates in the nuclei of the lateral lemniscus on the contralateral side of the brainstem (see Figure 12.12). These particular path-ways respond to sound arriving at one ear only and are thus referred to as monaural. Some cells in the lateral lemniscus nuclei signal the onset of sound, regardless of its intensity or frequency. Other cells in the lateral lem-niscus nuclei process other temporal aspects of sound, such as duration. The precise role of these pathways in processing temporal features of sound is not yet known. As with the outputs of the superior olivary nuclei, the path-ways from the nuclei of the lateral lemniscus converge at the midbrain. Integration in the Inferior Colliculus Auditory pathways ascending via the olivary and lemniscal complexes, as well as other projections that arise directly from the cochlear nucleus, project to the midbrain auditory center, the inferior colliculus. In examining how integration occurs in the inferior colliculus, it is again instructive to turn to the most completely analyzed auditory mechanism, the binaural system for localizing sound. As already noted, space is not mapped on the auditory receptor surface; thus the perception of auditory space must somehow be synthesized by circuitry in the lower brainstem and midbrain. Experiments in the barn owl, an extraordinarily proficient animal at localizing sounds, show that the convergence of binaural inputs in the midbrain produces something entirely new relative to the periphery—namely, a computed topo-graphical representation of auditory space. Neurons within this auditory space map in the colliculus respond best to sounds originating in a specific region of space and thus have both a preferred elevation and a preferred hor-izontal location, or azimuth. Although comparable maps of auditory space have not yet been found in mammals, humans have a clear perception of The Auditory System 307 308 Chapter Twelve both the elevational and azimuthal components of a sound’s location, sug-gesting that we have a similar auditory space map. Another important property of the inferior colliculus is its ability to process sounds with complex temporal patterns. Many neurons in the infe-rior colliculus respond only to frequency-modulated sounds, while others respond only to sounds of specific durations. Such sounds are typical com-ponents of biologically relevant sounds, such as those made by predators, or intraspecific communication sounds, which in humans include speech. The Auditory Thalamus Despite the parallel pathways in the auditory stations of the brainstem and midbrain, the medial geniculate complex (MGC) in the thalamus is an obligatory relay for all ascending auditory information destined for the cor-tex (see Figure 12.12). Most input to the MGC arises from the inferior col-liculus, although a few auditory axons from the lower brainstem bypass the inferior colliculus to reach the auditory thalamus directly. The MGC has sev-eral divisions, including the ventral division, which functions as the major thalamocortical relay, and the dorsal and medial divisions, which are orga-nized like a belt around the ventral division. In some mammals, the strictly maintained tonotopy of the lower brainstem areas is exploited by convergence onto MGC neurons, generating specific responses to certain spectral combinations. The original evidence for this state-ment came from research on the response properties of cells in the MGC of echolocating bats. Some cells in the so-called belt areas of the bat MGC respond only to combinations of widely spaced frequencies that are specific components of the bat’s echolocation signal and of the echoes that are reflected from objects in the bat’s environment. In the mustached bat, where this phenomenon has been most thoroughly studied, the echolocation pulse has a changing frequency (frequency-modulated, or FM) component that includes a fundamental frequency and one or more harmonics. The funda-mental frequency (FM1) has low intensity and sweeps from 30 kHz to 20 kHz. The second harmonic (FM2) is the most intense component and sweeps from 60 kHz to 40 kHz. Note that these frequencies do not overlap. Most of the echoes are from the intense FM2 sound, and virtually none arise from the weak FM1, even though the emitted FM1 is loud enough for the bat to hear. Apparently, the bat assesses the distance to an object by measuring the delay between the FM1 emission and the FM2 echo. Certain MGC neurons respond when FM2 follows FM1 by a specific delay, providing a mechanism for sensing such frequency combinations. Because each neuron responds best to a partic-ular delay, the population of MGC neurons encodes a range of distances. Bat sonar illustrates two important points about the function of the audi-tory thalamus. First, the MGC is the first station in the auditory pathway where selectivity for combinations of frequencies is found. The mechanism responsible for this selectivity is presumably the ultimate convergence of inputs from cochlear areas with different spectral sensitivities. Second, cells in the MGC are selective not only for frequency combinations, but also for specific time intervals between the two frequencies. The principle is the same as that described for binaural neurons in the medial superior olive, but in this instance, two monaural signals with different frequency sensitivity coincide, and the time difference is in the millisecond rather than the microsecond range. In summary, neurons in the medial geniculate complex receive convergent inputs from spectrally and temporally separate pathways. This complex, by virtue of its convergent inputs, mediates the detection of specific spectral and temporal combinations of sounds. In many species, including humans, vary-ing spectral and temporal cues are especially important features of communi-cation sounds. It is not known whether cells in the human medial geniculate are selective to combinations of sounds, but the processing of speech certainly requires both spectral and temporal combination sensitivity. The Auditory Cortex The ultimate target of afferent auditory information is the auditory cortex. Although the auditory cortex has a number of subdivisions, a broad distinc-tion can be made between a primary area and peripheral, or belt, areas. The primary auditory cortex (A1) is located on the superior temporal gyrus in the temporal lobe and receives point-to-point input from the ventral division of the medial geniculate complex; thus, it contains a precise tonotopic map. The belt areas of the auditory cortex receive more diffuse input from the belt areas of the medial geniculate complex and therefore are less precise in their tonotopic organization. The primary auditory cortex (A1) has a topographical map of the cochlea (Figure 12.15), just as the primary visual cortex (V1) and the primary somatic sensory cortex (S1) have topographical maps of their respective sensory The Auditory System 309 Frontal and parietal lobes removed (B) Left hemisphere Right hemisphere Secondary auditory cortex Primary auditory cortex Lateral sulcus Wernicke’s area Wernicke’s area (A) Primary auditory cortex Secondary auditory cortex (belt areas) Corresponds to base of cochlea 5 0 0 H z 10 00 H z 2000 Hz 4 0 0 0 H z 8 0 0 0 H z 1 6 , 0 0 0 H z Corresponds to apex of cochlea Figure 12.15 The human auditory cor-tex. (A) Diagram showing the brain in left lateral view, including the depths of the lateral sulcus, where part of the auditory cortex occupying the superior temporal gyrus normally lies hidden. The primary auditory cortex (A1) is shown in blue; the surrounding belt areas of the auditory cortex are in red. The primary auditory cortex has a tono-topic organization, as shown in this blowup diagram of a segment of A1 (right). (B) Diagram of the brain in left lateral view, showing locations of human auditory cortical areas related to processing speech sounds in the intact hemisphere. Right: An oblique section (plane of dashed line) shows the cortical areas on the superior surface of the tem-poral lobe. Note that Wernicke’s area, a region important in comprehending speech, is just posterior to the primary auditory cortex. 310 Chapter Twelve epithelia. Unlike the visual and somatic sensory systems, however, the cochlea has already decomposed the acoustical stimulus so that it is arrayed tonotopically along the length of the basilar membrane. Thus, A1 is said to comprise a tonotopic map, as do most of the ascending auditory structures between the cochlea and the cortex. Orthogonal to the frequency axis of the tonotopic map is a striped arrangement of binaural properties. The neurons in one stripe are excited by both ears (and are therefore called EE cells), while the neurons in the next stripe are excited by one ear and inhibited by the other ear (EI cells). The EE and EI stripes alternate, an arrangement that is reminiscent of the ocular dominance columns in V1 (see Chapter 11). Box E Representing Complex Sounds in the Brains of Bats and Humans Most natural sounds are complex, mean-ing that they differ from the pure tones or clicks that are frequently used in neu-rophysiological studies of the auditory system. Rather, natural sounds are tonal: they have a fundamental frequency that largely determines the “pitch” of the sound, and one or more harmonics of different intensities that contribute to the quality or “timbre” of a sound. The fre-quency of a harmonic is, by definition, a multiple of the fundamental frequency, and both may be modulated over time. Such frequency-modulated (FM) sweeps can rise or fall in frequency, or change in a sinusoidal or some other fashion. Occa-sionally, multiple nonharmonic frequen-cies may be simultaneously present in some communication or musical sounds. In some sounds, a level of spectral splat-ter or “broadband noise” is embedded within tonal or frequency modulated sounds. The variations in the sound spectrum are typically accompanied by a modulation of the amplitude envelop of the complex sound as well. All of these features can be visualized by performing a spectrographic analysis. How does the brain represent such complex natural sounds? Cognitive stud-ies of complex sound perception provide some understanding of how a large but limited number of neurons in the brain can dynamically represent an infinite variety of natural stimuli in the sensory environment of humans and other ani-mals. In bats, specializations for process-ing complex sounds are apparent. Stud-ies in echolocating bats show that both communication and echolocation sounds (Figure A) are processed not only within some of the same areas, but also within the same neurons in the auditory cortex. In humans, multiple modes of process-ing are also likely, given the large overlap within the superior and middle temporal gyri in the temporal lobe for the repre-sentation of different types of complex sounds. Asymmetrical representation is another common principle of complex sound processing that results in lateral-ized (though largely overlapping) repre-sentations of natural stimuli. Thus, speech sounds that are important for communication are lateralized to the left in the belt regions of the auditory cortex, whereas environmental sounds that are important for reacting to and recogniz-60 100 20 –0.5 0 0 20 40 60 0.5 Frequency (kHz) Amplitude (V) Noisy fSFM bUFM Harmonics of fb0 fb0 fb0 Time (ms) (A) Amplitude envelope (above) and spectrogram (below) of a composite syllable emitted by mustached bats for social communication. This composite consists of two simple syllables, a fixed Sinusoidal FM (fSFM) and a bent Upward FM (bUFM) that emerges from the fSFM after some overlap. Each syllable has its own fundamental (fa0 and fb0) and multiple harmonics. (Courtesy of Jagmeet Kanwal.) The auditory cortex obviously does much more than provide a tonotopic map and respond differentially to ipsi- and contralateral stimulation. Although the sorts of sensory processing that occur in the auditory cortex are not well understood, they are likely to be important to higher-order pro-cessing of natural sounds, especially those used for communication (Box E; see also Chapter 26). One clue about such processing comes from work in marmosets, a small neotropical primate with a complex vocal repertoire. The primary auditory cortex and belt areas of these animals are indeed orga-nized tonotopically, but also contain neurons that are strongly responsive to spectral combinations that characterize certain vocalizations. The responses The Auditory System 311 ing aspects of the auditory environment are represented in each hemisphere (Fig-ure B). Musical sounds that can either motivate us to march in war or to relax and meditate when coping with physical and emotional stress are highly lateral-ized to the right in the belt regions of the auditory cortex. The extent of lateraliza-tion for speech and possibly music may vary with sex, age, and training. In some species of bats, mice, and primates, pro-cessing of natural communication sounds appears to be lateralized to the left hemisphere. In summary, natural sounds are complex and their represen-tation within the sensory cortex tends to be asymmetric across the two hemi-spheres. References EHRET, G. (1987) Left hemisphere advantage in the mouse brain for recognizing ultrasonic communication calls. Nature 325: 249–251. ESSER, K.-H., C. J. CONDON, N. SUGA AND J. S. KANWAL (1997) Syntax processing by audi-tory cortical neurons in the FM-FM area of the mustached bat, Pteronotus parnellii. Proc. Natl. Acad. Sci. USA 94: 14019–14024. HAUSER, M. D. AND K. ANDERSSON (1994) Left hemisphere dominance for processing vocal-izations in adult, but not infant, rhesus mon-keys: Field experiments. Proc. Natl. Acad. Sci. USA 91: 3946-3948. KANWAL, J. S., J. KIM AND K. KAMADA (2000) Separate, distributed processing of environ-mental, speech and musical sounds in the cerebral hemispheres. J. Cog. Neurosci. (Supp.): p. 32. KANWAL, J. S., J. S. MATSUMURA, K. OHLEMILLER AND N. SUGA (1994) Acoustic ele-ments and syntax in communication sounds emitted by mustached bats. J. Acous. Soc. Am. 96: 1229–1254. KANWAL, J. S. AND N. SUGA (1995) Hemi-spheric asymmetry in the processing of calls in the auditory cortex of the mustached bat. Assoc. Res. Otolaryngol. 18: 104. (B) Top: Reconstructed functional magnetic resonance images of BOLD contrast signal change (average for 8 subjects) showing sig-nificant (p < 0.001) activation elicited by speech, environmental, and musical sounds on surface views of the left versus the right side of the human brain. Bottom: Bar graphs showing the total significant activation to each category of complex sounds in the core and belt areas of the auditory cortex for the left versus the right side. (Courtesy of Jagmeet Kanwal.) Speech Environmental Music Speech Environmental Music Left Right Left Right Left Right Sum of voxel values 20 0 10 Left Right Left Right Core Belt 12 0 6 Left Right Left Right Core Belt 12 0 6 Left Right Left Right Core Belt 312 Chapter Twelve of these neurons to the tonal stimuli do not accurately predict their responses to the spectral combinations, suggesting that, in accord with peripheral optimization, cortical processing is in part dedicated to detecting particular intraspecific vocalizations. Another clue about the role of the primary auditory cortex in the process-ing of intraspecific communication sounds comes from work in echolocating bats. Consistent with the essential role that echolocation plays in the survival of these crepuscular animals, certain regions of the bat primary auditory cor-tex, like those described in the MGC, are tuned in a systematic manner to the delays between frequency modulated pulses and their echoes, thus pro-viding information about target distance and velocity. These delay-tuned neurons can exhibit highly specific responses to intraspecific communication calls, suggesting that the same cortical neurons can serve these two distinct auditory functions (see Box E). Evidently the general ability of the mam-malian auditory cortex to detect certain spectral and temporal combinations of natural sounds has been exploited in bats to serve sonar-mediated naviga-tion, yielding these dual function neurons. Many of the dually specialized neurons are categorized as “combination-sensitive” neurons, i.e., neurons that show a nonlinear increase in their response magnitude when presented with a combination of tones and/or noise bands in comparison to the total magnitude of the response elicited by presenting each sound element separately. Combination-sensitive neurons are tuned to more than one frequency and are specialized to recognize com-plex species-specific sounds and extract information that is critical for sur-vival. This sensitivity to combinations of simple sound elements appears to be a universal property of neurons for the perception of complex sounds by many animal species, such as frogs, birds bats and nonhuman primates. Therefore, combination-sensitive neurons most likely partake in the recogni-tion of complex sounds in the human auditory cortex as well. Sounds that are especially important for intraspecific communication often have a highly ordered temporal structure. In humans, the best example of such time-varying signals is speech, where different phonetic sequences are perceived as distinct syllables and words (see Box A in Chapter 26). Behavioral studies in cats and monkeys show that the auditory cortex is especially important for processing temporal sequences of sound. If the auditory cortex is ablated in these animals, they lose the ability to discrimi-nate between two complex sounds that have the same frequency compo-nents but which differ in temporal sequence. Thus, without the auditory cor-tex, monkeys cannot discriminate one conspecific communication sound from another. The physiological basis of such temporal sensitivity likely requires neurons that are sensitive to time-varying cues in communication sounds. Indeed, electrophysiological recordings from the primary auditory cortex of both marmosets and bats show that some neurons that respond to intraspecific communication sounds do not respond as strongly when the sounds are played in reverse, indicating sensitivity to the sounds’ temporal features. Studies of human patients with bilateral damage to the auditory cortex also reveal severe problems in processing the temporal order of sounds. It seems likely, therefore, that specific regions of the human auditory cortex are specialized for processing elementary speech sounds, as well as other temporally complex acoustical signals, such as music (Box B). Thus, Wernicke’s area, which is critical to the comprehension of human language, lies within the secondary auditory area (Figure 12.15; see also Chapter 26). Summary Sound waves are transmitted via the external and middle ear to the cochlea of the inner ear, which exhibits a traveling wave when stimulated. For high-frequency sounds, the amplitude of the traveling wave reaches a maximum at the base of the cochlea; for low-frequency sounds, the traveling wave reaches a maximum at the apical end. The associated motions of the basilar membrane are transduced primarily by the inner hair cells, while the basilar membrane motion is itself actively modulated by the outer hair cells. Dam-age to the outer or middle ear results in conductive hearing loss, while hair cell damage results in a sensorineural hearing deficit. The tonotopic organi-zation of the cochlea is retained at all levels of the central auditory system. Projections from the cochlea travel via the eighth nerve to the three main divisions of the cochlear nucleus. The targets of the cochlear nucleus neu-rons include the superior olivary complex and nuclei of the lateral lemnis-cus, where the binaural cues for sound localization are processed. The infe-rior colliculus is the target of nearly all of the auditory pathways in the lower brainstem and carries out important integrative functions, such as process-ing sound frequencies and integrating the cues for localizing sound in space. The primary auditory cortex, which is also organized tonotopically, is essen-tial for basic auditory functions, such as frequency discrimination and sound localization, and also plays an important role in processing of intraspecific communication sounds. The belt areas of the auditory cortex have a less strict tonotopic organization and also process complex sounds, such as those that mediate communication. In the human brain, the major speech compre-hension areas are located in the zone immediately adjacent to the auditory cortex. The Auditory System 313 Additional Reading Reviews COREY, D. P. AND A. J. HUDSPETH (1979) Ionic basis of the receptor potential in a vertebrate hair cell. Nature 281: 675–677. COREY, D.P. (1999) Ion channel defects in hereditary hearing loss. Neuron. 22(2):217-9. DALLOS, P. (1992) The active cochlea. J. Neu-rosci. 12: 4575–4585. GARCIA-ANOVEROS, J. AND D. P. COREY (1997) The molecules of mechanosensation. Ann. Rev. Neurosci. 20: 567–597. HEFFNER, H. E. AND R. S. HEFFNER (1990) Role of primate auditory cortex in hearing. In Com-parative Perception, Volume II: Complex Signals. W. C. Stebbins and M. A. Berkley (eds.). New York: John Wiley. HUDSPETH, A. J. (1997) How hearing happens. Neuron 19: 947–950. HUDSPETH, A. J. (2000) Hearing and deafness. Neurobiol. Dis. 7: 511–514. HUDSPETH, A. J. AND M. KONISHI (2000) Audi-tory neuroscience: Development, transduc-tion, and integration. Proc. Natl. Acad. Sci. USA 97: 11690–11691. HUDSPETH, A. J., Y. CHOE, A. D. MEHTA AND P. MARTIN (2000) Putting ion channels to work: Mechanoelectrical transduction, adaptation, and amplification by hair cells. Proc. Natl. Acad. Sci. USA 97: 11765-11772. KIANG, N. Y. S. (1984) Peripheral neural pro-cessing of auditory information. In Handbook of Physiology, Section 1: The Nervous System, Volume III. Sensory Processes, Part 2. J. M. Brookhart, V. B. Mountcastle, I. Darian-Smith and S. R. Geiger (eds.). Bethesda, MD: Ameri-can Physiological Society. NEFF, W. D., I. T. DIAMOND AND J. H. CASSEDAY (1975) Behavioral studies of auditory discrim-ination. In Handbook of Sensory Physiology, Vol-umes V–II. W. D. Keidel and W. D. Neff (eds.). Berlin: Springer-Verlag. NELKEN, I. (2002) Feature detection by the auditory cortex. In Integrative Functions in the Mammalian Auditory Pathway, Springer Hand-book of Auditory Research, Volume 15. D. Oertel, R. Fay and A. N. Popper (eds.). New York: Springer-Verlag, pp. 358–416. SUGA, N. (1990) Biosonar and neural computa-tion in bats. Sci. Am. 262 (June): 60–68. Important Original Papers BARBOUR, D. L. AND X. WANG (2003) Contrast tuning in auditory cortex. Science. 299: 1073–1075. CRAWFORD, A. C. AND R. FETTIPLACE (1981) An electrical tuning mechanism in turtle cochlear hair cells. J. Physiol. 312: 377–412. FITZPATRICK, D. C., J. S. KANWAL, J. A. BUTMAN AND N. SUGA (1993) Combination-sensitive neurons in the primary auditory cortex of the mustached bat. J. Neurosci. 13: 931–940. COREY, D. P. AND A. J. HUDSPETH (1979) Ionic basis of the receptor potential in a vertebrate hair cell. Nature 281: 675–677. MIDDLEBROOKS, J. C., A. E. CLOCK, L. XU AND D. M. GREEN (1994) A panoramic code for sound location by cortical neurons. Science 264: 842–844. KNUDSEN, E. I. AND M. KONISHI (1978) A neural map of auditory space in the owl. Science 200: 795–797. JEFFRESS, L. A. (1948) A place theory of sound localization. J. Comp. Physiol. Psychol. 41: 35–39. 314 Chapter Twelve NELKEN, I., Y. ROTMAN AND O. BAR YOSEF (1999) Responses of auditory-cortex neurons to structural features of natural sounds. Nature 397: 154–157. SUGA, N., W. E. O’NEILL AND T. MANABE (1978) Cortical neurons sensitive to combinations of information-bearing elements of biosonar sig-nals in the mustache bat. Science 200: 778–781. VON BÉKÉSY, G. (1960) Experiments in Hearing. New York: McGraw-Hill. (A collection of von Békésy’s original papers.) Books PICKLES, J. O. (1988) An Introduction to the Physiology of Hearing. London: Academic Press. YOST, W. A. AND G. GOUREVITCH (EDS.) (1987) Directional Hearing. Berlin: Springer Verlag. YOST, W. A. AND D. W. NIELSEN (1985) Funda-mentals of Hearing. Fort Worth: Holt, Rinehart and Winston. Overview The vestibular system has important sensory functions, contributing to the perception of self-motion, head position, and spatial orientation relative to gravity. It also serves important motor functions, helping to stabilize gaze, head, and posture. The peripheral portion of the vestibular system includes inner ear structures that function as miniaturized accelerometers and inertial guidance devices, continually reporting information about the motions and position of the head and body to integrative centers in the brainstem, cere-bellum, and somatic sensory cortices. The central portion of the system includes the vestibular nuclei, which make extensive connections with brain-stem and cerebellar structures. The vestibular nuclei also directly innervate motor neurons controlling extraocular, cervical, and postural muscles. This motor output is especially important to stabilization of gaze, head orienta-tion, and posture during movement. Although we are normally unaware of its functioning, the vestibular system is a key component in postural reflexes and eye movements. Balance, gaze stabilization during head movement, and sense of orientation in space are all adversely affected if the system is dam-aged. These manifestations of vestibular damage are especially important in the evaluation of brainstem injury. Because the circuitry of the vestibular sys-tem extends through a large part of the brainstem, simple clinical tests of vestibular function can be performed to determine brainstem involvement, even on comatose patients. The Vestibular Labyrinth The main peripheral component of the vestibular system is an elaborate set of interconnected chambers—the labyrinth—that has much in common, and is in fact continuous with, the cochlea (see Chapter 12). Like the cochlea, the labyrinth is derived from the otic placode of the embryo, and it uses the same specialized set of sensory cells—hair cells—to transduce physical motion into neural impulses. In the cochlea, the motion is due to airborne sounds; in the labyrinth, the motions transduced arise from head move-ments, inertial effects due to gravity, and ground-borne vibrations (Box A). The labyrinth is buried deep in the temporal bone and consists of the two otolith organs (the utricle and saccule) and three semicircular canals (Fig-ure 13.1). The elaborate and tortuous architecture of these components explains why this part of the vestibular system is called the labyrinth. The utricle and saccule are specialized primarily to respond to linear accelerations of the head and static head position relative to the graviational axis, whereas the semicircular canals, as their shapes suggest, are specialized for responding to rotational accelerations of the head. Chapter 13 315 The Vestibular System 316 Chapter Thirteen The intimate relationship between the cochlea and the labyrinth goes beyond their common embryonic origin. Indeed, the cochlear and vestibular spaces are actually joined (see Figure 13.1), and the specialized ionic environ-ments of the vestibular end organ parallel those of the cochlea. The membra-nous sacs within the bone are filled with fluid (endolymph) and are collec-tively called the membranous labyrinth. The endolymph (like the cochlear endolymph) is similar to intracellular solutions in that it is high in K+ and low in Na+. Between the bony walls (the osseous labyrinth) and the membra-nous labyrinth is another fluid, the perilymph, which is similar in composi-tion to cerebrospinal fluid (i.e., low in K+ and high in Na+; see Chapter 12). The vestibular hair cells are located in the utricle and saccule and in three juglike swellings called ampullae, located at the base of the semicircular canals next to the utricle. Within each ampulla, the vestibular hair cells extend their hair bundles into the endolymph of the membranous labyrinth. As in the cochlea, tight junctions seal the apical surfaces of the vestibular hair cells, ensuring that endolymph selectively bathes the hair cell bundle while remaining separate from the perilymph surrounding the basal portion of the hair cell. Vestibular Hair Cells The vestibular hair cells, which like cochlear hair cells transduce minute dis-placements into behaviorally relevant receptor potentials, provide the basis for vestibular function. Vestibular and auditory hair cells are quite similar; a detailed description of hair cell structure and function has already been given in Chapter 12. As in the case of auditory hair cells, movement of the stereocilia toward the kinocilium in the vestibular end organs opens mechanically gated transduction channels located at the tips of the stere-ocilia, depolarizing the hair cell and causing neurotransmitter release onto (and excitation of) the vestibular nerve fibers. Movement of the stereocilia in the direction away from the kinocilium closes the channels, hyperpolarizing the hair cell and thus reducing vestibular nerve activity. The biphasic nature of the receptor potential means that some transduction channels are open in the absence of stimulation, with the result that hair cells tonically release Semicircular canals: Ampullae Endolymphatic duct Utricle Saccule Canal reuniens Cochlea Auditory part of cranial nerve VIII Vestibular part of cranial nerve VIII Facial nerve Scarpa’s ganglion Superior Posterior Horizontal Figure 13.1 The labyrinth and its innervation. The vestibular and audi-tory portions of the eighth nerve are shown; the small connection from the vestibular nerve to the cochlea contains auditory efferent fibers. General orien-tation in head is shown in Figure 12.3; see also Figure 13.8. transmitter, thereby generating considerable spontaneous activity in vestibu-lar nerve fibers (see Figure 13.6). One consequence of these spontaneous action potentials is that the firing rates of vestibular fibers can increase or decrease in a manner that faithfully mimics the receptor potentials produced by the hair cells (Box B). Importantly, the hair cell bundles in each vestibular organ have specific orientations (Figure 13.2). As a result, the organ as a whole is responsive to displacements in all directions. In a given semicircular canal, the hair cells in the ampulla are all polarized in the same direction. In the utricle and saccule, a specialized area called the striola divides the hair cells into two popula-tions with opposing polarities (Figure 13.2C; see also Figure 13.4C). The directional polarization of the receptor surfaces is a basic principle of organi-zation in the vestibular system, as will become apparent in the following descriptions of the individual vestibular organs. The Otolith Organs:The Utricle and Saccule Displacements and linear accelerations of the head, such as those induced by tilting or translational movements (see Box A), are detected by the two otolith organs: the saccule and the utricle. Both of these organs contain a The Vestibular System 317 (A) Cross-sectional view (C) (B) Top view Hair cells Supporting cells Nerve fibers Ampulla Sacculus Utricle Posterior Superior Inferior Anterior Saccular macula Utricular macula Ampulla of superior canal Kinocilium Stereocilia Direction of depolarizing deflection Striola Striola Anterior Lateral Posterior Medial Figure 13.2 The morphological polar-ization of vestibular hair cells and the polarization maps of the vestibular organs. (A) A cross section of hair cells shows that the kinocilia of a group of hair cells are all located on the same side of the hair cell. The arrow indicates the direction of deflection that depolar-izes the hair cell. (B) View looking down on the hair bundles. (C) In the ampulla located at the base of each semicircular canal, the hair bundles are oriented in the same direction. In the sacculus and utricle, the striola divides the hair cells into populations with opposing hair bundle polarities. 318 Chapter Thirteen sensory epithelium, the macula, which consists of hair cells and associated supporting cells. Overlying the hair cells and their hair bundles is a gelati-nous layer; above this layer is a fibrous structure, the otolithic membrane, in which are embedded crystals of calcium carbonate called otoconia (Figures 13.3 and 13.4A). The crystals give the otolith organs their name (otolith is Greek for “ear stones”). The otoconia make the otolithic membrane consid-erably heavier than the structures and fluids surrounding it; thus, when the head tilts, gravity causes the membrane to shift relative to the sensory epithelium (Figure 13.4B). The resulting shearing motion between the otolithic membrane and the macula displaces the hair bundles, which are embedded in the lower, gelatinous surface of the membrane. This displace-ment of the hair bundles generates a receptor potential in the hair cells. A shearing motion between the macula and the otolithic membrane also occurs when the head undergoes linear accelerations (see Figure 13.5); the greater relative mass of the otolithic membrane causes it to lag behind the macula temporarily, leading to transient displacement of the hair bundle. The similar effects exerted on otolithic hair cells by certain head tilts and linear accelerations would be expected to render these different stimuli per-ceptually equivalent when visual feedback is absent, as occurs in the dark or when the eyes are closed. Nevertheless, evidence suggests that subjects can discriminate between these two stimulus categories, apparently through combined activity of the otolith organs and the semicircular canals. As already mentioned, the orientation of the hair cell bundles is orga-nized relative to the striola, which demarcates the overlying layer of otoco-Figure 13.3 Scanning electron micro-graph of calcium carbonate crystals (otoconia) in the utricular macula of the cat. Each crystal is about 50 mm long. (From Lindeman, 1973.) Box A A Primer on Vestibular Navigation The function of the vestibular system can be simplified by remembering some basic terminology of classical mechanics. All bodies moving in a three-dimen-sional framework have six degrees of freedom: three of these are translational and three are rotational. The transla-tional elements refer to linear move-ments in the x, y, and z axes (the hori-zontal and vertical planes). Translational motion in these planes (linear accelera-tion and static displacement of the head) is the primary concern of the otolith organs. The three degrees of rotational freedom refer to a body’s rotation rela-tive to the x, y, and z axes and are com-monly referred to as roll, pitch, and yaw. The semicircular canals are primarily responsible for sensing rotational acceler-ations around these three axes. Roll: Rotation around x axis Pitch: Rotation around y axis Yaw: Rotation around z axis x y z nia (see Figure 13.4A). The striola forms an axis of mirror symmetry such that hair cells on opposite sides of the striola have opposing morphological polarizations. Thus, a tilt along the axis of the striola will excite the hair cells on one side while inhibiting the hair cells on the other side. The saccular macula is oriented vertically and the utricular macula horizontally, with a continuous variation in the morphological polarization of the hair cells The Vestibular System 319 (A) (B) (C) Saccular macula Utricular macula Striola Superior Anterior Lateral Striola Otoconia Striola Static tilt Gravitational force Otolithic membrane, gelatinous layer Reticular membrane Supporting cells Hair cells Saccular macula Utricular macula Anterior Figure 13.4 Morphological polarization of hair cells in the utricular and saccular maculae. (A) Cross section of the utricular macula showing hair bundles projecting into the gelatinous layer when the head is level. (B) Cross section of the utricular macula when the head is tilted. (C) Orientation of the utricular and saccular ma-culae in the head; arrows show orientation of the kinocilia, as in Figure 13.2. The saccules on either side are oriented more or less vertically, and the utricles more or less horizontally. The striola is a structural landmark consisting of small otoconia arranged in a narrow trench that divides each otolith organ. In the utricular mac-ula, the kinocilia are directed toward the striola. In the saccular macula, the kino-cilia point away from the striola. Note that, given the utricle and sacculus on both sides of the body, there is a continuous representation of all directions of body movement. 320 Chapter Thirteen Box B Adaptation and Tuning of Vestibular Hair Cells Hair Cell Adaptation The minuscule movement of the hair bundle at sensory threshold has been compared to the displacement of the top of the Eiffel Tower by a thumb’s breadth! Despite its great sensitivity, the hair cell can adapt quickly and continuously to static displacements of the hair bundle caused by large movements. Such adjust-ments are especially useful in the otolith organs, where adaptation permits hair cells to maintain sensitivity to small lin-ear and angular accelerations of the head despite the constant input from gravita-tional forces that are over a million times greater. In other receptor cells, such as photoreceptors, adaptation is accom-plished by regulating the second messen-ger cascade induced by the initial trans-duction event. The hair cell has to depend on a different strategy, however, because there is no second messenger system between the initial transduction event and the subsequent receptor poten-tial (as might be expected for receptors that respond so rapidly). Adaptation occurs in both directions in which the hair bundle displacement generates a receptor potential, albeit at different rates for each direction. When the hair bundle is pushed toward the kinocilium, tension is initially increased in the gating spring. During adaptation, tension decreases back to the resting level, perhaps because one end of the gating spring repositions itself along the shank of the stereocilium. When the hair bundle is displaced in the opposite direc-tion, away from the kinocilium, tension in the spring initially decreases; adapta-tion then involves an increase in spring tension. One theory is that a calcium-reg-ulated motor such as a myosin ATPase climbs along actin filaments in the stere-ocilium and actively resets the tension in the transduction spring. During sus-tained depolarization, some Ca2+ enters through the transduction channel, along with K+. Ca2+ then causes the motor to spend a greater fraction of its time unbound from the actin, resulting in slip-page of the spring down the side of the stereocilium. During sustained hyperpo-larization (Figure A), Ca2+ levels drop below normal resting levels and the motor spends more of its time bound to the actin, thus climbing up the actin fila-ments and increasing the spring tension. As tension increases, some of the previ-ously closed transduction channels open, admitting Ca2+ and thus slowing the motor’s progress until a balance is struck between the climbing and slipping of the motor. In support of this model, when internal Ca2+ is reduced artificially, spring tension increases. This model of hair cell adaptation presents an elegant molecular solution to the regulation of a mechanical process. Electrical Tuning Although mechanical tuning plays an important role in generating frequency selectivity in the cochlea, there are other mechanisms that contribute to this process in vestibular and auditory nerve cells. These other tuning mechanisms are especially important in the otolith organs, where, unlike the cochlea, there are no Stereocilium Kinocilium (A) Stereociliary pivot Motor protein “walks” along actin Actin filament Motor retensions gate spring Force of displacement Decreased Ca2+ 2 Motor retensions “spring,” causing fraction of channels to reopen 1 Stereocilia deflected (leftward), slackening “springs,” which closes channels, resulting in a decrease of [Ca2+]i (A) Adaptation is explained in the gating spring model by adjustment of the insertion point of tips links. Movement of the insertion point up or down the shank of the stereocilium, perhaps driven by a Ca2+-dependent protein motor, can continually adjust the resting tension of the tip link. (After Hudspeth and Gillespie, 1994.) The Vestibular System 321 obvious macromechanical resonances to selectively filter and/or enhance biologi-cally relevant movements. One such mechanism is an electrical resonance dis-played by hair cells in response to depo-larization: The membrane potential of a hair cell undergoes damped sinusoidal oscillations at a specific frequency in response to the injection of depolarizing current pulses (Figure B). The ionic mechanism of this process involves two major types of ion channels located in the membrane of the hair cell soma. The first of these is a voltage-acti-vated Ca2+ conductance, which lets Ca2+ into the cell soma in response to depolar-ization, such as that generated by the transduction current. The second is a Ca2+-activated K+ conductance, which is triggered by the rise in internal Ca2+ con-centration. These two currents produce an interplay of depolarization and repo-larization that results in electrical reso-nance (Figure C). Activation of the hair cell’s calcium-activated K+ conductance occurs 10 to 100 times faster than that of similar currents in other cells. Such rapid kinetics allow this conductance to gener-ate an electrical response that usually requires the fast properties of a voltage-gated channel. Although a hair cell responds to hair bundle movement over a wide range of frequencies, the resultant receptor poten-tial is largest at the frequency of electrical resonance. The resonance frequency rep-resents the characteristic frequency of the hair cell, and transduction at that fre-quency will be most efficient. This elec-trical resonance has important implica-tions for structures like the utricle and sacculus, which may encode a range of characteristic frequencies based on the different resonance frequencies of their constituent hair cells. Thus, electrical tuning in the otolith organs can generate enhanced tuning to biologically relevant frequencies of stimulation, even in the absence of macromechanical resonances within these structures. References Assad, J. A. and D. P. Corey (1992) An active motor model for adaptation by vertebrate hair cells. J. Neurosci. 12: 3291–3309. CRAWFORD, A. C. AND R. FETTIPLACE (1981) An electrical tuning mechanism in turtle cochlear hair cells. J. Physiol. 312: 377–412. HUDSPETH, A. J. (1985) The cellular basis of hearing: The biophysics of hair cells. Science 230: 745–752. HUDSPETH, A. J. AND P. G. GILLESPIE (1994) Pulling strings to tune transduction: Adapta-tion by hair cells. Neuron 12: 1–9. LEWIS, R. S. AND A. J. HUDSPETH (1988) A model for electrical resonance and frequency tuning in saccular hair cells of the bull-frog, Rana catesbeiana. J. Physiol. 400: 275–297. LEWIS, R. S. AND A. J. HUDSPETH (1983) Volt-age- and ion-dependent conductances in soli-tary vertebrate hair cells. Nature 304: 538–541. SHEPHERD, G. M. G. AND D. P. COREY (1994) The extent of adaptation in bullfrog saccular hair cells. J. Neurosci. 14: 6217–6229. 2 Ca2+ enters through voltage-gated channel Knob on kinocilium 3 Ca2+ activates K+ channel; K+ exits cells, repolarizing cell 4 K+ enters stereocilia, depolarizes cell (C) (B) Ca2+ K+ K+ K+ 1 Depolarization −5 ms Voltage (mV) ms 0 0 0.5 1.0 0 20 40 60 80 100 120 140 Current (nA) −10 0 10 15 0 20 40 60 80 100 120 140 Ca2+-dependent K+ channel Voltage-gated Ca2+ channel Stereocilia Electrical resonance (B) Voltage oscillations (upper trace) in an isolated hair cell in response to a depolarizing current injection (lower trace). (After Lewis and Hudspeth, 1983.) (C) Proposed ionic basis for electrical resonance in hair cells. (After Hudspeth, 1985.) 322 Chapter Thirteen located in each macula (as shown in Figure 13.4C, where the arrows indicate the direction of movement that produces excitation). Inspection of the exci-tatory orientations in the maculae indicates that the utricle responds to movements of the head in the horizontal plane, such as sideways head tilts and rapid lateral displacements, whereas the saccule responds to movements in the vertical plane (up–down and forward–backward movements in the sagittal plane). Note that the saccular and utricular maculae on one side of the head are mirror images of those on the other side. Thus, a tilt of the head to one side has opposite effects on corresponding hair cells of the two utricular maculae. This concept is important in understanding how the central connections of the vestibular periphery mediate the interaction of inputs from the two sides of the head (see the next section). How Otolith Neurons Sense Linear Forces The structure of the otolith organs enables them to sense both static dis-placements, as would be caused by tilting the head relative to the gravita-tional axis, and transient displacements caused by translational movements of the head. The mass of the otolithic membrane relative to the surrounding endolymph, as well as the otolithic membrane’s physical uncoupling from the underlying macula, means that hair bundle displacement will occur transiently in response to linear accelerations and tonically in response to tilting of the head. Therefore, both tonic and transient information can be conveyed by these sense organs. Figure 13.5 illustrates some of the forces produced by head tilt and linear accelerations on the utricular macula. These properties of hair cells are reflected in the responses of the vestibu-lar nerve fibers that innervate the otolith organs. The nerve fibers have a Forward Head tilt; sustained Upright Backward Forward acceleration Deceleration No head tilt; transient Figure 13.5 Forces acting on the head and the resulting displacement of the otolithic membrane of the utricular macula. For each of the positions and accelerations due to translational movements, some set of hair cells will be maximally excited, whereas another set will be maximally inhibited. Note that head tilts produce displacements similar to certain accelerations. steady and relatively high firing rate when the head is upright. The change in firing rate in response to a given movement can be either sustained or transient, thereby signaling either absolute head position or linear accelera-tion. An example of the sustained response of a vestibular nerve fiber inner-vating the utricle is shown in Figure 13.6. The responses were recorded from axons in a monkey seated in a chair that could be tilted for several seconds to produce a steady force. Prior to the tilt, the axon has a high firing rate, which increases or decreases depending on the direction of the tilt. Notice also that the response remains at a high level as long as the tilting force remains constant; thus, such neurons faithfully encode the static force being applied to the head (Figure 13.6A). When the head is returned to the original position, the firing level of the neurons returns to baseline value. Conversely, when the tilt is in the opposite direction, the neurons respond by decreasing their firing rate below the resting level (Figure 13.6B) and remain depressed as long as the static force continues. In a similar fashion, transient increases or decreases in firing rate from spontaneous levels signal the direction of lin-ear accelerations of the head. The range of orientations of hair bundles within the otolith organs enables them to transmit information about linear forces in every direction The Vestibular System 323 Figure 13.6 Response of a vestibular nerve axon from an otolith organ (the utricle in this example). (A) The stimu-lus (top) is a change in head tilt. The spike histogram shows the neuron’s response to tilting in a particular direc-tion. (B) A response of the same fiber to tilting in the opposite direction. (After Goldberg and Fernandez, 1976.) Time (s) 0 (A) 20 40 60 80 100 120 Discharge rate (spikes/s) 0 80 40 120 160 200 Time (s) 0 20 40 0 Discharge rate (spikes/s) 0 80 40 120 160 200 Start tilt End tilt Constant tilt 0 Constant tilt Start tilt End tilt (B) 324 Chapter Thirteen the body moves (see Figure 13.4C). The utricle, which is primarily concerned with motion in the horizontal plane, and the saccule, which is concerned with vertical motion, combine to effectively gauge the linear forces acting on the head at any instant in three dimensions. Tilts of the head off the horizon-tal plane and translational movements of the head in any direction stimulate a distinct subset of hair cells in the saccular and utricular maculae, while simultaneously suppressing the responses of other hair cells in these organs. Ultimately, variations in hair cell polarity within the otolith organs produce patterns of vestibular nerve fiber activity that, at a population level, can unambiguously encode head position and the forces that influence it. The Semicircular Canals Whereas the otolith organs are primarily concerned with head translations and orientation with respect to gravity, the semicircular canals sense head rotations, arising either from self-induced movements or from angular accel-erations of the head imparted by external forces. Each of the three semicir-cular canals has at its base a bulbous expansion called the ampulla (Figure 13.7), which houses the sensory epithelium, or crista, that contains the hair cells. The structure of the canals suggests how they detect the angular accel-erations that arise through rotation of the head. The hair bundles extend out of the crista into a gelatinous mass, the cupula, that bridges the width of the ampulla, forming a fluid barrier through which endolymph cannot circulate. As a result, the relatively compliant cupula is distorted by movements of the endolymphatic fluid. When the head turns in the plane of one of the semi-circular canals, the inertia of the endolymph produces a force across the cupula, distending it away from the direction of head movement and caus-ing a displacement of the hair bundles within the crista (Figure 13.8A,B). In contrast, linear accelerations of the head produce equal forces on the two sides of the cupula, so the hair bundles are not displaced. Unlike the saccular and utricular maculae, all of the hair cells in the crista within each semicircular canal are organized with their kinocilia pointing in the same direction (see Figure 13.2C). Thus, when the cupula moves in the appropriate direction, the entire population of hair cells is depolarized and activity in all of the innervating axons increases. When the cupula moves in the opposite direction, the population is hyperpolarized and neuronal activ-ity decreases. Deflections orthogonal to the excitatory–inhibitory direction produce little or no response. Each semicircular canal works in concert with the partner located on the other side of the head that has its hair cells aligned oppositely. There are three such pairs: the two pairs of horizontal canals, and the superior canal on each side working with the posterior canal on the other side (Figure 13.8C). Head rotation deforms the cupula in opposing directions for the two partners, resulting in opposite changes in their firing rates (Box C). Thus, the orientation of the horizontal canals makes them selectively sensitive to rota-tion in the horizontal plane. More specifically, the hair cells in the canal towards which the head is turning are depolarized, while those on the other side are hyperpolarized. For example, when the head accelerates to the left, the cupula is pushed toward the kinocilium in the left horizontal canal, and the firing rate of the rel-evant axons in the left vestibular nerve increases. In contrast, the cupula in the right horizontal canal is pushed away from the kinocilium, with a concomi-tant decrease in the firing rate of the related neurons. If the head movement is Crista Cupula Ampulla Membranous duct Nerve fibers Hair cells Hair bundle Figure 13.7 The ampulla of the pos-terior semicircular canal showing the crista, hair bundles, and cupula. The cupula is distorted by the fluid in the membranous canal when the head rotates. to the right, the result is just the opposite. This push–pull arrangement oper-ates for all three pairs of canals; the pair whose activity is modulated is in the plane of the rotation, and the member of the pair whose activity is increased is on the side toward which the head is turning. The net result is a system that provides information about the rotation of the head in any direction. How Semicircular Canal Neurons Sense Angular Accelerations Like axons that innervate the otolith organs, the vestibular fibers that inner-vate the semicircular canals exhibit a high level of spontaneous activity. As a result, they can transmit information by either increasing or decreasing their firing rate, thus more effectively encoding head movements (see above). The bidirectional responses of fibers innervating the hair cells of the semicircular canal have been studied by recording the axonal firing rates in a monkey’s The Vestibular System 325 Left posterior canal (PC) Right anterior canal (AC) Left anterior canal (AC) Right posterior canal (PC) (C) Left and right horizontal canals (A) Semicircular canal Hair cells Cupula Ampulla (B) Endolymph flow Angular acceleration Cupula displacement Figure 13.8 Functional organization of the semicircular canals. (A) The position of the cupula without angular acceleration. (B) Distortion of the cupula during angu-lar acceleration. When the head is rotated in the plane of the canal (arrow outside canal), the inertia of the endolymph creates a force (arrow inside the canal) that dis-places the cupula. (C) Arrangement of the canals in pairs. The two horizontal canals form a pair; the right anterior canal (AC) and the left posterior canal (PC) form a pair; and the left AC and the right PC form a pair. 326 Chapter Thirteen Box C Throwing Cold Water on the Vestibular System Testing the integrity of the vestibular sys-tem can indicate much about the condi-tion of the brainstem, particularly in comatose patients. Normally, when the head is not being rotated, the output of the nerves from the right and left sides are equal; thus, no eye movements occur. When the head is rotated in the horizontal plane, the vestibular afferent fibers on the side toward the turning motion increase their firing rate, while the afferents on the opposite side decrease their firing rate (Figures A and B). The net difference in firing rates then leads to slow movements of the eyes counter to the turning motion. This reflex response generates the slow component of a normal eye movement pattern called physiological nystagmus, which means “nodding” or oscillatory movements of the eyes (Figure B1). (The fast component is a saccade that resets the eye position; see Chapter 19.) Pathological nystagmus can occur if there is unilateral damage to the vestibu-lar system. In this case, the silencing of the spontaneous output from the dam-aged side results in an unphysiological difference in firing rate because the spon-taneous discharge from the intact side remains (Figure B2). The difference in fir-ing rates causes nystagmus, even though no head movements are being made. Responses to vestibular stimulation are thus useful in assessing the integrity of the brainstem in unconscious patients. If the individual is placed on his or her back and the head is elevated to about 30° above horizontal, the horizontal semicircular canals lie in an almost verti-cal orientation. Irrigating one ear with cold water will then lead to spontaneous eye movements because convection cur-rents in the canal mimic rotatory head movements away from the irrigated ear (Figure C). In normal individuals, these eye movements consist of a slow move-ment toward the irrigated ear and a fast movement away from it. The fast move-ment is most readily detected by the observer, and the significance of its direc-tion can be kept in mind by using the Axis of hair cells Body Fluid motion in horizontal ducts Afferent fibers of nerve VIII Increase in firing Decrease in firing Right horizontal canal (A) Left horizontal canal H e a d t u r n s Ampullae (A) View looking down on the top of a per-son’s head illustrates the fluid motion gener-ated in the left and right horizontal canals, and the changes in vestibular nerve firing rates when the head turns to the right. (B) In normal individuals, rotating the head elicits physiological nystagmus (1), which consists of a slow eye movement counter to the direc-tion of head turning. The slow component of the eye movements is due to the net differ-ences in left and right vestibular nerve firing rates acting via the central circuit dia-grammed in Figure 13.10. Spontaneous nys-tagmus (2), where the eyes move rhythmi-cally from side to side in the absence of any head movements, occurs when one of the canals is damaged. In this situation, net dif-ferences in vestibular nerve firing rates exist even when the head is stationary because the vestibular nerve innervating the intact canal fires steadily when at rest, in contrast to a lack of activity on the damaged side. Head rotation Slow eye movement Fast eye movement Increased firing Decreased firing Primary vestibular afferents Right horizontal canal Left horizontal canal Baseline firing No firing (2) Spontaneous nystagmus (1) Physiological nystagmus (B) The Vestibular System 327 mnemonic COWS (“Cold Opposite, Warm Same”). This same test can also be used in unconscious patients. In patients who are comatose due to dysfunction of both cerebral hemispheres but whose brainstem is intact, saccadic movements are no longer made and the response to cold water consists of only the slow movement component of the eyes to side of the irrigated ear (Figure D). In the presence of brainstem lesions involving either the vestibular nuclei themselves, the connections from the vestibular nuclei to oculomotor nuclei (the third, fourth, or sixth cranial nerves), or the peripheral nerves exiting these nuclei, vestibular responses are abolished (or altered, depending on the severity of the lesion). (2) Brainstem intact (1) Normal (3) MLF lesion (bilateral) (4) Low brainstem lesion Ocular reflexes in unconscious patients Ocular reflexes in conscious patients Warm H2O Cold H2O (D) Warm H2O S Cold H2O S Cold H2O Warm H2O S S Warm H2O S Cold H2O S F F F (D) Caloric testing can be used to test the function of the brainstem in an unconscious patient. The figures show eye movements resulting from cold or warm water irrigation in one ear for (1) a normal subject, and in three different conditions in an unconscious patient: (2) with the brainstem intact; (3) with a lesion of the medial longitudinal fas-ciculus (MLF; note that irrigation in this case results in lateral movement of the eye only on the less active side); and (4) with a low brainstem lesion (see Figure 13.10). 1 Warm H2O irrigation (C) 1 Cold H2O irrigation 3 Increased firing 3 Decreased firing Gravity (horizontal canals of reclining patient are nearly vertical) Right horizontal duct Left horizontal duct 2 Endolymph falls 2 Endolymph rises (C) Caloric testing of vestibular function is possible because irrigating an ear with water slightly warmer than body tem-perature generates convection currents in the canal that mimic the endolymph movement induced by turning the head to the irrigated side. Irrigation with cold water induces the opposite effect. These currents result in changes in the fir-ing rate of the associated vestibular nerve, with an increased rate on the warmed side and a decreased rate on the chilled side. As in head rotation and spontaneous nystagmus, net differences in firing rates generate eye movements. 328 Chapter Thirteen vestibular nerve. Seated in a chair, the monkey was rotated continuously in one direction during three phases: an initial period of acceleration, then a periord of several seconds at constant velocity, and finally a period of sud-den deceleration to a stop (Figure 13.9). The maximum firing rates observed correspond to the period of acceleration; the maximum inhibition corre-sponds to the period of deceleration. During the constant-velocity phase, the response adapts so that the firing rate subsides to resting level; after the movement stops, the neuronal activity decreases transiently before returning to the resting level. Neurons innervating paired semicircular canals have a complementary response pattern. Note that the rate of adaptation (on the order of tens of seconds) corresponds to the time it takes the cupula to return to its undis-torted state (and for the hair bundles to return to their undeflected position); adaptation therefore can occur while the head is still turning, as long as a constant angular velocity is maintained. Such constant forces are rare in nature, although they are encountered on ships, airplanes, and space vehi-cles, where prolonged acceleratory arcs are sometimes described. Central Pathways for Stabilizing Gaze, Head, and Posture The vestibular end organs communicate via the vestibular branch of cranial nerve VIII with targets in the brainstem and the cerebellum that process much of the information necessary to compute head position and motion. As with the cochlear nerve, the vestibular nerves arise from a population of bipolar neurons, the cell bodies of which in this instance reside in the vestibular nerve ganglion (also called Scarpa’s ganglion; see Figure 13.1). The distal processes of these cells innervate the semicircular canals and the otolith organs, while the central processes project via the vestibular portion of cranial nerve VIII to the vestibular nuclei (and also directly to the cere-bellum; Figure 13.10). The vestibular nuclei are important centers of integra-tion, receiving input from the vestibular nuclei of the opposite side, as well as from the cerebellum and the visual and somatic sensory systems. Because vestibular and auditory fibers run together in the eighth nerve, damage to this structure often results in both auditory and vestibular disturbances. The central projections of the vestibular system participate in three major classes of reflexes: (1) helping to maintain equilibrium and gaze during movement, (2) maintaining posture, and (3) maintaining muscle tone. The first of these reflexes helps coordinate head and eye movements to keep gaze fixated on objects of interest during movements (other functions include pro-tective or escape reactions; see Box D). The vestibulo-ocular reflex (VOR) in particular is a mechanism for producing eye movements that counter head movements, thus permitting the gaze to remain fixed on a particular point (Box C; see also Chapter 19). For example, activity in the left horizontal canal induced by leftward rotary acceleration of the head excites neurons in the left vestibular nucleus and results in compensatory eye movements to the right. This effect is due to excitatory projections from the vestibular nucleus to the contralateral nucleus abducens that, along with the oculomotor nucleus, help execute conjugate eye movements. For instance, horizontal movement of the two eyes toward the right requires contraction of the left medial and right lateral rectus muscles. Vestibular nerve fibers originating in the left horizontal semicircular canal project to the medial and lateral vestibular nuclei (see Figure 13.10). Excita-tory fibers from the medial vestibular nucleus cross to the contralateral abducens nucleus, which has two outputs. One of these is a motor pathway Time (s) 0 0 Discharge rate (spikes/s) 0 Acceleration Deceleration Constant velocity 60 120 40 80 120 Figure 13.9 Response of a vestibular nerve axon from the semicircular canal to angular acceleration. The stimulus (top) is a rotation that first accelerates, then maintains constant velocity, and then decelerates the head. The axon increases its firing above resting level in response to the acceleration, returns to resting level during constant velocity, then decreases its firing rate below rest-ing level during deceleration; these changes in firing rate reflect inertial effects on the displacement of the cupula. (After Goldberg and Fernan-dez, 1971.) that causes the lateral rectus of the right eye to contract; the other is an exci-tatory projection that crosses the midline and ascends via the medial longi-tudinal fasciculus to the left oculomotor nucleus, where it activates neurons that cause the medial rectus of the left eye to contract. Finally, inhibitory neurons project from the medial vestibular nucleus to the left abducens nucleus, directly causing the motor drive on the lateral rectus of the left eye to decrease and also indirectly causing the right medial rectus to relax. The consequence of these several connections is that excitatory input from the horizontal canal on one side produces eye movements toward the opposite side. Therefore, turning the head to the left causes eye movements to the right. In a similar fashion, head turns in other planes activate other semicircular canals, causing other appropriate compensatory eye movements. Thus, the VOR also plays an important role in vertical gaze stabilization in response to The Vestibular System 329 Rostral medulla Left eye Right eye Lateral rectus Lateral rectus Medial rectus Medial longitudinal fasciculus Oculomotor nucleus Abducens nucleus Midbrain Pons Scarpa’s ganglion Medial vestibular nucleus − + Figure 13.10 Connections underlying the vestibulo-ocular reflex. Projections of the vestibular nucleus to the nuclei of cranial nerves III (oculomotor) and VI (abducens). The connections to the ocu-lomotor nucleus and to the contralateral abducens nucleus are excitatory (red), whereas the connections to ipsilateral abducens nucleus are inhibitory (black). There are connections from the oculo-motor nucleus to the medial rectus of the left eye and from the adbucens nucleus to the lateral rectus of the right eye. This circuit moves the eyes to the right, that is, in the direction away from the left horizontal canal, when the head rotates to the left. Turning to the right, which causes increased activity in the right horizontal canal, has the opposite effect on eye movements. The projec-tions from the right vestibular nucleus are omitted for clarity. 330 Chapter Thirteen the linear vertical head oscillations that accompany locomotion, and in response to vertical angular accelerations of the head, as can occur when rid-ing on a swing. The rostrocaudal set of cranial nerve nuclei involved in the VOR (i.e., the vestibular, abducens, and oculomotor nuclei), as well as the VOR’s persistence in the unconscious state, make this reflex especially use-ful for detecting brainstem damage in the comatose patient (see Box C). Loss of the VOR can have severe consequences. A patient with vestibular damage finds it difficult or impossible to fixate on visual targets while the head is moving, a condition called oscillopsia (“bouncing vision”). If the damage is unilateral, the patient usually recovers the ability to fixate objects during head movements. However, a patient with bilateral loss of vestibular function has the persistent and disturbing sense that the world is moving when the head moves. The underlying problem in such cases is that infor-mation about head and body movements normally generated by the vestibu-lar organs is not available to the oculomotor centers, so that compensatory eye movements cannot be made. Descending projections from the vestibular nuclei are essential for pos-tural adjustments of the head, mediated by the vestibulo-cervical reflex (VCR), and body, mediated by the vestibulo-spinal reflex (VSR). As with the VOR, these postural reflexes are extremely fast, in part due to the small number of synapses interposed between the vestibular organ and the rele-vant motor neurons (Box D). Like the VOR, the VCR and the VSR are both compromised in patients with bilateral vestibular damage. Such patients exhibit diminished head and postural stability, resulting in gait deviations; they also have difficulty balancing. These balance defects become more pro-nounced in low light or while walking on uneven surfaces, indicating that balance normally is the product of vestibular, visual, and proprioceptive inputs. The anatomical substrate for the VCR involves the medial vestibular nucleus, axons from which descend in the medial longitudinal fasciculus to reach the upper cervical levels of the spinal cord (Figure 13.11). This path-way regulates head position by reflex activity of neck muscles in response to stimulation of the semicircular canals from rotational accelerations of the head. For example, during a downward pitch of the body (e.g., tripping), the superior canals are activated and the head muscles reflexively pull the head up. The dorsal flexion of the head initiates other reflexes, such as forelimb extension and hindlimb flexion, to stabilize the body and protect against a fall (see Chapter 16). The VSR is mediated by a combination of pathways, including the lateral and medial vestibulospinal tracts and the reticulospinal tract. The inputs from the otolith organs project mainly to the lateral vestibular nucleus, which in turn sends axons in the lateral vestibulospinal tract to the spinal cord (see Figure 13.11). These axons terminate monosynaptically on extensor motor neurons, and they disynaptically inhibit flexor motor neurons; the net result is a powerful excitatory influence on the extensor (antigravity) mus-cles. When hair cells in the otolith organs are activated, signals reach the medial part of the ventral horn. By activating the ipsilateral pool of motor neurons innervating extensor muscles in the trunk and limbs, this pathway mediates balance and the maintenance of upright posture. Decerebrate rigidity, characterized by rigid extension of the limbs, arises when the brainstem is transected above the level of the vestibular nucleus. Decerebrate rigidity in experimental animals is relieved when the vestibular nuclei are lesioned, underscoring the importance of the vestibular system to the maintenance of muscle tone. The tonic activation of extensor muscles in decerebrate rigidity suggests further that the vestibulospinal pathway is nor-mally suppressed by descending projections from higher levels of the brain, especially the cerebral cortex (see also Chapter 16). Vestibular Pathways to the Thalamus and Cortex In addition to these several descending projections, the superior and lateral vestibular nuclei send axons to the ventral posterior nuclear complex of the thalamus, which in turn projects to two cortical areas relevant to vestibular The Vestibular System 331 Mid-Pons Rostral medulla Spinal cord Medial vestibular nucleus Medial longitudinal fasciculus Lateral vestibulospinal tract Medial vestibulospinal tract Lateral vestibular nucleus Ventral horn Cerebellum Figure 13.11 Descending projections from the medial and lateral vestibular nuclei to the spinal cord underlie the VCR and VSR. The medial vestibular nuclei project bilaterally in the medial longitudinal fasciculus to reach the medial part of the ven-tral horns and mediate head reflexes in response to activation of semicircular canals. The lateral vestibular nucleus sends axons via the lateral vestibular tract to contact anterior horn cells innervating the axial and proximal limb muscles. Neu-rons in the lateral vestibular nucleus receive input from the cerebellum, allowing the cerebellum to influence posture and equilibrium. 332 Chapter Thirteen sensations (Figure 13.12). One of these cortical targets is just posterior to the primary somatosensory cortex, near the representation of the face; the other is at the transition between the somatic sensory cortex and the motor cortex (Brodmann’s area 3a; see Chapter 8). Electrophysiological studies of individ-ual neurons in these areas show that the relevant cells respond to proprio-ceptive and visual stimuli as well as to vestibular stimuli. Many of these neurons are activated by moving visual stimuli as well as by rotation of the body (even with the eyes closed), suggesting that these cortical regions are involved in the perception of body orientation in extrapersonal space. Con-Box D Mauthner Cells in Fish A primary function of the vestibular sys-tem is to provide information about the direction and speed of ongoing move-ments, ultimately enabling rapid, coordi-nated reflexes to compensate for both self-induced and externally generated forces. One of the most impressive and speediest vestibular-mediated reflexes is the tail-flip escape behavior of fish (and larval amphibians), a stereotyped response that allows a potential prey to elude its predators (Figure A; tap on the side of a fish tank if you want to observe the reflex). In response to a perceived risk, fish flick their tail and are thus pro-pelled laterally away from the approach-ing threat. The circuitry underlying the tail-flip escape reflex includes a pair of giant medullary neurons called Mauthner cells, their vestibular inputs, and the spinal cord motor neurons to which the Mauthner cells project. (In most fish, there is one pair of Mauthner cells in a stereotypic location. Thus, these cells can be consistently visualized and studied from animal to animal.) Movements in the water, such as might be caused by an approaching predator, excite saccular hair cells in the vestibular labyrinth. These receptor potentials are transmitted via the central processes of vestibular ganglion cells in cranial nerve VIII to the two Mauthner cells in the brainstem. As in the vestibulo-spinal pathway in humans, the Mauthner cells project directly to spinal motor neurons. The small number of synapses intervening between the receptor cells and the motor neurons is one of the ways that this cir-cuit has been optimized for speed by natural selection, an arrangement evi-dent in humans as well. The large size of the Mauthner axons is another; the axons from these cells in a goldfish are about 50 µm in diameter. The optimization for speed and direc-tion in the escape reflex also is reflected in the synapses vestibular nerve afferents make on each Mauthner cell (Figure B). These connections are electrical synapses that allow rapid and faithful transmis-sion of the vestibular signal. An appropriate direction for escape is promoted by two features: (1) each Mau-thner cell projects only to contralateral motor neurons; and (2) a local network of bilaterally projecting interneurons inhibits activity in the Mauthner cell away from the side on which the vestibular activity originates. In this way, the Mauthner cell on one side faithfully generates action potentials that command contractions of contralateral tail musculature, thus mov-ing the fish out of the path of the oncom-ing predator. Conversely, the Mauthner cell on the opposite side is silenced by the local inhibitory network during the response (Figure C). (A) (A) Bird’s-eye view of the sequential body orientations of a fish engaging in a tail-flip escape behavior, with time progressing from left to right. This behavior is largely mediated by vestibular inputs to Mauthner cells. sistent with this interpretation, patients with lesions of the right parietal cor-tex suffer altered perception of personal and extra-personal space, as dis-cussed in greater detail in Chapter 25. Summary The vestibular system provides information about the motion and position of the body in space. The sensory receptor cells of the vestibular system are located in the otolith organs and the semicircular canals of the inner ear. The The Vestibular System 333 The Mauthner cells in fish are analo-gous to the reticulospinal and vestibu-lospinal pathways that control balance, posture, and orienting movements in mammals. The equivalent behavioral responses in humans are evident in a friendly game of tag, or more serious endeavors. References EATON, R. C., R. A. BOMBARDIERI AND D. L. MEYER (1977) The Mauthner-initiated startle response in teleost fish. J. Exp. Biol. 66: 65–81. FURSHPAN, E. J. AND T. FURUKAWA (1962) Intra-cellular and extracellular responses of the several regions of the Mauthner cell of the goldfish. J. Neurophysiol. 25:732–771. JONTES, J. D., J. BUCHANAN AND S. J. SMITH (2000) Growth cone and dendrite dynamics in zebrafish embryos: Early events in synap-togenesis imaged in vivo. Nature Neurosci. 3: 231–237. O’MALLEY, D. M., Y. H. KAO AND J. R. FETCHO (1996) Imaging the functional organization of zebrafish hindbrain segments during escape behaviors. Neuron 17: 1145–1155. Right Mauthner cell Right Mauthner cell Left Mauthner cell Left Mauthner cell Lateral dendrite Electrical synapse Cranial nerve VIII Right cranial nerve VIII Left cranial nerve VIII Vestibular hair cells Axon cap Right axon Left axon Time 1 Time 2 Time 2 Time 1 Wave Midline Time Record Record Record Record (B) (C) (B) Diagram of synaptic events in the Mauthner cells of a fish in response to a disturbance in the water coming from the right. (C) Complementary responses of the right and left Mauthner cells mediating the escape response. Times 1 and 2 correspond to those indicated in Figure B. (After Furshpan and Furukuwa, 1962.) 334 Chapter Thirteen otolith organs provide information necessary for postural adjustments of the somatic musculature, particularly the axial musculature, when the head tilts in various directions or undergoes linear accelerations. This information rep-resents linear forces acting on the head that arise through static effects of gravity or from translational movements. The semicircular canals, in con-trast, provide information about rotational accelerations of the head. This lat-ter information generates reflex movements that adjust the eyes, head, and body during motor activities. Among the best studied of these reflexes are eye movements that compensate for head movements, thereby stabilizing the visual scene when the head moves. Input from all the vestibular organs is integrated with input from the visual and somatic sensory systems to pro-vide perceptions of body position and orientation in space. Ventral posterior nucleus complex of the thalamus Cerebrum Pons Muscle and cutaneous afferents Lateral and superior vestibular nuclei Postcentral gyrus Vestibular cortex Region near face representation of SI Posterior parietal cortex (Area 5) Vestibular cortex Region near face representation of SI Posterior parietal cortex (area 5) Figure 13.12 Thalamocortical path-ways carrying vestibular information. The lateral and superior vestibular nuclei project to the thalamus. From the thalamus, the vestibular neurons project to the vicinity of the central sulcus near the face representation. Sensory inputs from the muscles and skin also con-verge on thalamic neurons receiving vestibular input (see Chapter 9). Additional Reading Reviews BENSON, A. (1982) The vestibular sensory sys-tem. In The Senses, H. B. Barlow and J. D. Mol-lon (eds.). New York: Cambridge University Press. BRANDT, T. (1991) Man in motion: Historical and clinical aspects of vestibular function. A review. Brain 114: 2159–2174. FURMAN, J. M. AND R. W. BALOH (1992) Otolith-ocular testing in human subjects. Ann. New York Acad. Sci. 656: 431–451. GOLDBERG, J. M. (1991) The vestibular end organs: Morphological and physiological diversity of afferents. Curr. Opin. Neurobiol. 1: 229–235. GOLDBERG, J. M. AND C. FERNANDEZ (1984) The vestibular system. In Handbook of Physiology, Section 1: The Nervous System, Volume III: Sen-sory Processes, Part II, J. M. Brookhart, V. B. Mountcastle, I. Darian-Smith and S. R. Geiger (eds.). Bethesda, MD: American Physiological Society. HESS, B. J. (2001) Vestibular signals in self-ori-entation and eye movement control. News Physiolog. Sci. 16: 234–238. RAPHAN, T. AND B. COHEN. (2002) The vestibulo-ocular reflex in three dimensions. Exp. Brain Res. 145: 1–27. Important Original Papers GOLDBERG, J. M. AND C. FERNANDEZ (1971) Physiology of peripheral neurons innervating semicircular canals of the squirrel monkey, Parts 1, 2, 3. J. Neurophysiol. 34: 635–684. GOLDBERG, J. M. AND C. FERNANDEZ (1976) Physiology of peripheral neurons innervating otolith organs of the squirrel monkey, Parts 1, 2, 3. J. Neurophysiol. 39: 970–1008. LINDEMAN, H. H. (1973) Anatomy of the otolith organs. Adv. Oto.-Rhino.-Laryng. 20: 405–433. Books BALOH, R. W. AND V. HONRUBIA (2001) Clinical Neurophysiology of the Vestibular System, 3rd Ed. New York: Oxford University Press. BALOH, R. W. (1998) Dizziness, Hearing Loss, and Tinnitus. Philadelphia: F. A. Davis Com-pany. The Vestibular System 335 Overview Three sensory systems associated with the nose and mouth—olfaction, taste, and the trigeminal or general chemosensory system—are dedicated to the detection of chemicals in the environment. The olfactory system detects air-borne molecules called odorants. In humans, odors provide information about food, self, other people, animals, plants, and many other aspects of the environment. Olfactory information can influence feeding behavior, social interactions and, in many animals, reproduction. The taste (or gustatory) system detects ingested, primarily water-soluble molecules called tastants. Tastants provide information about the quality, quantity, and safety of in-gested food. Finally, the trigeminal chemosensory system provides informa-tion about irritating or noxious molecules that come into contact with skin or mucous membranes of the eyes, nose, and mouth. All three of these chemo-sensory systems rely on receptors in the nasal cavity, mouth, or on the face that interact with the relevant molecules and generate receptor and action potentials, thus transmitting information about chemical stimuli to appro-priate regions of the central nervous system. The Organization of the Olfactory System From an evolutionary perspective, the chemical senses—particularly olfac-tion—are deemed the “oldest” sensory systems; nevertheless, they remain in many ways the least understood of the sensory modalities. The olfactory system (Figure 14.1) is the most thoroughly studied component of the chemosensory triad and processes information about the identity, concentra-tion, and quality of a wide range of chemical stimuli that we associate with our sense of smell. These stimuli, called odorants, interact with olfactory receptor neurons found in an epithelial sheet—the olfactory epithelium— that lines the interior of the nose (Figure 14.1A,B). The axons arising from the receptor cells project directly to neurons in the olfactory bulb, which in turn sends projections to the pyriform cortex in the temporal lobe as well as other structures in the forebrain (Figure 14.1C). The olfactory system is thus unique among the sensory systems in that it does not include a thalamic relay from primary receptors en route to a neocortical (six-layered) region that processes the sensory information. Instead, the pyriform cortex is three-layered archicortex—considered to be phlogenetically older than the neo-cortex—and thus represents a specialized processing center dedicated to olfaction. Projections from the pyriform cortex relay olfactory information via the thalamus to association areas of the neocortex (see Figure 14.1C, D). The olfactory tract also projects to a number of other targets in the forebrain, including the hypothalamus and amygdala. The further processing that Chapter 14 337 The Chemical Senses 338 Chapter Fourteen Hippocampal formation (C) (E) (D) Hypothalamus Thalamus Orbitofrontal cortex Orbitofrontal cortex Amygdala Pyriform cortex Amygdala Olfactory tubercle Olfactory bulb targets Olfactory receptors Olfactory bulb Entorhinal cortex Pyriform cortex Olfactory nerve (I) Olfactory tract (A) Nasal cavity (B) Olfactory bulb Airborne odors Cribriform plate Olfactory nerve Olfactory epithelium Amygdala Olfactory tubercle Entorhinal cortex Pyriform cortex Olfactory tract Olfactory bulb Optic chiasm Olfactory bulb Cribriform plate Olfactory epithelium Region of olfactory bulb Figure 14.1 Organization of the human olfactory system. (A) Peripheral and central components of the primary olfactory pathway. (B) Enlargement of region boxed in (A) showing the relationship between the olfactory epithelium (which contains the olfactory receptor neurons) and the olfactory bulb (the central target of olfactory receptor neurons). (C) Dia-gram of the basic pathways for process-ing olfactory information. (D) Central components of the olfactory system. (E) fMRI images showing focal activity in the regions of the olfactory bulb, pyri-form cortex, and amygdala in a normal human being passively smelling odors. (From Savic et al., 2001.) occurs in these various regions identifies the odorant and initiates appropri-ate motor, visceral, and emotional reactions to olfactory stimuli. Despite its phylogenetic “age” and the unusual trajectory of olfactory information to the neocortex, the olfactory system abides by the basic princi-ple that governs other sensory modalities: interactions with stimuli—in this case, airborne chemical odorants—at the periphery are transduced and encoded by receptors into electrical signals, which are then relayed to higher-order centers. Nevertheless, less is known about the central organiza-tion of the olfactory system than other sensory pathways. For example, the somatic sensory and visual cortices described in the preceding chapters all feature spatial maps of the relevant receptor surface, and the auditory cortex features frequency and other maps. Whether analogous maps of specific odorants (e.g., rose or pine) or odorant attributes (e.g., sweet or acrid) exist in the olfactory bulb or pyriform cortex is not yet known. Indeed, until recently it has been difficult to imagine what sensory qualities would be rep-resented in an olfactory map, or what features might be processed in parallel as occurs in other sensory systems. Olfactory Perception in Humans In humans, olfaction is often considered the least acute of the senses, and a number of animals are obviously superior to humans in their olfactory abil-ities. This difference may reflect the larger number of olfactory receptor neu-rons (and odorant receptor molecules; see below) in the olfactory epithelium in many species and the proportionally larger area of the forebrain devoted to olfaction. In a 70-kg human, the surface area of the olfactory epithelium is approximately 10 cm2. In contrast, a 3-kg cat has about 20 cm2 of olfactory epithelium. Similarly, the relative size of the olfactory bulb and related struc-tures versus the cortical hemispheres in a rodent or carnivore is quite large compared to that in humans. Humans are nonetheless quite good at detect-ing and identifying airborne molecules in the environment (Figure 14.2). For instance, the major aromatic constituent of bell pepper (2-isobutyl-3-methoxypyrazine) can be detected at a concentration of 0.01 nM. However, the threshold concentrations for detection and identification of other odor-ants vary greatly. Ethanol, for example, cannot be identified until its concen-tration reaches approximately 2 mM. Small changes in molecular structure can also lead to large perceptual differences: The molecule D-carvone smells like caraway seeds, whereas L-carvone smells like spearmint. Since the number of odorants is very large, there have been several attempts to classify them in groups. The most widely used classification was developed in the 1950s by John Amoore, who divided odors into categories based on their perceived quality, molecular structure, and the fact that some people, called anosmics, have difficulty smelling one or another group. Amoore classified odorants as pungent, floral, musky, earthy, ethereal, camphor, peppermint, ether, and putrid; these categories are still used to describe odors, to study the cellular mechanisms of olfactory transduction, and to discuss the central representation of olfactory information. Nevertheless, this classi-fication remains entirely empirical. A further complication in rationalizing the perception of odors is that their quality may change with concentration. For example, at low concentrations indole has a floral odor, whereas at higher concentrations it smells putrid. Despite these problems, the longevity of Amoore’s scheme makes clear that the olfactory system can identify odor-ant classes that have distinct perceptual qualities. Indeed, humans can per-The Chemical Senses 339 340 Chapter Fourteen Figure 14.2 Chemical structure and human perceptual threshold for 12 com-mon odorants. Molecules perceived at low concentrations are more lipid-solu-ble, whereas those with higher thresh-olds are more water-soluble. (After Pelosi, 1994.) ceive distinct odorant molecules as a particular identifiable smell. Thus, coconuts, violets, cucumbers, and bell peppers all have a unique odor gener-ated by a specific molecule. Most naturally occurring odors, however, are blends of several odorant molecules, even though they are typically experi-enced as a single smell (such as the perceptions elicited by perfumes or the bouquet of a wine). Psychologists and neurologists have developed a variety of tests that mea-sure the ability to detect common odors. Although most people are able to consistently identify a broad range of test odorants, others fail to identify one or more common smells (Figure 14.3). Such chemosensory deficits, called anosmias, are often restricted to a single odorant, suggesting that a specific element in the olfactory system, either an olfactory receptor gene (see below) or genes that control expression or function of a specific odorant receptor gene, is inactivated. Nevertheless, genetic analysis of anosmic individuals has yet to confirm this possibility. Anosmias often target perception of distinct, noxious odorants. About 1 person in 1000 is insensitive to butyl mercaptan, the foul-smelling odorant released by skunks. More serious is the inability to 5α-Androst-16-en-3-one urinous 0.6 nM Geosmin earthy 0.1 nM 2-trans-6-cis-Nonadienal cucumber 0.07 nM β-Ionone violet 0.03 nM 2-Isobutyl-3-methoxypyrazine bell pepper 0.01 nM CH Ethanol alcoholic 2 mM Ethyl acetate ethereal 0.06 mM Benzaldehyde bitter almond 0.3 µM 4-Hydroxyoctanoic acid lactone coconut 0.05 µM Dimethylsulfide putrid 5 nM S OH O O O O H O O Cl Cl Cl O O O H 2,3,6-Trichloroanisole moldy 0.1 nM O Pentadecalactone musky 7 nM O O N N 90 80 70 60 50 40 30 20 10 0 Frequency (%) Number correct Anosmics Normal subjects 0 1−2 6−7 3 4 5 Figure 14.3 Anosmia is the inability to identify common odors. When subjects are presented with seven common odors (a test frequently used by neurologists), the vast majority of “normal” individuals can identify all seven odors correctly (in this case, baby powder, chocolate, cinnamon, coffee, mothballs, peanut butter, and soap). Some people, however, have difficulty identifying even these common odors. In this example, individuals previously identified as anosmics were presented with the same battery of odors, only a few could identify all of the odors (less than 15%), and more than half could not identify any of the odors. (After Cain and Gent, in Meiselman and Rivlin, 1986.) Figure 14.4 Normal decline in olfac-tory sensitivity with age. The ability to identify 80 common odorants declines markedly between 20 and 70 years of age. (After Murphy, 1986.) detect hydrogen cyanide (1 in 10 people), which can be lethal, or ethyl mer-captan, the chemical added to natural gas to aid in the detection of gas leaks. The ability to identify odors normally decreases with age. If otherwise healthy subjects are challenged to identify a large battery of common odor-ants, people between 20 and 40 years of age can typically identify about 50–75% of the odors, whereas those between 50 and 70 correctly identify only about 30–45% (Figure 14.4). A more radically diminished or distorted sense of smell can accompany eating disorders, psychotic disorders (espe-cially schizophrenia), diabetes, taking certain medications, and Alzheimer’s disease (all for reasons that remain obscure). Although the loss of human olfactory sensitivity is not usually a source of great concern, it can diminish the enjoyment of food and, if severe, can affect the ability to identify and respond appropriately to potentially dangerous odors such as spoiled food, smoke, or natural gas. The neural substrates for odor processing in humans includes all of the structures identified anatomically as part of the olfactory pathway: the olfac-tory bulb, pyriform and orbital cortices, amygdala and hypothalamus are all clearly activated by presentation of odorants in functional magnetic reso-nance images (fMRI) of normal human subjects (Figure 14.1E). Although fMRI cannot resolve differences in the local activity elicited by most individ-ual odors, some clear distinctions have been seen that support correspond-ing behavioral observations. Furthermore, the decline in olfactory ability with age mentioned above is matched by a decline in the level of activity in olfactory regions of the aging human brain. Physiological and Behavioral Responses to Odorants In addition to olfactory perceptions, odorants can elicit a variety of physio-logical responses. Examples are the visceral motor responses to the aroma of appetizing food (salivation and increased gastric motility) or to a noxious smell (gagging and, in extreme cases, vomiting). Olfaction can also influence reproductive and endocrine functions. Women housed in single-sex dormi-tories, for instance, have menstrual cycles that tend to be synchronized, a phenomenon that appears to be mediated by olfaction. Volunteers exposed to gauze pads from the underarms of women at different stages of their menstrual cycles also tend to experience synchronized menses, and this syn-chronization can be disrupted by exposure to gauze pads from men. Olfac-tion also influences mother–child interactions. Infants recognize their moth-ers within hours after birth by smell, preferentially orienting toward their mothers’ breasts and showing increased rates of suckling when fed by their mother compared to being fed by other lactating females, or when presented experimentally with their mother’s odor versus that of an unrelated female (see Chapter 23). By the same token, mothers can discriminate their own infant’s odor when challenged with a range of odor stimuli from infants of similar age. In other animals, including many mammals, species-specific odorants called pheromones play important roles in behavior, by influencing social, reproductive, and parenting behaviors (Box A). In rats and mice, odorants thought to be pheromones are detected by G-protein-coupled receptors located at the base of the nasal cavity in distinct, encapsulated chemosensory structures called vomeronasal organs (VNOs). In many mammals, VNOs project to the accessory olfactory bulb, which in turn projects to the hypothal-amus (where reproductive activity is generally regulated; see Chapter 29). VNOs are found bilaterally in only 8% of adult humans, and there is no clear The Chemical Senses 341 10 20 30 40 50 60 70 80 90 Percent correct Age (years) 20 30 40 50 60 70 342 Chapter Fourteen indication that these human structures have any significant function. The human genes encoding homologues of pheromone receptors expressed by VNO neurons in other mammals are mostly pseudogenes (i.e., the sequences have been mutated over the course of evolution so that these genes cannot be expressed). Thus, it is unlikely that human pheromone perception, if it exists, is mediated by the vomeronasal system, as is the case in other mammals. Nevertheless, recent observations suggest that exposure to androgen and estrogen-like compounds at concentrations below the level of conscious detection can elicit both behavioral responses and different patterns of brain activation in adult female and male human subjects (Figure 14.5). Thus, although most humans do not process pheromones by the vomeronasal sys-tem, other olfactory structures can evidently detect signals that may affect reproductive and other behaviors. The Olfactory Epithelium and Olfactory Receptor Neurons The transduction of olfactory information occurs in the olfactory epithelium, the sheet of neurons and supporting cells that lines approximately half of the nasal cavities. (The remaining surface is lined by respiratory epithelium, which lacks neurons and serves primarily as a protective surface.) The olfac-tory epithelium includes several cell types (Figure 14.6A). The most impor-tant of these is the olfactory receptor neuron, a bipolar cell that gives rise to a small-diameter, unmyelinated axon at its basal surface that transmits olfac-tory information centrally. At its apical surface, the receptor neuron gives rise to a single dendritic process that expands into a knoblike protrusion from which several microvilli, called olfactory cilia, extend into a thick layer of mucus. The mucus that lines the nasal cavity and controls the ionic milieu of the olfactory cilia is produced by secretory specializations (called Bowman’s glands) distributed throughout the epithelium. When the mucus layer becomes thicker, as during a cold, olfactory acuity decreases significantly. Two other cell classes, basal cells and sustentacular (supporting) cells, are also (A) Females (B) Males Anterior hypothalamus Posterior hypothalamus Figure 14.5 Differential patterns of activation in the hypothalamus of nor-mal human female (right) and male (left) subjects after exposure to an estrogen- or androgen-containing odor mix. (From Savic et al., 2001.) present in the olfactory epithelium. This entire apparatus—mucus layer and epithelium with neural and supporting cells—is called the nasal mucosa. The superficial location of the nasal mucosa allows the olfactory receptor neurons direct access to odorant molecules. Another consequence, however, is that these neurons are exceptionally exposed. Airborne pollutants, aller-gens, microorganisms, and other potentially harmful substances subject the olfactory receptor neurons to more or less continual damage. Several mecha-nisms help maintain the integrity of the olfactory epithelium in the face of this trauma. The ciliated cells of the respiratory epithelium, a non-neural epithelium found at the most external aspect of the nasal cavity, warms and moistens the inspired air. In addition, glandular cells throughout the epithe-lium secrete mucus, which traps and neutralizes potentially harmful agents. In both the respiratory and olfactory epithelium, immunoglobulins are secreted into the mucus, providing an initial defense against harmful anti-gens, and the sustentacular cells contain enzymes (cytochrome P450s and others) that catabolize organic chemicals and other potentially damaging molecules that enter the nasal cavity. The ultimate solution to this problem, however, is to replace olfactory receptor neurons in a normal cycle of degen-eration and regeneration. In rodents, the entire population of olfactory neu-rons is renewed every 6 to 8 weeks. This feat is accomplished by maintaining among the basal cells a population of precursors (stem cells) that divide to give rise to new receptor neurons (see Figure 14.6A). This naturally occur-ring regeneration of olfactory receptor cells provides an opportunity to investigate how neural precursor cells can successfully produce new neu-rons and reconstitute function in the mature central nervous system, a topic of broad clinical interest. Recent evidence suggests that many of the signal-ing molecules that influence neuronal differentiation, axon outgrowth, and synapse formation during development elsewhere in the nervous system (see Chapters 21 and 22) perform similar functions for regenerating olfactory The Chemical Senses 343 Odorant Odorant 0 −100 −200 −300 −400 Time (s) 0 1 2 3 4 5 6 0 1 2 3 4 5 6 (A) (B) Olfactory cilia Receptor cell axons (to olfactory bulb) Olfactory knob Mucus Odorants Mature receptor cell Pipette Cilia Odor Developing receptor cell Supporting cell Dividing stem cell Basal cell Bowman’s gland Odor Stimulation of olfactory cilia Stimulation of olfactory soma Cribriform plate Membrane current (pA) Record Record Figure 14.6 Structure and function of the olfactory epithelium. (A) Diagram of the olfactory epithelium showing the major cell types: olfactory receptor neu-rons and their cilia, sustentacular cells (that detoxify potentially dangerous chemicals), and basal cells. Bowman’s glands produce mucus. Nerve bundles of unmyelinated neurons and blood ves-sels run in the basal part of the mucosa (called the lamina propria). Olfactory receptor neurons are generated continu-ously from basal cells. (B) Generation of receptor potentials in response to odors takes place in the cilia of receptor neu-rons. Thus, odorants evoke a large inward (depolarizing) current when applied to the cilia (left), but only a small current when applied to the cell body (right). (A after Anholt, 1987; B after Firestein et al., 1991.) 344 Chapter Fourteen Box A Olfaction, Pheromones, and Behavior in the Hawk Moth Olfactory information guides essential behaviors in virtually all species. The importance of olfactory cues in repro-ductive behaviors has been particularly well characterized in the hawk moth, Manduca sexta. In Manduca, males iden-tify potential mates by following a plume of pheromones exuded by the female. Similarly, the female uses an olfactory cue—a molecule made by tobacco plants—to identify an appropriate site to lay eggs. These olfactory functions in the moths are sexually dimorphic: Only males respond to female pheromones, and only females detect the olfactory stimulus from the tobacco plant needed for egg-laying. These abilities are mediated by an olfactory system that shares some remarkable similarities with mammalian systems. Male and female moths have different olfactory receptor cells (and associated structures) on their antennae which generate receptor potentials in response to the female-specific pheromones or the tobacco plant odor-ants. These peripheral receptors project to olfactory recipient structures that are reminiscent of the mammalian olfactory bulb (see figure). The target structure in the moth—called the antennal lobe—is comprised of an array of iterated circuits that are referred to as glomeruli and are surprisingly similar in both structure and function to glomeruli in the mammalian olfactory bulb. In males, the antennal receptor neurons sensitive to the female pheromone project to a distinct subset of glomeruli called the macroglomerular complex. These glomeruli are specifically active in the presence of female pheromone and, if absent, prevent any behavioral response to the female scent. Finally, the development of these sexu-ally dimorphic central circuits is con-trolled by the periphery. If a male anten-nae is transplanted to a genotypically female moth, a macroglomerular com-plex develops in the antennal lobe. The female-specific pheromone has been identified, as have several receptor mole-cules specifically associated with the male or female olfactory pathway, respectively. Not surprisingly, pheromone receptors in the male are members of a special class of seven transmembrane odorant receptors found in other invertebrates and vertebrates. The matching of identified glomeruli with receptor cells expressing specific receptor molecules may be a general rule in olfactory systems. If so, the neurobiol-ogy of a sexually dimorphic olfactory behavior in the moth provides an ideal model system in which to study chemosensory processing of specific odorants. References FARKAS, S. R. AND H. H. SHOREY (1972) Chem-ical trial following by flying insects: A mech-anism for orientation to a distant odor source. Science 178: 67–68. MATSUMOTO, S. G. AND J. G. HILDEBRAND (1981) Olfactory mechanisms in the moth Manduca sexta: Response characteristics and morphology of central neurons in the anten-nal lobe. Proc. Roy. Soc. London B. 213: 249–277. SCHNEIDERMAN, A. M., S. G. MATSUMOTO AND J. G. HILDEBRAND (1982) Trans-sexually grafted antennae influence development of sexually dimorphic neurons in moth brain. Nature 298: 844–846. SCHNEIDERMAN, A. M., J. G. HILDEBRAND, M. M. BRENNAN AND J. H. TUMLINSON (1986) Trans-sexually grafted antennae alter pheromone-directed behavior in a moth. Nature 323: 801–803. STRAUSFELD, N. J. AND J. G. HILDEBRAND (1999) Olfactory systems: Common design, uncom-mon origin. Curr. Opin. Neurobiol. 9: 634–639. Male Female Antennal nerve Macroglomerular complex Antennal lobe neurons Glomeruli Glomeruli Male and female olfactory glomeruli in the antennal lobe are specialized for odorant-medi-ated behaviors. The male-specific macroglomerular complex (MCG) is essential for processing the female pheromone. receptor neurons in the adult. Understanding how the new olfactory recep-tor neurons differentiate into functional neurons, extend axons to the brain, and reestablish appropriate functional connections is obviously relevant to stimulating the regeneration of functional connections elsewhere in the brain after injury or disease (see Chapter 24). The Transduction of Olfactory Signals The cellular and molecular machinery for olfactory transduction is located in the cilia of olfactory receptor neurons (see Figure 14.6B). Despite their exter-nal appearance, olfactory cilia do not have the cytoskeletal features of motile cilia (the so-called 9 + 2 arrangement of microtubules). Odorant transduction begins with odorant binding to specific receptors on the external surface of cilia. Binding may occur directly, or by way of proteins in the mucus (called odorant binding proteins) that sequester the odorant and are thought to shuttle it to the receptor. Several additional steps then generate a receptor potential by opening ion channels. In mammals, the principal pathway involves cyclic nucleotide-gated ion channels, similar to those found in rod photoreceptors (see Chapter 10). The olfactory receptor neurons express an olfactory-specific G-protein (Golf), which activates an olfactory-specific adenylate cyclase (Figure 14.7A). Both of these proteins are restricted to the knob and cilia, consistent with the idea that odor transduction occurs in these portions of the olfactory receptor neuron. Stimulation of odorant receptor molecules leads to an increase in cyclic AMP (cAMP) which opens channels that permit Na+ and Ca2+ entry (mostly Ca2+), thus depolarizing the neuron. This depolarization, amplified by a Ca2+-activated Cl– current, is conducted passively from the cilia to the axon hillock region of the olfactory receptor neuron, where action potentials are generated and transmitted to the olfactory bulb. Olfactory receptor neurons are especially efficient at extracting a signal from chemosensory noise. Fluctuations in the cAMP concentration in an olfactory receptor neuron could, in theory, cause the receptor cell to be acti-vated in the absence of odorants. Such nonspecific responses do not occur, however, because the cAMP-gated channels are blocked at the resting poten-tial by the high Ca2+ and Mg2+ concentrations in mucus. To overcome this The Chemical Senses 345 Ca2+-CAM (A) Odorant molecule Active G-protein Active adenylate cyclase Receptor protein (Second messenger) Active Na+/ Ca2+ channel Ca2+-gated Cl− channel ATP GTP cAMP β γ cAMP Na+ Cl– Cl− Ca2+ Ca2+ Ca2+ Golf Na+/Ca2+ exchanger Na+ Conserved amino acids Variable amino acids C N (B) Figure 14.7 Olfactory transduction and olfactory receptor molecules. (A) Odorants in the mucus bind directly (or are shuttled via odorant binding pro-teins) to one of many receptor molecules located in the membranes of the cilia. This association activates an odorant-specific G-protein (Golf) that, in turn, activates an adenylate cyclase, resulting in the generation of cyclic AMP (cAMP). One target of cAMP is a cation-selective channel that, when open, permits the influx of Na+ and Ca2+ into the cilia, resulting in depolarization. The ensuing increase in intracellular Ca2+ opens Ca2+-gated Cl– channels that provide most of the depolarization of the olfac-tory receptor potential. The receptor potential is reduced in magnitude when cAMP is broken down by specific phos-phodiesterases to reduce its concentra-tion. At the same time, Ca2+ complexes with calmodulin (Ca2+-CAM) and binds to the channel, reducing its affinity for cAMP. Finally, Ca2+ is extruded through the Ca2+/Na+ exchange pathway. (B) The generic structure of putative olfac-tory odorant receptors. These proteins have seven transmembrane domains, plus a variable cell surface region and a cytoplasmic tail that interacts with G-proteins. As many as 1000 genes encode proteins of similar inferred structure in several mammalian species, including humans. Each gene presumably encodes an odorant receptor that detects a partic-ular set of odorant molecules. (Adapted from Menini, 1999.) 346 Chapter Fourteen voltage-dependent block, several channels must be opened at once. This requirement ensures that olfactory receptor neurons fire only in response to stimulation by odorants. Moreover, changes in the odorant concentration change the latency of response, the duration of the response, and/or the fir-ing frequency of individual neurons, each of which provides additional information about the environmental circumstances to the central stations in the system. Finally, like other sensory receptors, olfactory neurons adapt in the con-tinued presence of a stimulus. Adaptation is apparent subjectively as a decreased ability to identify or discriminate odors during prolonged expo-sure (e.g., decreased awareness of being in a “smoking” room at a hotel as more time is spent there). Physiologically, olfactory receptor neurons indi-cate adaptation by a reduced rate of action potentials in response to the con-tinued presence of an odorant. Adaptation occurs because of (1) increased Ca2+ binding by calmodulin, which decreases the sensitivity of the channel to cAMP; and (2) the extrusion of Ca2+ through the activation of Na+/Ca2+ exchange proteins, which reduces the depolarizing potential from Ca2+ acti-vated Cl– channels. Odorant Receptors Olfactory receptor molecules (Figure 14.7B) are homologous to a large fam-ily of other G-protein-linked receptors that includes β-adrenergic receptors, muscarinic acetylcholine receptors, and the photopigments rhodopsin and the cone opsins. In all invertebrates and vertebrates examined thus far, odor-ant receptor proteins have seven membrane-spanning hydrophobic domains, potential odorant binding sites in the extracellular domain of the protein, and the usual ability to interact with G-proteins at the carboxyl terminal region of their cytoplasmic domain. The amino acid sequences for these mol-ecules also show substantial variability, particularly in regions that code for the membrane-spanning domains. The specificity of olfactory signal trans-duction is presumably the result of this molecular variety of odorant recep-tor molecules present in the nasal epithelium. The numbers of odorant receptor genes in humans and other animals also varies widely (Figure 14.8A). Analysis of the complete human genome sequence has idenfied approximately 950 odorant receptor genes. In rodents (the mouse has been the animal of choice for such studies because of its well-established genetics), genome analysis has identified about 1500 differ-ent odorant receptor genes. Thus, in mammals, odorant receptors are the largest known gene family, representing between 3 and 5% of all genes. Figure 14.8 Odorant receptor genes. (A) The number of genes that encode odorant receptors in C. elegans, Drosophila, mice, and humans are indicated in the appropri-ate boxes. In each instance, we see the seven transmembrane domains characteristic of G-protein-coupled receptors (dark regions); however, the comparative size of each domain, plus the intervening cytoplasmic or cell surface domains, varies from species to species. In addition, splice sites (arrowheads) reflect introns in the genomic sequences of the two invertebrates; in contrast, the genes for mammalian odorant receptors lack introns. (B) The distribution of odorant receptor genes in the human genome. The relative number of genes is indicated by the green bar extend-ing toward the right from each chromosome. There are odorant receptor genes on each human chromosome except for chromosomes 20, 22, and the Y chromosome. (A after Dryer, 2000; B after Mombaerts, 2001.) ▼ (A) (B) TM1 TM2 TM3 TM4 TM5 TM6 TM7 D. melanogaster 60 TM1 TM2 TM3 TM4 TM5 TM6 TM7 C. elegans 1000 TM1 TM2 TM3 TM4 TM5 TM6 TM7 Mammal Mouse 1500 Human 950 20 Y X 22 21 19 13 14 17 18 16 15 6 11 12 9 10 8 7 1 4 2 3 5 348 Chapter Fourteen Additional sequence analysis of human and mouse odorant receptor genes, however, suggests that many—around 60% in human and 20% in mouse— are not transcribed. Thus, the numbers of functional odorant receptor pro-teins are estimated to be around 400 in humans and 1200 in mice. Similar analysis of complete genome sequences from the worm C. elegans and the fruit fly D. melanogaster indicate that there are approximately 1000 odorant receptor genes in the worm, but only about 60 in the fruit fly. The signifi-cance of these quite different numbers of odorant receptor genes is not known. Due to the large number of odorant receptor genes, expression in olfac-tory receptor neurons has only been confirmed for a limited subset (Figure 14.9). Messenger RNAs for different odorant receptor genes are expressed in subsets of olfactory neurons that occur in bilaterally symmetric patches of olfactory epithelium. Additional evidence for odorant receptor gene expres-sion comes from molecular genetic experiments where reporter proteins like β-galactosidase or green fluorescent protein have been inserted into odorant receptor gene loci. In these experiments (done primarily in mice and fruit flies) expression of the reporter protein is limited to individual olfactory receptor neurons and their processes in distinct regions of the olfactory epithelium. Genetic as well as cell biological analysis shows that each olfac-tory receptor neuron expresses only one or at most a few odorant receptor genes. Thus, different odors must activate molecularly and spatially distinct subsets of olfactory receptor neurons. Olfactory Coding Like other sensory receptor cells, individual olfactory receptor neurons are sensitive to a subset of stimuli. Presumably, depending on the particular olfactory receptor molecules they express, some olfactory receptor neurons exhibit marked selectivity to a particular chemical stimulus, whereas others are activated by a number of different odorant molecules (Figure 14.10A). In addition, olfactory receptor neurons can exhibit different thresholds for a particular odorant. That is, receptor neurons that are inactive at concentra-tions sufficient to stimulate some neurons are activated when exposed to higher concentrations of the same odorant. These characteristics suggest (A) (B) (C) (D) Figure 14.9 Odorant receptor gene expression. (A) Individual olfactory receptor neurons labeled immunohisto-chemically with the olfactory marker protein OMP (green label; OMP is selec-tive for all olfactory receptor neurons) and the olfactory receptor neuron-spe-cific adenylyl cyclase III (red label) that is limited to cilia. The labels are in regis-ter with the segregation of signal trans-duction components to this domain. (B) The distribution of OMP-expressing olfactory receptor neurons in the nasal epithelium of an adult mouse, demon-strated with a reporter transgene. The protuberances oriented diagonally from left to right represent individual turbinates within the olfactory epithe-lium. The remaining bony and soft-tis-sue structures of the nose have been dis-sected away. (C) The distribution of olfactory receptor neurons expressing the I7 odorant receptor. These cells are restricted to a distinct domain or zone in the epithelium. The inset photo shows that odorant receptor-expressing cells are indeed cilia-bearing olfactory recep-tor neurons. (D) Olfactory receptor neu-rons expressing the M81 odorant recep-tor are limited to a zone that is completely distinct from that of the I7 receptor. (A courtesy of C. Balmer and A. LaMantia; B–D from Bozza et al., 2002.) why the perception of an odor can change as a function of its concentration (Figure 14.10B). The relationship between physiological tuning of single olfactory receptor neurons and chemical specificity of single odorant recep-tor molecules remains unclear. At present, there is only one mammalian odorant receptor molecule, the I7 receptor, whose ligand specificity has been evaluated. This receptor has a high affinity for the aldehyde n-octanal, as well as some affinity for related molecules. While most of the molecular analysis has been done in rodents, humans can perceive n-octanal—it smells like freshly cut grass. Thus, it is possible that ligands for other individual odorant receptors eventually will be found, and these ligands will corre-spond to perceptually relevant odors. How olfactory receptor neurons represent the identity and concentration of a given odorant is a complex issue that is unlikely to be explained solely by the properties of the primary receptor neurons. Nevertheless, neurons with specific receptors are located in particular parts of the olfactory epithe-lium. As in other sensory systems, the topographical arrangement of recep-tor neurons expressing distinct odorant receptor molecules is referred to as space coding, although the meaning of this phrase in the olfactory system is much less clear than in vision, where a topographical map correlates with visual space. The coding of olfactory information also has a temporal dimen-sion. Sniffing, for instance, is a periodic event that elicits trains of action potentials and synchronous activity in populations of neurons. Information conveyed by timing is called temporal coding and occurs in a variety of species (Box B). The contribution of spatial or temporal coding to olfactory perception is not yet known. The Chemical Senses 349 Background 3.6 × 10–7 M 9.0 × 10–7 M 1.8 × 10–6 M 0 1 2 3 Time (s) 4 5 6 7 (B) 0 –800 0 –400 0 0 Stimulus on Stimulus off 4 6 0 4 Time (s) 6 0 4 6 –600 CINEOLE Neuron 1 (A) Neuron 2 Neuron 3 Membrane current (pA) ISOAMYL ACETATE ACETOPHENONE on off on off Odorant on Odorant off Figure 14.10 Responses of olfactory receptor neurons to selected odorants. (A) Neuron 1 responds similarly to three different odorants. In contrast, neuron 2 responds to only one of these odorants. Neuron 3 responds to two of the three stimuli. The responses of these receptor neurons were recorded by whole-cell patch clamp recording; downward deflections represent inward currents measured at a holding potential of –55 mV. (B) Responses of a single olfactory receptor neuron to changes in the con-centration of a single odorant, isoamyl acetate. The upper trace in each panel (red) indicates the duration of the odor-ant stimulus; the lower trace the neu-ronal response. The frequency and num-ber in each panel of action potentials increases as the odorant concentration increases. (A after Firestein, 1992; B after Getchell, 1986.) 350 Chapter Fourteen The Olfactory Bulb Transducing and relaying odorant information centrally from olfactory receptor neurons are only the first steps in processing olfactory signals. As the olfactory receptor axons leave the olfactory epithelium, they coalesce to form a large number of bundles that together make up the olfactory nerve Box B Temporal “Coding”of Olfactory Information in Insects Most studies of olfaction in mammals have emphasized the spatial patterns of receptors in the nose and glomeruli in the bulb that are activated by specific odorants. However, beginning with Edgar Adrian’s study of the hedgehog olfactory bulb in 1942, odor-induced temporal oscillations have been described in species as diverse as turtles and primates. A variety of functions have been proposed for these oscillatory phe-nomena, including identification of odor type and perception of odor intensity. Gilles Laurent and colleagues at Cali-fornia Institute of Technology have recently found that olfaction in insects does show an important temporal com-ponent related to behavior. By recording intracellularly from neurons in the anten-nal lobe in crickets (a structure analogous to the olfactory bulb in mammals; see also Box A) and extracellularly in the mushroom body (analogous to the mam-malian pyriform cortex), they found that the projection neurons in the antennal lobe (corresponding to mammalian mitral cells) respond to a given odor with a variety of temporal patterns that differ from odor to odor but are reproducible for the same odor. The figure here shows a schematic representation of these tem-poral aspects of the odor response of four such projection neurons. The upper panel shows a local field potential re-cording from the mushroom body (MB) that represents the synaptic activity of many neurons. During presentation of the odor, a pattern of activity is gener-ated by the synchronized firing of many projection neurons. Interestingly, this oscillation at 20–30 Hz is independent of the odor. Each small sphere in the lower panels represents the state of one of the four neurons before, during, and after the application of an odorant. White balls represents a silent or inhibited state, blue balls an active but unsynchronized state, and orange balls an active and synchro-nized state. The figure shows that at dif-ferent times during the odor presenta-tion, various neurons are in synchrony and thus contribute at different times to the field potential recorded in the mush-room body. Desynchronizing the neu-rons has the effect of eliminating the 20–30 Hz oscillation. Desynchronization does not modify the insects’ responses to odors, but eliminates their ability to dis-tinguish among similar odors. These observations suggest that coherent firing among neurons is an important component of olfactory pro-cessing in this species, and raise the pos-sibility that temporal coding is a more important aspect of mammalian olfac-tion than has so far been imagined. References ADRIAN, E. D. (1942) Olfactory reactions in the brain of the hedgehog. J. Physiol. (Lond.) 100: 459–473. FREEMAN, W. J. AND K. A. GRADJSKI (1987) Relation of olfactory EEG to behavior: Factor analysis. Behav. Neurosci. 101: 766–777. KAY L. M. AND G. LAURENT (1999) Odor- and context-dependent modulation of mitral cell activity in behaving rats. Nature Neurosci. 2: 1003–1009. LAM, Y.-W., L. B. COHEN, M. WACHOWIAK AND M. R. ZOCHOWSKI (2000) Odors elicit three different oscillations in the turtle olfactory bulb. J. Neurosci. 202: 749–762. LAURENT, G. (1999) A systems perspective on early olfactory coding. Science 286: 723–728. LAURENT, G., M. WEHR AND H. DAVIDOWITZ (1996) Temporal representation of odors in an olfactory network. J. Neurosci. 15: 3837–3847. STOPFER, M. AND G. LAURENT (1999) Short-term memory in olfactory network dynamics. Nature 402: 664–668. Antennal lobe neurons 1 2 3 4 Field membrane potential (MB) Time (ms) Odor on Odor off Temporal coding of olfactory information in insects. (From Laurent et al., 1996.) (cranial nerve I). Each olfactory nerve projects ipsilaterally to the olfactory bulb on that side, which lies on the ventral anterior aspect of the ipsilateral forebrain. The most distinctive feature of the olfactory bulb is an array of more or less spherical accumulations of neuropil 100–200 µm in diameter called glomeruli, which lie just beneath the surface of the bulb and receive the primary olfactory axons (Figure 14.11A–C). Although a remarkable fea-ture of the mammalian olfactory bulb, glomeruli are found in central ner-vous system regions that process olfaction in most animals, including insects like Drosophila (Figure 14.11A inset) and the moth (see Box A). In vertebrates, the olfactory bulb comprises several cell and neuropil layers that receive, process, and relay olfactory information. Within each glomerulus, the axons of the receptor neurons contact the api-cal dendrites of mitral cells, which are the principal projection neurons of the olfactory bulb. The cell bodies of the mitral cells are located in a distinct layer deep to the olfactory glomeruli and, in adults, extend a primary dendrite into a single glomerulus, where the dendrite gives rise to an elaborate tuft of branches onto which the primary olfactory axons synapse (Figure 14.11B and D). Each glomerulus in the mouse (where glomerular connectivity has been studied quantitatively) includes the apical dendrites of approximately 25 mitral cells, which receive innervation from approximately 25,000 olfactory receptor axons. This degree of convergence presumably serves to increase the sensitivity of mitral cells to ensure odor detection, and to increase the signal strength by averaging out uncorrelated noise. Each glomerulus also includes dendritic processes from two other classes of local circuit neurons: tufted cells and periglomerular cells (approximately 50 tufted cells and 25 periglomerular cells contribute to each glomerulus). Although it is generally assumed that these neurons sharpen the sensitivity of individual glomeruli, their function is unclear. Finally, granule cells, which constitute the innermost layer of the verte-brate olfactory bulb, synapse primarily on the basal dendrites of mitral cells within the external plexiform layer (Figure 14.11C,D). These cells lack an identifiable axon, and instead make dendrodendritic synapses on mitral cells. Granule cells are thought to establish local lateral inhibitory circuits as well as participating in synaptic plasticity in the olfactory bulb. In addition, olfactory granule cells and periglomerular cells are among the few classes of neurons in the forebrain that can be replaced throughout life. Granule cell precursors are maintained in a region outside of the olfactory bulb, within the cells that line the ventricles of the cortical hemispheres called the anterior subventricular zone (see Chapter 24). The neural stem cells in this region can give rise to postmitotic cells that then migrate through a region referred to as the rostral migratory stream that spans the territory between the frontal cor-tex and the olfactory bulb. Once these migrating neurons arrive in the olfac-tory bulb, they can differentiate into either mature granule or periglomerular cells. Although it is tempting to speculate about the functional significance of this ongoing generation of granule cells, little is known about how these newly generated cells influence olfactory function or odor perception. Bilaterally symmetrical subsets of glomeruli in the olfactory bulb (Figure 14.11E) receive input from olfactory receptor neurons that express distinct odorant receptor molecules. Thus, there is a special zone-to-zone projection between individual glomeruli in the olfactory bulb and groups of olfactory receptor neurons. As already mentioned, however, there is no obvious sys-tematic representation in this arrangement as there is, for example, in the somatic sensory or visual systems. Rather, there is an affinity between widely distributed cells in the olfactory epithelium and a limited ensemble The Chemical Senses 351 352 Chapter Fourteen Axons Axons (C) Olfactory epithelium Olfactory receptor cells Axons of olfactory receptor cells Cribriform plate Granule cells Glomerulus Periglomerular cell Mitral cell Tufted cell Lateral olfactory tract to olfactory cortex (D) (E) (A) (B) (C) Mitral cell layer Mitral cell layer Granule cell layer Granule cell layer Glomeruli Glomeruli External plexiform External plexiform layer layer Mitral cell layer Granule cell layer Glomeruli External plexiform layer Internal plexiform layer Internal plexiform layer Internal plexiform layer of target glomeruli. This arrangement suggests that individual glomeruli respond specifically (or at least selectively) to distinct odorants. Many inves-tigations have confirmed the selective (but not uniquely specific) responsive-ness of glomeruli to particular odorants using electrophysiological methods, voltage-sensitive dyes, and, most recently, intrinsic signals that depend on blood oxygenation (Figure 14.12). Such studies have also shown that increas-ing the odorant concentration increases the activity of individual glomeruli, as well as the number of glomeruli activated. While the exact mechanism by which these distributed patterns of activity represent odor quality and con-centration remains unclear, one useful metaphor is to consider the sheet of glomeruli in the olfactory bulb as a bank of lights on a movie marquee: the spatial distribution of active and inactive glomeruli provides a message that is unique for a given odorant at a particular concentration. Central Projections of the Olfactory Bulb Glomeruli in the olfactory bulb are the sole target of olfactory receptor neu-rons, and thus the only relay—via the axons of mitral and tufted cells—for olfactory information from the periphery to the rest of the brain. The mitral cell axons form a bundle—the lateral olfactory tract—that projects to the accessory olfactory nuclei, the olfactory tubercle, the entorhinal cortex, and portions of the amygdala (see Figure 14.1A). The major target of the olfac-tory tract is the three-layered pyriform cortex in the ventromedial aspect of The Chemical Senses 353 Figure 14.11 The organization of the mammalian olfactory bulb. (A) When the bulb is viewed from its dorsal surface (visualized here in a living mouse in which the overlying bone has been removed), olfactory glomeruli can be seen. The dense accumulation of dendrites and synapses that constitute glomeruli are stained here with a vital fluorescent dye that recognizes neuronal processes. The inset shows a similar arrangement of glomeruli in the mushroom body (the equivalent of the olfactory bulb) in Drosophila. (B) Among the major neuronal components of each glomerulus are the apical tufts of mitral cells, which project to the pyriform cortex and other bulb targets (see Figure 14.1C). In this image of a coronal section through the bulb, they have been labeled retrogradely by placing the lipophilic tracer Di-I in the lateral olfactory tract. (C) The cellular structure of the olfactory bulb, shown in a Nissl-stained coronal section. The five layers of the bulb are indicated. The glomerular layer includes the tufts of mitral cells, the axon terminals of olfactory receptor neurons, and periglomerular cells that define the margins of each glomeru-lus. The external plexiform layer is made up of lateral dendrites of mitral cells, cell bodies and lateral dendrites of tufted cells, and dendrites of granule cells that make dendrodendritic synapses with the other dendritic elements. The mitral cell layer is defined by the cell bodies of mitral cells, and mitral cell axons are found in the internal plexiform layer. Finally, granule cell bodies are densely packed into the granule cell layer. (D) Diagram of the laminar and circuit organization of the olfac-tory bulb, shown in a cutaway view from its medial surface. Olfactory receptor cell axons synapse with mitral cell apical dendritic tufts and periglomerular cell processes within glomeruli. Granule cells and mitral cell lateral dendrites constitute the major synaptic elements of the external plexiform layer. (E) Axons from olfac-tory receptor neurons that express a particular odorant receptor gene converge on a small subset of bilaterally symmetrical glomeruli. These glomeruli, indicated in the boxed area in the upper panel, are shown at higher magnification in the lower panel. The projections from the olfactory epithelium have been labeled by a reporter transgene inserted by homologous recombination (“knocked in”) into the genetic locus that encodes the particular receptor. (A from LaMantia et al., 1992; B,C from Pomeroy et al., 1990; E from Mombaerts et al., 1996.) ▲ 354 Chapter Fourteen Figure 14.12 Glomerular activity recorded by optical imaging (see Box C in Chapter 11). Dorsal surface of the olfactory bulb in a living rat monitored as increasing concentrations of amyl acetate are presented to the animal. The higher the concentration, the more intense the activity in the particular glomeruli that respond to the odor. The column at left shows the entire dorsal surface of the olfactory bulb; the col-umn at right shows a higher magnifica-tion of the individual glomeruli (indi-cated by the box in the left-hand column). (From Rubin and Katz, 1999.) the temporal lobe near the optic chiasm. Neurons in pyriform cortex respond to odors, and mitral cell inputs from glomeruli receiving odorant receptor-specific projections remain partially segregated. The further processing that occurs in this region, however, is not well understood. The axons of pyramidal cells in the pyriform cortex project in turn to sev-eral thalamic and hypothalamic nuclei and to the hippocampus and amyg-dala. Some neurons from pyriform cortex also innervate a region in the orbitofrontal cortex comprising multimodal neurons that respond to olfac-tory and gustatory stimuli. Information about odors thus reaches a variety of forebrain regions, allowing olfactory cues to influence cognitive, visceral, emotional, and homeostatic behaviors The Organization of the Taste System The taste system, acting in concert with the olfactory and trigeminal sys-tems, indicates whether food should be ingested. Once in the mouth, the chemical constituents of food interact with receptors on taste cells located in epithelial specializations called taste buds in the tongue. The taste cells transduce these stimuli and provide additional information about the iden-tity, concentration, and pleasant or unpleasant quality of the substance. This information also prepares the gastrointestinal system to receive food by causing salivation and swallowing (or gagging and regurgitation if the sub-stance is unpleasant). Information about the temperature and texture of food is transduced and relayed from the mouth via somatic sensory receptors from the trigeminal and other sensory cranial nerves to the thalamus and somatic sensory cortices (see Chapters 8 and 9). Of course, food is not simply 0.001% 0.01% 0.1% 1% 5% 10% 100% Amyl actetate concentration eaten for nutritional value; “taste” also depends on cultural and psychologi-cal factors. How else can one explain why so many people enjoy consuming hot peppers or bitter-tasting liquids such as beer? Like the olfactory system, the taste system includes both peripheral recep-tors and a number of central pathways (Figure 14.13). Taste cells (the periph-eral receptors) are found in taste buds distributed on the dorsal surface of the tongue, soft palate, pharynx, and the upper part of the esophagus (Fig-ure 14.13A; see also Figure 14.14). These cells make synapses with primary sensory axons that run in the chorda tympani and greater superior petrosal branches of the facial nerve (cranial nerve VII), the lingual branch of the glossopharyngeal nerve (cranial nerve IX), and the superior laryngeal branch The Chemical Senses 355 (B) Insula and frontal cortex Hypothalamus Amygdala Taste buds (ant. two-thirds of tongue) Cranial nerve VII Taste buds (post. one-third of tongue) Taste buds (epiglottis) VPM of thalamus Solitary nucleus of brainstem Cranial nerve IX Cranial nerve X Larynx Tongue VII X IX Axons from the nucleus of the solitary tract Nucleus of the solitary tract Gustatory cortex Gustatory cortex Ventral posterior medial nucleus of thalamus Ventral posterior medial nucleus of thalamus (frontal operculum) (insula) (A) Figure 14.13 Organization of the human taste system. (A) Drawing on the left shows the relationship between recep-tors in the oral cavity and upper alimentary canal, and the nucleus of the solitary tract in the medulla. The coronal sec-tion on the right shows the VPM nucleus of the thalamus and its connection with gustatory regions of the cerebral cor-tex. (B) Diagram of the basic pathways for processing taste information. 356 Chapter Fourteen of the vagus nerve (cranial nerve X) to innervate the taste buds in the tongue, palate, epiglottis, and esophagus, respectively (see Appendix A for a review of the cranial nerves). The central axons of these primary sensory neurons in the respective cranial nerve ganglia project to rostral and lateral regions of the nucleus of the solitary tract in the medulla (Figure 14.13B), which is also known as the gustatory nucleus of the solitary tract complex (recall that the posterior region of the solitary nucleus is the main target of afferent visceral sensory information related to the sympathetic and parasympathetic divi-sions of the visceral motor system; see Chapter 20). The distribution of these cranial nerves and their branches in the oral cav-ity is topographically represented along the rostral–caudal axis of the rostral portion of the gustatory nucleus; the terminations from the facial nerve are rostral, the glossopharyngeal are in the mid-region, and those from the vagus nerve are more caudal in the nucleus. Integration of taste and visceral sensory information is presumably facilitated by this arrangement. The cau-dal part of the nucleus of the solitary tract also receives innervation from subdiaphragmatic branches of the vagus nerve, which control gastric motil-ity. Interneurons connecting the rostral and caudal regions of the nucleus represent the first interaction between visceral and gustatory stimuli. This close relationship of gustatory and visceral information makes good sense, since an animal must quickly recognize if it is eating something that is likely to make it sick, and respond accordingly. Axons from the rostral (gustatory) part of the solitary nucleus project to the ventral posterior complex of the thalamus, where they terminate in the medial half of the ventral posterior medial nucleus. This nucleus projects in turn to several regions of the cortex, including the anterior insula in the tem-poral lobe and the operculum of the frontal lobe. There is also a secondary cortical taste area in the caudolateral orbitofrontal cortex, where neurons respond to combinations of visual, somatic sensory, olfactory, and gustatory stimuli. Interestingly, when a given food is consumed to the point of satiety, specific orbitofrontal neurons in the monkey diminish their activity to that tastant, suggesting that these neurons are involved in the motivation to eat (or not to eat) particular foods. Finally, reciprocal projections connect the nucleus of the solitary tract via the pons to the hypothalamus and amygdala (see Figure 14.13B). These projections presumably influence appetite, satiety, and other homeostatic responses associated with eating (recall that the hypothalamus is the major center governing homeostasis; see Chapter 20). Taste Perception in Humans Most taste stimuli are nonvolatile, hydrophilic molecules soluble in saliva. Examples include salts such as NaCl needed for electrolyte balance; essential amino acids such as glutamate needed for protein synthesis; sugars such as glucose needed for energy; and acids such as citric acid that indicate the palatability of various foods (oranges, in the case of citrate). Bitter-tasting molecules, including plant alkaloids like atropine, quinine, and strychnine, indicate foods that may be poisonous. Placing bitter compounds in the mouth usually deters ingestion unless one “acquires a taste” for the sub-stance, as for the quinine in tonic water. The taste system encodes information about the quantity as well as the identity of stimuli. In general, the higher the stimulus concentration, the greater the perceived intensity of taste. Threshold concentrations for most ingested tastants are quite high, however. For example, the threshold con-centration for citric acid is about 2 mM; for salt (NaCl), 10 mM; and for sucrose, 20 mM. (Recall that the perceptual threshold for some odorants is as low as 0.01 nM.) Because the body requires substantial concentrations of salts and carbohydrates, taste cells may respond only to relatively high con-centrations of these essential substances in order to promote an adequate intake. Clearly, it is advantageous for the taste system to detect potentially dangerous substances (e.g., bitter-tasting plant compounds that may be nox-ious or poisonous) at much lower concentrations. Thus the threshold con-centration for quinine is 0.008 mM, and for strychnine 0.0001 mM. As in olfaction, gustatory sensitivity declines with age. Adults tend to add more salt and spices to food than children. The decreased sensitivity to salt can be problematic for older people with electrolyte and/or fluid balance problems. Unfortunately, a safe and effective substitute for NaCl has not yet been developed. There is a common misconception that sweet is perceived at the tip of the tongue, salt along its posterolateral edges, sour along the mediolateral edges, and bitter on the back of the tongue. This arrangement was initially pro-posed in 1901 by Deiter Hanig, who measured taste thresholds for NaCl, sucrose, quinine, and hydrochloric acid (HCl). Hanig never said that other regions of the tongue were insensitive to these chemicals, but only indicated which regions were most sensitive. People missing the anterior part of their tongue (or who have facial nerve lesions) can still taste sweet and salty stim-uli. In fact, all of these tastes can be detected over the full surface the tongue (Figure 14.14A). However, different regions of the tongue do have different thresholds. Because the tip of the tongue is most responsive to sweet-tasting compounds, and because these compounds produce pleasurable sensations, information from this region activates feeding behaviors such as mouth movements, salivary secretion, insulin release, and swallowing. In contrast, responses to bitter compounds are greatest on the back of the tongue. Acti-vation of this region by bitter-tasting substances elicits protrusion of the tongue and other protective reactions that prevent ingestion. Sour-tasting compounds elicit grimaces, puckering responses, and massive salivary secre-tion to dilute the tastant. Based on general agreement across cultures, there are five perceptually distinct categories of taste: salt, sour, sweet, umami (from the Japanese word for delicious, umami refers to savory tastes, including monosodium gluta-mate and other amino acids), and bitter. However, there are obvious limita-tions to this classification. People experience a variety of taste sensations in addition to these five, including astringent (cranberries and tea), pungent (hot peppers and ginger), fat, starchy, and various metallic tastes, to name only a few. In addition, mixtures of chemicals may elicit entirely new taste sensations. But even though the “taste code” defined by the five primary taste classes is not yet fully understood, these tastes correspond to distinct classes of receptors in subsets of taste cells. Thus, taste perception is closely linked to the molecular biology of taste transduction. Idiosyncratic Responses to Tastants Taste responses vary among individuals. For example, many people (about 30–40% of the U.S. population) cannot taste the bitter compound phenylth-iocarbamide (PTC) but can taste molecules such as quinine and caffeine that also produce bitter sensations. Indeed, humans can be divided into two groups with quite different thresholds for bitter compounds containing the N—C=S group found in PTC. The difference between these individuals is the presence of a single autosomal gene (Ptc) with a dominant (tasters) and The Chemical Senses 357 358 Chapter Fourteen a recessive (non-tasters) allele. Interestingly, people who are extremely sensitive to PTC or its analogues—so-called called “supertasters”—have more taste buds than normal and tend to avoid certain foods such as grapefruit, green tea, and broccoli, all of which contain bitter-tasting com-pounds. Thus, an individual’s genetic makeup with respect to taste recep-tors has implications for diet, and even health. The relationship between taste perception and the molecular character of tastants is also variable. A number of quite different compounds taste sweet to humans. These include saccharides (glucose, sucrose, and fruc-tose), organic anions (saccharin), amino acids (aspartame, or Nutra-sweet®), L-phenyalanine methyl ester, and proteins (monellin and thau-matin). People can distinguish among different sweeteners, and some find saccharin to have a bitter-tasting component. One reason for such discrimination is that some of these compounds activate separate recep-tors. For example, saccharides activate cAMP pathways, whereas nonsac-(A) (B) Circumvallate papillae (cranial nerve IX) Taste pore Microvilli Taste cells Basal cell Synapse Gustatory afferent axons Foliate papilla Bitter Sour Sweet/ umami Salty Fungiform papillae (cranial nerve VII) (C) (D) Taste bud Papilla Trench Figure 14.14 Taste buds and the periph-eral innervation of the tongue. (A) Distri-bution of taste papillae on the dorsal sur-face of the tongue. Different responses to sweet, salty, sour, and bitter tastants recorded in the three cranial nerves that innervate the tongue and epiglottis are indicated at left. (B) Diagram of a circum-vallate papilla showing location of indi-vidual taste buds. (C) Light micrograph of a taste bud. (D) Diagram of a taste bud, showing various types of taste cells and the associated gustatory nerves. The api-cal surface of the receptor cells have microvilli that are oriented toward the taste pore. (C from Ross, Rommell and Kaye, 1995.) charide sweeteners such as amino acids activate IP3 pathways. Thus the per-ceptual experience of “sweet” encompasses much more than the taste of sucrose. It can be elicited by various sensory transduction mechanisms, and may generate sensory qualities different from those generated by sucrose. Taste sensitivity for salt also relies on a number of mechanisms. Not all salts, or even all monovalent chloride salts, activate the same pathway. Psy-chophysical studies have shown that amiloride, a diuretic that blocks Na+ entry through amiloride-sensitive Na+ channels, decreases the taste intensity of NaCl and LiCl, but not KCl. Although LiCl tastes salty, it cannot be used as a substitute for NaCl because it has profound effects on the central ner-vous system—clinically, LiCl is used to treat bipolar disorders. Sodium suc-cinate, NH4Cl, and CsCl do not taste exclusively salty. Indeed, CsCl has a bitter or salty-bitter taste that probably arises from the inhibition of K+ chan-nels. Additional evidence for a distinct receptor for NaCl comes from devel-opmental studies. Infants up to 4 months old can distinguish between water and sucrose (and lactose), water and acid, and water and bitter tastants, but they cannot distinguish between water and a 0.2 M NaCl solution. Thus, either the receptor for Na+ has not yet been expressed, or, if expressed, it is not yet functional. Infants between the ages of 4 and 6 months, however, can discriminate between NaCl solutions and water, and children can detect the full salty taste of NaCl at about 4 years of age. Clearly, a given individual’s perception of tastants results from many idiosyncracies of the taste system. These idiosyncracies may underlie per-sonal preferences and aversions that lead to individual variation in ingestive behaviors (eating and drinking). The French aphorism chacun à son goût (“each to his own taste”) reflects not only individual preferences but the biology of the taste-sensing system. The Organization of the Peripheral Taste System Approximately 4000 taste buds in humans are distributed throughout the oral cavity and upper alimentary canal. Taste buds are about 50 mm wide at their base and approximately 80 mm long, each containing 30 to 100 taste cells (the sensory receptor cells), plus a few basal cells (Figure 14.14B–D). About 75% percent of all taste buds are found on the dorsal surface of the tongue in small elevations called papillae (see Figure 14.14A). There are three types of papillae: fungiform (which contain about 25% of the total number of taste buds), circumvallate (which contain 50% of the taste buds), and foliate (which contain 25%). Fungiform papillae are found only on the anterior two-thirds of the tongue; the highest density (about 30/cm2) is at the tip. Fungiform papillae have a mushroom-like structure (hence their name) and typically have about 3 taste buds at their apical surface. There are 9 circumvallate papillae arranged in a chevron at the rear of the tongue. Each consists of a circular trench containing about 250 taste buds along the trench walls. Two foliate papillae are present on the posterolateral tongue, each hav-ing about 20 parallel ridges with about 600 taste buds in their walls. Thus, chemical stimuli on the tongue first stimulate receptors in the fungiform papillae and then in the foliate and circumvallate papillae. Tastants subse-quently stimulate scattered taste buds in the pharynx, larynx, and upper esophagus. Taste cells in individual taste buds (see Figure 14.14C,D) synapse with pri-mary afferent axons from branches of three cranial nerves: the facial (VII), glossopharyngeal (IX), and vagus (X) nerves (see Figure 14.13). The taste cells in fungiform papillae on the anterior tongue are innervated exclusively by the The Chemical Senses 359 360 Chapter Fourteen chorda tympani branch of the facial nerve; in circumvallate papillae, the taste cells are innervated exclusively by the lingual branch of the glossopharyngeal nerve; and in the palate they are innervated by the greater superior petrosal branch of the facial nerve. Taste buds of the epiglottis and esophagus are innervated by the superior laryngeal branch of the vagus nerve. The initiating events of chemosensory transduction occur in the taste cells, which have receptors on microvilli that emerge from the apical surface of the taste cell (see Figure 14.14D and 14.15). The apical surfaces of individ-ual taste cells in taste buds are clustered in a small opening (about 1 mm) near the surface of the tongue called a taste pore. The synapses that relay the receptor activity are made onto the afferent axons of the various cranial nerves at the basal surface. Like olfactory receptor neurons (and presumably for the same reasons), taste cells have a lifetime of only about 2 weeks and are normally regenerated from basal cells. Taste Receptors and the Transduction of Taste Signals The major perceptual categories of taste—salty, sour, sweet, umami, and bit-ter—are represented by five distinct classes of taste receptors. These recep-tors are found in the apical microvilli of taste cells. Salty and sour tastes are primarily elicited by ionic stimuli such as the positively charged ions in salts (like Na+ from NaCl), or the H+ in acids (acetic acid, for example, which gives vinegar its sour taste). These ions in salty and sour tastants initiate sen-sory transduction via specific ion channels: the amiloride-sensitive Na+ channel for salty tastes, and an H+-sensitive, cation-selective channel for sour (Figures 14.15 and 14.16). The receptor potential generated by the posi-tive inward current carried either by Na+ for salty or H+ for sour depolarizes the taste cell. This initial depolarization leads to the activation of voltage-gated Na+ channels in the basolateral aspect of the taste cell. This additional depolarization activates voltage-gated Ca2+ channels, leading to the release of neurotransmitter from the basal aspect of the taste cell and the activation of action potentials in ganglion cell axons (Figure 14.15). In humans and other mammals, sweet and amino acid (umami) receptors are heteromeric G-protein-coupled receptors that share a common seven-transmembrane receptor subunit called T1R3, which is paired with the T1R2 seven-transmembrane receptor for perception of sweet, or with the T1R1 receptor for amino acids (Figure 14.16). The T1R2 and T1R1 receptors are expressed in different subsets of taste cells, indicating that there are, respec-tively, sweet- and amino acid-selective cells in the taste buds (see Figure 14.17). Upon binding sugars or other sweet stimuli, the T1R2/T1R3 receptor initiates a G-protein-mediated signal transduction cascade that leads to the activation of the phospholipase C isoform PLCβ2, leading in turn to increased concentrations of inositol triphosphate (IP3) and to the opening of TRP channels (specifically the TRPM5 channel), which depolarizes the taste cell via increased intracellular Ca2+. Similarly, the T1R1/T1R3 receptor is broadly tuned to the 20 standard L-amino acids found in proteins (but not to their D-amino acid enantiomers). Transduction of amino acid stimuli via the T1R1/T1R3 receptor also reflects G-protein-coupled intracellular signaling leading to PLCβ2-mediated activation of the TRPM5 channel and depolariza-tion of the taste cell (see Figure 14.16). Another family of G-protein-coupled receptors known as the T2R recep-tors transduce bitter tastes. There are approximately 30 T2R subtypes en-coded by 30 genes in humans and other mammals, and multiple T2R sub-types are expressed in single taste cells. Nevertheless, T2R receptors are not expressed in the same taste cells as T1R1, 2, and 3 receptors. Thus, the recep-tor cells for bitter tastants are presumably a distinct class. Although the transduction of bitter stimuli relies on a similar mechanism to that for sweet and amino acid tastes, a taste cell-specific G-protein, gustducin, is found pri-marily in T2R-expressing taste cells and apparently contributes to the trans-duction of bitter tastes. The remaining steps in bitter transduction are similar to those for sweet and amino acids: PLCβ2-mediated activation of TRPM5 channels depolarizes the taste cell, resulting in the release of neurotransmit-ter at the synapse between the taste cell and sensory ganglion cell axon. The Chemical Senses 361 Transmitter release Endoplasmic reticulum Ca2+ Ca2+ K+ Na+ Ca2+ Second messengers Depolarization Sweet, bitter, umami (amino acid) Salt, acids (sour) Ion channel Na+ channel TRPM5 channel Ca2+ channel K+ channel Receptor G-protein Serotonin receptor Primary sensory neuron Action potential Basolateral domain Apical domain Figure 14.15 Basic components of sen-sory transduction in taste cells. Taste cells are polarized epithelial cells with an apical and a basolateral domain sepa-rated by tight junctions. Tastant-trans-ducing channels (salt and sour) and G-protein-coupled receptors (sweet, amino acid, and bitter) are limited to the apical domain. Intracellular signaling compo-nents that are coupled to taste receptor molecules (G-proteins and various sec-ond messenger-related molecules) are also enriched in the apical domain. Volt-age-regulated Na+, K+, and Ca2+ chan-nels that mediate release of neurotrans-mitter from presynaptic specializations at the base of the cell onto terminals of peripheral sensory afferents are limited to the basolateral domain, as is endo-plasmic reticulum that also modulates intracellular Ca2+ concentration and contributes to the release of neurotrans-mitter. The neurotransmitter serotonin, among others, is found in taste cells, and serotonin receptors are found on the sensory afferents. Finally, the TRPM5 channel, which facilitates G-protein-cou-pled receptor-mediated depolarization, is expressed in taste cells. Its localization to apical versus basal domains is not yet known. 362 Chapter Fourteen Figure 14.16 Molecular mechanisms of taste transduction via ion channels and G-protein-coupled receptors. Cation selectivity of the amiloride-sensi-tive Na+ versus the H+-sensitive proton channel provides the basis for speci-ficity of salt and sour tastes. In each case, positive current via the cation channel leads to depolarization of the cell. For sweet, amino acid (umami), and bitter tastants, different classes of G-protein-coupled receptors mediate transduction. For sweet tastants, het-eromeric complexes of the T1R2 and T1R3 receptors transduce stimuli via a PLCβ2-mediated, IP3-dependent mecha-nism that leads to activation of the TRPM5 Ca2+ channel. For amino acids, heteromeric complexes of T1R1 and T1R3 receptors transduce stimuli via the same PLCβ2/IP3/TRPM5-dependent mechanism. Bitter tastes are transduced via a distinct set of G-protein-coupled receptors, the T2R receptor subtypes.The details of T2R receptors are less well established; however, they apparently associate with the taste cell-specific G-protein gustducin, which is not found in sweet or amino acid recep-tor-expressing taste cells. Nevertheless, stimulus-coupled depolarization for bit-ter tastes relies upon the same PLCβ2/IP3/TRPM5-dependent mecha-nism used for sweet and amino acid taste transduction. Neural Coding in the Taste System In the taste system, neural coding refers to the way that the identity, concen-tration, and “hedonic” (pleasurable or aversive) value of tastants is repre-sented in the pattern of action potentials relayed to the brain. Neurons in the taste system (or in any other sensory system) might be specifically “tuned” to respond with a maximal change in electrical activity to a single taste stim-ulus. Such tuning is thought to rely on specificity at the level of the receptor cells, as well as on the maintenance of separate channels for the relay of this information from the periphery to the brain. This sort of coding scheme is referred to as a labeled line code, since responses in specific cells presum-ably correspond to distinct stimuli. The segregated expression of sweet, amino acid, and bitter receptors in different taste cells (Figure 14.17) is con-sistent with labeled line coding. Amiloride-sensitive Na+ channel Na+ H+-sensitive cation channel Salt Bitter Amino acids (umami) Sweet Acids (sour) IP3 T1R2 α β α β γ G-protein PLCβ2 α T1R3 T1R1 α β α β γ G-protein T1R3 TRPM5 channel Ca2+ PLCβ2 α T2R α β α β γ Gustducin TRPM5 channel IP3 Ca2+ H+ The results of molecular genetic experiments in mice are consistent with a labeled line code. Initial support came from studies in which the genes that specify the sweet and amino acid heteromeric receptors (T1R2 and T1R1) were inactivated in mice. Such mice lack behavioral responses to a broad range of sweet or amino acid stimuli, depending on the gene that has been inactivated. Moreover, recordings of electrical activity in the relevant branches of cranial nerves VII, IX, or X showed that action potentials in response to sweet or amino acid stimuli were lost in parallel with the genetic mutation and behavioral change. Finally, these deficits in transduction and perception were unchanged at a broad range of concentrations, indicating that the molecular specificity of each receptor is quite rigid—the remaining receptors could not respond, even at high concentrations of sweet or amino acid stimuli. These observations suggest that sweet and amino acid transduction and perception depend on labeled lines from the periphery. Bitter taste proved harder to analyze because of the larger number of T2R bitter receptors. To circumvent this challenge, Charles Zuker, Nicholas Ryba and colleagues took advantage of the shared aspects of intracellular signaling for sweet, amino acid, and bitter tastes (see Figure 14.16). Thus, if the genes for either the TRPM5 channel or PLCβ2 are inactivated, behavioral and physiological responses to sweet, amino acid, and bitter stimuli are abolished while salty and sour perception (and the related physiological responses) remain (Fig-ure 14.17). To evaluate whether taste cells expressing the T2R family of receptors provide a labeled line for bitter tastes, PLCβ2 was selectively re-expressed in T2R-expressing taste cells in a PLCb2 mutant mouse. Thus, in these mice, only the taste cells that normally express the T2R subset of taste cells (which expresses most of the T2R receptors in concert) can now tran-duce taste signals. If these cells provide a labeled line for bitter tastes, the “rescued” mice (i.e., those expressing PLCβ2 in T2R cells) should regain their perceptual and physiological responses to bitter taste, but not to sweet or amino acid tastes. This was indeed the result of the experiment—behavioral and physiological responses to bitter tastes, but not sweet or amino acid tastes, were restored to normal levels (see Figure 14.17). Evidently, taste cod-ing for sweet, amino acid, and bitter—as judged by taste perception and the related neural activity in peripheral nerves—reflects labeled lines established by the identity of the taste receptor proteins and the subsets of taste cells that express them. These observations support the labeled line hypothesis for primary tastes; however, they do not provide a full account of how either primary or com-plex tastes are represented in patterns of neural activity in central stations of the taste system (e.g., the solitary nucleus, the thalamus, or the insular cor-tex). Indeed, little is known about the representation of taste information in the CNS, either at the level of recordings from individual cells or the repre-sentation of tastes across an ensemble of neurons in relevant areas of the brainstem, thalamus, or cortex. Trigeminal Chemoreception The third of the major chemosensory systems, the trigeminal chemosensory system, consists of polymodal nociceptive neurons and their axons in the trigeminal nerve (cranial nerve V) and, to a lesser degree, nociceptive neu-rons whose axons run in the glossopharyngeal and vagus nerves (IX and X) (see Appendix A). These neurons and their associated endings are typically The Chemical Senses 363 364 Chapter Fourteen activated by chemicals classified as irritants, including air pollutants (e.g., sulfur dioxide), ammonia (smelling salts), ethanol (liquor), acetic acid (vine-gar), carbon dioxide (in soft drinks), menthol (in various inhalants sensa-tion; see Box A in Chapter 9), and capsaicin (the compound in hot chili pep-pers that elicits the characteristic burning sensation). Irritant-sensitive polymodal nociceptors alert the organism to potentially harmful chemical stimuli that have been ingested, respired, or come in contact with the face, and are closely tied to the trigeminal pain system discussed in Chapter 9. Trigeminal chemosensory information from the face, scalp, cornea, and mucous membranes of the oral and nasal cavities is relayed via the three major sensory branches of the trigeminal nerve: the ophthalmic, maxillary, Sweet (T1R2) Umami (T1R1) Bitter (T2Rs) (A) (B) (C) (D) (E) (F) (G) (H) (I) Behavioral response (relative to water) Sucrose (mM) 10 30 100 300 1000 8 6 4 2 0 Behavioral response (relative to water) Glutamate (mM) 12 3 10 30 100 10 8 6 4 2 0 Behavioral response (relative to water) Glutamate (mM) 12 3 10 30 100 10 8 6 4 2 0 Behavioral response (relative to water) Quinine (mM) 1.2 0.01 0.1 1.0 10 0.8 0.4 0.0 Behavioral response (relative to water) Quinine (mM) 1.2 0.01 0.1 1.0 10 0.8 0.4 0.0 Behavioral response (relative to water) Sucrose (mM) 10 30 100 300 1000 8 6 4 2 0 Taste cells Taste cells Lingual epithelium Lingual epithelium T2R–rescue Wild type Wild type PLCb2 –/– TRPM5 –/– T2R– rescue Wild type Wild type TRPM5 –/– PLCb2 –/– T2R–rescue Wild type Wild type PLCb2 –/– TRPM5 –/– and mandibular (Figure 14.18). The central target of these afferent axons is the spinal component of the trigeminal nucleus, which relays this informa-tion to the ventral posterior medial nucleus of the thalamus and thence to the somatic sensory cortex and other cortical areas that process facial irrita-tion and pain (see Chapter 9). Many compounds classified as irritants can also be recognized as odors or tastes; however, the threshold concentrations for trigeminal chemoreception are much higher than those for olfaction or taste. When potentially irritating compounds are presented to people who have lost their sense of smell, per-ceptual thresholds are found to be approximately 100 times higher than those of normal subjects who perceive the compounds as odors (Figure 14.19). Similar differences occur in identifying chemicals as tastes rather than irritants. Thus, 0.1 M NaCl has a salty taste, but 1.0 M NaCl is perceived as an irritant. Another common irritant is ethanol. When placed on the tongue at moderate temperatures and high concentrations—as in drinking vodka “neat”—ethanol produces a burning sensation. A variety of physiological responses mediated by the trigeminal chemo-sensory system are triggered by exposure to irritants. These include increased salivation, vasodilation, tearing, nasal secretion, sweating, de-creased respiratory rate, and bronchoconstriction. Consider, for instance, the experience that follows the ingestion of capsaicin (see Box A in Chapter 9). These reactions are generally protective in that they dilute the stimulus (tearing, salivation, sweating) and prevent inhaling or ingesting more of it. The receptors for irritants are primarily on the terminal branches of poly-modal nociceptive neurons, as described for the pain and temperature sys-tems in Chapter 9. Although these receptors respond to many of the same stimuli as olfactory receptor neurons (e.g., aldehydes, alcohols), they are probably not activated by the same mechanism; for instance, the G-protein-coupled receptors for odorants are found only in olfactory receptor neurons. With the exception of capsaicin and acidic stimuli, both of which activate cation-selective ion channels, little is known about the transduction mecha-nisms for irritants, or their central processing. The Chemical Senses 365 Figure 14.17 Specificity in peripheral taste coding supports the labeled line hypothesis. (A–C) Sweet (A), amino acid (B), and bitter (C) receptors are expressed in different subsets of taste cells. (D–E) The gene for the TRPM5 channel can be inac-tivated, or “knocked out,” in mice (TRPM5 –/–) and behavioral responses measured with a taste preference test. The mouse is presented with two drinking spouts, one with water and the other with a tastant; behavioral responses are measured as the frequency of licking of the two spouts. For pleasant tastes like sweet (sucrose; D) or umami (glutamate; E) control mice lick the spout with the tastant more frequently, and higher concentrations of tastant leads to increased response (blue lines). In TRPM5 –/– mice, this behavioral response (i.e., a preference for the tastant versus water) is eliminated at all concentrations (red lines). (F) For an aversive tastant like bitter quinine, control mice prefer water. This behavioral response—which is ini-tially low—is further diminished with higher quinine concentrations (blue line). Inactivation of TRPM5 also eliminates this behavioral response, regardless of tastant concentration (red line). (G–I) When the PLCb2 gene is knocked out, behavioral response to (G) sucrose, (H) glutamate, and (I) quinine are eliminated (red lines). When PLCb2 is re-expressed only in T2R-expressing taste cells, behavioral responses to sucrose and glutamate are not rescued (dotted green lines in G and H); however, the behavioral response to quinine is restored to normal levels (compare the blue and dotted green lines in I). (After Zhang et al., 2003.) ▲ Figure 14.18 Diagram of the branches of the trigeminal nerve that innervate the oral, nasal, and ocular cavities. The chemosensitive structures innervated by each trigeminal branch are indicated in parentheses. Mandibular nerve Ethmoid nerve (nose) Ciliary nerves (cornea) Lingual nerve (tongue) Inferior alveolar nerve (teeth) Maxillary nerve Ophthalmic nerve Trigeminal ganglion 366 Chapter Fourteen Summary The chemical senses—olfaction, taste, and the trigeminal chemosensory sys-tem—all contribute to sensing airborne or soluble molecules from a variety of sources. Humans and other mammals rely on this information for behaviors as diverse as attraction, avoidance, reproduction, feeding, and avoiding potentially dangerous circumstances. Receptor neurons in the olfactory epithelium transduce chemical stimuli into neuronal activity via the stimula-tion of G-protein-linked receptors; this interaction leads to elevated levels of second messengers such as cAMP, which in turn open cation-selective chan-nels. These events generate receptor potentials in the membrane of the olfac-tory receptor neuron, and ultimately action potentials in the afferent axons of these cells. Taste receptor cells, in contrast, use a variety of mechanisms for transducing chemical stimuli. These include ion channels that are directly activated by salts and amino acids, and G-protein-linked receptors that acti-vate second messengers. For both smell and taste, the spatial and temporal patterns of action potentials provide information about the identity and intensity of chemical stimuli. The trigeminal chemosensory system responds to irritants by means of mechanisms that are less well understood. Each of the approximately 10,000 odors that humans recognize (and an undeter-mined number of tastes and irritant molecules) is evidently encoded by the activity of a distinct population of receptor cells in the nose, tongue, and oral cavity. Olfaction, taste, and trigeminal chemosensation all are relayed via spe-cific pathways in the central nervous system. Receptor neurons in the olfac-tory system project directly to the olfactory bulb. In the taste system, infor-mation is relayed centrally by cranial sensory ganglion cells to the solitary nucleus in the brainstem. In the trigeminal chemosensory system, informa-tion is relayed via trigeminal ganglion cell projections to the spinal trigeminal nucleus in the brainstem. Each of these structures project in turn to many sites in the brain that process chemosensory information in ways that give rise to some of the most sublime pleasures that humans experience. Carbon chain length PEA Pyr Men 105 104 103 102 101 100 10−1 10−2 10−3 Threshold (ppm) 1 2 3 4 5 6 7 8 Normal subjects Anosmics Figure 14.19 Perceptual thresholds in anosmic and normal subjects for related organic chemicals. In anosmics, these chemicals are only detected as irritants at relatively high concentrations (indi-cated here in parts per million, ppm); in normal subjects, they are first detected at much lower concentrations as odors. The numbers 1–8 stand for the aliphatic alcohols from methanol to 1-octanol. Perceptual thresholds for three addi-tional common irritants—phenylethyl alcohol (PEA), pyridine (Pyr), and men-thol (Men)—are shown at the far right. (After Commetto-Muniz and Cain, 1990.) The Chemical Senses 367 Additional Reading Reviews BUCK, L. B. (2000) The molecular architecture of odor and pheromone sensing in mammals. Cell 100: 611–618. ERICKSON, R. P. (1985) Definitions: A matter of taste. In Taste, Olfaction, and the Central Ner-vous System. D. W. Pfaff (ed.). New York: Rockefeller University Press, p. 129. HERNESS, M. S. AND T. A. GILBERTSON (1999) Cellular mechanisms of taste transduction. Annu. Rev. Physiol. 61: 873–900. HILDEBRAND, J. G. AND G. M. SHEPHERD (1997) Mechanisms of olfactory discrimination: Con-verging evidence for common principles across phyla. Annu. Rev. Neurosci. 20: 595–631. KRUGER, L. AND P. W. MANTYH (1989) Gusta-tory and related chemosensory systems. In Handbook of Chemical Neuroanatomy, Vol. 7, Integrated Systems of the CNS, Part II. A. Björk-land, T. Hökfelt and L. W. Swanson (eds.). New York: Elsevier Science, pp. 323–410. LAURENT, G. (1999) A systems perspective on early olfactory coding. Science 286: 723–728. LINDEMANN, B. (1996) Taste reception. Physiol. Rev. 76: 719–766. MENINI, A. (1999) Calcium signaling and regu-lation in olfactory neurons. Curr. Opin. Neu-robiol. 9: 419–426. YAMAMOTO, T., T. NAGAI, T. SHIMURA AND Y. YASOSHIMA (1998) Roles of chemical mediators in the taste system. Jpn. J. Pharmacol. 76: 325–348. ZUTALL, F. AND T. LEINDERS-ZUTALL (2000) The cellular and molecular basis of odor adapta-tion. Chem. Senses 25: 473–481. Important Original Papers ADLER, E., M. A. HOON, K. L. MUELLER, J. CHRANDRASHEKAR, N. J. P. RYBA AND C. S. ZUCKER (2000) A novel family of mammalian taste receptors. Cell 100: 693–702. ASTIC, L. AND D. SAUCIER (1986) Analysis of the topographical organization of olfactory epithelium projections in the rat. Brain Res. Bull. 16(4): 455–462. AVANET, P. AND B. LINDEMANN (1988) Amiloride-blockable sodium currents in isolated taste receptor cells. J. Memb. Biol. 105: 245–255. BUCK, L. AND R. AXEL (1991) A novel multi-gene family may encode odorant receptors: A molecular basis for odor recognition. Cell 65: 175–187. CATERINA, M. J. AND 8 OTHERS (2000) Impaired nociception and pain sensation in mice lacking the capsaicin receptor. Science 288: 306–313. CHAUDHARI, N., A. M. LANDIN AND S. D. ROPER (2000) A metabotropic glutamate receptor variant functions as a taste receptor. Nature Neurosci. 3: 113–119. GRAZIADEI, P. P. C. AND G. A. MONTI-GRAZIADEI (1980) Neurogenesis and neuron regeneration in the olfactory system of mammals. III. Deaf-ferentation and reinnervation of the olfactory bulb following section of the fila olfactoria in rat. J. Neurocytol. 9: 145–162. KAY, L. M. AND G. LAURENT (2000) Odor- and context-dependent modulation of mitral cell activity in behaving rats. Nature Neurosci. 2: 1003–1009. MALNIC, B., J. HIRONO, T. SATO AND L. B. BUCK (1999) Combinatorial receptor codes for odors. Cell 96: 713–723. MOMBAERTS, P. AND 7 OTHERS (1996) Visualizing an olfactory sensory map. Cell 87: 675–686. NELSON, G., M. A. HOON, J. CHANDRASHEKAR, Y. ZHANG, N. J. P. RYBA AND C. S. ZUKER (2001) Mammalian sweet taste receptors. Cell 106: 381–390. NELSON, G. AND 6 OTHERS. (2002) An amino-acid taste receptor. Nature 416: 199–202. ROLLS, E. T. AND L. L. BAYLIS (1994) Gustatory, olfactory and visual convergence within pri-mate orbitofrontal cortex. J. Neurosci. 14: 5437–5452. SCHIFFMAN, S. S., E. LOCKHEAD AND F. W. MAES (1983) Amiloride reduces taste intensity of salts and sweeteners. Proc. Natl. Acad. Sci. USA 80: 6136–6140. VASSAR, R., S. K. CHAO, R. SITCHERAN, J. M. NUNEZ, L. B. VOSSHALL AND R. AXEL (1994) Topographic organization of sensory projec-tions to the olfactory bulb. Cell 79: 981–991. WONG, G. T., K. S. GANNON AND R. F. MAR-GOLSKEE (1996) Transduction of bitter and sweet taste by gustducin. Nature 381: 796–800. ZHANG, Y. AND 7 OTHERS. (2003) Coding of sweet, bitter, and umami tastes: Different receptor cells sharing similar signaling path-ways. Cell 112: 293–301. ZHAO, G. Q. AND 6 OTHERS (2003) The recep-tors for mammalian sweet and umami taste. Cell 115: 255–266. Books BARLOW, H. B. AND J. D. MOLLON (1989) The Senses. Cambridge: Cambridge University Press, Chapters 17–19. DOTY, R. L. (ED.) (1995) Handbook of Olfaction and Gustation. New York: Marcel Dekker. FARBMAN, A. I. (1992) Cell Biology of Olfaction. New York: Cambridge University Press. GETCHELL, T. V., L. M. BARTOSHUK, R. L. DOTY AND J. B. SNOW, JR. (1991) Smell and Taste in Health and Disease. New York: Raven Press. SIMON, S. A. AND S. D. ROPER (1993) Mecha-nisms of Taste Transduction. Boca Raton, FL: CRC Press. Movement and Its Central Control III Fluorescence photomicrograph showing motor axons (green) and neuromuscular synapses (orange) in transgenic mice that have been genetically engineered to express fluores-cent proteins. (Courtesy of Bill Snider and Jeff Lichtman.) UNIT III MOVEMENT AND ITS CENTRAL CONTROL 15 Lower Motor Neuron Circuits and Motor Control 16 Upper Motor Neuron Control of the Brainstem and Spinal Cord 17 Modulation of Movement by the Basal Ganglia 18 Modulation of Movement by the Cerebellum 19 Eye Movements and Sensory Motor Integration 20 The Visceral Motor System Movements, whether voluntary or involuntary, are produced by spa-tial and temporal patterns of muscular contractions orchestrated by the brain and spinal cord. Analysis of these circuits is fundamental to an understanding of both normal behavior and the etiology of a variety of neurological disorders. This unit considers the brainstem and spinal cord circuitry that make elementary reflex movements possible, as well as the circuits that organize the intricate patterns of neural activity responsible for more complex motor acts. Ultimately, all movements produced by the skeletal musculature are initiated by “lower” motor neurons in the spinal cord and brainstem that directly innervate skeletal muscles; the innervation of visceral smooth muscles is separately organized by the autonomic divisions of the visceral motor system. The lower motor neurons are controlled directly by local cir-cuits within the spinal cord and brainstem that coordinate individ-ual muscle groups, and indirectly by “upper” motor neurons in higher centers that regulate those local circuits, thus enabling and coordinating complex sequences of movements. Especially impor-tant are circuits in the basal ganglia and cerebellum that regulate the upper motor neurons, ensuring that movements are performed with spatial and temporal precision. Specific disorders of movement often signify damage to a par-ticular brain region. For example, clinically important and inten-sively studied neurodegenerative disorders such as Parkinson’s dis-ease, Huntington’s disease, and amyotrophic lateral sclerosis result from pathological changes in different parts of the motor system. Knowledge of the various levels of motor control is essential for understanding, diagnosing, and treating these diseases. Overview Skeletal (striated) muscle contraction is initiated by “lower” motor neurons in the spinal cord and brainstem. The cell bodies of the lower neurons are located in the ventral horn of the spinal cord gray matter and in the motor nuclei of the cranial nerves in the brainstem. These neurons (also called α motor neurons) send axons directly to skeletal muscles via the ventral roots and spinal peripheral nerves, or via cranial nerves in the case of the brain-stem nuclei. The spatial and temporal patterns of activation of lower motor neurons are determined primarily by local circuits located within the spinal cord and brainstem. Descending pathways from higher centers comprise the axons of “upper” motor neurons and modulate the activity of lower motor neurons by influencing this local circuitry. The cell bodies of upper motor neurons are located either in the cortex or in brainstem centers, such as the vestibular nucleus, the superior colliculus, and the reticular formation. The axons of the upper motor neurons typically contact the local circuit neu-rons in the brainstem and spinal cord, which, via relatively short axons, con-tact in turn the appropriate combinations of lower motor neurons. The local circuit neurons also receive direct input from sensory neurons, thus mediat-ing important sensory motor reflexes that operate at the level of the brain-stem and spinal cord. Lower motor neurons, therefore, are the final common pathway for transmitting neural information from a variety of sources to the skeletal muscles. Neural Centers Responsible for Movement The neural circuits responsible for the control of movement can be divided into four distinct but highly interactive subsystems, each of which makes a unique contribution to motor control (Figure 15.1). The first of these subsys-tems is the local circuitry within the gray matter of the spinal cord and the analogous circuitry in the brainstem. The relevant cells include the lower motor neurons (which send their axons out of the brainstem and spinal cord to innervate the skeletal muscles of the head and body, respectively) and the local circuit neurons (which are the major source of synaptic input to the lower motor neurons). All commands for movement, whether reflexive or voluntary, are ultimately conveyed to the muscles by the activity of the lower motor neurons; thus these neurons comprise, in the words of the great British neurophysiologist Charles Sherrington, the “final common path” for movement. The local circuit neurons receive sensory inputs as well as descending projections from higher centers. Thus, the circuits they form pro-vide much of the coordination between different muscle groups that is Chapter 15 371 Lower Motor Neuron Circuits and Motor Control 372 Chapter Fifteen Figure 15.1 Overall organization of neural structures involved in the control of movement. Four systems—local spinal cord and brainstem circuits, descending modulatory pathways, the cerebellum, and the basal ganglia— make essential and distinct contribu-tions to motor control. essential for organized movement. Even after the spinal cord is disconnected from the brain in an experimental animal such as a cat, appropriate stimula-tion of local spinal circuits elicits involuntary but highly coordinated limb movements that resemble walking. The second motor subsystem consists of the upper motor neurons whose cell bodies lie in the brainstem or cerebral cortex and whose axons descend to synapse with the local circuit neurons or, more rarely, with the lower motor neurons directly. The upper motor neuron pathways that arise in the cortex are essential for the initiation of voluntary movements and for com-plex spatiotemporal sequences of skilled movements. In particular, descend-ing projections from cortical areas in the frontal lobe, including Brodmann’s area 4 (the primary motor cortex), the lateral part of area 6 (the lateral pre-motor cortex), and the medial part of area 6 (the medial premotor cortex) are essential for planning, initiating, and directing sequences of voluntary movements. Upper motor neurons originating in the brainstem are responsi-ble for regulating muscle tone and for orienting the eyes, head, and body with respect to vestibular, somatic, auditory, and visual sensory information. Their contributions are thus critical for basic navigational movements, and for the control of posture. The third and fourth subsystems are complex circuits with output path-ways that have no direct access to either the local circuit neurons or the lower motor neurons; instead, they control movement by regulating the activity of the upper motor neurons. The third and larger of these subsys-tems, the cerebellum, is located on the dorsal surface of the pons (see Chap-ter 1). The cerebellum acts via its efferent pathways to the upper motor neu-rons as a servomechanism, detecting the difference, or “motor error,” between an intended movement and the movement actually performed (see Chapter 19). The cerebellum uses this information about discrepancies to Motor neuron pools Lower motor neurons Sensory inputs Local circuit neurons Lower motor neuron integration SKELETAL MUSCLES SPINAL CORD AND BRAINSTEM CIRCUITS DESCENDING SYSTEMS Upper Motor Neurons Planning, initiating, and directing voluntary movements Motor Cortex Brainstem Centers Basic movements and postural control BASAL GANGLIA Gating proper initiation of movement CEREBELLUM Sensory motor coordination mediate both real-time and long-term reductions in these motor errors (the latter being a form of motor learning). As might be expected from this account, patients with cerebellar damage exhibit persistent errors in move-ment. The fourth subsystem, embedded in the depths of the forebrain, con-sists of a group of structures collectively referred to as the basal ganglia (see Chapter 1). The basal ganglia suppress unwanted movements and prepare (or “prime”) upper motor neuron circuits for the initiation of movements. The problems associated with disorders of basal ganglia, such as Parkinson’s disease and Huntington’s disease, attest to the importance of this complex in the initiation of voluntary movements (see Chapter 17). Despite much effort, the sequence of events that leads from volitional thought to movement is still poorly understood. The picture is clearest, how-ever, at the level of control of the muscles themselves. It therefore makes sense to begin an account of motor behavior by considering the anatomical and physiological relationships between lower motor neurons and the mus-cle fibers they innervate. Motor Neuron–Muscle Relationships By injecting individual muscle groups with visible tracers that are trans-ported by the axons of the lower motor neurons back to their cell bodies, the lower motor neurons that innervate each of the body’s skeletal muscles can be seen in histological sections of the ventral horns of the spinal cord. Each lower motor neuron innervates muscle fibers within a single muscle, and all the motor neurons innervating a single muscle (called the motor neuron pool for that muscle) are grouped together into rod-shaped clusters that run parallel to the long axis of the cord for one or more spinal cord segments (Figure 15.2). An orderly relationship between the location of the motor neuron pools and the muscles they innervate is evident both along the length of the spinal cord and across the mediolateral dimension of the cord, an arrangement that in effect provides a spatial map of the body’s musculature. For example, the motor neuron pools that innervate the arm are located in the cervical enlargement of the cord and those that innervate the leg in the lumbar enlargement (see Chapter 1). The mapping, or topography, of motor neuron pools in the mediolateral dimension can be appreciated in a cross section through the cervical enlargement (the level illustrated in Figure 15.3). Thus, neurons that innervate the axial musculature (i.e., the postural muscles of the trunk) are located medially in the cord. Lateral to these cell groups are motor neuron pools innervating muscles located progressively more laterally in the body. Neurons that innervate the muscles of the shoulders (or pelvis, if one were to look at a similar section in the lumbar enlargement; see Figure 15.2) are the next most lateral group, whereas those that innervate the proxi-mal muscles of the arm (or leg) are located laterally to these. The motor neu-ron pools that innervate the distal parts of the extremities, the fingers or toes, lie farthest from the midline. This spatial organization provides clues about the functions of the descending upper motor neuron pathways described in the following chapter; some of these pathways terminate primarily in the medial region of the spinal cord, which is concerned with postural muscles, whereas other pathways terminate more laterally, where they have access to the lower motor neurons that control movements of the distal parts of the limbs, such as, the toes and the fingers. Two types of lower motor neuron are found in these neuronal pools. Small g motor neurons innervate specialized muscle fibers that, in combina-Lower Motor Neuron Circuits and Motor Control 373 374 Chapter Fifteen tion with the nerve fibers that innervate them, are actually sensory receptors called muscle spindles (see Chapter 8). The muscle spindles are embedded within connective tissue capsules in the muscle, and are thus referred to as intrafusal muscle fibers (fusal means capsular). The intrafusal muscle fibers are also innervated by sensory axons that send information to the brain and spinal cord about the length and tension of the muscle. The function of the γ motor neurons is to regulate this sensory input by setting the intrafusal mus-cle fibers to an appropriate length (see the next section). The second type of lower motor neuron, called a motor neurons, innervates the extrafusal mus-cle fibers, which are the striated muscle fibers that actually generate the forces needed for posture and movement. Although the following discussion focuses on the lower motor neurons in the spinal cord, comparable sets of motor neurons responsible for the control of muscles in the head and neck are located in the brainstem. The latter neu-rons are distributed in the eight motor nuclei of the cranial nerves in the medulla, pons, and midbrain (see Appendix A). Somewhat confusingly, but quite appropriately, these motor neurons in the brainstem are also called lower motor neurons. (B) (A) (C) L7 Medial gastrocnemius injection Soleus injection S1 Lower motor neurons Dorsal horn Ventral horn Figure 15.2 Organization of lower motor neurons in the ventral horn of the spinal cord demonstrated by labeling of their cell bodies following injection of a retrograde tracer in individual muscles. Neurons were identified by placing a retrograde tracer into the medial gas-trocnemius or soleus muscle of the cat. (A) Section through the lumbar level of the spinal cord showing the distribution of labeled cell bodies. Lower motor neu-rons form distinct clusters (motor pools) in the ventral horn. Spinal cord cross sections (B) and a reconstruction seen from the dorsal surface (C) illustrate the distribution of motor neurons innervat-ing individual skeletal muscles in both axes of the cord. The cylindrical shape and distinct distribution of different pools are especially evident in the dor-sal view of the reconstructed cord. The dashed lines in (C) represent individual lumbar and sacral spinal cord segments. (After Burke et al., 1977.) Figure 15.3 Somatotopic organization of lower motor neurons in a cross sec-tion of the ventral horn at the cervical level of the spinal cord. Motor neurons innervating axial musculature are located medially, whereas those inner-vating the distal musculature are located more laterally. The Motor Unit Most mature extrafusal skeletal muscle fibers in mammals are innervated by only a single α motor neuron. Since there are by far more muscle fibers than motor neurons, individual motor axons branch within muscles to synapse on many different fibers that are typically distributed over a relatively wide area within the muscle, presumably to ensure that the contractile force of the motor unit is spread evenly (Figure 15.4). In addition, this arrangement reduces the chance that damage to one or a few α motor neurons will signif-icantly alter a muscle’s action. Because an action potential generated by a Lower Motor Neuron Circuits and Motor Control 375 Proximal muscles Distal muscles Proximal muscles Distal muscles (A) (B) Motor neuron in spinal cord Muscle fibers innervated by a single motor neuron Figure 15.4 The motor unit. (A) Dia-gram showing a lower motor neuron in the spinal cord and the course of its axon to its target muscle. (B) Each motor neuron synapses with multiple fibers within the muscle. The motor neuron and the fibers it contacts define the motor unit. Cross section through the muscle shows the relatively diffuse distribution of muscle fibers (red dots) contacted by the motor neuron. 376 Chapter Fifteen motor neuron normally brings to threshold all of the muscle fibers it con-tacts, a single α motor neuron and its associated muscle fibers together con-stitute the smallest unit of force that can be activated to produce movement. Sherrington was again the first to recognize this fundamental relationship between an α motor neuron and the muscle fibers it innervates, for which he coined the term motor unit. Both motor units and the α motor neurons themselves vary in size. Small α motor neurons innervate relatively few muscle fibers and form motor units that generate small forces, whereas large motor neurons innervate larger, more powerful motor units. Motor units also differ in the types of muscle fibers that they innervate. In most skeletal muscles, the smaller motor units comprise small “red” muscle fibers that contract slowly and generate relatively small forces; but, because of their rich myoglobin content, plentiful mitochondria, and rich capillary beds, such small red fibers are resistant to fatigue (these units are also innervated by relatively small α motor neurons). These small units are called slow (S) motor units and are especially important for activities that require sustained muscular contrac-tion, such as the maintenance of an upright posture. Larger α motor neurons innervate larger, pale muscle fibers that generate more force; however, these fibers have sparse mitochondria and are therefore easily fatigued. These units are called fast fatigable (FF) motor units and are especially important for brief exertions that require large forces, such as running or jumping. A third class of motor units has properties that lie between those of the other two. These fast fatigue-resistant (FR) motor units are of intermediate size and are not quite as fast as FF units. They generate about twice the force of a slow motor unit and, as the name implies, are substantially more resistant to fatigue (Figure 15.5). These distinctions among different types of motor units indicate how the nervous system produces movements appropriate for different circum-stances. In most muscles, small, slow motor units have lower thresholds for activation than the larger units and are tonically active during motor acts that require sustained effort (standing, for instance). The thresholds for the large, fast motor units are reached only when rapid movements requiring great force are made, such as jumping. The functional distinctions between (A) (B) (C) Time (ms) Time (ms) 0 10 20 30 40 50 60 50 100 150 200 Time (min) 0 2 4 6 60 250 300 0 0 500 1000 1500 Slow Slow 0 100 0 0 100 100 Percent maximum force Fast fatigable Grams of force Fast fatigue-resistant Fast fatigable Fast fatigue-resistant Fast fatigable Slow Fast fatigue-resistant Figure 15.5 Comparison of the force and fatigability of the three different types of motor units. In each case, the response reflects stimulation of a single motor neuron. (A) Change in muscle tension in response to a single motor neuron action potential. (B) Tension in response to repetitive stimulation of the motor neurons. (C) Response to repeated stimulation at a level that evokes maximum tension. The ordinate represents the force generated by each stimulus. Note the strikingly different fatigue rates. (After Burke et al., 1974.) the various classes of motor units also explain some structural differences among muscle groups. For example, a motor unit in the soleus (a muscle important for posture that comprises mostly small, slow units) has an aver-age innervation ratio of 180 muscle fibers for each motor neuron. In contrast, the gastrocnemius, a muscle that comprises both small and larger units, has an innervation ratio of ~1000–2000 muscle fibers per motor neuron, and can generate forces needed for sudden changes in body position. More subtle variations are present in athletes on different training regimens. Thus, mus-cle biopsies show that sprinters have a larger proportion of powerful but rapidly fatiguing pale fibers in their leg muscles than do marathoners. Other differences are related to the highly specialized functions of particular mus-cles. For instance, the eyes require rapid, precise movements but little strength; in consequence, extraocular muscle motor units are extremely small (with an average innervation ratio of only 3!) and have a very high pro-portion of muscle fibers capable of contracting with maximal velocity. The Regulation of Muscle Force Increasing or decreasing the number of motor units active at any one time changes the amount of force produced by a muscle. In the 1960s, Elwood Henneman and his colleagues at Harvard Medical School found that pro-gressive increases in muscle tension could be produced by progressively increasing the activity of axons that provide input to the relevant pool of lower motor neurons. This gradual increase in tension results from the recruitment of motor units in a fixed order according to their size. By stimu-lating either sensory nerves or upper motor pathways that project to a lower motor neuron pool while measuring the tension changes in the muscle, Hen-neman found that in experimental animals only the smallest motor units in the pool are activated by weak synaptic stimulation. When synaptic input increases, progressively larger motor units that generate larger forces are recruited: As the synaptic activity driving a motor neuron pool increases, low threshold S units are recruited first, then FR units, and finally, at the highest levels of activity, the FF units. Since these original experiments, evi-dence for the orderly recruitment of motor units has been found in a variety of voluntary and reflexive movements. As a result, this systematic relation-ship has come to be known as the size principle. An illustration of how the size principle operates for the motor units of the medial gastrocnemius muscle in the cat is shown in Figure 15.6. When the animal is standing quietly, the force measured directly from the muscle tendon is only a small fraction (about 5%) of the total force that the muscle can generate. The force is provided by the S motor units, which make up about 25% of the motor units in this muscle. When the cat begins to walk, larger forces are necessary: locomotor activities that range from slow walk-ing to fast running require up to 25% of the muscle’s total force capacity. This additional need is met by the recruitment of FR units. Only movements such as galloping and jumping, which are performed infrequently and for short periods, require the full power of the muscle; such demands are met by the recruitment of the FF units. Thus, the size principle provides a simple solution to the problem of grading muscle force: The combination of motor units activated by such orderly recruitment optimally matches the physio-logical properties of different motor unit types with the range of forces required to perform different motor tasks. The frequency of the action potentials generated by motor neurons also contributes to the regulation of muscle tension. The increase in force that Lower Motor Neuron Circuits and Motor Control 377 378 Chapter Fifteen Figure 15.6 The recruitment of motor neurons in the cat medial gastrocne-mius muscle under different behavioral conditions. Slow (S) motor units pro-vide the tension required for standing. Fast fatigue-resistant (FR) units provide the additional force needed for walking and running. Fast fatigable (FF) units are recruited for the most strenuous activities, such as jumping. (After Walmsley et al., 1978.) occurs with increased firing rate reflects the summation of successive muscle contractions: The muscle fibers are activated by the next action potential before they have had time to completely relax, and the forces generated by the temporally overlapping contractions are summed (Figure 15.7). The low-est firing rates during a voluntary movement are on the order of 8 per sec-ond (Figure 15.8). As the firing rate of individual units rises to a maximum of about 20–25 per second in the muscle being studied here, the amount of force produced increases. At the highest firing rates, individual muscle fibers are in a state of “fused tetanus”—that is, the tension produced in individual motor units no longer has peaks and troughs that correspond to the individ-ual twitches evoked by the motor neuron’s action potentials. Under normal conditions, the maximum firing rate of motor neurons is less than that required for fused tetanus (see Figure 15.8). However, the asynchronous fir-ing of different lower motor neurons provides a steady level of input to the muscle, which causes the contraction of a relatively constant number of motor units and averages out the changes in tension due to contractions and relaxations of individual motor units. All this allows the resulting move-ments to be executed smoothly. Percent of motor neuron pool recruited Slow Fast fatigue-resistant Fast fatigable Jump Gallop Run Walk Stand 0 20 40 60 80 100 Percent maximum force 0 25 50 75 100 (A) (B) (C) (D) Single muscle twitches (5 Hz) Temporal summation (20 Hz) Unfused tetanus (80 Hz) Fused tetanus (100 Hz) Force Figure 15.7 The effect of stimulation rate on muscle tension. (A) At low fre-quencies of stimulation, each action potential in the motor neuron results in a single twitch of the related muscle fibers. (B) At higher frequencies, the twitches sum to produce a force greater than that produced by single twitches. (C) At a still higher frequency of stimu-lation, the force produced is greater, but individual twitches are still apparent. This response is referred to as unfused tetanus. (D) At the highest rates of motor neuron activation, individual twitches are no longer apparent (a con-dition called fused tetanus). Figure 15.8 Motor units recorded transcutaneously in a muscle of the human hand as the amount of volun-tary force produced is progressively increased. Motor units (represented by the lines between the dots) are initially recruited at a low frequency of firing (8 Hz); the rate of firing for each unit increases as the subject generates more and more force. (After Monster and Chan, 1977.) The Spinal Cord Circuitry Underlying Muscle Stretch Reflexes The local circuitry within the spinal cord mediates a number of sensory motor reflex actions. The simplest of these reflex arcs entails a sensory response to muscle stretch, which provides direct excitatory feedback to the motor neurons innervating the muscle that has been stretched (Figure 15.9). As already mentioned, the sensory signal for the stretch reflex originates in muscle spindles, the sensory receptors embedded within most muscles (see the previous section and Chapter 8). The spindles comprise 8–10 intrafusal fibers arranged in parallel with the extrafusal fibers that make up the bulk of the muscle (Figure 15.9A). Large-diameter sensory fibers, called Ia afferents, are coiled around the central part of the spindle. These afferents are the largest axons in peripheral nerves and, since action potential conduction velocity is a direct function of axon diameter (see Chapters 2 and 3), they mediate very rapid reflex adjustments when the muscle is stretched. The stretch imposed on the muscle deforms the intrafusal muscle fibers, which in turn initiate action potentials by activating mechanically gated ion channels in the afferent axons coiled around the spindle. The centrally projecting branch of the sensory neuron forms monosynaptic excitatory connections with the α motor neurons in the ventral horn of the spinal cord that innervate the same (homonymous) muscle and, via local circuit neurons, forms inhibitory connections with the α motor neurons of antagonistic (heterony-mous) muscles. This arrangement is an example of what is called reciprocal innervation and results in rapid contraction of the stretched muscle and simul-taneous relaxation of the antagonist muscle. All of this leads to especially rapid and efficient responses to changes in the length or tension in the muscle (Figure 15.9B). The excitatory pathway from a spindle to the α motor neurons innervating the same muscle is unusual in that it is a monosynaptic reflex; in most cases, sensory neurons from the periphery do not contact the lower motor neuron directly but exert their effects through local circuit neurons. This monosynaptic reflex arc is variously referred to as the “stretch,” “deep tendon,” or “myotatic” reflex, and it is the basis of the knee, ankle, jaw, biceps, or triceps responses tested in a routine neurological examination. The tap of the reflex hammer on the tendon stretches the muscle and there-fore excites an afferent volley of activity in the Ia sensory axons that inner-vate the muscle spindles. The afferent volley is relayed to the α motor neu-rons in the brainstem or spinal cord, and an efferent volley returns to the muscle (see Figure 1.5). Since muscles are always under some degree of Lower Motor Neuron Circuits and Motor Control 379 Voluntary force (grams) 12 16 20 24 4 8 Unit firing rate (Hz) 1 10 5 50 500 100 1000 380 Chapter Fifteen Resistance Passive stretch α Motor neuron Ia sensory neuron Muscle spindle Muscle Muscle Force required to hold glass Homonymous muscle Synergist (B) (A) Muscle spindle (C) Antagonist Inhibited Increase spindle afferent discharge Load Length change in muscle fiber Spindle receptor Disturbance (addition of liquid to glass) Descending facilitation and inhibition α Motor neuron α Motor neuron γ Motor neuron Capsule surrounding spindle Spindle afferent (Ia sensory neuron) + − stretch, this reflex circuit is normally responsible for the steady level of ten-sion in muscles called muscle tone. Changes in muscle tone occur in a vari-ety of pathological conditions, and it is these changes that are assessed by examination of tendon reflexes. In terms of engineering principles, the stretch reflex arc is a negative feed-back loop used to maintain muscle length at a desired value (Figure 15.9C). The appropriate muscle length is specified by the activity of descending upper motor neuron pathways that influence the motor neuron pool. Devia-tions from the desired length are detected by the muscle spindles, since increases or decreases in the stretch of the intrafusal fibers alter the level of activity in the sensory axons that innervate the spindles. These changes lead in turn to adjustments in the activity of the α motor neurons, returning the muscle to the desired length by contracting the stretched muscle and relax-ing the opposed muscle group, and by restoring the level of spindle activity to what it was before. The smaller γ motor neurons control the functional characteristics of the muscle spindles by modulating their level of excitability. As was described earlier, when the muscle is stretched, the spindle is also stretched and the rate of discharge in the afferent fibers increased. When the muscle shortens, however, the spindle is relieved of tension, or “unloaded,” and the sensory axons that innervate the spindle might therefore be expected to fall silent during contraction. However, they remain active. The γ motor neurons ter-minate on the contractile poles of the intrafusal fibers, and the activation of these neurons causes intrafusal fiber contraction—in this way maintaining the tension on the middle (or equatorial region) of the intrafusal fibers where the sensory axons terminate. Thus, co-activation of the α and γ motor neurons allows spindles to function (i.e., send information centrally) at all muscle lengths during movements and postural adjustments. The Influence of Sensory Activity on Motor Behavior The level of γ motor neuron activity often is referred to as γ bias, or gain, and can be adjusted by upper motor neuron pathways as well as by local reflex circuitry. The larger the gain of the stretch reflex, the greater the change in muscle force that results from a given amount of stretch applied to the intra-fusal fibers. If the gain of the reflex is high, then a small amount of stretch applied to the intrafusal fibers will produce a large increase in the number of α motor neurons recruited and a large increase in their firing rates; this in turn leads to a large increase in the amount of tension produced by the extrafusal fibers. If the gain is low, a greater stretch is required to generate the same amount of tension in the extrafusal muscle fibers. In fact, the gain of the stretch reflex is continuously adjusted to meet different functional requirements. For example, while standing in a moving bus, the gain of the stretch reflex can be modulated by upper motor neuron pathways to com-Lower Motor Neuron Circuits and Motor Control 381 Figure 15.9 Stretch reflex circuitry. (A) Diagram of muscle spindle, the sensory receptor that initiates the stretch reflex. (B) Stretching a muscle spindle leads to increased activity in Ia afferents and an increase in the activity of α motor neurons that innervate the same muscle. Ia afferents also excite the motor neurons that innervate synergistic muscles, and inhibit the motor neurons that innervate antago-nists (see also Figure 1.5). (C) The stretch reflex operates as a negative feedback loop to regulate muscle length. ▲ 382 Chapter Fifteen pensate for the variable changes that occur as the bus stops and starts or pro-gresses relatively smoothly. During voluntary movements, α and γ motor neurons are often co-activated by higher centers to prevent muscle spindles from being unloaded (Figure 15.10). In addition, the level of γ motor neuron activity can be modulated inde-pendently of α activity if the context of a movement requires it. In general, the baseline activity level of γ motor neurons is high if a movement is rela-tively difficult and demands rapid and precise execution. For example, recordings from cat hindlimb muscles show that γ activity is high when the animal has to perform a difficult movement such as walking across a narrow beam. Unpredictable conditions, as when the animal is picked up or han-dled, also lead to marked increases in γ activity and greatly increased spin-dle responsiveness. Gamma motor neuron activity, however, is not the only factor that sets the gain of the stretch reflex. The gain also depends on the level of excitability of the α motor neurons that serve as the efferent side of this reflex loop. Thus, in addition to the influence of descending upper motor neuron projections, other local circuits in the spinal cord can change the gain of the stretch reflex by excitation or inhibition of either α or γ motor neurons. Other Sensory Feedback That Affects Motor Performance Another sensory receptor that is important in the reflex regulation of motor unit activity is the Golgi tendon organ. Golgi tendon organs are encapsu-(A) α Motor neuron activation without γ (B) α Motor neuron activation with γ Stimulate α motor neuron Spindle afferent Extrafusal muscle ﬁbers Intrafusal muscle ﬁbers Stimulate α motor neuron Stimulate γ motor neuron Contraction Afferent activity Muscle force Contraction Afferent activity Muscle force Ia response ‘‘ﬁlled in’’ Stimulate Stimulate Stimulate Spindle afferent Record Record Record Record Figure 15.10 The role of γ motor neu-ron activity in regulating the responses of muscle spindles. (A) When α motor neurons are stimulated without activa-tion of γ motor neurons, the response of the Ia fiber decreases as the muscle con-tracts. (B) When both α and γ motor neurons are activated, there is no decrease in Ia firing during muscle shortening. Thus, the γ motor neurons can regulate the gain of muscle spindles so they can operate efficiently at any length of the parent muscle. (After Hunt and Kuffler, 1951.) lated afferent nerve endings located at the junction of a muscle and tendon (Figure 15.11A; see also Table 9.1). Each tendon organ is innervated by a sin-gle group Ib sensory axon (the Ib axons are slightly smaller than the Ia axons that innervate the muscle spindles). In contrast to the parallel arrangement of extrafusal muscle fibers and spindles, Golgi tendon organs are in series with the extrafusal muscle fibers. When a muscle is passively stretched, most of the change in length occurs in the muscle fibers, since they are more elas-Lower Motor Neuron Circuits and Motor Control 383 (A) (1) Muscle Spindles (2) Golgi Tendon Organs (1) Muscle Spindles (2) Golgi Tendon Organs Muscle fibers Capsule Tendon Collagen fibrils Axon GTO Ib afferent neuron Muscle stretched Muscle stretched Muscle contracted Muscle contracted Stimulate α motor neuron Spindle afferent Golgi tendon organ afferent Spindle afferent Stretch Muscle length Afferent activity Afferent activity Afferent activity Golgi tendon organ Golgi tendon organ afferent Stretch Shorten Shorten Extrafusal muscle fibers Intrafusal muscle fibers Stimulate α motor neuron Muscle length Afferent activity Muscle length Muscle length Stimulate Stimulate Record Record Record Record MUSCLE ACTIVELY CONTRACTED MUSCLE PASSIVELY STRETCHED (B) Figure 15.11 Comparison of the function of muscle spindles and Golgi tendon organs. (A) Golgi tendon organs are arranged in series with extrafusal muscle fibers because of their location at the junction of muscle and tendon. (B) The two types of muscle receptors, the muscle spindles (1) and the Golgi tendon organs (2), have different responses to passive muscle stretch (top) and active muscle contraction (bottom). Both afferents discharge in response to passively stretching the muscle, although the Golgi tendon organ discharge is much less than that of the spindle. When the extrafusal muscle fibers are made to contract by stimu-lation of their motor neurons, however, the spindle is unloaded and therefore falls silent, whereas the rate of Golgi tendon organ firing increases. (B after Patton, 1965.) 384 Chapter Fifteen Box A Locomotion in the Leech and the Lamprey All animals must coordinate body move-ments so they can navigate successfully in their environment. All vertebrates, including mammals, use local circuits in the spinal cord (central pattern genera-tors) to control the coordinated move-ments associated with locomotion. The cellular basis of organized locomotor activity, however, has been most thor-oughly studied in an invertebrate, the leech, and a simple vertebrate, the lamprey. Both the leech and the lamprey lack peripheral appendages for locomotion possessed by many vertebrates (limbs, flippers, fins, or their equivalent). Fur-thermore, their bodies comprise repeat-ing muscle segments (as well as repeat-ing skeletal elements in the lamprey). Thus, in order to move through the water, both animals must coordinate the movement of each segment. They do this by orchestrating a sinusoidal displace-ment of each body segment in sequence, so that the animal is propelled forward through the water. The leech is particularly well-suited for studying the circuit basis of coordi-nated movement. The nervous system in the leech consists of a series of intercon-nected segmental ganglia, each with motor neurons that innervate the corre-sponding segmental muscles (Figure A). These segmental ganglia facilitate elec-trophysiological studies, because there is a limited number of neurons in each and each neuron has a distinct identity. The neurons can thus be recognized and studied from animal to animal, and their electrical activity correlated with the sinusoidal swimming movements. A central pattern generator circuit coordinates this undulating motion. In the leech, the relevant neural circuit is an ensemble of sensory neurons, interneu-rons, and motor neurons repeated in each segmental ganglion that controls the local sequence of contraction and relaxation in each segment of the body wall muscula-ture (Figure B). The sensory neurons detect the stretching and contraction of the body wall associated with the se-quential swimming movements. Dorsal and ventral motor neurons in the circuit provide innervation to dorsal and ventral muscles, whose phasic contractions propel the leech forward. Sensory infor-mation and motor neuron signals are coordinated by interneurons that fire rhythmically, setting up phasic patterns of activity in the dorsal and ventral cells that lead to sinusoidal movement. The intrinsic swimming rhythm is established by a variety of membrane conductances that mediate periodic bursts of supra-threshold action potentials followed by well-defined periods of hyperpolarization. The lamprey, one of the simplest ver-tebrates, is distinguished by its clearly Dorsal muscle Ventral muscle Flattener muscle Posterior sucker EMGV EMGD Ventral cell Dorsal cell Head (B) LEECH (A) LEECH Segmental ganglion To muscles (A) The leech propels itself through the water by sequential contraction and relaxation of the body wall musculature of each segment. The segmental ganglia in the ventral midline coordi-nate swimming, each ganglion containing a population of identified neurons. (B) Electrical recordings from the ventral (EMGV) and dorsal (EMGD) muscles in the leech and the corre-sponding motor neurons show a reciprocal pattern of excitation for the dorsal and ventral muscles of a given segment. Lower Motor Neuron Circuits and Motor Control 385 segmented musculature and by its lack of bilateral fins or other appendages. In order to move through the water, the lamprey contracts and relaxes each mus-cle segment in sequence (Figure C), which produces a sinusoidal motion, much like that of the leech. Again, a cen-tral pattern generator coordinates this sinusoidal movement. Unlike the leech with its segmental ganglia, the lamprey has a continuous spinal cord that innervates its muscle segments. The lamprey spinal cord is simpler than that of other vertebrates, and several classes of identified neurons occupy stereotyped positions. This orderly arrangement again facilitates the identification and analysis of neurons that constitute the central pattern genera-tor circuit. In the lamprey spinal cord, the intrin-sic firing pattern of a set of intercon-nected sensory neurons, interneurons and motor neurons establishes the pat-tern of undulating muscle contractions that underlie swimming (Figure D). The patterns of connectivity between neu-rons, the neurotransmitters used by each class of cell, and the physiological prop-erties of the elements in the lamprey pat-tern generator are now known. Different neurons in the circuit fire with distinct rhythmicity, thus controlling specific aspects of the swim cycle (Figure E). Par-ticularly important are reciprocal inhib-itory connections across the midline that coordinate the pattern generating cir-cuitry on each side of the spinal cord. This circuitry in the lamprey thus pro-vides a basis for understanding the cir-cuits that control locomotion in more complex vertebrates. These observations on pattern gener-ating circuits for locomotion in relatively simple animals have stimulated parallel studies of terrestrial mammals in which central pattern generators in the spinal cord also coordinate locomotion. Although different in detail, terrestrial locomotion ultimately relies on the sequential movements similar to those that propel the leech and the lamprey through aquatic environments, and intrinsic physiological properties of spinal cord neurons that establish ryth-micity for coordinated movement. References GRILLNER, S., D. PARKER AND A. EL MANIRA (1998) Vertebrate locomotion: A lamprey per-spective. Ann. N.Y. Acad. Sci. 860: 1–18. MARDER, E. AND R. M. CALABRESE (1996) Prin-ciples of rhythmic motor pattern generation. Physiol. Rev. 76: 687–717. STENT, G. S., W. B. KRISTAN, W. O. FRIESEN, C. A. ORT, M. POON AND R. M. CALABRESE (1978) Neural generation of the leech swimming movement. Science 200: 1348–1357. Record Record Midline EV IV MV LV ED ID MD LD Ventral root Dorsal root Sensory inputs Sensory inputs Brainstem inputs (D) LAMPREY (C) In the lamprey, as this diagram indicates, the pattern of activity across segments is also highly coordinated. (D) The elements of the central pattern generator in the lamprey have been worked out in detail, providing a guide to understanding homologous cir-cuitry in more complex spinal cords. (E) As in the leech, different patterns of elec-trical activity in lamprey spinal neurons (neurons ED and LV in this example) corre-spond to distinct periods in the sequence of muscle contractions related to the swim cycle. LV ED (E) LAMPREY Duration of EMG activity in each segmental muscle 1 swim cycle Anterior Posterior (C) LAMPREY 386 Chapter Fifteen tic than the fibrils of the tendon. When a muscle actively contracts, however, the force acts directly on the tendon, leading to an increase in the tension of the collagen fibrils in the tendon organ and compression of the intertwined sensory receptors. As a result, Golgi tendon organs are exquisitely sensitive to increases in muscle tension that arise from muscle contraction but, unlike spindles, are relatively insensitive to passive stretch (Figure 15.11B). The Ib axons from Golgi tendon organs contact inhibitory local circuit neurons in the spinal cord (called Ib inhibitory interneurons) that synapse, in turn, with the α motor neurons that innervate the same muscle. The Golgi tendon circuit is thus a negative feedback system that regulates muscle ten-sion; it decreases the activation of a muscle when exceptionally large forces are generated and this way protects the muscle. This reflex circuit also oper-ates at reduced levels of muscle force, counteracting small changes in muscle tension by increasing or decreasing the inhibition of α motor neurons. Under these conditions, the Golgi tendon system tends to maintain a steady level of force, counteracting effects that diminish muscle force (such as fatigue). In short, the muscle spindle system is a feedback system that monitors and maintains muscle length, and the Golgi tendon system is a feedback system that monitors and maintains muscle force. Like the muscle spindle system, the Golgi tendon organ system is not a closed loop. The Ib inhibitory interneurons also receive synaptic inputs from a variety of other sources, including cutaneous receptors, joint receptors, muscle spindles, and descending upper motor neuron pathways (Figure 15.12). Acting in concert, these inputs regulate the responsiveness of Ib interneurons to activity arising in Golgi tendon organs. Figure 15.12 Negative feedback regula-tion of muscle tension by Golgi tendon organs. The Ib afferents from tendon organs contact inhibitory interneurons that decrease the activity of α motor neurons innervating the same muscle. The Ib inhibitory interneurons also receive input from other sensory fibers, as well as from descending pathways. This arrangement prevents muscles from generating exces-sive tension. Descending pathways Ib afferent Motor neuron Flexor muscle Extensor muscle Golgi tendon organ Ib inhibitory interneuron + Flexion Reflex Pathways So far, the discussion has focused on reflexes driven by sensory receptors located within muscles or tendons. Other reflex circuitry mediates the with-drawal of a limb from a painful stimulus, such as a pinprick or the heat of a flame. Contrary to what might be imagined given the speed with which we are able to withdraw from a painful stimulus, this flexion reflex involves several synaptic links (Figure 15.13). As a result of activity in this circuitry, stimulation of nociceptive sensory fibers leads to withdrawal of the limb from the source of pain by excitation of ipsilateral flexor muscles and recip-rocal inhibition of ipsilateral extensor muscles. Flexion of the stimulated limb is also accompanied by an opposite reaction in the contralateral limb (i.e., the contralateral extensor muscles are excited while flexor muscles are inhibited). This crossed extension reflex provides postural support during withdrawal of the affected limb from the painful stimulus. Like the other reflex pathways, local circuit neurons in the flexion reflex pathway receive converging inputs from several different sources, including other spinal cord interneurons and upper motor neuron pathways. Although the functional significance of this complex pattern of connectivity is unclear, changes in the character of the reflex following damage to descending path-ways provides some insight. Under normal conditions, a noxious stimulus is required to evoke the flexion reflex; following damage to descending path-ways, however, other types of stimulation, such as squeezing a limb, can sometimes produce the same response. This observation suggests that the descending projections to the spinal cord modulate the responsiveness of the local circuitry to a variety of sensory inputs. Spinal Cord Circuitry and Locomotion The contribution of local circuitry to motor control is not, of course, limited to reflexive responses to sensory inputs. Studies of rhythmic movements such as locomotion and swimming in animal models (Box A) have demonstrated that local circuits in the spinal cord called central pattern generators are fully capable of controlling the timing and coordination of such complex patterns of movement, and of adjusting them in response to altered circumstances (Box B). A good example is locomotion (walking, running, etc.). The movement of a single limb during locomotion can be thought of as a cycle consisting of two phases: a stance phase, during which the limb is extended and placed in contact with the ground to propel humans or other bipeds forward; and a swing phase, during which the limb is flexed to leave the ground and then brought forward to begin the next stance phase (Figure 15.14A). Increases in the speed of loco-motion reduce the amount of time it takes to complete a cycle, and most of the change in cycle time is due to shortening the stance phase; the swing phase remains relatively constant over a wide range of locomotor speeds. In quadrupeds, changes in locomotor speed are also accompanied by changes in the sequence of limb movements. At low speeds, for example, there is a back-to-front progression of leg movements, first on one side and then on the other. As the speed increases to a trot, the movements of the right forelimb and left hindlimb are synchronized (as are the movements of the left forelimb and right hindlimb). At the highest speeds (gallop), the movements of the two front legs are synchronized, as are the movements of the two hindlimbs (Figure 15.14B). Given the precise timing of the movement of individual limbs and the coordination among limbs that are required in this process, it is natural to Lower Motor Neuron Circuits and Motor Control 387 Figure 15.13 Spinal cord circuitry responsible for the flexion reflex. Stimu-lation of cutaneous receptors in the foot (by stepping on a tack in this example) leads to activation of spinal cord local circuits that withdraw (flex) the stimu-lated extremity and extend the other extremity to provide compensatory support. Cutaneous receptor Flexor muscle Extensor muscle Extensor muscle Motor neuron Cutaneous afferent fiber from nociceptor (Aδ) Stimulated leg flexes to withdraw Opposite leg extends to support + + 388 Chapter Fifteen Box B The Autonomy of Central Pattern Generators: Evidence from the Lobster Stomatogastric Ganglion A principle that has emerged from stud-ies of central pattern generators is that rhythmic patterns of firing elicit complex motor responses without need of ongo-ing sensory stimulation. A good example is the behavior mediated by a small group of nerve cells in lobsters and other crustaceans called the stomatogastric ganglion (STG) that controls the muscles of the gut (Figure A). This ensemble of 30 motor neurons and interneurons in the lobster is perhaps the most completely characterized neural circuit known. Of the 30 cells, defined subsets are essential for two distinct rhythmic movements: gastric mill movements that mediate grinding of food by “teeth” in the lob-ster’s foregut, and pyloric movements that propel food into the hindgut. Phasic firing patterns of the motor neurons and interneurons of the STG are directly cor-related with these two rhythmic move-ments. Each of the relevant cells has now been identified based on its position in the ganglion, and its electrophysiological and neuropharmacological properties characterized (Figures B and C). Patterned activity in the motor neu-rons and interneurons of the ganglion begins only if the appropriate neuromod-ulatory input is provided by sensory axons that originate in other ganglia. Depending upon the activity of the sen-sory axons, neuronal ensembles in the STG produce one of several characteristic rhythmic firing patterns. Once activated, however, the intrinsic membrane proper-ties of identified cells within the ensem-ble sustain the rhythmicity of the circuit in the absence of further sensory input. Another key fact that has emerged from this work is that the same neurons can participate in different programmed motor activities, as circumstances (A) Somatogastric ganglion Cardiac sac Brain Esophageal ganglion Esophagus Commissural ganglion Pyloric dilator muscle Constrictor muscles Pylorus Dorsal dilator muscle Gastric mill Motor nerve (A) Location of the lobster stomatogastric ganglion in relation to the gut. (B) Subset of identified neurons in the stomatogastric ganglion that generates gastric mill and pyloric activity. The abbreviations indicate individual identified neurons, all of which project to different pyloric muscles (except the AB neuron, which is an interneuron). (C) Recording from one of the neurons, the lateral pyloric or LP neuron, in this circuit show-ing the different patterns of activity elicited by several neuromodulators known to be involved in the normal synaptic interactions in this ganglion. Control Dopamine Proctolin Serotonin Pilocarpine AB PD VD IC PY LP (B) (C) Record assume that locomotion is accomplished by higher centers that organize the spatial and temporal activity patterns of the individual limbs. However, fol-lowing transection of the spinal cord at the thoracic level, a cat’s hindlimbs will still make coordinated locomotor movements if the animal is supported and placed on a moving treadmill (Figure 15.14C). Under these conditions, the speed of locomotor movements is determined by the speed of the tread-mill, suggesting that the movement is nothing more than a reflexive response to stretching the limb muscles. This possibility is ruled out, how-ever, by experiments in which the dorsal roots are also sectioned. Although the speed of walking is slowed and the movements are less coordinated than under normal conditions, appropriate locomotor movements are still observed. These and other observations in experimental animals show that the basic rhythmic patterns of limb movement during locomotion are not dependent on sensory input; nor are they dependent on input from descending projections from higher centers. Rather, each limb appears to have its own central pattern generator responsible for the alternating flexion and extension of the limb during locomotion (see Box B). Under normal con-ditions, the central pattern generators for the limbs are variably coupled to each other by additional local circuits in order to achieve the different sequences of movements that occur at different speeds. Although some locomotor movements can also be elicited in humans fol-lowing damage to descending pathways, these are considerably less effective than the movements seen in the cat. The reduced ability of the transected spinal cord to mediate rhythmic stepping movements in humans presum-ably reflects an increased dependence of local circuitry on upper motor neu-ron pathways. Perhaps bipedal locomotion carries with it requirements for postural control greater than can be accommodated by spinal cord circuitry alone. Whatever the explanation, the basic oscillatory circuits that control such rhythmic behaviors as flying, walking, and swimming in many animals also play an important part in human locomotion. The Lower Motor Neuron Syndrome The complex of signs and symptoms that arise from damage to the lower motor neurons of the brainstem and spinal cord is referred to as the “lower motor neuron syndrome.” In clinical neurology, this constellation of prob-lems must be distinguished from the “upper motor neuron syndrome” that results from damage to the descending upper motor neuron pathways (see Chapter 16 for a discussion of the signs and symptoms associated with dam-age to upper motor neurons). Lower Motor Neuron Circuits and Motor Control 389 demand. For example, the subset of neu-rons producing gastric mill activity over-laps the subset that generates pyloric activity. This economic use of neuronal subsets has not yet been described in the central pattern generators of mammals, but seems likely to be a feature of all such circuits. References HARTLINE, D. K. AND D. M. MAYNARD (1975) Motor patterns in the stomatogastric gan-glion of the lobster, Panulirus argus. J. Exp. Biol. 62: 405–420. MARDER, E. AND R. M. CALABRESE (1996) Prin-ciples of rhythmic motor pattern generation. Physiol. Rev. 76: 687–717. SELVERSTON, A. I., D. F. RUSSELL AND J. P. MILLER (1976) The stomatogastric nervous system: Structure and function of a small neural network. Progress in Neurobiology 7: 215–290. 390 Chapter Fifteen Damage to lower motor neuron cell bodies or their peripheral axons results in paralysis (loss of movement) or paresis (weakness) of the affected muscles, depending on the extent of the damage. In addition to paralysis and/or paresis, the lower motor neuron syndrome includes a loss of reflexes (areflexia) due to interruption of the efferent (motor) limb of the sensory motor reflex arcs. Damage to lower motor neurons also entails a loss of mus-cle tone, since tone is in part dependent on the monosynaptic reflex arc that links the muscle spindles to the lower motor neurons (see also Box D in Chapter 16). A somewhat later effect is atrophy of the affected muscles due to denervation and disuse. The muscles involved may also exhibit fibrilla-tions and fasciculations, which are spontaneous twitches characteristic of single denervated muscle fibers or motor units, respectively. These phenom-ena arise from changes in the excitability of denervated muscle fibers in the case of fibrillation, and from abnormal activity of injured α motor neurons in the case of fasciculations. These spontaneous contractions can be readily rec-ognized in an electromyogram, providing an especially helpful clinical tool in diagnosing lower motor neuron disorders (Box C). Swing Stance (A) (B) (C) LH Flexors EMG WALK LF RH RF LH TROT LF RH RF LH PACE LF RH RF LH GALLOP LF RH RF Time Extensors LH LF RH RF F E3 E1 E2 E3 F Stance Extensors Flexors Swing Level of transection of spinal cord Flexion Extension Figure 15.14 The cycle of locomotion for terrestrial mammals (a cat in this instance) is organized by central pattern generators. (A) The step cycle, showing leg flexion (F) and extension (E) and their relation to the swing and stance phases of locomotion. EMG indicates electromyographic recordings. (B) Com-parison of the stepping movements for different gaits. Brown bars, foot lifted (swing phase); gray bars, foot planted (stance phase). (C) Transection of the spinal cord at the thoracic level isolates the hindlimb segments of the cord. The hindlimbs are still able to walk on a treadmill after recovery from surgery, and reciprocal bursts of electrical activ-ity can be recorded from flexors during the swing phase and from extensors during the stance phase of walking. (After Pearson, 1976.) Summary Four distinct but highly interactive motor subsystems—local circuits in the spinal cord and brainstem, descending upper motor neuron pathways that control these circuits, the basal ganglia, and the cerebellum—all make essen-tial contributions to motor control. Alpha motor neurons located in the spinal cord and in the cranial nerve nuclei in the brainstem directly link the nervous system and muscles, with each motor neuron and its associated muscle fibers constituting a functional entity called the motor unit. Motor units vary in size, amount of tension produced, speed of contraction, and degree of fatigability. Graded increases in muscle tension are mediated by both the orderly recruitment of different types of motor units and an increase in motor neuron firing frequency. Local circuitry involving sensory inputs, local circuit neurons, and α and γ motor neurons are especially important in the reflexive control of muscle activity. The stretch reflex is a monosynaptic circuit with connections between sensory fibers arising from muscle spindles and the α motor neurons that innervate the same or syner-Lower Motor Neuron Circuits and Motor Control 391 Box C Amyotrophic Lateral Sclerosis Amyotrophic lateral sclerosis (ALS) is a neurodegenerative disease that affects an estimated 0.05% of the population in the United States. It is also called Lou Gehrig’s disease, after the New York Yankees baseball player who died of the disorder in 1936. ALS is characterized by the slow but inexorable degeneration of α motor neurons in the ventral horn of the spinal cord and brainstem (lower motor neurons), and of neurons in the motor cortex (upper motor neurons). Affected individuals show progressive weakness due to upper and/or lower motor neuron involvement, wasting of skeletal muscles due to lower motor neu-ron involvement, and usually die within 5 years of onset. Sadly, these patients are condemned to watch their own demise, since the intellect remains intact. No available therapy effectively prevents the inexorable progression of this disease. Approximately 10% of ALS cases are familial, and several distinct familial forms have been identified. An autoso-mal dominant form of familial ALS (FALS) is caused by mutations of the gene that encodes the cytosolic antioxi-dant enzyme copper/zinc superoxide dismutase (SOD1). Mutations of SOD1 account for roughly 20% of families with FALS. A rare autosomal recessive, juve-nile-onset form is caused by mutations in a protein called alsin, a putative GTPase regulator. Another rare type of FALS consists of a slowly progressive, autoso-mal dominant, lower motor neuron dis-ease without sensory symptoms, with onset in early adulthood; this form is caused by mutations of a protein named dynactin. How these mutant genes lead to the phenotype of motor neuron disease is uncertain. Defects of axonal transport have long been hypothesized to cause ALS. Evidence for this cause is that trans-genic mice with mutant SOD1 exhibit defects in slow axonal transport early in the course of the disease, and that dyn-actin binds to microtubules and thus that mutant dynactin may modify axonal transport along microtubules. However, whether defective axonal transport is the cellular mechanism by which these mutant proteins lead to motor neuron disease remains to be clearly established. Despite these uncertainties, demonstra-tion that mutations of each of these three genes can cause familial ALS has given scientists valuable clues about the molec-ular pathogenesis of at least some forms of this tragic disorder. References ADAMS, R. D. AND M. VICTOR (2001) Principles of Neurology, 7th Ed. New York: McGraw-Hill, pp. 1152–1158. HADANO, S. AND 20 OTHERS (2001) A gene encoding a putative GTPase regulator is mutated in familial amyotrophic lateral scle-rosis 2. Nature Genetics 29: 166–173. PULS, I. AND 13 OTHERS (2003) Mutant dyn-actin in motor neuron disease. Nature Genet-ics 33: 455–456, ROSEN, D. R. AND 32 OTHERS (1993) Mutations in Cu/Zn superoxide dismutase gene are associated with familial amyotrophic lateral sclerosis. Nature 362: 59–62. YANG, Y. AND 16 OTHERS (2001) The gene encoding alsin, a protein with three guanine-nucleotide exchange factor domains, is mutated in a form of recessive amyotrophic lateral sclerosis. Nature Genetics 29: 160–165. 392 Chapter Fifteen gistic muscles. Gamma motor neurons regulate the gain of the stretch reflex by adjusting the level of tension in the intrafusal muscle fibers of the muscle spindle. This mechanism sets the baseline level of activity in α motor neu-rons and helps to regulate muscle length and tone. Other reflex circuits pro-vide feedback control of muscle tension and mediate essential functions such as the rapid withdrawal of limbs from painful stimuli. Much of the spa-tial coordination and timing of muscle activation required for complex rhythmic movements such as locomotion are provided by specialized local circuits called central pattern generators. Because of their essential role in all of these circuits, damage to lower motor neurons leads to paralysis of the associated muscle and to other changes, including the loss of reflex activity, the loss of muscle tone, and eventually muscle atrophy. Additional Reading Reviews BURKE, R. E. (1981) Motor units: Anatomy, physiology and functional organization. In Handbook of Physiology, V. B. Brooks (ed.). Sec-tion 1: The Nervous System. Volume 1, Part 1. Bethesda, MD: American Physiological Soci-ety, pp. 345–422. BURKE, R. E. (1990) Spinal cord: Ventral horn. In The Synaptic Organization of the Brain, 3rd Ed. G. M. Shepherd (ed.). New York: Oxford University Press, pp. 88–132. GRILLNER, S. AND P. WALLEN (1985) Central pattern generators for locomotion, with spe-cial reference to vertebrates. Annu. Rev. Neu-rosci. 8: 233–261. HENNEMAN, E. (1990) Comments on the logi-cal basis of muscle control. In The Segmental Motor System, M. C. Binder and L. M. Mendell (eds.). New York: Oxford University Press, pp. 7–10. HENNEMAN, E. AND L. M. MENDELL (1981) Functional organization of the motoneuron pool and its inputs. In Handbook of Physiology, V. B. Brooks (ed.). Section 1: The Nervous Sys-tem. Volume 1, Part 1. Bethesda, MD: Ameri-can Physiological Society, pp. 423–507. LUNDBERG, A. (1975) Control of spinal mecha-nisms from the brain. In The Nervous System, Volume 1: The Basic Neurosciences. D. B. Tower (ed.). New York: Raven Press, pp. 253–265. PATTON, H. D. (1965) Reflex regulation of movement and posture. In Physiology and Bio-physics, 19th Ed., T. C. Rugh and H. D. Patton (eds.). Philadelphia: Saunders, pp. 181–206. PEARSON, K. (1976) The control of walking. Sci. Amer. 235 (Dec.): 72–86. PROCHAZKA, A., M. HULLIGER, P. TREND AND N. DURMULLER (1988) Dynamic and static fusimo-tor set in various behavioral contexts. In Mechanoreceptors: Development, Structure, and Function. P. Hnik, T. Soulup, R. Vejsada and J. Zelena (eds.). New York: Plenum, pp. 417–430. SCHMIDT, R. F. (1983) Motor systems. In Human Physiology. R. F. Schmidt and G. Thews (eds.). Berlin: Springer Verlag, pp. 81–110. Important Original Papers BURKE, R. E., D. N. LEVINE, M. SALCMAN AND P. TSAIRES (1974) Motor units in cat soleus mus-cle: Physiological, histochemical, and mor-phological characteristics. J. Physiol. (Lond.) 238: 503–514. BURKE, R. E., P. L. STRICK, K. KANDA, C. C. KIM AND B. WALMSLEY (1977) Anatomy of medial gastrocnemius and soleus motor nuclei in cat spinal cord. J. Neurophysiol. 40: 667–680. HENNEMAN, E., E. SOMJEN, AND D. O. CARPEN-TER (1965) Excitability and inhibitability of motoneurons of different sizes. J. Neurophys-iol. 28: 599–620. HUNT, C. C. AND S. W. KUFFLER (1951) Stretch receptor discharges during muscle contrac-tion. J. Physiol. (Lond.) 113: 298–315. LIDDELL, E. G. T. AND C. S. SHERRINGTON (1925) Recruitment and some other factors of reflex inhibition. Proc. R. Soc. London 97: 488–518. LLOYD, D. P. C. (1946) Integrative pattern of excitation and inhibition in two-neuron reflex arcs. J. Neurophysiol. 9: 439–444. MONSTER, A. W. AND H. CHAN (1977) Isometric force production by motor units of extensor digitorum communis muscle in man. J. Neu-rophysiol. 40: 1432–1443. WALMSLEY, B., J. A. HODGSON AND R. E. BURKE (1978) Forces produced by medial gastrocne-mius and soleus muscles during locomotion in freely moving cats. J. Neurophysiol. 41: 1203–1215. Books BRODAL, A. (1981) Neurological Anatomy in Relation to Clinical Medicine, 3rd Ed. New York: Oxford University Press. SHERRINGTON, C. (1947) The Integrative Action of the Nervous System, 2nd Ed. New Haven: Yale University Press. Overview The axons of upper motor neurons descend from higher centers to influence the local circuits in the brainstem and spinal cord that organize movements by coordinating the activity of lower motor neurons (see Chapter 15). The sources of these upper motor neuron pathways include several brainstem centers and a number of cortical areas in the frontal lobe. The motor control centers in the brainstem are especially important in ongoing postural con-trol. Each center has a distinct influence. Two of these centers, the vestibular nuclear complex and the reticular formation, have widespread effects on body position. Another brainstem center, the red nucleus, controls move-ments of the arms; also in the brainstem, the superior colliculus contains upper motor neurons that initiate orienting movements of the head and eyes. The motor and “premotor” areas of the frontal lobe, in contrast, are responsible for the planning and precise control of complex sequences of voluntary movements. Most upper motor neurons, regardless of their source, influence the generation of movements by directly affecting the activity of the local circuits in the brainstem and spinal cord (see Chapter 15). Upper motor neurons in the cortex also control movement indirectly, via pathways that project to the brainstem motor control centers, which, in turn, project to the local organizing circuits in the brainstem and cord. A major function of these indirect pathways is to maintain the body’s posture during cortically initiated voluntary movements. Descending Control of Spinal Cord Circuitry: General Information Some insight into the functions of the different sources of the upper motor neurons is provided by the way the lower motor neurons and local circuit neurons—the ultimate targets of the upper motor neurons—are arranged within the spinal cord. As described in Chapter 15, lower motor neurons in the ventral horn of the spinal cord are organized in a somatotopic fashion: The most medial part of the ventral horn contains lower motor neuron pools that innervate axial muscles or proximal muscles of the limbs, whereas the more lateral parts contain lower motor neurons that innervate the distal muscles of the limbs. The local circuit neurons, which lie primarily in the intermediate zone of the spinal cord and supply much of the direct input to the lower motor neurons, are also topographically arranged. Thus, the medial region of the intermediate zone of the spinal cord gray matter con-tains the local circuit neurons that synapse with lower motor neurons in the medial part of the ventral horn, whereas the lateral regions of the intermedi-ate zone contain local neurons that synapse primarily with lower motor neu-rons in the lateral ventral horn. Chapter 16 393 Upper Motor Neuron Control of the Brainstem and Spinal Cord 394 Chapter Sixteen The patterns of connections made by local circuit neurons in the medial region of the intermediate zone are different from the patterns made by those in the lateral region, and these differences are related to their respec-tive functions (Figure 16.1). The medial local circuit neurons, which supply the lower motor neurons in the medial ventral horn, have axons that project to many spinal cord segments; indeed, some project to targets along the entire length of the cord. Moreover, many of these local circuit neurons also have axonal branches that cross the midline in the commissure of the spinal cord to innervate lower motor neurons in the medial part of the contralateral hemicord. This arrangement ensures that groups of axial muscles on both sides of the body act in concert to maintain and adjust posture. In contrast, local circuit neurons in the lateral region of the intermediate zone have shorter axons that typically extend fewer than five segments and are pre-dominantly ipsilateral. This more restricted pattern of connectivity underlies the finer and more differentiated control that is exerted over the muscles of the distal extremities, such as that required for the independent movement of individual fingers during manipulative tasks. Differences in the way upper motor neuron pathways from the cortex and brainstem terminate in the spinal cord conform to these functional distinc-tions between the local circuits that organize the activity of axial and distal muscle groups. Thus, most upper motor neurons that project to the medial part of the ventral horn also project to the medial region of the intermediate zone; the axons of these upper motor neurons have collateral branches that terminate over many spinal cord segments, reaching medial cell groups on both sides of the spinal cord. The sources of these projections are primarily the vestibular nuclei and the reticular formation (see next section); as their terminal zones in the medial spinal cord gray matter suggest, they are con-cerned primarily with postural mechanisms (Figure 16.2). In contrast, descending axons from the motor cortex generally terminate in lateral parts of the spinal cord gray matter and have terminal fields that are restricted to only a few spinal cord segments (Figure 16.3). These corticospinal pathways are primarily concerned with precise movements involving more distal parts of the limbs. Two additional brainstem structures, the superior colliculus and the red nucleus, also contribute upper motor neuron pathways to the spinal cord (rubro means red; the adjective is derived from the rich capillary bed that gives the nucleus a reddish color in fresh tissue). The axons arising from the superior colliculus project to medial cell groups in the cervical cord, where they influence the lower motor neuron circuits that control axial muscula-ture of the neck (see Figure 16.2). These projections are particularly impor-tant in generating orienting movements of the head (the role of the superior colliculus in the generation of head and eye movements is covered in detail in Chapter 19). The red nucleus projections are also limited to the cervical level of the cord, but these terminate in lateral regions of the ventral horn and intermediate zone (see Figure 16.2). The axons arising from the red nucleus participate together with lateral corticospinal tract axons in the con-trol of the arms. The limited distribution of rubrospinal projections may seem surprising, given the large size of the red nucleus in humans. In fact, Long-distance local circuit neurons Commissural axons Short-distance local circuit neurons Motor nuclei (to axial muscles) Motor nuclei (to limb muscles) Figure 16.1 Local circuit neurons that supply the medial region of the ventral horn are situated medially in the inter-mediate zone of the spinal cord gray matter and have axons that extend over a number of spinal cord segments and terminate bilaterally. In contrast, local circuit neurons that supply the lateral parts of the ventral horn are located more laterally, have axons that extend over a few spinal cord segments, and terminate only on the same side of the cord. Descending pathways that contact the medial parts of the spinal cord gray matter are involved primarily in the control of posture; those that contact the lateral parts are involved in the fine control of the distal extremities. Figure 16.2 Descending projections from the brainstem to the spinal cord. Path-ways that influence motor neurons in the medial part of the ventral horn originate in the reticular formation, vestibular nucleus, and superior colliculus. Those that influence motor neurons that control the proximal arm muscles originate in the red nucleus and terminate in more lateral parts of the ventral horn. (A) COLLICULOSPINAL TRACT (B) RUBROSPINAL TRACT Cervical spinal cord Red nucleus Superior colliculus (C) RETICULOSPINAL TRACT Cervical spinal cord Pontine and medullary reticular formation Lateral and medial vestibular nuclei (D) VESTIBULOSPINAL TRACTS 396 Chapter Sixteen Pyramidal decussation Lateral corticospinal tract Brainstem Cerebrum Spinal cord (A) DIRECT CORTICAL PROJECTIONS Corticoreticulospinal tract Reticular formation (B) INDIRECT CORTICAL PROJECTIONS Primary motor cortex Medial and lateral premotor cortex Medial and lateral premotor cortex Primary somatic sensory cortex Primary motor cortex Primary somatic sensory cortex the bulk of the red nucleus in humans is a subdivision that does not project to the spinal cord at all, but relays information from the cortex to the cere-bellum (see Chapter 18). Motor Control Centers in the Brainstem: Upper Motor Neurons That Maintain Balance and Posture As described in Chapter 13, the vestibular nuclei are the major destination of the axons that form the vestibular division of the eighth cranial nerve; as such, they receive sensory information from the semicircular canals and the otolith organs that specifies the position and angular acceleration of the head. Many of the cells in the vestibular nuclei that receive this information are upper motor neurons with descending axons that terminate in the medial region of the spinal cord gray matter, although some extend more laterally to contact the neurons that control the proximal muscles of the limbs. The pro-jections from the vestibular nuclei that control axial muscles and those that influence proximal limb muscles originate from different cells and take dif-ferent routes (called the medial and lateral vestibulospinal tracts). Other upper motor neurons in the vestibular nuclei project to lower motor neurons in the cranial nerve nuclei that control eye movements (the third, fourth, and sixth cranial nerve nuclei). This pathway produces the eye movements that maintain fixation while the head is moving (see Chapters 13 and 19). The reticular formation is a complicated network of circuits located in the core of the brainstem that extends from the rostral midbrain to the caudal medulla and is similar in structure and function to the intermediate gray matter in the spinal cord (see Figure 16.4 and Box A). Unlike the well-defined sensory and motor nuclei of the cranial nerves, the reticular forma-tion comprises clusters of neurons scattered among a welter of interdigitat-ing axon bundles; it is therefore difficult to subdivide anatomically. The neurons within the reticular formation have a variety of functions, including cardiovascular and respiratory control (see Chapter 20), governance of myr-iad sensory motor reflexes (see Chapter 15), the organization of eye move-ments (see Chapter 19), regulation of sleep and wakefulness (see Chapter 27), and, most important for present purposes, the temporal and spatial coordination of movements. The descending motor control pathways from the reticular formation to the spinal cord are similar to those of the vestibu-lar nuclei; they terminate primarily in the medial parts of the gray matter where they influence the local circuit neurons that coordinate axial and prox-imal limb muscles (see Figure 16.2). Both the vestibular nuclei and the reticular formation provide information to the spinal cord that maintains posture in response to environmental (or self-induced) disturbances of body position and stability. As expected, the vestibu-lar nuclei make adjustments in posture and equilibrium in response to infor-Upper Motor Neuron Control of the Brainstem and Spinal Cord 397 Figure 16.3 Direct and indirect pathways from the motor cortex to the spinal cord. Neurons in the motor cortex that supply the lateral part of the ventral horn (A) to initiate movements of the distal limbs also terminate on neurons in the retic-ular formation (B) to mediate postural adjustments that support the movement. The reticulospinal pathway terminates in the medial parts of the ventral horn, where lower motor neurons that innervate axial muscles are located. Thus, the motor cor-tex has both direct and indirect routes by which it can influence the activity of spinal cord neurons. ▲ 398 Chapter Sixteen Box A The Reticular Formation If one were to exclude from the structure of the brainstem the cranial nerve nuclei, the nuclei that provide input to the cere-bellum, the long ascending and descend-ing tracts that convey explicit sensory and motor signals, and the structures that lie dorsal and lateral to the ventricu-lar system, what would be left is a cen-tral core region known as the tegmentum (Latin for “covering structure”), so named because it “covers” the ventral part of the brainstem. Scattered among the diffuse fibers that course through the tegmentum are small clusters of neurons that are collectively known as the reticu-lar formation. With few exceptions, these clusters of neurons are difficult to recog-nize as distinct nuclei in standard histo-logical preparations. Indeed, the modify-ing term reticular (“like a net”) was applied to this loose collection of neu-ronal clusters because the early neurohis-tologists envisioned these neurons as part of a sparse network of diffusely con-nected cells that extends from the inter-mediate gray regions of the cervical spinal cord to the lateral regions of the hypothalamus and certain nuclei along the midline of the thalamus. These early anatomical concepts were influenced by lesion experiments in ani-mals and clinical observations in human patients made in the 1930s and 40s. These studies showed that damage to the upper brainstem tegmentum produced coma, suggesting the existence of a neural system in the midbrain and ros-tral pons that supported normal con-scious brain states and transitions between sleep and wakefulness. These ideas were articulated most influentially by G. Moruzzi and H. Magoun when they proposed a “reticular activating sys-tem” to account for these functions and the critical role of the brainstem reticular formation. Current evidence generally supports the notion of an activating func-tion of the rostral reticular formation; however, neuroscientists now recognize the complex interplay of a variety of neu-rochemical systems (with diverse post synaptic effects) comprising distinct cell clusters in the rostral tegmentum, and a myriad of other functions performed by neuronal clusters in more caudal parts of the reticular formation. Thus, with the advent of more precise means of demon-strating anatomical connections, as well as more sophisticated means of identify-ing neurotransmitters and the activity patterns of individual neurons, the con-cept of a “sparse network” engaged in a common function is now obsolete. Nevertheless, the term reticular forma-tion remains, as does the daunting chal-lenge of understanding the anatomical complexity and functional heterogeneity of this complex brain region. Fortunately, two simplfying generalizations can be made. First, the functions of the different clusters of neurons in the reticular for-mation can be grouped into two broad categories: modulatory functions and pre-motor functions. Second, the modulatory functions are primarily found in the ros-tral sector of the reticular formation, whereas the premotor functions are localized in more caudal regions. Several clusters of large (“magnocel-lular”) neurons in the midbrain and ros-tral pontine reticular formation partici-pate—together with certain diencephalic nuclei—in the modulation of conscious states (see Chapter 27). These effects are accomplished by long-range, dien-cephalic projections of cholinergic neu-rons near the superior cerebellar pedun-cle, as well as the more widespread forebrain projections of noradrenergic neurons in the locus coeruleus and serotenergic neurons in the raphe nuclei. Generally speaking, these biogenic amine neurotransmitters function as neuromodulators (see Chapter 6) that alter the membrane potential and thus the firing patterns of thalamocortical and cortical neurons (the details of these effects are explained in Chapter 27). Also included in this category are the dopaminergic systems of the ventral midbrain that modulate cortico-striatal interactions in the basal ganglia (see Chapter 17) and the responsiveness of neurons in the prefrontal cortex and lim-bic forebrain (see Chapter 28). However, not all modulatory projections from the rostral reticular formation are directed toward the forebrain. Although not always considered part of the reticular formation, it is helpful to include in this functional group certain neuronal columns in the periaqueductal gray (sur-rounding the cerebral aqueduct) that project to the dorsal horn of the spinal cord and modulate the transmission of nociceptive signals (see Chapter 9). Reticular formation neurons in the caudal pons and medulla oblongata gen-erally serve a premotor function in the sense that they intergate feedback sen-sory signals with executive commands from upper motor neurons and deep cerebellar nuclei and, in turn, organize the efferent activities of lower visceral motor and certain somatic motor neu-rons in the brainstem and spinal cord. Examples of this functional category include the smaller (“parvocellular”) neurons that coordinate a broad range of motor activities, including the gaze cen-ters discussed in Chapter 19 and local circuit neurons near the somatic motor and branchiomotor nuclei that organize mastication, facial expressions, and a variety of reflexive orofacial behaviors such as sneezing, hiccuping, yawning, and swallowing. In addition, there are “autonomic centers” that organize the efferent activities of specific pools of pri-mary visceral motor neurons. Included in this subgroup are distinct clusters of neurons in the ventral-lateral medulla that generate respiratory rhythms, and others that regulate the cardioinhibitory mation from the inner ear. Direct projections from the vestibular nuclei to the spinal cord ensure a rapid compensatory response to any postural instability detected by the inner ear (see Chapter 13). In contrast, the motor centers in the reticular formation are controlled largely by other motor centers in the cortex or brainstem. The relevant neurons in the reticular formation initiate adjust-ments that stabilize posture during ongoing movements. The way the upper motor neurons of the reticular formation maintain posture can be appreciated by analyzing their activity during voluntary movements. Even the simplest movements are accompanied by the activa-tion of muscles that at first glance seem to have little to do with the primary purpose of the movement. For example, Figure 16.5 shows the pattern of muscle activity that occurs as a subject uses his arm to pull on a handle in response to an auditory tone. Activity in the biceps muscle begins about 200 Upper Motor Neuron Control of the Brainstem and Spinal Cord 399 output of neurons in the nucleus ambiguus and the dorsal motor nucleus of the vagus nerve. Still other clusters organize more complex activities that require the coordination of both somatic motor and visceral motor outflow, such as gagging and vomiting, and even laughing and crying. One set of neuronal clusters that does not fit easily into this rostral-caudal framework is the set of neurons that give rise to the reticulospinal projections. As described in the text, these neurons are distributed in both rostral and caudal sectors of the reticular formation and they give rise to long-range projections that innervate lower motor neuronal pools in the medial ventral horn of the spinal cord. The reticulospinal inputs serve to modulate the gain of segmental reflexes involving the muscles of the trunk and proximal limbs and to initiate certain stereotypical patterns of limb movement. In summary, the reticular formation is best viewed as a heterogeneous collection of distinct neuronal clusters in the brain-stem tegmentum that either modulate the excitability of distant neurons in the fore-brain and spinal cord or coordinate the firing patterns of more local lower motor neuronal pools engaged in reflexive or stereotypical somatic motor and visceral motor behavior. References BLESSING, W. W. (1997) Inadequate frame-works for understanding bodily homeostasis. Trends Neurosci. 20: 235–239 HOLSTEGE, G., R. BANDLER AND C. B. SAPER (EDS.) (1996) Progress in Brain Research, Vol. 107. Amsterdam: Elsevier. LOEWY, A. D. AND K. M. SPYER (EDS.) (1990) Central Regulation of Autonomic Functions. New York: Oxford. MASON, P. (2001) Contributions of the medullary raphe and ventromedial reticular region to pain modulation and other homeo-static functions. Annu. Rev. Neurosci. 24: 737–777. MORUZZI, G. AND H. W. MAGOUN (1949) Brain stem reticular formation and activation of the EEG. EEG Clin. Neurophys. 1: 455–476. Mesencephalic and rostral pontine reticular formation Modulates forebrain activity Caudal pontine and medullary reticular formation Premotor coordination of lower somatic and visceral motor neuronal pools Midbrain Pons Medulla Midsagittal view of the brain showing the longitudinal extent of the reticu-lar formation and highlighting the broad functional roles performed by neuronal clusters in its rostral (blue) and caudal (red) sectors. 400 Chapter Sixteen 3 2 1 Middle medulla Medullary reticular formation Inferior olive Hypoglossal nucleus Dorsal motor nucleus of vagus Medial lemniscus Medullary pyramid 3 Lower pons Middle cerebellar peduncle Abducens nucleus Pontine reticular formation Corticospinal fibers Fourth ventricle Medial lemniscus 2 Midbrain Superior colliculus Cerebral peduncle Substantia nigra Medial lemniscus 1 Mesencephalic reticular formation Figure 16.4 The location of the reticu-lar formation in relation to some other major landmarks at different levels of the brainstem. Neurons in the reticular formation are scattered among the axon bundles that course through the medial portion of the midbrain, pons, and medulla (see Box A). ms after the tone. However, as the records show, the contraction of the biceps is accompanied by a significant increase in the activity of a proximal leg muscle, the gastrocnemius (as well as many other muscles not monitored in the experiment). In fact, contraction of the gastrocnemius muscle begins well before contraction of the biceps. These observations show that postural control entails an anticipatory, or feedforward, mechanism (Figure 16.6). As part of the motor plan for moving the arm, the effect of the impending movement on body stability is “evalu-ated” and used to generate a change in the activity of the gastrocnemius muscle. This change actually precedes and provides postural support for the movement of the arm. In the example given in Figure 16.5, contraction of the biceps would tend to pull the entire body forward, an action that is opposed by the contraction of the gastrocnemius muscle. In short, this feedforward mechanism “predicts” the resulting disturbance in body stability and gener-ates an appropriate stabilizing response. The importance of the reticular formation for feedforward mechanisms of postural control has been explored in more detail in cats trained to use a forepaw to strike an object. As expected, the forepaw movement is accompa-nied by feedforward postural adjustments in the other legs to maintain the animal upright. These adjustments shift the animal’s weight from an even dis-tribution over all four feet to a diagonal pattern, in which the weight is carried mostly by the contralateral, nonreaching forelimb and the ipsilateral hindlimb. Lifting of the forepaw and postural adjustments in the other limbs can also be induced in an alert cat by electrical stimulation of the motor cortex. After pharmacological inactivation of the reticular formation, however, electrical stimulation of the motor cortex evokes only the forepaw movement, without the feedforward postural adjustments that normally accompany them. The results of this experiment can be understood in terms of the fact that the upper motor neurons in the motor cortex influence the spinal cord cir-cuits by two routes: direct projections to the spinal cord and indirect pro-jections to brainstem centers that in turn project to the spinal cord (see Fig-ure 16.3). The reticular formation is one of the major destinations of these latter projections from the motor cortex; thus, cortical upper motor neurons initiate both the reaching movement of the forepaw and also the postural adjustments in the other limbs necessary to maintain body stability. The forepaw movement is initiated by the direct pathway from the cortex to the spinal cord (and possibly by the red nucleus as well), whereas the postural adjustments are mediated via pathways from the motor cortex that reach the spinal cord indirectly, after an intervening relay in the reticular formation (the corticoreticulospinal pathway). Further evidence for the contrasting functions of the direct and indirect pathways from the motor cortex and brainstem to the spinal cord comes from experiments carried out by the Dutch neurobiologist Hans Kuypers, who examined the behavior of rhesus monkeys that had the direct pathway to the spinal cord transected at the level of the medulla, leaving the indirect descending upper motor neuron pathways to the spinal cord via the brain-stem centers intact. Immediately after the surgery, the animals were able to use axial and proximal muscles to stand, walk, run, and climb, but they had great difficulty using the distal parts of their limbs (especially their hands) independently of other body movements. For example, the monkeys could cling to the cage but were unable to reach toward and pick up food with their fingers; rather, they used the entire arm to sweep the food toward them. After several weeks, the animals recovered some independent use of their hands and were again able to pick up objects of interest, but this action still involved the concerted closure of all of the fingers. The ability to make independent, fractionated movements of the fingers, as in opposing the movements of the fingers and thumb to pick up an object, never returned. These observations show that following damage to the direct corticospinal pathway at the level of the medulla, the indirect projections from the motor cortex via the brainstem centers (or from brainstem centers alone) are capa-ble of sustaining motor behavior that involves primarily the use of proximal muscles. In contrast, the direct projections from the motor cortex to the spinal cord provide the speed and agility of movements, enabling a higher degree of precision in fractionated finger movements than is possible using the indirect pathways alone. Upper Motor Neuron Control of the Brainstem and Spinal Cord 401 Figure 16.6 Feedforward and feed-back mechanisms of postural control. Feedforward postural responses are “preprogrammed” and typically pre-cede the onset of limb movement (see Figure 16.4). Feedback responses are initiated by sensory inputs that detect postural instability. Figure 16.5 Anticipatory maintenance of body posture. At the onset of a tone, the subject pulls on a handle, contract-ing the biceps muscle. To ensure pos-tural stability, contraction of the gastroc-nemius muscle precedes that of the biceps. EMG refers to the electromyo-graphic recording of muscle activity. Gastrocnemius EMG 0 100 300 500 0 100 300 Tone Tone Time (ms) Time (ms) 500 Biceps EMG Feedforward for anticipated postural instability Feedback for unanticipated postural instability Postural adjustment Central command Limb movement Postural instability 402 Chapter Sixteen Figure 16.7 The primary motor cortex and the premotor area in the human cerebral cortex as seen in lateral (A) and medial (B) views. The primary motor cortex is located in the precentral gyrus; the premotor area is more rostral. Selective damage to the corticospinal tract (i.e., the direct pathway) in humans is rarely seen in the clinic. Nonetheless, this evidence in nonhuman primates showing that direct projections from the cortex to the spinal cord are essential for the performance of discrete finger movements helps explain the limited recovery in humans after damage to the motor cortex or to the internal capsule. Immediately after such an injury, such patients are typically paralyzed. With time, however, some ability to perform voluntary move-ments reappears. These movements, which are presumably mediated by the brainstem centers, are crude for the most part, and the ability to perform dis-crete finger movements such as those required for writing, typing, or but-toning typically remains impaired. The Corticospinal and Corticobulbar Pathways: Upper Motor Neurons That Initiate Complex Voluntary Movements The upper motor neurons in the cerebral cortex reside in several adjacent and highly interconnected areas in the frontal lobe, which together mediate the planning and initiation of complex temporal sequences of voluntary move-ments. These cortical areas all receive regulatory input from the basal ganglia and cerebellum via relays in the ventrolateral thalamus (see Chapters 17 and 18), as well as inputs from the somatic sensory regions of the parietal lobe (see Chapter 8). Although the phrase “motor cortex” is sometimes used to refer to these frontal areas collectively, more commonly it is restricted to the primary motor cortex, which is located in the precentral gyrus (Figure 16.7). The primary motor cortex can be distinguished from the adjacent “premotor” areas both cytoarchitectonically (it is area 4 in Brodmann’s nomenclature) and by the low intensity of current necessary to elicit movements by electrical stimulation in this region. The low threshold for eliciting movements is an indicator of a relatively large and direct pathway from the primary area to the lower motor neurons of the brainstem and spinal cord. This section and the next focus on the organization and functions of the primary motor cortex and its descending pathways, whereas the subsequent section addresses the con-tributions of the adjacent premotor areas. The pyramidal cells of cortical layer V (also called Betz cells) are the upper motor neurons of the primary motor cortex. Their axons descend to the brainstem and spinal motor centers in the corticobulbar and corti-cospinal tracts, passing through the internal capsule of the forebrain to enter the cerebral peduncle at the base of the midbrain (Figure 16.8). They then (A) Lateral view (B) Medial view Primary motor cortex Lateral premotor cortex Medial premotor cortex Medial premotor cortex Primary motor cortex Upper Motor Neuron Control of the Brainstem and Spinal Cord 403 Figure 16.8 The corticospinal and cor-ticobulbar tracts. Neurons in the motor cortex give rise to axons that travel through the internal capsule and coa-lesce on the ventral surface of the mid-brain, within the cerebral peduncle. These axons continue through the pons and come to lie on the ventral surface of the medulla, giving rise to the pyra-mids. Most of these pyramidal fibers cross in the caudal part of the medulla to form the lateral corticospinal tract in the spinal cord. Those axons that do not cross form the ventral corticospinal tract. Corticobulbar collaterals to reticular formation Corticospinal and corticobulbar tracts Internal capsule Cortex Midbrain Middle pons Middle medulla Caudal medulla Spinal cord Cerebral peduncle Pontine fiber bundles Pyramid Pyramidal decussation Lateral cortico-spinal tract Lower motor neuron Ventral cortico-spinal tract Trigeminal motor nucleus (V) Red nucleus Hypoglossal nucleus (XII) 404 Chapter Sixteen Box B Patterns of Facial Weakness and Their Importance for Localizing Neurological Injury The signs and symptoms pertinent to the cranial nerves and their nuclei are of spe-cial importance to clinicians seeking to pinpoint the neurological lesions that produce motor deficits. An especially instructive example is provided by the muscles of facial expression. It has long been recognized that the distribution of facial weakness provides important localizing clues indicating whether the underlying injury involves lower motor neurons in the facial motor nucleus (and/or their axons in the facial nerve) or the inputs that govern these neurons, which arise from upper motor neurons in the cerebral cortex. Damage to the facial motor nucleus or its nerve affects all the muscles of facial expression on the side of the lesion (lesion C in the figure); this is expected given the intimate anatomical and functional linkage between lower motor neurons and skele-tal muscles. A pattern of impairment that is more difficult to explain accompanies unilateral injury to the motor areas in the lateral frontal lobe (primary motor cor-tex, lateral premotor cortex), as occurs strokes that involve the middle cerebral artery (lesion A in the figure). Most patients with such injuries have difficulty controlling the contralateral muscles around the mouth but retain the ablility to symmetrically raise their eyebrows, wrinkle their forehead, and squint. Until recently, it was assumed that this pattern of inferior facial paresis with superior facial sparing could be attrib-uted to (presumed) bilateral projections from the face representation in the pri-mary motor cortex to the facial motor nucleus; in this conception, the intact ipsilateral corticobulbar projections were considered sufficient to motivate the con-tractions of the superior muscles of the face. However, recent tract-tracing stud-ies in non-human primates have sug-gested a different explanation. These studies demonstrate two important facts that clarify the relations among the face representations in the cerebral cortex and the facial motor nucleus. First, the corti-cobulbar projections of the primary motor cortex are directed predominantly toward the lateral cell columns in the contralateral facial motor nucleus, which control the movements of the perioral musculature. Thus, the more dorsal cell columns in the facial motor nucleus that innervate superior facial muscles do not receive significant input from the pri-mary motor cortex. Second, these dorsal cell columns are governed by an acces-Weakness of inferior facial muscles Weakness of superior and inferior facial muscle Upper motor neuron lesion Lower motor neuron lesion Facial nucleus Facial nerve Pons Face representation in right primary motor cortex Face representation in cingulate motor area A B C Organization of projections from cerebral cortex to the facial motor nucleus and the effects of upper and lower motor neuron lesions. run through the base of the pons, where they are scattered among the trans-verse pontine fibers and nuclei of the pontine gray matter, coalescing again on the ventral surface of the medulla where they form the medullary pyra-mids. The components of this upper motor neuron pathway that innervate cranial nerve nuclei, the reticular formation, and the red nucleus (that is, the corticobulbar tract) leave the pathway at the appropriate levels of the brain-stem (see Figure 16.8 and Box B ). At the caudal end of the medulla, most, but not all, of the axons in the pyramidal tract cross (or “decussate”) to enter the lateral columns of the spinal cord, where they form the lateral corticospinal tract. A smaller number of axons enters the spinal cord without crossing; these axons, which comprise the ventral corticospinal tract, terminate either ipsilaterally or contralaterally, after crossing in the midline (via spinal cord commissure). The ventral corticospinal pathway arises primarily from regions of the motor cortex that serve axial and proximal muscles. The lateral corticospinal tract forms the direct pathway from the cortex to the spinal cord and terminates primarily in the lateral portions of the ventral horn and intermediate gray matter (see Figures 16.3 and 16.8). The indirect pathway to lower motor neurons in the spinal cord runs, as already de-scribed, from the motor cortex to two of the sources of upper motor neurons in the brainstem: the red nucleus and the reticular formation. In general, the axons to the reticular formation originate from the parts of the motor cortex that project to the medial region of the spinal cord gray matter, whereas the axons to the red nucleus arise from the parts of the motor cortex that project to the lateral region of the spinal cord gray matter. Functional Organization of the Primary Motor Cortex Clinical observations and experimental work dating back a hundred years or more have provided a reasonably coherent picture of the functional organiza-tion of the motor cortex. By the end of the nineteenth century, experimental work in animals by the German physiologists G. Theodor Fritsch and Eduard Hitzig had shown that electrical stimulation of the motor cortex elicits con-tractions of muscles on the contralateral side of the body. At about the same time, the British neurologist John Hughlings Jackson surmised that the motor cortex contains a complete representation, or map, of the body’s musculature. Upper Motor Neuron Control of the Brainstem and Spinal Cord 405 sory motor area in the anterior cingulate gyrus, a cortical region that is associated with emotional processing (see Chapter 28). Therefore, a better interpretation is that strokes involving the middle cere-bral artery spare the superior aspect of the face because the relevant upper motor neurons are in the cingulum, which is supplied by the anterior cere-bral artery. An additional puzzle has also been resolved by these studies. Strokes involv-ing the anterior cerebral artery or subcor-tical lesions that interrupt the corticobul-bar projection (lesion B in the figure) sel-dom produce significant paresis of the superior facial muscles. Superior facial sparing in these situations may arise because this cingulate motor area sends descending projections through the corti-cobulbar pathway that bifuracte and innervate dorsal facial motor cell columns on both sides of the brainstem. Thus, the superior muscles of facial expression are controlled by symmetrical inputs from the cingulate motor areas in both hemispheres. References JENNY, A. B. AND C. B. SAPER (1987) Organiza-tion of the facial nucleus and corticofacial projection in the monkey: A reconsideration of the upper motor neuron facial palsy. Neu-rology 37: 930–939. KUYPERS, H. G. J. M. (1958) Corticobulbar connexions to the pons and lower brainstem in man. Brain 81: 364–489. MORECRAFT, R. J., J. L. LOUIE, J. L. HERRICK AND K. S. STILWELL-MORECRAFT (2001) Cortical innervation of the facial nucleus in the non-human primate: A new interpretation of the effects of stroke and related subtotal brain trauma on the muscles of facial expression. Brain 124: 176–208. 406 Chapter Sixteen Jackson reached this conclusion from his observation that the abnormal movements during some types of epileptic seizures “march” systematically from one part of the body to another. For instance, partial motor seizures may start with abnormal movements of a finger, progress to involve the entire hand, then the forearm, the arm, the shoulder, and, finally, the face. This early evidence for motor maps in the cortex was confirmed shortly after the turn of the nineteenth century when Charles Sherrington published his classical maps of the organization of the motor cortex in great apes, using focal electrical stimulation. During the 1930s, one of Sherrington’s stu-dents, the American neurosurgeon Wilder Penfield, extended this work by demonstrating that the human motor cortex also contains a spatial map of the body’s musculature. By correlating the location of muscle contractions with the site of electrical stimulation on the surface of the motor cortex (the same method used by Sherrington), Penfield mapped the representation of the muscles in the precentral gyrus in over 400 neurosurgical patients (Fig-ure 16.9). He found that this motor map shows the same disproportions observed in the somatic sensory maps in the postcentral gyrus (see Chapter 8). Thus, the musculature used in tasks requiring fine motor control (such as movements of the face and hands) occupies a greater amount of space in the Figure 16.9 Topographic map of the body musculature in the primary motor cortex. (A) Location of primary motor cortex in the precentral gyrus. (B) Sec-tion along the precentral gyrus, illustrat-ing the somatotopic organization of the motor cortex. The most medial parts of the motor cortex are responsible for con-trolling muscles in the legs; the most lateral portions are responsible for con-trolling muscles in the face. (C) Dispro-portional representation of various por-tions of the body musculature in the motor cortex. Representations of parts of the body that exhibit fine motor con-trol capabilities (such as the hands and face) occupy a greater amount of space than those that exhibit less precise motor control (such as the trunk). Corticospinal tract Corticobulbar tract (B) (C) Central sulcus Shoulder Neck Head Arm Hand Digits Thumb Eyes Nose Face Lips Jaw Tongue Throat Toes Genitalia Feet Leg Trunk (A) Primary motor cortex map than does the musculature requiring less precise motor control (such as that of the trunk). The behavioral implications of cortical motor maps are considered in Boxes C and D. The introduction in the 1960s of intracortical microstimulation (a more refined method of cortical activation) allowed a more detailed understand-ing of motor maps. Microstimulation entails the delivery of electrical cur-rents an order of magnitude smaller than those used by Sherrington and Penfield. By passing the current through the sharpened tip of a metal micro-electrode inserted into the cortex, the upper motor neurons in layer V that project to lower motor neuron circuitry can be stimulated focally. Although intracortical stimulation generally confirmed Penfield’s spatial map in the motor cortex, it also showed that the finer organization of the map is rather different than most neuroscientists imagined. For example, when microstim-ulation was combined with recordings of muscle electrical activity, even the smallest currents capable of eliciting a response initiated the excitation of several muscles (and the simultaneous inhibition of others), suggesting that organized movements rather than individual muscles are represented in the map (see Box C ). Furthermore, within major subdivisions of the map (e.g., arm, forearm, or finger regions), a particular movement could be elicited by stimulation of widely separated sites, indicating that neurons in nearby regions are linked by local circuits to organize specific movements. This interpretation has been supported by the observation that the regions responsible for initiating different movements overlap substantially. About the same time that these studies were being undertaken, Ed Evarts and his colleagues at the National Institutes of Health were pioneering a technique in which implanted microelectrodes were used to record the elec-trical activity of individual motor neurons in awake, behaving monkeys. In these experiments, the monkeys were trained to perform a variety of motor tasks, thus providing a means of correlating neuronal activity with volun-tary movements. Evarts and his group found that the force generated by contracting muscles changed as a function of the firing rate of upper motor neurons. Moreover, the firing rates of the active neurons often changed prior to movements involving very small forces. Evarts therefore proposed that the primary motor cortex contributes to the initial phase of recruitment of lower motor neurons involved in the generation of finely controlled move-ments. Additional experiments showed that the activity of primary motor neurons is correlated not only with the magnitude, but also with the direc-tion of the force produced by muscles. Thus, some neurons show progres-sively less activity as the direction of movement deviates from the neuron’s “preferred direction.” A further advance was made in the mid-1970s by the introduction of spike-triggered averaging (Figure 16.10). By correlating the timing of the cor-tical neuron’s discharges with the onset times of the contractions generated by the various muscles used in a movement, this method provides a way of measuring the influence of a single cortical motor neuron on a population of lower motor neurons in the spinal cord. Recording such activity from differ-ent muscles as monkeys performed wrist flexion or extension demonstrated that the activity of a number of different muscles is directly facilitated by the discharges of a given upper motor neuron. This peripheral muscle group is referred to as the “muscle field” of the upper motor neuron. On average, the size of the muscle field in the wrist region is two to three muscles per upper motor neuron. These observations confirmed that single upper motor neu-rons contact several lower motor neuron pools; the results are also consistent with the general conclusion that movements, rather than individual muscles, Upper Motor Neuron Control of the Brainstem and Spinal Cord 407 408 Chapter Sixteen are encoded by the activity of the upper motor neurons in the cortex (see Box C ). Finally, the relative amount of activity across large populations of neurons appears to encode the direction of visually-guided movements. Thus, the direction of movements in monkeys could be predicted by calculating a “neuronal population vector” derived simultaneously from the discharges of upper motor neurons that are “broadly tuned” in the sense that they dis-charge prior to movements in many directions (Figure 16.11). These observa-tions showed that the discharges of individual upper motor neurons cannot specify the direction of an arm movement, simply because they are tuned too broadly; rather, each arm movement must be encoded by the concurrent discharges of a large population of such neurons. The Premotor Cortex A complex mosaic of interconnected frontal lobe areas that lie rostral to the primary motor cortex also contributes to motor functions (see Figure 16.7). The upper motor neurons in this premotor cortex influence motor behavior Box C What Do Motor Maps Represent? Electrical stimulation studies carried out by the neurosurgeon Wilder Penfield and his colleagues in human patients (and by Sherrington and later Clinton Woolsey and his colleagues in experimental ani-mals) clearly demonstrated a systematic map of the body’s musculature in the pri-mary motor cortex (see text). The fine structure of this map, however, has been a continuing source of controversy. Is the map in the motor cortex a “piano key-board” for the control of individual mus-cles, or is it a map of movements, in which specific sites control multiple mus-cle groups that contribute to the genera-tion of particular actions? Initial experi-ments implied that the map in the motor cortex is a fine-scale representation of individual muscles. Thus, stimulation of small regions of the map activated single muscles, suggesting that vertical columns of cells in the motor cortex were responsi-ble for controlling the actions of particu-lar muscles, much as columns in the somatic sensory map are thought to ana-lyze particular types of stimulus informa-tion (see Chapter 8). More recent studies using anatomical and physiological techniques, however, have shown that the map in the motor cortex is far more complex than a colum-nar representation of particular muscles. Individual pyramidal tract axons are now known to terminate on sets of spinal motor neurons that innervate dif-ferent muscles. This relationship is evi-dent even for neurons in the hand repre-sentation of the motor cortex, the region that controls the most discrete, fraction-ated movements. Furthermore, cortical microstimulation experiments have shown that contraction of a single mus-cle can be evoked by stimulation over a wide region of the motor cortex (about 2–3 mm in macaque monkeys) in a com-plex, mosaic fashion. It seems likely that horizontal connections within the motor cortex and local circuits in the spinal cord create ensembles of neurons that coordinate the pattern of firing in the population of ventral horn cells that ulti-mately generate a given movement. Thus, while the somatotopic maps in the motor cortex generated by early studies are correct in their overall topog-raphy, the fine structure of the map is far more intricate. Unraveling these details of motor maps still holds the key to understanding how patterns of activity in the motor cortex generate a given movement. References BARINAGA, M. (1995) Remapping the motor cortex. Science 268: 1696–1698. LEMON, R. (1988) The output map of the pri-mate motor cortex. Trends Neurosci. 11: 501–506. PENFIELD, W. AND E. BOLDREY (1937) Somatic motor and sensory representation in the cere-bral cortex of man studied by electrical stim-ulation. Brain 60: 389–443. SCHIEBER, M. H. AND L. S. HIBBARD (1993) How somatotopic is the motor cortex hand area? Science 261: 489–491. WOOLSEY, C. N. (1958) Organization of somatic sensory and motor areas of the cere-bral cortex. In Biological and Biochemical Bases of Behavior, H. F. Harlow and C. N. Woolsey (eds.). Madison, WI: University of Wisconsin Press, pp. 63–81. Upper Motor Neuron Control of the Brainstem and Spinal Cord 409 Primary motor cortex (A) Detection of postspike facilitation Spikes of single cortical motor neuron Spinal motor neuron Electromyograph (EMG) Rectifier Trigger averager input (B) Postspike facilitation by cortical motor neuron Recording from cortical motor neuron n = 9000 spikes Spike-triggered average of EMG Cortical motor neuron spike Spike-triggered averaging Rectified EMG Time (ms) Record Figure 16.10 The influence of single cortical upper motor neurons on muscle activity. (A) Diagram illustrates the spike triggering average method for correlating muscle activity with the discharges of single upper motor neurons. (B) The response of a thumb muscle (bottom trace) follows by a fixed latency the single spike discharge of a pyramidal tract neuron (top trace). This technique can be used to determine all the muscles that are influenced by a given motor neuron (see text). (After Porter and Lemon, 1993.) 410 Chapter Sixteen both through extensive reciprocal connections with the primary motor cor-tex, and directly via axons that project through the corticobulbar and corti-cospinal pathways to influence local circuit and lower motor neurons of the brainstem and spinal cord. Indeed, over 30% of the axons in the corticospinal tract arise from neurons in the premotor cortex. In general, a variety of experiments indicate that the premotor cortex uses information from other cortical regions to select movements appropriate to the context of the action (see Chapter 25). The functions of the premotor cortex are usually considered in terms of the lateral and medial components of this region. As many as 65% of the Box D Sensory Motor Talents and Cortical Space Are special sensory motor talents, such as the exceptional speed and coordina-tion displayed by talented athletes, ballet dancers, or concert musicians visible in the structure of the nervous system? The widespread use of noninvasive brain imaging techniques (see Box A in Chap-ter 1) has generated a spate of studies that have tried to answer this and related questions. Most of these studies have sought to link particular sensory motor skills to the amount of brain space devoted to such talents. For example, a study of professional violinists, cellists, and classical guitarists purported to show that representations of the “finger-ing” digits of the left hand in the right primary somatic sensory cortex are larger than the corresponding represen-tations in nonmusicians. Although such studies in humans remain controversial (the techniques are only semiquantitative), the idea that greater motor talents (or any other abil-ity) will be reflected in a greater amount of brain space devoted to that task makes good sense. In particular, comparisons across species show that special talents are invariably based on commensurately sophisticated brain circuitry, which means more neurons, more synaptic con-tacts between neurons, and more sup-porting glial cells—all of which occupy more space within the brain. The size and proportion of bodily representations in the primary somatic sensory and motor cortices of various animals reflects species-specific nuances of mechanosen-sory discrimination and motor control. Thus, the representations of the paws are disproportionately large in the sensori-motor cortex of raccoons; rats and mice devote a great deal of cortical space to representations of their prominent facial whiskers; and a large fraction of the sen-sorimotor cortex of the star-nosed mole is given over to representing the elabo-rate nasal appendages that provide criti-cal mechanosensory information for this burrowing species. The link between behavioral competence and the alloca-tion of space is equally apparent in ani-mals in which a particular ability has diminished, or has never developed fully, during the course of evolution. Nevertheless, it remains uncertain how—or if—this principle applies to variations in behavior among members of the same species, including humans. For example, there does not appear to be any average hemisphere asymmetry in the allocation of space in either the pri-mary sensory or motor area, as mea-sured cytoarchitectonically. Some asym-metry might be expected simply because 90% of humans prefer to use the right hand when they perform challenging manual tasks. It seems likely that indi-vidual sensory motor talents among humans will be reflected in the allocation of an appreciably different amount of space to those behaviors, but this issue is just beginning to be explored with quan-titative methods that are adequate to the challenge. References CATANIA, K. C. AND J. H. KAAS (1995) Organi-zation of the somatosensory cortex of the star-nosed mole. J. Comp. Neurol. 351: 549–567. ELBERT, T., C. PANTEV, C. WIENBRUCH, B. ROCK-STROH AND E. TAUB (1995) Increased cortical representation of the fingers of the left hand in string players. Science 270: 305–307. WELKER, W. I. AND S. SEIDENSTEIN (1959) Somatic sensory representation in the cere-bral cortex of the raccoon (Procyon lotos). J. Comp. Neurol. 111: 469–501. WHITE, L. E., T. J. ANDREWS, C. HULETTE, A. RICHARDS, M. GROELLE, J. PAYDARFAR AND D. PURVES (1997) Structure of the human senso-rimotor system. II. Lateral symmetry. Cereb. Cortex 7: 31–47. WOOLSEY, T. A. AND H. VAN DER LOOS (1970) The structural organization of layer IV in the somatosensory region (SI) of mouse cerebral cortex. The description of a cortical field composed of discrete cytoarchitectonic units. Brain Res. 17: 205–242. neurons in the lateral premotor cortex have responses that are linked in time to the occurrence of movements; as in the primary motor area, many of these cells fire most strongly in association with movements made in a specific direction. However, these neurons are especially important in conditional motor tasks. That is, in contrast to the neurons in the primary motor area, when a monkey is trained to reach in different directions in response to a Upper Motor Neuron Control of the Brainstem and Spinal Cord 411 -500 0 500 1000 -500 0 500 1000 -500 0 500 1000 -500 0 500 1000 -500 0 500 1000 -1000 -1000 -500 0 500 1000 -1000 -500 0 500 1000 -1000 -1000 -1000 -1000 -1000 -500 0 500 1000 90° 180° 270° 0° Impulses/sec Direction of movement 20 40 60 45° 135° 225° 315° 90° 270° 0° 180° 135° 45° 315° 225° 90° 0° 0° (A) (C) (D) (B) Figure 16.11 Directional tuning of an upper motor neuron in the primary motor cortex. (A) A monkey is trained to move a joystick in the direction indicated by a light. (B) The activity of a single neuron was recorded during arm move-ments in each of eight different directions (zero indicates the time of movement onset, and each short vertical line in this raster plot represents an action potential). The activity of the neuron increased before movements between 90 and 225 degrees (yellow zone), but decreased in anticipation of movements between 0 and 315 degrees (purple zone). (C) Plot showing that the neuron’s discharge rate was greatest before movements in a particular direction, which defines the neuron’s “preferred direction.” (D) The black lines indi-cate the discharge rate of individual upper motor neurons prior to each direction of movement. By combining the responses of all the neurons, a “population vector” can be derived that represents the movement direction encoded by the simultaneous activity of the entire population. (After Georgeopoulos et al., 1986.) 412 Chapter Sixteen visual cue, the appropriately tuned lateral premotor neurons begin to fire at the appearance of the cue, well before the monkey receives a signal to actu-ally make the movement. As the animal learns to associate a new visual cue with the movement, appropriately tuned neurons begin to increase their rate of discharge in the interval between the cue and the onset of the signal to perform the movement. Rather than directly commanding the initiation of a movement, these neurons appear to encode the monkey’s intention to per-form a particular movement; thus, they seem to be particularly involved in the selection of movements based on external events. Further evidence that the lateral premotor area is concerned with move-ment selection comes from the effects of cortical damage on motor behavior. Lesions in this region severely impair the ability of monkeys to perform visually cued conditional tasks, even though they can still respond to the visual stimulus and can perform the same movement in a different setting. Similarly, patients with frontal lobe damage have difficulty learning to select a particular movement to be performed in response to a visual cue, even though they understand the instructions and can perform the movements. Individuals with lesions in the premotor cortex may also have difficulty per-forming movements in response to verbal commands. The medial premotor cortex, like the lateral area, mediates the selection of movements. However, this region appears to be specialized for initiating movements specified by internal rather than external cues. In contrast to lesions in the lateral premotor area, removal of the medial premotor area in a monkey reduces the number of self-initiated or “spontaneous” movements the animal makes, whereas the ability to execute movements in response to external cues remains largely intact. Imaging studies suggest that this corti-cal region in humans functions in much the same way. For example, PET scans show that the medial region of the premotor cortex is activated when the subjects perform motor sequences from memory (i.e., without relying on an external instruction). In accord with this evidence, single unit recordings in monkeys indicate that many neurons in the medial premotor cortex begin to discharge one or two seconds before the onset of a self-initiated move-ment. In summary, both the lateral and medial areas of the premotor cortex are intimately involved in selecting a specific movement or sequence of move-ments from the repertoire of possible movements. The functions of the areas differ, however, in the relative contributions of external and internal cues to the selection process. Damage to Descending Motor Pathways: The Upper Motor Neuron Syndrome Injury of upper motor neurons is common because of the large amount of cortex occupied by the motor areas, and because their pathways extend all the way from the cerebral cortex to the lower end of the spinal cord. Damage to the descending motor pathways anywhere along this trajectory gives rise to a set of symptoms called the upper motor neuron syndrome. This clinical picture differs markedly from the lower motor neuron syn-drome described in Chapter 15 and entails a characteristic set of motor deficits (Table 16.1). Damage to the motor cortex or the descending motor axons in the internal capsule causes an immediate flaccidity of the muscles on the contralateral side of the body and face. Given the topographical arrangement of the motor system, identifying the specific parts of the body that are affected helps localize the site of the injury. The acute manifestations tend to be most severe in the arms and legs: If the affected limb is elevated and released, it drops passively, and all reflex activity on the affected side is abolished. In contrast, control of trunk muscles is usually preserved, either by the remaining brainstem pathways or because of the bilateral projections of the corticospinal pathway to local circuits that control midline muscula-ture. The initial period of “hypotonia” after upper motor neuron injury is called spinal shock, and reflects the decreased activity of spinal circuits sud-denly deprived of input from the motor cortex and brainstem. After several days, however, the spinal cord circuits regain much of their function for reasons that are not fully understood. Thereafter, a consistent pattern of motor signs and symptoms emerges, including: 1. The Babinski sign. The normal response in an adult to stroking the sole of the foot is flexion of the big toe, and often the other toes. Following damage to descending upper motor neuron pathways, however, this stimulus elicits extension of the big toe and a fanning of the other toes (Figure 16.12). A similar response occurs in human infants before the maturation of the corticospinal pathway and pre-sumably indicates incomplete upper motor neuron control of local motor neuron circuitry. Upper Motor Neuron Control of the Brainstem and Spinal Cord 413 TABLE 16.1 Signs and Symptoms of Upper and Lower Motor Neuron Lesions Upper Motor Neuron Syndrome Lower Motor Neuron Syndrome Weakness Weakness or paralysis Spasticity Decreased superficial reflexes Increased tone Hypoactive deep reflexes Hyperactive deep reflexes Decreased tone Clonus Fasciculations and fibrillations Babinski’s sign Severe muscle atrophy Loss of fine voluntary movements (A) Normal plantar response (B) Extensor plantar response (Babinski sign) Fanning of toes Toes down (flexion) Up Figure 16.12 The Babinski sign. Fol-lowing damage to descending corti-cospinal pathways, stroking the sole of the foot causes an abnormal fanning of the toes and the extension of the big toe. 414 Chapter Sixteen 2. Spasticity. Spasticity is increased muscle tone (Box E), hyperactive stretch reflexes, and clonus (oscillatory contractions and relaxations of muscles in response to muscle stretching). Extensive upper motor neuron lesions may also be accompanied by rigidity of the extensor muscles of the leg and the flexor muscles of the arm (called decere-brate rigidity; see below). Spasticity is probably caused by the removal of inhibitory influences exerted by the cortex on the postural centers of the vestibular nuclei and reticular formation. In experimen-tal animals, for instance, lesions of the vestibular nuclei ameliorate the spasticity that follows damage to the corticospinal tract. Spasticity is also eliminated by sectioning the dorsal roots, suggesting that it represents an abnormal increase in the gain of the spinal cord stretch reflexes due to loss of descending inhibition (see Chapter 15). This increased gain is also thought to explain clonus (see Box E). Box E Muscle Tone Muscle tone is the resting level of tension in a muscle. In general, maintaining an appropriate level of muscle tone allows a muscle to make an optimal response to voluntary or reflexive commands in a given context. Tone in the extensor mus-cles of the legs, for example, helps main-tain posture while standing. By keeping the muscles in a state of readiness to resist stretch, tone in the leg muscles pre-vents the amount of sway that normally occurs while standing from becoming too large. During activities such as walk-ing or running, the “background” level of tension in leg muscles also helps to store mechanical energy, in effect enhancing the muscle tissue’s springlike qualities. Muscle tone depends on the resting level of discharge of α motor neu-rons. Activity in the Ia spindle affer-ents—the neurons responsible for the stretch reflex—is the major contributor to this tonic level of firing. As described in Chapter 15, the γ efferent system (by its action on intrafusal muscle fibers) regu-lates the resting level of activity in the Ia afferents and establishes the baseline level of α motor neuron activity in the absence of muscle stretch. Clinically, muscle tone is assessed by judging the resistance of a patient’s limb to passive stretch. Damage to either the α motor neurons or the Ia afferents carry-ing sensory information to the α motor neurons results in a decrease in muscle tone, called hypotonia. In general, dam-age to descending pathways that termi-nate in the spinal cord has the opposite effect, leading to an increase in muscle tone, or hypertonia (except during the phase of spinal shock—see text). The neural changes responsible for hyperto-nia following damage to higher centers are not well understood; however, at least part of this change is due to an increase in the responsiveness of α motor neurons to Ia sensory inputs. Thus, in experimental animals in which descend-ing inputs have been severed, the result-ing hypertonia can be eliminated by sec-tioning the dorsal roots. Increased resistance to passive move-ment following damage to higher centers is called spasticity, and is associated with two other characteristic signs: the clasp-knife phenomenon and clonus. When first stretched, a spastic muscle provides a high level of resistance to the stretch and then suddenly yields, much like the blade of a pocket knife (or clasp knife, in old-fashioned terminology). Hyperactiv-ity of the stretch reflex loop is the reason for the increased resistance to stretch in the clasp-knife phenomenon. The physi-ological basis for the inhibition that causes the sudden collapse of the stretch reflex (and loss of muscle tone) is thought to involve the activation of the Golgi tendon organs (see Chapter 15). Clonus refers to a rhythmic pattern of contractions (3–7 per second) due to the alternate stretching and unloading of the muscle spindles in a spastic muscle. Clonus can be demonstrated in the flexor muscles of the leg by pushing up on the sole of patient’s foot to dorsiflex the ankle. If there is damage to descending upper motor neuron pathways, holding the ankle loosely in this position gener-ates rhythmic contractions of both the gastrocnemius and soleus muscles. Both the increase in muscle tone and the pathological oscillations seen after dam-age to descending pathways are very dif-ferent from the tremor at rest and cog-wheel rigidity present in basal ganglia disorders such as Parkinson’s disease, phenomena discussed in Chapters 17 and 18. 3. A loss of the ability to perform fine movements. If the lesion involves the descending pathways that control the lower motor neurons to the upper limbs, the ability to execute fine movements (such as indepen-dent movements of the fingers) is lost. Although these upper motor neuron signs and symptoms may arise from damage anywhere along the descending pathways, the spasticity that fol-lows damage to descending pathways in the spinal cord is less marked than the spasticity that follows damage to the cortex or internal capsule. For example, the extensor muscles in the legs of a patient with spinal cord damage cannot support the individual’s body weight, whereas those of a patient with damage at the cortical level often can. On the other hand, lesions that interrupt the descending pathways in the brainstem above the level of the vestibular nuclei but below the level of the red nucleus cause even greater extensor tone than that which occurs after damage to higher regions. Sherrington, who first described this phenomenon, called the increased tone decerebrate rigidity. In the cat, the extensor tone in all four limbs is so great after lesions that spare the vestibulospinal tracts that the animal can stand without support. Patients with severe brainstem injury at the level of the pons may exhibit similar signs of decerebration, i.e., arms and legs stiffly extended, jaw clenched, and neck retracted. The relatively greater hypertonia following damage to the nervous system above the level of the spinal cord is presumably explained by the remaining activity of the intact descending pathways from the vestibular nuclei and reticular forma-tion, which have a net excitatory influence on these stretch reflexes. Summary Two sets of upper motor neuron pathways make distinct contributions to the control of the local circuitry in the brainstem and spinal cord. One set origi-nates from neurons in brainstem centers—primarily the reticular formation and the vestibular nuclei—and is responsible for postural regulation. The reticular formation is especially important in feedforward control of posture (that is, movements that occur in anticipation of changes in body stability). In contrast, the neurons in the vestibular nuclei that project to the spinal cord are especially important in feedback postural mechanisms (i.e., in producing movements that are generated in response to sensory signals that indicate an existing postural disturbance). The other major upper motor neuron path-way originates from the frontal lobe and includes projections from the pri-mary motor cortex and the nearby premotor areas. The premotor cortices are responsible for planning and selecting movements, whereas the primary motor cortex is responsible for their execution. The motor cortex influences movements directly by contacting lower motor neurons and local circuit neu-rons in the spinal cord and brainstem, and indirectly by innervating neurons in brainstem centers (in this case, the reticular formation and red nucleus) that in turn project to lower motor neurons and circuits. Although the brain-stem pathways can independently organize gross motor control, direct pro-jections from the motor cortex to local circuit neurons in the brainstem and spinal cord are essential for the fine, fractionated movements of the distal parts of the limbs, the tongue, and face that are especially important in our daily lives. Upper Motor Neuron Control of the Brainstem and Spinal Cord 415 416 Chapter Sixteen Additional Reading Reviews DUM, R. P. AND P. L. STRICK (2002) Motor areas in the frontal lobe of the primate. Physiol. Behav. 77: 677–682. GAHERY, Y. AND J. MASSION (1981) Coordina-tion between posture and movement. Trends Neurosci. 4: 199–202. GEORGEOPOULOS, A. P., M. TAIRA AND A. LUKA-SHIN (1993) Cognitive neurophysiology of the motor cortex. Science 260: 47–52. KUYPERS, H. G. J. M. (1981) Anatomy of the descending pathways. In Handbook of Physiol-ogy, Section 1: The Nervous System, Volume II, Motor Control, Part 1, V. B. Brooks (ed.). Bethesda, MD: American Physiological Society. NASHNER, L. M. (1979) Organization and pro-gramming of motor activity during posture control. In Reflex Control of Posture and Move-ment, R. Granit and O. Pompeiano (eds.). Prog. Brain Res. 50: 177–184. NASHNER, L. M. (1982) Adaptation of human movement to altered environments. Trends Neurosci. 5: 358–361. SHERRINGTON, C. AND S. F. GRUNBAUM (1901) Observations on the physiology of the cere-bral cortex of some of the higher apes. Proc. Roy. Soc. 69: 206–209. Important Original Papers EVARTS, E. V. (1981) Functional studies of the motor cortex. In The Organization of the Cere-bral Cortex, F. O. Schmitt, F. G. Worden, G. Adelman and S. G. Dennis (eds.). Cambridge, MA: MIT Press, pp. 199–236. GRAZIANO, M. S., C. C. TAYLOR, T. MOORE AND D. F. COOKE (2002) The cortical control of movement revisited. Neuron 36: 349–362. FETZ, E. E. AND P. D. CHENEY (1978) Muscle fields of primate corticomotoneuronal cells. J. Physiol. (Paris) 74: 239–245. FETZ, E. E. AND P. D. CHENEY (1980) Postspike facilitation of forelimb muscle activity by pri-mate corticomotoneuronal cells. J. Neuro-physiol. 44: 751–772. GEORGEOPOULOS, A. P., A. B. SWARTZ AND R. E. KETTER (1986) Neuronal population coding of movement direction. Science 233: 1416–1419. LAWRENCE, D. G. AND H. G. J. M. KUYPERS (1968) The functional organization of the motor system in the monkey. I. The effects of bilateral pyramidal lesions. Brain 91: 1–14. MITZ, A. R., M. GODSCHALK AND S. P. WISE (1991) Learning-dependent neuronal activity in the premotor cortex: Activity during the acquisition of conditional motor associations. J. Neurosci. 11: 1855–1872. ROLAND, P. E., B. LARSEN, N. A. LASSEN AND E. SKINHOF (1980) Supplementary motor area and other cortical areas in organization of vol-untary movements in man. J. Neurophysiol. 43: 118–136. SANES, J. N. AND W. TRUCCOLO (2003) Motor “binding”: Do functional assemblies in pri-mary motor cortex have a role? Neuron 38: 115–125. Books ASANUMA, H. (1989) The Motor Cortex. New York: Raven Press. BRODAL, A. (1981) Neurological Anatomy in Relation to Clinical Medicine, 3rd Ed. New York: Oxford University Press. BROOKS, V. B. (1986) The Neural Basis of Motor Control. New York: Oxford University Press. PASSINGHAM, R. (1993) The Frontal Lobes and Voluntary Action. Oxford: Oxford University Press. PENFIELD, W. AND T. RASMUSSEN (1950) The Cerebral Cortex of Man: A Clinical Study of Localization of Function. New York: Macmillan. PHILLIPS, C. G. AND R. PORTER (1977) Corti-cospinal Neurons: Their Role in Movement. Lon-don: Academic Press. PORTER, R. AND R. LEMON (1993) Corticospinal Function and Voluntary Movement. Oxford: Oxford University Press. SHERRINGTON, C. (1947) The Integrative Action of the Nervous System, 2nd Ed. New Haven: Yale University Press. SJÖLUND, B. AND A. BJÖRKLUND (1982) Brain-stem Control of Spinal Mechanisms. Amsterdam: Elsevier. Overview As described in the preceding chapter, motor regions of the cortex and brain-stem contain upper motor neurons that initiate movement by controlling the activity of local circuit and lower motor neurons in the brainstem and spinal cord. This chapter and the next discuss two additional regions of the brain that are important in motor control: the basal ganglia and the cerebellum. In contrast to the components of the motor system that harbor upper motor neurons, the basal ganglia and cerebellum do not project directly to either the local circuit or lower motor neurons; instead, they influence movement by regulating the activity of upper motor neurons. The term basal ganglia refers to a large and functionally diverse set of nuclei that lie deep within the cerebral hemispheres. The subset of these nuclei relevant to this account of motor function includes the caudate, putamen, and the globus pallidus. Two additional structures, the substantia nigra in the base of the midbrain and the subthalamic nucleus in the ventral thalamus, are closely associated with the motor functions of these basal ganglia nuclei and are included in the dis-cussion. The motor components of the basal ganglia, together with the sub-stantia nigra and the subthalamic nucleus, effectively make a subcortical loop that links most areas of the cortex with upper motor neurons in the pri-mary motor and premotor cortex and in the brainstem. The neurons in this loop respond in anticipation of and during movements, and their effects on upper motor neurons are required for the normal course of voluntary move-ments. When one of these components of the basal ganglia or associated structures is compromised, the patient cannot switch smoothly between commands that initiate a movement and those that terminate the movement. The disordered movements that result can be understood as a consequence of abnormal upper motor neuron activity in the absence of the supervisory control normally provided by the basal ganglia. Projections to the Basal Ganglia The motor nuclei of the basal ganglia are divided into several functionally distinct groups (Figure 17.1). The first and larger of these groups is called the corpus striatum, which includes the caudate and putamen. These two sub-divisions of the corpus striatum comprise the input zone of the basal ganglia, their neurons being the destinations of most of the pathways that reach this complex from other parts of the brain (Figure 17.2). The name corpus stria-tum, which means “striped body,” reflects the fact that the axon fascicles that pass through the caudate and putamen result in a striped appearance when cut in cross section. The destinations of the incoming axons from the Chapter 17 417 Modulation of Movement by the Basal Ganglia 418 Chapter Seventeen cortex are the dendrites of a class of cells called medium spiny neurons in the corpus striatum (Figure 17.3). The large dendritic trees of these neurons allow them to integrate inputs from a variety of cortical, thalamic, and brain-stem structures. The axons arising from the medium spiny neurons converge on neurons in the globus pallidus and the substantia nigra pars reticulata. The globus pallidus and substantia nigra pars reticulata are the main sources of output from the basal ganglia complex. Nearly all regions of the neocortex project directly to the corpus striatum, making the cerebral cortex the source of the largest input to the basal ganglia by far. Indeed, the only cortical areas that do not project to the corpus stria-tum are the primary visual and primary auditory cortices (Figure 17.4). Of those cortical areas that do innervate the striatum, the heaviest projections are from association areas in the frontal and parietal lobes, but substantial contributions also arise from the temporal, insular, and cingulate cortices. All of these projections, referred to collectively as the corticostriatal pathway, travel through the internal capsule to reach the caudate and putamen directly (see Figure 17.2). The cortical inputs to the caudate and putamen are not equivalent, how-ever, and the differences in input reflect functional differences between these two nuclei. The caudate nucleus receives cortical projections primarily from multimodal association cortices, and from motor areas in the frontal lobe that control eye movements. As the name implies, the association cortices do not process any one type of sensory information; rather, they receive inputs from a number of primary and secondary sensory cortices and associated (A) (B) Frontal cortex Cerebrum Putamen Midbrain Caudate nucleus VA/VL complex of thalamus Substantia nigra pars compacta Subthalamic nuclei Globus pallidus, external and internal segments Substantia nigra pars reticulata Cerebral cortex Caudate and putamen Substantia nigra pars reticulata Thalamus Substantia nigra pars compacta Subthalamic nucleus Globus pallidus and Superior colliculus − − − − + + + Figure 17.1 Motor components of the human basal ganglia. (A) Basic circuits of the basal ganglia pathway: (+) and (–) denote excitory and inhibitory connec-tions. (B) Idealized coronal section through the brain showing anatomical locations of structures involved in the basal ganglia pathway. Most of these structures are in the telencephalon, although the substantia nigra is in the midbrain and the thalamic and subthal-amic nuclei are in the diencephalon. The ventral anterior and ventral lateral thal-amic nuclei (VA/VL complex) are the targets of the basal ganglia, relaying the modulatory effects of the basal ganglia to upper motor neurons in the cortex. thalamic nuclei (see Chapter 25). The putamen, on the other hand, receives input from the primary and secondary somatic sensory cortices in the pari-etal lobe, the secondary (extrastriate) visual cortices in the occipital and tem-poral lobes, the premotor and motor cortices in the frontal lobe, and the auditory association areas in the temporal lobe. The fact that different corti-cal areas project to different regions of the striatum implies that the corticos-triatal pathway consists of multiple parallel pathways serving different func-tions. This interpretation is supported by the observation that the segregation is maintained in the structures that receive projections from the striatum, and in the pathways that project from the basal ganglia to other brain regions. There are other indications that the corpus striatum is functionally subdi-vided according to its inputs. For example, visual and somatic sensory corti-cal projections are topographically mapped within different regions of the putamen. Moreover, the cortical areas that are functionally interconnected at the level of the cortex give rise to projections that overlap extensively in the striatum. Anatomical studies by Ann Graybiel and her colleagues at the Massachusetts Institute of Technology have shown that regions of different cortical areas concerned with the hand (see Chapter 8) converge in specific rostrocaudal bands within the striatum; conversely, regions in the same corti-Modulation of Movement by the Basal Ganglia 419 Caudate Temporal cortex Frontal cortex Parietal cortex Midbrain Cerebrum Putamen Substantia nigra pars compacta Internal capsule Figure 17.2 Anatomical organization of the inputs to the basal ganglia. An idealized coronal section through the human brain, showing the projections from the cere-bral cortex and the substantia nigra pars comparta to the caudate and putamen. 420 Chapter Seventeen cal areas concerned with the leg converge in other striatal bands. These ros-trocaudal bands therefore appear to be functional units concerned with the movement of particular body parts. Another study by the same group showed that the more extensively cortical areas are interconnected by cortic-ocortical pathways, the greater the overlap in their projections to the striatum. A further indication of functional subdivision within the striatum is the spatial distribution of different types of medium spiny neurons. Although medium spiny neurons are distributed throughout the striatum, they occur in clusters of cells called “patches” or “striosomes,” in a surrounding “matrix” of neurochemically distinct cells. Whereas the distinction between the patches and matrix was originally based only on differences in the types of neuropep-tides contained by the medium spiny cells in the two regions, the cell types are now known to differ as well in the sources of their inputs from the cortex and in the destinations of their projections to other parts of the basal ganglia. For example, even though most cortical areas project to medium spiny neurons in both these compartments, limbic areas of the cortex (such as the cingulate gyrus; see Chapter 28) project more heavily to the patches, whereas motor and somatic sensory areas project preferentially to the neurons in the matrix. These differences in the connectivity of medium spiny neurons in the patches and matrix further support the conclusion that functionally distinct pathways pro-ject in parallel from the cortex to the striatum. (B) (A) Local circuit neuron Dopaminergic neuron Caudate Medium spiny neuron Medium spiny neuron Globus pallidus Putamen Substantia nigra pars reticulata Substantia nigra pars reticulata neuron Medium spiny neuron Globus pallidus or Cortical pyramidal neurons Medium spiny neuron External Internal Figure 17.3 Neurons and circuits of the basal ganglia. (A) Medium spiny neurons in the caudate and putamen. (B) Diagram showing convergent inputs onto a medium spiny neuron from corti-cal neurons, dopaminergic cells of the substantia nigra, and local circuit neu-rons. The primary output of the medium spiny cells is to the globus pal-lidus and to the substantia nigra pars reticulata. Figure 17.4 Regions of the cerebral cortex (shown in purple) that project to the caudate, putamen, and ventral stria-tum (see Box C) in both lateral (A) and medial (B) views. The caudate, puta-men, and ventral striatum receive corti-cal projections primarily from the asso-ciation areas of the frontal, parietal, and temporal lobes. The nature of the signals transmitted to the caudate and putamen from the cortex is not understood. It is known, however, that collateral axons of corticocortical, corticothalamic, and corticospinal pathways all form excita-tory glutamatergic synapses on the dendritic spines of medium spiny neu-rons (see Figure 17.3B). The arrangement of these cortical synapses is such that the number of contacts established between an individual cortical axon and a single medium spiny cell is very small, whereas the number of spiny neurons contacted by a single axon is extremely large. This divergence of axon terminals allows a single medium spiny neuron to integrate the influ-ences of thousands of cortical cells. The medium spiny cells also receive noncortical inputs from interneurons, from the midline and intralaminar nuclei of the thalamus, and from brainstem aminergic nuclei. In contrast to the cortical inputs to the dendritic spines, the local circuit neuron and thalamic synapses are made on the dendritic shafts and close to the cell soma, where they can modulate the effectiveness of corti-cal synaptic activation arriving from the more distal dendrites. The aminergic inputs are dopaminergic and they originate in a subdivision of the substantia nigra called pars compacta because of its densely packed cells. The dopamin-ergic synapses are located on the base of the spine, in close proximity to the cortical synapses, where they more directly modulate cortical input (see Figure 17.3B). As a result, inputs from both the cortex and the substantia nigra pars compacta are relatively far from the initial segment of the medium spiny neu-ron axon, where the nerve impulse is generated. Accordingly, the medium spiny neurons must simultaneously receive many excitatory inputs from cor-tical and nigral neurons to become active. As a result the medium spiny neu-rons are usually silent. When the medium spiny neurons do become active, their firing is associ-ated with the occurrence of a movement. Extracellular recordings show that these neurons typically increase their rate of discharge just before an impending movement. Neurons in the putamen tend to discharge in antici-pation of body movements, whereas caudate neurons fire prior to eye move-ments. These anticipatory discharges are evidently part of a movement selec-tion process; in fact, they can precede the initiation of movement by as much as several seconds. Similar recordings have also shown that the discharges of some striatal neurons vary according to the location in space of the target of a movement, rather than with the starting position of the limb relative to the target. Thus, the activity of these cells may encode the decision to move toward the target, rather than simply the direction and amplitude of the actual movement necessary to reach the target. Modulation of Movement by the Basal Ganglia 421 (A) Lateral view (B) Medial view Primary auditory cortex Primary visual cortex Primary visual cortex 422 Chapter Seventeen Projections from the Basal Ganglia to Other Brain Regions The medium spiny neurons of the caudate and putamen give rise to inhibitory GABAergic projections that terminate in another pair of nuclei in the basal ganglia complex: the internal division of the globus pallidus and a specific region of the substantia nigra called pars reticulata (because, unlike the pars compacta, axons passing through give it a netlike appear-ance). These nuclei are in turn the major sources of the output from the basal ganglia (Figure 17.5). The globus pallidus and substantia nigra pars reticu-lata have similar output functions. In fact, developmental studies show that pars reticulata is actually part of the globus pallidus, although the two even-tually become separated by fibers of the internal capsule. The striatal projec-tions to these two nuclei resemble the corticostriatal pathways in that they terminate in rostrocaudal bands, the locations of which vary with the loca-tions of their sources in the striatum. A striking feature of the projections from the medium spiny neurons to the globus pallidus and substantia nigra is the degree of their convergence onto pallidal and reticulata cells. In humans, for example, the corpus stria-tum contains approximately 100 million neurons, about 75% of which are (B) (A) Caudate Frontal cortex Globus pallidus, external segment Globus pallidus, internal segment Superior colliculus Subthalamic nucleus Frontal cortex Superior colliculus Globus pallidus internal VA/VL thalamic nuclear complex Substantia nigra pars reticulata Substantia nigra pars reticulata Caudate and putamen VA/VL complex (thalamus) + − − − − Putamen Figure 17.5 Functional organization of the outputs from the basal ganglia. (A) Diagram of the targets of the basal gan-glia, including the intermediate relay nuclei (the globus pallidus, internal and external segments, and the subthalamic nucleus), the superior colliculus, the thalamus, and the cerebral cortex. (B) An idealized coronal section through the human brain, showing the struc-tures and pathways diagrammed in (A). medium spiny neurons. In contrast, the main destination of their axons , the globus pallidus, comprises only about 700,000 cells. Thus, on average, more than 100 medium spiny neurons innervate each pallidal cell. The efferent neurons of the internal globus pallidus and substantia nigra pars reticulata together give rise to the major pathways that link the basal ganglia with upper motor neurons located in the cortex and in the brainstem (see Figure 17.5). The pathway to the cortex arises primarily in the internal globus pallidus and reaches the motor cortex after a relay in the ventral anterior and ventral lateral nuclei of the dorsal thalamus. These thalamic nuclei project directly to motor areas of the cortex, thus completing a vast loop that originates in multiple cortical areas and terminates (after relays in the basal ganglia and thalamus) back in the motor areas of the frontal lobe. In contrast, the axons from substantia nigra pars reticulata synapse on upper motor neurons in the superior colliculus that command eye movements, without an intervening relay in the thalamus (see Figure 16.2 and Chapter 19). This difference between the globus pallidus and substantia nigra pars reticulata is not absolute, however, since many reticulata axons also project to the thalamus where they contact relay neurons that project to the frontal eye fields of the premotor cortex (see Chapter 19). Because the efferent cells of both the globus pallidus and substantia nigra pars reticulata are GABAergic, the main output of the basal ganglia is inhibitory. In contrast to the quiescent medium spiny neurons, the neurons in both these output zones have high levels of spontaneous activity that tend to prevent unwanted movements by tonically inhibiting cells in the superior colliculus and thalamus. Since the medium spiny neurons of the striatum also are GABAergic and inhibitory, the net effect of the excitatory inputs that reach the striatum from the cortex is to inhibit the tonically active inhibitory cells of the globus pallidus and substantia nigra pars reticulata (Figure 17.6). Thus, in the absence of body movements, the globus pallidus neurons, for example, provide tonic inhibition to the relay cells in the ventral lateral and anterior nuclei of the thalamus. When the pallidal cells are inhibited by activity of the medium spiny neurons, the thalamic neurons are disinhibited and can relay signals from other sources to the upper motor neurons in the cortex. This disinhibition is what normally allows the upper motor neurons to send commands to local circuit and lower motor neurons that initiate movements. Conversely, an abnormal reduction in the tonic inhibition as a consequence of basal ganglia dysfunction leads to excessive excitability of the upper motor neurons, and thus to the involuntary movement syndromes that are characteristic of basal ganglia disorders such as Huntington’s dis-ease (Box A; see also Figure 17.9A). Evidence from Studies of Eye Movements The permissive role of the basal ganglia in the initiation of movement is per-haps most clearly demonstrated by studies of eye movements carried out by Okihide Hikosaka and Robert Wurtz at the National Institutes of Health (Figure 17.7). As described in the previous section, the substantia nigra pars reticulata is part of the output circuitry of the basal ganglia. Instead of pro-jecting to the cortex, however, it sends axons mainly to the deep layers of the superior colliculus. The upper motor neurons in these layers command the rapid orienting movements of the eyes called saccades (see Chapter 19). When the eyes are not scanning the environment, these upper motor neu-rons are tonically inhibited by the spontaneously active reticulata cells to prevent unwanted saccades. Shortly before the onset of a saccade, the tonic Modulation of Movement by the Basal Ganglia 423 424 Chapter Seventeen Figure 17.6 A chain of nerve cells arranged in a disinhibitory circuit. Top: Diagram of the connections between two inhibitory neurons, A and B, and an excitatory neuron, C. Bottom: Pattern of the action potential activity of cells A, B, and C when A is at rest, and when neu-ron A fires transiently as a result of its excitatory inputs. Such circuits are cen-tral to the gating operations of the basal ganglia. discharge rate of the reticulata neurons is sharply reduced by input from the GABAergic medium spiny neurons of the caudate, which have been acti-vated by signals from the cortex. The subsequent reduction in the tonic dis-charge from reticulata neurons disinhibits the upper motor neurons of the superior colliculus, allowing them to generate the bursts of action potentials that command the saccade. Thus, the projections from substantia nigra pars reticulata to the upper motor neurons act as a physiological “gate” that must be “opened” to allow either sensory or other, more complicated, signals from cognitive centers to activate the upper motor neurons and initiate a saccade. Upper motor neurons in the cortex are similarly gated by the basal ganglia but, as discussed earlier, the tonic inhibition is mediated mainly by the GABAergic projection from the internal division of the globus pallidus to the relay cells in the ventral lateral and anterior nuclei of the thalamus (see Fig-ures 17.5 and 17.6). Circuits within the Basal Ganglia System The projections from the medium spiny neurons of the caudate and puta-men to the internal segment of the globus pallidus and substantia nigra pars Transient excitatory inputs from cortex to A Excitatory inputs to C + + + + + + − − When A is at rest . . . A at rest A is excited B is tonically active . . . thereby inhibiting C . . . When A is transiently excited . . . B is transiently inhibited . . . and C is disinhibited so other inputs can excite it . . . leading to excitation of D so there is no excitation of D A B C D + Striatum Striatum Globus pallidus Globus pallidus VA/VL complex of thalamus VA/VL complex of thalamus Upper motor neuron in cortex Motor cortex To lower motor neurons Figure 17.7 The role of basal ganglia disinhibition in the generation of sac-cadic eye movements. (A) Medium spiny cells in the caudate nucleus respond with a transient burst of action potentials to an excitatory input from the cerebral cortex (1). The spiny cells inhibit the tonically active GABAergic cells in substantia nigra pars reticulata (2). As a result, the upper motor neu-rons in the deep layers of the superior colliculus are no longer tonically inhib-ited and can generate the bursts of action potentials that command a sac-cade (3, 4). (B) The temporal relation-ship between inhibition in substantia nigra pars reticulata (purple) and disin-hibition in the superior colliculus (yel-low) preceding a saccade to a visual tar-get. (After Hikosaka and Wurtz, 1989.) Modulation of Movement by the Basal Ganglia 425 Target onset Horizontal eye position Vertical eye position 100 spikes per second per trial Time (ms) 0 400 800 1200 1600 2000 – – + + Caudate nucleus Caudate nucleus Substantia nigra pars reticulata Substantia nigra pars reticulata Superior colliculus Superior colliculus Eye movement Projections to horizontal and vertical gaze centers (A) (B) Record Record Record Record Record Record Record Record Record 2 2 1 1 3 3 4 4 426 Chapter Seventeen reticulata are part of a “direct pathway” and, as just described, serve to release the upper motor neurons from tonic inhibition. This pathway is sum-marized in Figure 17.8A. A second pathway serves to increase the level of tonic inhibition and is called the “indirect pathway” (Figure 17.8B). This pathway provides a second route, linking the corpus striatum with the inter-Box A Huntington’s Disease In 1872, a physician named George Huntington described a group of patients seen by his father and grand-father in their practice in East Hampton, Long Island. The disease he defined, which became known as Huntington’s disease (HD), is characterized by the gradual onset of defects in behavior, cog-nition, and movement beginning in the fourth and fifth decades of life. The dis-order is inexorably progressive, resulting in death within 10 to 20 years. HD is inherited in an autosomal dominant pat-tern, a feature that has led to a much bet-ter understanding of its cause in molecu-lar terms. One of the more common inherited neurodegenerative diseases, HD usually presents as an alteration in mood (espe-cially depression) or a change in person-ality that often takes the form of in-creased irritability, suspiciousness, and impulsive or eccentric behavior. Defects of memory and attention may also occur. The hallmark of the disease, however, is a movement disorder consisting of rapid, jerky motions with no clear purpose; these choreiform movements may be confined to a finger or may involve a whole extremity, the facial musculature, or even the vocal apparatus. The move-ments themselves are involuntary, but the patient often incorporates them into apparently deliberate actions, presum-ably in an effort to obscure the problem. There is no weakness, ataxia, or deficit of sensory function. Occasionally, the dis-ease begins in childhood or adolescence. The clinical manifestations in juveniles include rigidity, seizures, more marked dementia, and a rapidly progressive course. A distinctive neuropathology is asso-ciated with these clinical manifestations: a profound but selective atrophy of the caudate and putamen, with some associ-ated degeneration of the frontal and tem-poral cortices (see Figure 17.9A). This pattern of destruction is thought to explain the disorders of movement, cog-nition, and behavior, as well as the spar-ing of other neurological functions. The availability of extensive HD pedi-grees has allowed geneticists to decipher the molecular cause of this disease. HD was one of the first human diseases in which DNA polymorphisms were used to localize the mutant gene, which in 1983 was mapped to the short arm of chromosome 4. This discovery led to an intensive effort to identify the HD gene within this region by positional cloning. Ten years later, these efforts culminated in identification of the gene (named Huntingtin) responsible for the disease. In contrast to previously recognized forms of mutations such as point muta-tions, deletions, or insertions, the muta-tion of Huntingtin is an unstable triplet repeat. In normal individuals, Huntingtin contains between 15 and 34 repeats, whereas the gene in HD patients con-tains from 42 to over 66 repeats. HD is one of a growing number of diseases attributed to unstable DNA seg-ments. Other examples are fragile X syn-drome, myotonic dystrophy, spinal and bulbar muscular atrophy, and spinocere-bellar ataxia type 1. In the latter two and HD, the repeats consist of a DNA seg-ment (CAG) that codes for the amino acid glutamine and is present within the coding region of the gene. The mechanism by which the in-creased number of polyglutamine repeats injures neurons is not clear. The leading hypothesis is that the increased numbers of glutamines alter protein folding, which somehow triggers a cas-cade of molecular events culminating in dysfunction and neuronal death. Inter-estingly, although Huntingtin is ex-pressed predominantly in the expected neurons in the basal ganglia, it is also present in regions of the brain that are not affected in HD. Indeed, the gene is expressed in many organs outside the nervous system. How and why the mutant Huntingtin uniquely injures stri-atal neurons is unclear. Continuing to elucidate this molecular pathogenesis will no doubt provide further insight into this and other triplet repeat diseases. References GUSELLA, J. F. AND 13 OTHERS (1983) A poly-morphic DNA marker genetically linked to Huntington’s disease. Nature 306: 234–238. HUNTINGTON, G. (1872) On chorea. Med. Surg. Reporter 26: 317. HUNTINGTON’S DISEASE COLLABORATIVE RESEARCH GROUP (1993) A novel gene contain-ing a trinucleotide repeat that is expanded and unstable on Huntington’s disease chro-mosomes. Cell 72: 971–983. WEXLER, A. (1995) Mapping Fate: A Memoir of Family, Risk, and Genetic Research. New York: Times Books. YOUNG, A. B. (2003) Huntingtin in health and disease. J. Clin. Invest. 111: 299–302. Figure 17.8 Disinhibition in the direct and indirect pathways through the basal ganglia. (A) In the direct pathway, transiently inhibitory projections from the caudate and putamen project to ton-ically active inhibitory neurons in the internal segment of the globus pallidus, which project in turn to the VA/VL complex of the thalamus. Transiently excitatory inputs to the caudate and putamen from the cortex and substantia nigra are also shown, as is the tran-siently excitatory input from the thala-mus back to the cortex. (B) In the indi-rect pathway (shaded yellow), transiently active inhibitory neurons from the caudate and putamen project to tonically active inhibitory neurons of the external segment of the globus pal-lidus. Note that the influence of nigral dopaminergic input to neurons in the indirect pathway is inhibitory. The globus pallidus (external segment) neu-rons project to the subthalamic nucleus, which also receives a strong excitatory input from the cortex. The subthalamic nucleus in turn projects to the globus pallidus (internal segment), where its transiently excitatory drive acts to oppose the disinhibitory action of the direct pathway. In this way, the indirect pathway modulates the effects of the direct pathway. nal globus pallidus and substantia nigra pars reticulata. In the indirect path-way, a population of medium spiny neurons projects to the lateral or exter-nal segment of the globus pallidus. This external division sends projections both to the internal segment of the globus pallidus and to the subthalamic nucleus of the ventral thalamus (see Figure 17.1). But, instead of projecting to structures outside of the basal ganglia, the subthalamic nucleus projects back to the internal segment of the globus pallidus and to the substantia nigra pars reticulata. As already described, these latter two nuclei project out of the basal ganglia, which thus allows the indirect pathway to influence the activity of the upper motor neurons. The indirect pathway through the basal ganglia apparently serves to mod-ulate the disinhibitory actions of the direct pathway. The subthalamic nucleus neurons that project to the internal globus pallidus and substantia Modulation of Movement by the Basal Ganglia 427 Frontal cortex Globus pallidus, internal segment Frontal cortex VA/VL complex of thalamus VA/VL complex of thalamus (transient) Globus pallidus, internal segment (A) Direct pathway + + − − Caudate/putamen + Cerebral cortex (transient) (transient) (transient) (tonic) Subthalamic nucleus (B) Indirect and direct pathways Indirect pathway − − − Caudate/putamen + + + + (transient) (transient) (transient) (transient) (transient) (tonic) − (tonic) Substantia nigra pars compacta Globus pallidus, external segment − − + D2 D1 D1 (transient) (transient) Substantia nigra pars compacta Cerebral cortex 428 Chapter Seventeen Figure 17.9 The pathological changes in certain neurological diseases provide insights about the function of the basal ganglia. (A) The size of the caudate and putamen (the striatum) (arrows) is dra-matically reduced in patients with Huntington’s disease. (B) Left: The mid-brain from a patient with Parkinson’s disease. The substantia nigra (pig-mented area) is largely absent in the region above the cerebral peduncles (arrows). Right: The mesencephalon from a normal subject, showing intact substantia nigra (arrows). (From Bradley et al., 1991.) nigra pars reticulata are excitatory. Normally, when the indirect pathway is activated by signals from the cortex, the medium spiny neurons discharge and inhibit the tonically active GABAergic neurons of the external globus pallidus. As a result, the subthalamic cells become more active and, by virtue of their excitatory synapses with cells of the internal globus pallidus and reticulata, they increase the inhibitory outflow of the basal ganglia. Thus, in contrast to the direct pathway, which when activated reduces tonic inhibi-tion, the net effect of activity in the indirect pathway is to increase inhibitory influences on the upper motor neurons. The indirect pathway can thus be regarded as a “brake” on the normal function of the direct pathway. Indeed, many neural systems achieve fine control of their output by a similar inter-play between excitation and inhibition. The consequences of imbalances in this fine control mechanism are appar-ent in diseases that affect the subthalamic nucleus. These disorders remove a source of excitatory input to the internal globus pallidus and reticulata, and thus abnormally reduce the inhibitory outflow of the basal ganglia. A basal ganglia syndrome called hemiballismus, which is characterized by violent, involuntary movements of the limbs, is the result of damage to the subthala-mic nucleus. The involuntary movements are initiated by abnormal dis-charges of upper motor neurons that are receiving less tonic inhibition from the basal ganglia. Another circuit within the basal ganglia system entails the dopaminergic cells in the pars compacta subdivision of substantia nigra and modulates the output of the corpus striatum. The medium spiny neurons of the corpus striatum project directly to substantia nigra pars compacta, which in turn sends widespread dopaminergic projections back to the spiny neurons. These dopaminergic influences on the spiny neurons are complex: The same nigral neurons can provide excitatory inputs mediated by D1 type dopamin-ergic receptors on the spiny cells that project to the internal globus pallidus (the direct pathway), and inhibitory inputs mediated by D2 type receptors on the spiny cells that project to the external globus pallidus (the indirect pathway). Since the actions of the direct and indirect pathways on the out-put of the basal ganglia are antagonistic, these different influences of the nigrostriatal axons produce the same effect, namely a decrease in the inhib-itory outflow of the basal ganglia. The modulatory influences of this second internal circuit help explain many of the manifestations of basal ganglia disorders. For example, Parkin-son’s disease is caused by the loss of the nigrostriatal dopaminergic neurons (Figure 17.9B and Box B). As mentioned earlier, the normal effects of the compacta input to the striatum are excitation of the medium spiny neurons that project directly to the internal globus pallidus and inhibition of the spiny neurons that project to the external globus pallidus cells in the indirect path-way. Normally, both of these dopaminergic effects serve to decrease the inhibitory outflow of the basal ganglia and thus to increase the excitability of the upper motor neurons (Figure 17.10A). In contrast, when the compacta cells are destroyed, as occurs in Parkinson’s disease, the inhibitory outflow of the basal ganglia is abnormally high, and thalamic activation of upper motor neurons in the motor cortex is therefore less likely to occur. In fact, many of the symptoms seen in Parkinson’s disease (and in other hypokinetic movement disorders) reflect a failure of the disinhibition nor-mally mediated by the basal ganglia. Thus, Parkinsonian patients tend to have diminished facial expressions and lack “associated movements” such as arm swinging during walking. Indeed, any movement is difficult to initi-ate and, once initiated, is often difficult to terminate. Disruption of the same (B) Parkinson's disease (A) Huntington's disease Box B Parkinson’s Disease: An Opportunity for Novel Therapeutic Approaches Parkinson’s disease is the second most common degenerative disease of the ner-vous system (Alzheimer’s disease being the leader; see Chapter 30). Described by James Parkinson in 1817, this disorder is characterized by tremor at rest, slowness of movement (bradykinesia), rigidity of the extremities and neck, and minimal facial expressions. Walking entails short steps, stooped posture, and a paucity of associated movements such as arm swinging. To make matters worse, in some patients these abnormalities of motor function are associated with dementia. Following a gradual onset between the ages of 50 and 70, the dis-ease progresses slowly and culminates in death 10 to 20 years later. The defects in motor function are due to the progressive loss of dopaminergic neurons in the substantia nigra pars com-pacta, a population that projects to and innervates neurons in the caudate and putamen (see text). Although the cause of the progressive deterioration of these dopaminergic neurons is not known, genetic investigations are providing clues to the etiology and pathogenesis. Whereas the majority of cases of Parkin-son’s disease are sporadic, there may be specific forms of susceptibility genes that confer increased risk of acquiring the dis-ease, just as the apoE4 allele increases the risk of Alzheimer’s disease. Familial forms of the disease caused by single gene mutations account for less than 10% of all cases, However, identification of these rare genes is likely give some insight into molecular pathways that may underlie the disease. Mutations of three distinct genes—a-synuclein, Parkin, and DJ-1—have been implicated in rare forms of this disease. Identification of these genes provides an opportunity to generate mutant mice carrying the mutant form of the human gene, poten-tially providing a useful animal model in which the pathogenesis can be elucidated and therapies can be tested. In contrast to other neurodegenera-tive diseases, such as Alzheimer’s dis-ease or amyotrophic lateral sclerosis, in Parkinson’s disease the spatial distribu-tion of the degenerating neurons is largely restricted to the substantia nigra pars compacta. This spatial restriction, combined with the defined and relatively homogeneous phenotype of the degener-ating neurons (i. e., dopaminergic neu-rons), has provided an opportunity for novel therapeutic approaches to this disorder. One strategy is so-called gene ther-apy. Gene therapy refers to the correction of a disease phenotype through the introduction of new genetic information into the affected organism. Although still in its infancy, this approach promises to revolutionize treatment of human dis-ease. One therapy for Parkinson’s dis-ease would be to enhance release of dopamine in the caudate and putamen. In principle, this could be accomplished by implanting cells genetically modified to express tyrosine hydroxylase, the enzyme that converts tyrosine to L-DOPA, which in turn is converted by a nearly ubiquitous decarboxylase into the neurotransmitter dopamine. The feasibil-ity of this approach has been demon-strated by transplanting tissue derived from the midbrain of human fetuses into the caudate and putamen, which pro-duces long-lasting symptomatic improvement in a majority of grafted Parkinson’s patients. (The fetal midbrain is enriched in developing neurons that express tyrosine hyroxylase and synthe-size and release dopamine.) To date, however, ethical, practical, and political considerations have limited use of fetal transplanted tissue. The effects of trans-planting non-neuronal cells genetically modified in vitro to express tyrosine hydroxylase are also being studied in patients with Parkinson’s disease, an approach that avoids some of these problems. An alternative strategy to treating Parkinsonian patients involves “neural grafts” using stem cells. Stem cells are self-renewing, multipotent progenitors with broad developmental potential (see Chapters 21 and 24). Instead of isolating mature dopaminergic neurons from the fetal midbrain for transplantation, this approach isolates neuronal progenitors at earlier stages of development, when these cells are actively proliferating. Crit-ical to this approach is to prospectively identify and isolate stem cells that are multipotent and self-renewing, and to identify the growth factors needed to promote differentiation into the desired phenotype (e.g., dopaminergic neurons). The prospective identification and isola-tion of multipotent mammalian stem cells has already been accomplished, and several factors likely to be important in differentiation of midbrain precursors into dopamine neurons have been identi-fied. Establishing the efficacy of this approach for Parkinson’s patients would increase the possibility of its application to other neurodegenerative diseases. Although therapeutic strategies like these remain experimental, it is likely that some of them will succeed. References BJÖRKLUND, A. AND U. STENEVI (1979) Recon-struction of the nigrostriatal dopamine path-way by intracerebral nigral transplants. Brain Res. 177: 555–560. DAUER, W. AND S. PRZEDBORSKI (2003) Parkin-son’s disease: Mechanisms and models. Neu-ron 39: 889–909. DAWSON, T. M. AND V. L. DAWSON (2003) Rare genetic mutations shed light on the patho-genesis of Parkinson disease. J. Clin. Invest. 111: 145–151. MORRISON, S. J., P. M. WHITE, C. ZOCK AND D. J. ANDERSON (1999) Prospective identification, isolation by flow cytometry, and in vivo self-renewal of multipotent mammalian neural crest stem cells. Cell 96: 737–749. YE, W., K. SHIMAMURA, J. L. RUBENSTEIN, M. A. HYNES AND A. ROSENTHAL (1998) FGF and Shh signals control dopaminergic and serotoner-gic cell fate in the anterior neural plate. Cell 93: 755–766. ZABNER, J. AND 5 OTHERS (1993) Adenovirus-mediated gene transfer transiently corrects the chloride transport defect in nasal epithe-lia of patients with cystic fibrosis. Cell 75: 207–216. 430 Chapter Seventeen Figure 17.10 Summary explanation of hypokinetic disorders such as Parkin-son’s disease and hyperkinetic disor-ders like Huntington’s disease. In both cases, the balance of inhibitory signals in the direct and indirect pathways is altered, leading to a diminished ability of the basal ganglia to control the thala-mic output to the cortex. (A) In Parkin-son’s disease, the inputs provided by the substantia nigra are diminished (thinner arrow), making it more difficult to generate the transient inhibition from the caudate and putamen. The result of this change in the direct pathway is to sustain the tonic inhibition from the globus pallidus (internal segment) to the thalamus, making thalamic excita-tion of the motor cortex less likely (thin-ner arrow from thalamus to cortex). (B) In hyperkinetic diseases such as Hunt-ington’s, the projection from the cau-date and putamen to the globus pal-lidus (external segment) is diminished (thinner arrow). This effect increases the tonic inhibition from the globus pal-lidus to the subthalamic nucleus (larger arrow), making the excitatory subthala-mic nucleus less effective in opposing the action of the direct pathway (thinner arrow). Thus, thalamic excitation of the cortex is increased (larger arrow), lead-ing to greater and often inappropriate motor activity. (After DeLong, 1990.) circuits also increases the discharge rate of the inhibitory cells in substantia nigra pars reticulata. The resulting increase in tonic inhibition reduces the excitability of the upper motor neurons in the superior colliculus and causes saccades to be reduced in both frequency and amplitude. Support for this explanation of hypokinetic movement disorders like Parkinson’s disease comes from studies of monkeys in which degeneration of the dopaminergic cells of substantia nigra has been induced by the neuro-toxin 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP). Monkeys (or humans) exposed to MPTP develop symptoms that are very similar to those of patients with Parkinson’s disease. Furthermore, a second lesion placed in the subthalamic nucleus results in significant improvement in the ability of these animals to initiate movements, as would be expected based on the cir-cuitry of the indirect pathway (see Figure 17.8B). Frontal cortex Increased excitation Less tonic inhibition Degenerated Degenerated Increased VA/VL complex of thalamus Subthalamic nucleus (B) Huntington’s disease (hyperkinetic) Cerebral cortex − − − − − Globus pallidus, external segment Globus pallidus, internal segment + + Diminished + Frontal cortex Decreased excitation More tonic inhibition Diminished Increased Increased Subthalamic nucleus (A) Parkinson’s disease (hypokinetic) Cerebral cortex − − − − − Globus pallidus, external segment Globus pallidus, internal segment + + + + + + Substantia nigra pars compacta VA/VL complex of thalamus Caudate/putamen Substantia nigra pars compacta Caudate/putamen D2 D1 − + D2 D1 Similarly, knowledge about the indirect pathway within the basal ganglia helps explain the motor abnormalities seen in Huntington’s disease (see Box A). In patients with Huntington’s disease, medium spiny neurons that pro-ject to the external segment of the globus pallidus degenerate (see Figure 17.9A). In the absence of their normal inhibitory input from the spiny neu-rons, the external globus pallidus cells become abnormally active; this activ-ity reduces in turn the excitatory output of the subthalamic nucleus to the internal globus pallidus (Figure 17.10B). In consequence, the inhibitory out-flow of the basal ganglia is reduced. Without the restraining influence of the basal ganglia, upper motor neurons can be activated by inappropriate sig-nals, resulting in the undesired ballistic and choreic (dancelike) movements that characterize Huntington’s disease. Importantly, the basal ganglia may exert a similar influence on other non-motor systems with equally significant clinical implications (Box C). As predicted by this account, GABA agonists and antagonists applied to substantia nigra pars reticulata of monkeys produce symptoms similar to those seen in human basal ganglia disease. For example, intranigral injection of bicuculline, which blocks the GABAergic inputs from the striatal medium spiny neurons to the reticulata cells, increases the amount of tonic inhibition on the upper motor neurons in the deep collicular layers. These animals exhibit fewer, slower saccades, reminiscent of patients with Parkinson’s dis-ease. In contrast, injections of the GABA agonist muscimol into substantia nigra pars reticulata decrease the tonic GABAergic inhibition of the upper motor neurons in the superior colliculus, with the result that the injected monkeys generate spontaneous, irrepressible saccades that resemble the involuntary movements characteristic of basal ganglia diseases such as hemiballismus and Huntington’s disease (Figure 17.11). Modulation of Movement by the Basal Ganglia 431 Left visual field Right visual field 0° 0° Fixation (A) (B) Substantia nigra pars reticulata Muscimol injection Figure 17.11 After the tonically active cells of substantia nigra pars reticulata are inactivated by an intranigral injection of muscimol (A), the upper motor neurons in the deep layers of the superior colliculus are disinhibited and the monkey generates spontaneous irrepressible saccades (B). The cells in both substantia nigra pars reticu-lata and the deep layers of the superior colliculus are arranged in spatially orga-nized motor maps of saccade vectors (see Chapter 19), and so the direction of the involuntary saccades—in this case toward the upper left quadrant of the visual field—depends on the precise location of the injection site in the substantia nigra. 432 Chapter Seventeen Box C Basal Ganglia Loops and Non-Motor Brain Functions Traditionally, the basal ganglia have been regarded as motor structures that regulate the initiation of movements. However, the basal ganglia are also cen-tral structures in anatomical circuits or loops that are involved in modulating non-motor aspects of behavior. These parallel loops originate in broad regions of the cortex, engage specific subdivi-sions of the basal ganglia and thalamus, and ultimately terminate in areas of the frontal lobe outside of the primary motor and premotor cortices. These non-motor loops (see figure) include a “prefrontal” loop involving the dorso-lateral prefrontal cortex and part of the caudate (see Chapter 25), a “limbic” loop involving the cingulate cortex and the ventral striatum (see Chapter 28), and an “oculomotor” loop that modu-lates the activity of the frontal eye fields (see Chapter 19). The anatomical similarity of these loops to the traditional motor loop sug-gests that the non-motor regulatory func-tions of the basal ganglia may be gener-ally the same as what the basal ganglia do in regulating the initiation of move-ment. For example, the prefrontal loop may regulate the initiation and termina-tion of cognitive processes such as plan-ning, working memory, and attention. By the same token, the limbic loop may reg-ulate emotional behavior and motivation. Indeed, the deterioration of cognitive and emotional function in both Huntington’s disease (see Box A) and Parkinson’s dis-ease (see Box B) could be the result of dis-ruption of these non-motor loops. Motor loop Motor, premotor, somatosensory cortex Putamen Lateral globus pallidus, internal segment Ventral lateral and ventral anterior nuclei Oculomotor loop Posterior parietal, prefrontal cortex Caudate (body) Globus pallidus, internal segment; substantia nigra pars reticulata Mediodorsal and ventral anterior nuclei Cortical input Cortical targets Cortical targets Cortical targets Cortical targets Striatum Pallidum Thalamus Prefrontal loop Dorsolateral prefrontal cortex Anterior caudate Mediodorsal and ventral anterior nuclei Globus pallidus, internal segment; substantia nigra pars reticulata Limbic loop Amygdala, hippocampus, orbitofrontal, anterior cingulate, temporal cortex Frontal cortex Ventral striatum Ventral pallidum Mediodorsal nucleus Primary motor, premotor, supplementary motor cortex Frontal eye field, supplementary eye field Dorsolateral prefrontal cortex Anterior cingulate, orbital frontal cortex Comparison of the motor and three non-motor basal ganglia loops. Summary The contribution of the basal ganglia to motor control is apparent from the deficits that result from damage to the component nuclei. Such lesions com-promise the initiation and performance of voluntary movements, as exem-plified by the paucity of movement in Parkinson’s disease and in the inap-propriate “release” of movements in Huntington’s disease. The organization of the basic circuitry of the basal ganglia indicates how this constellation of nuclei modulates movement. With respect to motor function, the system forms a loop that originates in almost every area of the cerebral cortex and eventually terminates, after enormous convergence within the basal ganglia, on the upper motor neurons in the motor and premotor areas of the frontal lobe and in the superior colliculus. The efferent neurons of the basal ganglia influence the upper motor neurons in the cortex by gating the flow of infor-mation through relays in the ventral nuclei of the thalamus. The upper motor neurons in the superior colliculus that initiate saccadic eye move-ments are controlled by monosynaptic projections from substantia nigra pars reticulata. In each case, the basal ganglia loop regulates movement by a process of disinhibition that results from the serial interaction within the basal ganglia circuitry of two GABAergic neurons. Internal circuits within the basal ganglia system modulate the amplification of the signals that are transmitted through the loop. Modulation of Movement by the Basal Ganglia 433 In fact, a variety of other disorders are now thought to be caused, at least in part, by damage to non-motor compo-nents of the basal ganglia. For example, patients with Tourette’s syndrome pro-duce inappropriate utterances and obscenities as well as unwanted vocal-motor “tics” and repetitive grunts. These manifestations may be a result of exces-sive activity in basal ganglia loops that regulate the cognitive circuitry of the prefrontal speech areas. Another exam-ple is schizophrenia, which some inves-tigators have argued is associated with aberrant activity within the limbic and prefrontal loops, resulting in hallucina-tions, delusions, disordered thoughts, and loss of emotional expression. In sup-port of the argument for a basal ganglia contribution to schizophrenia, antipsy-chotic drugs are known to act on dopaminergic receptors, which are found in high concentrations in the stria-tum. Still other psychiatric disorders, including obsessive-compulsive disor-der, depression, and chronic anxiety, may also involve dysfunctions of the limbic loop. A challenge for future research is therefore to understand more fully the relationships between the clini-cal problems and other largely unex-plored functions of the basal ganglia. References ALEXANDER, G. E., M. R. DELONG AND P. L. STRICK (1986) Parallel organization of func-tionally segregated circuits linking basal gan-glia and cortex. Annu. Rev. Neurosci. 9: 357–381. BHATIA, K. P. AND C. D. MARSDEN (1994) The behavioral and motor consequences of focal lesions of the basal ganglia in man. Brain 117: 859–876. BLUMENFELD, H. (2002) Neuroanatomy through Clinical Cases. Sunderland, MA: Sinauer Associates. DREVETS, W. C. AND 6 OTHERS (1997) Subgen-ual prefrontal cortex abnormalities in mood disorders. Nature 386: 824–827. GRAYBIEL, A. M. (1997) The basal ganglia and cognitive pattern generators. Schiz. Bull. 23: 459–469. JENIKE, M. A., L. BAER AND W. E. MINICHIELLO (1990) Obsessive Compulsive Disorders: Theory and Management. Chicago: Year Book Medical Publishers, Inc. MARTIN, J. H. (1996) Neuroanatomy: Text and Atlas. New York: McGraw-Hill. MIDDLETON, F. A. AND P. L. STRICK (2000) Basal ganglia output and cognition: Evidence from anatomical, behavioral, and clinical studies. Brain Cogn. 42: 183–200. 434 Chapter Seventeen Additional Reading Reviews ALEXANDER, G. E. AND M. D. CRUTCHER (1990) Functional architecture of basal ganglia cir-cuits: Neural substrates of parallel processing. Trends Neurosci. 13: 266–271. DELONG, M. R. (1990) Primate models of movement disorders of basal ganglia origin. Trends Neurosci. 13: 281–285. GERFEN, C. R. AND C. J. WILSON (1996) The basal ganglia. In Handbook of Chemical Neu-roanatomy, Vol. 12: Integrated Systems of the CNS, Part III. L. W. Swanson, A. Björklund and T. Hokfelt (eds.). New York: Elsevier Sci-ence Publishers, pp. 371–468. GOLDMAN-RAKIC, P. S. AND L. D. SELEMON (1990) New frontiers in basal ganglia research. Trends Neurosci. 13: 241–244. GRAYBIEL, A. M. AND C. W. RAGSDALE (1983) Biochemical anatomy of the striatum. In Chemical Neuroanatomy, P. C. Emson (ed.). New York: Raven Press, pp. 427–504. HIKOSAKA, O. AND R. H. WURTZ (1989) The basal ganglia. In The Neurobiology of Eye Move-ments, R. H. Wurtz and M. E. Goldberg (eds.). New York: Elsevier Science Publishers, pp. 257–281. KAJI, R. (2001) Basal ganglia as a sensory gat-ing devise for motor control. J. Med. Invest. 48: 142–146. MINK, J. W. AND W. T. THACH (1993) Basal gan-glia intrinsic circuits and their role in behav-ior. Curr. Opin. Neurobiol. 3: 950–957. POLLACK, A. E. (2001) Anatomy, physiology, and pharmacology of the basal ganglia. Neu-rol. Clin 19: 523–534. SLAGHT, S. J, T. PAZ, S. MAHON, N. MAURICE, S. CHARPIER AND J. M. DENIAU (2002) Functional organization of the circuits connecting the cerebral cortex and the basal ganglia. Implica-tions for the role of the basal ganglia in epilepsy. Epileptic Disord. Suppl 3: S9–S22. WILSON, C. J. (1990) Basal ganglia. In Synaptic Organization of the Brain. G. M. Shepherd (ed.). Oxford: Oxford University Press, Chapter 9. Important Original Papers ANDEN, N.-E., A. DAHLSTROM, K. FUXE, K. LARSSON, K. OLSON AND U. UNGERSTEDT (1966) Ascending monoamine neurons to the telen-cephalon and diencephalon. Acta Physiol. Scand. 67: 313–326. BRODAL, P. (1978) The corticopontine projec-tion in the rhesus monkey: Origin and princi-ples of organization. Brain 101: 251–283. CRUTCHER, M. D. AND M. R. DELONG (1984) Single cell studies of the primate putamen. Exp. Brain Res. 53: 233–243. DELONG, M. R. AND P. L. STRICK (1974) Rela-tion of basal ganglia, cerebellum, and motor cortex units to ramp and ballistic movements. Brain Res. 71: 327–335. DIFIGLIA, M., P. PASIK AND T. PASIK (1976) A Golgi study of neuronal types in the neostria-tum of monkeys. Brain Res. 114: 245–256. KEMP, J. M. AND T. P. S. POWELL (1970) The cor-tico-striate projection in the monkey. Brain 93: 525–546. KIM, R., K. NAKANO, A. JAYARAMAN AND M. B. CARPENTER (1976) Projections of the globus pallidus and adjacent structures: An autoradi-ographic study in the monkey. J. Comp. Neu-rol. 169: 217–228. KOCSIS, J. D., M. SUGIMORI AND S. T. KITAI (1977) Convergence of excitatory synaptic inputs to caudate spiny neurons. Brain Res. 124: 403–413. SMITH, Y., M. D. BEVAN, E. SHINK AND J. P. BOLAM (1998) Microcircuitry of the direct and indirect pathways of the basal ganglia. Neu-rosci. 86: 353–387. Books BRADLEY, W. G., R. B. DAROFF, G. M. FENICHEL AND C. D. MARSDEN (EDS.). (1991) Neurology in Clinical Practice. Boston: Butterworth-Heine-mann, Chapters 29 and 77. KLAWANS, H. L. (1989) Toscanini’s Fumble and Other Tales of Clinical Neurology. New York: Bantam, Chapters 7 and 10. Overview In contrast to the upper motor neurons described in Chapter 16, the efferent cells of the cerebellum do not project directly either to the local circuits of the brainstem and spinal cord that organize movement, or to the lower motor neurons that innervate muscles. Instead—like the basal ganglia—the cere-bellum influences movements by modifying the activity patterns of the upper motor neurons. In fact, the cerebellum sends prominent projections to virtually all upper motor neurons. Structurally, the cerebellum has two main components: a laminated cerebellar cortex, and a subcortical cluster of cells referred to collectively as the deep cerebellar nuclei. Pathways that reach the cerebellum from other brain regions (in humans, predominantly the cerebral cortex) project to both components; thus, the afferent axons send branches to both the deep nuclei and the cerebellar cortex. The output cells of the cere-bellar cortex project to the deep cerebellar nuclei, which give rise to the main efferent pathways that leave the cerebellum to regulate upper motor neurons in the cerebral cortex and brainstem. Thus, much like the basal ganglia, the cerebellum is part of a vast loop that receives projections from and sends projections back to the cerebral cortex and brainstem. The primary function of the cerebellum is evidently to detect the difference, or “motor error,” between an intended movement and the actual movement, and, through its projections to the upper motor neurons, to reduce the error. These correc-tions can be made both during the course of the movement and as a form of motor learning when the correction is stored. When this feedback loop is damaged, as occurs in many cerebellar diseases, the afflicted individuals make persistent movement errors whose specific character depends on the location of the damage. Organization of the Cerebellum The cerebellum can be subdivided into three main parts based on differ-ences in their sources of input (Figure 18.1; Table 18.1). By far the largest subdivision in humans is the cerebrocerebellum. It occupies most of the lat-eral cerebellar hemisphere and receives input from many areas of the cere-bral cortex. This region of the cerebellum is especially well developed in pri-mates. The cerebrocerebellum is concerned with the regulation of highly skilled movements, especially the planning and execution of complex spatial and temporal sequences of movement (including speech). The phylogeneti-cally oldest part of the cerebellum is the vestibulocerebellum. This portion comprises the caudal lobes of the cerebellum and includes the flocculus and the nodulus. As its name suggests, the vestibulocerebellum receives input from the vestibular nuclei in the brainstem and is primarily concerned with Chapter 18 435 Modulation of Movement by the Cerebellum 436 Chapter Eighteen (B) (C) (D) (A) Vermis Fourth ventricle Cerebellar peduncles Inferior Superior Middle Caudate nucleus Putamen Internal capsule Thalamus Midbrain Deep cerebellar nuclei Spinocerebellum Flocculus Flocculus Flocculus Cerebrocerebellum Vermis Vermis Nodulus Nodulus Nodulus Vestibulocerebellum Superior cerebellar peduncle Superior cerebellar peduncle Middle cerebellar peduncle Middle cerebellar peduncle Inferior cerebellar peduncle Cerebellar cortex Inferior cerebellar peduncle Dentate nucleus Interposed nuclei Fastigial nucleus Cerebrocerebellum Cerebrocerebellum Cerebrocerebellum Folia Figure 18.1 Overall organization and subdivisions of the cerebel-lum. (A) Dorsal view of the left cerebellar hemisphere also illus-trating the location of the deep cerebellar nuclei. The right hemi-sphere has been removed to show the cerebellar peduncles. (B) Removal from the brainstem reveals the cerebellar peduncles on the anterior aspect of the inferior surface. (C) Paramedian sagittal section through the left cerebellar hemisphere showing the highly convoluted cerebellar cortex. The small gyri in the cerebellum are called folia. (D) Flattened view of the cerebellar surface illustrating the three major subdivisions. the regulation of movements underlying posture and equilibrium. The last of the major subdivisions is the spinocerebellum. The spinocerebellum occupies the median and paramedian zone of the cerebellar hemispheres and is the only part that receives input directly from the spinal cord. The lat-eral part of the spinocerebellum is primarily concerned with movements of distal muscles, such as the relatively gross movements of the limbs in walk-ing. The central part, called the vermis, is primarily concerned with move-ments of proximal muscles, and also regulates eye movements in response to vestibular inputs. The connections between the cerebellum and other parts of the nervous system occur by way of three large pathways called cerebellar peduncles (Figures 18.1 to 18.3). The superior cerebellar peduncle (or brachium con-junctivum) is almost entirely an efferent pathway. The neurons that give rise to this pathway are in the deep cerebellar nuclei, and their axons project to upper motor neurons in the red nucleus, the deep layers of the superior col-liculus, and, after a relay in the dorsal thalamus, the primary motor and pre-motor areas of the cortex (see Chapter 16). The middle cerebellar peduncle (or brachium pontis) is an afferent pathway to the cerebellum; most of the cell bodies that give rise to this pathway are in the base of the pons, where they form the pontine nuclei (Figure 18.2). The pontine nuclei receive input from a wide variety of sources, including almost all areas of the cerebral cor-tex and the superior colliculus. The axons of the pontine nuclei, called trans-verse pontine fibers, cross the midline and enter the cerebellum via the Modulation of Movement by the Cerebellum 437 TABLE 18.1 Major Components of the Cerebellum Cerebellar cortex Cerebrocerebellum Spinocerebellum Vestibulocerebellum Deep cerebellar nuclei Dentate nucleus Interposed nuclei Fastigial nucleus Cerebellar peduncles Superior peduncle Middle peduncle Inferior peduncle Primary motor cortex Deep cerebellar nuclei Cerebellar cortex Superior cerebellar peduncle Pontine nuclei Vestibular nuclei Inferior olive Dorsal nucleus of Clarke VA/VL complex of thalamus Figure 18.2 Components of the brainstem and diencephalon related to the cerebellum. This sagittal section shows the major structures of the cerebellar system, including the cere-bellar cortex, the deep cerebellar nuclei, and the ventroante-rior and ventrolateral (VA/VL) complex (which is the target of some of the deep cerebellar nuclei). 438 Chapter Eighteen middle cerebellar peduncle (Figure 18.3). Each of the two middle cerebellar peduncles contain over 20 million axons, making this one of the largest path-ways in the brain. In comparison, the optic and pyramidal tracts contain only about a million axons. Most of these pontine axons relay information from the cortex to the cerebellum. Finally, the inferior cerebellar peduncle (or restiform body) is the smallest but most complex of the cerebellar peduncles, containing multiple afferent and efferent pathways. Efferent pathways in this peduncle project to the vestibular nuclei and the reticular formation; the afferent pathways include axons from the vestibular nuclei, the spinal cord, and several regions of the brainstem tegmentum. Projections to the Cerebellum The cerebral cortex is by far the largest source of inputs to the cerebellum, and the major destination of these inputs is the cerebrocerebellum (see Fig-ure 18.3 and Table 18.2). These pathways arise from a somewhat more cir-cumscribed area of the cortex than do those to the basal ganglia (see Chapter 17). The majority originate in the primary motor and premotor cortices of (B) Frontal cortex (A) Frontal/parietal cortex Pons Cerebellar cortex Midline Inferior olive Spinal cord Vestibular nucleus Parietal cortex Inferior cerebellar peduncle Middle cerebellar peduncle Cerebellar cortex Pontine nuclei Vestibular nuclei Inferior olive Dorsal nucleus of Clarke TABLE 18.2 Major inputs to the Cerebellum (via Inferior and Middle Cerebellar Peduncles) From cerebral cortex: Parietal cortex (secondary visual, primary and secondary somatic sensory) Cingulate cortex (limbic) Frontal cortex (primary and secondary motor) Other sources: Red nucleus Superior colliculus Spinal cord (Clarke’s column) Vestibular labyrinth and nuclei Reticular formation Inferior olivary nucleus Locus ceruleus Figure 18.3 Functional organization of the inputs to the cerebellum. (A) Diagram of the major inputs. (B) Idealized coronal and sagittal sections through the human brainstem and cerebrum, showing inputs to the cerebellum from the cortex, vestibular system, spinal cord, and brainstem. The cortical projections to the cere-bellum are made via relay neurons in the pons. These pontine axons then cross the midline within the pons and run to the cerebellum via the middle cerebellar peduncle. Axons from the inferior olive, spinal cord, and vestibular nuclei enter via the inferior cerebellar peduncle. the frontal lobe, the primary and secondary somatic sensory cortices of the anterior parietal lobe, and the secondary visual regions of the posterior pari-etal lobe (Figure 18.4). The visual input to the cerebellum originates mostly in association areas concerned with processing moving visual stimuli (i.e., the cortical targets of the magnocellular stream; see Chapter 11). Indeed, visually guided coordination of ongoing movement is one of the major tasks carried out by the cerebrocerebellum. Most of these cortical pathways relay in the pontine nuclei before entering the cerebellum (see Figure 18.3). Sensory pathways also project to the cerebellum (see Figure 18.3 and Table 18.2). Vestibular axons from the eighth cranial nerve and axons from the vestibular nuclei in the medulla project to the vestibulocerebellum. In addition, relay neurons in the dorsal nucleus of Clarke in the spinal cord (a group of relay neurons innervated by proprioceptive axons from the periph-ery; see Chapter 8) send their axons to the spinocerebellum. The vestibular and spinal inputs provide the cerebellum with information from the labyrinth in the ear, from muscle spindles, and from other mechanoreceptors that monitor the position and motion of the body. The somatic sensory input remains topographically mapped in the spinocerebellum such that there are orderly representations of the body surface within the cerebellum (Figure 18.5). These maps are “fractured,” however: That is, fine-grain electrophysi-ological analysis indicates that each small area of the body surface is repre-sented multiple times by spatially separated clusters of cells rather than by a specific site within a single continuous topographic map of the body surface. The vestibular and spinal inputs remain ipsilateral from their point of entry Modulation of Movement by the Cerebellum 439 Figure 18.4 Regions of the cerebral cortex that project to the cerebellum (shown in blue). The cortical projections to the cerebellum are mainly from the sensory association cortex of the parietal lobe and motor association areas of the frontal lobe. Spinocerebellum Flocculus Cerebrocerebellum Vermis Nodulus Figure 18.5 Somatotopic maps of the body surface in the cerebellum. The spinocerebellum contains at least two maps of the body. 440 Chapter Eighteen in the brainstem, traveling in the inferior cerebellar peduncle (see Figure 18.3B). This arrangement ensures that, in contrast to most areas of the brain, the right cerebellum is concerned with the right half of the body and the left cerebellum with the left half. Finally, the entire cerebellum receives modulatory inputs from the infe-rior olive and the locus ceruleus in the brainstem. These nuclei evidently participate in the learning and memory functions served by cerebellar cir-cuitry. Projections from the Cerebellum Except for a direct projection from the vestibulocerebellum to the vestibular nuclei, the cerebellar cortex projects to the deep cerebellar nuclei, which pro-ject in turn to upper motor neurons in the cortex (via a relay in the thalamus) and in the brainstem (Figure 18.6 and Table 18.3). There are four major deep (B) Primary motor and premotor cortex Cerebellar cortex Vestibular nuclei Inferior olive Dorsal nucleus of Clarke Ventral lateral complex (thalamus) Primary motor and premotor cortex Midline VL complex (thalamus) Deep cerebellar nuclei Cerebellar cortex (A) Superior cerebellar peduncle Deep cerebellar nuclei Pontine nuclei Figure 18.6 Functional organization of the outputs from the cerebellum to the cerebral cortex. (A) Tar-gets of the cerebellum. The axons of the deep cerebel-lar nuclei cross in the midbrain in the decussation of the superior cerebellar peduncle before reaching the thalamus. (B) Idealized coronal and sagittal sections through the human brainstem and cerebrum, show-ing the location of the structures and pathways dia-grammed in (A). Figure 18.7 Summary diagram of motor modulation by the cerebrocere-bellum. The central processing compo-nent, the cerebrocerebellar cortex, receives massive input from the cerebral cortex and generates signals that adjust the responses of upper motor neurons to regulate the course of a movement. Note that modulatory inputs also influence the processing of information within the cerebellar cortex. The output signals from the cerebellar cortex are relayed indirectly to the thalamus and then back to the motor cortex, where they modu-late the motor commands. nuclei: the dentate nucleus (by far the largest), two interposed nuclei, and the fastigial nucleus. Each receives input from a different region of the cere-bellar cortex. Although the borders are not distinct, in general, the cerebro-cerebellum projects primarily to the dentate nucleus, the spinocerebellum to the interposed nuclei, and the vestibulocerebellum to the fastigial nucleus. Pathways from the dentate nucleus are destined for the cortex via a relay in the ventral nuclear complex in the thalamus. Since each cerebellar hemi-sphere is concerned with the ispsilateral side of the body, this pathway must cross the midline if the motor cortex in each hemisphere, which is concerned with contralateral musculature, is to receive information from the appropri-ate cerebellum. Consequently, the dentate axons exit the cerebellum via the superior cerebellar peduncle, cross at the decussation of the superior cere-bellar peduncle in the caudal midbrain, and then ascend to the thalamus. The thalamic nuclei that receive projections from the deep cerebellar nuclei are segregated in two distinct subdivisions of the ventral lateral nuclear complex: the oral, or anterior, part of the posterolateral segment, and a region simply called “area X.” Both of these thalamic relays project directly to primary motor and premotor association cortices. Thus, the cerebellum has access to the upper motor neurons that organize the sequence of muscu-lar contractions underlying complex voluntary movements (see Chapter 16). Pathways leaving the deep cerebellar nuclei also project to upper motor neu-rons in the red nucleus, the superior colliculus, the vestibular nuclei, and the reticular formation (see Table 18.3 and Chapter 16). Anatomical studies using viruses to trace chains of connections between nerve cells have shown that large parts of the cerebrocerebellum send infor-mation back to non-motor areas of the cortex to form “closed loops.” That is, a region of the cerebellum projects back to the same cortical area that in turn projects to it. These closed loops run in parallel to “open loops” that receive input from multiple cortical areas and funnel output back to upper motor neurons in specific regions of the motor and premotor cortices (Figure 18.7). Circuits within the Cerebellum The ultimate destination of the afferent pathways to the cerebellar cortex is a distinctive cell type called the Purkinje cell (Figure 18.8). However, the input from the cerebral cortex to the Purkinje cells is indirect. Neurons in the pontine nuclei receive a projection from the cerebral cortex and then relay the information to the contralateral cerebellar cortex. The axons from the pontine nuclei and other sources are called mossy fibers because of the appearance of their synaptic terminals. Mossy fibers synapse on granule cells in the granule cell layer of the cerebellar cortex (see Figures 18.8 and 18.9). The cerebellar granule cells are widely held to be the most abundant class of neurons in the human brain. They give rise to specialized axons called parallel fibers that ascend to the molecular layer of the cerebellar cor-tex. The parallel fibers bifurcate in the molecular layer to form T-shaped branches that relay information via excitatory synapses onto the dendritic spines of the Purkinje cells. The Purkinje cells present the most striking histological feature of the cerebellum. Elaborate dendrites extend into the molecular layer from a sin-gle subjacent layer of these giant nerve cell bodies (called the Purkinje layer). Once in the molecular layer, the Purkinje cell dendrites branch extensively in a plane at right angles to the trajectory of the parallel fibers (Figure 18.8A). In this way, each Purkinje cell is in a position to receive input from a large number of parallel fibers, and each parallel fiber can contact a very large Modulation of Movement by the Cerebellum 441 TABLE 18.3 Output Targets of the Cerebellum Red nucleus Vestibular nuclei Superior colliculus Reticular formation Motor cortex (via relay in ventral lateral nuclei of thalamus) Thalamus Relay nuclei Cerebellar cortex Cortex Modulatory inputs 442 Chapter Eighteen Figure 18.8 Neurons and circuits of the cerebellum. (A) Neuronal types in the cerebellar cortex. Note that the vari-ous neuron classes are found in distinct layers. (B) Diagram showing convergent inputs onto the Purkinje cell from par-allel fibers and local circuit neurons [boxed region shown at higher magnifi-cation in (C)]. The output of the Pur-kinje cells is to the deep cerebellar nuclei. (C) Electron micrograph showing Purkinje cell dendritic shaft with three spines contacted by synapses from a trio of parallel fibers. (C courtesy of A. S. La Mantia and P. Rakic.) Granule cell Purkinje cell Purkinje cell Molecular layer Purkinje cell layer Basket cell Climbing fiber Purkinje cell axon Mossy fiber Granule cell Granule cell layer Parallel fiber Parallel fibers Mossy fibers Basket cell Parallel fiber/ Purkinje cell synapse Deep cerebellar nuclei neuron Climbing fiber (B) (A) Purkinje cell Stellate cell Golgi cell Purkinje cell dendrite Spines Parallel fiber synapse (C) number of Purkinje cells (on the order of tens of thousands). The Purkinje cells also receive a direct modulatory input on their dendritic shafts from the climbing fibers, all of which arise in the inferior olive (Figure 18.8B). Each Purkinje cell receives numerous synaptic contacts from a single climbing fiber. In most models of cerebellum function, the climbing fibers regulate movement by modulating the effectiveness of the mossy-parallel fiber con-nection with the Purkinje cells. The Purkinje cells project in turn to the deep cerebellar nuclei. They are the only output cells of the cerebellar cortex. Since Purkinje cells are GABAergic, the output of the cerebellar cortex is wholly inhibitory. How-ever, the neurons in the deep cerebellar nuclei receive excitatory input from the collaterals of the mossy and climbing fibers. The Purkinje cell inhibition of the deep nuclei neurons serves to modulate the level of this excitation (Figure 18.9). Inputs from local circuit neurons modulate the inhibitory activity of Purk-inje cells and occur on both dendritic shafts and the cell body. The most powerful of these local inputs are inhibitory complexes of synapses made around the Purkinje cell bodies by basket cells (see Figure 18.8A,B). Another type of local circuit neuron, the stellate cell, receives input from the parallel fibers and provides an inhibitory input to the Purkinje cell dendrites. Finally, the molecular layer contains the apical dendrites of a cell type called Golgi cells; these neurons have their cell bodies in the granular cell layer. The Golgi cells receive input from the parallel fibers and provide an inhibitory feedback to the cells of origin of the parallel fibers (the granule cells). This basic circuit is repeated over and over throughout every subdivision of the cerebellum in all mammals and is the fundamental functional module of the cerebellum. Modulation of signal flow through these modules pro-vides the basis for both real-time regulation of movement and the long-term changes in regulation that underlie motor learning. The flow of signals through this admittedly complex intrinsic circuitry is best described in refer-ence to the Purkinje cells (see Figure 18.9). The Purkinje cells receive two types of excitatory input from outside of the cerebellum, one directly from the climbing fibers and the other indirectly via the parallel fibers of the gran-ule cells. The Golgi, stellate, and basket cells control the flow of information through the cerebellar cortex. For example, the Golgi cells form an inhibitory feedback that may limit the duration of the granule cell input to the Purkinje cells, whereas the basket cells provide lateral inhibition that may focus the Modulation of Movement by the Cerebellum 443 Granule cell Purkinje cell Parallel fiber Mossy fiber To thalamus (motor cortex) Deep cerebellar nuclear cell From inferior olive From pontine nuclei (cerebral cortex), spinal cord, vestibular system + + + + + + + Granule cell layer Purkinje cell layer Molecular layer Climbing fiber + Figure 18.9 Excitatory and inhibitory connections in the cerebellar cortex and deep cerebellar nuclei. The excitatory input from mossy fibers and climbing fibers to Purkinje cells and deep nuclear cells is basically the same. Additional con-vergent input onto the Purkinje cell from local circuit neu-rons (basket and stellate cells) and other Purkinje cells estab-lishes a basis for the comparison of ongoing movement and sensory feedback derived from it. The Purkinje cell output to the deep cerebellar nuclear cell thus generates an error cor-rection signal that can modify movements already begun. The climbing fibers modify the efficacy of the parallel fiber–Purkinje cell connection, producing long-term changes in cerebellar output. (After Stein, 1986.) 444 Chapter Eighteen Box A Prion Diseases Creutzfeldt-Jakob disease (CJD) is a rare but devastating neurological disorder characterized by cerebellar ataxia, myoclonic jerks, seizures, and the fulmi-nant progression of dementia. The onset is usually in middle age, and death typi-cally follows within a year. The distinc-tive histopathology of the disease, termed “spongiform degeneration,” con-sists of neuronal loss and extensive glial proliferation, mainly in the cortex of the cerebellum and cerebrum; the peculiar spongiform pattern is due to vacuoles in the cytoplasm of neurons and glia. CJD is the only human disease known to be transmitted by inoculation (either orally or into the bloodstream) or inherited through the germline! In contrast to other transmissible diseases mediated by microorganisms such as viruses or bacte-ria, the agent in this case is a protein called a prion. Observations dating back some 30 years suggested that CJD was infective. The major clue came from scrapie, a once-obscure disease of sheep that is also characterized by cerebellar ataxia, wast-ing, and intense itching. The ability to transmit scrapie from one sheep to another strongly suggested an infectious agent. Another clue came from the work of Carlton Gajdusek, a neurologist study-ing a peculiar human disease called kuru that occurred specifically in a group of New Guinea natives known to practice ritual cannibalism. Like CJD, kuru is a neurodegenerative disease characterized by devastating cerebellar ataxia and sub-sequent dementia, usually leading to death within a year. The striking similar-ities in the distinctive histopathology of scrapie and kuru—namely spongiform degeneration—suggested a common pathogenesis and led to the successful transmission of kuru to apes and chim-panzees in the 1960s, confirming that CJD was indeed infectious. The pro-longed period between inoculation and disease onset (months to years) led Gaj-dusek to suggest that the transmissible agent was what he called a “slow virus.” These extraordinary findings spurred an intensive search for the infectious agent. The transmission of scrapie from sheep to hamsters by Stanley Prusiner at the University of California at San Fran-cisco permitted biochemical characteri-zation of partially purified fractions of scrapie agent from hamster brain. Oddly, he found that the infectivity was extraordinarily resistant to ultraviolet irradiation or nucleases, both treatments that degrade nucleic acids. It therefore seemed unlikely that a virus could be the causal agent. Conversely, procedures that modified or degraded proteins markedly diminished infectivity. In 1982, Prusiner coined the term prion to refer to the agent causing these trans-missible spongiform encephalopathies. He chose the term to emphasize that the agent was a proteinaceous infectious particle (he made the abbreviation a lit-tle more euphonious in the process). Subsequently, a half dozen more dis-eases of animals—including the widely publicized bovine spongiform encephalopathy (BSE), or “mad cow dis-ease”—and four more human diseases have been shown to be caused by prions. Whether prions contain undetected nucleic acids or are really proteins remained controversial for some years. Prusiner strongly advocated a “protein only” hypothesis, a revolutionary con-cept with respect to transmissible dis-eases. He proposed that the prion is a protein consisting of a modified (scrapie) form (PrPSc) of the normal host protein (PrPC, for “prion protein control”), the propagation of which occurs by a confor-mational change of endogenous PrPC to PrPSc autocatalyzed by PrPSc. That is, the modified form of the protein (PrPSc) transforms the normal form (PrPC) into the modified form, much as crystals form in supersaturated solutions. Differ-ences in the secondary structure of PrPC and PrPSc evident by optical spec-troscopy supported this idea. An alterna-tive hypothesis, however, was that the agent is simply an unconventional nucleic acid-containing virus, and that the accumulation of PrPSc is an inciden-tal consequence of infection and cell death. A compelling body of evidence in support of the “protein only” hypothesis has emerged only in the past decade. First, PrPSc and scrapie infectivity co-purify by a number of procedures, including affinity chromatography using an anti-PrP monoclonal antibody; no nucleic acid has been detected in highly purified preparations, despite intensive efforts. Second, spongiform encephalop-athies can be inherited in humans, and the cause is now known to be a mutation (or mutations) in the gene coding for PrP. Third, transgenic mice carrying a mutant PrP gene equivalent to one of the mutations of inherited human prion dis-ease develop a spongiform encephalopa-thy. Thus, a defective protein is sufficient to account for the disease. Finally, trans-genic mice carrying a null mutation for PrP do not develop spongiform encephalopathy when inoculated with scrapie agent, whereas wild-type mice do. These results argue convincingly that PrPSc must indeed interact with endoge-nous PrPC to convert PrPC to PrPSc, prop-agating the disease in the process. The protein is highly conserved across mam-malian species, suggesting that it serves some essential function, although mice carrying a null mutation of PrP exhibit no detectable abnormalities. These advances notwithstanding, many questions remain. What is the mechanism by which the conformational transformation of PrPC to PrPSc occurs? How do mutations at different sites of the same protein culminate in the dis-tinct phenotypes evident in diverse prion diseases of humans? Are conformational changes of proteins a common mecha-spatial distribution of Purkinje cell activity. The Purkinje cells modulate the activity of the deep cerebellar nuclei, which are driven by the direct excita-tory input they receive from the collaterals of the mossy and climbing fibers. The modulation of cerebellar output also occurs at the level of the Pur-kinje cells (see Figure 18.9). This latter modulation may be responsible for the motor learning aspect of cerebellar function. According to a model pro-posed by Masao Ito and his colleagues at Tokyo University, the climbing fibers relay the message of a motor error to the Purkinje cells. This message produces long-term reductions in the Purkinje cell responses to mossy-paral-lel fiber inputs. This inhibitory effect on the Purkinje cell responses disinhibits the deep cerebellar nuclei (for an account of the probable cellular mechanism for this long-term reduction in the efficacy of the parallel fiber synapse on Purkinje cells; see Chapter 24). As a result, the output of the cerebellum to the various sources of upper motor neurons is enhanced, in much the way that this process occurs in the basal ganglia (see Chapter 17). Cerebellar Circuitry and the Coordination of Ongoing Movement As expected for a structure that monitors and regulates motor behavior, neu-ronal activity in the cerebellum changes continually during the course of a movement. For instance, the execution of a relatively simple task like flip-ping the wrist back and forth elicits a dynamic pattern of activity in both the Purkinje cells and the deep cerebellar nuclear cells that closely follows the ongoing movement (Figure 18.10). Both types of cells are tonically active at rest and change their frequency of firing as movements occur. The neurons respond selectively to various aspects of movement, including extension or contraction of specific muscles, the position of the joints, and the direction of the next movement that will occur. All this information is therefore encoded by changes in the firing frequency of Purkinje cells and deep cerebellar nuclear cells. As these neuronal response properties predict, cerebellar lesions and dis-ease tend to disrupt the modulation and coordination of ongoing move-ments (Box A). Thus, the hallmark of patients with cerebellar damage is dif-ficulty producing smooth, well-coordinated movements. Instead, movements tend to be jerky and imprecise, a condition referred to as cerebellar ataxia. Many of these difficulties in performing movements can be explained as dis-ruption of the cerebellum’s role in correcting errors in ongoing movements. Normally, the cerebellar error correction mechanism ensures that move-Modulation of Movement by the Cerebellum 445 nism of other neurodegenerative dis-eases? And do these findings suggest a therapy for the dreadful manifestations of spongiform encephalopathies? Despite these unanswered questions, this work remains one of the most excit-ing chapters in modern neurological research, and rightly won Nobel Prizes in Physiology or Medicine for both Gaj-dusek (in 1976) and Prusiner (in 1997). References BUELER, H. AND 6 OTHERS (1993) Mice devoid of PrP are resistant to scrapie. Cell 73: 1339–1347. GAJDUSEK, D. C. (1977) Unconventional viruses and the origin and disappearance of kuru. Science 197: 943–960. GIBBS, C. J., D. C. GAJDUSEK, D. M. ASHER AND M. P. ALPERS (1968) Creutzfeldt-Jakob disease (spongiform encephalopathy): Transmission to the chimpanzee. Science 161: 388–389. PRUSINER, S. B. (1982) Novel proteinaceous infectious particles cause scrapie. Science 216: 136–144. PRUSINER, S. V., M. R. SCOTT, S. J. DEARMOND AND G. E. COHEN (1998) Prion protein biol-ogy. Cell 93: 337–348. RHODES, R. (1997) Deadly Feasts: Tracking the Secrets of a Terrifying New Plague. New York: Simon and Schuster. SOTO, C. (2003) Unfolding the role of protein misfolding in neurodegenerative diseases. Nature Rev. Neurosci. 4: 49–60. 446 Chapter Eighteen Figure 18.10 Activity of Purkinje cells (A) and deep cerebellar nuclear cells (B) at rest (upper traces) and during move-ment of the wrist (lower traces). The lines below the action potential records show changes in muscle tension, recorded by electromyography. The durations of the wrist movements are indicated by the colored blocks. Both classes of cells are tonically active at rest. Rapid alternating movements result in the transient inhibition of the tonic activity of both cell types. (After Thach, 1968.) ments are modified to cope with changing circumstances. As described ear-lier, the Purkinje cells and the deep cerebellar nuclear cells recognize poten-tial errors by comparing patterns of convergent activity that are concurrently available to both cell types; the deep nuclear cells then send corrective sig-nals to the upper motor neurons in order to maintain or improve the accu-racy of the movement. As in the case of the basal ganglia, studies of the oculomotor system (sac-cades in particular) have contributed greatly to understanding the contribu-tion that the cerebellum makes to motor error reduction. For example, cut-ting part of the tendon to the lateral rectus muscles in one eye of a monkey weakens horizontal eye movements by that eye (Figure 18.11). When a patch is then placed over the normal eye to force the animal to use its weak eye, the saccades performed by the weak eye are initially hypometric; as expected, they fall short of visual targets. Then, over the next few days, the amplitude of the saccades gradually increases until they again become accurate. If the patch is then switched to cover the weakened eye, the saccades performed by the normal eye are now hypermetric. In other words, over a period of a few days the nervous system corrects the error in the saccades made by the weak eye by increasing the gain in the saccade motor system. Lesions in the vermis of the spinocerebellum (see Figure 18.1) eliminate this ability to reduce the motor error. Similar evidence of the cerebellar contribution to movement has come from studies of the vestibulo-ocular reflex (VOR) in monkeys and humans. The VOR works to keep the eyes trained on a visual target during head movements (see Chapter 13). The relative simplicity of this reflex has made it possible to analyze some of the mechanisms that enable motor learning as a process of error reduction. When a visual image on the retina shifts its posi-tion as a result of head movement, the eyes must move at the same velocity in the opposite direction to maintain a stable percept. In these studies, the (A) PURKINJE CELL (B) DEEP NUCLEAR CELL During alternating movement During alternating movement At rest At rest Figure 18.11 Contribution of the cere-bellum to the experience-dependent modification of saccadic eye move-ments. Weakening of the lateral rectus muscle of the left eye causes the eye to undershoot the target (1). When the experimental subject (in this case a mon-key) is forced to use this eye by patch-ing the right eye, multiple saccades must be generated to acquire the target (2). After 5 days of experience with the weak eye, the gain of the saccadic sys-tem has been increased and a single sac-cade is now used to fixate the target. (3) This adjustment of the gain of the sac-cadic eye movement system depends on an intact cerebellum. (After Optican and Robinson, 1980.) adaptability of the VOR to changes in the nature of incoming sensory infor-mation is challenged by fitting subjects (either monkeys or humans) with magnifying or minifying spectacles (Figure 18.12). Because the glasses alter the size of the visual image on the retina, the compensatory eye movements, which would normally have maintained a stable image of an object on the retina, are either too large or too small. Over time, subjects (whether mon-keys or humans) learn to adjust the distance the eyes must move in response to head movements to accord with the artificially altered size of the visual field. Moreover, this change is retained for significant periods after the spec-tacles are removed and can be detected electrophysiologically in recordings from cerebellar Purkinje cells and neurons in the deep cerebellar nuclei. Information that reflects this change in the sensory context of the VOR must therefore be learned and remembered to eliminate the artificially introduced Modulation of Movement by the Cerebellum 447 Apply patch on left eye Left eye (weak) Partial sectioning of lateral rectus tendon Target Time Eye Position Right eye (normal) Time Position Position Position Position Position 1 2 Move patch to right eye 3 5 days after patching right eye With patch Time Time With patch Time Time With patch 3° 25° 448 Chapter Eighteen error. Once again, if the cerebellum is damaged or removed, the ability of the VOR to adapt to the new conditions is lost. These observations support the conclusion that the cerebellum is critically important in error reduction dur-ing motor learning. Cerebellar circuitry also provides real-time error correction during ongo-ing movements. This function is accomplished by changes in the tonically inhibitory activity of Purkinje cells that in turn influence the tonically excita-tory deep cerebellar nuclear cells. The resulting effects on the ongoing activ-ity of the deep cerebellar nuclear cells adjust the cerebellar output signals to the upper motor neurons in the cortex and brainstem. Further Consequences of Cerebellar Lesions As mentioned in the preceding discussion, patients with cerebellar damage, regardless of the causes or location, exhibit persistent errors in movement. These movement errors are always on the same side of the body as the dam-age to the cerebellum, reflecting the cerebellum’s unusual status as a brain structure in which sensory and motor information is represented ipsilater-ally rather than contralaterally. Furthermore, somatic, visual, and other inputs are represented topographically within the cerebellum; as a result, the movement deficits may be quite specific. For example, one of the most com-mon cerebellar syndromes is caused by degeneration in the anterior portion of the cerebellar cortex in patients with a long history of alcohol abuse (Fig-ure 18.13). Such damage specifically affects movement in the lower limbs, which are represented in the anterior spinocerebellum (see Figure 18.5). The consequences include a wide and staggering gait, with little impairment of arm or hand movements. Thus, the topographical organization of the cere-Head and eyes move in a coordinated manner to keep image on retina VOR out of register Minifying glasses VOR gain reset After several hours Minifying glasses t n e m e v o m d a e H E y e m o v e m e n t t n e m e v o m d a e H E y e m o v e m e n t Normal vestibulo-ocular reflex (VOR) Eyes move too far in relation to image movement on the retina when the head moves Eyes move smaller distances in relation to head movement to compensate t n e m e v o m d a e H E y e m o v e m e n t Figure 18.12 Learned changes in the vestibulo-ocular reflex in monkeys. Nor-mally, this reflex operates to move the eyes as the head moves, so that the retinal image remains stable. When the animal observes the world through minifying spec-tacles, the eyes initially move too far with respect to the “slippage” of the visual image on the retina. After some practice, however, the VOR is reset and the eyes move an appropriate distance in relation to head movement, thus compensating for the altered size of the visual image. Figure 18.13 The pathological changes in a variety of neurological diseases pro-vide insights about the function of the cerebellum. In this example, chronic alcohol abuse has caused degeneration of the anterior cerebellum (arrows), while leaving other cerebellar regions intact. The patient had difficulty walk-ing but little impairment of arm move-ments or speech. The orientation of this paramedian sagittal section is the same as Figure 18.1C. (From Victor et al., 1959.) bellum allows cerebellar damage to disrupt the coordination of movements performed by some muscle groups but not others. The implication of these pathologies is that the cerebellum is normally capable of integrating the moment-to-moment actions of muscles and joints throughout the body to ensure the smooth execution of a full range of motor behaviors. Thus, cerebellar lesions lead first and foremost to a lack of coordi-nation of ongoing movements (Box B). For example, damage to the vestibu-locerebellum impairs the ability to stand upright and maintain the direction of gaze. The eyes have difficulty maintaining fixation; they drift from the tar-get and then jump back with a corrective saccade, a phenomenon called nys-tagmus. Disruption of the pathways to the vestibular nuclei may also result in a loss of muscle tone. In contrast, patients with damage to the spinocere-bellum have difficulty controlling walking movements; they have a wide-based gait with small shuffling movements, which represents the inappro-priate operation of groups of muscles that normally rely on sensory feedback to produce smooth, concerted actions. The patients also have diffi-culty performing rapid alternating movements such as the heel-to-shin and/or finger-to-nose tests, a sign referred to as dysdiadochokinesia. Over-and underreaching may also occur (called dysmetria). During the move-ment, tremors—called action or intention tremors—accompany over- and undershooting of the movement due to disruption of the mechanism for detecting and correcting movement errors. Finally, lesions of the cerebro-cerebellum produce impairments in highly skilled sequences of learned movements, such as speech or playing a musical instrument. The common denominator of all of these signs, regardless of the site of the lesion, is the inability to perform smooth, directed movements. Summary The cerebellum receives input from regions of the cerebral cortex that plan and initiate complex and highly skilled movements; it also receives innerva-tion from sensory systems that monitor the course of movements. This arrangement enables a comparison of an intended movement with the actual movement and a reduction in the difference, or “motor error.” The correc-tions of motor error produced by the cerebellum occur both in real time and over longer periods, as motor learning. For example, the vestibulo-ocular reflex allows an observer to fixate an object of interest while the head moves; however, lenses that change image size produce a long-term change in the gain of this reflex that depends on an intact cerebellum. Knowledge of cere-bellar circuitry suggests that motor learning is mediated by climbing fibers that ascend from the inferior olive to contact the dendrites of the Purkinje cells in the cerebellar cortex. Information provided by the climbing fibers modulates the effectiveness of the second major input to the Purkinje cells, which arrives via the parallel fibers from the granule cells. The granule cells receive information about the intended movement from the vast number of mossy fibers that enter the cerebellum from multiple sources, including the cortico-ponto-cerebellar pathway. As might be expected, the output of the cerebellum from the deep cerebellar nuclei projects to all the major sources of upper motor neurons described in Chapter 16. The effects of cerebellar disease provide strong support for the idea that the cerebellum regulates the performance of movements. Thus, patients with cerebellar disorders show severe ataxias in which the site of the lesion determines the particular move-ments affected. Modulation of Movement by the Cerebellum 449 ➘ ➘ 450 Chapter Eighteen Box B Genetic Analysis of Cerebellar Function Since the early 1950s, investigators inter-ested in motor behavior have identified and studied strains of mutant mice in which movement is compromised. These mutant mice are easy to spot: following induced or spontaneous mutagenesis, the “screen” is simply to look for animals that have difficulty moving. Genetic analysis suggested that some of these abnormal behaviors could be explained by single autosomal recessive or semidominant mutations, in which homozygotes are most severely affected. The strains were given names like reeler, weaver, lurcher, staggerer, and leaner that reflected the nature of the motor dys-function they exhibited (see table). The relatively large number of mutations that compromise movement suggested it might be possible to understand some aspects of motor circuits and function at the genetic level. A common feature of the mutants is ataxia resembling that associated with cerebellar dysfunction in humans. Indeed, all the mutations are associated with some form of cerebellar pathology. The pathologies associated with the reeler and weaver mutations are particularly striking. In the reeler cerebellum, Purkinje cells, granule cells, and interneurons are all displaced from their usual laminar positions, and there are fewer granule cells than normal. In weaver, most of the granule cells are lost prior to their migra-tion from the external granule layer (a proliferative region where cerebellar granule cells are generated during devel-opment), leaving only Purkinje cells and interneurons to carry on the work of the cerebellum. Thus, these mutations caus-ing deficits in motor behavior impair the development and final disposition of the neurons that comprise the major process-ing circuits of the cerebellum (see Figure 18.8). Efforts to characterize the cellular mechanisms underlying these motor deficits were unsuccessful, and the mo-lecular identity of the affected genes remained obscure until recently. In the past few years, however, both the reeler and weaver genes have been identified and cloned. The reeler gene was cloned through a combination of good luck and careful observation. In the course of making transgenic mice by inserting DNA frag-ments in the mouse genome, investiga-tors in Tom Curran’s laboratory created a new strain of mice that behaved much like reeler mice and had similar cerebellar pathology. This “synthetic” reeler muta-tion was identified by finding the posi-tion of the novel DNA fragment—which turned out to be on the same chromo-Motor Mutations in Mice Chromosome Mutation Inheritance affected Behavioral and morphological characteristics reeler (rl) Autosomal 5 Reeling ataxia of gait, dystonic postures, and tremors. Systematic recessive malposition of neuron classes in the forebrain and cerebellum. Small cerebellum, reduced number of granule cells. weaver (wv) Autosomal ? Ataxia, hypotonia, and tremor. Cerebellar cortex reduced in recessive volume. Most cells of external granular layer degenerate prior to migration. leaner (tg1a) Autosomal 8 Ataxia and hypotonia. Degeneration of granule cells, particularly recessive in the anterior and nodular lobes of the cerebellum. Degen-eration of a few Purkinje cells. lurcher (lr) Autosomal 6 Homozygote dies. Heterozygote is ataxic with hesitant, lurching semidominant gait and has seizures. Cerebellum half normal size; Purkinje cells degenerate; granule cells reduced in number. nervous (nr) Autosomal 8 Hyperactivity and ataxia. Ninety percent of Purkinje cells die recessive between 3 and 6 weeks of age. Purkinje cell degeneration (pcd) Autosomal 13 Moderate ataxia. All Purkinje cells degenerate between the fif-recessive teenth embryonic day and third month of age. staggerer (sg) Autosomal 9 Ataxia with tremors. Dendritic arbors of Purkinje cells are simple recessive (few spines). No synapses of Purkinje cells with parallel fibers. Granule cells eventually degenerate. (Adapted from Caviness and Rakic, 1978.) Modulation of Movement by the Cerebellum 451 some as the original reeler mutation. Fur-ther analysis showed that the same gene had indeed been mutated, and the reeler gene was subsequently identified. Remarkably, the protein encoded by this gene is homologous to known extracellu-lar matrix proteins such as tenascin, laminin, and fibronectin (see Chapter 21). This finding makes good sense, since the pathophysiology of the reeler muta-tion entails altered cell migration, result-ing in misplaced neurons in the cerebel-lar cortex as well as the cerebral cortex and hippocampus. Molecular genetic techniques have also led to cloning the weaver gene. Using linkage analysis and the ability to clone and sequence large pieces of mammalian chromosomes, Andy Peterson and his colleagues “walked” (i.e., sequentially cloned) several kilobases of DNA in the chromosomal region to find where the weaver gene mapped. By comparing nor-mal and mutant sequences within this region, they determined weaver to be a mutation in a K+ channel that resembles the Ca2+-activated K+ channels found in cardiac muscle. How this particular mol-ecule influences the development of granule cells or causes their death in the mutants is not yet clear. The story of the proteins encoded by the reeler and weaver genes indicates both the promise and the challenge of a genetic approach to understanding cere-bellar function. Identifying motor mutants and their pathology is reason-ably straightforward, but understanding their molecular genetic basis depends on hard work and good luck. References CAVINESS, V. S. JR. AND P. RAKIC (1978) Mecha-nisms of cortical development: A view from mutations in mice. Annu. Rev. Neurosci. 1: 297–326. D’ARCANGELO, G., G. G. MIAO, S. C. CHEN, H. D. SOARES, J. I. MORGAN AND T. CURRAN (1995) A protein related to extracellular matrix pro-teins deleted in the mouse mutation reeler. Nature 374: 719–723. PATIL, N., D. R. COX, D. BHAT, M. FAHAM, R. M. MEYERS AND A. PETERSON (1995) A potas-sium channel mutation in weaver mice impli-cates membrane excitability in granule cell differentiation. Nature Genetics 11: 126–129. RAKIC, P. AND V. S. CAVINESS JR. (1995) Cortical development: A view from neurological mutants two decades later. Neuron 14: 1101–1104. (A) reeler (rl/rl) (B) weaver (wv/wv) Purkinje cell Basket cell Purkinje axon Purkinje axon Climbing fiber Mossy fiber Purkinje cell Golgi cell Climbing fiber Misplaced granule cell Mossy fiber The cerebellar cortex is disrupted in both the reeler and weaver mutations. (A) The cerebellar cortex in homozygous reeler mice. The reeler mutation causes the major cell types of the cere-bellar cortex to be displaced from their normal laminar positions. Despite the disorganization of the cerebellar cortex in reeler mutants, the major inputs—mossy fibers and climbing fibers—find appropriate targets. (B) The cerebellar cortex in homozygous weaver mice. The granule cells are missing, and the major cerebellar inputs synapse inappropriately on the remaining neurons. (After Rakic, 1977.) 452 Chapter Eighteen Additional Reading Reviews ALLEN, G. AND N. TSUKAHARA (1974) Cerebro-cerebellar communication systems. Physiol. Rev. 54: 957–1006. GLICKSTEIN, M. AND C. YEO (1990) The cerebel-lum and motor learning. J. Cog. Neurosci. 2: 69–80. LISBERGER, S. G. (1988) The neural basis for learning of simple motor skills. Science 242: 728–735. OHYAMA, T., W. L. NORES, M. MURPHY, AND M. D. MAUK (2003) What the cerebellum com-putes. Trends Neurosci. 26: 222–227. ROBINSON, F. R. AND A. F. FUCHS (2001) The role of the cerebellum in voluntary eye move-ments. Annu. Rev. Neurosci. 24: 981–1004. STEIN, J. F. (1986) Role of the cerebellum in the visual guidance of movement. Nature 323: 217–221. THACH, W. T., H. P. GOODKIN AND J. G. KEATING (1992) The cerebellum and adaptive coordina-tion of movement. Annu. Rev. Neurosci. 15: 403–442. Important Original Papers ASANUMA, C., W. T. THACH AND E. G. JONES (1983) Distribution of cerebellar terminals and their relation to other afferent terminations in the ventral lateral thalamic region of the mon-key. Brain Res. Rev. 5: 237–265. BRODAL, P. (1978) The corticopontine projec-tion in the rhesus monkey: Origin and princi-ples of organization. Brain 101: 251–283. DELONG, M. R. AND P. L. STRICK (1974) Rela-tion of basal ganglia, cerebellum, and motor cortex units to ramp and ballistic movements. Brain Res. 71: 327–335. ECCLES, J. C. (1967) Circuits in the cerebellar control of movement. Proc. Natl. Acad. Sci. USA 58: 336–343. MCCORMICK, D. A., G. A. CLARK, D. G. LAVOND AND R. F. THOMPSON (1982) Initial localization of the memory trace for a basic form of learn-ing. Proc. Natl. Acad. Sci. USA 79: 2731–2735. THACH, W. T. (1968) Discharge of Purkinje and cerebellar nuclear neurons during rapidly alternating arm movements in the monkey. J. Neurophysiol. 31: 785–797. THACH, W. T. (1978) Correlation of neural dis-charge with pattern and force of muscular activity, joint position, and direction of intended next movement in motor cortex and cerebellum. J. Neurophysiol. 41: 654–676. VICTOR, M., R. D. ADAMS AND E. L. MANCALL (1959) A restricted form of cerebellar cortical degeneration occurring in alcoholic patients. Arch. Neurol. 1: 579–688. Books BRADLEY, W. G., R. B. DAROFF, G. M. FENICHEL AND C. D. MARSDEN (EDS.) (1991) Neurology in Clinical Practice. Boston: Butterworth-Heine-mann, Chapters 29 and 77. ITO, M. (1984) The Cerebellum and Neural Con-trol. New York: Raven Press. KLAWANS, H. L. (1989) Toscanini’s Fumble and Other Tales of Clinical Neurology. New York: Bantam, Chapters 7 and 10. Overview Eye movements are, in many ways, easier to study than movements of other parts of the body. This fact arises from the relative simplicity of muscle actions on the eyeball. There are only six extraocular muscles, each of which has a specific role in adjusting eye position. Moreover, there are only four stereotyped kinds of eye movements, each with its own control circuitry. Eye movements have therefore been a useful model for understanding the mech-anisms of motor control. Indeed, much of what is known about the regula-tion of movements by the cerebellum, basal ganglia, and vestibular system has come from the study of eye movements (see Chapters 13, 17, and 18). Here the major features of eye movement control are used to illustrate the principles of sensory motor integration that also apply to more complex motor behaviors. What Eye Movements Accomplish Eye movements are important in humans because high visual acuity is restricted to the fovea, the small circular region (about 1.5 mm in diameter) in the central retina that is densely packed with cone photoreceptors (see Chapter 10). Eye movements can direct the fovea to new objects of interest (a process called “foveation”) or compensate for disturbances that cause the fovea to be displaced from a target already being attended to. As demonstrated several decades ago by the Russian physiologist Alfred Yarbus, eye movements reveal a good deal about the strategies used to inspect a scene. Yarbus used contact lenses with small mirrors on them (see Box A) to document (by the position of a reflected beam) the pattern of eye movements made while subjects examined a variety of objects and scenes. Figure 19.1 shows the direction of a subject’s gaze while viewing a picture of Queen Nefertiti. The thin, straight lines represent the quick, ballistic eye movements (saccades) used to align the foveas with particular parts of the scene; the denser spots along these lines represent points of fixation where the observer paused for a variable period to take in visual information (little or no visual perception occurs during a saccade, which occupies only a few tens of milliseconds). The results obtained by Yarbus, and subsequently many others, showed that vision is an active process in which eye move-ments typically shift the view several times each second to selected parts of the scene to examine especially interesting features. The spatial distribution of the fixation points indicates that much more time is spent scrutinizing Nefertiti’s eye, nose, mouth, and ear than examining the middle of her cheek or neck. Thus, eye movements allow us to scan the visual field, pausing to focus attention on the portions of the scene that convey the most significant Chapter 19 453 Eye Movements and Sensory Motor Integration 454 Chapter Nineteen information. As is apparent in Figure 19.1, tracking eye movements can be used to determine what aspects of a scene are particularly arresting. Adver-tisers now use modern versions of Yarbus’ method to determine which pic-tures and scene arrangements will best sell their product. The importance of eye movements for visual perception has also been demonstrated by experiments in which a visual image is stabilized on the retina, either by paralyzing the extraocular eye muscles or by moving a scene in exact register with eye movements so that the different features of the image always fall on exactly the same parts of the retina (Box A). Stabi-lized visual images rapidly disappear, for reasons that remain poorly under-stood. Nonetheless, these observations on motionless images make it plain that eye movements are also essential for normal visual perception. The Actions and Innervation of Extraocular Muscles Three antagonistic pairs of muscles control eye movements: the lateral and medial rectus muscles, the superior and inferior rectus muscles, and the superior and inferior oblique muscles. These muscles are responsible for movements of the eye along three different axes: horizontal, either toward the nose (adduction) or away from the nose (abduction); vertical, either elevation or depression; and torsional, movements that bring the top of the eye toward the nose (intorsion) or away from the nose (extorsion). Horizontal move-ments are controlled entirely by the medial and lateral rectus muscles; the medial rectus muscle is responsible for adduction, the lateral rectus muscle for abduction. Vertical movements require the coordinated action of the superior and inferior rectus muscles, as well as the oblique muscles. The rel-ative contribution of the rectus and oblique groups depends on the horizon-tal position of the eye (Figure 19.2). In the primary position (eyes straight ahead), both of these groups contribute to vertical movements. Elevation is due to the action of the superior rectus and inferior oblique muscles, while depression is due to the action of the inferior rectus and superior oblique muscles. When the eye is abducted, the rectus muscles are the prime vertical movers. Elevation is due to the action of the superior rectus, and depression is due to the action of the inferior rectus. When the eye is adducted, the oblique muscles are the prime vertical movers. Elevation is due to the action of the inferior oblique muscle, while depression is due to the action of the superior oblique muscle. The oblique muscles are also primarily responsible for torsional movements. The extraocular muscles are innervated by lower motor neurons that form three cranial nerves: the abducens, the trochlear, and the oculomotor (Figure 19.3). The abducens nerve (cranial nerve VI) exits the brainstem from the pons–medullary junction and innervates the lateral rectus muscle. The trochlear nerve (cranial nerve IV) exits from the caudal portion of the mid-brain and supplies the superior oblique muscle. In distinction to all other cranial nerves, the trochlear nerve exits from the dorsal surface of the brain-stem and crosses the midline to innervate the superior oblique muscle on the contralateral side. The oculomotor nerve (cranial nerve III), which exits from the rostral midbrain near the cerebral peduncle, supplies all the rest of the extraocular muscles. Although the oculomotor nerve governs several differ-ent muscles, each receives its innervation from a separate group of lower motor neurons within the third nerve nucleus. In addition to supplying the extraocular muscles, a distinct cell group within the oculomotor nucleus innervates the levator muscles of the eyelid; the axons from these neurons also travel in the third nerve. Finally, the third Figure 19.1 The eye movements of a subject viewing a picture of Queen Nefertiti. The bust at the top is what the subject saw; the diagram on the bottom shows the subject’s eye movements over a 2–minute viewing period. (From Yarbus, 1967.) Figure 19.3 Organization of the cra-nial nerve nuclei that govern eye move-ments, showing their innervation of the extraocular muscles. The abducens nucleus innervates the lateral rectus muscle; the trochlear nucleus innervates the superior oblique muscle; and the oculomotor nucleus innervates all the rest of the extraocular muscles (the medial rectus, inferior rectus, superior rectus, and inferior oblique). Superior rectus Inferior rectus Right Left Inferior oblique Superior oblique Lateral rectus Superior rectus Inferior rectus Lateral rectus Inferior oblique Superior oblique Medial rectus Left eye Right eye Cranial nerve III Superior rectus Lateral rectus Medial rectus Superior oblique Inferior oblique Oculomotor nucleus Abducens nucleus Cranial nerve VI Cranial nerve IV Trochlear nucleus Midbrain Caudal midbrain Pons Inferior rectus Figure 19.2 The contributions of the six extraocular muscles to vertical and horizontal eye movements. Horizontal movements are mediated by the medial and lateral rectus muscles, while verti-cal movements are mediated by the superior and inferior rectus and the superior and inferior oblique muscle groups. 456 Chapter Nineteen Box A The Perception of Stabilized Retinal Images Visual perception depends critically on frequent changes of scene. Normally, our view of the world is changed by sac-cades, and tiny saccades that continue to move the eyes abruptly over a fraction of a degree of visual arc occur even when the observer stares intently at an object of interest. Moreover, continual drift of the eyes during fixation progressively shifts the image onto a nearby but different set of photoreceptors. As a consequence of these several sorts of eye movements (Figure A), our point of view changes more or less continually. The importance of a continually changing scene for normal vision is dra-matically revealed when the retinal image is stabilized. If a small mirror is attached to the eye by means of a contact lens and an image reflected off the mir-ror onto a screen, then the subject neces-sarily sees the same thing, whatever the position of the eye: Every time the eye moves, the projected image moves exactly the same amount (Figure B). Under these circumstances, the stabilized image actually disappears from percep-tion within a few seconds! A simple way to demonstrate the rapid disappearance of a stabilized reti-nal image is to visualize one’s own reti-nal blood vessels. The blood vessels, which lie in front of the photoreceptor layer, cast a shadow on the underlying receptors. Although normally invisible, the vascular shadows can be seen by moving a source of light across the eye, a phenomenon first noted by J. E. Purkinje more than 150 years ago. This perception can be elicited with an ordinary penlight pressed gently against the lateral side of the closed eyelid. When the light is wig-gled vigorously, a rich network of black blood vessel shadows appears against an orange background. (The vessels appear black because they are shadows.) By starting and stopping the movement, it is readily apparent that the image of the blood vessel shadows disappears within a fraction of a second after the light source is stilled. The conventional interpretation of the rapid disappearance of stabilized images is retinal adaptation. In fact, the phenom-enon is at least partly of central origin. Stabilizing the retinal image in one eye, for example, diminishes perception through the other eye, an effect known as interocular transfer. Although the explanation of these remarkable effects is not entirely clear, they emphasize the point that the visual system is designed to deal with novelty. References BARLOW, H. B. (1963) Slippage of contact lenses and other artifacts in relation to fading and regeneration of supposedly stable retinal images. Q. J. Exp. Psychol. 15: 36–51. COPPOLA, D. AND D. PURVES (1996) The ex-traordinarily rapid disappearance of entopic images. Proc. Natl. Acad. Sci. USA 96: 8001–8003. HECKENMUELLER, E. G. (1965) Stabilization of the retinal image: A review of method, effects and theory. Psychol. Bull. 63: 157–169. KRAUSKOPF, J. AND L. A. RIGGS (1959) Interocu-lar transfer in the disappearance of stabilized images. Amer. J. Psychol. 72: 248–252. Screen Mirrors Contact lens Mirror on contact lens Light from projector Mirrors Adjustable return path (B) Diagram illustrating one means of producing sta-bilized retinal images. By attaching a small mirror to the eye, the scene projected onto the screen will always fall on the same set of retinal points, no mat-ter how the eye is moved. A) Diagram of the types of eye movements that continually change the retinal stimulus during fixation. The straight lines indicate microsaccades and the curved lines drift; the structures in the background are photo-receptors drawn approximately to scale. The normal scanning movements of the eyes (saccades) are much too large to be shown here, but obviously contribute to the changes of view that we continually experience, as do slow tracking eye movements (although the fovea tracks a particular object, the scene nonetheless changes). (After Pritchard, 1961.) Photoreceptor cells in retina Drift Tiny saccade Figure 19.4 The metrics of a saccadic eye movement. The red line indicates the position of a fixation target and the blue line the position of the fovea. When the target moves suddenly to the right, there is a delay of about 200 ms before the eye begins to move to the new target position. (After Fuchs, 1967.) nerve carries axons that are responsible for pupillary constriction (see Chap-ter 11) from the nearby Edinger-Westphal nucleus. Thus, damage to the third nerve results in three characteristic deficits: impairment of eye movements, drooping of the eyelid (ptosis), and pupillary dilation. Types of Eye Movements and Their Functions There are four basic types of eye movements: saccades, smooth pursuit movements, vergence movements, and vestibulo-ocular movements. The functions of each type of eye movement are introduced here; in subsequent sections, the neural circuitry responsible for three of these types of move-ments is presented in more detail (see Chapters 13 and 18 for further discus-sion of neural circuitry underlying vestibulo-ocular movements). Saccades are rapid, ballistic movements of the eyes that abruptly change the point of fixation. They range in amplitude from the small movements made while reading, for example, to the much larger movements made while gazing around a room. Saccades can be elicited voluntarily, but occur reflexively whenever the eyes are open, even when fixated on a target (see Box A). The rapid eye movements that occur during an important phase of sleep (see Chapter 27) are also saccades. The time course of a saccadic eye movement is shown in Figure 19.4. After the onset of a target for a saccade (in this example, the stimulus was the movement of an already fixated tar-get), it takes about 200 milliseconds for eye movement to begin. During this delay, the position of the target with respect to the fovea is computed (that is, how far the eye has to move), and the difference between the initial and intended position, or “motor error” (see Chapter 18), is converted into a motor command that activates the extraocular muscles to move the eyes the correct distance in the appropriate direction. Saccadic eye movements are said to be ballistic because the saccade-generating system cannot respond to subsequent changes in the position of the target during the course of the eye movement. If the target moves again during this time (which is on the order of 15–100 ms), the saccade will miss the target, and a second saccade must be made to correct the error. Smooth pursuit movements are much slower tracking movements of the eyes designed to keep a moving stimulus on the fovea. Such movements are under voluntary control in the sense that the observer can choose whether or not to track a moving stimulus (Figure 19.5). (Saccades can also be voluntary, but are also made unconsciously.) Surprisingly, however, only highly trained observers can make a smooth pursuit movement in the absence of a moving target. Most people who try to move their eyes in a smooth fashion without a moving target simply make a saccade. The smooth pursuit system can be tested by placing a subject inside a rotating cylinder with vertical stripes. (In practice, the subject is more often seated in front of a screen on which a series of horizontally moving vertical bars is presented to conduct this “optokinetic test.”) The eyes automatically follow a stripe until they reach the end of their excursion. There is then a quick saccade in the direction opposite to the movement, followed once again by smooth pursuit of a stripe. This alternating slow and fast move-ment of the eyes in response to such stimuli is called optokinetic nystag-mus. Optokinetic nystagmus is a normal reflexive response of the eyes in response to large-scale movements of the visual scene and should not be confused with the pathological nystagmus that can result from certain kinds of brain injury (for example, damage to the vestibular system or the cerebel-lum; see Chapters 13 and 18). Eye Movements and Sensory Motor Integration 457 Right Left Time Eye position Target position 200 ms 458 Chapter Nineteen Figure 19.5 The metrics of smooth pursuit eye movements. These traces show eye movements (blue lines) track-ing a stimulus moving at three different velocities (red lines). After a quick sac-cade to capture the target, the eye move-ment attains a velocity that matches the velocity of the target. (After Fuchs, 1967.) Vergence movements align the fovea of each eye with targets located at different distances from the observer. Unlike other types of eye movements in which the two eyes move in the same direction (conjugate eye move-ments), vergence movements are disconjugate (or disjunctive); they involve either a convergence or divergence of the lines of sight of each eye to see an object that is nearer or farther away. Convergence is one of the three reflex-ive visual responses elicited by interest in a near object. The other compo-nents of the so-called near reflex triad are accommodation of the lens, which brings the object into focus, and pupillary constriction, which increases the depth of field and sharpens the image on the retina (see Chapter 10). Vestibulo-ocular movements stabilize the eyes relative to the external world, thus compensating for head movements. These reflex responses pre-vent visual images from “slipping” on the surface of the retina as head posi-tion varies. The action of vestibulo-ocular movements can be appreciated by fixating an object and moving the head from side to side; the eyes automati-cally compensate for the head movement by moving the same distance but in the opposite direction, thus keeping the image of the object at more or less the same place on the retina. The vestibular system detects brief, transient changes in head position and produces rapid corrective eye movements (see Chapter 13). Sensory information from the semicircular canals directs the eyes to move in a direction opposite to the head movement. Although the vestibular system operates effectively to counteract rapid movements of the head, it is relatively insensitive to slow movements or to persistent rotation of the head. For example, if the vestibulo-ocular reflex is tested with continuous rotation and without visual cues about the move-ment of the image (i.e.,with eyes closed or in the dark), the compensatory eye movements cease after only about 30 seconds of rotation. However, if the same test is performed with visual cues, eye movements persist. The com-pensatory eye movements in this case are due to the activation of the smooth pursuit system, which relies not on vestibular information but on visual cues indicating motion of the visual field. Neural Control of Saccadic Eye Movements The problem of moving the eyes to fixate a new target in space (or indeed any other movement) entails two separate issues: controlling the amplitude of Time (s) 15 10 20 5 0 Eye movement (degrees) 0.5 0 1.0 1.5 20° 15° 10° Eye movement Target movement Catch-up saccade /s /s /s movement (how far), and controlling the direction of the movement (which way). The amplitude of a saccadic eye movement is encoded by the duration of neuronal activity in the lower motor neurons of the oculomotor nuclei. As shown in Figure 19.6, for instance, neurons in the abducens nucleus fire a burst of action potentials prior to abducting the eye (by causing the lateral rectus muscle to contract) and are silent when the eye is adducted. The amplitude of the movement is correlated with the duration of the burst of action potentials in the abducens neuron. With each saccade, the abducens neurons reach a new baseline level of discharge that is correlated with the position of the eye in the orbit. The steady baseline level of firing holds the eye in its new position. The direction of the movement is determined by which eye muscles are activated. Although in principle any given direction of movement could be specified by independently adjusting the activity of individual eye muscles, the complexity of the task would be overwhelming. Instead, the direction of eye movement is controlled by the local circuit neurons in two gaze centers in the reticular formation, each of which is responsible for generating move-ments along a particular axis. The paramedian pontine reticular formation (PPRF) or horizontal gaze center is a collection of local circuit neurons near the midline in the pons responsible for generating horizontal eye move-ments (Figure 19.7). The rostral interstitial nucleus or vertical gaze center is located in the rostral part of the midbrain reticular formation and is respon-sible for vertical movements. Activation of each gaze center separately results in movements of the eyes along a single axis, either horizontal or ver-tical. Activation of the gaze centers in concert results in oblique movements whose trajectories are specified by the relative contribution of each center. An example of how the PPRF works with the abducens and oculomotor nuclei to generate a horizontal saccade to the right is shown in Figure 19.7. Neurons in the PPRF innervate cells in the abducens nucleus on the same side of the brain. There are, however, two types of neurons in the abducens nucleus. One type is a lower motor neuron that innervates the lateral rectus Eye Movements and Sensory Motor Integration 459 Movement of eye 5 ms Medial Firing of abducens neuron Medial Neuron in abducens nucleus Lateral Lateral rectus muscle Lateral Time Record Figure 19.6 Motor neuron activity in relation to saccadic eye movements. The experimental setup is shown on the right. In this example, an abducens lower motor neuron fires a burst of activity (upper trace) that precedes and extends throughout the movement (solid line). An increase in the tonic level of firing is associated with more lateral displacement of the eye. Note also the decline in firing rate during a saccade in the opposite direction. (After Fuchs and Luschei, 1970.) 460 Chapter Nineteen Figure 19.7 Simplified diagram of syn-aptic circuitry responsible for horizontal movements of the eyes to the right. Acti-vation of local circuit neurons in the right horizontal gaze center (the PPRF; orange) leads to increased activity of lower motor neurons (red and green) and internuclear neurons (blue) in the right abducens nucleus. The lower motor neurons innervate the lateral rec-tus muscle of the right eye. The inter-nuclear neurons innervate lower motor neurons in the contralateral oculomotor nucleus, which in turn innervate the medial rectus muscle of the left eye. muscle on the same side. The other type, called internuclear neurons, send their axons across the midline and ascend in a fiber tract called the medial longitudinal fasciculus, terminating in the portion of the oculomotor nucleus that contains lower motor neurons innervating the medial rectus muscle. As a result of this arrangement, activation of PPRF neurons on the right side of the brainstem causes horizontal movements of both eyes to the right; the converse is of course true for the PPRF neurons in the left half of the brainstem. Neurons in the PPRF also send axons to the medullary reticular forma-tion, where they contact inhibitory local circuit neurons. These local circuit neurons, in turn, project to the contralateral abducens nucleus, where they terminate on lower motor neurons and internuclear neurons. In conse-quence, activation of neurons in the PPRF on the right results in a reduction in the activity of the lower motor neurons whose muscles would oppose movements of the eyes to the right. This inhibition of antagonists resembles the strategy used by local circuit neurons in the spinal cord to control limb muscle antagonists (see Chapter 15). Although saccades can occur in complete darkness, they are often elicited when something attracts attention and the observer directs the foveas toward the stimulus. How then is sensory information about the location of a target in space transformed into an appropriate pattern of activity in the horizontal and vertical gaze centers? Two structures that project to the gaze centers are demonstrably important for the initiation and accurate targeting of saccadic eye movements: the superior colliculus of the midbrain, and a region of the frontal lobe that lies just rostral to premotor cortex, known as Left eye Right eye Lateral rectus Medial rectus Medial longitudinal fasciculus Left oculomotor nucleus Right abducens nucleus Midbrain Pons Right PPRF the frontal eye field (Brodmann’s area 8). Upper motor neurons in both of these structures, each of which contains a topographical motor map, dis-charge immediately prior to saccades. Thus, activation of a particular site in the superior colliculus or in the frontal eye field produces saccadic eye movements in a specified direction and for a specified distance that is inde-pendent of the initial position of the eyes in the orbit. The direction and dis-tance are always the same for a given stimulation site, changing systemati-cally when different sites are activated. Both the superior colliculus and the frontal eye field also contain cells that respond to visual stimuli; however, the relation between the sensory and motor responses of individual cells is better understood for the superior col-liculus. An orderly map of visual space is established by the termination of retinal axons within the superior colliculus (see Chapter 11), and this sensory map is in register with the motor map that generates eye movements. Thus, neurons in a particular region of the superior colliculus are activated by the presentation of visual stimuli in a limited region of visual space. This activa-tion leads to the generation of a saccade that moves the eye by an amount just sufficient to align the foveas with the region of visual space that pro-vided the stimulation (Figure 19.8). Neurons in the superior colliculus also respond to auditory and somatic stimuli. Indeed, the location in space for these other modalities also is mapped in register with the motor map in the colliculus. Topographically organized maps of auditory space and of the body surface in the superior colliculus can therefore orient the eyes (and the head) in response to a vari-ety of different sensory stimuli. This registration of the sensory and motor maps in the colliculus illustrates an important principle of topographical maps in the motor system, namely to provide an efficient mechanism for sensory motor transformations (Box B). Eye Movements and Sensory Motor Integration 461 5° 5° −40° −40° 0° 0° 40° (B) Visual space Left visual field Right visual field (A) Superior colliculus 20° 10° 0° −10° −20° 30° Lateral Rostral Caudal Left Right Medial Lateral 20° 10° 10° 0° 20° 30° 1 1 2 2 3 3 4 4 5 5 6 7 8 8 7 6 20° 20° Visual receptive fields Eye movements induced by stimulating indicated sites in (A) Figure 19.8 Evidence for sensory motor transformation obtained from electrical recording and stimulation in the superior colliculus. (A) Surface views of the supe-rior colliculus illustrating the location of eight separate electrode recording and stim-ulation sites. (B) Map of visual space showing the receptive field location of the sites in (A) (white circles), and the amplitude and direction of the eye movements elicited by stimulating these sites electrically (arrows). In each case, electrical stimulation results in eye movements that align the fovea with a region of visual space that cor-responds to the visual receptive field of the site. (After Schiller and Stryker, 1972.) 462 Chapter Nineteen The functional relationship between the frontal eye field and the superior colliculus in controlling eye movements is similar to that between the motor cortex and the red nucleus in the control of limb movements (see Chapter 16). The frontal eye field projects to the superior colliculus, and the superior colliculus projects to the PPRF on the contralateral side (Figure 19.9). (It also projects to the vertical gaze center, but for simplicity the discussion here is Box B Sensory Motor Integration in the Superior Colliculus The superior colliculus is a laminated structure in which the differences between the layers provide clues about how sensory and motor maps interact to produce appropriate movements. As discussed in the text, the superficial or “visual” layer of the colliculus receives input from retinal axons that form a topographic map. Thus, each site in the superficial layer is activated maximally by the presence of a stimulus at a partic-ular point of visual space. In contrast, neurons in the deeper or “motor” layers generate bursts of action potentials that command saccades, effectively generat-ing a motor map; thus, activation of dif-ferent sites generates saccades having different vectors. The visual and motor maps are in register, so that visual cells responding to a stimulus in a specific region of visual space are located directly above the motor cells that com-mand eye movements toward that same region (see Figure 19.8). The registration of the visual and motor maps suggests a simple strategy for how the eyes might be guided toward an object of interest in the visual field. When an object appears at a par-ticular location in the visual field, it will activate neurons in the corresponding part of the visual map. As a result, bursts of action potentials are generated by the subjacent motor cells to com-mand a saccade that rotates the two eyes just the right amount to direct the foveas toward that same location in the visual field. This behavior is called “visual grasp” because successful sen-sory motor integration results in the accurate foveation of a visual target. This seemingly simple model, for-mulated in the early 1970s when the col-licular maps were first found, assumes point to point connections between the visual and motor maps. In practice, however, these connections have been difficult to demonstrate. Neither the anatomical nor the physiological meth-ods available at the time were suffi-ciently precise to establish these postu-lated synaptic connections. At about the same time, motor neurons were found to command saccades to nonvisual stimuli; moreover, spontaneous sac-cades occur in the dark. Thus, it was clear that visual layer activity is not always necessary for saccades. To con-fuse matters further, animals could be trained not to make a saccade when an object appeared in the visual field, showing that the activation of visual neurons is sometimes insufficient to command saccades. The fact that activ-ity of neurons in the visual map is nei-ther necessary nor sufficient for eliciting saccades led investigators away from the simple model of direct connections between corresponding regions of the two maps, toward models that linked the layers indirectly through pathways that detoured through the cortex. Eventually, however, new and better methods resolved this uncertainty. Techniques for filling single cells with axonal tracers showed an overlap be-tween descending visual layer axons and ascending motor layer dendrites, in accord with direct anatomical connec-tions between corresponding regions of the maps. At the same time, in vitro whole-cell patch clamp recording (see Box A in Chapter 4) permitted more dis-criminating functional studies that dis-tinguished excitatory and inhibitory inputs to the motor cells. These experi-ments showed that the visual and motor layers do indeed have the func-tional connections required to initiate the command for a visually guided sac-cadic eye movement. A single brief elec-trical stimulus delivered to the superfi-cial layer generates a prolonged burst of action potentials that resembles the command bursts that normally occur just before a saccade (see figure). These direct connections presumably provide the substrate for the very short latency reflex-like “express saccades” that are unaffected by destruction of the frontal eye fields. Other visual and non-visual inputs to the deep layers proba-bly explain why activation of the retina is neither necessary nor sufficient for the production of saccades. References LEE, P. H., M. C. HELMS, G. J. AUGUSTINE AND W. C. HALL (1997) Role of intrinsic synaptic circuitry in collicular sensorimotor integra-tion. Proc. Natl. Acad. Sci. USA 94: 13299–13304. limited to the PPRF.) The frontal eye field can thus control eye movements by activating selected populations of superior colliculus neurons. This corti-cal area also projects directly to the contralateral PPRF; as a result, the frontal eye field can also control eye movements independently of the superior col-liculus. The parallel inputs to the PPRF from the frontal eye field and supe-rior colliculus are reflected in the deficits that result from damage to these Eye Movements and Sensory Motor Integration 463 OZEN, G., G. J. AUGUSTINE AND W. C. HALL (2000) Contribution of superficial layer neu-rons to premotor bursts in the superior col-liculus. J. Neurophysiol. 84: 460–471. SCHILLER, P. H. AND M. STRYKER (1972) Sin-gle-unit recording and stimulation in supe-rior colliculus of the alert rhesus monkey. J. Neurophysiol. 35: 915–924. SPARKS, D. L. AND J. S. NELSON (1987) Sen-sory and motor maps in the mammalian superior colliculus. TINS 10: 312–317. WURTZ, R. H. AND J. E. ALBANO (1980) Visual-motor function of the primate supe-rior colliculus. Annu. Rev. Neurosci. 3: 189–226. Time (ms) Record Stimulate Retina Visual layer Superior colliculus Motor layer Other inputs Gaze center Saccade (A) (B) (C) Target position Eye position Visual cell Motor cell Current (pA) Membrane potential (mV) Time (ms) −20 −40 0 0 20 40 −100 −200 100 200 EPSCs Action potentials 0 200 400 600 Saccade Visual cell axon Visual cell dendrites Motor cell dendrites (A) The superior colliculus receives visual input from the retina and sends a command signal to the gaze centers to initiate a sac-cade (see text). In the experiment illustrated here, a stimulating electrode activates cells in the visual layer and a patch clamp pipette records the response evoked in a neuron in the subjacent motor layer. The cells in the visual and motor layers were subsequently labeled with a tracer called biocytin. This experiment demonstrates that the terminals of the visual neuron are located in the same region as the dendrites of the motor neuron. (B) The onset of a target in the visual field (top trace) is followed after a short interval by a saccade to foveate the target (second trace). In the superior colliculus, the visual cell responds shortly after the onset of the target, while the motor cell responds later, just before the onset of the saccade. (C) Bursts of excitatory postsynaptic currents (EPSCs) recorded from a motor layer neuron in response to a brief (0.5 ms) current stimu-lus applied via a steel wire electrode in the visual layer (top; see arrow). These synaptic currents generate bursts of action potentials in the same cell (bottom). (B after Wurtz and Albano, 1980; C after Ozen et al., 2000.) 464 Chapter Nineteen Figure 19.9 The relationship of the frontal eye field in the right cerebral hemisphere (Brodmann’s area 8) to the superior colliculus and the horizontal gaze center (PPRF). There are two routes by which the frontal eye field can influ-ence eye movements in humans: indi-rectly by projections to the superior col-liculus, which in turn projects to the contralateral PPRF, and directly by pro-jections to the contralateral PPRF. structures. Injury to the frontal eye field results in an inability to make sac-cades to the contralateral side and a deviation of the eyes to the side of the lesion. These effects are transient, however; in monkeys with experimentally induced lesions of this cortical region, recovery is virtually complete in two to four weeks. Lesions of the superior colliculus change the accuracy, fre-quency, and velocity of saccades; yet saccades still occur, and the deficits also improve with time. These results suggest that the frontal eye fields and the superior colliculus provide complementary pathways for the control of sac-cades. Moreover, one of these structures appears to be able to compensate (at least partially) for the loss of the other. In support of this interpretation, com-bined lesions of the frontal eye field and the superior colliculus produce a dramatic and permanent loss in the ability to make saccadic eye movements. These observations do not, however, imply that the frontal eye fields and the superior colliculus have the same functions. Superior colliculus lesions Cerebrum Superior colliculus PPRF (horizontal gaze center) Midbrain Pons Frontal eye field Primary motor cortex produce a permanent deficit in the ability to perform very short latency reflex-like eye movements called “express saccades.” The express saccades are evidently mediated by direct pathways to the superior colliculus from the retina or visual cortex that can access the upper motor neurons in the colliculus without extensive, and more time-consuming, processing in the frontal cortex (see Box B). In contrast, frontal eye field lesions produce per-manent deficits in the ability to make saccades that are not guided by an external target. For example, patients (or monkeys) with a lesion in the frontal eye fields cannot voluntarily direct their eyes away from a stimulus in the visual field, a type of eye movement called an “antisaccade.” Such lesions also eliminate the ability to make a saccade to the remembered loca-tion of a target that is no longer visible. Finally, the frontal eye fields are essential for systematically scanning the visual field to locate an object of interest within an array of distracting objects (see Figure 19.1). Figure 19.10 shows the responses of a frontal eye field neuron during a visual task in which a monkey was required to foveate a target located within an arrray of distracting objects. This frontal eye field Eye Movements and Sensory Motor Integration 465 Time from target (ms) 0 100 200 300 Time from target (ms) 0 100 200 300 Time from target (ms) 0 100 200 300 Response field Distractor Activity (Hz) 50 100 Target Saccade initiation Saccade initiation Saccade initiation (1) Target in response field (A) (B) (2) Target adjacent to response field (3) Target distant from response field Trials Record Frontal eye field Figure 19.10 Responses of neurons in the frontal eye fields. (A) Locus of the left frontal eye field on a lateral view of the rhesus monkey brain. (B) Activation of a frontal eye field neuron during visual search for a target. The vertical tickmarks represent action potentials, and each row of tick marks is a different trial. The graphs below show the aver-age frequency of action potentials as a function of time. The change in color from green to purple in each row indi-cates the time of onset of a saccade toward the target. In the left trace (1), the target (red square) is in the part of the visual field “seen” by the neuron, and the response to the target is similar to the response that would be generated by the neuron even if no distractors (green squares) were present (not shown). In the right trace (3), the target is far from the response field of the neu-ron. The neuron responds to the distrac-tor in its response field. However, it responds at a lower rate than it would to exactly the same stimulus if the square were not a distractor but a target for a saccade (left trace). In the middle trace (2), the response of the neuron to the distractor has been sharply reduced by the presence of the target in a neighbor-ing region of the visual field. (After Schall, 1995.) 466 Chapter Nineteen neuron discharges at different levels to the same stimulus, depending on whether the stimulus is the target of the saccade or a “distractor,” and on the location of the distractor relative to the actual target. For example, the differ-ences between the middle and the left and right traces in Figure 19.10 demonstrate that the response to the distractor is much reduced if it is located close to the target in the visual field. Results such as these suggest that lateral interactions within the frontal eye fields enhance the neuronal responses to stimuli that will be selected as saccade targets, and that such interactions suppress the responses to uninteresting and potentially distract-ing stimuli. These sorts of interactions presumably reduce the occurrence of unwanted saccades to distracting stimuli in the visual field. Neural Control of Smooth Pursuit Movements Smooth pursuit movements are also mediated by neurons in the PPRF, but are under the influence of motor control centers other than the superior col-liculus and frontal eye field. (The superior colliculus and frontal eye field are exclusively involved in the generation of saccades.) The exact route by which visual information reaches the PPRF to generate smooth pursuit movements is not known (a pathway through the cerebellum has been sug-gested). It is clear, however, that neurons in the striate and extrastriate visual areas provide sensory information that is essential for the initiation and accurate guidance of smooth pursuit movements. In monkeys, neurons in the middle temporal area (which is largely concerned with the perception of moving stimuli and a target of the magnocellular stream; see Chapter 11) respond selectively to targets moving in a specific direction. Moreover, dam-age to this area disrupts smooth pursuit movements. In humans, damage of comparable areas in the parietal and occipital lobes also results in abnormal-ities of smooth pursuit movements. Unlike the effects of lesions to the frontal eye field and the superior colliculus, the deficits are in eye movements made toward the side of the lesion. For example, a lesion of the left parieto-occipi-tal region is likely to result in an inability to track an object moving from right to left. Neural Control of Vergence Movements When a person wishes to look from one object to another object that are located at different distances from the eyes, a saccade is made that shifts the direction of gaze toward the new object, and the eyes either diverge or con-verge until the object falls on the fovea of each eye. The structures and path-ways responsible for mediating the vergence movements are not well under-stood, but appear to include several extrastriate areas in the occipital lobe (see Chapter 11). Information about the location of retinal activity is relayed through the two lateral geniculate nuclei to the cortex, where the informa-tion from the two eyes is integrated. The appropriate command to diverge or converge the eyes, which is based largely on information from the two eyes about the amount of binocular disparity (see Chapter 11), is then sent via upper motor neurons from the occipital cortex to “vergence centers” in the brainstem. One such center is a population of local circuit neurons located in the midbrain near the oculomotor nucleus. These neurons generate a burst of action potentials. The onset of the burst is the command to generate a ver-gence movement, and the frequency of the burst determines its velocity. There is a division of labor within the vergence center, so that some neurons command convergence movements while others command divergence movements. These neurons also coordinate vergence movements of the eyes with accommodation of the lens and pupillary constriction to produce the near reflex discussed in Chapter 10. Summary Despite their specialized function, the systems that control eye movements have much in common with the motor systems that govern movements of other parts of the body. Just as the spinal cord provides the basic circuitry for coordinating the actions of muscles around a joint, the reticular formation of the pons and midbrain provides the basic circuitry that mediates movements of the eyes. Descending projections from higher-order centers in the superior colliculus and the frontal eye field innervate the brainstem gaze centers, pro-viding a basis for integrating eye movements with a variety of sensory infor-mation that indicates the location of objects in space. The superior colliculus and the frontal eye field are organized in a parallel as well as a hierarchical fashion, enabling one of these structures to compensate for the loss of the other. Eye movements, like other movements, are also under the control of the basal ganglia and cerebellum (see Chapters 17 and 18); this control ensures the proper initiation and successful execution of these relatively sim-ple motor behaviors, thus allowing observers to interact efficiently with the universe of things that can be seen. Eye Movements and Sensory Motor Integration 467 Additional Reading Reviews FUCHS, A. F., C. R. S. KANEKO AND C. A. SCUD-DER (1985) Brainstem control of eye move-ments. Annu. Rev. Neurosci. 8: 307–337. HIKOSAKA, O AND R. H. WURTZ (1989) The basal ganglia. In The Neurobiology of Saccadic Eye Movements: Reviews of Oculomotor Research, Volume 3. R. H. Wurtz and M. E. Goldberg (eds.). Amsterdam: Elsevier, pp. 257–281. ROBINSON, D. A. (1981) Control of eye move-ments. In Handbook of Physiology, Section 1: The Nervous System, Volume II: Motor Control, Part 2. V. B. Brooks (ed.). Bethesda, MD: American Physiological Society, pp. 1275–1319. SCHALL, J. D. (1995) Neural basis of target selection. Reviews in the Neurosciences 6: 63–85. SPARKS, D. L. AND L. E. MAYS (1990) Signal transformations required for the generation of saccadic eye movements. Annu. Rev. Neu-rosci. 13: 309–336. ZEE, D. S. AND L. M. OPTICAN (1985) Studies of adaption in human oculomotor disorders. In Adaptive Mechanisms in Gaze Control: Facts and Theories. A Berthoz and G. Melvill Jones (eds.). Amsterdam: Elsevier, pp. 165–176. Important Original Papers FUCHS, A. F. AND E. S. LUSCHEI (1970) Firing patterns of abducens neurons of alert mon-keys in relationship to horizontal eye move-ments. J. Neurophysiol. 33: 382–392. OPTICAN, L. M. AND D. A. ROBINSON (1980) Cerebellar-dependent adaptive control of pri-mate saccadic system. J. Neurophysiol. 44: 1058–1076. SCHILLER, P. H. AND M. STRYKER (1972) Single unit recording and stimulation in superior colliculus of the alert rhesus monkey. J. Neu-rophysiol. 35: 915–924. SCHILLER, P. H., S. D. TRUE AND J. L. CONWAY (1980) Deficits in eye movements following frontal eye-field and superior colliculus abla-tions. J. Neurophysiol. 44: 1175–1189. Books HALL, W. C. AND A. MOSCHOVAKIS (EDS.) (2004) The Superior Colliculus: New Approaches for Studying Sensorimotor Integration. Methods and New Frontiers in Neuroscience Series. New York: CRC Press. LEIGH, R. J. AND D. S. ZEE (1983) The Neurology of Eye Movements. Contemporary Neurology Series. Philadelphia: Davis. SCHOR, C. M. AND K. J. CIUFFREDA (EDS.) (1983) Vergence Eye Movements: Basic and Clinical Aspects. Boston: Butterworth. YARBUS, A. L. (1967) Eye Movements and Vision. Basil Haigh (trans.). New York: Plenum Press. Overview The visceral (or autonomic) motor system controls involuntary functions mediated by the activity of smooth muscle fibers, cardiac muscle fibers, and glands. The system comprises two major divisions, the sympathetic and parasympathetic subsystems (the specialized innervation of the gut provides a further semi-independent division and is usually referred to as the enteric nervous system). Although these divisions are always active at some level, the sympathetic subsystem mobilizes the body’s resources for dealing with challenges of one sort or another. Conversely, parasympathetic activity pre-dominates during states of relative quiescence, so that energy sources previ-ously expended can be restored. This continuous neural regulation of the expenditure and replenishment of the body’s resources contributes impor-tantly to the overall physiological balance of bodily functions called home-ostasis. Whereas the major controlling centers for somatic motor activity are the primary and secondary motor cortices in the frontal lobes and a variety of related subcortical nuclei, the major locus of central control in the visceral motor system is the hypothalamus and the complex (and ill-defined) cir-cuitry that it controls in the brainstem reticular formation and spinal cord. The status of both principal divisions of the visceral motor system is modu-lated by descending pathways from these centers to preganglionic neurons in the brainstem and spinal cord, which in turn determine the activity of the primary visceral motor neurons in autonomic ganglia. The autonomic regu-lation of several organ systems of particular importance in clinical practice (including cardiovascular function, control of the bladder, and the gover-nance of the reproductive organs) is considered in more detail as specific examples of visceral motor control. Early Studies of the Visceral Motor System Although humans must always have been aware of involuntary motor reac-tions to stimuli in the environment (e.g., narrowing of the pupil in response to bright light, constriction of superficial blood vessels in response to cold or fear, increased heart rate in response to exertion), it was not until the late nineteenth century that the neural control of these and other visceral func-tions came to be understood in modern terms. The researchers who first rationalized the workings of the visceral motor system were Walter Gaskell and John Langley, two British physiologists at Cambridge University. Gaskell, whose work preceded that of Langley, established the overall anatomy of the system and carried out early physiological experiments that demonstrated some of its salient functional characteristics (e.g., that the heartbeat of an experimental animal is accelerated by stimulating the out-Chapter 20 469 The Visceral Motor System 470 Chapter Twenty flow of the upper thoracic spinal cord segments). Based on these and other observations, Gaskell concluded in 1866 that “every tissue is innervated by two sets of nerve fibers of opposite characters,” and he further surmised that these actions showed “the characteristic signs of opposite chemical processes.” Using similar electrical stimulation techniques in experimental animals, Langley went on to establish the function of autonomic ganglia (which har-bor the primary visceral motor neurons), defined the terms “preganglionic” and “postganglionic” (see below), and coined the phrase autonomic nervous system (which is commonly used as a synonym for “visceral motor system,” although certain somatic motor activities may also be considered “auto-nomic”; see Chapter 28). Langley’s work on the pharmacology of the auto-nomic system initiated the classical studies indicating the roles of acetyl-choline and the catecholamines in visceral motor function, and in neurotransmitter function more generally (see Chapter 6). In short, Langley’s ingenious physiological and anatomical experiments established in detail the general proposition put forward by Gaskell on circumstantial grounds. The third major figure in the pioneering studies of the visceral motor sys-tem was Walter Cannon at Harvard Medical School, who during the early to mid-1900s devoted his career to understanding visceral motor functions in relation to homeostatic mechanisms generally, and to the emotions and higher brain functions in particular (see Chapter 28). Like Gaskell and Lang-ley before him, this work was based primarily on electrical stimulation in experimental animals, but included activation of brainstem and other brain regions as well as the peripheral components of the system. He also estab-lished the effects of denervation in the visceral motor system, laying some of the basis for much further work on what is now referred to as “neuronal plasticity” (see Chapter 24). Distinctive Features of the Visceral Motor System Chapters 15 and 16 discussed in detail the organization of lower motor neu-rons in the central nervous system, their relationships to striated muscle fibers, and the means by which their activities are governed by higher motor centers. With respect to the efferent systems that govern the actions of smooth muscle fibers, cardiac muscle fibers, and glands, it is instructive to recognize the anatomical and functional features of the visceral motor sys-tem that distinguish it from the somatic motor system. First, although it is useful to recognize medial (postural control) and lat-eral (distal extremity control) components of the somatic motor system (see Chapters 15 and 16), the anatomical and functional distinctions that justify this division of the somatic motor system are not nearly so great as they are for the three subsystems that comprise the visceral motor system. Second, the lower motor neurons of the visceral motor system are located outside of the central nervous system; the cell bodies of primary visceral motor neurons are found in autonomic ganglia that are either close to the spinal cord (sympathetic division) or embedded in a neural plexus (plexus means “network”) very near or in the target organ (parasympathetic and enteric divisions). Third, the contacts between visceral motor neurons and target tissues are much less differentiated than the neuromuscular junctions of the somatic motor system. Visceral motor axons tend to be highly branched and give rise to many synaptic terminals at varicosities (swellings) along the length of the terminal axonal branch. Moreover, the surfaces of the target tissue usually lack the highly ordered structure of the motor endplates that characterizes postsynaptic target sites on striated muscle fibers. As a consequence, the neurotransmitters released by visceral motor terminals often diffuse for hun-dreds of microns before binding to postsynaptic receptors—a far greater dis-tance than at the synaptic cleft of the somatic neuromuscular junction. Fourth, visceral motor terminals release a variety of neurotransmitters, including primary small-molecule neurotransmitters (which differ depend-ing on whether the motor neuron in question is sympathetic or parasympa-thetic), and one or more of a variety of co-neurotransmitters that may be a different small-molecule type or a neuropeptide (see Chapter 6). These neu-rotransmitters in turn interact with a diverse set of postsynaptic receptors that mediate a myriad of postsynaptic effects in the target tissues. It should be clear, then, that while the major effect of somatic motor activation on stri-ated muscle is nearly the same throughout the body, the effects of visceral motor activation are remarkably varied. This fact should come as no sur-prise, given the challenge of maintaining homeostasis across the many organ systems of the body in the face of variable environmental conditions and dynamic behavioral contingencies. Finally, whereas the principal actions of the somatic motor system are governed by motor cortical areas in the posterior frontal lobe (discussed in Chapter 16), the activities of the visceral motor system are coordinated by a distributed set of cortical and subcortical structures in the ventral and medial parts of the forebrain; collectively, these structures comprise a central autonomic network. In the remaining sections of this chapter, the sympathetic and parasympa-thetic divisions and the enteric nervous system are separately considered. General principles of visceral motor control and the central and reflexive coordination of visceral motor and somatic motor activity are illustrated in more detail later in the chapter, in a discussion of specific autonomic reflexes related to cardiovascular control, urination, and sexual functioning. The Sympathetic Division of the Visceral Motor System Activity of the neurons that make up the sympathetic division of the visceral motor system ultimately prepares individuals for “flight or fight,” as Can-non famously put it. Cannon meant that, in extreme circumstances, height-ened levels of sympathetic neural activity allow the body to make maximum use of its resources (particularly its metabolic resources), thereby increasing the chances of survival or success in threatening or otherwise challenging situations. Thus, during high levels of sympathetic activity, the pupils dilate and the eyelids retract (allowing more light to reach the retina and the eyes to move more efficiently); the blood vessels of the skin and gut constrict (rerouting blood to muscles, thus allowing them to extract a maximum of available energy); the hairs stand on end (making our hairier ancestors look more fearsome); the bronchi dilate (increasing oxygenation); the heart rate accelerates and the force of cardiac contraction is enhanced (maximally per-fusing skeletal muscles and the brain); and digestive and other vegetative functions become quiescent (thus diminishing activities that are temporarily inappropriate) (Figure 20.1). At the same time, sympathetic activity stimu-lates the adrenal medulla to release epinephrine and norepinephrine into the bloodstream and mediates the release of glucagon and insulin from the pan-creas, further enhancing energy mobilizing (or catabolic) functions. The neurons in the central nervous system that drive these effects are located in the spinal cord. They are arranged in a column of preganglionic The Visceral Motor System 471 472 Chapter Twenty Figure 20.1 Overview of the sympathetic (left side of the figure) and parasympa-thetic (right side of the figure) divisions of the visceral motor system. Sympathetic division Parasympathetic division Inhibits salivation Stimulates salivation Relaxes airways Constricts airways Parasympathetic ganglia Sympathetic ganglia Accelerates heartbeat Slows heartbeat Stimulates secretion by sweat glands Stimulates gall- bladder to release bile Stimulates digestion Stomach Gallbladder Dilates blood vessels in intestines and rectum Stimulates urinary bladder to contract Stimulates penile erection Cervical Superior cervical ganglion Thoracic Lumbar Sacral Cranial Cranial Liver Pancreas Dilates pupil Constricts blood vessels Noradrenergic neurons Postganglionic Postganglionic Cholinergic neurons Preganglionic Celiac ganglion Cervical Thoracic Lumbar Sacral Stellate ganglion Inhibits digestion Stimulates glucose production and release Stimulates secretion of epinephrine and norepinephrine from adrenal gland Stimulates ejaculation Relaxes urinary bladder Inferior mesenteric ganglion Superior mesenteric ganglion To lower extremities via spinal nerves Ciliary ganglion Stimulates release of insulin and glucagon Figure 20.2 Organization of the pre-ganglionic spinal outflow to sympa-thetic ganglia. (A) General organization of the sympathetic division of the vis-ceral motor system in the spinal cord and the preganglionic outflow to the sympathetic ganglia that contain the primary visceral motor neurons. (B) Cross section of thoracic spinal cord at the level indicated, showing location of the sympathetic preganglionic neurons in the intermediolateral cell column of the lateral horn. neurons that extends from the uppermost thoracic to the upper lumbar seg-ments (T1 to L2 or L3; Table 20.1) in a region of the spinal cord gray matter called the intermediolateral column or lateral horn (Figure 20.2). The pre-ganglionic neurons that control sympathetic outflow to the organs in the The Visceral Motor System 473 Spinal cord C1 T1 L1 S1 Coc1 Sympathetic trunk Sympathetic chain ganglion Peripheral nerve To blood vessels and skin To viscera Gray communicating ramus White communicating ramus Prevertebral ganglion Dorsal root ganglion Lateral horn Lateral horn Intermediolateral cell column Intermediolateral cell column T1−L3 Dorsal horn Intermediate gray zone Ventral horn Visceral efferent fibers Thoracic spinal cord (A) (B) 474 Chapter Twenty Eye Lacrimal gland Submandibular and sublingual glands Parotid gland Head, neck (blood vessels, sweat glands, piloerector muscles) Upper extremity Heart Bronchi, lungs Stomach Pancreas Ascending small intestine, transverse large intestine Descending large intestine, sigmoid, rectum Adrenal gland Ureter, bladder Lower extremity Upper thoracic spinal cord (C8–T7) T3–T6 Middle thoracic spinal cord (T1–T5) Lower thoracic spinal cord (T6–T10) T9–L2 T11–L2 T10–L2 Superior cervical ganglion Stellate and upper thoracic ganglia Superior cervical and upper thoracic ganglia Upper thoracic ganglia Celiac ganglion Celiac ganglion Celiac, superior, and inferior mesenteric ganglia Inferior mesenteric hypogastric, and pelvic plexus Cells of gland are modified neurons Hypogastric and pelvic plexus Lower lumbar and upper sacral ganglia Pupillary dilation Tearing Vasoconstriction Vasoconstriction Sweat secretion, vasocon-striction, piloerection Sweat secretion, vasocon-striction, piloerection Increased heart rate and stroke volume, dilation of coronary arteries Vasodilation, bronchial dilation Inhibition of peristaltic move-ment and gastric secretion, vasoconstriction Vasoconstriction, insulin secretion Inhibition of peristaltic movement and secretion Inhibition of peristaltic movement and secretion Catecholamine secretion Relaxation of bladder wall muscle and contraction of internal sphincter Sweat secretion, vasocon-striction, piloerection Sympathetic Division Target organ Location of preganglionic Location of ganglionic Actions neurons neurons TABLE 20.1 Summary of the Major Functions of the Visceral Motor System The Visceral Motor System 475 Eye Lacrimal gland Submandibular and sublingual glands Parotid gland Head, neck (blood vessels, sweat glands, piloerector muscles) Upper extremity Heart Bronchi, lungs Stomach Pancreas Ascending small intestine, transverse large intestine Descending large intestine, sigmoid, rectum Adrenal gland Ureter, bladder Lower extremity Edinger-Westphal nucleus Superior salivatory nucleus Superior salivatory nucleus Inferior salivatory nucleus None None Nucleus ambiguus Dorsal motor nucleus of the vagus nerve Dorsal motor nucleus of the vagus nerve Dorsal motor nucleus of the vagus nerve Dorsal motor nucleus of the vagus nerve Dorsal motor nucleus of the vagus nerve S3–S4 None S2–S4 None Ciliary ganglion Pterygopalatine ganglion Submandibular ganglion Otic ganglion None None Cardiac plexus Pulmonary plexus Myenteric and submucosal plexus Pancreatic plexus Ganglia in the myenteric and submucosal plexus Ganglia in the myenteric and submucosal plexus None Pelvic plexus None Secretion of tears Secretion of saliva, vasodilation Secretion of saliva, vasodilation None None Reduced heart rate Bronchial constriction and secretion Peristaltic movement and secretion Secretion of digestive enzymes Peristaltic movement and secretion Peristaltic movement and secretion None Contraction of bladder wall and inhibition of internal sphincter None Parasympathetic Division Target organ Location of preganglionic Location of ganglionic Actions neurons neurons Pupillary constriction, accommodation TABLE 20.1 Summary of the Major Functions of the Visceral Motor System (continued) 476 Chapter Twenty head and thorax are in the lowest cervical segment and the upper and mid-dle thoracic segments, whereas those that control the abdominal and pelvic organs and targets in the lower extremities are in the lower thoracic and upper lumbar segments. The axons that arise from these spinal pregan-glionic neurons typically extend only a short distance, terminating in a series of paravertebral or sympathetic chain ganglia, which, as the name implies, are arranged in a chain that extends along most of the length of the vertebral column (see Figure 20.1). These preganglionic pathways to the ganglia are known as the white communicating rami because of the relatively light color imparted to the rami by the myelinated axons they contain (see Figure 20.2A). Roughly speaking, these preganglionic spinal neurons are compara-ble to somatic motor interneurons (see Chapter 15). The neurons in sympathetic ganglia are the primary or lower motor neu-rons of the sympathetic division in that they directly innervate smooth mus-cles, cardiac muscle, and glands. The postganglionic axons arising from these paravertebral sympathetic chain neurons travel to various targets in the body wall, joining the segmental spinal nerves of the corresponding spinal segments by way of the gray communicating rami. These rami are another set of short linking nerves, so named because the unmyelinated postganglionic axons give them a somewhat darker appearance than the myelinated preganglionic linking nerves (see Figure 20.2A). In addition to innervating the sympathetic chain ganglia, the pregan-glionic axons that govern the viscera extend a longer distance from the spinal cord in the splanchnic nerves to reach sympathetic ganglia that lie in the chest, abdomen, and pelvis. These prevertebral ganglia include sympathetic ganglia in the cardiac plexus, the celiac ganglion, the superior and inferior mesenteric ganglia, and sympathetic ganglia in the pelvic plexus (note that ganglion is the singular form, and ganglia plural). The postganglionic axons arising from the prevertebral ganglia provide sympathetic innervation to the heart, lungs, gut, kidneys, pancreas, liver, bladder, and reproductive organs (many of these organs also receive some postganglionic innervation from neurons in the sympathetic chain ganglia). Finally, a subset of thoracic pre-ganglionic fibers in the splanchnic nerves innervate the adrenal medulla, which is generally regarded as a sympathetic ganglion modified for a specific endocrine function—namely, the release of catecholamines into the circula-tion to enhance a widespread sympathetic response to stress. In summary, sympathetic axons contribute to virtually all peripheral nerves, carrying innervation to an enormous range of targets (see Table 20.1). Cannon’s memorable truism that the sympathetic activity prepares the ani-mal for “fight or flight” notwithstanding, the sympathetic division of the vis-ceral motor system is tonically active to maintain sympathetic target function at appropriate levels whatever the circumstances. Nor should the sympathetic system be thought of as responding in an all-or-none fashion; many specific sympathetic reflexes operate more or less independently, as might be expected from the obvious need to specifically control various organ func-tions (e.g., the heart during exercise, the bladder during urination, and the reproductive organs during sexual intercourse, as described in later sections). The Parasympathetic Division of the Visceral Motor System In contrast to the sympathetic division, the preganglionic outflow from the central nervous system to the ganglia of the parasympathetic division stems from neurons whose distribution is limited to the brainstem and the sacral part of the spinal cord (see Figure 20.1). The cranial preganglionic innervation arising from the brainstem, which is analogous to the preganglionic sympa-thetic outflow from the spinal cord, includes the Edinger-Westfall nucleus in the midbrain (which innervates the ciliary ganglion via the oculomotor nerve and mediates the diameter of the pupil in response to light; see Chapter 11), the superior and inferior salivatory nuclei in the pons and medulla (which innervate the salivary glands and tear glands, mediating salivary secretion and the production of tears), a visceral motor division of the nucleus ambiguus in the medulla and the dorsal motor nucleus of the vagus nerve, which is also in the medulla. The more dorsal part of the dorsal motor nucleus of the vagus nerve primarily governs glandular secretion via the parasympathetic ganglia located in the viscera of the thorax and abdomen, whereas the more ventral part of the nucleus controls the motor responses of the heart, lungs, and gut elicited by the vagus nerve (e.g., slowing of the heart rate and constricting the bronchioles). Neurons in the ventral-lateral part of the nucleus ambiguus also provide an important source of cardio-inhibitory innervation to the cardiac ganglia via the vagus nerve. In addition, other pre-ganglionic neurons in the nucleus ambiguus innervate parasympathetic gan-glia in the submandibular salivary glands and the mediastinum (a different division of the nucleus ambiguus provides branchiomotor innervation of stri-ated muscle in the pharynx and larynx). The location of the parasympathetic brainstem nuclei is shown in Figure 20.3A and B. The sacral preganglionic innervation arises from neurons in the lateral gray matter of the sacral segments of the spinal cord, which are located in much the same position as the sympathetic preganglionic neurons in the intermediolateral column of the thoracic cord (Figure 20.3C,D). The axons from these neurons travel in the splanchnic nerves to innervate parasympa-thetic ganglia in the lower third of the colon, rectum, bladder, and reproduc-tive organs. The parasympathetic ganglia innervated by preganglionic outflow from both cranial and sacral levels are in or near the end organs they serve. In this way they differ from the ganglionic targets of the sympathetic system (recall that both the paravertebral chain and prevertebral ganglia are located rela-tively far from their target organs; see Figure 20.1). An important anatomical difference between sympathetic and parasympathetic ganglia at the cellular level is that sympathetic ganglion cells tend to have extensive dendritic arbors and are, as might be expected from this arrangement, innervated by a large number of preganglionic fibers. Parasympathetic ganglion cells have few if any dendrites and consequently are each innervated by only one or a few preganglionic axons (see Box B in Chapter 22). The overall function of the parasympathetic system, as Gaskell, Langley, and later Cannon demonstrated, is generally opposite to that of the sympa-thetic system, serving to increase metabolic and other resources during peri-ods when the animal’s circumstances allow it to “rest and digest.” In con-trast to the sympathetic functions enumerated earlier, the activity of the parasympathetic system constricts the pupils, slows the heart rate, and increases the peristaltic activity of the gut. At the same time, diminished activity in the sympathetic system allows the blood vessels of the skin and gut to dilate, the piloerector muscles to relax, and the outflow of cate-cholamines from the adrenal medulla to decrease. Although most organs do (as Gaskell surmised) receive innervation from both the sympathetic and parasympathetic divisions of the visceral motor system, some receive only sympathetic innervation. These exceptional tar-gets include the sweat glands, the adrenal medulla, the piloerector muscles of the skin, and most arterial blood vessels (see Table 20.1). The Visceral Motor System 477 478 Chapter Twenty Parasympathetic preganglionic axon Parasympathetic postganglionic axon To viscera Dorsal root ganglion Visceral efferent axons Sacral spinal cord (C) Pelvic splanchnic nerve Spinal cord C1 T1 L1 S1 Coc1 Dorsal horn Intermediate gray zone Ventral horn (D) Parasympathetic preganglionic neurons (S1−S5) Oculomotor nerve (III) Edinger-Westphal nucleus Salivatory nuclei Facial nerve (VII) and glossopharyngeal nerve (IX) Vagus nerve (X) Middle medulla Upper medulla Midbrain (A) (B) Dorsal motor nucleus of vagus Dorsal motor nucleus of vagus Nucleus ambiguus Nucleus ambiguus Salivatory nuclei Edinger-Westphal nucleus Figure 20.3 Organization of the preganglionic outflow to parasympathetic gan-glia. (A) Dorsal view of brainstem showing the location of the nuclei of the cranial part of the parasympathetic division of the visceral motor system. (B) Cross section of the brainstem at the relevant levels [indicated by horizontal lines in (A)] showing location of these parasympathetic nuclei. (C) Main features of the parasympathetic preganglionics in the sacral segments of the spinal cord. (D) Cross section of the sacral spinal cord showing location of sacral preganglionic neurons. Figure 20.4 Organization of the enteric component of the visceral motor system. (A) Sympathetic and parasym-pathetic innervation of the enteric ner-vous system, and the intrinsic neurons of the gut. (B) Detailed organization of nerve cell plexuses in the gut wall. The neurons of the submucus plexus (Meiss-ner’s plexus) are concerned with the secretory aspects of gut function, and the myenteric plexus (Auerbach’s plexus) with the motor aspects of gut function (e.g., peristalsis). The Enteric Nervous System An enormous number of neurons are specifically associated with the gas-trointestinal tract to control its many functions; indeed, more neurons are said to reside in the human gut than in the entire spinal cord. As already noted, the activity of the gut is modulated by both the sympathetic and the parasympathetic divisions of the visceral motor system. However, the gut also has an extensive system of nerve cells in its wall (as do its accessory organs such as the pancreas and gallbladder) that do not fit neatly into the sympathetic or parasympathetic divisions of the visceral motor system (Fig-ure 20.4A). To a surprising degree, these neurons and the complex enteric The Visceral Motor System 479 Preganglionic sympathetic axon Postganglionic sympathetic axon Vagus nerve (X) Postganglionic parasympathetic neuron Prevertebral ganglion Submucus (Meissner’s) plexus Myenteric (Auerbach’s) plexus Mucosa Longitudinal muscle layer Circular muscle layer (A) (B) Gastrointestinal tract Intrinsic neurons of gut plexuses Dorsal motor nucleus of vagus 480 Chapter Twenty plexuses in which they are found operate more or less independently according to their own reflex rules; as a result, many gut functions continue perfectly well without sympathetic or parasympathetic supervision (peri-stalsis, for example, occurs in isolated gut segments in vitro). Thus, most investigators prefer to classify the enteric nervous system as a separate com-ponent of the visceral motor system. The neurons in the gut wall include local and centrally projecting sensory neurons that monitor mechanical and chemical conditions in the gut, local circuit neurons that integrate this information, and motor neurons that influ-ence the activity of the smooth muscles in the wall of the gut and glandular secretions (e.g., of digestive enzymes, mucus, stomach acid, and bile). This complex arrangement of nerve cells intrinsic to the gut is organized into (1) the myenteric (or Auerbach’s) plexus, which is specifically concerned with regulating the musculature of the gut; and (2) the submucus (or Meissner’s) plexus, which is located, as the name implies, just beneath the mucus mem-branes of the gut and is concerned with chemical monitoring and glandular secretion (Figure 20.4B). As already mentioned, the preganglionic parasympathetic neurons that influence the gut are primarily in the dorsal motor nucleus of vagus nerve in the brainstem and the intermediate gray zone in the sacral spinal cord seg-ments. The preganglionic sympathetic innervation that modulates the action of the gut plexuses derives from the thoraco-lumbar cord, primarily by way of the celiac, superior, and inferior mesenteric ganglia. Sensory Components of the Visceral Motor System Although the focus of this unit is “movement and its central control,” it is also important to understand the sources of visceral sensory information and the means by which this input becomes intergrated in the central ner-vous system. Generally speaking, afferent activity arising from the viscera serves two important functions: (1) it provides feedback input to local reflexes that modulate moment-to-moment visceral motor activity within individual organs; and (2) it serves to inform higher integrative centers of more complex patterns of stimulation that may signal potentially threaten-ing conditions and/or require the coordination of more widespread visceral motor, somatic motor, neuroendocrine, and behavioral activities (Figure 20.5). The nucleus of the solitary tract in the medulla is the central structure in the brain that receives visceral sensory information and distributes it accordingly to serve both purposes. The afferent fibers that provide this visceral sensory input arise from cell bodies that lie in the dorsal root ganglia (as is the case of somatic sensory modalities; see Chapters 8 and 9) and the sensory ganglia associated with the glossopharyngeal and vagus cranial nerves. However, there are far fewer visceral sensory neurons (by a factor of about 10) in comparison to mechanosensory neurons that innervate the skin and deeper somatic struc-tures. This relative sparseness of peripheral visceral sensory innervation accounts in part for why most visceral sensations are diffuse and difficult to localize precisely. The spinal visceral sensory neurons in the dorsal root ganglia send axons peripherally, through symapthetic nerves, ending in sensory receptor spe-cializations such as nerve endings that are sensitive to pressure or stretch (in the walls of the heart, bladder, and gastrointestinal tract); endings that inner-vate specialized chemosensitive cells (oxygen-sensitive cells in the carotid bodies); or nociceptive endings that respond to damaging stretch, ischemia, Figure 20.5 Distribution of visceral sensory information by the nucleus of the solitary tract to serve either local reflex responses or more complex hor-monal and behavioral responses via integration within a central autonomic network. As illustrated in Figure 20.7, forebrain centers also provide input to visceral motor effector systems in the brainstem and spinal cord. or the presence of irritating chemicals. The central axonal processes of these dorsal root ganglion neurons terminate on second-order neurons and local interneurons in the dorsal horn and on intermediate gray regions of the spinal cord. Some primary visceral sensory axons terminate near the lateral horn, where the preganglionic neurons of sympathetic and parasympathetic divisions are located; these terminals mediate visceral reflex activity in a manner not unlike the segmental somatic motor reflexes described in Chap-ter 15. In the dorsal horn, many of the second-order neurons that receive visceral sensory inputs are actually neurons of the anterolateral system, which also receive nociceptive and/or crude mechanosensory input from more superfi-cial sources (see Chapter 9). As described in Box A of Chapter 9, this is one means by which painful visceral sensations may be “referred” to more superficial somatic territories. Axons of these second-order visceral sensory neurons travel rostrally in the ventrolateral white matter of the spinal cord and the lateral sector of the brainstem and eventually reach the ventral pos-terior complex of the thalamus. However, the axons of other second-order visceral sensory neurons terminate before reaching the thalamus; the princi-pal target of these axons is the nucleus of the solitary tract (Figure 20.6). Other brainstem targets of second-order visceral sensory axons are visceral motor centers in the medullary reticular formation (see Box A in Chapter 16). In the last decade, it has become clear that visceral sensory information, especially axons related to painful visceral sensations, also ascends the cen-tral nervous system by another spinal pathway. Second-order neurons whose cell bodies are located near the central canal of the spinal cord send their axons through the dorsal columns to terminate in the dorsal column The Visceral Motor System 481 Preganglionic neurons Hormonal and behavioral response Medial and ventral forebrain Central integration Reflex activity Visceral motor response Nucleus of the solitary tract Visceral sensory input 482 Chapter Twenty Figure 20.6 Organization of sensory input to the visceral motor system. Afferent input from the cranial nerves relevant to visceral sensation (as well as afferent input ascending from the spinal cord not shown here) converge on the caudal division of the nucleus of the solitary tract (the rostral division is a gustatory relay; see Chapter 14). nuclei, where third-order neurons relay visceral nociceptive signals to the ventral posterior thalamus. Although the existence of this visceral pain path-way in the dorsal columns complicates the simplistic view of the dorsal col-umn–medial lemniscal pathway as a discriminitive mechanosensory projec-tion and the anterolateral system as a pain pathway, mounting empirical and clinical evidence highlights the importance of this newly discovered dorsal column pain pathway in the central transmission of visceral nociception (see Box B in Chapter 9). In addition to these spinal visceral afferents, general visceral sensory inputs from thoracic and upper abdominal organs, as well as from viscera in the head and neck, enter the brainstem directly via the glossopharyngeal and vagus cranial nerves (see Figure 20.6). These glossopharyngeal and vagal visceral afferents also terminate in the nucleus of the solitary tract. This nucleus, as described in the next section, integrates a wide range of vis-ceral sensory information and transmits this information directly (and indi-rectly) to relevant visceral motor nuclei, the brainstem reticular formation, as well as several key regions in the medial and ventral forebrain that coordi-nate visceral motor activity (see Figure 20.5). Finally, unlike the somatic sensory system (where virtually all sensory signals gain access to conscious neural processing), sensory fibers related to the viscera convey only limited information to consciousness. For example, most of us are completely unaware of the subtle changes in peripheral vas-cular resistance that raise or lower our mean arterial blood pressure, yet such covert visceral afferent information is essential for the functioning of auto-nomic reflexes and the maintenance of homeostasis. Typically, it is only painful visceral sensations and signals that are integrated into emotional experience and expression (see Chapter 28) that enter conscious awareness. Nucleus of the solitary tract, rostral gustatory division Nucleus of the solitary tract, caudal visceral sensory division Vagus nerve (X) Glossopharyngeal nerve (IX) Visceral afferents Second order visceral afferents Figure 20.7 A central autonomic net-work for the control of visceral motor function. Overview of connections within the central autonomic network. The distribution of visceral sensory information within this network is illus-trated on the right side of the figure and the generation of visceral motor com-mands is shown on the left. However, extensive interconnections among auto-nomic centers in the forebrain (between the amygdala and associated cortical regions or hypothalamus, for example) militate against a strict parsing of this network into afferent and efferent limbs. The hypothalamus is a key structure in this network that integrates visceral sen-sory input and higher order visceral motor signals (see Box A). Central Control of Visceral Motor Functions The nucleus of the solitary tract—and in particular, the caudal part of this nucleus—is a key integrative center for reflexive control of visceral motor function and an important relay of visceral sensory information to other brainstem nuclei and forebrain structures (Figure 20.7; see also Figure 20.5). The rostral part of this nucleus, as described in Chapter 14, is a gustatory relay receiving input from primary taste afferents (cranial nerves VII, IX, and X) and sending projections to the gustatory nucleus in the ventral-posterior thalamus. The caudal visceral sensory part of the nucleus of the solitary tract provides input to primary visceral motor nuclei, such as the dorsal motor nucleus of the vagus nerve and the nucleus ambiguus. It also projects to “premotor” autonomic centers in the medullary reticular formation, and to The Visceral Motor System 483 Thalamus Hypothalamus Amygdala Preganglionic neurons in brainstem and spinal cord Autonomic centers in brainstem reticular formation Insular cortex Medial prefrontal cortex Primary motor neurons in autonomic ganglia Spinal visceral sensory neurons; Cranial nerves IX and X Nucleus of the solitary tract End organs (smooth muscle, cardiac muscle, and glands) Parabrachial nucleus 484 Chapter Twenty Box A The Hypothalamus The hypothalamus is located at the base of the forebrain, bounded by the optic chiasm rostrally and the midbrain tegmentum caudally. It forms the floor and ventral walls of the third ventricle and is continuous through the infundi-bular stalk with the posterior pituitary gland, as illustrated in Figure A. Given its central position in the brain and its proximity to the pituitary, it is not sur-prising that the hypothalamus integrates information from the forebrain, brain-stem, spinal cord, and various intrinsic chemosensitive neurons. What is surprising about this struc-ture is the remarkable diversity of home-ostatic functions that are governed by this relatively small region of the fore-brain. The diverse functions in which hypothalamic involvement is at least partially understood include: the control of blood flow (by promoting adjustments in cardiac output, vasomotor tone, blood osmolarity, and renal clearance, and by motivating drinking and salt consump-tion); the regulation of energy metabolism (by monitoring blood glucose levels and regulating feeding behavior, digestive functions, metabolic rate, and tempera-ture); the regulation of reproductive activity (by influencing gender identity, sexual orientation and mating behavior and, in females, by governing menstrual cycles, pregnancy, and lactation); and the coordi-nation of responses to threatening conditions (by governing the release of stress hor-mones, modulating the balance between sympathetic and parasympathetic tone, and influencing the regional distribution of blood flow). Despite the impressive scope of hypo-thalamic control, the individual compo-nents of the hypothalamus utilize similar physiological mechanisms to exert their influence over these many functions (Fig-ure B). Thus, hypothalamic circuits receive sensory and contextual information, com-pare that information with biological set Hypothalamus Hypothalamus (Compares input to biological set points) Contextual information (Cerebral cortex, amygdala, hippocampal formation) Sensory inputs (Visceral and somatic sensory pathways, chemosensory and humoral signals) Visceral motor, somatic motor, neuroendocrine, behavioral responses (B) Physiological mechanisms underlying hypothalamic function. Lateral and medial preoptic nuclei Suprachiasmatic nucleus Supraoptic nucleus Paraventricular nucleus Anterior nucleus Dorsomedial nucleus Ventromedial nucleus Arcuate nucleus Posterior area Mammillary body Anterior pituitary Posterior pituitary Tuber cinereum Optic chiasm Anterior commissure Fornix Thalamus Hypothalamic sulcus Anterior region Tuberal region Lateral-posterior region 1 2 3 4 Infundibular stalk (A) Diagram of the human hypothalamus, illustrating its major nuclei. The Visceral Motor System 485 points, and activate relevant visceral mo-tor, neuroendocrine, and somatic motor effector systems that restore homeostasis and/or elicit appropriate behavioral responses. Like the overlying thalamus—and consistent with the scope of hypothala-mic functions—the hypothalamus com-prises a large number of distinct nuclei, each with its own specific pattern of con-nections and functions. The nuclei, most of which are intricately interconnected, can be grouped in three longitudinal regions referred to as periventricular, medial, and lateral. They can also be grouped along the anterior–posterior dimension, the groups being those nuclei in the anterior (or preoptic), tuberal, and posterior regions (Figure C). The anterior-pariventricular group contains the suprachiasmatic nucleus, which receives direct retinal input and drives circadian rhythms (see Chapter 27). More scattered neurons in the periventricular region (located along the wall of the third ven-tricle) manufacture peptides known as releasing or inhibiting factors that con-trol the secretion of a variety of hor-mones by the anterior pituitary. The axons of these neurons project to the median eminence, a region at the junc-tion of the hypothalamus and pituitary stalk, where the peptides are secreted into the portal circulation that supplies the anterior pituitary. The medial-tuberal region nuclei (“tuberal” refers to the tuber cinereum, the anatomical name given to the middle portion of the inferior surface of the hypothalamus) include the paraventricu-lar and supraoptic nuclei, which contain the neurosecretory neurons whose axons extend into the posterior pituitary. With appropriate stimulation, these neurons secrete oxytocin or vasopressin (antidi-uretic hormone) directly into the blood-stream. Other neurons in the paraventric-ular nucleus project to autonomic centers in the reticular formation, as well as pre-ganglionic neurons of the sympathetic and parasympathetic divisions in the (1) (3) (2) (4) Lateral preoptic nucleus Medial preoptic nucleus Suprachiasmatic nucleus Optic chiasm Optic chiasm Anterior commissure Lateral ventricle Third ventricle Third ventricle Lateral nucleus Anterior nucleus Supraoptic nucleus Paraventricular nucleus Periventricular nucleus Periventricular nucleus Optic tract Lateral nucleus Supraoptic nucleus Optic tract Dorsomedial nucleus Ventromedial nucleus Dorsal nucleus Dorsal thalamus Third ventricle Mammillary body Posterior nucleus Lateral nucleus Dorsal thalamus Subthalamic nucleus (C) Coronal sections through the human hypothalamus (see Figure A for location of sections 1–4). Color coding of the nuclei illustrates the two dimensions by which hypothalamic nuclei are subdivided (see text). Blue, red, and green illustrate nuclei in the anterior, tuberal, and pos-terior regions, respectively. The relative shading of these hues illustrates the three mediolateral zones: Lighter shading represents nuclei in the periventricular zone, whereas darker shades represent medial zone nuclei. Nuclei in the lateral zone are stippled. (1) Section through the anterior region illustrating the preoptic and suprachiasmatic nuclei. (2) Rostral tuberal region. (3) Caudal tuberal region. (4) Section through the posterior region illustrating the mammillary bodies. Continued on next page 486 Chapter Twenty higher integrative centers in the amygdala (specifically, the central group of amygdaloid nuclei; see Box B in Chapter 28) and hypothalamus (see Box A and below). In addition, the nucleus of the solitary tract projects to the parabrachial nucleus (so named because it envelopes the superior cerebellar peduncle, which is also known by its Latin name, the brachium conjunc-tivum). The parabrachial nucleus, in turn, provides additional visceral sen-sory relays to the hypothalamus, amygdala, thalamus, and medial prefrontal and insular cortex (see Figure 20.7; for clarity, the cortical projections of the parabrachial nucleus are omitted). Although one might propose that the posterior insular cortex serves as the primary visceral sensory area and the medial prefrontal cortex as the pri-mary visceral motor area, it is more useful to emphasize the interactions among these cortical areas and related subcortical structures; taken together, they constitute a central autonomic network. This network accounts for the integration of visceral sensory information with input from other sensory modalities and higher cognitive centers that process semantic and emotional experiences. Involuntary visceral reactions such as blushing in response to consciously embarrassing stimuli, vasoconstriction and pallor in response to fear, and autonomic responses to sexual situations are examples of the inte-grated activity of this network. Indeed, autonomic function is intimately related to emotional processing, as emphasized in Chapter 28. A key component of this central autonomic network that deserves special consideration is the hypothalamus. This heterogeneous collection of nuclei in the base of the diencephalon serves as the major center for the coordination and expression of visceral motor activity (Box A). The major outflow from the relevant hypothalamic nuclei is directed toward “autonomic centers” in the reticular formation; these centers can be thought of as dedicated premotor circuits that coordinate the efferent activity of preganglionic visceral motor neurons. They organize specific visceral functions such as cardiac reflexes, Box A The Hypothalamus (continued) brainstem and spinal cord; these cells are thought to exert hypothalamic control over the visceral motor system. The par-aventricular nucleus receives inputs from other hypothalamic zones, which are in turn related to the cerebral cortex, hip-pocampus, amygdala, and other central structures that are all capable of influenc-ing visceral motor function. Also in the region of the hypothala-mus are the dorsomedial and ventrome-dial nuclei, which are involved in feed-ing, reproductive and parenting behavior, thermoregulation, and water balance. These nuclei receive inputs from struc-tures of the limbic system, as well as from visceral sensory nuclei in the brainstem (e.g., the nucleus of the solitary tract). Finally, the lateral region of the hypo-thalamus is really a rostral continuation of the midbrain reticular formation (see Box A in Chapter 16). Thus, the neurons of the lateral region are not grouped into nuclei, but are scattered among the fibers of the medial forebrain bundle, which runs through the lateral hypothalamus. These cells control behavioral arousal and shifts of attention, especially as related to reproductive activities. In summary, the hypothalamus regu-lates an enormous range of physiological and behavioral activities and serves as the key controlling center for visceral motor activity and for homeostatic func-tions generally. References SAPER, C. B. (1990) Hypothalamus. In The Human Nervous System. G. Paxinos (ed.). San Diego: Academic Press, pp. 389–414. SWANSON, L. W. (1987) The hypothalamus. In Handbook of Chemical Neuroanatomy, Vol. 5: Integrated Systems of the CNS, Part I: Hypothal-amus, Hippocampus, Amygdala, Retina. A. Björklund and T. Hokfelt (eds.). Amsterdam: Elsevier, pp. 1–124. SWANSON, L. W. AND P. E. SAWCHENKO (1983) Hypothalamic integration: Organization of the paraventricular and supraoptic nuclei. Annu. Rev. Neurosci. 6: 269–324. reflexes that control the bladder, reflexes related to sexual function, and other critical autonomic reflexes underlying respiration and vomiting (see Box A in Chapter 16). In addition to these important connections to the reticular formation, hypothalamic control of visceral motor function is also exerted more directly by projections to the cranial nerve nuclei that contain parasympathetic pre-ganglionic neurons, and to the sympathetic and parasympathetic pregan-glionic neurons in the spinal cord. Nevertheless, the autonomic centers of the reticular formation and the preganglionic visceral motor neurons that they control are competent to function autonomously should disease or injury impede the governance of the hypothalamus over the many bodily systems that maintain homeostasis. The general organization of this central autonomic control is summarized in Figure 20.7; some important clinical manifestations of damage to this descending system are illustrated in Box B; Box C shows the relevance of this central control to one prevalent category of human disorder (obesity). Neurotransmission in the Visceral Motor System The neurotransmitter functions of the visceral motor system are of enor-mous importance in clinical practice, and drugs that act on the autonomic system are among the most important in the clinical armamentarium. More-over, autonomic transmitters have played a major role in the history of efforts to understand synaptic function. Consequently, neurotransmission in the visceral motor system deserves special comment (see also Chapter 6). Acetylcholine is the primary neurotransmitter of both sympathetic and parasympathetic preganglionic neurons. Nicotinic receptors on autonomic ganglion cells are ligand-gated ion channels that mediate a so-called fast EPSP (much like nicotinic receptors at the neuromuscular junction). In con-trast, muscarinic acetylcholine receptors on ganglion cells are members of the 7-transmembrane G-protein-linked receptor family, and they mediate slower synaptic responses (see Chapters 6 and 7).The primary action of mus-carinic receptors in autonomic ganglion cells is to close K+ channels, making the neurons more excitable and generating a prolonged EPSP. Acting in con-cert with the muscarinic activities are neuropeptides that serve as co-neuro-transmitters at the ganglionic synapses. As described in Chapter 6, peptide neurotransmitters also tend to exert slowly developing and long-lasting effects on postsynaptic neurons. As a result of these two acetylcholine recep-tor types and a rich repertoire of neuropeptide transmitters, ganglionic syn-apses mediate both rapid excitation and a slower modulation of autonomic ganglion cell activity. The postganglionic effects of autonomic ganglion cells on their smooth muscle, cardiac muscle, or glandular targets are mediated by two primary neurotransmitters: norepinephrine (NE) and acetylcholine (ACh). For the most part, sympathetic ganglion cells release norepinephrine onto their tar-gets (a notable exception is the cholinergic sympathetic innervation of sweat glands), whereas parasympathetic ganglion cells typically release acetyl-choline. As expected from the foregoing account, these two neurotransmit-ters usually have opposing effects on their target tissue—contraction versus relaxation of smooth muscle, for example. As described in Chapters 6 and 7, the specific effects of either ACh or NE are determined by the type of receptor expressed in the target tissue, and the downstream signaling pathways to which these receptors are linked. Periph-eral sympathetic targets generally have two subclasses of noradrenergic The Visceral Motor System 487 Chapter Twenty Box B Horner’s Syndrome The characteristic clinical presentation of damage to the pathway that controls the sympathetic division of the visceral motor system to the head and neck is called Horner’s syndrome, after the Swiss ophthalmologist who first described this clinical picture in the mid-nineteenth century. The main features, as illustrated in Figure A, are decreased diameter of the pupil on the side of the lesion (miosis), a droopy eyelid (ptosis), and a sunken appearance of the affected eye (enophthalmos). Less obvious signs are decreased sweating, increased skin temperature, and flushing of the skin on the same side of the face and neck. All these signs are explained by a loss of sympathetic tone due to damage somewhere along the pathway that con-nects visceral motor centers in the hypo-thalamus and reticular formation with sympathetic preganglionic neurons in the intermediolateral cell column of the thoracic spinal cord (Figure B). Lesions that interrupt these fibers often spare the descending parasympathetic pathways, which are located more medially in the brainstem and are more diffuse. The sympathetic preganglionic targets that are affected by such lesions include the neurons in the intermediolateral column in spinal segments T1–T3 that control the dilator muscle of the iris and the tone in smooth muscles of the eyelid and globe, the paralysis of which leads to miosis, ptosis, and enophthalmos. The flushing and decreased sweating are likewise the result of diminished sympathetic tone, in this case governed by intermediolateral column neurons in somewhat lower tho-racic segments (∼T3–T8). Damage to the descending sympathetic pathway in the brainstem will, of course, affect sweating and vascular tone in the rest of the body on the side of the lesion. However, if the damage is to the upper thoracic outflow (as is more typical), the upper thoracic chain, or the superior cervical ganglion, then the manifestations of Horner’s syn-drome will be limited to the head and neck. Typical causes in these sites are stab or gunshot wounds or other trau-matic injuries to the head and neck, and tumors of the apex of the lung, thyroid, or cervical lymph nodes. (B) Region of descending hypothalamic and reticular fibers for sympathetic control Intermediolateral cell column Sympathetic chain ganglia Spinal cord Superior cervical ganglion Carotid plexus Pupillary dilator muscle Hypothalamus Reticular formation in ventrolateral medulla (A) Major features of the clinical presentation of Horner’s syndrome. (B) Diagram of the descending sympathetic pathways arising in the hypothalamus and reticular formation that can be interrupted to cause Horner’s syndrome. Damage to the preganglionic neurons in the upper thoracic cord, to the superior cervical ganglion, or to the cervical sympathetic trunk can also cause Horner’s syndrome (see also Figure 20.1). The transverse lines indicate the level of the sections shown at right. Ipsilateral pupillary constriction (miosis) Drooping of eyelid (ptosis) Apparent sinking of eyeball (enophthalmos) (A) 488 receptors in their cell membranes, referred to as α and β receptors. Like mus-carinic ACh receptors, both α and β receptors and their subtypes belong to the 7-transmembrane G-protein-coupled class of cell surface receptors. The different distribution of these receptors in sympathetic targets allows for a variety of postsynaptic effects mediated by norepinephrine released from postganglionic sympathetic nerve endings (Table 20.2). The effects of acetylcholine released by parasympathetic ganglion cells onto smooth muscles, cardiac muscle, and glandular cells also vary accord-ing to the subtypes of muscarinic cholinergic receptors found in the periph-eral target (Table 20.3). The two major subtypes are known as M1 and M2 receptors, M1 receptors being found primarily in the gut and M2 receptors in the cardiovascular system. (Another subclass of muscarinic receptors, M3, occurs in both smooth muscle and glandular tissues.) Muscarinic receptors are coupled to a variety of intracellular signal transduction mechanisms that modify K+ and Ca2+ channel conductances. They can also activate nitric oxide synthase, which promotes the local release of NO in some parasympa-thetic target tissues (see, for example, the section below on autonomic con-trol of sexual function). In contrast to the relatively restricted responses generated by norepineph-rine and acetylcholine released by sympathetic and parasympathetic gan-glion cells, respectively, neurons of the enteric nervous system achieve an enormous diversity of target effects by virtue of many different neurotrans-The Visceral Motor System 489 TABLE 20.2 Summary of Adrenergic Receptor Types and Some of Their Effects in Sympathetic Targets Receptor Tissue Response α1 Smooth muscle of blood Contraction of smooth muscle vessels, iris, ureter, hairs, uterus, bladder Smooth muscle of gut Relaxation of smooth muscle Heart muscle Positive inotropic effect (β1 >> α1) Salivary gland Secretion Adipose tissue Glycogenolysis, gluconeogenesis Sweat glands Secretion Kidney Na+ reabsorbed α2 Adipose tissue Inhibition of lipolysis Pancreas Inhibition of insulin release Smooth muscle of blood Contraction vessels β1 Heart muscle Positive inotropic effect; positive chronotropic effect Adipose tissue Lipolysis Kidney Renin release β2 Liver Glycogenolysis, gluconeogenesis Skeletal muscle Glycogenolysis, lactate release Smooth muscle of bronchi, Relaxation uterus, gut, blood vessels Pancreas Insulin secretion Salivary glands Thickened secretions Box C Obesity and the Brain Obesity and its relationship to a broad range of diseases—including diabetes, cardiovascular disease and cancer—has become a major public health concern in most developed countries, particularly the United States. Whereas the signature of obesity is obviously an excess of body fat, the underlying cause or causes are generally thought to lie in abnormal reg-ulation by the brain circuits that control appetite and satiety. This fact makes weight loss particularly difficult for many obese individuals. Thus, understanding of the central nervous systems mecha-nisms that regulate food intake and metabolism are essential for developing effective strategies to combat this very serious health problem. The brain regulates appetite and sati-ety (the feeling of fullness following a meal) via the neural activity that is mod-ulated by chemical signals that are secreted into the circulation by fat storing adipose tissues throughout the body. Since this feedback loop entails some of the central components of the visceral motor system, in addition to endocrine mechanisms via insulin and growth hor-mone, it is discussed here. The peptide ghrelin is secreted by the stomach prior to feeding, presumably as a signal of hunger; adipocytes (the cells that concen-trate lipid in fatty tissues) secrete leptin into the circulation following feeding, presumably as a signal for satiety. The receptors for these peptides are concen-trated in small groups of neurons in the ventrolateral and anterior hypothalamus (see Box A), which contact additional hypothalamic neurons in the arcuate region. These grehlin- and leptin-respon-sive cells modulate the activity of neu-rons expressing the opiomelanocortin propeptide (POMC) and the subsequent secretion of α-melanocyte secreting hor-mone (α-MSH), one of the peptides encoded by the POMC transcript. This hormone evidently regulates appetite and satiety by acting on specific receptors (particularly the melanocortin receptor subtype called MCR-4) located on addi-tional populations of hypothalamic and brainstem neurons (particularly those in the nucleus of the solitary tract), as well as by endocrine mechanisms that remain poorly understood. The interactions of leptin, grehlin, α-MSH and MCR-4 were first determined in animal models. Two recessive muta-tions in mice—the obese (ob/ob) and the misnamed diabetic (db/db) mice—were identified based on excessive body weight and failure to regulate food intake. When each mutation was cloned, the mutant gene in ob mice turned out to be the gene for leptin, and the db gene that for the leptin receptor. Mutations in the POMC (Figure A) and MCR4 genes also lead to obesity in mice. The results of inactivation of the ghrelin gene are less clear; however, pharmacological and physiological studies associate changes in ghrelin levels with altered feeding and weight loss. Studies in mice have thus provided a solid framework for examin-ing the physiological mechanisms regu-lating food intake in humans. Nonethe-less, their relevance to morbid human obesity remained unclear until recently. Genetic analysis of individuals in human pedigrees with extreme obesity (measured body mass indices and weight/height ratios) revealed mutations in one or more of the leptin, leptin recep-tor, or MCR4 genes. As a result, these individuals have little sense of satiety after eating, and thus fail to regulate food intake based on signals other than gastric distension and pain. How this patho-physiology is related to less extreme degrees of obesity is not yet known, but is being intensely studied because of its implications for normal weight control. The emerging understanding of body weight regulation by hypothalamic cir-cuits that are modulated by feedback from by hormonal signals from fat tissues has provided new ways of thinking about pharmacological therapies for weight control. While leptin mimetics have proven generally ineffective, leptin administration in human subjects with leptin deficiencies does reduce food intake and obesity (Figure B). Currently, there is great interest in drugs that modu-late α-MSH signaling via MCR-4. Al-though no effective pharmacological therapies presently exist, there is hope that such drugs, when combined with behavioral changes in dietary practices, will effectively combat this often intractable and increasingly common health problem. References O’RAHILLY, S., I. S. FAROOQI, G. S. H. YEO AND B. G. CHALLIS (2003) Human obesity—lessons from monogenic disorders. Endocrinology 144: 3757–3764. SCHWARTZ, M. W., S. C. WOODE, D. PORTE, R. J. SEELY AND D. G. BASKIN (2000) Central nervous system control of food intake. Nature 404: 661–671. SAPER, C. B., T. C. CHOU AND J. K. ELMQUIST (2002) The need to feed: Homeostatic and hedonic control of eating. Neuron 36: 199–21. (A) (B) (A) A POMC knockout mouse (left) and a wild-type littermate (right). (B) The effect of leptin treatment in a human. At age 3 years, the subject weighed 42 kg (left); at age 7 years, following treatment, the same child weighed 32 kg (right). (A from Yaswen et al., 1999, B from O’Rahilly et al., 2003.) mitters, most of which are neuropeptides associated with specific cell groups in either the myenteric or submucous plexuses mentioned earlier. The details of these agents and their actions are beyond the scope of this intro-ductory account. Visceral Motor Reflex Functions Many examples of specific autonomic functions could be used to illustrate in more detail how the visceral motor system operates. The three outlined here—control of cardiovascular function, control of the bladder, and control of sexual function—have been chosen primarily because of their importance in human physiology and clinical practice. Autonomic Regulation of Cardiovascular Function The cardiovascular system is subject to precise reflex regulation so that an appropriate supply of oxygenated blood can be reliably provided to different body tissues under a wide range of circumstances. The sensory monitoring for this critical homeostatic process entails primarily mechanical (barosen-sory) information about pressure in the arterial system and, secondarily, chemical (chemosensory) information about the levels of oxygen and carbon dioxide in the blood. The parasympathetic and sympathetic activity relevant to cardiovascular control is determined by the information supplied by these sensors. The mechanoreceptors (called baroreceptors) are located in the heart and major blood vessels; the chemoreceptors are located primarily in the carotid bodies, which are small, highly specialized organs located at the bifurcation of the common carotid arteries (some chemosensory tissue is also found in the aorta). The nerve endings in baroreceptors are activated by deformation as the elastic elements of the vessel walls expand and contract. The chemore-ceptors in the carotid bodies and aorta respond directly to the partial pres-sure of oxygen and carbon dioxide in the blood. Both afferent systems con-vey their status via the vagus nerve to the nucleus of the solitary tract (Figure 20.8), which relays this information to the hypothalamus and the rel-evant autonomic centers in the reticular formation. The afferent information derived from changes in arterial pressure and blood gas levels reflexively modulates the activity of the relevant visceral The Visceral Motor System 491 TABLE 20.3 Summary of Cholinergic Receptor Types and Some of Their Effects in Parasympathetic Targets Receptor Tissue Response Nicotinic Most parasympathetic targets Relatively fast post-(and all autonomic ganglion cells) synaptic response Muscarinic Smooth muscles and glands Smooth muscle contrac-(M1) of the gut tion and glandular secretion (relatively slow response) Muscarinic Smooth and cardiac muscle Smooth muscle contrac-(M2) of cardiovascular system tion; some inotropic effect on cardiac muscle Muscarinic Smooth muscles and glands Smooth muscle contrac-(M3) of all targets tion, glandular secretion 492 Chapter Twenty motor pathways and, ultimately, of target smooth and cardiac muscles and other more specialized structures. For example, a rise in blood pressure acti-vates baroreceptors that, via the pathway illustrated in Figure 20.8, inhibit the tonic activity of sympathetic preganglionic neurons in the spinal cord. In parallel, the pressure increase stimulates the activity of the parasympathetic preganglionic neurons in the nucleus ambiguus and the dorsal motor nucleus of the vagus that influence heart rate. The carotid chemoreceptors also have some influence, but this is a less important drive than that stem-ming from the baroreceptors. As a result of this shift in the balance of sympathetic and parasympathetic activity, the stimulatory noradrenergic effects of postganglionic sympathetic Baroreceptor afferents Chemoreceptor afferents Heart Carotid body Vagus nerve (X) Glossopharyngeal nerve (IX) Nucleus ambiguus Nucleus of the solitary tract Preganglionic neurons in intermediolateral cell column of upper thoracic spinal cord (T1−T5) Postganglionic sympathetic fibers Postganglionic parasympathetic fibers Sympathetic chain ganglion Cardiac plexus Figure 20.8 Autonomic control of cardiovascular function. innervation on the cardiac pacemaker and cardiac musculature is reduced (these effects are abetted by the decreased output of catecholamines from the adrenal medulla and the decreased vasoconstrictive effects of sympathetic innervation on the peripheral blood vessels). At the same time, activation of the cholinergic parasympathetic innervation of the heart decreases the dis-charge rate of the cardiac pacemaker in the sinoatrial node and slows the ventricular conduction system. These parasympathetic influences are medi-ated by an extensive series of parasympathetic ganglia in and near the heart, which release acetylcholine onto cardiac pacemaker cells and cardiac muscle fibers. As a result of this combination of sympathetic and parasympathetic effects, heart rate and the effectiveness of atrial and ventricular mycoardial contraction are reduced and the peripheral arterioles dilate, thus lowering the blood pressure. In contrast to this sequence of events in response to raised blood pressure, a fall in blood pressure (as might occur from blood loss) has the opposite effect—it inhibits parasympathetic activity while increasing sympathetic activity. As a result, norepinephrine is released from sympathetic postgan-glionic terminals, increasing the rate of cardiac pacemaker activity and enhancing cardiac contractility, at the same time increasing release of cate-cholamines from the adrenal medulla (which further augments these and many other sympathetic effects that enhance the response to this threatening situation). Norepinephrine released from the terminals of sympathetic gan-glion cells also acts on the smooth muscles of the arterioles to increase the tone of the peripheral vessels, particularly those in the skin, subcutaneous tissues, and muscles, thus shunting blood away from these tissues to those organs where oxygen and metabolites are urgently needed to maintain func-tion (e.g., brain, heart, and kidneys in the case of blood loss). If these reflex sympathetic responses fail to raise the blood pressure sufficiently (in which case the patient is said to be in shock), the vital functions of these organs begin to fail, often catastrophically. A more mundane circumstance that requires a reflex autonomic response to a fall in blood pressure is standing up. Rising quickly from a prone posi-tion produces a shift of some 300–800 milliliters of blood from the thorax and abdomen to the legs, resulting in a sharp (approximately 40%) decrease in the output of the heart. The adjustment to this normally occurring drop in blood pressure (called orthostatic hypotension) must be rapid and effective, as evidenced by the dizziness sometimes experienced in this situation. Indeed, normal individuals can briefly lose consciousness as a result of blood pool-ing in the lower extremities, which is the usual cause of fainting among healthy individuals who stand still for abnormally long periods. The sympathetic innervation of the heart arises from the preganglionic neurons in the intermediolateral column of the spinal cord, extending from roughly the first through fifth thoracic segments (see Table 20.1). The pri-mary visceral motor neurons are in the adjacent thoracic paravertebral and prevertebral ganglia of the cardiac plexus. The parasympathetic pregan-glionics, as already mentioned, are in the nucleus ambiguus and the dorsal motor nucleus of the vagus nerve, projecting to parasympathetic ganglia in and around the heart and great vessels. Autonomic Regulation of the Bladder The autonomic regulation of the bladder provides a good example of the interplay between components of the somatic motor system that are subject to volitional control (we obviously have voluntary control over urination), The Visceral Motor System 493 494 Chapter Twenty and the sympathetic and parasympathetic divisions of the visceral motor system, which operate involuntarily. The arrangement of afferent and efferent innervation of the bladder is shown in Figure 20.9. The parasympathetic control of the bladder muscula-ture, the contraction of which causes bladder emptying, originates with neu-rons in the sacral spinal cord segments (S2–S4) that innervate visceral motor neurons in parasympathetic ganglia in or near the bladder wall. Mechanore-ceptors in the bladder wall supply visceral afferent information to the spinal cord and to higher autonomic centers in the brainstem (primarily the nucleus of the solitary tract), which in turn project to the various central Inferior mesenteric and pelvic ganglia Urinary bladder External sphincter Afferents to brainstem nuclei Postganglionic sympathetic axons Postganglionic parasympathetic axons Parasympathetic ganglia in pelvic pathway Parasympathetic preganglionic axons Dorsal root ganglion Sympathetic preganglionic neurons (T10−L2) Parasympathetic preganglionic neurons (S2−S4) Sacral spinal cord (S2−S4) Visceral afferent axons Somatic motor axons Urethra Descending somatic motor inputs Descending brainstem inputs Figure 20.9 Autonomic control of bladder function. coordinating centers for bladder function in the pontine reticular formation and anterior-medial hypothalamus. The sympathetic innervation of the bladder originates in the lower tho-racic and upper lumbar spinal cord segments (T10–L2), the preganglionic axons running to sympathetic neurons in the inferior mesenteric ganglion and the ganglia of the pelvic plexus. The postganglionic fibers from these ganglia travel in the hypogastric and pelvic nerves to the bladder, where sympathetic activity causes the internal urethral sphincter to close (postgan-glionic sympathetic fibers also innervate the blood vessels of the bladder, and in males the smooth muscle fibers of the prostate gland). Stimulation of this pathway in response to a modest increase in bladder pressure from the accumulation of urine thus closes the internal sphincter and inhibits the con-traction of the bladder wall musculature, allowing the bladder to fill. At the same time, moderate distension of the bladder inhibits parasympathetic activity (which would otherwise contract the bladder and allow the internal sphincter to open). When the bladder is full, afferent activity conveying this information centrally increases parasympathetic tone and decreases sympa-thetic activity, causing the internal sphincter muscle to relax and the bladder to contract. In this circumstance, the urine is held in check by the voluntary somatic motor innervation of the external urethral sphincter muscle (see Fig-ure 20.9). The voluntary control of the external sphincter is mediated by a-motor neurons of the ventral horn in the sacral spinal cord segments (S2–S4), which cause the striated muscle fibers of the sphincter to contract. During bladder filling (and subsequently, until circumstances permit urination) these neu-rons are active, keeping the external sphincter closed and preventing bladder emptying. During urination (or voiding, as clinicians often call this process), this tonic activity is temporarily inhibited, leading to relaxation in the exter-nal sphincter muscle. Thus, urination results from the coordinated activity of sacral parasympathetic neurons and temporary inactivity of the a-motor neurons of the voluntary motor system. The central governance of these events stems from the reticular formation of the rostral pons, the relevant pontine circuitry being referred to as the mic-turition center (micturition is also “medicalese” for urination). As many as five other central regions have been implicated in the coordination of urinary functions, including the locus coeruleus, the anterior-medial hypothalamus, the septal nuclei, and several cortical regions. The cortical regions primarily concerned with the voluntary control of bladder function include the para-central lobule, the cingulate gyrus, and the prefrontal cortex. This functional distribution accords with the motor representation of perineal musculature in the medial part of the primary motor cortex (see Chapter 16), and the planning functions of the frontal lobes (see Chapter 25), which are equally pertinent to bodily functions (remembering to stop by the bathroom before going on a long trip, for instance). Importantly, paraplegic patients, or patients who have otherwise lost descending control of the sacral spinal cord, continue to exhibit autonomic regulation of bladder function, since urination is eventually stimulated reflexively at the level of the sacral cord by sufficient bladder distension. Unfortunately, this reflex is not fully efficient in the absence of descending motor control, resulting in a variety of problems in paraplegics and others with diminished or absent central control of bladder function. The major dif-ficulty is incomplete bladder emptying, which often leads to chronic urinary tract infections from the culture medium provided by retained urine, and thus the need for an indwelling catheter to ensure adequate drainage. The Visceral Motor System 495 496 Chapter Twenty Autonomic Regulation of Sexual Function Much like control of the bladder, sexual responses are mediated by the coor-dinated activity of sympathetic, parasympathetic, and somatic innervation. Although these reflexes differ in detail in males and females, basic similari-ties allow the two sexes to be considered together, not only in humans but in mammals generally. The relevant autonomic effects include: (1) the media-tion of vascular dilation, which causes penile or clitoral erection; (2) stimula-tion of prostatic or vaginal secretions; (3) smooth muscle contraction of the vas deferens during ejaculation in males or rhythmic vaginal contractions during orgasm in females; and (4) contractions of the somatic pelvic muscles that accompany orgasm in both sexes. Like the urinary tract, the reproductive organs receive preganglionic parasympathetic innervation from the sacral spinal cord, preganglionic sym-pathetic innervation from the outflow of the lower thoracic and upper lum-bar spinal cord segments, and somatic motor innervation from a-motor neu-rons in the ventral horn of the lower spinal cord segments (Figure 20.10). The sacral parasympathetic pathway controlling the sexual organs in both males and females originates in the sacral segments S2–S4 and reaches the target organs via the pelvic nerves. Activity of the postganglionic neurons in the relevant parasympathetic ganglia causes dilation of penile or clitoral arteries, and a corresponding relaxation of the smooth muscles of the venous (cavernous) sinusoids, which leads to expansion of the sinusoidal spaces. As a result, the amount of blood in the tissue is increased, leading to a sharp rise in the pressure and an expansion of the cavernous spaces (i.e., erection). The mediator of the smooth muscle relaxation leading to erection is not acetylcholine (as in most postganglionic parasympathetic actions), but nitric oxide (see Chapter 7). The drug sildenafil (Viagra), for instance, acts by stimulating the activity of guanylate cyclase, which increases the conversion of GTP to cyclic GMP, mimicking the action of NO on the cGMP pathway, thus enhancing the relaxation of the venous sinusoids and promoting erec-tion in males with erectile dysfunction. Parasympathetic activity also pro-vides excitatory input to the vas deferens, seminal vesicles, and prostate in males, or vaginal glands in females. In contrast, sympathetic activity causes vasoconstriction and loss of erec-tion. The lumbar sympathetic pathway to the sexual organs originates in the thoraco-lumbar segments (T1–L2) and reaches the target organs via the cor-responding sympathetic chain ganglia and the inferior mesenteric and pelvic ganglia, as in the case of the autonomic bladder control. The afferent effects of genital stimulation are conveyed centrally from somatic sensory endings via the dorsal roots of S2–S4, eventually reaching the somatic sensory cortex (reflex sexual excitation may also occur by local stimulation, as is evident in paraplegics). The reflex effects of such stimula-tion are increased parasympathetic activity, which, as noted, causes relaxation of the smooth muscles in the wall of the sinusoids and subsequent erection. Finally, the somatic component of reflex sexual function arises from a-motor neurons in the lumbar and sacral spinal cord segments. These neu-rons provide excitatory innervation to the bulbocavernosus and ischiocaver-nosus muscles, which are active during ejaculation in males and mediate the contractions of the perineal (pelvic floor) muscles that accompany orgasm in both male and females. Sexual functions are governed centrally by the anterior-medial and medial-tuberal zones of the hypothalamus, which contain a variety of nuclei pertinent to visceral motor control and reproductive behavior (see Box A). Although they remain poorly understood, these nuclei act as integrative cen-ters for sexual responses and are also thought to be involved in more com-plex aspects of sexuality, such as sexual preference and gender identity (see Chapter 29). The relevant hypothalamic nuclei receive inputs from several areas of the brain, including—as one might imagine—the cortical and sub-cortical structures concerned with emotion, hedonic reward, and memory (see Chapters 28 and 30). The Visceral Motor System 497 Inferior mesenteric and pelvic ganglia Afferents to brainstem nuclei Postganglionic parasympathetic axons Parasympathetic ganglia in pelvic pathway Parasympathetic preganglionic axons Dorsal root ganglion Sympathetic preganglionic neurons (T11−L2) Parasympathetic preganglionic neurons (S2−S4) Sacral spinal cord (S2−S4) Somatic sensory afferent axons Somatic motor axons innervating perineal muscles Descending somatic motor inputs Descending brainstem inputs Penis Postganglionic sympathetic axons Figure 20.10 Autonomic control of sexual function in the human male. 498 Chapter Twenty Additional Reading Reviews ANDERSSON, K.-E. AND G. WAGNER (1995) Physiology of penile erections. Physiol. Rev. 75: 191–236. BROWN, D. A., F. C. ABOGADIE, T. G. ALLEN, N. J. BUCKLEY, M. P. CAULFIELD, P. DELMAS, J. E. HALEY, J. A. LAMAS AND A. A. SELYANKO (1997) Muscarinic mechanisms in nerve cells. Life Sciences 60(13–14): 1137–1144. COSTA, M. AND S. J. H. BROOKES (1994) The enteric nervous system. Am. J. Gastroenterol. 89: S129–S137. DAMPNEY, R. A. L. (1994) Functional organiza-tion of central pathways regulating the car-diovascular system. Physiol. Rev. 74: 323–364. GERSHON, M. D. (1981) The enteric nervous system. Annu. Rev. Neurosci. 4: 227–272. MUNDY, A. R. (1999) Structure and function of the lower urinary tract. In Scientific Basis of Urology, A. R. Mundy, J. M. Fitzpatrick, D. E. Neal, and N. J. R. George (eds.). Oxford: Isis Medical Media Ltd., pp. 217–242. PATTON, H. D. (1989) The autonomic nervous system. In Textbook of Physiology: Excitable Cells and Neurophysiology, Vol. 1, Section VII: Emo-tive Responses and Internal Milieu, H. D. Pat-ton, A. F. Fuchs, B. Hille, A. M. Scher, and R. Steiner (eds.). Philadelphia: Saunders, pp. 737–758. PRYOR, J. P. (1999) Male sexual function. In Sci-entific Basis of Urology, A. R. Mundy, J. M. Fitz-patrick, D. E. Neal and N. J. R. George (eds). Oxford: Isis Medical Media, pp. 243–255. Important Original Papers JANSEN, A. S. P., X. V. NGUYEN, V. KARPITSKIY,T. C. METTENLEITER AND A. D. LOEWY (1995) Cen-tral command neurons of the sympathetic nervous system: Basis of the fight or flight response. Science 270: 644–646. LANGLEY, J. N. (1894) The arrangement of the sympathetic nervous system chiefly on obser-vations upon pilo-erector nerves J. Physiol. (Lond.) 15: 176–244. LANGLEY, J. N. (1905) On the reaction of nerve cells and nerve endings to certain poisons chiefly as regards the reaction of striated mus-cle to nicotine and to curare. J. Physiol. (Lond.) 33: 374–473. LICHTMAN, J. W., D. PURVES AND J. W. YIP (1980) Innervation of sympathetic neurones in the guinea-pig thoracic chain. J. Physiol. 298: 285–299. RUBIN, E. AND D. PURVES (1980) Segmental or-ganization of sympathetic preganglionic neu-rons in the mammalian spinal cord. J. Comp. Neurol. 192: 163–174. Books APPENZELLER, O. (1997) The Autonomic Nervous System: An Introduction to Basic and Clinical Concepts, 5th Ed. Amsterdam: Elsevier Bio-medical Press. BLESSING, W. W. (1997) The Lower Brainstem and Bodily Homeostasis. New York: Oxford Univer-sity Press. BRADING, A. (1999) The Autonomic Nervous Sys-tem and Its Effectors. Oxford: Blackwell Science. BURNSTOCK, G. AND C. H. V. HOYLE (1995) The Autonomic Nervous System, Vol. 1: Autonomic Neuroeffector Mechanism. London: Harwood Academic. CANNON, W. B. (1932) The Wisdom of the Body. New York: Norton. FURNESS, J. B. AND M. COSTA (1987) The Enteric Nervous System. Edinburgh: Churchill Livingstone. GABELLA, G. (1976) Structure of the Autonomic Nervous System. London: Chapman and Hall. LANGLEY, J. N. (1921) The Autonomic Nervous System. Cambridge, England: Heffer & Sons. LOEWY, A. D. AND K. M. SPYER (eds.) (1990) Central Regulation of Autonomic Functions. New York: Oxford. PICK, J. (1970) The Autonomic Nervous System: Morphological, Comparative, Clinical and Surgi-cal Aspects. Philadelphia: J.B. Lippincott Com-pany. RANDALL, W. C. (ed.) (1984) Nervous Control of Cardiovascular Function. New York: Oxford University Press. Summary Sympathetic and parasympathetic ganglia, which contain the primary vis-ceral motor neurons that innervate smooth muscles, cardiac muscle, and glands, are controlled by preganglionic neurons in the spinal cord and brain-stem. The sympathetic preganglionic neurons that govern ganglion cells in the sympathetic division of the visceral motor system arise from neurons in the thoracic and upper lumbar segments of the spinal cord; parasympathetic preganglionic neurons, in contrast, are located in the brainstem and sacral spinal cord. Sympathetic ganglion cells are distributed in the sympathetic chain (paravertebral) and prevertebral ganglia, whereas the parasympathetic motor neurons are more widely distributed in ganglia that lie within or near the organs they control. Most autonomic targets receive inputs from both the sympathetic and parasympathetic systems, which act in a generally antago-nistic fashion. The diversity of autonomic functions is achieved primarily by different types of receptors for the two primary classes of postganglionic autonomic neurotransmitters, norepinephrine in the case of the sympathetic division and acetylcholine in the parasympathetic division. The visceral motor system is regulated by sensory feedback provided by dorsal root and cranial nerve sensory ganglion cells that make local reflex connections in the spinal cord or brainstem and project to the nucleus of the solitary tract in the brainstem, and by descending pathways from the hypothalamus and brain-stem reticular formation, the major controlling centers of the visceral motor system (and of homeostasis more generally). The importance of the visceral motor control of organs such as the heart, bladder, and reproductive organs— and the many pharmacological means of modulating autonomic function— have made visceral motor control a central theme in clinical medicine. The Changing Brain IV A mammalian embryo in which cells in the developing nervous system responding to the signaling molecule retinoic acid have been labeled by means of a reporter gene. (Courtesy of Anthony-Samuel LaMantia and Elwoood Linney.) UNIT IV THE CHANGING BRAIN 21 Early Brain Development 22 Construction of Neural Circuits 23 Modification of Brain Circuits as a Result of Experience 24 Plasticity of Mature Synapses and Circuits Although we think of ourselves as the same person throughout life, the structural and functional state of the brain changes dramatically over the human lifespan. The initial development of the nervous sys-tem entails the generation and differentiation of neurons, the forma-tion of axonal pathways, and the elaboration of vast numbers of syn-apses. Each of these events relies upon the interplay of secreted signals, their receptors, and transcriptional regulators, as well as adhesion and recognition molecules that determine appropriate identity, positions, and connections for developing neurons. The cir-cuits that emerge from these processes mediate an increasingly com-plex array of behaviors. Subsequent experience during postnatal life—and the activity-dependent molecular mechanisms that trans-late experience into changes in neuronal growth and gene expres-sion— continues to shape neural circuits, the related behavioral repertoires, and ultimately cognitive abilities. These changes are most pronounced during developmental windows in early life called critical periods. Even in maturity, however, synaptic connections can be modified as new skills and memories are acquired and older ones are forgotten; even some new neurons can be generated in a few spe-cialized regions. Some of the mechanisms used during early devel-opment are evidently retained and adapted to mediate these ongo-ing changes in the mature brain. Finally, like any other organ system, the brain is subject to dis-ease and traumatic insults. Some of these processes call repair mech-anisms into play; however, the capacity of the mature brain for repair or regeneration is limited. Diseases like amyotrophic lateral sclerosis, Parkinson’s disease, and Alzheimer’s disease all reflect pathologies of processes that normally contribute to neuronal development and to the subsequent maintenance and modification of neural circuitry. Overview The elaborate architecture of the adult brain is the product of genetic instruc-tions, cell-to-cell signals, and eventually interactions between the developing child and the external world. The early development of the nervous system is dominated by events that occur prior to the formation of synapses and are therefore activity-independent. These early events include the establishment of the primordial nervous system in the embryo, the initial generation of neurons from undifferentiated precursor cells, the formation of the major brain regions, and the migration of neurons from sites of generation to their final positions. These processes set the stage for the subsequent formation of axon pathways and synaptic connections. When any of these processes goes awry—because of genetic mutation, disease, or exposure to drugs or chemi-cals—the consequences can be disastrous. Indeed, most congenital brain defects result from interference with the normal mechanisms of activity-independent neuronal development. With the advent of powerful new tech-niques, the cellular and molecular machinery underlying these extraordinar-ily complex events is beginning to be understood. The Initial Formation of the Nervous System: Gastrulation and Neurulation Well before the patch of cells that will eventually become the brain and spinal cord appears, polarity (anterior versus posterior, medial versus lateral) and the primitive cell layers required for the subsequent formation of the nervous system are established in the embryo. Critical to this early frame-work in all vertebrate embryos is the process of gastrulation. This invagina-tion of the developing embryo (which starts out as a single sheet of cells) produces the three primitive cell layers or germ layers: the outer layer, or ectoderm; the middle layer, or mesoderm; and the inner layer, or endoderm (Figure 21.1). Based on the position of the invaginating mesoderm and endoderm, gastrulation defines the midline, anterior–posterior, and dosal– ventral axes of all vertebrate embryos. One key consequence of gastrulation is the formation of the notochord, a distinct cylinder of mesodermal cells that extends along the midline of the embryo from mid-anterior to posterior. The notochord forms from an aggre-gation of mesoderm that invaginates and extends inward from a surface indentation called the primitive pit, which subsequently elongates to form the primitive streak. As a result of these cell movements during gastrula-tion, the notochord comes to define the embryonic midline, and thus the major axis of symmetry for the entire body. The ectoderm that lies immedi-ately above the notochord, called the neuroectoderm, gives rise to the entire nervous system. Chapter 21 501 Early Brain Development 502 Chapter Twenty-One Figure 21.1 Neurulation in the mam-malian embryo. On the left are dorsal views of the embryo at several different stages of early development; each boxed view on the right is a midline cross sec-tion through the embryo at the same stage. (A) During late gastrulation and early neurulation, the notochord forms by invagination of the mesoderm in the region of the primitive streak. The ecto-derm overlying the notochord becomes defined as the neural plate. (B) As neu-rulation proceeds, the neural plate begins to fold at the midline (adjacent to the notochord), forming the neural groove and ultimately the neural tube. The neural plate immediately above the notochord differentiates into the floor-plate, whereas the neural crest emerges at the lateral margins of the neural plate (farthest from the notochord). (C) Once the edges of the neural plate meet in the midline, the neural tube is complete. The mesoderm adjacent to the tube then thickens and subdivides into structures called somites—the precursors of the axial musculature and skeleton. (D) As development continues, the neural tube adjacent to the somites becomes the rudimentary spinal cord, and the neural crest gives rise to sensory and auto-nomic ganglia (the major elements of the peripheral nervous system). Finally, the anterior ends of the neural plate (anterior neural folds) grow together at the midline and continue to expand, eventually giving rise to the brain. In addition to specifying the basic topography of the embryo and deter-mining the position of the nervous system, the notochord is required for subsequent neural differentiation (see Figure 21.1). Thus, the notochord (along with the primitive pit) sends inductive signals to the overlying ecto-derm that cause a subset of neuroectodermal cells to differentiate into neural precursor cells. During this process, called neurulation, the midline ecto-derm that contains these cells thickens into a distinct columnar epithelium called the neural plate. The lateral margins of the neural plate then fold inward, eventually transforming the neural plate into a tube. This neural tube subsequently gives rise to the brain and spinal cord. The progenitor cells of the neural tube are known as neural precursor cells. These precursors are dividing neural stem cells (Box A) that produce Mesoderm Mesoderm Endoderm Endoderm Notochord Notochord Floorplate Somite Ectoderm Ectoderm (A) 18 days (B) 20 days (C) 22 days (D) 24 days Neural plate Neural plate Notochord Primitive streak Neural groove Central canal Neural crest Neural crest Neural tube Anterior neural fold Sensory ganglion Sensory ganglion Anterior neural fold Neural tube Neural tube Spinal cord Somites Rhombencephalon Neural crest Neural plate/tube Pre-somitic mesoderm Floorplate Floorplate Somite Spinal chord Notochord more precursors, all with the capacity to give rise to neurons, astrocytes, and oligodendroglial cells. Eventually, subsets of these neural precursor cells will generate non-dividing neuroblasts that differentiate into neurons. Not all cells in the neural tube, however, are neural precursors. The cells at the ven-tral midline of the neural tube differentiate into a special strip of epithelial-like cells called the floorplate (reflecting their proximity to the notochord), which provides molecular signals to specify the neuroblast cells. The posi-tion of the floorplate at the ventral midline defines the dorsoventral polarity of the neural tube and further influences the differentiation of neural precur-sor cells. Inductive signals from both the notochord and floorplate lead to differentiation of cells in the ventral portion of the neural tube that eventu-ally give rise to spinal and hindbrain motor neurons (which are thus closest to the ventral midline). Precursor cells farther away from the ventral midline give rise to sensory relay neurons within the spinal cord and hindbrain. At the most dorsal limit of the neural tube, a third population of cells emerges in the region where the edges of the folded neural plate join together. Because of their location, this set of precursors is called the neural crest (Figure 21.2). The neural crest cells migrate away from the neural tube through loosely packed mesenchymal cells that fill the spaces between the neural tube, embryonic epidermis, and somites. Subsets of neural crest cells follow specific pathways that expose them to additional inductive signals that influence their differentiation. As a result, neural crest cells give rise to a variety of progeny, including the neurons and glia of the sensory and vis-ceral motor (autonomic) ganglia, the neurosecretory cells of the adrenal gland, and the neurons of the enteric nervous system. Neural crest cells also contribute to variety of non-neural structures such as pigment cells, carti-lage, and bone, particularly in the face and skull. The Molecular Basis of Neural Induction The essential consequence of gastrulation and neurulation for the develop-ment of the nervous system is the emergence of a population of neural pre-cursors from a subset of ectodermal cells. Through a variety of experimental manipulations, primarily involving extirpation or transplantation of differ-1 4 3 2 1 4 3 2 Neural crest Neural tube Notochord Floorplate Ectoderm Somite (A) (B) Notochord Floorplate Pre-somitic mesoderm Neural crest Neural groove Mesenchymal cells Figure 21.2 The neural crest. (A) Cross section through a developing mam-malian embryo at a stage similar to that in Figure 21.1B. The neural crest cells are established based on their position at the boundary of the embryonic epi-dermis and neuroectoderm. Arrows indicate the initial migratory route of undifferentiated neural crest cells. (B) Four distinct migratory paths lead to differentiation of neural crest cells into specific cell types and structures. Cells that follow pathways (1) and (2) give rise to sensory and autonomic ganglia, respectively. The precursors of adrenal neurosecretory cells migrate along path-way (3) and eventually aggregate around the dorsal portion of the kidney. Cells destined to become non-neural tis-sues (for example, melanocytes) migrate along pathway (4). Each pathway per-mits the migrating cells to interact with different kinds of cellular environments, from which they receive inductive sig-nals (see Figure 21.11). (After Sanes, 1988.) 504 Chapter Twenty-One Box A Stem Cells: Promise and Perils One of the most highly publicized issues in biology over the past several years has been the use of stem cells as a possible way of treating a variety of neurodegen-erative conditions, including Parkinson’s, Huntington’s, and Alzheimer’s diseases. Amidst the social, political, and ethical debate set off by the promise of stem cell therapies, an issue that tends to get lost is what, exactly, is a stem cell? Neural stem cells are an example of a broader class of stem cells called somatic stem cells. These cells are found in vari-ous tissues, either during development or in the adult. All somatic stem cells share two fundamental characteristics: they are self-renewing, and upon termi-nal division and differentiation they can give rise to the full range of cell classes within the relevant tissue. Thus, a neural stem cell can give rise to another neural stem cell or to any of the main cell classes found in the central and peripheral nervous system (inhibi-tory and excitatory neurons, astrocytes, and oligodendrocytes; Figure A). A neural stem cell is therefore distinct from a progenitor cell, which is incapable of continuing self-renewal and usually has the capacity to give rise to only one class of differentiated progeny. An oligoden-droglial progenitor, for example, contin-ues to give rise to oligodendrocytes until its mitotic capacity is exhausted; a neural stem cell, in contrast, can generate more stem cells as well as a full range of differ-entiated neural cell classes, presumably indefinitely. Neural stem cells, and indeed all classes of somatic stem cells, are distinct from embryonic stem cells. Embryonic stem cells (also known as ES cells) are derived from pre-gastrula embryos. ES cells also have the potential for infinite self-renewal and can give rise to all tis-sue and cell types throughout the organ-ism including germ cells that can gener-ate gametes (recall that somatic stem cells can only generate tissue specific cell types). There is some debate about the capacity of somatic stem cells to assume embryonic stem cell properties. Some experiments with hematopoetic and neural stem cells indicate that these cells can give rise to appropriately differ-entiated cells in other tissues; however, some of these experiments have not been replicated. The ultimate therapeutic promise of stem cells—neural or other types—is their ability to generate newly differenti-ated cell classes to replace those that may have been lost due to disease or injury. Such therapies have been imagined for some forms of diabetes (replacement of islet cells that secrete insulin) and some hematopoetic diseases. In the nervous system, stem cell therapies have been suggested for replacement of dopaminer-gic cells lost to Parkinson’s disease and replacing lost neurons in other degenera-tive disorders. While intriguing, this projected use of stem cell technology raises some signifi-cant perils. These include insuring the controlled division of stem cells when introduced into mature tissue, and iden-tifying the appropriate molecular instruc-tions to achieve differentiation of the desired cell class. Clearly, the latter chal-lenge will need to be met with a fuller understanding of the signaling and tran-scriptional regulatory steps used during development to guide differentiation of relevant neuron classes in the embryo. At present, there is no clinically vali-dated use of stem cells for human thera-peutic applications in the nervous sys-tem. Nevertheless, some promising work in mice and other experimental animals indicates that both somatic and ES cells can acquire distinct identities if given appropriate instructions in vitro (i.e., prior to introduction into the host), and if delivered into a supportive host envi-ronment. For example, ES cells grown in the presence of platelet-derived growth factor, which biases progenitors toward glial fates, can generate oligodendroglial cells that can myelinate axons in myelin-deficient rats. Similarly, ES cells pre-treated with retinoic acid matured into motor neurons when introduced into the (A) (i) (ii) (iii) (A) A single “neurosphere” consisting of clon-ally related neural stem cells from the adult forebrain is shown at top. Neurosphere-derived stem cells can differentiate to produce (i) GABAergic neurons, (ii) astrocytes, and (iii) oligodendrogila. ent portions of developing embryos, embryologists recognized early on that this process depends on signals arising from cells in the primitive pit and notochord. Because a wide variety of chemical agents and physical manipu-lations are able to mimic some of the effects of these endogenous signals, their nature remained a mystery for several decades. It is now clear that the generation of cell identity—of which neural induction is but one mecha-nism—results from the spatial and temporal control of different sets of genes by endogenous signaling molecules (Figure 21.3). These inducing signals— including those from the primitive pit and notochord—are, not surprisingly, molecules that modulate gene expression. The increasingly sophisticated effort to understand exactly how these inductive signals work has therefore focused on molecules that can modify patterns of gene expression. One of the first of these inductive signals to be identified was retinoic acid, a derivative of vitamin A and a member of the steroid/thyroid superfamily of hormones (Figure 21.3 and Box B). Retinoic acid activates a unique class of transcription factors—the retinoid receptors—that modulate the expression of a number of target genes. Peptide hormones provide another class of inductive signals, including those that belong to the fibroblast growth factor (FGF) and transforming growth factor (TGF) families. Within the TGF fam-ily, the bone morphogenetic proteins (BMPs) are particularly important for a variety of events in neural induction and differentiation; these will be dis-Early Brain Development 505 developing spinal cord (Figure B). While such experiments suggest that a combi-nation of proper instruction and correct placement can lead to appropriate differ-entiation, there are still many issues to be resolved before the promise of stem cells for nervous system repair becomes a reality. References BRAZELTON, T. R., F. M. V. ROSSI, G. I. KESHET AND H. M. BLAU (2000) From marrow to brain: Expression of neuronal phenotypes in adult mice. Science 290: 1776–1779. BRUSTLE, O. AND 7 OTHERS (1999) Embryonic stem cell derived glial precursors: A source of myelinating transplants. Science 285: 754–756. CASTRO, R. F., K. A. JACKSON, M. A. GOODELL, C. S. ROBERTSON, H. LIU AND H. D. SHINE (2002) Failure of bone marrow cells to transd-ifferentiate into neural cells in vivo. Science 297: 1299. MEZEY, E., K. J. CHANDROSS, G. HARTA, R. A. MAKI AND S. R. MCKERCHER (2000) Turning blood into brain: Cells bearing neuronal anti-gens generated in vivo from bone marrow. Science 290: 1779–1782. SEABERG, R. M. AND D. VAN DER KUOY. (2003) Stem and progenitor cells: The premature desertion of rigorous definition. TINS 26: 125–131. WICHTERLE, H., I. LIEBERAM, J. A. PORTER AND T. M. JESSELL (2002) Directed differentiation of embryonic stem cells into motor neurons. Cell 110: 385–397. (B) Injection of stem cells into spinal cord (B) Top left: Schematic of the injection of flu-orescently labeled embryonic stem (ES) cells into the spinal cord of a host chicken embryo. Bottom left: ES cells integrate into the host spinal cord and apparently extend axons. Top right: the progeny of the grafted ES cells are seen in the ventral horn of the spinal cord. They have motor neuron-like morphologies, and their axons extend into the ventral root. (From Wichterle et al., 2002.) 506 Chapter Twenty-One Box B Retinoic Acid:Teratogen and Inductive Signal In the early 1930s, investigators noticed that vitamin A deficiency during preg-nancy in animals led to a variety of fetal malformations. The most severe abnor-malities affected the developing brain, which was often grossly malformed. At about the same time, experimental stud-ies yielded the surprising finding that excess vitamin A caused similar defects. These observations suggested that a fam-ily of compounds—metabolic precursors or derivatives of vitamin A called retinoids—are teratogenic. (Teratogenesis is the term for birth defects induced by exogenous agents.) The retinoids include the alcohol form of vitamin A (retinol), the aldehyde form (retinal), and the acid form (retinoic acid). Subsequent experi-ments in animals confirmed that other retinoids produce birth defects similar to those generated by too much—or too lit-tle—vitamin A. The disastrous conse-quences of exposure to exogenous retin-oids during human pregnancy were underscored in the early 1980s when the drug Accutane® (the trade name for iso-retinoin, or 13-cis-retinoic acid) was intro-duced as a treatment for severe acne. Women who took this drug during preg-nancy had an increased number of spon-taneous abortions and children born with a range of birth defects. Despite the im-portance of these several findings, the reasons for the adverse effects of retin-oids on fetal development remained ob-scure well into the late twentieth century. An important insight into teratogenic potential of retinoids came when embry-ologists working on limb development in chicks found that retinoic acid mimics the inductive ability of tissues in the limb bud. Still the mystery remained as to just what retinoic acid (or its absence) was doing to influence or compromise devel-opment. An important answer came in the mid-1980s, when the receptors for retinoic acid were discovered. These receptors are members of the steroid/ thyroid hormone receptor superfamily; when they bind retinoic acid or similar ligands, the receptors act as transcription factors to activate specific genes. Further-more, careful biochemical analysis showed that retinoic acid was synthe-(B) (A) (A) At left, retinoic acid activates gene expression in a subset of cells in the normal developing forebrain of a mid-gestation mouse embryo (blue areas indicate β-galac-tosidase reaction product, an indicator of gene expression in this experiment). At right, after maternal ingestion of a small quantity of retinoic acid (0.00025 mg/g of maternal weight), gene expression is ectopically acti-vated throughout the forebrain. (B) At left, the brain of a normal mouse at term; at right, the grossly abnormal brain of a mouse whose mother ingested this same amount of retinoic acid at mid-gestation. (A from Anchan et al., 1997; B from Linney and LaMantia, 1994.) cussed in more detail later in this chapter. Another peptide hormone essential for neural induction is sonic hedgehog (shh). Shh is thought to be particu-larly important for differentiation of neurons—including motor neurons—in the ventral portion of the neural tube. Finally, members of the Wnt family of secreted signals (vertebrate homologues of the wingless gene of Drosophila) can modulate several aspects of neural induction and differentiation includ-ing some aspects of neural crest differentiation. Each of these molecules is produced by a variety of embryonic tissues—including the notochord, the floorplate, and the neural ectoderm itself, as well as tissues like somites that are adjacent to the developing nervous system—and they bind to surface receptors on nearby cells. In some cases, these signals have graded effects based upon the distance of target cells from the source of the inductive signal. These effects may represent a diffusion gradient of the signal, or graded activity due to distribution of receptors or other signaling components. Other signals are more specific in their action, being most effective at the bound-aries between distinct cell populations. The results of inductive signaling include changes in shape, motility, and gene expression in the target cells. The receptors for inductive signals, their locations, and their mode of action are clearly essential elements in determing the consequences of induc-tive signaling (Figure 21.3). The receptors for the FGF and BMP families of peptide signals are protein kinases. FGF receptors are tyrosine kinases that bind FGF with the cooperation of extracellular matrix components including heparan sulfate proteoglycan. Upon binding, activation of the intracellular kinase domains of the FGF receptors leads to activation of the RAS/MAP kinase pathway (see Chapter 7). This signaling can modify cytoskeletal and cytoplasmic components and thus alter the shape or motility of a cell, or it can in regulate gene expression, particularly genes that influence cell prolif-eration. BMP receptors are serine threonine kinases that phosphorylate a group of cytoplasmic proteins called SMADs. Upon phosphorylation, SMAD multimers translocate to the nucleus and interact with other DNA-binding proteins, thus modulating gene expression. Early Brain Development 507 sized by embryonic tissues. Subsequent studies have shown that retinoic acid acti-vates gene expression at several sites in the embryo including the developing brain (see figure). Among the most im-portant targets for retinoic acid regulation are genes for other inductive signals in-cluding sonic hedgehog and Hox genes (see Box C). Thus, an excess or deficiency of retinoic acid can disrupt normal devel-opment by eliciting inappropriate pat-terns of retinoid-induced gene expression. The role of retinoic acid as both a ter-atogen and an endogenous signaling molecule implies that the retinoids cause birth defects by mimicking the normal signals that influence gene expression. The story provides a good example of how teratogenic, clinical, cellular, and molecular observations can be combined to explain seemingly bizarre develop-mental pathology. References EVANS, R. M. (1988) The steroid and thyroid hormone receptor superfamily. Science 240: 889–895. JOHNSON R. L. AND C. J. TABIN (1997) Molecu-lar models for vertebrate limb development. Cell 90: 979–990 LAMANTIA, A.-S., M. C. COLBERT AND E. LIN-NEY (1993) Retinoic acid induction and regional differentiation prefigure olfactory pathway formation in the mammalian fore-brain. Neuron 10: 1035–1048. LAMMER, E. J. AND 11 OTHERS (1985) Retinoic acid embryopathy. N. Engl. J. Med. 313: 837–841. SCHARDEIN, J. L. (1993) Chemically Induced Birth Defects, 2nd Ed. New York: Marcel Dekker. THALLER, C. AND G. EICHELE (1987) Identifica-tion and spatial distribution of retinoids in the developing chick limb bud. Nature 327: 625–628. TICKLE, C., B. ALBERTS, L. WOLPERT AND J. LEE (1982) Local application of retinoic acid to the limb bud mimics the action of the polarizing region. Nature 296: 564–565. WARKANY, J. AND E. SCHRAFFENBERGER (1946) Congenital malformations induced in rats by maternal vitamin A deficiency. Arch. Oph-thalmol. 35: 150–169. 508 Chapter Twenty-One Some inductive signals use more indirect signaling routes. For example, the transduction of signals via sonic hedgehog depends on the cooperative bind-ing of two surface receptors followed by internalization of the receptor. The internalized complexes influence nuclear translocation of transcription factors (including Gli1) and subsequent modulation of gene expression. The trans-duction of Wnt signals has a similarly circuitous route, leading ultimately to the nucleus. Wnt receptors, including a family of proteins with the fanciful name “frizzled,” initiate a cascade of events after Wnt binding that leads to the degradation of a cytoplasmic protein complex that normally prevents the translocation of β-catenin from the cytoplasm to the nucleus. Once freed from this inhibition, β-catenin enters the nucleus and influences expression of a number of downstream genes. A particularly distinctive aspect neural induction is the mechanism by which the BMPs influence neural differentiation (see Figure 21.3). As the name suggests, these peptide hormones, which are members of the TGF-β family, elicit osteogenesis from mesodermal cells. If ectodermal cells are exposed to BMPs, they assume an epidermal fate. But how then does the (A) Sonic Hedgehog (shh) (D) Bone morphogenetic protein (BMP) (E) Wnt (B) Retinoic acid (RA) (C) Fibroblast growth factor (FGF) DNA Gli1 Smoothened RA RA RA binding protein ? RA receptor Co–A Patched protein shh DNA ras Receptor tyrosine kinase SNF/Grb2 Extracellular matrix MAP kinase Gli1 DNA Receptor serine kinase SMAD Co– SMAD BMP DNA β–catenin LEF/TCF Frizzled protein Wnt Noggin/ chordin DNA FGF Dishevelled/ APC/axin Figure 21.3 Major inductive signaling pathways in vertebrate embryos. Schematics of ligands, receptors, and primary intracellular signaling mole-cules for retinoic acid (RA); members of the FGF and TGF-β superfamily of pep-tide hormones; sonic hedgehog (shh); and the Wnt family of signals. Each of these pathways contributes to the initial establishment of the neural ectoderm, as well as to the subsequent differentiation of distinct classes of neurons and glia throughout the brain. ectoderm manage to become neuralized, given the fact that BMPs are pro-duced by the somites and surrounding mesodermal tissue? All of these struc-tures are in position to signal to the neuroectoderm, and therefore to convert it to epidermis. This fate is evidently avoided in the neural plate by the local activity of other inductive signaling molecules such as noggin and chordin— two members of a broad class of endogenous antagonists that modulate sig-naling via the TGF-β family (including that of the BMPs). Both of these mole-cules bind directly to the BMPs and thus prevent their binding to BMP receptors. In this way, the neuroectoderm is “rescued” from becoming epi-dermis. Such negative regulation has reinforced the speculation that becom-ing a neuron is actually the “default” fate for embryonic ectodermal cells. Some of these molecular signals have been implicated in determining the fates of specific classes of cells in the developing nervous system act after the initial differentiation of the neural plate, tube and neural crest (Figure 21.4). As mentioned above, sonic hedgehog (shh) is essential for the differentiation of motor neurons in the ventral spinal cord (Figure 21.4D), as well as some classes of neurons and glia in the forebrain; TGF-β family signals (including the BMPs) are important for the establishment of dorsal cells in the spinal cord—as well as the neural crest—and can influence other neuron classes in dorsal positions throughout the forebrain. The Wnt family of signals also is essential for the differentiation of neural crest, cerebellar granule cells, and Early Brain Development 509 (B) ssh (C) noggin (D) Ventral Dorsal Notochord Floorplate (A) Neural crest TGF-β family: BMPs, dorsalin; retinoic acid, noggin Sonic hedgehog, retinoic acid, noggin, and chordin Sensory relay neurons (to thalamus) Primary motor neurons (to muscles) Notochord Figure 21.4 Localized inductive signals influence axes and cellular identity in the developing neural tube. (A) Local signals associated with the dorsal-ventral axis. This distribution of signaling molecules is seen in those regions of the neural tube that give rise to the spinal cord and hind-brain. (B) Expression of shh mRNA is limited to the notochord and floor-plate of the developing spinal cord. This localized expression is thought to establish a gradient of secreted shh peptide extending throughout most of the ventral spinal cord. (C) The endogenous TGF-β antagonist noggin is expressed both in the notochord and in the dorsal medial neural tube (a region referred to as the roofplate). (D) The identity of motor (yellow) and sensory relay neurons (green) in the ventral versus the dorsal spinal cord, respectively, is thought to reflect the graded local activity of signals like shh, noggin, and others. This impression has been confirmed in studies that disrupt the balance of local inductive signals. 510 Chapter Twenty-One forebrain neurons. Thus, inductive signals can serve multiple purposes throughout neural development. Awareness of the molecules involved in neural induction has provided a much more informed way of thinking about the etiology and prevention of a number of congenital disorders of the nervous system. Anomalies like spina bifida (failure of the posterior neural tube to close completely), anencephaly (failure of the anterior neural tube to close at all), holoprosencephaly (dis-rupted regional differentiation of the forebrain), and other brain malforma-tions (often accompanied by mental retardation) can result from environ-mental insults that disrupt inductive signaling or from the mutation of genes that participate in this process. As already described, excessive intake of vit-amin A can impede neural tube closure and differentiation or disrupt later aspects of neuronal differentiation (see Box B). Embryonic exposure to a variety of other drugs—alcohol and thalidomide are good examples—can also elicit pathological differentiation of the embryonic nervous system by providing inductive signals at inappropriate times or places. Altered choles-terol metabolism can compromise sonic hedgehog signaling. Furthermore, dietary insufficiency of substances such as folic acid can disrupt neural tube formation by compromising cellular mechanisms essential for normal cell division and motility. Because the consequences of disordered neural induc-tion are so severe, pregnant women are well advised to avoid virtually all drugs and dietary supplements except those specifically prescribed by a physician, especially during the first trimester of pregnancy. Formation of the Major Brain Subdivisions Soon after neural tube formation, the forerunners of the major brain regions become apparent as a result of morphogenetic movements that bend, fold, and constrict the neural tube. Initially, the anterior end of the tube forms a crook, giving it the shape of a cane handle (Figure 21.5A). The end of the cane nearest the sharper bend, the cephalic flexure, balloons out to form the forebrain, or prosencephalon. The midbrain, or mesencephalon, forms as a bulge above the cephalic flexure. The hindbrain, or rhombencephalon, forms in the long, relatively straight stretch between the cephalic flexure and the more caudal cervical flexure. Caudal to the cervical flexure, the neural tube forms the precursor of the spinal cord. This bending and folding con-Figure 21.5 Regional specification of the developing brain. (A) Early in gestation the neural tube becomes subdivided into the prosencephalon (at the anterior end of the embryo), mesencephalon, and rhombencephalon. The spinal cord differentiates from the more posterior region of the neural tube. The initial bending of the neural tube at its anterior end leads to a cane shape. At right is a longitudinal section of the neural tube at this stage, showing the position of the major brain regions. (B) Fur-ther development distinguishes the telencephalon and diencephalon from the pros-encephalon; two other subdivisions—the metencephalon and myelencephalon— derive from the rhombencephalon. These subregions give rise to the rudiments of the major functional subdivisions of the brain, while the spaces they enclose eventu-ally form the ventricles of the mature brain. At right is a longitudinal section of the embryo at the developmental stage shown in (B). (C) The fetal brain and spinal cord are clearly differentiated by the end of the second trimester. Several major subdivi-sions, including the cerebral cortex and cerebellum, are clearly seen from the lateral surfaces. At right is a cross section through the forebrain at the level indicated showing the nascent sulci and gyri of the cerebral cortex, as well as the differentia-tion of thalamic nuclei. ▲ stricts or enlarges the lumen enclosed by the developing neural tube. These lumenal spaces eventually become the ventricles of the mature brain (Figure 21.5B; see also Appendix B). Once the primitive brain regions are established in this way, they undergo at least two more rounds of partitioning, each of which produces additional regions in the adult (Figure 21.5C). Thus, the lateral aspects of the rostral prosencephalon forms the telencephalon. The two bilaterally symmetric telencephalic vesicles include dorsal and ventral territories. The dorsal terri-(A) Cervical flexure Cephalic flexure Mesencephalon Prosencephalon Rhombencephalon Optic vesicle Spinal cord Cranial and spinal ganglia (B) Telencephalon Mesencephalon Metencephalon Myelencephalon Pontine flexure Optic vesicle (from diencephalon) Spinal cord Diencephalon Diencephalon (thalamus) (C) Cerebral hemisphere Lateral fissure Central sulcus Cerebellum Olfactory bulb Spinal cord Metencephalon Myelencephalon Prosencephalon Rhombencephalon Mesencephalon Spinal cord Telencephalon Diencephalon Mesencephalon Metencephalon Myelencephalon Third ventricle Future cerebral aqueduct Lateral ventricle Optic vesicle Fourth ventricle Central canal Spinal cord Lateral ventricles Basal ganglia Cerebral cortex Early Brain Development 511 512 Chapter Twenty-One tory will give rise to the rudiments of the cerebral cortex and hippocampus, while the ventral territory gives rise to the basal ganglia (derived from embryonic structures called the ganglionic eminences), basal forebrain nuclei, and olfactory bulb. The more caudal portion of the prosencephalon forms the diencephalon, which contains the rudiments of the thalamus and hypothalamus, as well as a pair of lateral outpocketings (the optic cups) from which the neural portion of the retina will form. The dorsal portion of the mesencephalon gives rise to the superior and inferior colliculi, while the ventral portion gives rise to a collection of nuclei known as the midbrain tegmentum. The rostral part of the rhombencephalon becomes the meten-cephalon and gives rise to the adult cerebellum and pons. Finally, the caudal part of the rhombencephalon becomes the myelencephalon and gives rise to the adult medulla. How can a simple tube of neuronal precursor cells produce such a variety of brain structures? At least part of the answer comes from the observation made early in the twentieth century that much of the neural tube is orga-nized into repeating units called neuromeres. This discovery led to the idea Box C Homeotic Genes and Human Brain Development The notion that particular genes can influence the establishment of distinct regions in an embryo arose from efforts to catalog single-gene mutations that affect development of the fruit fly Drosophila. In the 1960s and 1970s, E. B. Lewis at the California Institute of Tech-nology reported a number of mutations that resulted in either the duplication of a distinct body segment or the appear-ance of an inappropriate structure at an ectopic location in the fly. These genes were called homeotic genes because they were able to convert segments of one sort to those of another (homeo is Greek for “similar”). Subsequently, studies by C. Nusslein-Volhard and E. Wieschaus demonstrated the existence of numerous such “master control” genes, each form-ing part of a cascade of gene expression leading to the distinctive segmentation of the developing embryo. (In 1995, Lewis, Nusslein-Volhard, and Wieschaus shared a Nobel Prize for these discoveries.) Homeotic genes code for DNA-bind-ing proteins—that is, transcription fac-tors—that bind to a particular sequence of genomic DNA called the “homeobox.” Similar genes have been found in most species, including humans. Using an approach known as cloning by homol-ogy, at least four “clusters” of homeobox genes have been identified in virtually all vertebrates that have been examined. The genes of each cluster are closely, but not consecutively, spaced on a single chromosome. Other motifs identified in Drosophila have led to the discovery of additional families of DNA-binding pro-teins, which have again been found in a variety of species. Importantly, a number of develop-mental anomalies in mice and humans have been associated with mutations in the homeotic or other developmental con-trol genes initially identified in the fly. Relatively rare diseases like aniridia, Waardenburg syndrome, and Greig cephalopolysyndactyly syndrome (all disorders that disrupt the nervous system and peripheral structures like the iris or the digits) have been associated with human genes that are homologues of Drosophila developmental control genes. In addition, several other developmental disorders including autism and various forms of mental retardation can be asso-ciated with mutations or polymorphisms of homeobox genes (see text). Thus, the initial insights into the molecular control of development gleaned from genetic studies of Drosophila have opened new avenues for exploring the molecular basis of developmental disorders in humans. References ENGELKAMP, D. AND V. VAN HEYNINGEN (1996) Transcription factors in disease. Curr. Opin. Genet. Dev. 6: 334–42. GEHRING, W. J. (1993) Exploring the homeo-box. Gene 135: 215–221. GRUSS, P. AND C. WALTHER (1992) Pax in development. Cell 69: 719–721. LEWIS, E. B. (1978) A gene complex control-ling segmentation in Drosophila. Nature 276: 565–570. NUSSLEIN-VOLHARD, C. AND E. WIESCHAUS (1980) Mutations affecting segment number and polarity in Drosophila. Nature 287: 795–801. READ, A. P. AND V. E. NEWTON (1997) Waar-denburg syndrome. J. Med. Genet. 34: 656–665. SHIN, S. H., P. KOGERMAN, E. LINDSTROM, R. TOFTGARD AND L. G. BIESECKER (1999) Gli3 mutations in human disorders mimic Drosophila cubitus interruptus protein func-tions and localization. Proc. Natl. Acad. Sci. USA 96: 2880–2884. that the process of segmentation—used by all animal embryos at the earliest stages of development to establish regional identity in the body—might also establish regional identity in the developing brain. Enthusiasm for this hypoth-esis was stimulated by observations of the development of the body plan of the fruit fly Drosophila. In the fly, early expression of a class of genes called homeotic or homeobox genes (Box C) guides the differentiation of the embryo into distinct segments that give rise to the head, thorax, and abdomen (Figure 21.6). These genes code for DNA-binding proteins that can modulate the expression of other genes. Similar homeobox genes in mammals (referred to as Hox genes) have also been identified. In some cases their pattern of expression coincides with, or even precedes, the forma-tion of morphological features such as the various bends, folds, and constrictions that signify the progressive regional-ization of the developing neural tube, particularly in the hindbrain and spinal cord (Figure 21.6 and Box D). (B) (A) (C) Time Mesothorax Metathorax Abdominal segments T1 T2 A7 A8 A1 A3 A4 A5 A6 A2 T1 T2 T3 A1 A2 A3 A4 A5 A6 A7 A8 Head Prothorax T3 lab pb Dfd Scr ftz Antp Ubx abd–A abd–B bcd, zen HoxA HoxB bcd kr h wg HoxC HoxD Hox1 Hox2 Hox3 Hox4 Hox5 Hox6 (central) Hox7 (Posterior) C10 C11 C12 D10 D11 D12 A1 A2 A3 A4 A5 A6 A7 A9 A10 A11 A13 B1 B2 B3 B4 B5 B6 B7 B9 B8 B13 D1 D3 D4 D9 D8 D13 C4 C5 C6 C9 C8 C13 Human Anterior Drosophila Hox cluster Ancestral Hox cluster Posterior Anterior Posterior Figure 21.6 Sequential gene expression divides the embryo into regions and segments. (A) The relationship of the embryonic segments in the Drosophila larva, defined by sequential gene expression, to the body plan of the mature fruit fly. (B) Temporal pattern of expres-sion of four genes that influence the establishment of the body plan in Drosophila. A series of sections through the anterior-posterior midline of the embryo are shown from early to later stages of development (top to bottom in each row). Initially, expression of the gene bicoid (bcd) helps define the anterior pole of the embryo. Next, krüp-pel (kr) is expressed in the middle and then at the poste-rior end of the embryo, defining the anterior-posterior axis. Then hairy (h) is expressed, which helps to delin-eate the domains that will eventually form the mature segmented body of the fly. Finally, the wingless (wg) gene is expressed, further refining the organization of individual segments. (C) Parallels between Drosophila segmental genes (the inferred “ancestral” homeobox genes from which invertebrate and vertebrate segmental genes evolved) and human Hox genes. Human Hox genes have apparently been duplicated twice, leading to four independent groups, each on a distinct human chromosome. The anterior-to-posterior pattern of Hox gene expression in both flies and mammals (including humans) follows the 3′-to-5′ orientation of these genes on their respective chromosomes. (A after Gilbert, 1994, and Lawrence, 1992; B from Ingham, 1988; C after Veraksa and Mc Ginnis, 2000.) 514 Chapter Twenty-One Box D Rhombomeres An interesting parallel between early embryonic segmentation and early brain development was noticed around the turn of the nineteenth century. Several embryologists reported repeating units in the early neural plate and neural tube, which they called neuromeres. In the late 1980s, A. Lumsden, R. Keynes, and their colleagues, as well as R. Krumlauf, R. Wilkinson, and colleagues, noticed fur-ther that combinations of homeobox (Hox) and related genes (see Box C) are expressed in banded patterns in the developing chick nervous system, espe-cially in the hindbrain (the common name for the rhombencephalon and its derivatives). These expression domains defined rhombomeres, which in the chick (as well as in most mammals), are a series of seven transient bulges in the developing rhombencephalon corre-sponding to the neuromeres described earlier. Rhombomeres are sites of differ-ential cell proliferation (cells at rhom-bomere boundaries divide faster than cells in the rest of the rhombomere), dif-ferential cell mobility (cells from any one rhombomere cannot easily cross into adjacent rhombomeres), and differential cell adhesion (cells prefer to stick to those of their own rhombomere). Later in development, the pattern of axon outgrowth from the cranial motor nerves also correlates with the earlier rhombomeric pattern. Cranial motor nerves (see Appendix A) originate either from a single rhombomere or from spe-cific pairs of neighboring rhombomeres (transplantation experiments indicate that rhombomeres are in fact specified in pairs). Thus, Hox gene expression proba-bly represents an early step in the forma-(A) Trigeminal ganglion Geniculate ganglion (VII) r1 r2 r3 r4 r5 r6 r7 Spiral and Scarpa’s ganglia (VIII) Jugular/nodose ganglia (X) Petrosal ganglion (IX) Otic vesicle Abducens nerve Trochlear nerve Trigeminal motor nerve Facial motor nerve Glosso-pharyngeal nerve Vagus nerve Hypoglossal nerve (B) (C) Rhombomeres in the developing chicken hindbrain and their relationship to the differentia-tion of the cranial nerves. (A) Diagram of the chick hindbrain, indicating the position of the cranial ganglia and nerves and their rhombomeric origin (rhombomeres denoted as r1 to r7). (B) Section through early chicken hindbrain, showing bulges that will eventually become rhombomeres (in this example, r3 to r5). (C) Differential patterns of transcription factor expression (in this case, krx20, a Hox-like gene) define rhombomeres at early stages of devel-opment, well before the cranial nerves that will eventually emerge from them are apparent. (A courtesy of Andrew Lumsden; B,C from Wilkinson and Krumlauf, 1990.) The patterned expression of Hox genes, as well as other developmentally regulated transcription factors (many with homology to other patterning genes that influence development in Drosophila) and signaling molecules, does not by itself determine the fate of a group of embryonic neural precur-sors. Instead, this aspect of regionally distinct transcription factor expression during early brain development contributes to a broader series of genetic and cellular processes that eventually produce fully differentiated brain regions with appropriate classes of neurons and glia. Genetic Abnormalities and Altered Human Brain Development The recent explosion of information about molecules that influence brain development provides a basis for reevaluating the causes of a number of con-genital brain malformations, as well as various forms of mental retardation. For instance, some forms of hydrocephalus (caused by impeded flow of cere-brospinal fluid, which increases pressure and results in enlarged ventricles and eventually cortical atrophy as a result of compression) can be traced to mutations of genes on the X chromosome, especially those in the L1 cell adhesion molecule (see Chapter 22). Similarly, fragile-X syndrome, the most common form of congenital mental retardation, is associated with triplet repeats in a subset of genes on the X chromosome, particularly the fragile-X protein, which is involved in stabilizing dendritic processes and synapses. Beyond these X-linked abnormalities, there are at least two genetic disor-ders that compromise the nervous system generated by single gene muta-tions in homeobox-like transcription factors. Aniridia (characterized by loss Early Brain Development 515 tion of cranial nerves in the developing brain. Mutation or ectopic activation of Hox genes in mice alters the position of specific cranial nerves, or prevents their formation. Mutation of the HoxA-1 gene by homologous recombination—the so-called “knockout” strategy for targeting mutations to specific genes—prevents normal formation of rhombomeres. In these animals, development of the exter-nal, middle, and inner ear is also com-promised, and cranial nerve ganglia are fused and located incorrectly. Con-versely, when the HoxA-1 gene is expressed in a rhombomere where it is usually not seen, the ectopic expression causes changes in rhombomere identity and subsequent differentiation. It is likely that problems in rhombomere for-mation are the underlying cause of con-genital nervous system defects involv-ing cranial nerves, ganglia, and peripheral structures derived from the cranial neural crest (the part of the neural crest that arises from the hind-brain). The exact relationship between early patterns of rhombomere-specific gene transcription and subsequent cranial nerve development remains a puzzle. Nevertheless, the correspondence between these repeating units in the embryonic brain and similar iterated units in the development of the insect body (see Figure 21.5) suggests that dif-ferential expression of transcription fac-tors in specific regions is essential for the normal development of many species. In a wide variety of animals, spatially and temporally distinct patterns of transcrip-tion factor expression coincide with spa-tially and temporally distinct patterns of differentiation, including the differentia-tion of the nervous system. The idea that the bulges and folds in the neural tube are segments defined by patterns of gene expression provides an attractive frame-work for understanding the molecular basis of pattern formation in the develop-ing vertebrate brain. References CARPENTER, E. M., J. M. GODDARD, O. CHISA-KA, N. R. MANLEY AND M. CAPECCHI (1993) Loss of HoxA-1 (Hox-1.6) function results in the reorganization of the murine hindbrain. Development 118: 1063–1075. GUTHRIE, S. (1996) Patterning the hindbrain. Curr. Opin. Neurobiol. 6: 41–48. LUMSDEN, A. AND R. KEYNES (1989) Segmental patterns of neuronal development in the chick hindbrain. Nature 337: 424–428. VON KUPFFER, K. (1906) Die morphogenie des central nerven systems. In Handbuch der ver-gleichende und experiementelle Entwick-lungslehreder Wirbeltiere, Vol. 2, 3: 1–272. Fis-cher Verlag, Jena. WILKINSON, D. G. AND R. KRUMLAUF (1990) Molecular approaches to the segmentation of the hindbrain. TINS 13: 335–339. ZHANG, M. AND 9 OTHERS (1993) Ectopic HoxA-1 induces rhombomere transformation in mouse hindbrain. Development 120: 2431–2442. 516 Chapter Twenty-One of the iris in the eye and mild mental retardation) and Waardenburg syn-drome (characterized by craniofacial abnormalities, spina bifida, and hear-ing loss) are caused by mutations in the Pax6 and Pax3 genes, respectively, both of which produce transcription factors (see Box C). Finally, develop-mental disorders such as autism and other severe social or learning impair-ments have been linked in some cases to mutations in specific genes (includ-ing some of the Wnt family), as well as to microdeletions or duplications of specific chromosomal regions. Perhaps the best known example of this class of neurodevelopmental disorders is Down syndrome or trisomy 21, which is caused by the duplication of part or all of chromosome 21, usually due to failure of meiosis during the final stages of oogenesis. This duplication leads to three copies of the genes on chromosome 21; an as yet unknown subset of these genes leads to increased levels of the relevant proteins and altered neural development. Although the connections between these aberrant genes and the resulting anomalies of brain development are not yet understood, such correlations provide a starting point for exploring the molecular pathogenesis of many congenital disorders of the nervous system. The Initial Differentiation of Neurons and Glia Once the neural tube has developed into a rudimentary brain and spinal cord, the generation and differentiation of the permanent cellular elements of the brain—neurons and glia—begins in earnest. As noted in Chapter 1, the mature human brain contains about 100 billion neurons and many more glial cells, all generated over the course of only a few months from a small population of precursor cells. Except for a few specialized cases (see Chapter 24), the entire neuronal complement of the adult brain is produced during a time window that closes before birth; thereafter, precursor cells disappear, and few if any new neurons can be added to replace those lost by age or injury in most brain regions. The precursor cells are located in the ventricu-lar zone, the innermost cell layer surrounding the lumen of the neural tube, and a region of extraordinary mitotic activity. It has been estimated that in humans, about 250,000 new neurons are generated each minute during the peak of cell proliferation during gestation. The dividing precursor cells in the ventricular zone undergo a stereo-typed pattern of cell movements as they progress through the mitotic cycle, leading to the formation of either new stem cells or postmitotic neuroblasts that differentiate into neurons (Figure 21.7). As cells become postmitotic, they leave the ventricular zone and migrate to their final positions in the developing brain. Knowing when the neurons destined to populate a given brain region are “born”—that is, when they become postmitotic (determined by performing birthdating studies; Box E)—has given considerable insight into how different regions of the brain are constructed. Different populations of spinal cord neurons as well as nuclei of the brainstem and thalamus are distinguished by the times when their component neurons are generated, and some of these distinctions are influenced by local differences in signal-ing molecules and transcription factors that characterize the precursors (see Figure 21.9). In the cerebral cortex, most neurons of the six layers of the cor-tex are generated in an inside-out manner (see Box F for an intriguing excep-tion to this rule). The firstborn cells are eventually located in the deepest lay-ers, while later generations of neurons migrate radially from the site of their final division in the ventricular zone through the older cells and come to lie superficial to them (Figure 21.8). Indeed, in most regions of the brain where Early Brain Development 517 Box E Neurogenesis and Neuronal Birthdating The process by which neurons are gener-ated is generally referred to as neurogen-esis. The time at which neurogenesis occurs for any particular neuron is called its neuronal “birthdate.” At some point in development, stem cells—the dividing cells that populate the proliferative zones of the developing brain—undergo asym-metrical divisions that produce both another stem cell and a neuronal precur-sor (called a neuroblast) that will never again undergo cell division. Because neurons are generally unable to reenter the cell cycle once they have left it, the point at which a neuronal precursor leaves the cycle defines the birthdate of the resulting neuron. In animals with extraordinarily sim-ple nervous systems, such as the worm Caenorhabditis elegans, it is possible to directly monitor in a microscope each embryonic stem cell as it undergoes its characteristic series of cell divisions, and to thereby determine when a specific neuron is born. In the vastly more com-plex vertebrate brain, however, this approach is not feasible. Instead, neuro-biologists rely on the characteristics of the cell cycle itself to label cells according to their date of birth. When cells are actively replicating DNA, they take up nucleotides—the building blocks of DNA (see Figure 21.6). Cell birthdating studies use a labeled nucleotide that can be incorporated only into newly synthe-sized DNA—usually tritium-labeled thymidine or a chemically distinctive analog of thymidine (the DNA-specific nucleotide) such as bromodeoxyuridine (BrDU)—at a known time in the organ-ism’s developmental history. All stem cells that are actively synthesizing DNA incorporate the labeled tag and pass it on to their descendants. Because the labeled probe is only available for minutes to hours after being injected, if a stem cell continues to divide, the levels of the labeled probe in the cell’s DNA are quickly diluted. However, if a cell under-goes only a single division after incorpo-rating the label and produces a postmi-totic neuroblast, that neuron retains high levels of the labeled DNA indefinitely. Once the animal has matured, histologi-cal sections prepared from the brain show the labeled neurons. The most heavily labeled cells are those that incor-porated the tag just before their final division; they are therefore said to have been “born” at the time of injection. One of the earliest insights obtained from this approach was that the layers of the cerebral cortex develop in an “inside-out” fashion (see Figure 21.7). In certain mutant mice, such as reeler (see Box B in Chapter 18), birthdating studies show that the oldest cells end up erroneously in the most superficial layers and the most recently generated cells in the deepest as a result of defective migration. Although neuronal birthdates do not, in themselves, tell the lineage of cells, or when they acquire specific phenotypic or molecular features, they mark a major transition in the genetic programs that dictate when and how nerve cells differ-entiate. References ANGEVINE, J. B. JR. AND R. L. SIDMAN (1961) Autoradiographic study of cell migration during histogenesis of the cerebral cortex in the mouse. Nature 192: 766–768. CAVINESS, V. S. JR. AND R. L. SIDMAN (1973) Time of origin of corresponding cell classes in the cerebral cortex of normal and reeler mutant mice: An autoradiographic analysis. J. Comp. Neurol. 148: 141–151. GRATZNER, H. G. (1982) Monoclonal antibody to 5-bromo and 5-iododeoxyuridine. A new reagent for the detection of DNA replication. Science 218: 474–475. MILLER, M. W. AND R. S. NOWAKOWSKI (1988) Use of bromodeoxyuridine immunohisto-chemistry to examine the proliferation, migration, and time of origin of cells in the central nervous system. Brain Res. 457: 44–52. Birthdate Lineage Molecular “mapping” [3H]Thymidine or BrDU Injection of stable tracer Label with a specific probe for glia Label with a specific probe for neurons Additional divisions dilute label S phase M phase 518 Chapter Twenty-One neurons are arranged into layered structures (hippocampus, cerebellum, superior colliculus) there is a systematic relationship between the layers and the time of cell origin. Thus, each layer consists of a cohort of cells generated during a specific developmental period. The implication of this phenomenon is that common periods of neurogenesis are important for the development of the cell types and connections that characterize each layer. The Generation of Neuronal Diversity The neuronal precursor cells in the ventricular zone of the embryonic brain look and act more or less the same. Yet these precursors ultimately give rise to postmitotic cells that are enormously diverse in form and function. The spinal cord, cerebellum, cerebral cortex, and subcortical nuclei (including the basal ganglia and thalamus) each contain several neuronal cell types distin-guished by morphology, neurotransmitter content, cell surface molecules, and the types of synapses they make and receive. On an even more basic level, the stem cells of the ventricular zone produce both neurons and glia— cells with markedly different properties and functions. How and when are these different cell types determined? The bulk of the evidence favors the view that neuronal differentiation is based primarily on local cell–cell interactions followed by distinct histories of transcriptional regulation via a “code” of transcription factors expressed in each cell (Figure 21.9). Historically, most experimental approaches to this issue have relied on transplantation strategies, such as moving bits of a par-Neural tube lumen (ventricle) Pial surface Neural tube lumen (ventricle) Pial surface Neural tube lumen (ventricle) Pial surface G1 stage Mitosis S stage G2 stage G1 stage Mitosis S stage G2 stage G1 stage Mitosis S stage G2 stage G1 stage Mitosis S stage G2 stage Neural tube lumen (ventricle) Pial surface 3 During G2, cell grows and nucleus migrates toward lumen again 4 In M phase (mitosis), cells lose their connections to pial surface, divide, and extend new processes toward the pial surface 2 During S stage, nucleus and surrounding cytoplasm migrate toward the pial surface and DNA replicates 1 In G1 , nucleus is near ventricular surface G1 arrest/ postmitotic neuroblast Postmitotic neuroblasts Figure 21.7 Dividing precursor cells in the vertebrate neuroepithelium (neural plate and neural tube stages) are attached both to the pial (outside) sur-face of the neural tube and to its ventric-ular (lumenal) surface. The nucleus of the cell translocates between these two limits within a narrow cylinder of cyto-plasm. When cells are closest to the outer surface of the neural tube, they enter a phase of DNA synthesis (the S stage); after the nucleus moves back to the ventricular surface (the G2 stage), the precursor cells lose their connection to the outer surface and enter mitosis (the M stage). When mitosis is complete, the two daughter cells extend processes back to the outer surface of the neural tube, and the new precursor cells enter a resting (G1) phase of the cell cycle. At some point a precursor cell generates either another stem cell that will go on dividing and a daughter cell—a neurob-last—that will not divide further, or two postmitotic daughter cells. ticular brain region to a different location in the brain of a host animal to determine whether the transplanted cells acquire the host phenotype or retain their original fate during subsequent development. In general, when very young precursor cells are transplanted, they tend to acquire the host phenotype. Transplanted cells at increasingly older ages, however, usually retain the original phenotype. The use of genetic approaches, particularly in simple, so-called “model” organisms such as fruit flies and the worm Caenorhabditis elegans, has made clear the essential role of local cell–cell interactions, and has indicated some of the molecules that mediate these processes in neural fate determination. In the fruit fly eye, the position and identity of a variety of photoreceptor cells with distinct visual functions relies upon signaling mediated by cell surface ligands on one class of cells and specific receptor kinases on adjacent cells (Figure 21.10). In C. elegans, the determination of midline neurons reflects their lineage, the proper functioning of genes involved in cell–cell signaling, and whether subsets of precursors survive or die during pro-grammed cell death, or apoptosis. Similar local interactions have been invoked to explain differentiation of a number of neuronal and glial classes in the developing vertebrate brain. Per-haps not surprisingly, many of the signaling molecules that are essential for initial steps of neural induction and regionalization—retinoic acid, the FGFs, BMPs, shh, and Wnts—all influence the genesis of specific classes of neurons and glia via local cell–cell interactions (see Figure 21.9). Some of the addi-tional signaling molecules that contribute to these processes in the vertebrate brain include the notch family of cell surface ligands and their receptors, the delta family which tend to maintain precursors in a less differentiated state. Among the targets of these signals, a subset of transcription factor genes known as the bHLH genes (named for a shared basic helix-loop-helix amino acid motif that defines the DNA binding domain) has emerged as central to subsequent differentiation of distinct neural or glial fates. These molecular details provide an outline of how general cell classes are established; however, there is presently no clear and complete explanation for how any specific neuronal class achieves its identity. This gap in knowl-edge presents a problem in using neural stem cells to generate replacements for specific cell classes lost in neurodegenerative diseases or after brain injury (see Box A). Early Brain Development 519 30 I II III IVa IVb IVc V VI White matter Cortical layers Days of gestation Cortical neurogenesis 40 50 60 70 80 90 100 110 120 130 140 150 160 Birth Figure 21.8 Generation of cortical neu-rons during the gestation of a rhesus monkey (a span of about 165 days). The final cell divisions of the neuronal pre-cursors, determined by maximal incor-poration of radioactive thymidine administered to the pregnant mother (see Box E), occur primarily during the first half of pregnancy and are complete on or about embryonic day 105. Each short horizontal line represents the posi-tion of a neuron heavily labeled by maternal injection of radiolabeled thymidine at the time indicated by the corresponding vertical line. The numer-als on the left designate the cortical lay-ers. The earliest generated cells are found in a transient layer called the sub-plate (a few of these cells survive in the white matter) and in layer I (the Cajal-Retzius cells). (After Rakic, 1974.) Neuronal Migration The cellular positioning that constrains local signaling depends on migration of postmitotic neuroblasts in the fetal brain. Migration is a ubiquitous feature of development that brings cells into appropriate spatial relationships. In the ner-vous system, migration during development brings different classes of neurons together so that they can interact appro-priately. The final location of a postmitotic nerve cell is pre-sumably especially critical, since neural function depends on precise connections made by neurons and their targets. In short, the developing presynaptic and postsynaptic elements must be in the right place at the right time. After their final mitosis in the ventricular zone, most neu-roblasts migrate substantial distances. For neurons of the cen-tral nervous system, this migration remains within the limits of the neural tube. However, neurons of the peripheral ner-vous system, which come from the neural crest, arise from cells that have often journeyed a considerable distance through several embryonic environments (see Figure 21.2). Even within the central nervous system, the significant dis-tances traversed are obvious in large animals like primates. To form the cerebral cortex, for example, neurons must some-times travel several millimeters from the ventricular zone to the pial surface. A good deal is now known about the mechanics of how neurons move from their birthplace to their final destina-Neuroectoderm Noggin/ chordin Neural tube Neural induction Organizer centers Neural patterning TGF-βs Sonic hedgehog BMPs Floor plate Roof plate Floor plate Roof plate BMPs Epidermis Floor plate Ectoderm Neurons Neuronal precursors Notch Oligodendrocytes precursors Oligodendrocytes Proneural bHLHs Olig1/2 Nkx2.1 Notch/ Nrg bHLH genes Astrocyte precursors Astrocytes Proneural bHLHs 1 2 3 Astrogliogenesis Oligodendrogenesis Neurogenesis 5 4 6 Ependyma 7 Figure 21.9 Essential molecular and cellular mecha-nisms that guide neuronal and glial differentiation in the neural ectoderm. (1–3) The steps by which ecto-derm acquires its identity as neural ectoderm. Genera-tion of neural precursors, or stem cells, relies first on the balance of BMP and its endogenous antagonists like noggin and chordin in the developing embryo. Next, local sources of inductive signals, including TFG-β fam-ily members and sonic hedgehog, establish gradients that influence subsequent neural precursor identities, as well as identifying local “organizers” (such as the floorplate and roofplate) that define the cellular identity of the inductive signaling centers. (4–7) Steps thought to define neurons, oligodendroglia, and astrocytes from multipotent neuronal precursors. Balanced signaling activity of notch and transcriptional control of the bHLH proneural genes (named based on their ability to bias neural progenitor cells toward a differentiate neural fate) influence neurogenesis. Similarly, antago-nistic transcriptional regulation via either the bHLH genes or three additional transcription factors, Olig1, Olig2, and Nkx2.2, influence the generation of oligo-dendroglia. Continued antagonism between bHLH genes, notch signaling, and the signal molecule neureglin (Nrg) is thought to influence the generation of mature astrocytes. Finally, in the adult brain, cells adjacent to the ventricles (which apparently have avoided becoming differentiated) remain as ependymal cells. These may included a subpopulation of neural stem cells (see Box A). (After Kintner, 2002.) tion. Depending on the area of the developing nervous system in which they originate, migrating neurons follow one of two strategies. Neural crest cells are largely guided along distinct migratory pathways by specialized adhe-sion molecules in the extracellular matrix or by molecules on the surfaces of cells in the embryonic periphery (see Figure 21.2). At different developmen-tal stages, similar molecules are probably used to guide axonal outgrowth (see Chapter 22). In contrast, neurons in many regions, including the cerebral cortex, cerebellum, hippocampus, and spinal cord, are guided to their final destinations by crawling along a particular type of glial cell, called radial glia, which act as cellular guides (Figure 21.11). Histological observations of embryonic brains made by Wilhelm His and Ramon y Cajál during the nineteenth and early twentieth centuries sug-gested that neuroblasts crawled along glial guides to their final locations (Figure 21.11A). These observations were supported by analyses of electron microscopic images of fixed tissue in the 1960s and 1970s (Figure 21.11B,C), which fit well with the orderly relationship between birthdates and final position of distinct cell types in the cerebellum and cerebral cortex (see Fig-ure 21.7 and Box E). Subsequently, innovations in cell culture techniques and light microscopy made it possible to observe the process of migration directly. When radial glial cells and immature neurons are isolated from the developing cerebellum or cerebral cortex and mixed together in vitro, the neurons attach to the glial cells, assume the characteristic shape of migrating cells seen in vivo, and begin moving along the glial processes. Indeed, the membrane constituents of glial cells, when coated onto thin glass fibers, sup-port this sort of normal migration. Several cell surface adhesion molecules, extracellular matrix adhesion molecules, and associated signal transduction molecules apparently mediate this process. Many of these molecules are also essential for subsequent steps in neural development, such as axon growth and guidance (see Chapter 22). Although in many regions of the brain—par-ticularly those that give rise to nuclear cell groups—neurons migrate with-out the benefit of glial guides (Box F) migration along radial glial fibers is always seen in regions where cells are organized into layers, such as the cerebral cortex, hippocampus, and cerebellum. Both neuropathological Early Brain Development 521 Corneal lens (A) Crystalline cone Receptor cell Nerve to brain Ommatidium (C) (B) boss sev 6 4 3 5 2 1 8 7 Figure 21.10 Development of the com-pound eye of the fruit fly Drosophila pro-vides an example of how cell–cell inter-actions can determine cell fate. (A) Scanning electron micrograph of the eye in Drosophila. (B) Diagram of the struc-ture of the fly eye. The eye consists of an array of identical ommatidia, each com-prising an array of eight photoreceptors. (C) Arrangement of photoreceptors within each ommatidium and the cell–cell signaling that determines their fate. A membrane-bound ligand on R8 (the boss gene product) binds to a recep-tor (encoded by the sevenless gene, sev) on the R7 cell. These interactions even-tually lead to the changes in gene expression that determine the fate of an R7 cell. The arrows between R8 and the remaining receptor cells indicate inter-actions necessary for determining the fates of R1–R6. (A courtesy of T. Venka-tesh; B,C after Rubin, 1989.) 522 Chapter Twenty-One observations and more recent molecular and genetic studies indicate that some forms of mental retardation, epilepsy, and other neurological problems arise from the abnormal migration of cerebral cortical neurons (see Box B in Chapter 18). Relatively little is known about the specific messages that neurons receive as they migrate in the central nervous system. It is apparent, however, that moving through a changing cellular environment has important conse-quence for the differentiation of neurons. Such effects are most thoroughly documented in the migration of neural crest cells, where the migratory paths of precursor cells are related to both the ultimate position in the body and neuronal identity. The distinct signals along these pathways can be secreted molecules (including some of the peptide hormones used at earlier times for neural induction), cell surface ligands and receptors (adhesion molecules and other signals), or extracellular matrix molecules (see Chapter 22). These signals are made available from somites, visceral epithelial structures like the developing dorsal aorta, mesodermally derived mesenchymal cells, and the neural crest cells themselves. (A) (B) (C) Ventricle Pial surface Pial surface Cortical plate Intermediate zone Radially migrating cell Radial glial Radial glial process Radial glial cell body Ventricular zone Trailing process Radial glial process Migrating neuron Leading process Non-radially migrating cell αv Integrin, laminin, fibronectin, NGCAM (L1) CDK5/P35, neuregulin, NMDA-R1, α3 β1 Integrin Figure 21.11 Radial migration in the developing cortex. (A) Section through the developing forebrain showing radial glial processes from the ventricular to the surfaces. Micrograph shows migrat-ing neurons labeled with an antibody to neuregulin, specific for migrating corti-cal neurons. (B) Enlargement of boxed area in (A). Migrating neurons are inti-mately apposed to radial glial cells, which guide them to their final position in the cortex. Some cells take a nonra-dial migratory route, which can lead to wide dispersion of neurons derived from the same precursor (see Box F). (C) A single neuroblast migrates upon a radial glial process (based on serial reconstruction of EM sections as well as in vitro assays of migration, as shown in the accompanying micrograph). Cell adhesion and other signaling molecules or receptors found on the surface of either the neuron (green) or the radial glial process (tan) are indidated in the respective boxes. (After Rakic, 1974; micrographs courtesy of E. S. Anton and P. Rakic.) Of particular significance is the fact that specific peptide hormone growth factors cause neural crest cells to differentiate into distinct phenotypes (Fig-ure 21.12). These effects depend on the location of the neuronal precursor cell along a migratory pathway, different signals being available at different points. Such position-dependent cues are probably not restricted to the peripheral nervous system; in the cerebellum, for example, different patterns of genes are expressed in migrating granule neurons at different locations, implying the existence of different signals (as yet unknown) along the migratory path. Thus, neuronal migration involves much more than the mechanics of moving cells from one place to another. As in the case of inductive events during the initial formation of the nervous system, stereotyped movements bring different classes of cells into contact with one another, thereby provid-ing a means of constraining cell–cell signaling to specific times and places. Early Brain Development 523 Neural crest progenitor Leukocyte inducing factor (LIF) Stem cell factor Ciliary neurotrophic factory Sensory neuron Sympathetic progenitor Chromaffin cell progenitor Chromaffin cell Adrenergic neuron Cholinergic neuron Melanocyte Glucocorticoids Glucocorticoids FGF2 NGF Figure 21.12 Cell signaling during the migration of neural crest cells. The establish-ment of each precursor type relies on signals provided by one of several specific pep-tide hormones. The availability of each signal depends on the migratory pathway. 524 Chapter Twenty-One Box F Mixing It Up: Long-Distance Neuronal Migration For many years, developmental neurobi-ologists assumed that position was des-tiny in the developing brain. For exam-ple, if a neuron was found in the thalamus, cerebellum, or cerebral cortex in the adult brain, it most likely came from a neural progenitor cell in the embryonic brain region that gave rise to the thalamus, cerebellum, or cerebral cor-tex. The identification of rhombomeres and subsequent evidence that these domains are compartments between which little mixing of cells occurs rein-forced this notion. Nevertheless, a few observations hinted that all neurogenesis might not be local, and eventually led to a new idea of how neuronal classes in a variety of brain regions are integrated into mature structures and circuits. The initial indication of this tendency for subsets of neurons to wander came in the late 1960s with a report that neurons in the pulvinar, a thalamic nucleus assumed to be derived from the dien-cephalon, were actually generated in the telencephalon. This observation received little notice until the mid 1980s, when a series of experiments using chick–quail chimeras suggested that a major portion of granule cells in the cerebellum (small local circuit neurons) were actually gen-erated outside the rhombencephalon (the embryonic region associated with the generation of the cerebellum). Most of these extrinsic cells were thought to migrate from the mesencephalon (associ-ated with the generation of the superior and inferior colliculus in the adult brain) into the external granule cell layer of the cerebellum. Together, these findings implied that adult brain structures might be derived from a broad range of embry-onic brain subdivisions. Around the same time, several inves-tigators noticed a small but consistent proportion of cells in the cerebral cortex whose migratory route was apparently tangential rather than radial (via radial glial guides). These observations were the focus of a lively debate that neverthe-less failed to explain the significance of the apparent “escapees” from the radial migration framework in the developing cortex. Moreover, lineage analysis sug-gested that cortical projection neurons, interneurons, astrocytes and oligoden-droglia were probably not derived from the same precursor pools. There was lit-tle consensus about these disparate observations until the mid 1990s when several groups realized that there was a massive migration of cells from the ven-tral forebrain—the region of the gan-glionic eminence that gives rise to the caudate, putamen, and globus pallidus— to the cerebral cortex (Figure A). More-over, these ventrally derived cells were not just any cell types; they constituted distinct classes of GABAergic interneu-rons in the cortex and olfactory bulb, as well as oligodendroglia throughout the entire forebrain. Newly generated gran-ule and periglomular interneurons in the mature olfactory bulb are derived from a remnant of the ganglionic eminence called the anterior subventricular zone, which persists at the surface of the mature lateral ventricles. A mosaic of transcriptional regulators whose expression and activity is restricted to various domains in the ven-tral forebrain orchestrates this long dis-tance migration of distinct cell types (Figure B). When subsets of these tran-scription factors are mutated, migration of cells from the ventral forebrain to the cortex is dramatically diminished (Figure C), and the numbers of GABAergic interneurons is similarly reduced. The mechanisms for specifying cell identity, migration and destination remain unknown; nevertheless, this regional diversity is apparently a consistent fea-ture of neurogenesis in mammalian brains. Nevertheless, not all neurons par-ticipate in this long-distance migration. In the human brain, for example, some GABAergic interneurons are generated locally in the cortical rudiment, in addi-tion to those that migrate from the ven-tral forebrain. These locally generated interneurons apparently use the same radial glial migratory route as their glu-tamatergic neighbors. The developmental and functional significance of this mixing of offspring from progenitors in various embryonic brain regions remains unknown. Per-haps the range and number of cell–cell interactions necessary to generate func-tionally distinct cell types is so large that the appropriate population can only be determined by exposing subsets of cells to a variety of environments, and then having those cells act as messen-gers to deliver additional molecular sig-nals at a new location. Regardless of the purpose of this arduous journey, its con-sequence is the orderly establishment of cellular diversity in a number of brain regions. References ANDERSON, S. A., D. D. EISENSTAT, L. SHI AND J. L. RUBENSTEIN (1997) Interneuron migration from basal forebrain to neocortex: Depen-dence on Dlx genes. Science 278: 474–476. HE, W., C. INGRAHAM, L. RISING, S. GODERIE AND S. TEMPLE (2001) Multipotent stem cells from the mouse basal forebrain contribute GABAergic neurons and oligodendrocytes to the cerebral cortex during embryogenesis. J. Neurosci. 21: 8854–8862. MARTINEZ, S. AND R. M. ALVARADO-MALLART (1989) Rostral cerebellum originates from the caudal portion of the so-called “mesen-cephalic” vesicle: A study using chick/quail chimeras. Eur. J. Neurosci. 6: 549–560. PARNAVELAS, J. G., J. A. BARFIELD, E. FRANKE AND M. B. LUSKIN (1991) Separate progenitor cells give rise to pyramidal and nonpyrami-dal neurons in the rat telencephalon. Cereb. Cortex 1: 463–468. RAKIC, P. AND R. L. SIDMAN (1969) Telen-cephalic origin of pulvinar neurons in the fetal human brain. Z. Anat. Entwicklungs-gesch. 129: 53–82. Summary The initial development of the nervous system depends on an intricate inter-play of cellular movements and inductive signals. In addition to an early establishment of regional identity and cellular position as a result of mor-phogenesis, substantial migration of neuronal precursors is necessary for the subsequent differentiation of distinct classes of neurons, as well as for the eventual formation of specialized patterns of synaptic connections (see Chapter 22). The fate of individual precursor cells is not determined simply by their mitotic history; rather, the information required for differentiation arises largely from interactions between the developing cells and the subse-quent activity of distinct transcriptional regulators. All of these events are dependent on the same categories of molecular and cellular phenomena: cell–cell signaling, changes in motility and adhesion, transcriptional regula-tion, and, ultimately, cell-specific changes in gene expression. The molecules that participate in signaling during early brain development are the same as the signals used by mature cells: hormones, transcription factors, other sec-ond messengers (see Chapter 7), as well as cell adhesion molecules. As might be expected, the identification and characterization of these molecules in the developing brain has begun to explain a variety of congenital neuro-logical defects. Signaling and regulation of gene expression during early neural development are especially vulnerable to the effects of genetic muta-tions, and to the actions of the many drugs and toxins that can compromise the elaboration of a normal nervous system. Early Brain Development 525 WICHTERLE, H., D. H. TURNBULL, S. NERY, G. FISHELL AND A. ALVAREZ-BUYLLA (2001) In utero fate mapping reveals distinct migratory pathways and fates of neurons born in the mammalian basal forebrain. Development 128: 3759–3771. (B) (A) (C) LGE LGE OB Cx LGE MGE Mash1 + Dix1/2 Gli3 + Ngn1/2 Nkx2.1+ Mash1 + Dix1/2 (A) Migration of cells from the ventral fore-brain to the neocortex during late gestation in the mouse. A tracer has been placed in the lateral ganglionic eminence, and labeled cells can be seen streaming toward the cor-tex, as well as in residence in the developing cortical plate. (B) Schematic of transcrip-tional regulators associated with the primary divisions of the ganglionic eminence (lateral and medial), and the basic migratory routes taken by cells in each division (arrows). (C) Diminished migration of cells from the ven-tral forebrain in mice with null mutations of both Dlx1 and Dlx2 (expressed throughout the lateral and medial ganglionic eminence). 526 Chapter Twenty-One Additional Reading Reviews ANDERSON, D. J. (1993) Molecular control of cell fate in the neural crest: The sympatho-adrenal lineage. Annu. Rev. Neurosci. 16: 129– 158. CAVINESS, V. S. JR. AND P. RAKIC (1978) Mecha-nisms of cortical development: A view from mutations in mice. Annu. Rev. Neurosci. 1: 297–326. FRANCIS, N. J. AND S. C. LANDIS (1999) Cellular and molecular determinants of sympathetic neuron development. Annu. Rev. Neurosci. 22: 541–566. HATTEN, M. E. (1993) The role of migration in central nervous system neuronal develop-ment. Curr. Opin. Neurobiol. 3: 38–44. INGHAM, P. (1988) The molecular genetics of embryonic pattern formation in Drosophila. Nature 335: 25–34. JESSELL, T. M. AND D. A. MELTON (1992) Dif-fusible factors in vertebrate embryonic induc-tion. Cell 68: 257–270. KESSLER, D. S. AND D. A. MELTON (1994) Verte-brate embryonic induction: Mesodermal and neural patterning. Science 266: 596–604. KEYNES, R. AND R. KRUMLAUF (1994) Hox genes and regionalization of the nervous system. Annu. Rev. Neurosci. 17: 109–132. KINTNER C. (2002) Neurogenesis in embryos and in adult neural stem cells. J. Neurosci. 22: 639–643. LEWIS, E. M. (1992) The 1991 Albert Lasker Medical Awards. Clusters of master control genes regulate the development of higher organisms. JAMA 267: 1524–1531. LINNEY, E. AND A.-S. LAMANTIA (1994) Reti-noid signaling in mouse embryos. Adv. Dev. Biol. 3: 73–114. RICE, D. S. AND T. CURRAN (1999) Mutant mice with scrambled brains: Understanding the signaling pathways that control cell position-ing in the CNS. Genes Dev. 13: 2758–2773. RUBENSTEIN, J. L. R. AND P. RAKIC (1999) Genetic control of cortical development. Cere-bral Cortex 9: 521–523. SANES, J. R. (1989) Extracellular matrix mole-cules that influence neural development. Annu. Rev. Neurosci. 12: 491–516. SELLECK, M. A. , T. Y. SCHERSON AND M. BRON-NER-FRASER (1993) Origins of neural crest cell diversity. Dev. Biol. 159: 1–11. ZIPURSKY, S. L. AND G. M. RUBIN (1994) Deter-mination of neuronal cell fate: Lessons from the R7 neuron of Drosophila. Annu. Rev. Neu-rosci. 17: 373–397. Important Original Papers ANCHAN, R. M., D. P. DRAKE, C. F. HAINES, E. A. GERWE AND A.-S. LAMANTIA (1997) Disrup-tion of local retinoid-mediated gene expres-sion accompanies abnormal development in the mammalian olfactory pathway. J. Comp. Neurol. 379: 171–184. ANGEVINE, J. B. AND R. L. SIDMAN (1961) Auto-radiographic study of cell migration during histogenesis of cerebral cortex in the mouse. Nature 192: 766–768. BULFONE, A., L. PUELLES, M. H. PORTEUS, M. A. FROHMAN, G. R. MARTIN AND J. L. RUBENSTEIN (1993) Spatially restricted expression of Dlx-1, Dlx-2 (Tes-1), Gbx-2, and Wnt-3 in the embry-onic day 12.5 mouse forebrain defines poten-tial transverse and longitudinal segmental boundaries. J. Neurosci. 13: 3155–3172. EKSIOGLU, Y. Z. AND 12 OTHERS (1996) Periven-tricular heterotopia: An X-linked dominant epilepsy locus causing aberrant cerebral corti-cal development. Neuron 16: 77–87. ERICSON, J., S. MORTON, A. KAWAKAMI, H. ROE-LINK AND T. M. JESSELL (1996) Two critical peri-ods of sonic hedgehog signaling required for the specification of motor neuron identity. Cell 87: 661–673. GALILEO, D. S., G. E. GRAY, G. C. OWENS, J. MAJORS AND J. R. SANES (1990) Neurons and glia arise from a common progenitor in chicken optic tectum: Demonstration with two retroviruses and cell type-specific anti-bodies. Proc. Natl. Acad. Sci. USA 87: 458–462. GRAY, G. E. AND J. R. SANES (1991) Migratory paths and phenotypic choices of clonally related cells in the avian optic tectum. Neuron 6: 211–225. HAFEN, E., K. BASLER, J. E. EDSTROEM AND G. M. RUBIN (1987) Sevenless, a cell-specific homeotic gene of Drosophila, encodes a puta-tive transmembrane receptor with a tyrosine kinase domain. Science 236: 55–63. HEMMATI-BRIVANLOU, A. AND D. A. MELTON (1994) Inhibition of activin receptor signaling promotes neuralization in Xenopus. Cell 77: 273–281. KRAMER, H., R. L. CAGAN AND S. L. ZIPURSKY (1991) Interaction of bride of sevenless mem-brane-bound ligand and the sevenless tyro-sine-kinase receptor. Nature 352: 207–212. LANDIS, S. C. AND D. L. KEEFE (1983) Evidence for transmitter plasticity in vivo: Developmen-tal changes in properties of cholinergic sym-pathetic neruons. Dev. Biol. 98: 349–372. LIEM, K. F. JR., G. TREMML AND T. M. JESSELL (1997) A role for the roof plate and its resident TGFβ-related proteins in neuronal patterning in the dorsal spinal cord. Cell 91: 127–138. MCMAHON, A. P. AND A. BRADLEY (1990) The wnt-1 (int-1) protooncogene is required for the development of a large region of the mouse brain. Cell 62: 1073–1085. NODEN, D. M. (1975) Analysis of migratory behavior of avian cephalic neural crest cells. Dev. Biol. 42: 106–130. PATTERSON, P. H. AND L. L. Y. CHUN (1977) The induction of acetylcholine synthesis in pri-mary cultures of dissociated rat sympathetic neurons. Dev. Biol. 56: 263–280. RAKIC, P. (1971) Neuron-glia relationship dur-ing granule cell migration in developing cere-bral cortex. A Golgi and electronmicroscopic study in Macacus rhesus. J. Comp. Neurol. 141: 283–312. RAKIC, P. (1974) Neurons in rhesus monkey visual cortex: Systematic relation between time of origin and eventual disposition. Sci-ence 183: 425–427. SAUER, F. C. (1935) Mitosis in the neural tube. J. Comp. Neurol. 62: 377–405. SPEMANN, H. AND H. MANGOLD (1924) Induc-tion of embryonic primordia by implantation of organizers from a different species. Trans-lated into English by V. Hamburger and reprinted in Foundations of Experimental Em-bryology, B. H. Willier and J. M. Oppenheimer (eds.) (1974). New York: Hafner Press. STEMPLE, D. L. AND D. J. ANDERSON (1992) Iso-lation of a stem cell for neurons and glia from the mammalian neural crest. Cell 71: 973–985. WALSH, C. AND C. L. CEPKO (1992) Widespread dispersion of neuronal clones across func-tional regions of the cerebral cortex. Science 255: 434–440. YAMADA, T., M. PLACZEK, H. TANAKA, J. DODD AND T. M. JESSELL (1991) Control of cell pattern in the developing nervous system. Polarizing activity of the floor plate and notochord. Cell 64: 635–647. ZIMMERMAN, L. B, J. M. DE JESUS-ESCOBAR AND R. M. HARLAND (1996) The Spemann orga-nizer signal noggin binds and inactivates bone morphogenetic protein 4. Cell 86: 599– 606. Books LAWRENCE, P. A. (1992) The Making of a Fly: The Genetics of Animal Design. Oxford: Blackwell Scientific. MOORE, K. L. (1988) The Developing Human: Clinically Oriented Embryology, 4th Ed. Phila-delphia: W. B. Saunders Company. Overview Two central features of neural circuits must be established after neurons are generated and have migrated to their final positions. First, nerve cells in dif-ferent regions must be linked together via axon pathways. Second, orderly synaptic connections must be made among appropriate pre- and postsynap-tic partners. The cellular mechanisms that generate axon outgrowth and syn-apse formation are thus the major determinants of neural circuits that will eventually control behavior. The directed growth of axons and the recogni-tion of synaptic targets is mediated by a specialization at the tip of each growing axon called the growth cone. Growth cones detect and respond to signaling molecules that identify correct pathways, prohibit incorrect trajec-tories, and ultimately facilitate functional synaptic partnerships. These include cell surface adhesion molecules and diffusible signals that either attract or repel growing axons. In addition, secreted growth factors influence axon growth and synapse formation as well as regulating appropriate num-bers of connections between axons and their targets. As in other instances of intercellular communication, a variety of receptors and second messenger molecules transduce the signals provided to the growth cone. Thus cell–cell signals initiate intracellular events that underlie directed growth of the axon, the conversion of the growth cone into a presynaptic specialization, and the elaboration of a distinct postsynaptic site. The end results of the dynamic processes are a wealth of well-defined peripheral and central axon pathways and complex neural circuits that allow animals to behave in ever more sophisticated ways as they mature. The Axonal Growth Cone Among the many extraordinary features of nervous system development, one of the most fascinating is the ability of growing axons to navigate over millimeters or even centimeters, through complex embryonic terrain, to find appropriate synaptic partners. In 1910, Ross G. Harrison, who first observed axons extending in a living tadpole in vitro, noted that “The growing fibers are clearly endowed with considerable energy and have the power to make their way through the solid or semi-solid protoplasm of the cells of the neural tube. But we are at present in the dark with regard to the conditions which guide them to specific points.” Harrison’s observations indicate the central features of axonal growth. First, the energy and power of growing axons reflect the cellular properties of the growth cone, a specialized structure at the tip of the extending axon. Growth cones are highly motile structures that explore the extracellular envi-Chapter 22 527 Construction of Neural Circuits 528 Chapter Twenty-Two ronment, determine the direction of growth, and then guide the extension of the axon in that direction. The primary morphological characteristic of a growth cone is a sheetlike expansion of the growing axon at its tip called a lamellapodium. When examined in vitro, numerous fine processes called filopodia rapidly form and disappear from the terminal expansion, like fin-gers reaching out to sense the environment (Figure 22.1). The cellular mech-anisms that underlie these complex searching movements have become a focus of cell biological studies of axon growth and guidance. This aspect of growth cone mobility reflects rapid, controlled rearrangement of cytoskeletal elements—particularly molecules related to the actin cytoskeleton—which modulate changes in growth cone shape, and ultimately the course of the axon through developing tissues. These rearrangements are regulated by sig-nals transduced from the environment through receptors and channels on the growth cone extracellular surface (see below, and Figure 22.2). The growth cone, therefore, can use actin-based and other cytoskeletally medi-ated mechanisms to generate force, cause filopodial extension, and thus pro-mote further exploration of the local environment. Santiago Ramón y Cajal, Harrison’s contemporary, noted further that when growth cones move along an established pathway pioneered by other axons, they tend to be simple in shape (see Figure 22.3B). In contrast, when a growing axon first extends in a new direction or reaches a region where a choice must be made about the direction to take, the structure (and presum-ably motility) of its growth cone undergoes dramatic changes. The growth cone flattens and extends numerous filopodia, much as it does in a culture dish, suggesting an active search for appropriate cues to direct subsequent growth. These changes of growth cone shape at “decision points” have been observed in both the peripheral and central nervous system. In the periph-ery, the growth cones of motor neurons undergo shape changes as they enter the primordia of muscles in immature limbs, presumably facilitating the selection of appropriate targets in the developing musculature. In the central nervous system, growth cones in developing spinal cord, olfactory and optic nerves also change shape when they reach critical points in their trajectories. An example of the functional significance of growth cone exploration is the decision made by subsets of retinal axons at the optic chiasm where the par-tial crossing or decussation of retinal axons is important for establishing the circuitry for binocular vision. The growth cones of retinal axons slow down and acquire a complex shape as they “choose” whether or not to cross the midline. Perhaps not surprisingly, this growth cone behavior reflects a com-bination of local molecular cues at the developing optic chiasm as well as the identity of retinal ganglion cells based upon position in the retina (Box A). Non-Diffusible Signals for Axon Guidance The complex behavior of growth cones during axonal extension suggests the presence of specific cues that cause the growth cone to move in a particular direction. In addition, the growth cone itself must have a specialized array of receptors and transduction mechanisms to respond to these cues. The cues themselves—the “condition(s) which guide … growth cones” referred to by Harrison—remained elusive for more than half a century after his initial observations of axon growth. The identity of some of the relevant molecules has been established over the last 30 years. These signals comprise a large group of molecules associated with cell adhesion and cell-cell recognition throughout the organism, as well as with directed axon or growth cone motility in the developing nervous system. The association of specific cell Construction of Neural Circuits 529 (A) (B) (C) Lamelipodia Filopodia Microtubule subunits G–actin F–actin assembly F–actin depolymerization Microtubule and organelle movement Attractive cue Leading edge Repulsive cue Figure 22.1 Basic structure of the growth cone. (A) A growth cone from a cultured sensory ganglion neuron, labeled for actin (red) and tubulin (green). Actin predom-inates in the filopodial extensions of the growth cone. Tubulin is the predominant cytoskeletal protein in the axon, extending into the lamellapodium of the growth cone. (B) Distinct classes of actin and tubulin are seen in discrete regions. At left, fil-amentous actin (F-actin; red) is enriched in the growth cone lamellapodia. Tyrosi-nated microtubules are the primary constituents of the lamellar region of the growth cone (middle left; green). Actylated microtubules are restricted to the axonal region (middle right; blue). On the far right, a merged image shows the restricted distribution of each distinct cytoskeletal element. (C) Distribution and dynamics of cytoskeletal elements in the growth cone. Globular actin (G-actin) can be incorporated into F-actin at the leading edge of the filopodium in response to attractive cues. Repulsive cues support the disassembly and retrograde flow of G-actin toward the lamellapodium. Organized microtubules make up the cytoskeletal core of the axon, while more broadly dispersed, dynamic microtubules or micro-tubule subunits are found in apposition to F- and G-actin in the lamellapodium. (A courtesy of X. Zhou and W. Snider; B courtesy of E. Dent and F. Gertler; C after Kolodkin et al., 2003.) 530 Chapter Twenty-Two Box A Choosing Sides: Axon Guidance at the Optic Chiasm The functional requirement that a subset of axons from retinal ganglion cells in each eye to cross while the remainder projects to the ipsilateral side of the brain was predicted based on optical princi-ples—most notably by Issac Newton— and confirmed (much later) by neu-roanatomists and neurophysiologists (see Chapter 11). The partial crossing, or decussation, of retinal axons is most striking in primates including humans, where approximately half of the axons cross and the other half do not. All other mammals have crossed and uncrossed retinal projections; however, the percent-age of uncrossed axons diminishes from 20–30% in carnivores to less than 5% in most rodents. The frequency of uncrossed axons decreases even more in other vertebrates; thus in amphibians, fish, and birds most or all of the retinal projection is crossed. For both functional and evolutionary reasons, the partial decussation of the retinal pathways and its variable extent in different species has engaged the imagination of biologists and others interested in vision. For developmental neurobiologists this phenomenon raises an obvious question: How do retinal ganglion cells choose sides so that some project con-tralaterally and others ipsilaterally? This question is central to understanding how the peripheral visual projection is orga-nized to construct two accurate visual hemifield maps that superimpose points of space seen jointly by the two eyes (see Chapter 11). It also speaks to the more general issue in neural development of how axons distinguish ipsilateral and contralateral targets. It is clear that the laterality of retinal axons is determined by initial cell iden-tity and axon guidance mechanisms rather than by regressive processes that subsequently select or sculpt these pro-jections. Thus, the distinction between the nasal and temporal retinal regions that project ipsilaterally and contralater-ally is already apparent in the retina as well as in axon trajectories at the midline and in the developing optic tract, long before the axons reach their targets. In the retina, this specificity is seen as a “line of decussation,” or border, between ipsilaterally and contralaterally project-ing retinal ganglion cells, detected exper-imentally by injecting a retrograde tracer into the nascent optic tract of very young embryos. In the retinas of such embryos there is a distinct boundary between the population of retinal ganglion cells pro-jecting ipsilaterally in one eye (found in the temporal retina), and a complemen-tary boundary for contralaterally project-ing cells in the other eye (see figure). A molecular basis for this specificity was initially suggested by studies of albino mammals, including mice and humans. In albinos, where single gene mutation disrupts melanin synthesis throughout the animal, including in the pigment epithelium of the retina, the ipsilateral component of the retinal projection from each eye is dramatically reduced, the line of decussation in the retina is disrupted, and the distribution of glia and other cells in the vicinity of the optic chiasm is altered. These and other observations suggested that identity of retinal axons with respect to decussation is established in the retina, and further reinforced by axonal “choices” influenced by cues pro-vided by cells within the optic chiasm. Cell biological analysis of growth cone morphologies showed that the chi-asm is indeed a region where growth cones explore the molecular environment in a particularly detailed way, presum-ably to make choices pertinent to di-rected growth. Furthermore, molecular analysis showed that specialized neu-roepithelial cells in and around the chi-asm express a number of cell adhesion molecules associated with axon guid-ance. Interestingly, some of these mole-cules—particularly netrins, slits, and their robo receptors—do not influence decussation in the chiasm as they do at other regions of the nervous system. Instead, they are expressed in cells where the chiasm forms, apparently constrain-ing its location on the ventral surface of the diencephalon. The establishment of ipsilateral versus contralateral identity is evidently more dependent on the zinc finger transcription factor Zic2, as well as cell adhesion molecules of the ephrin family. Zic2, which is expressed specifi-cally in the temporal retina, is associated with the expression of a distinct Eph receptor, EphB1, in the axons arising from temporal retinal ganglion cells. The ephrin B2 ligand, which is recognized as a repellent of EphB1 axons, is found in midline glial cells in the optic chiasm. In support of the functional importance of these molecules, disrupting Zic2, EphB1 or ephrin B2 function diminishes the degree of ipsilateral projection in devel-oping mice; in accord with this finding, neither Zic2 nor ephrin B2 is expressed in vertebrate species that lack ipsilateral projections. These observations thus provide a molecular framework for the identifica-tion of retinal ganglion cells and the sort-ing of their projections at the optic chi-asm. How this sorting is related to the topopgraphy of tectal, thalamic, and cor-tical representations is not yet known. Most observations suggest that retinal topography is not faithfully preserved among axons in the optic tracts. The identity and position of axons from nasal and temporal retinas whose retinal gan-glion cells “see” a common point in the binocular hemifield must therefore be restored in the thalamus, and subse-quently retained or re-established in the thalamic projections to cortex. Choosing sides at the chiasm is only a first step in establishing maps of visual space. adhesion molecules with axon growth is based upon experiments either in vitro, where addition or removal of a particular molecule results in modify-ing the relevant behavior of growing axons, or in vivo where genetic muta-tion, deletion or manipulation disrupts the growth, guidance or targeting of a particular axon projection (see Box A). Despite their daunting number, molecules that are known to influence axon growth and guidance can be grouped into families of ligands and their receptors (Figure 22.2). The extracellular matrix molecules and their integrin receptors, the Ca2+-independent cell adhesion molecules (CAMs), the Ca2+-dependent cell adhesion molecules (cadherins), and the ephrins and eph receptors (see below) are the major classes of non-diffusible axon guidance molecules. The extracellular matrix cell adhesion molecules were the first to be associated with axon growth. The most prominent members of this group are the laminins, the collagens, and fibronectin. As their family name indi-cates, laminin, collagen, and fibronectin are all found in a macromolecular complex or matrix outside of the cell (Figure 22.3). The matrix components can be secreted by the cell itself or its neighbors; however, rather than diffus-ing away from the cell after secretion, these molecules form polymers and create a more durable local extracellular substance. A broad class of recep-tors, known collectively as integrins, bind specifically to these molecules (see Figure 22.2). Integrins themselves do not have kinase activity or other direct signaling capacity. Instead, the binding of laminin, collagen, or Construction of Neural Circuits 531 References GUILLERY, R. W. (1974) Visual pathways in albinos. Sci. Am. 230: 44–54. GUILLERY, R. W., C. A. MASON AND J. S. TAYLOR (1995) Developmental determi-nants at the mammalian optic chiasm. J. Neurosci. 15: 4727–4737. HERRERA, E. AND 8 OTHERS (2003) Zic2 patterns binocular vision by specifying the uncrossed retinal projection. Cell 114: 545–557. RASBAND, K., M. HARDYV AND C. B. CHIEN (2003) Generating X: Formation of the optic chiasm. Neuron 39: 885–888. WILLIAMS, S. E. AND 9 OTHERS (2003) Ephrin-B2 and EphB1 mediate retinal axon divergence at the optic chiasm. Neuron 39: 919–935. (A) There is a small population of Zic2-expressing retinal ganglion cells (arrow-heads) in the ventrotemporal region of the normal retina (at left, mounted flat by making several radial cuts). At right, the normal projection of one eye via the optic nerve (ON), through the optic chiasm (OC), and into the optic tract (OT) has been traced using a lipophilic dye placed in one eye. After the chiasm, labeled axons can be seen both in the contralateral (contra) as well as the ipsilateral (ipsi) optic tract. (B) When Zic2 function is diminished in a mouse heterozygous for a Zic2 “knock-down” mutation (in which expression of Zic2 protein is diminished, but not elimi-nated, in the ventrotemporal retina), the number of ipsilateral axons in the optic tract is similarly diminished. (C) When Zic2 function is further diminished in homozygous Zic2 knock-down animals, the ipsilateral projection can no longer be detected in the optic tract; thus, each of the optic tracts consist of contralateral axons. (From Herrera et al., 2003.) (A) +/+ (B) Zic2kd/+ (C) Zic2kd/kd OT Contra Ipsi ON OC Contra Ipsi Contra Ipsi fibronectin to integrins triggers a cascade of events—perhaps via interactions with cytoplasmic kinases and other soluble signaling molecules—that gen-erally stimulates growth and elongation. These changes include fluctuations in levels of intracellular messengers such as calcium and inositol trisphos-phate (IP3), and the activation of additional intracellular kinase pathways (F) Ephrins (A) Extracellular matrix molecules (D) Netrin/slit family (E) Semaphorins Semaphorins Neuropilin Plexin Actin Rho/ GAPs Ephrins Bi–directional signaling Eph (tyrosine kinase receptor) Rho/ GAPs Slit Netrin DCC UNC5 Robo Rho/GAPs (B) CAMs L1 NCAM (C) Cadherins β–catenin Actin Phosphatases Tyrosine kinases α–catenin Actin Ca2+ Cadherins α β Kinases/other signaling molecules Integrin receptors Kinases/other signaling molecules Further signal transduction ECM Actin Kinases/other signaling molecules Figure 22.2 Several families of ligands and receptors constitute the major classes of axon guidance molecules. These ligand–receptor pairs can be either attractive or repulsive, depending on the identity of the molecules and the context in which they signal the growth cone. (A) Extracellular matrix molecules serve as the ligands for multiple integrin receptors. (B) Homophilic, Ca2+-independent cell adhesion mole-cules (CAMs) are at once ligands and receptors. (C) Ca2+-dependent adhesion mole-cules, or cadherins, are also capable of homophilic binding. (D) The netrin/slit fam-ily of attractive and repulsive secreted signals acts through two distinct receptors, DCC (“deleted in colorectal cancer”), which binds netrin, and robo, the receptor for slit. (E) Semaphorins are primarily repulsive cues that can either be bound to the cell surface or secreted. Their receptors (the plexins and neuropilin) are found on growth cones. (F) Ephrins, which can be transmembrane- or membrane-associated, signal via the Eph receptors, which are receptor tyrosine kinases. (see Chapter 7). The role of extracellular matrix molecules in axon guidance is particularly clear in the embryonic periphery. Axons extending through peripheral tissues grow through loosely arrayed mesenchymal cells that fill the interstices of the embryo, and the spaces between these mesenchymal cells are rich in extracellular matrix molecules. Axons also grow along the interface of mesenchyme and epithelial tissues including the epidermis, where an organized sheet of extracellular matrix components called the basal lamina provides a supportive substrate. In addition, in peripheral nerves, matrix molecules are secreted by glial cells (Schwann cells) associated with growing axons. In tissue culture as well as in the embryo, different extracellular matrix molecules have different capacities to stimulate axon growth. Thus, the relative availability of differ-ent matrix molecules can influence the speed or direction of a growing axon. The role of matrix molecules in the central nervous system is less clear. Some of the same molecules are present in the extracellular space but are not orga-nized into orderly substrates like the basal lamina in the periphery, and have therefore been harder to study. Construction of Neural Circuits 533 (A) (B) Contact–mediated attraction Fasciculated growth cones Pioneer growth cone Chemoattraction Contact–mediated Repulsion Target trophic support Chemorepulsion (C) Figure 22.3 Growth cone interactions with the environment. (A) Potential classes of cues and their effects on grow-ing axons. Attractant cues, either secreted or bound to the cell surface, can guide a growth cone to a particular domain, or help maintain growing axons as distinct bundles, or fascicles. (B) Growth cone morphology varies in a single axon pathway. Examples of axons at different points in their trajectory between the dorsal horn and the ventral midline. When the axons are growing in the dorsal spinal cord, the growth cones are simple, with few apparent filopodia. When these axons reach a “choice point” (presumably one rich in chemoattractant and repulsive cues) such as the floorplate at the ventral mid-line, the growth cones become more complex, with broader lamellapodia and multiple filopodial extensions. (C) Sum-mary of growth cone responses to the range of cues available in the environ-ment. (B courtesy of C. Mason; C after Huber et al., 2003.) 534 Chapter Twenty-Two The CAMs and cadherins are distinguished by their presence on both growing axons and growth cones as well as surrounding cells or targets (see Figure 22.3). Moreover, both CAMs and cadherins have dual functions as lig-ands and receptors, usually via homophilic binding. Some of the CAMs, especially the L1 CAM, have been associated with the bundling, or fasicula-tion, of groups of axons as they grow. Cadherins have been suggested as important determinants of final target selection in the transition from grow-ing axon to synapse (see below). For both CAMs and cadherins, the unique ability of each class to function as both ligand and receptor (e.g., L1 is its own receptor) may be important for recognition between specific sets of axons and targets. Both these classes rely upon a somewhat indirect route of signal transduction. The Ca2+-independent molecules interact with cytoplas-mic kinases to initiate cellular responses, while the cadherins engage the APC/β-catenin pathway (also activated by Wnts; see Chapter 21). The importance of adhesive interactions in axon growth and guidance mediated by these molecules is underscored by the pathogenesis of several inherited human developmental or neurological disorders. These syn-dromes—X-linked hydrocephalus, MASA (an acronym for mental retarda-tion, aphasia, shuffling gait, and adducted thumbs), Kalman’s syndrome (which compromises reproductive and chemosensory function) and X-linked spastic paraplegia—are all consequences of mutations in genes encoding cell surface adhesion molecules. These mutations can also lead to the absence of the corpus callosum, which connects the two cerebral hemispheres, and of the corticospinal tract, which carries cortical information to the spinal cord. Con-genital anomalies such as these (which are fortunately rare) are now under-stood to arise from errors in the signaling mechanisms normally responsible for axon navigation via cell surface adhesion molecules. Diffusible Signals for Axon Guidance: Chemoattraction and Repulsion Another major challenge in establishing appropriate patterns of connectivity is attracting axons to distant targets, and insuring that the axons do not stray into inappropriate regions en route. Several additional molecules are respon-sible for this aspect of axon growth and guidance. With remarkable fore-sight, Cajal proposed early in the twentieth century that target-derived sig-nals selectively influenced axonal growth cones, thereby attracting them to appropriate destinations. In addition to the chemoattraction predicted by Cajal, it was long supposed that there might also be chemorepellent signals that discouraged axon growth toward a particular region. Despite the clear importance of chemoattraction and repulsion in constructing pathways and circuits, the identity of the signals themselves remained uncertain until the last 15 years or so. One problem was the vanishingly small amounts of such factors expressed in the developing embryo. Another was that of distin-guishing tropic molecules—which guide growing axons toward a source— from trophic molecules—which support the survival and growth of neurons and their processes once an appropriate target has been contacted (see below). These problems were solved by laborious biochemical purification and analysis of attractive or repulsive activities from vertebrate (chick) embryos, and genetic analysis of axon growth in both Drosophila and C. ele-gans; this work eventually led to the identification of several genes that code for chemotropic factors. Remarkably, the identity and function of chemoat-tractants and chemorepellents across phyla is highly conserved. The best-characterized class of chemoattractant molecules is the netrins (from the Sanskrit “to guide”; Figure 22.4). In chick embryos, the netrins were identified as proteins with chemoattractant activity following bio-chemical purification. In C. elegans, netrins were first recognized as the prod-uct of a gene that influenced axon growth and guidance (the first such gene was called Unc-6 for “uncoordinated,” which describes the behavioral phe-notype of the mutant worms; the cause is misrouted axons as a result of the absence of netrin). The netrins themselves have high homology to extracellu-lar matrix molecules like laminin (see Figure 22.2) and in some cases may actually interact with the extracellular matrix to influence directed axon growth. Netrin signals are transduced by specific receptors including the molecule DCC (deleted in colorectal cancer) as well as other co-receptors. Like many cell surface adhesion molecules, netrin receptors have repeated (A) Dorsal Ventral Floor plate Roof plate Commissural neurons Notochord (B) Floor plate Netrin Slit Sema3 Repelled by Slit and semaphorins, insensitive to netrin Slit silences netrin attraction ? Attracted by netrin, insensitive to Slit and semaphorins (C) DRG MN Figure 22.4 Chemotropic molecules (netrins) in the developing spinal cord. (A) Commissural neurons send axons to the ventral region of the spinal cord, including a specific region called the floorplate. (B) Opposing activities of netrin and slit at the ventral midline of the spinal cord. This molecular guid-ance system ensures that the axons relaying pain and temperature via the anterolateral pathway cross the midline at appropriate levels of the spinal cord and remain on the contralateral side until they reach their targets in the thal-amus. (C) At left, labeled commissural axons (red) descend through the spinal cord, pass the motor column (MC), and cross the midline into the anterior (ven-tral) commissure of the spinal cord. At right, the netrin gene of a mouse has been homozygously inactivated, and the commissural axons do not fasiculate, nor do they cross at the ventral midline (arrowheads). (A after Serafini et al., 1994; B after Dickinson, 2002; C from Serafini et al., 1996.) Construction of Neural Circuits 535 536 Chapter Twenty-Two amino acid motifs in their extracellular domain, a transmembrane domain and an intracellular domain with no known enzymatic activity. Thus, there must be indirect routes of signal transduction following netrin binding to its receptor. Netrins are often found at the midline in the developing nervous system. Indeed, their initial characterization was guided by the observation that there seemed to be a chemoattractive signal in the spinal cord that influ-enced the growth of spinothalamic axons from the dorsal horn toward the ventral midline (see Figure 22.4). After their initial purification and cloning, netrins were localized to the floorplate, which defines the ventral midline in the developing spinal cord. Consistent with their expression and in vitro activity, mutation of the netrin-1 gene disrupts the development of the spinal cord anterior commissure as well as axon pathways that cross the midline in the forebrain: the corpus callosum, anterior commissure and hippocampal commissure. The secreted factor “slit” and its receptor “robo” (named for the phenotypes of Drosophilia mutants in which these genes were first iden-tified) are important for preventing an axon from straying back over the midline once it has crossed initially in response to netrin. The combination of these molecules (and most likely others) and the relationships between their signaling pathways are thought to orchestrate the unidirectional cross-ing of axons at the midline—a process that is essential for the construction of some aspect of all major sensory, motor, and associational pathways in the mammalian brain. Much of the research on axon guidance has focused on molecules that encourage axon outgrowth or attract growing neurons. Constructing the nervous system, however, also entails telling axons where not to grow. Two broad classes of chemorepellent molecules have been described. The first is associated with central nervous system myelin. These molecules—referred to as the NoGo’s—and their receptors are evidently important after injury to the adult brain, where they inhibit axon growth at regions of CNS damage (see Chapter 24); however, their role in initial axon growth and guidance is less clear. In addition to the NoGo’s, some protein components of the myelin sheath, including myelin basic protein, also can be chemorepulsive for grow-ing axons. Molecules belonging to the second class of chemorepellents are active during neural development. These molecules, called semaphorins (semaphor is the Greek word for “signal”; see Figure 22.2E), are eventually bound to cell surfaces or to the extracellular matrix, where they can prevent the extension of nearby axons (Figure 22.5). Their receptors, like those for cell surface adhesion molecules, are transmembrane proteins (including the plexins and a protein called neuropilin) whose cytoplasmic domains have no known catalytic activity, but can complex with intercellular kinases and other signaling molecules. Much of the initial characterization of semaphorin chemorepellent activ-ity emerged from studies of invertebrates—particularly Drosophila—where mutation or manipulation of these genes can cause axons to grow abnor-mally. Studies with cultured vertebrate neurons indicated that the sema-phorins can cause collapse of growth cones and cessation of axon extension. The activity of these molecules in developing vertebrates, however, has been harder to demonstrate in vivo. For example, inappropriate growth or target-ing of axons is not apparent when single semaphorin genes are deleted in mice; nevertheless, local introduction of semaphorins can lead to altered axon trajectories due to avoidance of the exogenous semaphorin. The sema-phorins represent the largest family of chemorepellants. None of these mol-ecules alone, however, explains the initial choices and resulting trajectories of developing axons. It is nonetheless clear that the semaphorins make an important contribution to the orderly construction of axon pathways in both the periphery and in the central nervous system. The Formation of Topographic Maps In the somatic sensory, visual, and motor systems, neuronal connections are arranged such that neighboring points in the periphery are represented at similarly adjacent locations in the appropriate regions of the central nervous system (see Chapters 8, 11, and 16). In other systems (e.g., the auditory and olfactory systems), there are also orderly representations of various stimulus attributes like frequency or receptor identity. How do growing axons dis-tribute themselves with such fidelity within target regions in the brain? In the early 1960s, Roger Sperry, who later did pioneering work on the functional specialization of the cerebral hemispheres (see Chapter 26), artic-ulated the chemoaffinity hypothesis, based primarily on work in the visual system of frogs and goldfish. In these animals, the terminals of retinal gan-glion cells form a precise topographic map in the optic tectum (the tectum is homologous to the mammalian superior colliculus). When Sperry crushed the optic nerve and allowed it to regenerate (fish and amphibians, unlike mammals, can regenerate axonal tracts in their central nervous system; see Chapter 24), he found that retinal axons reestablished the same pattern of connections in the tectum. Even if the eye was rotated 180°, the regenerating axons grew back to their original tectal destinations (causing some behav-ioral confusion for the frog: Figure 22.6B). Accordingly, Sperry proposed that each tectal cell carries an “identification tag”; he further supposed that the growing terminals of retinal ganglion cells have complementary tags, such that they seek out a specific location in the tectum. In modern parlance, these “chemical” tags are cell adhesion or recognition molecules, and the “affinity” that they engender is a selective binding of receptor molecules on the growth cone to corresponding molecules on the tectal cells that signal their relative positions. Figure 22.5 Semaphorins promote growth cone collapse and axon repul-sion. (A) Time-lapse series showing a growth cone exposed to semaphorin. (B) In the presence of nerve growth factor (NGF), explant cultures of chick dorsal root ganglia extend halos of neurites that originate from different neuronal subpopulations. (C) Co-culture of a gan-glion with non-neuronal cells (+) trans-fected with the gene for semaphorin III (collapsin) results in asymmetrical growth of the ganglion cell neurites as a result of chemorepulsion. Control cells not transfected with the gene [(–) in panel B] have no effect on the pattern of outgrowth. (A from Dontchev and Letourneau, 2002; B, C from Messer-smith et al., 1995.) (B) (C) (NGF) (NGF) (+) (–) (A) 0 min 15 min after Sema3A 30 min after Sema3A Construction of Neural Circuits 537 538 Chapter Twenty-Two (A) (C) (D) (B) TECTUM Dorsal Ventral A D B C Fly Normal Rotated Posterior Posterior Anterior Anterior A D B C RETINA EphA4 ephrin-A5 Nasal Migrating growth cone Temporal ephrin-A5 Anterior Posterior A P A P A P A P A P A P A P Nasal axons Temporal axons Figure 22.6 Mechanisms of topographic mapping in the vertebrate visual system. (A) Posterior retinal axons project to the anterior tectum and anterior retinal axons to the posterior tectum. When the optic nerve of a frog is surgically interrupted, the axons regenerate with the appropriate specificity. (B) Even if the eye is rotated after severing the optic nerve, the axons regenerate to their original position in the tec-tum. This topographic constancy is evident from the frog’s behavior: When a fly is presented above, the frog consistently strikes downward, and vice versa. (C) An in vitro assay for cell surface molecules that contribute to topographic specificity in the optic tectum. A set of alternating stripes (90 µm wide) of membranes from anterior (A) and posterior (P) optic tectum of chicks was laid down on a glass coverslip. The posterior membranes have fluorescent particles added to make the boundaries of the stripes apparent (top of panels). Explants of retina from either nasal or temporal retina were placed on the stripes. Temporal axons prefer to grow on anterior mem-branes and are repulsed by posterior membranes. In contrast, nasal retinal axons grow equally well on both stripes. (D) Complementary gradients of Eph receptors (in afferent cells and their growth cones) and ephrins (in the target cells) lead to dif-ferential affinities and topograpic mapping. In this model, a growth cone with a high concentration of Eph receptors would be more likely to recognize a lower con-centration of ligand, whereas a growth cone with low Eph receptor concentration would recognize a higher concentration of ligand. (A, B after Sperry, 1963; C from Walter et al., 1987; D after Wilkinson, 2001.) Further experiments in the amphibian and avian visual systems made the strictest form of the chemoaffinity hypothesis—labeling of each tectal loca-tion by a different recognition molecule—untenable. Rather than precise “lock and key” affinity, the behavior of growing axons suggested that there are gradients of cell surface molecules to which growing axons respond to establish the basic axes of the retinotopic map. Normally, axons from the temporal region of the retina innervate the anterior pole of the tectum and avoid the posterior pole. Embryological experiments in which temporal and nasal regions of the retina or anterior and posterior regions of the tectum were reversed in their position suggested that there was some specificity. This specificity, however, was not absolute—if only posterior tectum was available to temporal retina axons, the axons would innervate the normally inhospitable target. Subsequent in vitro analysis showed that the specificity was generated by a comparison between different substrates. Temporal reti-nal axons, when presented with a choice of cell membranes derived from anterior or posterior tectal regions as a substrate, grow exclusively on ante-rior membranes, avoiding membranes derived from the “wrong” region of the tectum (Figure 22.6C). The positive interactions probably are due to increased adhesion of the growth cones to the substrate, whereas the failure to grow into inappropriate regions may result from repulsive interactions that tend to collapse the growth cones (see above). A likely candidate for the negative guidance signal for temporal axons in the posterior tectum was subsequently purified, and its gene cloned. The pro-tein—initially called RAGS (repulsive axon guidance signal) and later re-named ephrin-A5—belongs to a family of ephrin ligands and Eph receptors (see Figure 22.2). Subsequent work has associated several members of this molecular family with topographic mapping in the visual system as well as formation of axon pathways like the anterior commissure and migration of subpopulations of neural crest cells (Figure 22.6D). Ephrin ligands are cell adhesion-like molecules that can be either transmembrane or membrane-associated proteins. Eph receptors belong to the single transmembrane domain tyrosine receptor kinase family, and thus can directly transduce a sig-nal from an Eph ligand. Subsequent work has also suggested that the Ephrin ligands can generate intercellular signals upon binding with the Eph recep-tors via interactions with cytoplasmic kinases and related molecules. Disrup-tion of the genes for the Eph ligands or their receptors results in subtle disruptions in the topographic organization of the retinocollicular or retino-thalamic projection. These observations accord with the idea that chemo-affinity operates by a system of gradients in the retina and tectum that give axons and their targets markers of position, rather than a unique lock and key sort of recognition. The Eph receptors and their ligands provide a model of how graded molecular information can help organize topographic axonal growth in the visual system and other regions of the developing brain. Selective Synapse Formation After reaching the correct target or target region, axons must make a further local determination about which particular cells to innervate among a vari-ety of potential local synaptic partners. The choices available to an axon include: establish synaptic contacts; retract and regrow to another target; or fail to form stable connections (a choice that can result in the death of the parent neuron). Because of the complexity of brain circuitry, this issue has been studied most thoroughly in the peripheral nervous system, particularly Construction of Neural Circuits 539 540 Chapter Twenty-Two in the innervation of muscle fibers (Box B) and autonomic ganglion cells by spinal cord motor neurons. Synaptic specificity was first explored by British physiologist John Langley at the end of the nineteenth century. Pregan-glionic sympathetic neurons located at different levels of the spinal cord innervate cells in sympathetic chain ganglia in a stereotyped and selective manner (Figure 22.7; see also Chapter 20). In the superior cervical ganglion, for example, cells from the highest thoracic level (T1) innervate ganglion cells that project in turn to targets in the eye, whereas neurons from a some-what lower level (T4) innervate ganglion cells that cause constriction of the blood vessels of the ear. Since the axons of all these neurons run together in the cervical sympathetic trunk to arrive at the ganglion, the mechanisms underlying the differential innervation of the ganglion cells must occur at the level of synapse formation rather than axon guidance to the general vicinity of target cells (see above). Anticipating Sperry by more than 50 years in a different context, Langley concluded that selective synapse formation is based on differential affinities of the pre- and postsynaptic elements. Subsequent studies based on intracellular recordings from individual neurons in the superior cervical ganglion have shown, however, that the selective affinities between pre- and postsynaptic neurons are not especially restrictive. Thus, synaptic connections to ganglion cells made by pregan-glionic neurons of a particular spinal level are preferred, but synaptic con-tacts from neurons at other levels are not excluded (much like the rules that govern axon guidance). Furthermore, if the innervation to the superior cer-vical ganglion from a particular spinal level is surgically interrupted, record-ings made some weeks later indicate that new connections are established by residual axons arising from what would normally be inappropriate spinal segments. The novel connections also establish a pattern of segmental pref-erences, as if the system had attempted to achieve the best match it could under the altered circumstances. Despite this relative selectivity during syn-apse formation, a quite different line of work has shown that where a synapse forms on the target cell (at least if the cell is a muscle fiber) is tightly con-trolled by a set of molecules that are now understood in some detail (see Box B). Perhaps not surprisingly, these molecules include variants of several of the cell adhesion molecules that influence growth cone behavior (see below). There are some absolute restrictions to synaptic associations. Thus, neu-rons do not innervate nearby glial or connective tissue cells, and many in-stances have been described in which various nerve and target cell types show little or no inclination to establish connections with one another. When synaptogenesis does proceed, however, neurons and their targets in both the central and peripheral nervous systems appear to associate according to a continuously variable system of preferences—much like the old song “if you can’t be with the one you love, love the one you’re with.” Such biases guide the pattern of innervation that arises in development (or reinnervation) with-out limiting it in any absolute way. The target cells residing in muscles, auto-nomic ganglia, or elsewhere are certainly not equivalent, but neither are they unique with respect to the innervation they can receive. This relative promis-cuity can cause problems following neural injury, since regenerated patterns of peripheral innervation are not always appropriate (see Chapter 24). Several observations show that many of the same adhesion molecules that participate in axon guidance contribute to the identification and stabilization of a synaptic site on target cells, as well as to the ability of a growing axon to recognize specific sites as optimal. Ephrins have been suggested to con-tribute to this process, as have cadherins. In both cases the diversity of lig-ands and receptors makes these adhesion molecule families attractive candi-Targets in the ear Targets in the eye Superior cervical ganglion Cervical sympathetic trunk Rostral Caudal Preganglionic axons arising from different segments of the spinal cord T1 T2 T3 T4 T5 T6 Figure 22.7 Evidence that synaptic connections between mammalian neu-rons form according to specific affinities between different classes of pre- and postsynaptic cells. In the superior cervi-cal ganglion, preganglionic neurons located in particular spinal cord seg-ments (T1, for example) innervate gan-glion cells that project to particular peripheral targets (the eye, for example). Establishment of these preferential syn-aptic relationships indicates that selec-tive neuronal affinities are a major determinant of neural connectivity. dates. This speculation has an intriguing parallel in Drosophila. In the fly, the gene for the cell adhesion molecule DSCAM (the fly ortholog of the mam-malian down syndrome cell adhesion molecule, the gene for which is located on chromosome 21, the chromosome that is duplicated in Down syndrome) has approximately 38,000 isoforms based upon the numbers of exons in the gene and predicted splicing (Figure 22.8A). In the fly, DSCAM is expressed at synaptic sites in the developing nervous system. It is not yet clear whether or not individual splice isoforms are differentially expressed at distinct syn-aptic sites; however, if this is the case, the genomic diversity may contribute Construction of Neural Circuits 541 (A) DSCAM (B) Gamma protocadherin (C) mRNA Protein Introns Exon 4 Exon 6 Exon 9 1 1 1 1 2 12 48 33 Exon 17 Genomic DNA Genomic DNA Pcdhα αV Pcdhα γV αC γC Pcdhβ Figure 22.8 Potential molecular medi-ators of synapse identity. (A) Organiza-tion of the DSCAM gene in Drosophila. Each of four multiple-exon regions (4, 6, 9, and 17) has several alternative splice variants, and different combinations of these four regions yields a potential 37,000 isoforms of the DSCAM protein that can be expressed at distinct synap-tic sites in the fly’s developing nervous system. (B) Similar variability of multi-ple alternative exons is seen in the mam-malian gene for γ-protocadherin. (C) Distinct γ-protocadherin isoforms (green) are expressed at subsets of syn-aptic contacts on dendrites of hippocam-pal neurons in culture, suggesting that different synaptic sites may have differ-ent complements of adhesion molecules perhaps conferring specifity to those synaptic junctions. (A after Schmucker et al., 2000; B after Wang et al., 2002; C from Phillips et al., 2003.) 542 Chapter Twenty-Two Box B Molecular Signals That Promote Synapse Formation Synapses require a precise organization of presynaptic and postsynaptic elements in order to function properly (see Chap-ters 4–7). At the neuromuscular junction, for example, synaptic vesicles and the related release machinery are located at sites in the nerve terminal called active zones; and, in the postsynaptic muscle cell, acetylcholine receptors and other synapse-specific molecules are localized in high density exactly subjacent to the presynaptic active zones. During the past 25 years, a number of investigators have identified some of the molecular cues that guide the formation of these care-fully apposed elements. Their efforts have met with the greatest success at the neuromuscular junction, where a mole-cule called agrin is now known to be responsible for initiating some of the events that lead to the formation of a fully functional synapse. Agrin was originally identified as a result of its influence in the reinnervation of frog neuromuscular junctions follow-ing damage to the motor nerve. In mature skeletal muscle, each fiber typi-cally receives a single synaptic contact at a highly specialized region called the end plate (see Chapter 5). U. J. McMa-han, Josh Sanes, and their colleagues at Harvard and later Stanford and Wash-ington Universities found that regenerat-ing axons reinnervate the original end plate site precisely. In seeking to deter-mine the molecular signals underlying this phenomenon, they took advantage of the fact that each muscle fiber is sur-rounded by a sheath of extracellular matrix called the basal lamina. When muscle fibers degenerate, they leave the basal lamina behind (as do degenerating axons); moreover, a specific infolding of the basal lamina at the former end plate site allows its continued identification. Remarkably, presynaptic nerve terminals differentiate at these original sites even when the associated muscle fibers are absent. Equally remarkable is that regen-erating muscle fibers form postsynaptic specializations—such as densely packed acetylcholine receptors—at precisely these same basal lamina locations in the absence of nerve fibers! These findings show that the signal(s) guiding synapse formation remain in the extracellular environment after removal of either nerve or muscle, presumably in the basal lamina “ghost” that surrounds each muscle fiber. Using a bioassay based on the aggre-gation of acetylcholine receptors to ana-lyze the constituents of the basal lamina, Day 15 Day 16 Day 18 Control Agrin-deficient Development of neuromuscular junctions in agrin-deficient mice. Diaphragm muscles from control (left) and agrin-deficient (right) mice at embryonic day 15, 16, and 18 were double-stained for acetylcholine receptors and axons, then drawn with a camera lucida. The develop-ing muscle fibers run vertically. In both control and mutant muscles, an intramuscular nerve (black) and aggregates of AChRs (red) are present by embryonic day 15. In controls, axonal branches and AChR clusters are confined to a band at the central end plate at all stages. Mutant AChR aggregates are smaller, less dense, and less numerous; axons form fewer branches and their synaptic relationships are disorganized. (From Gautam et al., 1996.) to synaptic diversity. While the mammalian orthologue of DSCAM does not show a similar diversity, some members of the protocadherin family do (Fig-ure 22.8B,C). The possibility that protocadherin splice isoforms might invest synaptic sites with unique identities has thus been raised. Trophic Interactions and the Ultimate Size of Neuronal Populations The formation of synaptic contacts between growing axons and their synap-tic partners marks the beginning of a new stage of development. Once syn-aptic contacts are established, neurons become dependent in some degree on the presence of their targets for continued survival and differentiation; in the absence of synaptic targets, the axons and dendrites of developing neurons atrophy and the innervating nerve cells may eventually die. This long-term dependency between neurons and their targets is referred to as trophic interaction. The word trophic is taken from the Greek trophé, meaning, roughly, “nourishment.” Despite this nomenclature, the sustenance pro-vided to neurons by trophic interactions is not the sort derived from metabo-lites such as glucose or ATP. Rather, the dependence is based on specific sig-naling molecules called neurotrophic factors. Neurotrophic factors, like some other intercellular signaling molecules (mitogens and cytokines, for example), originate from target tissues and regulate neuronal differentiation, growth, and ultimately survival. These factors (referred to as neurotrophins Construction of Neural Circuits 543 McMahan and colleagues isolated and purified agrin. Agrin is a proteoglycan found in both mammalian motor neu-rons and muscle fibers; it is also abun-dant in brain tissue. The neuronal form of agrin is synthesized by motor neu-rons, transported down their axons, and released from growing nerve fibers. Agrin binds to a postsynaptic receptor whose activation leads to a clustering of acetylcholine receptors and, evidently, to subsequent events in synaptogenesis. Support for the role of agrin as an orga-nizer of synaptic differentiation is the finding by Sanes and his collaborators that genetically engineered mice that lack the gene for agrin develop in utero with few neuromuscular junctions (see figure). Importantly, mice lacking only neural agrin were as severely impaired as mice lacking both nerve and muscle agrin. Animals missing the agrin recep-tor also fail to develop neuromuscular junctions and die at birth. Agrin is there-fore one of the first examples of a presy-naptically derived molecule that pro-motes postsynaptic differentiation in tar-get cells. Because synapse formation requires an ongoing dialogue between pre- and postsynaptic partners, it is likely that postsynaptically derived organizers of presynaptic differentiation also exist. Based on the studies of basal lamina mentioned above, Sanes and his collabo-rators identified one such group of mole-cules, the β2-laminins (originally called s-laminin). Mice lacking β2-laminin show deficits in differentiation of motor nerve terminals and, unexpectedly, of terminal-associated glial (Schwann) cells. However, presynaptic defects in β2-laminin mutants are considerably less severe than postsynaptic defects in agrin mutants, suggesting that additional important retrograde signals remain to be identified. References BURGESS, R. W., Q. T. NGUYEN, Y.-J. SON, J. W. LICHTMAN AND J. R. SANES (1999) Alterna-tively spliced isoforms of nerve- and muscle-derived agrin: Their roles at the neuromuscu-lar junction. Neuron 23: 33–44. DECHIARA, T. M. AND 14 OTHERS (1996) The receptor tyrosine kinase MuSK is required for neuromuscular junction formation in vivo. Cell 85: 501–512. GAUTAM, M. AND 6 OTHERS (1996) Defective neuromuscular synaptogenesis in agrin-defi-cient mutant mice. Cell 85: 525–535. MCMAHAN, U. J. (1990) The agrin hypothesis. Cold Spring Harbor Symp. Quant. Biol. 50: 407–418. NOAKES, P. G., M. GAUTAM, J. MUDD, J. R. SANES AND J. P. MERLIE (1995) Aberrant differ-entiation of neuromuscular junctions in mice lacking S-laminin/laminin β2. Nature 374: 258–262. PATTON, B. L., A. Y. CHIU AND J. R. SANES (1998) Synaptic laminin prevents glial entry into the synaptic cleft. Nature 393: 698–701. SANES, J. R., L. M. MARSHALL AND U. J. MCMAHAN (1978) Reinnervation of muscle fiber basal lamina after removal of myofibers. J. Cell Biol. 78: 176–198. 544 Chapter Twenty-Two for short) are unique in that, unlike inductive signaling molecules and cell adhesion molecules, their expression is limited primarily to neurons as well as some non-neural targets like muscles, and they are first detected after the initial populations of postmitotic neurons have been generated in the nascent central and peripheral nervous systems. Why should neurons depend so strongly on their targets, and what spe-cific cellular and molecular interactions mediate this dependence? The answer to the first part of this question lies in the changing scale of the developing nervous system and the body it serves, and the related need to precisely match the number of neurons in particular populations with the size of their targets. The basic mechanisms by which neurons are initially generated have already been considered in Chapter 21. There is, however, one more issue in generating the final complement of neurons. A general— and surprising—strategy in the development of vertebrates is the production of an initial surplus of nerve cells (on the order of two- or threefold); the final population is subsequently established by the death of those neurons that fail to interact successfully with their intended targets (see below). The elim-ination of supernumerary neurons is now known to be mediated by neu-rotrophic factors. Evidence that targets play a major role in determining the size of the neu-ronal populations that innervate them has come from an ongoing series of studies dating from the start of the twentieth century. The seminal observa-tion was that the removal of a limb bud from a chick embryo results, at later embryonic stages, in a striking reduction in the number of nerve cells (α motor neurons) in the corresponding portions of the spinal cord (Figure 22.9A,B). These supernumerary neurons die due to a lack of trophic support. The interpretation of these experiments is that neurons, in the spinal cord in this case, compete with one another for a resource present in the target (the developing limb) that is available in limited supply. In support of this idea, many neurons that would normally have died can be rescued by augment-ing the amount of target available—in this example, by adding another limb that can be innervated by the same spinal segments that innervate the nor-mal limb—thereby providing extra trophic support (Figure 22.9C,D). Thus, the size of nerve cell populations in the adult is not fully determined in advance by a rigid genetic program. It can be modified by idiosyncratic neu-ron–target interactions in each developing individual. Limb bud ablation (A) (B) (C) Spinal cord section Missing limb Normal Transplantation of supernumerary limb bud 1 week later Spinal cord section Extra limb Normal Ventral horn 1 week later (D) Figure 22.9 Effect of removing or aug-menting neural targets on the survival of related neurons. (A) Limb bud ampu-tation in a chick embryo at the appropri-ate stage of development (about 2.5 days of incubation) depletes the pool of motor neurons that would have inner-vated the missing extremity. (B) A cross section of the lumbar spinal cord in an embryo that underwent this surgery about a week earlier. The motor neurons (dots) in the ventral horn that would have innervated the hindlimb degener-ate almost completely after embryonic amputation; a normal complement of motor neurons is present on the other side. (C) Adding an extra limb bud before the normal period of cell death rescues neurons that normally would have died. (D) Such augmentation leads to an abnormally large number of limb motor neurons (dots) on the side related to the extra limb. (After Hamburger, 1958, 1977, and Hollyday and Ham-burger, 1976.) Figure 22.10 Major features of synap-tic rearrangement during the first few weeks of postnatal life in the mam-malian peripheral nervous system. In ganglia comprising neurons without dendrites (A) and in muscles (B), each axon innervates more target cells at birth than in maturity. In both muscles and ganglia, however, the size and com-plexity of the terminal arbor on each tar-get cell increases. Thus, each axon elabo-rates more and more terminal branches and synaptic endings on the target cells it will innervate in maturity. The com-mon denominator of this process is not a net loss of synapses, but the focusing by each axon of a progressively increas-ing amount of synaptic machinery on fewer target cells. (After Purves and Lichtman, 1980.) Further Competitive Interactions in the Formation of Neuronal Connections Once neuronal populations are established by this winnowing, trophic inter-actions continue to modulate the formation of synaptic connections, begin-ning in embryonic life and extending far beyond birth. Among the problems that must be solved during the establishment of innervation is ensuring that each target cell is innervated by the right number of axons, and that each axon innervates the right number of target cells. Getting these numbers right is another major achievement of trophic interactions between developing neurons and target cells, and is necessary for establishing appropriate cir-cuits to support specific functional demands of each individual organism. Studying synaptic refinement in the complex circuitry of the cerebral cor-tex or other regions of the central nervous system is a formidable challenge. As a result, many basic ideas about the ongoing modification of developing brain circuitry have come from simpler, more accessible systems, most notably the vertebrate neuromuscular junction and autonomic ganglion cells (Figure 22.10). Adult skeletal muscle fibers and neurons in some classes of autonomic ganglia (parasympathetic neurons) are each innervated by a single axon. Initially, however, each of these target cells is innervated by axons from several neurons, a condition termed polyneuronal innervation. In such cases, inputs are gradually lost during early postnatal development until only one remains. This process of loss is generally referred to as synapse elimination, although the elimination actually refers to a reduction in the number of dif-ferent axonal inputs to the target cells, not to a reduction in the overall num-ber of synapses made on the postsynaptic cells. In fact, the overall number of synapses (individual specialized sites for release of neurotransmitter) in the peripheral nervous system increases steadily during the course of develop-Construction of Neural Circuits 545 At birth Muscle fibers In maturity (A) Ganglion cells (B) Muscle cells 546 Chapter Twenty-Two ment, as is the case throughout the brain. A variety of experiments have shown that the elimination of some initial inputs to muscle and ganglion cells is a process in which synapses originating from different neurons compete with one another for “ownership” of an individual target cell (see Box B). Importantly, such competition is thought to be modulated by patterns of electrical activity in the pre- and postsynaptic partners. For example, if acetylcholine receptors at the neuromuscular junction are blocked by curare (a potent antagonist of the acetylcholine receptor; see Chapter 6), polyneu-ronal innervation persists. Blocking presynaptic action potentials in the motor neuron axons (by silencing the nerve with tetrodotoxin, a sodium channel blocker) also prevents the reduction of polyneuronal innervation. Blocking neural activity, therefore, reduces (or delays) competitive interac-tions and the associated synaptic rearrangements. The object of this competition is not known. Some of the phenomena of activity-dependent competition in muscles and autonomic ganglia (as well as in more complex central nervous system structures) could be explained by postulating that (1) synapses require a certain minimal level of trophic support to persist, (2) the relevant factors are secreted in limited amounts by the postsynaptic (target) cells in response to synaptic activation, and (3) syn-apses can only avail themselves of trophic support if their activity and that of the target cell coincide. There is, however, little direct evidence for this sce-nario. Equally plausible is the idea that active synapses provide a destabiliz-ing signal that weakens asynchronously firing inputs. Thus, how activity achieves its effects on synaptic connectivity remains a key question. The most useful insights into the nature of synaptic rearrangement during development have come from direct observation of this process (Figure 22.11). Using different-colored fluorescent dyes that stain either the presyn-aptic terminal or the postsynaptic receptors synaptic rearrangement Jeff Lichtman and his colleagues have followed the same neuromuscular junc-tion over days, weeks, or longer. These observations have yielded some unexpected results. Competition between synapses arising from different motor neurons does not involve the active displacement of the “losing” input by the eventual “winner.” Instead, it appears that the inputs of the two competitors gradually segregate. The “losing” axon then atrophies and retracts from the synaptic site. This is accomplished by a loss of the corre-sponding postsynaptic specializations associated with the “loser.” Neuro-transmitter receptors beneath the terminal branches that eventually will be eliminated are also lost. This receptor loss occurs before the nerve terminal (A) (B) (C) Figure 22.11 Synapse elimination at neuromuscular junctions. (A) Several neuromuscular junctions (arrows) from a mouse fetus (embryonic day 17). The red and green terminals are synapses from two different axons that converge at each of several junctions. (B) A single neuromuscular junction at higher mag-nification during a late stage of competi-tion in which one of the synaptic inputs is close to elimination (white arrow). The “losing” input has completely seg-regated from the other axon, and the synaptic area on the muscle fiber that it occupies (labeled red with an acetyl-choline antibody) is disappearing as the nerve is being eliminated (arrowheads). (C) This image illustrates the outcome of synaptic competition just after the losing axon (green) has withdrawn, leaving a red axon and its terminal. Note that the “loser” (green axon) has a retraction bulb at the end (arrow), and the “win-ning” axon (red) is significantly thicker. (Courtesy of J. W. Lichtman.) has withdrawn and presumably reduces the synaptic strength of the input, which causes a further loss of postsynaptic receptors, leading to further reduction in the strength of the input. The downward spiral of synaptic effi-cacy presumably results in withdrawal of the presynaptic terminal. The remaining terminals then continue to enlarge and strengthen in place as the end plate region expands during postnatal muscle growth. A generally similar reorganization of synaptic innervation is evident in a variety of other peripheral and central nervous system regions. In the peripheral nervous system, the number of presynaptic axons innervating each neuron can also decrease, as demonstrated by studies of certain auto-nomic ganglia. A similar process has been described in the central nervous system. In the cerebellum, each adult Purkinje cell is innervated by a single climbing fiber (see Chapter 18); however, during early development, each Purkinje cell receives multiple climbing fiber inputs. Finally, in the visual cortex, initial binocular innervation of cells is eliminated to establish segre-gated molecularly driven inputs (see Chapter 23). The pattern of synaptic connections that emerges in the adult is not simply a consequence of the bio-chemical identities of synaptic partners or other determinate developmental rules. Rather, the mature wiring plan is the result of a much more flexible process in which neuronal connections are formed, removed, and remodeled according to local circumstances that reflect molecular constraints as well as ongoing electrical activity. These interactions guarantee that every target cell is innervated—and continues to be innervated—by the right number of inputs and synapses, and that every innervating axon contacts the right number of target cells with an appropriate number of synaptic endings. Thus, the regulation of convergence (the number of inputs to a target cell) and divergence (the number of connections made by a neuron) in the devel-oping nervous system is another key consequence of trophic interactions among neurons and their targets. The regulation of convergence and diver-gence by neurotrophic interactions is also importantly influenced by the form of neurons, particularly the elaboration of dendrites (Box C), a feature that is also subject to neurotrophic control (see below). Thus, trophic interactions regulate three essential steps in the formation of mature neural circuits: matching numbers of afferents to the available target space; regulating the degree of innervation of individual afferents and their postsynaptic partners, and modulating the growth and shape of axonal and dendritic branches. Molecular Basis of Trophic Interactions The three major functions of neurotrophic signaling—survival of a subset of neurons from a considerably larger population, subsequent formation and maintenance of appropriate numbers of connections, and the elaboration of axonal and dendritic branches to support these connections—can be ratio-nalized in part by the supply and availability of trophic factors. These rules entail several general assumptions about neurons and their targets (which may be other neurons, muscles, or other peripheral structures). First, neu-rons depend on the availability of some minimum amount of trophic factor for survival, and subsequently for the persistence of appropriate numbers of target connections. Second, target tissues synthesize and make available to developing neurons appropriate trophic factors. Third, targets produce trophic factors in limited amounts; in consequence, the survival of develop-ing neurons (and later, the persistence of neuronal connections and growth and further differentiation of neurons) depends on neuronal competition for Construction of Neural Circuits 547 Box C Why Do Neurons Have Dendrites? Perhaps the most striking feature of neu-rons is their diverse morphology. Some classes of neurons have no dendrites at all; others have a modest dendritic arbor-ization; still others have an arborization that rivals the complex branching of a fully mature tree (see Figures 1.2 and 1.6). Why should this be? Although there are many reasons for this diversity, neu-ronal geometry influences the number of different inputs that a target neuron re-ceives by modulating competitive inter-actions among the innervating axons. Evidence that the number of inputs a neuron receives depends on its geometry has come from studies of the peripheral autonomic system, where it is possible to stimulate the full complement of axons innervating an autonomic ganglion and its constituent neurons. This approach is not usually feasible in the central ner-vous system because of the anatomical complexity of most central circuits. Since individual postsynaptic neurons can also be labeled via an intracellular recording electrode, electrophysiological measure-ments of the number of different axons innervating a neuron can routinely be correlated with target cell shape. In both parasympathetic and sympathetic gan-glia, the degree of preganglionic conver-gence onto a neuron is proportional to its dendritic complexity. Thus, neurons that lack dendrites altogether are generally innervated by a single input, whereas neurons with increasingly complex den-dritic arborizations are innervated by a proportionally greater number of differ-ent axons (see figure). This correlation of neuronal geometry and input number holds within a single ganglion, among different ganglia in a single species, and among homologous ganglia across a range of species. Since ganglion cells that have few or no dendrites are initially innervated by several different inputs (see text), confining inputs to the limited arena of the developing cell soma evi-dently enhances competition between them, whereas the addition of dendrites to a neuron allows multiple inputs to persist in peaceful coexistence. Impor-tantly, the dendritic complexity of at least some classes of autonomic ganglion cells is influenced by neurotrophins. A neuron innervated by a single axon will clearly be more limited in the scope of its responses than a neuron inner-vated by 100,000 inputs (1 to 100,000 is the approximate range of convergence in the mammalian brain). By regulating the number of inputs that neurons receive, dendritic form greatly influences func-tion. References HUME, R. I. AND D. PURVES (1981) Geometry of neonatal neurons and the regulation of synapse elimination. Nature 293: 469–471. PURVES, D. AND R. I. HUME (1981) The relation of postsynaptic geometry to the number of presynaptic axons that innervate autonomic ganglion cells. J. Neurosci. 1: 441–452. PURVES, D. AND J. W. LICHTMAN (1985) Geo-metrical differences among homologous neu-rons in mammals. Science 228: 298–302. PURVES, D., E. RUBIN, W. D. SNIDER AND J. W. LICHTMAN (1986) Relation of animal size to convergence, divergence and neuronal num-ber in peripheral sympathetic pathways. J. Neurosci. 6: 158–163. SNIDER, W. D. (1988) Nerve growth factor promotes dendritic arborization of symapa-thetic ganglion cells in developing mammals. J. Neurosci. 8: 2628–2634. 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 0.2 mm (A) (B) Number of primary dendrites Number of innervating axons 2 3 4 5 7 Number of innervating axons = 1 The number of axons inner-vating ciliary ganglion cells in adult rabbits. (A) Neurons studied electrophysiologically and then labeled by intracellu-lar injection of a marker enzyme have been arranged in order of increasing dendritic complexity. The number of axons innervating each neu-ron is indicated. (B) This graph summarizes observa-tions on a large number of cells. There is a strong correla-tion between dendritic geome-try and input number. (After Purves and Hume, 1981.) the available factor. One much-studied trophic molecule, the protein called nerve growth factor (NGF), has provided support for these assumptions. Although the story of nerve growth factor certainly does not explain all aspects of trophic interactions, it has been a useful paradigm for under-standing in more detail the manner in which neural targets influence the survival and connections of the nerve cells that innervate them. NGF was discovered in the early 1950s by Rita Levi-Montalcini and Vik-tor Hamburger at Washington University. On the basis of experiments involving the survival of motor neurons after removal of developing limb buds (see Figure 22.9), they made an informed guess that the target tissues provided some sort of signal to the relevant neurons, and that limited amounts of this agent explained the apparently competitive nature of nerve cell death. Accordingly, Levi-Montalcini and Hamburger undertook a series of experiments to explore the source and nature of the postulated signal, focusing on dorsal root and sympathetic ganglion neurons rather than the spinal cord neurons. A former student of Hamburger’s had earlier removed a limb from a chick embryo and replaced it with a piece of mouse tumor. The surprising outcome of this experiment was that the tumor apparently furnished an even more potent stimulus than the limb, causing an enlarge-ment of the sensory and sympathetic ganglia that normally innervate the appendage. In further experiments, Levi-Montalcini and Hamburger pro-vided evidence that the tumor (a mouse sarcoma) secreted a soluble factor that stimulated the survival and growth of both sensory and sympathetic ganglion cells. Levi-Montalcini then devised a bioassay for the presumed agent and, in collaboration with Stanley Cohen, isolated and characterized the molecule—which had by then been named nerve growth factor for its ability to induce the massive outgrowth of neurites from explanted ganglia (Figure 22.12). (The term “neurite” is used to describe neuronal branches when it is not known whether they are axons or dendrites.) NGF was identi-fied as a protein and was substantially purified from a rich biological source, the salivary glands of the male mouse. Subsequently, its amino acid sequence and 3 dimensional structure was determined and the cDNAs encoding NGF cloned in several species. Support for the idea that NGF is important for neuronal survival in more physiological circumstances emerged from a number of further observations. Depriving developing mice of NGF by the chronic administration of an NGF antiserum or other strategies resulted in adult mice lacking most NGF-dependent neurons (Figure 22.12). Conversely, injection of exogenous NGF into newborn rodents caused enlargement of sympathetic ganglia, an effect opposite that of NGF deprivation. Neurons in ganglia in treated animals were both more numerous and larger; there was also more neuropil between cell bodies, suggesting an overgrowth of axons, dendrites, and other cellular elements. The dramatic influence of NGF on cell survival, together with what was known about the significance of neuronal death in development, suggested that NGF is indeed a target-derived signal that serves to match the number of nerve cells to the number of target cells. The ability of NGF to support neuronal survival (and of NGF deprivation to enhance cell death) is not in itself unassailable proof of a physiological role for this factor in development. In particular, these observations provided no direct evidence for NGF synthesis by (and uptake from) neuronal targets. This gap was filled by another series of ingenious experiments in several lab-oratories that showed NGF to be present in sympathetic targets, and to be quantitatively correlated with the density of sympathetic innervation. Fur-thermore, messenger RNA for NGF was demonstrated in targets innervated Construction of Neural Circuits 549 550 Chapter Twenty-Two Figure 22.12 Effect of NGF on the out-growth of neurites. (A) A chick sensory ganglion taken from an 8-day-old embryo and grown in organ culture for 24 hours in the absence of NGF. Few, if any, neuronal branches grow out into the plasma clot in which the explant is embedded. (B) A similar ganglion in identical culture conditions 24 hours after the addition of NGF to the medium. NGF stimulates a halo of neu-rite outgrowth from the ganglion cells. (C, D) Effect of NGF on the survival of sympathetic ganglion cells. (C) The sur-vival of newborn rat sympathetic gan-glion cells grown in culture for 30 days evaluated quantitatively as a function of NGF concentration. Dose-response curves such as this one confirm the strict dependence of these neurons on the availability of NGF. (D) Cross section of a superior cervical ganglion from a nor-mal 9-day-old mouse (top) compared to a similar section from a littermate injected daily since birth with NGF anti-serum (bottom). The ganglion of the treated mouse shows marked atrophy, with obvious loss of nerve cells. (A, B from Purves and Lichtman, 1985, cour-tesy of R. Levi-Montalcini; C after Chun and Patterson, 1977; D from Levi-Mon-talcini, 1972.) by sympathetic and sensory ganglia, but not in the ganglia themselves or in targets innervated by other types of nerve cells. As might be expected from such specificity, the NGF-sensitive neurons were also shown to have receptor molecules for the trophic factor (see next section). Importantly, the NGF message appears only after ingrowing axons have reached their targets; this fact makes it unlikely that secreted NGF acts in vivo as a chemotropic (guid-ance) molecule (like netrins and other cell adhesion molecules discussed ear-lier). Finally, the great majority of sympathetic neurons are lacking in mice in which the gene encoding NGF has been deleted. In sum, several decades of work in a number of laboratories have shown that NGF mediates cell survival among two specific neuronal populations in birds and mammals (sympathetic neurons and a subpopulation of sensory ganglion cells). These observations include the death of the relevant neurons in the absence of NGF; the survival of a surplus of neurons in the presence of augmented levels of the factor; the presence and production of NGF in neu-ronal targets; and the existence of receptors for NGF in innervating nerve ter-minals. Indeed, these observations define the criteria that must be satisfied in order to conclude that a given molecule is indeed a neurotrophic factor. Although NGF remains the most thoroughly studied neurotrophic factor, it was apparent from the outset that only certain classes of nerve cells respond to NGF. Work from a number of laboratories in the late 1980’s and early 1990’s has shown that NGF is only one member of a family of related trophic molecules, the neurotrophins. At present, there are three well-char-Number of surviving neurons (2103) NGF concentration (µg/ml) 3 2 1 1 0.5 5 10 (A) (B) (C) (D) Control NGF BDNF NT–3 DRG NG SG Control NGF BDNF NT–3 DRG NG SG (A) (B) Dorsal root ganglion Spinal cord Free nerve ending NGF Muscle spindle NT3 Merkel disk BDNF Hair follicle NT4/5 Construction of Neural Circuits 551 Figure 22.13 The influence of neu-rotrophins. (A) Effect of NGF, BDNF, and NT-3 on the outgrowth of neurites from explanted, dorsal root ganglia (left column), nodose ganglia (middle col-umn), and sympathetic ganglia (right column). The specificities of these sev-eral neurotrophins are evident in the ability of NGF to induce neurite out-growth from sympathetic and dorsal root ganglia, but not from nodose gan-glia (which are cranial nerve sensor gan-glia that have a different embryological origin from dorsal root ganglia); of BDNF to induce neurite outgrowth from dorsal root and nodose ganglia, but not from sympathetic ganglia; and of NT-3 to induce neurite outgrowth from all three types of ganglia. (B) Specific influ-ence of neurotrophins in vivo. Distinct classes of peripheral somatosensory receptors and the dorsal root ganglion cells that give rise to these sensory end-ings depend on different trophic factors in specific target tissues. (A from Maisonpierre et al., 1990; B after Bibel and Barde, 2000.) acterized members of the neurotrophin family in addition to NGF: brain-derived neurotrophic factor (BDNF), neurotrophin-3 (NT-3), and neu-rotrophin 4/5 (NT-4/5) (Box D). Although several neurotrophins are homolo-gous in amino acid sequence and structure, they are very different in their specificity (Figure 22.13). For example, NGF supports the survival of (and neurite outgrowth from) sympathetic neurons, while another family mem-ber—BDNF—cannot. Conversely, BDNF, but not NGF, can support the sur-552 Chapter Twenty-Two Box D The Discovery of BDNF and the Neurotrophin Family During the 30 years or so that work with NGF showed it to fulfill all the criteria for a target-derived neurotrophic factor (see text), it became clear that NGF affected only a few specific populations of peripheral neurons. It was therefore presumed that other neurotrophic factors must exist that followed similar rules, but supported the survival and growth of other classes of neurons. In particular, whereas NGF was shown to be secreted by the peripheral targets of primary sen-sory and sympathetic neurons, other fac-tors were presumably produced by tar-get neurons in the brain and spinal cord that supported the central projections of sensory neurons. The serendipity of the mouse salivary gland and its extraordinary levels of NGF was not repeated for these addi-tional factors, however, and the hunt for the neurotrophic factors presumed to act in the central nervous system proved to be a long and arduous one. Indeed, it was not until the 1980s that the pioneer-ing work of Yves Barde, Hans Thoenen, and their colleagues succeeded in identi-fying and purifying a factor from the brain that they named brain-derived neurotrophic factor (BDNF). As with NGF, this factor was purified on the basis of its ability to promote the sur-vival and neurite outgrowth of sensory neurons. However, BDNF is expressed at such vanishingly small levels that over a million-fold purification was necessary before the protein could be identified! Thereafter, microsequencing and recombinant DNA technology allowed rapid progress even from the scant amounts of purified BDNF protein that were available. By 1989, Barde’s group had succeeded in cloning the cDNA for BDNF. Surprisingly—despite its entirely different origin and distinct neuronal specificity—BDNF turned out to be a close relative of NGF. Based on the homologies between the primary struc-tures of NGF and BDNF, the following year six independent laboratories (including Barde’s) reported the cloning of a third member of the neurotrophin family, neurotrophin-3 (NT-3). At pre-sent, four members of the neurotrophin family have been reported in a variety of vertebrate species (see text). Experiments on BDNF and other members of the neurotrophin family over last decade have supported the conclusion that the survival and growth of different neuronal populations in both the PNS and CNS is dependent on different neurotrophins, relationships that are mediated by expression of membrane receptors that are specific for each neuro-trophin (see figure). However, the dra-matic relationship between the survival of neuronal populations and neurotrophins has not been found in the CNS, where BDNF, NT-3, and NT-4/5, as well as their receptors, are primarily expressed. The most striking demonstration of this differ-ence has been in “knockout” mice in which individual genes encoding neuro-trophins or Trk receptors have been de-leted: While these genetic deletions have led to predictable deficits in the PNS (see text), they have generally had minimal impact on CNS structure and function. Thus, the part played by neurotro-phins in the CNS remains much less cer-tain. One possibility is that these neuro-trophins are more involved in regulating neuronal differentiation and phenotype in the CNS than in supporting neuronal survival per se. In this regard, the expres-sion of neurotrophins is tightly regulated by electrical and synaptic activity, sug-gesting that they may also influence experience-dependent processes during the formation of circuits in the CNS. References HOFER, M. M. AND Y.-A. BARDE (1988) Brain-derived neurotrophic factor prevents neu-ronal death in vivo. Nature 331: 261–262. HOHN, A., J. LEIBROCK, K. BAILEY AND Y. -A. BARDE (1990) Identification and characteriza-tion of a novel member of the nerve growth factor/brain-derived neurotrophic factor family. Nature 344: 339–341. HORCH, H. W., A. KRUITTGEN, S. D. PORTBURY AND L. C. KATZ (1999) Destabilization of cor-tical dendrites and spines by BDNF. Neuron 23: 353–364. LEIBROCK, J. AND 7 OTHERS (1989) Molecular cloning and expression of brain-derived neu-rotrophic factor. Nature 341: 149–152 SNIDER, W. D. (1994) Functions of the neu-rotrophins during nervous system develop-ment: What the knockouts are teaching us. Cell 77: 627–638. Neurotrophins influence dendritic arbors in the developing cerebral cortex. The cell on the left was transfected with the gene for green fluorescent protein (GFP) alone, the one on the right with GFP plus the gene encoding BDNF. Within a day, BDNF-transfected neurons grow elabo-rate dendritic branches, reminiscent of the NGF-induced halo in peripheral ganglia (see Fig-ure 22.12B). (From Horch et al., 1999.) Figure 22.14 Evidence that NGF can influence neurite growth by local action. Three compartments of a culture dish (A, B, C) are separated from one another by a plastic divider sealed to the bottom of the dish with grease. Isolated rat sympathetic ganglion cells plated in compartment A can grow through the grease seal and into compartments B and C. (A magnified view looking down on the compartments is shown below.) Growth into a lateral chamber occurs as long as the compartment con-tains an adequate concentration of NGF. Subsequent removal of NGF from a compartment causes a local regression of neurites without affecting the sur-vival of cells or neurites in the other compartments. These observations show that neuritic growth can be locally controlled by neurotrophins. (After Campenot, 1981.) vival of certain sensory ganglion neurons, which have a different embryonic origin. NT-3 supports both of these populations. Given the diverse systems whose growth and connectivity must be coordinated during neural develop-ment, this specificity makes good sense. Neurotrophin Signaling All of the biological observations on neurotrophic interactions suggest that signaling via the neurotrophins will activate at least 3 different kinds of responses: cell survival/death, synapse stabilization/elimination, and process growth/retraction. This impression was initially generated by exper-iments that presented NGF to subsets of neural processes without exposing the cell body to the factor (Figure 22.14). The result of this experiment indi-cated that NGF could act locally to stimulate neurite growth—even while other processes of the same cell, deprived of NGF, are retracting. In addition, physiological experiments indicated that NGF and other neurotrophins could influence synaptic activity and plasticity, again independent of their effects on cell survival. Thus, there is a high degree of selectivity of neu-rotrophin actions, depending on the neurotrophic factor available, the stage of differentiation of the responding neuron as well as the cellular domains where neurotrophic signaling takes place. The selective actions of the neurotrophins arise from their interactions with two classes of receptors: the Trk (for tyrosine kinase) receptors and the p75 receptor. There are three Trk receptors, each of which is a single trans-membrane protein with a cytoplasmic tyrosine kinase domain. TrkA is pri-marily a receptor for NGF, TrkB a receptor for BDNF and NT-4/5, and TrkC a receptor for NT-3 (Figure 22.15). In addition, all neurotrophins can activate the p75 receptor protein. The interactions between neurotrophins and p75 demonstrate another level of selectivity and specificity of neurotrophin sig-naling. All neurotrophins are secreted in an unprocessed form that under-goes subsequent proteolytic cleavage. The p75 receptor has high affinity for unprocessed neurotrophins, and low affinity for the processed ligands, while the Trk receptors have high affinity for processed ligands only. The expres-sion of a particular Trk receptor subtype or p75 therefore confers the capac-ity to respond to the corresponding neurotrophin. Since neurotrophins, Trk Construction of Neural Circuits 553 NGF removed from compart-ments A and B Keep NGF in compartment; continued proliferation of branches NGF NGF NGF Well B Well A Well C Neurite regression No NGF No NGF Well B NGF Well C Well A Teflon insert separating compartments A,B, and C Grease seal C B A A C B 554 Chapter Twenty-Two receptors and p75 are expressed only in subsets of neurons, the selective binding between ligand and receptor accounts for the specificity of the rele-vant neurotrophic interactions. Signaling via either the Trk receptors or the p75 receptor can lead to changes in the three domains that are sensitive to neurotrophic signaling: cell survival/death, cell and process growth/differentiation, and activity dependent synaptic stabilization or elimination. Each receptor class (Trk or p75) can engage distinct intracellular signaling cascades that lead to changes in cell state (motility, adhesion, etc.) or gene expression and thus result in the known consequences of neurotrophic interactions (Figure 22.16). Thus, understanding the specific effects of neurotrophic interactions for any cell relies on at least three pieces of information: the neurotrophins locally avail-able, the combination of receptors on the relevant neuron, and the intracellu-lar signaling pathways expressed by that neuron. The subtlety and diversity of neuronal circuits is thus set during development by different combina-tions of neurotrophins, their receptors, and signal transduction mechanisms that in concert determine the numbers of neurons, their shape, and their pat-terns of connections. Presumably, disruption of these neurotrophin-depen-dent processes, either during development or in the adult brain, can result in neurodegenerative conditions in which neurons die due to lack of appropri-ate trophic support, with devastating consequences for the circuits that the cells define, and the behaviors that are controlled by those circuits. Indeed, the pathogenic mechanisms of neurodegenerative diseases as diverse as amyotrophic lateral sclerosis (ALS), Parkinson’s, Huntington’s, and Alz-heimer’s diseases may all reflect deficiencies of neurotrophic regulation. Summary Neurons in the developing brain must integrate a variety of molecular sig-nals in order to determine where to send their axons, whether to live or die, what cells to form synapses on, how many synapses to make, and whether Inside Outside BDNF TrkB receptor p75 receptor TrkC receptor TrkA receptor NT-3 NT-4/5 NGF BDNF NT-4/5 NT-3 NGF (A) (B) Figure 22.15 Neurotrophin receptors and their specificity for the neuro-trophins. (A) The Trk family of receptor tyrosine kinases for the neurotrophins. TrkA is primarily a receptor for NGF, TrkB a receptor for BDNF and NT-4/5, and TrkC a receptor for NT-3. Because of the high degree of structural homol-ogy among both the neurotrophins and the Trk receptors, there is some degree of cross-activation between factors and receptors. For example, NT-3 can bind to and activate TrkB under some condi-tions, as indicated by the dashed arrow. These distinct receptors allow various neurons to respond selectively to the different neurotrophins. (B) The p75 low-affinity neurotrophin receptor binds all neurotrophins at low affinities (as its name implies). This receptor confers the ability to respond to a broad range of neurotrophins upon fairly broadly dis-tributed classes of neurons in the peripheral and central nervous systems. to retain them. Fixed and/or diffusible adhesive, chemotropic, chemorepul-sive, and trophic molecules all regulate the trajectory of growing axons and the synaptic connections they make with target cells. These developmental interactions occur over weeks, months, and to some extent may continue at a low level over the entire lifetime of the animal—as body size and func-tional demands change. Cell adhesion molecules influence the initial target-ing of axons to appropriate target zones by modulating the direction and extent of growth cone motility. The earliest effects of trophic agents are on cell survival and differentiation. Once the appropriate number of neurons is established, trophic signals continue to govern the establishment of neural connections, particularly the extent of axonal and dendritic arborizations. Defects in the early guidance of axons are responsible for a variety of con-genital neurological syndromes, and conditions thought to reflect trophic dysfunction may underlie degenerative diseases such as amyotrophic lateral sclerosis and Parkinson’s disease. Understanding the molecular basis of axon guidance, synapse formation, and trophic signaling began a century ago and has now burgeoned into a broad effort that continues to identify additional factors and signaling pathways to illuminate their varied roles in both the developing and adult brain. A further goal that now seems within reach is the application of this knowledge to understanding a spectrum of previously intractable neurological diseases. Construction of Neural Circuits 555 Inside Outside Trk receptor p75 receptor (A) (B) PI 3 kinase PKB Akt kinase Cell survival Cell death Neurite growth MAP Kinase ras Kinases Neurite outgrowth and neuronal differentiation Activity– dependent plasticity Ca2+ release PLC RhoA NADE SC1 DAG PKC IP3 Cell cycle arrest Figure 22.16 Signaling through the neurotrophins and their receptors. (A) Signaling via Trk dimers can lead to a variety of cellular responses, depending on the intracellular signaling cascade engaged by the receptor after binding to the ligand. The possibilities include cell survival (via the protein kinase C/AKT pathway); neurite growth (via the MAP-Kinase pathway); and activity-depen-dent plasticity (via the Ca2+/calmodulin and PKC pathways). (B) Signaling via the p75 pathway can lead to neurite growth via interaction with Rho kinases, or cell cycle arrest and cell death via other distinct intracellular signaling cas-cades. 556 Chapter Twenty-Two Additional Reading Reviews CULOTTI, J. G. AND D. C. MERZ (1998) DCC and netrins. Curr. Opin. Cell Biol. 10: 609–613. HUBER, A. B., A. L. KOLODKIN, D. D. GINTY AND J. F. CLOUTIER (2003) Signaling at the growth cone: Ligand-receptor complexes and the con-trol of axon growth and guidance. Annu. Rev. Neurosci. 26: 509–563. LEVI-MONTALCINI, R. (1987) The nerve growth factor 35 years later. Science 237: 1154–1162. LEWIN, G. R. AND Y. A. BARDE (1996) Physiol-ogy of the neurotrophins. Annu. Rev. Neu-rosci. 19: 289–317. LICHTMAN, J. W. AND H. COLEMAN (2000) Syn-apse elimination and indelible memory. Neu-ron 25: 269–278. PURVES, D. AND J. W. LICHTMAN (1978) Forma-tion and maintenance of synaptic connections in autonomic ganglia. Physiol. Rev. 58: 821–862. PURVES, D. AND J. W. 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Physiol. (Lond.) 261: 387–422. CAMPENOT, R. B. (1977) Local control of neu-rite development by nerve growth factor. Proc. Natl. Acad. Sci. USA 74: 4516–4519. DONTCHEV, V. D. AND P. C. LETOURNEAU (2002) Nerve growth factor and semaphorin 3A sig-naling pathways interact in regulating sen-sory neuronal growth cone motility. J. Neu-rosci. 22: 6659–6669. DRESCHER, U., C. KREMOSER, C. HANDWERKER, J. LOSCHINGER, M. NODA AND F. BONHOEFFER (1995) In vitro guidance of retinal ganglion cell axons by RAGS, a 25 kDa tectal protein related to ligands for Eph receptor tyrosine kinases. Cell 82: 359–370. FREDETTE, B. J. AND B. RANSCHT (1994) T-cad-herin expression delineates specific regions of the developing motor axon-hindlimb projec-tion pathway. J. Neurosci. 14: 7331–7346. FARINAS, I., K. R. JONES, C. BACKUS, X. Y. WANG AND L. F. REICHARDT (1994) Severe sensory and sympathetic deficits in mice lacking neu-rotrophin-3. Nature 369: 658–661. KAPLAN, D. R., D. MARTIN-ZANCA AND L. F. PARADA (1991) Tyrosine phosphorylation and tyrosine kinase activity of the trk proto-onco-gene product induced by NGF. Nature 350: 158–160. KENNEDY, T. E., T. SERAFINI, J. R. DE LA TORRE AND M. TESSIER-LAVIGNE (1994) Netrins are dif-fusible chemotropic factors for commissural axons in the embryonic spinal cord. Cell 78: 425–435. KOLODKIN, A. L., D. J. MATTHES AND C. S. GOODMAN (1993) The semaphorin genes encode a family of transmembrane and secreted growth cone guidance molecules. Cell 75: 1389–1399. LANGLEY, J. N. (1895) Note on regeneration of pre-ganglionic fibres of the sympathetic. J. Physiol. (Lond.) 18: 280–284. LEVI-MONTALCINI, R. AND S. COHEN (1956) In vitro and in vivo effects of a nerve growth-stimulating agent isolated from snake venom. Proc. Natl. Acad. Sci. USA 42: 695–699. LICHTMAN, J. W. (1977) The reorganization of synaptic connexions in the rat submandibular ganglion during post-natal development. J. Physiol. (Lond.) 273: 155–177. LICHTMAN, J. W., L. MAGRASSI AND D. PURVES (1987) Visualization of neuromuscular junc-tions over periods of several months in living mice. J. Neurosci. 7: 1215-1222. LUO, Y., D. RAIBLE AND J. A. RAPER (1993) Col-lapsin: A protein in brain that induces the col-lapse and paralysis of neuronal growth cones. Cell 75: 217–227. MESSERSMITH, E. K., E. D. LEONARDO, C. J. SHATZ, M. TESSIER-LAVIGNE, C. S. GOODMAN AND A. L. KOLODKIN (1995) Semaphorin III can function as a selective chemorepellent to pat-tern sensory projections in the spinal cord. Neuron 14: 949–959. OPPENHEIM, R. W., D. PREVETTE AND S. HOMMA (1990) Naturally occurring and induced neu-ronal death in the chick embryo in vivo requires protein and RNA synthesis: Evidence for the role of cell death genes. Dev. Biol. 138: 104–113. SERAFINI, T., AND 6 OTHERS (1996) Netrin-1 is required for commissural axon guidance in the developing vertebrate nervous system. Cell 87: 1001–1014. SPERRY, R. W. (1963) Chemoaffinity in the orderly growth of nerve fiber patterns and connections. Proc. Natl. Acad. Sci. USA 50: 703–710. WALTER, J., S. HENKE-FAHLE AND F. BONHOEFFER (1987) Avoidance of posterior tectal mem-branes by temporal retinal axons. Develop-ment 101: 909–913. Books LETOURNEAU, P. C., S. B. KATER AND E. R. MACAGNO (EDS.) (1991) The Nerve Growth Cone. New York: Raven Press. LOUGHLIN, S. E. AND J. H. FALLON (EDS.) (1993) Neurotrophic Factors. San Diego, CA: Acade-mic Press. PURVES, D. (1988) Body and Brain: A Trophic Theory of Neural Connections. Cambridge, MA: Harvard University Press. RAMÓN Y CAJAL, S. (1928) Degeneration and Regeneration of the Nervous System. R. M. May (ed.). New York: Hafner Publishing. Overview The rich diversity of human personalities, abilities, and behavior is undoubt-edly generated by the uniqueness of individual human brains. These fasci-nating neurobiological differences among humans derive from both genetic and environmental influences. The first steps in the construction of the brain’s circuitry—the establishment of distinct brain regions, the generation of neurons, the formation of major axon tracts, the guidance of growing axons to appropriate targets, and the initiation of synaptogenesis—rely largely on the intrinsic cellular and molecular processes described in the pre-vious chapters. Once the basic patterns of brain connections are established, however, patterns of neuronal activity (including those that are elicited by experience) modify the synaptic circuitry of the developing brain. Neuronal activity generated by interactions with the outside world in postnatal life thus provides a mechanism by which the environment can influence brain structure and function. Many of the effects of activity are transduced via sig-naling pathways that modify levels of intracellular Ca2+ and thus influence local cytoskeletal organization as well as gene expression (see Chapter 7). This activity-mediated influence on the developing brain is most consequen-tial during temporal windows called critical periods. As humans and other mammals mature, the brain becomes increasingly refractory to the lessons of experience, and the cellular mechanisms that modify neural connectivity become less effective. Critical Periods The cellular and molecular mechanisms outlined in Chapters 21 and 22 con-struct a nervous system of impressive anatomical complexity. These mecha-nisms and their developmental consequences are sufficient to create some remarkably sophisticated innate or “instinctual” behaviors (see Box A in Chapter 30). For most animals, the behavioral repertoire, including foraging, fighting, and mating strategies, largely relies on patterns of connectivity established by intrinsic developmental mechanisms. However, the nervous systems of complex (“higher”) animals, including humans, clearly adapt to and are influenced by the particular circumstances of an individual’s envi-ronment. These environmental factors are especially influential in early life, during temporal windows called critical periods. In some cases, such as the acquisition of language, instructive influences from the environment are obviously required for the normal development of the behavior (i.e., expo-sure to the individual’s native language). Moreover, some behaviors, such as imprinting in birds (Box A), are expressed only if animals have certain spe-Chapter 23 557 Modification of Brain Circuits as a Result of Experience 558 Chapter Twenty-Three Box A Built-In Behaviors The idea that animals already possess a set of behaviors appropriate for a world not yet experienced has always been dif-ficult to accept. However, the preemi-nence of instinctual responses is obvious to any biologist who looks at what ani-mals actually do. Perhaps the most thor-oughly studied examples occur in young birds. Hatchlings emerge from the egg with an elaborate set of innate behaviors. First, of course, is the complex behavior that allows the chick to escape from the egg. Having emerged, a variety of addi-tional abilities indicate how much early behavior is “preprogrammed” (see Box A in Chapter 30). In a series of seminal observations, Konrad Lorenz, working with geese, showed that goslings follow the first large, moving object that they see and hear during their first day of life. Although this object is normally the mother goose, Lorenz found that goslings can imprint on a wide range of animate and inanimate objects presented during this period, including Lorenz himself (see figure). The window for imprinting in goslings is less than a day: If animals are not exposed to an appro-priate stimulus during this time, they will never form the appropriate parental relationship. Once imprinting occurs, however, it is irreversible, and geese will continue to follow inappropriate objects (male conspecifics, people, or even inani-mate objects). In many mammals, audi-tory and visual systems are poorly devel-oped at birth, and maternal imprinting relies on olfactory and/or gustatory cues. For example, during the first week of life (but not later), infant rats develop a lifelong preference to odors associated with their mother’s nipples. As in birds, this variety of filial imprinting also plays a role in their social development and later sexual preferences. Imprinting is a two-way street, with parents (especially mothers) rapidly forming exclusive bonds with their off-spring. This phenomenon is especially important in animals like sheep that live in large groups or herds and produce off-spring at about the same time of year. Ewes have a critical period 2–4 hours after giving birth during which they imprint on the scent of their own lamb. Following this time, they rebuff approaches by other lambs. The relevance of this work to primates was underscored in the 1950s by Harry Harlow and his colleagues at the Univer-sity of Wisconsin. Harlow isolated mon-keys within a few hours of birth and raised them in the absence of either a natural mother or a human substitute. In the best-known of these experiments, the baby monkeys had one of two maternal surrogates: a “mother” constructed of a wooden frame covered with wire mesh that supported a nursing bottle, or a sim-ilarly shaped object covered with ter-rycloth. When presented with this choice, the baby monkeys preferred the terrycloth mother and spent much of their time clinging to it, even if the feed-ing bottle was with the wire mother. Harlow took this to mean that newborn monkeys have a built-in need for mater-nal care and have at least some innate idea of what a mother should be like. More recently, a number of other endogenous behaviors have been care-fully studied in infant monkeys, includ-ing a naïve monkey’s fear reaction to the presentation of certain objects (e.g., a snake) and the “looming” response (fear elicited by the rapid approach of any for-midable object). Most of these built-in behaviors have analogs in human infants. Taken together, these observations make plain that many complicated behaviors, emotional responses, and other predilections are well established in the nervous system prior to any signif-icant experience, and that the need for certain kinds of early experience for nor-mal development is predetermined. These built-in behaviors and their neural substrates have presumably evolved to give newborns a better chance of surviv-ing in a predictably dangerous world. References HARLOW, H. F. (1959) Love in infant monkeys. Sci. Amer. 2 (September): 68–74. HARLOW, H. F. AND R. R. ZIMMERMAN (1959) Affectional responses in the infant monkey. Science 130: 421–432. LORENZ, K. (1970) Studies in Animal and Human Behaviour. Translated by R. Martin. Cambridge, MA: Harvard University Press. MACFARLANE, A. J. (1975) Olfaction in the development of social preferences in the human neonate. Ciba Found. Symp. 33: 103–117. SCHAAL, B. E., H. MONTAGNER, E. HERTLING, D. BOLZONI, A. MOYSE AND R. QUICHON (1980) Les stimulations olfactives dans les relations entre l’enfant et la mère. Reprod. Nutr. Dev. 20(3b): 843–858. TINBERGEN, N. (1953) Curious Naturalists. Gar-den City, NY: Doubleday. Konrad Lorenz, followed by imprinted geese. (Photograph courtesy of H. Kacher.) cific experiences during a sharply restricted time in early postnatal (or posthatching; see Box A) development. On the other hand, critical periods for sensory and motor skills, or complex behaviors such as human language, are longer and much less well delimited. Despite the fact that critical periods vary widely in both the behaviors affected and their duration, they all share some basic properties. A critical period is defined as the time during which a given behavior is especially sus-ceptible to, and indeed requires, specific environmental influences to develop normally. Once this period ends, the behavior is largely unaffected by subse-quent experience (or even by the complete absence of the relevant experi-ence). Conversely, failure to be exposed to appropriate stimuli during the crit-ical period is difficult or in some cases impossible to remedy subsequently. While psychologists and ethologists (biologists who study the natural behavior of animals) have long recognized that early postnatal or posthatch-ing life is a period of special sensitivity to environmental influences, their studies of critical periods focused on behavior. Work in the last few decades has increasingly examined the underlying changes in the relevant brain cir-cuits and their mechanisms. The Development of Language: Example of a Human Critical Period Many animals communicate by means of sound, and some (humans and songbirds are examples) learn these vocalizations. There are, in fact, provocative similarities in the development of human language and bird-song (Box B). Many other animal vocalizations, like alarm calls in mammals and birds, are innate, and require no experience to be correctly produced. For example, quail raised in isolation or deafened at birth so that they never hear conspecifics nonetheless produce the full repertoire of species-specific vocalizations. In contrast, humans obviously require extensive postnatal experience to produce and decode speech sounds that are the basis of lan-guage. The various forms of early language exposure, including the “baby talk” that parents and other adults often use to communicate with children as they begin to acquire language may actually serve to emphasize impor-tant perceptual distinctions that facilitate proper language production and comprehension. Importantly, this linguistic experience, to be effective, must occur in early life. The requirement for perceiving and practicing language during a critical period is apparent in studies of language acquisition in congenitally deaf chil-dren. Whereas most babies begin producing speechlike sounds at about 7 months (babbling), congenitally deaf infants show obvious deficits in their early vocalizations, and such individuals fail to develop language if not pro-vided with an alternative form of symbolic expression (such as sign language; see Chapter 26). If, however, these deaf children are exposed to sign language at an early age (from approximately six months onward), they begin to “bab-ble” with their hands just as a hearing infant babbles audibly. This suggests that, regardless of the modality, early experience shapes language behavior (Figure 23.1). Children who have acquired speech but subsequently lose their hearing before puberty also suffer a substantial decline in spoken language, presumably because they are unable to hear themselves talk and thus lose the opportunity to refine their speech by auditory feedback during the final stages of the critical period for language. Examples of pathological situations in which normal children were never exposed to a significant amount of language make the same point. In one Modification of Brain Circuits as a Result of Experience 559 Figure 23.1 Manual “babbling” in two deaf infants raised by deaf, signing par-ents compared to manual babble in three hearing infants. Babbling was judged by scoring hand positions and shapes that showed some resemblance to the components of American Sign Language. In deaf infants, meaningful hand shapes increase as a percentage of manual activity between ages 10 and 14 months. Hearing children raised by hearing, speaking parents do not pro-duce similar hand shapes. (After Petito and Marentette, 1991.) Age (months) 0 20 40 60 80 Manual babbling (% manual activity) 9 10 11 12 13 14 15 Deaf infants Hearing infants 560 Chapter Twenty-Three well-documented case, a girl was raised by deranged parents until the age of 13 under conditions of almost total language deprivation. Despite intense subsequent training, she never learned more than a rudimentary level of communication. This and other examples of so-called “feral children” starkly define the importance of early experience for language development as well as other aspects of social communication and personality. In contrast to the devastating effects of deprivation on children, adults retain their abil-ity to speak and comprehend language even if decades pass without expo-sure to human communication (a fictional example would be Robinson Cru-soe). In short, the normal acquisition of human speech is subject to a critical period: The process is sensitive to experience or deprivation during a restricted period of life (before puberty) and is relatively refractory to similar experience or deprivations in adulthood. On a more subtle level, the phonetic structure of the language an indi-vidual hears during early life shapes both the perception and production of speech. Many of the thousands of human languages and dialects use appre-Box B Birdsong Anyone witnessing language develop-ment in a child cannot help but be amazed at how quickly learning takes place. This facility contrasts with the adult acquisition of a new language, which can be a painfully slow process that never produces complete fluency. In fact, many learned behaviors are acquired during a period in early life when experience exerts an especially potent influence on subsequent behav-ior. Particularly well characterized is the sensitive period for learning courtship songs by oscine songbirds such as canaries and finches. In these species, the quality of early sensory exposure is the major determinant of subsequent perceptual and behavioral capabilities. Furthermore, developmental periods for learning these and other behaviors are restricted during postnatal life, suggest-ing that the nervous system changes in some manner to become refractory to further experience. Understanding how critical periods are regulated has many implications, not least the possibility of reactivating this enhanced learning capacity in adults. Nonetheless, such periods are often highly specialized for the acquisition of species-typical behav-iors and are not merely times of general enhanced learning. Avian song learning illustrates the interactions between intrinsic and envi-ronmental factors in this developmental process. Many birds sing to attract mates, but oscine songbirds are special in that their courtship songs are dependent on auditory and vocal experience. The sensitive period for song learning com-prises an initial stage of sensory acquisi-tion, when the juvenile bird listens to and memorizes the song of a nearby adult male tutor (usually of its own species), and a subsequent stage of vocal learning, when the young bird matches its own song to the now-memorized tutor model via auditory feedback. This sensory motor learning stage ends with the onset of sexual maturity, when songs become acoustically stable, or crystal-lized. In all species studied to date, young songbirds are especially impres-sionable during the first two months after hatching and then become refrac-tory to further exposure to tutor song as they age. The impact of this early experi-ence is profound, and the memory it generates can remain intact for months, and perhaps years, before the onset of the vocal practice phase. Even constant exposure to other songs after sensory acquisition during the sensitive period ends does not affect this memory: The songs heard during sensory acquisition, but not later, are those that the bird vocally mimics. Early auditory experi-ence is crucial to the bird’s Darwinian success. In the absence of a tutor, or if raised only in the presence of another species, birds produce highly abnormal “isolate” songs, or songs of the foster species, neither of which succeeds in attracting females of their own kind. Two other features of song learning indicate an intrinsic predisposition for this specialized form of vocal learning. First, juveniles often need to hear the tutor song only 10 or 20 times to then vocally mimic it many months later. Sec-ond, when presented with a variety of songs played from tape recordings that include their own and other species’ songs, juvenile birds preferentially copy the song of their own species, even with no external reinforcement. These obser-vations show that juveniles are not really ciably different speech elements (called phonemes) to produce spoken words (examples are the phonemes ba and pa in English; see Chapter 26). Very young human infants can perceive and discriminate between differ-ences in all human speech sounds, and are not innately biased towards phonemes characteristic of any particular language. However, this universal perceptual capacity does not persist. For example, adult Japanese speakers cannot reliably distinguish between the r and l sounds in English, presum-ably because this phonemic distinction is not made in Japanese and thus not reinforced by experience during the critical period. Nonetheless, 4-month-old Japanese infants can make this discrimination as reliably as 4-month-olds raised in English-speaking households (as indicated by increased suckling frequency or head turning in the presence of a novel stimulus). By 6 months of age, however, infants begin to show preferences for phonemes in their native language over those in foreign languages, and by the end of their first year no longer respond robustly to phonetic ele-ments peculiar to non-native languages. The ability to perceive these Modification of Brain Circuits as a Result of Experience 561 “naïve,” but are innately biased to learn the songs of their own species over those of others. In short, intrinsic factors make the nervous system of oscine birds espe-cially sensitive to songs that are species-typical. It is likely that similar biases influence human language learning. References DOUPE, A. AND P. KUHL (1999) Birdsong and human speech: Common themes and mecha-nisms. Annu. Rev. Neurosci. 22: 567–631. kHz 8 6 4 2 0 0 0.5 1.0 1.5 2.0 2.5 Time (s) i i i a b c d a b c d a b c d motif (B) (C) Stage Time (days) 0 50 100 110 10 20 30 40 60 70 80 90 Sensory acquisition Sensory motor learning Crystallized song (A) (A) A pair of zebra finches (the male is on the right), a species that has been the subject of many song acquisition studies. (B) Spec-trogram of the typical adult song. The male’s song comprises characteristic repeating ele-ments including introductory notes (i), and single or multi-note syllables (a–d). Syllables are grouped into motifs; both syllable struc-ture and order are learned in this species. (C) Chronology of song acquisition in the zebra finch. (Courtesy of Rich Mooney.) 562 Chapter Twenty-Three phonemic contrasts, when attended to, evidently persists for several more years, as evidenced by the fact that children can learn to speak a second language without accent and with fluent grammar until about age 7 or 8. After this age, however, performance gradually declines no matter what the extent of practice or exposure (Figure 23.2). A number of changes in the developing brain could explain these obser-vations. One possibility is that experience acts selectively to preserve the cir-cuits in the brain that perceive phonemes and phonetic distinctions. The absence of exposure to non-native phonemes would then result in a gradual atrophy of the connections representing those sounds, accompanied by a declining ability to distinguish between them. In this formulation, circuits that are used are retained, whereas those that are unused get weaker (and presumably disappear). Alternatively, experience could promote the growth of rudimentary circuitry pertinent to the experienced sounds. Recent com-parisons of patterns of activity in children (age 7–10) and adults performing very specific word processing tasks suggest that different brain regions are activated for the same task in children and adults. While the significance of such differences is not clear—they may reflect anatomical plasticity associ-ated with critical periods, or distinct modes of performing language tasks in children versus adults—there is nevertheless an indication that brain circuits change to accommodate language function during early life. Critical Periods in Visual System Development Although critical periods for language and other distinctively human behav-iors are in some ways the most compelling examples of this phenomenon, it is difficult if not impossible to study the underlying changes in the human brain. A much clearer understanding of how changes in connectivity might contribute to critical periods has come from studies of the developing visual system in experimental animals with highly developed visual abilities—par-ticularly cats and monkeys. In an extraordinarily influential series of experi-ments, David Hubel and Torsten Wiesel found that depriving animals of normal visual experience during a restricted period of early postnatal life irreversibly alters neuronal connections (and functions) in the visual cortex. These observations provided the first evidence that the brain translates the effects of early experience (that is, patterns of neural activity) into more or less permanently altered wiring. To understand these experiments and their implications, it is important to review the organization and development of the mammalian visual system. Recall that information from the two eyes is first integrated in the primary visual (striate) cortex, where most afferents from the lateral geniculate nucleus of the thalamus terminate (see Chapter 11). In some mammals—car-nivores, anthropoid primates, and humans—the afferent terminals form an alternating series of eye-specific domains in cortical layer IV called ocular dominance columns (Figure 23.3). As already described in Chapter 11, ocu-lar dominance columns can be visualized by injecting tracers, such as radioactive proline, into one eye; the tracer is then transported along the visual pathway to specifically label the geniculocortical terminals (i.e., syn-aptic terminals in the visual cortex) corresponding to that eye (Figure 23.3, Box C). In the adult macaque monkey, the domains representing the two eyes are stripes of about equal width (0.5 mm) that occupy roughly equal areas of layer IV of the primary visual cortex. Electrical recordings confirm that the cells within layer IV of macaques respond strongly or exclusively to stimulation of either the left or the right eye, while neurons in layers above Figure 23.2 Learning language. (A) Maps derived from fMRI in adults and children performing visual word pro-cessing tasks. Images are sagittal sec-tions with the front of the brain toward the left. The top row shows the range of active areas (left) and foci of activity based on group averages (right) for chil-dren ages 7–10. The bottom row shows analogous results for adults performing the same task. (B) A critical period for learning language is shown by the decline in language ability (fluency) of non-native speakers of English as a function of their age upon arrival in the United States. The ability to score well on tests of English grammar and vocab-ulary declines from approximately age 7 onward. (A after Schlaggar et. al., 2002; B after Johnson and Newport, 1989.) Age of arrival (years) Relative fluency Native speakers Areas activated Children age 7–10 Adults Focal differences 3−7 8−10 11−16 17−39 (A) (B) and below layer IV integrate inputs from the left and right eyes and respond to visual stimuli presented to either eye. Ocular dominance is thus apparent in two related phenomena: the degree to which individual cortical neurons are driven by stimulation of one eye or the other, and domains (stripes) in cortical layer IV in which the majority of neurons are driven exclusively by one eye or the other. The clarity of these patterns of connectivity and the pre-cision by which experience via the two eyes can be manipulated led to the series of experiments described in the following section that greatly clarified the neurobiological processes underlying critical periods. Effects of Visual Deprivation on Ocular Dominance As described in Chapter 11, if an electrode is passed at a shallow angle through the cortex while the responses of individual neurons to stimulation of one or the other eye are being recorded, detailed assessment of ocular dominance can be made at the level of individual cells (see Figure 11.13). In their original studies, Hubel and Wiesel assigned neurons to one of seven ocular dominance categories, and this classification scheme has become standard in the field. Group 1 cells were defined as being driven only by stimulation of the contralateral eye; group 7 cells were driven entirely by the Modification of Brain Circuits as a Result of Experience 563 1 Radioactive proline injected in eye 2 Transynaptic transport through the LGN terminates in layer IV of the primary visual cortex Cortical layers I−III Optic radiation Lateral geniculate nucleus Optic tract Optic nerve LGN Visual cortex Visual cortex Visual cortex 3 Terminations are visible as bright bands on the autoradiogram C C C I I I C C C I I I Figure 23.3 Ocular dominance columns (which in most anthropoid pri-mates are really stripes or bands) in layer IV of the primary visual cortex of an adult macaque monkey. Diagram indicates the labeling procedure (see also Box C); following transynaptic transport, the pattern of geniculocortical terminations related to that eye is visible as a series of bright stripes in this autoradiogram of a section through layer IV in the plane of the cortex (that is, as if looking down on the cortical surface). The dark areas are the zones occupied by geniculocortical terminals related to the other eye. The pattern of human ocular dominance columns is shown in Figure 12.10. (From LeVay, Wiesel, and Hubel, 1980.) 564 Chapter Twenty-Three Box C Transneuronal Labeling with Radioactive Amino Acids Uptake and incorporation into proteins Labeled amino acids Terminal labeling Anterograde axonal transport Terminal labeling Retina Thalamus Cortex Transneuronal transport Anterograde axonal transport Unlike many brain structures, ocular dominance columns are not easily visible by means of conventional histology. Thus, the striking cortical patterns evi-dent in cats and monkeys were not seen until the early 1970s, when the technique of anterograde tracing using radioactive amino acids was introduced. In this approach, an amino acid commonly found in proteins (usually proline) is radioactively tagged and injected into the area of interest. Neurons in the vicin-ity take up the label from the extracellu-lar space and incorporate it into newly made proteins. Some of these proteins are involved in the maintenance and function of the neuron’s synaptic termi-nals; thus, they are shipped via antero-grade transport from the cell body to nerve terminals, where they accumulate. After a suitable interval, the tissue is fixed, and sections are made, placed on glass slides, and coated with a sensitive photographic emulsion. The radioactive decay of the labeled amino acids in the proteins causes silver grains to form in the emulsion. After several months of exposure, a heavy concentration of silver grains accumulates over the regions that contain synapses originating from the injected site. For example, injections into the eye will heavily label the terminal fields of retinal ganglion cells in the lat-eral geniculate nucleus. Transneuronal transport takes this process a step further. After tagged pro-teins reach the axon terminals, a fraction is actually released into the extracellular space, where the proteins are degraded into amino acids or small peptides that retain their radioactivity. An even smaller fraction of this pool of labeled amino acids is taken up by the postsyn-aptic neurons, incorporated again into proteins, and transported to synaptic ter-minals of the second set of neurons. Because the label passes from the presyn-aptic terminals of one set of cells to the postsynaptic target cells, the process is called transneuronal transport. By such transneuronal labeling, the chain of con-nections originating from a particular structure can be visualized. In the case of the visual system, proline injections into one eye label appropriate layers of the lateral geniculate nucleus (as well as other retinal ganglion cell targets such as the superior colliculus), and subse-quently the terminals in the visual cortex of the geniculate neurons receiving inputs from that eye. Thus, when sec-tions of the visual cortex are viewed with dark-field illumination to make the silver grains glow a brilliant white against the unlabeled background, ocular domi-nance columns in layer IV are easily seen (see Figure 23.3). References COWAN, W. M., D. I. GOTTLIEB, A. HENDRICK-SON, J. L. PRICE AND T. A. WOOLSEY (1972) The autoradiographic demonstration of axonal connections in the central nervous system. Brain Res. 37: 21–51 GRAFSTEIN, B. (1971) Transneuronal transfer of radioactivity in the central nervous sys-tem. Science 172: 177–179. GRAFSTEIN, B. (1975) Principles of anterograde axonal transport in relation to studies of neu-ronal connectivity. In The Use of Axonal Trans-port for Studies in Neuronal Connectivity, W. M. Cowan and M. Cuénod (eds.). Amsterdam: Elsevier, pp. 47–68. Transneuronal transport. A neuron in the retina is shown taking up a radioactive amino acid, incorporating it into proteins, and moving the proteins down the axons and across the extra-cellular space between neurons. This process is repeated in the thalamus, and eventually label accumulates in the thalamocortical terminals in layer IV of the primary visual cortex. ipsilateral eye. Neurons driven equally well by either eye were assigned to group 4. Using this approach, they found that the ocular dominance distrib-ution across the cortical layers in primary visual cortex is roughly Gaussian in a normal adult (cats were used in these experiments). Most cells were acti-vated to some degree by both eyes, and about a quarter were more activated by either the contralateral or ipsilateral eye (Figure 23.4A). Hubel and Wiesel then asked whether this normal distribution of ocular dominance could be altered by visual experience. When they simply closed one eye of a kitten early in life and let the animal mature to adulthood (which takes about 6 months), a remarkable change was observed. Electro-physiological recordings now showed that very few cortical cells could be driven from the deprived eye; that is, the ocular dominance distribution had shifted such that nearly all cells were driven by the eye that had remained Modification of Brain Circuits as a Result of Experience 565 (A) Normal adult 1 Ocular dominance group Period of deprivation (months) Contralateral Ipsilateral 60 40 20 10 10 20 2 3 4 5 6 7 NR 1 2 3 4 5 6 7 1 2 3 4 5 6 7 NR NR 2.5 0 38 0 38 12 0 38 (B) Monocular deprivation in kitten (C) Monocular deprivation in adult Number of cells Birth Exp Birth Exp Birth Exp Contralateral Eyelid sutured closed Ipsilateral Contralateral Ipsilateral Equal Equal Equal 20 Eyelid sutured closed Figure 23.4 Effect of early closure of one eye on the distribution of cortical neurons driven by stimulation of both eyes. (A) Ocular dominance distribution of single unit recordings from a large number of neurons in the primary visual cortex of normal adult cats. Cells in group 1 were activated exclusively by the contralateral eye, cells in group 7 by the ipsilateral eye. Diagrams below these graphs indicate procedure, and bars indicate duration of deprivation (purple). “Exp” = time at which experimental observations were made. (B) Following closure of one eye from 1 week after birth until 2.5 months of age (indicated by the bar underneath the graph), no cells could be acti-vated by the deprived (contralateral) eye. Some cells could not be activated by either eye (NR). Note that the closed eye is opened at the time of the experimental observa-tions, and that the recordings are not restricted to any particular cortical layer. (C) A much longer period of monocular deprivation in an adult cat has little effect on ocular dominance (although overall cortical activity is diminished). In this case, the contralat-eral eye was closed from 12 to 38 months of age. (A after Hubel and Wiesel, 1962; B after Wiesel and Hubel, 1963; C after Hubel and Wiesel, 1970.) 566 Chapter Twenty-Three open (Figure 23.4B). Recordings from the retina and lateral geniculate layers related to the deprived eye indicated that these more peripheral stations in the visual pathway worked quite normally. Thus, the absence of cortical cells that responded to stimulation of the closed eye was not a result of retinal degeneration or a loss of retinal connections to the thalamus. Rather, the deprived eye had been functionally disconnected from the visual cortex. Consequently, such animals are behaviorally blind in the deprived eye. This “cortical blindness,” or amblyopia, is permanent (see next section). Even if the formerly deprived eye is subsequently left open indefinitely, little or no recovery occurs. Remarkably, the same manipulation—closing one eye—had no effect on the responses of cells in the visual cortex of an adult cat (Figure 23.4C). If one eye of a mature cat was closed for a year or more, both the ocular domi-nance distribution measured across all cortical layers and the animal’s visual behavior were indistinguishable from normal when tested through the reopened eye. Thus, sometime between the time a kitten’s eyes open (about a week after birth) and a year of age, visual experience determines how the visual cortex is wired with respect to eye dominance. After this time, depri-vation or manipulation has little or no permanent, detectable effect. In fact, further experiments showed that eye closure is effective only if the depriva-tion occurs during the first 3 months of life. In keeping with the ethological observations described earlier in the chapter, Hubel and Wiesel called this period of susceptibility to visual deprivation the critical period for the devel-opment of ocular dominance. During the height of the critical period (about 4 weeks of age in the cat), as little as 3 to 4 days of eye closure profoundly alters the ocular dominance profile of the striate cortex (Figure 23.5). Similar experiments in the monkey have shown that the same phenomenon occurs in primates, although the critical period is longer (up to about 6 months of age). 20 10 30 1 2 3 4 5 6 7 1 2 3 4 5 6 7 (A) 3-Day monocular deprivation (B) 6-Day monocular deprivation Number of cells Ocular dominance group 1 0 2 1 0 2 Birth Exp Birth Exp Contralateral Ipsilateral Equal Contralateral Ipsilateral Equal Eyelid sutured closed Period of deprivation (months) Figure 23.5 The consequences of a short period of monocular deprivation at the height of the critical period in the cat. Just 3 days of deprivation in this example (A) produced a significant shift of cortical innervation in favor of the non-deprived eye; 6 days of deprivation (B) produced an almost a com-pete shift. Bars below each histogram indicate the period of deprivation, as in Figure 23.4. (After Hubel and Wiesel, 1970.) Thus the key advance arising from Hubel and Wiesel’s early work was to show that visual deprivation causes changes in cortical connectivity that influence the functional response properties of individual neurons (Figure 23.6). The implications of altered cortical circuitry as a result of experience was amply confirmed by subsequent anatomical studies. In monkeys, the alternating stripelike patterns of geniculocortical axon terminals in layer IV representing the two eyes that define ocular dominance columns—is already present at birth (Figure 23.6A). Thus, the visual cortex is clearly not a blank slate on which the effects of experience are later inscribed. Nevertheless, ani-mals deprived of vision in one eye from birth develop abnormal patterns of ocular dominance stripes in the visual cortex (Figure 23.6B). The stripes related to the open eye are substantially wider than normal, whereas the stripes representing the deprived eye are correspondingly diminished. The absence of cortical neurons that respond to the deprived eye in electrophysio-logical studies is not simply a result of the relatively inactive inputs withering away. If this were the case, one would expect to see areas of layer IV devoid of any thalamic innervation. Instead, inputs from the active (open) eye take over some of the territory that formerly belonged to the inactive (closed) eye. Hubel and Wiesel interpreted these results as demonstrating a competi-tive interaction between the two eyes during the critical period (see Chapter 22).In summary, the cortical representation of both eyes starts out equal, and in a normal animal, this balance is retained if both eyes experience roughly comparable levels of visual stimulation. When, however, an imbalance in visual experience is induced by monocular deprivation, the active eye gains a competitive advantage and replaces many of the synaptic inputs from the closed eye, such that few if any neurons can be driven by the deprived eye (see Figure 22.4B). These observations in experimental animals have impor-tant implications for children with birth defects or ocular injuries that cause an imbalance of inputs from the two eyes. Unless the imbalance is corrected during the critical period, the child may ultimately have poor binocular fusion, diminished depth perception, and degraded acuity; in other words, the child’s vision may be permanently impaired (see the next section). The idea that a competitive imbalance underlies the altered distribution of inputs after deprivation has been confirmed by closing both eyes shortly after birth, thereby equally depriving all visual cortical neurons of normal experi-ence during the critical period. The arrangement of ocular dominance Modification of Brain Circuits as a Result of Experience 567 Figure 23.6 Effect of monocular depri-vation on ocular dominance columns in the macaque monkey. (A) In normal monkeys, ocular dominance columns seen as alternating stripes of roughly equal width are already present at birth. (B) The picture is quite different after monocular deprivation. This dark-field autoradiograph shows a reconstruction of several sections through layer IV of the primary visual cortex of a monkey whose right eye was sutured shut from 2 weeks of age to 18 months, when the animal was sacrificed. Two weeks before death, the normal (left) eye was injected with radiolabeled amino acids (see Box C). The columns related to the nonde-prived eye (white stripes) are much wider than normal, whereas as those related to the deprived eye are shrunken. (A from Horton and Hocking, 1999; B from Hubel et al., 1977.) (A) (B) 568 Chapter Twenty-Three recorded some months later is, by either electrophysiological or anatomical criteria, much closer to normal than if just one eye is closed. Although sev-eral peculiarities in the response properties of cortical cells are apparent, roughly normal proportions of neurons representing the two eyes are pre-sent. Because there is no imbalance in the visual activity of the two eyes (both sets of related cortical inputs being deprived), both eyes retain their territory in the cortex. If disuse atrophy of the closed-eye inputs were the main effect of deprivation, then binocular deprivation during the critical period would cause the visual cortex to be largely unresponsive. Experiments using techniques that label individual axons from the lateral geniculate nucleus terminating in layer IV have shown in greater detail what happens to the arborizations of individual neurons after visual deprivation (Figure 23.7). As noted, monocular deprivation causes a loss of cortical terri-tory related to the deprived eye, with a concomitant expansion of the open eye’s territory. At the level of single axons, these changes are reflected in an increased extent and complexity of the arborizations related to the open eye, and a decrease in the size and complexity of the arborizations related to the deprived eye. Individual neuronal arborizations can be substantially altered after as little as one week of deprivation, and perhaps even less. This latter finding highlights the ability of developing thalamic and cortical neurons to rapidly remodel their connections—presumably making and breaking syn-apses—in response to environmental circumstances. Visual Deprivation and Amblyopia in Humans These developmental phenomena in the visual system of experimental ani-mals accord with clinical problems in children who have experienced similar deprivation. The loss of acuity, diminished stereopsis, and problems with fusion that arise from early deficiencies of visual experience is called ambly-opia (from the Greek meaning “dim sight”). In humans, amblyopia is most often the result of strabismus—a misalign-ment of the two eyes due to improper control of the direction of gaze by the eye muscles and referred to colloquially as “lazy eye.” Depending on the muscles affected, the misalignment can produce convergent strabismus, Layer III IV V Layer III IV V Layer III IV V Layer III IV V Open eye 0.5 mm (A) Short-term monocular deprivation (B) Long-term monocular deprivation Open eye Deprived eye Deprived eye Figure 23.7 Terminal arborizations of lateral geniculate nucleus axons in the visual cortex can change rapidly in response to monocular deprivation during the critical period. (A) After only a week of monocular deprivation, axons from the deprived eye have greatly reduced numbers of branches compared with those from the open eye. (B) Deprivation for longer periods does not result in appreciably larger changes. Numbers on the left of each figure indicate cortical layers. (After Antonini and Stryker, 1993.) called esotropia (“cross-eyed”), or divergent strabismus, called exotropia. These alignment errors are surprisingly common, affecting about 5% of chil-dren. Since such misalignments produce double vision, the response of the visual system in some of these individuals is to suppress input from one eye by mechanisms that are not completely understood, but are thought to reflect competitive interactions during the critical period. Functionally, how-ever, the suppressed eye eventually comes to have very low acuity and may render the affected individual effectively blind in that eye. Thus, early surgi-cal correction of ocular misalignment (by adjusting lengths of extraocular muscles) has become an essential treatment for strabmismic children. Another cause of visual deprivation in humans is cataracts. Cataracts, which can be caused by several congenital conditions, render the lens opaque. Dis-eases such as onchocerciasis (“river blindness,” a parasitic infection caused by the nematode Onchocerca volvulus) and trachoma (caused by Chlamydia trachomatis, a small, bacteria-like organism) affect millions of people in unde-veloped tropical regions, often inducing corneal opacity in one or both eyes. A cataract in one eye is functionally equivalent to monocular deprivation in experimental animals; left untreated in children, this defect also results in an irreversible effect on the visual acuity of the deprived eye. If either the cataract or corneal opacity is removed before about 4 months of age, how-ever, the consequences of monocular deprivation are largely avoided. As expected from Hubel and Wiesel’s work, bilateral cataracts, which are simi-lar to binocular deprivation in experimental animals, produce less dramatic deficits even if treatment is delayed. Apparently, unequal competition dur-ing the critical period for normal vision (e.g., that caused by monocular deprivation) is more deleterious than the complete abrogation of visual input that occurs with binocular deprivation. In keeping with the findings in experimental animals, the visual abilities of individuals monocularly deprived of vision as adults (by cataracts or corneal scarring, for example) are much less affected, even after decades, when vision is restored (although there may be important psychological consequences of restoring sight after prolonged binocular blindness, as has been engagingly described by the neurologist Oliver Sacks among others). Nor is there any evidence of anatomical change in this circumstance. For instance, a patient whose eye was surgically removed in adulthood showed normal ocular dominance columns when his brain was examined post-mortem many years later (see Figure 11.10). Thus, one can detect evidence of critical period phenomena for visual cortical development and behavior in the visual system of humans based upon careful examination of patients with opthalmic disease or other lesions. Mechanisms by which Neuronal Activity Affects the Development of Neural Circuits How, then, are differences in patterns of neural activity translated into changes in neural circuitry? In 1949, the psychologist D. O. Hebb hypothe-sized that coordinated activity of a presynaptic terminal and a postsynaptic neuron strengthens the synaptic connection between them. Hebb’s postulate, as it has come to be known, was originally formulated to explain the cellular basis of learning and memory (see Chapter 24), but this general concept has been widely applied to situations that involve long-term modifications in synaptic strength, including those that occur during development of neural circuits. In this context, Hebb’s postulate implies that synaptic terminals strengthened by correlated activity will be retained or sprout new branches, Modification of Brain Circuits as a Result of Experience 569 570 Chapter Twenty-Three whereas those that are persistently weakened by uncorrelated activity will eventually lose their hold on the postsynaptic cell (Figure 23.8; see also Chapter 22). In the visual system, the action potentials of the thalamocortical inputs related to one eye are presumably better correlated with each other than with the activity related to the other eye—at least in layer IV. If sets of correlated inputs tend to dominate the activity of groups of locally con-nected postsynaptic cells, this relationship would exclude uncorrelated inputs. Thus, patches of cortex occupied exclusively by inputs representing one eye or the other could arise. In this scenario, ocular dominance column rearrangements in layer IV are generated by cooperation between inputs carrying similar patterns of activity, and competition between inputs carry-ing dissimilar patterns. Monocular deprivation, which dramatically changes ocular dominance columns, clearly alters both the levels and patterns of neural activity between the two eyes. However, to specifically test the role of correlated activity in driving the competitive postnatal rearrangement of cortical con-nections, it is necessary to create a situation in which activity levels in each eye remain the same but the correlations between the two eyes are altered. This circumstance can be created in experimental animals by cutting one of the extraocular muscles in one eye. As already mentioned, this condition, in which the two eyes can no longer be aligned, is called strabismus. The major consequence of strabismus is that corresponding points on the two retinas are no longer stimulated by objects in the same location in visual space at the same time. As a result, differences in the visually evoked patterns of activity between the two eyes are far greater than normal. Unlike monocular depri-vation, however, the overall amount of activity in each eye remains roughly the same; only the correlation of activity arising from corresponding retinal points is changed. Layer IV cell Left eye Strengthening of synapses that correlate with output pattern Layer IV cell Right eye Figure 23.8 Representation of Hebb’s postulate as it might operate during development of the visual system. The cell represents a postsynaptic neuron in layer IV of the primary visual cortex. Early in development, inputs from the two eyes converge on single postsynap-tic cells. The two sets of presynaptic inputs, however, have different patterns of electrical activity (represented by the short vertical bars). In the example here, the three left eye inputs are better able to activate the postsynaptic cell; as a result, their activity is highly correlated with the postsynaptic cell’s activity. According to Hebb’s postulate, these synapses are therefore strengthened. The inputs from the right eye carry a different pattern of activity that is less well correlated with the majority of the activity elicited in the postsynaptic cell. These synapses gradually weaken and are eventually eliminated (right-hand side of figure), while the correlated inputs form additional synapses. The effects of strabismus in experimental animals provide an illustration of the basic validity of Hebb’s postulate. Recall that misalignment of the two eyes can, depending on the details of the situation, lead to suppression of the input from one and eventual loss of the related cortical connections. In other instances, however, input from the two eyes is retained. The anatomi-cal pattern of ocular dominance columns in layer IV of cats in which input from both eyes remains (but is asynchronous) is sharper than normal, imply-ing that the uncoordinated patterns of activity have actually accentuated the normal separation of cortical inputs from the two eyes. In addition, the ocu-lar asynchrony prevents the binocular convergence that normally occurs in cells above and below layer IV: ocular dominance histograms from such ani-mals show that most cells in all layers are driven exclusively by one eye or the other (Figure 23.9). Evidently, strabismus not only accentuates the com-petition between the two sets of thalamic inputs in layer IV, but also pre-vents binocular interactions in the other layers, which are mediated by local connections originating from cells in layer IV. Even before visual experience exerts these effects, innate mechanisms have ensured that the basic outlines of a functional system are present. These intrinsic mechanisms establish the general circuitry required for vision, but allow modifications to accommodate the individual requirements that occur with changes in head size or eye alignment. Normal visual experience evi-dently validates the initial wiring, preserving, augmenting, or adjusting the normal arrangement. In the case of abnormal experience, such as monocular deprivation, the mechanisms that allow these adjustments result in more dramatic anatomical (and ultimately behavioral) changes, such as those that occur in amblyopia. The eventual decline of this capacity to remodel cortical (and subcortical) connections is presumably the cellular basis of critical peri-ods in a variety of neural systems, including the development of language and other higher brain functions. By the same token, these differences in Modification of Brain Circuits as a Result of Experience 571 40 20 60 160 80 1 2 3 4 5 6 7 1 2 3 4 5 6 7 (A) Normal animals (B) Strabismic animals Number of cells Ocular dominance group Contralateral Ipsilateral Equal Contralateral Ipsilateral Equal Ocular dominance Ocular dominance Figure 23.9 Ocular dominance histograms obtained by electrophysiological recordings in normal adult cats (A) and adults cats in which strabismus was induced during the critical period (B). The data in (A) is the same as that shown in Figure 23.3A. The number of binocular cells is sharply decreased as a consequence of strabismus; most of the cells are dri-ven exclusively by stimulation of one eye or the other. This enhanced segregation of the inputs presumably results from the greater discrepancy in the patterns of activity between the two eyes as a result of surgically interfering with normal conjugate vision. (After Hubel and Wiesel, 1965.) 572 Chapter Twenty-Three plasticity as a function of age presumably provide a neurobiological basis for the general observation that human behavior is much more susceptible to normal or pathological modification early in development than later on a concept with obvious educational, psychiatric, and social implications. Although many cellular and molecular mechanisms have been proposed to explain these effects (see Chapter 24), the specific mechanisms responsible for creating and eventually terminating critical periods remain largely unknown. Cellular and Molecular Correlates of Activity-Dependent Plasticity during Critical Periods A further question for understanding how experience changes neural cir-cuits during critical periods is how patterns of activity are transduced to modify connections and to make these changes permanent. Clearly, the steps that initiate these processes must rely on signals generated by the synaptic activity associated with sensory experience or motor performance—the basic neural processes by which experience is represented. Neurotransmitters and a number of other signaling molecules, including neurotrophic factors, are obvious candidates for initiating changes that occur with correlated or repeated activity. Indeed, mice that lack genes for a number of neurotrans-mitters or receptors exhibit changes in experience-dependent visual cortical plasticity. These signals—neurotransmitters and other secreted molecules like neurotrophins—are all thought to ultimately influence levels of intracel-lular Ca2+, particularly in postsynaptic cells (Figure 23.10). Increased Ca2+ concentration in the affected cells can activate a number of kinases, includ-ing Ca2+ /calmodulin kinase (CaMK) II, leading to phosphorylation-depen-dent modifications of the cytoskeleton and changes in dendritic and axonal branching. In addition, changes in Ca2+ can activate other kinases found in the nucleus, including CaMK IV (see Chapter 7). The kinases in the nucleus in turn can activate transcription factors like CREB (cyclic nucleotide response element binding transcription factor) via phosphorylation. When activation occurs, these DNA binding proteins can then influence gene expression, and thus alter the transcriptional state of the neuron to reflect experience-driven functional changes. Such changes may include—but are unlikely to be limited to—transcription of neurotrophin genes like BDNF. Whether this sequence is correct or complete remains uncertain, but it pro-vides a plausible scenario for the molecular and cellular events underlying activity-dependent plasticity. Evidence for Critical Periods in Other Sensory Systems Although the neural basis of critical periods has been most thoroughly stud-ied in the mammalian visual system, similar phenomena exist in a number of sensory systems, including the auditory, somatic sensory and olfactory systems. In the auditory system, experiments on the role of auditory experi-ence and neural activity in owls (who use auditory information to localize prey) indicate that neural circuits for auditory localization are similarly shaped by experience. Thus, deafening an owl or altering neural activity during early postnatal development compromises the bird’s ability to local-ize sounds and can alter the neural circuits that mediate this capacity. The development of song in many species of birds provides another auditory example, as described in Chapter 12. In the somatic sensory system, cortical maps can be changed by experience during a critical period of postnatal development. In mice or rats, for instance, the anatomical patterns of “whisker barrels” in the somatic sensory cortex (see Chapter 8) can be altered by abnormal sensory experience during a narrow window in early postnatal life. And, as outlined in Chapter 14, behavioral studies in the olfac-tory system indicate that exposure to maternal odors for a limited period can alter the ability to respond to such odorants, a change that can persist throughout life. Clearly, the phenomenon of critical periods is general in development of sensory perceptual abilities and motor skills. Summary An individual animal’s history of interaction with the environment—its “experience”—helps to shape neural circuitry and thus determines subse-quent behavior. In some cases, experience functions primarily as a switch to activate innate behaviors. More often, however, experience during a specific time in early life (referred to as a “critical period”) helps shape the adult behavioral repertoire. Critical periods influence behaviors as diverse as maternal bonding and the acquisition of language. Although it is possible to define the behavioral consequences of critical periods for these complex Modification of Brain Circuits as a Result of Experience 573 DNA CREB VGCC BDNF Pi Pi Ca2+ Ca2+ /calmodulin kinase IV Ca2+ /calmodulin kinase IV Endoplasmic reticulum Ligand-gated ion channel NMDA–R AMPA–R Cytoskeleton Ca2+ Ca2+ Ca2+ (C) (B) (A) Figure 23.10 Transduction of electrical activity into cellular change via Ca2+ signaling. (A) A target neuron, showing two possible sites of action—the cell soma and the distal dendrites—for activity-dependent increases in Ca2+ sig-naling. (B) Correlated or sustained activ-ity leads to increased Ca2+ conductances and increased intracellular Ca2+ concen-tration, which results in activation of Ca2+/calmodulin kinase IV (CaMKIV) in the nucleus. CaMKIV then activates Ca2+-regulated transcription factors like CREB. The target genes for activated CREB may include neurotrophic signals like BDNF, which when secreted by a cell may help stabilize or promote the growth of active synapses on that cell. (C) Local increases in Ca2+ signaling in distal dendrites due to correlated or sus-tained activity may lead to local increases in Ca2+ concentration which, via kinases like CaMKIV, modify cytoskeletal elements (actin- or tubulin-based structures). Changes in these ele-ments lead to local changes in dendritic structure. In addition, increased local Ca2+ concentration may influence local translation of transcripts in the endo-plasmic reticulum (ER), including tran-scripts for neurotransmitter receptors and other modulators of postsynaptic responses. Increased Ca2+ may also influence the trafficking of these pro-teins, their interaction with local scaf-folds for cytoplasmic proteins, and their insertion into the postsynaptic mem-brane. (After Wong and Ghosh, 2002.) 574 Chapter Twenty-Three functions, their biological basis has been more difficult to understand. The most accessible and thoroughly studied example of a critical period is the one pertinent to the establishment of normal vision. These studies show that experience is translated into patterns of neuronal activity that influence the function and connectivity of the relevant neurons. In the visual system, and other systems as well, competition between inputs with different patterns of activity is an important determinant of adult connectivity. Correlated pat-terns of activity in afferent axons tend to stabilize connections and con-versely a lack of correlated activity can weaken or eliminate connections. When normal patterns of activity are disturbed during a critical period in early life (experimentally in animals or by pathology in humans), the con-nectivity in the visual cortex is altered, as is visual function. If not reversed before the end of the critical period, these structural and functional alter-ations of brain circuitry are difficult or impossible to change. In normal development, the influence of activity on neural connectivity presumably enables the maturing brain to store the vast amounts of information that reflect the specific experience of the individual. Additional Reading Reviews KATZ, L. C. AND C. J. SHATZ (1996) Synaptic activity and the construction of cortical cir-cuits. Science 274: 1133–1138. KNUDSEN, E. I. (1995) Mechanisms of experi-ence-dependent plasticity in the auditory localization pathway of the barn owl. J. Comp. Physiol. 184(A): 305–321. SHERMAN, S. M. AND P. D. SPEAR (1982) Organi-zation of visual pathways in normal and visu-ally deprived cats. Physiol. Rev. 62: 738–855. WIESEL, T. N. (1982) Postnatal development of the visual cortex and the influence of environ-ment. Nature 299: 583–591. WONG, W. O. AND A. GHOSH (2002) Activity-dependent regulation of dendritic growth and patterning. Nat. Rev. Neurosci. 10: 803–812. Important Original Papers ANTONINI, A. AND M. P. STRYKER (1993) Rapid remodeling of axonal arbors in the visual cor-tex. Science 260: 1819–1821. CABELLI, R. J., A. HOHN AND C. J. SHATZ (1995) Inhibition of ocular dominance column for-mation by infusion of NT-4/5 or BDNF. Sci-ence 267: 1662–1666. HORTON, J. C. AND D. R. HOCKING (1999) An adult-like pattern of ocular dominance columns in striate cortex of newborn monkeys prior to visual experience. J. Neurosci. 16: 1791–1807. HUBEL, D. H. AND T. N. WIESEL (1965) Binocu-lar interaction in striate cortex of kittens reared with artificial squint. J. Neurophysiol. 28: 1041–1059. HUBEL, D. H. AND T. N. WIESEL (1970) The period of susceptibility to the physiological effects of unilateral eye closure in kittens. J. Physiol. 206: 419–436. HUBEL, D. H., T. N. WIESEL AND S. LEVAY (1977) Plasticity of ocular dominance columns in monkey striate cortex. Phil. Trans. R. Soc. Lond. B. 278: 377–409. KUHL, P. K., K. A. WILLIAMS, F. LACERDA, K. N. STEVENS AND B. LINDBLOM (1992) Linguistic experience alters phonetic perception in infants by 6 months of age. Science 255: 606–608. LEVAY, S., T. N. WIESEL AND D. H. HUBEL (1980) The development of ocular dominance columns in normal and visually deprived monkeys. J. Comp. Neurol. 191: 1–51. RAKIC, P. (1977) Prenatal development of the visual system in the rhesus monkey. Phil. Trans. R. Soc. Lond. B. 278: 245–260. STRYKER, M. P. AND W. HARRIS (1986) Binocular impulse blockade prevents the formation of ocular dominance columns in cat visual cor-tex. J. Neurosci. 6: 2117–2133. WIESEL, T. N. AND D. H. HUBEL (1965) Compar-ison of the effects of unilateral and bilateral eye closure on cortical unit responses in kit-tens. J. Neurophysiol. 28: 1029–1040. Books CURTISS, S. (1977) Genie: A Psycholinguistic Study of a Modern-Day “Wild Child.” New York: Academic Press. HUBEL, D. H. (1988) Eye, Brain, and Vision. Sci-entific American Library Series. New York: W. H. Freeman. PURVES, D. (1994) Neural Activity and the Growth of the Brain. Cambridge: Cambridge University Press. Overview The capacity of the nervous system to change—generally referred to as neural plasticity—is obvious during the development of neural circuits. However, the adult brain must also possess substantial plasticity in order to learn new skills, establish new memories, and respond to injury throughout life. Although the mechanisms responsible for ongoing changes in the adult brain are not completely understood, altered neural function in maturity appears to rely primarily on carefully regulated changes in the strength of existing synapses. Experiments carried out in a variety of animals, ranging from sea slugs to primates, have shown that synaptic strength can be altered over periods that range from milliseconds to months. The molecular mecha-nisms underlying these changes are post-translational modifications of pro-teins and, in the case of longer-lasting effects, changes in gene expression. To some extent, changes in synaptic circuitry can also occur by localized forma-tion of new axon terminals and dendritic processes. More extensive changes occur when the adult nervous system is damaged by trauma or disease, although regeneration of connections in the brain and spinal cord is sharply limited. Modest optimism regarding this unfortunate clinical situation is warranted by the observation that new neurons can be generated through-out life in a limited number of brain regions, suggesting that new cells can be integrated into existing circuits. Synaptic Plasticity Underlies Behavioral Modification in Invertebrates An obvious obstacle to exploring change in the brains of humans and other mammals is the enormous number of neurons and the complexity of synap-tic connections. As a consequence, it is difficult to unambiguously attribute a behavioral modification to changes in the properties of specific neurons or synapses. One way to circumvent this dilemma is to examine plasticity in far simpler nervous systems. The assumption in this strategy is that plasticity is so fundamental that its essential cellular and molecular underpinnings are likely to be conserved in the nervous systems of very different organisms. One of the most successful examples of this approach has been that of Eric Kandel and his colleagues at Columbia University using the marine mollusk Aplysia californica (Figure 24.1A). This sea slug has only a few tens of thousands of neurons, many of which are quite large (up to 1 mm in diameter) and in stereotyped locations within the ganglia that make up the animal’s nervous system (Figure 24.1B). These attributes make it practical to monitor the electrical and chemical signaling of specific, identifiable nerve Chapter 24 575 Plasticity of Mature Synapses and Circuits 576 Chapter Twenty-Four Gill Siphon Tail Head Mantle Right connective Left connective (B) (A) Dorsal surface Siphon nerve Genital-pericardial nerve Branchial nerve Ganglion cell bodies Magnitude of gill contraction (C) (D) (E) 4 8 12 0 4 8 12 0 4 8 12 0 4 8 12 0 Time (s) Time (s) Time (s) Time (s) Touch siphon Touch siphon Touch siphon Trial 1 Trial 6 Trial 13 Shock tail and touch siphon Trial 14 50 0 200 100 150 Gill withdrawal (% first response) Time (hrs) –2 0 4 2 Time (days) 0 4 6 8 2 With one tail shock No shock Single tail shock 1000 500 100 Gill withdrawal (% first response) 4 single tail shocks 4 trains of tail shocks 4 trains/day, for 4 days No shocks Tail shocks Figure 24.1 Short-term sensitization of the Aplysia gill withdrawal reflex. (A) Diagram of the animal. (B) The abdomi-nal ganglion of Aplysia. The cell bodies of many of the neurons involved in gill withdrawal can be recognized by their size, shape, and position within this ganglion. (C) Changes in the gill with-drawal behavior due to habituation and sensitization. The first time that the siphon is touched, the gill contracts vig-orously. Repeated touches elicit smaller gill contractions due to habituation. Subsequently pairing a siphon touch with an electrical shock to the tail restores a large and rapid gill contrac-tion, due to short-term sensitization. (D) A short-term sensitization of the gill withdrawal response is observed fol-lowing the pairing of a single tail shock with a siphon touch. (E) Repeated applications of tail shocks causes pro-longed sensitization of the gill with-drawal response. (After Squire and Kandel, 1999.) cells, and to define the synaptic circuits involved in mediating the limited behavioral repertoire of Aplysia. Aplysia exhibit several elementary forms of behavioral plasticity. One form is habituation, a process that causes the animal to become less responsive to repeated occurrences of a stimulus. Habituation is found in many other species, including humans. For example, when dressing we initially experi-ence tactile sensations due to clothes stimulating our skin, but habituation quickly causes these sensations to fade. Similarly, a light touch to the siphon of an Aplysia results in withdrawal of the animal’s gill, but habituation causes the gill withdrawal to become weaker during repeated stimulation of the siphon (Figure 24.1C). The gill withdrawal response of Aplysia exhibits another form of plasticity called sensitization. Sensitization is a process that allows an animal to generalize an aversive response elicited by a noxious stimulus to a variety of other, non-noxious stimuli. In Aplysia that have habituated to siphon touching, sensitization of gill withdrawal is elicited by pairing a strong electrical stimulus to the animal’s tail with another light touch of the siphon. This pairing causes the siphon stimulus to again elicit a strong withdrawal of the gill (Figure 24.1C, right) because the noxious stim-ulus to the tail sensitizes the gill withdrawal reflex to light touch. Even after a single stimulus to the tail, the gill withdrawal reflex remains enhanced for at least an hour (Figure 24.1D). With repeated pairing of tail and siphon stimuli, this behavior can be altered for days or weeks (Figure 24.1E), demonstrating a simple form of long-term memory. The small number of neurons in the Aplysia nervous system makes it pos-sible to define the neural circuits involved in gill withdrawal and to monitor the activity of individual neurons in these circuits. Although hundreds of neurons are ultimately involved in producing this simple behavior, the activ-ities of only a few different types of neurons can account for gill withdrawal and its plasticity during habituation and sensitization. These critical neurons include mechanosensory neurons that innervate the siphon, motor neurons that innervate muscles in the gill, and interneurons that receive inputs from a variety of sensory neurons (Figure 24.2A). Touching the siphon activates the mechanosensory neurons, which form excitatory synapses that release glutamate onto both the interneurons and the motor neurons; thus, touching the siphon increases the probability that both these postsynaptic targets will produce action potentials. The interneurons form excitatory synapses on motor neurons, further increasing the likelihood of the motor neurons firing action potentials in response to mechanical stimulation of the siphon. When the motor neurons are activated by the summed synaptic excitation of the sensory neurons and interneurons, they release acetylcholine that excites the muscle cells of the gill, producing gill withdrawal. Synaptic activity in this circuit is modified during habituation and sensi-tization. During habituation, transmission at the glutamatergic synapse between the sensory and motor neurons is decreased (Figure 24.2B, left). This weakening of synaptic transmission, termed synaptic depression, is thought to be responsible for the decreasing ability of siphon stimuli to evoke gill contractions during habituation. Synaptic depression has subse-quently been shown to be due to a reduction in the number of synaptic vesi-cles available for release, with a concomitant reduction in the amount of glu-tamate released from the presynaptic sensory neuron. In contrast, sensitization modifies the function of this circuit by recruiting additional neurons. The tail shock that evokes sensitization activates sensory neurons that innervate the tail. These sensory neurons in turn excite modulatory Plasticity of Mature Synapses and Circuits 577 578 Chapter Twenty-Four Figure 24.2 Synaptic mechanisms underlying short-term sensitization. (A) Neural circuitry involved in sensitiza-tion. Normally, touching the siphon skin activates sensory neurons that excite interneurons and gill motor neu-rons, yielding a contraction of the gill muscle. A shock to the animal’s tail stimulates modulatory interneurons that alter synaptic transmission between the siphon sensory neurons and gill motor neurons, resulting in sensitiza-tion. (B) Changes in synaptic efficacy at the sensory-motor synapse during short-term sensitization. Prior to sensiti-zation, activating the siphon sensory neurons causes an EPSP to occur in the gill motor neurons. Activation of the serotonergic modulatory interneurons enhances release of transmitter from the sensory neurons onto the motor neu-rons, increasing the EPSP in the motor neurons and causing the motor neurons to more strongly excite the gill muscle. (C) Time course of the serotonin-induced facilitation of transmission at the sensory motor synapse. (After Squire and Kandel, 1999.) interneurons that release serotonin on to the presynaptic terminals of the sensory neurons of the siphon (see Figure 24.2A). Serotonin enhances trans-mitter release from the siphon sensory neuron terminals, leading to increased synaptic excitation of the motor neurons (Figure 24.2B). This mod-ulation of the sensory neuron-motor neuron synapse lasts approximately an hour (Figure 24.2C), which is similar to the duration of the short-term sensi-tization of gill withdrawal produced by applying a single stimulus to the tail (Figure 24.1D). Thus, the short-term sensitization apparently is due to recruitment of additional synaptic elements that modulate synaptic trans-mission in the gill withdrawal circuit. (B) (C) −50 −50 −40 −25 0 0 min 20 min 50 min 50 min 20 s 100 200 300 100 200 300 100 200 300 100 200 300 0 Stimulate tail nerve Time (ms) 0 Time (ms) 0 Time (ms) 0 Time (ms) Sensory neuron action potential (mV) Motor neuron EPSP (mV) (A) Interneuron Motor neuron Gill Modulatory interneuron Tail Siphon skin Sensory neuron Sensory neuron Stimulus shock + + 100 0 300 500 Motor neuron EPSP (% control) Time (mins) 0 50 40 30 20 10 The mechanism thought to be responsible for the enhancement of gluta-matergic transmission during short-term sensitization is shown in Figure 24.3A. Serotonin released by the facilitatory interneurons binds to G-protein-coupled receptors on the presynaptic terminals of the siphon sensory neu-rons (step 1), which stimulates production of the second messenger, cAMP (step 2). cAMP binds to the regulatory subunits of protein kinase A (PKA; step 3), liberating catalytic subunits of PKA that are then able to phosphory-late several proteins, probably including K+ channels (step 4). The net effect of the action of PKA is to reduce the probability that the K+ channels open during a presynaptic action potential. This effect prolongs the presynaptic action potential, thereby opening more presynaptic Ca2+ channels (step 5). Finally, the enhanced influx of Ca2+ into the presynaptic terminals increases the amount of transmitter released onto motor neurons during a sensory neuron action potential (step 6). In summary, short-term sensitization of gill withdrawal is mediated by a signal transduction cascade that involves neu-rotransmitters, second messengers, one or more protein kinases, and ion channels. This cascade ultimately enhances synaptic transmission between the sensory and motor neurons within the gill withdrawal circuit. The same serotonin-induced enhancement of glutamate release that medi-ates short-term sensitization is also thought to underlie long-term sensitiza-tion. However, during long-term sensitization this circuitry is affected for up to several weeks. The prolonged duration of this form of plasticity is evi-dently due to changes in gene expression and thus protein synthesis (Figure 24.3B). With repeated training (that is, additional tail shocks), the serotonin-activated PKA involved in short-term sensitization now phosphorylates— and thereby activates—the transcriptional activator CREB (see Chapter 7). CREB binding to the cAMP responsive elements (CREs) in regulatory regions of nuclear DNA increases the rate of transcription of downstream genes. Although the changes in genes and gene products that follow CRE activation have been difficult to sort out, two consequences of gene activa-tion have been identified. First, CREB stimulates the synthesis of an enzyme, ubiquitin hydroxylase, that stimulates degradation of the regulatory subunit of PKA. This causes a persistent increase in the amount of free catalytic sub-unit, meaning that some PKA is persistently active and no longer requires serotonin to be activated. CREB also stimulates another transcriptional acti-vator protein, called C/EBP. C/EBP stimulates transcription of other, unknown genes that cause addition of synaptic terminals, yielding a long-term increase in the number of synapses between the sensory and the motor neurons. Such structural increases are not seen following short-term sensiti-zation and may represent the ultimate cause of the long-lasting change in overall strength of the relevant circuit connections that produce a long-last-ing enhancement in the gill withdrawal response. These studies of Aplysia, and related work on other invertebrates such as the fruit fly (Box A), have led to several generalizations about the neural mechanisms underlying plasticity in the adult nervous system that presum-ably extend to mammals and other vertebrates. First, behavioral plasticity can clearly arise from plastic changes in the efficacy of synaptic transmis-sion. Second, these changes in synaptic function can be either short-term effects that rely on post-translational modification of existing synaptic pro-teins, or long-term changes that require changes in gene expression, new protein synthesis, and perhaps even growth of new synapses (or the elimi-nation of existing ones). The following sections explore the evidence for these generalizations in neuronal circuits and synapses of the mature mam-malian nervous system. Plasticity of Mature Synapses and Circuits 579 580 Chapter Twenty-Four (A) Ca2+ K+ Ca2+ channel K+ channel ATP cAMP Facilitatory interneuron Sensory neuron Motor neuron Serotonin receptor G-protein Adenylyl cyclase Glutamate receptor 1 2 3 4 5 6 Protein kinase A Regulatory subunits Catalytic subunits (B) Facilitatory interneuron Sensory neuron Motor neuron Ubiquitin hydrolase DNA C/EBP CREB Nucleus Pi Pi cAMP Unidentified proteins responsible for synaptic growth Persistent PKA Figure 24.3 Mechanism of presynaptic enhancement underlying behavioral sensi-tization. (A) Short-term sensitization is due to an acute, PKA-dependent enhance-ment of glutamate release from the presynaptic terminals of sensory neurons. See text for explanation. (B) Long-term sensitization is due to changes in gene expres-sion, causing expression of proteins that change PKA activity and lead to changes in synapse growth. (After Squire and Kandel, 1999.) Plasticity of Mature Synapses and Circuits 581 Box A Genetics of Learning and Memory in the Fruit Fly As part of a renaissance in the genetic analysis of simple organisms in the mid-1970s, several investigators recognized that the genetic basis of learning and memory might be effectively studied in the fruit fly, Drosophila melanogaster. In the intervening quarter-century, this approach has yielded some fundamental insights. Although learning and memory has certainly been one of the more diffi-cult problems tackled by Drosophila geneticists, their efforts have been sur-prisingly successful. A number of genetic mutations have been discovered that to alter learning and memory, and the iden-tification of these genes has provided a valuable framework for studying the cel-lular mechanisms of these processes. The initial problem in this work was to develop behavioral tests that could identify abnormal learning and/or mem-ory defects in large populations of flies. This challenge was met by Seymour Ben-zer and his colleagues Chip Quinn and Bill Harris at the California Institute of Technology, who developed the olfactory and visual learning tests that have become the basis for most subsequent analyses of learning and memory in the fruit fly (see figure). Behavioral para-digms pairing odors or light with an aversive stimulus allowed Benzer and his colleagues to assess associative learn-ing in flies. The design of an ingenious testing apparatus controlled for non-learning-related sensory cues that had previously complicated such behavioral testing. Moreover, the apparatus allowed large numbers of flies to be screened rel-atively easily, expediting the analysis of mutagenized populations. These studies led to the identification of an ever-increasing number of single gene mutations that disrupt learning and/or memory in flies. The behavioral and molecular studies of the mutants (given whimsical but descriptive names like dunce, rutabaga, and amnesiac) sug-gested that a central pathway for learn-ing and memory in the fly is signal transduction mediated by the cyclic nucleotide cAMP. Thus, the gene prod-ucts of the dunce, rutabaga, and amnesiac loci are, respectively, a phosphodi-esterase (which degrades cAMP), an adenylyl cyclase (which converts ATP to cAMP), and a peptide transmitter that stimulates adenylyl cyclase. This conclu-sion about the importance of cAMP has been confirmed by the finding that genetic manipulation of the CREB tran-scription factor also interferes with learn-ing and memory in normal flies. These observations in Drosophila accord with conclusions reached in stud-ies of Aplysia and mammals (see text) and have emphasized the importance of cAMP-mediated learning and memory in a wide range of additional species. References QUINN, W. G., W. A. HARRIS AND S. BENZER (1974) Conditioned behavior in Drosophila melanogaster. Proc. Natl. Acad. Sci. USA 71: 708–712. TULLY, T. (1996) Discovery of genes involved with learning and memory: An experimental synthesis of Hirshian and Benzerian perspec-tives. Proc. Natl. Acad. Sci. USA 93: 13460–13467. WADDELL, S. AND W. G. QUINN (2001) Flies, genes, and learning. Annu. Rev. Neurosci. 24: 1283–1309. WEINER, J. (1999) Time, Love, Memory: A Great Biologist and His Quest for the Origins of Behav-ior. New York: Knopf. (B) (A) Wild-type dunce rutabaga dunce, rutabaga Single-gene mutants Double mutant 0 20 40 60 80 100 Performance index (A) The fruit fly, Drosophila melanogaster. (B) Performance of nor-mal and mutant flies on an olfactory learning task. The perfor-mance of both dunce and rutabaga mutants on this task is dimin-ished by at least 50%. Flies that are mutant at both the dunce and rutabaga locus show a larger decrease in performance, suggesting that the two genes disrupt different but related aspects of learn-ing. (B after Tully, 1996.) 582 Chapter Twenty-Four Short-Term Synaptic Plasticity in the Mammalian Nervous System Evidence for synaptic plasticity in the mammalian nervous system is wide-spread; indeed, it is probably safe to conclude that all chemical synapses are capable of plastic change. Synaptic plasticity mechanisms at mammalian synapses, like their invertebrate counterparts, occur on time scales ranging from milliseconds to days, weeks, or longer. The short-term forms of plas-ticity—those lasting for minutes or less—have been studied in greatest detail at peripheral neuromuscular synapses, the same synapses that proved so valuable for understanding basic mechanisms of synaptic transmission (Chapter 5). Repeated activation of the neuromuscular junction triggers several changes that vary in both direction and duration (Figure 24.4). Synaptic facilitation, which is a transient increase in synaptic strength, occurs when two or more action potentials invade the presynaptic terminal in close suc-cession. Facilitation results in more neurotransmitter being released by each succeeding action potential, causing the postsynaptic end plate potential (EPP) to increase progressively. Synaptic facilitation is most likely the result of prolonged elevation of presynaptic calcium levels following synaptic activity. Although the entry of Ca2+ into the presynaptic terminal occurs within a millisecond or two after an action potential invades (see Chapter 5), the mechanisms that return Ca2+ to resting levels are much slower. Thus, when action potentials arrive close together in time, calcium builds up within the terminal and allows more neurotransmitter to be released by a subsequent presynaptic action potential. A high-frequency burst of presyn-aptic action potentials (referred to as tetanus) can yield an even more pro-longed elevation of presynaptic calcium levels, causing another form of syn-aptic plasticity called post-tetanic potentiation (PTP). PTP is delayed in its onset and typically enhances transmitter release for up to a few minutes after the train of stimuli ends. The difference in duration distinguishes PTP from synaptic facilitation. PTP also is thought to arise from calcium-depen-dent processes, perhaps including activation of presynaptic protein kinases, that enhance the ability of incoming calcium ions to trigger fusion of synap-tic vesicles with the plasma membrane. Synaptic transmission also can be diminished following repeated synaptic activity. Such synaptic depression occurs when many presynaptic action potentials occur in rapid succession and depends on the amount of neuro-transmitter that has been released (see Figure 24.4). Depression arises because of the progressive depletion of the pool of synaptic vesicles available for fusion in this circumstance. During synaptic depression, the strength of the synapse declines until this pool can be replenished via the mechanisms involved in recycling of synaptic vesicles (see Chapter 5). During repeated synaptic activity, these various types of plasticity can interact in complex ways. For example, at the neuromuscular synapse, repeated activity first facilitates synaptic transmission, and depletion of syn-aptic vesicles then allows depression to dominate and weaken the synapse (see Figure 24.4). After the stimulus train ends, the invasion of the terminal by another action potential causes enhanced transmitter release (i.e., post-tetanic potentiation). These forms of short-term plasticity are observed at virtually all chemical synapses and continually modify synaptic strength. Thus, the efficacy of chemical synaptic transmission changes dynamically as a consequence of the recent history of synaptic activity. Long-Term Synaptic Plasticity in the Mammalian Nervous System Facilitation, depression, and post-tetanic potentiation can briefly modify synaptic transmission. While these mechanisms are probably responsible for many short-lived changes in brain circuitry, they cannot provide the basis for memories or other manifestations of behavioral plasticity that persist for weeks, months, or years. As might be expected, many synapses in the mam-malian central nervous system exhibit long-lasting forms of synaptic plastic-ity that are plausible substrates for more permanent changes in behavior. Because of their duration, these forms of synaptic plasticity are widely believed to be cellular correlates of learning and memory. Thus, a great deal of effort has gone into understanding how they are generated. Some patterns of synaptic activity in the CNS produce a long-lasting increase in synaptic strength known as long-term potentiation (LTP), whereas other patterns of activity produce a long-lasting decrease in synap-tic strength, known as long-term depression (LTD). LTP and LTD are broad terms that describe only the direction of change in synaptic efficacy; in fact, different cellular and molecular mechanisms can be involved in producing LTP or LTD at different synapses. In general, these different forms of synap-tic plasticity are produced by different histories of activity, and are mediated by different complements of intracellular signal transduction pathways in the nerve cells involved. Plasticity of Mature Synapses and Circuits 583 Time (ms) 0 −100 −80 10 Membrane potential (mV) 20 40 50 60 70 80 90 100 110 30 Record Facilitation Depression Stimulus ceases Post-tetanic potentiation (minutes later) −90 Stimulate axon Record postsynaptic EPPs Stimulate Record Figure 24.4 Short-term plasticity at the neuromuscular synapse. Electrical recording of EPPs elicited in a muscle fiber by a train of electrical stimuli applied to the presyn-aptic motor nerve. Facilitation of the EPP occurs at the beginning of the stimulus train and is followed by depression of the EPP. After the train of stimuli ends, EPPs are larger than before the train. This phenomenon is called post-tetanic potentiation. (After Katz, 1966.) 584 Chapter Twenty-Four Figure 24.5 Diagram of a section through the rodent hippocampus show-ing the major regions, excitatory path-ways, and synaptic connections. Long-term potentiation has been observed at each of the three synaptic connections shown here. Long-Term Potentiation of Hippocampal Synapses LTP has been most thoroughly studied at excitatory synapses in the mam-malian hippocampus, an area of the brain that is especially important in the formation and/or retrieval of some forms of memory (see Chapter 30). In humans, functional imaging shows that the human hippocampus is acti-vated during certain kinds of memory tasks, and that damage to the hip-pocampus results in an inability to form certain types of new memories. In rodents, hippocampal neurons fire action potentials only when an animal is in certain locations. Such “place cells” appear to encode spatial memories, an interpretation supported by the fact that hippocampal damage prevents rats from developing proficiency in spatial learning tasks (see Figure 30.7). Although many other brain areas are involved in the complex process of memory formation, storage, and retrieval, these observations have led many investigators to study LTP of hippocampal synapses. Work on LTP began in the late 1960s, when Terje Lomo and Timothy Bliss, working in the laboratory of Per Andersen in Oslo, Norway, discovered that a few seconds of high-frequency electrical stimulation can enhance synaptic transmission in the rabbit hippocampus for days or even weeks. More recently, however, progress in understanding the mechanism of LTP has relied heavily on in vitro studies of slices of living hippocampus. The arrangement of neurons allows the hippocampus to be sectioned such that most of the relevant circuitry is left intact. In such preparations, the cell bod-ies of the pyramidal neurons lie in a single densely packed layer that is read-ily apparent (Figure 24.5). This layer is divided into several distinct regions, the major ones being CA1 and CA3. “CA” refers to cornu Ammon, the Latin for Ammon’s horn—the ram’s horn that resembles the shape of the hip-Hippocampus Mossy fibers Schaffer collaterals Perforant path (from entorhinal cortex) CA3 Dentate gyrus CA1 CA1 pyramidal cell CA3 pyramidal cell + + + Granule cell Figure 24.6 Long-term potentiation of Schaffer collateral-CA1 synapses. (A) Arrangement for recording synaptic transmission; two stimulating electrodes (1 and 2) each activate separate popula-tions of Schaffer collaterals, thus provid-ing test and control synaptic pathways. (B) Left: Synaptic responses recorded in a CA1 neuron in response to single stimuli of synaptic pathway 1, minutes before and one hour after a high-fre-quency train of stimuli. The high-fre-quency stimulus train increases the size of the EPSP evoked by a single stimulus. Right: Responses produced by stimulat-ing synaptic pathway 2, which did not receive high-frequency stimulation, is unchanged. (C) The time course of changes in the amplitude of EPSPs evoked by stimulation of pathways 1 and 2. High-frequency stimulation of pathway 1 causes a prolonged enhance-ment of the EPSPs in this pathway (pur-ple). This potentiation of synaptic trans-mission in pathway 1 persists for several hours, while the amplitude of EPSPs produced by pathway 2 (orange) remains constant. (After Malinow et al., 1989.) pocampus. The dendrites of pyramidal cells in the CA1 region form a thick band (the stratum radiatum), where they receive synapses from Schaffer col-laterals, the axons of pyramidal cells in the CA3 region. Much of the work on LTP has focused on the synaptic connections between the Schaffer collaterals and CA1 pyramidal cells. Electrical stimulation of Schaffer collaterals gener-ates excitatory postsynaptic potentials (EPSPs) in the postsynaptic CA1 cells (Figure 24.6A,B). If the Schaffer collaterals are stimulated only two or three times per minute, the size of the evoked EPSP in the CA1 neurons remains constant. However, a brief, high-frequency train of stimuli to the same axons causes LTP, which is evident as a long-lasting increase in EPSP amplitude (Figure 24.6C). LTP occurs not only at the excitatory synapses of the hip-pocampus shown in Figure 24.5, but at many other synapses in a variety of brain regions, including the cortex, amygdala, and cerebellum. Plasticity of Mature Synapses and Circuits 585 Time (min) EPSP amplitude (% of control) −15 0 High frequency stimulation 200 100 15 30 45 60 Pathway 2 Pathway 1 −60 −55 −50 −65 0 25 50 Time (ms) 75 100 EPSP membrane potential (mv) After tetanus Before tetanus 0 25 50 75 100 Stimulus Stimulus 300 Schaffer collaterals CA1 pyramidal cell CA3 pyramidal cells LTP of tetanized pathway Pathway 1 Pathway 2 Record Stimulus 2 Stimulus 1 (A) (B) (C) Before tetanus to pathway 1 After tetanus to pathway 1 586 Chapter Twenty-Four Figure 24.7 Pairing presynaptic and postsynaptic activity causes LTP. Single stimuli applied to a Schaffer collateral synaptic input evokes EPSPs in the post-synaptic CA1 neuron. These stimuli alone do not elicit any change in synap-tic strength. However, when the CA1 neuron’s membrane potential is briefly depolarized (by applying current pulses through the recording electrode) in con-junction with the Schaffer collateral stimuli, there is a persistent increase in the EPSPs. (After Gustafsson et al., 1987.) LTP of the Schaffer collateral synapse exhibits several properties that make it an attractive neural mechanism for information storage. First, LTP is state-dependent: The state of the membrane potential of the postsynaptic cell determines whether or not LTP occurs (Figure 24.7). If a single stimulus to the Schaffer collaterals—which would not normally elicit LTP—is paired with strong depolarization of the postsynaptic CA1 cell, the activated Schaf-fer collateral synapses undergo LTP. The increase occurs only if the paired activities of the presynaptic and postsynaptic cells are tightly linked in time, such that the strong postsynaptic depolarization occurs within about 100 ms of presynaptic transmitter release. Recall that a requirement for coincident activation of presynaptic and postsynaptic elements is the central postulate of Donald Hebb’s early theories of the synaptic changes underlying the selective maintenance of neuronal connections (see Chapter 22). LTP also exhibits the property of input specificity: When LTP is induced by the stimulation of one synapse, it does not occur in other, inactive synapses that contact the same neuron (see Figure 24.6). Thus, LTP is restricted to acti-vated synapses rather than to all of the synapses on a given cell (Figure 24.8A). This feature of LTP is consistent with its involvement in memory for-mation (or at least the storage of specific information). If activation of one set of synapses led to all other synapses—even inactive ones—being potenti-ated, it would be difficult to selectively enhance particular sets of inputs, as is presumably required to store specific information. Another important property of LTP is associativity (Figure 24.8B). As noted, weak stimulation of a pathway will not by itself trigger LTP. How-ever, if one pathway is weakly activated at the same time that a neighboring pathway onto the same cell is strongly activated, both synaptic pathways undergo LTP. This selective enhancement of conjointly activated sets of syn-aptic inputs is often considered a cellular analog of associative or classical Time (min) 0 10 20 30 40 50 60 70 EPSP amplitude (mv) Test Strong depolarizing pulses paired with EPSPs 0 2 4 Schaffer collaterals CA1 pyramidal cell CA3 pyramidal cell Record Stimulus LTP conditioning. More generally, associativity is expected in any network of neurons that links one set of information with another. Although there is clearly a gap between understanding LTP of hippocam-pal synapses and understanding learning, memory, or other aspects of behavioral plasticity in mammals, this form of synaptic plasticity provides a plausible neural mechanism for long-lasting changes in a part of the brain that is known to be involved in the formation of certain kinds of memories. Molecular Mechanisms Underlying LTP Despite the fact that LTP was discovered more than 30 years ago, its molecu-lar underpinnings were not well understood until recently. A key advance in this effort occurred in the mid-1980s, when it was discovered that antago-nists of the NMDA type of glutamate receptor prevent LTP, but have no effect on the synaptic response evoked by low-frequency stimulation of the Schaffer collaterals. At about the same time, the unique biophysical proper-ties of the NMDA receptor were first appreciated. As described in Chapter 6, the NMDA receptor channel is permeable to Ca2+, but is blocked by physio-logical concentrations of Mg2+. This property provides a critical insight into how LTP is induced. Thus, during low-frequency synaptic transmission, glu-tamate released by the Schaffer collaterals binds to both NMDA-type and AMPA/kainate-type glutamate receptors. While both types of receptors bind glutamate, if the postsynaptic neuron is at its normal resting membrane potential, the NMDA channels will be blocked by Mg2+ ions and no current will flow (Figure 24.9, left). Because blockade of the NMDA channel by Mg2+ is voltage-dependent, the function of the synapse changes markedly when the postsynaptic cell is depolarized. Thus, conditions that induce LTP, such as high-frequency stimulation (as in Figure 24.6), will cause a prolonged depolarization that results in Mg2+ being expelled from the NMDA channel (Figure 24.9, right). Removal of Mg2+ allows Ca2+ to enter the postsynaptic neuron and the resulting increase in Ca2+ concentration within the dendritic spines of the postsynaptic cell turns out to be the trigger for LTP (Box B). The Plasticity of Mature Synapses and Circuits 587 (A) Specificity Pathway 1: Active Pathway 2: Inactive Pathway 1: Strong stimulation Pathway 2: Weak stimulation (B) Associativity Synapse not strengthened Synapse strengthened Synapse strengthened Synapse strengthened Figure 24.8 Properties of LTP at a CA1 pyramidal neuron receiving synaptic inputs from two independent sets of Schaffer collateral axons. (A) Strong activity initiates LTP at active synapses (pathway 1) without initiating LTP at nearby inactive synapses (pathway 2). (B) Weak stimulation of pathway 2 alone does not trigger LTP. However, when the same weak stimulus to pathway 2 is activated together with strong stimula-tion of pathway 1, both sets of synapses are strengthened. 588 Chapter Twenty-Four NMDA receptor thus behaves like a molecular “and” gate: The channel opens (to induce LTP) only when glutamate is bound to NMDA receptors and the postsynaptic cell is depolarized to relieve the Mg2+ block of the NMDA channel. Thus, the NMDA receptor can detect the coincidence of two events. These properties of the NMDA receptor can account for many of the char-acteristics of LTP. The specificity of LTP (see Figure 24.8A) can be explained by the fact that NMDA channels will be opened only at synaptic inputs that are active and releasing glutamate, thereby confining LTP to these sites. With respect to associativity (see Figure 24.8B), a weakly stimulated input releases glutamate, but cannot sufficiently depolarize the postsynaptic cell to relieve the Mg2+ block. If neighboring inputs are strongly stimulated, however, they provide the “associative” depolarization necessary to relieve the block. The state dependence of LTP, evident as the induction of LTP by the pairing of weak synaptic input with depolarization (see Figure 24.7), should work sim-ilarly: The synaptic input releases glutamate, while the coincident depolar-ization relieves the Mg2+ block of the NMDA receptor. Several sorts of observations have confirmed that a rise in the concentra-tion of Ca2+ in the postsynaptic CA1 neuron, due to Ca2+ ions entering through NMDA receptors, serves as a second messenger signal that induces LTP. Imaging studies, for instance, have shown that activation of NMDA receptors causes increases in postsynaptic Ca2+ levels. Furthermore, injection of Ca2+ chelators blocks LTP induction, whereas elevation of Ca2+ levels in postsynaptic neurons potentiates synaptic transmission. Ca2+ induces LTP by activating complicated signal transduction cascades that include protein kinases in the postsynaptic neuron. At least two Ca2+-activated protein kinases have been implicated in LTP induction (Figure 24.10): Ca2+/calmod-ulin-dependent protein kinase (CaMKII) and protein kinase C (PKC; see Na+ Glutamate Mg2+ blocks NMDA receptor Mg2+ expelled from channel Na+ Ca2+ Presynaptic terminal At resting potential During postsynaptic depolarization Presynaptic terminal Dendritic spine of postsynaptic neuron Na+ AMPA receptor NMDA receptor Na+ AMPA receptor NMDA receptor Na+ Ca2+ LTP Figure 24.9 The NMDA receptor channel can open only during depolarization of the postsynaptic neuron from its normal resting level. Depolarization expels Mg2+ from the NMDA channel, allowing current to flow into the postsynaptic cell. This leads to Ca2+ entry, which in turn triggers LTP. (After Nicoll et al., 1988.) Chapter 7). CaMKII seems to play an especially important role: This enzyme is the most abundant postsynaptic protein at Schaffer collateral synapses, and pharmacological inhibition or genetic deletion of CaMKII prevents LTP. The downstream targets of these kinases are not yet fully known, but appar-ently include the AMPA class of glutamate receptors. Recent efforts have clarified the mechanism(s) responsible for the expres-sion of LTP, namely how LTP causes synapses to be strengthened for pro-longed periods. The most likely explanation is that LTP arises from changes in the sensitivity of the postsynaptic cell to glutamate. Several recent obser-vations indicate that excitatory synapses can dynamically regulate their postsynaptic glutamate receptors and can even add new AMPA receptors to “silent” synapses that did not previously have postsynaptic AMPA receptors (Box C). The “expression” or maintenance of LTP apparently is due to such insertion of AMPA receptors into the postsynaptic membrane (as opposed to its “induction,” which relies on the activity of the NMDA receptors). For example, synaptic activity that induces LTP can elicit postsynaptic responses Plasticity of Mature Synapses and Circuits 589 AMPA receptors Glutamate NMDA receptor Na+ Na+ Ca2+ Na+ Ca2+ Protein kinase C Ca2+/ Calmodulin kinase II Presynaptic terminal Dendritic spine of postsynaptic neuron Substrate phosphorylation Insert additional AMPA receptors Figure 24.10 Mechanisms underlying LTP. During glutamate release, the NMDA channel opens only if the postsynaptic cell is sufficiently depolarized. The Ca2+ ions that enter the cell through the channel activate postsynaptic protein kinases. These kinases may act postsynaptically to insert new AMPA receptors into the postsynap-tic spine, thereby increasing the sensitivity to glutamate. 590 Chapter Twenty-Four Box B Dendritic Spines Many synapses in the brain involve small protrusions from dendritic branches known as spines (Figure A). Spines are distinguished by the presence of globular tips called spine heads; when spines are present, the synapses inner-vating dendrites are made from these heads. Spine heads are connected to the main shafts of dendrites by narrow links called spine necks (Figure B). Just beneath the site of contact between the terminals and the spine heads are intra-cellular structures called postsynaptic densities (Figure C). The number, size, and shape of dendritic spines are quite variable and can, at least in some cases, change dynamically over time (see Fig-ure 24.14B). Since the earliest description of these structures by Santiago Ramón y Cajal in the late 1800s, dendritic spines have fas-cinated generations of neuroscientists, inspiring many speculations about their function. One of the earliest conjectures was that the narrow spine neck electri-cally isolates synapses from the rest of the neuron. Given that the size of spine necks can change, such a mechanism could cause the physiological effect of individual synapses to vary over time, thereby providing a cellular mechanism for forms of synaptic plasticity such as LTP and LTD. However, subsequent measurements of the properties of spine necks indicate that these structures would be relatively ineffective in attenu-ating the flow of electrical current between spine heads and dendrites. Another theory—currently the most popular functional concept—postulates that spines create biochemical compart-ments. This idea is based on the supposi-tion that the spine neck could prevent diffusion of biochemical signals from the spine head to the rest of the dendrite. Several observations are consistent with this notion. First, measurements show that the spine neck does indeed serve as a barrier to diffusion, slowing the rate of molecular movement by a factor of 100 or more. Second, spines are found only at excitatory synapses, where it is known that synaptic transmission generates (A) 50 µm 5 µm 3 µm (A) Cajal’s classic drawings of dendritic spines. Left, Dendrites of cortical pyramidal neurons. Right, higher-magnification images of several different types of dendritic spines. (B) High-resolution electron microscopic reconstruction of a small region of the den-drite of a hippocampal pyramidal neuron. (C) Electron micrograph of a cross section through an excitatory synapse. (A from DeFelipe and Jones, 1988; B from Harris, 1994; C from Kennedy, 2000.) (C) (B) Dendrite Spine neck Spine head Postsynaptic density Presynaptic terminal Postsynaptic density Spine Dendrite 1 µm 0.5 µm Plasticity of Mature Synapses and Circuits 591 many diffusible signals, most notably the second messenger Ca2+. Finally, fluores-cence imaging shows that synaptic Ca2+ signals can indeed be restricted to den-dritic spines (Figure D). Nevertheless, there are counterargu-ments to the hypothesis that spines pro-vide relatively isolated biochemical com-partments. For example, it is known that other second messengers, such as IP3, can diffuse out of the spine head and into the dendritic shaft. Presumably this difference in diffusion is due to the fact that IP3 signals last longer than Ca2+ sig-nals, allowing IP3 sufficient time to over-come the diffusion barrier of the spine neck. Another relevant point is that post-synaptic Ca2+ signals are highly local-ized, even at excitatory synapses that do not have spines. Thus, in at least some instances, spines are neither necessary nor sufficient for localization of synaptic second messenger signaling. A final and less controversial idea is that the purpose of spines is to serve as reservoirs where signaling proteins, such as the downstream molecular targets of Ca2+ and IP3, can be concentrated. Con-sistent with this possibility, glutamate receptors are highly concentrated on spine heads, and the postsynaptic den-sity comprises dozens of proteins involved in intracellular signal transduc-tion (Figure E). According to this view, the spine head is the destination for these signaling molecules during the assembly of synapses, as well as the tar-get of the second messengers that are produced by the local activation of gluta-mate receptors. Although the function of dendritic spines remains enigmatic, Cajal undoubtedly would be pleased at the enormous amount of attention that these tiny synaptic structures continue to com-mand, and the real progress that has been made in understanding the variety of things they are capable of doing. References GOLDBERG, J. H., G. TAMAS, D. ARONOV AND R. YUSTE (2003) Calcium microdomains in aspiny dendrites. Neuron 40: 807–821. HARRIS, K. M. (1994) Serial electron microscopy as an alternative or complement to confocal microscopy for the study of syn-apses and dendritic spines in the central ner-vous system. In Three-Dimensional Confocal Microscopy: Volume Investigation of Biological Specimens. New York: Academic Press. HARRIS, K. M. AND J. K. STEVENS (1988) Den-dritic spines of rat cerebellar Purkinje cells: serial electron microscopy with reference to their biophysical characteristics. J. Neurosci. 8: 4455–4469. KENNEDY, M. B. (2000) Signal-processing machines at the postsynaptic density. Science 290: 750–754. MIYATA, M. AND 9 OTHERS (2000) Local cal-cium release in dendritic spines required for long-term synaptic depression. Neuron 28: 233–244. NIMCHINSKY, E. A., B. L. SABATINI AND K. SVO-BODA (2002) Structure and function of den-dritic spines. Annu. Rev. Physiol. 64: 313–353. SABATINI, B. L., T. G. OERTNER AND K. SVO-BODA (2002) The life cycle of Ca2+ ions in den-dritic spines. Neuron 33: 439–452. SHENG, M. AND M. J. KIM (2002) Postsynaptic signaling and plasticity mechanisms. Science 298: 776–780. YUSTE, R. AND D. W. TANK (1996) Dendritic integration in mammalian neurons, a century after Cajal. Neuron 16: 701–716. (D) (E) 1 µm NMDA–R RTK NMDA–R mGluR Kalirin Rac AKA PKA PP2B PP1 Src PYK2 Ras Raf MEK ERK Rap SPAR SPAR GKAP GKAP GKAP GKAP PSD–95 PSD–95 PSD–95 PSD–95 PSD–95 CaMKII Shank Shank nNOS nNOS SynGAP SynGAP H H H H H H SER IP3 receptors (D) Localized Ca2+ signal (green) produced in the spine of a hippocampal pyramidal neuron following activation of a glutamatergic synapse. (E) Postsynaptic densities include dozens of signal transduction molecules, including gluta-mate receptors (NMDA-R; mGluR), tyrosine kinase recep-tors (RTK), and many intracellular signal transduction mol-ecules, most notably the protein kinase CaMKII. (D from Sabatini et al., 2002; E after Sheng and Kim, 2002.) 592 Chapter Twenty-Four mediated by AMPA receptors at silent synapses (Figure 24.11A). Such rapid insertion of new AMPA receptors also can occur at “non-silent” excitatory synapses. Further, fluorescently tagged AMPA receptors can be seen to move into synapses under conditions that induce LTP (Figure 24.11B). Addition of these new AMPA receptors would be expected to increase the response of the postsynaptic cell to released glutamate, strengthening synaptic transmis-sion as long as LTP is maintained. Under some circumstances, LTP also can cause a sustained increase in the ability of presynaptic terminals to release glutamate. Because LTP clearly is triggered by the actions of Ca2+ within the postsynaptic neuron (see Figure 24.10), this presynaptic potentiation requires that a retrograde signal (perhaps NO) spread from the postsynaptic region to the presynaptic terminals. Long-Term Synaptic Depression If synapses simply continued to increase in strength as a result of LTP, even-tually they would reach some level of maximum efficacy, making it difficult to encode new information. Thus, to make synaptic strengthening useful, other processes must selectively weaken specific sets of synapses. Long-term depression (LTD) is such a process. In the late 1970s, LTD was found to occur at the synapses between the Schaffer collaterals and the CA1 pyramidal cells in the hippocampus. Whereas LTP at these synapses requires brief, high-fre-quency stimulation, LTD occurs when the Schaffer collaterals are stimulated at a low rate—about 1 Hz—for long periods (10–15 minutes). This pattern of 0 20 40 60 80 (A) Spine 1 Spine 2 Time (ms) Stimulation Before LTP After LTP Excitatory postsynaptic current (pA) (B) Spine 1 Spine 2 2 µm Before stimulus After stimulus Figure 24.11 Insertion of postsynaptic AMPA receptors during LTP. (A) LTP induces AMPA receptor responses at silent synapses in the hippocampus. Prior to inducing LTP, no EPSCs are elicited at -65 mV at this silent synapse (upper trace). After LTP induction, the same stimulus produces EPSCs that are mediated by AMPA receptors (lower trace). (B) Distribution of fluorescently labeled AMPA recep-tor subunits (GluR1) before and 30 minutes after a high-frequency stimulus that can induce LTP. While the AMPA receptors of spine 1 did not change, there was a rapid delivery of AMPA receptors into spine 2 following the stimulus. (A after Liao et al., 1995; B from Shi et al., 1999.) Figure 24.12 Long-term synaptic depression in the hippocampus. (A) Electrophysiological procedures used to monitor transmission at the Schaffer col-lateral synapses on to CA1 pyramidal neurons. (B) Low-frequency stimulation (1 per second) of the Schaffer collateral axons causes a long-lasting depression of synaptic transmission. (C) Mecha-nisms underlying LTD. A low-amplitude rise in Ca2+ concencentration in the postsynaptic CA1 neuron activate post-synaptic protein phosphatases, which cause internalization of postsynaptic AMPA receptors, thereby decreasing the sensitivity to glutamate released from the Schaffer collateral terminals. (B after Mulkey et al., 1993.) activity depresses the EPSP for several hours and, like LTP, is specific to the activated synapses (Figure 24.12A,B). Moreover, LTD can erase the increase in EPSP size due to LTP, and, conversely, LTP can erase the decrease in EPSP size due to LTD. This complementarity suggests that LTD and LTP reversibly affect synaptic efficiency by acting at a common site. Plasticity of Mature Synapses and Circuits 593 Schaffer collaterals CA1 pyramidal cell CA3 pyramidal cell Record Stimulus (A) Time (min) 0 15 30 45 60 75 EPSP amplitude (% of control) 100 50 150 1-Hz stimulus LTD (B) (C) AMPA receptors Glutamate NMDA receptor Na+ Na+ Ca2+ Na+ Ca2+ Protein phosphatases Presynaptic terminal Dendritic spine of postsynaptic neuron Dephosphorylate substrates Internalization of AMPA receptors 594 Chapter Twenty-Four LTP and LTD at the Schaffer collateral-CA1 synapses actually share sev-eral key elements. Both require activation of NMDA-type glutamate recep-tors and the resulting entry of Ca2+ into the postsynaptic cell. The major determinant of whether LTP or LTD arises appears to be the amount of Ca2+ in the postsynaptic cell: Small rises in Ca2+ lead to depression, whereas large increases trigger potentiation. As noted above, LTP is at least partially due to activation of CaMKII, which phosphorylates target proteins. LTD, on the other hand, appears to result from activation of Ca2+-dependent phos-phatases that cleave phosphate groups from these target molecules (see Chapter 7). Evidence in support of this idea is that phosphatase inhibitors prevent LTD, but have no effect on LTP. The different effects of Ca2+ during LTD and LTP may arise from the selective activation of protein phosphatases and kinases by low and high levels of Ca2+. While the phosphatase sub-strates important for LTD have not yet been identified, it is possible that LTP Box C Silent Synapses Several recent observations indicate that postsynaptic glutamate receptors are dynamically regulated at excitatory syn-apses. Early insight into this process came from the finding that stimulation of some glutamatergic synapses generates no postsynaptic electrical signal when the postsynaptic cell is at its normal rest-ing membrane potential (Figure A). However, once the postsynaptic cell is depolarized, these “silent synapses” can transmit robust postsynaptic electrical responses. The fact that transmission at such synapses can be turned on or off in response to postsynaptic activity sug-gests an interesting and simple means of modifying neural circuitry. Silent synapses are especially preva-lent in development and have been found in many brain regions, including the hippocampus, cerebral cortex, and spinal cord. The silence of these synapses is evidently due to the voltage-depen-dent blockade of NMDA receptors by Mg2+ (see text and Chapter 6). At the normal resting membrane potential, pre-synaptic release of glutamate evokes no postsynaptic response at such synapses because their NMDA receptors are blocked by Mg2+. However, depolariza-tion of the postsynaptic neuron displaces the Mg2+, allowing glutamate release to induce postsynaptic responses mediated by NMDA receptors. Glutamate released at silent synapses evidently binds only to NMDA recep-tors. How, then, does glutamate release avoid activating AMPA receptors? One possibility is that glutamate released onto neighboring neurons diffuses to synapses on the neuron from which the electrical recording is being made. In this case, the diffusing glutamate may be pre-sent at concentrations sufficient to acti-vate the high-affinity NMDA receptors, but not the low-affinity AMPA receptors. A second possibility is that a silent syn-apse has both AMPA and NMDA recep-tors, but its AMPA receptors are some-how not functional. Finally, some excitatory synapses may have only 0 5 10 15 20 Stimulation Time (ms) +55 mV −65 mV (A) (B) Excitatory postsynaptic current (pA) 10 µm AMPA-R NMDA-R AMPA-R and NMDA-R (A) Electrophysiological evidence for silent synapses. Stimulation of some axons fails to acti-vate synapses when the postsynaptic cell is held at a negative potential (–65 mV, upper trace). However, when the postsynaptic cells is depolarized (+55 mV), stimulation produces a robust response (lower trace). (B) Immunofluorescent localization of NMDA receptors (green) and AMPA receptors (red) in a cultured hippocampal neuron. Many dendritic spines are positive for NMDA receptors but not AMPA receptors, indicating NMDA receptor-only synapses. (A after Liao et al., 1999; B courtesy of M. Ehlers.) and LTD phosphorylate and dephosphorylate the same set of regulatory proteins to control the efficacy of transmission at the Schaeffer collateral-CA1 synapse. Just as LTP at this synapse is associated with insertion of AMPA receptors, LTD is often associated with a loss of synaptic AMPA receptors. This loss probably arises from internalization of AMPA receptors into the postsynaptic cell (Figure 24.12C), due to the same sort of clathrin-dependent endocytosis mechanisms important for synaptic vesicle recycling in the presynaptic terminal (see Chapter 5). A somewhat different form of LTD is observed in the cerebellum (see Chap-ter 18). LTD of synaptic inputs onto cerebellar Purkinje cells was first described by Masao Ito and colleagues in Japan in the early 1980s. Purkinje neurons in the cerebellum receive two distinct types of excitatory input: climb-ing fibers and parallel fibers (Figure 24.13A; see Chapter 18). LTD reduces the strength of transmission at the parallel fiber synapse (Figure 24.13B) and has Plasticity of Mature Synapses and Circuits 595 NMDA receptors. Accumulating evi-dence supports the latter explanation. Most compelling are immunocytochemi-cal experiments demonstrating the pres-ence of excitatory synapses that have only NMDA receptors (green spots in Figure B). Such NMDA receptor-only synapses are particularly abundant early in postnatal development and decrease in adults (Figure C). Thus, at least some silent synapses are not a separate class of excitatory synapses that lack AMPA receptors, but rather an early stage in the ongoing maturation of the glutamatergic synapse (Figure D). Evidently, AMPA and NMDA receptors are not inextrica-bly linked at excitatory synapses, but are targeted via independent cellular mecha-nisms. Such synapse-specific glutamate receptor composition implies sophisti-cated mechanisms for regulating the localization of each type of receptor. Dynamic changes in the trafficking of AMPA and NMDA receptors can strengthen or weaken synaptic transmis-sion and are important in LTP and LTD, as well as in the maturation of gluta-matergic synapses. Although silent synapses have begun to whisper their secrets, much remains to be learned about their physiological importance and the molecular mecha-nisms that mediate rapid recruitment or removal of synaptic AMPA receptors. References GOMPERTS, S. N., A. RAO, A. M. CRAIG, R. C. MALENKA AND R. A. NICOLL (1998) Postsynap-tically silent synapses in single neuron cul-tures. Neuron 21: 1443–1451. LIAO, D., N. A. HESSLER AND R. MALINOW (1995) Activation of postsynaptically silent synapses during pairing-induced LTP in CA1 region of hippocampal slice. Nature 375: 400–404. LUSCHER, C., R. A. NICOLL, R. C. MALENKA AND D. MULLER (2000) Synaptic plasticity and dynamic modulation of the postsynaptic membrane. Nature Neurosci. 3: 545–550. PETRALIA, R. S. AND 6 OTHERS (1999) Selective acquisition of AMPA receptors over postnatal development suggests a molecular basis for silent synapses. Nature Neurosci. 2: 31–36. (C) (D) Silent synapse NMDA-R only Functional synapse AMPA-P + NMDA-R NMDA-R NMDA-R AMPA-R Synaptic cleft Juvenile Pre Pre Post Post Adult Maturation Presynaptic terminal Postsynaptic spine NMDA-R NMDA-R AMPA-R 0.1 µm (C) Electron microscopy of excitatory synapses in CA1 stratum radiatum of the hippocampus from 10-day-old or 5-week-old (adult) rats double-labeled for AMPA receptors and NMDA receptors. The presynaptic terminal (pre), synaptic cleft, and postsynaptic spine (post) are indicated. AMPA receptors are abundant at the adult synapse, but absent from the younger synapse. (D) Diagram of glutamatergic synapse maturation. Early in postnatal development, many excitatory synapses contain only NMDA receptors. As synapses mature, AMPA recep-tors are recruited. (C from Petralia et al., 1999.) 596 Chapter Twenty-Four Time (minutes) (A) (C) (B) 3 0 4 5 6 7 Parallel fiber EPSP amplitude (mV) −20 0 20 40 60 80 Pair CF and PF Granule cell Purkinje cell Parallel fibers Climbing fiber CF Stimulus PF Stimulus Record Parallel fiber Climbing fiber Purkinje cell dendritic spine Synapse weakened Synapse weakened Climbing fiber depolarizes Vm (D) AMPA receptors Presynaptic terminal of parallel fiber Dendritic spine of Purkinje cell mGluR Glutamate Phospholipase C PIP2 IP3 DAG PKC Phosphorylate substrate proteins Release Ca2+ Ca2+ Ca2+ Climbing fiber depolarizes VM Endoplasmic reticulum Long-term depression Internalization of AMPA receptors Na+ Figure 24.13 Long-term synaptic depression in the cerebellum. (A) Experimental arrangement. Synaptic responses were recorded from Purkinje cells following stim-ulation of parallel fibers and climbing fibers. (B) Pairing stimulation of climbing fibers (CF) and parallel fibers (PF) causes LTD that reduces the parallel fiber EPSP. (C) LTD requires depolarization of the Purkinje cell, produced by climbing fiber activation, as well as signals generated by active parallel fiber synapses. (D) Mecha-nism underlying cerebellar LTD. Glutamate released by parallel fibers activates both AMPA receptors and metabotropic glutamate receptors. The latter produces two second messengers, DAG and IP3, which interact with Ca2+ that enters when climb-ing fiber activity opens voltage-gated Ca2+ channels. This leads to activation of PKC, which triggers clathrin-dependent internalization of postsynaptic AMPA receptors to weaken the parallel fiber synapse. (B after Sakurai, 1987.) recently been found to depress transmission at the climbing fiber synapse as well. This form of LTD has been implicated in the motor learning that medi-ates the coordination, acquisition, and storage of complex movements within the cerebellum. Although the role of LTD in cerebellar motor learning remains controversial, it has nonetheless been a useful model system for understand-ing the cellular mechanisms of long-term synaptic plasticity. Cerebellar LTD is associative in that it occurs only when climbing fibers and parallel fibers are activated at the same time (Figure 24.13C). The asso-ciativity arises from the combined actions of two distinct intracellular signal transduction pathways that are activated in the postsynaptic Purkinje cell due to the activity of climbing fiber and parallel fiber synapses. In the first pathway, glutamate released from the parallel fiber terminals activates at two types of receptors, the AMPA-type and metabotropic glutamate recep-tors (see Chapter 7). Glutamate binding to the AMPA receptor results in membrane depolarization, whereas binding to the metabotropic receptor produces the second messengers inositol trisphosphate (IP3) and diacylglyc-erol (DAG) (see Chapter 7). The second signal transduction pathway, initi-ated by climbing fiber activation, causes a large influx of Ca2+ through volt-age-gated channels and a subsequent increase in intracellular Ca2+ concentration. These second messengers work together to cause an ampli-fied rise in intracellular Ca2+ concentration, due to IP3 and Ca2+ triggering release of Ca2+ from IP3-sensitive intracellular stores, and the synergistic acti-vation of PKC by Ca2+ and DAG (Figure 24.13D). While the downstream substrate proteins that are phosphorylated by PKC are still be determined, it is known that the net effect is to cause an internalization of AMPA receptors via clathrin-dependent endocytosis (Figure 24.13D). This loss of AMPA receptors decreases the response of the postsynaptic Purkinje cell to gluta-mate release from the presynaptic terminals of the parallel fibers. Thus, in contrast to LTD in the hippocampus, cerebellar LTD requires the activity of a protein kinase, rather than a phosphatase, and does not involve Ca2+ entry through the NMDA type of glutamate receptor (which is not present in mature Purkinje cells). However, the net effect is the same in both cases: internalization of AMPA receptors is a common mechanism for decreased efficacy of both hippocampal and cerebellar synapses during LTD. Changes in Gene Expression Cause Enduring Changes in Synaptic Function during LTP and LTD The initial basis of long-lasting forms of synaptic plasticity in the mam-malian CNS, such as LTP and LTD, entails post-translational changes that lead to altered distribution or density of postsynaptic AMPA receptors. Stud-ies in Aplysia, however, showed that while a short-term form of serotonin-induced synaptic plasticity also has a post-translational origin, the long-term form of synaptic plasticity requires changes in gene expression (see Figure 24.4). This principle also appears to apply to long-lasting forms of synaptic plasticity in the mammalian CNS. Whereas hippocampal LTP has an early phase that involves post-translation mechanisms, it also has a later phase that depends on changes in gene expression and the synthesis of new pro-teins. Thus, blocking protein synthesis prevents LTP measured several hours after a stimulus but does not affect LTP measured at earlier times. This late phase of LTP is initiated by transcription factors such as CREB, which stim-ulate the expression of still other transcriptional regulators (Figure 24.14A). In addition, there is also evidence that the number and size of synaptic con-Plasticity of Mature Synapses and Circuits 597 598 Chapter Twenty-Four (A) Short–term Long–term (C) (B) Top view Side view 50 m LTP Presynaptic terminal NMDA receptor NMDA receptor AMPA receptor AMPA receptor Dendritic spines of postsynaptic neuron Ca2+ Ca2+ calmodulin Protein kinases Ca2+ ATP cAMP Protein kinase A CREB Pi Pi Transcriptional regulators Synapse growth proteins Figure 24.14 Mechanisms responsible for long-lasting changes in synaptic transmission during LTP. (A) The late component of LTP is due to PKA acti-vating the transsciptional regulator CREB, which turns on expression of a number of genes that produce long-last-ing changes in PKA activity and syn-apse structure. (B,C) Structural changes associated with LTP in the hippocam-pus. (B) The dendrites of a CA1 pyrami-dal neuron were visualized by filling the cell with a fluorescent dye. (C) New dendritic spines (white arrows) can be observed to appear approximately 1 hour after a stimulus that induces LTP. The presence of novel spines raises the possibility that LTP may arise, in part, from formation of new synapses. (A after Squire and Kandel, 1999; B and C after Engert and Bonhoeffer, 1999.) tacts increases during LTP (Figure 24.14B,C). Thus, it is likely that some of the proteins newly synthesized during LTP are involved in construction of new synaptic contacts. While evidence for late components of hippocampal LTD is unclear, CREB may also be required for a late phase of LTD in the cerebellum. In summary, behavioral plasticity requires activity-dependent synaptic changes that lead to changes in the functional connections within and among neural circuits. These changes in the efficacy and local geometry of connectivity provide a basis not only for learning, memory, and other forms of plasticity, but also some pathologies. Thus, abnormal patterns of neuronal activity, such as those that occur in epilepsy, can stimulate abnormal changes in synaptic connections that may further increase the frequency and severity of seizures (Box D). Despite the substantial advances in understanding the cellular and molecular bases of some forms of plasticity, how selective changes of synaptic strength encode memories or other complex behavioral modifications in the mammalian brain is simply not known. Plasticity in the Adult Cerebral Cortex In addition to these cellular and molecular studies of synaptic plasticity, a good deal is now known about plasticity of adult cortical maps and of the receptive field properties of mature cortical neurons. Until the late 1970s, it was assumed that significant reorganization of cortical circuitry happened primarily during early postnatal development. This conclusion was based on the evidence for critical periods described in the preceding chapter, and on the relative permanence of neural deficits after CNS trauma in adults. This view has to some extent been modified by evidence that topographic maps in the somatic sensory cortex of adult monkeys are actually capable of appreciable reorganization. As described in Chapter 8, the four cortical areas that define the primate somatic sensory cortex (Brodmann’s areas 3a, 3b, 1, and 2) each contain a complete topographic representation of the body sur-face. Jon Kaas and Michael Merzenich took advantage of this arrangement by carefully defining the normal spatial organization of topographic maps in these regions. They then amputated a digit (or cut one of the nerves that innervate the hand) and reexamined topographical maps in the same animals several weeks later. Surprisingly, the somatic sensory cortex had changed: The cortical neurons that had been deprived of their normal peripheral input now responded to stimulation of other parts of the animal’s hand (Figure 24.15). For example, if the third digit was amputated, cortical neurons that formerly responded to stimulation of digit 3 responded to stimulation of dig-its 2 or 4. Thus, the central representation of the remaining digits had expanded to take over the cortical territory that had lost its main input. Such “functional re-mapping” also occurs in the somatic sensory nuclei in the thal-amus and brainstem; indeed, some of the reorganization of cortical circuits Plasticity of Mature Synapses and Circuits 599 (A) Owl monkey brain (C) Hand representation two months after digit 3 amputation 1 2 4 5 1 2 (B) Normal hand representation Caudal Lateral Medial 4 5 3 3b 1 Somatic sensory cortex Hand representation Figure 24.15 Functional changes in the somatic sensory cortex of an owl monkey following amputation of a digit. (A) Diagram of the somatic sensory cortex in the owl monkey, showing the approximate location of the hand representation. (B) The hand representation in the animal before amputation; the numbers correspond to different digits. (C) The cortical map determined in the same animal two months after amputation of digit 3. The map has changed substantially; neurons in the area formerly responding to stimulation of digit 3 now respond to stimulation of digits 2 and 4. (After Merzenich et al., 1984.) 600 Chapter Twenty-Four may depend on this concurrent subcortical plasticity. This sort of adjustment in the somatic sensory system may contribute to the altered sensation of phantom limbs after amputation (see Box D in Chapter 9). Similar plastic changes now have been demonstrated in the visual, auditory, and motor cor-tices, suggesting that some ability to reorganize after peripheral deprivation or injury is a general property of the mature neocortex. Appreciable changes in cortical representation also can occur in response to more physiological changes in sensory or motor experience. For instance, if a monkey is trained to use a specific digit for a particular task that is repeated many times, the functional representation of that digit determined Box D Epilepsy:The Effect of Pathological Activity on Neural Circuitry Epilepsy is a brain disorder characterized by periodic and unpredictable seizures mediated by the rhythmic firing of large groups of neurons. It seems likely that abnormal activity generates plastic changes in cortical circuitry that are criti-cal to the pathogenesis of the disease. The importance of neuronal plasticity in epilepsy is indicated most clearly by an animal model of seizure production called kindling. To induce kindling, a stimulating electrode is implanted in the brain, often in the amygdala (a compo-nent of the limbic system that makes and receives connections with the cortex, thalamus, and other limbic structures, including the hippocampus; see Chapter 28). At the beginning of such an experi-ment, weak electrical stimulation, in the form of a low-amplitude train of electri-cal pulses, has no discernible effect on the animal’s behavior or on the pattern of electrical activity in the brain (labora-tory rats or mice have typically been used for such studies). As this weak stimulation is repeated once a day for several weeks, it begins to produce behavioral and electrical indications of seizures. By the end of the experiment, the same weak stimulus that initially had no effect now causes full-blown seizures. This phenomenon is essentially perma-nent; even after an interval of a year, the same weak stimulus will again trigger a seizure. Thus, repetitive weak activation produces long-lasting changes in the excitability of the brain that time cannot reverse. The word kindling is therefore quite appropriate: A single match can start a devastating fire. The changes in the electrical patterns of brain activity detected in kindled ani-mals resemble those in human epilepsy. The behavioral manifestations of epilep-tic seizures in human patients range from mild twitching of an extremity to loss of consciousness and uncontrollable convulsions. Although many highly accomplished people have suffered from epilepsy (Alexander the Great, Julius Caesar, Napoleon, Dostoyevsky, and van Gogh, to name a few), seizures of suffi-cient intensity and frequency can obvi-ously interfere with many aspects of daily life. Moreover, uncontrolled con-vulsions can lead to excitotoxicity (see Box D in Chapter 6). Up to 1% of the population is afflicted, making epilepsy one of the most common neurological problems. Modern thinking about the causes (and possible cures) of epilepsy has focused on where seizures originate and the mechanisms that make the affected region hyperexcitable. Most of the evi-dence suggests that abnormal activity in small areas of the cerebral cortex (called foci) provide the triggers for a seizure that then spreads to other synaptically connected regions. For example, a seizure originating in the thumb area of the right motor cortex will first be evi-dent as uncontrolled movement of the left thumb that subsequently extends to other more proximal limb muscles, whereas a seizure originating in the visual association cortex of the right hemisphere may be heralded by complex hallucinations in the left visual field. The behavioral manifestations of seizures therefore provide important clues for the neurologist seeking to pinpoint the abnormal region of cerebral cortex. Epileptic seizures can be caused by a variety of acquired or congenital factors, including cortical damage from trauma, stroke, tumors, congenital cortical dysge-nesis (failure of the cortex to grow prop-erly), and congenital vascular malforma-tions. One rare form of epilepsy, Rasmussen’s encephalitis, is an autoim-mune disease that arises when the immune system attacks the brain, using both humoral (i.e. antibodies) and cellu-lar (lymphocytes and macrophages) agents that can destroy neurons. Some forms of epilepsy are heritable, and more than a dozen distinct genes have been demonstrated to underlie unusual types of epilepsy. However, most forms of familial epilepsy (such as juvenile myoclonic epilepsy and petit mal epi-lepsy) are caused by the simultaneous inheritance of more than one mutant gene. by electrophysiological mapping can expand at the expense of the other dig-its (Figure 24.16). In fact, significant changes in receptive fields of somatic sensory neurons can be detected when a peripheral nerve is blocked tem-porarily by a local anesthetic. The transient loss of sensory input from a small area of skin induces a reversible reorganization of the receptive fields of both cortical and subcortical neurons. During this period, the neurons assume new receptive fields that respond to tactile stimulation of the skin surrounding the anesthetized region. Once the effects of the local anesthetic subside, the receptive fields of cortical and subcortical neurons return to their usual size. The common experience of an anesthetized area of skin feel-Plasticity of Mature Synapses and Circuits 601 No effective prevention or cure exists for epilepsy. Pharmacological therapies that successfully inhibit seizures are based on two general strategies. One approach is to enhance the function of inhibitory synapses that use the neuro-transmitter GABA; the other is to limit action potential firing by acting on volt-age-gated Na+ channels. Commonly used antiseizure medications include carbamazepine, phenobarbital, pheny-toin (Dilantin®), and valproic acid. These agents, which must be taken daily, suc-cessfully inhibit seizures in 60–70% of patients. In a small fraction of patients, the epileptogenic region can be surgi-cally excised. In extreme cases, physi-cians resort to cutting the corpus callo-sum to prevent the spread of seizures (most of the “split-brain” subjects described in Chapter 26 were patients suffering from intractable epilepsy). One of the major reasons for controlling epileptic activity is to prevent the more permanent plastic changes that would ensue as a consequence of abnormal and excessive neural activity. References SCHEFFER, I. E. AND S. F. BERKOVIC (2003) The genetics of human epilepsy. Trends Pharm. Sci. 24: 428–433. ENGEL, J. JR. AND T. A. PEDLEY (1997) Epilepsy: A Comprehensive Textbook. Philadelphia: Lip-pincott-Raven Publishers. McNamara, J. O. (1999) Emerging insights into the genesis of epilepsy. Nature 399: A15–A22. Onset of seizure Position of recording electrodes P3 – O1 C3 – P3 F3 – C3 FP1 – F3 P4 – O2 C4 – P4 F4 – C4 Fp2 – F4 0 1 2 Time (s) 3 4 Electroencephalogram (EEG) recorded from a patient during a seizure. The traces show rhyth-mic activity that persisted much longer than the duration of this record. This abnormal pat-tern reflects the synchronous firing of large numbers of cortical neurons. (The designations are various positions of electrodes on the head; see Box C in Chapter 27 for additional informa-tion about EEG recordings.) (After Dyro, 1989.) 602 Chapter Twenty-Four ing disproportionately large—following dental anesthesia—may be a conse-quence of this temporary change. Despite these intriguing observations, the mechanism, purpose, and sig-nificance of the reorganization of sensory and motor maps that occurs in adult cortex are not known. Clearly, limited changes in cortical circuitry can occur in the adult brain, even though the basic features of cortical organiza-tion—such as ocular dominance columns and the broader topographical organization of inputs from the thalamus—remain fixed (see Chapter 23). If a greater degree of cortical plasticity were possible, recovery from brain injury would be far more vigorous and effective than centuries of clinical observation have shown it to be. Given their rapid and reversible character, most of these changes in cortical function probably reflect alterations in the strength of synapses already present. Recovery from Neural Injury These various observations on adult plasticity indicate that normal experi-ence can alter the strength of existing synapses and even elicit some local remodeling of synapses and circuits. More extensive growth and remodeling are stimulated by nervous system injury. As just noted, however, this remodeling rarely results in full restoration of lost function. Traumatic injury, interruption of blood supply, and degenerative diseases all can damage axons in peripheral nerves, or neuronal cell bodies and syn-Before differential stimulation 4 5 3 2 1 5 4 3 2 1 After differential stimulation 4 1 mm 5 3 1 2 Figure 24.16 Functional expansion of a cortical representation by a repetitive behavioral task. An owl monkey was trained in a task that required heavy usage of digits 2, 3, and occasionally 4. The map of the digits in the primary somatic sensory cortex prior to training is shown. After several months of “practice,” a larger region of the cortex contained neurons activated by the dig-its used in the task. Note that the spe-cific arrangements of the digit represen-tations are somewhat different from the monkey shown in Figure 24.14, indicat-ing the variability of the cortical repre-sentation in particular animals. (After Jenkins et al., 1990.) Figure 24.17 Different responses to injury in the peripheral (A) and central (B) nervous systems. Damage to a peripheral nerve leads to series of cellular responses, collectively called Wallerian degeneration (after Augustus Waller, the nineteenth century English physician who first described these phenomena). Distal to the site of injury, axons disconnected from their cell bodies degenerate, and invading macrophages remove the cellular debris. Schwann cells that formerly ensheathed the axons proliferate, align to form longitudinal arrays, and increase their produc-tion of neurotrophic factors that can promote axon regeneration. Schwann cell sur-faces and the extracellular matrix also provide a favorable substratum for the exten-sion of regenerating axons. In the CNS, the removal of myelin debris is relatively slow, and the myelin membranes produce inhibitory molecules that can block axon growth (see Chapter 23). Astrocytes at the site of injury also interfere with regenera-tion. Proximal to the injury, neuron cell bodies react to peripheral nerve injury by inducing expression of growth-related genes, including those for major compo-nents of axonal growth cones. Following CNS injury, however, neurons typically fail to activate these growth-associated genes. ▼ apses in the more complex circuitry of the brain or spinal cord. When peripheral nerves are injured, the damaged axons regenerate vigorously and can re-grow over distances of many centimeters or more. Under favorable circumstances, these regenerated axons can also reestablish synaptic connec-tions with their targets in the periphery. In contrast, CNS axons typically fail to regenerate (Figure 24.17). As a result, axonal damage in the retina, spinal cord, or the rest of the brain leads to permanent blindness, paralysis, and other disabilities. What, then, explains this difference in the regeneration of Plasticity of Mature Synapses and Circuits 603 (A) Peripheral nervous system Injury to peripheral nerve Injury to CNS axon Macrophages rapidly remove myelin debris Proliferating Schwann cells promote axon regeneration Schwann cells Axon gowth- promoting signals Proximal to injury Distal to injury Growth cone Regenerated axon Oligodendrocytes Prolonged clearing of myelin debris Inhibitory factors disrupt axon extension Astrocytes Time Time Expression of growth-related genes (B) Central nervous system Proximal to injury Distal to injury 604 Chapter Twenty-Four peripheral nerves compared to axonal regeneration in the brain or spinal cord? Successful regeneration in peripheral nerves depends on two critical condi-tions. First, the injured neuron must respond to axon interruption by initiating a program of gene expression that can support axon elongation. Many of the genes involved in the outgrowth of axons over comparatively short distances during embryonic development (see Chapter 23) are not normally expressed in adult neurons. Interruption of axons reactivates expression of some of these genes in the peripheral nervous system, but not in the adult CNS. Axons dam-aged in the long tracts of the brain or spinal cord, particularly at sites far from their cell bodies, rarely re-express these genes. Second, once a damaged neu-ron initiates a genetic program that can support axon regrowth, the emerging growth cones must encounter an environment that can support and guide the regrowing axons. In peripheral nerves, damage or degeneration triggers changes that produce a favorable environment for axon elongation. Schwann cells and other non-neuronal cells respond to axonal injury by elaborating cell adhesion molecules, extracellular matrix components, and an array of neu-rotrophins and other signals that promote axon growth (see Chapter 22). Equally important, damaged peripheral nerves are invaded by macrophages that rapidly remove fragments of degenerating axons and myelin that might otherwise inhibit the growth of regenerating axons. In contrast, damage to axonal tracts in the adult CNS triggers a very dif-ferent set of changes. First, the relative distances for specific growth are far longer than they were in the developing brain and spinal cord. Moreover, as axons and their myelin sheaths break down, the remnants are not cleared efficiently and can persist for many weeks, posing a substantial impediment to regeneration. This inhibition appears to reflect the activity of inhibitory signals produced by glia and other cells at the site of injury, including a pro-tein called Nogo that blocks axon extension by interacting with advancing growth cones (see Chapter 22). Nogo is produced primarily by oligodendro-cytes, the glia that normally form myelin sheaths around CNS axons. The contributions of Nogo to axon regeneration remains unclear. Blocking its function with specific antibodies can enhance growth of axons in the mature injured CNS; however, genetic inactivation of Nogo (or its receptor) in mice does not result in significantly enhanced axon regeneration in the CNS fol-lowing injury. To make matters worse, astrocytes reacting to CNS injury express addi-tional inhibitors of axon extension, and the cytokines released by microglia or macrophages as part of the inflammatory response to injury also diminish axon growth. As a consequence, even if a central neuron initiates a genetic program for regeneration, growth cones emerging from the site of a lesion in the adult CNS encounter an array of circumstances that impede continued growth and reestablishment of connections. The contributions of the intrinsic capacity for growth in mature CNS neu-rons versus the local axonal environment in CNS regeneration was explored in detail by Albert Aguayo and his co-workers at McGill University in the 1980s. They grafted segments of peripheral nerve into sites in the CNS, such as optic nerve, spinal cord, or other locations, and then determined whether neurons were able to regenerate axons through the peripheral grafts. Their studies showed that at least some CNS axons are able to take advantage of the more supportive growth environment of the peripheral nerve, regenerat-ing over distances of many centimeters and in some cases restoring appro-priate synaptic connections (Box E). This demonstration that CNS axons can sometimes regenerate successfully into a peripheral nerve graft sparked intensive efforts by many labs to pro-duce a similarly supportive environment for axon growth within the long tracts of the brain or spinal cord. For example, Martin Schwab and his collab-orators showed that implanting cells engineered to secrete antibodies against inhibitory proteins, including Nogo, alleviated some of the inhibitory proper-ties of CNS myelin and other cells at the site of axon injury in experimental animals. Another approach was to introduce cells that provide a more sup-portive environment for regenerating axons in the damaged CNS. Schwann cells, neural stem cells (see next section), and specialized glial cells from the olfactory nerve all can be grown in tissue culture and introduced into the brains or spinal cords of experimental animals, where they modestly improve axon regrowth and, in some cases, may contribute to limited functional recovery. In short, regeneration in adults is held in check by ongoing suppression of genes required for effective axon elongation. Injury to the peripheral ner-vous system readily induces expression of this genetic program, while inter-ruption of mammalian CNS axons does not. Once CNS neurons have acti-vated these genes, in principle regrowth could be enhanced by removal or neutralization of inhibitory molecules, minimizing local inflammatory responses, and by the introduction of cells that provide a more supportive growth environment. These strategies, however, have not been proven clini-cally useful, and functional loss after brain and spinal cord injury remains a daunting clinical challenge. Generation of Neurons in the Adult Brain It has long been known that mature, differentiated neurons do not divide (see Chapter 21). It does not follow, however, that all the neurons in the adult brain are produced during embryonic development, even though this inter-pretation has generally been assumed. The merits of this assumption were initially challenged in the 1960s, in experiments indicating that interneurons in a variety of brain regions could be labeled with tritiated thymidine injected in the adult, rather than during early development. This finding suggested that some interneurons—particularly in the olfactory bulb and hippocampus—are generated in the mature rather than in the developing animal. Moreover, a variety of experiments in fish, frogs, and birds indicated a limited generation of new neurons throughout life in these species, espe-cially in animals (like goldfish) where there is significant continuing growth of the entire organism throughout the course of its life. In songbirds, new neurons are able to extend dendrites, generate synaptic and action poten-tials, and project long axons to establish appropriate connections with other brain nuclei. Production of new neurons is apparent in many parts of the birds’ brains, but seems especially prominent in areas involved in song pro-duction (see Box B in Chapter 23). These observations showed that the adult brain can generate at least some new nerve cells and incorporate them into neural circuits (see also Chapter 14). The production of new neurons in the mammalian adult brain has now been examined (or re-examined) in mice, rats, monkeys, and humans. In all these cases, new nerve cells in the CNS have been restricted to just two regions of the brain: (1) The granule cell layer of the olfactory bulb; and (2) the dentate gyrus of the hippocampus (Figure 24.18). Furthermore, the new nerve cells are primarily local circuit neurons or interneurons. New neurons Plasticity of Mature Synapses and Circuits 605 606 Chapter Twenty-Four with long distance projections have not been observed. Each of these popula-tions in the olfactory bulb and hippocampus is apparently generated from nearby sites near the surface of the lateral ventricle. At least some of these new nerve cells become integrated into functional synaptic circuits. Evidently, a limited production of new neurons occurs continually in just a few specific loci. The ultimate functional significance for the addition of such cells in mammals or other animals remains unknown. If differentialted neurons cannot divide (see Chapter 21), how does the adult brain generate these nerve cells? The answer emerged with the discov-ery that the subventricular zone (a population of cells adjacent to the ven-tricular space found in the cortical hemispheres and hippocampus that pro-Box E Why Aren’t We More Like Fish and Frogs? The central nervous system of adult mammals, including humans, recovers only poorly from injury. As indicated in the text, once severed, major axon tracts (such as those in the spinal cord) never regenerate. The devastating conse-quences of these injuries—e.g., loss of movement and the inability to control basic bodily functions—has led many neuroscientists to seek ways of restoring the connections of severed axons. There is no a priori reason for this biological failure, since “lower” vertebrates—e.g., lampreys, fish, and frogs—can regenerate a severed spinal cord or optic nerve. Even in mammals, the inability to regen-erate axonal tracts is a special failing of the central nervous system; peripheral nerves can and do regenerate in adult animals, including humans. Why, then, not the central nervous system? At least a part of the answer to this puzzle apparently lies in the molecular cues that promote and inhibit axon out-growth. In mammalian peripheral nerves, axons are surrounded by a basement membrane (a proteinaceous extracellular layer composed of collagens, glycopro-teins, and proteoglycans) secreted in part by Schwann cells, the glial cells associ-ated with peripheral axons. After a peripheral nerve is crushed, the axons within it degenerate; the basement mem-brane around each axon, however, per-sists for months. One of the major com-ponents of the basement membrane is laminin, which (along with other growth-promoting molecules in the basement membrane) forms a hospitable environ-ment for regenerating growth cones. The surrounding Schwann cells also react by releasing neurotrophic factors, which fur-ther promote axon elongation (see text). This peripheral environment is so favor-able to regrowth that even neurons from the central nervous system can be induced to extend into transplanted seg-ments of peripheral nerve. Albert Aguayo and his colleagues at the Montreal Gen-eral Hospital found that grafts derived from peripheral nerves can act as “bridges” for central neurons (in this case, retinal ganglion cells), allowing them to grow for over a centimeter (Fig-ure A); they even form a few functional synapses in their target tissues (Figure B). These several observations suggest that the failure of central neurons to regenerate is not due to an intrinsic inability to sprout new axons, but rather to something in the local environment that prevents growth cones from extend-ing. This impediment could be the absence of growth-promoting factors— such as the neurotrophins—or the pres-ence of molecules that actively prevent axon outgrowth. Studies by Martin Schwab and his colleagues point to the latter possibility. Schwab found that cen-tral nervous system myelin contains an inhibitory component that causes growth cone collapse in vitro and prevents axon growth in vivo. This component, recog-nized by a monoclonal antibody called IN-1, is found in the myelinated portions of the central nervous system but is absent from peripheral nerves. IN-1 also recognizes molecules in the optic nerve and spinal cord of mammals, but is miss-ing in the same sites in fish, which do regenerate these central tracts. Nogo-A, the primary antigen recognized by the IN-1 antibody, is secreted by oligoden-drocytes, but not by Schwann cells in the peripheral nervous system. Most dra-matically, the IN-1 antibody increases the extent of spinal cord regeneration when provided at the site of injury in rats with spinal cord damage. All this implies that the human central nervous system dif-fers from that of many “lower” verte-brates in that humans and other mam-mals present an unfavorable molecular environment for regrowth after injury. Why this state of affairs occurs is not known. One speculation is that the extra-ordinary amount of information stored in mammalian brains puts a premium on a stable pattern of adult connectivity. duces neurons during development) retains some neural stem cells in the adult. The term “stem cells” refers to a population of cells that are self-renewing—each cell can divide symmetrically to give rise to more cells like itself, but also can divide asymmetrically, giving rise to a new stem cell plus one or more differentiated cells. Thus a neural stem cell can give rise to the full complement of basic cell classes found in neural tissue—i.e., neurons, astrocytes, and oligodendroglia (see Box A in Chapter 21), as well as more stem cells. Adult stem cells can be isolated not only from the anterior sub-ventricular zone (near the olfactory bulb) and dentate gyrus, but from many other parts of the forebrain, cerebellum, midbrain, and spinal cord, although they do not apparently produce any new neurons in these sites. Plasticity of Mature Synapses and Circuits 607 At present there is only one modestly helpful treatment for CNS injuries such as spinal cord transection. High doses of a steroid, methylprednisolone, immedi-ately after the injury prevents some of the secondary damage to neurons result-ing from the initial trauma. Although it may never be possible to fully restore function after such injuries, enhancing axon regeneration, blocking inhibitory molecules and providing additional trophic support to surviving neurons could in principle allow sufficient recov-ery of motor control to give afflicted individuals a better quality of life than they now enjoy. The best “treatment,” however, is to prevent such injuries from occurring, since there is now very little that can be done after the fact. References BRAY, G. M., M. P. VILLEGAS-PEREZ, M. VIDAL-SANZ AND A. J. AGUAYO (1987) The use of peripheral nerve grafts to enhance neuronal survival, promote growth and permit termi-nal reconnections in the central nervous sys-tem of adult rats. J. Exp. Biol. 132: 5–19. SCHNELL, L. AND M. E. SCHWAB (1990) Axonal regeneration in the rat spinal cord produced by an antibody against myelin-associated neurite growth inhibitors. Nature 343: 269–272. SO, K. F. AND A. J. AGUAYO (1985) Lengthy regrowth of cut axons from ganglion cells after peripheral nerve transplantation into the retina of adult rats. Brain Res. 359: 402–406. VIDAL-SANZ, M., G. M. BRAY, M. P. VILLEGAS-PEREZ, S. THANOS AND A. J. AGUAYO (1987) Axonal regeneration and synapse formation in the superior colliculus by retinal ganglion cells in the adult rat. J. Neurosci. 7: 2894–2909. Optic nerves Site of nerve crush Sciatic nerve graft Superior colliculus (A) (B) Implantation of a section of peripheral nerve into the central nervous system facilitates the extension of central axons. (A) Mammalian retinal ganglion neurons, which do not normally regenerate following a crush injury, will grow for many millimeters into a graft derived from the sciatic nerve. (B) If the distal end of the graft is inserted into a normal target of retinal gan-glion cells, such as the superior colliculus, a few regenerating axons invade the target and form functional synapses, as shown in this electron micrograph (arrowheads). The dark mate-rial is an intracellularly transported label that identifies particular synaptic terminals as origi-nating from a regenerated retinal axon. (A after So and Aguayo, 1985; B from Bray et al., 1991.) 608 Chapter Twenty-Four Why the generation of neurons is so restricted in the adult brain is not understood. Nevertheless, the fact that new neurons can be generated in at least a few regions of the adult brain shows that this phenomenon can occur in the adult CNS. The ability of newly generated neurons to integrate into some synaptic circuits adds to the available mechanisms for plasticity in the adult brain. Thus, many investigators have begun to explore the potential use of stem cells for the repair of circuits damaged by traumatic injury or degenerative disease. Figure 24.18 Neurogenesis in the adult mammalian brain. (A) Neural precursors in the epithelial lining of the anterior lateral ventricles in the fore-brain (a region called the anterior sub-ventricular zone, or SVZ) give rise to postmitotic neuroblasts that migrate to the olfactory bulb via a distinctive path-way known as the rostral migratory stream or RMS. Neuroblasts that migrate to the bulb via the RMS become either olfactory bulb granule cells or periglomerular cells; both cell types function as interneurons in the bulb. (B) In the mature hippocampus, a popu-lation of neural precursors is resident in the basal aspect of the granule cell layer of the dentate gyrus. These precursors give rise to postmitotic neuroblasts that translocate from the basal aspect of the granule cell layer to more apical levels. In addition, some of these neuroblasts elaborate dendrites and a local axonal process and apparently become GABAergic interneurons within the dentate gyrus. (After Gage, 2000.) Lateral wall of lateral ventricle RMS Proliferating precursors in the anterior subventricular zone Olfactory bulb (A) (B) Corpus callosum Cerebral cortex Cerebellum Hippocampal formation CA1 CA3 Molecular layer Dentate gyrus Proliferation Translocation Differentiation 3 2 1 Plasticity of Mature Synapses and Circuits 609 Additional Reading Reviews BARRES, B. A. (1999) A new role for glia: Gen-eration of neurons! Cell 97: 667–670. BLISS, T. V. P. AND G. L. COLLINGRIDGE (1993) A synaptic model of memory: Long-term poten-tiation in the hippocampus. Nature 361: 31–39. BREDT, D. S. AND R A. NICOLL (2003) AMPA receptor trafficking at excitatory synapses. Neuron 40: 361–379. 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LOMO (1973) Long-lasting potentiation of synaptic transmission in the dentate area of the anaesthetized rabbit fol-lowing stimulation of the perforant path. J. Physiol. 232: 331–356. BRAGER, D.H., X. CAI AND S.M. THOMPSON (2003) Activity-dependent activation of pre-synaptic protein kinase C mediates post-tetanic potentiation. Nature Neurosci. 6:551-552. BREGMAN, B. S., E. KUNKEL-BAGDEN, L. SCHNELL, H. N. DAI, D. GAO AND M. E. SCHWAB (1995) Recovery from spinal cord injury mediated by antibodies to neurite growth inhibitors. Nature 378: 498–501. CHUNG, H. J., J. P. STEINBERG, R. L. HUGANIR AND D. J. LINDEN (2003) Requirement of AMPA receptor GluR2 phosphorylation for cerebellar long-term depression. Science 300: 1751–1755. Summary The adult nervous system exhibits plastic change in a variety of circum-stances. Studies of behavioral plasticity in several invertebrates and of the neuromuscular junction suggest that modification of synaptic strength is responsible for much of the ongoing change in synaptic function in adults. Synapses exhibit many forms of plasticity that occur over a broad temporal range. At the shortest times (seconds to minutes), facilitation, post-tetanic potentiation, and depression provide rapid but transient modifications based on alterations in Ca2+ signaling and synaptic vesicle pools at recently active synapses. Longer-lasting forms of synaptic plasticity such as LTP and LTD are also based on Ca2+ and other intracellular second messengers. In these more enduring forms of plasticity, protein phosphorylation and changes in gene expression greatly outlast the period of synaptic activity and can yield persistent changes in synaptic strength (hours to days or longer). Different brain regions evidently use one or more of these strategies to learn new behaviors and acquire new memories. Neuronal damage can also induce plastic changes. Peripheral neurons can regenerate axons fol-lowing damage, though the capacity of CNS axons to regenerate is severely limited. In addition, neural stem cells are present in certain regions of the adult brain, allowing the production of some new neurons in a few brain regions. These various forms of adult plasticity can modify the function of the mature brain and provide some hope for improving the limited ability of the CNS to recover successfully from trauma and neurological disease. 610 Chapter Twenty-Four COLLINGRIDGE, G. L., S. J. KEHL AND H. MCLEN-NAN (1983) Excitatory amino acids in synaptic transmission in the Schaffer collateral-com-missural pathway of the rat hippocampus. J. Physiol. 334: 33–46. ENGERT, F. AND T. BONHOEFFER (1999) Dendritic spine changes associated with hippocampal long-term synaptic plasticity. Nature 399: 66–70. ERIKSSON, P. S. AND 6 OTHERS (1998) Neurogen-esis in the adult human hippocampus. Nature Medicine 4: 1313–1317. FAGGIN, B. M., K. T. NGYUEN AND M. A. L. NICOLELIS (1997) Immediate and simultaneous sensory reorganization at cortical and subcor-tical levels of the somatosensory system. Proc. Natl. Acad. Sci. U.S.A. 94: 9428–9433. FINCH, E. A. AND G. J. AUGUSTINE (1998) Local calcium signaling by IP3 in Purkinje cell den-drites. Nature 396: 753–756. GILBERT, C. D. AND T. N. WIESEL (1992) Recep-tive field dynamics in adult primary visual cortex. Nature 356: 150–152. GOLDMAN, S. A. AND F. NOTTEBOHM (1983) Neuronal production, migration, and differ-entiation in a vocal control nucleus of the adult female canary brain. Proc. Natl. Acad. Sci. USA 80: 2390–2394. GUSTAFSSON, B., H. WIGSTROM, W.C. ABRAHAM, AND Y.Y. HUANG (1987) Long-term potentia-tion in the hippocampus using depolarizing current pulses as the conditioning stimulus to single volley synaptic potentials. J. Neurosci. 7: 774–780. HAYASHI, Y., S. H. SHI, J. A. ESTEBAN, A. PICCINI, J. C. PONCER AND R. MALINOW (2000) Driving AMPA receptors into synapses by LTP and CaMKII: Requirement for GluR1 and PDZ domain interaction. Science 287: 2262–2267. JENKINS, W. M., M. M. MERZENICH, M. T. OCHS, E. ALLARD AND T. GUIC-ROBLES (1990) Func-tional reorganization of primary somato-sensory cortex in adult owl monkeys after behaviorally controlled tactile stimulation. J. Neurophysiol. 63: 82–104. KATZ, B. AND R. MILEDI (1968) The role of cal-cium in neuromuscular facilitation. J. Physiol. (Lond.) 195: 481–492. KAUER, J. A., R. C. MALENKA AND R. A. NICOLL (1988) A persistent postsynaptic modification mediates long-term potentiation in the hip-pocampus. Neuron 1: 911–917. KEMPERMANN, G., H. G. KUHN AND F. H. GAGE (1997) More hippocampal neurons in adult mice living in an enriched environment. Nature 386: 493–495. LASHLEY, K. S. (1950) In search of the engram. Symp. Soc. Exp. Biol. 4: 454–482. LIAO, D., N. A. HESSLER AND R. MALINOW (1995) Activation of postsynaptically silent synapses during pairing-induced LTP in CA1 region of hippocampal slice. Nature 375: 400–404. MALENKA, R. C., J. A. KAUER, R. S. ZUCKER AND R. A. NICOLL (1988) Postsynaptic calcium is sufficient for potentiation of hippocampal synaptic transmission. Science 242: 81–84. MALINOW, R., H. SCHULMAN, AND R. W. TSIEN (1989) Inhibition of postsynaptic PKC or CaMKII blocks induction but not expression of LTP. Science 245: 862–866. MCDONALD, J. W. AND 7 OTHERS (1999) Trans-planted embryonic stem cells survive, differ-entiate and promote recovery in injured rat spinal cord. Nature Medicine 5: 1410–1412. MERZENICH, M. M., R. J. NELSON, M. P. STRYKER, M. S. CYNADER, A. SCHOPPMANN AND J. M. ZOOK (1984) Somatosensory cortical map changes following digit amputation in adult monkeys. J. Comp. Neurol. 224: 591–605. MULKEY, R. M., C. E. HERRON AND R. C. MALENKA (1993) An essential role for protein phosphatases in hippocampal long-term depression. Science 261: 1051–1055. NEUMANN, S. AND C. J. WOOLF (1999) Regener-ation of dorsal column fibers into and beyond the lesion site following adult spinal cord injury. Neuron 23: 83–91. NICOLELIS, M. A. L., R. C. S. LIN, D. J. WOOD-WARD AND J. K. CHAPIN (1993) Induction of immediate spatiotemporal changes in tha-lamic networks by peripheral block of ascend-ing cutaneous information. Nature 361: 533–536. O’KEEFE, J. (1990) A computational theory of the hippocampal cognitive map. Prog. Brain Res. 83: 301–312. RAMON-CUETO, A., M. I. CORDERO, F. F. SANTOS-BENITO AND J. AVILA (2000) Functional recovery of paraplegic rats and motor axon regenera-tion in their spinal cords by olfactory ensheathing glia. Neuron 25: 425–435. SAKURAI, M. (1987) Synaptic modification of parallel fibre-Purkinje cell transmission in in vitro guinea-pig cerebellar slices. J. Physiol. (Lond) 394: 463–480. SHEN, Y., C. HANSEL AND D. J. LINDEN (2002) Glutamate release during LTD at cerebellar climbing fiber-Purkinje cell synapses. Nature Neurosci. 5: 725–726. SHI, S. H. AND 6 OTHERS (1999) Rapid spine delivery and redistribution of AMPA recep-tors after synaptic NMDA receptor activation. Science 284: 1811–1816. SILVA, A. J., R. PAYLOR, J. M. WEHNER AND S. TONEGAWA (1992) Impaired spatial learning in alpha-calcium-calmodulin kinase II mutant mice. Science 257: 206–211. SQUIRE, L. R., J. G. OJEMANN, F. M MIEZEN, S. E. PETERSEN, T. O. VIDEEN AND M. E. RAICHLE (1995) Activation of the hippocampus in nor-mal humans: A functional anatomical study of memory. Proc. Natl. Acad. Sci. USA 89: 1837–1841. ZAKHARENKO, S. S., L. ZABLOW AND S. A. SIEGELBAUM (2001) Visualization of changes in presynaptic function during long-term synap-tic plasticity. Nature Neurosci. 4: 711–717. Books BAUDRY, M. AND J. D. DAVIS (1991) Long-Term Potentiation: A Debate of Current Issues. Cam-bridge, MA: MIT Press. LANDFIELD, P. W. AND S. A. DEADWYLER (EDS.) (1988) Long-Term Potentiation: From Biophysics to Behavior. New York: A. R. Liss. SQUIRE, L. R. AND E. R. KANDEL (1999) Memory: From Mind to Molecules. New York: Scientific American Library. Complex Brain Functions V The function of the frontal cor-tex was first suggested by a dramatic accident that occur-red in 1848. An explosion drove a tamping rod through the frontal part of the brain of a railroad worker named Phineas P. Gage. Remarkably, Gage sur-vived, and his subsequent behavioral deficits stimulated much thinking about complex brain functions. The illustration here is a reconstruction of the trajectory of the rod based on Gage’s skull, which is housed in the Warren Museum at Har-vard Medical School. (Courtesy of H. Damasio.) UNIT V COMPLEX BRAIN FUNCTIONS 25 The Association Cortices 26 Language and Speech 27 Sleep and Wakefulness 28 Emotions 29 Sex, Sexuality, and the Brain 30 Memory The awareness of physical and social circumstances, the ability to have thoughts and feelings (emotions), to be sexually attracted to others, to express these things to our fellow humans by language, and to store such information in memory certainly rank among the most intriguing functions of the human brain. Given their impor-tance in daily life—and for human culture generally—it is not sur-prising that much of the human brain is devoted to these and other complex mental functions. The intrinsic interest of these aspects of human behavior is unfortunately equaled by the difficulty—both technical and conceptual—involved in unraveling their neurobiolog-ical underpinnings. Nonetheless, a good deal of progress has been made in deciphering the structural and functional organization of the relevant brain regions. Especially important has been the steady accumulation of case studies during the last century or more that, by the signs and symptoms resulting from damage to specific brain regions, have indicated much about the primary location of various complex brain functions. More recently, the advent of noninvasive brain imaging techniques has provided a much deeper understand-ing of some of these abilities in normal human subjects as well as in neurological patients. Finally, complementary electrophysiological experiments in nonhuman primates and other experimental animals have begun to elucidate the cellular correlates of many of these func-tions. Taken together, these observations have established a rapidly growing body of knowledge about these more complex aspects of the human brain. This general domain of investigation has come to be called “cognitive neuroscience,” a field that promises to loom ever larger in the new century. Overview The association cortices include most of the cerebral surface of the human brain and are largely responsible for the complex processing that goes on between the arrival of input in the primary sensory cortices and the genera-tion of behavior. The diverse functions of the association cortices are loosely referred to as cognition, which literally means the process by which we come to know the world. (“Cognition” is perhaps not the best word to indicate this wide range of neural functions, but it has become part of the working vocab-ulary of neurologists and neuroscientists.) More specifically, cognition refers to the ability to attend to external stimuli or internal motivation; to identify the significance of such stimuli; and to make meaningful responses. Given the complexity of these tasks, it is not surprising that the association cortices receive and integrate information from a variety of sources, and that they influence a broad range of cortical and subcortical targets. Inputs to the asso-ciation cortices include projections from the primary and secondary sensory and motor cortices, the thalamus, and the brainstem. Outputs from the asso-ciation cortices reach the hippocampus, the basal ganglia and cerebellum, the thalamus, and other association cortices. Insight into the function of these cortical regions has come primarily from observations of human patients with damage to one or another of these areas. Noninvasive brain imaging of normal subjects, functional mapping at neurosurgery, and elec-trophysiological analysis of comparable brain regions in non-human pri-mates have generally confirmed clinical deductions. Together, these studies indicate that, among other functions, the parietal association cortex is espe-cially important for attending to stimuli in the external and internal envi-ronment, that the temporal association cortex is especially important for identifying the nature of such stimuli, and that the frontal association cortex is especially important for planning appropriate behavioral responses. The Association Cortices The preceding chapters have considered in some detail the parts of the brain responsible for encoding sensory information and commanding movements (i.e., the primary sensory and motor cortices). But these regions account for only a fraction (perhaps a fifth) of the cerebral cortex (Figure 25.1). The con-sensus has long been that much of the remaining cortex is concerned with attending to complex stimuli, identifying the relevant features of such stim-uli, recognizing the related objects, and planning appropriate responses (as well as storing aspects of this information). Collectively, these integrative abilities are referred to as cognition, and it is evidently the association cor-Chapter 25 613 The Association Cortices 614 Chapter Twenty-Five Figure 25.1 Lateral and medial views of the human brain, showing the extent of the association cortices in blue. The primary sensory and motor regions of the neocortex are shaded in yellow. Notice that the primary cortices occupy a relatively small fraction of the total area of the cortical mantle. The remain-der of the neocortex—defined by exclu-sion as the association cortices—is the seat of human cognitive ability. The term association refers to the fact that these regions of the cortex integrate (associate) information derived from other brain regions. tices in the parietal, temporal, and frontal lobes that make cognition possible. (The extrastriate cortex of the occipital lobe is equally important in cognition; its functions, however, are largely concerned with vision, and much of what is known about these areas has been discussed in Chapter 11.) These other areas of the cerebral cortex are referred to collectively as the association cor-tices (see Figure 25.1). An Overview of Cortical Structure Before delving into a more detailed account of the functions of these cortical regions, it is important to have a general understanding of cortical structure and the organization of its canonical circuitry. Most of the cortex that covers the cerebral hemispheres is neocortex, defined as cortex that has six cellular layers, or laminae. Each layer comprises more or less distinctive populations of cells based on their different densities, sizes, shapes, inputs, and outputs. The laminar organization and basic connectivity of the human cerebral cor-tex are summarized in Figure 25.2A and Table 25.1. Despite an overall uni-formity, regional differences based on these laminar features have long been apparent (Box A), allowing investigators to identify numerous subdivisions of the cerebral cortex (Figure 25.2B). These histologically defined subdivi-sions are referred to as cytoarchitectonic areas, and, over the years, a zealous band of neuroanatomists has painstakingly mapped these areas in humans and in some of the more widely used laboratory animals. Early in the twentieth century, cytoarchitectonically distinct regions were identified with little or no knowledge of their functional significance. Even-tually, however, studies of patients in whom one or more of these cortical Primary sensory and motor areas Association cortices TABLE 25.1 The Major Connections of the Neocortex Sources of cortical input Targets of cortical output Other cortical regions Other cortical regions Hippocampal formation Hippocampal formation Amygdala Amygdala Thalamus Thalamus Brainstem modulatory systems Caudate and putamen (striatum) Brainstem Spinal cord areas had been damaged, supplemented by electrophysiological mapping in both laboratory animals and neurosurgical patients, supplied this informa-tion. This work showed that many of the regions neuroanatomists had dis-tinguished on histological grounds are also functionally distinct. Thus, cytoarchitectonic areas can sometimes be identified by the physiological response properties of their constituent cells, and often by their patterns of local and long-distance connections. Despite significant variations among different cytoarchitectonic areas, the circuitry of all cortical regions has some common features (Figure 25.3). First, each cortical layer has a primary source of inputs and a primary output tar-get. Second, each area has connections in the vertical axis (called columnar or radial connections) and connections in the horizontal axis (called lateral or horizontal connections). Third, cells with similar functions tend to be arrayed in radially aligned groups that span all of the cortical layers and receive inputs that are often segregated into radial or columnar bands. Finally, interneurons within specific cortical layers give rise to extensive local axons that extend horizontally in the cortex, often linking functionally similar groups of cells. The particular circuitry of any cortical region is a variation on this canonical pattern of inputs, outputs, and vertical and horizontal pat-terns of connectivity. Specific Features of the Association Cortices These generalizations notwithstanding, the connectivity of the association cortices is appreciably different from primary and secondary sensory and motor cortices, particularly with respect to inputs and outputs. For instance, two thalamic nuclei that are not involved in relaying primary motor or sen-sory information provide much of the subcortical input to the association The Association Cortices 615 1 2 3 1 2 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 17 17 18 18 19 19 19 20 37 37 20 21 22 23 24 26 27 28 29 30 31 32 34 35 36 38 38 39 40 42 43 41 44 45 46 47 (B) (A) White matter I II IV V VI Descending axon (output) Stellate cell Dendrites Local axon collateral (local circuitry) Pyramidal cell III Figure 25.2 The structure of the human neocortex, including the associ-ation cortices. (A) A summary of the cellular composition of the six layers of the neocortex. (B) Based on variations in the thickness, cell density, and other histological features of the six neocorti-cal laminae, the human brain can be divided into numerous cytoarchitec-tonic areas, in this case those recog-nized by the neuroanatomist Korbinian Brodmann in his seminal monograph in 1909. (See Box A for additional details.) 616 Chapter Twenty-Five Figure 25.3 Canonical neocortical cir-cuitry. Green arrows indicate outputs to the major targets of each of the neocorti-cal layers in humans; orange arrow indi-cates thalamic input (primarily to layer IV); purple arrows indicate input from other cortical areas; and blue arrows indicate input from the brainstem mod-ulatory systems to each layer. cortices: the pulvinar projects to the parietal association cortex, while the medial dorsal nuclei project to the frontal association cortex. Several other thalamic nuclei, including the anterior and ventral anterior nuclei, innervate the association cortices as well. Unlike the thalamic nuclei that receive peripheral sensory information and project to primary sensory cortices, the input to these association cortex-projecting nuclei comes from other regions of the cortex. In consequence, the signals coming into the association cortices via the thalamus reflect sensory and motor information that has already been processed in the primary sen-sory and motor areas of the cerebral cortex, and is being fed back to the association regions. The primary sensory cortices, in contrast, receive thala-mic information that is more directly related to peripheral sense organs (see, for example, Chapter 8). Similarly, much of the thalamic input to primary motor cortex is derived from the thalamic nuclei related to the basal ganglia and cerebellum rather than to other cortical regions (see Unit III). A second major difference in the sources of innervation to the association cortices is their enrichment in direct projections from other cortical areas, called corticocortical connections (see Figure 25.3). Indeed, these connec-tions form the majority of the input to the association cortices. Ipsilateral corticocortical connections arise from primary and secondary sensory and motor cortices, and from other association cortices within the same hemi-sphere. Corticocortical connections also arise from both corresponding and noncorresponding cortical regions in the opposite hemisphere via the corpus callosum and anterior commissure, which together are referred to as inter-hemispheric connections. In the association cortices of humans and other primates, corticocortical connections often form segregated bands or columns in which interhemispheric projection bands are interdigitated with bands of ipsilateral corticocortical projections. Another important source of innervation to the association areas is sub-cortical, arising from the dopaminergic nuclei in the midbrain, the noradren-Other cortical areas Other cortical areas Other cortical areas, opposite hemisphere Subcortical structures (e.g., striatum, superior colliculus) Thalamus I II III IV V VI White matter Thalamus Brainstem modulatory systems The Association Cortices 617 Box A A More Detailed Look at Cortical Lamination Much knowledge about the cerebral cor-tex is based on descriptions of differ-ences in cell number and density throughout the cortical mantle. Nerve cell bodies, because of their high meta-bolic rate, are rich in basophilic sub-stances (RNA, for instance), and there-fore tend to stain darkly with reagents such as cresyl violet acetate. These Nissl stains (named after F. Nissl, who first described this technique when he was a medical student in nineteenth-century Germany) provide a dramatic picture of brain structure at the histological level. The most striking feature revealed in this way is the distinctive lamination of the cortex in humans and other mammals, as seen in the figure. In humans, there are three to six cortical layers, which are usu-ally designated by roman numerals, with letters for laminar subdivisions (layers IVa, IVb, and IVc in the visual cortex, for example). Each of the cortical laminae in the so-called neocortex (which covers the bulk of the cerebral hemispheres and is defined by six layers) has characteristic func-tional and anatomical features (see Fig-ures 25.2 and 25.3). For example, cortical layer IV is typically rich in stellate neu-rons with locally ramifying axons; in the primary sensory cortices, these neurons receive input from the thalamus, the major sensory relay from the periphery. Layer V, and to a lesser degree layer VI, contain pyramidal neurons whose axons typically leave the cortex. The generally smaller pyramidal neurons in layers II and III (which are not as distinct as their roman numeral assignments suggest) have primarily corticocortical connec-tions, and layer I contains mainly neu-ropil. Korbinian Brodmann, who early in the twentieth century devoted his career to an analysis of brain regions distin-guished in this way, described about 50 distinct cortical regions, or cytoarchitec-tonic areas (see Figure 25.2B). These structural features of the cerebral cortex continue to figure importantly in discus-sions of the brain, particularly in struc-tural/functional correlation of intensely studied regions such as the primary sen-sory and motor cortices. Not all of the cortical mantle is six-layered neocortex. The hippocampus, for example, which lies deep in the temporal lobe and has been implicated in acquisi-tion of declarative memories (see Chapter 30), has only three or four laminae. The hippocampal cortex is regarded as evolu-tionarily more primitive, and is therefore called archicortex to distinguish it from the six-layered neocortex. Another, pre-sumably more primitive, type of cortex, called paleocortex (paleo = ancient), gener-ally has three layers and is found on the ventral surface of the cerebral hemi-spheres and along the parahippocampal gyrus in the medial temporal lobe. The functional significance of differ-ent numbers of laminae in neocortex, archicortex, and paleocortex is not known, although it seems likely that the greater number of layers in neocortex reflects more complex information pro-cessing than in archi- or paleocortex. The general similarity of neocortical structure across the entire cerebrum clearly sug-gests that there is a common denomina-tor of cortical operation, although no one has yet deciphered what it is. Archicortex (hippocampus) Paleocortex (pyriform cortex) Neocortex (motor cortex) Neocortex (visual cortex) I II III I II III IV I II III IV V VI I II III V VI Major types of cortex in the cerebral mantle, based primarily on the different numbers of laminae apparent in histological sections. 618 Chapter Twenty-Five ergic and serotonergic nuclei in the brainstem reticular formation, and cholinergic nuclei in the brainstem and basal forebrain. These diffuse inputs project to different cortical layers and, among other functions, determine mental state along a continuum that ranges from deep sleep to high alert (see Chapter 27). The general wiring plan for the association cortices is summarized in Fig-ure 25.4. Despite this degree of interconnectivity, the extensive inputs and outputs of the association cortices should not be taken to imply that every-thing is simply connected to everything else in these regions. On the con-trary, each association cortex is defined by a distinct, if overlapping, subset of thalamic, corticocortical, and subcortical connections. It is nonetheless dif-ficult to conclude much about the role of these different cortical areas based solely on connectivity (this information is, in any event, quite limited for the human association cortices; most of the evidence comes from anatomical tracing studies in non-human primates, supplemented by the limited path-way tracing that can be done in human brain tissue postmortem). As a result, inferences about the function of human association areas continue to depend critically on observations of patients with cortical lesions. Damage to the association cortices in the parietal, temporal, and frontal lobes, respec-tively, results in specific cognitive deficits that indicate much about the oper-ations and purposes of each of these regions. These deductions have largely been corroborated by patterns of neural activity observed in the homologous regions of the brains of experimental animals, as well as in humans using noninvasive imaging techniques. Caudate and putamen VA/VL Thalamus MD, LP, pulvinar Cerebellum Brainstem modulatory inputs ASSOCIATION CORTICES Association cortex of the contralateral hemisphere Cerebral cortex Other primary and secondary sensory cortical regions Frontal, parietal, temporal Motor and premotor cortex Corresponding cortical areas Non-corresponding cortical areas Figure 25.4 Summary of the overall connectivity of the association cortices. Lesions of the Parietal Association Cortex: Deficits of Attention In 1941, the British neurologist W. R. Brain reported three patients with uni-lateral parietal lobe lesions in whom the primary problem was varying degrees of attentional difficulty. Brain described their peculiar deficiency in the following way: Though not suffering from a loss of topographical memory or an inability to describe familiar routes, they nevertheless got lost in going from one room to another in their own homes, always making the same error of choosing a right turning instead of a left, or a door on the right instead of one on the left. In each case there was a massive lesion in the right parieto-occipital region, and it is suggested that this … resulted in an inattention to or neglect of the left half of external space. The patient who is thus cut off from the sensations which are necessary for the construction of a body scheme may react to the situation in several different ways. He may remember that the limbs on his left side are still there, or he may periodically forget them until reminded of their presence. He may have an illusion of their absence, i.e. they may ‘feel absent’ although he knows that they are there; he may believe that they are absent but allow himself to be con-vinced by evidence to the contrary; or, finally, his belief in their absence may be unamenable to reason and evidence to the contrary and so constitute a delusion. W. R. Brain, 1941 (Brain 64: pp. 257 and 264) This description is generally considered the first account of the link between parietal lobe lesions and deficits in attention or perceptual awareness. Based on a large number of patients studied since Brain’s pioneering work, these deficits are now referred to as contralateral neglect syndrome. The hallmark of contralateral neglect is an inability to attend to objects, or even one’s own body, in a portion of space, despite the fact that visual acuity, somatic sensation, and motor ability remain intact. Affected individuals fail to report, respond to, or even orient to stimuli presented to the side of the body (or visual space) opposite the lesion (Figure 25.5). They may also have difficulty performing complex motor tasks on the neglected side, including The Association Cortices 619 (A) “Draw a house” (B) “Bisect the line” Model Patient’s copy (C) “Cancel the line” Figure 25.5 Characteristic perfor-mance on visuospatial tasks by individ-uals suffering from contralateral neglect syndrome. In (A), the patient was asked to draw a house by copying the figure on the left; on the right is the subject’s imitation. In (B), the patient was asked to draw a vertical line through the cen-ter of (i.e., bisect) a horizontal line. In (C), the patient was asked to cross out each of the lines presented on the page (A, B adapted from Posner and Raichle, 1994; C from Blumenfeld, 2002.) 620 Chapter Twenty-Five dressing themselves, reaching for objects, writing, drawing, and, to a lesser extent, orienting to sounds (the motor deficits are called apraxias). The signs of neglect can be as subtle as a temporary lack of contralateral attention that rapidly improves as the patient recovers, or as profound as permanent denial of the existence of the side of the body and extrapersonal space opposite the lesion. Since Brain’s original description of contralateral neglect and its rela-tionship to lesions of the parietal lobe, it has been generally accepted that the parietal cortex, particularly the inferior parietal lobe, is the primary cortical region (but not the only region) governing attention (Figure 25.6A). Importantly, contralateral neglect syndrome is specifically associated with damage to the right parietal cortex. The unequal distribution of this particu-lar cognitive function between the hemispheres is thought to arise because the right parietal cortex mediates attention to both left and right halves of the body and extrapersonal space, whereas the left hemisphere mediates attention primarily to the right (Figure 25.6B). Thus, left parietal lesions tend to be compensated by the intact right hemisphere. In contrast, when the right parietal cortex is damaged, there is little or no compensatory capacity in the left hemisphere to mediate attention to the left side of the body or extrapersonal space. (A) (B) Less overlap Normal Right hemisphere lesion (severe left neglect) Left hemisphere lesion (minimal right neglect) Partial bilateral lesion (severe right neglect) More overlap Figure 25.6 Neuroanatomy of attention. (A) Composite of the loca-tion of the underlying lesions in eight patients diagnosed with con-tralateral neglect syndrome. The site of damage was ascertained from CT scans (see Box B in Chapter 1). While the lesions include parietal cortical areas, frontal areas, and the temporal lobe of the right hemi-sphere, the region of the right parietal lobe indicated by the dashed line is most often affected. (B) Schematic illustration of hemispheric asymmetry in attention inferred from neglect patients. In normal sub-jects, the right parietal cortex dominates the control of attention, as indicated by the thicker rays. A right parietal lesion (purple) results in severe left neglect, whereas a left parietal lesion leads to only minimal right neglect due to preserved attention within the right hemisphere. Bilateral parietal lesions cause right neglect due to a lack of attentive processing in both hemispheres. (A after Heilman and Valenstein, 1985; B after Blumenfeld, 2002.) This interpretation has been confirmed by noninvasive imaging of pari-etal lobe activity during specific attention tasks carried out by normal sub-jects. Such studies show that blood flow is increased in both the right and left parietal cortices when subjects are asked to perform tasks in the right visual field requiring selective attention to distinct aspects of a visual stimulus such as its shape, velocity, or color. However, when a similar challenge is pre-sented in the left visual field, only the right parietal cortex is activated (Figure 25.7). There is also evidence of increased activity in the right frontal cortex during such tasks (see Figure 25.6A). This latter observation suggests that regions outside the parietal lobe also contribute to attentive behavior, and perhaps to some aspects of the pathology of neglect syndromes. Overall, however, metabolic mapping is consistent with the clinical fact that con-tralateral neglect typically arises from a right parietal lesion, and endorses the broader idea of hemispheric specialization for attention, in keeping with hemispheric specialization for a number of other cognitive functions (see below and Chapter 26). Interestingly, patients with contralateral neglect are not simply deficient in their attentiveness to the left visual field, but to the left sides of objects generally. For example, when asked to cross out lines distributed throughout the visual field, contralateral neglect patients, as expected, tend to bisect more lines on the right side of the field than on the left, consistent with a dis-ruption in attentiveness to the left visual field (see Figure 25.5C). The lines they draw, however, tend to be biased towards the right side of each non-vertical line, wherever the line happens to be in the visual field. These obser-vations suggest that attentiveness relies on a frame of reference anchored to the locations of objects and their relative dimensions. Disruptions in spatial frames of reference are also associated with lesions of the parietal cortex that are more dorsal and medial than those typically associated with classical neglect. Such damage often presents as a triad of visuospatial deficits known as Balint’s syndrome (named after an Austrian-Hungarian neurologist). These three signs are: an inability to perceive parts of a complex visual scene as a whole (called simultanagnosia); deficits in visu-ally guided reaching (optic ataxia); and difficulty in voluntary scanning of visual scenes (ocular apraxia). In contrast to classical neglect, optic ataxia and ocular apraxia typically remit when movements are guided by non-visual cues. These observations suggest that the parietal cortex participates in the construction of spatial representations that can guide both attention and movement. The Association Cortices 621 (A) Attending to the left visual field (B) Attending to the right visual field L R L R Figure 25.7 In confirmation of the impressions derived from neurological patients with parietal lobe damage, the right parietal cortex of normal subjects is highly active during tasks requiring attention. (A) A subject has been asked to attend to objects in the left visual field; only the right parietal cortex is active. (B) When attention is shifted from the left visual field to the right, the right parietal cortex remains active, but activity is apparent in the left parietal cortex as well. This arrangement im-plies that damage to the left parietal lobe does not generate right-sided hem-ineglect because the right parietal lobe also serves this function. (After Posner and Raichle, 1994.) 622 Chapter Twenty-Five Lesions of the Temporal Association Cortex: Deficits of Recognition Clinical evidence from patients with lesions of the association cortex in the temporal lobe indicates that one of the major functions of this part of the brain is the recognition and identification of stimuli that are attended to, particularly complex stimuli. Thus, damage to either temporal lobe can result in difficulty recognizing, identifying, and naming different categories of objects. These disorders, collectively called agnosias (from the Greek for “not knowing”), are quite different from the neglect syndromes. As noted, patients with right parietal lobe damage often deny awareness of sensory information in the left visual field (and are less attentive to the left sides of objects generally), despite the fact that the sensory systems are intact (an individual with contralateral neglect syndrome typically withdraws his left arm in response to a pinprick, even though he may not admit the arm’s exis-tence). Patients with agnosia, on the other hand, acknowledge the presence of a stimulus, but are unable to report what it is. These latter disorders have both a lexical aspect (a mismatching of verbal or other cognitive symbols with sensory stimuli; see Chapter 26) and a mnemonic aspect (a failure to recall stimuli when confronted with them again; see Chapter 30). One of the most thoroughly studied agnosias following damage to the temporal association cortex in humans is the inability to recognize and iden-tify faces. This disorder, called prosopagnosia (prosopo, from the Greek for “face” or “person”), was recognized by neurologists in the late nineteenth century and remains an area of intense investigation. After damage to the inferior temporal cortex, typically on the right, patients are often unable to identify familiar individuals by their facial characteristics, and in some cases cannot recognize a face at all. Nonetheless, such individuals are perfectly aware that some sort of visual stimulus is present and can describe particu-lar aspects or elements of it without difficulty. An example is the case of L.H., a patient described by the neuropsycholo-gist N. L. Etcoff and colleagues. (The use of initials to identify neurological patients in published reports is standard practice.) This 40-year-old minister and social worker had sustained a severe head injury as the result of an automobile accident when he was 18. After recovery, L.H. could not recog-nize familiar faces, report that they were familiar, or answer questions about faces from memory. He was nonetheless able to lead a fairly normal and pro-ductive life. He could still identify other common objects, could discriminate subtle shape differences, and could recognize the sex, age, and even the “lik-ability” of faces. Moreover, he could identify particular people by non-facial cues such as voice, body shape, and gait. The only other category of visual stimuli he had trouble recognizing was animals and their expressions, though these impairments were not as severe as for human faces. Noninva-sive brain imaging showed that L.H.’s prosopagnosia was the result of dam-age to the right temporal lobe. More recently, imaging studies in normal subjects have confirmed that the inferior temporal cortex mediates face recognition and that nearby regions are responsible for categorically different recognition functions (Figure 25.8). In general, lesions of the right temporal cortex lead to agnosia for faces and objects, whereas lesions of the corresponding regions of the left temporal cortex tend to result in difficulties with language-related material. (Recall that the primary auditory cortex is on the superior aspect of the temporal lobe; as described in the following chapter, the cortex adjacent to the audi-tory cortex in the left temporal lobe is specifically concerned with language.) The lesions that typically cause recognition deficits are in the inferior tempo-ral cortex in or near the so-called fusiform gyrus; those that cause language-related problems in the left temporal lobe tend to be on the lateral surface of the cortex. Consistent with these conclusions, direct cortical stimulation in subjects whose temporal lobes are being mapped for neurosurgery (typically removal of an epileptic focus) may have a transient prosopagnosia as a con-sequence of this abnormal activation of the relevant regions of the right tem-poral cortex. Prosopagnosia and related agnosias involving objects are specific instances of a broad range of functional deficits that have as their hallmark the inability to recognize a complex sensory stimulus as familiar, and to identify and name that stimulus as a meaningful entity in the environment. Depending on the laterality, location, and size of the lesion in temporal cor-tex, agnosias can be as specific as for human faces, or as general as an inabil-ity to name most familiar objects. Lesions of the Frontal Association Cortex: Deficits of Planning The functional deficits that result from damage to the human frontal lobe are diverse and devastating, particularly if both hemispheres are involved. This broad range of clinical effects stems from the fact that the frontal cortex has a wider repertoire of functions than any other neocortical region (consistent with the fact that the frontal lobe in humans and other primates is the largest of the brain’s lobes and comprises a greater number of cytoarchitectonic areas). The particularly devastating nature of the behavioral deficits after frontal lobe damage reflects the role of this part of the brain in maintaining what is normally thought of as an individual’s “personality.” The frontal cortex inte-The Association Cortices 623 MR signal change Time (s) Face area White matter 1.00% 0.80% 0.60% 0.40% 0.20% 0.00% −0.20% −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 (A) (B) R L Figure 25.8 Functional brain imaging of temporal lobe during face recognition. (A) Face stimulus presented to a normal subject at time indicated by arrow. Graph shows activity change in the relevant area of the right temporal lobe. (B) Location of fMRI activity in the right inferior temporal lobe. (Courtesy of Greg McCarthy.) 624 Chapter Twenty-Five grates complex perceptual information from sensory and motor cortices, as well as from the parietal and temporal association cortices. The result is an appreciation of self in relation to the world that allows behaviors to be planned and executed normally. When this ability is compromised, the afflicted individual often has difficulty carrying out complex behaviors that are appropriate to the circumstances. These deficiencies in the normal ability to match ongoing behavior to present or future demands are, not surpris-ingly, interpreted as a change in the patient’s “character.” The case that first called attention to the consequences of frontal lobe damage was that of Phineas Gage, a worker on the Rutland and Burlington Railroad in mid-nineteenth-century Vermont. In that era, the conventional way of blasting rock was to tamp powder into a hole with a heavy metal rod. Gage, the popular and respected foreman of the crew, was undertaking this procedure one day in 1848 when his tamping rod sparked the powder, setting off an explosion that drove the rod, which was about a meter long and 4 or 5 centimeters in diameter, through his left orbit (eye socket), destroying much of the frontal part of his brain in the process (see the illus-tration on page 612). Gage, who never lost consciousness, was promptly taken to a local doctor who treated his wound. An infection set in, presum-ably destroying additional frontal lobe tissue, and Gage was an invalid for several months. Eventually he recovered and was to outward appearances well again. Those who knew Gage, however, were profoundly aware that he was not the “same” individual that he had been before. A temperate, hard-working, and altogether decent person had, by virtue of this accident, been turned into an inconsiderate, intemperate lout who could no longer cope with normal social intercourse or the kind of practical planning that had allowed Gage the social and economic success he enjoyed before. The physician who looked after Gage until his death in 1863 summarized his impressions of Gage’s personality as follows: [Gage is] fitful, irreverent, indulging at times in the grossest profanity (which was not previously his custom), manifesting but little deference for his fel-lows, impatient of restraint or advice when it conflicts with his desires, at times pertinaciously obstinate, yet capricious and vacillating, devising many plans of future operations, which are no sooner arranged than they are aban-doned in turn for others appearing more feasible. A child in his intellectual capacity and manifestations, he has the animal passions of a strong man. Previous to his injury, although untrained in the schools, he possessed a well-balanced mind, and was looked upon by those who knew him as a shrewd, smart businessman, very energetic and persistent in executing all his plans of operation. In this regard his mind was radically changed, so decidedly that his friends and acquaintances said he was ‘no longer Gage.’ J. M. Harlow, 1868 (Publications of the Massachusetts Medical Society 2: 339–340) Another classic case of frontal lobe deficits was that of a patient followed for many years by the neurologist R. M. Brickner during the 1920s and 30s. Joe A., as Brickner referred to his patient, was a stockbroker who at age 39 underwent bilateral frontal lobe resection because of a large tumor. After the operation, Joe A. had no obvious sensory or motor deficits; he could speak and understand verbal communication and was aware of people, objects, and temporal order in his environment. He acknowledged his illness and retained a high degree of intellectual power, as judged from an ongoing abil-ity to play an expert game of checkers. Nonetheless, Joe A.’s personality had undergone a dramatic change. This formerly restrained, modest man became boastful of professional, physical, and sexual prowess, showed little The Association Cortices 625 Box B Psychosurgery The consequences of frontal lobe destruc-tion have been all too well documented by a disturbing yet fascinating episode in twentieth-century medical practice. Dur-ing the period from 1935 through the 1940s, neurosurgical destruction of the frontal lobe (frontal lobotomy or leukot-omy) was a popular treatment for certain mental disorders. More than 20,000 of these procedures were performed, mostly in the United States. Enthusiasm for this approach to men-tal disease grew from the work of Egas Moniz, a respected Portuguese neurolo-gist, who, among other accomplish-ments, did pioneering work on cerebral angiography before becoming the lead-ing advocate of psychosurgery. Moniz recognized that the frontal lobes were important in personality structure and behavior, and concluded that interfering with frontal lobe function might alter the course of mental diseases such as schizo-phrenia and other chronic psychiatric disorders. He also recognized that destroying the frontal lobe would be rel-atively easy to do and, with the help of Almeida Lima, a neurosurgical col-league, introduced a simple surgical pro-cedure for indiscriminately destroying most of the connections between the frontal lobe and the rest of the brain (see figure). In the United States, the neurologist Walter Freeman at George Washington University School of Medicine, in collab-oration with neurosurgeon James Watts, became an equally strong advocate of this approach. Freeman devoted his life to treating a wide variety of mentally disturbed patients in this way. He popu-larized a form of the procedure that could be carried out under local anesthe-sia and traveled widely across the United States to demonstrate this technique and encourage its use. Although it is easy in retrospect to be critical of this zealotry in the absence of either evidence or sound theory, it is important to remember that effective psychotropic drugs were not then avail-able, and patients suffering from many of the disorders for which leukotomies were done were confined under custo-dial conditions that were at best dismal, and at worst brutal. Rendering a patient relatively tractable, albeit permanently altered in personality, no doubt seemed the most humane of the difficult choices that faced psychiatrists and others deal-ing with such patients in that period. With the advent of increasingly effec-tive psychotropic drugs in the late 1940s and the early 1950s, frontal lobotomy as a psychotherapeutic strategy rapidly dis-appeared, but not before Moniz was awarded the Nobel Prize for Physiology or Medicine in 1949. The history of this instructive episode in modern medicine has been compellingly told by Eliot Valenstein, and his book on the rise and fall of psychosurgery should be read by anyone contemplating a career in neurol-ogy, neurosurgery, or psychiatry. References BRICKNER, R. M. (1932) An interpretation of function based on the study of a case of bilat-eral frontal lobectomy. Proceedings of the Association for Research in Nervous and Mental Disorders 13: 259–351. BRICKNER, R. M. (1952) Brain of patient A after bilateral frontal lobectomy: Status of frontal lobe problem. Arch. Neurol. Psychia-try 68: 293–313. FREEMAN, W. AND J. WATTS (1942) Psy-chosurgery: Intelligence, Emotion and Social Behavior Following Prefrontal Lobotomy for Mental Disorders. Springfield, IL: Charles C. Thomas. MONIZ, E. (1937) Prefrontal leukotomy in the treatment of mental disorders. Am. J. Psychi-atry 93: 1379–1385 VALENSTEIN, E. S. (1986) Great and Desperate Cures: The Rise and Decline of Psychosurgery and Other Radical Treatments for Mental Illness. New York: Basic Books. Damaged area The surgical technique for frontal leukotomy under local anes-thesia described and advocated by Egas Moniz and Almeida Lima. The “leukotome” was inserted into the brain at approxi-mately the angles shown. When the leukotome was in place, a wire “knife” was extended and the handle rotated. The right side of the figure depicts a horizontal slice of the brain (parallel to the top of the skull) with Moniz’s estimate of the extent of the damage done by the procedure. (After Moniz, 1937.) 626 Chapter Twenty-Five restraint in conversation, and was unable to match the appropriateness of what he said to his audience. Like Gage, his ability to plan for the future was largely lost, as was much of his earlier initiative and creativity. Even though he retained the ability to learn complex procedures, he was unable to return to work and had to rely on his family for support and care. The effects of widespread frontal lobe damage documented by these case studies encompass a wide range of cognitive disabilities, including impaired restraint, disordered thought, perseveration (i.e., repetition of the same behavior), and the inability to plan appropriate action. Recent studies of patients with focal damage to particular regions of the frontal lobe also sug-gest that some of the processes underlying these deficits may be localized anatomically, with working memory functions (see Chapter 30) situated more dorsolaterally and planning and social restraint functions located more ventromedially. Some of these functions can be clinically assessed using standardized tests such as the Wisconsin Card Sorting Task for planning (see Box C), the delayed response task for working memory, and the “go-nogo” task for inhibition of inappropriate responses. All these observations are con-sistent with the idea that the common denominator of the cognitive func-tions subserved by the frontal cortex is the selection, planning, and execu-tion of appropriate behavior, particularly in social contexts. Sadly, the effects of damage to the frontal lobes have also been docu-mented by the many thousands of frontal lobotomies (“leukotomies”) per-formed in the 1930s and 40s as a means of treating mental illness (Box B). The rise and fall of this “psychosurgery” provides a compelling example of the frailty of human judgment in medical practice, and of the conflicting approaches of neurologists, neurosurgeons, and psychiatrists in that era to the treatment of mental disease. “Attention Neurons”in the Monkey Parietal Cortex These clinical and pathological observations clearly indicate distinct cogni-tive functions for the parietal, temporal, and frontal lobes. They do not, how-ever, provide much insight into how the nervous system represents this information in nerve cells and their interconnections. The apparent functions of the association cortices implied by clinical observations stimulated a num-ber of informative electrophysiological studies in non-human primates, par-ticularly macaque (usually rhesus) monkeys. As in humans, a wide range of cognitive abilities in monkeys are medi-ated by the association cortices of the parietal, temporal, and frontal lobes (Figure 25.9A). Moreover, these functions can be tested using behavioral paradigms that assess attention, identification, and planning capabilities— the broad functions respectively assigned to the parietal, temporal, and frontal association cortices in humans. Needless to say, it is far more practi-cal to study neuronal activity in relation to cognitive functions in experi-mental animals. Using implanted electrodes, recordings can be made from single neurons in the brains of awake, behaving monkeys to assess the activ-ity of individual cells in the association cortices as various cognitive tasks are performed (Figure 25.9B). An example is neurons apparently related to the attentive functions of the parietal cortex. These particular studies of cellular electrophysiology and behavior take advantage of the fact that monkeys can be trained to selec-tively attend to particular objects or events and report their experience in a variety of nonverbal ways, typically by looking at a response target or manipulating a joystick. Thus, attention-sensitive neurons can be identified by changes in neuronal activity associated with simultaneous changes in the attentive behavior of the animal. As might be expected from the clinical evi-dence in humans, neurons in specific regions of the parietal cortex of the rhe-sus monkey are activated when the animal attends to a target but not when the same stimulus is ignored (Figure 25.10B). In another study, monkeys were rewarded with different amounts of fruit juice (a highly desirable treat) for attending to each of a pair of simultane-ously illuminated targets (Figure 25.10C). Not surprisingly, the frequency with which monkeys attended to each target varied with the amount of juice they could expect for doing so. Moreover, the activity of some neurons in parietal cortex also varied systematically as a function of the amount of juice associated with each target, and therefore the amount of attention paid by the monkey to the target. Thus, the primate parietal cortex contains neurons that respond specifically when the animal attends to a behaviorally mean-ingful stimulus, and the vigor of the response reflects the amount of atten-tion paid to the stimulus. “Recognition Neurons”in the Monkey Temporal Cortex In keeping with human deficits of recognition following temporal lobe lesions, neurons with responses that correlate with the recognition of specific The Association Cortices 627 (B) (A) Frontal lobe Recording electrode Juice reward mechanism Restraint chair Stimulus screen Response bar Temporal lobe Parietal lobe Occipital lobe Figure 25.9 Recording from single neurons in the brain of an awake, behaving rhesus monkey. (A) Lateral view of the rhesus monkey brain showing the parietal (red), temporal (green), and frontal (blue) cortices. The occipital cortex is shaded purple. (B) The animal is seated in a chair and gently restrained. Several weeks before data collection begins, a recording well is placed through the skull using a sterile surgical technique. For electrophysiological recording experiments, a tung-sten microelectrode is inserted through the dura and arachnoid, and into the cortex. The screen and the response bar in front of the monkey are for behavioral testing. In this way, individual neurons can be monitored while the monkey performs specific cognitive tasks. 628 Chapter Twenty-Five stimuli are present in the temporal cortex of rhesus monkeys (Figure 25.11). The behavior of these neurons in the vicinity of the superior temporal sulcus is generally consistent with one of the major functions ascribed to the human temporal cortex—namely, the recognition and identification of com-plex stimuli. For example, some neurons in the inferior temporal gyrus of the rhesus monkey cortex respond specifically to the presentation of a mon-key face. These cells are often quite selective; thus, some respond only to the frontal view of a face and others only to profiles (Figure 25.11B,C). Further-more, the cells are not easily deceived. When parts of faces or generally sim-ilar objects are presented, such cells typically fail to respond. In principle, it is unlikely that such “face cells” are tuned to specific faces or objects, and no cells have so far been found that are selective for a particular face. However, it is not hard to imagine that populations of neurons differently responsive to various features of faces or other objects could act in concert to enable the recognition of such complex sensory stimuli. In fact, recent studies 50 25 75 100 (B) (C) (A) Attend target Ignore target On Off Record Posterior parietal cortex 0 50 25 75 100 1.0 0.5 Relative amount of juice Attention to target (% maximum) 0 1.0 0.5 Relative amount of juice Neuronal firing rate (% maximum) Figure 25.10 Selective activation of neurons in the parietal cortex of a rhesus monkey as a function of attention (in this case, attention is directed to a light asso-ciated with a fruit juice reward). (A) Region of recording. (B) Although the baseline level of activity of the neuron being studied here remains unchanged when the monkey ignores a visual target (left), firing rate increases dramatically when the monkey attends to the same stimulus (right). The histograms indicate action poten-tial frequency per unit time. (C) When given a choice of where to attend, the mon-key pays increasing attention to a particular visual target when more fruit juice reward can be expected for doing so (left), and the firing rate of a parietal neuron under study increases accordingly (B after Lynch et al., 1977. C after Platt and Glimcher, 1999.) have suggested that neurons in the temporal cortex may be organized in a columnar arrangement similar to that in the primary visual cortex (see Chap-ter 11). Each column is thought to represent different arrangements of complex features making up an object, while the center of neuronal activity within this map indicates the object in view. In keeping with this general idea, optical imaging (see Box C in Chapter 11) of the surface of the temporal cortex shows that large populations of neurons are activated when monkeys view an object comprising several different geometric features. The locus of this activity in the (B) (C) 1 2 3 4 5 6 1 2 3 4 5 6 (A) Inferior temporal cortex Record Figure 25.11 Selective activation of face cells in the inferior temporal cortex of a rhesus monkey. (A) Region of recording. (B) The neuron being recorded from in this case responds selectively to faces seen from the front. Scrambled parts of faces (stimulus 2) or faces with parts omitted (stimulus 3) do not elicit a maximal response. The cell responds best to different monkey faces, as long as they are complete and viewed from the front (stimulus 4); the cell also responds to a bearded human face (stim-ulus 5), although not quite as robustly. An irrelevant stimulus (a hand; stimulus 6) does not elicit a response. (C) In this example, the neuron being recorded from responds to profiles of faces. A face viewed from the front (stimulus 1), 30° (stimulus 2), or 60° (stimulus 3) is not as effective as a true profile (stimulus 4). The cell responds to profiles of different monkeys (stimulus 5), but is unrespon-sive to an irrelevant stimulus (a brush; stimulus 6). (After Desimone et al., 1984.) The Association Cortices 629 630 Chapter Twenty-Five upper layers of the cortex shifts systematically when object features, such as the orientation of a face, are systematically altered (Figure 25.12). These fur-ther observations suggest that object identification relies on graded signals carried by a population of neurons rather than on the specific output of one or a few cells selective for a particular object. “Planning Neurons”in the Monkey Frontal Cortex In confirmation of the human clinical evidence about the function of the frontal association cortices, neurons that appear to be specifically involved in planning have been identified in the frontal cortices of rhesus monkeys. The behavioral test used to study cells in the monkey frontal cortex is called the delayed response task (Figure 25.13A). Variants of this task are used to assess frontal lobe function in a variety of situations, including the Left 90 Face rotation Left Right Left 45 Front Right 45 Right 90 (A) (B) Figure 25.12 Topography of object representation. (A) Schematic of possi-ble columnar organization of object rep-resentations in the inferotemporal cor-tex. Each cortical column is thought to signal a particular object class or point of view, with relatively smooth transi-tions between object features across columns. (B) Systematic movement of the active region of inferotemporal cor-tex with rotation of the face. Intrinsic signal optical images (below) were obtained for the views of five different positions of the face. Contours circum-scribing significant cortical activation by these five different views are shown on the right. (A after Tanaka, 2001; B after Wang et al., 1996.) The Association Cortices 631 Food morsel Cue Delay Response 3 Screen is raised and monkey uncovers well containing food 1 Food is placed in randomly selected well visible to monkey Empty dish Screen is lowered and food covered for a standard time 2 Dorsolateral prefrontal cortex Record Cue Delay Response (C) Stimulus (food morsel) presented (A) (B) (D) No stimulus presented Figure 25.13 Activation of neurons near the principal sulcus of the frontal lobe dur-ing delayed response task. (A) Illustration of task. The experimenter randomly varies the well in which the food is placed. The monkey watches the morsel being covered, and then the screen is lowered for a standard time. When the screen is raised, the monkey is allowed to uncover only one well to retrieve the food. Normal monkeys learn this task quickly, usually performing at a level of 90% correct after less than 500 training trials, whereas monkeys with frontal lesions perform poorly. (B) Region of recording. (C) Activity of a delay-specific neuron in the prefrontal cortex of a rhesus monkey recorded during the delayed response task shown in (A). The histograms show the number of action potentials during the cue, delay, and response periods. The neuron begins firing when the screen is lowered and remains active throughout the delay period. (D) When the screen is lowered and raised but no food is presented, the same neuron is less active. (After Goldman-Rakic, 1987.) 632 Chapter Twenty-Five Box C Neuropsychological Testing Sort by color Sort by shape Sort by number Long before PET scanning and func-tional MRI were used to evaluate normal and abnormal cognitive function, several “low-tech” methods proved to be reliable means of assessing these abilities in human subjects. From the late 1940s onward, psychologists and neurologists developed a battery of behavioral tests— generally called neuropsychological tests—to evaluate the integrity of cogni-tive function and to help localize lesions. One of the most frequently used mea-sures is the Wisconsin Card Sorting Task illustrated here. In this test, the examiner places four cards with symbols that dif-fer in number, shape, or color before the subject, who is given a set of response cards with similar symbols on them. The subject is then asked to place an appro-priate response card in front of the stim-ulus card based on a sorting rule estab-lished, but not stated, by the examiner (i.e., sort by color, number, or shape). The examiner then indicates whether the response is “right” or “wrong.” After 10 consecutive correct responses, the exam-iner changes the sorting rule simply by saying “wrong.” The subject must then ascertain the new sorting rule and per-form 10 correct trials. The sorting rule is then changed again, until six cycles have been completed. In 1963, the neuropsychologist Brenda Milner at the Montreal Neurological Institute showed that patients with frontal lobe lesions have consistently poor performance in the Wisconsin Card Sorting Task. By comparing patients with known brain lesions as a result of surgery for epilepsy or tumor, Milner was able to demonstrate that this impair-ment is fairly specific for frontal lobe damage. Particularly striking is the inability of frontal lobe patients to use previous information to guide subse-quent behavior. A widely accepted expla-nation for the sensitivity of the Wiscon-sin Card Sorting Task to frontal lobe deficits is the “planning” aspect of this test. To respond correctly, the subject must retain information about the previ-ous trial, which is then used to guide behavior on future trials. Processing this sort of information is characteristic of frontal lobe function. A variety of other neuropsychological tests have been devised to evaluate the functional integrity of other cognitive functions. These include tasks in which a patient is asked to identify familiar faces in a series of pictures, and others in which “distractors” interfere with the patient’s ability to attend to salient stim-ulus features. An example of the latter is the Stroop Interference Test, in which patients are asked to read the names of colors presented in color-conflicting print clinical evaluation of frontal lobe function in humans (Box C). In the delayed response task, the monkey watches an experimenter place a food morsel in one of two wells; both wells are then covered. Subsequently, a screen is low-ered for an interval of a few seconds to several minutes (the delay). When the screen is raised, the monkey gets only one chance to uncover the well containing food and receive the reward. Thus, the animal must decide that he wants the food, remember where it is placed, recall that the cover must be removed to obtain the food, and keep all this information available during the delay so that it can be used to get the reward. The monkey’s ability to carry out this task is diminished or abolished if the area anterior to the motor region of the frontal cortex—called the prefrontal cortex—is destroyed bilaterally (which is in accord with clinical findings in human patients). Some neurons in the prefrontal cortex, particularly those in and around the principal sulcus (Figure 25.13B), are activated when monkeys perform the delayed response task, and they are maximally active during the period of the delay, as if their firing represented information about the location of the food morsel maintained from the presentation part of the trial (i.e., the cognitive information needed to guide behavior when the screen is raised; Figure 25.12C,D). Such neurons return to a low level of activity during the actual motor phase of the task, suggesting that they represent working mem-ory and planning (see Chapter 30) rather than the actual movement itself. Delay-specific neurons in the prefrontal cortex are also active in monkeys that have been trained to perform a variant of the delayed response task in which well-learned movements are produced in the absence of any cue. Evi-dently, these neurons are equally capable of using stored information to guide behavior. Thus, if a monkey is trained to associate eye movements to a particular target with a delayed reward, the delay-associated neurons in the prefrontal cortex will fire during the delay, even if the monkey moves his eyes to the appropriate region of the visual field in the absence of the target. In addition to maintaining cognitive information during short delays, some neurons in prefrontal cortex also appear to participate directly in longer range planning of sequences of movements. When monkeys are trained to perform a motor sequence, such as turning a joystick to the left, then right, then left again, some neurons in prefrontal cortex fire at a partic-ular point in the sequence (such as the third response), regardless of which movement (e.g., left or right) is made. Prefrontal neurons have also been found that are selective for each position in a learned motor sequence, thus ruling out the possibility that these neurons merely encode task difficulty or proximity to reward as the monkey nears the end of the series of responses. Similar neurons have been found in the supplementary eye field in pre-The Association Cortices 633 (for example, the word “green” printed in red ink). This sort of challenge evalu-ates both attention and identification abilities. The simplicity, economy, and accumu-lated experience with such tests continue to make them a valuable means of evalu-ating cognitive functions. References BERG, E. A. (1948) A simple objective tech-nique for measuring flexibility in thinking. J. Gen. Psychol. 39: 15–22. LEZAK, M. D. (1995) Neuropsychological Assess-ment, 3rd Ed. New York: Oxford University Press. MILNER, B. (1963) Effects of different brain lesions on card sorting. Arch. Neurol. 9: 90–100. MILNER, B. AND M. PETRIDES (1984) Behav-ioural effects of frontal-lobe lesions in man. Trends Neurosci. 4: 403–407. 634 Chapter Twenty-Five Box D Brain Size and Intelligence The fact that so much of the brain is occu-pied by the association cortices raises a fundamental question: does more of it provide individuals with greater cogni-tive ability? Humans and other animals obviously vary in their talents and pre-dispositions for a wide range of cognitive behaviors. Does a particular talent imply a greater amount of neural space in the service of that function? Historically, the most popular ap-proach to the issue of brain size and behavior in humans has been to relate the overall size of the brain to a broad index of performance, conventionally measured in humans by “intelligence tests.” This way of studying the relation-ship between brain and behavior has caused considerable trouble. In general terms, the idea that the size of brains from different species reflects intelli-gence represents a simple and apparently valid idea (see figure). The ratio of brain weight to body weight for fish is 1:5000; for reptiles it is about 1:1500; for birds, 1:220; for most mammals, 1:180; and for humans, it is 1:50. If intelligence is defined as the full spectrum of cognitive performance, surely no one would dis-pute that a human is more intelligent than a mouse, or that this difference is explained in part by the 3000-fold differ-ence in the size of the brains of these species. Does it follow, however, that rel-atively small differences in the size of the brain among related species, strains, gen-ders, or individuals—differences that often persist even after correcting for body size—are also a valid measure of cognitive abilities? Certainly no issue in neuroscience has provoked more heated debate than the notion that alleged dif-ferences in brain size among races (or the demonstrable differences in brain size between men and women) reflect differ-ences in performance. The passion attending this controversy has been gen-erated not only by the scientific issues involved, but also by the specters of racism and misogyny. Nineteenth-century enthusiasm for brain size as a simple measure of human performance was championed by some remarkably astute scientists (including Darwin’s cousin Francis Galton and the French neurologist Paul Broca), as well as others whose motives and methods are now suspect (see Gould, 1978, 1981 for a fascinating and authoritative com-mentary). Broca, one of the great neurol-ogists of his day and a gifted observer, not only thought that brain size reflected intelligence, but was of the opinion (as was just about every other nineteenth-century male scientist) that white Euro-pean males had larger and better devel-oped brains than anyone else. Based on what was known about the human brain in the late nineteenth century, it was per-haps reasonable for Broca to consider it, like the liver or the lung, as an organ having a largely homogeneous function. Ironically, it was Broca himself who laid the groundwork for the modern view that the brain is a heterogeneous collec-tion of highly interconnected but func-tionally discrete systems (see Chapter 26). Nonetheless, the simplistic nine-teenth-century approach to brain size and intelligence has persisted in some quarters well beyond its time. There are at least two reasons why measures such as brain weight or cranial capacity are not easily interpretable indices of intelligence, even though small observed differences may be statistically valid. First is the obvious difficulty of defining and accurately measuring intel-ligence , particularly among humans with different educational and cultural backgrounds. Second is the functional diversity and connectional complexity of Rat Weasel Cat Squirrel monkey Macaque monkey Chimp Porpoise Human 3 cm frontal cortex that are selective for particular sequences of eye movements. When these regions of prefrontal cortex are inactivated pharmacologically, monkeys lose the ability to execute sequences of movements from memory. These further observations endorse the notion, first inferred from studies of individuals like Phineas Gage, that the frontal lobe contributes specifically to the cognitive functions that use stored information to plan and guide appro-priate behavior. In short, the existence of planning-specific neurons in the frontal cortex of rhesus monkeys, as well as attention-specific cells in the parietal cortex and recognition-specific cells in the temporal cortex, supports the functions of these cortical areas inferred from clinical evidence in humans. Nonetheless, functional localization, whether inferred by examining human patients or by recording single neurons in monkeys, is an imprecise business. The observa-tions summarized here are only a rudimentary guide to thinking about how complex cognitive information is represented and processed in the brain, and how the relevant brain areas and their constituent neurons contribute to such important but still ill-defined qualities as personality, intelligence (Box D), or other cognitive functions that define what it means to be a human being. Summary The majority of the human cerebral cortex is devoted to tasks that transcend encoding primary sensations or commanding motor actions. Collectively, the association cortices mediate these cognitive functions of the brain—broadly defined as the ability to attend to, identify, and act meaningfully in response The Association Cortices 635 the brain. Imagine assessing the relation-ship between body size and athletic abil-ity, which might be considered the somatic analogue of intelligence. Body weight, or any other global measure of somatic phenotype, would be a woefully inadequate index of athletic ability. Although the evidence would presum-ably indicate that bigger is better in the context of sumo wrestling or basketball, more subtle somatic features would no doubt be correlated with extraordinary ability in Ping-Pong, gymnastics, or fig-ure skating. The diversity of somatic function vis-à-vis athletic ability con-founds the interpretation of any simple measure such as body size. The implications of this analogy for the brain are straightforward. Any pro-gram that seeks to relate brain weight, cranial capacity, or some other measure of overall brain size to individual perfor-mance ignores the reality of the brain’s functional diversity. Thus, quite apart from the political or ethical probity of attempts to measure “intelligence” by brain size, by the yardstick of modern neuroscience (or simple common sense), this approach will inevitably generate more heat than light. A more rational approach to the issue has become feasi-ble in the last few years, which is to relate the size of measurable regions of known function (the primary visual cor-tex, for example) to the corresponding functions (visual performance), as well as to cellular features such as synaptic density and dendritic arborization. These correlations have greater promise for exploring the sensible idea that better performance will always be based on more underlying neural machinery. References BROCA, P. (1861) Sur le volume et la forme du cerveau suivant les individus et suivant les races. Bull. Soc. Anthrop. 2: 139–207, 301–321. GALTON, F. (1883) Inquiries into Human Faculty and Its Development. London: Macmillan. GOULD, S. J. (1978) Morton’s ranking of races by cranial capacity. Science 200: 503–509. GOULD, S. J. (1981) The Mismeasure of Man. New York: W. W. Norton and Company. GROSS, B. R. (1990) The case of Phillipe Rush-ton. Acad. Quest. 3: 35–46. SPITZKA, E. A. (1907) A study of the brains of six eminent scientists and scholars belonging to the American Anthropometric Society, together with a description of the skull of Professor E. D. Cope. Trans. Amer. Phil. Soc. 21: 175–308. WALLER, A. D. (1891) Human Physiology. Lon-don: Longmans, Green. Additional Reading Reviews BEHRMANN, M. (1999) Spatial frames of refer-ence and hemispatial neglect. In The Cognitive Neurosciences, 2nd Ed. M. Gazzaniga (ed.). Cambridge, MA: MIT Press, pp. 651–666. DAMASIO, A. R. (1985) The frontal lobes. In Clinical Neuropsychology, 2nd Ed. K. H. Heil-man and E. Valenstein (eds.). New York: Oxford University Press, pp. 409–460. DAMASIO, A. R., H. DAMASIO AND G. W. VAN HOESEN (1982) Prosopagnosia: Anatomic basis and behavioral mechanisms. Neurology 32: 331–341. DESIMONE, R. (1991) Face-selective cells in the temporal cortex of monkeys. J. Cog. Neurosci. 3: 1–8. FILLEY, C. M. (1995) Neurobehavioral Anatomy. Ch. 8, Right hemisphere syndromes. Boulder: University of Colorado Press, pp. 113–130. GOLDMAN-RAKIC, P. S. (1987) Circuitry of the prefrontal cortex and the regulation of behav-ior by representational memory. In Handbook of Physiology. Section 1, The Nervous System. Vol. 5, Higher Functions of the Brain, Part I. F. Plum (ed.). Bethesda: American Physiological Society, pp. 373–417. HALLIGAN, P. W. AND J. C. MARSHALL (1994) Toward a principled explanation of unilateral neglect. Cog. Neuropsych. 11(2): 167–206. LÁDAVAS, E., A. PETRONIO AND C. UMILTA (1990) The deployment of visual attention in the intact field of hemineglect patients. Cortex 26: 307–317. MACRAE, D. AND E. TROLLE (1956) The defect of function is visual agnosia. Brain 77: 94–110. POSNER, M. I. AND S. E. PETERSEN (1990) The attention system of the human brain. Annu. Rev. Neurosci. 13: 25–42. VALLAR, G. (1998) Spatial hemineglect in humans. Trends Cog. Sci. 2(3): 87–96. Important Original Papers BRAIN, W. R. (1941) Visual disorientation with special reference to lesions of the right cere-bral hemisphere. Brain 64: 224–272. COLBY C. L., J. R. DUHAMEL AND M. E. GOLD-BERG (1996) Visual, presaccadic, and cognitive activation of single neurons in monkey lateral intraparietal area. J. Neurophysiol. 76: 2841– 2852. DESIMONE, R., T. D. ALBRIGHT, C. G. GROSS AND C. BRUCE (1984) Stimulus-selective properties of inferior temporal neurons in the macaque. J. Neurosci. 4: 2051–2062. ETCOFF, N. L., R. FREEMAN AND K. R. CAVE (1991) Can we lose memories of faces? Con-tent specificity and awareness in a prosopag-nosic. J. Cog. Neurosci. 3: 25–41. FUNAHASHI, S., M. V. CHAFEE AND P. S. GOLD-MAN-RAKIC (1993) Prefrontal neuronal activity in rhesus monkeys performing a delayed anti-saccade task. Nature 365: 753–756. FUSTER, J. M. (1973) Unit activity in prefrontal cortex during delayed-response performance: Neuronal correlates of transient memory. J. Neurophysiol. 36: 61–78. GESCHWIND, N. (1965) Disconnexion syn-dromes in animals and man. Parts I and II. Brain 88: 237–294. HARLOW, J. M. (1868) Recovery from the pas-sage of an iron bar through the head. Publica-tions of the Massachusetts Medical Society 2: 327–347. MOUNTCASTLE, V. B., J. C. LYNCH, A. GEOR-GOPOULOUS, H. SAKATA AND C. ACUNA (1975) Posterior parietal association cortex of the monkey: Command function from operations within extrapersonal space. J. Neurophys. 38: 871–908. PLATT, M. L. AND P. W. GLIMCHER (1999) Neural correlates of decision variables in pari-etal cortex. Nature 400: 233–238. TANJI, J. AND K. SHIMA (1994) Role for supple-mentary motor area cells in planning several movements ahead. Nature 371: 413–416. WANG, G., K. TANAKA AND M. TANIFUJI (1996) Optical imaging of functional organization in the monkey inferotemporal cortex. Science 272: 1665–1668. Books BRICKNER, R. M. (1936) The Intellectual Func-tions of the Frontal Lobes. New York: Macmillan. DAMASIO, A. R. (1994) Descartes’ Error: Emo-tion, Reason and the Human Brain. New York: Grosset/Putnam. DEFELIPE, J. AND E. G. JONES (1988) Cajal on the Cerebral Cortex: An Annotated Translation of the Complete Writings. New York: Oxford Univer-sity Press. GAREY, L. J. (1994) Brodmann’s “Localisation in the Cerebral Cortex.” London: Smith-Gordon. (Translation of K. Brodmann’s 1909 book. Leipzig: Verlag von Johann Ambrosius Barth.) GLIMCHER, P. W. (2003) Decisions, Uncertainty, and the Brain: The Science of Neuroeconomics. Cambridge, MA: MIT Press. HEILMAN, H. AND E. VALENSTEIN (1985) Clinical Neuropsychology, 2nd Ed, Chapters 8, 10, and 12. New York: Oxford University Press. KLAWANS, H. L. (1988) Toscanini’s Fumble, and Other Tales of Clinical Neurology. Chicago: Con-temporary Books. KLAWANS, H. L. (1991) Newton’s Madness. New York: Harper Perennial Library. POSNER, M. I. AND M. E. RAICHLE (1994) Images of Mind. New York: Scientific American Library. SACKS, O. (1987) The Man Who Mistook His Wife for a Hat. New York: Harper Perennial Library. SACKS, O. (1995) An Anthropologist on Mars. New York: Alfred A. Knopf. 636 Chapter Twenty-Five to complex external or internal stimuli. Descriptions of patients with cortical lesions, functional brain imaging of normal subjects, and behavioral and electrophysiological studies of non-human primates have established the general purpose of the major association areas. Thus, parietal association cortex is involved in attention and awareness of the body and the stimuli that act on it; temporal association cortex is involved in the recognition and identification of highly processed sensory information; and frontal associa-tion cortex is importantly involved in guiding complex behavior by planning responses to ongoing stimulation (or remembered information), matching such behaviors to the demands of a particular situation. More than any other brain regions, the association areas support the mental processes that make us human. Overview One of the most remarkable cortical functions in humans is the ability to associate arbitrary symbols with specific meanings to express thoughts and emotions to ourselves and others by means of written and spoken language. Indeed, the achievements of human culture rest largely upon this kind of communication, and a person who for one reason or another fails to develop a facility for language as a child is severely incapacitated. Studies of patients with damage to specific cortical regions and normal subjects studied by functional brain imaging indicate that linguistic abilities of humans depend on the integrity of several specialized areas of the association cortices in the temporal and frontal lobes. In the vast majority of people, these primary lan-guage functions are located in the left hemisphere: the linkages between speech sounds and their meanings are mainly represented in the left tempo-ral cortex, and the circuitry for the motor commands that organize the pro-duction of meaningful speech is mainly found in the left frontal cortex. Despite this left-sided predominance for the “lexical” aspects of language, the emotional (affective) content of speech is governed largely by the right hemisphere. Studies of congenitally deaf individuals have shown further that the cortical areas devoted to sign language are the same as those that organize spoken and heard communication. The regions of the brain devoted to language are therefore specialized for symbolic representation and communication, rather than for heard and spoken language as such. Understanding functional localization and hemispheric lateralization of lan-guage is especially important in clinical practice. The loss of language is such a devastating blow that neurologists and neurosurgeons make every effort to identify and preserve those cortical areas involved in its compre-hension and production. The need to map language functions in patients for the purpose of sparing these regions of the brain has provided another rich source of information about the neural organization of this critical human attribute. Language Is Both Localized and Lateralized It has been known for more than a century that two regions in the frontal and temporal association cortices of the left cerebral hemisphere are espe-cially important for normal human language. That language abilities are both localized and lateralized is not surprising; ample evidence of the local-ization and lateralization of other cognitive functions was reviewed in Chapter 25. The unequal representation of language functions in the two cerebral hemispheres provides an especially compelling example of this phenomenon. Chapter 26 637 Language and Speech 638 Chapter Twenty-Six Although the concept of lateralization has already been introduced in describing the unequal functions of the parietal lobes in attention and of the temporal lobes in recognizing different categories of objects, it is in language that this idea has been most thoroughly documented. Because language is so important to human beings, its lateralization has given rise to the misleading idea that one hemisphere in humans is actually “dominant” over the other— namely, the hemisphere in which the major capacity for language resides. The true significance of lateralization for language or any other cognitive ability, however, lies in the efficient subdivision of complex functions between the hemispheres, rather than in any superiority of one hemisphere over the other. Indeed, pop psychological dogmas about cortical redundancy notwithstanding, it is a safe presumption is that every region of the brain is doing something important. A first step in the proper consideration of these issues is recognizing that the cortical representation of language is distinct from the circuitry con-cerned with the motor control of the larynx, pharynx, mouth, and tongue— the structures that produce speech sounds (Box A). Cortical representation is also distinct from, although clearly related to, the circuits underlying the auditory perception of spoken words and the visual perception of written words in the primary auditory and visual cortices, respectively (Figure 26.1). Whereas the neural substrates for language as such depend on these essen-tial motor and sensory functions, the regions of the brain that are specifically devoted to language transcend these more basic elements. The main concern of the areas of cortex that represent language is using of a system of symbols for purposes of communication—spoken and heard, written and read, or, in the case of sign language, gestured and seen. Thus, the essential function of the cortical language areas, and indeed of language, is symbolic representa-tion. Obedience to a set of rules for using these symbols (called grammar), ordering them to generate useful meanings (called syntax), and giving utter-ances the appropriate emotional valence (called prosody), are all important and readily recognized regardless of the particular mode of representation and expression. Given the profound biological and social importance of communication among the members of a species, it is not surprising that other animals com-municate in ways that, while grossly impoverished compared to human lan-guage, nonetheless suggest the sorts of communicative skills and interac-tions from which human language evolved in the brains of our prehominid ancestors (Box B). Aphasias The distinction between language and the related sensory and motor capac-ities on which it depends was first apparent in patients with damage to spe-cific brain regions. Clinical evidence of this sort showed that the ability to move the muscles of the larynx, pharynx, mouth, and tongue can be com-promised without abolishing the ability to use spoken language to commu-nicate (even though a motor deficit may make communication difficult). Similarly, damage to the auditory pathways can impede the ability to hear without interfering with language functions per se (as is obvious in individ-uals who have become partially or wholly deaf later in life). Damage to spe-cific brain regions, however, can compromise essential language functions while leaving the sensory and motor infrastructure of verbal communication intact. These syndromes, collectively referred to as aphasias, diminish or abolish the ability to comprehend and/or to produce language, while sparing Broca's area Primary auditory cortex Primary motor cortex Primary somatic sensory cortex Wernicke's area Primary visual cortex Figure 26.1 Diagram of the major brain areas involved in the comprehen-sion and production of language. The primary sensory, auditory, visual, and motor cortices are indicated to show the relation of Broca’s and Wernicke’s lan-guage areas to these other areas that are necessarily involved in the comprehen-sion and production of speech, albeit in a less specialized way. the ability to perceive the relevant stimuli and to produce intelligible words. Missing in these patients is the capacity to recognize or employ the symbolic value of words, thus depriving such individuals of the linguistic under-standing, grammatical and syntactical organization, and appropriate intona-tion that distinguishes language from nonsense (Box C). The localization of language function to a specific region (and to some degree a hemisphere) of the cerebrum is usually attributed to the French neurologist Paul Broca and the German neurologist Carl Wernicke, who made their seminal observations in the late 1800s. Both Broca and Wernicke examined the brains of individuals who had become aphasic and later died. Based on correlations of the clinical picture and the location of the brain damage, Broca suggested that language abilities were localized in the ventro-posterior region of the frontal lobe (Figures 26.1 and 26.2). More importantly, he observed that the loss of the ability to produce meaningful language— as opposed to the ability to move the mouth and produce words—was usually associated with damage to the left hemisphere. “On parle avec l’hemisphere gauche,” Broca concluded. The preponderance of aphasic syn-dromes associated with damage to the left hemisphere has supported his claim that one speaks with the left hemisphere, a conclusion amply con-firmed by a variety of modern studies using functional imaging (albeit with some important caveats, discussed later in the chapter). Although Broca was basically correct, he failed to grasp the limitations of thinking about language as a unitary function localized in a single cortical region. This issue was better appreciated by Wernicke, who distinguished between patients who had lost the ability to comprehend language and those who could no longer produce language. Wernicke recognized that some aphasic patients do not understand language but retain the ability to produce utterances with reasonable grammatical and emotional content. He concluded that lesions of the posterior and superior temporal lobe on the left side tend to result in a deficit of this sort. In contrast, other patients continue to comprehend language but lack the ability to organize or control the lin-guistic content of their response. Thus, they produce nonsense syllables, transposed words, and utter grammatically incomprehensible phrases. These deficits are associated with damage to the posterior and inferior region of the left frontal lobe, an area that Broca emphasized as an important substrate for language (see Figures 26.1 and 26.2). Language and Speech 639 1 2 3 4 5 6 7 8 9 10 11 17 18 19 20 37 21 22 22 38 39 40 42 43 41 44 45 46 47 Wernicke’s area Broca’s area Figure 26.2 The relationship of the major language areas to the classical cytoarchitectonic map of the cerebral cortex. As discussed in Chapter 25, about 50 histologically distinct regions (cytoarchitectonic areas) have been described in the human cerebral cortex. Whereas primary sensory and motor functions are sometimes coextensive with these areas, more general cognitive functions like attention, identification, and planning typically encompass a number of different cytoarchitectonic areas in one or more cortical lobes. The language functions described by Broca and Wernicke are associated with at least three of the cytoarchitectonic areas defined by Brodmann (area 22, at the junction of the parietal and temporal lobes [Wernicke’s area]; and areas 44 and 45, in the ventral and posterior region of the frontal lobe [Broca’s area]), and are not coextensive with any of them. 640 Chapter Twenty-Six As a consequence of these early observations, two rules about the local-ization of language have been taught ever since. The first is that lesions of the left frontal lobe in a region referred to as Broca’s area affect the ability to produce language efficiently. This deficiency is called motor or expressive Box A Speech The organs that produce speech include the lungs, which serve as a reservoir of air; the larynx, which is the source of the periodic stimulus quality of “voiced” sounds; and the pharynx, oral, and nasal cavities and their included structures (e.g., tongue, teeth, and lips), which modify (or filter) the speech sounds that eventually emanate from the speaker. The fundamentally correct idea that the larynx is the “source” of speech sounds and the rest of the vocal tract acts as a fil-ter that modulates the sound energy of the source is an old one, having been proposed by Johannes Mueller in the nineteenth century. Although the physiological details are complex, the general operation of the vocal apparatus is simple. Air expelled from the lungs accelerates as it passes through a constricted opening between the vocal folds (“vocal cords”) called the glottis, thus decreasing the pressure in the air stream (according Bernoulli’s principle). As a result, the vocal folds come together until the pressure buildup in the lungs forces them open again. The ongoing repetition of this process results in an oscillation of sound wave pressure, the frequency of which is determined primarily by the muscles that control the tension on the vocal cords. The frequen-cies of these oscillations—which are the basis of voiced speech sounds—range from about 100 to about 400 Hz, depend-ing on the gender, size, and age of the speaker. The larynx has many other conse-quential effects on the speech signal that create additional speech sounds. For instance, the vocal folds can open sud-denly to produce what is called a glottal stop (as in the beginning of the exclama-tion “Idiot!”). Alternatively, the vocal folds can hold an intermediate position for the production of consonants such as h, or they can be completely open for “unvoiced” consonants such as s or f (i.e., speech sounds that don’t have the peri-odic quality derived from vocal fold oscillations). In short, the larynx is impor-tant in the production of virtually all vocal sounds. The vocal system can be thought of as a sort of musical instrument capable of extraordinary subtlety and exquisite modulation. As in the sound produced by a musical instrument, however, the primary source of oscillation (e.g., the reed of a clarinet or the vocal folds in speech) is hardly the whole story. The entire pathway between the vocal folds and the lips (and nostrils) is equally criti-cal in determining speech sounds, as is the structure of a musical instrument. The key determinants of the sound that emanates from an instrument are its nat-ural resonances, which shape or filter the sound pressure oscillation. For the vocal tract, the resonances that modulate the air stream generated by the larynx are called formants. The resonance fre-Lips Laryngeal ventricle Thyroid cartilage Esophagus Trachea Tongue Nasal cavity Nasal pharynx Soft palate Oral pharynx Epiglottis Pharynx Larynx False vocal fold Vocal fold aphasia, also known as Broca’s aphasia. (Such aphasias must be specifically distinguished from dysarthria, which is the inability to move the muscles of the face and tongue that mediate speaking.) The deficient motor-planning aspects of expressive aphasias accord with the complex motor functions of Language and Speech 641 quency of the major formant arises from the fact that the approximate length of the vocal tract is 17 cm, which is the quarter wavelength of a 68-cm sound wave; quarter wavelengths determine the resonances of pipes open at one end, which is essentially what the vocal tract is. Since the speed of sound is about 33,500 cm/sec, the lowest resonance fre-quency of an open tube or pipe of this length will be 33,500/68 or about 500 Hz; additional resonant frequencies will occur at the odd harmonics of this major formant (e.g., 1500 Hz, 2500 Hz, etc.). The result of these physical facts about the vocal tract is that any power in the laryn-geal source at these formant frequencies will be reinforced, and any other power will, in varying degrees, be filtered out. Of course, this general statement is con-plicated by the further fact that the shape of the vocal tract changes to produce dif-ferent speech sounds. Thus, in addition to the effects of the larynx, specific speech sounds are generated by dynamic effects imposed by the configuration of the rest of the vocal tract. In any given language, the basic speech sounds are called phonemes. (The sound stimuli as such are referred to as phones.) Phonemes are used to make up syllables, which are used in turn to make up words, which are used to create sentences. There are about 40 phonemes in English, and these are about equally divided between vowel and consonant speech sounds. Vowel sounds are by and large the voiced (peri-odic) elements of speech (i.e., the ele-mental sounds in any language gener-ated by the oscillation of the vocal cords). In contrast, consonant sounds involve rapid changes in the sound sig-nal and are more complex. In English, consonants begin and/or end syllables, each of which entails a vowel sound. Consonant sounds are categorized according to the site in the vocal tract that determines them (the place of articu-lation), or the physical way they are gen-erated (the manner of articulation). With respect to place, there are labial conso-nants (such as p and b), dental conso-nants ( f and v), palatal consonants (sh), and glottal consonants (h) (among many others). With respect to manner, there are plosive, fricative, nasal, liquid, and semi-vowel consonants. Plosives are produced by blocking the flow of air somewhere in the vocal tract, fricatives by producing turbulence, nasals by directing the flow of air through the nose, and so on. A further variation on the use of con-sonants is found in the “click languages” of southern Africa, of which about 30 survive today. Each of these languages has 4–5 different click sounds that are double consonants (the consonant equiv-alent of dipthongs) made by sucking the tongue down from the roof of the mouth. It should be obvious then that speech stimuli are enormously complex (there are more than 200 phonemes in human languages). To make matters worse, Alvin Liberman, working at the Haskins Laboratory at Yale University, showed that there is no one-to-one correspon-dence between phonemes (as defined above) and phones (i.e., the specific acoustic elements in speech). Because speech sounds changes continuously, they cannot be split up into discrete seg-ments, as the concept of phonemes implies. This fact is now recognized as a fundamental problem that undermines any strictly phonemic approach to lan-guage. Moreover, the phones for different vowels (or at least the formants) overlap in natural speech of men, women, and children. Evidence from studies of illiter-ates suggests that phonemes are probably more related to learning how to read and spell than to actually hearing speech, implying that syllables or words are much better candidates for the natural units of speech perception. Given this complexity, it is remark-able that we can communicate so readily. A clue to the obvious success of humans in this task is computer-based speech recognition programs. These programs achieve the very substantial success they currently enjoy by virtue of prolonged empirical training rather than in the a priori application of any logical rules. References BAGLEY, W.C. (1900–1901) The apperception of the spoken sentence: A study in the psy-chology of language. Am. J. Psychol. 12: 80–130. LIBERMAN, A. M. (1996) Speech: A Special Code. Cambridge, MA: MIT Press. LIBERMAN, A. M. AND I. G. MATTINGLY (1985). The motor theory of speech perception revised. Cognition 21: 1–36. MILLER, G. A. (1991) The Science of Words, Chapter 4, “The spoken word.” New York: Scientific American Library. MILLER, G. A. AND J. C. R. LICKLIDER (1950) The intelligibility of interrupted speech. J. Acoust. Soc. Am. 22: 167–173. PLOMP, R. (2002) The Intelligent Ear: On the Nature of Sound Perception. Mahwah, NJ: Erlbaum. WARREN, R. M. (1999) Auditory Perception: A New Analysis and Synthesis, Chapter 7, “Speech.” Cambridge: Cambridge University Press. 642 Chapter Twenty-Six Box B Do Other Animals Have Language? Over the centuries, theologians, natural philosophers, and a good many modern neuroscientists have argued that lan-guage is uniquely human, this extraordi-nary behavior being seen as setting us qualitatively apart from our fellow ani-mals. However, the gradual accumula-tion of evidence during the last 75 years demonstrating highly sophisticated sys-tems of communication in species as diverse as bees, birds, monkeys, and whales has made this point of view increasingly untenable, at least in a broad sense (see Box B in Chapter 23). Until recently, however, human language has appeared unique in the ability to associate specific meanings with arbi-trary symbols, ad infinitum. In the dance of the honeybee described so beautifully by Karl von Frisch, for example, each symbolic movement made by a foraging bee that returns to the hive encodes only a single meaning, whose expression and appreciation has been hardwired into the nervous systems of the actor and the respondents. A series of controversial studies in great apes, however, have indicated that the rudiments of the human symbolic communication are evident in the behav-ior of our closest relatives. Although early efforts were sometimes patently misguided (initial attempts to teach chimpanzees to speak were without merit simply because these animals lack the necessary vocal apparatus), modern work on this issue has shown that if chimpanzees are given the means to communicate symbolically, they demon-strate some surprising talents. While techniques have varied, most psycholo-gists who study chimps have used some form of manipulable symbols that can be arranged to express ideas in an inter-pretable manner. For example, chimps can be trained to manipulate tiles or other symbols (such as the gestures of sign language) to rep-resent words and syntactical constructs, allowing them to communicate simple demands, questions, and even sponta-neous expressions. The most remarkable results have come from increasingly sophisticated work with chimps using keyboards with a variety of symbols (Figure A). With appropriate training, chimps can choose from as many as 400 different symbols to construct expres-sions, allowing the researchers to have something resembling a rudimentary conversation with their charges. The more accomplished of these animals are alleged to have “vocabularies” of several thousand words or phrases, equivalent to a child 3 or 4 years of age (how they use these words compared to a child, however, is much less impressive). Given the challenge this work pre-sents to some long-held beliefs about the uniqueness of human language, it is not surprising that these claims continue to stir up debate and are not universally accepted. Nonetheless, the issues raised certainly deserve careful consideration by anyone interested in human language abilities and how our remarkable sym-bolic skills may have evolved from the communicative capabilities of our ances-tors. The pressure for the evolution of some form of symbolic communication in great apes seems clear enough. Etholo-gists studying chimpanzees in the wild have described extensive social commu-nication based on gestures, the manipu-lation of objects, and facial expressions. This intricate social intercourse is likely to be the antecedent of human language; one need only think of the importance of gestures and facial expressions as ancil-lary aspects of our own speech to appre-ciate this point. (The sign language stud-ies described later in the chapter are also pertinent here.) Whether the regions of the temporal, parietal, and frontal cortices that support human language also serve these sym-Burrito 1 2 3 5 4 1 2 3 5 4 H R U T P JUM Symbols Meanings Car Raisin Ham-burger Sherman Egg Sue's office Groom Log cabin Chow Stick Out-doors Rose Fire TV Rock Yes Orange Bread Hose Hurt Look Get Hug No Milk Hotdog Can opener Water Jump Tree house Burrito Straw Turtle Come Criss-cross Ice Hide Goodbye Midway Pine needle (A) Section of keyboard showing lexical symbols used to study symbolic communication in great apes. (From Savage-Rumbaugh et al., 1998.) the posterior frontal lobe and its proximity to the primary motor cortex already discussed (see Chapters 15 and 25). The second rule is that damage to the left temporal lobe causes difficulty understanding spoken language, a deficiency referred to as sensory or recep-tive aphasia, also known as Wernicke’s aphasia. (Deficits of reading and writing—alexias and agraphias—are separate disorders that can arise from damage to related but different brain areas; most aphasics, however, also have difficulty with these closely linked abilities as well.) Receptive aphasia generally reflects damage to the auditory association cortices in the posterior temporal lobe, a region referred to as Wernicke’s area. A final broad category of language deficiency syndromes is conduction aphasia. These disorders arise from lesions to the pathways connecting the relevant temporal and frontal regions, such as the arcuate fasciculus in the subcortical white matter that links Broca’s and Wernicke’s areas. Interruption of this pathway may result in an inability to produce appropriate responses to heard communication, even though the communication is understood. In a classic Broca’s aphasia, the patient cannot express himself appropri-ately because the organizational aspects of language (its grammar and syn-Language and Speech 643 bolic functions in the brains of great apes (Figure B) is an important question that remains to be tackled. In addition, field studies of vervets and other monkey species have shown that the alarm calls of these animals differ according to the nature of the threat. Thus, ethologists Dorothy Cheney and Robert Seyfarth found that a specific alarm call uttered when a vervet monkey spotted a leopard caused nearby vervets to take to the trees; in contrast, the alarm call given when a monkey saw an eagle caused other monkeys to look skyward. More recent studies of monkey calls by Marc Hauser and his collaborators have greatly extended this sort of work. Although much uncertainty remains, in light of this evidence only someone given to extraordinary anthropocentrism would continue to argue that symbolic communication is a uniquely human attribute. In the end, it may turn out to be that human language, for all its seem-ing complexity, is based on the same general scheme of inherent and acquired neural associations that appears to be the basis of any animal communication. References CERUTTI, D. AND D. RUMBAUGH (1993) Stimu-lus relations in comparative primate perspec-tive. Psychological Record 43: 811–821. GHAZANFAR, A. A. AND M. D. HAUSER (2001) The auditory behavior of primates: a neu-roethological perspective. Curr. Opin. Biol. 16: 712–720. GOODALL, J. (1990) Through a Window: My Thirty Years with the Chimpanzees of Gombe. Boston: Houghton Mifflin Company. GRIFFIN, D. R. (1992) Animal Minds. Chicago: The University of Chicago Press. HAUSER, M .D. (1996) The Evolution of Commu-nication. Cambridge, MA: Bradford/MIT Press. HELTNE, P. G. AND L. A. MARQUARDT (EDS.) (1989) Understanding Chimpanzees. Cam-bridge, MA: Harvard University Press. MILES, H. L. W. AND S. E. HARPER (1994) “Ape language” studies and the study of human language origins. In Hominid Culture in Pri-mate Perspective, D. Quiatt and J. Itani (eds.). Niwot, CO: University Press of Colorado, pp. 253–278. SAVAGE-RUMBAUGH, S., J. MURPHY, R. A. SEV-CIK, K. E. BRAKKE, S. L. WILLIAMS AND D. M. RUMBAUGH (1993) Language Comprehension in Ape and Child. Monographs of the Society for Research in Child Development, Serial No. 233, Vol. 58, Nos. 3, 4. SAVAGE-RUMBAUGH, S., S. G. SHANKER, AND T. J. TAYLOR (1998) Apes, Language, and the Human Mind. New York: Oxford University Press. SEFARTH, R.,M. AND D.,I. CHENEY (1984) The natural vocalizations of non-human pri-mates. Trends Neurosci. 7: 66–73. TERRACE, H. S. (1983) Apes who “talk”: Lan-guage or projection of language by their teachers? In Language in Primates: Perspectives and Implications, J. de Luce and H. T. Wilder (eds.). New York: Springer-Verlag, pp. 19–42. WHITEN, A., J. GOODALL, W. C. MCGREW, T. NISHIDA, V. REYNOLDS, Y. SUGIYAMA, C. E. G. TUTIN, R. W. WRANGHAM AND C. BOESCH (1999) Cultures in chimpanzees. Nature 399: 682–685. VON FRISCH, K. (1993) The Dance Language and Orientation of Bees (Transl. by Leigh E. Chad-wick). Cambridge, MA: Harvard University Press. WALLMAN, J. (1992) Aping Language. New York: Cambridge University Press. (B) The brains of great apes are remarkably simi-lar to those of humans, including regions that, in humans, support language. The areas comparable to Broca’s area and Wer-nicke’s area are indicated. 644 Chapter Twenty-Six tax) have been disrupted, as shown in the following example reported by Howard Gardner (who is the interlocutor). The patient was a 39-year-old Coast Guard radio operator named Ford who had suffered a stroke that affected his left posterior frontal lobe. ‘I am a sig…no…man…uh, well,…again.’ These words were emitted slowly, and with great effort. The sounds were not clearly articulated; each syllable as uttered harshly, explosively, in a throaty voice. With practice, it was possible to understand him, but at first I encountered considerable difficulty in this. ‘Let me help you,’ I interjected. ‘You were a signal…’ ‘A sig-nal man…right,’ Ford completed my phrase triumphantly. ‘Were you in the Coast Guard?’ ‘No, er, yes, yes, …ship…Massachu…chusetts…Coastguard …years.’ He raised his hands twice, indicating the number nineteen. ‘Oh, you were in the Coast Guard for nineteen years.’ ‘Oh…boy…right…right,’ he replied. ‘Why are you in the hospital, Mr. Ford?’ Ford looked at me strangely, as if to say, Isn’t it patently obvious? He pointed to his paralyzed arm and said, ‘Arm no good,’ then to his mouth and said, ‘Speech…can’t say…talk, you see.’ Howard Gardner, 1974. (The Shattered Mind: The Person after Brain Damage, pp. 60–61.) In contrast, the major difficulty in Wernicke’s aphasia is putting together objects or ideas and the words that signify them. Thus, in a Wernicke’s aphasia, speech is fluent and well structured, but makes little or no sense because words and meanings are not correctly linked, as is apparent in the following example (again from Gardner). The patient in this case was a 72-year-old retired butcher who had suffered a stroke affecting his left posterior temporal lobe. Boy, I’m sweating, I’m awful nervous, you know, once in a while I get caught up, I can’t get caught up, I can’t mention the tarripoi, a month ago, quite a lit-tle, I’ve done a lot well, I impose a lot, while, on the other hand, you know what I mean, I have to run around, look it over, trebbin and all that sort of stuff. Oh sure, go ahead, any old think you want. If I could I would. Oh, I’m taking the word the wrong way to say, all of the barbers here whenever they stop you it’s going around and around, if you know what I mean, that is tying and tying for repucer, repuceration, well, we were trying the best that we could while another time it was with the beds over there the same thing… Ibid., p. 68. The major differences between these two classical aphasias are summarized in Table 26.1. Despite the validity of Broca’s and Wernicke’s original observations, the classification of language disorders is considerably more complex. An effort to refine the nineteenth-century categorization of aphasias was undertaken TABLE 26.1 Characteristics of Broca’s and Wernicke’s Aphasias Broca’s aphasiaa Wernicke’s aphasiab Halting speech Fluent speech Tendency to repeat phrases or words Little spontaneous repetition (perseveration) Disordered syntax Syntax adequate Disordered grammar Grammar adequate Disordered structure of Contrived or inappropriate words individual words Comprehension intact Comprehension not intact a Also called motor, expressive, or production aphasia b Also called sensory or receptive aphasia Language and Speech 645 Box C Words and Meaning When Samuel Johnson (Figure A) com-piled his Dictionary of English Language in 1755 under the sponsorship of Oxford University, he defined only 43,500 entries. The current Oxford English Dictio-nary, a lineal descendant of Johnson’s seminal work and most recently revised in the 1980s, contains over 500,000 defini-tions! This quantitative difference is not the result of an increase in the number of English words since the eighteenth cen-tury, but rather is an indication of the dif-ficulty collecting the enormous number of words we use in daily communication; the average college-educated speaker of English is said to have a working vocab-ulary of more than 100,000 words. Using words appropriately is made even more difficult by the fact that word meanings are continually changing, and by the enormous ambiguity of the words we do use. There is far more to a lexi-con—be it a dictionary or a region of the left temporal cortex—than simply attach-ing meanings to words. Even when the meaning of a word is known, it must be understood in a particular context (Fig-ure B) and used according to the rules of grammar and syntax in order to produce effective communication. From the points of view of both neu-roscience and linguistics, two related questions about words and grammar (i.e., the rules for putting words together to form sentences) are especially germane in relation to this chapter. First, what is the nature of the neural machinery that allows us to learn language? And second, why do humans have such a profound drive to learn language? The major twen-tieth-century figure who has grappled with these questions is linguist Noam Chomsky, working at the Massachusetts Institute of Technology. Chomsky, while not interested in brain structure has argued that the complexity of language is such that it cannot simply be learned. He therefore proposed that language must be predicated on a “universal grammar” laid down in the evolution of our species. Although this argument is undoubtedly correct (the basic neural machinery for language, like all aspects of brain cir-cuitry that support adult behavior, is indeed constructed during the normal development of each individual, primar-ily as a result of inheritance; see Chapters 22 and 23), Chomsky’s eschewing of neu-robiology avoids the central question of how, in evolutionary or developmental terms, this machinery comes to be and how it encodes words and strings them together into meaningful sentences. Whatever the mechanisms eventually prove to be, much of the language we use is obviously learned by making neuronal associations between arbitrary symbols and the objects, concepts, and interrela-tionships they signify in the real world. As such, human language provides a rich source for understanding how the rele-vant parts of the human cortex and their constituent neurons work to produce the enormous facility for making associa-tions, which appears to be a fundamental (perhaps the fundamental) aspect of all cortical functions. References CHOMSKY, N. (1975) Reflections on Language. New York: Pantheon/Random House. CHOMSKY, N. (1980) Rules and Representations. New York: Columbia University Press. CHOMSKY, N. (1981) Knowledge of language: Its elements and origins. Philos. Trans. Roy. Soc. Lond. B 295: 223-234. MILLER, G. A. (1991) The Science of Words. New York: Scientific American Library. PINKER, S. (1994) The Language Instinct. New York: W. Morrow and Co. WINCHESTER, S. (2003) The Meaning of Every-thing: The Story of the Oxford English Dictio-nary. Oxford UK: Oxford University Press. (B) The importance of context. When a person says “I’m going to our house on the lake,” the meaning of the expression obviously depends on usage and context, rather than on the literal structure of the sentence uttered. This example indicates the enormous complexity of the task we all accomplish routinely. How this is done, even in principle, remains a central puzzle in language. (From Miller, 1991.) (A) Samuel Johnson 646 Chapter Twenty-Six by the American neurologist Norman Geschwind during the 1950s and early 1960s. Based on clinical and anatomical data from a large number of patients and on the better understanding of cortical connectivity gleaned by that time from animal studies, Geschwind concluded correctly that several other regions of the parietal, temporal, and frontal cortices are critically involved in human linguistic capacities. Basically, he showed that damage to these additional areas results in identifiable, if more subtle, language deficits. His clarification of the definitions of language disorders has been largely con-firmed by functional brain imaging in normal subjects, and remains the basis for much contemporary clinical work on language and aphasias. A Dramatic Confirmation of Language Lateralization Until the 1960s, observations about language localization and lateralization were based primarily on patients with brain lesions of varying severity, loca-tion, and etiology. The inevitable uncertainties of clinical findings allowed skeptics to argue that language function (or other complex cognitive func-tions) might not be lateralized (or even localized) in the brain. Definitive evi-dence supporting the inferences from neurological observations came from studies of patients whose corpus callosum and anterior commissure had been severed as a treatment for medically intractable epileptic seizures. (Recall that a certain fraction of severe epileptics are refractory to medical treatment, and that interrupting the connection between the two hemi-spheres remains an effective way of treating epilepsy in highly selected patients; see Box C in Chapter 24). In such patients, investigators could assess the function of the two cerebral hemispheres independently, since the major axon tracts that connect them had been interrupted. The first studies of these so-called split-brain patients were carried out by Roger Sperry and his colleagues at the California Institute of Technology in the 1960s and 1970s, and established the hemispheric lateralization of language beyond any doubt; this work also demonstrated many other functional differences between the left and right hemispheres (Figure 26.3) and continues to stand as an extraordinary contribution to the understanding of brain organization. Figure 26.3 Confirmation of hemispheric specialization for language obtained by studying individuals in whom the connections between the right and left hemi-spheres have been surgically divided. (A) Single-handed, vision-independent stere-ognosis can be used to evaluate the language capabilities of each hemisphere in split-brain patients. Objects held in the right hand, which provides somatic sensory information to the left hemisphere, are easily named; objects held in the left hand, however, are not readily named by these patients. (B) Visual stimuli or simple instructions can be given independently to the right or left hemisphere in normal and split-brain individuals. Since the left visual field is perceived by the right hemi-sphere (and vice versa; see Chapter 11), a briefly presented (tachistoscopic) instruc-tion in the left visual field is appreciated only by the right brain (assuming that the individual maintains fixation on a mark in the center of the viewing screen). In nor-mal subjects, activation of the right visual cortex leads to hemispheric transfer of visual information via the corpus callosum to the left hemisphere. In split-brain patients, information presented to the left visual field cannot reach the left hemi-sphere, and patients are unable to produce a verbal report regarding the stimuli. However, such patients are able to provide a verbal report of stimuli presented to the right visual field. A wide range of hemispheric functions can be evaluated using this tachistoscopic method, even in normal subjects. The list (above right) enumer-ates some of the different functional abilities of the left and right hemispheres, as deduced from a variety of behavioral tests in split-brain patients. ▲ To evaluate the functional capacity of each hemisphere in split-brain patients, it is essential to provide information to one side of the brain only. Sperry, Michael Gazzaniga (a key collaborator in this work), and others devised several simple ways to do this, the most straightforward of which was to ask the subject to use each hand independently to identify objects without any visual assistance (Figure 26.3A). Recall from Chapter 8 that somatic sensory information from the right hand is processed by the left hemisphere, and vice versa. By asking the subject to describe an item being manipulated by one hand or the other, the language capacity of the relevant hemisphere could be examined. Such testing showed clearly that the two hemispheres differ in their language ability (as expected from the post-mortem correlations described earlier). Language and Speech 647 (B) (A) (C) Right visual field Left visual field Right visual field Left visual field Right visual field Left visual field Normal individual Fixation point Right visual cortex Left visual cortex Broca's area Split-brain individual Split-brain individual Fixation point Right visual cortex Left visual cortex Broca's area Right visual cortex Left visual cortex Broca's area Fixation point Speech Rudimentary speech Spatial abilities Writing Stereognosis (right hand) Left hemisphere functions Right hemisphere functions Analysis of right visual field Analysis of left visual field Stereognosis (left hand) Lexical and syntactic language Emotional coloring of language 648 Chapter Twenty-Six Using the left hemisphere, split-brain patients were able to name objects held in the right hand without difficulty. In contrast, and quite remarkably, an object held in the left hand could not be named! Using the right hemi-sphere, subjects could produce only an indirect description of the object that relied on rudimentary words and phrases rather than the precise lexical symbol for the object (for instance, “a round thing” instead of “a ball”), and some could not provide any verbal account of what they held in their left hand. Observations using special techniques to present visual information to the hemispheres independently (a method called tachistoscopic presentation; Figure 26.3B) showed further that the left hemisphere can respond to written commands, whereas the right hemisphere can typically respond only to non-verbal stimuli (e.g., pictorial instructions, or, in some cases, rudimentary written commands). These distinctions reflect broader hemispheric differ-ences summarized by the statement that the left hemisphere in most humans is specialized for (among other things) the verbal and symbolic pro-cessing important in communication, whereas the right hemisphere is spe-cialized for (among other things) visuospatial and emotional processing (see Figure 26.3). The ingenious work of Sperry and his colleagues on split-brain patients put an end to the century-long controversy about language lateralization; in most individuals, the left hemisphere is unequivocally the seat of the major language functions (although see Box D). It would be wrong to suppose, however, that the right hemisphere has no language capacity. As noted, in some individuals the right hemisphere can produce rudimentary words and phrases, and it is normally the source of emotional coloring of language (see below and Chapter 28). Moreover, the right hemisphere in many split-brain patients understands language to a modest degree, since these patients can respond to simple visual commands presented tachistoscopically in the left visual field. Consequently, Broca’s conclusion that we speak with our left brain is not strictly correct; it would be more accurate to say that we under-stand language and speak very much better with the left hemisphere than with the right, and thus that the contributions of the two hemispheres to the overall goals of communication are different. Anatomical Differences between the Right and Left Hemispheres The differences in language function between the left and right hemispheres have naturally inspired neurologists and neuropsychologists to find a struc-tural correlate of this behavioral lateralization. One hemispheric difference that has received much attention over the years was identified in the late 1960s by Norman Geschwind and his colleagues at Harvard Medical School, who found an asymmetry in the superior aspect of the temporal lobe known as the planum temporale (Figure 26.4). This area was significantly larger on the left side in about two-thirds of human subjects studied postmortem, a difference that has also been found in higher apes, but not in other primates. Because the planum temporale is near (although certainly not congruent with) the regions of the temporal lobe that contain cortical areas essential to language (i.e., Wernicke’s area and other auditory association areas), it was initially suggested that this leftward asymmetry reflected the greater involvement of the left hemisphere in language. Nonetheless, these anatom-ical differences in the two hemispheres of the brain, which are recognizable at birth, are unlikely to be an anatomical correlate of the lateralization of lan-guage functions. The fact that a detectable planum asymmetry is present in only 67% of human brains, whereas the preeminence of language in the left hemisphere is evident in 97% of the population, argues that this association has some other cause. The structural correlate of the functional left–right dif-ferences in hemispheric language abilities, if indeed there is one at a gross anatomical level, is simply not clear, as is the case for the lateralized hemi-spheric functions described in Chapter 25. Mapping Language Functions The pioneering work of Broca and Wernicke, and later Geschwind and Sperry, clearly established differences in hemispheric function. Several tech-niques have since been developed that allow hemispheric attributes to be assessed in neurological patients with an intact corpus callosum, and in nor-mal subjects. One method that has long been used for the clinical assessment of lan-guage lateralization was devised in the 1960s by Juhn Wada at the Montreal Neurological Institute. In the so-called Wada test, a short-acting anesthetic (e.g., sodium amytal) is injected into the left carotid artery; this procedure transiently “anesthetizes” the left hemisphere and thus tests the functional capabilities of the affected half of the brain. If the left hemisphere is indeed “dominant” for language, then the patient becomes transiently aphasic while carrying out an ongoing verbal task like counting. The anesthetic is rapidly diluted by the circulation, but not before its local effects on the hemisphere on the side of the injection can be observed. Since this test is potentially dangerous, its use is limited to neurological and neurosurgical patients. Language and Speech 649 Frontal and parietal lobes removed (A) (C) (B) Planum temporale measurements of 100 adult and 100 infant brains Left hemisphere Right hemisphere Right planum temporale Left planum temporale Right side Left side Infant Adult 20.7 37.0 11.7 18.4 Figure 26.4 Asymmetry of the right and left human temporal lobes. (A) The superior portion of the brain has been removed as indicated to reveal the dorsal surface of the temporal lobes in the right-hand diagram (which presents a dorsal view of the horizontal plane). A region of the surface of the temporal lobe called the planum temporale is signifi-cantly larger in the left hemisphere of most (but far from all) individuals. (B) Measurements of the planum temporale in adult and infant brains. The mean size of the planum temporale is expressed in arbitrary planimetric units to get around the difficulty of measuring the curvature of the gyri within the planum. The asymmetry is evident at birth and per-sists in adults at roughly the same mag-nitude (on average, the left planum is about 50% larger than the right). (C) A magnetic resonance image in the frontal plane, showing this asymmetry (arrows) in a normal adult subject. 650 Chapter Twenty-Six Box D Language and Handedness Approximately 9 out of 10 people are right-handed, a proportion that appears to have been stable over thousands of years and across all cultures in which handedness has been examined. Hand-edness is usually assessed by having individuals answer a series of questions about preferred manual behaviors, such as “Which hand do you use to write?”; “Which hand do you use to throw a ball?”; or “Which hand do you use to brush your teeth?” Each answer is given a value, depending on the preference indicated, providing a quantitative mea-sure of the inclination toward right- or left-handedness. Anthropologists have determined the incidence of handedness in ancient cultures by examining arti-facts; the shape of a flint ax, for example, can indicate whether it was made by a right- or left-handed individual. Hand-edness in antiquity has also been assessed by examining the incidence of figures in artistic representations who are using one hand or the other. Based on this evidence, the human species appears always to have been a right-handed one. Handedness, or its equivalent, is not peculiar to humans; many studies have demonstrated paw preference in animals ranging from mice to monkeys that is, at least in some ways, similar to human handedness. Whether an individual is right- or left-handed has a number of interesting consequences. As will be obvious to left-handers, the world of human artifacts is in many respects a right-handed one (Figure A). Implements such as scissors, knives, coffee pots, and power tools are constructed for the right-handed major-ity. Books and magazines are also designed for right-handers (compare turning this page with your left and right hands), as are golf clubs and guitars. By the same token, the challenge of pen-manship is different for left- and right-handers by virtue of writing from left to right (Figure B). Perhaps as a conse-quence of such biases, the accident rate for left-handers in all categories (work, home, sports) is higher than for right-handers, including the rate of traffic fatalities. However, there are also some advantages to being left-handed. For example, an inordinate number of inter-national fencing champions have been left-handed. The reason for this fact is simply that the majority of any individ-ual’s opponents will be right-handed; therefore, the average fencer, whether right- or left-handed, is less practiced at parrying thrusts from left-handers. Hotly debated in recent years have been the related questions of whether being left-handed is in any sense “patho-logical,” and whether being left-handed entails a diminished life expectancy. No one disputes the fact that there is cur-rently a surprisingly small number of left-handers among the elderly (Figure C). These data have come from studies of the Opens to the left for right- handed filling Right-handed Left-handed Left hand blocked Opening designed for right-handed reach (A) Examples of common objects designed for use by the right-handed majority. Language and Speech 651 general population and have been sup-ported by information gleaned from The Baseball Encyclopedia (in which longevity and other characteristics of a large num-ber of healthy left- and right-handers have been recorded because of interest in the U.S. national pastime). Two explanations of this peculiar finding have been put forward. Stanley Coren and his collaborators at the Uni-versity of British Columbia have argued that these statistics reflect a higher mor-tality rate among left-handers partly as a result of increased accidents, but also because of other data that show left-handedness to be associated with a vari-ety of pathologies (there is, for instance, a higher incidence of left-handedness among individuals classified as mentally retarded). Coren and others have sug-gested that left-handedness may arise because of developmental problems in the pre- and/or perinatal period. If true, then a rationale for decreased longevity would have been identified that might combine with greater proclivity to acci-dents in a right-hander’s world. An alternative explanation, however, is that the diminished number of left-handers among the elderly is primarily a reflection of sociological factors—namely, a greater acceptance of left-handed chil-dren today compared to the first half of the twentieth century. In this view, there are fewer older left-handers now because in earlier generations parents, teachers, and other authority figures encouraged (and sometimes insisted on) right-hand-edness. The weight of the evidence favors the sociological explanation. The relationship between handed-ness and other lateralized functions— language in particular—has long been a source of confusion. It is unlikely that there is any direct relationship between language and handedness, despite much speculation to the contrary. The most straightforward evidence on this point comes from the results of the Wada test described in the text. The large number of such tests carried out for clinical pur-poses indicate that about 97% of humans, including the majority of left-handers, have their major language functions in the left hemisphere (although it should be noted that right hemispheric dominance for language is much more common among left-han-ders). Since most left-handers have lan-guage function on the side of the brain opposite the control of their preferred hand, it is hard to argue for any strict relationship between these two lateral-ized functions. In all likelihood, handed-ness, like language, is first and foremost an example of the advantage of having any specialized function on one side of the brain or the other to make maximum use of the available neural circuitry in a brain of limited size. References BAKAN, P. (1975) Are left-handers brain dam-aged? New Scientist 67: 200–202. COREN, S. (1992) The Left-Hander Syndrome: The Causes and Consequence of Left-Handedness. New York: The Free Press. DAVIDSON, R. J. AND K. HUGDAHL (EDS.) (1995) Brain Asymmetry. Cambridge, MA: MIT Press. SALIVE, M. E., J. M. GURALNIK AND R. J. GLYNN (1993) Left-handedness and mortality. Am. J. Pub. Health 83: 265–267. Right-handed writing Left-handed writing (B) Writing techniques for right- and left-handed individuals. The percentage of left-handers in the normal population as a function of age (based on more than 5000 individuals). Taken at face value, these data indicate that right-handers live longer than left-handers. Another possi-bility, however, is that the paucity of elderly left-handers at present may simply reflect changes over the decades in the social pres-sures on children to become right-handed. (From Coren, 1992.) Age (years) 16 14 12 10 8 6 4 2 0 Percent left-handed 10 20 30 40 50 60 70 80 (C) 652 Chapter Twenty-Six Less invasive (but less definitive) ways to test the cognitive abilities of the two hemispheres in normal subjects include positron emission tomography, functional magnetic resonance imaging (see Box C in Chapter 1), and the sort of tachistoscopic presentation used so effectively by Sperry and his col-leagues (even when the hemispheres are normally connected, subjects show delayed verbal responses and other differences when the right hemisphere receives the instruction). Application of these various techniques, together with noninvasive brain imaging, has amply confirmed the hemispheric lat-eralization of language functions. More importantly, such studies have pro-vided valuable diagnostic tools to determine, in preparation for neuro-surgery, which hemisphere is “eloquent”: although most individuals have the major language functions in the left hemisphere, a few—about 3% of the population—do not (the latter are much more often left-handed; see Box D). Once the appropriate hemisphere is known by these means, neurosur-geons typically map language functions more precisely by electrical stimula-tion of the cortex during the surgery to further refine their approach to the problem at hand. By the 1930s, the neurosurgeon Wilder Penfield and his colleagues at the Montreal Neurological Institute had already carried out a detailed localization of cortical capacities in a large number of patients (see Chapter 8). Penfield used electrical mapping techniques adapted from neuro-physiological work in animals to delineate the language areas of the cortex prior to removing brain tissue in the treatment of tumors or epilepsy. Such intraoperative mapping guaranteed that the cure would not be worse than the disease and has been widely used ever since, with increasingly sophisti-cated stimulation and recording methods. As a result, a wealth of more detailed information about language localization has emerged. Penfield’s observations, together with more recent studies performed by George Ojemann and his group at the University of Washington, have fur-ther advanced the conclusions inferred from postmortem correlations and other approaches. As expected, intraoperative studies using electrophysio-logical recording methods have shown that a large region of the perisylvian cortex of the left hemisphere is clearly involved in language production and comprehension (Figure 26.5). A surprise, however, has been the variability in language localization from patient to patient. Ojemann found that the brain regions involved in language are only approximately those indicated by older textbook treatments, and that their exact locations differ unpredictably among individuals. Equally unexpected, bilingual patients do not necessar-Broca’s area Wernicke’s area 50 37 20 43 29 50 45 23 18 42 36 79 9 27 19 14 26 8 29 36 29 26 19 14 5 2 7 19 21 32 0 0 0 0 0 Central sulcus (A) (B) Lateral sulcus Figure 26.5 Evidence for the variabil-ity of language representation among individuals, determined by electrical stimulation during neurosurgery. (A) Diagram from Penfield’s original study illustrating sites in the left hemisphere at which electrical stimulation interfered with speech. (B) Diagrams summarizing data from 117 patients whose language areas were mapped by electrical record-ing at the time of surgery. The number in each red circle indicates the (quite variable) percentage of patients who showed interference with language in response to stimulation at that site. Note also that many of the sites that elicited interference fall outside the classic lan-guage areas (Broca’s area, shown in pur-ple; Wernicke’s area, shown in blue). (A after Penfield and Roberts, 1959; B after Ojemann et al., 1989.) ily use the same bit of cortex for storing the names of the same objects in two different languages. Moreover, although single neurons in the temporal cor-tex in and around Wernicke’s area respond preferentially to spoken words, they do not show preferences for a particular word. Rather, a wide range of words can elicit a response in any given neuron. Despite these advances, neurosurgical studies are complicated by their intrinsic difficulty and to some extent by the fact that the brains of the patients in whom they are carried out are not normal. The advent of positron emission tomography in the 1980s, and more recently functional magnetic resonance imaging, has allowed the investigation of the language regions in normal subjects by noninvasive brain imaging (Figure 26.6). Recall that these Language and Speech 653 Figure 26.6 Language-related regions of the left hemisphere mapped by positron emission tomography (PET) in a normal human subject. Subjects reclined within the PET scanner and fol-lowed instructions on a special display (these details are not illustrated). The left panels indicate the task being prac-ticed prior to scanning. The PET scan images are shown on the right. Lan-guage tasks such as listening to words and generating word associations elicit activity in Broca’s and Wernicke’s areas, as expected. However, there is also activity in primary and association sen-sory and motor areas for both active and passive language tasks. These observa-tions indicate that language processing involves cortical regions in addition to the classic language areas. (From Posner and Raichle, 1994.) Passively viewing words Listening to words Speaking words Generating word associations “Table” “Table” “Chair” 654 Chapter Twenty-Six Figure 26.7 Different regions in the temporal lobe are activated by different word categories using PET imaging. Dotted lines show location of the rele-vant temporal regions in these horizon-tal views. Note the different patterns of activity in the temporal lobe in response to each stimulus catagory. (After Dama-sio et al., 1996.) techniques reveal the areas of the brain that are active during a particular task because the related electrical activity increases local metabolic activity and therefore local blood flow (see Boxes B and C in Chapter 1). Much like Ojemann’s studies in neurosurgical patients, the results of this approach, particularly in the hands of Marc Raichle, Steve Petersen, and their col-leagues at Washington University in St. Louis, have challenged excessively rigid views of the localization and lateralization of linguistic function. Although high levels of activity occur in the expected regions, large areas of both hemispheres are activated in word recognition or production tasks. Finally, Hanna Damasio and her colleagues at the University of Iowa have shown that distinct regions of the temporal cortex are activated by tasks in which subjects named particular people, animals, or tools (Figure 26.7). This arrangement helps explain the clinical finding that when a relatively limited region of the temporal lobe is damaged (usually by a stroke on the left side), language deficits are sometimes restricted to a particular category of objects. These studies are also consistent with Ojemann’s electrophysiological stud-ies, indicating that language is apparently organized according to categories of meaning rather than individual words. Taken together, such studies are rapidly augmenting the information available about how language is repre-sented in the brain. The Role of the Right Hemisphere in Language Because exactly the same cytoarchitectonic areas exist in the cortex of both hemispheres, a puzzling issue remains. What do the comparable areas in the right hemisphere actually do? In fact, language deficits often do occur fol-lowing damage to the right hemisphere. The most obvious effect of such lesions is an absence of the normal emotional and tonal components of lan-guage—called prosodic elements—that impart additional meaning to verbal communication. This “coloring” of speech is critical to the message con-veyed, and in some languages (e.g., Mandarin Chinese) is even used to change the literal meaning of the word uttered. These deficiencies, referred to as aprosodias, are associated with right-hemisphere damage to the corti-cal regions that correspond to Broca’s and Wernicke’s areas and associated regions in the left hemisphere. The aprosodias emphasize that although the left hemisphere (or, better put, distinct cortical regions within that hemi-sphere) figures prominently in the comprehension and production of lan-guage for most humans, other regions, including areas in the right hemi-sphere, are needed to generate the full richness of everyday speech. People Animals L R L R Tools L R High Level of activity Low Figure 26.8 Signing deficits in congen-itally deaf individuals who had learned sign language from birth and later suf-fered lesions of the language areas in the left hemisphere. Left hemisphere damage produced signing problems in these patients analogous to the aphasias seen after comparable lesions in hearing, speaking patients. In this example, the patient (upper panels) is expressing the sentence “We arrived in Jerusalem and stayed there.” Compared to a normal control (lower panels), he cannot prop-erly control the spatial orientation of the signs. The direction of the correct signs and the aberrant direction of the “aphasic” signs are indicated in the upper left-hand corner of each panel. (After Bellugi et al., 1989.) In summary, whereas the classically defined regions of the left hemi-sphere operate more or less as advertised, a variety of more recent studies have shown that other left- and right-hemisphere areas clearly make a sig-nificant contribution to generation and comprehension of language. Sign Language The implication of at least some aspects of the foregoing account is that the cortical organization of language does not simply reflect specializations for hearing and speaking; the language regions of the brain appear to be more broadly organized for processing symbols pertinent to social communica-tion. Strong support for this conclusion has come from studies of sign lan-guage in individuals deaf from birth. American Sign Language has all the components (e.g., grammar, syntax, and emotional tone) of spoken and heard language. Based on this knowl-edge, Ursula Bellugi and her colleagues at the Salk Institute examined the cortical localization of sign language abilities in patients who had suffered lesions of either the left or right hemisphere. All these deaf individuals never learned language, had been signing throughout their lives, had deaf spouses, were members of the deaf community, and were right-handed. The patients with left-hemisphere lesions, which in each case involved the lan-guage areas of the frontal and/or temporal lobes, had measurable deficits in sign production and comprehension when compared to normal signers of similar age (Figure 26.8). In contrast, the patients with lesions in approxi-Language and Speech 655 Arrive Stay There Patient with signing deficit: Arrive Stay There Correct form: 656 Chapter Twenty-Six mately the same areas in the right hemisphere did not have signing “aphasias.” Instead, as predicted from other hearing patients with similar lesions, right hemisphere abilities such as visuospatial processing, emotional processing and the emotional tone evident in signing were impaired. Although the number of subjects studied was necessarily small (deaf signers with lesions of the language areas are understandably difficult to find), the capacity for signed and seen communication is evidently represented pre-dominantly in the left hemisphere, in the same areas as spoken language. This evidence accords with the idea that the language regions of the brain are specialized for the representation of social communication by means of symbols, rather than for heard and spoken language per se. The capacity for seen and signed communication, like its heard and spo-ken counterpart, emerges in early infancy. Careful observation of babbling in hearing (and, eventually, speaking) infants shows the production of a pre-dictable pattern of sounds related to the ultimate acquisition of spoken lan-guage. Thus, babbling prefigures true language, and indicates that an innate capacity for language imitation is a key part of the process by which a full-blown language is ultimately acquired. The offspring of deaf, signing par-ents “babble” with their hands in gestures that are apparently the forerun-ners of signs (see Figure 23.1). Like verbal babbling, the amount of manual babbling increases with age until the child begins to form accurate, mean-ingful signs. These observations indicate that the strategy for acquiring the rudiments of symbolic communication from parental or other cues—regard-less of the means of expression—is similar. Summary A variety of methods have all been used to understand the organization of language in the human brain. This effort began in the nineteenth century by correlating clinical signs and symptoms with the location of brain lesions determined postmortem. In the twentieth century, additional clinical obser-vations together with studies of split-brain patients, mapping at neuro-surgery, transient anesthesia of a single hemisphere, and noninvasive imag-ing techniques such as PET and ƒMRI have greatly extended knowledge about the neural substrates of language. Together, these various approaches show that the perisylvian cortices of the left hemisphere are especially important for normal language in the vast majority of humans. The right hemisphere also contributes importantly to language, most obviously by giving it emotional tone. The similarity of the deficits after comparable brain lesions in congenitally deaf individuals and their speaking counterparts have shown further that the cortical representation of language is indepen-dent of the means of its expression or perception (spoken and heard, versus gestured and seen). The specialized language areas that have been identified are evidently the major components of a widely distributed set of brain regions that allow humans to communicate effectively by means of symbols that can be attached to objects, concepts and feelings. Additional Reading Reviews BELLUGI, U., H. POIZNER AND E. S. KLIMA (1989) Language, modality, and the brain. Trends Neurosci. 12: 380–388. DAMASIO, A. R. (1992) Aphasia. New Eng. J. Med. 326: 531–539. DAMASIO, A. R. AND H. DAMASIO (1992) Brain and language. Sci. Amer. 267 (Sept.): 89–95. DAMASIO, A. R. AND N. GESCHWIND (1984) The neural basis of language. Annu. Rev. Neu-rosci. 7: 127–147. ETCOFF, N. L. (1986) The neurophysiology of emotional expression. In Advances in Clinical Neuropsychology, Volume 3, G. Goldstein and R. E. Tarter (eds.). New York: Quantum, pp. 127–179. LENNEBERG, E. H. (1967) Language in the con-text of growth and maturation. In Biological Foundations of Language. New York: John Wiley and Sons, pp. 125–395. OJEMANN, G. A. (1983) The intrahemispheric organization of human language, derived with electrical stimulation techniques. Trends Neurosci. 4: 184–189. OJEMANN, G. A. (1991) Cortical organization of language. J. Neurosci. 11: 2281–2287. SPERRY, R. W. (1974) Lateral specialization in the surgically separated hemispheres. In The Neurosciences: Third Study Program, F. O. Schmitt and F. G. Worden (eds.). Cambridge, MA: The MIT Press, pp. 5–19. SPERRY, R. W. (1982) Some effects of discon-necting the cerebral hemispheres. Science 217: 1223–1226. Important Original Papers CREUTZFELDT, O., G. OJEMANN AND E. LETTICH (1989) Neuronal activity in the human tempo-ral lobe. I. Response to Speech. Exp. Brain Res. 77: 451-475. CARAMAZZA, A. AND A. E. HILLIS (1991) Lexical organization of nouns and verbs in the brain. Nature 349: 788-790. DAMASIO, H., T. J. GRABOWSKI, D. TRANEL, R. D. HICHWA AND A. DAMASIO (1996) A neural basis for lexical retrieval. Nature 380: 499-505. EIMAS, P. D., E. R. SIQUELAND, P. JUSCZYK AND J. VIGORITO (1971) Speech perception in infants. Science 171: 303–306. GAZZANIGA, M. S. (1998) The split brain revis-ited. Sci. Amer. 279 (July): 50–55. GAZZANIGA, M. S., R. B. LURY AND G. R. MAN-GUN (1998) Ch. 8, Language and the Brain. In Cognitive Neuroscience: The Biology of the Mind. New York: W. W. Norton and Co., pp. 289–321. GAZZANIGA, M. S. AND R. W. SPERRY (1967) Language after section of the cerebral com-missures. Brain 90: 131–147. GESCHWIND, N. AND W. LEVITSKY (1968) Human brain: Left-right asymmetries in tem-poral speech region. Science 161: 186–187. OJEMANN, G. A. AND H. A. WHITAKER (1978) The bilingual brain. Arch. Neurol. 35: 409–412. PETERSEN, S. E., P. T. FOX, M. I. POSNER, M. MINTUN AND M. E. RAICHLE (1988) Positron emission tomographic studies of the cortical anatomy of single-word processing. Nature 331: 585–589. PETTITO, L. A. AND P. F. MARENTETTE (1991) Babbling in the manual mode: Evidence for the ontogeny of language. Science 251: 1493–1496. WADA, J. A., R. CLARKE AND A. HAMM (1975) Cerebral hemispheric asymmetry in humans: Cortical speech zones in 100 adult and 100 infant brains. Arch. Neurol. 32: 239–246. WESTBURY, C. F., R. J. ZATORRE AND A. C. EVANS (1999) Quantifying variability in the planum temporale: A probability map. Cerebral Cor-tex 9: 392–405. Books GARDNER, H. (1974) The Shattered Mind: The Person After Brain Damage. New York: Vintage. LENNEBERG, E. (1967) The Biological Foundations of Language. New York: Wiley. PINKER, S. (1994) The Language Instinct: How the Mind Creates Language. New York: William Morrow and Company. POSNER, M. I. AND M. E. RAICHLE (1994) Images of Mind. New York: Scientific American Library. Language and Speech 657 Overview Sleep—which is defined behaviorally by the normal suspension of con-sciousness and electrophysiologically by specific brain wave criteria—con-sumes fully a third of our lives. Sleep occurs in all mammals, and probably in all vertebrates. We crave sleep when deprived of it and, to judge from some animal studies, continued sleep deprivation can ultimately be fatal. Surprisingly, however, this peculiar state is not the result of a simple diminu-tion of brain activity; for example, in REM (rapid eye movement) sleep, the brain is about as active as it is when people are awake. Rather, sleep is a series of precisely controlled brain states, the sequence of which is governed by a group of brainstem nuclei that project widely throughout the brain and spinal cord. The reason for such high levels of brain activity during REM sleep, the significance of dreaming, and the basis of the restorative effect of sleep are all topics that remain poorly understood. The clinical importance of sleep is obvious from the prevalence of sleep disorders (insomnias). In any given year about 40 million Americans suffer from chronic sleep disorders, and an additional 30 million experience occasional (at least a few days each month) sleeping problems that are severe enough to interfere with their daily activities. Why Do Humans (and Many Other Animals) Sleep? To feel rested and refreshed upon awakening, most adults require 7–8 hours of sleep, although this number varies among individuals (Figure 27.1A). As a result, a substantial fraction of our lives is spent in this mysterious state. For infants, the requirement is much higher (17 hours a day or more), and teenagers need on average about 9 hours of sleep. As people age, they tend to sleep more lightly and for shorter times at night, although their need for sleep is probably not much less than in early adulthood (Figure 27.1B). Thus, older adults often “make up” for shorter and lighter nightly sleep periods by napping during the day. Getting too little sleep creates a “sleep debt” that must be repaid in the following days. In the meantime, judgment, reaction time, and other functions are in varying degrees impaired. Poor sleep there-fore has a price, sometimes with tragic consequences. In the United States alone, fatigue is estimated to contribute to more than 100,000 highway acci-dents each year, resulting in some 70,000 injuries and 1,500 deaths. Sleep (or at least a physiological period of quiescence) is a highly con-served behavior that occurs in animals ranging from fruit flies to humans (Box A). Despite this prevalence, why we sleep is not well understood. Since an animal is particularly vulnerable while sleeping, there must be evolution-ary advantages that outweigh this considerable disadvantage. Shakespeare Chapter 27 659 Sleep and Wakefulness 660 Chapter Twenty-Seven called sleep “nature’s soft nurse,” emphasizing (as have many others) the restorative nature of sleep. From a perspective of energy conservation, one function of sleep is to replenish brain glycogen levels, which fall during the waking hours. In addition, since it is generally colder at night, more energy would have to be expended to keep warm were we nocturnally active. Body temperature has a 24-hour cycle (as do many other indices of activity and stress), reaching a minimum at night and thus reducing heat loss (Figure 27.2). As might be expected, metabolism measured by oxygen consumption decreases during sleep. Another plaausible reason is that humans and many other animals that sleep at night are highly dependent on visual information to find food and avoid predators. Whatever the reasons for sleeping, in mammals sleep is evidently neces-sary for survival. Sleep-deprived rats lose weight despite increasing food intake and progressively fail to regulate body temperature as their core tem-perature increases several degrees. They also develop infections, suggesting some compromise of the immune system. Rats completely deprived of sleep Conception Birth Age in years Sleep Awake Death Hours in the day −1 0 1 10 20 100 24 16 8 0 Percentage of subjects 0 25 50 75 4.5 6.5 8.5 10.5 Sleep length (hours) (A) (B) Figure 27.1 The duration of sleep. (A) The duration of sleep each night in adults is normally distributed with a mean of 7.5 hours and a standard devia-tion of about 1.25 hours. Thus, each night about two-thirds of the population sleeps between 6.25 and 8.75 hours. (B) The duration of daily sleep as a function of age. (After Hobson, 1989.) Time of day (hours) 0 5 10 15 0 5 10 15 20 36 37 38 Cortisol (ug/100mL) Growth hormone (ng/mL) Tempreature (ºC) 24 18 12 6 24 18 12 6 20 Figure 27.2 Circadian rhythmicity of core body temperature, and of growth hormone and cortisol levels in the blood. In the early evening, core temper-ature begins to decrease whereas growth hormone begins to increase. The level of cortisol, which reflects stress, begins to increase in the morning and stays elevated for several hours. die within a few weeks (Figure 27.3A,B). In humans, lack of sleep leads to impaired memory and reduced cognitive abilities and, if the deprivation per-sists, mood swings and often hallucinations. Patients with the genetic dis-ease fatal familial insomnia—as the name implies—die within several years of onset. This disease, which appears in middle age, is characterized by hallu-cinations, seizures, loss of motor control, and the inability to enter a state of deep sleep (see the section “Stages of Sleep”). Sleep and Wakefulness 661 Box A Styles of Sleep in Different Species A wide variety of animals have a rest–activity cycle that often (but not always) occurs in a daily (circadian) rhythm. Even among mammals, how-ever, the organization of sleep depends very much on the species in question. As a general rule, predatory animals can indulge, as humans do, in long, uninter-rupted periods of sleep that can be noc-turnal or diurnal, depending on the time of day when the animal acquires food, mates, cares for its young, and deals with life’s other necessities. The survival of animals that are preyed upon, how-ever, depends much more critically on continued vigilance. Such species—as diverse as rabbits and giraffes—sleep during short intervals that usually last no more than a few minutes. Shrews, the smallest mammals, hardly sleep at all. An especially remarkable solution to the problem of maintaining vigilance during sleep is shown by dolphins and seals, in whom sleep alternates between the two cerebral hemispheres (see fig-ure). Thus, one hemisphere can exhibit the electroencephalographic signs of wakefulness, while the other shows the characteristics of sleep (see Box C and Figure 27.5). In short, although periods of rest are evidently essential to the proper functioning of the brain, and more generally to normal homeostasis, the manner in which rest is obtained depends on the particular needs of each species. References ALLISON, T. AND D. V. CICCHETTI (1976) Sleep in mammals: Ecological and constitutional correlates. Science 194: 732–734. ALLISON, T. H. AND H. VAN TWYVER (1970) The evolution of sleep. Natural History 79: 56–65. ALLISON, T., H. VAN TWYVER AND W. R. GOFF (1972) Electrophysiological studies of the echidna, Tachyglossus aculeatus. Arch. Ital. Biol. 110: 145–184. Atlantic bottlenose dolphin (Tursiops truncatus) 1 4 2 5 3 6 1 2 3 4 Time (s) 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 Time (s) Time (s) Time (s) Time (s) Time (s) Sleep Awake Some animals can sleep one hemisphere at a time. These EEG tracings were taken simul-taneously from left and right cerebral hemi-spheres of a dolphin. Slow-wave sleep is apparent in the left hemisphere (recording sites 1–3); the right hemisphere, however, shows low-voltage, high-frequency waking activity (sites 4–6). (After Mukhametov, Supin, and Polyakova, 1977.) 662 Chapter Twenty-Seven The longest documented period of voluntary sleeplessness in humans is 453 hours, 40 minutes (approximately 19 days)—a record achieved without any pharmacological stimulation. The young man involved recovered after a few days, during which he slept more than normal, but otherwise seemed none the worse for wear. The Circadian Cycle of Sleep and Wakefulness Human sleep occurs with circadian (circa = about; dia = day) periodicity, and biologists interested in circadian rhythms have explored a number of ques-tions about this daily cycle. What happens, for example, when individuals are prevented from sensing the cues they normally use to distinguish night and day? This question has been addressed by placing volunteers in an environment such as a cave or bunker that lacks external time cues (Figure 27.4). In a typical experiment of this sort, subjects undergo a 5- to 8-day period that included social interactions, meals at normal times, and temporal cues (radio, TV). During this acclimation period, the subjects arose and went to sleep at the usual times and maintained a 24-hour sleep–wake cycle. After removing these normal cues, however, the subjects awakened later each day, and the cycle of sleep and wakefulness gradually lengthened to about 26 hours. When the volunteers returned to a normal environment, the 24-hour cycle was rapidly restored. Thus, humans (and many other animals; see Box B) have an internal “clock” that operates even in the absence of external information about the time of day; under these conditions, the clock is said to be “free-running.” (A) Experimental setup (B) Experimental animals Days of sleep deprivation Food intake 0 7 14 21 28 Experimental rat Control rat Feeder Feeder Motor Gears to rotate cage floor Onset of non-REM sleep in experimental rat triggers floor movement EEG EEG Body weight Death Figure 27.3 The consequences of total sleep deprivation in rats. (A) In this apparatus, an experimental rat is kept awake because the onset of sleep (detected electroencephalographically) triggers movement of the cage floor. The control rat (brown) can thus sleep intermittently, whereas the experimental animal (white) cannot. (B) After two to three weeks of sleep deprivation, the experimental animals begin to lose weight, fail to control their body temperature, and even-tually die. (After Bergmann et al., 1989.) Figure 27.4 Rhythm of waking (blue lines) and sleeping (red lines) of a vol-unteer in an isolation chamber with and without cues about the day–night cycle. Numbers represent the mean ± stan-dard deviation of a complete wake–sleep cycle in each condition. Tri-angles represent times when the rectal temperature was maximum. (After Aschoff, 1965, as reproduced in Schmidt et. al., 1983) Presumably, circadian clocks evolved to maintain appropriate periods of sleep and wakefulness and to control other daily rhythms in spite of the vari-able amount of daylight and darkness in different seasons and at different places on the planet. To synchronize physiological processes with the day-night cycle (called photoentrainment), the biological clock must detect decreases in light levels as night approaches. The receptors that sense these light changes are, not surprisingly, in the outer nuclear layer of the retina, as demonstrated by the fact that removing or covering the eyes abolishes pho-toentrainment. The detectors are not, however, the rods or cones (Figure 27.5A). Rather, these cells lie within the ganglion cell layer of the primate and murine retinas. Unlike rods and cones that are hyperpolarized when acti-vated by light (see Chapter 11), this special class of ganglion cells contains a novel photopigment called melanopsin and are depolarized by light. The function of these unusual photoreceptors is evidently to encode environmen-tal illumination and to set the biological clock. This regulation is achieved via axons running the retinohypothalmic tract (Figure 27.5B), which projects to the suprachiasmatic nucleus (SCN) of the anterior hypothalamus, the site of the circadian control of homeostatic functions. Activation of the SCN evokes responses in neurons whose axons first syn-apse in the paraventricular nucleus of the hypothalamus and descend to the preganglionic sympathetic neurons in intermediolateral zone in the lateral horns of the thoracic spinal cord. As described in Chapter 20, these pregan-Sleep and Wakefulness 663 664 Chapter Twenty-Seven glionic neurons modulate neurons in the superior cervical ganglia whose postganglionic axons project to the pineal gland (pineal means “pinecone-shaped”) in the midline near the dorsal thalamus (Figure 27.5B). The pineal gland synthesizes the sleep-promoting neurohormone melatonin (N-acetyl-5-methoxytryptamine) from tryptophan, and secretes melatonin into the bloodstream where it modulates the brainstem circuits that ultimately gov-(A) (C) Intermediolateral cell column Spinal cord Superior cervical ganglion Hypothalamus Suprachiasmatic nucleus Optic chiasm Paraventricular nucleus Retinal ganglion cell Pineal gland 1 2 3 4 5 6 7 8 9 10 0 Time (min) Membrane potential (mV) Wavelength (nm) Log relative sensitivity 400 500 600 700 0 –2 –4 –6 2 4 6 8 10 12 2 4 6 8 PM AM Time of day 20 0 40 60 80 Melatonin production (pg/mL) (B) Photosensitive RGCs Photosensitive RGCs Green cones Rods Cone Figure 27.5 Photoreceptors responsible for signaling circadian light changes. (A) Functional and structural properties of photosensitive retinal ganglion cells in the rat. Increasing the light intensity produces a burst of action potentials in these cells. The spectral sensitivity of these cells compared to rods and one of the standard cone types is also shown. (B) Schematic summary of targets influ-enced by these photosensitive retinal ganglion cells. Projections to the SCN form the retinohypothalamic tract. (C) The 24-hour cycle of melatonin production. ern the sleep–wake cycle. Melatonin synthesis increases as the light in the environment decreases and reaches a maximum between 2 A.M. and 4:00 A.M. (Figure 27.5C). In the elderly, the pineal gland produces less melatonin, perhaps explaining why older people sleep less at night and are more often afflicted with insomnia. Melatonin has been used to promote sleep in elderly insomniacs and to reduce disruption of the biological clocks that occurs with jet lag, but whether these therapies are really effective remains unclear. Most sleep researchers consider the superior chiasmatic nucleus to be the “master clock.” Evidence for this conclusion is that its removal of the SCN in experimental animals abolishes their circadian rhythm of sleep and waking. Furthermore, when SCN cells are placed in organ culture, they exhibit char-acteristic circadian rhythms (Box B). The SCN also governs other functions that are synchronized with the sleep–wake cycle, including body tempera-ture, hormone secretion (e.g., cortisol), blood pressure, and urine production (see Figure 27.2). In adults, urine production is reduced at night because of the circadian regulation of antidieuretic hormone (ADH or vasopressin) pro-duction. Some children and elderly individuals lack this circadian control (albeit for different reasons), as evidenced by bed-wetting. Stages of Sleep The normal cycle of human sleep and wakefulness implies that, at specific times, various neural systems are being activated while others are being turned off. For centuries—indeed up until the 1950s—most people who thought about sleep considered it a unitary phenomenon whose physiology was essentially passive and whose purpose was simply restorative. In 1953, however, Nathaniel Kleitman and Eugene Aserinksy showed, by means of electroencephalographic (EEG) recordings from normal subjects, that sleep actually comprises different stages that occur in a characteristic sequence. Over the first hour after retiring, humans descend into successive stages of sleep (Figure 27.6). These characteristic stages are defined primarily by electroencephalographic (EEG) criteria (Box C). Initially, during “drowsi-Sleep and Wakefulness 665 Awake Stage I Stage II Stage III Stage IV REM sleep Sleep spindle Stage Time (min) 0 10 20 30 40 50 60 70 Figure 27.6 EEG recordings during the first hour of sleep. The waking state with the eyes open is characterized by high-frequency (15–60 Hz), low-ampli-tude activity (∼30 µV) activity. This pat-tern is called beta activity. Descent into stage I non-REM sleep is characterized by decreasing EEG frequency (4–8 Hz) and increasing amplitude (50–100 µV), called theta waves. Descent into stage II non-REM sleep is characterized by 10–12 Hz oscillations (50–150 µV) called spindles, which occur periodically and last for a few seconds. Stage III non-REM sleep is characterized by slower waves at 2–4 Hz (100–150 µV). Stage IV sleep is defined by slow waves (also called delta waves) at 0.5–2 Hz (100–200 µV). After reaching this level of deep sleep, the sequence reverses and a period of rapid eye movement sleep, or REM sleep, ensues. REM sleep is charac-terized by low-voltage, high-frequency activity similar to the EEG activity of individuals who are awake. (Adapted from Hobson, 1989.) 666 Chapter Twenty-Seven ness,” the frequency spectrum of the electroencephalogram is shifted toward lower values and the amplitude of the cortical waves increases slightly. This drowsy period, called stage I sleep, eventually gives way to light or stage II sleep, which is characterized by a further decrease in the frequency of the EEG waves and an increase in their amplitude, together with intermittent Box B Molecular Mechanisms of Biological Clocks Virtually all plants and animals adjust their physiology and behavior to the 24-hour day–night cycle under the gover-nance of circadian clocks. Molecular bio-logical studies have now indicated much about the genes and proteins that make up the machinery of these clocks, a story that began about 30 years ago. In the early 1970s, Ron Konopka and Seymour Benzer, working at the Califor-nia Institute of Technology, discovered three mutant strains of fruit flies whose circadian rhythms were abnormal. Fur-ther analysis showed the mutants to be alleles of a single locus, which Konopka and Benzer called the period or per gene. In the absence of normal environmental cues (that is, in constant light or dark), wild-type flies have periods of activity geared to a 24-hour cycle; pers mutants have 19 hour rhythms, per1 mutants have 29-hour rhythms, and per0 mutants have no apparent rhythm. About 10 years later, Michael Young at Rockefeller University and Jeffrey Hall and Michael Rosbash at Brandeis Uni-versity independently cloned the first of the three per genes. Cloning a gene does not necessarily reveal its function, how-ever, and so it was in this case. Nonethe-less, the gene product Per, a nuclear pro-tein, is found in many Drosophila cells pertinent to the production of the fly’s circadian rhythms. Moreover, normal flies show a circadian variation in the amount of per mRNA and Per protein, whereas per0 flies, which lack a circadian rhythm, do not show this circadian rhythmicity of gene expression. Diagram illustrating molecular feedback loop that governs circadian clocks. (After Okamura et al., 1999.) CRY−PER2 CRY−PER2 C−B C−B Cry E-boxes Ccg E-boxes Per1, 2, 3 PER1 PER2 CCG CLOCK (C) CRY PER3 E-boxes Bmal1 Clk BMAL1 (B) Nucleus Cytoplasm Light-dependent transcription of Clk and Bmal1 genes B and C proteins are synthesized and associate as dimers C−B dimers bind to E-boxes and act as transcriptional enhancers Synthesis and modification of temporally regulated proteins CRY−PER2 proteins associate as dimers and diffuse into nucleus CRY binds and inhibits C−B PER2 stimulates transcription of Bmal1 and Clk 5 6 7 1 2 3 4 + + − high-frequency spike clusters called sleep spindles. Sleep spindles are peri-odic bursts of activity at about 10–12 Hz that generally last 1–2 seconds and arise as a result of interactions between thalamic and cortical neurons. In stage III sleep, which represents moderate to deep sleep, the number of spindles decreases, whereas the amplitude of the EEG activity increases fur-ther and the frequency continues to fall. In the deepest level of sleep, stage IV sleep, also known as slow-wave sleep, the predominant EEG activity consists of very low frequency (0.5–2 Hz), high-amplitude fluctuations called delta waves, the characteristic slow waves for which this phase of sleep is named. (Note that these can also be thought of as reflecting synchronized electrical activity of cortical neurons.) The entire sequence from drowsiness to deep stage IV sleep usually takes about an hour. These four sleep stages are called non-rapid eye movement (non-REM) sleep, and its most prominent feature is slow-wave (stage IV) sleep. It is more difficult to awaken people from slow-wave sleep, which is therefore considered to be the deepest stage of sleep. Following a period of slow-wave sleep, however, EEG recordings show that the stages of sleep reverse, enter-ing a quite different state called rapid eye movement (REM) sleep. In REM sleep, EEG recordings are remarkably similar to those of the awake state (see Figure 27.6). After about 10 minutes in REM sleep, the brain typically cycles back through the non-REM sleep stages. Slow-wave sleep usually occurs Many of the genes and proteins responsible for circadian rhythms in fruit flies have now been discovered in mam-mals. In mice, the circadian clock arises from the temporally regulated activity of proteins (in capital letters) and genes (in italics), including CRY (cryptochrome), CLOCK (C) (Circadian locomotor output cycles kaput), BMAL1 (B) (brain and mus-cle, ARNT-like), PER1 (Period1), PER2 (Period2), PER3 (Period3), and vasopressin prepropressophysin (VP) (clock-controlled genes; ccg). These genes and their pro-teins give rise to transcription/transla-tion autoregulatory feedback loops with both excitatory and inhibitory compo-nents (see figure). The key points to understanding this system are: (1) that the concentrations of BMAL1 (B) and the three PER proteins cycle in counterpoint; (2) that PER2 is a positive regulator of the Bmal1 loop; and (3) that CRY is a negative regulator of the period and cryptochrome loops. The two positive components of this loop are influenced, albeit indirectly, by light or temperature. At the start of the day, the transcrip-tion of Clk and Bmal1 commencences, and the proteins CLOCK (C) and BMAL1 (B) are synthesized in tandem. When the concentrations of C and B increase sufficiently, they associate as dimers and bind to regulatory DNA sequences (E-boxes) that act as a circa-dian transcriptional enhancers of the genes Cry, Per1, Per2, Per3, and CCG. As a result, the proteins PER1, 2, and 3, CRY, and proteins such as VP are produced. These proteins then diffuse from the nucleus into the cytoplasm, where they are modified. Although the functions of PER1 and PER3 remain to be elucidated, when the cytoplasmic concentrations of PER2 and CRY increase, they associate as CRY–PER2, and diffuse back into the nucleus. Here, PER2 stimulates the syn-thesis of C, and B, and CRY binds to C–B dimers, inhibiting their ability to stimu-late the synthesis of the other genes. The complete time course of these feedback loops is 24 hours. References CASHMORE, A. R. (2003) Cryptochromes: Enabling plants and animals to determin cir-cadian time. Cell 114: 537–543. DUNLAP, J. C. (1993) Genetic analysis of circa-dian clocks. Annu. Rev. Physiol. 55: 683–727. KING, D. P. AND J. S. TAKAHASHI (2000) Molec-ular mechanism of circadian rhythms in mammals. Annu. Rev. Neurosci. 23: 713–742. HARDIN, P. E., J. C. HALL AND M. ROSBASH (1990) Feedback of the Drosophila period gene product on circadian cycling of its messenger RNA levels. Nature 348: 536–540. OKAMURA, H. AND 8 OTHERS (1999) Photic induction of mPer1 and mPer2 in Cry-defi-cient mice lacking a biological clock. Science 286: 2531–2534. REN, D. AND J. D. MILLER (2003) Primary cell culture of suprachiasmiatic nucleus. Brain Res. Bull. 61: 547–553. SHEARMAN , L. P. AND 10 OTHERS (2000) Inter-acting molecular loops in the mammalian cir-cadian clock. Science 288: 1013–1019. TAKAHASHI, J. S. (1992) Circadian clock genes are ticking. Science 258: 238–240. VITATERNA, M. H. AND 9 OTHERS (1994) Muta-genesis and mapping of a mouse gene, clock, essential for circadian behavior. Science 264: 719–725. Sleep and Wakefulness 667 668 Chapter Twenty-Seven Box C Electroencephalography Although electrical activity recorded from the exposed cerebral cortex of a monkey was reported in 1875, it was not until 1929 that Hans Berger, a psychiatrist at the University of Jena, first made scalp recordings of this activity in humans. Since then, the electroencephalogram, or EEG, has received mixed press, touted by some as a unique opportunity to under-stand human thinking and denigrated by others as too complex and poorly re-solved to allow anything more than a superficial glimpse of what the brain is actually doing. The truth lies somewhere in between. Certainly no one disputes that electroencephalography has pro-vided a valuable tool to both researchers and clinicians, particularly in the fields of sleep physiology and epilepsy. The major advantage of electroen-cephalography, which involves the appli-cation of a set of electrodes to standard positions on the scalp (Figure A), is its great simplicity. Its most serious limita-tion is poor spatial resolution, allowing localization of an active site only to within several centimeters. Four basic EEG phenomena have been defined in humans (albeit somewhat arbitrarily). The alpha rhythm is typically recorded in awake subjects with their eyes closed. By definition, the frequency of the alpha rhythm is 8–13 Hz, with an amplitude that is typically 10–50 mV. Lower-ampli-tude beta activity is defined by frequen-cies of 14–60 Hz and is indicative of mental activity and attention. The theta and delta waves, which are characterized by frequencies of 4–7 Hz and less than 4 Hz, respectively, imply drowsiness, sleep, or one of a variety of pathological conditions; these slow waves in normal individuals are the signature of stage IV non-REM sleep. The way these phenom-ena are generated is indicated in Figures B and C. Far and away the most obvious com-ponent of these various oscillations is the alpha rhythm. Its prominence in the occipital region—and its modulation by eye opening and closing—implies that it is somehow linked to visual processing, as was first pointed out in 1935 by the British physiologist E. D. Adrian. In fact, evidence from very large numbers of subjects suggests that at least several dif-ferent regions of the brain have their own characteristic rhythms; for example, within the alpha band (8–13 Hz), one rhythm, the classic alpha rhythm, is asso-ciated with visual cortex, one (the mu rhythm) with the sensory motor cortex around the central sulcus, and yet an-other (the kappa rhythm) with the audi-tory cortex. Inion Sylvian fissure Central sulcus F2 F3 C2 P2 O O1 Fp F7 T3 T5 P3 C Electroencephalographic leads (A) The electroencephalogram represents the voltage recorded between two electrodes applied to the scalp. Typically, pairs of electrodes are placed in 19 standard positions distributed over the head. Letters indicate position (F = frontal, P = parietal, T = temporal, O = occipital, C = central). The recording obtained from each pair of electrodes is somewhat different because each samples the activity of a population of neurons in a different brain region. Sleep and Wakefulness 669 In the 1940s, Edward W. Dempsey and Robert Morrison showed that these EEG rhythms depend in part on activity in the thalamus, since thalamic lesions can reduce or abolish the oscillatory cor-tical discharge (although some oscilla-tory activity remains even after the thala-mus has been inactivated). At about the same time, H. W. Magoun and G. Moruzzi showed that the reticular acti-vating system in the brainstem is also important in modulating EEG activity. For example, activation of the reticular formation changes the cortical alpha rhythm to beta activity, in association with greater behavioral alertness. In the 1960s, Per Andersen and his colleagues in Sweden further advanced these stud-ies by showing that virtually all areas of the cortex participate in these oscillatory rhythms, which reflect a feedback loop between neurons in the thalamus and cortex (see text). The cortical origin of EEG activity has been clarified by animal studies, which have shown that the source of the cur-rent that causes the fluctuating scalp potential is primarily the pyramidal neu-rons and their synaptic connections in the deeper layers of the cortex (Figures B and C). (This conclusion was reached by noting the location of electrical field reversal upon passing an electrode verti-cally through the cortex from surface to white matter.) In general, oscillations come about either because membrane voltage of thalamocortical cells fluctuates spontaneously, or as a result of the recip-rocal interaction of excitatory and inhibitory neurons in circuit loops. The oscillations of the EEG are thought to arise from the latter mechanism. Despite these intriguing observations, the functional significance of these corti-cal rhythms is not known. The purpose of the brain’s remarkable oscillatory activity is a puzzle that has defied elec-troencephalographers and neurobiolo-gists for more than 60 years. Scalp Skull Dura mater Arachnoid Subarachnoid space Pia mater Efferent axons Afferent axons EEG electrode Active synapses (B) An electrode on the scalp measures the activity of a very large number of neurons in the underlying regions of the brain, each of which generates a small electrical field that changes over time. This activity (which is thought to be mostly synaptic) makes the more superficial extracellular space negative with respect to deeper cortical regions. The EEG electrode mea-sures a synchronous signal because many thousands of cells are responding in the same man-ner at more or less the same time. (Adapted from Bear et al., 2001.) Continued on next page 670 Chapter Twenty-Seven again in the second round of this continuing cycling, but generally not dur-ing the rest of the night (see Figure 27.7). On average, four additional peri-ods of REM sleep occur, each having a longer duration. In summary, the typical 8 hours of sleep experienced each night actually comprise several cycles that alternate between non-REM and REM sleep, and the brain is quite active during much of this supposedly dormant, restful time. The amount of daily REM sleep decreases from about 8 hours at birth to 2 hours at 20 years to only about 45 minutes at 70 years of age (see Figure 27.1B). The reasons for this change over the human lifespan are not known. Box C Electroencephalography (continued) References ADRIAN, E. D. AND K. YAMAGIWA (1935) The origin of the Berger rhythm. Brain 58: 323–351. ANDERSEN, P. AND S. A. ANDERSSON (1968) Physiological Basis of the Alpha Rhythm. New York: Appleton-Century-Crofts. CATON, R. (1875) The electrical currents of the brain. Brit. Med. J. 2: 278. DA SILVA, F. H. AND W. S. VAN LEEUWEN (1977) The cortical source of the alpha rhythm. Neu-rosci. Letters 6: 237–241. DEMPSEY, E. W. AND R. S. MORRISON (1943) The electrical activity of a thalamocortical relay system. Amer. J. Physiol. 138: 283–296. NIEDERMEYER, E. AND F. L. DA SILVA (1993) Electroencephalography: Basic Principles, Clini-cal Applications, and Related Fields. Baltimore: Williams & Wilkins. NUÑEZ, P. L. (1981) Electric Fields of the Brain: The Neurophysics of EEG. New York: Oxford University Press. 1 2 3 4 5 6 EEG sum Irregular 1 2 3 4 5 6 EEG sum Synchronized 1 2 3 4 5 6 (C) Generation of the synchronous activity that characterizes deep sleep. In the pyrami-dal cell layer below the EEG electrode, each neuron receives thousands of synaptic inputs. If the inputs are irregular or out of phase, their algebraic sum will have a small amplitude, as occurs in the waking state. If, on the other hand, the neurons at activated at approximately the same time, then the EEG waves will be in phase and the ampli-tude will be much greater, as occurs in the delta waves that characterize stage IV sleep. (Adapted from Bear et al., 2001.) Physiological Changes in Sleep States A variety of additional physiological changes take place during the different stages of sleep (Figure 27.7). Periods of non-REM sleep are characterized by slow, rolling eye movements and by decreases in muscle tone, body move-ments, heart rate, breathing, blood pressure, metabolic rate and temperature. All these parameters reach their lowest values during stage IV sleep. Periods of REM sleep, in contrast, are accompanied by increases in blood pressure, heart rate, and metabolism to levels almost as high as those found in the awake state. REM sleep, as the name implies, is also characterized by rapid, ballistic eye movements, pupillary constriction, paralysis of many large mus-cle groups (although obviously not the diaphragm), and the twitching of the smaller muscles in the fingers, toes, and the middle ear. Spontaneous penile erection also occurs during REM sleep, a fact that is clinically important in determining whether a complaint of impotence has a physiological or psy-chological basis. REM sleep has been observed in all mammals and in at least some birds. Despite the similarity of EEG recordings obtained in REM sleep and in wakefulness, the two conditions are clearly not equivalent brain states. REM sleep is characterized by dreaming, which entails a sort of visual hallucina-tion, often characterized by increased emotion and a lack of self-reflection and volitional control. Since most muscles are inactive during REM sleep, the motor responses to dreams are relatively minor. (Sleepwalking, which is most common in children from ages 4–12, and sleeptalking actually occur during non-REM sleep and are not usually accompanied or motivated by dreams.) The relative physical paralysis during REM sleep arises from increased activity in GABAergic neurons in the pontine reticular formation that project to inhibitory neurons that synapse in turn with lower motor neu-rons in the spinal cord (Figure 27.8). Increased activity of descending inhibitory projections from the pons to the dorsal column nuclei also causes a diminished response to somatic sensory stimuli. Taken together, these observations have led to the aphorism that non-REM sleep is characterized by an inactive brain in an active body, whereas REM sleep is characterized by an active brain in an inactive body. Clearly, however, several sensory and motor systems are sequentially activated and inactivated during the differ-ent stages of sleep. The Possible Functions of REM Sleep and Dreaming Despite this wealth of descriptive information about the stages of sleep and an intense research effort, the functional purposes of the various sleep states remain poorly understood. Whereas most sleep researchers accept the idea that the purpose of non-REM sleep is at least in part restorative, the function of REM sleep remains a matter of considerable controversy. A possible clue about the purposes of REM sleep is the prevalence of dreams during these epochs of the sleep cycle. The time of occurrence of dreams during sleep was determined by waking volunteers during either non-REM or REM sleep and asking them if they were dreaming. Subjects awakened from REM sleep usually recalled elaborate, vivid and emotional dreams; subjects awakened during non-REM sleep reported fewer dreams, which, when they did occur, were more conceptual, less vivid, and less emo-Sleep and Wakefulness 671 672 Chapter Twenty-Seven Figure 27.7 Physiological changes in a volunteer during the various sleep states in a typical 8-hour sleep period. (A) The duration of REM sleep increases from 10 min-utes in the first cycle to up to 50 minutes in the final cycle; note that slow-wave (stage IV) sleep is attained only in the first two cycles. (B) The upper panels show the elec-tro-oculogram (EOG) and the lower panels show changes in various muscular and autonomic functions. Movement of neck muscles was measured using an elec-tromyogram (EMG). Other than the few slow eye movements approaching stage I sleep, all other eye movements evident in the EOG occur in REM sleep. The greatest EMG activity occurs during the onset of sleep and just prior to awakening. The heart rate (beats per minute) and respiration (breaths per minute) slow in non-REM sleep, but increase almost to the waking levels in REM sleep. Finally, penile erection (strain gauge units) occurs only during REM sleep. (After Foulkes and Schmidt, 1983.) EEG stages Heart rate Respiration Penile erection Wake Stage I Stage II Stage III Stage IV 0 0 1 2 3 4 5 6 7 8 10 20 30 14 18 22 26 55 65 75 EOG EMG REM REM REM REM REM REM REM REM REM REM Time (hours) (A) (B) tion-laden. Thus dreaming can also occur during light non-REM sleep, near the onset of sleep and before awakening. Dreams have been studied in a variety of ways, perhaps most notably within the psychoanalytic framework aimed at revealing unconscious thought processes considered to be at the root of neuroses. Sigmund Freud’s The Interpretation of Dreams, published in 1900, speaks eloquently to the com-plex relationship between conscious and unconscious mentation. Specifi-cally, Freud thought that during dreaming the “ego” relaxes its hold on the “id,” or subconscious. For the most part, these ideas are now out of fashion, but to give Freud his due, at the time he made these speculations little was known about neurobiology of the brain in general and sleep in particular. Since Freud’s time, several other explanations of dreams have been pro-posed. One idea is that dreaming releases behaviors less commonly enter-tained in the waking state (e.g., frank aggression). Studies have found that about 60% of dream content is associated with sadness, apprehension, or anger; 20% with happiness or excitement; and (somewhat surprisingly) only 10% with sexual feelings or acts. Another suggestion is that dreaming evolved to dispose of unwanted memories that accumulate during the day. A further plausible idea about the function of dreams is that they help con-solidate learned tasks, perhaps by strengthening synaptic activity associated Pontine reticular formation GABA GABA Glycine Glycine Glu Glu ACh ACh ACh NE 5–HT Skeletal muscle Inhibition of lower motor neurons results in paralysis Inhibition of cells in the dorsal column nuclei results in a diminished response to somatic sensory stimuli DCN Midbrain Medulla Pons DCN Midbrain Pontine reticular formation Thalamus To cortex Ventral horn of spinal cord Figure 27.8 Diagram of the circuitry involved in the decreased sensation and muscle paralysis that occurs during REM sleep. Sleep and Wakefulness 673 674 Chapter Twenty-Seven with recent experiences. This hypothesis is supported by studies of remem-bered spatial location in rodents, and by experiments in humans that show a sleep-dependent improvement in learning. However, some experts, such as Allan Hobson, take the more skeptical view that dream content may be “as much dross as gold, as much cognitive trash as treasure, as much informa-tional noise as a signal of something.” Nevertheless, most people, including most sleep researchers, at least privately give some credence to the signifi-cance of dream content. Adding to this uncertainty about the purposes of REM sleep and dream-ing is the fact that depriving human subjects of REM sleep for as much as two weeks has little or no obvious effect on their behavior. The apparent innocuousness of REM sleep deprivation contrasts markedly with the devas-tating effects of total sleep deprivation mentioned earlier. The implication of these findings is that we can get along without REM sleep but need non-REM sleep in order to survive. In summary, the questions of why we have REM sleep and why we dream basically remain unanswered. Neural Circuits Governing Sleep From the descriptions of the various physiological states that occur during sleep, it is clear that periodic charges in the balance of excitation and inhibi-tion must occur in many neural circuits. What follows is a brief overview of these incompletely understood circuits and the interactions among them that govern sleeping and wakefulness. In 1949, Horace Magoun and Giuseppe Moruzzi provided one of the first clues about the circuits involved in the sleep–wake cycle. They found that electrically stimulating a group of cholinergic neurons near the junction of the pons and midbrain causes a state of wakefulness and arousal. This region of the brainstem was given the name reticular activating system (Fig-ure 27.9A; see also Box A in Chapter 16). Their work implied that wakeful-ness requires special activating circuitry—that is, wakefulness is not just the presence of adequate sensory experience. About the same time, the Swiss physiologist Walter Hess found that stimulating the thalamus in an awake cat with low-frequency pulses produced a slow-wave sleep (Figure 27.9B). These seminal experiments showed that sleep entails a patterned interaction between the thalamus and cortex. The saccade-like eye movements that define REM sleep arise because, in the absence of external visual stimuli, endogenously generated signals from Reticular activating system Thalamus Stimulation Stimulation Awake (A) Sleep (B) Awake Sleep Stimulate Stimulate Figure 27.9 Activation of specific neural circuits triggers sleep and wake-fulness. (A) Electrical stimulation of the cholinergic neurons near the junction of pons and midbrain (the reticular activat-ing system) causes a sleeping cat to awaken. (B) Slow electrical stimulation of the thalamus causes an awake cat to fall asleep. Graphs show EEG recordings before and during stimulation. Sleep and Wakefulness 675 Box D Consciousness As the text explains, the mechanisms of sleep and wakefulness determine mental status at any moment on a continuum that normally ranges from stage IV sleep to high alert. There is, however, another way that “wakefulness” has been consid-ered, namely from the perspective of con-sciousness as such. Although the brain-stem circuits and projections supporting consciousness are beginning to be under-stood, these neurological aspects of consciousness are—not surprisingly— insufficient to satisfy philosophers, theologians, and neuroscientists inter-ested in the broader issues that the phe-nomenon of consciousness raises. The common concern of these diverse groups is the more general basis of self-awareness, in particular whether other animals have this mental property and whether machines could ever be self-aware in the way humans are. With respect to the first of these issues, despite a longstanding debate about conscious-ness in other animals, it would be foolish to assert that humans are alone in pos-sessing this obviously useful biological attribute. However, from a purely logical vantage it is impossible, strictly speaking, to know whether any being other than ourselves is conscious; as philosophers have long pointed out, we must inevitably take the consciousness of others on faith (or on the basis of common sense). Nonetheless, it is reasonable to assume that animals with brains structured much like ours (other primates and, to a consid-erable degree, mammals generally) have in some measure the same ability to be self-aware as we do. The ability to reflect on the past and plan for the future that is made possible by self-awareness is surely an advantage that evolution would have to some degree inculcated in the very sim-ilar brains of higher primates. At what phylogenetic level this assumption about self-awareness falls below the definition of consciousness as we know it in our-selves is, of course, unclear. But a reason-able supposition would be that conscious-ness is present in animals in proportion to the complexity of their brains and behav-iors—particularly those behaviors that are sophisticated enough to benefit from reflecting on past outcomes and future eventualities. The question of whether machines can ever be conscious is a much more contentious issue, but is also subject to common sense informed by some knowledge of how brains work. If one rejects dualism (the Cartesian proposi-tion that consciousness, or “mind,” is an entity beyond the ken of physics, chem-istry, and biology, and not therefore sub-ject to the rules of these disciplines), it follows that a structure could be built by sufficiently wise agents that either mim-icked our own consciousness by being effectively isomorphic with brains, or achieved consciousness using physically different elements (e.g., computer ele-ments) in sufficiently biological ways to allow self-awareness. There are, of course, some caveats (not to mention the objections of those people who find such thinking unacceptable on “moral” grounds). An interesting argu-ment in this respect was put forward by the philosopher John Searle to rebut those who imagine that present-day computers, because their operations in some ways resemble mental processes, can already be considered to have the rudiments of con-sciousness. His famous “Chinese Room” analogy describes a cubicle in which workers are handed English letters that they then translate into Chinese charac-ters. The workers themselves have no knowledge of English or Chinese, but simply a set of rules that enables the char-acters to be efficiently translated. The out-put of the room is sensible statements in Chinese. Yet the workers have no knowl-edge of the meaning of the information they are dealing with or of the room’s larger purpose. Searle uses this image to emphasize that meaningful output from a computer, however sophisticated, cannot provide evidence for consciousness or self-awareness within it. Despite this clever argument deflating simplistic asser-tions that extant machines exhibit a rudi-mentary form of consciousness, Searle does not dispute the notion that nothing in principle stands in the way of con-structing conscious entities. A great deal of literature on the subject notwithstanding, these fascinating ques-tions about consciousness are not readily subject to neurobiological investigation. Although a number of contemporary sci-entists have advocated the idea that neu-robiology will soon reveal the “basis” of consciousness (Nobel Laureates seem especially prone to this sort of pontifica-tion; these include such outspoken indi-viduals as John Eccles, Francis Crick, and Gerald Edelman), such revelations are not likely. A more plausible scenario is that as information grows about the nature of other animals, about comput-ers, and indeed about the brain, the ques-tion “What is consciousness?” may sim-ply fade from center stage in much the same way that the question “What is life?” (which stirred up a similar debate early in the twentieth century) was asked less and less frequently as biologists and others recognized it as an ill-posed prob-lem that admitted no definite answer. References CHURCHLAND, P. M. AND P. S. CHURCHLAND (1990) Could a machine think? Sci. Am. 262 (Jan.): 32–37. CRICK, F. (1995) The Astonishing Hypothesis: The Scientific Search for the Soul. New York: Touchstone. CRICK, F. AND C. KOCH (1998) Consciousness and neuroscience. Cerebral Cortex 8: 97–107. PENROSE, R. (1996) Shadows of the Mind: A Search for the Missing Science of Consciousness. Oxford: Oxford University Press. SEARLE, J. R. (1992) The Rediscovery of the Mind. Cambridge, MA: MIT Press. SEARLE, J. R. (2000) Consciousness. Annu. Rev. Neurosci. 23: 557–578. TONONI, G. AND G. EDELMAN (1998) Con-sciousness and complexity. Science 282: 1846–1851. 676 Chapter Twenty-Seven the pontine reticular formation are transmitted to the motor region of the superior colliculus. As described in Chapter 19, collicular neurons project to the paramedialpontine reticular formation (PPRF) and the rostral intersti-tial nucleus, which coordinates timing and direction of eye movements. REM sleep is also characterized by EEG waves that originate in the pontine reticular formation and propagate through the lateral geniculate nucleus of the thalamus to the occipital cortex. These pontine-geniculo-occipital (PGO) waves provide a useful marker for the beginning of REM sleep; they also indicate yet another neural network by which brainstem nuclei can acti-vate the cortex. Human fMRI and PET (see Box A in Chapter 1) studies have been used to compare brain activity in the awake state and in REM sleep, as well as the phenomenon of consciousness more generally (Box D). Activity in the amyg-dala, parahippocampus, pontine tegmentum, and anterior cingulate cortex all increase in REM sleep, whereas activity in the dorsolateral prefrontal and posterior cingulate cortices decreases (Figure 27.10). The increase in limbic system activity, coupled with a marked decrease in the influence of the frontal cortex during REM sleep, presumably explains some characteristics of dreams (e.g., their emotionality and their often inappropriate social con-tent; see Chapter 25 for the normal role of the frontal cortex in determining behavior that is appropriate to circumstances in the waking state). Dorsolateral prefrontal cortex Amygdala Anterior cingulate cortex Posterior cingulate cortex Pontine tegmentum Parahippocampal gyrus Inactivated during REM sleep Activated during REM sleep Figure 27.10 Diagram showing cortical regions whose activity is increased or decreased during REM sleep. (After Hobson et al., 1989.) Figure 27.11 Important nuclei in regulation of the sleep–wake cycle. (A) A variety of brainstem nuclei using several different neurotransmitters determines mental status on a continuum that ranges from deep sleep to a high level of alertness. These nuclei include: (left) the cholinergic nuclei of the pons–midbrain junction and the raphe nuclei; and (right) the locus coeruleus and the tuberomammillary nuclues. All have widespread ascending and descending connections to other regions (arrows), which explains their numerous effects. Curved arrows along the perimeter of the cortex indicate the innervation of lateral cortical regions not shown in this plane of section. (B) Location of hypothalamic nuclei involved in sleep. (C) Activation of VLPO induces sleep. Orexin-containing neurons project to different nuclei and produce arousal. It is generally agreed that a key component of the reticular activating sys-tem is a group of cholinergic nuclei near the pons–midbrain junction that project to thalamocortical neurons (Figure 27.11). The relevant neurons in the nuclei are characterized by high discharge rates during waking and in REM sleep, and by quiescence during non-REM sleep. When stimulated, these nuclei cause “desynchronization” of the electroencephalogram (that is, a shift of EEG activity from high-amplitude, synchronized waves to lower-Sleep and Wakefulness 677 (B) (C) Pons Medulla Corpus callosum Cerebral cortex To spinal cord (A) Pons Medulla Corpus callosum Cerebral cortex Thalamus Paraventricular nucleus Mammillary body Tuber cinereum Optic chiasm Anterior commissure Fornix Thalamus Hypothalamic sulcus Tubero– mammillary nucleus (TMN) Ventrolateral preoptic nucleus (VLPO) Suprachiasmatic nucleus (SCN) Lateral hypothalamic area (orexin neurons) Thalamus Cholinergic nuclei Raphe nuclei Locus coeruleus Tuberomammillary nucleus of hypothalamus Hypothalamus Orexin neurons VPLO Brainstem nuclei Cholinergic nuclei Raphe nuclei Locus coeruleus Tuberomammillary nucleus To cerebral cortex, basal forebrain 678 Chapter Twenty-Seven amplitude, higher-frequency, desynchronized ones; see Box C). These fea-tures imply that activity of cholinergic neurons in the reticular activating system is a primary cause of wakefulness and REM sleep, and that their rel-ative inactivity is important for producing non-REM sleep. Activity of these neurons is not, however, the only neuronal basis of wakefulness; also involved are the noradrenergic neurons of the locus coeruleus; the serotonergic neurons of the raphe nuclei; and the histamine-containing neurons in the tuberomammillary nucleus (TMN) of the hypo-thalamus (Figure 27.11). The activation of these cholinergic, monoaminergic, and histamine-containing networks together produces the awake state. The locus coeruleus and raphe nuclei are modulated by the TMN neurons located near the tuberal region that synthesize the peptide orexin (also called hypercretin). Orexin promotes waking, and thus may have useful applications in jobs where operators need to stay alert. On the other hand, antihistamines inhibit the histamine-containing TMN network, and thus tend to make people drowsy. The three circuits responsible for the awake state are periodically inhib-ited by neurons in the ventrolateral preoptic nucleus (VLPO) of the hypo-thalamus (see Figure 27.11). Thus, activation of VLPO neurons contributes to the onset of sleep, and lesions of VLPO neurons tend to produce insomnia. These complex interactions and effects are summarized in Table 27.1. Both monoaminergic and cholinergic systems are active during the waking state and suppressed during REM sleep. Thus, decreased activity of the mono-aminergic and cholinergic systems leads to the onset of non-REM sleep. In REM sleep, monoaminergic and serotonin neurotransmitter levels markedly decrease, while cholinergic levels increase to approximately the levels found in the awake state. TABLE 27.1 Summary of the Cellular Mechanisms that Govern Sleep and Wakefulness Activity state Brainstem nuclei Neurotransmitter of the relevant responsible involved brainstem neurons WAKEFULNESS Cholinergic nuclei of Acetylcholine Active pons-midbrain junction Locus coeruleus Norepinephrine Active Raphe nuclei Serotonin Active Tuberomammillary nuclei Orexin Active NON-REM SLEEP Cholinergic nuclei of Acetylcholine Decreased pons-midbrain junction Locus coeruleus Norepinephrine Decreased Raphe nuclei Serotonin Decreased REM SLEEP ON Cholinergic nuclei of Acetylcholine Active (PGO waves) pons-midbrain junction Raphe nuclei Serotonin Inactive REM SLEEP OFF Locus coeruleus Norepinephrine Active With so many systems and transmitters involved in the different phases of sleep, it is not surprising that a wide variety of drugs can influence the sleep cycle (Box E). Thalamocortical Interactions The effects of brainstem nuclei on mental status are achieved by modulating the rhythmicity of interactions between the thalamus and the cortex. Thus, the activity of several ascending systems from the brainstem decreases both the rhythmic bursting of the thalamocortical neurons and the related syn-chronized activity of cortical neurons (hence the diminution and ultimate disappearance of high-voltage, low-frequency slow waves during waking and REM sleep; see Box C). To appreciate how different sleep states reflect modulation of thalamocor-tical activity, it is useful to consider the electrophysiological responses of the relevant neurons. Thalamocortical neurons receive ascending projections from the locus coeruleus (noradregeneric), raphe nuclei (serotonin), reticular activating system (acetylcholine), TMN (histamine) and, as their name implies, project to cortical pyramidal cells. The primary characteristic of thal-amocortical neurons is that they can be in one of two stable electrophysiolog-ical states (Figure 27.12): an intrinsic oscillatory or bursting state, and a ton-ically active or firing state that is generated when the neurons are depolarized as occurs when the reticular activating system generates wake-fulness; (see Figure 27.11). In the tonic firing state, thalamocortical neurons transmit information to the cortex that is correlated with the spike trains encoding peripheral stimuli. In contrast, when thalamocortical neurons are in the oscillatory/bursting mode, the neurons in the thalamus become synchro-Sleep and Wakefulness 679 Sleep Sleep Awake −65 −85 −45 −25 −65 −85 −45 −25 Na+/K+ action potentials Ca2+ spike Brainstem inputs induce waking 1 4 8 12 0 200 400 600 800 1000 16 20 Time (s) Time (s) Membrane potential (mV) Membrane potential (mV) Figure 27.12 Recordings from a thalamocortical neuron, showing the oscillatory mode corresponding to a sleep state, and the tonically active mode corresponding to an awake state. An expanded view of oscillatory phase is shown below. Bursts of action potentials are evoked only when the thalamocortical neuron is hyperpolarized sufficiently to activate low-threshold calcium channels. These bursts account for the spindle activity seen in EEG recordings in stage II sleep (see Figure 27.6 and 27.13). Depolarizing the cell either by injecting current or by stimulating the reticular activating system transforms this oscillatory activity into a toni-cally active mode. (After McCormick and Pape, 1990.) 680 Chapter Twenty-Seven nized with those in the cortex, essentially “disconnecting” the cortex from the outside world. During slow-wave sleep, when EEG recordings show the low-est frequency and the highest amplitude, this disconnection is maximal. The oscillatory state of thalamocortical neurons can be transformed into the tonically active state by activity in the cholinergic or monoaminergic pro-jections from the brainstem nuclei (Figure 27.13). Moreover, the oscillatory state is stabilized by hyperpolarizing the relevant thalamic cells. Such hyper-polarization can occur as a consequence of stimulation by GABAergic neu-rons in the thalamic reticular nucleus. These neurons receive ascending − + + + + Cortical pyramidal cell Reticular cell Cerebral cortex Thalamus Thalamocortical cell (C) (A) (B) 0.5 0 1.0 1.5 2.0 2.5 3.0 Time (s) 2 0 4 6 8 10 12 14 16 Time (s) Membrane potential (mV) Membrane potential (mV) Membrane potential (mV) Reticular cell Thalamocortical cell Cortical pyramidal cell Figure 27.13 Thalamocortical feedback loop and the generation of sleep spin-dles. (A) Diagram showing excitatory (+) and inhibitory (–) connections between thalamocortical cells, pyramidal cells in the cortex, and thalamic retic-ular cells, which provide the basis for sleep spindle generation. Inputs into thalamocotical and thalamic reticular cells are not shown. (B) EEG recordings illustrating sleep spindles (the bottom trace is filtered to accentuate the spin-dles). (C) The responses from individual thalamic reticular cells, thalamocorti-cal cells, and cortical cells during the generation of the middle spindle (boxed in panel B). The bursting behavior of the thalamocortical neurons elicits spikes in cortical cells, which is then evident as spindles in EEG recordings. (After Steriade et al., 1993.) information from the brainstem and descending projections from cortical neurons, and they contact the thalamocortical neurons. When neurons in the reticular nucleus undergo a burst of activity, they cause thalamocortical neu-rons to generate short bursts of action potentials, which in turn generate spindle activity in cortical EEG recordings (indicating a lighter sleep state; see Figures 27.5 and 27.13). In brief, the control of sleep and wakefulness depends on brainstem and hypothalamic modulation of the thalamus and cortex. It is this thalamocorti-cal loop that generates the EEG signature of mental function along the con-tinuum of deep sleep to high alert. The major components of the brainstem modulatory system are the cholinergic nuclei of the pons–midbrain junction; the noradrenergic cells of the locus coeruleus in the pons; the serotonergic raphe nuclei; and GABAergic neurons in the VLPO. All of these nuclei can exert both direct and indirect effects on the overall cortical activity that determines sleep and wakefulness. The relationship among the various sleep–wake states is summarized in the scheme shown in Figure 27.14. Sleep Disorders As noted earlier, an estimated 40% of the U.S. population experiences some kind of sleep disorder during their lifetime. Sleep problems occur more fre-quently with advancing age and are more prevalent in women than in men. These problems range from simply annoying to life-threatening. The most prevalent problems are insomnia, sleep apnea, “restless legs” syndrome, and narcolepsy. Insomnia is the inability to sleep for a sufficient length of time (or deeply enough) to produce refreshment. This all-too-common problem has many Sleep and Wakefulness 681 Activation High Low Waking NREM sleep REM sleep NREM sleep REM sleep Aminergic Modulation Cholinergic Information source External Internal Figure 27.14 Summary scheme of sleep–wake states. In the waking state, activa-tion is high, modulation is aminergic, and the information source is external. In REM sleep, activation is also high, the modulation is cholinergic, and the informa-tion source is internal. The other states can likewise be remembered in terms of this general diagram. (After Hobson, 1989.) 682 Chapter Twenty-Seven causes. Short-term insomnia can arise from stress, jet lag, or simply drinking too much coffee. A frequent cause is altered circadian rhythms associated with working night shifts. These problems can usually be prevented by improving sleep habits, avoiding stimulants like caffeine at night, and in some cases taking sleep-promoting medications. More serious insomnia is associated with psychiatric disorders such as depression (see Chapter 28) that presumably affect the balance between the cholinergic, adrenergic, and serotinergic systems that control the onset and duration of the sleep cycles. Long-term insomnia is a particular problem in the elderly, both because aged individuals are subject to more depression and because they frequently take medications that can affect the relevant neurotransmitter systems. Sleep apnea refers to a pattern of interrupted breathing during sleep that affects about 18 million Americans, most often obese, middle aged males. A person suffering from sleep apnea may wake up dozens or even hundreds of times during the night, with the result that they experience little or no slow-wave sleep and spend less time in REM sleep (Figure 27.15). These individu-Box E Drugs and Sleep It is not surprising that many drugs may affect sleep patterns; the reason is that many neurotransmitters (e.g., acetyl-choline, serotonin, norepinepherine, and histamine) are involved in regulating the various states of sleep (see Table 27.1). A simple but useful way of looking at these effects is that in the waking state, the aminergic system is especially active (see Figure 27.14). During non-REM sleep, aminergic and cholinergic input both decrease, but aminergic activity decreases more, such that cholinergic inputs become dominant. Thus there are two major ways drugs alter the sleep pattern: by changing the relative activity of the inputs in any of the three states, or by changing when the different sleep states will commence. For example, insomnia will ensue if, during the waking state, the aminergic input is increased relative to the cholinergic input; in contrast, hyper-somnia occurs when there is increased cholinergic activity relative to the aminer-gic input. Because of the large number of people who suffer with sleep disorders, numer-ous drugs are available to treat these problems. One class of commonly used drugs is the benzodiapines. As shown in the figure, these drugs increase the time to onset of the deeper stages of sleep. Stimulant drugs that prevent sleep are also commonly used, especially caffeine, which is an adenosine receptor antago-nist (adenosine induces sleep). Wake Stage I/REM Stage II Stage III Stage IV Wake Stage I/REM Stage II Stage III Stage IV Wake Stage I/REM Stage II Slow wave sleep 1 0 2 3 4 5 6 7 8 9 Time (hours) Placebo Benzodiazepines Caffeine Compared to a placebo, benzodiazepines hasten the onset and depth of sleep, whereas caf-feine has the opposite effect. als are continually tired and often suffer from depression that exacerbates the problem. In some high-risk individuals, sleep apnea may even lead to death from respiratory arrest. The underlying problem is that the airway in susceptible individuals collapses during breathing, thus blocking airflow. In normal sleep, breathing slows and muscle tone decreases throughout the body, including the tone of the pharynx. If the output of the brainstem cir-cuitry regulating commands to the chest wall or to pharyngeal muscles is decreased sufficiently, or if the airway is compressed because of obesity, the pharynx tends to collapse as the muscles relax during the normal cycle of breathing. As a result, oxygen levels decrease and CO2 levels rise. The rise in CO2 reflexively causes inspiration, which tends to shift the individual from Stage I sleep to the waking state. A third sleep disorder is restless legs syndrome, a problem that affects about 12 million (mostly elderly) Americans. The characteristic of this syn-drome is unpleasant crawling, prickling, or tingling sensations in one or both legs and feet, and an urge to move them about to obtain relief. These sensations occur when the person lies down or sits for prolonged periods of time. The result is constant leg movement during the day and fragmented sleep at night. The neurobiology of this problem is not understood. In mild cases, a hot bath, massaging the legs, or eliminating caffeine may alleviate the problem. In more severe cases, medications such as benzodiazepines may help. The best-understood sleep disorder is narcolepsy, a chronic disorder that affects about 250,000 people (mostly men) in the United States. It is the sec-ond leading cause of daytime drowsiness, ranking just behind sleep apnea. Individuals with narcolepsy have frequent “REM sleep attacks” during the day, in which they enter REM sleep from wakefulness without going through non-REM sleep. These “sleep attacks” can last from 30 seconds to 30 minutes or more. The onset of sleep in such individuals can be so abrupt that they fall down, with potentially disastrous consequences; this phenom-enon is called cataplexy, referring to a temporary loss of muscle control. Insights into the causes of narcolepsy have come from studies of dogs suffer-Sleep and Wakefulness 683 Wake Stage I Stage II Stage III Stage IV 1 2 3 4 5 6 7 Time (hours) Figure 27.15 Sleep apnea. The sleep pattern of a patient with obstructive sleep apnea. In this condition, patients awake frequently and never descend into stages III or IV sleep. The brief descents below stage I in the record represent short periods of REM sleep. (After Carskadon and Dement, 1989, based on data from G. Nino-Murcia.) 684 Chapter Twenty-Seven ing from a genetic disorder similar to the human disease. In these animals, narcolepsy is caused by a mutation of the orexin-2 receptor gene (Orx2). As already described, orexins are neuropeptides homologous to secretin and are found exclusively in cells in the tuberal region of the hypothalamus, where they project to target nuclei responsible for wakefulness (see Figure 27.11). Evidence from both dogs and mice suggests that the Orx2 mutation causes hyperexcitability of the neurons that generate REM sleep, and/or impair-ment of the circuits that inhibit REM sleep. Clinically, narcoleptics are treated using stimulants such as methylphenidate (Ritalin™), amphetamines, or modafanil (Provigil™) to increase their overall level of arousal. Summary All animals exhibit a restorative cycle of rest following activity, but only mammals divide the period of rest into distinct phases of non-REM and REM sleep. Why humans (and many other animals) need a restorative phase of suspended consciousness accompanied by decreased metabolism and lowered body temperature is not known. Even more mysterious is why the human brain is periodically active during sleep at levels not appreciably dif-ferent from the waking state (that is, the neural activity during REM sleep). Despite the electroencephalographic similarities, the psychological states of wakefulness and REM sleep are obviously different. The highly organized sequence of human sleep states is actively generated by nuclei in the brain-stem, most importantly the cholinergic nuclei of the pons–midbrain junction, the noradrenergic cells of the locus coeruleus, and the serotonergic neurons of the raphe nuclei. The activity of the relevant cell groups controls the degree of mental alertness on a continuum from deep sleep to waking atten-tiveness. These brainstem systems are in turn influenced by a circadian clocks located in the suprachiasmatic nucleus and VLPO of the hypothala-mus. The clock adjusts periods of sleep and wakefulness to appropriate durations during the 24-hour cycle of light and darkness that is fundamental to life on Earth. Additional Reading Reviews COLWELL, C. S. AND S. MICHEL. (2003) Sleep and circadian rhythms: Do sleep centers talk back to the clock? Nature Neurosci. 10:1005–1006. DAVIDSON, A. J. AND M. MENAKER (2003) Birds of a feather clock together—sometimes: Social synchronization of circadian rhythms. Curr. Opin. Neurobiol. 13: 765–769. HOBSON, J. A. (1990) Sleep and dreaming. J. Neurosci. 10: 371–382. HOBSON, J. A., R. STRICKGOLD AND E. F. PACE-SCHOTT (1998) The neuropsychology of REM sleep and dreaming. NeuroReport 9: R1–R14. LU J., M. A. GRECO, P. SHIROMANI AND C. B. SAPER (2000) Effect of lesions of the ventrolat-eral preoptic nucleus on NREM and REM sleep. J. Neurosci. 20: 3830–3842. MCCARLEY, R. W. (1995) Sleep, dreams and states of consciousness. In Neuroscience in Medicine, P. M. Conn (ed.). Philadelphia: J. B. Lippincott, pp. 535–554. MCCORMICK, D. A. (1989) Cholinergic and noradrenergic modulation of thalamocortical processing. Trends Neurosci. 12: 215–220. MCCORMICK, D. A. (1992) Neurotransmitter actions in the thalamus and cerebral cortex. J. Clin. Neurophysiol. 9: 212–223. POSNER, M. I. AND S. DEHAENE (1994) Atten-tional networks. Trends Neurosci. 17: 75–79. PROVENCIO, I. AND 5 OTHERS (2000) A novel human opsin in the inner retina. J. Neurosci. 20: 600–605. SAPER, C. B. AND F. PLUM (1985) Disorders of consciousness. In Handbook of Clinical Neurol-ogy, Volume 1 (45): Clinical Neuropsychology, J. A. M. Frederiks (ed.). Amsterdam: Elsevier Science Publishers, pp. 107–127. SIEGEL, J. M. (2000) Brainstem mechanisms generating REM sleep. In Principles and Prac-tice of Sleep Medicine, 3rd Ed. M. H. Kryger, T. Roth and W. C. Dement (eds.). New York: W. B. Saunders. STERIADE, M. (1992) Basic mechanisms of sleep generation. Neurol. 42: 9–18. STERIADE, M. (1999) Coherent oscillations and short-term plasticity in corticothalamic net-works. TINS 22: 337–345, STERIADE, M., D. A. MCCORMICK AND T. J. SEJNOWSKI (1993) Thalamocortical oscillations in the sleeping and aroused brain. Science 262: 679–685. WILLIE, J. T. AND 13 OTHERS. (2003) Distinct narcolepsy syndromes in orexin receptor-2 and orexin null mice: Molecular genetic dis-section of non-REM and REM sleep regula-tory processes. Neuron 38: 715–730 WILSON, M. A. (2002) Hippocampal memory formation, plasticity, and the role of sleep. Neurobiol. Learn. Mem. 3: 565–569. Important Original Papers ASCHOFF, J. (1965) Circadian rhythms in man. Science 148: 1427–1432. ASERINSKY, E. AND N. KLEITMAN (1953) Regu-larly occurring periods of eye motility, and concomitant phenomena, during sleep. Sci-ence 118: 273–274. COLWELL, C. S. AND S. MICHEL (2003) Sleep and circadian rhythms: Do sleep centers talk back to the clock? Nature Neurosci. 6: 1005–1006. DEMENT, W. C. AND N. KLEITMAN (1957) Cyclic variation in EEG during sleep and their rela-tion to eye movements, body motility and dreaming. Electroenceph. Clin. Neurophysiol. 9: 673–690. MORUZZI, G. AND H. W. MAGOUN (1949). Brain stem reticular formation and activation of the EEG. Electroenceph. Clin. Neurophysiol. 1: 455–473. RIBEIRO, S. AND 7 OTHERS (2004) Long-lasting novelty-induced neuronal reverberation dur-ing slow-wave sleep in multiple forebrain areas. PLoS Biology January 20: E24. ROFFWARG, H. P., J. N. MUZIO AND W. C. DEMENT (1966) Ontogenetic development of the human sleep-dream cycle. Science 152: 604–619. VON SCHANTZ, M. AND S. N. ARCHER (2003) Clocks, genes, and sleep. J. Roy. Soc. Med. 96: 486–489. Books FOULKES, D. (1999) Children’s Dreaming and the Development of Consciousness. Cambridge, MA: Harvard University Press. HOBSON, J. A. (2002) Dreaming. New York: Oxford University Press. HOBSON, J. A. (1989) Sleep. New York: Scien-tific American Library. LAVIE, P. (1996). The Enchanted World of Sleep. (Transl. by A. Barris.) New Haven: Yale Uni-versity Press. Sleep and Wakefulness 685 Overview The subjective feelings and associated physiological states known as emo-tions are essential features of normal human experience. Moreover, some of the most devastating psychiatric problems involve emotional (affective) dis-orders. Although everyday emotions are as varied as happiness, surprise, anger, fear, and sadness, they share some common characteristics. All emo-tions are expressed through both visceral motor changes and stereotyped somatic motor responses, especially movements of the facial muscles. These responses accompany subjective experiences that are not easily described, but which are much the same in all human cultures. Because emotional expression is closely tied to the visceral motor system, it entails the activity of the central brain structures that govern preganglionic autonomic neurons in the brainstem and spinal cord. Historically, the higher order neural cen-ters that coordinate emotional responses have been grouped under the rubric of the limbic system. More recently, however, several brain regions in addition to the classical limbic system have been shown to play a pivotal role in emotional processing, including the amygdala and several cortical areas in the orbital and medial aspects of the frontal lobe. This broader constellation of cortical and subcortical regions encompasses not only the central components of the visceral motor system but also regions in the forebrain and diencephalon that motivate lower motor neuronal pools con-cerned with the somatic expression of emotional behavior. Effectively, the concerted action of these diverse brain regions constitutes an emotional motor system. The same forebrain structures that process emotional signals participate in a variety of complex brain functions, including rational deci-sion making, the interpretation and expression of social behavior, and even moral judgments. Physiological Changes Associated with Emotion The most obvious signs of emotional arousal involve changes in the activity of the visceral motor (autonomic) system (Chapter 20). Thus, increases or decreases in heart rate, cutaneous blood flow (blushing or turning pale), piloerection, sweating, and gastrointestinal motility can all accompany vari-ous emotions. These responses are brought about by changes in activity in the sympathetic, parasympathetic, and enteric components of the visceral motor system, which govern smooth muscle, cardiac muscle, and glands throughout the body. As discussed in Chapter 20, Walter Cannon argued that intense activity of the sympathetic division of the visceral motor system prepares the animal to fully utilize metabolic and other resources in chal-lenging or threatening situations. Conversely, activity of the parasympa-Chapter 28 687 Emotions 688 Chapter Twenty-Eight thetic division (and the enteric division) promotes a building up of meta-bolic reserves. Cannon further suggested that the natural opposition of the expenditure and storage of resources is reflected in a parallel opposition of the emotions associated with these different physiological states. As Cannon pointed out, “The desire for food and drink, the relish of taking them, all the pleasures of the table are naught in the presence of anger or great anxiety.” Activation of the visceral motor system, particularly the sympathetic divi-sion, was long considered an all-or-nothing process. Once effective stimuli engaged the system, it was argued, a widespread discharge of all of its com-ponents ensued. More recent studies have shown that the responses of the autonomic nervous system are actually quite specific, with different patterns of activation characterizing different situations and their associated emo-tional states. Indeed, emotion-specific expressions produced voluntarily can elicit distinct patterns of autonomic activity. For example, if subjects are given muscle-by-muscle instructions that result in facial expressions recog-nizable as anger, disgust, fear, happiness, sadness, or surprise without being told which emotion they are simulating, each pattern of facial muscle activ-ity is accompanied by specific and reproducible differences in visceral motor activity (as measured by indices such as heart rate, skin conductance, and skin temperature). Moreover, autonomic responses are strongest when the facial expressions are judged to most closely resemble actual emotional expression and are often accompanied by the subjective experience of that emotion. One interpretation of these findings is that when voluntary facial expressions are produced, signals in the brain engage not only the motor cortex but also some of the circuits that produce emotional states. Perhaps this relationship helps explain how good actors can be so convincing. Nev-ertheless, we are quite adept at recognizing the difference between a con-trived facial expression and the spontaneous smile that accompanies a pleas-ant emotional state (Box A). This evidence, along with many other observations, indicates that one source of emotion (but certainly not the only source) is sensory drive from muscles and internal organs. This input forms the sensory limb of reflex cir-cuitry that allows rapid physiological changes in response to altered condi-tions. However, physiological responses can also be elicited by complex and idiosyncratic stimuli mediated by the forebrain. For example, an anticipated tryst with a lover, a suspenseful episode in a novel or film, stirring patriotic or religious music, or dishonest accusations can all lead to autonomic activa-tion and strongly felt emotions. The neural activity evoked by such complex stimuli is relayed from the forebrain to visceral and somatic motor nuclei via the hypothalamus and brainstem reticular formation, the major structures that coordinate the expression of emotional behavior (see the next section). In summary, emotion and sensorimotor behavior are inextricably linked. As William James put it more than a century ago: What kind of an emotion of fear would be left if the feeling neither of quick-ened heart-beats nor of shallow breathing, neither of trembling lips nor of weakened limbs, neither of goose-flesh nor of visceral stirrings, were present, it is quite impossible for me to think … I say that for us emotion dissociated from all bodily feeling is inconceivable. William James, 1893 (Psychology: p. 379.) The Integration of Emotional Behavior In 1928, Phillip Bard reported the results of a series of experiments that pointed to the hypothalamus as a critical center for coordination of both the Figure 28.1 Midsagittal view of a cat’s brain, illustrating the regions sufficient for the expression of emotional behav-ior. (A) Transection through the mid-brain, disconnecting the hypothalamus and brainstem, abolishes “sham rage.” (B) The integrated emotional responses associated with “sham rage” survive removal of the cerebral hemispheres as long as the caudal hypothalamus remains intact. (After LeDoux, 1987.) visceral and somatic motor components of emotional behavior (see Box A in Chapter 20). Bard removed both cerebral hemispheres (including the cortex, underlying white matter, and basal ganglia) in a series of cats. When the anesthesia had worn off, the animals behaved as if they were enraged. The angry behavior occurred spontaneously and included the usual autonomic correlates of this emotion: increased blood pressure and heart rate, retraction of the nictitating membranes (the thin connective tissue sheets associated with feline eyelids), dilation of the pupils, and erection of the hairs on the back and tail. The cats also exhibited somatic motor components of anger, such as arching the back, extending the claws, lashing the tail, and snarling. This behavior was called sham rage because it had no obvious target. Bard showed that a complete response occurred as long as the caudal hypothala-mus was intact (Figure 28.1). Sham rage could not be elicited, however, when the brain was transected at the junction of the hypothalamus and mid-brain (although some uncoordinated components of the response were still apparent). Bard suggested that whereas the subjective experience of emotion might depend on an intact cerebral cortex, the expression of coordinated emotional behaviors does not necessarily entail cortical processes. He also emphasized that emotional behaviors are often directed toward self-preser-vation (a point made by Charles Darwin in his classic book on the evolution of emotion), and that the functional importance of emotions in all mammals is consistent with the involvement of phylogenetically older parts of the ner-vous system. Complementary results were reported by Walter Hess, who showed that electrical stimulation of discrete sites in the hypothalamus of awake, freely moving cats could also lead to a rage response, and even to subsequent attack behavior. Moreover, stimulation of other sites in the hypothalamus caused a defensive posture that resembled fear. In 1949, a share of the Nobel Prize in Physiology or Medicine was awarded to Hess “for his discovery of the functional organization of the interbrain [hypothalamus] as a coordina-tor of the activities of the internal organs.” Experiments like those of Bard and Hess led to the important conclusion that the basic circuits for orga-nized behaviors accompanied by emotion are in the diencephalon and the brainstem structures connected to it. Furthermore, their work emphasized that the control of the involuntary motor system is not entirely separable from the control of the voluntary pathways, an important consideration in understanding the motor aspects of emotion, as discussed below. The routes by which the hypothalamus and other forebrain structures influence the visceral and somatic motor systems are complex. The major targets of the hypothalamus lie in the reticular formation, the tangled web of nerve cells and fibers in the core of the brainstem (see Box A in Chapter 16). This structure contains over 100 identifiable cell groups, including some of the nuclei that control the brain states associated with sleep and wakeful-ness described in the previous chapter. Other important circuits in the retic-ular formation control cardiovascular function, respiration, urination, vomit-ing, and swallowing. The reticular neurons receive hypothalamic input from and feed into both somatic and autonomic effector systems in the brainstem and spinal cord. Their activity can therefore produce widespread visceral motor and somatic motor responses, often overriding reflex function and sometimes involving almost every organ in the body (as implied by Can-non’s dictum about the sympathetic preparation of the animal for fight or flight). In addition to the hypothalamus, other sources of descending projections from the forebrain to the brainstem reticular formation contribute to the Emotions 689 Hypothalamus Cerebral cortex Medulla Pons Midbrain (B) “Sham rage” remains Hypothalamus Cerebral cortex Medulla Pons Midbrain (A) No “sham rage” 690 Chapter Twenty-Eight Box A Facial Expressions: Pyramidal and Extrapyramidal Contributions In 1862, the French neurologist and physiologist G.-B. Duchenne de Boulogne published a remarkable trea-tise on facial expressions. His work was the first to systematically examine the contributions of small groups of cranial muscles to the expressions that commu-nicate the richness of human emotion. Duchenne reasoned that “one would be able, like nature herself, to paint the expressive lines of the emotions of the soul on the face of man.” In so doing, he sought to understand how the coordi-nated contractions of groups of muscles express distinct, pan-cultural emotional states. To achieve this goal, he pioneered the use of transcutaneous electrical stim-ulation (then called “faradization” after the British chemist and physicist Michael Faraday) to activate single muscles and small groups of muscles in the face, dor-sal surface of the head, and neck. Duchenne also documented the faces of his subjects with another technological innovation: photography (Figure A). His seminal contribution was the identifica-tion of muscles and muscle groups, such as the obicularis oculi, that cannot be activated by force of the will, but are only “put into play by the sweet emo-tions of the soul.” Duchenne concluded that the emotion-driven contraction of these muscle groups surrounding the eyes, together with the zygomaticus major, convey the genuine experience of happiness, joy and laughter. In recogni-tion of these insights, psychologists sometimes refer to this facial expression as the “Duchenne smile.” In normal individuals, such as the Parisian shoemaker illustrated in Figure A, the difference between a forced smile (produced by voluntary contraction or electrical stimulation of facial muscles) and a spontaneous (emotional) smile testifies to the convergence of descend-ing motor signals from different fore-brain centers onto premotor and motor neurons in the brainstem that control the facial musculature. In contrast to the Duchenne smile, the contrived smile of volition (sometimes called a “pyramidal smile”) is driven by the motor cortex, which communicates with the brainstem and spinal cord via the pyramidal tracts. The Duchenne smile is motivated by accessory motor areas in the prefrontal cortex (see Box B in Chapter 16) and ventral parts of the basal ganglia that access brainstem nuclei via multisynap-tic, “extrapyramidal” pathways through the brainstem reticular formation. Studies of patients with specific neurological injury to these separate descending systems of control have fur-ther differentiated the forebrain centers responsible for control of the muscles of facial expression (Figure B). Patients with unilateral facial paralysis due to damage of descending pathways from the motor cortex (upper motor neuron syndrome; see Chapter 16) have considerable diffi-culty moving their lower facial muscles on one side, either voluntarily or in response to commands, a condition called voluntary facial paresis (Figure B, left panels). Nonetheless, many such (1) (A) (2) (3) (4) (A) Duchenne and one of his subjects undergoing “faradization” of the muscles of facial expression (1). Bilateral electrical stimulation of the zygomaticus major mimicked a genuine expression of happiness (2), although closer examination shows insufficient contraction of the obicularis oculi (surrounding the eyes) compared to spontaneous laughter (3). Stimulation of the brow and neck produced an expression of “terror mixed with pain, torture … that of the damned” (4); however, the subject reported no discomfort or emotional experience consistent with the evoked contractions. Emotions 691 individuals produce symmetrical invol-untary facial movements when they laugh, frown, or cry in response to amus-ing or distressing stimuli. In such patients, pathways from regions of the forebrain other than the classical motor cortex in the posterior frontal lobe remain available to activate facial move-ments in response to stimuli with emo-tional significance. A much less common form of neuro-logical injury, called emotional facial paresis, demonstrates the opposite set of impairments, i.e., loss of the ability to express emotions by using the muscles of the face without loss of volitional control (Figure B, right panels). Such individuals are able to produce symmetrical pyrami-dal smiles, but fail to display sponta-neous emotional expressions involving the facial musculature contralateral to the lesion. These two systems are dia-grammed in Figure C. References DUCHENNE DE BOULOGNE, G.-B. (1862) Mecan-isme de la Physionomie Humaine. Paris: Edi-tions de la Maison des Sciences de l’Homme. Edited and translated by R. A. Cuthbertson (1990). Cambridge: Cambridge University Press. HOPF, H. C., W. MÜLLER-FORELL AND N. J. HOPF (1992) Localization of emotional and volitional facial paresis. Neurol. 42:1918–1923. TROSCH, R. M., G. SZE, L. M. BRASS AND S. G. WAXMAN (1990) Emotional facial paresis with striatocapsular infarction. J. Neurol. Sci. 98:195–201. WAXMAN, S. G. (1996) Clinical observations on the emotional motor system. In Progress in Brain Research, Vol. 107. G. Holstege, R. Ban-dler and C. B. Saper (eds.). Amsterdam: Else-vier, pp. 595–604. Facial motor paresis Emotional motor paresis Voluntary smile Response to humor (B) (C) The complementary deficits demonstrated in Figure B are explained by selective lesions of one of two anatomically and functionally distinct sets of descending projections that motivate the muscles of facial expression. (C) VOLITIONAL MOVEMENT Descending “pyramidal” and “extrapyramidal” projections from motor cortex and brainstem NEURAL SYSTEMS FOR EMOTIONAL EXPRESSION Descending “extrapyramidal” projections from medial forebrain and hypothalamus Motor neuron pools in facial nucleus Activation of facial muscles Pyramidal smile Duchenne smile Emotional facial paresis Voluntary facial paresis (B) Left panels: Mouth of a patient with a lesion that destroyed descending fibers from the right motor cortex displaying voluntary facial paresis. When asked to show her teeth, the patient was unable to contract the muscles on the left side of her mouth (upper left), yet her spontaneous smile in response to a humorous remark is nearly symmetrical (lower left). Right panels: Face of a child with a lesion of the left forebrain that interrupted descending pathways from nonclassical motor cortical areas, producing emotional facial paresis. When asked to smile volitionally, the contractions of the facial muscles are nearly symmetrical (upper right). In spontaneous response to a humorous comment, however, the right side of the patient’s face fails to express emotion (lower right). 692 Chapter Twenty-Eight expression of emotional behavior. Collectively, these additional centers in the forebrain are considered part of the limbic system, which is described in the following section. These descending influences on the expression of somatic and visceral motor behavior arise outside of the classic motor cortical areas in the posterior frontal lobe. NEURAL SYSTEMS FOR EMOTION Somatic motor system (Chapters 16–20) Visceral motor system (Chapter 21) Volitional Non-volitional Non-volitional (A) (B) VOLITIONAL MOVEMENT Descending “pyramidal” and “extrapyramidal” projections from motor cortex and brainstem EMOTIONAL EXPRESSION Descending “extrapyramidal” projections from “limbic” centers of ventral-medial forebrain and hypothalamus Lateral Fine control of distal extremities Medial Posture, proximal extremities Medial Gain setting, rhythmical reflexes Specific emotional behaviors Lateral Brainstem reticular formation MOTOR NEURON POOLS Motor neurons of cranial nerve nuclei and ventral horn Autonomic preganglionic neurons Muscle contraction and movement Activation of smooth muscle and glands Thus, the descending control of emotional expression entails two parallel systems that are anatomically and functionally distinct (Figure 28.2). The voluntary motor component described in detail in Chapters 15 through 20 comprises the classical motor areas of the posterior frontal lobe and related circuitry in the basal ganglia and cerebellum. The descending pyramidal and extrapyramidal projections from the motor cortex and brainstem ultimately convey the impulses responsible for voluntary somatic movements. In addi-tion to the descending systems that govern volitional movements, several cortical and subcortical structures in the medial frontal lobe and ventral parts of the forebrain, including related circuitry in the ventral part of the basal ganglia and hypothalamus, give rise to separate descending projec-tions that run parallel to the pathways of the volitional motor system. These descending projections of the medial and ventral forebrain terminate on vis-ceral motor centers in the brainstem reticular formation, preganglionic auto-nomic neurons, and certain somatic premotor and motor neuron pools that also receive projections from volitional motor centers. The two types of facial paresis illustrated in Box A underscore this dual nature of descending motor control. In short, the somatic and visceral activities associated with unified emo-tional behavior are mediated by the activity of both the somatic and visceral motor neurons, which integrate parallel, descending inputs from a constella-tion of forebrain sources. The remaining sections of the chapter are devoted to the organization and function of the forebrain centers that specifically govern the experience and expression of emotional behavior. The Limbic System Attempts to understand the effector systems that control emotional behavior have a long history. In 1937, James Papez (pronouced “Papes”) first proposed that specific brain circuits are devoted to emotional experience and expression (much as the occipital cortex is devoted to vision, for instance). In seeking to understand what parts of the brain serve this function, he began to explore Emotions 693 Figure 28.2 Components of the nervous system that organize the expression of emotional experience. (A) The neural systems that help convey emotion include forebrain centers that govern the nonvolitional expression of somatic motor behav-ior and the visceral motor system. (B) Diagram of the descending systems that con-trol somatic and visceral motor effectors. Motor cortical areas in the posterior frontal lobe give rise to descending projections that, together with secondary pro-jections arising in the brainstem, are organized into medial and lateral components. As described in Chapter 16, these descending projections account for volitional somatic movements. Functionally and anatomically distinct centers in the forebrain govern the expression of nonvolitional somatic motor and visceral motor functions, which are coordinated to meditate emotional behavior. “Limbic” centers in the ventral-medial forebrain and hypothalamus also give rise to medial and lateral descending projections. For both systems of descending projections, the lateral components elicit specific behaviors (e.g., volitional digit movements and emo-tional facial expressions), while the medial components support and modulate the execution of such behaviors. The descending projections of both systems terminate in several integrative centers in the brainstem reticular formation, as well as the motor neuronal pools of the brainstem and spinal cord. In addition, the limbic fore-brain centers innervate components of the visceral motor system that govern pre-ganglionic autonomic neurons in the brainstem and spinal cord. ▲ 694 Chapter Twenty-Eight Figure 28.3 The so-called limbic lobe includes the cortex on the medial aspect of the cerebral hemisphere that forms a rim around the corpus callosum and diencephalon, including the cingulate gyrus (lying above the corpus callosum) and the parahippocampal gyrus. Histor-ically, the olfactory bulb and olfactory cortex (not illustrated here) have also been considered to be important ele-ments of the limbic lobe. the medial aspects of the cerebral hemisphere. In the 1850s, Paul Broca used the term “limbic lobe” to refer to the part of the cerebral cortex that forms a rim (limbus is Latin for rim) around the corpus callosum and diencephalon on the medial face of the hemispheres (Figure 28.3). Two prominent components of this region are the cingulate gyrus, which lies above the corpus callosum, and the parahippocampal gyrus, which lies in the medial temporal lobe. For many years, these structures, along with the olfactory bulbs, were thought to be concerned primarily with the sense of smell. Indeed, Broca con-sidered the olfactory bulbs to be the principal source of input to the limbic lobe. Papez, however, speculated that the function of the limbic lobe might be more related to emotions. He knew from the work of Bard and Hess that the hypothalamus influences the expression of emotion; he also knew, as every-one does, that emotions reach consciousness, and that higher cognitive func-tions affect emotional behavior. Ultimately, Papez showed that the cingulate cortex and hypothalamus are interconnected via projections from the mam-millary bodies (part of the posterior hypothalamus) to the anterior nucleus of the dorsal thalamus, which projects in turn to the cingulate gyrus. The cingulate gyrus (and many other cortical regions as well) projects to the hip-pocampus. Finally, he showed that the hippocampus projects via the fornix (a large fiber bundle) back to the hypothalamus. Papez suggested that these pathways provided the connections necessary for cortical control of emo-tional expression, and they became known as the “Papez circuit.” Over time, the concept of a forebrain circuit for the control of emotional expression, first elaborated by Papez, has been revised to include parts of the orbital and medial prefrontal cortex, ventral parts of the basal ganglia, the mediodorsal nucleus of the thalamus (a different thalamic nucleus than the one emphasized by Papez), and a large nuclear mass in the temporal lobe anterior to the hippocampus, called the amygdala. This set of structures, together with the parahippocampal gyrus and cingulate cortex, is generally referred to as the limbic system (Figure 28.4). Thus, some of the structures that Papez originally described (the hippocampus, for example) now appear to have little to do with emotional behavior, whereas the amygdala, which was hardly mentioned by Papez, clearly plays a major role in the experience and expression of emotion (Box B). Cingulate gyrus Fornix Corpus callosum Temporal lobe Parahippocampal gyrus Cut edge of midbrain Figure 28.4 Modern conception of the limbic system. Two especially important components of the limbic system not emphasized in early anatomical accounts are the orbital and medial pre-frontal cortex and the amygdala. These two telencephalic regions, together with related structures in the thalamus, hypo-thalamus and ventral striatum, are espe-ically important in the experience and expression of emotion (colored green). Other parts of the limbic system, includ-ing the hippocampus and the mammi-lary bodies of the hypothalamus, are no longer considered important neural cen-ters for processing emotion (colored blue). About the same time that Papez proposed that these structures were important for the integration of emotional behavior, Heinrich Klüver and Paul Bucy were carrying out a series of experiments on rhesus monkeys in which they removed a large part of both medial temporal lobes, thus destroying much of the limbic system. They reported a set of abnormal behaviors in these animals that is now known as the Klüver-Bucy syndrome (Box C). Among the most prominent changes was visual agnosia: the ani-mals appeared to be unable to recognize objects, although they were not blind, a deficit similar to that sometimes seen in human patients following lesions of the temporal cortex (see Chapter 25). In addition, the monkeys dis-played bizarre oral behaviors. For instance, these animals would put objects into their mouths that normal monkeys would not. They exhibited hyperac-tivity and hypersexuality, approaching and making physical contact with Emotions 695 Cingulate gyrus Fornix Ventral basal ganglia Corpus callosum Temporal lobe Parahippocampal gyrus Cut edge of midbrain Orbital and medial prefrontal cortex Amygdala Hippocampus Mammillary body Anterior nucleus of the thalamus Mediodorsal nucleus of the thalamus Hypothalamus Anterior commissure Optic chiasm Mammillothalamic tract 696 Chapter Twenty-Eight Box B The Anatomy of the Amygdala The amygdala is a complex mass of gray matter buried in the anterior-medial por-tion of the temporal lobe, just rostral to the hippocampus (Figure A). It com-prises multiple, distinct subnuclei and cortical regions that are richly connected to other nearby cortical areas on the ven-tral and medial aspect of the hemispheric surface. The amygdala (or amygdaloid complex, as it is often called) can best be thought of in terms of three major func-tional and anatomical subdivisions, each of which has a unique set of connections with other parts of the brain (Figures B and C). The medial group of subnuclei has extensive connections with the olfac-tory bulb and the olfactory cortex. The basal-lateral group, which is especially large in humans, has major connections with the cerebral cortex, especially the orbital and medial prefrontal cortex of the frontal lobe and the associational cor-tex of the anterior temporal lobe. The central and anterior group of nuclei is characterized by connections with the hypothalamus and brainstem, including such visceral sensory structures as the nucleus of the solitary tract and the parabrachial nucleus. The amygdala thus links cortical regions that process sensory information with hypothalamic and brainstem effec-tor systems. Cortical inputs provide information about highly processed visual, somatic sensory, visceral sensory, and auditory stimuli. These pathways from sensory cortical areas distinguish the amygdala from the hypothalamus, which receives relatively unprocessed visceral sensory inputs. The amygdala also receives sensory input directly from some thalamic nuclei, the olfactory bulb, and visceral sensory relays in the brain-stem. Physiological studies have confirmed this convergence of sensory information. Thus, many neurons in the amygdala respond to visual, auditory, somatic Amygdala Medial group Central group (A) (B) Basal-lateral group (A) Coronal section through the forebrain at the level of the amygdala; box indicates the region illustrated in panel (B). (B) Histological section through the human amygdala, stained with silver salts to reveal the presence of myelinated fiber bundles. These bundles subdivide major nuclei and cortical regions within the amygdaloid complex. (Courtesy of Joel Price.) virtually anything in their environment; most importantly, they showed marked changes in emotional behavior. Because they had been caught in the wild, the monkeys had typically reacted with hostility and fear to humans before their surgery. Postoperatively, however, they were virtually tame. Motor and vocal reactions generally associated with anger or fear were no longer elicited by the approach of humans, and the animals showed little or no excitement when the experimenters handled them. Nor did they show fear when presented with a snake—a strongly aversive stimulus for a nor-mal rhesus monkey. Klüver and Bucy concluded that this remarkable change in behavior was at least partly due to the interruption of the pathways described by Papez. A similar syndrome has been described in humans who have suffered bilateral damage of the temporal lobes. When it was later demonstrated that the emotional disturbances of the Klüver–Bucy syndrome could be elicited by removal of the amygdala alone, attention turned more specifically to the role of this structure in the control of emotional behavior. The Importance of the Amygdala Experiments first performed in the late 1950s by John Downer at University College London vividly demonstrated the importance of the amygdala in aggressive behavior. Downer removed one amygdala in rhesus monkeys, at Emotions 697 sensory, visceral sensory, gustatory, and olfactory stimuli. Moreover, highly com-plex stimuli are often required to evoke a neuronal response. For example, there are neurons in the basal-lateral group of nuclei that respond selectively to the sight of faces, very much like the “face” neurons in the inferior temporal cortex (see Chapter 25). In addition to sensory inputs, the pre-frontal and temporal cortical connections of the amygdala give it access to more overtly cognitive neocortical circuits, which integrate the emotional signifi-cance of sensory stimuli and guide com-plex behavior. Finally, projections from the amyg-dala to the hypothalamus and brainstem (and possibly as far as the spinal cord) allow it to play an important role in the expression of emotional behavior by influencing activity in both the somatic and visceral motor efferent systems. Reference PRICE, J. L., F. T. RUSSCHEN AND D. G. AMARAL (1987) The limbic region II: The amygdaloid complex. In Handbook of Chemical Neu-roanatomy, Vol. 5, Integrated Systems of the CNS, Part I, Hypothalamus, Hippocampus, Amygdala, Retina. A. Björklund and T. Hök-felt (eds.). Amsterdam: Elsevier, pp. 279–388. Ventral basal ganglia Orbital and medial prefrontal cortex Amygdala (basal-lateral nuclei) (C) Mediodorsal nucleus of the thalamus (C) The amygdala (specifically, the basal-lateral group of nuclei) participates in a “triangular” circuit linking the amygdala, the thalamic mediodorsal nucleus (directly and indirectly via the ventral parts of the basal ganglia), and the orbital and medial prefrontal cortex. These complex interconnec-tions allow direct interactions between the amygdala and prefrontal cortex, as well as indirect modulation via the circuitry of the ventral basal ganglia. 698 Chapter Twenty-Eight the same time transecting the optic chiasm and the commissures that link the two hemispheres (principally, the corpus callosum and anterior commis-sure; see Chapter 26). In so doing, he produced animals with a single amyg-dala that had access only to visual inputs from the eye on the same side of the head. Downer found that the animals’ behavior depended on which eye was used to view the world. When the monkeys were allowed to see with the eye on the side of amygdala lesion, they behaved in some respects like those described by Klüver and Bucy; for example, they were relatively placid in the presence of humans. If, however, they were allowed to see only with the eye on the side of the intact amygdala, they reverted to their normal fear-ful and often aggressive behavior. Thus, in the absence of the amygdala, a monkey does not interpret the significance of the visual stimulus presented by an approaching human in the same way as a normal animal. Importantly, only visual stimuli presented to the eye on the side of the ablation produced this abnormal state; thus if the animal was touched on either side, a full aggressive reaction occurred, implying that somatic sensory information about both sides of the body had access to the remaining amygdala. These anecdotal data, taken together with what is now a rich trove of empirical results and clinical observations in both experimental animals and humans show that the amygdala mediates neural processes that invest sensory expe-rience with emotional significance. Box C The Reasoning Behind an Important Discovery Paul Bucy explains why he and Heinrich Klüver removed the temporal lobes in monkeys: When we started out, we were not trying to find out what removal of the temporal lobe would do, or what changes in behavior of the monkeys it would produce. What we found out was completely unexpected! Heinrich had been experimenting with mescaline. He had even taken it himself and had experienced hal-lucinations. He had written a book about mescaline and its effects. Later Heinrich gave mescaline to his monkeys. He gave everything to his monkeys, even his lunch! He noticed that the monkeys acted as though they experienced paraesthe-sias in their lips. They licked, bit and chewed their lips. So he came to me and said, “Maybe we can find out where mescaline has its actions in the brain.” So I said, “OK.” We began by doing a sensory den-ervation of the face, but that didn’t make any difference to the mesca-line-induced behavior. So we tried motor denervation. That didn’t make any difference, either. Then we had to sit back and think hard about where to look. I said to Hein-rich, “This business of licking and chewing the lips is not unlike what you see in cases of temporal lobe epilepsy. Patients chew and smack their lips inordinately. So, let’s take out the uncus.” Well, we could just as well take out the whole temporal lobe, including the uncus. So we did. We were especially fortunate with our first animal. This was an older female.… She had become vicious—absolutely nasty. She was the most vicious animal you ever saw; it was dangerous to go near her. If she didn’t hurt you, she would at least tear your clothing. She was the first animal on which we operated. I removed one tempo-ral lobe.… The next morning my phone was ringing like mad. It was Heinrich, who asked, “Paul, what did you do to my monkey? She is tame!” Subsequently, in operating on non-vicious animals, the taming effect was never so obvious. That stimulated our getting the other temporal lobe out as soon as we could evaluate her. When we removed the other temporal lobe, the whole syndrome blossomed. Excerpt from an interview of Bucy by K. E. Livingston in 1981. K. E. Livingston (1986) Epilogue: Reflections on James Wenceslas Papez, According to Four of his Colleagues. In The Limbic System: Functional Organization and Clinical Disorders. B. K. Doane and K. E. Livingston (eds.). New York: Raven Press. To better understand the role of the amygdala in evaluating stimuli, and to define more precisely the specific circuits and mechanisms involved, sev-eral other animal models of emotional behavior have since been developed. One of the most useful is based on conditioned fear responses in rats. Con-ditioned fear develops when an initially neutral stimulus is repeatedly paired with an inherently aversive one. Over time, the animal begins to respond to the neutral stimulus with behaviors similar to those elicited by the threatening stimulus (i.e., it learns to attach a new meaning to the neu-tral stimulus). Studies of the parts of the brain involved in the development of conditioned fear in rats have begun to shed some light on this process. Joseph LeDoux and his colleagues at New York University trained rats to associate a tone with a mildly aversive foot shock delivered shortly after onset of the sound. To assess the animals’ responses, they measured blood pressure and the length of time the animals crouched without moving (a fearful reaction called “freezing”). Before training, the rats did not react to the tone, nor did their blood pressure change when the tone was presented. After training, however, the onset of the tone caused a marked increase in blood pressure and prolonged periods of behavioral freezing. Using this par-adigm, LeDoux and his collegues worked out the neural circuitry that estab-lished the association between the tone and fear (Figure 28.5). First, they demonstrated that the medial geniculate nucleus is necessary for the devel-opment of the conditioned fear response. This result is not surprising, since all auditory information that reaches the forebrain travels through the medial geniculate nucleus of the dorsal thalamus (see Chapter 12). They went on to show, however, that the responses were still elicited if the con-nections between the medial geniculate and auditory cortex were severed, leaving only a direct projection between the medial geniculate and the basal-lateral group of nuclei in the amygdala. Furthermore, if the part of the medial geniculate that projects to the amygdala was also destroyed, the fear Emotions 699 Output to circuits that influence somatomotor and autonomic activity Auditory cortex Amygdala Other projections (including somatic sensory pathways) Medial geniculate nucleus Auditory pathways 1 3 4 5 2 Figure 28.5 Pathways in the rat brain that mediate the association of auditory and aversive somatic sensory stimuli. Information processed by the auditory centers in the brainstem is relayed to the auditory cortex via the medial genicu-late nucleus (1). The amygdala receives auditory information indirectly via the auditory cortex (2) and directly from one subdivision of the medial geniculate (3). The amygdala also receives sensory information about other sensory modal-ities, including pain (4). Thus, the amyg-dala is in a position to associate diverse sensory inputs, leading to new behav-ioral and autonomic responses to stim-uli that were previously devoid of emo-tional content (5). 700 Chapter Twenty-Eight Figure 28.6 Model of associative learn-ing in the amygdala relevant to emo-tional function. Most neutral sensory inputs are relayed to principal neurons in the amygdala by projections from “higher order” sensory processing areas that represent objects (e.g., faces). If these sensory inputs depolarize amyg-dalar neurons at the same time as inputs that represent other sensations with pri-mary reinforcing value, then associative learning occurs by strengthening synap-tic linkages between the previously neu-tral inputs and the neurons of the amyg-dala (see Chapter 24 for synaptic mechanisms of learning). The output of the amygdala then informs a variety of integrative centers responsible for the somatic and visceral motor expression of emotion, and for modifying behavior relevant to seeking rewards and avoid-ing punishment. (After Rolls, 1999.) responses were abolished. Subsequent work in LeDoux’s laboratory estab-lished that projections from the central group of nuclei in the amygdala to the midbrain reticular formation are critical in the expression of freezing behavior, while other projections from this group to the hypothalamus con-trol the rise in blood pressure. Since the amygdala is a site where neural activity produced by both tones and shocks can be processed, it is reasonable to suppose that the amygdala is also the site where learning about fearful stimuli occurs. These results, among others, have led to the broader hypothesis that the amygdala partici-pates in establishing associations between neutral sensory stimuli, such as a mild auditory tone or the sight of inanimate object in the environment, and other stimuli that have some primary reinforcement value (Figure 28.6). The neutral sensory input can be stimuli in the external environment, stimuli Outputs Primary reinforcers (e.g., taste, touch, pain) Inputs Neutral sensory stimuli (e.g., visual, auditory stimuli related to an object) Inputs Hypothalamus and brainstem Visceral motor effector systems to prepare body for action Outputs Orbital and medial prefrontal cortex Implicit motor actions Explicit conscious processing to obtain rewards, avoid punishers and implement long–term plan Learning Learning Learning Learning communicated centrally via the special sensory afferent systems, or internal stimuli derived from activation of visceral sensory receptors. The stimuli with primary reinforcement value include sensory stimuli that are inherently rewarding, such as the sight, smell, and taste of food, or stimuli with nega-tive valences such as an aversive taste, loud sounds, or painful mechanical stimulation. The associative learning process itself is probably a Hebbian-like mechanism (see Chapters 23 and 24) that strengthens the connections relaying the information about the neutral stimulus, provided that they acti-vate the postsynaptic neurons in the amygdala at the same time as inputs pertaining to the primary reinforcer. The discovery that long-term potentia-tion (LTP) occurs in the amygdala provides further support for this hypoth-esis. Indeed, the acquisition of conditioned fear in rats is blocked by infusion into the amygdala of NMDA antagonists, which prevents the induction of LTP. Finally, the behavior of patients with selective damage to the anterior-medial temporal lobe indicates that the amygdala plays a similar role in the human experience of fear (Box D). The Relationship between Neocortex and Amygdala As these observations on the limbic system (and the amygdala in particular) make plain, understanding the neural basis of emotions also requires under-standing the role of the cerebral cortex. In animals like the rat, most behav-ioral responses are highly stereotyped. In more complex brains, however, individual experience is increasingly influential in determining responses to special and even idiosyncratic stimuli. Thus in humans, a stimulus that evokes fear or sadness in one person may have little or no effect on the emo-tions of another. Although the pathways underlying such responses are not well understood, the amygdala and its interconnections with an array of neo-cortical areas in the prefrontal cortex and anterior temporal lobe, as well as several subcortical structures, appear to be especially important in the higher order processing of emotion. In addition to its connections with the hypo-thalamus and brainstem centers that regulate visceral motor function, the amygdala has significant connections with several cortical areas in the orbital and medial aspects of the frontal lobe (see Box B). These cortical fields associ-ate information from every sensory modality (including information about visceral activities) and can thus integrate a variety of inputs pertinent to moment-to-moment experience. In addition, the amygdala projects to the thalamus (specifically, the mediodorsal nucleus), which projects in turn to these same cortical areas. Finally, the amygdala innervates neurons in the ventral portions of the basal ganglia that receive the major cortico-striatal pro-jections from the regions of the prefrontal cortex thought to process emotions. Considering all these seemingly arcane anatomical connections, the amyg-dala emerges as a nodal point in a network that links together the cortical (and subcortical) brain regions involved in emotional processing. Clinical evidence concerning the significance of this circuitry linked through the amygdala has come from functional imaging studies of patients suffering from depression (Box E), in which this set of interrelated forebrain structures displays abnormal patterns of cerebral blood flow, especially in the left hemisphere. More generally, the amygdala and its connections to the prefrontal cortex and basal ganglia are likely to influence the selection and initiation of behaviors aimed at obtaining rewards and avoiding punish-ments (recall that the process of motor program selection and initiation is an important function of basal ganglia circuitry; see Chapter 17). The parts of Emotions 701 702 Chapter Twenty-Eight Studies of fear conditioning in rodents show that the amygdala plays a critical role in the association of an innocuous auditory tone with an aversive mechani-cal sensation. Does this finding imply that the human amygdala is similarly involved in the experience of fear and the expression of fearful behavior? Recent reports of at least one extraordi-nary patient support the idea that the amygdala is indeed a key brain center for the experience of fear. The patient (S.M.) suffers from a rare, autosomal recessive condition called Urbach-Wiethe disease, a disorder that causes bilateral calcification and atro-phy of the anterior-medial temporal lobes. As a result, both of S.M.’s amyg-dalas are extensively damaged, with lit-tle or no detectable injury to the hip-pocampal formation or nearby temporal neocortex (Figure A). She has no motor or sensory impairment, and no notable deficits in intelligence, memory, or lan-guage function. However, when asked to rate the intensity of emotion in a series of photographs of facial expres-sions, she cannot recognize the emotion of fear (Figure B). Indeed, S.M.’s ratings of emotional content in fearful facial expressions were several standard devi-ations below the ratings of control patients who had suffered brain dam-age outside of the anterior-medial tem-poral lobe. The investigators next asked S.M. (and the brain-damaged control sub-jects) to draw facial expressions of the same set of emotions from memory. Although the subjects obviously dif-fered in artistic abilities and the detail of their renderings, S.M. (who has some artistic experience) produced skillful pictures of each emotion, except for fear (Figure C). At first, she could not pro-duce a sketch of a fearful expression and, when prodded to do so, explained that “she did not know what an afraid Brain-damaged controls Patient S.M. Happy Surprised Afraid Disgusted Sad Neutral Angry Happy Surprised Afraid Disgusted Sad Neutral Angry Relative emotional content Relative emotional content (B) Hippocampus Amygdala Amygdala (A) (A) MRI showing the extent of brain damage in patient S.M; note the bialateral destruction of the amygdala and the preservation of the hippocampus. (B) Patients with brain damage outside of the anterior-medial temporal lobe and patient S.M. rated the emotional content of a series of facial expressions. Each colored line represents the intensity of the emotions judged in the face. S.M. recognized happi-ness, surprise, anger, disgust, sadness, and neutral qualities in facial expressions about as well as controls. However, she failed to recognize fear (orange lines). (A courtesy of R. Adolphs.) Box D Fear and the Human Amygdala: A Case Study the prefrontal cortex interconnected with the amygdala are also involved in organizing and planning future behaviors; thus, the amygdala may provide emotional input to overt (and covert) deliberations of this sort (see the later section on “Emotion, Reason, and Social Behavior”). Finally, it is likely that interactions between the amygdala, the neocortex and related subcortical circuits account for what is perhaps the most enig-matic aspect of emotional experience: the highly subjective “feelings” that attend most emotional states. Although the neurobiology of such experience is not understood, it is reasonable to assume that emotional feelings arise as a consequence of a more general cognitive capacity for self-awareness. In this conception, feelings entail both the immediate conscious experience of implicit emotional processing (arising from amygdala–neocortical circuitry) and explicit processing of semantically based thought (arising from hip-pocampal–neocortical circuitry; see Chapter 30). Thus, feelings are plausibly Emotions 703 face would look like.” After several failed attempts, she produced the sketch of a cowering figure with hair standing on end, evidently because she knew these clichés about the expression of fear. In short, S.M. has a severely limited concept of fear and, consequently, fails to recognize the emotion of fear in facial expressions. Studies of other individu-als with bilateral destruction of the amygdala are consistent with this account. As might be expected, S.M.’s deficiency also limits her ability to expe-rience fear in situations where this emo-tion is appropriate. Despite the adage “have no fear,” to truly live without fear is to be deprived of a crucial neural mechanism that facil-itates appropriate social behavior, helps make advantageous decisions in critical circumstances, and, ultimately, pro-motes survival. References ADOLPHS, R., D. TRANEL, H. DAMASIO AND A. R. DAMASIO (1995) Fear and the human amygdala. J. Neurosci. 15: 5879–5891. BECHARA, A., H. DAMASIO, A. R. DAMASIO AND G. P. LEE (1999) Differential contributions of the human amygdala and ventromedial pre-frontal cortex to decision-making. J. Neu-rosci. 19: 5473–5481. Happy Sad Surprised Disgusted Angry Afraid (C) (C) Sketches made by S.M. when asked to draw facial expressions of emotion. 704 Chapter Twenty-Eight Box E Affective Disorders Although some degree of disordered emotion is present in virtually all psychi-atric problems, in affective (mood) disor-ders the essence of the disease is an abnormal regulation of the feelings of sadness and happiness. The most severe of these afflictions are major depression and manic depression. (Manic depres-sion is also called “bipolar disorder,” since such patients experience alternat-ing episodes of depression and eupho-ria.) Depression, the most common of the major psychiatric disorders, has a life-time incidence of 10–25% in women and 5–12% in men. For clinical purposes, depression (as distinct from bereavement or neurotic unhappiness) is defined by a set of standard criteria. In addition to an abnormal sense of sadness, despair, and bleak feelings about the future (depres-sion itself), these criteria include disor-dered eating and weight control, disor-dered sleeping (insomnia or hyper-somnia), poor concentration, inappropri-ate guilt, and diminished sexual interest. The personally overwhelming quality of major depression has been compellingly described by patient/authors such as William Styron, and by afflicted psych-ologists such as Kay Jamison. The depressed patient’s profound sense of despair has been nowhere better expressed than by Abraham Lincoln, who during a period of depression wrote: I am now the most miserable man living. If what I feel were equally distributed to the whole human family, there would not be one cheerful face on earth. Whether I shall ever be better, I cannot tell; I awfully forebode I shall not. To remain as I am is impossible. I must die or be better, it appears to me. Indeed, about half the suicides in this country occur in individuals with clinical depression. Not many decades ago, depression and mania were considered disorders that arose from circumstances or a neu-rotic inability to cope. It is now univer-sally accepted that these conditions are neurobiological disorders. Among the strongest lines of evidence for this con-sensus are studies of the inheritance of these diseases. For example, the concor-dance of affective disorders is high in monozygotic compared to dizygotic twins. It has also become possible to study the brain activity of patients suf-fering from affective disorders by non-invasive brain imaging (see Figure). In at least one condition, unipolar depression, abnormal patterns of blood flow are apparent in the “triangular” circuit inter-connecting the amygdala, the mediodor-sal nucleus of the thalamus, and the orbital and medial prefrontal cortex (see Box B). Of particular interest is the sig-nificant correlation of abnormal blood flow in the amygdala and the clinical severity of depression, as well as the observation that the abnormal blood flow pattern in the prefrontal cortex returns to normal when the depression has abated. Despite evidence for a genetic predis-position and an increasing understand-ing of the brain areas involved, the cause of these conditions remains unknown. The efficacy of a large number of drugs Areas of increased blood flow in the left amygdala, orbital, and medial pre-frontal cortex (A) and in a location in the left medial thalamus consistent with the mediodorsal nucleus (B) from a sample of patients diagnosed with unipolar clinical depression. The “hot” colors indicate statistically significant increases in blood flow, compared to a sample of nondepressed subjects. (From Drevets and Raichle, 1994.) (A) (B) Amygdala Orbital and medial prefrontal cortex Mediodorsal nucleus of the thalamus L R conceived as the product of an emotional working memory that sustains neural activity related to the processing of these various elements of emo-tional experience. Given the evidence for working memory functions in the prefrontal cortex (see Chapter 25), this portion of the frontal lobe—especially the orbital and medial sector—is the likely neural substrate where such asso-ciations are maintained in conscious awareness (Figure 28.7). Cortical Lateralization of Emotional Functions Since functional asymmetries of complex cortical processes are common-place (see Chapters 25 and 26), it should come as no surprise that the two hemispheres make different contributions to the governance of emotion. Emotionality is lateralized in the cerebral hemispheres in at least two ways. First, as discussed in Chapter 26, the right hemisphere is especially important for the expression and comprehension of the affective aspects of speech. Thus, patients with damage to the supra-Sylvian portions of the pos-terior frontal and anterior parietal lobes on the right side may lose the ability Emotions 705 that influence catecholaminergic and serotonergic neurotransmission strongly implies that the basis of the disease(s) is ultimately neurochemical (see Figure 6.12 for an overview of the projections of these neural systems). The majority of patients (about 70%) can be effectively treated with one of a variety of drugs (including tricyclic antidepressants, monoamine oxidase inhibitors, and selective serotonin reuptake inhibitors). Most successful are drugs that selec-tively block the uptake of serotonin without affecting the uptake of other neurotransmitters; these drugs are com-monly known as selective serotonin reuptake inhibitors, or SSRIs. Three such inhibitors—fluoxetine (Prozac®), sertra-line (Zoloft®), and paroxetine (Paxil®)— are especially effective in treating depression and have few of the side effects of the older, less specific drugs. Perhaps the best indicator of the success of these drugs has been their wide acceptance: although the first SSRI’s were approved for clinical use only in the late 1980s, they are now among the most prescribed pharmaceuticals. Most depressed patients who use drugs such as the SSRI’s report that they lead fuller lives and are more energetic and organized. Based on such informa-tion, these drugs are sometimes used not only to combat depression but also to “treat” individuals who have no defin-able psychiatric disorder. This abuse raises important social questions, similar to those posed by Aldous Huxley in his 1932 novel, where the mythical drug “Soma” was routinely administered to the inhabitants of his fictitious Brave New World to keep them content and docile. Presumably there is a middle ground between excessive suffering and exces-sive tranquility. References BREGGIN, P. R. (1994) Talking Back to Prozac: What Doctors Won’t Tell You about Today’s Most Controversial Drug. New York: St. Martin’s Press. DREVETS, W. C. AND M. E. RAICHLE (1994) PET imaging studies of human emotional disor-ders. In The Cognitive Neurosciences, M. S. Gazzaniga (ed.). Cambridge, MA: MIT Press, pp. 1153–1164. FREEMAN, P. S., D. R. WILSON AND F. S. SIERLES (1993) Psychopathology. In Behavior Science for Medical Students, F. S. Sierles (ed.). Balti-more: Williams and Wilkins, pp. 239–277. GREENBERG, P. E., L. E. STIGLIN, S. N. FINKEL-STEIN AND E. R. BERNDT (1993) The economic burden of depression in 1990. J. Clin. Psychi-atry 54: 405–424. JAMISON, K. R. (1995) An Unquiet Mind. New York: Alfred A. Knopf. JEFFERSON, J. W. AND J. H. GRIEST (1994) Mood disorders. In Textbook of Psychiatry, J. A. Tal-bott, R. E. Hales and S. C. Yudofsky (eds.). Washington: American Psychiatric Press, pp. 465–494. ROBINS, E. (1981) The Final Months: A Study of the Lives of 134 Persons Who Committed Suicide. New York: Oxford University Press. STYRON, W. (1990) Darkness Visible: A Memoir of Madness. New York: Random House. WONG, D. T. AND F. P. BYMASTER (1995) Devel-opment of antidepressant drugs: Fluoxetin (Prozac®) and other selective serotonin uptake inhibitors. Adv. Exp. Med. Biol. 363: 77–95. WONG, D. T., F. P. BYMASTER AND E. A. ENGLE-MAN (1995) Prozac® (fluoxetine, Lilly 110140), the first selective serotonin uptake inhibitor and an antidepressant drug: Twenty years since its first publication. Life Sci. 57(5): 411–441. WURTZEL, E. (1994). Prozac Nation: Young and Depressed in America. Boston: Houghton-Mifflin. 706 Chapter Twenty-Eight to express emotion by modulation of their speech patterns (recall that this loss of emotional expression is referred to as aprosody or aprosodia, and that similar lesions in the left hemisphere give rise to Broca’s aphasia). Patients with aprosodia tend to speak in a monotone, no matter what the circum-stances or meaning of what is said. For example, one such patient, a teacher, had trouble maintaining discipline in the classroom. Because her pupils (and even her own children) couldn’t tell when she was angry or upset, she had to resort to adding phrases such as “I am angry and I really mean it” to indicate the emotional significance of her remarks. The wife of another patient felt her husband no longer loved her because he could not imbue his speech with cheerfulness or affection. Although such patients cannot express emotion in speech, they nonetheless experience normal emotional feelings. A second way in which the hemispheric processing of emotionality is asymmetrical concerns mood. Both clinical and experimental studies indi-cate that the left hemisphere is more importantly involved with what can be thought of as positive emotions, whereas the right hemisphere is more involved with negative ones. For example, the incidence and severity of depression (see Box E) is significantly higher in patients with lesions of the left anterior hemisphere compared to any other location. In contrast, patients with lesions of the right anterior hemisphere are often described as unduly cheerful. These observations suggest that lesions in the left hemisphere result in a relative loss of positive feelings, facilitating depression, whereas lesions of the right hemisphere result in a loss of negative feelings, leading to inappropriate optimism. Hemispheric asymmetry related to emotion is also apparent in normal individuals. For instance, auditory experiments that introduce sound into one ear or the other indicate a right-hemisphere superiority in detecting the emotional nuances in speech. Moreover, when facial expressions are specifi-Immediate conscious experience of emotional feelings (Working memory in prefrontal cortex) Hippocampal-dependent explicit memory Amygdala-dependent associative learning Triggering (interoceptive and exteroceptive) stimuli Figure 28.7 Neural model for the awareness of emotional feelings. The highly sub-jective feelings associated with emotional experience presumably arise from neural systems in the prefrontal cortex that produce awareness of emotional processing. (After LeDoux, 2000.) cally presented to either the right or the left visual hemifield, the depicted emotions are more readily and accurately identified from the information in the left hemifield (that is, the hemifield perceived by the right hemisphere; see Chapters 11 and 26). Finally, kinematic studies of facial expressions show that most individuals more quickly and fully express emotions with the left facial musculature than with the right (recall that the left lower face is con-trolled by the right hemisphere, and vice versa) (Figure 28.8). Taken together, this evidence is consistent with the idea that the right hemisphere is more intimately concerned with both the perception and expression of emotions than is the left hemisphere. However, it is important to remember that, as in the case of other lateralized behaviors (language, for instance), both hemi-spheres participate in processing emotion. Emotion, Reason, and Social Behavior The experience of emotion—even on a subconscious level—has a powerful influence on other complex brain functions, including the neural faculties Emotions 707 Figure 28.8 Asymmetrical smiles on some famous faces. Studies of normal sub-jects show that facial expressions are often more quickly and fully expressed by the left facial musculature than the right, as suggested by examination of these exam-ples (try covering one side of the faces and then the other). Since the left lower face is governed by the right hemisphere, some psychologists have suggested that the majority of humans are “left-faced,” in the same general sense that most of us are right-handed. (After Moscovitch and Olds, 1982; images from Microsoft® Encarta Encyclopedia 98.) 708 Chapter Twenty-Eight responsible for making rational decisions and the interpersonal judgments that guide social behavior. Evidence for this statement has come principally from studies of patients with damage to parts of the orbital and medial pre-frontal cortex, as well as patients with injury or disease involving the amyg-dala (see Box D). Such patients often have impairments in emotional process-ing, especially of the emotions engendered by complex personal and social situations, and they have difficulty making advantageous decisions (see also Chapter 25). Adding to this body of evidence are results from brain imaging studies in normal subjects in which investigators have mapped the brain structures that participate in the necessary emotional and social appraisals. Antonio Damasio and his colleagues at the University of Iowa have sug-gested that such decision-making entails the rapid evaluation of a set of pos-sible outcomes with respect to the future consequences associated with each course of action. It seems plausible that the generation of conscious or sub-conscious mental images that represent the consequences of each contin-gency triggers emotional states that involve either actual alterations of somatic and visceral motor function, or the activation of neural representa-tions of such activity. Whereas William James proposed that we are “afraid because we tremble,” Damasio and his colleagues suggest a vicarious repre-sentation of motor action and sensory feedback in the neural circuits of the frontal and parietal lobes. It is these vicarious states, according to Damasio, that give mental representations of contingencies the emotional valence that helps an individual to identify favorable or unfavorable outcomes. Experimental studies of fear conditioning have implied just such a role for the amygdala in associating sensory stimuli with aversive consequences. For example, the patient described in Box D showed an impaired ability to rec-ognize and experience fear, together with impairment in rational decision-making. Similar evidence of the emotional influences on decision-making have also come from studies of patients with lesions in the orbital and medial prefrontal cortex. These clinical observations suggest that the amyg-dala and prefrontal cortex, as well as their striatal and thalamic connections, are not only involved in processing emotions, but also participate in the complex neural processing responsible for rational thinking. These same neural networks are engaged by sensory stimuli (e.g., facial expressions) that convey important cues pertinent to appraising social circumstances and con-ventions. Thus, when judging the trustworthiness of human faces—a task of considerable importance for successful interpersonal relations—neural activ-ity in the amygdala is specifically increased, especially when the face in question is deemed untrustworthy (Figure 28.9). It is not surprising, then, that subjects with bilateral damage to the amygdala differ from control sub-jects in their appraisals of trustworthiness; indeed, individuals with such impairments often show inappropriately friendly behavior toward strangers in real-life social situations. Such evidence adds further weight to the idea that emotional processing is crucial for competent performance in a wide variety of complex brain functions. Summary The word “emotion” covers a wide range of states that have in common the association of visceral motor responses, somatic behavior, and powerful sub-jective feelings. The visceral motor responses are mediated by the visceral motor nervous system, which is itself regulated by inputs from many other parts of the brain. The organization of the somatic motor behavior associated with emotion is governed by circuits in the limbic system, which includes the hypothalamus, the amygdala, and several regions of the cerebral cortex. Although a good deal is known about the neuroanatomy and transmitter chemistry of the different parts of the limbic system, there is still a dearth of information about how this complex circuitry mediates specific emotional states. Similarly, neuropsychologists, neurologists and psychiatrists are only now coming to appreciate the important role of emotional processing in other complex brain functions, such as decision-making and social behavior. A variety of other evidence indicates that the two hemispheres are differ-ently specialized for the governance of emotion, the right hemisphere being the more important in this regard. The prevalence and social significance of human emotions and their disorders ensure that the neurobiology of emo-tion will be an increasingly important theme in modern neuroscience. Emotions 709 (A) z values 0.2 0.0 0.1 0.3 Low Med Implicit (B) Explicit High Low Med High 0.4 Signal change in left amygdala (%) 0.2 0.0 0.1 0.3 Low Med Implicit Explicit High Low Med High 0.4 Signal change in right amygdala (%) (C) 0 1 2 3 4 5 6 Amygdala Amygdala Figure 28.9 Activation of the amygdala during judgments of trustworthiness. (A) Functional MRI shows increased neural activation bilaterally in the amygdala when normal subjects appraise the trustworthiness of human faces; activity is also increased in the right insular cortex. (B, C) The degree of activation is greatest when subjects evaluate faces that are considered untrustworthy (Low, Med and High indi-cate ratings of trustworthiness; Low = untrustworthy). The same effect was observed when subjects were instructed to evaluate the trustworthiness of the faces (explicit condition) or whether the faces were those of high school or university students (implicit condition). (After Winston et al., 2002; A courtesy of J. Winston.) 710 Chapter Twenty-Eight Additional Reading Reviews ADOLPHS, R. (2003) Cognitive neuroscience of human social behavior. Nature Rev. Neurosci. 4: 165–178. APPLETON, J. P. (1993) The contribution of the amygdala to normal and abnormal emotional states. Trends Neurosci. 16: 328–333. CAMPBELL, R. (1986) Asymmetries of facial action: Some facts and fancies of normal face movement. In The Neuropsychology of Face Per-ception and Facial Expression, R. Bruyer (ed.). Hillsdale, NJ: Erlbaum, pp. 247–267. DAVIS, M. (1992) The role of the amygdala in fear and anxiety. Annu. Rev. Neurosci. 15: 353–375. LEDOUX, J. E. (1987) Emotion. In Handbook of Physiology, Section 1, The Nervous System, Vol. 5. F. Blum, S. R. Geiger, and V. B. Mountcastle (eds.). Bethesda, MD: American Physiological Society, pp. 419–459. SMITH, O. A. AND J. L. DEVITO (1984) Central neural integration for the control of auto-nomic responses associated with emotion. Annu. Rev. Neurosci. 7: 43–65. Important Original Papers BARD, P. (1928) A diencephalic mechanism for the expression of rage with special reference to the sympathetic nervous system. Am. J. Physiol. 84: 490–515. DOWNER, J. L. DE C. (1961) Changes in visual agnostic functions and emotional behaviour following unilateral temporal pole damage in the “split-brain” monkey. Nature 191: 50–51. EKMAN, P., R. W. LEVENSON AND W. V. FRIESEN (1983) Autonomic nervous system activity distinguishes among emotions. Science 221: 1208–1210. KLÜVER, H. AND P. C. BUCY (1939) Preliminary analysis of functions of the temporal lobes in monkeys. Arch. Neurol. Psychiat. 42: 979–1000. MACCLEAN, P. D. (1964) Psychosomatic dis-ease and the “visceral brain”: Recent develop-ments bearing on the Papez theory of emo-tion. In Basic Readings in Neuropsychology, R. L. Isaacson (ed.). New York: Harper & Row, Inc., pp. 181–211. PAPEZ, J. W. (1937) A proposed mechanism of emotion. Arch. Neurol. Psychiat. 38: 725–743. ROSS, E. D. AND M.-M. MESULAM (1979) Domi-nant language functions of the right hemi-sphere? Prosody and emotional gesturing. Arch. Neurol. 36: 144–148. Books APPLETON, J. P. (ed.) (1992) The Amygdala: Neu-robiological Aspects of Emotion, Memory and Mental Dysfunction. New York: Wiley-Liss. CORBALLIS, M. C. (1991) The Lopsided Ape: Evo-lution of the Generative Mind. New York: Oxford University Press. DAMASIO, A. R. (1994) Descartes Error: Emotion, Reason, and the Human Brain. New York: Avon Books. DARWIN, C. (1890) The Expression of Emotion in Man and Animals, 2nd Ed. In The Works of Charles Darwin, Vol. 23, 1989. London: William Pickering. HELLIGE, J. P. (1993) Hemispheric Asymmetry: What’s Right and What’s Left. Cambridge, MA: Harvard University Press. HOLSTEGE, G., R. BANDLER AND C. B. SAPER (eds.) (1996) Progress in Brain Research, Vol. 107. Amsterdam: Elsevier. JAMES, W. (1890) The Principles of Psychology, Vols. 1 and 2. New York: Dover Publications (1950). LEDOUX, J. (1998) The Emotional Brain: The Mysterious Underpinnings of Emotional Life. New York: Simon and Schuster. ROLLS, E. T. (1999) The Brain and Emotion. Oxford: Oxford University Press. Overview “Vive la difference.” “Isn’t that just like a (wo)man?” “It’s on the Y chromo-some.” These expressions denote pleasure (or displeasure) with phenotypic sexual differences—how females and males look and behave. Sex-related differences in the phenotypic expression of genotype are called sexual dimorphisms. While some of the behavioral distinctions involved may be rooted in cultural or social norms, sexual dimorphisms arise primarily because the brains of females and males are in some respects different. In the rat (the animal in which most experimental work has been done), several structures in female and male brains clearly differ in the number, size, and connectivity of their constituent neurons. In humans and other primates, structural differences are less obvious but nonetheless present. In both rats and humans, sexually dimorphic brain structures tend to cluster around the third ventricle in the anterior hypothalamus and are an integral part of the system that governs visceral motor behavior. Other sexual dimorphisms are apparent in cerebral cortical structures, implying differences in more com-plex regulatory and other behaviors. The development of these structural differences depends primarily on the early effect of gonadal steroid hor-mones on maturing brain circuits, an influence that apparently continues to some extent throughout life. The functional consequences of sexual dimor-phisms in rodents are beginning to be well understood. Although the signif-icance of such differences in humans is less clear, they provide a plausible neural basis for the wide variety of human sexual behavior. Sexually Dimorphic Behavior Many animal behaviors differ between the sexes and are therefore referred to as sexually dimorphic (dimorphic means having two forms). However, dimorphic behaviors and their neural substrates often overlap. Mounting behaviors in male and female rodents, for example, depend on social context and life history, as well as on hormones and the brain structures that pro-duce them. Some sexually dimorphic behaviors are simply part of the reproductive repertoire, whereas others are associated with cognitive functions. An exam-ple of dimorphic behavior related to reproduction is apparent in songbirds. In many species, the male produces complex song, but the female does not. Song production arises from the activity of specific brain nuclei; as described in Chapter 23, these nuclei are much larger in males than in females. The size of song control nuclei increases in females treated with testosterone or estradiol during development, and these “masculinized” females sing. Chapter 29 711 Sex, Sexuality, and the Brain 712 Chapter Twenty-Nine Rodents also exhibit sexually dimorphic behaviors associated with repro-duction. Examples include the priming of the genitalia for sexual inter-course, and a stereotypical position assumed while having sex (typically lor-dosis for females and mounting for males). Just as courting and behaviors associated with the sex act can be dimor-phic, other more complex reproductive behaviors such as building nests, car-ing for the young, foraging for food, nursing, and so on can take different forms in female and male. In humans, the different behaviors of males and females can be far subtler, including sexual identity, the choice of a sexual partner, and behaviors that are not related directly to sexual or reproductive function, such as spatial thinking and use of language. In humans, as in other animals, the full range of these behavioral differ-ences is necessarily based on the details of the underlying neural circuitry. Accordingly, neurobiologists have long looked for differences between the brains of females and males that might explain sexually dimorphic behav-iors. As described later in this chapter, they have found many examples. Dif-ferences in the nervous system, like the behavioral differences they give rise to, are also referred to as sexually dimorphic. Bear in mind, however, that whereas brain and behavioral differences in songbirds or rodents usually have two distinct forms, in human females and males these differences tend to vary along a continuum. What Is Sex? Human sexual behaviors are—quite obviously—less stereotyped than those of rodents. Like memory, language, sleep, and other higher order brain func-tions, sexual behavior (especially when its neurobiological underpinnings are considered) is by no means simple to sort out, or even to categorize. Roughly speaking, the concept of sex can be subdivided into three cate-gories: chromosomal sex, phenotypic sex, and gender. Chromosomal sex refers specifically to an individual’s sex chromosomes. Most humans have either two X chromosomes or one X and one Y chromosome, with XX being a chromosomal female and XY a chromosomal male. Phenotypic sex refers to an individual’s sex as determined by their internal and external genitalia, the expression of secondary sex characteristics, and their behavior. In the prototypical case, during development the XX genotype leads to an individ-ual with ovaries, oviducts, uterus, cervix, clitoris, labia, and vagina—i.e., a phenotypic female. The XY genotype leads to a person with testicles, epi-didymis, vas deferens, seminal vesicles, penis, and scrotum—a phenotypic male (Box A). Gender, as the term is most often used, refers to an individual’s subjec-tive perception of their sex and their sexual orientation, which is harder to define than chromosomal or phenotypic sex. It should also be apparent that some people consider gender to be a political and social construct. For pre-sent purposes, however, gender entails self-appraisal according to the traits most often associated with one sex or the other (called gender traits), which are influenced by societal expectations and cultural norms as well as by biol-ogy. Sexual orientation also entails self-appraisal in the context of culture. To understand the neurobiology of sex, it is helpful to think of chromosomal sex as largely immutable; phenotypic sex as modifiable by developmental processes, hormone treatments, and/or surgery; and gender as a more com-plex social and cultural construct that an individual may or may not want to accept. Clearly, chromosomal sex, phenotypic sex, and gender will not always be aligned. Genetic variations in alignment can challenge the usual definitions of female and male, and for the affected individuals can lead to psychosocial conflicts, sexual dysfunction, and other problems. These variations include individuals who are chromosomally XO (Turner’s syndrome), XXY (Kline-felter’s syndrome), and XYY, with each of these genotypes having a particu-lar phenotype. Other genetic variations entail mutations in genes coding for hormone receptors or for the hormones themselves. For instance in some XX individuals, a metabolic disorder called congenital adrenal hyperplasia (CAH) leads to overactive adrenals during maturation, resulting in abnor-mally high levels of circulating androgens and hence (along with severe salt imbalance), an ambiguous sexual phenotype. In addition to having a large clitoris and fused labia at birth, women with CAH often exhibit behavioral traits more often associated with boys than girls as children, and as adults they may be more likely to form homosexual relationships than are mem-bers of control groups. By analogy with the studies in rodents, high levels of circulating androgens may stimulate sexually dimorphic brain circuitry to have a male rather than female organization, leading to more aggressive play and the eventual choice of a female sexual partner. An example of a mutation in a gene responsible for hormone receptors is androgen insensitivity syndrome (AIS), also called testicular feminization. In an XY individual with AIS, the testes form and secrete testosterone and Müllerian-inhibiting hormone, as in normal males (see Box A). The deficiency of receptors for these androgens, however, leads to the development of female external genitalia in an individual who is chromosomally male. Thus, people with complete androgen insensitivity syndrome look like females and self-identify as female, even though they have a Y chromosome. Since they are generally not aware of their condition until puberty (when they fail to menstruate), such individuals see themselves as female and are experienced by the rest of society as female. As a result of the lack of androgen receptors, the gender identity of androgen-insensitive individuals matches their exter-nal sexual phenotype, but not their chromosomal sex. Androgen-insensitive individuals also present one of the strongest arguments that brain circuits in primates are masculinized primarily by the action of androgens (as opposed to the effects of estrogens, which are the masculinizing agent in rodents). Another variation in the alignment of chromosomal sex, phenotype, and gender occurs in certain chromosomal males who are phenotypic females early in life, but whose sexual phenotype changes at puberty. As infants and children, the genitalia of these individuals resembles that of females more than of males because they lack an enzyme, 5-a-reductase, that promotes the early development of male genitalia (see Box A). Such children have labia with an enlarged clitoris; since their testes have not descended by birth, they are generally raised as females. At puberty, however, when the testicular secretion of androgen becomes high, the clitoris enlarges into a penis and the testes descend, changing these individuals into phenotypic males. In the Dominican Republic and Haiti, where this congenital syndrome has been thoroughly studied in a particular pedigree, the condition is referred to collo-quially as “testes-at-twelve.” Now that the condition is well recognized in areas where it is prevalent, the children in these pedigrees are raised with the understanding that their genitalia will change. But even if the situation goes unrecognized, such individuals generally change their gender identification at puberty, and most eventually assume a male role, for reasons that are fur-ther considered in Box B. Sex, Sexuality, and the Brain 713 714 Chapter Twenty-Nine Box A The Development of Male and Female Phenotypes The presence of either two X chromo-somes or an X and a Y chromosome in the cells of an embryo sets in motion events that establish phenotypical sex, including the sexually dimorphic devel-opment of the brain. The relevant neural effects are determined by the production of hormones, which depends in turn on the presence of either female or male gonads. The early stages of human embryonic development follow a plan that produces common precursors for the gonads. By about the sixth week of gestation, the primordial gonads have formed from somatic mesenchyme tissue, near the developing kidneys. Cells in the gonads differentiate into supporting and hor-mone-producing cells; the germline cells, which divide by meiosis rather than mitosis and eventually become ova or sperm have a different origin, and migrate to the gonads from the yolk sac. Attached to the primordial gonads are two sets of tubes—the Müllerian and Wolffian ducts—that are the progenitors of the internal genitalia. Developing simultaneously is an undifferentiated structure called the urogenital groove, the progenitor of the external genitalia. The primary genetic influence on the development of the typical male pheno-type is the sex-determining region on the Y chromosome, the Sry gene. When this region of the chromosome is activated during development, it turns on the pro-duction of a protein called testicular determining factor (TDF). It is TDF that instructs the testes to begin developing. Once activated, the male primordial gonads begin to produce testosterone (elaborated by the Leydig cells). The cells of the testes also secrete Müllerian-inhibiting hormone, which prevents the Müllerian ducts from developing and allows the Wolffian ducts to develop into the epididymis, vas deferens, and semi-Genital tubercle (A) (B) (C) (D) (E) (F) (G) (H) Urogenital membrane Urogenital fold Phallus Developing glans penis Male Female Developing glans clitoris Urethral groove 4−7 weeks 9 weeks 11 weeks 12 weeks Urethral groove Fused urogenital folds Glans penis Fused labioscrotal folds Perineum Anus Urethral groove Scrotum External urethral orifice Body of penis Scrotum Labium minus Labium majus Anus Clitoris Urethral orifice Vagina Glans clitoris Development of human female and male external genitalia. (A, B) Indifferent stage, weeks 4–7 of gestation. (D, F, H) Differentiation in the female genitalia at weeks 9, 11, and 12, respec-tively. (C, E, G) Differentiation in the male genitalia at the same intervals. (After Moore, 1977.) The general term used to describe all these variations is intersexuality. Intersexuality is apparent in 1 to 2% of all live births. In addition to the more clearly defined categories of Klinefelter’s syndrome, Turner’s syndrome, AIS, 5-a-reductase deficiency, and CAH, the many subtle permutations and combinations of genes, hormones, and environment clearly present a large number of biological and behavioral possibilities. Hormonal Influences on Sexual Dimorphism The development of sexual dimorphisms in the central nervous system is ultimately an outcome of chromosomal sex. Chromosomal combinations usually determine the phenotype of the gonads; the gonads, in turn, are responsible for producing most of the circulating sex hormones (see Box A). Differences in circulating hormones lead to a variety of differential effects on the individual’s development, including their physical appearance, response to pharmacological treatments, susceptibility to certain diseases, and brain development. The establishment of phenotypic dimorphisms under the influence of dif-ferent relative amounts of circulating hormones has been best studied in rodents. This work has shown that different levels of hormones at critical times organizes and/or activates circuits generating female- or male-typical behavior. Males have an early surge of testosterone, which masculinizes the genitalia and nervous system, and ultimately behavior. Paradoxically, many of the effects of testosterone on the rodent brain are really due to estrogens Sex, Sexuality, and the Brain 715 nal vesicles. Under these influences, the tissue around the urogenital groove becomes the penis and scrotum. Androgens alone, however, are not sufficient for male differentiation. Ken Korach’s group at the National Institute for Environmental Health Sciences has demonstrated that estrogens are also needed for the hormonal differentiation of the testes. More specifically, XY mice lacking estrogen receptors develop testes, but there is disruption of spermatogene-sis and ultimately degeneration of the seminiferous tubules, leading to sterility. Thus the presence of TDF and the conse-quent production of androgens early in life lead to the differentiation of the male body and brain, but estrogens are also essential for the full development of the male phenotype. In XX embryos, the absence of TDF, testosterone, and Müllerian-inhibiting hormone allows the indifferent gonad to differentiate into an ovary, the Wolffian ducts to degenerate, and the Müllerian ducts to develop into the oviducts, uterus, and cervix. The tissue around the urogenital groove becomes the clitoris, labia, and vagina. In short, the early absence of androgens leads to the differ-entiation of a female body and brain. However, development of the female phenotype also depends on estrogens; the absence of both α and β estrogen receptors results in ovaries that resemble testes, with structures resembling semi-niferous tubule (including Sertoli-like cells) and the expression of Müllerian-inhibiting hormone. References COUSE, J. F., S. C. HEWITT, D. O. BUNCH, M. SAR, V. R. WALKER, B. J. DAVIS AND K. S. KORACH (1999) Postnatal sex reversal of the ovaries in mice lacking estrogen receptors alpha and beta. Science 286: 2328–2331. EDDY, E. M., T. F. WASHBURN, D. O. BUNCH, E. H. GOULDING, B. C. GLADEN, D. B. LUBAHN AND K. S. KORACH (1996) Targeted disruption of the estrogen receptor gene in male mice causes alteration of spermatogenesis and infertility. Endocrinology 137: 4796–4805. JOHNSON, M. H. AND B. J. EVERITT (1988) Essential Reproduction, 3rd Ed., pp. 1–34. Oxford: Blackwell Scientific. KOOPMAN, P., J. GUBBAY, N. VIVIAN, P. GOOD-FELLOW AND R. LOVELL-BADGE (1991) Male development of chromosomally female mice transgenic for Sry. Nature 351: 117–121. SINCLAIR, A. H., P. BERTA, M. S. PALMER, J. R. HAWKINS, B. L. GRIFFITHS, M. J. SMITH, J. W. FOSTER, A. M. FRISCHAUF, R. LOVELL-BADGE AND P. N. GOODFELLOW (1990) A gene from the human sex-determining region encodes a protein with homology to a conserved DNA-binding motif. Nature 346: 240–242. 716 Chapter Twenty-Nine in the developmental window two weeks prenatal to two weeks postnatal: rodent neurons contain an enzyme (aromatase) that converts testosterone to estradiol, a form of estrogen. Thus, the surge of testosterone in developing males is effectively a surge of estradiol. Although testosterone is popularly considered the “male” hormone and estrogen the “female” hormone, the active agent in the brains of both male and female rodents is estradiol. Once the conversion of testosterone to estradiol has occurred, estradiol can influence gene transcription by binding with intracellular receptors (α-and β-estrogen receptors) that regulate gene transcription (Figure 30.1). In Box B The Case of Bruce/Brenda In the early 1960s, identical XY twins were born to a Canadian couple. When the twins were 7 months old, the parents had them circumcised. The surgeon, per-forming the operation using an electro-cautery knife, burned one of the twins’ penises so severely that the penis was, in essence, destroyed. The medical consen-sus conveyed to the parents by the local physicians was that the disfigured twin would be unable to have a normal het-erosexual life, would be shunned by his peers, and would suffer in a variety of other ways. Given this dire prognosis, the parents consulted an eminent sex researcher, John Money at Johns Hopkins University, to help them decide what should be done. After meeting with the family, Money advocated that they surgically reassign the child’s sex and raise the boy as a girl. The parents consented, and at age 17 months the child’s testes were removed and his scrotum reshaped to resemble a vulva. The little boy, Bruce, became known as Brenda within the family and personal circle; Money’s medical records and published papers used the pseudo-nyms “John” and “Joan.” The parents did everything they could to raise Brenda as a normal female. Although Money’s published reports were optimistic, subsequent interviews with the family, including the child him-self, indicated that the truth was far more complex, and indeed deeply prob-lematic. In a detailed follow-up of the case, Milton Diamond of the University of Hawaii and Keith Sigmundson described the struggle that Brenda suf-fered from the earliest age. The child refused to wear dresses, urinated stand-ing up, always felt that something was wrong, and refused to comply with the hormone treatments that were initiated at puberty. At the age of 14, Brenda demanded to know the truth, and her equally frustrated parents reluctantly gave an account of the early events that had resulted in the current situation. Ironically, Brenda was greatly relieved to understand why “she” had always been subject to such deeply conflicting feelings, which had sometimes made life so miserable that “she” contemplated sui-cide. Brenda immediately reverted to male dress and behavior and started going by the name of David. David, who is now nearly 40, eventually underwent surgery to be reconfigured as a pheno-typic male. He married, adopted his wife’s children, and has lived a relatively conventional life as a father and husband. This case underscores the fact that, in the words of Diamond and Sigmundson, “the evidence [is] overwhelming that normal humans are not psychosocially neutral at birth but are, in keeping with their mammalian heritage, predisposed and biased to interact with environmen-tal, familial, and social forces in either a male or female mode.” Cases like David’s raise serious moral and ethical questions about the assignment of gen-der when, for one reason or another, that option is open. Since there is no indica-tion at birth how the brain has been shaped by early exposure to hormones, in many cases there is insufficient infor-mation to know with what sex the child, or the adult, will ultimately identify. In David’s case, a grievous mistake was made by failing to understand the over-whelming influence on the brain of cir-culating androgens during early sexual development. David, whose surname is Reimer, is the subject of the biography by J. Colapinto listed below, and has wel-comed the opportunity to make his case known in the interest of preventing such mistakes in the future. References COLAPINTO, J. (2000) As Nature Made Him: The Boy Who was Raised as a Girl. New York: Harper Collins. DIAMOND, M. AND H. K. SIGMUNDSON (1997) Sex reassignment at birth: Long-term review and clinical implications. Arch. Ped. Adolesc. Med. 151: 298–304. DREGER, A. D. (1998) “Ambiguous sex” or ambiguous medicine? The Hastings Center Report 28: 24–35. mammals generally, fetuses are exposed to estrogens generated by the maternal ovary and placenta. Why doesn’t this estrogen interfere with sex-ual differentiation in female offspring? Apparently, the answer is that devel-oping mammals have a circulating protein called a-fetoprotein that binds circulating estrogens. The female brain is kept from early exposure to large amounts of estrogens, since estrogens are bound by α-fetoprotein; the male brain, however, is exposed via early testosterone surge; testosterone is not affected by α-fetoprotein, and is aromatized to estradiol only once inside neurons. The conversion of testosterone to estrogen may not be as important in humans and other primates, where evidence suggests that sexual differenti-ation of the brain relies more on androgens and androgen receptors. It is also androgens that bear most of the responsibility for stimulating sex drive in females as well as males. For this reason, XY individuals with AIS can be “super-feminine” in their behavior and rarely choose females as sexual partners. Finally, the influence of hormones in humans and other animals may be reinforced by sex differences established by genetic effects that are unre-lated to hormonal differences during development. For example, Ingrid Reisert, working at the Universitat Albert-Einstein in Germany established that there are sex differences in the development of dopaminergic fibers in cell cultures prepared from the diencephalon prior to sexual differentiation. More recently, Geert DeVries and his colleagues at the University of Massa-chusetts created unusual male (XX with Sry; see Box A) and female (XY without Sry) transgenic mice. In these animals, testes development occurred independently of the X or Y chromosome, thus demonstrating that XY mice with ovaries are, at least in some respects, more masculinized (measured by the density of vasopressin-immunoreactive fibers in the lateral septum) than XX mice with testes. Complex as this configuration of chromosomal sex and phenotype may be, the experiment shows that at least one sexually dimorphic trait (the density of vasopressin fibers in the midbrain) depends on the presence of the Y chromosome, but not on the presence of testes and the androgens they secrete postnatally. This observation supports the notion that hormone-independent sex differences are a part of the developmental plan. This idea has also been examined in birds. Arthur Arnold and his group at the University of California at Los Angeles have shown that the well-known song patterns existing in male but not in female zebra finches are driven in part by genetic mechanisms that operate independently of hormone levels. These several studies raise the possibility that mechanisms in addition to hormones contribute to the sexual diversity of humans—a point that is important to bear in mind during the following discussion of the hormone-driven sex differences in rodents. Sex, Sexuality, and the Brain 717 HO Cholesterol O C CH3 O Progesterone O OH Testosterone 5-α-Reductase Aromatase 5-α-Dihydrotestosterone O H OH 17-β-Estradiol HO OH Figure 29.1 All sex steroids are synthesized from cholesterol. Cholesterol is first converted to progesterone, the common precursor, by four enzymatic reactions (rep-resented by the four arrows). Progesterone can then be converted into testosterone via another series of enzymatic reactions; testosterone in turn is converted to 5-a-dihydrotestosterone via 5-a-reductase, or to 17-b-estradiol via an aromatase. 17-b-estradiol mediates most of the known hormonal effects in the brains of both female and male rodents. 718 Chapter Twenty-Nine The Effect of Sex Hormones on Neural Circuitry Gonadal steroids—whether estrogens or androgens—stimulate sexually dimorphic patterns of development by binding to estrogen or androgen receptors. These receptors, which are transcription factors activated by hor-mone binding, influence gene transcription and, ultimately, the development of an array of targets, including sexually dimorphic neural circuits. (See Box C for further details about the actions of sex hormones.) During development, and to some extent throughout life, estradiol stimu-lates brain dimorphisms by increasing size, nuclear volume, dendritic length, dendritic branching, dendritic spine density, and synaptic connectiv-ity of the sensitive neurons. One of the first demonstrations of such effects was provided by Dominique Toran-Allerand at Columbia University, who Box C The Actions of Sex Hormones Sex hormones, which include progestins, androgens, and estrogens, are all steroids derived from a common precursor, cho-lesterol (see Figure 29.1). Despite the common tendency to the contrary, it is not really correct to think of estrogens as “female” and androgens as “male.” Females and males synthesize both estro-gens and androgens, but in ratios that are very different. Both sexes also have androgen and estrogen receptors in the brain, although there are some regional sex differences in receptor density Because sex steroids are lipids, they do not need membrane receptors to enter cells; they simply diffuse through the lipid bilayer. However, neurons and other cells have the capacity to select, concen-trate, and retain specific steroids by means of receptors and binding proteins in both the cytoplasm and nucleus. Dif-ferent areas of the adult brain have differ-ent steroid receptor patterns, with over-lapping distributions of receptor types. Thus, particular brain regions can be tar-gets for the actions of different classes of steroids (Figure A). For instance, estradiol receptors are sparsely distributed in the neocortex of rodents, but are prevalent in preoptic and hypothalamic areas and the anterior pituitary. Conversely, whereas receptors for 5-a-dihydrotestosterone (5-DHT) are found only in certain nuclei in the septum and hypothalamus, both estradiol and 5-DHT receptors are abun-dant in the frontal, prefrontal, and cingu-late areas of the cortex. Some neurons express receptors for more than one steroid and, as a result, hormones can have a synergistic effect. For example, all neurons with proges-terone receptors also express estrogen Corpus callosum Plane of section Hippocampus Midbrain Cerebellum Olfactory bulb Septum Pituitary Preoptic area Hypothalamus (A) (A) Distribution of estradiol-sensitive neu-rons illustrated in a sagittal section of the rat brain. Animals were given radioactively labeled estradiol; dots represent regions where the label accumulated. In the rat, most estradiol-sensitive neurons are located in the preoptic area, hypothalamus, and amygdala. (After McEwen, 1976.) noted the striking consequences of adding estrogens to fetal hypothalamic explants (Figure 29.2). Estradiol can also stimulate an increase of the number of synaptic contacts neurons receive in adult animals. For example, during periods of high circulating estrogen in the estrous cycle of female rodents (or after administration of estrogens) there is an increase in the density of spines and synapses on the apical dendrites of pyramidal neurons in the hip-pocampus (Figure 29.3). These changes in neuronal circuitry presumably underlie differences in learning and memory over the estrous cycle (e.g., dif-ferences in the spatial navigation of rodents). Other hormonally generated differences in brain circuits leading to differ-ences in reproductive behaviors in both female and male rodents have been documented by administering testosterone (or estrogens) to females, or by Sex, Sexuality, and the Brain 719 receptors. Although female reproductive behaviors can be elicited by estrogen alone, the behavior is greatly facilitated in females given estrogen followed by progesterone. Steroids can have a direct effect on neural activity by altering the permeabil-ity of the membrane to neurotransmitters and their precursors, or by altering the function of neurotransmitter receptors (Figure B). This type of effect has a latency-to-onset of seconds to minutes and makes it possible for sex steroids to explicitly modulate the efficacy of neural signaling. Sex steroids can also have an indirect effect on neural activity by forming non-covalent bonds with steroid receptors, or by affecting other signaling pathways. Binding to a steroid receptor causes a conformational change that allows the receptor to bind to specific DNA-recog-nition elements called hormone-respon-sive elements. Steroid receptor co-activa-tors, which are members of a family of co-activators that modulate the activity of steroid receptors, can enhance the effects of steroids by (1) opening up chromatin structure and (2) stabilizing the preinitiation complex at the level of the relevant promoter. Consequently, hormones can alter gene expression, leading to changes in the synthesis of specific proteins (Figure B). Such indirect hormonal actions have a latency-to-onset of minutes to hours. Most sexually dimorphic differences in the brains of females and males are thought to arise by the indirect actions of hormones on gene expression. References BROWN, T. J., J. YU, M. GAGNON, M. SHARMA AND N. J. MACLUSKY (1996) Sex differences in estrogen receptor and progestin receptor induction in the guinea pig hypothalamus and preoptic area. Brain Res. 725: 37–48. MCEWEN, B. S., P. G. DAVIS, B. S. PARSONS AND D. W. PFAFF (1979) The brain as a target for steroid hormone action. Annu. Rev. Neurosci. 2: 65–112. ROWAN, B. G., N. L. WEIGEL AND B. W. O’MAL-LEY (2000) Phosphorylation of steroid recep-tor coactivator-1: Identification of the phos-phorylation sites and phosphorylation through the mitogen-activated protein kinase pathway. J. Biol. Chem. 275: 4475–4483. TSAI, M.-J. AND B. W. O’MALLEY (1994) Molec-ular mechanisms of action of steroid/thyroid receptor superfamily members. Annu. Rev. Biochem. 63: 451–486. Presynaptic cell (B) Postsynaptic cell Estrogen Estrogen receptor/ transcription factor Nuclear envelope DNA Receptor bound to DNA Neuron Steroid Direct action Indirect action Promotes or inhibits transcription Alters membrane permeability Alters neuro-transmitter . synthesis . release . reuptake (B) Steroids have direct and indirect effects on neurons. Dashed line shows direct effects of hormones on the pre- or postsynaptic membrane, which alters neurotransmitter release, and affects neurotransmitter recep-tors. Solid line shows indirect effects of hor-mones, which act at the level of the nucleus to alter protein synthesis. (After McEwen et al., 1978.) 720 Chapter Twenty-Nine depriving males of testosterone by castrating them at birth. Geoffrey Raisman and Pauline Field, then working at Oxford University, found a greater num-ber of synapses on spines in the preoptic region of the hypothalamus in nor-mal female rats compared to the equivalent region in males. This difference is directly under the influence of hormones during development. Castrating males within 12 days of birth increased the density of these synapses to female levels, whereas administration of testosterone to developing females led to a reduction of preoptic spine synapses to male levels. Neonatal castra-tion also affects other aspects of brain function. Unlike intact males, male rats castrated soon after birth respond to estradiol with a surge of luteinizing hormone (which, in the presence of ovaries, would lead to ovulation); and treatment of newborn females with testosterone leads to the loss of the luteinizing hormone surge. Subsequently, Roger Gorski and his colleagues at the University of Cali-fornia at Los Angeles discovered a nucleus in the male rodent hypothalamus that is so small as to be essentially missing in the female; logically enough, they called this structure the sexually dimorphic nucleus (SDN). This sex difference also develops under the influence of hormones; Gorski found that the SDN in male rats could be reduced in size to that of the female by castra-tion within the first 2 weeks after birth. Similarly, the size of the female SDN could be increased to that of the male by early administration of androgens. Since the preoptic area is crucial for the display of male sex behavior in many species, the sex difference in the SDN seemed likely to be related to male sexual function. Indeed, female rodents given testosterone early in development exhibit mounting behavior, whereas male rodents deprived of testosterone exhibit lordosis (i.e., a behavior receptive to mounting). Nonetheless, the exact role of the SDN plays in these behavioral sex differ-ences is not clear. In short, the development of sexually dimorphic structures in the rodent brain is primarily under the control of circulating sex hormones, with some determined at least in part by genes on the Y chromosome. Again, the effect of hormones is less certain and may be more complex in the primate brain. For example, Kim Wallen at Emory University investigated the role of social conditions in establishing some of the sex-typical behaviors of rhesus mon-keys that were once thought to be solely determined by hormones. He found that although rough-and-tumble play and mounting (typical juvenile behav-ior for this species) were exhibited less frequently by females than by males, the environment in which the animals were reared affected the degree of this sex difference. Moreover, when reared with only their own sex, males dis-played more and females less of these behaviors. Thus, while the propensity for such sex-typical juvenile behaviors may be established by hormonal actions, their expression is shaped by the environment in which the animal develops. It is not difficult to extrapolate from these studies to humans, where it seems especially important to consider both nature and nurture in the development of differences between sexes. Other Central Nervous System Dimorphisms Specifically Related to Reproductive Behaviors Other sexual dimorphisms in the central nervous system influence behaviors ranging from the control of motor responses in reproductive behaviors to aspects of cognition. This section briefly reviews additional examples specif-ically related to reproductive behavior; the following section considers sex-ual dimorphisms related to cognitive abilities. Figure 29.2 Estrogen causes exuberant outgrowth of neurites in hypothalamic explants from newborn mice. (A) Con-trol explant showing only a few silver-impregnated processes growing from the explant. (B) An estradiol-treated explant has many more neurites grow-ing from its center. (From Toran-Allerand, 1978.) (A) (B) Perhaps the best example of sexual dimorphism related to motor control of a reproductive behavior is the difference in size of a nucleus in the lumbar segment of the rat spinal cord called the spinal nucleus of the bulbocaver-nosus. The motor neurons of this nucleus innervate two striated muscles of the perineum, the bulbocavernosus and levator ani (Figure 29.4A). In males, the bulbocavernosus and levator ani attach to the penis and play a role both in urination and copulation. In female rats, the bulbocavernosus is absent and the levator ani is dramatically reduced in size. Marc Breedlove and his colleagues first showed that the spinal nucleus containing the motor neu-rons that innervate the bulbocavernosus is absent in female rats but is quite large in males (Figure 29.4B,C). Breedlove and Nancy Forger then demon-strated that the development of this dimorphism in the spinal cord depends on the maintenance of target muscles by circulating androgens. Since devel-oping males have high levels of circulating sex steroids and females do not, these muscles largely degenerate in developing female rats, leaving the motor neurons to atrophy in the absence of trophic support (see Chapter 23). As with most sexual dimorphisms, the analogous situation in humans is considerably less clear than in experimental animals. In humans, the spinal cord structure that corresponds to the spinal nucleus of the bulbocavernosus in rats is called Onuf’s nucleus. Onuf’s nucleus consists of two cell groups in the sacral cord, the dorsal medial and the ventral lateral groups. The dor-sal medial group is not sexually dimorphic; however, human females have fewer neurons in the ventral lateral group than males (Figure 29.4D). In con-Sex, Sexuality, and the Brain 721 20 18 16 14 12 10 8 6 4 2 0 Dendritic spines/10 µm Dendritic spine density Dendritic morphology High progesterone and high estrogen Progesterone and estrogen at basal levels Progesterone receptor agonist Dendritic spines (1) (2) (3) Figure 29.3 Changes in the dendrites of rat hippocampal neurons following vari-ous hormonal regimes. Left: Dendritic spine density under each of the indicated conditions (recall that dendritic spines, which are small extensions from the den-dritic shaft, are sites of synapses). Right: Tracings of representative apical dendrites from hippocampal pyramidal neurons: (1) After administration of progesterone and estrogen in high dosage. (2) After administration of progesterone and estrogen at basal levels. (3) After administration of a progesterone receptor antagonist. (After Woolley and McEwen, 1992.) 722 Chapter Twenty-Nine (B) (C) (D) Motor neuron count 400 800 1200 1600 2000 2400 Ventral-lateral group (VL) Dorsal-medial group (DM) Female Male (A) Male rat pelvis Colon Anus Lavator ani Bulbouretheral gland Penis Medial bulbocavernosus muscle Ischiocavernosus muscle Lateral bulbocavernosus muscle Figure 29.4 The number of spinal motor neurons related to the perineal muscles is different in female and male rodents. (A) Diagram of the perineal region of a male rat. (B) A histological cross section through the fifth lumbar segment of the male. Arrows indicate the spinal nucleus of the bulbocavernosus. (C) Same region of the spinal cord in the female rat. There is no equivalent grouping of densely stained neurons. (D) Histograms showing motor neuron counts in the dorsal-medial and ventral-lateral groups of Onuf’s nucleus in human females and males. (A after Breedlove and Arnold, 1984; B and C from Breedlove and Arnold, 1983; D after Forger and Breedlove, 1986.) trast to rodents, human females retain a bulbocavernosus muscle throughout life (which serves to constrict the vagina), but the muscle is smaller than in the male. The difference in nuclear size in humans, as in rats, presumably reflects the difference in the number of muscle fibers the motor neurons must innervate. A variety of reproductive behaviors, including desire, priming, and par-enting behaviors, are governed by the hypothalamus. Neurons in the medial preoptic area of the primate anterior hypothalamus apparently mediate at least some of these behaviors (Figure 29.5). In rhesus monkeys, physiological recordings from hypothalamic neurons during sexual activity show that neurons of the medial preoptic area of the anterior hypothalamus fire during different components of the sexual act. Such recordings have been carried out on male monkeys sitting in a flexible restraining chair that allows the male to gain access to a receptive female by pressing a bar, which brings the female close enough to allow the male to mount her. In this way, the responses of hypothalamic neurons can be correlated with “desire” (number of bar presses) and mating behavior (contact, mounting, intromission, thrusting). Neurons in the medial preoptic area of the male hypothalamus fire rapidly before sexual behavior, but decrease their activity upon contact with the female and mating (Figure 29.6). In contrast, neurons in the dorsal anterior hypothalamus begin firing at the onset of mating and continue to fire vigorously during intercourse. Although these studies do not speak to sexual dimorphism, they provide direct evidence about the variety of sexual behaviors mediated by the hypothalamus. Sex, Sexuality, and the Brain 723 Medial preoptic area (nucleus) Supraoptic nucleus Suprachiasmatic nucleus Paraventricular nucleus Anterior hypothalamic area (anterior nucleus) Dorsomedial nucleus Ventromedial nucleus Optic chiasm Anterior commissure Fornix Thalamus Hypothalamic sulcus Endocrine organs Thalamus and neocortex Hippocampus Anterior hypothalamus Amygdala Other regions of hypothalamus Pituitary Endocrine feedback to all brain regions above Motor output via brainstem and spinal cord (B) (A) Figure 29.5 Organization of the com-ponents of the hypothalamus involved in regulating sexual functions. (A) The human hypothalamus, illustrating the location of the anterior hypothalamic area and other nuclei in which sexual dimorphisms have been observed in either humans or experimental animals. (B) Diagram of the major relationships of the anterior hypothalamus with other brain regions. Blue arrows denote neural connections; yellow arrows denote hormonal links; purple arrow denotes a combination of hormonal and neural connections. Although this infor-mation comes largely from studies of rodents, it is reasonable to assume that these interactions are characteristic of mammals. 724 Chapter Twenty-Nine Such studies of rodents and non-human primates have stimulated a vari-ety of further observations in the human hypothalamus. The most thor-oughly documented examples of sexually dimorphic hypothalamic nuclei in humans have been described by Laura Allen and Roger Gorski at the Uni-versity of California at Los Angeles and by Dick Swaab and his colleagues at the Netherlands Institute for Brain Research. Swaab first found a sex differ-ence in the anterior hypothalamus of humans in a cell group that they named the sexually dimorphic nucleus (by analogy with the SDN of rats). Subsequently, Allen and Gorski discovered that there are actually four cell groupings within the anterior hypothalamus of humans, which they called the interstitial nuclei of the anterior hypothalamus (INAH). The INAH are numbered 1 to 4, from dorsolateral to ventromedial; INAH-1 corresponds to the nucleus initially discovered by Swaab (Figure 29.7). Allen and Gorski reported that INAH-2 and INAH-3 can be more than twice as large in males as they are in females. What might account for these somewhat discrepant findings? First, human studies are always complicated by the difficulty of obtaining human brains that meet the criteria of uniformity applied to the brains of experimental ani-mals. Second, it takes a long time to acquire a large enough number of human brains to confidently interpret the results. Swaab and colleagues sug-gested that INAH-1 and 2 change in size over time; thus the age of the sub-jects studied might also influence observed sex differences. For instance, INAH-1 is evidently about the same size in females and males up until 2–4 years of age; it then becomes larger in males until approximately 50 years of age, when it decreases in size in both sexes. Although generally larger in males, INAH-2 is larger in females of childbearing age than in prepubescent and postmenopausal females. Changes in nuclear size with age in humans presumably arise as a result of changing levels of circulating sex steroids. Despite the difficulties inherent in the interpretation of such studies, one aspect of human reproduction in which these hypothalamic nuclei have been implicated is the choice of a sexual partner. In addition to heterosexual behavior, some humans express sexual behaviors toward both females and males (bisexuality), and some only toward members of their own pheno-typic sex (homosexuality). Still other people are interested the opposite sex Female in view Bar presses bring male to female Mating sequence Ejaculation 100 50 Action potentials/sec Time (min) 1 0 2 3 4 5 6 7 8 Figure 29.6 Many neurons in the primate hypothalamus are actively associated with sexual behavior. This example shows a histogram of neuronal activity recorded in the medial preoptic area in a male monkey exposed to a receptive female (see text). The firing rate of the neuron changes during different phases of sexual activ-ity. (After Oomura et al., 1983.) but with a gender identity that is at odds with their phenotypic sex (trans-genderism). Based on experimental work in animals and evidence that rela-tively simple sexual behaviors are influenced by brain dimorphisms, explaining these more complex behaviors in the same general way has been an attractive possibility. To investigate this issue, Simon LeVay, then working at the Salk Institute, compared the INAH of females, heterosexual males, and homosexual males. LeVay first confirmed Allen and Gorski’s findings that of the four INAH nuclei, at least two are sexually dimorphic. He went on to discover that one of these nuclei—INAH-3—is more than twice as large in male heterosexuals as in male homosexuals (Figure 29.8A) and sug-gested that this difference is related to sexual orientation. These studies have since been replicated by William Byne at the Mount Sinai School of Medicine, who confirmed the sexual dimorphism in INAH-3, although the difference was less than that reported by Allen and by LeVay. Byne concluded that INAH-3 in the gay men studied was intermediate in Sex, Sexuality, and the Brain 725 1 2 3 4 Third ventricle Paraventricular nucleus Supraoptic nucleus (A) (B) Male Female (C) (D) 1 1 1 1 2 2 3 4 4 3 Figure 29.7 Sexual dimorphisms in the interstitial nuclei of the human anterior hypothalamus (INAH). (A) Diagrammatic coro-nal section through the anterior hypothalamus. The four intersti-tial nuclei of the anterior hypothalamus (red) are indicated by the numbers 1–4. (B–D) Micrographs showing the interstitial nuclei from a male (left column) and a female (right column). The male examples were taken from the left side of the brain, female examples from the right side at the same level. (B) INAH-1. (C) INAH-1 and 2. Note that INAH-2 is less compact in the female. (D) INAH-3 and 4. INAH-4 is well represented in both the male and female, whereas INAH-3 is clearly less distinct in the female. (B–D from Allen et al., 1989.) 726 Chapter Twenty-Nine size between heterosexual men and women. The difference between the size of INAH-3 in the heterosexual and gay men in the study was of borderline significance, and thus neither a strong confirmation nor a refutation of ear-lier work. Other researchers have suggested that dimorphisms of additional hypo-thalamic nuclei are related to sexual orientation and gender identity. Dick Swaab and Michel Hofman at the Netherlands Institute for Brain Research studied the suprachiasmatic nucleus of the hypothalamus, which lies just above the optic chiasm in both rodents and humans and generates circadian (A) INAH-3 (B) Suprachiasmatic nucleus Heterosexual male Homosexual male 0.1 0.2 0.3 0.4 0.5 0.6 Volume (mm3) Hetero-sexuals (No AIDS) Homo-sexuals (AIDS) Hetero-sexuals (AIDS) 25 50 75 100 125 Total cell number (×103) Hetero-sexuals (No AIDS) Homo-sexuals (AIDS) Hetero-sexuals (AIDS) Volume Number of neurons Figure 29.8 Brain dimorphisms in heterosexual and homosexual human males. (A) Micrographs showing difference in INAH-3 between heterosexual and homo-sexual males. Arrowheads outline the nucleus. (B) The suprachiasmatic nucleus may also differ between homosexual and heterosexual males. The suprachiasmatic nucleus of homosexual males appears to be larger (left histogram) and to contain more neurons (right histogram) than that of heterosexual males with or without AIDS (which could be a significant variable in such studies). (A from LeVay, 1991; B after Swaab and Hofman, 1990.) rhythms (see Figure 29.5A and Chapter 27). In examining the suprachias-matic nuclei of females, heterosexual males, and homosexual males, Swaab and Hofman found the volume of the suprachiasmatic nucleus to be almost twice as large in male homosexuals compared to male heterosexuals (Figure 29.8B). They found no difference, however, between the size of the suprachi-asmatic nucleus in females and heterosexual males. Like LeVay, they sug-gested that the difference in nuclear size between homosexual and hetero-sexual men might be related to sexual orientation. This same group reported another dimorphism that may be related to gender identity. In comparing male-to-female transgendered individuals to non-transgendered males, they found that another hypothalamic structure, the bed nucleus of the stria termi-nalis, is smaller in transgendered males, being closer in size to that of females. The history of these several research efforts highlights the difficulty of car-rying out controlled studies that measure small differences in the human brain and the importance of reliable replication. Taken together, however, the sum of this evidence suggests a plausible explanation of the continuum of human sexuality: small differences in the relevant brain structures generate significant differences in sexual identity and behavior. By analogy with rodents, it seems likely these human brain dimorphisms are established by the early influence of hormones acting on the brain nuclei that mediate vari-ous aspects of sexuality. For instance, low levels of circulating androgens in a male early in life could lead to a relatively feminine brain in chromosomal males, whereas high levels of circulating androgens in females could lead to a relatively masculinized brain in chromosomal females. As attractive as this hypothesis may be, the development of sexuality in humans is almost certainly a good deal more complicated. Although LeVay’s findings support the idea that homosexuality is related to “feminization” of the male brain (recall that INAH-3 in gay males is smaller than in straight males), Swaab and Hofman’s data on the size of the suprachiasmatic nucleus undermine the interpretation that the male homosexual’s brain is simply “feminized” by a lack of androgens early in development. Whereas they found a difference in the volume of this suprachiasmatic nucleus between homosexual and heterosexual males, in contrast to LeVay they found no difference in the volume of this nucleus between females and het-erosexual males. In addition, the development of the INAH-1 dimorphism (see above) occurs between 2 and 4 years of age—long after the first testos-terone surge in males. These discrepancies suggest that the development of sexually dimorphic nuclei in humans does not depend solely on early hor-mone levels. As discussed earlier, genetic effects of the Y chromosome independent of those influencing the production of hormones can affect sexually dimorphic traits. It should also be remembered that adult neural circuits also have some plasticity (see Chapter 24 and the following section), leaving open the possi-bility that behavior, experience, and changes in circulating hormone levels combine to generate dimorphisms at later life stages. In apparent confirma-tion of this suggestion, Breedlove and colleagues have reported that the pos-terodorsal nucleus of the medial amygdala has a greater volume in male rats than in female, but that castration of adult males and androgen treatment of adult females reverses this effect. Thus, the question of whether we are sim-ply “born that way” with respect to sexuality remains difficult to answer. Like most developmental events, a combination of intrinsic and extrinsic fac-tors are involved. Sex, Sexuality, and the Brain 727 728 Chapter Twenty-Nine Despite all these uncertainties, work over the last decade has clearly placed human sexuality on a much firmer biological footing. This is a welcome advance over the not-too-distant past when unusual sexual behavior was commonly explained in social, Freudian, or moralistic terms. Brain Dimorphisms Related to Cognitive Function Evidence for sexually dimorphic behavior in humans that is not directly related to reproductive functions comes mainly from clinical observations. For example, neurologists have reported that females suffer aphasia less often than males after damage to the left hemisphere. This observation led to the suggestion that language functions are to some degree differently repre-sented in females and males. To explore this issue, Doreen Kimura at the University of Western Ontario looked at the language ability in right-handed patients with unilateral lesions of the left cerebral cortex. She found that females were more likely to suffer aphasia if the damage was to the anterior left hemisphere, whereas males were more likely to suffer aphasia if the damage was located posteriorly. Kimura’s data suggest that language areas of the female brain are more anteriorly represented and thus less vulnerable to stroke. Susan Rossell and her colleagues at University College London have sug-gested other such sexual dimorphisms in the human brain. Using fMRI to measure activation during a lexical visual field task (a language task that shows replicable sex differences related to speed and accuracy), Rossell and colleagues found more brain activity in response to such challenges in females than in males. Females show greater activation of the right hemisphere areas, especially in the inferior frontal, inferior posterior, and middle temporal gyri. In addition, females have a left visual field advantage when the task is pre-sented visually, showing faster reaction times than males. In males, activation is more lateralized to the left hemisphere, especially the inferior posterior tem-poral lobe and the fusiform and lingual gyri. These studies and the earlier work by Kimura suggest that females and males use overlapping but some-what different cortical areas to carry out language tasks. The performance of tasks that depend more on one hemisphere than the other has also been examined in females and males. One simple test for visuospatial differences entails how well girls and boys are able to identify shapes after feeling them with the right or left hand while blindfolded. Both sexes perform equally well with either hand up to about 6 years of age. Thereafter, boys start scoring better when they use their left hand, whereas girls continue to score equally well with either hand up to 13 years of age, when they also begin to do better with their left hand. This study suggests that boys develop the right hemispheric lateralization of visuospatial skills earlier than girls. The idea that females and males develop lateralized functions at different rates is supported by studies of the development of the prefrontal cortex of non-human primates. Removing the prefrontal cortex before 15 to 18 months of age does not affect motor-planning functions in female rhesus monkeys, although the same lesion in male monkeys at this age diminishes these skills. In a similar vein, Matthias Riepe and his colleagues at the University of Ulm have reported that human females and males use different strategies to navigate in an unfamiliar environment. Males trying to find their way out of a three-dimensional virtual reality maze use the geometry of the whole scene and “escape” from the maze in a little more than 2 minutes on aver-age. Females tend to use local landmarks or clues and take about a minute longer to get out. Functional brain imaging shows that both sexes use the right hippocampus during this task, but that men use the left hippocampus as well. Conversely, women tend to use the right prefrontal cortex, whereas men do not. Involvement of the inferior parietal lobe is also different in females and males. The two sides of this structure are thought to mediate different aspects of visual processing, with the left side more involved in perceptions such as judging how fast something is moving or mentally rotat-ing three-dimensional objects, and the right side mediating working mem-ory of spatial relationships. Finally, Godfrey Pearlson and his colleagues at Johns Hopkins University have determined that the right parietal lobe is larger than the left in females, whereas in males the left parietal lobe is larger than the right. None of these studies is in itself compelling, but taken together they sup-port the idea that the two sexes to some degree use different cognitive strate-gies, and that these differences affect some aspects of behavior. Hormone-Sensitive Brain Circuits in Adult Animals As mentioned earlier, there is growing evidence that some brain circuits con-tinue to change over the course of an individual’s life, depending on both experience and hormonal milieu. For example, changes in the brain circuits of adult rats occur in conjunction with parenting behavior. Michael Merzenich, Judith Stern and their colleagues at the University of California at San Francisco have shown that the cortical representation of the ventrum (chest wall) is altered in the somatic sensory cortex of the lactating female. As determined by electrophysiological mapping, the representation of the ventrum is approximately twice as large in nursing females as in non-lactat-ing controls. Moreover, the receptive fields of the neurons representing the skin of the ventrum in lactating females are decreased to about a third of that of non-lactating females (Figure 29.9). Both the increase in cortical rep-resentation and the decrease in receptive field size highlight the fact that changes in behavior can be reflected in changes of cortical circuitry in adult animals. Another example of adult plasticity under hormonal control is the altered connections between cells of the female rat hypothalamus after giving birth. In females prior to pregnancy, the relevant hypothalamic neurons are iso-lated from each other by thin astrocytic processes. Under the influence of the hormonal environment prevailing during birth and lactation, the glial processes retract and the oxytocin- and vasopressin-secreting neurons become electrically coupled by gap junctions (Figure 29.10). Before the female gives birth, these neurons fire independently; during lactation, how-ever, they fire synchronously, releasing pulses of oxytocin into the maternal circulation. These surges of oxytocin cause the contraction of smooth mus-cles in the mammary glands, and hence milk ejection. Interestingly, the changes are thought to be mediated by olfactory cues, since the lactating cir-cuits can be induced in virgin females simply by placing them in the vicinity of pups. These examples of adult plasticity suggest that some of the sexual circuits of the brain are malleable not only during development, but to some degree throughout life under the effects of experience and the changing hormonal milieu. Sex, Sexuality, and the Brain 729 730 Chapter Twenty-Nine (D) Receptive field size (cm2) 0 5 10 15 Non-lactating control Lactating Virgin control (B) Nonlactating rat (18 days postpartum) Ventrum Hindlimb Dorsum Tail NCR Forelimb Neck Neck Tail Hindlimb Dorsum NCR HL Forelimb NCR NCR Neck Tail NCR Ventrum Ventrum Ventrum NCR NCR Location of nipples on ventrum Primary somatic sensory cortex (A) Female rat (B) Nonlactating rat (18 days postpartum) (C) Lactating rat (19 days postpartum) Figure 29.9 Changes in the cortical representation of the chest wall in the rat pri-mary somatic sensory cortex during lactation. (A) Ventrum of the female rat; dots mark the position of nipples. (B) Diagram of somatic sensory cortex in a nonlactat-ing control rat, showing the amount of cortex normally activated by stimulation of the ventrum. Squares mark electrode penetrations; colors signify the estimated rep-resentation. (C) Similar diagram from a 19-day postpartum, lactating rat. Note the expansion of the representation of the ventrum. NCR, no cutaneous response. (D) Histogram of receptive field sizes of single neurons in nonlactating control, lactat-ing, and virgin control rats. The receptive field sizes of neurons in lactating mothers are decreased. (B–C after Xerri et al., 1994.) Figure 29.10 Changes in neurons of the rat supraoptic nucleus during lacta-tion. Left: Before birth, the relevant neu-rons and their dendrites are isolated from each other by astrocytic processes (blue). Right: During nursing of the young, the astrocytic processes with-draw, and neurons and their dendrites show close apposition (arrow pairs) that allows electrical synapses to form between adjacent neurons (see Chapter 5). (From Modney and Hatton, 1990.) Summary Differences in female and male behaviors ranging from copulation to cogni-tion are linked to differences in brain structure. Although the neural basis for these sexual dimorphisms is much clearer in experimental animals, the evidence for sex-related differences in the human brain has grown rapidly in recent years. The region of the brain in which the most clear-cut struc-tural dimorphisms occur is the anterior hypothalamus, which governs reproductive behavior. In rats and monkeys, the nuclei in this region play a role not only in the mechanics of sex, but also in desire, parenting, and sex-ual orientation. In the rodent, sexual dimorphisms develop primarily as a result of hormonal action on neurons during early development. On the strength of this knowledge about sexual development in experimental ani-mals, neurobiological explanations for a variety of human sexual behaviors have been proposed. Such models remain controversial because the sexual dimorphisms of the human brain and their functional significance are nei-ther fully established nor well understood. In addition, only a few such studies have been replicated. Nevertheless, it seems likely that a deeper understanding of how the dynamic interplay between behavior, genetics, hormones, and environment influence the brain throughout life will even-tually explain the fascinating continuum of human sexuality. Sex, Sexuality, and the Brain 731 Additional Reading Reviews BLACKLESS, M., A. CHARUVASTRA, A. DERRYCK, A. FAUSTO-STERLING, K. LAUZANNE AND E. LEE (2000) How sexually dimorphic are we? Review and synthesis. Am. J. Human Biol. 12: 151–166. MACLUSKY, N. J. AND F. NAFTOLIN (1981) Sex-ual differentiation of the central nervous sys-tem. Science 211: 1294–1302. MCEWEN, B. S. (1999) Permanence of brain sex differences and structural plasticity of the adult brain. PNAS 96: 7128–7129. SMITH, C. L AND B. W. O’MALLEY (1999) Evolv-ing concepts of selective estrogen receptor action: From basic science to clinical applica-tions. Trends Endocrinol. Metab. 10: 299–300. SWAAB, D. F. (1992) Gender and sexual orien-tation in relation to hypothalamic structures. Horm. Res. 38 (Suppl. 2): 51–61. SWAAB, D. F. AND M. A. HOFMAN (1984) Sexual differentiation of the human brain: A histori-cal perspective. In Progress in Brain Research, Vol. 61. G. J. De Vries (ed.). Amsterdam: Else-vier, pp. 361–374. Important Original Papers ALLEN, L. S., M. HINES, J. E. SHRYNE AND R. A. GORSKI (1989) Two sexually dimorphic cell groups in the human brain. J. Neurosci. 9: 497–506. ALLEN, L. S., M. F. RICHEY, Y. M. CHAI AND R. A. GORSKI (1991) Sex differences in the corpus callosum of the living human being. J. Neu-rosci. 11: 933–942. BEYER, C., B. EUSTERSCHULTE, C. PILGRIM, AND I. REISERT (1992) Sex steroids do not alter sex dif-ferences in tyrosine hydroxylase activity of dopaminergic neurons in vitro. Cell Tissue Res. 270: 547–552. BREEDLOVE, S. M. AND A. P. ARNOLD (1981) Sex-ually dimorphic motor nucleus in the rat lum-bar spinal cord: Response to adult hormone manipulation, absence in androgen-insensi-tive rats. Brain Res. 225: 297–307. BYNE, W., M. S. LASCO, E. KERUETHER, A. SHIN-WARI, L. JONES AND S. TOBET (2000) The intersti-tial nuclei of the human anterior hypothala-mus: Assessment for sexual variation in volume and neuronal size, density, and num-ber. Brain Res. 856: 254–258. BYNE, W., S. TOBET, L. A. MATTIACE, M. S. LASCO, E. KEMETHER, M. A. EDGAR, S. MORGELLO, M. S. BUCHBAUM AND L. B. JONES (2002) The interstitial nuclei of the human anterior hypothalamus: An investigation of variation with sex, sexual orientation, and HIV status. Horm. Behav. 40: 86–92. COOKE, B. M., G. TABIBNIA AND S. M. BREEDLOVE (1999) A brain sexual dimorphism controlled by adult circulating androgens. PNAS 96: 7538–7540. DEVRIES, G. J., W. F. RISSMAN, R. B. SIMMERLY, L. Y. YANG, E. M. SCORDALAKES, C. J. AUGER, A. SWAIN, R. LOVELL-BADGE, P. S. BURGOYNE AND A. P. ARNOLD (2002) A model system for study of sex chromosome effects on sexually dimor-phic neural and behavioral traits. J. Neurosci. 22: 9005–9014. FORGER, N. G. AND S. M. BREEDLOVE (1987) Motoneuronal death during human fetal development. J. Comp. Neurol. 264: 118–122. FREDERIKSE, M. E., A. LU, E. AYLWARD, P. BARTA AND G. PEARLSON (1999) Sex differences in the inferior parietal lobule. Cerebral Cortex 9: 896–901. GORSKI, R. A., J. H. GORDON, J. E. SHRYNE AND A. M. SOUTHAM (1978) Evidence for a mor-phological sex difference within the medial preoptic area of the rat brain. Brain Res. 143: 333–346. GRON, G., A. P. WUNDERLICH, M. SPITZER, R. TOMCZAK, AND M. W. RIEPE (2000) Brain activa-tion during human navigation: Gender differ-ent neural networks as substrate of perfor-mance. Nat. Neurosci. 3: 404–408. LEVAY, S. (1991) A difference in hypothalamic structure between heterosexual and homosex-ual men. Science 253: 1034–1037. LASCO, M. S., T. J. JORDAN, M. A. EDGAR, C. K. PETITO AND W. BYNE (2002) A lack of dimor-phism of sex or sexual orientation in the human anterior commissure. Brain Res. 936: 95–98. MEYER-BAHLBURG, H. F. L., A. A. EHRHARDT, L. R. ROSEN AND R. S. GRUEN (1995) Prenatal estrogens and the development of homosex-ual orientation. Dev. Psych. 31:12–21. MODNEY, B. K. AND G. I. HATTON (1990) Moth-erhood modifies magnocellular neuronal interrelationships in functionally meaningful ways. In Mammalian Parenting, N. A. Krasne-gor and R. S. Bridges (eds.). New York: Oxford University Press, pp. 306–323. RAISMAN, G. AND P. M. FIELD (1973) Sexual dimorphism in the neuropil of the preoptic area of the rat and its dependence on neonatal androgen. Brain Res. 54: 1–29. ROSSELL, S. L., E. T. BULLMORE, S. C. R. WILLIAMS AND A. S. DAVID (2002) Sex differ-ences in functional brain activation during a lexical visual field task. Brain Lang. 80: 97–105. SWAAB, D. F. AND E. FLIERS (1985) A sexually dimorphic nucleus in the human brain. Sci-ence 228: 1112–1115. WALLEN, K. (1996) Nature needs nurture: The interaction of hormonal and social influences on the development of behavioral sex differ-ences in Rhesus monkeys. Horm. Behav. 30: 364–378. WOOLLEY, C. S. AND B. S. MCEWEN (1992) Estradiol mediates fluctuation in hippocam-pal synapse density during the estrous cycle in the adult rat. J. Neurosci. 12: 2549–2554. XERRI, C., J. M. STERN AND M. M. MERZENICH (1994) Alterations of the cortical representa-tion of the rat ventrum induced by nursing behavior. J. Neurosci. 14: 1710–1721. ZHOU, J.-N., M. A. HOFMAN, L. J. G. GOOREN AND D. F. SWAAB (1995) A sex difference in the human brain and its relation to transsexuality. Nature 378: 68–70. Books FAUSTO-STERLING, A. (2000) Sexing the Body. New York: Basic Books. GOY, R. W. AND B. S. MCEWEN (1980) Sexual Differentiation of the Brain. Cambridge, MA: MIT Press. LEVAY, S. (1993) The Sexual Brain. Cambridge, MA: MIT Press. LEVAY, S. AND S. M. VALENTE (2003). Human Sex-uality. Sunderland, MA: Sinauer Associates. 732 Chapter Twenty-Nine Overview One of the most intriguing of the brain’s complex functions is the ability to store information provided by experience and to retrieve much of it at will. Without this ability, many of the cognitive functions discussed in the preced-ing chapters could not occur. Learning is the name given to the process by which new information is acquired by the nervous system and is observable through changes in behavior. Memory refers to the encoding, storage, and retrieval of learned information. Equally fascinating (and important) is the normal ability to forget information. Pathological forgetfulness, or amnesia, has been especially instructive about the neurological underpinnings of memory; amnesia is defined as the inability to learn new information or to retrieve information that has already been acquired. The importance of memory in daily life has made understanding these several phenomena one of the major challenges of modern neuroscience, a challenge that has only begun to be met. The mechanisms of plasticity that provide plausible cellu-lar and molecular bases for some aspects of information storage have been considered in Chapters 22 through 24. The present chapter summarizes the broader organization of human memory, surveys the major clinical manifes-tations of memory disorders, and considers the implications of these disor-ders for ultimately understanding human memory in more detailed terms. Qualitative Categories of Human Memory Humans have at least two qualitatively different systems of information stor-age, which are generally referred to as declarative memory and nondeclara-tive memory (Figure 30.1; see also Box A). Declarative memory is the storage (and retrieval) of material that is available to consciousness and can be expressed by language (hence, “declarative”). Examples of declarative mem-ory are the ability to remember a telephone number, a song, or the images of some past event. Nondeclarative memory (sometimes referred to as proce-dural memory), on the other hand, is not available to consciousness, at least not in any detail. Such memories involve skills and associations that are, by and large, acquired and retrieved at an unconscious level. Remembering how to dial the telephone, how to sing a song, how to efficiently inspect a scene, or making the myriad associations that occur continuously are all examples of memories that fall in this category. It is difficult or impossible to say how we do these things, and we are not conscious of any particular memory during their occurrence. In fact, thinking about such activities may actually inhibit the ability to perform them efficiently (thinking about exactly how to stroke a tennis ball or swing a golf club often makes matters worse). Chapter 30 733 Memory 734 Chapter Thirty Figure 30.1 The major qualitative cate-gories of human memory. Declarative memory includes those memories that can be brought to consciousness and expressed as remembered events, images, sounds, and so on. Nondeclara-tive, or procedural, memory includes motor skills, cognitive skills, simple classical conditioning, priming effects, and other information that is acquired and retrieved unconsciously. While it makes good sense to divide human learning and memory into categories based upon the accessibility of stored information to conscious awareness, this distinction becomes problematic when considering learning and memory processes in animals. From an evolutionary point of view, it is unlikely that declarative memory arose de novo in humans with the develop-ment of language. Although some researchers continue to argue for different classifications in humans and other animals, recent studies suggest that sim-ilar memory processes operate in all mammals and that these memory func-tions are subserved by homologous neural circuitry. In other mammals, declarative memory typically refers to the storage of information which could, in principle, be declared through language (e.g., “the cheese is in the box in the corner”) and that is dependent on the integrity of the medial tem-poral lobe and its associated structures (discussed later in the chapter). Non-declarative memory in other animals, as in humans, can be thought of as referring to the learning and storage of sensory associations and motor skills that are not dependent on the medial temporal portions of the brain. Temporal Categories of Memory In addition to the types of memory defined by the nature of what is remem-bered, memory can also be categorized according to the time over which it is effective. Although the details are still debated by both psychologists and neurobiologists, three temporal classes of memory are generally accepted (Figure 30.2). The first of these is immediate memory. By definition, imme-diate memory is the routine ability to hold ongoing experiences in mind for Daily episodes Words and their meanings Motor skills Priming cues Puzzle- solving skills Declarative (available to consciousness) Nondeclarative (generally not available to consciousness) Memory History Associations Immediate memory (fractions of a second− seconds) Working memory (seconds−minutes) Forgetting Long-term memory (days−years) Consolidation Figure 30.2 The major temporal cate-gories of human memory. fractions of a second. The capacity of immediate memory is very large and each sensory modality (visual, verbal, tactile, and so on) appears to have its own memory register. Working memory, the second temporal category, is the ability to hold information in mind for seconds to minutes once the present moment has Memory 735 Box A Phylogenetic Memory A category of information storage not usually considered in standard accounts is memories that arise from the experi-ence of the species over the eons, estab-lished by natural selection acting on the cellular and molecular mechanisms of neural development. Such stored infor-mation does not depend on postnatal experience, but on what a given species has typically encountered in its environ-ment. These “memories” are no less con-sequential than those acquired by indi-vidual experience and are likely to have much underlying biology in common with the memories established during an individual’s lifetime. (After all, phyloge-netic and ontogenetic memories are based on neuronal connectivity.) Information about the experience of the species, as expressed by endogenous or “instinctive” behavior, can be quite sophisticated, as is apparent in examples collected by ethologists in a wide range of animals, including primates. The most thoroughly studied instances of such behaviors are those occurring in young birds. Hatchlings arrive in the world with an elaborate set of innate behaviors. First is the complex behavior that allows the young bird to emerge from the egg. Having hatched, a variety of additional behaviors indicate how much of its early life is dependent on inherited informa-tion. Hatchlings of precocial species “know” how to preen, peck, gape their beaks, and carry out a variety of other complex acts immediately. In some species, hatchlings automatically crouch down in the nest when a hawk passes overhead but are oblivious to the over-flight of an innocuous bird. Konrad Lorenz and Niko Tinbergen used hand-held silhouettes to explore this phenome-non in naïve herring gulls, as illustrated in the figure shown here. “It soon became obvious,” wrote Tinbergen, “that … the reaction was mainly one to shape. When the model had a short neck so that the head protruded only a little in front of the line of the wings, it released alarm, independent of the exact shape of the dummy.” Evidently, the memory of what the shadow of a predator looks like is built into the nervous system of this species. Examples in primates include the innate fear that newborn monkeys have of snakes and looming objects. Despite the relatively scant attention paid to this aspect of memory, it is proba-bly the most important component of the stored information in the brain that determines whether or not an individual survives long enough to reproduce. References TINBERGEN, N. (1969) Curious Naturalists. Gar-den City, NY: Doubleday. TINBERGEN, N. (1953) The Herring Gull’s World. New York: Harper & Row. LORENZ, K. (1970) Studies in Animal and Human Behaviour. (Translated by R. Martin.) Cambridge, MA: Harvard University Press. DUKAS, R. (1998) Cognitive Ecology. Chicago: University of Chicago Press. Direction of movement (A) (B) (A) Niko Tinbergen at work. (B) Sil-houettes used to study alarm reac-tions in hatchlings. The shapes that were similar to the shadow of the bird’s natural predators (red arrows) when moving in the appropriate direction elicited escape responses (crouching, crying, seeking cover); silhouettes of songbirds and other innocuous species (or geometrical forms) elicited no obvious response. (From Tinbergen, 1969.) 736 Chapter Thirty passed. An everyday example of working memory is searching for a lost object; working memory allows the hunt to proceed efficiently, avoiding places already inspected. A conventional way of testing the integrity of working memory at the bedside is to present a string of randomly ordered digits, which the patient is then asked to repeat; surprisingly, the normal “digit span” is only 7–9 numbers. The third temporal category is long-term memory and entails the reten-tion of information in a more permanent form of storage for days, weeks, or even a lifetime. There is general agreement that the so-called engram—the physical embodiment of the long-term memory in neuronal machinery— depends on long-term changes in the efficacy of transmission of the relevant synaptic connections, and/or the actual growth and reordering of such con-nections. As discussed in Chapter 24, there is good reason to think that both these varieties of synaptic change occur. Evidence for a continual transfer of information from working memory to long-term memory, or consolidation (Figure 30.2), is apparent in the phe-nomenon of priming. Priming is typically demonstrated by presenting sub-jects with a set of items to which they are exposed under false pretenses. For example, a list of words can be given with the instruction that the subjects are to identify some feature that is actually extraneous to the experiment (e.g., whether the words are verbs, adjectives, or nouns). Sometime thereafter (e.g., the next day) the same individuals are given a different test in which they are asked to fill in the missing letters of words with whatever letters come to mind. The test list actually includes fragments of words that were presented in the first test, mixed among fragments of words that were not. Subjects fill in the letters to make the words that were presented earlier at a higher rate than expected by chance, even though they have no specific memory of the words that were seen initially; moreover, they are faster at filling in letters to make words that were seen earlier than new words. Prim-ing shows that information previously presented is influential, even though we are entirely unaware of its effect on subsequent behavior. The signifi-cance of priming is well known—at least intuitively—to advertisers, teach-ers, spouses, and others who want to influence the way we think and act. Despite the prevalence of such transfer, the information stored in this process is not particularly reliable. Consider, for instance, the list of words in Table 30.1A. If the list is read to a group of students who are immediately asked to identify which of several items were on the original list and which were not (Table 30.1B), the result is surprising. Typically, about half the stu-dents report that the word “sweet” was included in the list in Table 30.1A; moreover, they are quite certain about it! The mechanism of such erroneous “recognition” is presumably the strong associations that have previously been made between the words on the list in Table 30.1A and the word “sweet,” which bias the students to think that “sweet” was a member of the original set. Clearly, memories, even those we feel quite confident about, are often false. The Importance of Association in Information Storage The normal human capacity for remembering relatively meaningless infor-mation is surprisingly limited (as noted, a string of about 7–9 numbers or other arbitrary items). This capacity, however, can be increased dramatically. For example, a college student who for some months spent an hour each day practicing the task of remembering randomly presented numbers was able to recall a string of up to about 80 digits (Figure 30.3). He did this primarily TABLE 30.1 The Fallibility of Human Memorya (A)Initial list (B)Subsequent of words test list candy taste sour point sugar sweet bitter chocolate good sugar taste nice tooth nice honey soda chocolate heart cake eat pie aAfter hearing the words in list A read aloud, sub-jects were asked to identify which of the items in list B had also been on list A. See text for the results. by making subsets of the string of numbers he was given signify dates or times at track meets (he was a competitive runner)—in essence, giving meaningless items a meaningful context. This same strategy of association is used by most professional “mnemonists,” who amaze audiences by appar-ently prodigious feats of memory. Similarly, a good chess player can remem-ber the position of many more pieces on a briefly examined board than a poor player, presumably because the positions have much more significance for individuals who know the intricacies of the game than for neophytes (Figure 30.4). Thus, the capacity of working memory very much depends on Memory 737 Practice (5-day blocks) 0 10 20 30 40 50 60 70 80 Digit span 5 15 25 35 Figure 30.3 Increasing the digit span by practice (and the development of associa-tional strategies). During many months involving one hour of practice a day for 3–5 days a week, this subject increased his digit span from 7 to 79 numbers. Random digits were read to him at the rate of one per second. If a sequence was recalled cor-rectly, one digit was added to the next sequence. (After Ericsson et al., 1980.) Figure 30.4 The retention of briefly presented information depends on past experience, context, and its perceived importance. (A) Board position after white’s twenty-first move in game 10 of the 1985 World Chess Championship between A. Karpov (white) and G. Kas-parov (black). (B) A random arrange-ment of the same 28 pieces. (C, D) After briefly viewing the board from the real game, master players reconstruct the positions of the pieces with much greater efficiency than beginning play-ers. With a randomly arranged board, however, beginners perform as well or better than accomplished players. (After Chase and Simon, 1973.) (C) Real game (D) Randomly arranged Black Black (A) (B) Black White Black White 1 2 3 4 5 6 7 Trials Correct pieces 4 8 12 16 20 24 0 Master Beginner 1 2 3 4 5 6 7 Trials Correct pieces 4 8 12 16 20 24 0 Master Beginner 738 Chapter Thirty what the information in question means to the individual and how readily it can be associated with information that has already been stored. The ability of humans to remember significant information in the normal course of events is, in fact, enormous. Consider Arturo Toscanini, the late conductor of the NBC Philharmonic Orchestra, who allegedly kept in his head the complete scores of more than 250 orchestral works, as well as the music and librettos for some 100 operas. Once, just before a concert in St. Louis, the first bassoonist approached Toscanini in some consternation because he had just discovered that one of the keys on his bassoon was bro-ken. After a minute or two of deep concentration, the story goes, Toscanini turned to the alarmed bassoonist and informed him that there was no need for concern, since that note did not appear in any of the bassoon parts for the evening’s program. A parallel example of a prodigious quantitative memory is the mathe-matician Alexander Aitken. After an undistinguished career in elementary school, the 13-year-old Aitken was greatly taken with the manipulation of numbers. For the next four years he undertook, as a personal challenge, to master mental calculation. He began by memorizing the value of π to 1000 places, and could soon do calculations in his head with such facility that he became a local celebrity. When asked for the squares of three-digit numbers, he was able to give these almost instantly. The square roots for each were produced to five significant digits in 2–3 seconds; the squares of four-digit numbers allegedly took him about 5 seconds. Aitken went on to become a professor of mathematics at Edinburgh and was eventually elected a Fellow of the Royal Society for his contributions to numerical mathematics, statis-tics, and matrix algebra. At the age of 30 or so, he began to lose his enthusi-asm for “mental yoga,” as he called his penchant. In part, his waning enthu-siasm stemmed from the realization that the advent of calculators was making his prowess obsolete (it was then 1930). He also discovered that the last 180 digits of π that he had memorized as a boy were wrong; he had taken the values from the published work of another mental calculator, who erred in an era when there was no way to check the correct value. In fact, Aitken’s feat has long since been superseded. In 1981, an Indian mnemonist memorized the value of π to 31,811 places, only to have a Japanese mne-monist increase this record to 40,000 places a few years later! Toscanini’s and Aitken’s mental processes in these feats were not rote learning, but a result of the fascination that aficionados bring to their special interests (Box B). Although few can boast the mnemonic prowess of such individuals, the human ability to remember the things that deeply interest us—whether baseball statistics, soap opera plots, or the details of brain struc-ture—is amazing. Forgetting Some years ago, a poll showed that 84% of psychologists agreed with the statement “everything we learn is permanently stored in the mind, although sometimes particular details are not accessible.” The 16% who thought oth-erwise should get the higher marks. Common sense indicates that, were it not for forgetting, our brains would be impossibly burdened with the welter of useless information that is briefly encoded in our immediate memory “buffer.” In fact, the human brain is very good at forgetting. In addition to the unreliable performance on tests such as the example in Table 30.1, Figure 30.5 shows that the memory of the appearance of a penny (an icon seen thousands of times since childhood) is uncertain at best, and that people gradually forget what they have seen over the years (TV shows, in this case). Clearly we forget things that have no particular importance, and unused memories deteriorate over time. The ability to forget unimportant information may be as critical for nor-mal life as retaining information that is significant. One sort of evidence for this presumption is rare individuals who have difficulty with the normal erasure of information. Perhaps the best-known case is a subject studied over several decades by the Russian psychologist A. R. Luria, who referred to the Memory 739 Box B Savant Syndrome A fascinating developmental anomaly of human memory is seen in rare individu-als who until recently were referred to as idiots savants; the current literature tends to use the less pejorative phrase savant syndrome. Savants are people who, for a variety of poorly understood reasons (typically brain damage in the perinatal period), are severely restricted in most mental activities but extraordinarily competent and mnemonically capacious in one particular domain. The grossly disproportionate skill compared to the rest of their limited mental life can be striking. Indeed, these individuals— whose special talent may be in calcula-tion, history, art, language, or music—are usually diagnosed as severely retarded. Many examples could be cited, but a summary of one such case suffices to make the point. The individual whose history is summarized here was given the fictitious name “Christopher” in a detailed study carried out by psycholo-gists Neil Smith and Ianthi-Maria Tsim-pli. Christopher was discovered to be severely brain damaged at just a few weeks of age (perhaps as the result of rubella during his mother’s pregnancy, or anoxia during birth; the record is uncertain in this respect). He had been institutionalized since childhood because he was unable to care for himself, could not find his way around, had poor hand-eye coordination, and a variety of other deficiencies. Tests on standard IQ scales were low, consistent with his general inability to cope with daily life. Scores on the Wechsler Scale were, on different occasions, 42, 67, and 52. Despite his severe mental incapacita-tion, Christopher took an intense interest in books from the age of about three, par-ticularly those providing factual infor-mation and lists (e.g., telephone directo-ries and dictionaries). At about six or seven he began to read technical papers that his sister sometimes brought home from work, and he showed a surprising proficiency in foreign languages. His special talent in the acquisition and use of language (an area in which savants are often especially limited) grew rapidly. As an early teenager, Christopher could translate from—and communicate in—a variety of languages in which his skills were described as ranging from rudi-mentary to fluent; these included Dan-ish, Dutch, Finnish, French, German, modern Greek, Hindi, Italian, Norwe-gian, Polish, Portuguese, Russian, Span-ish, Swedish, Turkish, and Welsh. This extraordinary level of linguistic accom-plishment is all the more remarkable since he had no formal training in lan-guage even at the elementary school level, and could not play tic-tac-toe or checkers because he was unable to grasp the rules needed to make moves in these games. The neurobiological basis for such extraordinary individuals is not under-stood. It is fair to say, however, that savants are unlikely to have an ability in their areas of expertise that exceeds the competency of normally intelligent indi-viduals who focus passionately on a par-ticular subject (several examples are given in the text). Presumably, the savant’s intense interest in a particular cognitive domain is due to one or more brain regions that continue to work rea-sonably well. Whether because of social feedback or self-satisfaction, savants clearly spend a great deal of their mental time and energy practicing the skill they can exercise more or less normally. The result is that the relevant associations they make become especially rich, as Christopher’s case demonstrates. References MILLER, L. K. (1989) Musical Savants: Excep-tional Skill in the Mentally Retarded. Hillsdale, New Jersey: Lawrence Erlbaum Associations. SMITH, N. AND I.-M. TSIMPLI (1995) The Mind of a Savant: Language Learning and Modularity. Oxford, England: Basil Blackwell Ltd. HOWE, M. J. A. (1989) Fragments of Genius: The Strange Feats of Idiots Savants. Routledge, New York: Chapman and Hall. 740 Chapter Thirty subject simply as “S.” Luria’s description of an early encounter gives some idea why S, then a newspaper reporter, was so interesting: I gave S a series of words, then numbers, then letters, reading them to him slowly or presenting them in written form. He read or listened attentively and then repeated the material exactly as it had been presented. I increased the number of elements in each series, giving him as many as thirty, fifty, or even seventy words or numbers, but this too, presented no problem for him. He did not need to commit any of the material to memory; if I gave him a series of words or numbers, which I read slowly and distinctly, he would listen atten-tively, sometimes ask me to stop and enunciate a word more clearly, or, if in doubt whether he had heard a word correctly, would ask me to repeat it. Usually during an experiment he would close his eyes or stare into space, fix-ing his gaze on one point; when the experiment was over, he would ask that we pause while he went over the material in his mind to see if he had retained it. Thereupon, without another moment’s pause, he would reproduce the series that had been read to him. A. R. Luria (1987), The Mind of a Mnemonist, pp. 9–10 S’s phenomenal memory, however, did not always serve him well. He had difficulty ridding his mind of the trivial information that he tended to focus on, sometimes to the point of incapacitation. As Luria put it: Thus, trying to understand a passage, to grasp the information it contains (which other people accomplish by singling out what is most important) (B) a (A) Time event occurred (years ago) 80 70 60 50 40 2 0 4 6 8 10 12 14 Percent correct f k b g l c h m d i n e j o Figure 30.5 Forgetting. (A) Different versions of the “heads” side of a penny. Despite innumerable exposures to this familiar design, few people are able to pick out (a) as the authentic version. Clearly, repeated information is not necessarily retained. (B) The deterioration of long-term memories was evaluated in this exam-ple by a multiple-choice test in which the subjects were asked to recognize the names of television programs that had been broadcast for only one season during the past 15 years. Forgetting of stored information that is no longer used evidently occurs gradually and progressively over the years (chance performance = 25%). (A after Rubin and Kontis, 1983; B after Squire, 1989.) became a tortuous procedure for S, a struggle against images that kept rising to the surface in his mind. Images, then, proved an obstacle as well as an aid to learning in that they prevented S from concentrating on what was essential. Moreover, since these images tended to jam together, producing still more images, he was carried so far adrift that he was forced to go back and rethink the entire passage. Consequently, a simple passage—a phrase, for that mat-ter—would turn out to be a Sisyphean task. Ibid., p. 113 Although forgetting is a normal and apparently essential mental process, it can also be pathological, a condition called amnesia. Some of the causes of memory loss are listed in Table 30.2. An inability to establish new memories following neurological insult is called anterograde amnesia, whereas diffi-culty retrieving memories established prior to the precipitating neuropathol-ogy is called retrograde amnesia. Anterograde and retrograde amnesia are often present together, but can be dissociated under various circumstances. Amnesias following bilateral lesions of the temporal lobe and diencephalon have given particular insight into where and how at least some categories of memory are formed and stored, as discussed in the next section. Brain Systems Underlying Declarative Memory Formation Three extraordinary clinical cases of amnesia have been especially revealing about the brain systems responsible for the short-term storage and consoli-dation of declarative information and are now familiar to neurologists and psychologists as patients H.M., N.A., and R.B. (Box C). Taken together, these cases provide dramatic evidence of the importance of midline diencephalic and medial temporal lobe structures—the hippocampus, in particular—in establishing new declarative memories (Figure 30.6). These patients also demonstrate that there is a different anatomical substrate for anterograde and retrograde amnesia, since in each of these individuals, memory for events prior to the precipitating injury was largely retained. The devastating deficiency is (or was, in the case of R.B.) the inability to establish new memories. Retrograde amnesia—the loss of memory for events preceding an injury or illness—is more typical of the generalized Memory 741 TABLE 30.2 Causes of Amnesia Causes Examples Site of damage Vascular occlusion of Patient R.B. (Box C) Bilateral medial temporal lobe, both posterior cerebral the hippocampus in arteries particular Midline tumors — Medial thalamus bilaterally (hippocampus and other related structures if tumor is large enough) Trauma Patient N.A. (Box C) Bilateral medial temporal lobe Surgery Patient H.M. (Box C) Bilateral medial temporal lobe Infections Herpes simplex Bilateral medial temporal lobe encephalitis Vitamin B1 deficiency Korsakoff’s Medial thalamus and syndrome mammillary bodies Electroconvulsive therapy — Uncertain (ECT) for depression 742 Chapter Thirty Box C Clinical Cases That Reveal the Anatomical Substrate for Declarative Memories The Case of H.M. H.M. had suffered minor seizures since age 10 and major seizures since age 16. At the age of 27, he underwent surgery to correct his increasingly debilitating epilepsy. A high school graduate, H.M. had been working as a technician in a small electrical business until shortly before the time of his operation. His attacks involved generalized convulsions with tongue biting, incontinence, and loss of consciousness (all typical of grand mal seizures). Despite a variety of med-ications, the seizures remained uncon-trolled and increased in severity. A few weeks before his surgery, H.M. became unable to work and had to quit his job. On September 1, 1953, surgeons per-formed a bilateral medial temporal lobe resection in which the amygdala, uncus, hippocampal gyrus, and anterior two-thirds of the hippocampus were re-moved. At the time, it was unclear that bilateral surgery of this kind would cause a profound memory defect. Severe amnesia was evident, however, upon H.M.’s recovery from the operation, and his life was changed radically. The first formal psychological exam of H.M. was conducted nearly 2 years after the operation, at which time a pro-found memory defect was still obvious. Just before the examination, for instance, H.M. had been talking to the psycholo-gist; yet he had no recollection of this experience a few minutes later, denying that anyone had spoken to him. He gave the date as March 1953 and seemed oblivious to the fact that he had under-gone an operation, or that he had be-come incapacitated as a result. None-theless, his score on the Wechsler-Bellevue Intelligence Scale was 112, a value not significantly different from his preoperative IQ. Various psychological tests failed to reveal any deficiencies in perception, abstract thinking, or reason-ing; he seemed highly motivated and, in the context of casual conversation, nor-mal. Importantly, he also performed well on tests of the ability to learn new skills, such as mirror writing or puzzle solving (that is, his ability to form procedural memories was intact). Moreover, his early memories were easily recalled, showing that the structures removed during H.M.’s operation are not a perma-nent repository for such information. On the Wechsler Memory Scale (a specific test of declarative memory), however, he performed very poorly, and he could not recall a preceding test-set once he had turned his attention to another part of the exam. These deficits, along with his obvious inability to recall events in his daily life, all indicate a profound loss of short-term declarative memory function. During the subsequent decades, H.M. has been studied extensively, primarily by Brenda Milner and her colleagues at the Montreal Neurological Institute. His memory deficiency has continued unabated, and, according to Milner, he has little idea who she is in spite of their acquaintance for nearly 50 years. Sadly, he has gradually come to appreciate his predicament. “Every day is alone,” H.M. reports, “whatever enjoyment I’ve had and whatever sorrow I’ve had.” The Case of N.A. N.A. was born in 1938 and grew up with his mother and stepfather, attending public schools in California. After a year of junior college, he joined the Air Force. In October of 1959 he was assigned to the Azores as a radar technician and remained there until December 1960, when a bizarre accident made him a cel-ebrated neurological case. N.A. was assembling a model air-plane in his barracks room while, unbe-knownst to him, his roommate was prac-ticing thrusts and parries with a minia-ture fencing foil behind N.A.’s chair. N.A. turned suddenly and was stabbed through the right nostril. The foil pene-trated the cribriform plate (the structure through which the olfactory nerve enters the brain) and took an upward course into the left forebrain. N.A. lost con-sciousness within a few minutes (pre-sumably because of bleeding in the region of brain injury) and was taken to a hospital. There he exhibited a right-sided weakness and paralysis of the right eye muscles innervated by the third cra-nial nerve. Exploratory surgery was undertaken and the dural tear repaired. Gradually he recovered and was sent home to California. After some months, his only general neurological deficits were some weakness of upward gaze and mild double vision. He retained, however, a severe anterograde amnesia for declarative memories. MRI studies first carried out in 1986 showed exten-sive damage to the thalamus and the medial temporal lobe, mostly on the right side; the mammillary bodies also appeared to be missing bilaterally. The exact extent of his lesion, however, is not known, as N.A. remains alive and well. N.A.’s memory from the time of his injury over 40 years ago to the present has remained impaired and, like H.M., he fails badly on formal tests of new learning ability. His IQ is 124, and he shows no defects in language skills, per-ception, or other measures of intelli-gence. He also learns new procedural skills quite normally. His amnesia is not as dense as that of H.M. and is more ver-bal than spatial. He can, for example, draw accurate diagrams of material pre-sented to him earlier. Nonetheless, he loses track of his possessions, forgets what he has done, and tends to forget Memory 743 who has come to visit him. He has only vague impressions of political, social, and sporting events that have occurred since his injury. Watching television is difficult because he tends to forget the storyline during commercials. On the other hand, his memory for events prior to 1960 is extremely good; indeed, his lifestyle tends to reflect the 1950s. The Case of R.B. At the age of 52, R.B. suffered an ischemic episode during cardiac bypass surgery. Following recovery from anes-thesia, a profound amnesic disorder was apparent. As in the cases of H.M. and N.A., his IQ was normal (111), and he showed no evidence of cognitive defects other than memory impairment. R.B. was tested extensively for the next five years, and, while his amnesia was not as severe as that of H.M. or N.A., he consis-tently failed the standard tests of the ability to establish new declarative mem-ories. When R.B. died in 1983 of conges-tive heart failure, a detailed examination of his brain was carried out. The only significant finding was bilateral lesions of the hippocampus—specifically, cell loss in the CA1 region that extended the full rostral–caudal length of the hippo-campus on both sides. The amygdala, thalamus, and mammillary bodies, as well as the structures of the basal fore-brain, were normal. R.B.’s case is particu-larly important because it suggests that hippocampal lesions alone can result in profound anterograde amnesia for declarative memory. References CORKIN, S. (1984) Lasting consequences of bilateral medial temporal lobectomy: Clinical course and experimental findings in H.M. Semin. Neurol. 4: 249–259. CORKIN, S., D. G. AMARAL, R. G. GONZÁLEZ, K. A. JOHNSON AND B. T. HYMAN (1997) H. M.’s medial temporal lobe lesion: Findings from MRI. J. Neurosci. 17: 3964-3979. HILTS, P. J. (1995) Memory’s Ghost: The Strange Tale of Mr. M. and the Nature of Memory. New York: Simon and Schuster. MILNER, B., S. CORKIN AND H.-L. TEUBER (1968) Further analysis of the hippocampal amnesic syndrome: A 14-year follow-up study of H.M. Neuropsychologia 6: 215–234. SCOVILLE, W. B. AND B. MILNER (1957) Loss of recent memory after bilateral hippocampal lesions. J. Neurol. Neurosurg. Psychiat. 20: 11–21. SQUIRE, L. R., D. G. AMARAL, S. M. ZOLA-MOR-GAN, M. KRITCHEVSKY AND G. PRESS (1989) Description of brain injury in the amnesic patient N.A. based on magnetic resonance imaging. Exp. Neurol. 105: 23–35. TEUBER, H. L., B. MILNER AND H. G. VAUGHN (1968) Persistent anterograde amnesia after stab wound of the basal brain. Neuropsy-chologia 6: 267–282. ZOLA-MORGAN, S., L. R. SQUIRE AND D. AMA-RAL (1986) Human amnesia and the medial temporal region: Enduring memory impair-ment following a bilateral lesion limited to the CA1 field of the hippocampus. J. Neu-rosci. 6: 2950–2967. (A) (B) (C) (D) Damaged area Anterior Posterior MRI images of the brain of patient H.M. (A) Sagittal view of the right hemi-sphere; the area of the ante-rior temporal lobectomy is indicated by the white dotted line. The intact posterior hip-pocampus is the banana-shaped object indi-cated by the white arrow. (B–D) Coronal sec-tions at approximately the levels indicated by the red lines in (A). Image (B) is the most rostral and is at the level of the amygdala. The amygdala and the associated cortex are entirely missing. Image (C) is at the level of the rostral hippocampus; again, this struc-ture and the associated cortex have been removed. Image (D) is at the caudal level of the hippocampus; the posterior hippocam-pus appears intact, although somewhat shrunken. Outlines below give a clearer indi-cation of the parts of H.M.’s brain that have been ablated (black shading). (From Corkin et al., 1997.) Chapter Thirty lesions associated with head trauma and neurodegenerative disorders, such as Alzheimer’s disease (Box D). Although a degree of retrograde amnesia can occur with the more focal lesions that cause anterograde amnesia, the long-term storage of memories is presumably distributed throughout the brain (see the next section). Thus, the hippocampus and related diencephalic structures indicated in Figure 30.6 form and consolidate declarative memo-ries that are ultimately stored elsewhere. Other causes of amnesia have also provided some insight into the parts of the brain relevant to various aspects of memory (see Table 30.2). Korsakoff’s syndrome, for example, occurs in chronic alcoholics as a result of thiamine (vitamin B1) deficiency. In such cases, loss of brain tissue occurs bilaterally in the mammillary bodies and the medial thalamus, for reasons that are not well understood. Studies of animals with lesions of the medial temporal lobe have largely corroborated these findings with human patients. For example, one test of the presumed equivalent of declarative memory formation in animals involves placing rats into a pool filled with opaque water, thus concealing a submerged platform; note that the pool is surrounded by prominent visual landmarks (Figure 30.7). Normal rats at first search randomly until they find Fornix Hippocampus Hippocampus Optic nerve Mammillary body Lateral ventricle Temporal lobe Fornix Thalamus Amygdala Rhinal cortex Mammillary body Prefrontal cortex Basal forebrain (A) Brain areas associated with declarative memory disorders (B) Ventral view of hippocampus and related structures with part of temporal lobes removed Tail of the caudate nucleus Inferior horn of the lateral ventricle Hippocampus Hippocampal fissure Optic tract Inferior portion of the temporal lobe (C) Hippocampus in coronal section Corpus callosum Figure 30.6 Brain areas that, when damaged, tend to give rise to declarative memory disor-ders. By inference, declarative memory is based on the physiological activity of these structures. (A) Studies of amnesic patients have shown that the formation of declarative memories depends on the integrity of the hippocampus and its subcortical connections to the mammil-lary bodies and dorsal thalamus. (B) Diagram showing the location of the hippocampus in a cutaway view in the horizontal plane. (C) The hippocampus as it would appear in a histologi-cal section in the coronal plane, at approxi-mately the level indicated by the line in (B). 744 the submerged platform. After repeated testing, however, they learn to swim directly to the platform no matter where they are initially placed in the pool. Rats with lesions to the hippocampus and nearby structures cannot learn to find the platform, suggesting that remembering the location of the platform Memory 745 Figure 30.7 Spatial learning and mem-ory in rodents depends on the hip-pocampus. (A) Rats are placed in a cir-cular tank about the size and shape of a child’s wading pool filled with opaque (milky) water. The surrounding envi-ronment contains visual cues such as windows, doors, a clock, and so on. A small platform is located just below the surface. As rats search for this resting place, the pattern of their swimming (indicated by the traces in C) is moni-tored by a video camera. (B) After a few trials, normal rats rapidly reduce the time required to find the platform, whereas rats with hippocampal lesions do not. Sample swim paths of normal rats (C) and hippocampal lesioned rats (D) on the first and tenth trials. Rats with hippocampal lesions are unable to remember where the platform is located (B after Eichenbaum, 2000; C,D after Schenk and Morris, 1985). (C) Control rat ( ) (D) Rat with hippocampus lesioned First trial After 10 trials First trial After 10 trials Hidden platform 0 10 20 30 40 50 60 Trials 0 2–6 7–12 13–18 Hippocampus-lesioned Control Video camera Mean latency (B) (A) 746 Chapter Thirty relative to the configuration of visual landmarks depends on the same neural structures critical to declarative memory formation in humans. Like-wise, destruction of the hippocampus and parahippocampal gyrus in mon-keys severely impairs their ability to perform delayed-response tasks (see Figure 25.13). These studies suggest that primates and other mammals depend on medial temporal structures such as the hippocampus and para-hippocampal gyrus to encode and consolidate memories of events and objects in time and space, just as humans use these same brain regions for the initial encoding and consolidation of declarative memories. Brain Systems Underlying Long-Term Storage of Declarative Memory Revealing though they have been, clinical studies of amnesic patients have provided relatively little insight into the long-term storage of declarative information in the brain (other than to indicate quite clearly that such infor-mation is not stored in the midline diencephalic and medial temporal lobe structures that are affected in anterograde amnesia). Nonetheless, a good deal of evidence implies that the cerebral cortex is the major long-term repository for many aspects of declarative memory. One line of evidence comes from observations of patients undergoing electroconvulsive therapy (ECT). Individuals with severe depression are often treated by the passage of enough electrical current through the brain to cause the equivalent of a full-blown seizure (this procedure is done under anesthesia, in well-controlled circumstances). This remarkably useful treat-ment was discovered because depression in epileptics was perceived to remit after a spontaneous seizure (see Box C in Chapter 24). However, ECT often causes both anterograde and retrograde amnesia. Patients typically do not remember the treatment itself or the events of the preceding days, and even their recall of events of the previous 1–3 years can be affected. Animal stud-ies (rats tested for maze learning, for example) have confirmed the amnesic consequences of ECT. The memory loss usually clears over a period of weeks to months. However, to mitigate this side effect (which may be the result of excitotoxicity; see Box B in Chapter 6), ECT is often delivered to only one hemisphere at a time. The nature of amnesia following ECT supports the conclusion that long-term declarative memories are widely stored in the cerebral cortex, since this is the part of the brain predominantly affected by this therapy. A second line of evidence comes from patients with damage to associa-tion cortex outside the medial temporal lobe. Since different cortical regions have different cognitive functions (see Chapters 25 and 26), it is not surpris-ing that these sites store information that reflects the cognitive function of that part of the brain. For example, the lexicon that links speech sounds and their symbolic significance is located in the association cortex of the superior temporal lobe, and damage to this area typically results in an inability to link words and meanings (Wernicke’s aphasia; see Chapter 26). Presumably, the widespread connections of the hippocampus to the language areas serve to consolidate declarative information in these and other language-related cor-tical sites (Figure 30.8). By the same token, the inability of patients with tem-poral lobe lesions to recognize objects and/or faces suggests that such mem-ories are stored there (see Chapter 25). A third sort of evidence supporting the hypothesis that declarative mem-ories are stored in cortical areas specialized for processing particular types of information comes from neuroimaging of human subjects recalling vivid memories. In one such study, subjects first examined words paired with either pictures or sounds. Their brains were then scanned while they were asked to recall whether each test word was associated with either a picture or a sound. Functional images based on these scans showed that the cortical areas activated when subjects viewed pictures or heard sounds were reacti-vated when these percepts were vividly recalled. In fact, this sort of reactiva-tion can be quite specific. Thus, different classes of visual images—such as faces, houses, or chairs—tend to reactivate the same small regions of the visual association cortex that were activated when the objects were actually perceived (Figure 30.9). These neuroimaging studies reinforce the conclusion that declarative memories are stored widely in specialized areas of the cerebral cortex. Retrieving such memories appears to involve the medial temporal lobe, as well as regions of the frontal cortex. Frontal cortical areas located on the dor-solateral and anterolateral aspect of the brain, in particular, are activated when normal subjects attempt to retrieve declarative information from long-term memory. Moreover, patients with damage to these areas often fail to accurately recall the details of a memory and sometimes resort to confabula-tion to fill in the missing information. Finally, whereas the ability of patients such as H.M., N.A., and R.B. to remember facts and events from the period of their lives preceding their lesions clearly demonstrates that the medial temporal lobe is not necessary for retrieving declarative information held in long-term memory, other studies have suggested that these structures may be important for recalling declarative memories during the early stages of consolidation and storage in the cerebral cortex. Memory 747 Medial view Lateral view Hippocampus Widespread projections from association neocortex converge on the hippocampal region. The output of the hippocampus is ultimately directed back to these same neocortical areas. Figure 30.8 Connections between the hippocampus and possible declarative mem-ory storage sites. The rhesus monkey brain is shown because these connections are much better documented in non-human primates than in humans. Projections from numerous cortical areas converge on the hippocampus and the related structures known to be involved in human memory; most of these sites also send projections to the same cortical areas. Medial and lateral views are shown, the latter rotated 180° for clarity. (After Van Hoesen, 1982.) 748 Chapter Thirty Brain Systems Underlying Nondeclarative Learning and Memory H.M., N.A., and R.B. had no difficulty establishing or recalling nondeclarative memories, indicating that this information is laid down by using an anatom-ical substrate different from that used in declarative memory formation. Non-declarative memory apparently involves the basal ganglia, prefrontal cortex, amygdala, sensory association cortex, and cerebellum, but not the medial temporal lobe or midline diencephalon. In support of this interpretation, per-ceptual priming (the influence of previously studied information on subse-quent performance, unavailable to conscious recall) depends critically on the integrity of sensory association cortex. For example, lesions of the visual asso-ciation cortex produce profound impairments in visual priming but leave declarative memory formation intact. Likewise, simple sensory-motor condi-tioning, such as learning to blink following a tone that predicts a puff of air directed at the eye, relies on the normal activation of neural circuits in the cerebellum. Ischemic damage to the cerebellum following infarcts of the superior cerebellar artery or the posterior inferior cerebellar artery cause pro-found deficits in classical eyeblink conditioning without interfering with the Figure 30.9 Reactivation of visual cor-tex during vivid remembering of visual view images. (A) Subjects were instructed to view either images of objects (houses, faces, and chairs) (left) or imagine the objects in the absence of the stimulus (right). (B) (Left) Bilateral regions of ventral temporal cortex are specifically activated during perception of houses (yellow), faces (red), and chairs (blue). (Right) When subjects recall these objects, the same regions preferentially activated during the per-ception of each object class are reacti-vated. (After Ishai et al., 2000). Chairs Faces Houses Imagery Perception (B) (A) ability to lay down new declarative memories. Evidence from such double-dissociations endorses the idea that independent brain systems govern the formation and storage of declarative and nondeclarative memories. A brain system that appears to be especially important for complex motor learning involves the signaling loops that connect the basal ganglia and pre-frontal cortex (see Chapter 17). Damage to either structure profoundly inter-feres with the ability to learn new motor skills. Thus, patients with Hunting-ton’s disease, which causes atrophy of the caudate and putamen (see Figure 17.9B), perform poorly on motor skill learning tests such as manually track-ing a spot of light, tracing curves using a mirror, or reproducing sequences of finger movements. Because the loss of dopaminergic neurons in the sub-stantia nigra interferes with normal signaling in the basal ganglia (see Figure 17.9A), patients with Parkinson’s disease show similar deficits in motor skill learning, as do patients with prefrontal lesions caused by tumors or strokes. Neuroimaging studies have largely corroborated these findings, revealing activation of the basal ganglia and prefrontal cortex in normal subjects per-forming these same skill-learning tests. Activation of the basal ganglia and prefrontal cortex has also been observed in animals carrying out rudimen-tary motor learning and sequencing tasks. The dissociation of memory systems supporting declarative and nonde-clarative memory suggests the scheme for long-term information storage dia-grammed in Figure 30.10. The generality of the diagram only emphasizes the rudimentary state of present thinking about exactly how and where long-term memories are stored. A reasonable guess is that each complex memory is instantiated in an extensive network of neurons whose activity depends on synaptic weightings that have been molded and modified by experience. Memory and Aging Although it is all too obvious that our outward appearance changes with age, we tend to imagine that the brain is much more resistant to the ravages of time. Unfortunately, the evidence suggests that this optimistic view is not justified. From early adulthood onward, the average weight of the normal human brain, as determined at autopsy, steadily decreases (Figure 30.11). In elderly individuals, this effect can also be observed with noninvasive imag-ing as a slight but nonetheless significant shrinkage of the brain. Counts of synapses in the cerebral cortex generally decrease in old age (although the number of neurons probably does not change very much), suggesting that it is mainly the connections between neurons (i.e., neuropil) that are lost as Memory 749 Acquisition and storage of declarative information Long-term storage (a variety of cortical sites: Wernicke’s area for the meanings of words, temporal cortex for the memories of objects and faces, etc.) Short-term memory storage (hippocampus and related structures) Acquisition and storage of nondeclarative information Long-term storage (cerebellum, basal ganglia, premotor cortex, and other sites related to motor behavior) Short-term memory storage (sites unknown but presumably widespread) Figure 30.10 Summary diagram of the acquisition and storage of declarative versus nondeclarative information. 750 Chapter Thirty Box D Alzheimer’s Disease Dementia is a syndrome characterized by failure of recent memory and other intellectual functions that is usually insidious in onset but steadily pro-gresses. Alzheimer’s disease (AD) is the most common dementia, accounting for 60–80% of cases in the elderly. It afflicts 5–10% of the population over the age of 65, and as much as 45% of the popula-tion over 85. The earliest sign is typically an impairment of recent memory func-tion and attention, followed by failure of language skills, visual–spatial orienta-tion, abstract thinking, and judgment. Inevitably, alterations of personality accompany these defects. The tentative diagnosis of Alz-heimer’s disease is based on these char-acteristic clinical features, and can only be confirmed by the distinctive cellular pathology evident on postmortem exam-ination of the brain. The histopathology consists of three principal features (illus-trated in the figure): (1) collections of intraneuronal cytoskeletal filaments called neurofibrillary tangles; (2) extracel-lular deposits of an abnormal protein in a matrix called amyloid in so-called senile plaques; and (3) a diffuse loss of neurons. These changes are most apparent in neo-cortex, limbic structures (hippocampus, amygdala, and their associated cortices), and selected brainstem nuclei (especially the basal forebrain nuclei). Although the vast majority of AD cases arise sporadically, the disorder is inherited in an autosomal dominant pat-tern in a small fraction (less than 1%) of patients. Identification of the mutant gene in a few families with an early-onset autosomal dominant form of the disease has provided considerable insight into the kinds of processes that go awry in Alzheimer’s. Investigators suspected that the mutant gene responsible for familial AD might reside on chromosome 21, primar-ily because similar clinical and neu-ropathologic features often occur in indi-viduals with Down’s syndrome (a syndrome typically caused by an extra copy of chromosome 21), but with a much earlier onset (at about age 30 in most cases). The prominence of amyloid deposits in AD further suggested that a mutation of a gene encoding amyloid precursor protein is somehow involved. The gene for amyloid precursor protein (APP) was cloned by D. Goldgaber and colleagues, and found to reside on chro-mosome 21. This discovery eventually led to the identification of mutations of the APP gene in almost 20 families with the early-onset autosomal dominant form of AD. It should be noted, however, that only a few of the early-onset fami-lies, and none of the late-onset families, exhibited these particular mutations. The mutant genes underlying two additional autosomal dominant forms of AD have been subsequently identified (presenilin 1 and presenilin 2). Thus, mutation of any one of several genes appears to be suffi-cient to cause a heritable form of AD. The most common form of Alzhei-mer’s occurs late in life, and although the relatives of affected individuals are at a greater risk, the disease is clearly not inherited in any simple sense. The central role of APP in the families with (A) (B) Neurofibrillary tangle Amyloid plaque (A) Histological section of the cerebral cortex from a patient with Alzheimer’s disease, show-ing characteristic amyloid plaques and neurofibrillary tangles. (B) Distribution of pathologic changes (including plaques, tangles, neuronal loss, and gray matter shrinkage) in Alzheimer’s disease. Dot density indicates severity of pathology. (A from Roses, 1995, courtesy of Gary W. Van Hoesen; B after Blumenfeld, 2002, based on Brun and Englund, 1981.) Memory 751 the early-onset form of the disease nonetheless suggested that APP might be linked to the chain of events culmi-nating in the “spontaneous” forms of Alzheimer’s disease. In particular, bio-chemists Warren Strittmatter and Guy Salvesen theorized that pathologic depo-sition of proteins complexed with a derivative of APP might be responsible. To test this idea, they immobilized a recombinant form of the APP derivative on nitrocellulose paper and searched for proteins in the cerebrospinal fluid of patients with Alzheimer’s disease that bound with high affinity. One of the pro-teins they detected was apolipoprotein E (ApoE), a molecule that normally chap-erones cholesterol through the blood-stream. This discovery was especially pro-vocative in light of a discovery made by Margaret Pericak-Vance, Allen Roses, and their colleagues at Duke University Med-ical Center, who found that affected members of some families with the late-onset form of the inherited disease ex-hibited an association with genetic mark-ers on chromosome 19. This finding was of particular interest because a gene encoding an isoform of apolipoprotein E (the e4 allele) is located in the same region of chromosome 19 implicated by the family studies. As a result, they began to explore the association of the different alleles of apolipoprotein E with affected members in families with a late-onset but inherited form of Alzheimer’s disease. There are three major alleles of apolipoprotein E, e2, e3, and e4. The fre-quency of allele e3 in the general popula-tion is 0.78, and the frequency of allele e4 is 0.14. The frequency of the ε4 allele in late-onset familial AD patients, however, is 0.52—almost 4 times higher than the general population. Thus, the inheritance of the e4 allele is a risk factor for late-onset AD. In fact, people homozygous for e4 are about 8 times more likely to develop AD compared to individuals homozygous for ε3. Among individuals in late-onset Alzheimer’s families with no copies of e4, only 20% develop AD by age 75 compared to 90% of individuals with two copies of e4. An increased asso-ciation of the e4 allele has also been shown in the sporadic form of AD, an especially important discovery because this category constitutes by far the most common form of the disease. It is not known whether the ε4 allele of ApoE itself is responsible for the increased risk, or whether it is linked to another gene on chromosome 19 that is the real culprit. The fact that ApoE binds avidly to amyloid plaques in AD brains favors the idea that the e4 allele of ApoE itself is the problem. However, in con-trast to the mutations of APP or presenilin 1 and presenilin 2 that cause familial forms of AD, inheriting the e4 form of ApoE is not sufficient to cause AD; rather, inheriting this gene simply increases the risk of developing AD. Moreover, some of the individuals with early-onset forms of familial AD do not have the e4 allele. Thus, a variety of related molecular anomalies appear to underlie AD. A possible common denominator of AD at the cellular level is the “amyloid cascade” hypothesis. A prominent con-stituent of the amyloid plaques is an abnormal cleavage product of APP called amyloid-β peptide (or β-A4). The cascade hypothesis proposes that accumulation of β-A4 is critical to the pathogenesis of AD. Others, however, argue that extra-cellular deposition of β-A4 may not be a key event in the pathogenesis of AD because the density of the β-A4 plaques correlates only poorly with severity of the dementia (the degree of dementia being much better correlated with the density of neurofibrillary tangles). More-over, a transgenic mouse model of AD based on a presenilin 1 mutation exhibits neurodegeneration without amyloid plaque formation. Clearly, AD has a complex pathology and probably reflects a variety of related molecular and cellular abnormalities. It is unlikely that this important problem will be understood without a great deal more research, much hyperbole in the lay press notwithstanding. References CHUI, D. H., H. AND 12 OTHERS (1999) Trans-genic mice with Alzheimer presenilin 1 muta-tions show accelerated neurodegeneration without amyloid plaque formation. Nature Med. 5: 560–564. CITRON, M., T. OLTERSDORF, C. HAASS, L. MCCONLOGUE, A. Y. HUNG, P. SEUBERT, C. VIGO-PELFREY, I. LIEBERBURG AND D. J. SELKOE (1992) Mutation of the β-amyloid precursor protein in familial Alzheimer’s disease increases β-protein production. Nature 360: 672–674. CORDER, E. H., A. M. SAUNDERS, W. J. STRITT-MATTER, D. E. SCHMECHEL, P. C. GASKELL, G. W. SMALL, A. D. ROSES, J. L. HAINES AND M. A. PERICAK-VANCE (1993) Gene dose of apolipo-protein E type 4 allele and the risk of Alz-heimer’s disease in late-onset families. Sci-ence 261: 921–923. GOLDGABER, D., M. I. LERMAN, O. W. MCBRIDE, U. SAFFIOTTI AND D. C. GAJDUSEK (1987) Characterization and chromosomal localization of a cDNA encoding brain amy-loid of Alzheimer’s disease. Science 235: 877–880. LI, T. AND 17 OTHERS. (2000) Photoactivated g-secretase inhibitors directed to the active site covalently label presenilin 1. Nature 405: 689–694. MURRELL, J., M. FARLOW, B. GHETTI AND M. D. BENSON (1991) A mutation in the amyloid precursor protein associated with hereditary Alzheimer’s disease. Science 254: 97–99. ROGAEV, E. I. AND 20 OTHERS. (1995) Familial Alzheimer’s disease in kindreds with mis-sense mutations in a gene on chromosome 1 related to the Alzheimer’s disease type 3 gene. Nature 376: 775–778. SHERRINGTON, R. AND 33 OTHERS. (1995) Cloning of a gene bearing missense muta-tions in early-onset familial Alzheimer’s dis-ease. Nature 375: 754–760. 752 Chapter Thirty Figure 30.11 Brain size as a function of age. The human brain reaches its maximum size (measured by weight in this case) in early adult life and decreases progressively thereafter. This decrease evidently represents the grad-ual loss of neural circuitry in the aging brain, which presumably underlies the progressively diminished memory func-tion in older individuals. (After Deka-ban and Sadowsky, 1978.) humans grow old (consistent with the idea that the networks of connections that represent memories—i.e., the engrams—gradually deteriorate). These several observations accord with the difficulty older people have in making associations (e.g., remembering names or the details of recent experi-ences) and with declining scores on tests of memory as a function of age. The normal loss of some memory function with age means that there is a large gray zone between individuals undergoing normal aging and patients suffer-ing from age-related dementias such as Alzheimer’s disease (see Box D). Just as regular exercise slows the deterioration of the neuromuscular sys-tem with age, age-related neurodegeneration and associated cognitive decline may be slowed in elderly individuals who make a special effort to continue using the full range of human memory abilities (i.e, both declara-tive and nondeclarative memory tasks). Although cognitive decline with age is ultimately inevitable, neuroimaging studies suggest that high-performing older adults may to some degree offset declines in processing efficacy through compensatory activation of cortical tissue that is less fully used dur-ing remembering in poorly performing older adults (Figure 30.12). Age (years) 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Brain weight (kg) Females Males 0 1 3 5 10 20 30 40 50 60 70 80 90 Old–Low Old–High Young R L R L R L Figure 30.12 Compensatory activa-tion of memory areas in high-function-ing older adults. During remembering, activity in prefrontal cortex was restricted to the right prefrontal cortex (following radiological conventions, the brain images are left-right reversed) in both young participants and elderly subjects with poor recall. In contrast, elderly subjects with relatively good memory showed activation in both right and left prefrontal cortex. (After Cabeza et al., 2002). Summary Human memory entails a number of biological strategies and anatomical substrates. Primary among these are a system for memories that can be expressed by means of language and can be made available to the conscious mind (declarative memory), and a separate system that concerns skills and associations that are essentially prelinguistic, operating at a largely uncon-scious level (nondeclarative or procedural memory). Based on evidence from amnesic patients and knowledge about normal patterns of neural connec-tions in the human brain, the hippocampus and associated midline dien-cephalic and medial temporal lobe structures are critically important in lay-ing down new declarative memories, although not in storing them (a process that occurs primarily in the association cortices). In contrast, nondeclarative memories for motor and other unconscious skills depends on the integrity of the premotor cortex, basal ganglia, and cerebellum, and is not affected by lesions that impair the declarative memory system. The common denomina-tor of these categories of stored information is generally thought to be alter-ations in the strength and number of the synaptic connections in the cerebral cortices that mediate associations between stimuli and the behavioral re-sponses to them. Memory 753 Additional Reading Reviews BUCKNER, R. L. (2000) Neuroimaging of mem-ory. In The New Cognitive Neurosciences, M. Gazzaniga (ed.). Cambridge, MA: MIT Press, pp. 817–840. BUCKNER, R. L. (2002) The cognitive neuro-science of remembering. Nat. Rev. Neurosci. 2: 624–634. CABEZA, R. (2001) Functional neuroimaging of cognitive aging. In Handbook of Functional Neu-roimaging of Cognition, R. Cabeza and A. King-stone (eds.). Cambridge, MA: MIT Press, pp. 331–377. ERICKSON, C. A., B. JAGADEESH AND R. DESI-MONE (2000) Learning and memory in the inferior temporal cortex of the macaque. In The New Cognitive Neurosciences, M. Gazza-niga (ed.). Cambridge, MA: MIT Press, pp. 743–752. MISHKIN, M. AND T. APPENZELLER (1987) The anatomy of memory. Sci. Am. 256(6): 80–89. PETRI, H. AND M. MISHKIN (1994) Behaviorism, cognitivism, and the neuropsychology of memory. Am. Sci. 82: 30–37. SCHACTER, D. L. AND R. L. BUCKNER (1998) Priming and the brain. Neuron 20: 185–195. SQUIRE, L. R. AND B. J. KNOWLTON (2000) The medial temporal lobe, the hippocampus, and the memory systems of the brain. In The New Cognitive Neurosciences, M. Gazzaniga (ed.). Cambridge, MA: MIT Press, pp. 765–779. SQUIRE, L. R. (1992) Memory and hippocam-pus: A synthesis from findings with rats, mon-keys, and humans. Psych. Rev. 99: 195–230. THOMPSON, R. F. (1986) The neurobiology of learning and memory. Science 223: 941–947. ZACKS, R. T., L. HASHER AND K. Z. H. LI (1999) Human memory. In The Handbook of Aging and Cognition. F. I. M. Craik and T. A. Salthouse (eds.). Mahwah, New Jersey: Lawrence Erl-baum Associates, pp. 293–357. ZOLA-MORGAN, S. M. AND L. R. SQUIRE (1993) Neuroanatomy of memory. Annu. Rev. Neu-rosci. 16: 547–563. Important Original Papers CABEZA, R., N. D. ANDERSON, J. K. LOCANTORE AND A. R. MCINTOSH (2002) Aging gracefully: Compensatory brain activity in high-perform-ing older adults. NeuroImage 17: 1394–1402. GOBET, F. AND H. A. SIMON (1998) Expert chess memory: Revisiting the chunking hypothesis. Memory 6: 225–255. ISHAI, A., L. G. UNGERLEIDER AND J. V. HAXBY (2000) Distributed neural systems for the gen-eration of visual images. Neuron 28: 979–990. SCOVILLE, W. B. AND B. MILNER (1957) Loss of recent memory after bilateral hippocampal lesions. J. Neurol. Neurosurg. Psychiat. 20: 11–21. SQUIRE, L. R. (1989) On the course of forget-ting in very long-term memory. J. Exp. Psy-chol. 15: 241–245. ZOLA-MORGAN, S. M. AND L. R. SQUIRE (1990) The primate hippocampal formation: Evi-dence for a time-limited role in memory stor-age. Science 250: 288–290. Books BADDELEY, A. (1982) Your Memory: A User’s Guide. New York: Macmillan. CRAIK, F. I. M. AND T. A. SALTHOUSE (1999) The Handbook of Aging and Cognition. Mahwah, New Jersey: Lawrence Erlbaum Associates. DUKAS, R. (1998) Cognitive Ecology: The Evolu-tionary Ecology of Information Processing and Decision Making. Chicago: University of Chi-cago Press. GAZZANIGA, M. S. (2000) The New Cognitive Neurosciences, 2nd Ed. Cambridge MA: MIT Press. GAZZANIGA, M. S., R. B. IVRY AND G. R. MAN-GUN (1998) Cognitive Neuroscience: The Biology of the Mind. New York: W. W. Norton & Com-pany. LURIA, A. R. (1987) The Mind of a Mnemonist. Translated by Lynn Solotaroff. Cambridge, MA: Harvard University Press. NEISSER, U. (1982) Memory Observed: Remem-bering in Natural Contexts. San Francisco: W. H. Freeman. PENFIELD, W. AND L. ROBERTS (1959) Speech and Brain Mechanisms. Princeton, NJ: Princeton University Press. SAPER, C. B. AND F. PLUM (1985) Handbook of Clinical Neurology, Vol. 1(45): Clinical Neuro-psychology, P. J. Vinken, G. S. Bruyn and H. L. Klawans (eds.). New York: Elsevier, pp. 107–128. SCHACTER, D. L. (1997) Searching for Memory: The Brain, the Mind, and the Past. New York: Basic Books. SCHACTER, D. L. (2001) The Seven Sins of Mem-ory: How the Mind Forgets and Remembers. Houghton Mifflin Co. SMITH, S. B. (1983) The Great Mental Calculators: The Psychology, Methods, and Lives of Calculat-ing Prodigies, Past and Present. New York: Columbia University Press. SQUIRE, L. R. (1987) Memory and Brain. New York: Oxford University Press, pp. 202–223. ZECHMEISTER, E. B. AND S. E. NYBERG (1982) Human Memory: An Introduction to Research and Theory. Monterey, CA: Brooks/Cole Pub-lishing. The brainstem, comprising the midbrain, pons, and medulla, is continuous rostrally with the diencephalon (thalamus and hypothalamus) and with the spinal cord caudally. Although the medulla, pons, and midbrain participate in myriad specific functions, the integrated actions of these brainstem com-ponents give rise to three fundamental functions. First, the brainstem is the target or source for the cranial nerves that deal with sensory and motor func-tion in the head and neck (Figure A1; Table A1). Second, the brainstem pro-vides a “thruway” for all of the ascending sensory tracts from the spinal cord; the sensory tracts for the head and neck (the trigeminal system); the descending motor tracts from the forebrain; and local pathways that link eye movement centers. Finally, the brainstem is involved in regulating the level of consciousness, primarily though the extensive forebrain projections of a por-tion of the brainstem core, the reticular formation (see Box A in Chapter 16). Understanding the internal anatomy of the brainstem is generally regarded as essential for the practice of clinical medicine. Brainstem struc-tures are compressed into a relatively small volume that has a regionally restricted vascular supply (see Appendix B, Figure B7). Thus, vascular acci-dents in the brainstem—which are common—result in distinctive, and often devastating, combinations of functional deficits (see Appendix B, Box A). These deficits can be used both for diagnosis and for better understanding of the intricate anatomy of the medulla, pons, and midbrain. Unlike the spinal cord, which is relatively homogeneous in appearance along its length, the surface appearance of each brainstem subdivision is characterized by unique bumps and bulges formed by the underlying gray matter (nuclei) or white matter (tracts) (Figures A1 and A2). The midbrain contains the superior and inferior colliculi defining its dorsal surface, or tectum (meaning “roof”). Several midbrain nuclei, including the substantia nigra, lie in the ventral portion or tegmentum (meaning “covering”) of the midbrain. The other noteworthy anatomical feature of the midbrain is the presence of the prominent cerebral peduncles that are visible from the ven-tral surface. The pons is caudal to the midbrain and is easily recognized by the mass of decussating fibers on its ventral surface that give this subdivison its name; pons literally means “bridge.” The cerebellum is attached to the dorsal aspect of the pons by three large white matter tracts, the superior, middle and infe-rior cerebellar peduncles. Each of these tracts contains either efferent (supe-rior) or afferent (inferior and middle) axons from or to the cerebellum. There is a series of swellings on the dorsal and ventral surfaces of the medulla that reflect many of the major structures in this part of the brain-stem. Laterally, the inferior olivary complex can be seen. Adjacent and Appendix A 755 The Brainstem and Cranial Nerves 756 Appendix A slightly medial to the olivary complex are ridges that represent the vagal and hypoglossal nuclei. The pyramids are prominent swellings on the ventral surface of the medulla, reflecting the underlying descending corticospinal tract (see Figure 16.8). The surface features of the midbrain, pons, and medulla can be used as landmarks for locating the source and termination of the majority of cranial nerves in the brainstem. Unlike the spinal nerves, the entry and exit points of the cranial nerves are not regularly arrayed along the length of the brain-stem. Two cranial nerves, the olfactory nerve (I) and the optic nerve (II), enter the forebrain directly. The remaining cranial nerves enter and exit at distinct regions of the ventral (and in one case, the dorsal) surface of the midbrain, pons, and medulla (Figure A1). The oculomotor nerve (III) exits into the space between the two cerebral peduncles on the ventral surface of the midbrain. The trochlear nerve (IV) associated with the caudal midbrain is the only cranial nerve to exit on the dorsal surface of the brainstem. The trigeminal nerve (V)—the largest cranial nerve—exits the ventrolateral pons through the middle cerebellar peduncle. The abducens nerve (VI), facial nerve (VII), and vestibulocochlear nerve (VIII) emerge in a medial to lat-eral manner, respectively, at the junction of the pons and medulla. The glos-sopharyngeal nerve (IX) and the vagus nerve (X) are associated with the lat-eral medulla, whereas the hypoglossal nerve (XII) exits the ventromedial medulla between the pyramids and the inferior olive. The spinal accessory nerve (XI) does not originate in the brainstem but, as its name implies, exits the lateral portion of the upper cervical spinal cord. Table A1 describes the major functions of the cranial nerves. TABLE A1 The Cranial Nerves and Their Primary Functions Cranial nerve I II III IV V VI VII VIII IX X XI XII Name Olfactory nerve Optic nerve Oculomotor nerve Trochlear nerve Trigeminal nerve Abducens nerve Facial nerve Vestibulocochlear (auditory) nerve Glossopharyngeal nerve Vagus nerve Spinal accessory nerve Hypoglossal nerve Sensory and/or motor Sensory Sensory Motor Motor Sensory and motor Motor Sensory and motor Sensory Sensory and motor Sensory and motor Motor Motor Major function Sense of smell Vision Eye movements; papillary constriction and accommodation; muscles of eyelid. Eye movements Somatic sensation from face, mouth, cornea; muscles of mastication Eye movements Controls the muscles of facial expression; taste from anterior tongue; lacrimal and salivary glands Hearing; sense of balance Sensation from pharynx; taste from posterior tongue; carotid baroreceptors Autonomic functions of gut; sensation from pharynx; muscles of vocal cords; swallowing Shoulder and neck muscles Movements of tongue Cranial nerve nuclei within the brainstem are the targets of cranial sen-sory nerves or the source of cranial motor nerves (Figure A2; Table A2). Cra-nial nerve nuclei that receive sensory input (analogous to the dorsal horns of the spinal cord) are located separately from those that give rise to motor out-put (which are analogous to the ventral horns). The primary sensory neu-rons that innervate these nuclei are found in ganglia associated with the cra-nial nerves—similar to the relationship between dorsal root ganglia and the spinal cord. In general, sensory nuclei are found laterally in the brainstem, whereas motor nuclei are located more medially (Figure A3). There are three types of brainstem motor nuclei: somatic motor nuclei project to striated muscles; branchial motor nuclei project to muscles derived from embryonic structures called branchial arches (these arches give rise to the muscles—and bones—of the jaws and other cranio-facial structures); and visceral motor nuclei project to peripheral ganglia that innervate smooth muscle or glan-dular targets, similar to preganglionic motor neurons in the spinal cord that innervate autonomic ganglia. Finally, the major ascending or descending tracts—carrying sensory or motor information to or from the brain—are found in the lateral and basal regions of the brainstem (Figure A3). The rostral–caudal organization of the cranial nerve nuclei (all of which are bilaterally symmetric) reflects the rostrocaudal distribution of head and neck structures (see Figure A2 and Tables A1 and A2). The more caudal the nucleus, the more caudally located the target structures in the periphery. For example, the spinal accessory nucleus in the cervical spinal cord and caudal medulla provides motor innervation for neck and shoulder muscles, and the motor nucleus of the vagus nerve provides preganglionic innervation for The Brainstem and Cranial Nerves 757 Location of cells whose axons form the nerve Nasal epithelium Retina Oculomotor nucleus in midbrain; Edinger-Westphal nucleus in midbrain Trochlear nucleus in midbrain Trigeminal motor nucleus in pons; trigeminal sensory ganglion (the gasserian ganglion) Abducens nucleus in midbrain Facial motor nucleus; superior salivatory nuclei in pons; trigeminal (gasserian) ganglion Spiral ganglion; vestibular (Scarpa’s) ganglion Nucleus ambiguus; inferior salivatory Dorsal motor nucleus of vagus; vagal nerve ganglion Spinal accessory nucleus; nucleus ambiguus; intermediolateral column of spinal cord Hypoglossal nucleus of medulla Clinical test of function Test sense of smell with standard odor Measure acuity and integrity of visual field Test eye movements (patient can’t look up, down, or medially if nerve involved); look for ptosis, pupillary dilation Can’t look downward when eye abducted Test sensation on face; palpate masseter muscles and temporal muscle Can’t look laterally Test facial expression plus taste on anterior tongue Test audition with tuning fork; vestibular function with caloric test Test swallowing; pharyngeal gag reflex Test above plus hoarseness Test sternocleidomastoid and trapezius muscles Test deviation of tongue during protrusion (points to side of lesion) 758 Appendix A Midbrain Pons Medulla Spinal cord Cerebral peduncle Middle cerebellar peduncle Inferior olive Medullary pyramid Spinal cord Hypoglossal nerve (XII) Vestibulocochlear nerve (VIII) Facial nerve (VII) Abducens nerve (VI) Trigeminal nerve (V) Trochlear nerve (IV) Oculomotor nerve (III) Optic nerve (II) Mammillary body Optic tract Optic chiasm Accessory nerve (XI) Vagus nerve (X) Glossopharyngeal nerve (IX) Pons Cranial nerves Sensory cranial nerves Motor cranial nerves Mixed (sensory and motor) cranial nerves Color key for drawing at left: Figure A1 At left is a ventral view of the brainstem showing the locations of the cranial nerves as they enter or exit the midbrain, pons, and medulla. Nerves that are exclusively sensory are indicated in yellow, motor nerves are in blue, and mixed sensory/motor nerves are in green. At right, the territories included in each of the brainstem subdivisions (midbrain, violet; pons, green; medulla, pink) are indicated. aAssociated cranial nerves are shown in parentheses. TABLE A2 Classification and Location of the Cranial Nerve Nucleia Oculomotor nucleus (III) Midbrain Pons Medulla Trochlear nucleus (IV) Abducens nucleus (VI) Hypoglossal nucleus (XII) Trigeminal motor nucleus (V) Facial nucleus (VII) Nucleus ambiguus (IX, X) Spinal accessory nucleus (XI) Edinger-Westphal nucleus (III) Superior salivatory nucleus (VII) Inferior salivatory nucleus (IX) Dorsal motor nucleus of vagus (X) Trigeminal sensory: mesencephalic nucleus (V, VII, IX, X) Trigeminal sensory: principal nucleus (V, VII, IX, X) Trigeminal sensory: spinal nucleus (V, VII, IX, X) Nucleus of the solitary tract (VII, IX, X) Location Somatic motor Branchial motor Visceral motor General sensory Special sensory Visceral sensory Vestibular nuclei (VIII) Cochlear nuclei (VIII) many enteric and visceral targets. In the pons, the sensory and motor nuclei are primarily concerned with somatic sensation from the face (the principal trigeminal nuclei); movement of the jaws and the muscles of facial expres-sion (the trigeminal motor and facial nuclei); and abduction of the eye (the abducens nuclei). Further rostrally, in the mesencephalic portion of the brainstem, are nuclei concerned primarily with eye movements (the oculo-motor and trochlear nuclei) and preganglionic parasympathetic innervation of the iris (the Edinger-Westphal nuclei). While this list is not complete, it indicates the basic order of the rostral–caudal organization of the brainstem. Neurologists assess combinations of cranial nerve deficits to infer the loca-tion of brainstem lesions, or to place the source of brain dysfunction either in the spinal cord or brain. The most common brainstem lesions reflect the vas-cular territories that supply subsets of cranial nerve nuclei as well as ascend-ing and descending tracts (see Appendix B, Figure B7). For example, an occlusion of the posterior inferior cerebellar artery (PICA), a branch of the vertebral artery that supplies the lateral region of the mid- and rostral medulla, results in damage to three cranial nerve nuclei and several tracts (see the “Upper medulla” section in Figure A3). Accordingly, there are func-tional deficits that reflect the loss of the spinal trigeminal nucleus, the vestibu-lar nucleus, and the nucleus ambiguus (which contains motor neurons that project to the larynx and pharynx) on the same side as the lesion. In addition, ascending pathways from the spinal cord that relay pain and temperature from the contralateral body surface are disrupted, leading to a contralateral loss of these functions. Finally, the inferior cerebellar peduncle, which con-tains projections that relay information about body position to the cerebellum for postural control, is damaged. This loss results in ataxia (clumsiness) on The Brainstem and Cranial Nerves 759 Superior colliculus Inferior colliculus Superior cerebellar peduncle Middle cerebellar peduncle Inferior cerebellar peduncle Fourth ventricle (space above surface) Edinger-Westphal nucleus Oculomotor nucleus Trochlear nucleus Abducens nucleus Facial motor nucleus Principal trigeminal nucleus Spinal trigeminal nucleus Trigeminal motor nucleus Vestibular nuclei Cochlear nuclei Salivatory nuclei Nucleus of the solitary tract Hypoglossal nucleus Dorsal motor nucleus of vagus Accessory nucleus Nucleus ambiguus Midbrain Pons Medulla Spinal cord Thalamus Somatic motor Branchial motor Visceral motor General sensory Visceral sensory Special sensory Color key for drawing at left: Figure A2 At left, a “phantom” view of the dorsal surface of the brainstem shows the locations of the brainstem cranial nerve nuclei that are either the target or the source of the cranial nerves. (See Table A1 for the relationship between each cranial nerve and cranial nerve nuclei.) With the exception of the cranial nerve nuclei associated with the trigeminal nerve, there is fairly close correspondence between the location of the cranial nerve nuclei in the midbrain, pons, and medulla and the location of the associated cranial nerves. At right, the territories of the major brainstem subdivisions are indicated (viewed from the dorsal surface). 760 Appendix A Lower pons Midbrain Middle pons Middle medulla Caudal medulla Upper medulla Superior colliculus Superior cerebellar peduncle Middle cerebellar peduncle Middle cerebellar peduncle Inferior cerebellar peduncle Fourth ventricle Edinger-Westphal nucleus Oculomotor nucleus Abducens nucleus Facial nucleus Principal trigeminal nucleus Spinal trigeminal nucleus Spinal trigeminal nucleus Spinal trigeminal nucleus Spinal trigeminal nucleus Trigeminal motor nucleus Vestibular nuclei Vestibular nuclei Vestibular nuclei Cochlear nuclei Nucleus of the solitary tract Nucleus of the solitary tract Nucleus of the solitary tract Hypoglossal nucleus Hypoglossal nucleus Dorsal motor nucleus of vagus Dorsal motor nucleus of vagus Nucleus ambiguus Substantia nigra Pyramidal tract Medial lemniscus Inferior olivary nucleus Medullary pyramid Nucleus gracilis Nucleus cuneatus Medial lemniscus 5 6 4 3 2 1 5 6 4 3 2 1 Somatic motor Branchial motor Visceral motor General sensory Visceral sensory Special sensory Color key for cranial nerve nuclei: Figure A3 Transverse sections through the brainstem and spinal cord showing internal organization along the rostral–caudal axis. The locations of the cranial nerve nuclei, ascending, and descending tracts are indicated in each representative section. The identity of the nuclei (somatic sensory or motor; visceral sensory or motor; branchial sen-sory or motor) is indicated using the same color key as in Figure A2. The vascular territories for these brainstem sections are illustrated in Appendix B, Figure B7. References BLUMENFELD, H. (2002) Neuroanatomy through Clinical Cases. Sunderland, MA: Sinauer Asso-ciates. BRODAL, P. (1992) The Central Nervous System: Structure and Function. New York: Oxford Uni-versity Press. CARPENTER, M. B. AND J. SUTIN (1983) Human Neuroanatomy, 8th Ed. Baltimore, MD: Wil-liams and Wilkins. ENGLAND, M. A. AND J. WAKELY (1991) Color Atlas of the Brain and Spinal Cord: An Introduc-tion to Normal Neuroanatomy. St. Louis: Mosby Yearbook. HAINES, D. E. (1995) Neuroanatomy: An Atlas of Structures, Sections, and Systems, 2nd Ed. Balti-more: Urban and Schwarzenberg. MARTIN, J. H. (1996) Neuroanatomy: Text and Atlas, 2nd Ed. Stamford, CT: Appleton and Lange. The Brainstem and Cranial Nerves 761 the side of the lesion. Anatomical relationships and shared vascularization, rather than any functional principle, unite these deficits and allow clinical localization of brainstem damage. For both clinicians and neurobiologists, understanding the brainstem requires integrating anatomical information with knowledge about functional organization and pathology. The Blood Supply of the Brain and Spinal Cord Understanding the blood supply of the brain and spinal cord is crucial for the practice of medicine, particularly for neurology and neurosurgery. Dam-age to major blood vessels by trauma or stroke results in combinations of functional defects reflecting local cell death as well as the disruption of axons passing through the region compromised by the vascular damage. Thus, a firm knowledge of the major cerebral blood vessels and the neu-roanatomical territories they perfuse facilitates the initial diagnoses of a broad range of brain damage and disease. The entire blood supply of the brain and spinal cord depends on two sets of branches from the dorsal aorta. The vertebral arteries arise from the sub-clavian arteries, and the internal carotid arteries are branches of the common carotid arteries. The vertebral arteries and the ten medullary arteries that arise from segmental branches of the aorta provide the primary vasculariza-tion of the spinal cord. These medullary arteries join to form the anterior and posterior spinal arteries (Figure B1). If any of the medullary arteries are obstructed or damaged (during abdominal surgery, for example), the blood supply to specific parts of the spinal cord may be compromised. The pattern of resulting neurological damage differs according to whether supply to the posterior or anterior artery is interrupted. As might be expected from the arrangement of ascending and descending neural pathways in the spinal cord, loss of the posterior supply generally leads to loss of sensory functions, whereas loss of the anterior supply more often causes motor deficits. Anterior to the spinal cord and brainstem, the internal carotid arteries branch to form two major cerebral arteries, the anterior and middle cerebral arteries. The right and left vertebral arteries come together at the level of the pons on the ventral surface of the brainstem to form the midline basilar artery. The basilar artery joins the blood supply from the internal carotids in an arterial ring at the base of the brain (in the vicinity of the hypothalamus and cerebral peduncles) called the circle of Willis. The posterior cerebral arteries arise at this confluence, as do two small bridging arteries, the ante-rior and posterior communicating arteries. Conjoining the two major sources of cerebral vascular supply via the circle of Willis presumably improves the chances of any region of the brain continuing to receive blood if one of the major arteries becomes occluded (see Box A). The major branches that arise from the internal carotid artery—the ante-rior and middle cerebral arteries—form the anterior circulation that supplies the forebrain (Figure B2). These arteries branch from the internal carotids within the circle of Willis. Each gives rise to branches that supply the cortex and branches that penetrate the basal surface of the brain, supplying deep Appendix B 763 Vascular Supply, the Meninges, and the Ventricular System 764 Appendix B structures such as the basal ganglia, thalamus, and internal capsule. Particu-larly prominent are the lenticulostriate arteries that branch from the middle cerebral artery. These arteries supply the basal ganglia and thalamus. The posterior circulation of the brain supplies the posterior cerebral cortex, the midbrain, and the brainstem; it comprises arterial branches arising from the posterior cerebral, basilar, and vertebral arteries. The pattern of arterial dis-tribution is similar for all the subdivisions of the brainstem: midline arteries supply medial structures, lateral arteries supply the lateral brainstem, and dorsal-lateral arteries supply dorsal-lateral brainstem structures and the cerebellum (Figures B2 and B3). Among the most important dorsal-lateral arteries (also called long circumferential arteries) are the posterior inferior cerebellar artery (PICA) and the anterior inferior cerebellar artery (AICA), which supply distinct regions of the medulla and pons. These arteries, as well as branches of the basilar artery that penetrate the brainstem from its ventral and lateral surfaces (called paramedian and short circumferential arteries), are especially common sites of occlusion and result in specific func-tional deficits of cranial nerve, somatic sensory, and motor function (see Appendix A). The physiological demands served by the blood supply of the brain are particularly significant because neurons are more sensitive to oxygen depri-vation than other kinds of cells with lower rates of metabolism. In addition, the brain is at risk from circulating toxins, and is specifically protected in this respect by the blood-brain barrier (see below). As a result of the high meta-bolic rate of neurons, brain tissue deprived of oxygen and glucose as a result of compromised blood supply is likely to sustain transient or permanent damage. Brief loss of blood supply (referred to as ischemia) can cause cellu-lar changes, which, if not quickly reversed, can lead to cell death. Sustained loss of blood supply leads much more directly to death and degeneration of the deprived cells. Strokes—an anachronistic term that refers to the death or dysfunction of brain tissue due to vascular disease—often follow the occlu-(A) (B) (C) Basilar artery Posterior inferior cerebellar artery Posterior spinal artery Vertebral artery Anterior spinal artery Posterior spinal artery Medullary arteries Vasocorona Sulcal artery Anterior spinal artery Ventral Dorsal Figure B1 Blood supply of the spinal cord. (A) View of the ventral (anterior) surface of the spinal cord. At the level of the medulla, the vertebral arteries give off branches that merge to form the anterior spinal artery. Approximately 10 to 12 segmental arteries (which arise from various branches of the aorta) join the anterior spinal artery along its course. These segmental arteries are known as medullary arteries. (B) The vertebral arteries (or the posterior infe-rior cerebellar artery) give rise to paired posterior spinal arteries that run along the dorsal (posterior) surface of the spinal cord. (C) Cross section through the spinal cord, illustrating the distribu-tion of the anterior and posterior spinal arteries. The anterior spinal arteries give rise to numerous sulcal branches that supply the anterior two-thirds of the spinal cord. The posterior spinal arteries supply much of the dorsal horn and the dorsal columns. A network of vessels known as the vasocorona con-nects these two sources of supply and sends branches into the white matter around the margin of the spinal cord. Vascular Supply, the Meninges, and the Ventricular System 765 (B) Anterior cerebral artery (A) Middle cerebral artery Portion of temporal lobe removed Posterior inferior cerebellar artery Vertebral artery Posterior communicating artery Anterior communicating artery Anterior inferior cerebellar artery Basilar artery Internal carotid artery Posterior cerebral artery (to midbrain) Basilar artery (to pons) (C) Anterior cerebral artery Middle cerebral artery Internal carotid artery Anterior communicating artery Lenticulostriate arteries (D) Anterior cerebral artery Posterior cerebral artery Posterior cerebral artery Middle cerebral artery Anterior cerebral artery Figure B2 The major arteries of the brain. (A) Ventral view (compare with Figure 1.13B). The enlargement of the boxed area shows the circle of Willis. (B) Lateral and (C) midsagittal views showing the location of the cerebral arteries. Colorized insets below illustrate the cortical territories supplied by the anterior (yellow), middle (green), and posterior (pur-ple) cerebral arteries. (D) Idealized frontal sec-tion showing course of middle cerebral artery. 766 Appendix B sion of (or hemorrhage from) the brain’s arteries (Box A). Historically, stud-ies of the functional consequences of strokes, and their relation to vascular territories in the brain and spinal cord, provided information about the loca-tion of various brain functions. The location of the major language functions in the left hemisphere, for instance, was discovered in this way in the latter part of the nineteenth century (see Chapter 26). Now, noninvasive functional imaging techniques based on blood flow (see Box A In Chapter 1) have largely supplanted the correlation of clinical signs and symptoms with the location of tissue damage observed at autopsy. The Blood-Brain Barrier The interface between the walls of capillaries and the surrounding tissue is important throughout the body, as it keeps vascular and extravascular concen-Upper medulla Midbrain Middle pons Caudal medulla Posterior inferior cerebellar artery Anterior inferior cerebellar artery Basilar artery Basilar artery Posterior cerebral artery and superior cerebellar artery Posterior inferior cerebellar artery Vertebral artery and anterior spinal artery Vertebral artery Anterior spinal artery Posterior spinal artery Posterior inferior cerebellar artery Anterior inferior cerebellar artery Posterior cerebral artery (to midbrain) Posterior communicating artery Basilar artery (to pons) Vertebral artery (to medulla) (B) (A) Superior cerebellar artery Figure B3 Blood supply of the three subdivisions of the brainstem. (A) Dia-gram of major blood supply. (B) Sec-tions through different levels of the brainstem indicating the territory sup-plied by each of the major brainstem arteries. trations of ions and molecules at appropriate levels in these two compart-ments. In the brain, this interface is especially significant and has been accorded an alliterative name, “the blood-brain barrier.” The special properties of the blood-brain barrier were first observed by the nineteenth-century bacte-riologist Paul Ehrlich, who noted that intravenously injected dyes leaked out of capillaries in most regions of the body to stain the surrounding tissues; the brain, however, remained unstained. Ehrlich wrongly concluded that the brain had a low affinity for the dyes; his student, Edwin Goldmann, showed that such dyes do not traverse the specialized walls of brain capillaries. The restriction of large molecules like Ehrlich’s dyes (and many smaller molecules) to the vascular space is the result of tight junctions between neighboring capillary endothelial cells in the brain (Figure B4). Such junc-tions are not found in capillaries elsewhere in the body, where the spaces between adjacent endothelial cells allow much more ionic and molecular Vascular Supply, the Meninges, and the Ventricular System 767 Box A Stroke Stroke is the most common neurological cause for admission to a hospital, and is the third leading cause of death in the United States (after heart disease and cancer). The term “stroke” refers to the sudden appearance of a limited neuro-logical deficit, such as weakness or paral-ysis of a limb, or the sudden inability to speak. The onset of the deficit within sec-onds, minutes, or hours marks the prob-lem a vascular one. Brain function is exquisitely dependent on a continuous supply of oxygen, as evidenced by the onset of unconsciousness within about 10 seconds of blocking its blood supply (by cardiac arrest, for instance). The damage to neurons is at first reversible, but eventually becomes permanent if the blood supply is not promptly restored. Strokes can be subdivided into three main types: thrombotic, embolic, and hemorrhagic. The thrombotic variety is caused by a local reduction of blood flow arising from an atherosclerotic buildup in one of the cerebral blood vessels that eventually occludes it. Alternatively, a reduction of blood flow can arise when an embolus (meaning an object loose in the bloodstream) dislodges from the heart (or from an atherosclerotic plaque in the carotid or vertebral arteries) and travels to a cerebral artery (or arteriole) where it forms a plug. A hemorrhagic stroke occurs when a cerebral blood ves-sel ruptures, as can occur as a result of hypertension, a congenital aneurysm (bulging of a vessel), or a congenital arte-rio-venous malformation. The relative frequency of thrombotic, embolic, and hemorrhagic strokes is approximately 50%, 30%, and 20%, respectively. The diagnosis of stroke relies primar-ily on an accurate history and a compe-tent neurological examination. Indeed, the neurologist C. Miller Fisher, a master of bedside diagnosis, remarked that medical students and residents should learn neurology “stroke by stroke.” Understanding the portion of the brain supplied by each of the major arteries (see text) enables an astute clinician to identify the occluded blood vessel. More recently, imaging techniques such as CT scans and MRI (see Box A in Chapter 1) have greatly facilitated the physician’s ability to identify and local-ize small hemorrhages and regions of permanently damaged tissue. Moreover, Doppler ultrasound, magnetic resonance angiography, and imaging of blood ves-sels by direct infusion of radio-opaque dye can now pinpoint atherosclerotic plaques, aneurysms, and other vascular abnormalities. Several therapeutic approaches to strokes are feasible. Dissolving a throm-botic plug by tissue plasminogen activa-tor (TPA) and other compounds is now standard clinical practice for selected stroke victims. Furthermore, recent un-derstanding of some of the mechanisms by which ischemia injures brain tissue has made pharmacological strategies to minimize neuronal injury after stroke a potentially effective possibility (see Box D in Chapter 6). Hemorrhagic strokes are treated neurosurgically by finding and stopping the bleeding from the defective vessel (when that is technically possible). These approaches can minimize func-tional loss; however, strokes remain a serious health risk from which there is never full recovery. The inability of the mature brain to replace large populations of damaged or dead neurons, or to repair long axon tracts once they have been compromised, invariably prevents the complete restoration of lost functions. Reference ADAMS, R. D., M. VICTOR AND A. H. ROPPER (2001) Principles of Neurology, 7th Ed. New York: McGraw-Hill, Ch. 34, pp. 821–924. 768 Appendix B traffic. The structure of tight junctions was first demonstrated in the 1960s by Tom Reese, Morris Karnovsky, and Milton Brightman. Using electron microscopy after the injection of electron-dense intravascular agents such as lanthanum salts, they showed that the close apposition of the endothelial cell membranes prevented such ions from passing (panel B in Figure B4). Sub-stances that traverse the walls of brain capillaries must move through the endothelial cell membranes. Accordingly, molecular entry into the brain should be determined by an agent’s solubility in lipids, the major con-stituent of cell membranes. Nevertheless, many ions and molecules not read-ily soluble in lipids do move quite readily from the vascular space into brain tissue. A molecule like glucose, the primary source of metabolic energy for neurons and glial cells, is an obvious example. This paradox is explained by the presence of specific transporters for glucose and other critical molecules and ions. In addition to tight junctions, astrocytic “end feet” (the terminal regions of astrocytic processes) surround the outside of capillary endothelial cells. The reason for this endothelial–glial allegiance is unclear, but may reflect an influence of astrocytes on the formation and maintenance of the blood-brain barrier. The brain, more than any other organ, must be carefully shielded from abnormal variations in its ionic milieu, as well as from the potentially toxic molecules that find their way into the vascular space by ingestion, infection, or other means. The blood-brain barrier is thus important for protection and homeostasis. It also presents a significant problem for the delivery of drugs to the brain. Large (or lipid-insoluble) molecules can be introduced to the brain, but only by transiently disrupting the blood-brain barrier with hyper-osmotic agents like mannitol. The Meninges The cranial cavity is conventionally divided into three regions called the anterior, middle, and posterior cranial fossae. Surrounding and supporting the brain within this cavity are three protective tissue layers, which also extend down the brainstem and the spinal cord. Together these layers are Astrocyte foot process Nucleus Capillary Brain capillary endothelial cell Tight junction (A) (B) Figure B4 The cellular basis of the blood-brain barrier. (A) Diagram of a brain capillary in cross section and reconstructed views, showing endothe-lial tight junctions and the investment of the capillary by astrocytic end feet. (B) Electron micrograph of boxed area in (A), showing the appearance of tight junctions between neighboring endothe-lial cells (arrows). (A after Goldstein and Betz, 1986; B from Peters et al., 1991.) called the meninges (Figure B5). The outermost layer of the meninges is called the dura mater (meaning “hard mother,” because it is thick and tough). The middle layer is called the arachnoid mater because of spiderlike processes called arachnoid trabiculae that extend from it toward the third layer, the pia mater, a thin, delicate layer of cells that closely invests the sur-face of the brain. Since the pia closely adheres to the brain as its surface curves and folds, whereas the arachnoid does not, there are places—called cisterns—where the subarachnoid space enlarges to form significant collec-tions of CSF. The major arteries supplying the brain course through the sub-Vascular Supply, the Meninges, and the Ventricular System 769 Dura mater Arachnoid Superior sagittal sinus Superior sagittal sinus Arachnoid granulation Pia mater Dura mater Arachnoid matter Subarachnoid space filled with spinal fluid Posterior cranial fossae Artery Choroid plexus of 4th ventricle Choroid plexus of lateral ventricle Anterior cranial fossa Dura mater Arachnoid mater Subarachnoid space Arachnoid trabeculae Pia mater Artery Perivascular space Cerebral cortex White matter Arachnoid villi or granulations Middle cranial fossa Figure B5 The meninges. Upper left panel is a midsagittal view showing the three layers of the meninges in relation to the skull and brain. Right panels are blowups to show detail. 770 Appendix B Dura mater Arachnoid Superior sagittal sinus Subarachnoid space filled with CSF Posterior cranial fossae Fourth ventricle Choroid plexus Lateral ventricle Cerebral aqueduct Third ventricle Arachnoid villi or granulations Foramen of Magendie Foramen of Monro arachnoid space where they give rise to branches that penetrate the substance of the hemispheres. The subarachnoid space is therefore a frequent site of bleeding following trauma. A collection of blood between the meningeal layers is referred to as a subdural or subarachnoid hemorrhage, as distinct from bleeding within the brain itself. The Ventricular System The cerebral ventricles are a series of intercon-nected, fluid-filled spaces that lie in the core of the forebrain and brainstem (Figures B6 and B7). These spaces are filled with cerebrospinal fluid (CSF) that is produced by a modified vascular structure referred to as the choroid plexus, which is present in each of the ventricles. The cerebrospinal fluid percolates through the ven-tricular system and flows into the subarachnoid space through perforations in the thin covering of the fourth ventricle (see Figure B6); it is even-tually absorbed by specialized structures called arachnoid villi or granulations (see Figure B5), and returned to the venous circulation. The presence of ventricular spaces in the various subdi-visions of the brain reflects the fact that the ventricles are the adult derivatives of the open space or lumen of the embryonic neural tube (see Chapter 21). Although they have no unique function, the ventricular spaces present in sections through the brain provide another useful guide to location (Figure B8). The largest of these spaces are the lat-eral ventricles (formerly called the first and second ventri-cles), one within each of the cerebral hemispheres. These particular ventricles are best seen in frontal sections, where their ventral surface is usually defined by the basal gan-glia, their dorsal surface by the corpus callosum, and their medial surface by the septum pellucidum, a membranous tissue sheet that forms part of the midline sagittal surface of the cerebral hemispheres. The lateral ventricles, like sev-eral telencephalic structures, possess a “C” shape that is formed by the non-uniform growth of the cerebral hemi-spheres during embryonic development (see Figure 21.5). CSF flows from the lateral ventricles through small open-ings (called the interventricular foramen, or the foramen of Monro) into a narrow midline space between the right and left thalamus, the third ventricle. The third ventricle is continuous caudally with the cerebral aqueduct (also referred to as the aqueduct of Sylvius), which runs though the midbrain. At its caudal end, the aqueduct opens into the fourth ventricle, a larger space in the dorsal pons and medulla. The fourth ventricle, covered on its dorsal aspect by the cerebellum, narrows caudally to form the central canal of the spinal cord. Figure B6 Circulation of cerebrospinal fluid. CSF is produced by the choroid plexus and flows from the lateral ven-tricles through the interventricular fora-men (foramen of Monro) into the third ventricle, through the cerebral aqueduct and into the fourth ventricle. CSF exits the ventricular system through several foramen associated with the fourth ven-tricle into the subarachnoid space sur-rounding the central nervous system. CSF is eventually absorbed by arach-noid granulations and returned to the venous circulation. Vascular Supply, the Meninges, and the Ventricular System 771 Figure B7 The ventricular system of the human brain. (A) Location of the ventricles as seen in a transparent left lateral view. (B) Dorsal view of the ven-tricles. (C) Table showing the ventricu-lar spaces associated with each of the major subdivisions of the brain. (See Chapter 21 for an account of brain development that more fully explains the origin of the ventricular spaces.) Right lateral ventricle Central part of left lateral ventricle (A) (B) Occipital horn of lateral ventricle Occipital horn of lateral ventricle Fourth ventricle Choroid plexus Cerebral aqueduct Third ventricle Choroid plexus Left lateral ventricle Interventricular foramen of Monro Frontal horn of lateral ventricle Central canal (C) Telencephalon (forebrain) EMBRYONIC BRAIN Diencephalon Metencephalon Cerebellum Cerebral cortex Basal ganglia Hippocampus Olfactory bulb Basal forebrain Dorsal thalamus Hypothalamus Pons Myelencephalon Spinal cord Medulla Midbrain (superior and inferior colliculi) Lateral ventricles Third ventricle Central canal Cerebral aqueduct ADULT BRAIN DERIVATIVES ASSOCIATED VENTRICULAR SPACE Rhombencephalon Prosencephalon Spinal cord Mesencephalon Fourth ventricle Fourth ventricle Central sulcus Postcentral gyrus Left cerebral hemisphere Right cerebral hemisphere Interventricular foramen of Monro Fourth ventricle Third ventricle Cerebral aqueduct Frontal horn of lateral ventricle Temporal horn of lateral ventricle 772 Appendix B The normal total volume of CSF in the ventricular system is approxi-mately 140 mL. The choroid plexus produces approximately 500 mL of CSF per day, so that the entire volume present in the system is turned over sev-eral times a day. Thus, impaired absorption or obstruction of CSF flow results in an excess of cerebrospinal fluid in the intracranial cavity, a condi-tion called hydrocephalus (literally, “water head”). Corpus callosum (A) (C) (B) Corpus callosum Lateral ventricle Fornix Third ventricle Hippocampus Mammillary body Lateral ventricle (temporal horn) Thalamus Caudate Caudate Putamen Putamen Globus pallidus Tail of caudate nucleus Internal capsule Level of section shown in (A) Level of section shown in (B) White matter Optic chiasm Basal forebrain nuclei Anterior commissure Temporal lobe Cerebral cortex (gray matter) Basal ganglia Amygdala Internal capsule Figure B8 The ventricular system as seen in coronal brain sections. (A, B) Location the ventricles in coronal section. Notice that the lateral ventricle appears twice in section (B). (C) A transparent view of the ventricular system indicating the approxi-mate location of the sections in (A) and (B). References BLUMENFELD, H. (2002) Neuroanatomy through Clinical Cases. Sunderland, MA: Sinauer Asso-ciates. BRIGHTMAN, M. W. AND T. S. REESE (1969) Junc-tions between intimately opposed cell mem-branes in the vertebrate brain. J. Cell Biol. 40: 648–677. BRODAL, P. (1992) The Central Nervous System: Structure and Function. New York: Oxford Uni-versity Press. CARPENTER, M. B. AND J. SUTIN (1983) Human Neuroanatomy, 8th Ed. Baltimore, MD: Wil-liams and Wilkins. ENGLAND, M. A. AND J. WAKELY (1991) Color Atlas of the Brain and Spinal Cord: An Introduc-tion to Normal Neuroanatomy. St. Louis: Mosby Yearbook. GOLDSTEIN, G. W. AND A. L. BETZ (1986) The blood-brain barrier. Sci. Amer. 255(3):74–83 HAINES, D. E. (1995) Neuroanatomy: An Atlas of Structures, Sections, and Systems, 2nd Ed. Balti-more: Urban and Schwarzenberg. MARTIN, J. H. (1996) Neuroanatomy: Text and Atlas, 2nd Ed. Stamford, CT: Appleton and Lange. NETTER, F. H. (1983) The CIBA Collection of Medical Illustrations, Vols. I and II. PETERS, A., S. L. PALAY AND H. DEF. WEBSTER (1991) The Fine Structure of the Nervous System: Neurons and Their Supporting Cells, 3rd Ed. Oxford University Press, New York. SCHMIDLEY, J. W. AND E. F. MAAS (1990) Cere-brospinal fluid, blood-brain barrier and brain edema. In Neurobiology of Disease, A. L. Pearl-man and R.C. Collins (eds.). New York: Oxford University Press, Chapter 19, pp. 380–398. REESE, T. S. AND M. J. KARNOVSKY (1967) Fine structural localization of a blood–brain barrier to exogenous peroxidase. J. Cell Biol. 34: 207–217. WAXMAN, S. G. AND J. DEGROOT (1995) Correla-tive Neuroanatomy, 22nd Ed. Norwalk, CT: Appleton and Lange. Vascular Supply, the Meninges, and the Ventricular System 773 acetylcholine Neurotransmitter at motor neuron synapses, in autonomic ganglia and a variety of central synapses; binds to two types of receptors: ligand-gated ion channels (nicotinic receptors) and G-protein-coupled receptors (mus-carinic receptors). achromatopsia, cerebral Loss of color vision as a result of damage to extrastriate visual cortex. action potential The electrical signal conducted along axons (or muscle fibers) by which information is conveyed from one place to another in the nervous system. activation The time-dependent opening of ion channels in response to a stimulus, typically membrane depolariza-tion. adaptation The phenomenon of sensory receptor adjustment to different levels of stimulation; critical for allowing sen-sory systems to operate over a wide dynamic range. adenylyl cyclase Membrane-bound enzyme that can be acti-vated by G-proteins to catalyze the synthesis of cyclic AMP from ATP. adhesion molecules see cell adhesion molecules. adrenaline see epinephrine. adrenal medulla The central part of the adrenal gland that, under visceral motor stimulation, secretes epinephrine and norepinephrine into the bloodstream. adrenergic Refers to synaptic transmission mediated by the release of norepinephrine or epinephrine. adult The mature form of an animal, usually defined by the ability to reproduce. afferent An axon that conducts action potentials from the periphery toward the central nervous system. agnosia The inability to name objects. alpha (a) motor neurons Neurons in the ventral horn of the spinal cord that innervate skeletal muscle. amacrine cells Retinal neurons that mediate lateral interac-tions between bipolar cell terminals and the dendrites of ganglion cells. amblyopia Diminished visual acuity as a result of the failure to establish appropriate visual cortical connections in early life. amnesia The pathological inability to remember or establish memories; retrograde amnesia is the inability to recall existing memories, whereas anterograde amnesia is the inability to lay down new memories. amphetamine A synthetically produced central nervous sys-tem stimulant with cocaine-like effects; drug abuse may lead to dependence. ampullae The juglike swellings at the base of the semicircu-lar canals that contain the hair cells and cupulae (see also cupulae). amygdala A nuclear complex in the temporal lobe that forms part of the limbic system; its major functions concern autonomic, emotional, and sexual behavior. androgen insensitivity syndrome A condition in which, due to a defect in the gene that codes for the androgen receptor, testosterone cannot act on its target tissues. anencephaly A congenital defect of neural tube closure, in which much of the brain fails to develop. anosmia Loss of the sense of smell. anterior Toward the front; sometimes used as a synonym for rostral, and sometimes as a synonym for ventral. anterior commissure A small midline fiber tract that lies at the anterior end of the corpus callosum; like the callosum, it serves to connect the two hemispheres. anterior hypothalamus Region of the hypothalamus con-taining nuclei that mediate sexual behaviors; not to be con-fused with region in rodent called the medial preoptic area, which lies anterior to hypothalamus and also contains nuclei that mediate sexual behavior (most notably the sex-ually dimorphic nucleus). anterograde A movement or influence acting from the neu-ronal cell body toward the axonal target. anterolateral pathway (anterolateral system) Ascending sensory pathway in the spinal cord and brainstem that car-ries information about pain and temperature to the thala-mus. antiserum Serum harvested from an animal immunized to an agent of interest. aphasia The inability to comprehend and/or produce lan-guage as a result of damage to the language areas of the cerebral cortex (or their white matter interconnections). apoptosis Cell death resulting from a programmed pattern of gene expression; also known as “programmed cell death.” aprosodia The inability to infuse language with its normal emotional content. arachnoid mater One of the three coverings of the brain that make up the meninges; lies between the dura mater and the pia mater. areflexia Loss of reflexes. association cortex Defined by exclusion as those neocortical regions that are not involved in primary sensory or motor processing. associativity In the hippocampus, the enhancement of a weakly activated group of synapses when a nearby group is strongly activated. astrocytes One of the three major classes of glial cells found in the central nervous system; important in regulating the ionic milieu of nerve cells and, in some cases, transmitter reuptake. astrotactin A cell surface molecule that causes neurons to adhere to radial glial fibers during neuronal migration. athetosis Slow, writhing movements seen primarily in patients with disorders of the basal ganglia. ATPase pumps Membrane pumps that use the hydrolysis of ATP to translocate ions against their electrochemical gradi-ents. atrophy The physical wasting away of a tissue, typically muscle, in response to disuse or other causes. attention The selection of a particular sensory stimulus or mental process for further analysis. Glossary G-1 G-2 Glossary auditory meatus Opening of the external ear canal. auditory space map Topographic representation of sound source location, as occurs in the inferior colliculus. autonomic nervous system The components of the nervous system (peripheral and central) concerned with the regula-tion of smooth muscle, cardiac muscle, and glands (see also visceral motor system). axon The neuronal process that carries the action potential from the nerve cell body to a target. axoplasmic transport The process by which materials are carried from nerve cell bodies to their terminals (antero-grade transport), or from nerve cell terminals to the neu-ronal cell body (retrograde transport). baroreceptors Sensory receptors in the visceral motor sys-tem that respond to changes in blood pressure. basal ganglia A group of nuclei lying deep in the subcortical white matter of the frontal lobes that organize motor behav-ior. The caudate and putamen and the globus pallidus are the major components of the basal ganglia; the subthalamic nucleus and substantia nigra are often included. basal lamina (basement membrane) A thin layer of extracel-lular matrix material (primarily collagen, laminin, and fibronectin) that surrounds muscle cells and Schwann cells. Also underlies all epithelial sheets. basilar membrane The membrane that forms the floor of the cochlear duct, on which the cochlear hair cells are located. basket cells Inhibitory interneurons in the cerebellar cortex whose cells bodies are located within the Purkinje cell layer and whose axons make basketlike terminal arbors around Purkinje cell bodies. binocular Referring to both eyes. biogenic amines The bioactive amine neurotransmitters; includes the catecholamines (epinephrine, norepinephrine, dopamine), serotonin, and histamine. bipolar cells Retinal neurons that provide a direct link between photoreceptor terminals and ganglion cell dendrites. bisexuality Sexual attraction to members of both the oppo-site and the same phenotypic sex. blastomere A cell produced when the egg undergoes cleavage. blastula An early embryo during the stage when the cells are typically arranged to form a hollow sphere. blind spot The region of visual space that falls on the optic disk; due to the lack of photoreceptors in the optic disk, objects that lie completely within the blind spot are not perceived. blood-brain barrier A diffusion barrier between the brain vasculature and the substance of the brain formed by tight junctions between capillary endothelial cells. bouton (synaptic bouton) A swelling specialized for the release of neurotransmitter that occurs along or at the end of an axon. bradykinesia Pathologically slow movement. brain-derived neutrophic factor (BDNF) One member of a family of neutrophic factors, the best-known constituent of which is nerve growth factor. brainstem The portion of the brain that lies between the diencephalon and the spinal cord; comprises the midbrain, pons, and medulla. Broca’s aphasia Difficulty producing speech as a result of damage to Broca’s area in the left frontal lobe. Broca’s area An area in the left frontal lobe specialized for the production of language. CA1 A region of the hippocampus that shows a robust form of long-term potentiation. CA3 A region of the hippocampus containing the neurons that form the Schaffer collaterals. cadherins A family of calcium-dependent cell adhesion mol-ecules found on the surfaces of growth cones and the cells over which they grow. calcarine sulcus The major sulcus on the medial aspect of the occipital lobe; the primary visual cortex lies largely within this sulcus. cAMP response element binding protein (CREB) A protein activated by cyclic AMP that binds to specific regions of DNA, thereby increasing the transcription rates of nearby genes. cAMP response elements (CREs) Specific DNA sequences that bind transcription factors activated by cAMP (see also cAMP response element binding protein). carotid bodies Specialized tissue masses found at the bifur-cation of the carotid arteries in humans and other mam-mals that respond to the chemical composition of the blood (primarily the partial pressure of oxygen and carbon dioxide). catecholamine A term referring to molecules containing a catechol ring and an amino group; examples are the neuro-transmitters epinephrine, norepinephrine, and dopamine. cauda equina The collection of segmental ventral and dorsal roots that extend from the caudal end of the spinal cord to their exit from the spinal canal. caudal Posterior, or “tailward.” caudate nucleus One of the three major components of the basal ganglia (the other two are the globus pallidus and putamen). cell adhesion molecules A family of molecules on cell sur-faces that cause them to stick to one another (see also fibronectin and laminin). central nervous system The brain and spinal cord of verte-brates (by analogy, the central nerve cord and ganglia of invertebrates). central pattern generator Oscillatory spinal cord or brain-stem circuits responsible for programmed, rhythmic move-ments such as locomotion. central sulcus A major sulcus on the lateral aspect of the hemispheres that forms the boundary between the frontal and parietal lobes. The anterior bank of the sulcus contains the primary motor cortex; the posterior bank contains the primary sensory cortex. cerebellar ataxia A pathological inability to make coordinated movements associated with lesions to the cerebellum. cerebellar cortex The superficial gray matter of the cerebel-lum. cerebellar peduncles The three bilateral pairs of axon tracts (inferior, middle, and superior cerebellar peduncles) that carry information to and from the cerebellum. cerebellum Prominent hindbrain structure concerned with motor coordination, posture, and balance. Composed of a three-layered cortex and deep nuclei; attached to the brain-stem by the cerebellar peduncles. cerebral aqueduct The portion of the ventricular system that connects the third and fourth ventricles. cerebral cortex The superficial gray matter of the cerebral hemispheres. cerebral peduncles The major fiber bundles that connect the brainstem to the cerebral hemispheres. cerebrocerebellum The part of the cerebellar cortex that receives input from the cerebral cortex via axons from the pontine relay nuclei. cerebrospinal fluid A normally clear and cell-free fluid that fills the ventricular system of the central nervous system; produced by the choroid plexus in the third ventricle. cerebrum The largest and most rostral part of the brain in humans and other mammals, consisting of the two cerebral hemispheres. c-fos Cellular Feline Osteosarcoma gene product; a transcrip-tion factor that binds as a heterodimer, thus activating gene transcription. chemical synapses Synapses that transmit information via the secretion of chemical signals (neurotransmitters). chemoaffinity (chemoaffinity hypothesis) The idea that nerve cells bear chemical labels that determine their connectivity. chemotaxis The movement of a cell up (or down) the gradi-ent of a chemical signal. chemotropism The growth of a part of a cell (axon, dendrite, filopodium) up (or down) a chemical gradient. chimera An experimentally generated embryo (or organ) comprising cells derived from two or more species (or other genetically distinct sources). cholinergic Referring to synaptic transmission mediated by acetylcholine. chorea Jerky, involuntary movements of the face or extremi-ties associated with damage to the basal ganglia. choreoathetosis The combination of jerky, ballistic, and writhing movements that characterizes the late stages of Huntington’s disease. choroid plexus Specialized epithelium in the ventricular sys-tem that produces cerebrospinal fluid. chromosome Nuclear organelle that bears the genes. ciliary body Circular band of muscle surrounding the lens; contraction allows the lens to round up during accommo-dation. cingulate cortex Cortex of the cingulate gyrus that surrounds the corpus callosum; important in emotional and visceral motor behavior. cingulate gyrus Prominent gyrus on the medial aspect of the hemisphere, lying just superior to the corpus callosum; forms a part of the limbic system. cingulate sulcus Prominent sulcus on the medial aspect of the hemisphere. circadian rhythms Variations in physiological functions that occur on a daily basis. circle of Willis Arterial anastomosis on the ventral aspect of the midbrain; connects the posterior and anterior cerebral circulation. cisterns Large, cerebrospinal-fluid-filled spaces that lie within the subarachnoid space. class A taxonomic category subordinate to phylum; com-prises animal orders. climbing fibers Axons that originate in the inferior olive, ascend through the inferior cerebellar peduncle, and make terminal arborizations that invest the dendritic tree of Purk-inje cells. clone The progeny of a single cell. cochlea The coiled structure within the inner ear where vibrations caused by sound are transduced into neural impulses. cognition A general term referring to higher order mental processes; the ability of the central nervous system to attend, identify, and act on complex stimuli. collapsin A molecule that causes collapse of growth cones; a member of the semaphorin family of signaling mole-cules. colliculi The two paired hillocks that characterize the dorsal surface of the midbrain; the superior colliculi concern vision, the inferior colliculi audition. competition The struggle among nerve cells, or nerve cell processes, for limited resources essential to survival or growth. concha A component of the external ear. conduction aphasia Difficulty producing speech as a result of damage to the connection between Wernicke’s and Broca’s language areas. conduction velocity The speed at which an action potential is propagated along an axon. conductive hearing loss Diminished sense of hearing due reduced ability of sounds to be mechanically transmitted to the inner ear. Common causes include occlusion of the ear canal, perforation of the tympanic membrane, and arthritic degeneration of the middle ear ossicles. Contrast with sen-sorineural hearing loss. cone opsins The three distinct photopigments found in cones; the basis for color vision. cones Photoreceptors specialized for high visual acuity and the perception of color. congenital adrenal hyperplasia Genetic deficiency that leads to overproduction of androgens and a resultant masculin-ization of external genitalia in genotypic females. conjugate The paired movements of the two eyes in the same direction, as occurs in the vestibulo-ocular reflex (see also vergence movements and vestibulo-ocular reflex). conspecific Fellow member of a species. contralateral On the other side. contralateral neglect syndrome Neurological condition in which the patient does not acknowledge or attend to the left visual hemifield or the left half of the body. The syndrome typically results from lesions of the right parietal cortex. contrast The difference, usually expressed in terms of a per-centage in luminance, between two territories in the visual field (can also apply to color when specified as spectral contrast). convergence Innervation of a target cell by axons from more than one neuron. cornea The transparent surface of the eyeball in front of the lens; the major refractive element in the optical pathway. coronal Referring to a plane through the brain that runs par-allel to the coronal suture (the mediolateral plane). Synony-mous with frontal plane. corpus callosum The large midline fiber bundle that con-nects the cortices of the two cerebral hemispheres. corpus striatum General term applied to the caudate and putamen; name derives from the striated appearance of these basal ganglia nuclei in sections of fresh material. cortex The superficial mantle of gray matter covering the cerebral hemispheres and cerebellum, where most of the neurons in the brain are located. Glossary G-3 G-4 Glossary cortico-cortical connections Connections made between cortical areas in the same hemisphere or betweem the two hemispheres via the cerebral commissures (the corpus cal-losum and the anterior commissure). corticospinal tract Pathway carrying motor information from the primary and secondary motor cortices to the brain stem and spinal cord. co-transmitters Two or more types of neurotransmitters within a single synapse; may be packaged into separate populations of synaptic vesicles or co-localized within the same synaptic vesicles. cranial nerve ganglia The sensory ganglia associated with the cranial nerves; these correspond to the dorsal root gan-glia of the spinal segmental nerves. cranial nerve nuclei Nuclei in the brainstem that contain the neurons related to cranial nerves III–XII. cranial nerves The 12 pairs of nerves arising from the brain-stem that carry sensory information toward (and some-times motor information away from) the central nervous system. CREB see cAMP response element binding protein. crista The hair cell-containing sensory epithelium of the semicircular canals. critical period A restricted developmental period during which the nervous system is particularly sensitive to the effects of experience. cuneate nuclei Sensory relay nuclei that lie in the lower medulla; they contain the second-order sensory neurons that relay mechanosensory information from peripheral receptors in the upper body to the thalamus. cupulae Gelatinous structures in the semicircular canals in which the hair cell bundles are embedded. cytoarchitectonic areas Distinct regions of the neocortical mantle identified by differences in cell size, packing density, and laminar arrangement. decerebrate rigidity Excessive tone in extensor muscles as a result of damage to descending motor pathways at the level of the brainstem. declarative memory Memories available to consciousness that can be expressed by language. decussation A crossing of fiber tracts in the midline. deep cerebellar nuclei The nuclei at the base of the cerebel-lum that relay information from the cerebellar cortex to the thalamus. delayed response genes Genes that are synthesized de novo after a cell is stimulated; usually refers to transcriptional acti-vator proteins that are synthesized after preexisting tran-scription factors are first activated by an inducing stimulus. delayed response task A behavioral paradigm used to test cognition and memory. delta waves Slow (<4 Hz) electroencephalographic waves that characterize stage IV (slow-wave) sleep. dendrite A neuronal process arising from the cell body that receives synaptic input. denervation Removal of the innervation to a target. dentate gyrus A region of the hippocampus; so named because it is shaped like a tooth. depolarization The displacement of a cell’s membrane potential toward a less negative value. dermatome The area of skin supplied by the sensory axons of a single spinal nerve. determination Commitment of a developing cell or cell group to a particular fate. dichromatic Referring to the majority of mammals (and most color-blind humans), which have only two instead of three cone pigments to mediate color vision. diencephalon Portion of the brain that lies just rostral to the midbrain; comprises the thalamus and hypothalamus. differentiation The progressive specialization of developing cells. dihydrotestosterone A more potent form of testosterone that masculinizes the external genitalia. disinhibition Arrangement of inhibitory and excitatory cells in a circuit that generates excitation by the transient inhibi-tion of a tonically active inhibitory neuron. disjunctive eye movements Movements of the two eyes in opposite directions (see also vergence movements). distal Farther away from a point of reference (the opposite of proximal). divergence The branching of an axon to innervate multiple target cells. dopamine A catecholamine neurotransmitter. dorsal Referring to the back. dorsal column nuclei Second-order sensory neurons in the lower medulla that relay mechanosensory information from the spinal cord to the thalamus; comprises the cuneate and gracile nuclei. dorsal columns Major ascending tracts in the spinal cord that carry mechanosensory information from the first-order sensory neurons in dorsal root ganglia to the dorsal column nuclei; also called the posterior funiculi. dorsal horn The dorsal portion of the spinal cord gray mat-ter; contains neurons that process sensory information. dorsal root ganglia (DRG) The segmental sensory ganglia of the spinal cord; contain the first-order neurons of the dorsal column/medial lemniscus and spinothalamic path-ways. dorsal roots The bundle of axons that runs from the dorsal root ganglia to the dorsal horn of the spinal cord, carrying sensory information from the periphery. dura mater The thick external covering of the brain and spinal cord; one of the three components of the meninges, the other two being the pia mater and arachnoid mater. dynorphins A class of endogenous opioid peptides. dysarthria Difficulty producing speech as a result of damage to the primary motor centers that govern the muscles of articulation; distinguished from aphasia, which results from cortical damage. dysmetria Inaccurate movements due to faulty judgment of distance. Characteristic of cerebellar pathology. dystonia Lack of muscle tone. early inward current The initial electrical current, measured in voltage clamp experiments, that results from the voltage-dependent entry of a cation such as Na+ or Ca2+; produces the rising phase of the action potential. ectoderm The most superficial of the three embryonic germ layers; gives rise to the nervous system and epidermis. Edinger-Westphal nucleus Midbrain nucleus containing the autonomic neurons that constitute the efferent limb of the pupillary light reflex. efferent An axon that conducts information away from the central nervous system. electrical synapses Synapses that transmit information via the direct flow of electrical current at gap junctions. electrochemical equilibrium The condition in which no net ionic flux occurs across a membrane because ion concentra-tion gradients and opposing transmembrane potentials are in exact balance. electrogenic Capable of generating an electrical current; usu-ally applied to membrane transporters that create electrical currents while translocating ions. embryo The developing organism before birth or hatching. end plate current (EPC) Postsynaptic current produced by neu-rotransmitter release and binding at the motor end plate. end plate potential (EPP) Depolarization of the membrane potential of skeletal muscle fiber, caused by the action of the transmitter acetylcholine at the neuromuscular synapse. endocrine Referring to the release of signaling molecules whose effects are made widespread by distribution in the general circulation. endocytosis A budding off of vesicles from the plasma mem-brane, which allows uptake of materials in the extracellular medium. endoderm The innermost of the three embryonic germ layers. endogenous opioids Peptides in the central nervous system that have the same pharmacological effects as morphine and other derivatives of opium. endolymph The potassium-rich fluid filling both the cochlear duct and the membranous labyrinth; bathes the apical end of the hair cells. endorphins One of a group of neuropeptides that are ago-nists at opioid receptors, virtually all of which contain the sequence Tyr-Gly-Gly-Phe. end plate The complex postsynaptic specialization at the site of nerve contact on skeletal muscle fibers. engram The term used to indicate the physical basis of a stored memory. enkephalins A general term for endogenous opioid peptides. ependyma The epithelial lining of the canal of the spinal cord and the ventricles. ependymal cells Epithelial cells that line the ventricular sys-tem. epidermis The outermost layer of the skin; derived from the embryonic ectoderm. epigenetic Referring to influences on development that arise from factors other than genetic instructions. epinephrine (adrenaline) Catecholamine hormone and neu-rotransmitter that binds to α- and β-adrenergic G-protein-coupled receptors. epineurium The connective tissue surrounding axon fascicles of a peripheral nerve. epithelium Any continuous layer of cells that covers a sur-face or lines a cavity. equilibrium potential The membrane potential at which a given ion is in electrochemical equilibrium. estradiol One of the biologically important C18 class of steroid hormones capable of inducing estrous in females. eukaryote An organism that contains cells with nuclei. excitatory postsynaptic potential (EPSP) Neurotransmitter-induced postsynaptic potential change that depolarizes the cell, and hence increases the likelihood of initiating a post-synaptic action potential. exocytosis A form of cell secretion resulting from the fusion of the membrane of a storage organelle, such as a synaptic vesicle, with the plasma membrane. explant A piece of tissue maintained in culture medium. external segment A subdivision of the globus pallidus. extracellular matrix A matrix composed of collagen, laminin, and fibronectin that surrounds most cells (see also basal lamina). extrafusal muscle fibers Fibers of skeletal muscles; a term that distinguishes ordinary muscle fibers from the special-ized intrafusal fibers associated with muscle spindles. face cells Neurons in the temporal cortex of rhesus monkeys that respond specifically to faces. facilitation The increased transmitter release produced by an action potential that follows closely upon a preceding action potential. family A taxonomic category subordinate to order; com-prises genera. fasciculation The aggregation of neuronal processes to form a nerve bundle; also refers to the spontaneous discharge of motor units after muscle denervation. a-fetoprotein A protein that actively sequestors circulating estrogens. fetus The developing mammalian embryo at relatively late stages when the parts of the body are recognizable. fibrillation Spontaneous contractile activity of denervated muscle fibers. fibroblast growth factor (FGF) A peptide growth factor, orig-inally defined by its mitogenic effects on fibroblasts; also acts as an inducer during early brain development. fibronectin A large cell adhesion molecule that binds integrins. filopodium Slender protoplasmic projection, arising from the growth cone of an axon or a dendrite, that explores the local environment. fissure A deep cleft in the brain; distinguished from sulci, which are shallower cortical infoldings. flexion reflex Polysynaptic reflex mediating withdrawal from a painful stimulus. floorplate Region in the ventral portion of the developing spinal cord; important in the guidance and crossing of growing axons. folia The name given to the gyral formations of the cerebel-lum. forebrain The anterior portion of the brain that includes the cerebral hemispheres (includes the telencephalon and dien-cephalon). fornix An axon tract, best seen from the medial surface of the divided brain, that interconnects the hypothalamus and hippocampus. fourth ventricle The ventricular space that lies between the pons and the cerebellum. fovea Area of the retina specialized for high acuity in the center of the macula; contains a high density of cones and few rods. foveola Capillary and rod-free zone in the center of the fovea. frontal lobe One of the four lobes of the brain; includes all the cortex that lies anterior to the central sulcus and supe-rior to the lateral fissure. Glossary G-5 G-6 Glossary G-protein-coupled receptors (metabotropic receptors) A large family of neurotransmitter or hormone receptors, characterized by seven transmembrane domains; the bind-ing of these receptors by agonists leads to the activation of intracellular G-proteins. G-proteins Term for two large groups of proteins—the het-erotrimeric G-proteins and the small-molecule G-proteins— that can be activated by exchanging bound GDP for GTP. gamma (g) motor neurons Class of spinal motor neurons specifically concerned with the regulation of muscle spin-dle length; these neurons innervate the intrafusal muscle fibers of the spindle. ganglion (plural, ganglia) Collections of hundreds to thou-sands of neurons found outside the brain and spinal cord along the course of peripheral nerves. ganglion cell A neuron located in a ganglion. gap junction A specialized intercellular contact formed by channels that directly connect the cytoplasm of two cells. gastrula The early embryo during the period when the three embryonic germ layers are formed; follows the blas-tula stage. gastrulation The cell movements (invagination and spread-ing) that transform the embryonic blastula into the gastrula. gender identification Self-perception of one’s alignment with the traits associated with being a phenotypic female or male in a given culture. gene A hereditary unit located on the chromosomes; genetic information is carried by linear sequences of nucleotides in DNA that code for corresponding sequences of amino acids. genome The complete set of an animal’s genes. genotype The genetic makeup of an individual. genotypic sex Sexual characterization according to the com-plement of sex chromosomes; XX is a genotypic female, and XY is a genotypic male. genus A taxonomic division that comprises a number of closely related species within a family. germ cell The egg or sperm (or the precursors of these cells). germ layers The three primary layers of the developing embryo from which all adult tissues arise: ectoderm, meso-derm, and endoderm. glia (neuroglial cells) The support cells associated with neu-rons (astrocytes, oligodendrocytes, and microglia in the central nervous system; Schwann cells in peripheral nerves; and satellite cells in ganglia). globus pallidus One of the three major nuclei that make up the basal ganglia in the cerebral hemispheres; relays infor-mation from the caudate and putamen to the thalamus. glomeruli Characteristic collections of neuropil in the olfac-tory bulbs; formed by dendrites of mitral cells and termi-nals of olfactory receptor cells, as well as processes from local interneurons. glutamate-glutamine cycle A metabolic cycle of glutamate release and resynthesis involving both neuronal and glial cells. Golf A G-protein found uniquely in olfactory receptor neu-rons. Golgi tendon organs Receptors located in muscle tendons that provide mechanosensory information to the central nervous system about muscle tension. gracile nuclei Sensory nuclei in the lower medulla; these second-order sensory neurons relay mechanosensory infor-mation from the lower body to the thalamus. gradient A systematic variation of the concentration of a mol-ecule (or some other agent) that influences cell behavior. granule cell layer The layer of the cerebellar cortex where granule cell bodies are found. Also used to refer to cell-rich layers in neocortex and hippocampus. gray matter General term that describes regions of the cen-tral nervous system rich in neuronal cell bodies and neu-ropil; includes the cerebral and cerebellar cortices, the nuclei of the brain, and the central portion of the spinal cord. Green Fluorescent Protein (GFP) A protein, originally dis-covered in a light-emitting jellyfish, that generates green fluorescent light. GFP is widely used as a genetic tag in flu-orescence microscopy. It allows observation of specific neu-rons and some of their components over time in living cells, or even in whole organisms. Especially exciting has been the ability to monitor changes neuronal structure over time. growth cone The specialized end of a growing axon (or den-drite) that generates the motive force for elongation. gyri The ridges of the infolded cerebral cortex (the valleys between these ridges are called sulci). hair cells The sensory cells within the inner ear that trans-duce mechanical displacement into neural impulses. helicotrema The opening at the apex of the cochlea that joins the scala vestibuli and scala tympani. Hensen’s node see primitive pit. heterotrimeric G-proteins A large group of proteins consist-ing of three subunits (α, β, and γ) that can be activated by exchanging bound GDP with GTP resulting in the liberation of two signaling molecules—αGTP and the βγ-dimer. higher-order neurons Neurons that are relatively remote from peripheral targets. hindbrain see rhombencephalon. hippocampus A cortical structure in the medial portion of the temporal lobe; in humans, concerned with short-term declarative memory, among many other functions. histamine A biogenic amine neurotransmitter derived from the amino acid histidine. homeobox genes A set of master control genes whose expression establishes the early body plan of developing organisms (see also homeotic mutant). homeotic mutant A mutation that transforms one part of the body into another (e.g., insect antennae into legs). Affects homeobox genes. homologous Technically, referring to structures in different species that share the same evolutionary history; more gen-erally, referring to structures or organs that have the same general anatomy and perform the same function. homosexuality Sexual attraction to an individual of the same phenotypic sex. horizontal cells Retinal neurons that mediate lateral interac-tions between photoreceptor terminals and the dendrites of bipolar cells. horseradish peroxidase A plant enzyme widely used to stain nerve cells (after injection into a neuron, it generates a visible precipitate by one of several histochemical reac-tions). Huntington’s disease An autosomal dominant genetic dis-order in which a single gene mutation results in personal-ity changes, progressive loss of the control of voluntary movement, and eventually death. Primary target is the basal ganglia. hydrocephalus Enlarged cranium as a result of increased cerebrospinal fluid pressure (typically due to a mechanical outflow blockage). hyperalgesia Increased perception of pain. hyperkinesia Excessive movement. hyperpolarization The displacement of a cell’s membrane potential toward a more negative value. hypokinesia A paucity of movement. hypothalamus A collection of small but critical nuclei in the diencephalon that lies just inferior to the thalamus; governs reproductive, homeostatic, and circadian functions. imprinting A rapid and permanent form of learning that occurs in response to early experience. inactivation The time-dependent closing of ion channels in response to a stimulus, such as membrane depolarization. inducers Chemical signals originating from one set of cells that influence the differentiation of other cells. induction The ability of a cell or tissue to influence the fate of nearby cells or tissues during development by chemical signals. inferior colliculi (singular, colliculus) Paired hillocks on the dorsal surface of the midbrain; concerned with auditory processing. inferior olive (inferior olivary nucleus) Prominent nucleus in the medulla; a major source of input to the cerebellum. infundibulum The connection between the hypothalamus and the pituitary gland; also known as the pituitary stalk. inhibitory postsynaptic potential (IPSP) Neurotransmitter-induced postsynaptic potential change that tends to decrease the likelihood of a postsynaptic action potential. innervate Establish synaptic contact with a target. innervation Referring to all the synaptic contacts of a target. input The innervation of a target cell by a particular axon; more loosely, the innervation of a target. input elimination The developmental process by which the number of axons innervating some classes of target cells is diminished. instructive A developmental influence that dictates the fate of a cell rather than simply permitting differentiation to occur. insula The portion of the cerebral cortex that is buried within the depths of the lateral fissure. integral membrane proteins Proteins that possess hydro-phobic domains that are inserted into membranes. integration The summation of excitatory and inhibitory syn-aptic conductance changes by postsynaptic cells. integrins A family of receptor molecules found on growth cones that bind to cell adhesion molecules such as laminin and fibronection. intention tremor Tremor that occurs while performing a vol-untary motor act. Characteristic of cerebellar pathology. internal arcuate tract Mechanosensory pathway in the brain-stem that runs from the dorsal column nuclei to form the medial lemniscus. internal capsule Large white matter tract that lies between the diencephalon and the basal ganglia; contains, among others, sensory axons that run from the thalamus to the cor-tex and motor axons that run from the cortex to the brain-stem and spinal cord. interneuron Technically, a neuron in the pathway between primary sensory and primary effector neurons; more gen-erally, a neuron that branches locally to innervate other neurons. interstitial nuclei of the anterior hypothalamus (INAH) Four cell groups located slightly lateral to the third ventricle in the anterior hypothalamus of primates; thought to play a role in sexual behavior. intrafusal muscle fibers Specialized muscle fibers found in muscle spindles. invertebrate An animal without a backbone (includes about 97% of extant animals). in vitro Referring to any biological process studied outside of the organism (literally, “in glass”). in vivo Referring to any biological process studied in an intact living organism (literally “in life”). ion channels Integral membrane proteins possessing pores that allow certain ions to diffuse across cell membranes, thereby conferring selective ionic permeability. ion exchangers Membrane transporters that translocate one or more ions against their concentration gradient by using the electrochemical gradient of other ions as an energy source. ionotropic (ionotropic receptors) Receptors in which the ligand binding site is an integral part of the receptor mol-ecule. ion pumps see transporters. ipsilateral On the same side of the body. iris Circular pigmented membrane behind the cornea; perfo-rated by the pupil. ischemia Insufficient blood supply. kinocilium A true ciliary structure which, along with the stereocilia, comprises the hair bundle of vestibular and fetal cochlear hair cells in mammals (it is not present in the adult mammalian cochlear hair cell). Korsakoff’s syndrome An amnesic syndrome seen in chronic alcoholics. labyrinth Referring to the internal ear; comprises the cochlea, vestibular apparatus, and the bony canals in which these structures are housed. lamellipodia The leading edge of a motile cell or growth cone, which is rich in actin filaments. laminae (singular, lamina) Cell layers that characterize the neocortex, hippocampus, and cerebellar cortex. The gray matter of the spinal cord is also arranged in laminae. laminin A large cell adhesion molecule that binds integrins. late outward current The delayed electrical current, mea-sured in voltage clamp experiments, that results from the voltage-dependent efflux of a cation such as K+. Produces the repolarizing phase of the action potential. lateral columns The lateral regions of spinal cord white mat-ter that convey motor information from the brain to the spinal cord. lateral (Sylvian) fissure The cleft on the lateral surface of the brain that separates the temporal and frontal lobes. lateral geniculate nucleus (LGN) A nucleus in the thalamus that receives the axonal projections of retinal ganglion cells in the primary visual pathway. lateral olfactory tract The projection from the olfactory bulbs to higher olfactory centers. lateral posterior nucleus A thalamic nucleus that receives its major input from sensory and association cortices and pro-Glossary G-7 G-8 Glossary jects in turn to association cortices, particularly in the pari-etal and temporal lobes. lateral superior olive (LSO) The auditory brainstem struc-ture that processes interaural intensity differences and, in humans, mediates sound localization for stimuli greater than 3 kHz. learning The acquisition of novel behavior through experi-ence. lens Transparent structure in the eye whose thickening or flattening in response to visceral motor control allows light rays to be focused on the retina. lexical The quality of associating a symbol (e.g., a word) with a particular object, emotion, or idea. lexicon Dictionary. Sometimes used to indicate region of brain that stores the meanings of words. ligand-gated ion channels Term for a large group of neuro-transmitter receptors that combine receptor and ion channel functions into a single molecule. limb bud The limb rudiment of vertebrate embryos. limbic lobe Cortex that lies superior to the corpus callosum on the medial aspect of the cerebral hemispheres; forms the cortical component of the limbic system. limbic system Term that refers to those cortical and subcor-tical structures concerned with the emotions; the most prominent components are the cingulate gyrus, the hip-pocampus, and the amygdala. lobes The four major divisions of the cerebral cortex (frontal, parietal, occipital, and temporal). local circuit neurons General term referring to neurons whose activity mediates interactions between sensory sys-tems and motor systems; interneuron is often used as a synonym. locus coeruleus A small brainstem nucleus with widespread adrenergic cortical and descending connections; important in the governance of sleep and waking. long-term Lasting days, weeks, months, or longer. long-term depression A persistent weakening of synapses based on recent patterns of activity. long-term memory Memories that last days, weeks, months, years, or a lifetime. long-term potentiation (LTP) A persistent strengthening of synapses based on recent patterns of activity. lower motor neuron Spinal motor neuron; directly innervates muscle (also referred to as a or primary motor neuron). lower motor neuron syndrome Signs and symptoms arising from damage to a motor neurons; these include paralysis or paresis, muscle atrophy, areflexia, and fibrillations. macroscopic Visible with the naked eye. macroscopic currents Ionic currents flowing through large numbers of ion channels distributed over a substantial area of membrane. macula The central region of the retina that contains the fovea (the term derives from the yellowish appearance of this region in ophthalmoscopic examination); also, the sen-sory epithelia of the otolith organs. magnocellular A component of the primary visual pathway specialized for the perception of motion; so named because of the relatively large cells involved. mammal An animal the embyros of which develop in a uterus and the young of which begin to suckle at birth (technically, a member of the class Mammalia). mammillary bodies Small prominences on the ventral sur-face of the diencephalon; functionally, part of the caudal hypothalamus. map The ordered projection of axons from one region of the nervous system to another, by which the organization of the body (or some function) is reflected in the organization of the nervous system. mechanoreceptors Receptors specialized to sense mechani-cal forces. medial Located nearer to the midsagittal plane of an animal (the opposite of lateral). medial dorsal nucleus A thalamic nucleus that receives its major input from sensory and association cortices and pro-jects in turn to association cortices, particularly in the frontal lobe. medial geniculate complex The major thalamic relay for auditory information. medial lemniscus Axon tract in the brainstem that carries mechanosensory information from the dorsal column nuclei to the thalamus. medial longitudinal fasciculus Axon tract that carries exci-tatory projections from the abducens nucleus to the con-tralateral oculomotor nucleus; important in coordinating conjugate eye movements. medial superior olive (MSO) The auditory brainstem struc-ture that processes interaural time differences and serves to compute the horizontal location of a sound source. medium spiny neuron The principal projection neuron of the caudate and putamen. medulla The caudal portion of the brainstem, extending from the pons to the spinal cord. meduallary pyramids Longitudinal bulges on the ventral aspect of the medulla that signify the corticospinal tracts at this level of the neuraxis. Meissner’s corpuscles Encapsulated cutaneous mechano-sensory receptors specialized for the detection of fine touch and pressure. membrane conductance The reciprocal of membrane resis-tance. Changes in membrane conductance result from, and are used to describe, the opening or closing of ion channels. meninges The external covering of the brain; includes the pia, arachnoid, and dura mater. Merkel’s disks Encapsulated cutaneous mechanosensory receptors specialized for the detection of fine touch and pressure. mesencephalon see midbrain. mesoderm The middle of the three germ layers; gives rise to muscle, connective tissue, skeleton, and other structures. mesopic Light levels at which both the rod and cone systems are active. metabotropic (metabotropic receptors) Refers to receptors that are indirectly activated by the action of neurotransmit-ters or other extracellular signals, typically through the aegis of G-protein activation. Meyer’s loop That part of the optic radiation that runs in the caudal portion of the temporal lobe. microglial cells One of the three main types of central ner-vous system glia; concerned primarily with repairing dam-age following neural injury. microscopic currents Ionic currents flowing through single ion channels. midbrain (mesencephalon) The most rostral portion of the brainstem; identified by the superior and inferior colliculi on its dorsal surface, and the cerebral penduncles on its ventral aspect. middle cerebellar peduncle Large white matter tract that carries axons from the pontine relay nuclei to the cerebel-lar cortex. miniature end plate potential (MEPP) Small, spontaneous depolarization of the membrane potential of skeletal mus-cle cells, caused by the release of a single quantum of acetylcholine. mitral cells The major output neurons of the olfactory bulb. mnemonic Having to do with memory. modality A category of function. For example, vision, hear-ing, and touch are different sensory modalities. molecular layer The layer of the cerebellar cortex containing the apical dendrites of Purkinje cells, parallel fibers from granule cells, a few local circuit neurons, and the synapses between these elements. monoclonal antibody An antibody molecule raised from a clone of transformed lymphocytes. morphine A plant alkaloid that gives opium its analgesic properties. morphogen A molecule that influences morphogenesis. morphogenesis The generation of animal form. morphology The study of the form and structure of organ-isms; or, more commonly, the form and structure of an ani-mal or animal part. motor Pertaining to movement. motor cortex The region of the cerebral cortex lying anterior to the central sulcus concerned with motor behavior; includes the primary motor cortex in the precentral gyrus and associated cortical areas in the frontal lobe. motor neuron By usage, a nerve cell that innervates skeletal muscle. Also called primary or α motor neuron. motor neuron pool The collection of motor neurons that innervates a single muscle. motor system A broad term used to describe all the central and peripheral structures that support motor behavior. motor unit A motor neuron and the skeletal muscle fibers it innervates; more loosely, the collection of skeletal muscle fibers innervated by a single motor neuron. mucosa Term referring the mucus membranes lining the nose, mouth, gut, and other epithelial surfaces. muscarinic receptors A group of G-protein-coupled acetyl-choline receptors activated by the plant alkaloid muscarine. muscle spindle Highly specialized sensory organ found in most skeletal muscles; provides mechanosensory informa-tion about muscle length. muscle tone The normal, ongoing tension in a muscle; mea-sured by resistance of a muscle to passive stretching. myelin The multilaminated wrapping around many axons formed by oligodendrocytes or Schwann cells. myelination Process by which glial cells wrap axons to form multiple layers of glial cell membrane that increase axonal conduction velocity. myotatic reflex (stretch reflex) A fundamental spinal reflex that is generated by the motor response to afferent sensory information arising from muscle spindles. myotome The part of each somite that contributes to the development of skeletal muscles. Na+/K+ transporter (or Na+ pump) A type of ATPase trans-porter in the plasma membrane of most cells that is respon-sible for accumulating intracellular K+ and extruding intra-cellular Na+. nasal (nasal division) Referring to the region of the visual field of each eye in the direction of the nose. near reflex Reflexive response induced by changing binocu-lar fixation to a closer target; includes convergence, accom-modation, and pupillary constriction. neocortex The six-layered cortex that forms the surface of most of the cerebral hemispheres. Nernst equation A mathematical relationship that predicts the equilibrium potential across a membrane that is perme-able to only one ion. nerve A collection of peripheral axons that are bundled together and travel a common route. nerve growth factor (NGF) A neurotrophic protein re-quired for survival and differentiation of sympathetic gan-glion cells and certain sensory neurons. Preeminent mem-ber of the neurotrophin family of growth factors. netrins A family of diffusible molecules that act as attractive or repulsive cues to guide growing axons. neural cell adhesion molecule (N-CAM) Molecule that helps bind axons together and is widely distributed in the devel-oping nervous system. Structurally related to immunoglo-bin. neural crest A group of progenitor cells that forms along the dorsum of the neural tube and gives rise to peripheral neu-rons and glia (among other derivatives). neural plate The thickened region of the dorsal ectoderm of a neurula that gives rise to the neural tube. neural tube The primordium of the brain and spinal cord; derived from the neural ectoderm. neurite A neuronal branch (usually used when the process in question could be either an axon or a dendrite, such as the branches of isolated nerve cells in tissue culture). neuroblast A dividing cell, the progeny of which develop into neurons. neurogenesis The development of the nervous system. neuroglial cells see glia. neuroleptics A group of antipsychotic agents that cause indif-ference to stimuli by blocking brain dopamine receptors. neuromere A segment of the rhombencephalon (synonym for rhombomere). neuromuscular junction The synapse made by a motor axon on a skeletal muscle fiber. neuron Cell specialized for the conduction and transmission of electrical signals in the nervous system. neuronal geometry The spatial arrangement of neuronal branches. neuron-glia cell adhesion molecule (Ng-CAM) A cell adhe-sion molecule, structurally related to immunoglobin mole-cules, that promotes adhesive interactions between neurons and glia. neuropeptides A general term describing a large number of peptides that function as neurotransmitters or neurohor-mones. neuropil The dense tangle of axonal and dendritic branches, and the synapses between them, that lies between neuronal cell bodies in the gray matter of the brain and spinal cord. Glossary G-9 G-10 Glossary neurotransmitter Substance released by synaptic terminals for the purpose of transmitting information from one nerve cell to another. neurotrophic factors A general term for molecules that pro-mote the growth and survival of neurons. neurotrophic hypothesis The idea that developing neurons compete for a limited supply of trophic factors secreted by their targets. neurotrophins A family of trophic factor molecules that pro-mote the growth and survival of several different classes of neurons. neurula The early vertebrate embryo during the stage when the neural tube forms from the neural plate; follows the gastrula stage. neurulation The process by which the neural plate folds to form the neural tube. nociceptors Cutaneous and subcutaneous receptors (usually free nerve endings) specialized for the detection of harmful (noxious) stimuli. nodes of Ranvier Periodic gaps in the myelination of axons where action potentials are generated. non-rapid eye movement (non-REM) sleep Collectively, those phases of sleep characterized by the absence of rapid eye movements. norepinephrine (noradrenaline) Catecholamine hormone and neurotransmitter that binds to α- and β-adrenergic receptors, both of which are G-protein-coupled receptors. notochord A transient, cylindrical structure of mesodermal cells underlying the neural plate (and later the neural tube) in vertebrate embryos. Source of important inductive sig-nals for spinal cord. nucleus (plural, nuclei) Collection of nerve cells in the brain that are anatomically discrete, and which typically serve a particular function. nucleus proprius Region of the dorsal horn of the spinal cord that receives information from nociceptors. nystagmus Literally, a nodding movement. Refers to repeti-tive movements of the eyes normally elicited by large-scale movements of the visual field (optokinetic nystagmus). Nystagmus in the absence of appropriate stimuli usually indicates brainstem or cerebellar pathology. occipital lobe The posterior lobe of the cerebral hemisphere; primarily devoted to vision. ocular dominance columns The segregated termination pat-terns of thalamic inputs representing the two eyes in pri-mary visual cortex of some mammalian species. odorants Molecules capable of eliciting responses from receptors in the olfactory mucosa. olfactory bulb Olfactory relay station that receives axons from cranial nerve I and transmits this information via the olfactory tract to higher centers. olfactory epithelium Pseudostratified epithelium that con-tains olfactory receptor cells, supporting cells, and mucus-secreting glands. olfactory receptor neurons Bipolar neurons in olfactory epithelium that contain receptors for odorants. olfactory tracts see lateral olfactory tract. oligodendrocytes One of three classes of central neuroglial cells; their major function is to elaborate myelin. ontogeny The developmental history of an individual ani-mal; also used as a synonym for development. Onuf’s nucleus Sexually dimorphic nucleus in the human spinal cord that innervates striated perineal muscles medi-ating contraction of the bladder in males, and vaginal con-striction in females. opioid Any natural or synthetic drug that has pharmacolog-ical actions similar to those of morphine. opsins Proteins in photoreceptors that absorb light (in humans, rhodopsin and the three specialized cone opsins). optic chiasm The junction of the two optic nerves on the ventral aspect of the diencephalon, where axons from the nasal parts of each retina cross the midline. optic cup see optic vesicle. optic disk The region of the retina where the axons of retinal ganglion cells exit to form the optic nerve. optic nerve The nerve (cranial nerve II) containing the axons of retinal ganglion cells; extends from the eye to the optic chiasm. optic radiation Portion of the internal capsule that com-prises the axons of lateral geniculate neurons that carry visual information to the striate cortex. optic tectum The first central station in the visual pathway of many vertebrates (analogous to the superior colliculus in mammals). optic tract The axons of retinal ganglion cells after they have passed through the region of the optic chiasm en route to the lateral geniculate nucleus of the thalamus. optic vesicle The evagination of the forebrain vesicle that generates the retina and induces lens formation in the over-lying ectoderm. optokinetic eye movements Movements of the eyes that compensate for head movements; the stimulus for optoki-netic movements is large-scale motion of the visual field. optokinetic nystagmus Repeated reflexive responses of the eyes to ongoing large-scale movements of the visual scene. orbital (and medial prefrontal) cortex Division of the pre-frontal cortex that lies above the orbits in the most rostral and ventral extension of the sagittal fissure; important in emotional processing and rational decision-making. order A taxonomic category subordinate to class; comprises animal families. orientation selectivity A property of many neurons in visual cortex in which they respond to edges presented over a narrow range of orientations. oscillopsia An inability to fixate visual targets while the head is moving as a result of vestibular damage. ossicles The bones of the middle ear otoconia The calcium carbonate crystals that rest on the otolithic membrane overlying the hair cells of the sacculus and utricle. otolithic membrane The gelatinous membrane on which the otoconia lie and in which the tips of the hair bundles are embedded. otoliths Dense calcific structures (literally “ear stones”); important in generating the vestibular signals pertinent to balance. outer segment Portion of photoreceptors made up of mem-branous disks that contain the photopigment responsible for initiating phototransduction. oval window Site where the middle ear ossicles transfer vibrational energy to the cochlea. overshoot The peak, positive-going phase of an action poten-tial, caused by high membrane permeability to a cation such as Na+ or Ca2+. oxytocin A 9-amino-acid neuropeptide that is both a putative neurotransmitter and a neurohormone. Pacinian corpuscle Encapsulated mechanosensory receptor specialized for the detection of high-frequency vibrations. Papez’s circuit System of interconnected brain structures (mainly cingulate gyrus, hippocampus, and hypothalamus) in the medial aspect of the telencephalon and diencephalon described by James Papez. Participates in emotional process-ing, short-term declarative memory, and autonomic func-tions. paracrine Term referring to the secretion of hormone-like agents whose effects are mediated locally rather than by the general circulation. parallel fibers The bifurcated axons of cerebellar granule cells that synapse on dendritic spines of Purkinje cells. paralysis Complete loss of voluntary motor control. paramedian pontine reticular formation (PPRF) Neurons in the reticular formation of the pons that coordinate the actions of motor neurons in the abducens and oculomotor nuclei to generate horizontal movements of the eyes; also known as the “horizontal gaze center.” parasympathetic nervous system A division of the visceral motor system in which the effectors are cholinergic gan-glion cells located near target organs. paresis Partial loss of voluntary motor control; weakness. parietal lobe The lobe of the brain that lies between the frontal lobe anteriorly, and the occipital lobe posteriorly. Parkinson’s disease A neurodegenerative disease of the sub-stantia nigra that results in a characteristic tremor at rest and a general paucity of movement. parvocellular Referring to the component of the primary visual pathway specialized for the detection of detail and color; so named because of the relatively small cells involved. passive current flow Current flow across neuronal mem-branes that does not entail the action potential mechanism. patch clamp An extraordinarily sensitive voltage clamp method that permits the measurement of ionic currents flowing through individual ion channels. periaqueductal gray matter Region of brainstem gray matter that contains, among others, nuclei associated with the modulation of pain perception. perilymph The potassium-poor fluid that bathes the basal end of the cochlear hair cells. perineurium The connective tissue that surrounds a nerve fascicle in a peripheral nerve. peripheral nervous system All nerves and neurons that lie outside the brain and spinal cord. permissive An influence during development that permits differentiation to occur but does not specifically instruct cell fate. phasic Transient firing of action potentials in response to a prolonged stimulus; the opposite of tonic. phenotype The visible (or otherwise discernible) characteris-tics of an animal that arise during development. phenotypic sex The visible body characteristics associated with sexual behaviors. phospholipase A2A G-protein-activated enzyme that hydro-lizes membrane phospholipids at the inner leaflet of the plasma membrane to release fatty acids such as arachadonic acid. phospholipase CA G-protein-activated enzyme that hydro-lizes membrane phospholipids at the inner leaflet of the plasma membrane to release a diacylglycerol and an inosi-tol phosphate such as inositol trisphosphate (IP3). photopic vision Vision at high light levels that is mediated entirely by cones. phylogeny The evolutionary history of a species or other tax-onomic category. phylum A major division of the plant or animal kingdom that includes classes having a common ancestry. pia mater The innermost of the three layers of the meninges, which is closely applied to the surface of the brain. pigment epithelium Pigmented coat underlying the retina important in the normal turnover of photopigment in rods and cones. pineal gland Midline neural structure lying on the dorsal surface of the midbrain; important in the control of circa-dian rhythms (and, incidentally, considered by Descartes to be the seat of the soul). pinna A component of the external ear. pituitary gland Endocrine structure comprising an anterior lobe made up of many different types of hormone-secreting cells, and a posterior lobe that secretes neuropeptides pro-duced by neurons in the hypothalamus. placebo An inert substance that when administered may, because of the circumstances, have physiological effects. planum temporale Region on the superior surface of the temporal lobe posterior to Heschl’s gyrus; notable because it is larger in the left hemisphere in about two-thirds of humans. plasticity Term that refers to structural or functional changes in the nervous system. polarity Referring to a continually graded organization along one of the major axes of an animal. polymodal Responding to more than one sensory modality. polyneuronal innervation A state in which neurons or mus-cle fibers receive synaptic inputs from multiple, rather than single, axons. pons One of the three components of the brainstem, lying between the midbrain rostrally and the medulla caudally. pontine-geniculate-occipital (PGO) waves Characteristic encephalographic waves that signal the onset of rapid eye movement sleep. pontine relay nuclei Collections of neurons in the pons that receive input from the cerebral cortex and send their axons across the midline to the cerebellar cortex via the middle cerebellar peduncle. pore A structural feature of membrane ion channels that allows ions to diffuse through the channel. pore loop An extracellular domain of amino acids, found in certain ion channels, that lines the channel pore and allows only certain ions to pass. postcentral gyrus The gyrus that lies just posterior to the cen-tral sulcus; contains the primary somatic sensory cortex. posterior Toward the back; sometimes used as a synonym for caudal or dorsal. postganglionic Referring to axons that link visceral motor neurons in autonomic ganglia to their targets. Glossary G-11 G-12 Glossary postsynaptic current (PSC) The current produced in a post-synaptic neuron by the binding of neurotransmitter released from a presynaptic neuron. postsynaptic Referring to the component of a synapse spe-cialized for transmitter reception; downstream at a syn-apse. postsynaptic potential (PSP) The potential change pro-duced in a postsynaptic neuron by the binding of neuro-transmitter released from a presynaptic neuron. post-tetanic potentiation (PTP) An enhancement of synaptic transmission resulting from high-frequency trains of action potentials. precentral gyrus The gyrus that lies just anterior to the cen-tral sulcus; contains the primary motor cortex. prefrontal cortex Cortical regions in the frontal lobe that are anterior to the primary and association motor cortices; thought to be involved in planning complex cognitive behaviors and in the expression of personality and appro-priate social behavior. preganglionic Referring to neurons and axons that link vis-ceral motor neurons in spinal cord and brainstem to auto-nomic ganglia. premotor cortex Motor association areas in the frontal lobe anterior to primary motor cortex; thought to be involved in planning or programming of voluntary movements. pre-proproteins The first protein translation products syn-thesized in a cell. These polypeptides are usually much larger than the final, mature peptide, and often contain sig-nal sequences that target the peptide to the lumen of the endoplasmic reticulum. presynaptic Referring to the component of a synapse spe-cialized for transmitter release; upstream at a synapse. pretectum A group of nuclei located at the junction of the thalamus and the midbrain; these nuclei are important in the pupillary light reflex, relaying information from the retina to the Edinger-Westphal nucleus. prevertebral (prevertebral ganglia) Sympathetic ganglia that lie anterior to the spinal column (distinct from the sympathetic chain ganglia). primary auditory cortex The major cortical target of the neu-rons in the medial geniculate nucleus. primary motor cortex A major source of descending projec-tions to motor neurons in the the spinal cord and cranial nerve nuclei; located in the precentral gyrus (Brodmann’s area 4) and essential for the voluntary control of movement. primary neuron A neuron that directly links muscles, glands, and sense organs to the central nervous system. primary sensory cortex Any one of several cortical areas receiving the thalamic input for a particular sensory modality. primary visual cortex see striate cortex. primary visual pathway (retinogenticulocortical pathway) Pathway from the retina via the lateral genticulate nucleus of the thalamus to the primary visual cortex; carries the information that allows conscious visual perception. primate An order of mammals that includes lemurs, tarsiers, marmosets, monkeys, apes, and humans (technically, a member of this order). priming A phenomenon in which the memory of an initial exposure is expressed unconsciously by improved perfor-mance at a later time. primitive pit The thickened anterior end of the primitive streak; an important source of inductive signals during early development. primitive streak Axial thickening in the ectoderm of the gastrulas of reptiles, birds, and mammals; the mesoderm forms by the ingression of cells at this site. procedural memory Unconscious memories such as motor skills and associations. production aphasia Aphasia that derives from cortical dam-age to those centers concerned with the motor aspects of speech. promoter DNA sequence (usually within 35 nucleotides upstream of the start site of transcription) to which the RNA polymerase and its associated factors bind to initiate transcription. proproteins Partially processed forms of proteins containing peptide sequences that play a role in the correct folding of the final protein. proprioceptors Sensory receptors (usually limited to mech-anosensory receptors) that sense the internal forces acting on the body; muscle spindles and Golgi tendon organs are the preeminent examples. prosencephalon The part of the brain that includes the dien-cephalon and telencephalon (derived from the embryonic forebrain vesicle). prosody (adjective, prosodic) The emotional tone or quality of speech. prosopagnosia The inability to recognize faces; usually asso-ciated with lesions to the right inferior temporal cortex. proteoglycan Molecule consisting of a core protein to which one or more long, linear carbohydrate chains (glycos-aminoglycans) are attached. proximal Closer to a point of reference (the opposite of distal). psychotropic Referring to drugs that alter behavior, mood, and perception. pulvinar A thalamic nucleus that receives its major input from sensory and association cortices and projects in turn to association cortices, particularly in the parietal lobe. pupil The perforation in the iris that allows light to enter the eye. pupillary light reflex The decrease in the diameter of the pupil that follows stimulation of the retina. Purkinje cell The large principal projection neuron of the cerebellar cortex that has as its defining characteristic an elaborate apical dendrite. putamen One of the three major nuclei that make up the basal ganglia. pyramidal tract White matter tract that lies on the ventral surface of the medulla and contains axons descending from motor cortex to the spinal cord. pyriform cortex Component of cerebral cortex in the tempo-ral lobe pertinent to olfaction; so named because of its pearlike shape. radial glia Glial cells that contact both the luminal and pial surfaces of the neural tube, providing a substrate for neu-ronal migration. ramus Branch; typically applied to the white and gray com-municating rami that carry visceral motor axons to the seg-mental nerves. raphe nuclei A collection of serotonergic nuclei in the brain-stem tegmentum; important in the governance of sleep and waking. rapid eye movement (REM) sleep Phase of sleep character-ized by low-voltage, high-frequency electroencephalo-graphic activity accompanied by rapid eye movements. receptive field Region of a receptor surface (e.g., the body surface or the retina) that causes a sensory nerve cell (or axon) to respond. receptor A molecule specialized to bind any one of a large number of chemical signals, preeminently neurotransmitters. receptor neuron A neuron specialized for the transduction of energy in the environment into electrical signals. receptor potential The membrane potential change elicited in receptor neurons during sensory transduction. 5-a-reductase Enzyme that converts testosterone to dihy-drotestosterone. reflex A stereotyped (involuntary) motor response elicited by a defined stimulus. refractory period The brief period after the generation of an action potential during which a second action potential is difficult or impossible to elicit. remodeling Change in the anatomical arrangement of neural connections. reserpine An antihypertensive drug that is no longer used due to side effects such as behavioral depression. resting potential The inside-negative electrical potential that is normally recorded across all cell membranes. reticular activating system Region in the brainstem tegmen-tum that, when stimulated, causes arousal; involved in modulating sleep and wakefulness. reticular formation A network of neurons and axons that occupies the core of the brainstem, giving it a reticulated appearance in myelin-stained material; major functions include control of respiration and heart rate, posture, and state of consciousness. retina Laminated neural component of the eye that contains the photoreceptors (rods and cones) and the initial process-ing machinery for the primary (and other) visual pathways. retinoic acid A derivative of vitamin A that acts as an inducer during early brain development. retinotectal system The pathway between ganglion cells in the retina and the optic tectum of vertebrates. retrograde A movement or influence acting from the axon terminal toward the cell body. reversal potential The membrane potential of a post-synaptic neuron (or other target cell) at which the action of a given neurotransmitter causes no net current flow. rhodopsin The photopigment found in rods. rhombencephalon The part of the brain that includes the pons, cerebellum, and medulla (derived from the embry-onic hindbrain vesicle). rhombomere Segment of the developing rhombencephalon. rising phase The initial, depolarizing, phase of an action potential, caused by the regenerative, voltage-dependent influx of a cation such as Na+ or Ca2+. rods Photoreceptors specialized for operating at low light levels. rostral Anterior, or “headward.” rostral interstitial nucleus Neurons in the midbrain reticular formation that coordinate the actions of neurons in the ocu-lomotor nuclei to generate vertical movements of the eye; also known as the “vertical gaze center.” saccades Ballistic, conjugate eye movements that change the point of foveal fixation. sacculus The otolith organ that detects linear accelerations and head tilts in the vertical plane. sagittal Referring to the anterior-posterior plane of an ani-mal. saltatory conduction Mechanism of action potential propaga-tion in myelinated axons; so named because action poten-tials “jump” from one node of Ranvier to the next due to generation of action potentials only at these sites. Scarpa’s ganglion The ganglion containing the bipolar cells that innervate the semicircular canals and otolith organs. Schaffer collaterals The axons of cells in the CA3 region of hippocampus that form synapses in the CA1 region. Schwann cells Neuroglial cells in the peripheral nervous sys-tem that elaborate myelin (named after the nineteenth-cen-tury anatomist and physiologist Theodor Schwann). sclera The external connective tissue coat of the eyeball. scotoma A defect in the visual field as a result of pathological changes in some component of the primary visual pathway. scotopic Referring to vision in dim light, where the rods are the operative receptors. second-order neurons Projection neurons in a sensory path-way that lie between the primary receptor neurons and the third-order neurons. segment One of a series of more or less similar anterior-pos-terior units that make up segmental animals. segmentation The anterior-posterior division of animals into roughly similar repeating units. semaphorins A family of diffusible, growth-inhibiting mole-cules (see also collapsin). semicircular canals The vestibular end organs within the inner ear that sense rotational accelerations of the head. sensitization Increased sensitivity to stimuli in an area sur-rounding an injury. Also, a generalized aversive response to an otherwise benign stimulus when it is paired with a nox-ious stimulus. sensorineural hearing loss Diminished sense of hearing due to damage of the inner ear or its related central auditory structures. Contrast with conductive hearing loss. sensory Pertaining to sensation. sensory aphasia Difficulty in communicating with language that derives from cortical damage to those areas concerned with the comprehension of speech. sensory ganglia see dorsal root ganglia. sensory system Term sometimes used to describe all the components of the central and peripheral nervous system concerned with sensation. sensory transduction Process by which energy in the envi-ronment is converted into electrical signals by sensory receptors. serotonin A biogenic amine neurotransmitter derived from the amino acid tryptophan. sexually dimorphic Having two different forms depending on genotypic or phenotypic sex. short-term memory Memories that last from seconds to min-utes. silver stain A classical method for visualizing neurons and their processes by impregnation with silver salts (the best-Glossary G-13 G-14 Glossary known technique is the Golgi stain, developed by the Ital-ian anatomist Camillo Golgi in the late nineteenth century). size principle The orderly recruitment of motor neurons by size to generate increasing amounts of muscle tension. sleep spindles Bursts of electroencephalographic activity, at a frequency about 10–14 Hz and lasting a few seconds; spindles characterize the initial descent into non-REM sleep. small molecule neurotransmitters Referring to the non-pep-tide neurotransmitters such as acetylcholine, the amino acids glutamate, aspartate, GABA, and glycine, as well as the biogenic amines. smooth pursuit eye movements Slow, tracking movements of the eyes designed to keep a moving object aligned with the fovea. soma (plural, somata) The cell body. somatic cells Referring to the cells of an animal other than its germ cells. somatic sensory cortex That region of the cerebral cortex concerned with processing sensory information from the body surface, subcutaneous tissues, muscles, and joints; located primarily in the posterior bank of the central sulcus and on the postcentral gyrus. somatic sensory system Components of the nervous system involved in processing sensory information about the mechanical forces active on both the body surface and on deeper structures such as muscles and joints. somatotopic maps Cortical or subcortical arrangements of sensory pathways that reflect the organization of the body. somites Segmentally arranged masses of mesoderm that lie alongside the neural tube and give rise to skeletal muscle, vertebrae, and dermis. species A taxonomic category subordinate to genus; mem-bers of a species are defined by extensive similarities, including the ability to interbreed. specificity Term applied to neural connections that entail specific choices between neurons and their targets. spina bifida A congenital defect in which the neural tube fails to close at its posterior end. spinal cord The portion of the central nervous system that extends from the lower end of the brainstem (the medulla) to the cauda equina. spinal ganglia see dorsal root ganglia. spinal nucleus of the bulbocavernosus Sexually dimorphic collection of neurons in the lumbar region of the rodent spinal cord that innervate striated perineal muscles. spinal shock The initial flaccid paralysis that accompanies damage to descending motor pathways. spinal trigeminal tract Brainstem tract carrying fibers from the trigeminal nerve to the spinal nucleus of the trigeminal complex (which serves as the relay for painful stimulation of the face). spinocerebellum Region of the cerebellar cortex that receives input from the spinal cord, particularly Clarke’s column in the thoracic spinal cord. spinothalamic pathway see anterolateral pathway. spinothalamic tract Ascending white matter tract carrying information about pain and temperature from the spinal cord to the VP nuclear complex in the thalamus; also referred to as the anterolateral tract. split-brain patients Individuals who have had the cerebral commissures divided in the midline to control epileptic seizures. sporadic Cases of a disease that apparently occur at random in a population; contrasts with familial or inherited. stem cells Undifferentiated cells from which other cells, including neurons, can be derived. stereocilia The actin-rich processes that, along with the kinocilium, form the hair bundle extending from the apical surface of the hair cell; site of mechanotransduction. stereopsis The perception of depth that results from the fact that the two eyes view the world from slightly different angles. strabismus Developmental misalignment of the two eyes; may lead to binocular vision being compromised. stria vascularis Specialized epithelium lining the cochlear duct that maintains the high potassium concentration of the endolymph. striate cortex Primary visual cortex in the occipital lobe (also called Brodmann’s area 17). So named because the promi-nence of layer IV in myelin-stained sections gives this region a striped appearance. striatum (neostriatum) see corpus striatum. striola A line found in both the sacculus and utricle that divides the hair cells into two populations with opposing hair bundle polarities. subarachnoid space The cerebrospinal fluid—filled space over the surface of the brain that lies between the arach-noid and the pia. substance P An 11-amino acid neuropeptide; the first neu-ropeptide to be characterized. substantia nigra Nucleus at the base of the midbrain that receives input from a number of cortical and subcortical structures. The dopaminergic cells of the substantia nigra send their output to the caudate/putamen, while the GABAergic cells send their output to the thalamus. subthalamic nucleus A nucleus in the ventral diencephalon that receives input from the caudate/putamen and partici-pates in the modulation of motor behavior. sulci (singular, sulcus) The infoldings of the cerebral hemi-sphere that form the valleys between the gyral ridges. summation The addition in space and time of sequential synaptic potentials to generate a larger than normal post-synaptic response. superior colliculus Laminated structure that forms part of the roof of the midbrain; plays an important role in orient-ing movements of the head and eyes. suprachiasmatic nucleus Hypothalamic nucleus lying just above the optic chiasm that receives direct input from the retina; involved in light entrainment of circadian rhythms. Sylvian fissure see lateral fissure. sympathetic nervous system A division of the visceral motor system in vertebrates comprising, for the most part, adrenergic ganglion cells located relatively far from the related end organs. synapse Specialized apposition between a neuron and its target cell for transmission of information by release and reception of a chemical transmitter agent. synaptic cleft The space that separates pre- and postsynaptic neurons at chemical synapses. synaptic depression A short-term decrease in synaptic strength resulting from the depletion of synaptic vesicles at active synapses. synaptic vesicle recycling A sequence of budding and fusion reactions that occurs within presynaptic terminals to main-tain the supply of synaptic vesicles. synaptic vesicles Spherical, membrane-bound organelles in presynaptic terminals that store neurotransmitters. syncytium A group of cells in protoplasmic continuity. target (neural target) The object of innervation, which can be either non-neuronal targets, such as muscles, glands, and sense organs, or other neurons. taste buds Onion-shaped structures in the mouth and phar-ynx that contain taste cells. tectorial membrane The fibrous sheet overlying the apical surface of the cochlear hair cells; produces a shearing motion of the stereocilia when the basilar membrane is dis-placed. tectum A general term referring to the dorsal region of the brainstem (tectum means “roof”). tegmentum A general term that refers to the central gray matter of the brainstem. telencephalon The part of the brain derived from the anterior part of the embryonic forebrain vesicle; includes the cere-bral hemispheres. temporal (temporal division) Referring to the region of the visual field of each eye in the direction of the temple. temporal lobe The hemispheric lobe that lies inferior to the lateral fissure. terminal A presynaptic (axonal) ending. tetraethylammonium A quaternary ammonium compound that selectively blocks voltage-sensitive K+ channels; elimi-nates the delayed K+ current measured in voltage clamp experiments. tetrodotoxin An alkaloid neurotoxin, produced by certain puffer fish, tropical frogs, and salamanders, that selectively blocks voltage-sensitive Na+ channels; eliminates the initial Na+ current measured in voltage clamp experiments. thalamus A collection of nuclei that forms the major compo-nent of the diencephalon. Although its functions are many, a primary role of the thalamus is to relay sensory informa-tion from lower centers to the cerebral cortex. thermoreceptors Receptors specialized to transduce changes in temperature. threshold The level of membrane potential at which an action potential is generated. tight junction A specialized junction between epithelial cells that seals them together, preventing most molecules from passing across the cell sheet. tip links The filamentous structures that link the tips of adja-cent stereocilia; thought to mediate the gating of the hair cell’s transduction channels. tonic Sustained activity in response to an ongoing stimulus; the opposite of phasic. tonotopy the topographic mapping of frequency across the surface of a structure, which originates in the cochlea and is preserved in ascending auditory structures, including the auditory cortex. transcription factors A general term applied to proteins that regulate transcription, including basal transcription factors that interact with the RNA polymerase to initiate transcrip-tion, as well as those that bind elsewhere to stimulate or repress transcription. transcriptional activator proteins Proteins that bind DNA and activate the transcription of DNA. transducin G-protein involved in the phototransduction cas-cade. transduction see sensory transduction. transforming growth factor (TGF) A class of peptide growth factors that acts as an inducer during early development. transgenderism Gender identification with the opposite phe-notypic sex. transmitter see neurotransmitter. transporters (active transporters) Cell membrane molecules that consume energy to move ions up their concentration gradients, thus restoring and/or maintaining normal con-centration gradients across cell membranes. trichomatic Referring to the presence of three different cone types in the human retina, which generate the initial steps in color vision by differentially absorbing long, medium, and short wavelength light. tricyclic antidepressants A class of antidepressant drugs named for their three-ringed molecular structure; thought to act by blocking the reuptake of biogenic amines. trigeminal ganglion The sensory ganglion associated with the trigeminal nerve (cranial nerve V). Trk receptors The receptors for the neurotrophin family of growth factors. trophic The ability of one tissue or cell to support another; usually applied to long-term interactions between pre- and postsynaptic cells. trophic factor (agent) A molecule that mediates trophic inter-actions. trophic interactions Referring to the long-term interdepen-dence of nerve cells and their targets. trophic molecules see trophic factor. tropic An influence of one cell or tissue on the direction of movement (or outgrowth) of another. tropic molecules Molecules that influence the direction of growth or movement. tropism Orientation of growth in response to an external stimulus. tuning curve Referring to a common physiological test in which the receptive field properties of neurons are gauged against a varying stimulus such that maximum sensitivity or maximum responsiveness can be defined by the peak of the tuning curve. tympanic membrane The eardrum. undershoot The final, hyperpolarizing phase of an action potential, typically caused by the voltage-dependent efflux of a cation such as K+. upper motor neuron A neuron that gives rise to a descend-ing projection that controls the activity of lower motor neu-rons in the brainstem and spinal cord. upper motor neuron syndrome Signs and symptoms that result from damage to descending motor systems; these include paralysis, spasticity, and a positive Babinski sign. utricle The otolith organ that senses linear accelerations and head tilts in the horizontal plane. vasopressin A 9-amino-acid neuropeptide that acts as a neu-rotransmitter, as well as a neurohormone. Glossary G-15 G-16 Glossary ventral Referring to the belly; the opposite of dorsal. ventral horn The ventral portion of the spinal cord gray mat-ter; contains the primary motor neurons. ventral posterior complex Group of thalamic nuclei that receives the somatic sensory projections from the dorsal column nuclei and the trigeminal nuclear complex. ventral posterior lateral nucleus Component of the ventral posterior complex of thalamic nuclei that receives brain-stem projections carrying somatic sensory information from the body (excluding the face). ventral posterior medial nucleus Component of the ventral posterior complex of thalamic nuclei that receives brain-stem projections related to somatic sensory information from the face. ventral roots The collection of nerve fibers containing motor axons that exit ventrally from the spinal cord and contribute the motor component of each segmental spinal nerve. ventricles The fluid-filled spaces in the vertebrate brain that represent the lumen of the embryonic neural tube. ventricular zone The sheet of cells closest to the ventricles in the developing neural tube. vergence movements Disjunctive movements of the eyes (convergence or divergence) that align the fovea of each eye with targets located at different distances from the observer. vertebrate An animal with a backbone (technically, a mem-ber of the subphylum Vertebrata). vesicle Literally, a small sac. Used to refer to the organelles that store and release transmitter at nerve endings. Also used to refer to any of the three dilations of the anterior end of the neural tube that give rise to the three major sub-divisions of the brain. vestibulocerebellum The part of the cerebellar cortex that receives direct input from the vestibular nuclei or vestibu-lar nerve. vestibulo-ocular reflex Involuntary movement of the eyes in response to displacement of the head. This reflex allows retinal images to remain stable while the head is moved. visceral (noun, viscera) Referring to the internal organs of the body cavity. visceral motor system The component of the motor system (also known as the autonomic nervous system) that moti-vates and governs visceral motor behavior. visceral nervous system Synonymous with autonomic ner-vous system. visual field The area in the external world normally seen by one or both eyes (referred to, respectively, as the monocular and visual binocular fields). vital dye A reagent that stains cells when they are alive. voltage clamp A method that uses electronic feedback to control the membrane potential of a cell, simultaneously measuring transmembrane currents that result from the opening and closing of ion channels. voltage-gated Term used to describe ion channels whose opening and closing is sensitive to membrane potential. Wallerian degeneration The process by which the distal portion of a damaged axon segment degenerates; named after Augustus Waller, a nineteenth-century physician and neuroanatomist. Wernicke’s aphasia Difficulty comprehending speech as a result of damage to Wernicke’s language area. Wernicke’s area Region of cortex in the superior and poste-rior region of the left temporal lobe that helps mediate lan-guage comprehension. Named after the nineteenth-century neurologist, Carl Wernicke. white matter A general term that refers to large axon tracts in the brain and spinal cord; the phrase derives from the fact that axonal tracts have a whitish cast when viewed in the freshly cut material. working memory Memories held briefly in mind that enable a particular task to be accomplished (e.g., efficiently search-ing a room for a lost object). Chapter 1 Studying the Nervous Systems of Humans and Other Animals Figure 1.3 PETERS, A., S. L. PALAY AND H. DEF. WEBSTER (1991) The Fine Structure of the Nervous System: Neurons and Their Supporting Cells, 3rd Ed. Oxford University Press, New York. Figure 1.4E SALA, K., K. FUTAI, K. YAMAMOTO, P. F. WORLEY, Y. HAYASHI AND M. SHENG (2003) Inhibition of dendritic spine morphogenesis and synaptic transmission by activity-inducible protein Homer1a. J. Neurosci. 23: 6327–6337. Figure 1.4F MATUS, A. (2000) Actin dynamics and synap-tic plasticity. Science 290: 754–758. Figure 1.5A–C JONES, E. G. AND M. W. COWAN (1983) The nervous tissue. In The Structural Basis of Neurobiology, E. G. Jones (ed.). New York: Elsevier, Chapter 8. Chapter 2 Electrical Signals of Nerve Cells Figures 2.7 & 2.8 HODGKIN, A. L. AND B. KATZ (1949) The effect of sodium ions on the electrical activity of the giant axon of the squid. J. Physiol. (Lond.) 108: 37–77. Chapter 3 Voltage-Dependent Membrane Permeability Figures 3.1, 3.2, 3.3 & 3.4 HODGKIN, A. L. AND A. F. 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Phil. Trans. R. Soc. Lond. B. 278: 377–409. Figure 23.7 ANTONINI, A. AND M. P. STRYKER (1993) Rapid remodeling of axonal arbors in the visual cortex. Science 260: 1819–1821. Figure 23.9 HUBEL, D. H. AND T. N. WIESEL (1965) Binocular interaction in striate cortex of kittens reared with artificial squint. J. Neurophysiol. 28: 1041–1059. Figure 23.10 WONG, R. O. AND A. GHOSH (2002) Activity-dependent regulation of dendritic growth and patterning. Nature Rev. Neurosci. 3: 803–812. Chapter 24 Plasticity of Mature Synapses and Circuits Figures 24.1 –24.3 SQUIRE, L. R. AND E. R. KANDEL (1999) Memory: From Mind to Mole-cules. New York: Scientific American Library. Figure 24.4 KATZ, B. (1966) Nerve, Muscle and Synapse. New York: McGraw Hill. Figure 24.4 SCHENK, F. AND R. G. MORRIS (1985) Dissociation between components of spatial memory in rats after recovery from the effects of retrohippocam-pal lesions. Exp. Brain Res. 58: 11–27. Fig-ure 24.6 MALINOW, R., H. SCHULMAN, AND R. W. TSIEN (1989) Inhibition of postsynaptic PKC or CaMKII blocks induction but not expression of LTP. Science 245: 862–866. Figure 24.7 GUSTAFSSON, B., H. WIGSTROM, W.C. ABRAHAM, AND Y.Y. HUANG (1987) Long-term potentiation in the hippocampus using depolarizing current pulses as the conditioning stimulus to single volley syn-aptic potentials. J. Neurosci. 7: 774–780. Figure 24.9 NICOLL, R. A., J. A. KAUER AND R. C. MALENKA (1988) The current excite-ment in long-term potentiation. Neuron. 1: 97–103. Figure 24.11A LIAO, D., N. A. HESSLER AND R. MALINOW (1995) Activation of postsynaptically silent synapses during pairing-induced LTP in CA1 region of hip-pocampal slice. Nature 375: 400–404. Fig-ure 24.11B SHI, S. H. AND 6 OTHERS (1999) Rapid spine delivery and redistribution of AMPA receptors after synaptic NMDA receptor activation. Science 284: 1811–1816. Figure 24.12 MULKEY, R. M., C. E. HERRON AND R. C. MALENKA (1993) An essential role for protein phosphatases in hippocampal long-term depression. Science 261: 1051–1055. Figure 24.13B SAKURAI, M. (1987) Synaptic modification of parallel fibre-Purkinje cell transmission in in vitro guinea-pig cerebellar slices. J. Physiol. (Lond) 394: 463–480. Figure 24.14A SQUIRE, L. R. AND E. R. KANDEL (1999) Mem-ory: From Mind to Molecules. New York: Sci-entific American Library. Figure 24.14B ENGERT, F. AND T. BONHOEFFER (1999) Den-dritic spine changes associated with hip-pocampal long-term synaptic plasticity. Nature 399: 66–70. Figure 24.15 MERZENICH, M. M., R. J. NELSON, M. P. STRYKER, M. S. CYNADER, A. SCHOPPMANN AND J. M. ZOOK (1984) Somatosensory cortical map changes following digit amputation in adult monkeys. J. Comp. Neurol. 224: 591–605. Box C DYRO, F. M. (1989) The EEG Handbook. Boston: Little, Brown and Company. Figure 24.16 JENKINS, W. M., M. M. MERZENICH, M. T. OCHS, E. ALLARD AND T. GUIC-ROBLES (1990) Functional reorganization of primary somatosensory cortex in adult owl monkeys after behaviorally controlled tactile stimulation. J. Neurophysiol. 63: 82–104. Figure 24.18 GAGE, F. H. (2000) Mammalian neural stem cells. Science 287: 1433–1438. Chapter 25 The Association Cortices Figure 25.5A,B & 25.7 POSNER, M. I. AND M. E. RAICHLE (1994) Images of Mind. New York: Scientific American Library. Figure 25.5C & 25.6B BLUMENFELD, H. (2002) Neuroanatomy through Clinical Cases. Sunderland, MA: Sin-auer Associates. Figure 25.6A HEILMAN, H. AND E. VALENSTEIN (1985) Clinical Neu-ropsychology, 2nd Ed. New York: Oxford Uni-versity Press. Figure 25.10B LYNCH, J. C., V. B. MOUNTCASTLE, W. H. TALBOT AND T. C. YIN (1977) Parietal lobe mechanisms for directed visual attention. J. Neurophys. 40: 362–369. Figure 25.10C PLATT, M. L. AND P. W. GLIMCHER (1999) Neural correlates of decision variables in parietal cortex. Nature 400: 233–238. Figure 25.11 DESIMONE, R., T. D. ALBRIGHT, C. G. GROSS AND C. BRUCE (1984) Stimulus-selective properties of inferior tem-poral neurons in the macaque. J. Neurosci. 4: 2051–2062. Figure 25.12A TANAKA, S. (2001) Computational approaches to the architecture and operations of the prefrontal cortical circuit for working memory. Prog. Neuro-Psychopharm. Biol. Psychiat. 25: 259–281. Figure 25.12B WANG, G., K. TANAKA AND M. TANIFUJI (1996) Optical imag-ing of functional organization in the monkey inferotemporal cortex. Science 272: 1665– 1668. Figure 25.13 GOLDMAN-RAKIC, P. S. (1987) Circuitry of the prefrontal cortex and the regulation of behavior by representa-tional memory. In Handbook of Physiology. Sec-tion 1, The Nervous System. Vol. 5, Higher Functions of the Brain, Part I. F. Plum (ed.). Bethesda: American Physiological Society, pp. 373–417. Chapter 26 Language and Lateralization Figure 26.5A PENFIELD, W. AND L. ROBERTS (1959) Speech and Brain Mechanisms. Prince-ton, NJ: Princeton University Press, 1959) Figure 26.5B OJEMANN, G. A., I. FRIED AND E. LETTICH (1989) Electrocorticographic (EcoG) correlates of language. Electroen-cephalo. Clin. Neurophys. 73: 453–463. Fig-ure 26.6 POSNER, M. I. AND M. E. RAICHLE (1994) Images of Mind. New York: Scientific American Library. Figure 26.7 DAMASIO, H., T. J. GRABOWSKI, D. TRANEL, R. D. HICHWA AND A. DAMASIO (1996) A neural basis for lex-ical retrieval. Nature 380: 499-505. Figure 26.8 BELLUGI, U., H. POIZNER AND E. S. KLIMA (1989) Language, modality, and the brain. Trends Neurosci. 12: 380–388. Chapter 27 Sleep and Wakefulness Figures 27.1, 27.6, & 27.10 HOBSON, J. A. (1989) Sleep. New York: Scientific American Library. Box A MUKHAMETOV, L. M., A. Y. SUPIN AND I. G. POLYAKOVA (1977) Interhem-ispheric asymmetry of the electroencephalo-graphic sleep patterns in dolphins. Brain Res. 134: 581–584. Figure 27.3 Bergmann, B. M., C. A. Kushida, C. A. EVERSON, M. A. GILLILAND, W. OBERYMEYER AND A. RECHTSCHAFFEN (1989) Sleep deprivation in the rat: II. Methodology. Sleep 12: 5–12. Fig-ure 27.4 ASCHOFF, J. (1965) Circadian rhythms in man. Science 148: 1427–1432. Box C Figures B & C BEAR, M., M. A. PAR-ADISO AND B. CONNORS (2001) Neuroscience: Exploring the Brain, 2nd Ed. Philadelphia: Williams & Wilkins/Lippincott. Figure 27.7 FOULKES, D. AND M. SCHMIDT (1983) Temporal sequence and unit composition in dream reports from different stages of sleep. Sleep 6: 265–280. Figure 27.12 MCCORMICK, D. A. AND H. C. PAPE (1990) Properties of a hyper-polarization-activated cation current and its role in rhythmic oscillation in thalamic relay neurones. J. Physiol. 431: 291–318. Figure 27.13 STERIADE, M., D. A. MCCORMICK AND T. J. SEJNOWSKI (1993) Thalamocortical oscilla-tions in the sleeping and aroused brain. Sci-ence 262: 679–685. Figure 27.14 HOBSON, J. A. (1999) Consciousness. New York: Scientific American Library. Chapter 28 Emotions Figure 28.1 LEDOUX, J. E. (1987) Emotion. In Handbook of Physiology, Section 1, The Nervous System, Vol. 5. F. Blum, S. R. Geiger, and V. B. Mountcastle (eds.). Bethesda, MD: American Physiological Society, pp. 419–459. Figure 28.6 ROLLS, E. T. (1999) The Brain and Emo-tion. Oxford: Oxford University Press. Fig-ure 28.7 LEDOUX, J. E. (2000) Emotion cir-cuits in the brain. Annu. Rev. Neurosci. 23: 155–184. Figure 28.8 MOSCOVITCH, M. AND J. OLDS (1982) Asymmetries in spontaneous facial expressions and their possible relation to hemispheric specialization. Neuropsy-chologia 20: 71–81. Figure 28.9B WINSTON, J. S., B. A. STRANGE, J. O’DOHERTY AND R. J. DOLAN (2002) Automatic and intentional brain responses during evaluation of trust-worthiness of faces. Nature Neurosci. 5: 277–283. Chapter 29 Sex, Sexuality, and the Brain Box A MOORE, K. L. (1977) The Developing Human, 2nd Ed. Philadelphia: W. B. Saun-ders, p. 219. Box C Figure A MCEWEN, B. S. (1976) Interactions between hormones and nerve tissue. Sci. Am. 235: 48–58. Box C Figure B MCEWEN, B. S., P. G. DAVIS, B. PAR-SONS AND D. W. PFAFF (1978) The brain as a target for steroid hormone action. Ann. Rev. Neurosci. 2: 65–112. Figure 29.2 TORAND-ALLERAND, C. D. (1978) Gonadal hormones and brain development. Cellular aspects of sexual differentiation. Amer. Zool. 18: 553–565. Figure 29.3 WOOLLEY, C. S. AND B. S. MCEWEN (1992) Estradiol mediates fluc-tuation in hippocampal synapse density dur-ing the estrous cycle in the adult rat. J. Neu-rosci. 12: 2549–2554. Figure 29.4A BREEDLOVE, S. M. AND A. P. ARNOLD (1984) Sexually dimorphic motor nucleus in the rat lumbar spinal cord: Response to adult hor-mone manipulation, absence in androgen-insensitive rats. Brain Res. 225: 297–307. Figure 29.4B,C BREEDLOVE, S. M. AND A. P. ARNOLD (1983) Hormonal control of a devel-oping neuromuscular system. II. Sensitive periods for the androgen-induced masculin-ization of the rat spinal nucleus of the bulbo-cavernosus. J. Neurosci. 3: 424–432. Figure 29.4D FORGER, N. G. AND S. M. BREEDLOVE (1986) Sexual dimorphism in human and canine spinal cord: Role of early androgen. Proc. Natl. Acad. Sci. USA 83: 7527–7530. Figure 29.6 OOMURA, Y., H. YOSHIMATSU AND S. AOU (1983) Medial preoptic and hypothala-mic neuronal activity during sexual behavior of the male monkey. Brain Res. 266: 340–343. Figure 29.7B–D ALLEN, L. S., M. HINES, J. E. SHYRNE AND R. A. GORSKI (1989) Two sexually dimorphic cell groups in the human brain. J. Neurosci. 9: 497–506. Figure 29.8A LEVAY, S. (1991) A difference in hypothalamic struc-ture between heterosexual and homosexual men. Science 253: 1034–1037. Figure 29.8B SWAAB, D. F. AND M. A. HOFFMAN (1990) An enlarged suprachiasmatic nucleus in homo-sexual men. Brain Res. 537: 141–148. Figure 29.9B–C XERRI, C., J. M. STERN AND M. M. MERZENICH (1994) Alterations of the cortical representation of the rat ventrum induced by nursing behavior. J. Neurosci. 14: 1710–1721. Figure 29.10 MODNEY, B. K. AND G. I. HAT-TON (1990) Motherhood modifies magnocel-lular neuronal interrelationships in function-ally meaningful ways. In Mammalian Parenting, N. A. Krasnegor and R. S. Bridges (eds.). New York: Oxford University Press, pp. 306–323. Chapter 30 Human Memory Figure 30.3 ERICSSON, K. A., W. G. CHASE, AND S. FALOON (1980) Acquisition of a mem-ory skill. Science. 208: 1181–1182. Figure 30.4 CHASE W. G. AND H. A. SIMON (1973) The Mind’s Eye in Chess in Visual Information Processing, W. G. Chase, ed. New York: Acad-emic Press, pp. 215–281. Figure 30.5A RUBIN, D. C. AND T. C. KONTIS (1983) A schema for common cents. Mem. Cog. 11: 335–341. Figure 30.5B SQUIRE, L. R. (1989) On the course of forgetting in very long-term memory. J. Exp. Psychol. 15: 241–245. Fig-ure 30.7B EICHENBAUM, H. (2000). A cortical-Illustration Source References SR-5 SR-6 Illustration Source References hippocampal system for declarative mem-ory. Nat. Rev. Neurosci. 1: 41–50. Figure 30.7C,D SCHENK, F. AND R. G. MORRIS (1985) Dissociation between components of spatial memory in rats after recovery from the effects of retrohippocampal lesions. Exp. Brain Res. 58: 11–28. Figure 30.8 VAN HOESEN, G. W. (1982) The parahippocampal gyrus. Trends Neurosci. 5: 345–350. Figure 30.9 ISHAI, A., L. G. UNGERLEIDER, A. MAR-TIN AND J. V. HAXBY (2000) The representa-tion of objects in the human occipital and temporal cortex. J. Cog. Neurosci. 12 Suppl 2: 35–51. Figure 30.11 DEKABAN, A. S. AND D. SADOWSKY (1978) Changes in brain weights during the span of human life: Relation of brain weights to body heights and body weights. Ann. Neurol. 4: 345–356. Box D Figure A ROSES, A. (1995) Apolipoprotein E and Alzheimer disease. Science & Medicine September/October 1995, 16–25. Box D Figure B BLUMEN-FELD, H. (2002) Neuroanatomy through Clinical Cases. Sunderland, MA: Sinauer Associates; BRUN, A. AND E. ENGLUND (1981) Regional pattern of degeneration in Alzheimer’s dis-ease: Neuronal loss and histopathalogical grading. Histopathology 5: 459–564. ABCR gene, 243 abducens nerve (cranial nerve VI), 329, 454, 514, 756, 756–758 abducens nucleus, 759, 760 acceleration angular, 325–328, 328 perception of, 315, 322–323 accessory nucleus, 759 accomodation, 231, 231–234 Accutane® (isoretinoin, 13-cis-retinoic acid), 506 acetyl coenzyme A (acetyl CoA), 131 acetylcholine (ACh) function, 129, 131, 131–135 identification, 96 metabolism, 132 preganglionic neurons and, 487 release, 102 structure, 130 synthesis, 131 acetylcholine receptors (AChRs), 116, 116–117, 132–133, 133, 135, 542, 543 acetylcholinesterase (AChE), 132 acid-sensitive ion channels (ASICs), 78, 361 aconitine, 82 acromelic acid, 137 “across-neuron” hypothesis, 364 actin, localization, 6, 529 actin cytoskeleton, 528 action potentials all-or-nothing character, 35 conduction velocity, 59, 62 extracellular recordings, 12 function, 7 ion channels and, 69–73 ionic basis, 44, 44–46 long-distance signaling by, 56–61 membrane permeability and, 47 myotatic reflexes, 13 nomenclature, 45–46 permeabilities and, 40 phases, 45, 45–46 production, 34 propagation, 59, 59 reconstruction, 54–56, 55 saltatory propagation, 63, 64 threshold, 57 time course, 61 action tremors, 449 active transporters, 35–36, 36, 86–87 acupuncture, 225 acute brain injury, 145 Aδ nociceptors, 210 adaptation, 320, 320–321, 346 to light, 254–255, 257 addiction, 134–135 adenosine, 152–153 adenosine triphosphate (ATP), 130, 131, 152–153 adenylyl cyclase, 171 adrenal glands, 474–475 adrenal medulla, 471 β-adrenergic receptor blockers, 150 adrenergic receptors, 150, 489 Adrian, Edgar, 350, 668 affective disorders, 704–705 afferent neurons function, 12 mechanosensory information, 201–204 sensory fibers and, 383 somatic sensory system and, 193 from viscera, 480 α-agatoxins, 137 age/aging brain function and, 752 handedness and, 651 hearing loss, 285 macular degeneration, 243 memory and, 749–752 odor perception, 341, 341 sleep requirements, 659 age-related macular degenera-tion (AMD), 243 agnosias, 622 agraphias, 643 agrin, 542–543 Aguayo, Albert, 604, 606–607 Aiken, Alexander, 738 alarm calls, 643 albinos, 530 alcohol abuse, 448, 744 Allen, Laura, 724–725 allergic reactions, 151 allodynia, 221 α-toxins, 82, 82 Alzheimer’s disease, 341, 504, 744, 750, 750–751 amacrine cells, retinal, 3, 234, 236 Amanita muscaria, 136 amblyopia, 568–569 ametropia, 232 amino acids radioisotopic labeling, 564 structures, 130 tastants (umami), 357–363, 364 aminoglycoside antibiotics, 285 4-aminopyridine (4-AP), 104, 105 amnesia, 741, 741, 743, 744 Amoore, John, 339 AMPA (α-amino-3-hydroxyl-5-methyl-4-isoxazole-propi-onate) receptors changes, 595, 597–599 clathrin-dependent internal-ization, 596 long-term potentiation and, 589 subunits, 138, 139 function, 142 light perception and, 252 long-term depression and, 592, 592 long-term potentiation and, 589 structure, 162 amphetamines, 149, 684 amplitude, sound waves, 283 ampullae, 316, 316, 324, 324 amputations, 599–602 amygdala anatomy, 696–697, 696–697 associative learning and, 700 blood flow, 704 fear and, 702–703 function, 20, 697–701 judgments of trustworthiness and, 709 location, 19, 20, 694, 772 neocortex and, 701, 703 nondeclarative memory and, 748–749 amyloid-β peptide (β-A4), 751 amyloid plaques, 750 amyloid precursor protein (APP), 750–751 amyotrophic lateral sclerosis (ALS), 393, 393 Anamerta cocculus, 137 anandamide, 158, 212 Anderson, Per, 584, 669 androgen insensitivity syndrome (AIS), 713 androgen receptors, 719 anencephaly, 509 aniridia, 513, 515 anomalous trichromats, 248 anopsias, 267 anosmias, 340, 340, 365, 366 anterior, definition, 16, 17 anterior cerebral arteries, 763, 765 anterior chamber, eye, 229 anterior circulation, 763 anterior commissure, 484, 485, 772 anterior communicating artery, 765 anterior inferior cerebellar artery (AICA), 764, 765 anterior nucleus of the dorsal thalamus, 694 anterior pituitary gland, 484 anterior spinal arteries, 763, 764 anterograde amnesia, 741, 746 anterolateral system, 213 antibiotics, 285 antibody labeling, 10–11 antidiuretic hormones (ADH; vasopressin), 665 antihistamines, 151, 678 apamin, 82 aphasias, 638–646 Aplysia californica (sea slug), 575, 576, 577, 578 apnea, 682–683, 683 apolipoprotein E (ApoE), 751 apoptosis, 239, 519. see also cell death APP gene, 750 apraxias, 620 aprosodias, 654, 706 aprosody, 706 APV (2-amino-5-phosphono-valerate), 142 aqueous humor, 229 Arachidonylglycerol, 158 arachnoid mater, 768, 769 arachnoid villi, 769 arborization, dendrite, 4, 176 archicortex, 617, 617 in olfactory system, 357 area X, 441 Areca catechu (betel nuts), 136, 137 arecoline, 137 areflexia, 392 arms, neural control of, 394 Index I-1 Italic type indicates the information will be found in an illustration. I-2 Index Arnold, Arthur, 717 aromatase, 716 arrestin, 240 Aserinsky, Eugene, 665 aspartate, structure, 130 aspirin, 221 association, memory and, 736–738 association cortices, 613–636 anatomy, 613–616, 614, 618 connectivity, 618 lesions, 619–621 planning deficits, 623–626 specific features, 615–618 associational systems, 14 associative learning, 700 associativity, 586–587 astrocytes, 8, 9, 603, 768 ataxias, 759 ATPase pumps, 86–87 atropine, 135, 137 attention deficits, 619–621 neuroanatomy of, 620 parietal cortex and, 626–627, 628, 629 audible spectrum, mammals, 284 auditory cortex, 309, 309–312 auditory meatus, 287, 291 auditory nerve fibers function, 285 location, 292 response properties, 302 timing, 301–303 tuning, 301–303 auditory space maps, 307 auditory system, 283–314, 304, 572 Auerbach’s plexus, 479, 480 autism, development, 515–516 autoimmune diseases, 600 autonomic ganglia, 16, 470 autonomic motor division, 14. see also visceral nervous system autonomic nervous system, 16, 470, 688 axes, neural system terminology, 16–18, 17 axial (horizontal) sections, defini-tion, 16, 17 axon hillocks, 7 axon terminals. see presynaptic terminals axons CNS function, 15 dendritic complexity and, 548 filopodia, 528 function, 7 growth cones, 527–528, 533 histology, 5 lamellapodia, 528 membrane leakiness, 56 neural cell tracings, 3 passive current flow, 58 structure, 7 synapse formation, 543–544 Babinski sign, 66, 413, 413 baclofen, 137 bactrachotoxin, 82 balance, motor control centers, 397–402 Balint’s syndrome, 621 ballistic eye movements. see saccades banded krait (Bungarus multicin-tus), 136, 136 barbiturates, 146 Bard, Phillip, 688–689 Barde, Yves, 552 Barnard, Eric, 75 baroreceptors, 491 basal forebrain nuclei, 510, 772 basal ganglia circuits, 420, 424–428, 430–432 disinhibition pathway, 427 formation, 510 functions, 20, 417–424, 432, 432, 748–749 location, 19, 20, 772 loops, 432, 432–433 motor components, 375, 418 organization of inputs, 419 projections from, 422, 422–423 projections to, 417–421 ventral parts, 694 basal lamina, 531 basilar arteries, 763, 764, 765 basilar membranes, 290, 291, 292, 294, 295 basket cells, 442, 442–443 bats, 284, 310–311 BDNF gene, 180 bed nucleus of the stria termi-nalis, 727 Beecher, Henry, 224 behavior analysis, 24–27 behavioral modification, 575–581 behaviors, innate, 557–559 Békésky, Georg von, 292, 293 belladona, 137 Bell’s palsy, 289 Bellugi, Ursula, 655 belt areas, auditory cortex, 309 benign familial neonatal convulsions, 85 benperidol, 148 Benzer, Seymour, 581, 666 benzodiazepines, 146, 682 Berger, Hans, 668 beta-toxins, 82, 82 betel nuts (Areca catechu), 136, 137 Betz cells, 402 bHLH genes, 517 Bialek, William, 301 biceps muscles, 399–400 bicoid (bcd) gene, 512 biculline, 137 binocular fields, 265 binocularity, 270 biogenic amines, 129, 147–152 biological clocks, 666–667 bipolar cells, retinal, 3, 234, 251 bipolar disorders, 704 birds, 557–559, 572, 735 birdsong, 559–561, 560 bisexuality, 724 bitemporal hemianopsia, 268 bitter taste, 357–363 blind spots, 259, 262 Bliss, Timothy, 584 blood flow, PET imaging, 26 blood oxygenation level-depen-dent (BOLD) changes, 27 blood pressure, 493 blood supply brain, 763–773 sexual function and, 496 spinal cord, 763–773 traumatic injury and, 602 blood vessel regulation, 471, 474–475, 491–493, 492 blood–brain barrier, 764, 766–768, 768 BMAL1 proteins, 667 body axes, terminolgy, 16–18, 17 body surface, tactile discrimina-tion, 196 body temperature, core, 660 bone morphogenetic proteins (BMPs), 505, 507, 508 botulinum toxins, 108, 115 Bowman’s glands, 342 brachium conjunctivum. see superior cerebellar pedun-cles brachium pontis. see middle cerebellar peduncles bradykinin, 220–221 brain age/aging and, 752 altered development, 515–516 anatomy, 18–20, 19 blood supply, 763–773 cat, 689 catecholamine distribution, 149 CNS function, 14 declarative memory forma-tion, 741–746, 744 development, 511 dimorphisms, 728–729 early development, 501–526 estradiol-sensitive neurons, 718 functional imaging, 25–27, 311 generation of neurons, 605–608 glycogen levels, 660 great ape, 643 hemisphere differences, 648–649 kindling, 600 language localization, 638 learning and, 748–749 longitudinal axis, 17 major arteries, 765 mammalian, 209 marijuana and, 160–161 memory and, 746–748 modification by experience, 557–574 modular structures, 209 new nerve cell production, 605–606 during REM sleep, 659 sexual dimorphism, 726 size and intelligence, 634–635 somatotopic organization, 22 sound representation in, 310–311 subdivision formation, 510–515 brain imaging, 25–27 brain-derived neurotrophic fac-tor (BDNF), 550–552 brainstem anatomy, 755–761 blood supply, 766 caloric testing, 327 CNS function, 18 cochlear information to, 303 components, 437 decerebrate rigidity and, 415 descending projections, 395 dorsal surface, 759 indirect projections to, 401 location, 19 motor control centers, 393, 397–402 nociception, 213 projections, 618 somatic sensory system, 21 transverse section, 760 trigeminal nerve ganglia and, 203 ventral view, 758 Brain, W. R., 619 branchial motor nuclei, 398, 757 breeding behaviors, 722 Breedlove, Marc, 721 Brewster, David, 272 Brickner, R.M., 624 Brightman, Milton, 767 Broca, Paul, 634, 639, 694 Broca’s aphasia, 641, 643–644, 644 Broca’s area, 638, 640, 643, 652, 653 Brodmann, Korbinian, 615, 617 Brodmann’s areas, 639 1, 203, 599 2, 203 3, 599 4, 374, 402 8, 460, 464 17, 260 3a, 203, 599 3b, 203 cytoarchitectonic areas, 615, 617 V1, 260 bromodeoxyuridine (BrDu), 517 bronchi, motor control, 474–475 Bucy, Paul, 695, 698 bulbocavernosus, 721 bullfrogs, 301, 303 α-bungarotoxin, 133–134, 136 Bungarus multicintus (banded krait), 136, 136 Byne, William, 725 C/EBP, 579 c-fos gene, 180 c-fos protein, 181 Ca2+/calmodulin kinase IV, 179, 180 Ca2+-independent cell adhesion molecules (CAMs), 532 CA1 region, 585 inputs, 594–595, 595 long term potentiation and, 584–585 long-term potentiation and, 586, 586 visualization, 598 CA3 region long term potentiation and, 584–585 cadherins, 529, 532, 533–534 cadmium, 107 Caenorhabditis elegans, 2, 347, 348, 517–519, 534–535 Cajal, Santiago Ramón y, 3–4, 521, 528, 590 calcarine sulcus, 266, 267, 270 calcineurin, 178 calcitonin gene-related peptide (CGRP), 221 calcium/calmodulin kinase (CaMK) II, 176, 177, 572, 588–589, 589 calcium carbonate, 318, 318 calcium channels episodic ataxia type 2 and, 85 hair cells and, 320–321 muscarinic receptors and, 489 night blindness and, 85 olfaction and, 345 photoreceptors and, 237 signal transduction and, 300 topology, 79 voltage-dependent, 107 voltage-gated, 76, 96 voltage-sensitive, 237 calcium ions (Ca2+) activity-dependent plasticity and, 572 CREB activation and, 573 long-term potentiation and, 588, 588, 589 LTD mechanisms, 593 neurotransmitter release and, 99, 107–110 NMDA receptor binding of, 141 potassium channels activated by, 76 as second messenger, 169, 172–174, 173, 579 signaling, 31, 589 calcium pump, 174 calmodulin, 159, 174 caloric testing, 327 cAMP (cyclic adenosine monophosphate), 78, 174 taste pathway, 358, cAMP-dependent protein kinases (PKAs), 176, 177 cAMP response element-binding protein (CREB), 579 cAMP response elements (CREs), 179 canal reuniens, 316 cannabinoid receptors, 157 Cannibis satva, 160, 160 Cannon, Walter, 470, 476, 477, 687 capillaries, blood-brain barrier, 768 capsaicin, 211, 212, 212 carbamazepine, 601 carbon dioxide chemoreceptors, 491 cardiac muscle, 687 cardiovascular function, 491–493, 492 CaRE (calcium response ele-ment), 179 carotid body, 492 cataplexy, 683 cataracts, 231, 569 catechol O-methyltransferase (COMT), 149 catecholamines biosynthesis, 147 brain distribution, 149 functional features, 131 structures, 130 tyrosine hydroxylase regula-tion, 185 visceral motor control, 474–475 β-catenin, 508, 534 cats brain, 689 brain size, 634 emotional behavior, 689 ocular dominance, 571 visual cortex, 566, 566 cauda equina, 17 caudal, definition, 16, 17 caudate, 417, 421, 772 caudate nuclei, 418, 418, 425, 436, 772 cell adhesion molecules (CAMs), 528–534, 532 cell-associated signaling mole-cules, 167–168, 168 cell bodies, 3, 5, 10–11 cell cycle, neuroepithelium, 518 cell death, 764. see also apoptosis cell-impermeant signaling mole-cules, 167–168, 168 cell membranes, 32–35 cell-permeant signaling mole-cules, 167–168, 168 cell–cell interactions, 518, 521, 528 center–surround, 249–254, 255, 256 central autonomic network, 486 central canal, 502 central nervous system (CNS) components, 14, 15, 20 dimorphisms, 720–728 new nerve cell production, 605–606 recovery, 603 subdivisions, 18–20, 17 central pattern generators (CPGs), 389, 390–391, 392 central sulcus, 18, 19, 193, 511 Centruroides sculpturatus (scor-pion), 82 cephalic flexure, 510, 511 cerci, crickets, 197 cerebellar ataxia, 84, 239 cerebellar nuclei, 436 cerebellar peduncles, 437 cerebellum circuits within, 441–443, 442, 443, 445 CNS function, 18 components, 437 formation, 510, 511 function, 18 genetic analysis of function, 450–451 lesions, 448–449 location, 17, 19, 755 LTD in, 595, 596, 597 motor systems and, 374–375 movement modulation by, 435–452 nondeclarative memory and, 748–749 organization, 435–438, 436 output targets, 441 projections from, 440, 440–441 projections to, 438, 438–440, 439 somatotopic maps, 439, 439 cerebral achromatopsia, 280 cerebral aqueduct, 511 cerebral cortex Alzheimer’s disease and, 750, 750–751 formation, 510 language areas, 652 layers, 516 location, 772 motor areas, 402 plasticity, 599–602, 602 somatic sensory system and, 21 cerebral hemispheres, 18 cerebrocerebellum, 435, 436 cerebrospinal fluid (CSF), 770, 770 cerebrum basal ganglia pathway, 418 inputs, 438 location, 17 mechanosensory pathway, 203 pain perception, 217 somatic sensory system and, 21, 193 cervical enlargement, 17 cervical flexure, 510 cervical nerve emergence, 17 cGMP (cyclic guanosine monophosphate), 174. see also G-proteins cGMP-gated channels, 78, 238 channel-linked receptors. see ion channels, ligand-gated channelopathies, 84–85 charybdotoxin, 82 chemical synapses, 7, 94, 96, 97 chemoaffinity hypothesis, 537 chemoattractants, 534 chemoreception, 363–366, 365, 366 chemoreceptors, 491 chemorepellents, 534 Cheney, Dorothy, 643 chess, memory and, 737 chick embryos, 544 chimpanzees, 624, 634 Chlamydia trachomatis, 569 chlordiazepoxide (Librium®), 148 chloride ion channels, 76, 78, 79, 122 chlorpromazine, 148 cholesterol, 717 choline acetyltransferase (CAT), 131 cholinergic nuclei, 677 cholinergic receptors, 491 Chomsky, Noam, 645 Chondodendron tomentosum, 136 chordin, 508 choroid, 229 choroid plexus, 769, 770 chromosomal sex, 712 chronic sleep disorders, 659 ciliary body, 229 ciliary ganglion, 261 ciliary muscles, 231–234 ciliary neurotrophic factor, 523 cingulate cortex, 216, 217 cingulate gyrus, 694 circadian rhythms, 662–665 core body temperature, 660 cortisol levels, 660 growth hormone levels, 660 regulation, 281 rest–activity cycles, 661 circle of Willis, 763, 765 circumvallate papillae, 358, 359 CL1, neurotransmitter release and, 115 clathrin, 114 climbing fibers, 442, 442, 597 clitoral erection, 496 CLOCK proteins, 667 cloning, genes, 666 clonus, 414 clostridial toxins, 115 Clostridium bacteria, 107–108 CNS. see central nervous system co-transmitters, definition, 98 cocaine, 134, 149 coccygeal nerves, 17 cochlea anatomy, 292 brainstem projections from, 303 function, 289–290 implants, 290–291, 291 location, 288, 316 traveling waves, 293 cochlear nerves, 288 cochlear nuclei, 286, 759, 760 cognitive function aging and, 752 brain dimorphisms, 728–729 definition, 613–614 sleep and, 661 cognitive neuroscience, 24 Cohen, Stanley, 549 coincidence detectors, 305 Cole, Kenneth, 2, 3 collagens, 531 color blindness, 248 color constancy, 247, 247 color contrast, 247, 247 Index I-3 I-4 Index color vision absorption spectra, 246 cone cells and, 245–249 deficiencies, 248 perception, 247 commissures, CNS, 15 communication animal, 642–643 context and, 645 emotional tone and, 656 sign language, 655–656 symbols and, 638 theories of, 3–4 complex cells, 270 computerized tomographic (CT) imaging, 25, 25 concha, 287, 288, 288 conductances, depolarization and, 53, 54 conduction aphasia, 643 conduction velocity, 59, 63–65, 65 conductive hearing loss, 289 cones (photoreceptors) circadian rhythms and, 664 color vision and, 245–249 distribution, 244–245 functional specialization, 240–244 hyperpolarization, 663, 664 intracellular recording, 237 pigments, 245–246 retinal, 235 structure, 241 cone snails (Conus sp.), 136, 137 congenital adrenal hyperplasia (CAH), 713 congenital myasthenic syn-dromes, 107 congenital night blindness (CSNB), X-linked, 85 conjugate eye movements, 458 conotoxins, 136 consciousness, 675 consolidation, 736 context, communication and, 645, 645 contractions, spontaneous, 392 contralateral neglect syndrome, 619, 619, 620–621 Conus sp. (cone snails), 136, 137 convergence, 547 convulsions. see seizures coordination cerebellar lesions and, 448–449 hypothalamic control, 484–486 locomotion, 386–387, 389, 391 movements, 397 copper/zinc superoxide dismu-tase, 393 cornea, 229, 231 coronal sections, definition, 16, 17 corpus callosum, 601, 772 corpus striatum, 417, 418–419 cortex, 331–332 cortical cells, 23 cortical layers, 10–11, 562–563, 563 cortical mapping, 652 cortices, PNS function, 15 corticobulbar tract, 402 corticocortical connections, 616 corticoreticulospinal tract, 396 corticospinal tract, 402–405, 403 corticostriatal pathway, 418 cortisol levels, 660 courting behaviors, 711–712 cranial fossae, 768 cranial motor nerves, 18 cranial nerve ganglia, 12 cranial nerve nuclei, 18, 455, 758 cranial nerve I (olfactory nerve), 338, 756, 756–758 cranial nerve II (optic nerve), 235–236, 259, 261, 756, 756–758 cranial nerve III (oculomotor nerve), 230, 756, 756–758 cranial nerve IV (trochlear nerve), 454, 514, 756, 756–758 cranial nerve V (trigeminal nerve) characterization, 756–757 chemoreception, 363–365, 365 function, 289 location, 756 mechanosensory system, 202–204 rhombomeres and, 514 subdivisions, 203 cranial nerve VI (abducens nerve), 329, 454, 514, 756, 756–758 cranial nerve VII (facial nerve) characterization, 756–758 function, 289 injury to, 404 location, 316, 756 taste and, 355, 359 cranial nerve VIII (vestibulo-cochlear nerve) characterization, 756–758 damage to, 290 location, 316, 756 tuning curves, 300 vestibular end organs and, 328–331 cranial nerve IX (glossopharyn-geal nerve) autonomic regulation, 492 characterization, 756–758 chemoreception, 363 location, 482, 756 rhombomeres and, 514 taste and, 355, 359 cranial nerve X (vagus nerve) autonomic regulation, 492 cardioinhibitory outputs, 398–399 characterization, 756–758 chemoreception, 363 heart rate and, 96, 98 location, 756 rhombomeres and, 514 taste and, 359 cranial nerve XI (spinal accessory nerve), 756, 756–758 cranial nerve XII (hypoglossal nerve), 514, 756, 756–758 cranial nerves anatomy, 755–761 brainstem, dorsal view, 759 brainstem, ventral view, 758 formation, 514 primary functions, 756–757 cranial sensory ganglia, 18 cranial sensory nerves, 18 CREB (cAMP response element-binding protein), 179–180, 180, 572, 573, 579, 597, 599 CREs (cAMP response elements), 179 Creutzfeldt-Jakob disease (CJD), 444–445 cribriform plate, 338 crickets, 197, 197, 350 crista, 324 critical periods brain function and, 557 human language, 559, 559–562 ocular dominance, 562–568, 566 synaptic plasticity and, 572 cross-eyed (esotropia) strabis-mus, 569 crossed extension reflex, 389 CRY protein, 667 Cryptochrome (Cry) gene, 667 culture, taste and, 355 cuneate nuclei, 193, 200, 201 cuneate tract, 200, 201 cupula, 324 curare, 136 Curran, Thom, 450 Curtis, David, 143 cutaneous sensory receptors, 189–194 cyclic adenosine monophosphate (cAMP). see cAMP cyclic guanosine monophosphate (cGMP), 174. see also G-pro-teins cyclic nucleotides degradation, 173 ion channels gated by, 76, 78 production, 173 as second messengers, 174–175 cyclooxygenase (COX) inhibitors, 221, 222 cytoarchitectonic areas, 614–614, 639 cytoskeleton, 4, 6 actin, 528 Damasio, Antonio, 708 Damasio, Hanna, 654 Darwin, Charles, 689 DAT, 149 db gene, 490 DCC, 535 de Nó, Rafael Lorente, 209 deafness, sign language and, 655. see also hearing loss decerebrate rigidity, 330–331, 415 declarative memory, 733–734, 734 brain structures in, 741–746, 744 clinical cases, 742–743 information acquisition, 749 information storage, 749 long-term storage and, 746–748 decussation, definition, 200, 530 deep brain stimulation, 225 delayed response genes, 181 delayed response tasks, 630, 631, 633 deletion mutations, 516 delta family, 517 delta waves, 667 dementias, 750–751 Dempsey, Edward W., 668 dendrites arborization, 4, 176, 552 effect of hormones on, 721 estrogens and, 720 histology, 5 neural cell tracings, 3 neuronal, 548, 548 dendritic spines, 590–591 dendrotoxin, 82 dentate gyrus, 606 dentate nuclei, 436, 440 depolarization conductances and, 53, 54 ionic currents and, 49, 50 membrane, 34 neurotransmitter release, 99 depression, 704 dermatomes, 21, 204 desensitization, 212 deuteranopia, 248 DeVries, Geert, 717 diabetes, odor perception and, 341 diacylglycerol (DAG), 158, 173, 175 Diamond, Milton, 716 diazepam (Valium®), 146, 148 dichromacy, 248 dieldrin, 137 diencephalon, 17, 18, 437, 510, 511 Digenea simplex (red alga), 137 dihydrotestosterone, 717 5-α-dihydrotestosterone recep-tors, 694 dihydroxyphenylalanine (DOPA), 147 Dilantin® (phenytoin), 601 direct projections, 401 disconjugate eye movements, 458 disinhibitory circuits, 423, 424 disjunctive eye movements, 458 dissociated sensory loss, 213, 216 divergence, 547 diversity, cellular, 520 DNA labeling, 517 promoter regions, 178 transcription steps, 179 dolphins, 284, 661, 661 domoate, 137 L-DOPA, 429 DOPA decarboxylase, 149 dopamine brain distribution, 149 effector pathways, 172 function, 139, 147 structure, 130 synthesis, 147, 147, 149 varieties of, 139 dopamine β-hydroxylase, 150 dopamine receptors, 135 dorsal, definition, 16, 17 dorsal column, 200 dorsal column-medial lemniscus system, 199–202, 201, 213, 219 dorsal lateral geniculate nucleus, 260 dorsal motor nucleus of the vagus nerve, 477, 759, 760 dorsal nucleus of Clarke, 437, 439 dorsal raphe, 225 dorsal root ganglia (DRG) axons, 201 dermatomes, 204 description, 12 pathways, 21, 22 somatic sensory system and, 20, 21, 193 visceral sensory neurons, 480–481 dorsal (sensory) roots, 201 dorsolateral tract of Lissauer, 213 dorsomedial nucleus, 484, 485 Down syndrome, 516 Downer, John, 697–698 downstream (5′) regulatory sequences, 1 DRG. see dorsal root ganglia Drosophila melanogaster (fruit flies) amnesiac mutation, 581 axon growth, 534, 536 bicoid (bcd) gene, 512 body plan, 511, 513 DSCAM gene, 541, 541 dunce mutation, 581 eye development, 521 gene expression sequence, 512 genome size, 2 hairy (h) gene, 512 homeotic genes, 513 krüppel (kr) gene, 512 learning, 581 memory, 581 odorant receptors, 347, 348 olfactory learning, 581 per gene, 666 rutabaga mutation, 581 wingless gene homolog, 506 wingless (wg) gene, 512 drug addiction, 134–135 drugs, sleep and, 682 DSCAM gene, 541, 541 Duchenne de Boulogne, G.-B., 690 dura mater, 768, 769 Dutchman’s breeches, 137 dynamin, 114 dynorphins, 227 dysarthria, 641 dysdiadochokinesia, 449 eardrums (tympanic mem-branes), 287 early inward currents, 50–51, 51 ears external anatomy, 287–288 human, anatomy, 288 integrating information, 303–307 internal anatomy, 289–294 sensitivity, 284, 293 vestibular system, 315–335 eating disorders, 341 echolocation, 309 ectoderm, 501, 502 Edinger-Westphal nucleus, 260, 261, 477, 759, 760 efferent neurons, 12 Ehrlich, Paul, 767 electrical signaling, 32–47, 94, 94–95 electrical synapses, 93–95, 94 electrochemical equilibria, 36, 37–39, 39–41 electroconvulsive therapy (ECT), 746 electroencephalograms (EEGs) dolphin, 661 epileptic seizure, 601 sleep, 665, 665 thalamocortical neuron firing, 679, 680 waveforms, 668–670 electroencephalography, 668–670 electrogenic pumps, 87 electromyography, 409 electrophysiological recording, 13, 23, 627 embryology, 771 brain development, 501–526, 511 cell diversity and, 520 eye development, 234 neurulation, 502 sex phenotypes, 714 embryonic stem cells, 504 emmetropia, 232, 232–233 emotions, 687–710 awareness of, 706 cortical lateralization, 705–707 dreams and, 673 facial expressions, 690–691 hemispheric asymmetry, 706–707 integration of behaviors, 688–689, 693 neural systems for expression, 691, 692 physiological changes, 687–688 processing, 656 social behaviors and, 707–708 encapsulated sensory receptors, 189, 194–195 end plate currents (EPCs), 116, 117–121, 118, 120 end plate potentials (EPPs), 102, 102–104 electronic recording, 583 membrane potentials and, 116–121 myasthenia gravis and, 140 potassium ion movement and, 120 sodium ion movement and, 120 end plates, 102, 542, 547 endocannabinoids, 131, 157, 158, 159 endocrine signaling, 165, 166 endocytosis, definition, 105 endoderm, 501, 502 endogenous opioids, 226 endolymph, 299, 299, 316 endoplasmic reticulum, 5f, 78 endorphins, 227 endothelial cells, capillary, 768 engrams, 736, 752 enkephalins, 227 enophthalmos, 488 enteric nervous system, 479–480 enteric system, 16 enzyme-linked receptors, 169, 169–170 enzyme markers, 10–11 Eph receptors, 529, 538, 539 EphB1, 530 ephrin-A5, 539 ephrin B2 ligand, 530 ephrin ligands, 539 ephrins, 532, 538 epilepsy, 406, 600–601 epinephrine (adrenaline) biosynthetic pathway, 147, 147 brain distribution, 149 release, 471 structure, 130 varieties of, 139 episodic ataxias, 84–85 equilibrium, vestibular system and, 328–329 equilibrium potential, 37 esophagus, 215, 640 estradiol, 716, 717 estrogen receptors, 694, 719 estrogens, 720 estropia (cross-eyed), 569 Etcoff, N.L., 622 ethacrynic acid, 285 ethanol, 339 eustachian tubes, 288 Evarts, Ed, 407 excitatory amino acid trans-porters (EAATs), 137, 141 excitatory postsynaptic potentials (EPSPs), 121–123, 124, 239, 578, 585 excitotoxicity, 145 exocytosis, 105, 106, 298 exons, transcription, 1 exotropia, 569 experience, brain modification and, 557–574 experimental allergic encephalomyelitis (EAE), 66 express saccades, 465 expressive aphasia, 640–641 external auditory meatus, 288 extorsion, definition, 230 extracellular matrix, 529, 532 extracellular recordings, 13 extracellular signal-regulated kinases (ERKs). see mitogen-activated protein kinases (MAPKs) extraocular muscles, 454–455, 455, 457 extrastriate visual areas, 278–281, 279, 281 eye movements diagram, 454 extraocular muscles in, 455 functions, 457–458 horizontal, 460 saccadic, 458–466 sensory integration and, 453–467 stabilized images and, 456, 456 eyelids, 471 eyes anatomy, 229–230, 230 central vision pathways, 259–282 coordination, 263, 328–329 critical periods, 562–568, 565 development, 234 frontal field, 464 Horner’s syndrome, 488 movements, 240, 241, 418, 423–424, 425 retinal surface, 260 visceral motor control, 474–475 vision, 229–257 vision deprivation studies, 565 face asymmetrical smiles, 707 emotions and, 690–691, 690–691 patterns of weakness, 404, 404–405 recognition of, 629 sensory information from, 202, 202–206 Urbach-Wiethe disease and, 702–703 facial motor nerve, 514 facial motor nucleus, 404, 404, 759, 760 facial nerve (cranial nerve VII) characterization, 756–758 injury to, 404 location, 316, 756 taste and, 355, 359 familial hemiplegic migraine (FHM), 84 familial infantile myasthenia, 107 far cells, 271 faradization, 690 fast fatigable (FF) motor units, 378, 379 fast fatigue-resistant (FR) motor units, 378, 379 fastigial nucleus, 436, 441 fatal familial insomnia, 661 fatigability, of motor units, 378 Fatt, Paul, 102 fear, 699, 702–703 feedback mechanisms, 401 feedforward mechanisms, 400, 401 females cognitive function, 728–729 phenotypic sex, 714, 714–715 fentanyl, 155 feral children, 560 Index I-5 I-6 Index α-fetoprotein, 717 fibroblast growth factor (FGF) family, 505, 508, 523 fibroblast growth factor (FGF) receptor, 507 fibronectin, 531 Field, Pauline, 720 fight or flight, 471 filopodia, 528, 529 first-order neurons, 201 first pain, 210, 211 fish, Mauthner cells, 332–333 Fisher, C. Miller, 767 flexion reflex, 389, 389 flocculus, 435, 436 floorplate, 503, 503 Florey, Ernst, 143 fluorescent dyes, 10–11 fluoxetine (Prozac®), 148 fMRI. see functional magnetic resonance imaging folia, location, 436 foliate papillae, 358, 359 folic acid deficiency, 509 foramen of Monro, 770, 771 force, muscle, 379–380 forebrain, 18–20, 19, 510, 608 Forger, Nancy, 721 forgetting, 738–741, 740 formants, 640–641 fornix, 694, 772 Fourier transform, 283 fourth ventricle CNS function, 18 formation, 511 location, 436, 759, 760, 770 fovea, 244, 245, 260 foveation, 453 foveola, 244 fragile-X syndrome, 515 free nerve endings, 189, 190, 193 free sensory receptors, 189 Freeman, Walter, 625 frequencies, echolocation, 309 frequency, sound, 283 Freud, Sigmund, 673 Frisch, Karl von, 624 Fritsch, G. Theodor, 405 frogs, 538 frontal cortex, 630–635, 631, 747 frontal eye field (Brodmann’s area 8), 460, 464, 465 frontal leukotomy, 625 frontal lobes, 18, 19, 216, 419, 623–626 frontal lobotomy, 625 frontal (coronal) sections, 17, 17 fruit flies. see Drosophila melanogaster functional magnetic resonance imaging (fMRI), 25–27, 26, 27 language function mapping, 649–654 odor perception and, 341 sleep–wake cycles, 676 visual areas, 279, 280 fungiform papillae, 358, 359 G-protein-coupled receptors (GPCRs), 124–125. see also metabotropic receptors activation, 150, 361, 362 description, 169, 170 effect of serotonin on, 579 effector pathways, 172 light perception and, 252 nociception and, 221 taste perception and, 362–363, 362, 364 G-proteins, 124–125 activation, 125, 167 binding, 139 molecular targets, 170–171 olfactory-specific, 345 types of, 171 GABA epilepsy therapy and, 601 functional features, 131, 143–147 inhibitory response, 146 metabolism, 144 photoreception and, 255, 257 postsynaptic potentials and, 122 receptor types, 146 structure, 130, 146 subunits, 138 varieties of, 139 GABA transaminase, 143 Gage, Phineas, 624 gait, cerebellar lesions and, 449 Gajdusek, Carlton, 444–445 Galton, Francis, 634 γ bias, 383 γ efferent system, 414 γ motor neurons, 200, 200, 375–376, 383, 384 ganglia, PNS function, 15 ganglion cells, 3, 234, 259–263, 261, 538, 548 circadian rhythm sensors, 663, 664 on- and off-center, 249–254, 255, 256 ganglionic eminences, 510 gap junctions, 94, 95 GAPs (GTPase-activating pro-teins), 171 Gardener, Howard, 644 Gaskell, Walter, 469, 477 gastrulation, 501–503 gate theory of pain, 226 gating spring model, 320 gaze, 328–329, 425, 459 Gazzaniga, Michael, 647 gender. see also females; males; sexual dimorphism definition, 712 odor perception and, 341–342, 342 gender identity, 724–725 gene expression, 506, 506–507, 512 generalized epilepsy with febrile seizures (GEFS), 85 generator potentials, 192 genes cloning, 666 components, 1 ion channel diversity and, 73–74 transcription, 579 genetic analysis, 450–451 geniculate ganglion, 514 genitalia, 713 genomes, 2 germ layers, 501 germline cells, 714 Geschwind, Norman, 646, 648 ghrelin gene, 490 giraffes, 661 glands, emotional arousal and, 687 glaucoma, 230 glia. see neuroglia glial cells, 533 glial processes, 8 globus pallidus basal ganglia pathway, 418, 422, 422 efferent cells, 423 external segment, 427 Huntington’s disease and, 431 internal division of, 422 location, 772 glomeruli, 351, 354 glossopharyngeal nerve (cranial nerve IX) autonomic regulation, 492 characterization, 756–758 location, 482, 756 rhombomeres and, 514 taste and, 355, 359 glottal stop, 640 glucagon release, 471 glucocorticoids, 523 glutamate effector pathways, 172 functional features, 131, 137–139, 141, 143–145 long-term potentiation and, 589 photoreceptors, 255 silent synapses and, 594–595 structure, 130 synthesis, 137, 141 glutamate-glutamine cycle, 139 glutamate receptors, 74, 76, 121–122, 139, 252 glutamic acid decarboxylase (GAD), 143 glutaminase, 137 glycine, 130, 131, 138, 143–147, 144 glycogen, 660 Goldgaber, D., 750 Goldman equation, 39–40 Goldmann, Edwin, 767 Golgi, Camillo, 3–4 Golgi apparatus, 5 Golgi cells, 442, 443 Golgi technique, 3 Golgi tendon organs characteristics, 192 innervation, 201 negative feedback, 388, 388 reflex regulation, 384–385, 385 Gorski, Roger, 720, 724–725 gracile nuclei, 191, 200, 201 gracile tract, 200, 201 grafts, neural, 604–607 grammar, 634–644, 638 granule cell layer, 606 granule cells, 441, 442 gray matter, 15, 750 Graybiel, Ann, 419 Greig cephalopolysyndactylyl syndrome, 513 growth, after injury, 602 growth cones, 527–528, 533, 606 semaphorins and, 537 structure, 529 growth hormone, 660 GTP-binding proteins. see G-pro-teins GTPase-activating proteins (GAPs), 171 guanylyl cyclase, 159, 171 Gurdon, John, 75 gustatory nucleus, 356 gustducin, 361 gut, 471, 479. see also intestinal tract gyri, 18, 19, 204, 309, 606, 694 habituation, 577 Hagoun, H., 398 hair, standing on end, 471 hair cells adaptation, 320, 320–321 anatomy, 296 bending, 295 bundles, 296, 318–319, 324, 325 depolarization, 321 environmental insults, 290 function, 285, 293–294, 296 hearing loss and, 285 location, 292 polarization, 317, 319 signal transduction, 294–300, 297 transduction, 294–300 tuning, 320, 320–321 vestibular, 316–317, 320–321 hairy (h) gene, 512 Hall, Jeffrey, 666 haloperidol, 148 Hamburger, Victor, 549 handedness, 650–651 Hanig, Deiter, 357 haptics, 201 Harlow, Harry, 558 Harris, Bill, 581 Harrison, Ross G., 527 Hauser, Marc, 643 hawk moths (Manduca sexta), 344 head angular acceleration, 397 rotations, 324 sense of position, 315, 318, 322 visceral motor control, 474–475 hearing, 559 hearing loss acquired, 285 conductive, 289, 290 monaural, 290 sensorineural, 289, 290–291 heart autonomic regulation, 491–493, 492 pacemaker, 493 pain referral patterns, 215 parasympathetic regulation of, 477 visceral motor control, 474–475 visceral nervous system and, 471 Hebb, D.O., 569 Hebbs postulate, 569–571, 570 helicotrema, 291 hemiballismus, 428, 431 hemispheres, differences, 648–649 Henneman, Elwood, 379 HERG channels, 77 heroin addiction, 135 Hess, Walter, 674, 689 heteronomous hemianopsia, 268 heterosexuality, 726 heterotrimeric G-proteins, 170 Heuser, John, 104, 105 Hikosaka, Okihide, 423 hindbrain formation, 510 hippocampus, 694 declarative memory and, 742–743, 746–748, 747 dentate gyrus, 606 formation, 510 location, 19, 20, 772 long-term potentiation, 584–587 LTD mechanisms, 593 memory formation and, 741 rodent, 584 spatial learning and, 744–746, 745 His, Wilhelm, 521 histamine-containing neurons in the tuberomammillary nucleus, 676, 677, 678 histamines, 679 biosynthetic pathway, 147 brain distribution, 151 functional features, 131, 151 structure, 130 synthesis, 152 histidine, 152 Hitzig, Eduard, 405 Hobson, Allan, 674 Hodgkin, Alan, 41, 43, 49–54 Hofman, Michel, 726 holoprosencephaly, 509 homeobox genes. see homeotic genes homeostasis, sleep and, 661 homeotic genes, 513 homonymous hemianopsia, 267 homonymous quadrantanopsia, 268 homosexuality, 724–725, 726 homunculus, 205 horizontal cells, retinal, 234, 236, 255, 256, 257 horizontal eye movements, 460 horizontal gaze center, 459 horizontal (transverse) section, 16–17, 17 hormone-responsive elements, 719 hormones, 341, 715–718, 729. see also specific hormones Horner’s syndrome, 488, 488 horseradish peroxidase (HRP), 105, 106, 106 Hox genes, 506, 512, 513, 514–515 Hubel, David, 209, 269, 562, 563 Hudspeth, A.J., 294 human T lymphotropic virus-1, 66 humans amblyopia, 568–569 audible spectrum, 284 brain size, 634 ear sensitivity, 284 eye development, 234 genome size, 2, 2 language development, 559–562 olfactory perception, 339–341 ororant receptors, 347 somatotropic map, 205 sound representation in brain, 310–311 taste perception, 356–358 taste system, 355, 356–361 vision deprivation studies, 567–569 visual areas, 280 Huntingtin protein, 426 Huntington, George, 426 Huntington’s disease, 423, 426, 428, 428, 430, 431, 504 Huxley, Andrew, 49–54 hydrocephalus, 515, 770 X-linked, 534 γ-hydroxybutyrate, 143–144 5-hydroxytryptamine. see sero-tonin (5-HT) 5-hydroxytryptophan, 152 hyperacusis, 289 hyperalgesia, 220 hypercretin, 678 hyperkinetic disorders, 430 hyperopia, 232, 232 hyperpolarization, 34, 55, 237, 298–299 hyperpolarized cation channels (HCNs), 361 hypersomnia, 682 hypertonia, 414 hypoglossal nerve (cranial nerve XII), 514, 756, 756–758 hypoglossal nucleus, 759, 760 hypokinetic disorders, 430 hypothalamic sulcus, 484 hypothalamus central autonomic network and, 486–487 emotional behaviors and, 689 formation, 510 function, 20 location, 19, 20, 261 organization, 723 pain perception and, 216 sections, 484, 485 sexual behaviors and, 496–497, 724 suprachiasmatic nucleus, 263 visceral motor control, 484–486 hypotonia, 414 ibotenic acid, 137 ibuprofen, 221 imaging, brain, 24–27, 25 imidazoleamine, 130 immediate early genes, 180, 181 immediate memory, 734 impedance, definition, 289 imprinting, critical periods, 557–559 IN-1 antibody, 606 inactivation, 53, 73 incus, 288, 289 Inderol® (propanolol), 150 indirect projections, 401 indoleamine, 130 inductive signals, 502, 508, 509 inferior, positional definition, 16, 17 inferior cerebellar peduncles, 436, 438, 755, 759 inferior colliculus, 286, 304, 307–308, 755, 759 inferior divisions, 265 inferior oblique muscles, 230 inferior olivary nucleus, 760 inferior olive, 437, 438, 758 inferior parietal lobe, 620 inferior rectus muscles, 230 inferior salivatory nuclei, 477 inflammation, 220 information storage, 736–738 infundibular stalk, 484 inhibitory postsynaptic poten-tials (IPSPs), 121–123, 124 innate behaviors, 557–559 inner ears, 288, 289–294, 299. see also ears inner hair cells, 300–301. see also hair cells inositol trisphosphate (IP3), 173, 175, 362 dendritic spines and, 591 receptors, 174 insects, 350, 350 insomnia, 661, 681–682 instinctual behaviors, 557 insula, 216, 217 insulin release, 471 integrins, 168, 529, 531 intelligence, brain size and, 634–635 intention tremors, 449 interhemispheric connections, 616 intermediate relay ganglia, 422 intermediolateral column, 473 internal arcuate tract, 200 internal capsule, 436, 772 internal carotid arteries, 763, 765 interneurons axon length, 7 eye movements and, 460 function, 12 generation in adults, 605 intracellular recordings, 13, 14 serotonin release, 578 interposed nuclei, 436, 441 Interpretation of Dreams, The, 673 intersexuality, 715 interstitial nuclei of the anterior hypothalamus (INAH), 724–725 interventricular foramen, 770 intestinal tract, 474–475, 479–480. see also gut intorsion, definition, 230 intracellular receptors, 169, 170 intracellular recordings, 13, 13 intracellular signaling, 166, 172–175, 173 intracortical microstimulation, 407 intrafusal muscle fibers, 200, 200 introns, location, 1 invertebrates, 575–581 IP3. see inositol triphosphate ion channels ACh-activated, 116–121 action potentials and, 69–73 cyclic nucleotide-gated, 76 diseases related to, 84–85 diversity, 73–74 effect of tetraethylammonium ions, 51, 52 effect of tetrodotoxin, 51, 52 G-protein activation of, 171 heat-activated, 78–79 inactivation, 73 ion gradients and, 36, 36–37 ligand-gated, 76, 78, 124–125, 125, 169 (see also ionotropic receptors) mechanically-gated, 381 molecular structure, 79–85 pores, 81 properties, 69–70 refractory period, 61–63 selectivity filters, 81, 119 stretch-activated, 78–79 taste receptor function and, 360–361 topology, 79 toxins, 82 voltage-gated, 73, 76, 76–78, 77 voltage-sensitive, 71 Xenopus oocytes, 75 ion exchangers, 86–87 ionic currents, 49–52 ionotropic receptors, 124–125. ipratropium, 135 iris, characterization, 229 ischemia, 764 isoretinoin (13-cis-retinoic acid), 506 Ito, Masao, 595 Jackson, John Hughlings, 405 James, William, 688 Johnson, Samuel, 645, 645 joint receptors, 192 Joro spider, 137 jorotoxin, 137 jugular ganglia, 514 Julesz, Bela, 272 Index I-7 I-8 Index juvenile myoclonic epilepsy, 600 K-cell pathway, 278 Kaas, Jon, 599 kainate, 137 kainate receptors, 139 function, 142 light perception and, 252 structure, 142 Kalman’s syndrome, 534 Kandel, Eric, 575 Karnovsky, Morris, 767 Katz, Bernard, 41, 43, 102, 107 Keynes, Richard, 87, 514 Kimura, Doreen, 728 kindling, 600 kinocilia, 296, 316–317, 319, 324–325 Kleitman, Nathaniel, 665 Klinefelter’s syndrome, 713 Klüver, Heinrich, 695, 698 Klüver-Bucy syndrome, 695, 697 “knee jerk” reflex, 11–14, 12 koniocellular pathway, 278 Konopka, Ron, 666 Korach, Ken, 715 Korsakoff’s syndrome, 744 Kravitz, Edward, 143 Krumlauf, R., 514 krüpple (kr) gene, 512 krx20 gene, 514 Kuffler, Stephen, 23, 249, 253, 269 kuru disease, 444 Kuypers, Hans, 401 KV1 channels, 77 KV2.1 channels, 77 L1 CAM, 534 labeled line coding auditory, 301 taste system, 362–363, 364 labyrinth, vestibular, 315–316, 316 lacrimal glands, 474–475 lactation, 729, 730, 731 Lambert-Eaton myasthenic syn-drome (LEMS), 107 lamellapodia, 528 β2-laminin, 543 laminins, 531 lampreys, 386–387, 387 Land, Edwin, 247 Land Mondrians, 247 Langley, John N., 114, 469, 470, 477, 540 language animal use of, 642–643 association cortex lesions and, 622 brain areas, 638 context and, 645 critical periods, 559–562 handedness and, 650–651 lateralization, 646–648 learning of, 562 localization, 637–638 right hemisphere and, 654–655 savant syndrome and, 739 sign language, 655–656 large dense-core vesicles, 100, 111 larynx, 640, 640–641 late outward currents, 51 lateral, definition, 16 lateral corticospinal tract, 405 lateral fissure, 19, 511 lateral geniculate nucleus, 261, 263, 270, 275, 568 lateral horn, spinal cord, 473 lateral olfactory tract, 353 lateral premotor cortex, 374, 410–412 lateral preoptic nuclei, 484, 485 lateral rectus muscles, 230 lateral superior olive (LSO), 306, 306–307 lateral tegmental system, 150 lateral ventricles, 18, 485, 770, 772 lateralization, 637–638, 646–648 α-latritoxin, 115 Laurent, Gilles, 350 leaner (tg1aI) mice, 450, 450 learning definition, 733 genetics of, 581 language, 559–562, 562 nondeclarative, 748–749 spatial, 744–746, 745 LeDoux, Joseph, 699 leeches, 386, 386–387 left-handedness, 650–651 Leiurus quinquestriatus (scorpion), 82 lens, eye, 231 lenticulostriate arteries, 765 leptins, effect of, 490 leukocyte inducing factor, 523 LeVay, Simon, 725, 727 Levi-Montalcini, Rita, 549 Lewis, E.B., 513 Liberman, Alvin, 641 Librium® (chlordiazepoxide), 148 ligand-gated ion channels, 124–125, 138 light adaptation, 240, 253–256 light intensity, perception of, 250–251 Lima, Almeida, 625 limbic lobe, 694 limbic system, 692, 693–695, 695, 697 Lincoln, Abraham, 704 Lindstrom, Jon, 140 lips, speech and, 640, 640 lithium chloride (LiCl), taste, 359 Llinás, Rodolfo, 107 lobes locations, 19 nomenclature, 18 lobsters, 390, 390–391 local circuit neurons, 11, 373 locomotion central pattern generators and, 392 lampreys, 386–387, 387 leech, 386, 386–387 spinal cord circuitry and, 389–391 locus coeruleus, 150, 225, 398, 676, 677 Loewi, Otto, 96, 98, 98 Lomo, Terje, 584 long-term depression (LTD), 182–184, 583, 592–599, 596 long-term memory, 736, 746–748, 749 long-term potentiation (LTP), 583, 584–587, 701 AMPA receptors, 592, 592 function, 589 gene expression changes and, 597–599 long lasting changes, 598 molecular mechanisms, 587–592 properties of, 586–587, 587 Schaffer collateral-CA1 syn-apses, 585, 586 longitudinal sections, 16, 18 Lorenz, Konrad, 558, 558, 735 Lou Gehrig’s disease, 393 loudness, 283 low-threshold receptors, 195, 200, 201 lower extremities, 474–475 lower motor neuron syndrome, 391–393, 413 lower motor neurons description, 373 motor control, 373–395 spinal cord, 376, 377 sympathetic ganglia, 476 visceral nervous system, 470 Lucas, D.R., 145 lumbar enlargement, 17 lumbar nerves, 17 luminance, 242, 249–254, 255, 256, 263 Lumsden, A., 514 lungs, motor control, 474–475 lurcher (lr) mice, 450, 450 Luria, A.R., 739–741 lysophosphatidylinositol, 158 lysophospholipase C, 158 M ganglion cells, 275, 277–278 macaques, 634 macroscopic currents, 71, 117 macula lutea, 260 maculae, saccular, 319 maculae, utricular, 318, 318, 319, 319 macular degeneration, 243 macular sparing, 268 magnesium ions, 141, 587–588, 588 magnetic resonance imaging (MRI), 25–27, 25, 26, 27, 66, 311. see also functional mag-netic resonance imaging magnocellular layers, 275 magnocellular streams, 275, 276 Magoun, Horace, 669, 674 males cognitive function, 728–729 phenotypic sex, 714, 714–715 sexual function, 497 malleus, 288, 289 mammals audible spectrum, 284 neurons, 41, 582–583 olfactory bulbs, 352 ororant receptors, 347 mammillary bodies, 484, 485, 694, 758, 772 mandibular branches, 203 Manduca sexta (hawk moth), 344, 344 manic depression, 704 mapping, language functions, 649–654 marijuana, 161 Mariotte, Edmé, 262 marmosets, 311 MASA, 534 Mauthner cells, 332–333, 333 maxillary nerves, 203 MCR4 genes, 490 mechanoreceptors, 189, 193–199, 491 mechanosensory discrimination, 193–197 mechanosensory neurons, 577 mechanosensory pathways, 201 mechanosensory system, 201–203 medial, definition, 16 medial dorsal nuclei, 616 medial gastrocnemius muscles, 379, 380 medial geniculate complex (MGC), 304, 309 medial geniculate nucleus, 699 medial leminiscus, 193, 200, 201, 760 medial longitudinal fasciculus, 329, 460 medial nucleus of the trapezoid body (MNTB), 306, 306–307 medial prefrontal cortex, 694 medial premotor cortex, 374, 412 medial preoptic nuclei, 484, 485 medial rectus muscles, 230 medial superior olive (MSO), 305, 305 medium spiny neurons, 418, 420, 420–421, 423 medulla CNS function, 18 cranial nerve nuclei, 758 epinephrine localization, 150 formation, 510 location, 17, 758, 759 mechanosensory pathway, 203 pain perception, 217 reticular formation neurons in, 398 somatic sensory system and, 193 transverse section, 760 medullary arteries, 763, 764 medullary pyramids, 405, 758, 760 Meissner’s corpuscles, 189, 190, 193, 194 Meissner’s plexus, 480 melanocortin receptor 4 (MCR-4), 490 α-melanocyte-secreting hormone (α-MSH), 490 melanopsin, 263, 663 melatonin (N-acetyl-5-methoxytryptamine), 664, 665 Melzack, Ronald, 226 membrane conductance, 52–54, 53 membrane potentials creation of, 37–39 current amplitude and, 50, 50 effect of toxins, 82 end plate currents and, 118 feedback cycles, 56, 56, 57 intracellular recordings, 13 ion fluxes and, 39 Na+/K+ pumps and, 89 nerve cell, 32–35 permeabilities and, 40 recording, 34 membranes leakiness, 56 passive properties, 60–61 permeability, 34, 35 voltage-dependent permeabil-ity, 47–67 memory aging and, 749–752, 752 Alzheimer’s disease and, 750–751 definition, 733 fallibility, 736 forgetting and, 738–741 formation, 741–746 genetics of, 581 practice and, 737 qualitative categories, 733–734, 734 retention and, 737 temporal categories, 734, 734–736 meninges, 763–773, 768, 769 meperidine, 155 Merkel’s disks, 193, 195, 195 Merzenich, Michael, 599, 729 mescaline, 698 mesencephalic nucleus, 3 mesencephalon, 510, 511 mesoderm, 501, 502 mesopic vision, 241 metabotropic receptors, 124–125, 125, 139. see also G-protein-coupled receptors metencephalon, 510, 511 methadone, 155 methionine enkephalin, 130 methylphenidate (Ritalin™), 684 methylprednisolone, 607 Meyer’s loop, 268 mice, 2, 410, 490, 490 microelectrodes, 23, 32, 627 microglial cells, 8, 9 microscopic currents, 71 micturition, 495 mid-pons, 203, 217 midbrain anatomy, 755 basal ganglia pathway, 418 CNS function, 18 cranial nerve nuclei, 758 formation, 510 location, 17, 436, 758, 759 mechanosensory pathway, 203 periaqueductal gray area, 216 somatic sensory system and, 193 transverse section, 760 vasopressin in, 717 middle cerebellar peduncles cerebellar pathways and, 438 location, 436, 437, 755, 758, 759, 760 middle cerebral arteries, 763, 765 middle cranial fossa, 769 middle ears, 288, 289. see also ears middle pons, 760 middle temporal area (MT), 278–280 midget ganglia, 242, 244 midline myelotomy, 218 midsagittal sections, 16, 17 migraine headaches, 84 migration neuronal, 520–525 radial glia, 522 Miledi, Ricardo, 75, 107 Milner, Brenda, 632, 742 miniature end plate potentials (MEPPs), 102, 103, 104, 140 miosis, 488 mitochondria, 5 mitogen-activated protein kinases (MAPKs), 177–178, 180 mitral cells, 351 modafanil (Provigil™), 684 molecular layer, 441, 442 molecular signaling, 165–186, 166 Money, John, 716 Moniz, Egas, 625 monkeys, 401, 558, 567 monoamine oxidase (MAO), 149 monoamine oxidase (MAO) inhibitors, 148 monomeric G-proteins, 170 monosodium glutamate, 357 monosynaptic reflex arcs, 381 morphine, 155 Morrison, Robert, 668 Moruzzi, Giuseppe, 398, 669, 674 mossy fibers, 441, 442 mother–child interactions, 341 motor aphasia, 640 motor behaviors, 688 motor control, 373–395 motor cortex, 394, 396, 617, 617 motor mutations, in mice, 450–451 motor neurons acetylcholine release, 104 differentiation, 508 function, 12–13 intracellular recordings, 13 limb bud removal, 544 perineal muscles, 722 pool, 375, 380 stem cell-derived, 504 α motor neurons, 393 motor system function, 14 motor units, 377, 377–379, 378, 380, 381 Mountcastle, Vernon, 23, 209 movement basal ganglia and, 417–424 cerebellar lesions and, 448–449 cerebellar modulation of, 435–452 coordination, 445–448 fine control, 414, 415 limbs, 389, 391 neural control, 373–375, 374 selection process, 421 sensory feedback and, 384–388 MRI (magnetic resonance imag-ing), 25–27, 25, 26, 27, 66, 311. see also functional mag-netic resonance imaging Mueller, Johannes, 640 Müllerian ducts, 714, 715 Müllerian-inhibiting syndrome, 714 multiple sclerosis (MS), 63, 66 muscarine, 136, 171 muscarinic acetylcholine recep-tors (mAChR), 135, 139, 491 muscarinic cholinergic receptors, 489 muscimol, 137, 431, 431 muscle spindles anatomy, 200 characteristics, 192 proprioception, 200–201 reflex regulation, 385 stretch reflexes, 382 stretch reflexes and, 383 muscles cardiac, 493 force generation, 407 motor neuron pool, 375 regulation of force, 379–380 stretch reflexes, 381–383 tension, 380 tone, 328–329, 383, 414, 448–449 topographical organization, 406 upper motor neuron syn-drome, 412–414 mushroom bodies (MBs), 350 music, 286–287, 294 mutagenesis, 79 mutations, motor, 450, 450–451 myasthenia gravis, 140–141 myasthenic syndromes, 107 myelencephalon, 510, 511 myelin, 9, 63 myelin sheaths, 5, 9 myelinated stria, 266 myelination, 63–65, 66 myenteric plexus, 479, 480 myopia, 232, 232–233 myotactic reflex, 14. see also stretch reflexes myotatic spinal reflexes, 11–14, 12, 14 myotonia, 84 Na+/Ca2+ exchangers, 174 Na+/H+ exchangers, 87 Na+/K+ ATPase pumps, 86–87 Na+/K+ pumps, 87–89, 88, 89 naloxone, 224 narcolepsy, 681, 683–684 nasal cavity, 338, 640 nasal division, 264–265 nasal mucosa, 343 nasal pharynx, 640 Nathans, Jeremy, 248 navigation, vestibular, 318 near cells, 271 neck, 394, 474–475 negative feedback loops, 382, 388, 388 Neher, Erwin, 71, 107 neocortex amygdala and, 701, 703 anatomy, 614, 615 canonical circuitry, 616 lamination, 617, 617 major connections, 614 motor cortex, 617 visual cortex, 617 neostigmine, 140 Nernst equation, 36, 37 nerve cells. see neurons nerve grafts, 606–607 nerve growth factor (NGF), 182, 182, 220–221, 523, 537 identification, 549 neurite growth, 553 neurite outgrowth and, 550, 550, 551 trophic interactions, 547, 549–553 nervous (nr) mice, 450, 450 nervous systems cellular components, 2–4 cellular diversity, 9–11, 10 composition, 14–16 functional analysis, 23–24 initial formation, 501–503 neural induction, 503–510 upright posture and, 16–17 netrin/slit family proteins, 532 netrins, 534–535, 535, 536 netrins, function, 535 neural cell adhesion molecules (NCAMs), 168 neural circuits, 11–13 neural coding, taste system, 362–363, 364 neural crest, 502, 503, 503, 523, 523 neural groove, 503 neural injury, recovery, 602–605 neural plate, 502, 502 neural plexus, 470 neural precursor cells, 502 neural stem cells, 502, 607–608 neural tube, 502, 502, 509, 509 neurexins, 115 neurites, 549, 550, 553 neuroanatomy, terminology, 16–18 neuroblasts, 503, 517, 520 neuroectoderm, 501 neuroethology, 24 neurofibrillary tangles, 750, 750 neurogenesis, 517 in adult brain, 605–609, 608 Index I-9 I-10 Index neuroglia, 4, 8, 8–9, 10–11, 516–518 neurokinin A, 155 neuromeres, 510, 514–515 neuromuscular junctions, 102, 542, 542–543, 546 neuromuscular synapses, 140–141 “neuron doctrine,” 3 neuronal signal transduction, 181–184 neurons afferent, 12 anticipatory discharges, 421 birthdating, 517 communication theories, 3–4 cytoskeletal elements, 6 dendrites, 548, 548 diversity, 518–520 effect of estradiol, 719 efferent, 12 electrical signaling, 32–47 function, 4–7 generation during gestation, 519 generation in adult brain, 605–608 initial differentiation, 516–518 ionic currents, 47–49 long-distance migration, 524–525 loss in AD, 750 markers, 10–11 membrane leakiness, 56, 59 migration, 520–525 molecular signaling, 165–186 PNS function, 15 population sizes, 544, 544 receptive fields, 23 structure, 4–5 thalamocortical, 679, 680 neuropathic pain, 223 neuropeptides composition, 129 functional features, 131 lengths, 155 neuropeptide γ, 155 neuropeptide K, 155 release, 98, 111 synthesis, 100 neuropilin, 536 neuropils, 11, 351 neuropsychological testing, 632–633 α-neurotoxin, 136 neurotoxins, 136–137 neurotransmitter receptors, 8, 99, 99, 114–116 neurotransmitters calcium in secretion of, 107–110 calcium ion channels and, 76 categories, 129 criteria defining, 99 functional features, 131 ligand-gated channels and, 78 mechanisms of transmission, 110–114, 113 metabolism, 101 packaging, 100 presynaptic proteins and release, 112 properties of, 96–102 quantal release, 102–103, 104 release, 103–105, 124 storage, 8 synaptic vesicles and, 96, 105 toxins and, 115 visceral nervous system, 471 neurotrophic factors, 543, 603 neurotrophins, 543–544, 550, 551, 552, 553–554, 555 neurulation, 501–503, 502 Newhouse, J.P., 145 nicotine, 136 Nicotinia tabacum, 136 nicotinic acetylcholine receptor (nAChR), 132–135, 133, 138, 491 night blindness, 84, 85, 239 Nissl staining, 10–11, 617 nitric oxide (NO), 131, 159, 159–160 nitric oxide synthase (NOS), 159, 489 NMDA (N-methyl-D-aspartate) receptors, 139, 141, 587–588, 594–595 function, 142, 588 structure, 142 subunits, 138 NMRA receptors, 141 Nobel Prizes, 513 Camillo Golgi, 4 Carlton Gajdusek, 444–445 Charles Sherrington, 4 Stanley Prusiner, 444–445 Walter Hess, 689 nociceptors, 189, 209–211, 210 nodes of Ranvier, 5, 63 nodose ganglia, 514 nodulus, 435, 436 noggin, 508 Nogo protein, 604, 606 NoGos, 536 non-rapid eye movement (non-REM) sleep, 667 nondeclarative memory, 733–734, 734, 748–749, 749 nonsteroidal anti-inflammatory drugs (NSAIDs), 221 noradrenergic neurons of the locus coeruleus, 677, 678 noradrenergic receptors, 487 norepinephrine (noradrenaline) biosynthetic pathway, 147, 147 brain distribution, 150 effector pathways, 172 function, 149 release, 471, 487, 493 structure, 130 varieties of, 139 norepinephrine transporter (NET), 150 notch family, 517 notochord, 501, 502, 503 Nottebohm, Fernando, 605 NSAIDS, 221 NSF (NEM-sensitive fusion pro-tein), 111 NSTX-3, 137 nuclear bag fibers, 200, 200 nuclear chain fibers, 200, 200 nuclear receptors, 181 nuclear signaling, 178–181 nuclei, 5, 15. see also specific nuclei nuclei of the lateral leminiscus, 307 nucleus ambiguus, 398–399, 477, 759, 760 nucleus cuneatus, 760 nucleus gracilis, 760 nucleus of the lateral leminiscus, 304 nucleus of the solitary tract, 480, 481 autonomic regulation, 492 gustatory nucleus, 356 location, 482, 759, 760 Nusslein-Volhard, C., 513 nystagmus, 326, 326, 457 ob gene, 490 obesity, genetic control, 490 obicularis oculi, 690 object recognition, 630 oblique muscles, 230 occipital lobes, 18, 19, 270 ocular apraxia, 621 ocular dominance, 274, 562–568, 571, 571 ocular dominance columns, 271, 275, 562–563, 563 oculomotor nerve (cranial nerve III), 230, 260, 329, 756, 756–760 odorants classification, 339 definition, 337 gender-specific responses, 342 perception thresholds, 340 responses to, 341–342 signal transduction, 339 off-center photoreceptors, 249–254, 255, 256 Ohm’s law, 52 Ojemann, George, 652 olfaction, learning, 581 olfactor marker protein (OMP), 348 olfactory bulbs antibody labeling, 10–11 central projections, 353–354 formation, 510, 511 function, 20, 350–353 granule cell layer, 606 location, 20, 351 Nissl staining, 10–11 olfaction and, 338 organization, 352 olfactory cilia, 342 olfactory coding, 348–350, 350 olfactory epithelium, 337, 338, 342–345, 343 olfactory nerve (cranial nerve I), 338, 756, 756–758 olfactory receptor neurons, 342–345, 348, 349, 351 olfactory system, 337–342, 338, 344–346 oligodendrocytes, 8, 9, 606 oligodendroglial cells, 504 Olney, John, 145 on-center photoreceptors, 249–254, 255, 256 Onchocerca volvulus, 569 onchoceriasis (river blindness), 569 Onuf’s nucleus, 721 ophthalmic artery, 260 ophthalmic nerves, 203 opioids peptides, 155, 156 opiomelanocortin propeptides (POMCs), 490 opsins, 237 optic ataxia, 621 optic chiasm, 259–260, 484, 485, 530–531, 758, 772 optic cups, 510 optic disk, 259, 260 optic illusions, 250 optic nerve (cranial nerve II), 235–236, 259, 261, 756, 756–758 optic radiation, 260, 261, 267 optic tectum, 538 optic tract, 260, 261, 485, 758 optic vesicle, 234 511 optical imaging, 277 optokinetic nystagmus, 457 oral pharynx, 640 orbital prefrontal cortex, 694 orexin, 678 orexin-2 receptor gene (Orx2), 684 organ of Corti, 292 organophosphates, 132 orgasm, 496 orientation-selective neurons, 270 orthostatic hypotension, 493 oscillopsia (bouncing vision), 330 ossicles, function, 289 otic vesicle, 514 otoconia, 318, 318 otolith organs, 315, 317–319, 322, 322–324, 323, 397 otolithic membrane, 318, 322 ototoxicity, drugs, 285 outer hair cells, 300–301. see also hair cells oval windows, 288, 289, 292 overshoot phase, 45, 46 owl monkey, 208, 599, 602 Oxford English Dictionary, 645 oxygen, chemoreceptors, 491 oxyhemoglobin, 276 oxytocin, 485, 729 P ganglion cells, 275, 277–278 p75 receptor protein, 553, 554, 555 Pacinian corpuscles, 32, 33, 192, 194, 195 pain, 209–228 affective-motivational aspect, 216, 217 central pathways, 213–221, 214 control of perception, 224 descending systems, 225–227, 226 dorsal column pathway, 218 gate theory of, 226 modulation, 225–227 pathways, 21–22, 21 perception, 210–211, 211 phantom, 222–223 placebo effects, 224–225 referred, 215 sensitization to, 220–223 tissue damage and, 220 visceral, 218, 219 paleocortex, 617, 617 panacrine signaling, 165, 166 pancreas, motor control, 474–475 Papez, James, 693, 694 papillae, tongue, 358, 359 papilledema, 259 parabrachial nuclei, 225, 486 parahippocampal gyrus, 694 parallel fibers (PFs), 183–184, 441, 442 parallel pathways, 20–22, 21 paralysis, 84, 392 paramedialpontine reticular for-mation (PPRF), 676 paramedian arteries, 764 paramedian pontine reticular for-mation (PPRF), 459, 460–463, 464 paraplegia, 495 parasagittal sections, 16, 17 parasympathetic division, 16, 472, 475, 687 parasympathetic ganglia, 477, 478 paraventricular nucleus, 484, 485 paravertebral symphathetic chain neurons, 476 paresis, definition, 392 parietal cortex, 626–627, 628, 629 parietal lobes, 18, 19, 281, 729 parieto-occipital sulcus, 19, 266, 270 Parkinson’s disease, 147, 149, 428, 428–430, 430, 504 parotid glands, 474–475 pars reticulata, 418, 418, 422 parvocellular layers, 275 parvocellular streams, 275, 276 passive current flow, 56, 58, 60–61 patch clamp method, 70, 70–71, 72, 73 Patrick, Jim, 140 Pax3 genes, 515 Pax6 genes, 515 Pearlson, Godfrey, 729 Penfield, Wilder, 406, 407, 408, 652 penile erection, 496 peptide neurotransmitters, 101, 130, 153–156 PER proteins, 667 perception, retinal images, 456 periaqueductal gray area, 216 Pericak-Vance, Margaret, 751 perilymph, 291, 299, 299, 316 perineal muscles, 722 period (per) gene, 666 peripheral nerves, 607 peripheral nervous system (PNS), 14, 15, 16, 21, 545, 603, 604 peripheral sensitization, 220 peripheral taste system, 359–360 peristalsis, 474–475, 479 permeability effect of steroids, 719 membrane, 35–36, 40, 46 postsynaptic changes, 116–121 receptor potentials and, 192 voltage-dependent, 47–67 personality, frontal lobe and, 623–626 PET (positron emission tomogra-phy), 26–27, 652, 653, 654 Peterson, Andy, 451 Peterson, Steve, 654 petit mal epilepsy, 600 petrosal ganglion, 514 “phantom limbs,” 198, 222–223 phantom pain, 222–223 phase, sound, 283 phase locking, 301, 302 phasic receptors, 194 phenobarbital, 601 phenotypic sex, 712, 714–715 phenylethanolamine-N-methyl-transferase, 150 phenylthiocarbamide (PTC), 357–358 phenytoin (Dilantin®), 601 pheromones, 341, 344 β-philanthotoxin, 137 phonemes, 641 phones, 641 phosphatidylethanolamine, 158 phosphatidylinositol, 158 phosphodiesterases, 240 phospholipase C (PLC), 171, 182, 182, in taste system, 360–363, 364 photoentrainment, 663 photopic vision, 241 photopigments, 235 photoreceptors, 235, 239. see also cones; rods circadian rhythms and, 663, 664 on- and off-center, 249–254, 255, 256 phototransduction, 236–240 phylogenetic memory, 735 pia mater, 769 picrotoxin, 137, 146 piloerection, 474–475 pineal glands, 664 pinna, 287, 288, 288 pitch, sound, 283 place cells, 584 placebo effects, 224–225 planning, deficits in, 623–626 planning functions, 630–635 planum temporale, 648–649 plasma membranes, 60–61, 104 plasticity, 575–610, 602 platelet-derived growth factor, 504 PLCβ2 channel, 360–363, 364 plexins, 536 PNS. see peripheral nervous sys-tem points of fixation, 265 polymodal nociceptors, 210, 212 polyneuronal innervation, 545 pons CNS function, 18 cranial nerve nuclei, 758 formation, 510 location, 17, 755, 758, 759 transverse section, 760 pons–midbrain junction, 677 pontine flexure, 511 pontine-geniculo-occipital (PGO) waves, 676 pontine nuclei, 437, 437 pontine reticular formation, 676 pores, 81, 95 porpoises, 634 positron emission tomography (PET), 26–27, 652, 653, 654 post-tetanic potentiation (PTP), 582 postcentral gyrus, 19, 204 posterior, definition, 16, 17 posterior cerebral arteries, 763–764, 765 posterior chamber, 229–230 posterior circulation, 763 posterior communicating arter-ies, 763, 765 posterior funiculi, 200 posterior inferior cerebellar artery (PICA), 759, 764, 764, 765 posterior spinal arteries, 763 postganglionic axons, 476 postspike facilitation, 409 postsynaptic currents (PSCs), 121 postsynaptic elements, 94, 99 postsynaptic potentials (PSPs), 121–124, 123, 124 postsynaptic receptors, 124–125, 136–137 postsynaptic specialization, 176 postural control anticipatory maintenance, 400–401, 401 cerebellar lesions and, 448–449 motor control centers, 393, 397–402 vestibular system and, 328–329 potassium channels, 77 2-pore, 77 benign familial neonatal con-vulsions and, 85 calcium-activated, 76, 77, 78 closing, 487 effect of toxins, 82 episodic ataxia type 1 and, 85 gating, 83 hair cell transduction and, 297 hair cells and, 320–321 inwardly-rectifying, 77 muscarinic receptors and, 489 patch clamp studies, 72–73, 73 tetrodotoxin and, 51 topology, 79 voltage-gated, 74, 77 weaver (wv) gene and, 451 X-ray crystallography, 81 potassium ions, 43, 43–44, 51, 53 PP1, regulation, 178 PP2A. see calcineurin pre-prokephalin A, 154 pre-proopiomelanocortin, 154 pre-propeptides, 153, 154 precentral gyrus, 19 predation, 661, 735 prefrontal cortex, 729, 748–749 preganglionic neurons, 471, 473, 473, 474–475, 478, 487 premotor area, 402 premotor cortex, 408–412 preoccipital notch, 19 presbyacusis, 285 presbyopia, 233 presenilin genes, 750, 751 pressure, pathways, 22 presynaptic elements, 94 presynaptic neurons, 99 presynaptic proteins, 112 presynaptic terminals, 5, 7, 103–104, 107–109, 176, 593 pretectum, 260, 261 prevertebral ganglia, 476 primary auditory cortex (A1), 304, 309 primary motor cortex, 614, 638 functional organization, 405–408 location, 402, 402, 437 topographical organization, 406, 408 primary sensory areas, 614 primary sensory endings, 200 primary somatic sensory cortex (SI), 21, 201–203, 638 primary visual cortex, 260, 269 primary visual pathway, 260, 275–278 priming, memory, 736 primitive pit, 501 primitive streak, 501 principal nucleus, 203 principal trigeminal nucleus, 759, 760 prion diseases, 444–445 procedural memory, 733 progesterone, 717 promoter regions, 178 propanolol (Inderol®), 150 propeptides, 153 proprioception, 22, 199–201 proprioceptors, 199–201 prosencephalon, 510, 511 prosodic elements, 654 prosody, 638 prosopagnosia, 622 prostaglandins, 220–221 prostate gland, 215 protanopia, 248 protein kinases activation, 177 function, 169–170, 175, 175 PKA, 179, 579 PKC, 176, 177, 588, 589, 596, 598 Index I-11 I-12 Index protein phosphatases, 175, 175, 178 protein tyrosine kinases, 176–177 protons, 78 Provigil® (modafanil), 684 Prozac® (fluoxetine), 148 Prusiner, Stanley, 444–445 psychosurgery, 625 psychotic disorders, 341 PTC (phenylthiocarbamide), 357–358 ptosis, 488 pulvinar, 524, 616 pupils characterization, 229 light reflex, 260, 261, 261 visceral motor control, 471, 474–475 purines, 130, 138, 139 Purkinje cell degeneration (pcd) mice, 450, 450 Purkinje cells, 3 activity of, 240 calcium signaling, 31 cerebellar, 441–442 cerebellar pathways and, 442 long-term depression and, 182–184, 595, 596, 597 Nissl staining, 10–11 signal transduction, 184 putamen, 417, 418, 421, 436, 772 pyramidal cells, 3, 10–11, 23, 354, 402 pyramidal decussation, 396 pyramidal tract, 760 pyramids, location, 755 pyridoxyl phosphate, 143 pyriform cortex, 337, 338, 353–354, 617 quinine, 356, 364 Quinn, Chip, 581 quisqualate, 137 Quisqualis indica, 137 radial glia, 521, 522 radioisotopes, 564 RAGS protein, 539 Raichle, Marc, 654 Raisman, Geoffrey, 720 random dot stereograms, 272–273, 272–273 raphe nuclei, 151, 151, 398, 676, 677 rapid eye movement (REM) sleep, 659, 667 circuitry, 673 cortical regions during, 676 drigs and, 682 EEG recording, 665, 672 functions, 671–674 sleep apnea and, 683 rapidly adapting receptors, 194 ras, 170–171, 179 Ras/MAP kinase pathway, 507 Rasmussen’s encephalitis, 600 rats aversive somatic sensory stim-uli, 699 brain size, 634 estradiol-sensitive neurons, 718 imprinting, 558 sensorimotor cortex, 410 sleep deprivation, 662 reason, social behavior and, 707–708 receptive aphasia, 643 receptive fields antagonistic surrounds, 254, 256 center responses, 255 crickets, 195 dynamic aspects, 198–199 neuron, 23 on- and off-center photorecep-tors, 249–254, 255, 256 plasticity, 729 receptor density and, 198 retinal, 249, 251–253 somatic sensory neurons, 196–199 receptor potentials, 13, 32, 192 receptors categories, 168–170, 169 neurotransmitter, 99 somatic sensory, 191–195, 193 reciprocal innervation, 381 recognition deficits in, 622–623 facial, 629 object topography, 630 temporal cortex and, 627–630 rectus muscles, 230 red alga (Digenea simplex), 137 red nucleus, 393, 394, 441 5-α-reductase, 713 reeler (rl) mice, 450, 450, 451, 517 Reese, Tom, 104, 105, 767 referred pain, 215 reflexes areflexia, 392 orofacial, 398 simple circuit, 12 vestibular system and, 328–329 visceral motor, 491 refractive errors, 232–233 refractory periods, 61–63 regenerative properties, 56 Reisert, Ingrid, 717 Reissner’s membrane, 300 relay nuclei, 20–22, 21 remodeling, after injury, 602 REM sleep. see rapid eye move-ment sleep reserpine, 148 rest–activity cycles, 661 restiform body. see inferior cere-bellar peduncles resting potentials conduction and, 62 ionic basis, 41, 42–43 neuron type and, 32 permeabilities and, 40 squid giant neurons, 43 restless legs syndrome, 683 reticular activating system, 674 reticular formation anatomy, 398–399, 399 function, 393, 397–399 gaze centers, 459 hypothalamic targets in, 689 location, 396, 399, 400 pain perception, 216, 217, 225 projections, 618 spinal cord projections from, 394 visceral motor centers, 481 “reticular theory,” 3 reticulata cells, 423–424 retina amacrine cells, 3 bipolar cells, 3 center–surround circuits, 249–254, 255, 256 characterization, 229 function, 234–236 ganglion cells, 3, 259–263, 538 image formation on, 231–234 Nissl staining, 10–11 quadrants, 264–267 structure, 235 surface, 260 retinal circuits, 249–254, 255, 256 retinal ganglion cells, 261 regeneration of, 606–607, 607 retinal pigment epithelium, 234 retinitis pigmentosa (RP), 236, 239 retinogeniculostriate pathway, 260 retinohypothalamic pathway, 263 retinoic acid, 504, 505, 506–507, 508 retinoid receptors, 505 retinotopic maps, 539 retrograde amnesia, 741, 746 reversal potentials, 117, 119, 122 Rexed’s laminae, 192, 195, 200 rhodopsin, 170, 238, 240 rhombencephalon, 502, 510, 511 rhombomeres, 514, 514–515 ribosomes, 5 Riepe, Matthias, 728 right-handedness, 650–651 right parietal cortex, 621 rimonabant, 158 rising phase, 45, 46 Ritalin™ (methylphenidate), 684 river blindness (onchoceriasis), 569 RNA, 178, 179 messenger, 10 RNA polymerases, 178–179 Roberts, Eugene, 143 rods (photoreceptors), 238, 241, 244, 245 circadian rhythms and, 664 function, 240–245 hyperpolarization, 663, 664 retinal, 235 rodents, 347, 348, 712. see also mice; rats Rosbash, Michael, 666 Roses, Allen, 751 Rossell, Susan, 728 rostral, definition, 16, 17 rostral interstitial nucleus, 459, 676 round windows, 288, 290, 292 Ruffini’s corpuscles, 192, 195, 195 Ruggero, M., 294 ryanodine receptors, 174 saccades, 240, 241, 423 antisaccades, 465 basal ganglia in, 425 express, 465 functions, 457 metrics, 457 neural control, 458–466, 459 perception during, 453 saccules, 315, 316 sacral nerves, 17 sagittal sections, 16, 17 Sakmann, Bert, 71, 107 saliva, 474–475, 477 salivatory nuclei, 759 saltatory propagation, 63, 64 salty taste, 356–363 Salvensen, Guy, 751 Sarin gas, 132 savant syndrome, 739 saxitoxin, 82 scala media, 290–291, 292 scala tympani, 290–291, 299 scala vestibuli, 290–291, 292 Scarpa’s ganglion, 316, 328, 514 Schaffer collateral synapses, 585, 585, 586, 586, 592, 593, 594–595 Schiller, Peter, 251 schizophrenia, 148, 341, 433 Schwab, Martin, 605, 606 Schwann cells, 9, 15, 533 neural recovery and, 603, 604, 606 sclera, 229 SCN. see suprachiasmatic nucleus SCN genes, 76 scopolamine, 135, 137 scorpions, 82 scotoma. see blind spots scotomas, 267 scotopic vision, 241–242 scrapie, 444–445 sea slug (Aplysia californica), 575, 576, 577, 578 Searle, John, 675 second messengers intracellular signaling, 172–175, 173 ion channel interactions, 78 mechanisms, 197 nuclear signaling, 178–181 targets, 175–178 second-order neurons, 200 second pain, 210, 211 sections, axes of, 16, 17 seizures, 406, 600–601, 601 selectivity filters, 81, 81 semaphorins, 532, 536, 537 semicircular canals, 315 function, 324–328 functional organization, 325 location, 288, 316 sense of acceleration and, 325–328 sensory information from, 397 sensitization, 220–223, 576, 577, 578, 580 sensorineural hearing loss, 289, 290–291 sensory aphasia, 643 sensory association cortex, 748–749 sensory ganglion, 502 sensory integration, 453–467 sensory maps, 197, 197 sensory motor talents, 410 sensory neurons, 12, 13, 14 sensory receptors, 14 sensory systems, 14 sensory transduction, 192 septum pellucidum, 770 serine threonine kinases, 176, 178, 507 serotogenergic neurons of the raphe nuclei, 678 serotonin (5-HT), 679 biosynthetic pathway, 147 brain distribution, 151 functional features, 131, 151–152 release, 578 structure, 130 subunits, 138 synthesis, 152 varieties of, 139 serotonin transporter (SERT), 152 7-transmembrane receptors. see metabotropic receptors sevenless (sev) gene, 521 sex autonomic regulation, 496–497, 497 brain and, 711–732 definition of, 712–715 drive, 717 neurons and, 722 phenotypes, 714 sexual behaviors, 724 sex hormones actions, 718–719 neural circuitry and, 718–720 synthesis, 717 sexual dimorphism behaviors, 711–712 brain, 726 central nervous system, 720–728 hormonal influence on, 715–718 INAH, 725 odor perception and, 341–342 olfaction and, 344 sexually dimorphic nucleus (SDN), 720 Seyfarth, Robert, 643 sham rage, 689 Sherrington, Charles, 3–4, 373, 378, 406, 407, 408 short circumferential arteries, 764 short-term memory, 749 Sigmundson, K., 716 sign language, 655–656 signal amplification, 166, 167 signal transduction hair cells, 294–300, 320–321 intracellular, 166 mechanoelectrical, 294–300 neuronal, 181–184 olfactory system, 345–346 taste cells, 360–361, 361, 362 sildenafil (Viagra®), 496 silent synapses, 594–595 simple cells, 270 simultanagnosia, 621 sine waves, 284, 284 single-photon emission comput-erized tomography (SPECT), 26 single-unit electrophysiological recordings, 13, 23, 23 size principle, 379 skin, 191–194, 195, 204 sleep deprivation, 662 disorders, 681–684 drugs and, 682 duration, 660 need for, 659–662 neural circuits, 674, 674, 676–678, 677 physiological changes in, 671, 672 rhythm of, 663 species-related styles, 661 stages, 666–667 wakefulness and, 659–658 sleep apnea, 682–683, 683 sleep debt, 659 sleep spindles, 667, 680 sleep–wake cycles, 664–665, 676, 677, 678 slit, function, 535, 536 slow axonal transport, 100 slow (S) motor units, 378, 379 slow-wave sleep, 661, 667 slowly adapting receptors, 194 small clear-core vesicles, 100 small G-proteins, 170 small-molecule co-transmitters, 111 small-molecule neurotransmit-ters, 101, 129 SMAT multimers, 507 smiles, asymmetrical, 707 Smith, Neil, 739 smooth muscles, 687 smooth pursuit movements, 457, 458, 466 SNAPs (soluble NSF-attachment proteins), 111, 113 SNARES (SNAP receptors), 108, 111, 113, 115 social behaviors, 707–708 sodium (Na), salty taste and, 359 sodium/calcium exchangers, 174 sodium channels effect of toxins, 82 generalized epilepsy with febrile seizures and, 85 genes, 76 ion current measurement, 72 photoreceptors and, 237 taste receptor function and, 360–361 tetrodotoxin and, 51 topology, 79 voltage-gated, 74 sodium/hydrogen ion exchang-ers, 87 sodium ion (Na+) pumps, 86–87 sodium ions action potentials and, 44, 44–46, 49 conductances, 53 early inward currents and, 51 membrane permeability and, 47 sodium/potassium ion ATPase pumps, 86–87 sodium/potassium pumps, 87–90, 88, 89 soft palate, 640 soma, neuron, 5 somatic motor division, 15 somatic motor nuclei, 757 somatic sensory cortex, 21 characterization, 203–206 cortical areas, 599 higher-order representations, 206 during lactation, 730 location, 20, 193 rat, 10–11 somatic sensory receptors, 191–194, 192 somatic sensory stimuli, 699 somatic sensory system, 20–22, 21, 22, 191–210 neurons, 196–199 organization, 191 thalamus, 203 somatic stem cells, 504 somatostatin release, 212 somatotopic maps, 22, 204–206, 205, 206, 222–223, 439, 439 somatotopy, 21, 22 somites, 502 songbirds, 605, 711–712, 717, 735 sonic hedgehog (shh), 506, 508, 509 sound distortion, 294 localization, 303–307 music and, 286–287 physics of, 283–284 representation in brain, 310–311 signal transduction, 294–300 speed of, 641 sour taste, 356–363 space coding, 349 spastic paraplegia, X-linked, 534 spasticity, 414 spatial learning, 744–746, 745 speech, anatomy of, 640–645 Sperry, Roger, 537, 646, 647 spike-triggered averaging, 407, 409 spina bifida, 509 spinal accessory nerve (cranial nerve XI), 756, 756–758 spinal accessory nuclei, 757 spinal cord, 17 blood supply, 763–773, 764 brainstem projections to, 395 cerebellar pathways and, 438 CNS function, 14, 18 descending control of, 393–397 direct projections to, 401 dissociated sensory loss, 216 formation, 508–509, 511 intermediolateral column, 473 lateral horn, 473 lateral view, 17 locomotion and, 389–391 longitudinal axis, 17 lower motor neurons, 376, 377 lumbar segments, 495 mechanosensory pathway, 203 motor cortex projections to, 396 nociception, 213 pain perception, 217 preganglionic neurons, 473 sacral segments, 494 somatic sensory system and, 21, 193 stretch reflexes and, 381–383 thoracic, 473 transverse section, 760 ventral horn, 394, 394 spinal motor neurons, 722 spinal nucleus, 203 spinal nucleus of the bulbocaver-nosus, 721 spinal shock, 413 spinal trigeminal nucleus, 759, 760 spinal trigeminal tract, 216 spinocerebellar degeneration, 84 spinocerebellum, 436, 437 spinothalamic (anterolateral) pathway, 200 spinothalamic tract, 213, 216 spiral ganglia, 292, 514 split-brain patients, 646, 646–648 spongiform degeneration, 444–445 squid, 41, 42, 42, 43, 48, 49 Sry gene, 714 stages of sleep, 666, 667 staggerer (sg) mice, 450, 450 staining, 10–11 stapes, 288, 289 star-nosed moles, 410 Stargardt disease, 243 stellate cells, 442, 442–443 stem cell factor, 523 stem cells embryonic, 504 neural, 502, 607–608 potential, 504–505 somatic, 504 stereocilia anatomy, 296 function, 294, 299 hair cell function and, 316–317 hearing loss and, 285 location, 292 tip links, 297 Stern, Judith, 729 steroid hormones, 168 steroids, 146 steroids hormones, 717 steropsis, 271, 271 Index I-13 I-14 Index stimuli, quality of, 192, 194 stomach, 474–475 stomatogastric ganglion (STG), 390, 390–391 strabismus, 271, 568 stretch reflexes, 381–383, 382 stria terminalis, 727 stria vascularis, 299 striate cortex columnar organization, 271, 273, 274, 275 functional organization, 269–271 location, 261 optic radiation to, 267 pathway mixing, 270 visuoptic organization, 266 striola, 316–317 Strittmatter, Warren, 751 strokes, 764, 767 Stroop Interference Test, 632–633 strychnine, 137 Strychnos nux-vomica, 137 sublingual glands, 474–475 submandibular glands, 474–475 submucus plexus, 480 substance P, 154–155, 212, 221 substantia nigra, 149 basal ganglia pathway, 418, 419, 422 dopaminergic cells, 420, 428–430 efferent cells, 423 location, 755, 760 muscimol and, 431, 431 saccadic eye movement and, 425 subthalamic nuclei, 418, 422, 427 succinic semialdehyde dehydro-genase, 143 sulcal artery, 764 sulci, 18, 19 superior, positional definition, 16, 17 superior cerebellar peduncles decussation of, 441 location, 436, 437, 437, 755, 759, 760 superior colliculus, 263 basal ganglia pathway, 422 eye movements and, 460 location, 261, 755, 759, 760 saccadic eye movement and, 425 sensory motor integration, 462–463 sensory motor transformation, 461 upper motor neuron path-ways, 394 upper motor neurons, 393 visual inputs, 463 superior divisions, visual fields, 265 superior oblique muscles, 230 superior olivary complex, 286 superior olive, 304 superior rectus muscles, 230 superior sagittal sinus, 769 superior salivary nuclei, 477 superior temporal gyrus, 309 “supertasters,” 358 superoxide dismutase (SOD), 393 suprachiasmatic nucleus (SCN), 726–727 activation, 663–664 of the hypothalamus, 263 location, 484, 485 projections to, 663 supraoptic nucleus, 484, 485, 731 Swaab, Dick, 724–725, 726 sweat, 474–475 sweet taste, 356–363, 364 Sylvian fissure, 19 symbols, communication and, 624, 638 sympathetic division autonomic nervous system, 16 emotional arousal and, 687 visceral motor system, 472, 473, 474 sympathetic ganglia, 476 synapses chemical, 7, 94, 96, 97 competition, 546–547 connection formation, 545–547 cytoskeletal elements, 6 electrical, 93–95, 94 elimination, 545, 546 formation, 542–543, 543–544 growth proteins, 598 histology, 5 LTD mechanisms, 592–597 neuromuscular, 140–141 plasticity, 565–610 rearrangement, 545 selective formation, 539, 539–543 silent, 594–595 specificity, 540 synapsin, 114 synaptic cleft, 7, 96, 97, 150 synaptic depression, 577 synaptic endings. see presynaptic terminals synaptic facilitation, 582 synaptic plasticity, 565–610 critical periods and, 572 dendritic spines and, 590–591 long-term, 583 LTD and, 183 short-term, 582–583, 583 synaptic potentials, 13, 33 synaptic transmission, 93–127 definition, 7 description, 166 membrane permeability changes, 116–121 neuromuscular junctions, 102 synaptic vesicles chemical synapses, 96 cycles, 106 description, 8 exocytosis, 105 local recycling, 105–107, 106 neurotransmitter release, 103–105 transmitter release, 105 synaptic zones, 10–11 synaptojanin, 114 synaptotagmin, 113, 114 syntax, 634–644, 638 syntaxin, 111, 113 tachistoscopic presentation, 648 tactile discrimination, 196, 201 tail-flip escape reflex, 332, 332 Takeuchi, Akira, 119 Takeuchi, Noriko, 119 tastants categories, 357 responses to, 357–363, 364 taste buds, 354, 355, 358, 359 taste cells, 354, 361 taste pores, 358, 359–360 taste system, 354–363, 364 neural coding, 362–363, 364 organization, 354–356, 355 peripheral, 359–360 receptors, 360–364, 362 tears, 474–475, 477 tectal cells, 537 tectorial membranes, 290, 292, 295 tegmentum, 398 telencephalon, 510, 511 temperature receptors, 21–22, 21, 214 temporal coding, 349, 350 temporal cortex, 627–630, 629 temporal divisions, 264–265 temporal lobes anatomy, 18, 19 asymmetry, 648 facial recognition and, 623 location, 772 memory formation and, 741 memory retrieval and, 747 visual areas, 280, 281 tension, 380, 388 tensor tympani, 289 teratogenesis, 506 terminal aborizations, 568 terminal boutons. see presynaptic terminals testicular determining factor (TDF), 714 testicular feminization, 713 testosterone, 716, 717 tetanus, fused, 380 tetanus toxins, 108, 115 tetraethylammonium ions, 51, 52 ∆9-tetrahydrocannabinol (THC), 160 tetrodotoxin, 51, 52, 72, 82, 107 thalamic nuclei, 441 thalamocortical neurons, 679, 679–681, 680 thalamus auditory, 308–309 basal ganglia pathway, 418 dorsal lateral geniculate nucleus, 260 formation, 510 function, 20 location, 19, 20, 436, 759 mediodorsal nucleus of, 694 somatic sensory components, 20, 21, 203–204, 204 ventral nuclei, 423 ventral posterior nucleus, 216 vestibular pathways to, 331–332 thermoceptors, classification, 191 thiamine deficiency, 744 third-order neurons, 204 third ventricle, 18, 485, 511, 770, 772 Thoenen, Hans, 552 thoracic nerves, 17 threshold potentials, 34, 57, 122 thyroid cartilage, 640 thyroid hormone (TH), 181 tight junctions, 767, 768 Tinbergen, Niko, 735 tinnitus, 300 tip links, 297 TMN. see tuberomammillary nucleus tongue, 358, 359, 640 tonic receptors, 194 tonotopy, 285–286, 293, 310 topographical organization, 20, 406, 408 maps, 537–539 Toran-Allerand, Dominique, 719 Toscanini, Arturo, 738 total circuit neurons. see interneurons touch, 22, 32, 33 Tourette’s syndrome, 433 toxins, 115, 768 T1R activation, 361–362 tracers, 11 trachea, 640 trachomas, 569 tracts, CNS function, 15 transcription, 179, 179–180 transcription factors, 178, 505, 514 transcriptional activator proteins. see transcription factors transducin, 238 transforming growth factor (TGF) family, 505, 508, 508 transgenderism, 725 transient receptor potentials (TRPs), 78, 211 transmissible spongiform encephalopathies, 444–445 transneuronal transport, 564, 564 transverse pontine fibers, 437 transverse (horizontal) sections, 16–17 traveling waves, 292, 293, 294 tremors, cerebellar lesions and, 449 trichromatic vision, 248 tricyclic antidepressants, 148 trigeminal brainstem complex, 203 trigeminal ganglia, 21, 203, 213 trigeminal leminiscus, 203 trigeminal motor nucleus, 759, 760 trigeminal nerve (cranial nerve V) characterization, 756–758 chemoreception, 363–365, 365 function, 289 location, 756 mechanosensory system, 200–201 rhombomeres and, 514 subdivisions, 203 trigeminal somatic sensory sys-tem, 203 trigeminal system, 755 trigeminothalamic leminiscus, 203 trigeminothalamic tract, 203, 203, 216 TrkA, B, C signaling, 182, 553, 554 trochlear nerve (cranial nerve IV), 454, 514, 756, 756–758 trochlear nucleus, 759 trophic interactions, 543 molecular basis, 547–551 trophic molecules, 534, 535 tropic molecules, 534 tropical spastic paraparesis (TSP), 66 T1R taste receptors, 360–363, 362, 364 TRPM5 channel, 360–363, 362, 364 trustworthiness, judgments of, 709 tryptophan, 152 Tsimpli, Ianthi-Maria, 739 tuberomammillary nucleus (TMN), 151, 676–689, 677 δ-tubocurarine, 136 tubulin, 6, 529 tuning auditory systems, 284 delay-tuned neurons, 312 tuning curves auditory nerve, 301, 302 upper motor neurons, 411 vestibular hair cells, 320–321 tuning forks, 284, 284 tunnel of Corti, 292 tunnel vision, 239 Turner’s syndrome, 713 twitches, spontaneous, 392 two-point discrimination tests, 196, 196 tympanic membranes (eardrums), 287, 288 tyrosine hydroxylase, 184, 185 tyrosine kinase receptors, 553–554, 554, 555 umami (taste category), 357–363, 364 Unc-6 gene, 534–535 undershoot phase, 45, 46, 55 upper extremities, 474–475 upper motor neuron syndrome, 412–414, 413 upper motor neurons, 374, 394, 409, 411 upstream (3′) regulatory sequences, 1 Urbach-Wiethe disease, 702–703 ureters, 215, 474–475 urinary bladder, 215, 493–495, 494 urination, 495 urine, 474–475, 665 urogenital groove, 714 utricles, 315, 316 uveal tract, 229 V4 area, 278–279, 279 vaginal contractions, 496 vagus nerve (cranial nerve X) autonomic regulation, 492 cardioinhibitory outputs, 398–399 characterization, 756–758 chemoreception, 363 heart rate and, 96, 98 location, 756 rhombomeres and, 514 taste and, 359 Valenstein, Eliot, 625 Valium® (diazepam), 146, 148 valproic acid, 601 vanilloid-like receptor (VLR-1, TRPV2), 211 vanilloid receptor (VR-1, TRPV1), 211, 220–221 varicosities, definition, 470 vascular supply, 763–773 vasoconstriction, 474–475 vasocorona, 764 vasopressin, 485 ventral, definition, 16, 17 ventral anterior nculei, 423 ventral corticospinal tract, 405 ventral lateral nuclei, 423 ventral posterior complex of the thalamus, 203 ventral posterior lateral (VPL) nucleus, 203 ventral posterior medial (VPM) nucleus, 201, 203, 216, 356 ventricular system anatomy, 772 blood supply, 763–773 circulation, 770, 771 CNS function, 18 embryology, 771 location, 19 ventricular zone, 516 ventrolateral preoptic nucleus (VLPO), 677, 678 ventromedial nucleus, 484, 485 veratridine, 82 vergence movements, 458, 466–467 vermis, 436, 437 vertebral arteries, 763, 764, 765 vertical gaze center, 459 vervet monkeys, 643 vesicular glutamate transporters (VGLUTs), 141 vesicular inhibitory acid trans-porters (VIAATs), 143, 147 vesicular monoamine transporter (VMAT), 149 vestibular end organs, 328–331 vestibular nerve ganglia, 328 vestibular nerves, 288 vestibular nuclear complex, 393 vestibular nuclei, 328 cerebellar pathways and, 438 descending projections, 331 function, 397 location, 437, 759, 760 projections from, 399 vestibular system, 315–335 caloric testing, 326–327, 327 dysfunction, 326–328 fluid motion, 326, 327 navigation and, 318 vestibules, location, 288 vestibulo-cervical reflex (VCR), 330 vestibulo-ocular eye movements, 458 vestibulo-ocular reflex (VOR), 240–241, 242, 328, 329, 329–330 vestibulo-spinal reflex (VSR), 330 vestibulocerebellum, 435, 436 vestibulocochlear nerve (cranial nerve VIII) characterization, 756–758 damage to, 290 location, 316, 756 tuning curves, 300 vestibular end organs and, 328–331 VGLUT transporters, 137 VGLUTs (vesicular glutamate transporters), 141 VIAATs (vesicular inhibitory acid transporters), 143 Viagra® (sildenafil), 496 visceral motor division, 15, 16, 687 visceral motor reflexes, 491 visceral motor system, 469–498 autonomic network for, 483 central control of functions, 483–487 distinctive features, 470–471 early studies, 469–470 enteric component, 479 hypothalamic control, 484–486 major functions, 474–475 neurotransmission in, 487–491 nuclei, 757 parasympathetic division of, 472, 476–478 sensory components, 480–482 sensory input, 482 sympathetic division of, 471–476, 472 vision central pathways, 259–282 critical periods, 562–568 deprivation studies, 563–569, 565, 567 the eye, 229–257 monocular deprivation, 570 visiospatial processing, 656 visual cortex, 276–277, 617, 617, 748 visual fields binocular, 265 deficits, 267–269, 268 lateralization, 647 retinoptic representation, 263–267, 264, 265 right parietal lobe and, 621 sexual dimorphism, 728–729 superior colliculus and, 239 targets, 465 vitreous humor, 230 VMAT (vesicular monoamine transporter), 149 vocal folds, 640, 640 “volley theory,” 301 voltage clamp method, 48, 48–49, 49 voltage-gated ion channels, 360–361, 361 voltage sensors, 73, 80, 83 voluntary facial paresis, 690–691 vomeronasal organs (VNOs), 341–342 VP protein, 667 Waardenburg syndrome, 513, 515 Wada, Juhn, 649 Wada test, 649 wakefulness, 659–658, 663, 674. see also sleep–wake cycles walking, 448–449 Wall, Patrick, 226 Watkins, Jeffrey, 143 Watts, James, 625 waveforms, sound, 283–284 weasels, 634 weaver (wv) gene, 450, 450, 451, 451 Weber test, 290 Wernicke, Carl, 639 Wernicke’s aphasia, 643–644, 644, 746 Wernicke’s area, 312, 638, 639, 643, 652, 653 whisker barrels, 572 whiskers, 199, 199, 410 white matter, 15 Wieschaus, E., 513 Wiesel, Torsten, 209, 269, 562, 563 Wilkinson, R., 514 Willis, Thomas, 140 Win 55,212-2, 158 wingless (wg) gene, 512 Wisconsin Card Sorting Task, 626, 632, 632 withdrawal syndrome, 134 Wnt family, 506, 508, 508–509, 516 Wolffian ducts, 714 Woolsey, Clinton, 408 words, meaning and, 645 working memory, 735–736 writing, handedness and, 651 Wurtz, Robert, 423 X chromosome, 515 X-ray crystallography, 80, 81 xanthines, 153 Xenopus oocytes, 75, 75 Y chromosomes, 717 Yarbus, Alfred, 453 Young, Michael, 666 Young, Thomas, 247 zebra finches, 561, 717 Zic2, 530, 531 zinc finger transcription factors, 530 zonule fibers, 231–234 Index I-15
13205	https://www.teachingmedicine.com/tutorial/us_lung/Seashore_barcode	Teaching Medicine - Tutorial: Lung Ultrasound You have been logged out, please login to use this function. Login Email is required Password is required [x] Remember me on this computer Forgot your password?Resend verification email?) or login with Facebook)Google) Practice any time anywhere Join Teaching Medicine to get personalized help with what you're practicing or to learn something completely new. We'll save all of your progress. Help students succeed with personalized practice Assign our practice cases Our Software does all the marking Our algorithms generate feedback You download the scores Join Teaching Medicine For Free as a learner an instructor or assistant Continue Have an Account? 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How to level up? Develop your skills by completing our Practice Cases! Choose Level Tutorial: Lung Ultrasound Seashore and Barcode in M mode Lessons 42 Times Practiced 1284 Cases Completed 1h 24m Total Time spent 1m 24s Average Time Progress Accuracy Efficiency Accuracy Efficiency )))))))) 1Normal Lung UltrasoundNormal Lung Ultrasound) 2A linesA lines) 3B linesB lines) 4Comet tailsComet tails) 5Seashore and Barcode in M modeSeashore and Barcode in M mode) 6Pleural EffusionPleural Effusion) 7PneumothoraxPneumothorax) 8Interstitial Lung PatternsInterstitial Lung Patterns) Previous) Next) Previous Next Lesson Seashore and Barcode in M mode M-Mode signs: we will discuss 2 signs found on M mode for lung ultrasound: Seashore (Waves on the Beach) sign Barcode sign What is M mode? M mode is a simple mode of ultrasound. In 2D ultrasound (what we are all familiar with), a 2 dimensional picture is created by multiple beams coming out of the ultrasound probe (left image). In M mode, only 1 beam is coming out of the probe (image on right) and this one beam records an image. A few milliseconds later, it does this again and the next image is placed BESIDE the first image. In the image on the left, the ultrasound beam is seen within the 2D image. In the right hand image, the yellow arrow shows how this single beam lines up images creating the M mode image.As time goes forward, these single lines are printed on the screen very closely beside each other. Seashore (Waves on the Beach) Sign the seashore sign is anormal findingand represents lung sliding the thick bright white line on the tracing is the pleural line superficial to the pleura ( chest muscles, skin, fat ) is not moving, creating the solitary linear lines indicating a lack of motion deep to the pleura is lung sliding causing irregular grainy ‘noise’ Now crank up your imagination! The superficial component looks like waves approaching the beach. The pleural line is the surf break. The lung artifact component looks like the sand on the beach. Go grab your Speedos! Barcode Sign when there is no movement, M mode creates straight lines (as seen in the "ocean" above) if there isno lung sliding, then there is no movementanywhere on the screen the barcode sign occurs when lung sliding is absent the barcode sign is anabnormal finding tip a barcode on its side to see the similarities (this is the barcode from my pair of men's Speedos) Summary: M mode is a very primitive form of ultrasound time is the axis moving from left to right on the screen the Seashore sign is a normal finding the Barcode sign indicates loss of lung sliding Previous) Next) Previous Next Lesson AboutFor InstructorsFor ResearchersContact Us Terms of Use Privacy Policy © 2005-2025 TeachingMedicine.com All rights reserved.
13206	https://www.convertunits.com/from/nanometers/to/micrometers	Convert nanometers to micrometers - Conversion of Measurement Units Convert nanometre to micrometre Please enable Javascript to use the unit converter. Note you can turn off most ads here: \| \| \| --- \| \| \| nanometers \| \| \| micrometers \| \| \| More information from the unit converter How many nanometers in 1 micrometers? The answer is 1000. We assume you are converting between nanometre and micrometre. You can view more details on each measurement unit: nanometers or micrometers The SI base unit for length is the metre. 1 metre is equal to 1000000000 nanometers, or 1000000 micrometers. Note that rounding errors may occur, so always check the results. Use this page to learn how to convert between nanometres and micrometres. Type in your own numbers in the form to convert the units! Quick conversion chart of nanometers to micrometers 1 nanometers to micrometers = 0.001 micrometers 10 nanometers to micrometers = 0.01 micrometers 50 nanometers to micrometers = 0.05 micrometers 100 nanometers to micrometers = 0.1 micrometers 200 nanometers to micrometers = 0.2 micrometers 500 nanometers to micrometers = 0.5 micrometers 1000 nanometers to micrometers = 1 micrometers Want other units? You can do the reverse unit conversion from micrometers to nanometers, or enter any two units below: Enter two units to convert \| \| \| --- \| \| From: \| \| \| To: \| \| \| \| \| Common length conversions Definition: Nanometre The SI prefix "nano" represents a factor of 10-9, or in exponential notation, 1E-9. So 1 nanometre = 10-9 metre. Definition: Micrometer A micrometre (American spelling: micrometer, symbol µm) is an SI unit of length equal to one millionth of a metre, or about a tenth of the size of a droplet of mist or fog. It is also commonly known as a micron, although that term is officially outdated. It can be written in the expanded mathmatical notation (1×10-6 m) The symbol µ is the "micro sign", which should look identical to the Greek letter mu (?) (the two may or may not look the same, depending on the font). The symbol "um" is sometimes used, when the µ and ? are not available, for example when using a typewriter. The micrometre is a common unit of measurement for wavelengths of infrared radiation. Some people (especially in astronomy and the semiconductor business) use the old name micron and/or the solitary symbol µ (both of which were official between 1879 and 1967) to denote a micrometre. This practice persists in the face of official discouragement, perhaps to help disambiguate between the unit of measurement and the micrometer, a measuring device. Metric conversions and more ConvertUnits.com provides an online conversion calculator for all types of measurement units. You can find metric conversion tables for SI units, as well as English units, currency, and other data. Type in unit symbols, abbreviations, or full names for units of length, area, mass, pressure, and other types. Examples include mm, inch, 70 kg, 150 lbs, US fluid ounce, 6'3", 10 stone 4, cubic cm, metres squared, grams, moles, feet per second, and many more!
13207	https://cdn.wou.edu/mathcenter/files/2015/09/Exponents-and-Logarithms.pdf	Properties of Exponents and Logarithms Exponents Let a and b be real numbers and m and n be integers. Then the following properties of exponents hold, provided that all of the expressions appearing in a particular equation are dened. 1. aman = am+n 2. (am)n = amn 3. (ab)m = ambm 4. am an = amn, a 6= 0 5. a b m = am bm , b 6= 0 6. am = 1 am, a 6= 0 7. a 1 n = n pa 8. a0 = 1, a 6= 0 9. a m n = n p am = n pa m where m and n are integers in properties 7 and 9. Logarithms Denition: y = loga x if and only if x = ay, where a > 0. In other words, logarithms are exponents. Remarks: log x always refers to log base 10, i.e., log x = log10 x. ln x is called the natural logarithm and is used to represent loge x, where the irrational number e 2:71828. Therefore, ln x = y if and only if ey = x. Most calculators can directly compute logs base 10 and the natural log. For any other base it is necessary to use the change of base formula: logb a = ln a ln b or log10 a log10 b. Properties of Logarithms (Recall that logs are only dened for positive values of x.) For the natural logarithm For logarithms base a 1. ln xy = ln x + ln y 1. loga xy = loga x + loga y 2. ln x y = ln x ln y 2. loga x y = loga x loga y 3. ln xy = y ln x 3. loga xy = y loga x 4. ln ex = x 4. loga ax = x 5. eln x = x 5. aloga x = x Useful Identities for Logarithms For the natural logarithm For logarithms base a 1. ln e = 1 1. loga a = 1, for all a > 0 2. ln 1 = 0 2. loga 1 = 0, for all a > 0 1
13208	https://lessons.unbounded.org/content_guides/7/ratios-unbound-a-guide-to-grade-6-mathematics-standards	Back to Enhance Instruction UnboundEd Mathematics Guide Ratios: Unbound A Guide to Grade 6 Mathematics Standards Download Guide ? What's in a Content Guide and how do I use it? Get answers to all your Content Guide questions, including what's in each part and how they can be used in your role at your school View FAQs 6.RP.A \| Understand ratio concepts and use ratio reasoning to solve problems. Welcome to the UnboundEd Mathematics Guide series! These guides are designed to explain what new, high standards for mathematics say about what students should learn in each grade, and what they mean for curriculum and instruction. This guide, the first for Grade 6, includes three parts. The first part gives a “tour” of the standards for Ratios & Proportional Relationships using freely available online resources that you can use or adapt for your class. The second part shows how Ratios & Proportional Relationships relate to other concepts in Grade 6. And the third part explains where Ratios & Proportional Relationships are situated in the progression of learning in Grades 3-8. Throughout all of our guides, we include a large number of sample math problems. We strongly suggest tackling these problems yourself to help best understand the methods and strategies we’re covering, and the potential challenges your students might face. Part 1: What do these standards say? The standards for Grade 6 contain a number of important ideas, so why begin this series with Ratios & Proportional Relationships? For starters, these standards are part of the “major work” of Grade 6, meaning they deserve a large majority of class time over the course of the school year.1 In this series, major clusters are denoted by a ▉. For more information on the major work of Grade 6, see the Student Achievement Partners guide Focus in Grade 6. In this series, major clusters are denoted by a ▉. For more information on the major work of Grade 6, see the Student Achievement Partners guide Focus in Grade 6. Prioritizing major work within the year ensures that those standards are sure to get the attention they deserve. Ratios are also important because they’re a crucial step on the path to algebra, connecting multiplication and division from the elementary grades to linear equations, slope and other concepts in Grades 7-12. Another reason that ratios are a great way to start the year is that they’re a “fresh” idea, introduced for the first time in Grade 6, and are accessible to any student with a basic understanding of whole-number multiplication. Moveover, some of the other work in Grade 6 (such as the standards for Expressions & Equations) is easier for students to understand once they have an understanding of ratios. So if you’re wondering where to start your year, ratios are a solid bet. In Grade 6, the standards in the Ratios & Proportional Relationships (RP) domain are grouped together into one cluster (called RP.A because it’s the first and only cluster). But this one cluster contains a number of essential mathematical ideas. Let’s take a look at what these standards say. 6.RP.A Understand ratio concepts and use ratio reasoning to solve problems. \| \| \| 6.RP.A.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes." 6.RP.A.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger." 6.RP.A.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams or equations. 6.RP.A.3.A Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables and plot the pairs of values on the coordinate plane. Use tables to compare ratios. 6.RP.A.3.B Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? 6.RP.A.3.C Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. 6.RP.A.3.D Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Expectations for unit rates in this grade are limited to non-complex fractions. \| The order of the standards doesn’t indicate the order in which they have to be taught. Standards are only a set of expectations for what students should know and be able to do by the end of each year; they don’t prescribe an exact sequence or curriculum. In this case, though, they are lined up pretty well: The first two standards name important conceptual understandings that students should have about ratios and rates, and the third says that students should be able to use these understandings to solve problems. It even goes on to give examples of the kinds of problems that students should encounter, as well as the types of strategies they should use. If you’re planning a unit on ratios, it makes sense to follow a similar sequence: Lay a conceptual foundation first, using simple problems, and then move on to more advanced applications of those ideas. And remember that instruction on ratios is probably going to involve working with more than one standard at once, since new concepts can often be introduced through real-world contexts and problems. Ratios and rates: Essential concepts As adults, we do ratio math all the time without naming the ideas involved. But teaching students who are new to ratios requires precise knowledge of what they’re being expected to learn. Let’s pause for a moment to think about the concepts in these standards: A ratio is a pair of non-negative numbers, A:B, which are not both 0 (such as 1:2, 5:3, etc.).2 Much of the information in this section is taken from the Draft 6-7 Progression on Ratios and Proportional Relationships, one of a series of papers that describes the big ideas behind the standards and how those ideas fit together. If you’re interested in learning more about ratios and proportional relationships, it’s a good resource. Much of the information in this section is taken from the Draft 6-7 Progression on Ratios and Proportional Relationships, one of a series of papers that describes the big ideas behind the standards and how those ideas fit together. If you’re interested in learning more about ratios and proportional relationships, it’s a good resource. Any two quantities can be associated in a ratio. Some examples of ratios which associate two quantities in this way are: I paid 1 dollar for every 4 pounds of flour. The ratio of dollars to pounds of flour is 1:4. For every 3 girls in the class, there are 2 boys. The ratio of girls to boys is 3:2. In the birdhouse at the zoo, the ratio of wings to beaks is 2:1. Ratios are most useful in situations which other, equivalent ratios have meaning. Equivalent ratios are the ratios obtained by multiplying the numbers in a ratio by the same positive number. So, for a class where the ratio of girls to boys is 3:2, we can generate equivalent ratios of 6:4, 9:6, 12:8, and so on. In context, this means that the class might have 6 girls and 4 boys, 9 girls and 6 boys, 12 girls and 8 boys, and so on. The number of students and the size of each group of boys and girls might change, but the ratios 3:2, 6:4, 9:6, and 12:8 are all equivalent. All of these are “in the same ratio.” The standards also focus on ratio language. In our last example, if the ratio of girls to boys is 3:2, we can say, “For every 3 girls there are 2 boys.” The phrase “for every” (and also “for each”) is an important piece of language that can be used to describe a ratio relationship.3 While “for every” will eventually take on a more widely applicable meaning in higher level math, in Grade 6, when used in a context associating two quantities, it is an indicator of a ratio relationship. While “for every” will eventually take on a more widely applicable meaning in higher level math, in Grade 6, when used in a context associating two quantities, it is an indicator of a ratio relationship. Ratios have companion unit rates. A unit rate of two quantities in a ratio is the number of units of the first quantity for every 1 unit of the second quantity. (This is what standard 6.RP.A.2 means when it says “a unit rate a/b associated with a ratio a:b.”) For example, each of these statements contains a ratio followed by its associated unit rate: A recipe uses 1 cup of sugar for every 2 cups of flour, so there is 1/2 cup of sugar for every cup of flour. Juice costs 96 cents for every 32 ounces, which is a rate of 3 cents for each ounce. A car travels 120 miles every 2 hours, which is a rate of 60 miles per hour. Note that in Grade 6, students only need to work with non-complex fractions (fractions of two whole numbers, not fractions of fractions). Starting in Grade 7, they’ll work with rates such as “1/2 mile for every 1/4 hour.” More on that in Part 3 of this guide. The importance of conceptual understanding Both standards 6.RP.A.1 and 6.RP.A.2 seem to focus on the language of ratio and rates. This is certainly an important aspect of these standards and deserves explicit attention. But at the heart of both standards is really the understanding of the concepts of ratio and unit rate, which will help students make sense of a variety of problems. (Remember, the cluster heading for these standards is, “Understand ratio concepts and use ratio reasoning to solve problems.”) As you plan lessons for these standards, think about how students can explain and show their understanding of ratios and rates in various ways. Ultimately, students should be able to define the concepts named above in their own words, as well as give examples and nonexamples of each. Problems that develop conceptual understanding Now that those we’ve established the basics, the natural question is: How do we get students to start thinking in terms of ratios and rates? Let’s take a look at three tasks that could be used as part of a unit to develop student understanding of these concepts. These aren’t the only tasks you’ll need to teach ratios, but they should give you a starting point for some of your lessons. Ratio language and notation The task in the box below presents opportunities for students to use ratio language, to examine how ratios are distinct from other types of relationships, and to relate ratio statements to their numerical representations. (6.RP.A.1) It could be the basis for an early lesson on ratio language and notation. Games at Recess The students in Mr. Hill’s class played games at recess. 6 boys played soccer 4 girls played soccer 2 boys jumped rope 8 girls jumped rope Afterward, Mr. Hill asked the students to compare the boys and girls playing different games. Mika said, “Four more girls jumped rope than played soccer.” Chaska said, “For every girl that played soccer, two girls jumped rope.” Mr. Hill said, “Mika compared the girls by looking at the difference and Chaska compared the girls using a ratio.” Compare the number of boys who played soccer and jumped rope using the difference. Write your answer as a sentence as Mika did. Compare the number of boys who played soccer and jumped rope using a ratio. Write your answer as a sentence as Chaska did. Compare the number of girls who played soccer to the number of boys who played soccer using a ratio. Write your answer as a sentence as Chaska did. “Games at Recess” by Illustrative Mathematics is licensed under CC BY 4.0. HideShow One interesting aspect of this task is how it contrasts ratio language with the language of difference, so that students begin to see how related quantities can be described in more than one way. Though this might seem obvious, it’s a good way to draw students’ attention to the fact that ratio relationships are distinct from the types of additive comparisons (“how many more” and “how many less”) that they may have seen in the elementary grades. Moreover, by contrasting their answers to parts (b) and (c), they’re able to see that situations often give rise to a number of possible ratio relationships. Since the directions for this task are fairly simple, you might also use it as an opportunity to explicitly teach ratio notation (e.g., 1:2). Or, if you’re using this task after your students have learned ratio notation, having them express each statement numerically could be a way to practice. You could even ask them to write several more ratio statements based on the information in the task to emphasize the various ratios in the problem. Equivalent ratios Soon after students start working with ratios, they should begin to see how one ratio implies a set of other, equivalent ratios. Ratio tables make it easy for students to see relationships among ratios: they present both an additive structure and a multiplicative structure, and students should be familiar with both. The task in the box below is taken from a lesson that does just that, encouraging students to discover and use more than one relationship in a table. Grade 6, Module 1, Lesson 10: Exit Ticket Show more than one way you could use the structure of the table to find the unknown value. Fill in the unknown values. \| \| \| --- \| \| Number of Weeks \| Amount of Money in Account \| \| 2 \| $350 \| \| 4 \| $700 \| \| 6 \| $1,050 \| \| 8 \| \| \| 10 \| \| Grade 6, Module 1, Lesson 10 Available from engageny.org/resource/grade-6-mathematics-module-1-topic-b-lesson-10; accessed 2015-05-29. Copyright © 2015 Great Minds. UnboundEd is not affiliated with the copyright holder of this work. When using this task (or one like it), it’s important to observe the ways in which they think about finding unknown values. Ask students to describe how they determined the amount of money in each row. Students who are able to see the multiplicative structure will be able to say things like, “I could see that each value in the second column is 175 times the corresponding value in the first column.” Students who are able to see the additive structure might say things like, “I could see that the values in the first column increase by two and the values in the second column increase by 350.” Though both observations are valid, it’s important that students see the multiplicative structure between quantities to get ready for questions like, “How much money would be left in the account after 26 weeks?” In that case, a student could find the answer by extending the table and continuing to add, but it’s far more efficient to multiply. If some students don’t see the multiplicative relationship at first, you (or another student) could illustrate it on the board, using arrows to show the patterns within the table. You might also choose to extend this task by adding another row of the table with a more challenging number of weeks (such as 11 or 26) to help students understand why the multiplicative structure is so valuable. Unit rates Unit rates are a natural extension of ratios. (6.RP.A.2) The task below is interesting because it uses unusual items to get students thinking about the notion of unit rate as “for every” or “per 1” of a second quantity, and to reinforce the importance of order in expressing rates. Hippos Love Pumpkins Hippos sometimes get to eat pumpkins as a special treat. If 3 hippos eat 5 pumpkins, how many pumpkins per hippo is that? Lindy made 24 jelly-bread sandwiches with a 16-ounce jar of jelly. How many ounces of jelly per sandwich is that? Purslane bought 350 rolls of toilet paper for the whole year. How many rolls of toilet paper per month is that? In the world's longest running experiment, scientists have tried to capture tar pitch dripping on camera. In the past 86 years, 9 drops have formed. How many years per drop is that? Imagine that 12 goats got into a dumpster behind a pizza parlor and ate 3 pizzas. How many goats per pizza would that be? “Hippos Love Pumpkins” by Illustrative Mathematics is licensed under CC BY 4.0. HideShow One way to extend this task might be to ask students to find two distinct rates in each situation (such as “goats per pizza” and “pizzas per goat”), or to ask why expressing a rate in a certain way might be useful (if a zookeeper is deciding how many pumpkins to buy for 8 hippos, for example). You could also ask some simple questions involving rate reasoning. (6.RP.A.3.B) (For example, “If Lindy makes 3 more sandwiches, how much jelly will she need?”) On the other hand, if you think your students might not be ready for the complexity of the numbers involved here, consider adding a couple of examples with very “clean” unit rates up front. Any situation with a whole-number unit rate would be fine (“Tanasia watched 3 shows and saw 18 commercials. How many commercials per show is that?”), as would a situation where the unit rate is a simple fraction like 1/2 (“Doug can eat 8 burgers in 4 minutes. How many minutes per burger is that?”). Helpful representations There are four specific representations named in these standards that students can use to better understand and solve problems with ratios and rates: tape diagrams, ratio tables, double number lines, and equations. Each of them is described below, but it’s a good idea to try them all yourself before using them in your lessons. You’ll probably find that each has strengths and limitations. It’s also important to know that students will need explicit instruction on why and how to use each type of representation. Introduce tape diagrams and double number lines early, when your students are working with simple problems. That way, they’ll have time to get to know these representations, and will be able to use them more effectively when problems become more challenging. Over time, they should see how the right tool can make complicated problems more manageable. Why not just use cross multiplication? Most adults have seen some version of the “cross multiplication” method of solving ratio problems, which involves writing equations like these and multiplying on the diagonal: This method relies on a multi-step algorithm that students often don’t understand, and they use it without realizing why it works. (In the equation above, why does multiplying 6 by 3, and then dividing by 2 yield the correct answer? Most students would have a hard time explaining.) When students don’t understand why a procedure works, it becomes more likely that they will misapply it. Though equations like this can be useful for solving ratio problems, the cross multiplication method isn’t required in Grade 6 for exactly this reason. The standards require students to build deep conceptual understanding of ratios and rate, which they can then use to solve problems. Over time, they should be able to use a variety of representations and methods to explain their thinking, rather than relying on a single method. Tape diagrams Tape diagrams (also known as bar models or strip diagrams) are thin rectangles resembling pieces of tape that can be divided into sections to represent parts of a problem. In the elementary grades, a tape diagram with two sections can represent a simple addition or subtraction problem; later on, a diagram with several equal-sized sections can represent a multiplication or division problem. Students can represent ratio problems using two tape diagrams “side by side” to represent the two quantities in a ratio relationship. Because they offer a handy way to visualize the elements of a problem, tape diagrams will probably be among the first tools you’ll use with students. They also help to build conceptual understanding of equivalent ratios, as in this task. Grade 6, Module 1, Lesson 3: Exercise 2 Shanni and Mel are using a ribbon to decorate a project in their art class. The ratio of the length of Shanni’s ribbon to the length of Mel’s ribbon is 7:3. Draw a tape diagram to represent this ratio. Grade 6, Module 1, Lesson 3 Available from engageny.org/resource/grade-6-mathematics-module-1-topic-lesson-3; accessed 2015-05-29. Copyright © 2015 Great Minds. UnboundEd is not affiliated with the copyright holder of this work. HideShow When used early in the unit on ratios, this task can help students understand the nature of equivalent ratios. Since each model has the same number of units, students can see that equivalent ratios all have the same unit rate. (This is one of the defining features of equivalent ratios.) You might push students to explain this concept by asking what all three ratios have in common, and then asking them to find another ratio that’s equivalent to the others (and prove its equivalence by using a model). Tape diagrams are also useful aids for problem-solving. The process of constructing a tape diagram from a problem requires students to read the problem, determine the quantities involved, and determine the relationships among those quantities. Once they’re able to represent the problem in diagram form, they should have a solid grasp of what operations they need to use to solve it. At first, students might find it tedious to create a diagram and then find a solution to the problem, but tape diagrams have two advantages. First, they help students slow down and think about each problem before they try just anything. Second, they allow students to decode very tricky problems that are difficult to solve using only an arithmetic method. Take this problem, for example. Grade 6, Module 1, Lesson 6: Exercise 1 The Business Direct Hotel caters to people who travel for different types of business trips. On Saturday night there is not a lot of business travel, so the ratio of the number of occupied rooms to the number of unoccupied rooms is 2: 5. However, on Sunday night the ratio of the number of occupied rooms to the number of unoccupied rooms is 6: 1 due to the number of business people attending a large conference in the area. If the Business Direct Hotel has 432 occupied rooms on Sunday night, how many unoccupied rooms does it have on Saturday night? Grade 6, Module 1, Lesson 6 Available from engageny.org/resource/grade-6-mathematics-module-1-topic-lesson-6; accessed 2015-05-29. Copyright © 2015 Great Minds. UnboundEd is not affiliated with the copyright holder of this work. HideShow Without drawing the diagrams first, the relationships between the two ratios (2:5 and 6:1) and the given quantity (432 occupied rooms on Sunday) might be tough to discern. But once students take the time to construct both tape diagrams, the situations becomes much more clear. Finding the solution just requires a few simple calculations, as shown here: 6 units = 432 rooms 1 unit = 432 ÷ 6 = 72 rooms 5 units = 72 × 5 = 360 rooms Ratio tables In addition to being a useful instructional tool, ratio tables are also useful for solving problems. They’re simple to construct, help students organize their work, and are adaptable to a variety of situations. This task is just one example. Mixing Concrete A mixture of concrete is made up of sand and cement in a ratio of 5:3. How many cubic feet of each are needed to make 160 cubic feet of concrete mix? “Mixing Concrete” by Illustrative Mathematics is licensed under CC BY 4.0. While students might represent this problem in a number of ways, a ratio table might be the fastest and simplest: They can easily record the facts given in the problem, as well as the quantities they need to find. The table below includes two extra columns, which aren’t required to solve the problem but might help struggling students. Asking them to explain how to complete these intermediate rows might give them a clue about how to get started. \| \| \| \| \| \| --- --- \| Sand \| 5 \| 10 \| \| ? \| \| Cement \| 3 \| \| 9 \| ? \| \| Total Mixture \| 8 \| 16 \| \| 160 \| Double number lines Just as the name implies, double number lines are diagrams containing two parallel number lines labeled with different units. They’re similar to ratio tables in that they allow students to easily scale quantities up or down, but also allow students to see the relationship between different units as in a tape diagram. (In particular, double number lines are handy where percents are involved, allowing students to make sense of problems beyond those that just require finding percent of a number.) The task below relates ounces of soda and grams of sugar, allowing students to solve based on a ratio of 20 grams of sugar to every 6 ounces of soda. Grade 6, Module 1, Lesson 12: Exercise 4 A school cafeteria has a restriction on the amount of sugary drinks available to students. Drinks may not have more than of sugar. Based on this restriction, what is the largest size cola (in ounces) the cafeteria can offer to students? My estimate is between 6 and 12 oz but closer to 6 ounces. I need to find of 6 and add it to 6. x= = 1 1= 7 A 7 oz cola is the largest size that the school cafeteria can offer to students. Grade 6, Module 1, Lesson 12 Available from engageny.org/resource/grade-6-mathematics-module-1-topic-b-lesson-12; accessed 2015-05-29. Copyright © 2015 Great Minds. UnboundEd is not affiliated with the copyright holder of this work. HideShow Notice how the double number line allows students to see where the answer falls in a range of equivalent ratios. The calculations shown are only one possible solution; students could also use unit rate reasoning, for example, to find the amount of soda per gram of sugar, and then multiply to find the amount of soda containing 25 grams of sugar. (If given a choice of methods, students will probably find yet more ways to solve.) Equations After students have had plenty of exposure to conceptual representations like ratio tables and tape diagrams, they may be ready to solve certain problems by writing equations. The “Mixing Concrete” problem above, for example, could be solved with equations. Notice, however, how closely these equations resemble portions of the table that students used to approach the problem at first. Learning to write equations like this should be the natural result of working with ratio tables, so that after enough “at bats,” students are able to explain how their equations are valid expressions of the problem situation. \| \| \| \| --- \| Sand \| 5 \| \| \| Cement \| 3 \| \| \| Total Mixture \| 8 \| 160 \| ↙ ↘ \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| --- --- --- --- --- --- --- \| \| \| \| \| \| --- \| Sand \| 5 \| \| \| Total Mixture \| 8 \| 160 \| ↓ \| \| \| \| \| --- \| Cement \| 3 \| \| \| Total Mixture \| 8 \| 160 \| ↓ \| It’s also important to note that when students “solve” these equations, they shouldn’t need to use abstract methods like “cross multiplication.” Rather, they’ll discover the unknown factor that relates two of the quantities in the problem and use that to calculate the answer. This way, they don’t have to employ any “tricks,” but can rely on established ideas about equivalent ratios and the relationship between multiplication and division. 8 cubic feet concrete × __ = 160 cubic feet concrete ↓ 8 cubic feet concrete × 20 = 160 cubic feet concrete ↓ 5 cubic feet sand × 20 = 100 cubic feet sand Applications of ratios and rates Once the concept of ratio has been introduced, students should get plenty of practice solving a variety of ratio problems. A balanced instructional unit will include problems that involve finding equivalent ratios and also problems that require students to work with ratio tables and graph ratio relationships on the coordinate plane. (6.RP.A.3.A) This example involves both: Students need to complete a ratio table based on a description of a situation, and then use their entries in the table to create a graph. Grade 6, Module 1, Lesson 14: Example 1 Kelli is traveling by train with her soccer team from Yonkers, NY to Morgantown, WV for a tournament. The distance between Yonkers and Morgantown is 400 miles. The total trip will take 8 hours. Dinner service starts once the train is 250 miles away from Yonkers. What is the minimum time the players will have to wait before they can have their meal? The minimum time is 5 hours. Grade 6, Module 1, Lesson 14 Available from engageny.org/resource/grade-6-mathematics-module-1-topic-b-lesson-14; accessed 2015-05-29. Copyright © 2015 Great Minds. UnboundEd is not affiliated with the copyright holder of this work. HideShow The questions that follow this problem (in the linked document) are interesting, first in how they explicitly help students set up the graph (students may require more or less guidance than this lesson plan suggests, but it’s good to think about how they’ll interact with the coordinate plane, which was only just introduced in Grade 5). Then, when looking at the completed graph, ask students to interpret the meaning of individual points (“What does this point represent in the context of distance and time?”). Constantly considering how the parts of a representation relate to the original situation is a good habit of mathematical thinking to encourage. It’s also worth pointing out that this lesson plan budgets quite a bit of time for this problem, allowing students to fully engage with all of its aspects. In addition to using equivalent ratios to solve problems, students should also be able to use unit rate thinking to solve problems. This task invites multiple solutions: students can set up a ratio table and “jump” to the values they need for each part, but they can also find a unit rate. Running at a Constant Speed A runner ran 20 miles in 150 minutes. If she runs at that speed, How long would it take her to run 6 miles? How far could she run in 15 minutes? How fast is she running in miles per hour? What is her pace in minutes per mile? “Running at a Constant Speed” by Illustrative Mathematics is licensed under CC BY 4.0. If this task is used in the course of a lesson and students are allowed to solve in several ways, it might be interesting to discuss the contrasts among the methods they used with the class. How are they similar and different, in terms of the operations involved? Which one is the most efficient? Ultimately, students should be comfortable with both methods--there will be times when thinking in terms of unit rates is preferable to thinking in terms of equivalent ratios, especially when the numbers involved are less “friendly” than the ones used here—and seeing the connection between the two is valuable. If we want to encourage students to try one method over another, consider the order of the questions: As they’re presented now, students may be inclined to set up a ratio table to answers parts (a) and (b). But if parts (c) and (d) were moved first, they might be more inclined to use a unit rate solution. One remarkable aspect of the ratio standards is that percents and measurement conversions, which in the past were often taught as isolated skills, are now treated as ratio situations. This is good news, as students are now able to approach them using the same type of reasoning and tools as with other ratio problems. This task is a fairly straightforward percent problem. Kendall’s Vase Kendall bought a vase that was priced at $450. In addition, she had to pay 3% sales tax. How much did she pay for the vase? “Kendall’s Vase” by Illustrative Mathematics is licensed under CC BY 4.0. One of the sample solutions shows a percent table (really, a type of ratio table) that illustrates the relationship between ratios and percents. Double number lines (like those shown in the section above) could also help students find the correct answer. Similar strategies can be employed to solve problems involving measurement conversions. The role of Mathematical Practices The standards don’t just include knowledge and skills; they also recognize the need for students to engage in certain important practices of mathematical thinking and communication. These “Mathematical Practices” have their own set of standards, which contain the same basic objectives for Grades K-12.4 You can read the full text of the Standards for Mathematical Practice here. You can read the full text of the Standards for Mathematical Practice here. (The idea is that students should cultivate the same habits of mind in increasingly sophisticated ways over the years.) But rather than being “just another thing” for teachers to incorporate into their classes, the practices are ways to help students arrive at the deep conceptual understandings required in each grade. In other words, the Practices help students get the content. The table below contains a few examples of how the Mathematical Practices might help students understand and work with ratios in Grade 6. \| \| \| --- \| \| Opportunities for Mathematical Practices: \| Teacher actions: \| \| Percents are a special kind of rate (a “rate per 100”) which is similar in structure to unit rate (a “rate per 1”). When students are allowed to notice and explain this concept, and then to apply it in a variety of problem contexts, they look for and make use of structure. (MP.7) \| Consider introducing percents by showing students examples in which it helps to compare several quantities on a “per 100” basis. (For an example, see Exercises 1-2 of this introductory lesson plan on percents). Ask them to explain how this approach is similar and different to using a unit rate. And when students are able to use the “per 100” structure of percents to solve problems (e.g. they figure out that a 25-cup recipe with 7 cups of sugar contains 28% sugar using multiplication by 4), you can have them explain their reasoning to the rest of the class. \| \| Students can model with mathematics (MP.4) when they solve real-world and mathematical problems using ratio and rate reasoning, especially when they make use of various representations in the modeling process. \| Show students a variety of ways to model ratio situations (such as those presented above: tape diagrams, ratio tables, double number lines, and equations), and during the course of the year, give them interesting problem contexts that require these models. Have students explain how their representations model the situation at hand, and why they selected a certain type of representation for a given situation. \| \| Students can reason abstractly and quantitatively (MP.2) when they work with the concept of a ratio, which abstracts a comparison between two quantities and implies other, related relationships. (For example, a ratio of 3:4 implies equivalent ratios of 6:8, 9:12, etc., and a unit rate of 3/4.) \| As a simple exploration activity, you might have students count intentionally constructed sets of objects—like checkers—where there is a consistent ratio of black checkers to red. To start, students are simply counting (quantifying) what they observe. Then you can guide students to look for patterns between the numbers of black and red checkers in each group. After examining several groups—perhaps one group per table of students—students should come to see the underlying structure of a black checkers to b red checkers. Finally, you can abstract this structure using ratio language (e.g. “For every a black checkers, there are b red checkers.”). \| Podcast clip: Importance of the Mathematical Practices with Andrew Chen and Peter Coe (start 30:33, end 43:39) Part 2: How do ratios relate to other parts of Grade 6? There are lots of connections among standards in Grade 6; if you think about the standards long enough, you’ll probably start to see these relationships everywhere.5 The idea that standards relate strongly to one another is known as coherence, and is a distinctive feature of the Common Core State Standards for Mathematics. If you’re interested in exploring more of the connections between standards, you might want to try the Student Achievement Partners Coherence Map web app. The idea that standards relate strongly to one another is known as coherence, and is a distinctive feature of the Common Core State Standards for Mathematics. If you’re interested in exploring more of the connections between standards, you might want to try the Student Achievement Partners Coherence Map web app. A few are so important, though, that they deserve special attention. The first is the relationship that the ratio and proportional reasoning standards have to one another. As mentioned above, it’s tough to work in one of these standards without working in others at the same time. When students are starting to understand the concepts of ratio and unit rate, (6.RP.A.1, 6.RP.A.2) they should be solving application problems that draw out these ideas. (6.RP.A.3) Exploring problems through ratio tables, for example, is a great way to see how ratio relationships work. And as students begin solving a wider variety of problems (rate problems, percent problems, measurement conversions), they’ll be cementing their core understandings of ratio and rate through application. Therefore, as you’re planning instruction for one standard, keep the others in mind: There may be clues about how to teach one standard hidden in another. Expressions & Equations: Reasoning about one-variable equations Another area of focus in Grade 6 is work with algebraic Expressions & Equations (EE). This is an area that deserves its own guide, but right now we’ll cover two particular ways that ratios can play a part in understanding these concepts. Many teachers will choose to begin their study of EE with standards that relate expressions to arithmetic operations from Grades K-5. (6.EE.A.2) When it comes time to write and solve equations for a variety of situations, (6.EE.B.7) though, ratio situations are a rich source of problems, and ratio reasoning can lend students insight into how to write equations to model a situation. This task is one such example: Firefighter Allocation A town's total allocation for firefighter's wages and beneﬁts in a new budget is $600,000. If wages are calculated at $40,000 per firefighter and beneﬁts at $20,000 per firefighter, write an equation whose solution is the number of firefighters the town can employ if they spend their whole budget. Solve the equation. “Firefighter Allocation” by Illustrative Mathematics is licensed under CC BY 4.0. The commentary and solutions that follow the task explain how to set up an equation to solve this problem. But writing expressions and equations is very abstract, and can be tough for many students when they try it the first time around. So how do students get to the point where they can write equations like the ones suggested? One way to get started is to help students see a ratio at work in this problem (for every firefighter it hires, the town spends $60,000) and explore it using a ratio table. You might guide students to build a table like the one below by asking: How much is the town spending per firefighter? How much for two firefighters? How do you know? What is the relationship between the first and second row? \| \| \| \| \| \| --- --- \| Firefighters \| 1 \| 2 \| 3 \| x \| \| Cost ($) \| 60,000 \| 120,000 \| 180,000 \| \| By applying the same type of unit rate reasoning they used to solve ratio problems, students can see why a good expression for the total cost of x firefighters is 60,000x. Some questions you might want to ask to help your students come to this realization are: What does the x represent? What does the box below x represent? What would the cost for 4, 5, and 6 firefighters be? How do you know? Can you write some expressions that show how to find the cost in each column of the table? What changes from one expression to the next, and what stays the same? How could these help you fill in the last box? Solving problems like this will help to prepare students for more work with algebraic equations and ratios in Grade 7. (7.RP.A.2.C) 600,000 = 60,000x ↑ unit rate Since this standard also requires that students work with equations involving additive relationships (equations of the form x + p = q), students should also learn to distinguish situations where two quantities are in a ratio relationship and when they’re not. A table may also help when introducing the difference between the two situations, as it allows students to easily see when there is no multiplicative relationship between rows. Expressions & Equations: Representing relationships between two variables In addition to writing and solving equations with one variable (like the one shown above), students also begin using equations in two variables to model the relationship between two quantities. (6.EE.C.9) This is where their journey toward modeling with functions, which continues through the rest of the middle grades and into high school, really begins. Many of the situations that they encounter will involve ratios and rates, so this is where prior experience with those concepts will come in handy. As an example, let’s look at this task: Chocolate Bar Sales Stephanie is helping her band collect money to fund a field trip. The band decided to sell boxes of chocolate bars. Each bar sells for $1.50 and each box contains 20 bars. Below is a partial table of monies collected for different numbers of boxes sold. \| \| \| --- \| \| Boxes Sold \| Money Collected \| \| 1 \| $30.00 \| \| 2 \| \| \| 3 \| \| \| 4 \| \| \| 5 \| $150.00 \| \| 6 \| \| \| 7 \| \| \| 8 \| \| Complete the table above for the values of . Write an equation for the amount of money, , that will be collected if boxes of chocolate bars are sold. Which is the independent variable and which is the dependent variable? Graph the equation using the ordered pairs from the table above. Calculate how much money will be collected if 100 boxes of chocolate bars are sold. The band collected $1530.00 from chocolate bar sales. How many boxes did they sell? “Chocolate Bar Sales” by Illustrative Mathematics is licensed under CC BY 4.0. HideShow Many parts of this problem should be familiar to students after studying ratios and rates: They’re making a table to represent the constant relationship between boxes and money, they’re graphing that relationship on the coordinate plane, and they’re using a rate to find unknown quantities. Part (b) is the tricky one, though, so let’s focus on that. The difficulty here is the same as in the previous task: Writing equations is very abstract, and students often have trouble seeing and expressing the relationship between variables. Not surprisingly, the questions you might ask to help students write the equation are also similar. (And fortunately, this problem has a table built into it, which can help students see the relationships involved.) You might ask: What is the cost per box? How do you know? What relationship do you see between columns in the table? Can you write some expressions to show how to find the cost in each row of the table? What changes from one expression to the next, and what stays the same? What if the number of boxes is b? Again, as students solve more problems like this, they’ll begin to see that they can model any two variables in a ratio relationship in the same way: dependent variable ↓ ↓ independent variable m = 30b ↑ unit rate This isn’t limited to quantities in a ratio relationship. Students should also see situations where there is an additive relationship between variables (e.g., x + 5 = y). Again, tables are helpful in allowing students to see that no multiplicative relationship exists in these cases. The Number System: Operations with decimals The last significant connection that we want to mention here is the relationship to operations with decimals. (6.NS.B.2, 6.NS.B.3) Because working fluently with multidigit decimals is a required fluency for Grade 6, students should be given frequent opportunities to use all four standard algorithms with decimals. As mentioned above, ratio and rate work is a good place to start the year; study of the standards in the Number System (NS) domain will likely occur later on in the year. However, once instruction on dividing multi-digit whole numbers (6.NS.B.2) and the four operations with multidigit decimals (6.NS.B.3) has occurred, ratio and rate problems are good ways to practice these skills and develop fluency while continuing to deepen their understanding of ratio. Take this problem, which invites students to use multiple algorithms: When making bread, a baker uses 2 ounces of yeast for every 8 pounds of flour. How much yeast does the baker need to make a batch of bread using 150 pounds of flour? Though there are a number of ways to solve this, one approach would be to calculate a unit rate (0.25 ounces of yeast per pound of flour) using the long division algorithm, and then multiply (again, using the standard algorithm) by the amount of flour in the larger batch to find the amount of yeast required. Students might interpret the problem using ratio reasoning and a representation like a ratio table or tape diagram, and then build fluency with decimal operations in calculating the solution. Part 3: Where do ratios come from, and where are they going? Ratios make their debut in Grade 6, but (as with most things) they’re part of a careful progression of prior learning. Knowing the lead-up to ratios will help you leverage content from previous grades in your lessons. And if your students are behind, seeing where ratios come from will allow you to adapt your curriculum and lessons to make new ideas accessible. Let’s look at the main threads that lead up to ratios in Grades K-5; then we’ll examine some ways that you might use this information to meet the unique needs of your students. After that, we’ll see where ratios are going in the next few years after Grade 6. Podcast clip: Importance of Coherence with Andrew Chen and Peter Coe (start 9:34, end 26:19) Where do ratios come from? Grades 3-5: Multiplication and division Starting in Grade 3, students are introduced to multiplication (and, in a related way, division) as an expression of equal groups. (3.OA.A.1, 3.OA.A.2) In Grade 4, they should begin to understand the idea of multiplicative comparison (the idea that one quantity is so many times more than another) and distinguish this from additive comparison (the idea that one quantity is simply so many more than another). (4.OA.A.1, 4.OA.A.2) The differences between these concepts are shown below: \| \| \| --- \| \| Multiplicative comparison “I have 2 apples and Samantha has 10 apples. How many times more does Samantha have than I do?” 2 × ___ = 10 \| Additive comparison “I have 2 apples and Niyah has 10 apples. How many more apples does Niyah have than I do?” 2 + ___ = 10 \| In Grade 5, students should expand their concept of multiplication again to interpret multiplication as scaling. (5.NF.B.5) This occurs in the context of work with fractions, but as in Grade 4, the focus is still on how two quantities are related by an unknown factor. In both Grades 4 and 5, reasoning about multiplication strongly resembles later thinking around ratios. When we line up a few problems from each grade, we can see students making their way toward ratios through the years. \| \| \| Grade 3 Liam bought 5 bunches of bananas. Each bunch has exactly 5 bananas. How many bananas does Liam have? Mrs. Oro needs 90 corn seeds. The Garden Center sells corn seeds in packs of 10 seeds each. Write a division equation showing how many packs of seeds Mrs. Oro should buy. (Source: “Introducing Multiplication and Division Unit Plan” by Student Achievement Partners is licensed under CC 0 1.0.) ➔ With multiplication and division problems like these, students use the ideas of multiplication as equal groups and division as an unknown factor. These are the foundation for all future work involving multiplication and division, including ratios. \| \| \| \| Grade 4 The Turner family uses 548 liters of water per day. The Hill family uses 3 times as much water per day. How much water does the Hill family use per day? How much water will they use per week? (Source: Grade 4, Module 3, Lesson 12 (teacher version) from EngageNY.org of the New York State Education Department is licensed under CC BY-NC-SA 3.0.) ➔ With multiplicative comparison problems like this one, students begin to reason about how two numbers might be related by a certain factor. They’ll use similar reasoning to scale numbers up and down by fractional factors in Grade 5 and to find equivalent ratios in Grade 6. \| \| \| \| Grade 5 A company uses a sketch to plan an advertisement on the side of a building. The lettering on the sketch is 3/4 inch tall. In the actual advertisement, the letters must be 34 times as tall. How tall will the letters be on the building? (Source: Grade 5, Module 4, Lesson 22 (teacher version) from EngageNY.org of the New York State Education Department is licensed under CC BY-NC-SA 3.0.) ➔ In this problem, we see students doing much the same thing as in Grade 4, only now their work involves fractions. The notion of scaling a quantity up or down will help when students solve problems with equivalent ratios in Grade 6. \| Grades 3-5: Fractions Though ratios are not fractions (ratios are mathematical relationships, and fractions are numbers), they’re certainly related: A complete understanding of unit rates, for example, requires knowledge of fractions.6 If you want to learn more about the differences between ratios and fractions (and why they matter), check out this article from the Strategic Education Research Partnership. If you want to learn more about the differences between ratios and fractions (and why they matter), check out this article from the Strategic Education Research Partnership. And there are other similarities: Equivalent ratios behave a lot like equivalent fractions, so students with substantial fraction experience will probably feel more comfortable around ratios. The standards formalize the concept of a fraction for the first time in Grade 3, when they’re identified in two ways: as part of a whole (3.NF.A.1) and as a number on the number line. (3.NF.A.2) In Grade 4, fractions develop into compositions of other, same-sized fractions (for example, students should see 1 2/3 as 1 + 2/3 or 3/3 + 2/3), allowing students to begin adding and subtracting fractions. (4.NF.B.3) Decimals are also introduced as “decimal fractions”—a special way of writing fractions with base-ten denominators. (4.NF.C.6) By Grade 5, students should see fractions as expressions of division, (5.NF.B.3) and should be able to fluently add, subtract, (5.NF.A.1) and to multiply them. (5.NF.B.4) (Only in Grade 6 are students required to completely master division of fractions by fractions (6.NS.A.1) and operations with multidigit decimals. (6.NS.B.3)) Lining up some example problems as we did before, we can see how the Standards prepare students to work with unit rates by Grade 6. \| \| \| Grade 3 Use the fractional units on the left to count up on the number line. Label the missing fractions on the blanks. (Source: Grade 3, Module 5, Lesson 21 (teacher version) from EngageNY.org of the New York State Education Department is licensed under CC BY-NC-SA 3.0.) ➔ As they begin work with fractions, students use the number line (along with other representations) to show how fractions are composed of unit fractions. (In this diagram, for example, they can see that 3/4 is composed of 3 intervals that are each 1/4 long.) They also begin to understand the ideas behind fraction equivalence by dividing the number line in different ways. \| \| \| \| Grade 4 Draw a number bond and write a number sentence to match the tape diagram. (Source: Grade 4, Module 5, Lesson 1 (teacher version) from EngageNY.org of the New York State Education Department is licensed under CC BY-NC-SA 3.0.) ➔ With problems like this, Grade 4 students learn to see fractions as sums of other fractions with the same unit size (in this example, 4/5 = 1/5 + 3/5). This will help them to develop methods for adding and subtracting fractions, and later, to understand multiplication of fractions by whole numbers. \| \| \| \| Grade 5 Carly and Gina read the following problem in their math class. Seven cereal bars were shared equally by 3 children. How much did each child receive? Carly and Gina solve the problem differently. Carly gives each child 2 whole cereal bars, and then divides the remaining cereal bar among the 3 children. Gina divides all the cereal bars into thirds and shares the thirds equally among the 3 children. a. Illustrate both girls’ solutions. b. Explain why they are both right. (Source: Grade 5, Module 4, Lesson 2 (teacher version) from EngageNY.org of the New York State Education Department is licensed under CC BY-NC-SA 3.0.) ➔ In this problem, students are asked to interpret the fraction 7/3 in two different ways. Notice the phrase “for each” in the question; this is basically a unit rate problem. Solving problems like this prepares students for a formal understanding of unit rates in Grade 6. \| Grades 3-5: Arithmetic patterns Students are also expected to work with arithmetic patterns in the elementary grades. In Grade 3, they look for and explain certain patterns in the multiplication table—noticing, for example, that every other number in the 2 sequence is a number in the 4 sequence. (3.OA.D.9) In Grade 4, this type of thinking should extend to other patterns outside of the multiplication table. (4.OA.C.5) And in Grade 5, they further their understanding by generating two arithmetic sequences, explaining the relationships between them, and plotting them on the coordinate plane. (5.OA.B.3) This sequence of problems shows how the standards build a foundation in number patterns that students can use when approaching ratios. \| \| \| Grade 3 The table shows products of the whole numbers 1 through 6. (a) Color all of the even products in the table. (b) Sometimes there are even numbers next to each other in the table. However, there are never odd numbers next to each other. Why is this true? (Source: “Patterns in the Multiplication Table” by Illustrative Mathematics is licensed under CC BY 4.0.) \| \| \| \| Grade 4 a. Starting with 9, list the first 10 multiples of 9. b. In the list in part (a), what patterns do you see with the digits in the 10's place? What patterns do you see with the digits in the 1's place? c. Using pictures, words or equations, explain the patterns you observed in part (b). (Source: “Multiples of Nine” by Illustrative Mathematics is licensed under CC BY 4.0.) \| \| \| \| Grade 5 Create a table of 3 values for x and y such that each y-coordinate is 3 more than the corresponding x-coordinate. (a) Plot each point on the coordinate plane. (b) Use a straightedge to draw a line connecting these points. (c) Give the coordinates of 2 other points that fall on this line with x-coordinates greater than 12. Source: Grade 5, Module 6, Lesson 8 (teacher version) from EngageNY.org of the New York State Education Department is licensed under CC BY-NC-SA 3.0. \| Ratios represent a capstone of this sequence, in that students are consolidating their ideas of multiplication, division and patterns into the concept of a ratio. When approaching ratios for the first time, it may help to present students with problems that result in two rows of a multiplication table. For example, a drink recipe requiring 2 cups of cranberry juice for every 5 cups of apple juice gives students two very familiar sequences, which can help them begin to understand ratios as multiplicative comparisons. Suggestions for students who are below grade level Adapting curriculum requires information, acquired via assessment, about what your students already know and can do, as well as what gaps in learning they may have. If, going into a unit on ratios, you know your students don’t have a solid grasp of the ideas named above (or haven’t encountered them at all), what can you do? It’s not practical (or even desirable) to reteach everything students should have learned in Grades 3-5; there’s plenty of new material in Grade 6, so the focus needs to be on grade-level standards. At the same time, there are strategic ways of wrapping up “unfinished learning” from prior grades and honing essential fluencies within a unit on ratios. Here are a few ideas for adapting your instruction to bridge the gaps students might have in the progressions outlined above. If a significant number of students don’t understand the notion of multiplicative comparison, you could plan a lesson or two on that idea before starting work with ratios. (This Grade 4 lesson, which includes several multiplicative comparison problems, might be helpful.) And if you think an entire lesson is too much, but your students could still use some review, you could create 2-3 multiplicative comparison problems as “warm-ups” to start your first few lessons on ratios. If a significant number of students don’t understand fractions as division, you could likewise plan a lesson or two on that before introducing rates. (This Grade 5 lesson, which involves some “for each” problems that lead nicely into unit rates, is one possible starting point.) Again, if you think that an entire lesson is too much, you could use some problems involving this idea as warm-ups for your first few rate lessons. If a significant number of students don’t understand the relationship between multiplication and division, you could plan a lesson or series of warm-ups on this idea. (This Grade 3 lesson offers some ideas of the types of models and problems you might use, and this Grade 4 lesson has some more advanced division problems that may be appropriate for older students.) If a significant number of students don’t understand the concept of equivalent fractions, or can’t fluently perform the procedures to find equivalent fractions, you could plan review lessons or a series of warm-ups on those topics. (This Grade 4 lesson might be a good place to start.) For students who lack fluency with multiplication and division facts, consider incorporating drills on these facts into your weekly routine. These can be fast-paced and joyful, and as students achieve improved fact fluency, they’ll be better able to perform the calculations involved in ratio problems. (For an example of this type of activity, see the instructions for a “sprint” on pages 11-13 of this document, as well as the sprint handout on pages 58-59 of this Grade 4 lesson plan.) Podcast clip: Coherence with Ratios in Grade 6 with Andrew Chen and Peter Coe (start 26:20, end 30:31) Beyond Grade 6: What’s next with ratios? Grades 7-8: Proportional relationships, linear equations and functions So how will students use their knowledge of ratios after Grade 6? This is an important question, because the answer defines the limits of instruction in Grade 6 and explains why it’s important to focus on a small number of essential concepts there. At the same time, knowing the next steps in the journey can help us focus our lessons on the knowledge and skills that matter most. Let’s recap, then: By the end of Grade 6, students should have a firm grasp of the concepts of ratio and rate, and should have extensive experience with a variety of ratio problems (including percents and measurement conversions, which they should see through the lens of ratio reasoning). From there, students move to Grade 7, where a few new things happen. First, ratio and rate problems get more challenging: Students will find unit rates of fractional quantities (7.RP.A.1) and will work on solving more complicated, multistep ratio and percent problems. (7.RP.A.3) Second, their concept of equivalent ratios will evolve into an understanding of proportional relationships, and students will explore these relationships through various representations. (7.RP.A.2.A) And third, the content the Ratios & Proportional Relationships and Expressions & Equations domains, which looked fairly distinct in Grade 6, will start to come together. (7.RP.A.2.C) In Grade 8, there is no separate group of standards for ratios and proportional relationships; these ideas merge completely with the algebra content in the Expressions & Equations domain and the Functions domain. The concept of unit rate evolves into slope, (8.EE.B.5) and students will discover important properties of slope. They explore the connection between proportional relationships (i.e. can be represented by an equation y = mx) and linear equations more generally (y = mx + b). (8.EE.B.6) And after being formally introduced to the concept of a function, students will model linear relationships with functions. (8.F.B.4) Students will rely on these concepts throughout high school and, in many cases, in post-secondary work as well. These are only brief summaries of the content in each grade, but hopefully they show how critical the learning in Grade 6 is to everything that follows. If students don’t have the time to develop deep conceptual understanding of ratios and unit rates in Grade 6, for example, the multistep problems that come in Grade 7 will be much more difficult. To highlight the limits of the expectations for each grade, as well as to show how each grade’s content depends on what came before, let’s take a look at one last progression of problems. \| \| \| Grade 6 Suppose you own a restaurant. You want to do some advertising, so you hire 2 students to deliver takeout menus around town. One student, Darla, delivers 350 menus in 2 hours, and another student, Drew, delivers 510 menus in 3 hours. You promise a $10 bonus to the fastest worker since time is money in the restaurant business. Who gets the bonus? (Source: Grade 6, Module 1, Lesson 23 (teacher version) from EngageNY.org of the New York State Education Department is licensed under CC BY-NC-SA 3.0.) ➔This is a relatively straightforward rate problem such as we’ve seen before in this guide. Notice the use of whole numbers: Non-complex fractions are not required in Grade 6. \| \| \| \| Grade 7 Anthony’s mother is making birthday cupcakes for 12 friends at daycare. The recipe calls for 3 1/3 cups of flour. This recipe makes 2 1/2 dozen cupcakes. Anthony’s mother has only 1 cup of flour. Is there enough flour for each of his friends to get a cupcake? (Source: Grade 7, Module 1, Lesson 11 (teacher version) from EngageNY.org of the New York State Education Department is licensed under CC BY-NC-SA 3.0.) ➔ This problem illustrates the additional layer of computational difficulty in Grade 7 work with rates: Now students are working with complex fractions. \| \| \| \| Grade 8 The information in the table below shows the function of time in minutes with respect to mowing an area of lawn in square feet. Write a function rule that describes the area in square feet mowed, y, in x minutes. Then use your function rule to find the area of lawn that can be mowed in 24 minutes. (Source: Grade 8, Module 5, Lesson 3 (teacher version) from EngageNY.org of the New York State Education Department is licensed under CC BY-NC-SA 3.0.) ➔ This problem is representative of Grade 8 work with linear functions, which relies on understandings of proportional relationships from Grades 6 and 7. Here, students aren’t just finding a unit rate, but using that rate to build a function that models the situation. \| If you’ve just finished this entire guide, congratulations! Hopefully it’s been informative, and you can return to it as a reference when planning lessons, creating units, or evaluating instructional materials. For more guides in this series, please visit our Enhance Instruction page. For more ideas of how you might use these guides in your daily practice, please visit our Frequently Asked Questions page. And if you’re interested in learning more about Ratios & Proportional Relationships in Grade 6, don’t forget these resources: Student Achievement Partners: Focus in Grade 6 Draft 6-7 Progression on Ratios and Proportional Relationships EngageNY: Grade 6 Module 1 Materials Illustrative Mathematics Grade 6 Tasks Endnotes In this series, major clusters are denoted by a ▉. For more information on the major work of Grade 6, see the Student Achievement Partners guide Focus in Grade 6. Much of the information in this section is taken from the Draft 6-7 Progression on Ratios and Proportional Relationships, one of a series of papers that describes the big ideas behind the standards and how those ideas fit together. If you’re interested in learning more about ratios and proportional relationships, it’s a good resource. While “for every” will eventually take on a more widely applicable meaning in higher level math, in Grade 6, when used in a context associating two quantities, it is an indicator of a ratio relationship. You can read the full text of the Standards for Mathematical Practice here. The idea that standards relate strongly to one another is known as coherence, and is a distinctive feature of the Common Core State Standards for Mathematics. If you’re interested in exploring more of the connections between standards, you might want to try the Student Achievement Partners Coherence Map web app. If you want to learn more about the differences between ratios and fractions (and why they matter), check out this article from the Strategic Education Research Partnership. FAQs 1. What is a Content Guide? In our work with high academic standards, we often hear educators ask, “What does standards-aligned instruction look like?” Our Content Guides aim to answer this question by providing an in-depth look at one or a few clusters of math standards at a time. The Content Guides are grade-level and content area-specific, and there are guides for each grade or course, from Kindergarten to Algebra II. If you want to learn more about teaching Ratios and Proportional Relationships in Grade 6, for example,our associated Content Guide will give you a comprehensive but accessible explanation about these standards, multiple Open Educational Resource (OER) examples that are aligned to the standards, and concrete suggestions to support the teaching of Grade 6 ratios and proportional reasoning. Our goal in creating the Content Guides has been to provide busy teachers with a practical and easy-to-read resource on what the grade-level math standards are saying, along with examples of instructional materials that support conceptual understanding, problem-solving, and procedural skill and fluency for students. It’s important to note that content guides are not meant to serve as a curriculum (or any kind of student-facing document), a guide or source material for test-preparation activities, or any kind of teacher evaluation tool. 2. What’s in a Content Guide? Each Content Guide is focused on a specific group of standards. Most Content Guides follow the same three-part structure: Part 1 makes clear the student skills and understandings described by this group of standards. This section illustrates the standards using multiple student tasks from freely available online sources. Teachers can use or adapt these tasks for their students. Part 2 explains how this group of standards is connected to other standards in the same grade. We highlight how these connections have implications for planning and teaching, and how this within-grade coherence can increase access for students. Part 2 also includes multiple student tasks from freely available online sources. Part 3 traces selected progressions of learning leading to grade-level content discussed in the specific Content Guide. This discussion segues into a series of concrete and practical suggestions for how teachers can leverage the progressions to teach students who may not be prepared for grade-level mathematics. Finally, Part 3 traces the progression to content in higher grades. 3. How can I use the Content Guides? Teachers who have read our Content Guides say they see benefits for all educators. Here are some suggestions for how different educators might use them. Teachers can use the Mathematics Content Guides to: Increase or refresh their knowledge of the standards and the expectations for what students should know by the end of the year. Adapt lessons and units using appropriate pre-requisites to support students who are behind grade-level. Gain access to the best available OER for math to use for introducing and/or reinforcing concepts Ensure their curriculum and/or units: Focus on the major work of the grade and the appropriate depth of each standard. Target the appropriate aspects of rigor—procedural skill and fluency, modeling and application, and conceptual understanding described by the standards. Help students make coherent connections within and across grades. Create or revise their lessons and questioning to focus on important concepts in the standards. Instructional coaches and school leaders can use the Mathematics Content Guides to: Refresh or increase their knowledge of the standards and the expectations for what students should know by the end of the year. Develop and communicate consistent expectations for lesson planning and instruction aligned to the standards. Provide a reference when planning and/or discussing instruction with teachers. Gain insight into what instruction and student work should look like in order to meet the demands of the standards. Develop and design content and standards-driven professional development sessions/workshops. Foster content rich, standards-based discussions among staff and build staff knowledge. Develop and/or revise school improvement plans in order to support and incorporate content and practice-based teaching and learning. 4. Why the Content Guides? The transition to higher standards has led teachers all over the country to make significant changes in their planning and instruction, but only one-third of teachers feel they are prepared to help their students pass the more rigorous standards-aligned assessments (Kane et.al., 2016). This is to be expected because the new high standards are a significant departure from prior standards. The standards require a deeper level of understanding of the math content they teach; a different progression of what students need to learn by which grade; as well as different pedagogy that emphasizes student conceptual understanding, problem solving and procedural fluency in equal intensity. The support for teachers to bring high standards to their classrooms, however, has lagged behind. Research shows that teacher training in the U.S. is currently insufficient in preparing teachers to teach the demanding new standards (Center for Research in Mathematics and Science Education, 2010). And though some resources exist that “unpack” the standards, few, if any, explain and illustrate the standards. “Unpacking” the standards one by one can also result in a disjointed presentation that neglects the structure and coherence of the standards. In creating the Content Guides, we aimed to provide busy teachers with a practical, easy-to-read resource on their grade-specific standards and how to help all students learn them. There is ample empirical evidence that when teachers have both strong knowledge of the math content that they teach, and the pedagogical knowledge to help students master that content knowledge, their students learn more (Baumert et. al., 2010; Hill, Rowan and Ball, 2005; Rockoff et. al., 2008). With the Content Guides in hand, we hope that teachers will find more success in helping their students make progress toward college- and career-readiness. 5. What is the relationship between the Content Guides and the Progressions? The Progressions documents describe the grade-to-grade development of understanding of mathematics. These were informed by research on children’s cognitive development as well as the logical structure of mathematics. The Progressions explain why standards are sequenced the way they are. The Content Guides often highlight key ideas from the Progressions, but do not add new standards or change the expectations of what students should know and be able to do; they aim to explain and illustrate a group of standards at a time using freely available online sources. While the OER tasks and lessons in the Content Guides are one way to meet the grade-level standards, they are not the only means for doing so. 6. How were the resources selected? We selected sample tasks and lessons from freely available online sources such as EngageNY, Illustrative Mathematics and Student Achievement Partners to illustrate the Standards. These sources are chosen because they are fully aligned to the new high standards based on national review of K-12 curricula or are created by organizations led by the writers of the new high standards. In addition, because they are open educational resources (OER), they are freely accessible for all uses. All UnboundEd materials are also OER, as part of our commitment to make high-quality, highly aligned content available to all educators. 7. Why are the Content Guides only about a few standards? Where are the rest of the standards? Each Content Guide addresses a subset of the standards for the grade. The standards addressed in the first set of Content Guides for each grade usually address high-priority content; these standards are also often a good choice for teaching at the beginning of the year. More information about the selection of standards can be found in the introduction to each Content Guide. Over time, we will develop additional Content Guides for each grade and update existing ones. We plan to have four Content Guides for each grade or course, from Kindergarten to Algebra II. The guides will be published in waves, with each wave consisting of one guide for each grade. We plan to release a second set of Content Guides for each grade by the end of the 2016-17 school year. 8. How do I stay informed about new Content Guides? If you would like to receive updates on content and events from UnboundEd, including new Content Guides, please sign up for UnboundEd announcements here. Understand ratio concepts and use ratio reasoning to solve problems. Understand ratio concepts and use ratio reasoning to solve problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. Solve unit rate problems including those involving unit pricing and constant speed. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. Solve unit rate problems including those involving unit pricing and constant speed. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. Look for and make use of structure. Model with mathematics. Reason abstractly and quantitatively. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Write, read, and evaluate expressions in which letters stand for numbers. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. Represent proportional relationships by equations. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. Interpret multiplication as scaling (resizing), by: Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. Understand a fraction as a number on the number line; represent fractions on a number line diagram. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. Use decimal notation for fractions with denominators 10 or 100. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. Use proportional relationships to solve multistep ratio and percent problems. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Represent proportional relationships by equations. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
13209	https://mathoverflow.net/questions/366572/diophantine-equation-of-a-factorial-type	nt.number theory - Diophantine equation of a factorial type - MathOverflow Join MathOverflow By clicking “Sign up”, you agree to our terms of service and acknowledge you have read our privacy policy. Sign up with Google OR Email Password Sign up Already have an account? Log in Skip to main content Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Visit Stack Exchange Loading… Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company, and our products current community MathOverflow helpchat MathOverflow Meta your communities Sign up or log in to customize your list. more stack exchange communities company blog Log in Sign up Home Questions Unanswered AI Assist Labs Tags Chat Users Hang on, you can't upvote just yet. You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation and how do I get it? Instead, you can save this post to reference later. Save this post for later Not now Thanks for your vote! You now have 5 free votes weekly. Free votes count toward the total vote score does not give reputation to the author Continue to help good content that is interesting, well-researched, and useful, rise to the top! To gain full voting privileges, earn reputation. Got it!Go to help center to learn more Diophantine equation of a factorial type Ask Question Asked 5 years, 2 months ago Modified5 years, 2 months ago Viewed 342 times This question shows research effort; it is useful and clear 2 Save this question. Show activity on this post. I'm interested in nontrivial solutions of Diophantine equations of the type a 2 b 3=c!(c−k)!a 2 b 3=c!(c−k)! For various values of k fixed, and of course a,b,c∈Z+a,b,c∈Z+ Does anyone have any insight into this type of equation or a good reference for further reading? My search is being swamped by irrelevant results. Edit: I changed n to c to emphasize that I am looking for a,b,c that solve this equation. Thus for k= 1, the equation becomes a 2 b 3=c a 2 b 3=c, which clearly has infinity many solutions. nt.number-theory reference-request Share Share a link to this question Copy linkCC BY-SA 4.0 Cite Improve this question Follow Follow this question to receive notifications edited Jul 25, 2020 at 21:14 G GG G asked Jul 25, 2020 at 20:23 G GG G 41 2 2 bronze badges 3 Look up Shorey Tijdeman and related on perfect powers of (products of) consecutive integers. It will get you a step closer, and most likely your results of interest will reference their work. Laishram has related material as well. Gerhard "Is Researching Sylvester And Schur" Paseman, 2020.07.25.Gerhard Paseman –Gerhard Paseman 2020-07-25 20:58:23 +00:00 Commented Jul 25, 2020 at 20:58 @Gerhard squarefull is far from perfect power, so it's not clear to me how much closer Shorey & Tijdeman will get us.Gerry Myerson –Gerry Myerson 2020-07-26 01:04:05 +00:00 Commented Jul 26, 2020 at 1:04 No, but if anyone has published on this problem recently, I can't think of any other paper they would reference. Gerhard "Maybe You Know Of One?" Paseman, 2020.07.25.Gerhard Paseman –Gerhard Paseman 2020-07-26 01:29:40 +00:00 Commented Jul 26, 2020 at 1:29 Add a comment\| 3 Answers 3 Sorted by: Reset to default This answer is useful 3 Save this answer. Show activity on this post. You may already know this, but numbers of the form a 2 b 3 a 2 b 3 are called powerful numbers. A closely related question that might provide information on your question is to ask for binomial coefficients that are powerful. A Google search of "powerful number" and "binomial coefficient" brought up the following paper of Granville: On the scarcity of powerful binomial coefficients Andrew Granville He proves that there are only finitely many powerful binomial coefficients, contingent on the abc conjecture. Share Share a link to this answer Copy linkCC BY-SA 4.0 Cite Improve this answer Follow Follow this answer to receive notifications answered Jul 25, 2020 at 21:03 Joe SilvermanJoe Silverman 48.2k 2 2 gold badges 154 154 silver badges 249 249 bronze badges 4 Is there literature on consecutive powerful numbers, or intervals containing many powerful numbers? Gerhard "Are Numbers More Powerful Together?" Paseman, 2020.07.25.Gerhard Paseman –Gerhard Paseman 2020-07-25 21:10:06 +00:00 Commented Jul 25, 2020 at 21:10 @GerhardPaseman Here's a reference with some information on that question: POWERFUL NUMBERS IN SHORT INTERVALS, JEAN-MARIE DE KONINCK, FLORIAN LUCA AND IGOR E. SHPARLINSKI, BULL. AUSTRAL. MATH. SOC. 71 (2005)Joe Silverman –Joe Silverman 2020-07-25 22:20:06 +00:00 Commented Jul 25, 2020 at 22:20 It is conjectured that there are never three consecutive powerful numbers.Gerry Myerson –Gerry Myerson 2020-07-26 01:09:37 +00:00 Commented Jul 26, 2020 at 1:09 Thanks for the help. This is exactly the type of thing I was looking for.G G –G G 2020-07-27 02:58:01 +00:00 Commented Jul 27, 2020 at 2:58 Add a comment\| This answer is useful 1 Save this answer. Show activity on this post. You might be interested in extensions to the Sylvester Schur theorem, which by your constraints shows that c is bigger than k^2 as the set of consecutive integers in the product must have a single multiple of q^2 for some prime q bigger than k. A paper of Saradha and Shorey from 2003, Almost Squares and Factorizations in Consecutive Integers, shows the sparsity of solutions to your equation where k-1 of the numbers on the right hand side multiply to a square. This may be useful for you in a citation search . Gerhard "Not Quite Almost Powerful Numbers" Paseman, 2020.07.25. Share Share a link to this answer Copy linkCC BY-SA 4.0 Cite Improve this answer Follow Follow this answer to receive notifications edited Jul 25, 2020 at 21:40 answered Jul 25, 2020 at 21:34 Gerhard PasemanGerhard Paseman 13.1k 3 3 gold badges 34 34 silver badges 64 64 bronze badges Add a comment\| This answer is useful 0 Save this answer. Show activity on this post. The smallest interesting case of k=2 k=2 reduces to a family of Pell equations paramaterized by b b: (2 c−1)2−b 3(2 a)2=1.(2 c−1)2−b 3(2 a)2=1. This gives infinitely many solutions. For example, for b=2 b=2, we have a series of solutions indexed by n n: c n+a n 8–√=(17+6 8–√)n+1 2.c n+a n 8=(17+6 8)n+1 2. Numerical values of c n c n are listed in OEIS A055792. Share Share a link to this answer Copy linkCC BY-SA 4.0 Cite Improve this answer Follow Follow this answer to receive notifications answered Jul 26, 2020 at 0:24 Max AlekseyevMax Alekseyev 38k 5 5 gold badges 83 83 silver badges 165 165 bronze badges 3 Also, given powerful numbers m and m+1, we have 4m(m+1) and (2m+1)^2 also powerful. Gerhard "Finally Remembered That Contest Problem" Paseman, 2020.07.25.Gerhard Paseman –Gerhard Paseman 2020-07-26 00:36:56 +00:00 Commented Jul 26, 2020 at 0:36 @Gerhard, yes, where the trick is finding consecutive powerful numbers. Numbers n n such that n n and n+1 n+1 are both powerful are tabulated at oeis.org/A060355Gerry Myerson –Gerry Myerson 2020-07-26 01:05:24 +00:00 Commented Jul 26, 2020 at 1:05 Ah. So you know about 2527 and 2626 already. Gerhard "No More Element Of Surprise" Paseman, 2020.07.25.Gerhard Paseman –Gerhard Paseman 2020-07-26 01:25:28 +00:00 Commented Jul 26, 2020 at 1:25 Add a comment\| You must log in to answer this question. 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13210	https://math.libretexts.org/Bookshelves/Differential_Equations/Differential_Equations_for_Engineers_(Lebl)/7%3A_Power_series_methods/7.3%3A_Singular_Points_and_the_Method_of_Frobenius	7.3.1 7.3.2 7.3.3 7.3.1 7.3.1 7.3.2 7.3.4 Skip to main content 7.3: Singular Points and the Method of Frobenius Last updated : Feb 23, 2025 Save as PDF 7.2: Series Solutions of Linear Second Order ODEs 7.E: Power series methods (Exercises) Page ID : 359 Jiří Lebl Oklahoma State University ( \newcommand{\kernel}{\mathrm{null}\,}) Examples While behavior of ODEs at singular points is more complicated, certain singular points are not especially difficult to solve. Let us look at some examples before giving a general method. We may be lucky and obtain a power series solution using the method of the previous section, but in general we may have to try other things. Example 7.3.17.3.1 Let us first look at a simple first order equation 2xy′−y=0. 2xy′−y=0.(7.3.1) Note that x=0x=0 is a singular point. If we only try to plug in y=∞∑k=0akxk, y=∑k=0∞akxk,(7.3.2) we obtain 0=2xy′−y=2x(∞∑k=1kakxk−1)−(∞∑k=0akxk)=a0+∞∑k=1(2kak−ak)xk. 0=2xy′−y=2x(∑k=1∞kakxk−1)−(∑k=0∞akxk)=a0+∑k=1∞(2kak−ak)xk.(7.3.3) First, a0=0a0=0. Next, the only way to solve 0=2kak−ak=(2k−1)ak0=2kak−ak=(2k−1)ak for k=1,2,3,…k=1,2,3,… is for ak=0ak=0 for all kk. Therefore we only get the trivial solution y=0y=0. We need a nonzero solution to get the general solution. Let us try y=xry=xr for some real number rr. Consequently our solution---if we can find one---may only make sense for positive xx. Then y′=rxr−1y′=rxr−1. So 0=2xy′−y=2xrxr−1−xr=(2r−1)xr. 0=2xy′−y=2xrxr−1−xr=(2r−1)xr. Therefore r=12r=12, or in other words y=x1/2y=x1/2. Multiplying by a constant, the general solution for positive xx is y=Cx1/2. y=Cx1/2. If C≠0C≠0 then the derivative of the solution "blows up" at x=0x=0 (the singular point). There is only one solution that is differentiable at x=0x=0 and that's the trivial solution y=0y=0. Not every problem with a singular point has a solution of the form y=xry=xr, of course. But perhaps we can combine the methods. What we will do is to try a solution of the form y=xrf(x) y=xrf(x) where f(x)f(x) is an analytic function. Example 7.3.27.3.2 Suppose that we have the equation 4x2y″−4x2y′+(1−2x)y=0, 4x2y′′−4x2y′+(1−2x)y=0,(7.3.4) and again note that x=0x=0 is a singular point. Let us try y=xr∞∑k=0akxk=∞∑k=0akxk+r, y=xr∑k=0∞akxk=∑k=0∞akxk+r,(7.3.5) where rr is a real number, not necessarily an integer. Again if such a solution exists, it may only exist for positive xx. First let us find the derivatives y′=∞∑k=0(k+r)akxk+r−1,y″=∞∑k=0(k+r)(k+r−1)akxk+r−2. y′y′′=∑k=0∞(k+r)akxk+r−1,=∑k=0∞(k+r)(k+r−1)akxk+r−2.(7.3.6) Plugging Equations 7.3.57.3.5 - 7.3.67.3.6 into our original differential equation (Equation 7.3.47.3.4) we obtain 0=4x2y″−4x2y′+(1−2x)y=4x2(∞∑k=0(k+r)(k+r−1)akxk+r−2)−4x2(∞∑k=0(k+r)akxk+r−1)+(1−2x)(∞∑k=0akxk+r)=(∞∑k=04(k+r)(k+r−1)akxk+r)−(∞∑k=04(k+r)akxk+r+1)+(∞∑k=0akxk+r)−(∞∑k=02akxk+r+1)=(∞∑k=04(k+r)(k+r−1)akxk+r)−(∞∑k=14(k+r−1)ak−1xk+r)+(∞∑k=0akxk+r)−(∞∑k=12ak−1xk+r)=4r(r−1)a0xr+a0xr+∞∑k=1(4(k+r)(k+r−1)ak−4(k+r−1)ak−1+ak−2ak−1)xk+r=(4r(r−1)+1)a0xr+∞∑k=1((4(k+r)(k+r−1)+1)ak−(4(k+r−1)+2)ak−1)xk+r. 0=4x2y′′−4x2y′+(1−2x)y=4x2(∑k=0∞(k+r)(k+r−1)akxk+r−2)−4x2(∑k=0∞(k+r)akxk+r−1)+(1−2x)(∑k=0∞akxk+r)=(∑k=0∞4(k+r)(k+r−1)akxk+r)−(∑k=0∞4(k+r)akxk+r+1)+(∑k=0∞akxk+r)−(∑k=0∞2akxk+r+1)=(∑k=0∞4(k+r)(k+r−1)akxk+r)−(∑k=1∞4(k+r−1)ak−1xk+r)+(∑k=0∞akxk+r)−(∑k=1∞2ak−1xk+r)=4r(r−1)a0xr+a0xr+∑k=1∞(4(k+r)(k+r−1)ak−4(k+r−1)ak−1+ak−2ak−1)xk+r=(4r(r−1)+1)a0xr+∑k=1∞((4(k+r)(k+r−1)+1)ak−(4(k+r−1)+2)ak−1)xk+r.(7.3.7) To have a solution we must first have (4r(r−1)+1)a0=0(4r(r−1)+1)a0=0. Supposing that a0≠0 we obtain 4r(r−1)+1=0. This equation is called the indicial equation. This particular indicial equation has a double root at r=12. OK, so we know what r has to be. That knowledge we obtained simply by looking at the coefficient of xr. All other coefficients of xk+r also have to be zero so (4(k+r)(k+r−1)+1)ak−(4(k+r−1)+2)ak−1=0. If we plug in r=12 and solve for ak we get ak=4(k+12−1)+24(k+12)(k+12−1)+1ak−1=1kak−1. Let us set a0=1. Then a1=11a0=1,a2=12a1=12,a3=13a2=13⋅2,a4=14a3=14⋅3⋅2,… Extrapolating, we notice that ak=1k(k−1)(k−2)⋯3⋅2=1k!. In other words, y=∞∑k=0akxk+r=∞∑k=01k!xk+1/2=x1/2∞∑k=01k!xk=x1/2ex. That was lucky! In general, we will not be able to write the series in terms of elementary functions. We have one solution, let us call it y1=x1/2ex. But what about a second solution? If we want a general solution, we need two linearly independent solutions. Picking a0 to be a different constant only gets us a constant multiple of y1, and we do not have any other r to try; we only have one solution to the indicial equation. Well, there are powers of x floating around and we are taking derivatives, perhaps the logarithm (the antiderivative of x−1) is around as well. It turns out we want to try for another solution of the form y2=∞∑k=0bkxk+r+(lnx)y1, which in our case is y2=∞∑k=0bkxk+1/2+(lnx)x1/2ex. We now differentiate this equation, substitute into the differential equation and solve for bk. A long computation ensues and we obtain some recursion relation for bk. The reader can (and should) try this to obtain for example the first three terms b1=b0−1,b2=2b1−14,b3=6b2−118,… We then fix b0 and obtain a solution y2. Then we write the general solution as y=Ay1+By2. Method of Frobenius Before giving the general method, let us clarify when the method applies. Let p(x)y″+q(x)y′+r(x)y=0 be an ODE. As before, if p(x0)=0, then x0 is a singular point. If, furthermore, the limits limx→x0 (x−x0)q(x)p(x)andlimx→x0 (x−x0)2r(x)p(x) both exist and are finite, then we say that x0 is a regular singular point. Example 7.3.3: Expansion around a regular singular point Often, and for the rest of this section, x0=0. Consider x2y″+x(1+x)y′+(π+x2)y=0. Write limx→0 xq(x)p(x)=limx→0 xx(1+x)x2=limx→0 (1+x)=1,limx→0 x2r(x)p(x)=limx→0 x2(π+x2)x2=limx→0 (π+x2)=π. So x=0 is a regular singular point. On the other hand if we make the slight change x2y″+(1+x)y′+(π+x2)y=0, then limx→0 xq(x)p(x)=limx→0 x(1+x)x2=limx→0 1+xx=DNE. Here DNE stands for does not exist. The point 0 is a singular point, but not a regular singular point. Let us now discuss the general Method of Frobenius1. Let us only consider the method at the point x=0 for simplicity. The main idea is the following theorem. Theorem 7.3.1 Method of Frobenius Suppose that p(x)y″+q(x)y′+r(x)y=0 has a regular singular point at x=0, then there exists at least one solution of the form y=xr∞∑k=0akxk. A solution of this form is called a Frobenius-type solution. The method usually breaks down like this. We seek a Frobenius-type solution of the form y=∞∑k=0akxk+r.We plug this y into equation (7.3.9). We collect terms and write everything as a single series. The obtained series must be zero. Setting the first coefficient (usually the coefficient of xr) in the series to zero we obtain the indicial equation, which is a quadratic polynomial in r. If the indicial equation has two real roots r1 and r2 such that r1−r2 is not an integer, then we have two linearly independent Frobenius-type solutions. Using the first root, we plug in y1=xr1∞∑k=0akxk,and we solve for all ak to obtain the first solution. Then using the second root, we plug in y2=xr2∞∑k=0bkxk,and solve for all bk to obtain the second solution. If the indicial equation has a doubled root r, then there we find one solution y1=xr∞∑k=0akxk,and then we obtain a new solution by plugging y2=xr∞∑k=0bkxk+(lnx)y1,into Equation (7.3.9) and solving for the constants bk. If the indicial equation has two real roots such that r1−r2 is an integer, then one solution is y1=xr1∞∑k=0akxk,and the second linearly independent solution is of the form y2=xr2∞∑k=0bkxk+C(lnx)y1,where we plug y2 into (7.3.9) and solve for the constants bk and C. Finally, if the indicial equation has complex roots, then solving for ak in the solution y=xr1∞∑k=0akxkresults in a complex-valued function---all the ak are complex numbers. We obtain our two linearly independent solutions2 by taking the real and imaginary parts of y. The main idea is to find at least one Frobenius-type solution. If we are lucky and find two, we are done. If we only get one, we either use the ideas above or even a different method such as reduction of order (Exercise 2.1.8) to obtain a second solution. Bessel Functions An important class of functions that arises commonly in physics are the Bessel functions3. For example, these functions appear when solving the wave equation in two and three dimensions. First we have Bessel's equation of order p: x2y″+xy′+(x2−p2)y=0. We allow p to be any number, not just an integer, although integers and multiples of 12 are most important in applications. When we plug y=∞∑k=0akxk+r into Bessel's equation of order p we obtain the indicial equation r(r−1)+r−p2=(r−p)(r+p)=0. Therefore we obtain two roots r1=p and r2=−p. If p is not an integer following the method of Frobenius and setting a0=1, we obtain linearly independent solutions of the form y1=xp∞∑k=0(−1)kx2k22kk!(k+p)(k−1+p)⋯(2+p)(1+p),y2=x−p∞∑k=0(−1)kx2k22kk!(k−p)(k−1−p)⋯(2−p)(1−p). Exercise 7.3.1 Verify that the indicial equation of Bessel's equation of order p is (r−p)(r+p)=0. Suppose that p is not an integer. Carry out the computation to obtain the solutions y1 and y2 above. Bessel functions will be convenient constant multiples of y1 and y2. First we must define the gamma function Γ(x)=∫∞0tx−1e−tdt. Notice that Γ(1)=1. The gamma function also has a wonderful property Γ(x+1)=xΓ(x). From this property, one can show that Γ(n)=(n−1)! when n is an integer, so the gamma function is a continuous version of the factorial. We compute: Γ(k+p+1)=(k+p)(k−1+p)⋯(2+p)(1+p)Γ(1+p),Γ(k−p+1)=(k−p)(k−1−p)⋯(2−p)(1−p)Γ(1−p). Exercise 7.3.2 Verify the above identities using Γ(x+1)=xΓ(x). We define the Bessel functions of the first kind of order p and −p as Jp(x)=12pΓ(1+p)y1=∞∑k=0(−1)kk!Γ(k+p+1)(x2)2k+p,J−p(x)=12−Γ(1−p)y2=∞∑k=0(−1)kk!Γ(k−p+1)(x2)2k−p. As these are constant multiples of the solutions we found above, these are both solutions to Bessel's equation of order p. The constants are picked for convenience. When p is not an integer, Jp and J−p are linearly independent. When n is an integer we obtain Jn(x)=∞∑k=0(−1)kk!(k+n)!(x2)2k+n. In this case it turns out that Jn(x)=(−1)nJ−n(x), and so we do not obtain a second linearly independent solution. The other solution is the so-called Bessel function of second kind. These make sense only for integer orders n and are defined as limits of linear combinations of Jp(x) and J−p(x) as p approaches n in the following way: Yn(x)=limp→ncos(pπ)Jp(x)−J−p(x)sin(pπ). As each linear combination of Jp(x) and J−p(x) is a solution to Bessel's equation of order p, then as we take the limit as p goes to n, Yn(x) is a solution to Bessel's equation of order n. It also turns out that Yn(x) and Jn(x) are linearly independent. Therefore when n is an integer, we have the general solution to Bessel's equation of order n y=AJn(x)+BYn(x), for arbitrary constants A and B. Note that Yn(x) goes to negative infinity at x=0. Many mathematical software packages have these functions Jn(x) and Yn(x) defined, so they can be used just like say sin(x) and cos(x). In fact, they have some similar properties. For example, −J1(x) is a derivative of J0(x), and in general the derivative of Jn(x) can be written as a linear combination of Jn−1(x) and Jn+1(x). Furthermore, these functions oscillate, although they are not periodic. See Figure 7.3.1 for graphs of Bessel functions. Example 7.3.4: Using Bessel functions to Solve a ODE Other equations can sometimes be solved in terms of the Bessel functions. For example, given a positive constant λ, xy″+y′+λ2xy=0, can be changed to x2y″+xy′+λ2x2y=0. Then changing variables t=λx we obtain via chain rule the equation in y and t: t2y″+ty′+t2y=0, which can be recognized as Bessel's equation of order 0. Therefore the general solution is y(t)=AJ0(t)+BY0(t), or in terms of x: y=AJ0(λx)+BY0(λx). This equation comes up for example when finding fundamental modes of vibration of a circular drum, but we digress. Footnotes Named after the German mathematician Ferdinand Georg Frobenius (1849 – 1917). See Joseph L. Neuringera, The Frobenius method for complex roots of the indicial equation, International Journal of Mathematical Education in Science and Technology, Volume 9, Issue 1, 1978, 71–77. Named after the German astronomer and mathematician Friedrich Wilhelm Bessel (1784 – 1846). 7.2: Series Solutions of Linear Second Order ODEs 7.E: Power series methods (Exercises)
13211	https://www.thoughtco.com/military-dictatorship-definition-and-examples-5091896	What Is a Military Dictatorship? Definition and Examples A military dictatorship is a form of government in which the military holds most or all political power. Military dictatorships may be ruled by a single high-ranking military officer or by a group of such officers. Military dictatorships are notorious for human rights abuses and the denial of political and social freedoms. Key Takeaways Military Dictatorship Military Dictatorship Definition and Characteristics In a military dictatorship, military leaders exercise substantial or complete control of the people and functions of government. As an autocratic form of government, a military dictatorship may be ruled by either a single military strongman whose authority is unlimited or by a group of high-ranking military officers—a “military junta”—who can to some extent limit the dictator’s authority. During the 19th century, for example, many Latin American countries struggling to reorganize after being freed from Spanish colonial rule, allowed military dictators to take power. These charismatic self-proclaimed leaders, known as “caudillos,” usually led private guerilla armies that had won control of former Spanish-held territories before setting their sights on vulnerable national governments. In most cases, military dictatorships come to power after the previous civilian government has been overthrown in a coup d'etat. Typically, the military dictator completely dissolves the civilian government. Occasionally, components of the civilian government structure may be restored after the coup d'etat but are strictly controlled by the military. In Pakistan, for example, while a series of military dictators have sporadically staged elections, they have fallen far short of the UN’s definition of “free and fair.” The secrecy of the ballot has been regularly compromised and military authorities often denied the rights to freedom of expression, association, assembly, and movement. Along with the suspension or revocation of constitutional rights and freedoms, an almost universal characteristic of a military dictatorship is the imposition of martial law or a permanent state of national emergency intended to distract the people with a constant fear of attack. Military regimes typically disregard human rights and go to extremes to silence political opposition. Ironically, military dictators have often justified their rule as a way of protecting the people from “harmful” political ideologies. For example, the threat of communism or socialism was often used to justify military regimes in Latin America. Playing on the public assumption that the military is politically neutral, military dictatorships may attempt to portray themselves as the people’s “savior” from corrupt and exploitive civilian politicians. For example, many military juntas adopt titles such as Poland’s “National Liberation Committee” in the early 1980s, or Thailand’s current “Peace & Order Maintaining Council.” Since their oppressive style of rule often spawns public dissent, military dictatorships often go out the same way they came in—through an actual or imminent coup d'etat or popular revolt. Military Juntas A military junta is a coordinated group of high-ranking military officers who exercise authoritarian or totalitarian rule over a country after taking power by force. Meaning “meeting” or “committee,” the term junta was first used about the Spanish military leaders who resisted Napoleon’s invasion of Spain in 1808 and later about the groups that helped Latin America win independence from Spain between 1810 and 1825. Like military dictatorships, military juntas often take power through a coup d'etat. Unlike pure military dictatorships, in which the power of a single dictator or “military strongman” is unlimited, the officers of a military junta can limit the dictator’s power. Unlike military dictators, the leaders of military juntas may end martial law, wear civilian clothing, and appoint former military officers to maintain de-facto control over local governments and political parties. Rather than all functions of the national government, military juntas may choose to control a more limited range of areas, such as foreign policy or national security. Military vs. Civilian Dictatorships In contrast to a military dictatorship, a civilian dictatorship is a form of autocratic government that does not draw its power directly from the armed forces. Unlike military dictatorships, civilian dictatorships do not have built-in access to an organized base of support like an army. Instead, civilian dictators take and hold on to power by controlling a dominant political party and the electoral process or by winning fanatical levels of popular support. Rather than the threat of military force, charismatic civilian dictators use techniques like mass distribution of bombastic propaganda and psychological warfare to create cult-like feelings of support and nationalism among the people. Civilian dictatorships that depend on political domination tend to be longer-lasting than personalistic cult-supported dictatorships. Without the automatic support of the armed forces, civilian dictators are less likely than military dictators to involve the country in foreign wars and to be ousted by insurrection or revolt. Civilian dictatorships are also more likely to be replaced by democracies or constitutional monarchies than are military dictatorships. Examples of 20th Century Military Dictatorships Once common throughout Latin America, Africa, and the Middle East, the prevalence of military dictatorships has been declining since the early 1990s. With the collapse of the Soviet Union and the end of the Cold War, it became harder for military regimes to seize power by using the threat of communism to gain the support of powerful Western democracies like the United States. While Thailand remains the only country currently ruled by a military dictatorship, dozens of other countries have been under military rule at some point during the 20th century. Thailand On May 22, 2014, the caretaker government of Thailand was overthrown in a bloodless coup d'etat led by General Prayuth Chan-ocha, commander of the Royal Thai Army. Prayuth established a military junta, the National Council for Peace and Order (NCPO), to govern the country. The junta repealed the constitution, declared martial law, and banned all forms of political expression. In 2017, the NCPO issued an interim constitution granting itself almost total power and establishing a puppet legislature, which unanimously elected Prayuth prime minister. Brazil From 1964 to 1985, Brazil was controlled by an authoritarian military dictatorship. After taking power in a coup d'etat, commanders of the Brazilian Army, backed by anti-communist interests, including the United States, enacted a new constitution that restricted freedom of speech and outlawed political opposition. The military regime gained popular support by encouraging nationalism, promising economic growth, and rejecting communism. Brazil officially restored democracy in 1988. Chile On September 11, 1973, Chile’s socialist government of Salvador Allende was overthrown in a coup d'etat backed by the United States. Over the next 17 years, a military junta headed by General Augusto Pinochet orchestrated the most brutal period of human rights abuses in Chilean history. During what it called the “national reconstruction,” Pinochet’s regime outlawed political participation, executed over 3,000 suspected dissidents, tortured tens of thousands of political prisoners, and forced some 200,000 Chileans into exile. Although Chile returned to democracy in 1990, the people continue to suffer from the effects of Pinochet’s military dictatorship on political and economic life. Argentina After overthrowing President Isabel Perón in a coup d'etat on March 24, 1976, a junta of right-wing military officers ruled Argentina until democracy was restored in December 1983. Operating under the official name of the National Reorganization Process, the junta persecuted social minorities, imposed censorship, and placed all levels of government under military control. During Argentina’s so-called “Dirty War” period of military dictatorship, as many as 30,000 citizens were killed or “disappeared.” In 1985, five leaders of the former ruling military junta were convicted of crimes against humanity. Greece From 1967 to 1974, Greece was ruled by an extreme right-wing military dictatorship known as the Regime of the Colonels. On April 21, 1976, a group of four Greek Army colonels overthrew the caretaker government in a coup d'etat. In just the first week of its reign, the junta jailed, tortured, and exiled over 6,000 suspected political opponents in the name of protecting Greece from communism. Their actions were so swift and brutal that by September 1967 the European Commission of Human Rights had charged the Regime of the Colonels with multiple gross violations of human rights. Sources and Reference Follow Us
13212	https://pynative.com/python-weighted-random-choices-with-probability/	Python Programming Python weighted random choices to choose from the list with different probability This lesson demonstrates ways to choose single or multiple elements from the list randomly with a different probability. Use the random.choices() function to get the weighted random samples in Python. Also, See: Python random data generation Exercise Python random data generation Quiz Let’s take the following example for a better understanding of the requirement. ``` import random sampleList = [10, 20, 30, 40] x = random.choice(sampleList) print(x)Code language: Python (python) ``` If you execute the random.choice() in the above code, it will give you 10, 20, 30, or 40 with equal probability. But what if you want to pick the element from the list with a different probability. For example, choose a list of items from any sequence in such a way that each element has a different probability of being selected. In other words, choose 4 elements from the list randomly with different probabilities. For example: Choose 10 – 10% of the time Choose 20 – 25% of the time Choose 30 – 50% of the time Choose 40 – 15% of the time There are 2 ways to make weighted random choices in Python If you are using Python 3.6 or above then use the s Else, use a numpy.random.choice() We will see how to use both one by one. Table of contents random.choices() Syntax Relative weights to choose elements from the list with different probability Cumulative weights to choose items from the list with different probability Choose a single element form list with different probability Probability of getting 6 or more heads from 10 spins Generate weighted random numbers Points to remember before implementing weighted random choices Numpy’s random.choice() to choose elements from the list with different probability Next Steps random.choices() Python 3.6 introduced a new function random.choices() in the random module. By using the choices() function, we can make a weighted random choice with replacement. You can also call it a weighted random sample with replacement. Syntax Let’s have a look at the syntax of this function. random.choices(population, weights=None, , cum_weights=None, k=1) None None 1Code language: Python(python) It returns a k sized list of elements chosen from the population with replacement. Parameters population: It is is sequence or data structure from which you want to choose data. weights or cum_weights: Define the selection probability for each element. weights: If a weights sequence is specified, random selections are made according to the relative weights. cum_weights: Alternatively, if a cum_weights sequence is given, the random selections are made according to the cumulative weights. k: The number of samples you want from a population. Note: You cannot specify both weights and cum_weights at the same time. As mentioned above we can define weights sequence using the following two ways Relative weights Cumulative weights Relative weights to choose elements from the list with different probability First, define the probability for each element. If you specified the probability using the relative weight, the selections are made according to the relative weights. You can set relative weights using the weight parameter. Example: Choose 5 elements from the list with different probability ``` import random numberList = [111, 222, 333, 444, 555] print(random.choices(numberList, weights=(10, 20, 30, 40, 50), k=5)) Output [555, 222, 555, 222, 555]Code language: Python (python) ``` Note: As you can see in the output, we received an item ‘555‘ three times because we assigned the highest weight to it. So it has the highest probability to be selected Weights sum is not 100 because they’re relative weights, not percentages. The following rule determines the weighted probability of selecting each element. Probability = element_weight/ sum of all weightsCode language: Python(python) In the above example, the probability of occurring each element is determined is as follows ``` The total weight is 10+20+30+40+50 = 150 List is [111, 222, 333, 444, 555] It returns 111 with probability 0.66 (10/150) It returns 222 with probability 0.13 (20/150) It returns 333 with probability 0.20 (30/150) It returns 444 with probability 0.26 (40/150) It returns 555 with probability 0.33 (50/150) ``` Cumulative weights to choose items from the list with different probability To make selections according to the cumulative weights, use the cum_weights parameter. Note: Python converts the relative weights to cumulative weights before making selections. So, I suggest you pass cumulative weights to saves time and extra work. he cumulative weight of each element is determined by using the following formula. cum_weight= Weight of previous element + own weight For example, the relative weights [5, 10, 15, 20] are equivalent to the cumulative weights [5, 15, 30, 50]. Let’s see how to use cumulative weights to choose 4 elements from a list with different probability. ``` import random nameList = ["Kelly", "Scott", "Emma", "Jon"] print(random.choices(nameList, cum_weights=(5, 15, 30, 50), k=4)) Output ['Jon', 'Kelly', 'Jon', 'Scott']Code language: Python (python) ``` Choose a single element form list with different probability ``` import random names = ["Kelly", "Scott", "Emma", "Jon"] for i in range(3): item = random.choices(names, cum_weights=(5, 15, 30, 50), k=1) print("Iteration:", i, "Weighted Random choice is", item)Code language: Python (python) ``` Output: Iteration: 0 Weighted Random choice is Jon Iteration: 1 Weighted Random choice is Kelly Iteration: 2 Weighted Random choice is Jon Note: we got “Jon” 3 times in the result because it has the highest probability of being selected Probability of getting 6 or more heads from 10 spins Use the cumulative weights to set the probability of getting the head of a coin to 0.61, and the tail of a coin to 0.39 (1 – 0.61 = 0.39) ``` import random we specified head and tail of a coin in string coin = "HT" Execute 3 times to verify we are getting 6 or more heads in every 10 spins for i in range(3): print(random.choices(coin, cum_weights=(0.61, 1.00), k=10))Code language: Python (python) ``` Output: ['H', 'H', 'H', 'H', 'H', 'H', 'H', 'T', 'H', 'T'] ['H', 'T', 'H', 'H', 'H', 'T', 'H', 'H', 'H', 'H'] ['H', 'T', 'T', 'T', 'H', 'T', 'H', 'H', 'H', 'H'] Generate weighted random numbers Given a range of integers, we want to generate five random numbers based on the weight. We need to specify the probability/weight for each number to be selected. Let’s see how to generate random numbers with a given (numerical) distribution with different probability ``` import random Generate 6 random numbers from a given range with weighted probability numbers = random.choices(range(10, 40, 5), cum_weights=(5, 15, 10, 25, 40, 65), k=6) print(numbers) Output [35, 35, 15, 10, 35, 35]Code language: Python (python) ``` Points to remember before implementing weighted random choices If you don’t specify the relative or cumulative weight, the random.choices() will choose elements with equal probability. The specified weights sequence must be of the same length as the population sequence. Don’t specify relative weights and cumulative weight at the same time to avoid Type Error (TypeError: Cannot specify both weights and cumulative weights). You can specify The weights or cum_weights only as integers, floats, and fractions but excludes decimals. Weights must be non-negative. Numpy’s random.choice() to choose elements from the list with different probability If you are using Python version less than 3.6, you can use the NumPy library to make weighted random choices. Install numpy using a pip install numpy. Using a numpy.random.choice() you can specify the probability distribution. numpy.random.choice(a, size=None, replace=True, p=None) None True NoneCode language: Python(python) a: It is the population from which you want to choose elements. for example, list. size: It is nothing but the number of elements you want to choose. p: It Used to specify the probability for each element to be selected. Note: Probabilities must sum to 1, i.e., when you specify probability weights for each element, the sum of all weights must be 1. Example: ``` import numpy as np numberList = [100, 200, 300, 400] Choose elements with different probabilities sampleNumbers = np.random.choice(numberList, 4, p=[0.10, 0.20, 0.30, 0.40]) print(sampleNumbers) Output [300 200 300 300] Code language: Python (python) ``` Next Steps I want to hear from you. What do you think of this article? Or maybe I missed one of the ways to generate weighted random choices? Either way, let me know by leaving a comment below. Also, try to solve the following Free exercise and quiz to have a better understanding of working with random data in Python. Python random data generation Exercise Python random data generation Quiz Did you find this page helpful? Let others know about it. Sharing helps me continue to create free Python resources. TweetF sharein shareP Pin About Vishal I’m Vishal Hule, the Founder of PYnative.com. As a Python developer, I enjoy assisting students, developers, and learners. Follow me on Twitter. Related Tutorial Topics: Python Python Random Python Exercises and Quizzes Free coding exercises and quizzes cover Python basics, data structure, data analytics, and more. 15+ Topic-specific Exercises and Quizzes Each Exercise contains 10 questions Each Quiz contains 12-15 MCQ Exercises Quizzes Loading comments... Please wait.
13213	https://www.youtube.com/watch?v=HyjLaUmBxxw	1-Digit Multiplication: A Step-By-Step Review \| Multiplying by a 1-Digit Number \| Math with Mr. J Math with Mr. J 1700000 subscribers 434 likes Description 45311 views Posted: 28 Mar 2022 Welcome to 1-Digit Multiplication: A Step-By-Step Review (Multiplying by a 1-Digit Number) with Mr. J! Need a refresher on single digit multiplication? You're in the right place! Everyone needs a refresher from time to time, so this video is for you if you're looking for help with how to multiply by a 1-digit number. Mr. J will go through a 3-digit by 1-digit multiplication problem, a 4-digit by 1-digit multiplication problem, and explain the steps of multiplying by a 1-digit number. About Math with Mr. J: This channel offers instructional videos that are directly aligned with math standards. Teachers, parents/guardians, and students from around the world have used this channel to help with math content in many different ways. All material is absolutely free. Click Here to Subscribe to the Greatest Math Channel On Earth: Follow Mr. J on Twitter: @MrJMath5 Email: math5.mrj@gmail.com Music: Hopefully this video is what you're looking for when it comes to multiplying by a 1-digit number. Have a great rest of your day and thanks again for watching! ✌️✌️✌️ 53 comments Transcript: [Music] welcome to math with mr j [Music] in this video i'm going to go through a quick review of one digit multiplication if it's been a while and you need a quick refresher this should be helpful whether you're in high school college continuing your education as an adult helping with an assignment or maybe you just learned this recently and need a quick refresher really no matter where you're at here are a couple of examples to help you out let's jump into number one where we have 439 times seven now the first thing that we're going to do we're going to line this up vertically so we're going to rewrite it up and down so let's go below the problem here and we have 439 times seven now we can start multiplying and we start with the ones place so we have a 9 in the ones place we need to do 7 times 9 to start with 7 times 9 is 63 so let's write our 3 and then carry our 6 and then we work our way left so next would be the tens place so we have a three in the tens place seven times three is twenty-one and then we add that carried six so twenty-one plus six is twenty-seven let's put our seven and carry the two and then we have the hundreds place so a four is in the hundreds place seven times four is twenty-eight plus two is thirty so we can put our zero now there are no more places to the left so let's just bring our three down into the thousands place put our comma and our final answer is three thousand seventy three let's move on to number two and do another example for number two we have 2864 times five so let's rewrite this vertically 2864 times five start with the ones and then we will work our way left so we have a four in the ones place five times four is twenty let's put our zero carry the two then we have the tens place where we have a six five times six is thirty plus the carry two is thirty two carry our three then we have the hundreds where we have an eight so five times eight is forty plus three is forty three carry our four and then lastly we have the thousands where we have a two so five times two is ten plus that carried 4 is 14. so we'll put our 4 and then we do not have any more places to the left so we just bring our 1 straight down we have a comma here and our final answer is 14 hundred twenty so there you have it there's a quick review of one digit multiplication i hope that helped thanks so much for watching until next time peace you
13214	https://math-in-the-middle.com/wp-content/uploads/2015/09/Integers-Rules-Notes.pdf	Integer Operations Integer Addition Rules:  If the signs are alike, just add the numbers and make answer positive if both numbers are positive and negative if both are negative ex: 4 + 3 = 7 ex: -4 + (-3) = -7  If the signs are different, subtract the numbers and take sign of the larger number ex: 12 + (-3) = 9 ex: 3 + (-12) = -9 Integer Subtraction Rules:  Change the subtraction sign to addition and flip the sign of the number after the subtraction sign (if it was negative, make it positive & if it was positive, make it negative). Then just follow integer addition rules. ex: 5 – (-10) 5 + (+10) = 15 ex: 5 – 10 5 + (-10) = -5 Integer Multiplication Rules:  Positive · Positive = Positive ex: 5 · 4 = 20  Negative · Negative = Positive ex: -5 · (-4) = 20  Positive · Negative = Negative ex: 5 · (-4) = -20  Negative · Positive = Negative ex: -5 · 4 = -20 Integer Division Rules:  Positive  Positive = Positive ex: 36  4 = 9  Negative  Negative = Positive ex: -36  (-4) = 9  Positive  Negative = Negative ex: 36  (-4) = -9  Negative  Positive = Negative ex: -36  4 = -9
13215	https://nyheritage.contentdm.oclc.org/digital/collection/p15281coll10/id/1010/	New York Heritage Digital Collections - New York Heritage Digital Collections Skip to main content ### Collections ### Organizations ### Exhibits ### About Advanced Search Loading... Collections Organizations Exhibits About Powered by CONTENTdm®
13216	https://lib.zu.edu.pk/ebookdata/Dentistry/BDS%202nd%20Year%20Books/Craig%E2%80%99s%20Restorative%20Dental%20Materials%2014th%20Edition.pdf	FOURTEENTH EDITION EDITED BY Ronald Sakaguchi, DDS, MS, PhD, MBA Professor, Division of Management School of Medicine Professor, Division of Biomaterials and Biomechanics Department of Restorative Dentistry School of Dentistry Oregon Health & Science University Portland, OR Jack Ferracane, PhD Professor and Chair, Department of Restorative Dentistry Division Director, Biomaterials and Biomechanics School of Dentistry Oregon Health & Science University Portland, OR John Powers, PhD Senior Vice President, Dental Consultants, Inc. (publisher of The Dental Advisor) Ann Arbor, MI Clinical Professor of Oral Biomaterials Department of Restorative Dentistry and Prosthodontics UTHealth School of Dentistry The University of Texas Health Science Center at Houston Houston, TX Craig’s RESTORATIVE DENTAL MATERIALS 3251 Riverport Lane St. Louis, Missouri 63043 CRAIG’S RESTORATIVE DENTAL MATERIALS, FOURTEENTH EDITION ISBN: 978-0-323-47821-2 Copyright © 2019 by Elsevier, Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further infor-mation about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treat-ment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evalu-ating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. With respect to any drug or pharmaceutical products identified, readers are advised to check the most current information provided (i) on procedures featured or (ii) by the manufacturer of each product to be administered, to verify the recommended dose or formula, the method and duration of administration, and contraindications. It is the responsibility of practitioners, relying on their own experience and knowledge of their patients, to make diagnoses, to determine dosages and the best treatment for each individual patient, and to take all appropriate safety precautions. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instruc-tions, or ideas contained in the material herein. Previous editions copyrighted 2012, 2006, 2002, 1997, 1993, 1989, 1985, 1980, 1975, 1971, 1968, 1964, and 1960 by Mosby, Inc., an affiliate of Elsevier Inc. Library of Congress Cataloging-in-Publication Data Names: Sakaguchi, Ronald L., editor. \| Ferracane, Jack L., editor. \| Powers, John M., 1946- editor Title: Craig’s restorative dental materials / edited by Ronald Sakaguchi, Jack Ferracane, John Powers Other titles: Restorative dental materials Description: Fourteenth edition. \| St. Louis, Missouri : Elsevier, \| Includes bibliographical references and index. Identifiers: LCCN 2017051980 \| ISBN 9780323478212 (pbk. : alk. paper) Subjects: \| MESH: Dental Materials \| Dental Atraumatic Restorative Treatment Classification: LCC RK652.5 \| NLM WU 190 \| DDC 617.6/95--dc23 LC record available at Senior Content Strategist: Jennifer Flynn-Briggs Senior Content Development Specialist: Ann Ruzycka Anderson Publishing Services Manager: Catherine Jackson Book Production Specialist: Kristine Feeherty Design Direction: Renee Duenow Printed in China Last digit is the print number: 9 8 7 6 5 4 3 2 1 Craig’s Restorative Dental Materials is dedicated to the memory of Dr. Robert G. Craig, who passed away on April 24, 2003. Following in the footsteps of the first editor, Dr. Floyd Peyton, Dr. Craig served as the lead editor of nine editions of this text. Dr. Craig was the Marcus L. Ward Professor Emeritus of Dentistry at the University of Michigan, where he had been on the faculty since 1957. He applied his background in chemistry and engineering to research problems in dental materials and contributed to the education of thousands of predoctoral, postgraduate, and graduate students. This text, which is now translated in numerous languages, reflects his commitment to the dissemination of accurate, current knowledge about dental materials in clinical practice. We also dedicate this text to the many mentors and colleagues with whom we have collaborated. Ron Sakaguchi Jack Ferracane John Powers This page intentionally left blank v Roberto R. Braga, DDS, MS, PhD Professor Department of Biomaterials and Oral Biology School of Dentistry University of São Paulo São Paulo, Brazil Chapter 5: Testing of Dental Materials and Biomechanics Chapter 13: Materials for Adhesion and Luting Isabelle L. Denry, DDS, PhD Professor Department of Prosthodontics and Dows Institute for Oral Health Research The University of Iowa College of Dentistry Iowa City, IA Chapter 11: Restorative Materials: Ceramics Jack L. Ferracane, PhD Professor and Chair Department of Restorative Dentistry Division Director Biomaterials and Biomechanics School of Dentistry Oregon Health & Science University Portland, OR Chapter 3: Materials-Centered Treatment Design Chapter 6: Biocompatibility and Tissue Reaction to Biomaterials Chapter 8: Preventive and Intermediary Materials Chapter 10: Restorative Materials: Metals Sharukh S. Khajotia, BDS, MS, PhD Associate Dean for Research University of Oklahoma College of Dentistry University of Oklahoma Health Sciences Center Oklahoma City, OK Chapter 2: The Oral Environment David B. Mahler, PhD† Professor Emeritus Division of Biomaterials and Biomechanics Department of Restorative Dentistry School of Dentistry Oregon Health & Science University Portland, OR Chapter 10: Restorative Materials: Metals Grayson W. Marshall Jr., DDS, MPH, PhD, Odont. Dr. h.c. (Malmö) Distinguished Professor Emeritus and Professor (Recalled) Division of Biomaterials and Bioengineering Department of Preventive and Restorative Dental Sciences University of California San Francisco San Francisco, CA Chapter 2: The Oral Environment Sally J. Marshall, PhD Distinguished Professor Emerita and Professor (Recalled) Division of Biomaterials and Bioengineering Department of Preventive and Restorative Dental Sciences University of California San Francisco San Francisco, CA Chapter 2: The Oral Environment John C. Mitchell, PhD Professor and Assistant Dean for Research Midwestern University College of Dental Medicine Glendale, AZ Chapter 6: Biocompatibility and Tissue Reaction to Biomaterials Chapter 15: Dental and Orofacial Implants Chapter 16: Tissue Engineering Sumita B. Mitra, PhD Corporate Scientist 3M Company (retired) St. Paul, MN Partner Mitra Chemical Consulting, LLC West St. Paul, MN Chapter 9: Restorative Materials: Resin Composites and Polymers Chapter 13: Materials for Adhesion and Luting Carmem S. Pfeifer, DDS, PhD Associate Professor Division of Biomaterials and Biomechanics Department of Restorative Dentistry School of Dentistry Oregon Health & Science University Portland, OR Chapter 4: Fundamentals of Materials Science Chapter 5: Testing of Dental Materials and Biomechanics Contributors †Deceased. vi CONTRIBUTORS John M. Powers, PhD Senior Vice President Dental Consultants, Inc. (publisher of The Dental Advisor) Ann Arbor, MI Clinical Professor of Oral Biomaterials Department of Restorative Dentistry and Prosthodontics UTHealth School of Dentistry The University of Texas Health Science Center at Houston Houston, TX Chapter 12: Replicating Materials: Impression and Casting Chapter 14: Digital Imaging and Processing for Restorations Ronald L. Sakaguchi, DDS, MS, PhD, MBA Professor Division of Management School of Medicine Professor Division of Biomaterials and Biomechanics Department of Restorative Dentistry School of Dentistry Oregon Health & Science University Portland, OR Chapter 1: Role and Significance of Restorative Dental Materials Chapter 3: Materials-Centered Treatment Design Chapter 4: Fundamentals of Materials Science Chapter 5: Testing of Dental Materials and Biomechanics Chapter 7: General Classes of Biomaterials Chapter 8: Preventive and Intermediary Materials Chapter 9: Restorative Materials: Resin Composites and Polymers Chapter 14: Digital Imaging and Processing for Restorations vii The fourteenth edition of this classic textbook has been extensively updated to include many recent developments in dental biomaterials science and new materials for clinical use. The book continues to be designed for predoctoral dental students and also provides an excellent update of dental bioma-terials science and clinical applications of restorative materials for students in graduate programs and residencies. Dr. Ron Sakaguchi returns as the lead editor of the fourteenth edition. Dr. Sakaguchi serves as pro-fessor in the Division of Management in the School of Medicine and professor, Division of Biomaterials and Biomechanics in the Department of Restorative Dentistry at Oregon Health & Science University (OHSU) in Portland, Oregon. He earned a BS in cyber-netics from the University of California Los Angeles (UCLA), a DDS from Northwestern University, an MS in prosthodontics from the University of Minnesota, a PhD in biomaterials and biomechanics from Thames Polytechnic (London, England; now the University of Greenwich), and an MBA summa cum laude in entrepreneurship from Babson College. Dr. Jack Ferracane is a new co-editor of the four-teenth edition. Dr. Ferracane serves as professor and chair of the Department of Restorative Dentistry and division director of Biomaterials and Biomechanics at Oregon Health & Science University (OHSU) in Portland, Oregon. He earned a BS in biology from the University of Illinois and an MS and a PhD in biological materials from Northwestern University. Dr. John M. Powers returns as a co-editor of the fourteenth edition. He served as the lead editor of the twelfth edition and contributed to the previous eight editions. Dr. Powers is clinical professor of oral biomaterials in the Department of Restorative Dentistry and Prosthodontics at the UTHealth School of Dentistry, The University of Texas Health Science Center at Houston, and senior vice presi-dent of Dental Consultants, Inc. (publisher of The Dental Advisor). Dr. Powers was formerly Director of the Houston Biomaterials Research Center. He earned a BS in chemistry and a PhD in mechanical engineering and dental materials at the University of Michigan. We thank our many chapter authors for their effort and expertise: Dr. Roberto Braga of the University of São Paulo; Dr. Isabelle Denry of the University of Iowa; Dr. Sharukh Khajotia of the University of Oklahoma; Dr. David Mahler of Oregon Health & Science University; Drs. Grayson and Sally Marshall of the University of California San Francisco (UCSF); Dr. John Mitchell of Midwestern University; Dr. Sumita Mitra of Mitra Chemical Consulting, LLC, and many years at 3M ESPE; and Dr. Carmem Pfeifer of Oregon Health & Science University. The organization of the fourteenth edition follows the format of the popular thirteenth edition. Chapters are organized by major clinical procedures. Chapter 3 has been extensively revised with a new focus on materials-centered treatment design. The treatment design approach proposed by Spear and Kokich is discussed where treatment planning starts with an assessment of overall esthetics, to which a consider-ation of function, structure, and biology are added. A new table presents a summary of the approach with queries for each stage, and relevant materials and properties to be considered. The discussion of material and mechanical properties and their testing in Chapters 4 and 5 is updated and modernized to improve understanding. The history of amalgam and its fabrication now appears in the online companion to Chapter 10, along with other legacy metals and alloys. Tissue engineering materials have been exten-sively updated, with new figures, in Chapter 16. A website accompanies this textbook. Included is the majority of the procedural, or materials han-dling, content that was in the twelfth and thirteenth editions. The website can be found at elsevier.com/Sakaguchi/restorative/, where you will also find extensive text and graphics to supple-ment the print version of the book. Ron Sakaguchi Jack Ferracane John Powers Preface This page intentionally left blank ix 1 Role and Significance of Restorative Dental Materials, 1 Scope of Materials Covered in Restorative Dentistry, 1 A Systems Approach to Restorative Materials, 2 Application of Various Sciences, 2 Future Developments in Biomaterials, 2 2 The Oral Environment, 5 Enamel, 5 The Mineral, 8 Dentin, 9 Physical and Mechanical Properties, 12 The Dentin-Enamel Junction, 15 Oral Biofilms and Restorative Dental Materials, 17 3 Materials-Centered Treatment Design, 23 Evidence-Based Dentistry, 23 Patient Evidence, 23 Scientific Evidence, 23 Planning for Dental Treatment, 24 4 Fundamentals of Materials Science, 29 Mechanical Properties, 29 Force, 29 Stress, 30 Stress-Strain Curves, 31 Viscoelasticity, 39 Dynamic Mechanical Properties, 42 Surface Mechanical Properties, 43 The Colloidal State, 45 Diffusion Through Membranes and Osmotic Pressure, 46 Adsorption, Absorption, and Sorption, 46 Surface Tension and Wetting, 47 Adhesion, 48 Optical Properties, 50 Color, 50 Measurement of Color, 50 Surface Finish and Thickness, 52 Opacity, Translucency, Transparency, and Opalescence, 53 Index of Refraction, 53 Optical Constants, 53 Thermal Properties, 56 Temperature, 56 Transition Temperatures, 56 Heat of Fusion, 57 Thermal Conductivity, 58 Specific Heat, 58 Thermal Diffusivity, 59 Coefficient of Thermal Expansion, 59 Electrical Properties, 60 Electrical Conductivity and Resistivity, 60 Dielectric Constant, 61 Electromotive Force, 61 Galvanism, 62 Electrochemical Corrosion, 63 Zeta-Potential, 63 Other Properties, 63 Tarnish and Discoloration, 63 Water Sorption, 64 Setting Time, 64 Shelf Life, 65 Summary, 65 5 Testing of Dental Materials and Biomechanics, 69 Compressive Strength, 69 Flexure, 69 Flexural Strength, 69 Permanent Bending, 71 Diametral Tensile Strength, 71 Shear Strength, 71 Torsion, 72 Fatigue Strength, 73 Fracture Toughness, 73 Fractographic Analysis, 73 Tear Strength and Tear Energy, 75 Hardness, 75 Brinell Hardness Test, 76 Knoop Hardness Test, 76 Vickers Hardness Test, 76 Rockwell Hardness Test, 76 Barcol Hardness Test, 77 Shore A Hardness Test, 77 Nanoindentation, 77 Wear, 78 Contents x CONTENTS Setting Time, 79 Measurement, 79 Dynamic Mechanical Analysis, 79 Rheology, 80 Differential Scanning Calorimetry, 80 Spectrometric Techniques, 80 Pycnometry, 81 Bond Strength Test Methods, 81 Macroshear Bond Strength Tests, 82 Macrotensile Bond Strength Tests, 83 Microtensile Bond Strength Tests, 83 Microshear Bond Strength Tests, 83 Push-Out Tests, 83 Methods for Measuring Shrinkage and Stress During the Cure of Resin Composites, 83 Mercury Dilatometer, 83 Bonded Disk, 84 AcuVol, 84 Managing Accurate Resin Curing Test, 84 Cavity Configuration Factor (C-Factor), 84 Stress Analysis and Design of Dental Structures, 85 Polymerization Stress Test, 86 Tensilometer, 86 Tensometer, 87 Crack Analysis, 87 Specifications for Restorative Materials, 87 American Dental Association Specifications, 88 American Dental Association Acceptance Program, 88 Index of Federal Specifications and Standards, 88 6 Biocompatibility and Tissue Reaction to Biomaterials, 91 Measuring Biocompatibility, 91 In Vitro Tests, 92 Animal Tests, 94 Usage Tests, 94 Correlation Among In Vitro, Animal, and Usage Tests, 95 Using In Vitro, Animal, and Usage Tests Together, 96 Standards That Regulate the Measurement of Biocompatibility, 97 Biocompatibility of Dental Materials, 98 Reactions of Pulp, 98 Reaction of Other Oral Soft Tissues to Restorative Materials, 105 Summary, 108 7 General Classes of Biomaterials, 113 Metals and Alloys, 113 Chemical and Atomic Structure of Metals, 113 Atomic Structure, 113 Physical Properties of Metals, 115 Polymers, 116 Basic Nature of Polymers, 116 Ceramics, 118 Composites, 120 8 Preventive and Intermediary Materials, 123 Pit and Fissure Sealants, 123 Light-Cured Sealants, 123 Air Inhibition of Polymerization, 123 Properties of Sealants, 123 Clinical Studies, 125 Application of Sealants, 125 Glass Ionomers as Sealants, 126 Flowable Composites as Sealants, 126 Glass Ionomers to Prevent the Progression of Caries, 127 Composition and Reaction, 127 Properties, 127 Resin-Modified Glass Ionomers, 128 Composition and Reaction, 129 Properties, 129 Manipulation, 130 Resin-Modified Glass Ionomers as Cavity Liners, 130 Calcium Hydroxide Cavity Liners, 130 Mineral Trioxide Aggregate, 131 Fluoride Varnishes, 131 Remineralization, 131 9 Restorative Materials: Resin Composites and Polymers, 135 Multipurpose Resin Composites, 136 Composition, 136 Polymerization Reactions, 144 Packaging of Composites, 147 Properties of Composites, 147 Physical Properties, 147 Mechanical Properties, 151 Clinical Properties, 152 Composites for Special Applications, 153 Microfilled Composites, 153 Bulk Fill Composites, 154 xi CONTENTS Syringeable Composites, 154 Laboratory Composites, 155 Core Build-Up Composites, 155 Provisional Composites, 155 Glass Ionomers, 156 Components and Setting Reaction of Conventional Glass Ionomer, 156 Cermets, 157 Components and Setting Reactions of Resin-Modified Glass Ionomers, 158 Tri-Cure Glass Ionomer System, 159 Nanoionomer, 160 Packaging of Glass Ionomers, 161 Clinical Applications of Glass Ionomers, 161 Properties of Glass Ionomers, 161 Compomers, 163 Composition and Setting Reaction, 163 Properties, 164 Manipulation, 164 Light-Curing Units, 164 Quartz-Tungsten-Halogen Light-Curing Units, 164 Blue Light-Emitting Diodes, 164 Prosthetic Applications of Polymers, 165 Physical Form and Composition, 165 Athletic Mouth Protectors, 166 10 Restorative Materials: Metals, 171 Metals for Direct Placement: Amalgam, 171 Composition and Morphology, 171 Amalgamation Processes: Admixed Alloys, 172 Physical and Mechanical Properties, 174 Bonding of Amalgam, 177 Dental Casting Alloys, 178 Types and Composition, 178 Metallic Elements Used in Dental Alloys, 180 Noble Alloys, 184 Base-Metal Alloys, 190 Wrought Alloys, 200 Microstructure, 200 Composition, 200 Properties, 201 Wrought Stainless Steel Alloys, 201 Wrought Nickel-Titanium Alloy, 203 Wrought Beta-Titanium Alloy, 204 11 Restorative Materials: Ceramics, 209 Classification of Dental Ceramics, 209 Classification by Application, 209 Classification by Fabrication Method, 209 Classification by Crystalline Phase, 209 General Applications of Ceramics in Prosthetic Dentistry, 210 Metal-Ceramic Crowns and Fixed Dental Prostheses, 210 All-Ceramic Crowns, Inlays, Onlays, and Veneers, 211 Mechanical and Thermal Properties of Dental Ceramics, 211 Toughening Mechanisms, 211 Test Methods, 212 Comparative Data, 213 Optical Properties of Dental Ceramics, 214 All-Ceramic Restorations, 215 Sintered All-Ceramic Materials, 215 Heat-Pressed All-Ceramic Materials, 216 Machinable All-Ceramic Materials, 217 Metal-Ceramic Restorations, 219 Requirements for a Metal-Ceramic System, 220 Metal-Ceramic Bonding, 221 Ceramics for Metal-Ceramic Restorations, 222 Effect of Design on Metal-Ceramic Restora-tions, 224 Failure and Repair of Metal-Ceramic Restorations, 225 12 Replicating Materials: Impression and Casting, 229 Purpose of Impression Materials, 229 Desirable Qualities, 229 Types of Impression Materials, 231 Alginate Hydrocolloids, 231 Elastomeric Impression Materials, 237 Occlusal Registration Materials, 250 Impression Trays, 250 Die, Cast, and Model Materials, 250 Desirable Qualities of a Cast or Die Material, 250 Dental Plaster and Stone, 251 Epoxy Die Materials, 251 Comparison of Impression and Die Materials, 251 Gypsum Products, 252 Chemical and Physical Nature of Gypsum Products, 252 Properties, 255 Manipulation, 260 Casting Investments, 260 Properties Required of an Investment, 261 Composition, 261 Calcium Sulfate–Bonded Investments, 262 Effect of Temperature on Investment, 262 Thermal and Hygroscopic Casting Investment, 265 Brazing Investment, 268 Investment for All-Ceramic Restorations, 268 xii CONTENTS 13 Materials for Adhesion and Luting, 273 Principles of Adhesion, 273 Adhesive Systems, 275 Bonding to Other Substrates, 280 Repair of Composite, Ceramic, and Ceramic-Metal Restorations, 282 Classification and Characteristics of Luting Agents, 282 Classification, 282 Biocompatibility, 283 Interfacial Sealing and Anticariogenic Activity, 283 Adhesion, 283 Mechanical Properties, 283 Handling Properties and Radiopacity, 283 Viscosity and Film Thickness, 284 Solubility, 284 Esthetics, 284 Acid-Base Cements, 284 Zinc Oxide-Eugenol and Noneugenol Cements, 284 Glass Ionomer, 285 Resin-Modified Glass Ionomer, 287 Calcium Aluminate/Glass Ionomer Cement, 289 Resin-Based Cements, 289 Resin Cements, 289 Self-Adhesive Resin Cements, 290 Resin Cements for Provisional Restorations, 292 14 Digital Imaging and Processing for Restorations, 295 Dental CAD/CAM Systems, 295 Digital Impressions, 296 Design Software, 297 Processing Devices, 298 Clinical Outcomes, 298 15 Dental and Orofacial Implants, 301 Classification, 301 Endosseous Implant, 301 Osseointegration and Biointegration, 301 Factors Affecting the Endosteal Implant, 304 Geometry, 304 Magnitude of the Force, 304 Duration of the Force, 304 Type of Force, 305 Implant Diameter, 305 Implant Length, 305 Surfaces and Biocompatibility, 305 Ion Release, 306 Surfaces, 306 Surface Alterations, 306 Surface Coatings, 308 Implant Materials and Processing, 308 Challenges and the Future, 309 16 Tissue Engineering, 313 Autograft, 313 Allograft, 313 Xenograft, 313 Alloplasts, 314 Strategies for Tissue Engineering, 314 Injection of Cells, 314 Guided Tissue Regeneration, 315 Cell Induction, 315 Cells Within Scaffold Matrices, 317 Stem Cells, 318 Biomaterials and Scaffolds, 320 Biological Materials, 320 Ceramic and Glass Materials, 320 Polymeric Materials, 321 Cell Culture Methods, 322 Tissue-Engineered Dental Tissues, 322 Appendix A: Conversion of Units, 327 Index, 331 1 Developments in materials science, stem cells, imag-ing, three-dimensional (3D) printing, and robotics have dramatically changed the way we look at the replacement of components of the human anatomy. The replacement of tooth structure lost to disease and injury continues to be a large part of general dental practice. Restorative dental materials are the foundation for the replacement of tooth structure. Form and function are important considerations in the replacement of lost tooth structure. Although tooth form and appearance are aspects most easily recognized, function of the teeth and supporting tissues contributes greatly to the quality of life. The links between oral and general health are widely accepted. Proper function of the elements of the oral cavity, including the teeth and soft tissues, is needed for eating, speaking, swallowing, and proper breathing. Restorative dental materials make the reconstruction of the dental hard tissues possible. In many areas, the development of dental materials has progressed more rapidly than for other anatomical prostheses. Because of their long-term success, patients often expect dental prostheses to outperform the natural materials they replace. The application of materials science is unique in dentistry because of the complexity of the oral cavity, which includes bacteria, high forces, ever changing pH, and a warm, fluid environment. The oral cavity is con-sidered to be the harshest environment for a material in the body. In addition, when dental materials are placed directly into tooth cavities as restorative materials, there are very specific requirements for manipulation of the material. Knowledge of materials science and biomechanics is very important when choosing materi-als for specific dental applications and when designing the best solution for restoration of tooth structure and replacement of teeth. A review of the history of dentistry may be found on the book’s website at sakaguchi/restorative. SCOPE OF MATERIALS COVERED IN RESTORATIVE DENTISTRY Restorative dental materials include representa-tives from the broad classes of materials: met-als, polymers, ceramics, and composites. Dental materials include such items as resin composites, cements, glass ionomers, ceramics, noble and base metals, amalgam alloys, gypsum materials, cast-ing investments, impression materials, denture base resins, and other materials used in restorative procedures. The demands for material character-istics and performance range from high flexibility required by impression materials to high stiffness required in crowns and fixed dental prostheses. Materials for dental implants require integration with bone. Some materials are cast to achieve excellent adaptation to existing tooth structure, whereas others are machined to produce very reproducible dimensions and structured geom-etries. When describing these materials, physi-cal and chemical characteristics are often used as criteria for comparison. To understand how a material works, we study its chemical structure, its physical and mechanical characteristics, and how it should be manipulated to produce the best performance. Most restorative materials are characterized by physical, chemical, and mechanical parameters that are derived from test data. Improvements in these characteristics might be attractive in labo-ratory studies, but the real test is the material’s performance in the mouth and the ability of the material to be manipulated properly by the den-tal team. In many cases, manipulative errors can negate the technological advances for the mate-rial. It is therefore very important for the dental team to understand fundamental materials science and biomechanics to select and manipulate dental materials appropriately. C H A P T E R 1 Role and Significance of Restorative Dental Materials 2 CRAIG’S RESTORATIVE DENTAL MATERIALS A SYSTEMS APPROACH TO RESTORATIVE MATERIALS The practice of clinical dentistry depends not only on a complete understanding of the various clinical techniques but also on an appreciation of the funda-mental biological, chemical, and physical principles that support the clinical applications. It is important to understand the “how” and “why” associated with the function of natural and synthetic dental materials. A systems approach to assessing the chemical, physical, and engineering aspects of dental materi-als and oral function, along with the physiological, pathological, and other biological studies of the tis-sues that support the restorative structures, provides the best patient outcomes. This integrative approach, when combined with the best available scientific evi-dence, clinician experience, patient preferences, and patient modifiers, results in the best patient-centered care. APPLICATION OF VARIOUS SCIENCES In the chapters that follow, fundamental characteris-tics of materials are presented along with numerous practical examples of how the basic principles relate to clinical applications. Test procedures and fabrica-tion techniques are discussed briefly but not empha-sized. Many of the details of manipulation are found on the book’s website at sakaguchi/restorative. A more complete understanding of fundamental principles of materials and mechanics is important for the clinician to design and provide a progno-sis for restorations. For example, the prognosis of long-span fixed dental prostheses, or bridges, is dependent on the stiffness and fracture resistance of the materials. When considering esthetics, the hardness of the material is an important property because it influences the ability to polish the mate-rial. Some materials release fluoride when exposed to water, which might be beneficial in high-caries-risk patients. When selecting a ceramic for in-office fabrication of an all-ceramic crown, the machining characteristic of ceramics is important. Implants have a range of bone and soft tissue adaptations that are dependent on surface texture, coatings, and implant geometry. These are just a few examples of the many interactions between the clinical perfor-mance of dental materials and fundamental scien-tific principles. The toxicity of and tissue reactions to dental mate-rials are receiving more attention as a wider variety of materials are being used and as federal agencies demonstrate more concern in this area. A further indication of the importance of the interaction of materials and tissues is the development of recom-mended standard practices and tests for the biologi-cal interaction of materials through the auspices of the American Dental Association (ADA). After many centuries of dental practice, we con-tinue to be confronted with the problem of replacing tooth tissue lost by either accident or disease. In an effort to constantly improve our restorative capa-bilities, the dental profession will continue to draw from materials science, product design, engineering, biology, chemistry, and the arts to further develop an integrated practice of dentistry. FUTURE DEVELOPMENTS IN BIOMATERIALS In the United States about 50% of adults aged 20 to 64 have lost at least one permanent tooth to an accident, periodontal disease, a failed root canal, or tooth decay. In adults aged 65 and older, almost 19% have lost all of their natural teeth. That number is twice as large for adults aged 75 and over than for adults aged 65 to 74 (CDC/NCHS, National Health and Nutrition Examination Survey, 2011–2012). For children aged 5 to 19 years, 18% have untreated den-tal caries. For adults aged 20 to 44, that number is 27%. The demand for restorative care is tremendous. Advances in endodontology and periodontology enable people to retain teeth longer, shifting restor-ative care from replacement of teeth to long-term restoration and maintenance. Development of suc-cessful implant therapies has encouraged patients to replace individual teeth with fixed, single-tooth restorations rather than with fixed or removable dental prostheses. For those patients with good access to dental care, single-tooth replacements with implants are becoming a more popular option because they do not involve the preparation of adjacent teeth as for a fixed, multiunit restoration. Research into implant coatings, surface textures, graded properties, alternative materials, and new geometries will continue to grow. For those with less access, removable prostheses will continue to be used. An emphasis on esthetics continues to be popular among consumers, and this will continue to drive the development and sales of tooth-whitening systems and esthetic restorations. There appears to be an emerging trend for a more natural looking appear-ance with some individuality as opposed to the uniform, sparkling white dentition that was previ-ously requested by many patients. This will encour-age manufacturers to develop materials that mimic natural dentition even more closely by providing the same depth of color and optical characteristics of natural teeth. 3 1. Role and Significance of Restorative Dental Materials With the aging of the population, restorations for exposed root surfaces and worn dentitions will become more common. These materials will need to function in an environment with reduced sali-vary flow and atypical salivary pH and chemistry. Adhesion to these surfaces will be more challenging. This segment of the population will be managing multiple chronic diseases with many medications and will have difficulty maintaining an adequate regimen of oral home care. Restorative materials will be challenged in this difficult environment. The interaction between the fields of biomaterials and molecular biology is growing rapidly. Advances in tissue regeneration will accelerate. Developments in nanotechnology are having a major impact on materials science. The properties we currently understand at the macro and micro levels will be very different at the nano level. Biofabrication and bioprinting methods are creating new structures and materials. This is a very exciting time for materials research, and clinicians will have much to look for-ward to in the near future as this body of research develops new materials for clinical applications. Bibliography Centers for Disease Control and Prevention and National Center for Health Statistics. National Health and Nutrition Examination Study. 2011–2012. Choi CK, Breckenridge MT, Chen CS. Engineered materials and the cellular microenvironment: a strengthening inter-face between cell biology and bioengineering. Trends Cell Biol. 2010;20(12):705–714. Denry I, Kelly JR. Emerging ceramic-based materials for dentistry. J Dent Res. 2014;93(12):1235–1242. Horowitz RA, Coelho PG. Endosseous implant: the journey and the future. Compend Contin Educ Dent. 2010;31(7):545–547. Jones JR, Boccaccini AR. Editorial: a forecast of the future for biomaterials. J Mater Sci Mater Med. 2006;17:963–964. Nakamura M, Iwanaga S, Henmi C, Arai K, Nishiyama Y. Biomatrices and biomaterials for future develop-ments of bioprinting and biofabrication. Biofabrication. 2010;2(1):014110. Rekow ED, Fox CH, Watson T, Petersen PE. Future inno-vation and research in dental restorative materials. Adv Dent Res. 2013;25(1):2–7. U.S. Department of Health and Human Services, Centers for Disease Control and Prevention (CDC) and National Center for Health Statistics (NCHS). Health, United States; 2015. U.S. Department of Health and Human Services. Oral Health in America: A Report of the Surgeon General—Executive Summary. Rockville, MD: U.S. Department of Health and Human Services, National Institute of Dental and Craniofacial Research, National Institutes of Health; 2000. This page intentionally left blank 5 The tooth contains three specialized calcified tissues: enamel, dentin, and cementum (Fig. 2.1). Enamel is unique in that it is the most highly calcified tissue in the body and contains the least organic content of any of these tissues. Enamel provides the hard outer cov-ering of the crown that allows efficient mastication. Dentin and cementum, like bone, are vital, hydrated, biological composite structures formed mainly of a collagen type I matrix reinforced with the calcium phosphate mineral called apatite. Dentin forms the bulk of the tooth and is joined to the enamel at the dentin-enamel junction (DEJ). The dentin of the tooth root is covered by cementum that provides connection of the tooth to the alveolar bone via the periodontal ligament. Although the structure of these tissues is often described in dental texts, the properties are often discussed only superficially. However, these proper-ties are important with regard to the interrelationships of the factors that contribute to the performance neces-sary for the optimum function of these tissues. In restorative dentistry we are interested in pro-viding preventive treatments that will maintain tissue integrity and replace damaged tissues with materials that ideally will mimic the natural appear-ance and performance of those tissues when neces-sary. Thus knowledge of the structure and properties of these tissues is desirable both as a yardstick to measure the properties and performance of restor-ative materials and as a guide to the development of materials that will mimic their structure and func-tion. In addition, many applications, such as dental bonding, require us to attach synthetic materials to the calcified tissues, and these procedures rely on detailed knowledge of the structure and properties of the adhesive tissue substrates. ENAMEL Fig. 2.1 shows a schematic diagram of a posterior tooth sectioned to reveal the enamel and dentin components. Enamel forms the hard outer shell of the crown and as the most highly calcified tissue is well suited to resisting wear due to mastication. Enamel is formed by ameloblasts starting at the DEJ and proceeding outward to the tooth surface. The ameloblasts exchange signals with odontoblasts located on the other side of the DEJ at the start of the enamel and dentin formation, and the odontoblasts move inward from the DEJ as the ameloblasts form-ing enamel move outward to form the enamel of the crown. Most of the enamel organic matrix composed of amelogenins and enamelins is resorbed during tooth maturation to leave a calcified tissue that is largely composed of mineral and a sparse organic matrix. The structural arrangement of enamel forms keyhole-shaped structures known as enamel prisms or rods that are about 5 μm across, as seen in Fig. 2.2. The overall composition is about 96% mineral by weight, with 1% lipid and protein and the remainder C H A P T E R 2 The Oral Environment Enamel Dentin Pulp Inner cervical Outer Inner FIG. 2.1 Schematic diagram of a tooth cut longitudi-nally to expose the enamel, dentin, and the pulp cham-ber. On the right side are illustrations of dentin tubules as viewed from the top, which show the variation in the tubule number with location. At the left is an illustration of the change in direction of the primary dentin tubules as secondary dentin is formed. (From Marshall SJ, Balooch M, Breunig T, et al. Human dentin and the dentin-resin adhesive interface. Acta Mater. 1998;46:2529–2539.) 6 CRAIG’S RESTORATIVE DENTAL MATERIALS being water. The organic portion and water probably play important roles in tooth function and pathology, and it is often more useful to describe the composition on a volume basis. On that basis we see the organic components make up about 3% and water 12% of the structure. The mineral is formed and grows into very long crystals of hexagonal shape about 40 nm across; these crystals have not been synthetically duplicated. There is some evidence that the crystals may span the whole enamel thickness, but this is difficult to prove because most preparation procedures lead to frac-ture of the individual crystallites. It appears that they are at least thousands of nanometers long. If this is true, then enamel crystals provide an extraordinary “aspect” ratio (length-to-width ratio) for a nanoscale material, and they are very different from the much smaller dentin crystals. The crystals are packed into enamel prisms or rods that are about 5 μm across, as shown in Fig. 2.2. These prisms are revealed easily by acid etching and extend in a closely packed array from the DEJ to the enamel surface and lie roughly perpen-dicular to the DEJ, except in cuspal areas where the rods twist and cross, known as decussation, which may increase fracture resistance. About 100 crystals of the mineral are needed to span the diameter of a prism, and the long axes of the crystals tend to align them-selves along the prism axes, as seen in Fig. 2.2. The crystals near the periphery of each prism deviate somewhat from the long axis toward the interface between prisms. The deviation in the tail of the prism is even greater. The individual crys-tals within a prism are also coated with a thin layer of lipid and/or protein that plays important roles in mineralization, although much remains to be learned about the details. Recent work suggests that this protein coat may lead to increased toughness of the enamel. The interfaces between prisms, or inter-rod enamel, contain the main organic components Interrod enamel Head Tail A B 40.0 30.0 20.0 10.0 0 0 10.0 20.0 30.0 40.0 C FIG. 2.2 Enamel microstructure showing a schematic diagram of keyhole-shaped enamel prisms or rods about 5 μm in diameter (B). Atomic force microscopy images showing prism cross sections (A) and along axes of the prisms (C). Crystallite orientation deviates in the interrod and tail area, and the organic content increases in the interrod area. (Modified from Habelitz S, Marshall SJ, Marshall GW, et al. Mechanical properties of human dental enamel on the nanometer scale. Arch Oral Biol. 2001;46:173–183.) 7 2. The Oral Environment of the structure and act as passageways for water and ionic movement. These areas are also known as prism sheaths. These regions are of vital importance in etching processes associated with bonding and other demineralization processes, such as caries. Etching of enamel with acids such as phosphoric acid, commonly used in enamel bonding, eliminates smear layers associated with cavity preparation, dissolves persisting layers of prismless enamel in deciduous teeth, and differentially dissolves enamel crystals in each prism. The pattern of etched enamel is categorized as type 1 (preferential prism core etch-ing; Fig. 2.2A), type 2 (preferential prism periphery etching; Fig. 2.3C), and type 3 (mixed or uniform). Sometimes these patterns appear side by side on the same tooth surface (Fig. 2.3E). No differences in C D E 25 m A B FIG. 2.3 Etching enamel. (A) Gel etchant dispensed on the enamel portion of the preparation. (B) Frosty appearance after etching, rinsing, and drying. (C) Magnified view of etch pattern with preferential prism periphery etch (type 1). (D) Bonding agent revealed after dissolving enamel. (E) Mixed etch patterns showing type 1 (light prisms with dark periphery) and type 2 (dark cores with light periphery) etching on the same surface. (C and D, After Marshall GW, Olson LM, Lee CV. SEM Investigation of the variability of enamel surfaces after simulated clinical acid etching for pit and fissure sealants. J Dent Res. 1975;54:1222–1231; E, After Marshall GW, Olson LM, Lee CV. SEM Investigation of the variability of enamel surfaces after simu-lated clinical acid etching for pit and fissure sealants. J Dent Res. 1975;54:1222–1231; E, from Marshall GW, Marshall SJ, Bayne SC. Restorative dental materials: scanning electron microscopy and x-ray microanalysis. Scanning Microsc. 1988;2:2007–2028.) 8 CRAIG’S RESTORATIVE DENTAL MATERIALS micromechanical bond strength of the different etch-ing patterns have been established. In a standard cav-ity preparation for a composite, the orientation of the enamel surfaces being etched could be perpendicular to enamel prisms (perimeter of the cavity outline), oblique cross section of the prisms (beveled occlusal or proximal margins), and axial walls of the prisms (cavity preparation walls). During the early stages of etching, when only a small amount of enamel crystal dissolution occurs, it may be difficult or impossible to detect the extent of the process. However, as the etching pattern begins to develop, the surface etched with phosphoric acid develops a frosty appearance (Fig. 2.3B), which has been used as the traditional clinical indicator for sufficient etching. This rough-ened surface provides the substrate for infiltration of bonding agents that can be polymerized after pen-etration of the etched enamel structure so that they form micromechanical bonds to the enamel when polymerized. With self-etching bonding agents, this frosty appearance cannot be detected. There are two other important structural varia-tions of enamel. Near the DEJ the enamel prism struc-ture is not as well developed in the very first enamel formed, so that the enamel very close to the DEJ may appear aprismatic or without the prism-like structure. Similarly, on the outer surface of the enamel, at com-pletion of the enamel surface, the ameloblasts degen-erate and leave a featureless layer, called prismless enamel, on the outer surface of the crown. This layer is more often observed in deciduous teeth and is often worn off in permanent teeth. However, if present, this causes some difficulty in getting an effective etching pattern and may require roughening of the surface or additional etching treatments. The outer surface of the enamel is of great clinical significance because it is the surface subjected to daily wear and undergoes repeated cycles of demineralization and remineral-ization. As a result of these cycles, the composition of the enamel crystals may change, for example, as a result of exposure to fluoride. Thus the properties of the enamel might be expected to vary from the exter-nal to the internal surface. Such variations, including a thin surface veneer of fluoride-rich apatite crystals, create differences in the enamel properties within the enamel. Enamel is usually harder at the occlusal and cuspal areas and less hard nearer the DEJ. Fig. 2.4 shows an example of the difference in hardness. THE MINERAL The mineral of all calcified tissues is a highly defec-tive relative of the mineral hydroxyapatite (HA). The biological apatites of calcified tissues are differ-ent from the ideal HA structure in that the defects and chemical substitutions generally make them weaker and more soluble in acids. HA has the simple formula Ca10(PO4)6(OH)2, with an ideal molar ratio of calcium to phosphorus (Ca/P) of 1.67 and a hex-agonal crystal structure. The apatite of enamel and dentin has a much more variable composition that depends on its formative history and other chemi-cal exposures during maturity. Thus the mineral in enamel and dentin is a calcium-deficient, carbonate-rich, and highly substituted form related to HA. Metal ions such as magnesium (Mg) and sodium (Na) may substitute for calcium, whereas carbonate substitutes for the phosphate and hydroxyl groups. These substitutions distort the structure and make it more soluble. Perhaps the most beneficial substitu-tion is the fluorine (F) ion, which substitutes for the hydroxyl group (OH) in the formula and makes the structure stronger and less soluble. Complete sub-stitution of F for (OH) in HA yields fluoroapatite mineral, Ca10(PO4)6(F)2, which is much less soluble than HA or the defective apatite of calcified tissues. It is worth noting that HA has attracted considerable attention as an implantable calcified tissue replace-ment. It has the advantage of being a purified and stronger form of the natural mineral and releases no harmful agents during biological degradation. Its major shortcoming is that it is extremely brittle and sensitive to porosity or defects, and therefore it frac-tures easily in load-bearing applications. The approximate carbonate contents of the enamel and dentin apatites are significantly different, about 3% and 5% carbonate, respectively. All other fac-tors being equal, this would make the dentin apatite more soluble in acids than the enamel apatite. Things are not equal, however, and the dentin apatite crys-tals are much smaller than the enamel crystals. This means that the dentin crystals present a higher sur-face area to attacking acids and contain many more Buccal Hardness (GPa) Lingual 6 5.5 5 4.5 4 3.5 3 2.5 FIG. 2.4 Nanoindentation mapping of the mechani-cal properties of human molar tooth enamel. (From Cuy JL, Mann AB, Livi KJ, et al. Nanoindentation mapping of the mechanical properties of human molar tooth enamel. Arch Oral Biol. 2002;47(4):281–291.) 9 2. The Oral Environment defects per unit volume and thus exhibit consider-ably higher solubility. Finally, as discussed further below, the dentin mineral occupies only about 50% of the dentin structure, so there is not as much apatite in the dentin as there is in the enamel. All of these factors multiply the susceptibility of dentin to acid attack and provide insight into the rapid spread of caries when it penetrates the DEJ. DENTIN Dentin is a complex hydrated biological com-posite structure that forms the bulk of the tooth. Furthermore, dentin is modified by physiological, aging, and disease processes that result in differ-ent forms of dentin. These altered forms of dentin may be the precise forms that are most important in restorative dentistry. Some of the recognized varia-tions include primary, secondary, reparative or ter-tiary, sclerotic, transparent, carious, demineralized, remineralized, and hypermineralized. These terms reflect alterations in the fundamental components of the structure as defined by changes in their arrange-ment, interrelationships, or chemistry. A number of these may have important implications for our ability to develop long-lasting adhesion or bonds to dentin. Primary dentin is formed during tooth develop-ment. Its volume and conformation, reflecting tooth form, vary with the size and shape of the tooth. Dentin is composed of about 50 volume percent (vol%) carbonate-rich, calcium-deficient apatite; 30 vol% organic matter, which is largely type I col-lagen; and about 20 vol% fluid, which is similar to plasma. Other noncollagenous proteins are thought to be involved in dentin mineralization and other functions such as controlling crystallite size and orientation. The role of noncollagenous proteins in biomineralization or simpler molecules that can mimic some of their functions may lead to dentin remineralization methods; however, these functions and possibilities are not discussed further in this text. The major components are distributed into distinc-tive morphological features to form a vital and com-plex hydrated composite in which the morphology varies with location and undergoes alterations with age or disease. The tubules, one distinct and impor-tant feature of dentin, represent the tracks taken by the odontoblastic cells from the DEJ or cementum at the root to the pulp chamber and appear as tunnels piercing the dentin structure (Fig. 2.5). The tubules converge on the pulp chamber, and therefore tubule density and orientation vary from location to location (see Fig. 2.1). Tubule number density is lowest at the DEJ and highest at the predentin surface at the junc-tion to the pulp chamber, where the odontoblastic cell bodies lie in nearly a close-packed array. Lower tubule densities are found in the root. The contents of the tubules include odontoblast processes, for all or part of their course, and fluid. The extent of the odontoblast process is still uncertain, but evidence is mounting that it extends to the DEJ. For most of its course, the tubule lumen is lined by a highly mineral-ized cuff of peritubular dentin approximately 0.5 to 1 μm thick (Fig. 2.6). Because the peritubular dentin forms after the tubule lumen has been formed, some argue that it may be more properly termed intratubu-lar dentin and contains mostly apatite crystals with little organic matrix. A number of studies have con-cluded that the peritubular dentin does not contain collagen and therefore might be considered a sepa-rate calcified tissue. The tubules are separated by intertubular dentin composed of a matrix of type I collagen reinforced by apatite (see Figs. 2.5 and 2.6). This arrangement means that the amount of intertu-bular dentin varies with location. The apatite crystals are much smaller (approximately 5 × 30 × 100 nm) than the apatite found in enamel and contain about 5% carbonate. The small crystallite size, defect struc-ture, and higher carbonate content lead to the greater dissolution susceptibility described above. Estimates of the size of tubules, the thickness of the peritubular region, and the amount of intertubu-lar dentin have been made in a number of studies. Calculations for occlusal dentin as a function of posi-tion from these data show that the percentage tubule area and diameter vary from about 22% and 2.5 μm near the pulp to 1% and 0.8 μm at the DEJ, respec-tively. Intertubular matrix area varies from 12% at the 30kv 2.00kx 959 5.0 FIG. 2.5 Scanning electron microscopy image of nor-mal dentin showing its unique structure as seen from two directions. At the top is a view of the tubules, each of which is surrounded by peritubular dentin. Tubules lie between the dentin-enamel junction and converge on the pulp chamber. The perpendicular surface at the bottom shows a fracture surface revealing some of the tubules as they form tunnel-like pathways toward the pulp. The tubule lumen normally contains fluid and processes of the odontoblastic cells. (From Marshall GW. Dentin: microstructure and charac-terization. Quintessence Int. 1993;24:606–617.) 10 CRAIG’S RESTORATIVE DENTAL MATERIALS predentin to 96% near the DEJ, whereas peritubular dentin ranges from over 60% down to 3% at the DEJ. Tubule densities are compared in Table 2.1 based on work by various investigators. It is clear that the structural components will vary considerably over their course and necessarily result in location-depen-dent variations in morphology, distribution of the structural elements, and important properties such as permeability, moisture content, and available surface area for bonding. They may also affect bond strength, hardness, and other properties. Because the odontoblasts come to rest just inside the dentin and line the walls of the pulp chamber after tooth formation, the dentin-pulp complex can be considered a vital tissue. This is different from mature enamel, which is acellular. Over time, sec-ondary dentin forms and the pulp chamber gradu-ally becomes smaller. The border between primary and secondary dentin is usually marked by a change in orientation of the dentin tubules. Furthermore, the odontoblasts react to form tertiary dentin in response to insults such as caries or tooth preparation, and this form of dentin is often less well organized than the primary or secondary dentin. Early enamel carious lesions may be reversed by remineralization treatments. However, effective remineralization treatments are not yet available for dentin, and therefore the current standard of care dictates surgical intervention to remove highly dam-aged tissue and then restoration as needed. Thus it is important to understand altered forms of dentin and the effects of such clinical interventions. When dentin is cut or abraded by dental instru-ments, a smear layer develops and covers the sur-face and obscures the underlying structure (Fig. 2.7). The bur cutting marks are shown in Fig. 2.7A and at higher magnification in Fig. 2.7B. Fig. 2.7C shows the smear layer thickness from the side and the development of smear plugs as the cut dentin debris is pushed into the dentin tubule lumen. The advantages and disadvantages of the smear layer have been extensively discussed for several decades. It reduces permeability and therefore aids in main-taining a drier field, and it reduces infiltration of nox-ious agents into the tubules and perhaps the pulp. However, it is now generally accepted that it is a hin-drance to dentin bonding procedures and therefore is normally removed or modified by some form of acid conditioning. Acid etching or conditioning allows for removal of the smear layer and alteration of the superficial dentin, opening channels for infiltration by bond-ing agents. Fig. 2.8 shows what happens in such an etching treatment. The tubule lumens widen as the peritubular dentin is preferentially removed because it is mostly mineral with sparse protein. The widened lumens form a funnel shape that is not very retentive. Fig. 2.9 shows these effects in a slightly different way. Unetched dentin in Fig. 2.9A (top) has small tubules and peritubular dentin, which is removed in A Peritubular dentin Intertubular dentin B P I 20 kv 5.0 kx 956 2.00 FIG. 2.6 Fracture surface of the dentin. (A) Viewed from the occlusal direction. (B) Viewed longitudinally. Peritubular (P; also called intratubular) dentin forms a cuff or lining around each tubule. The tubules are separated from one another by intertubular dentin (I). (Courtesy G.W. Marshall.) TABLE 2.1 Comparison of Mean Numerical Density of Tubules in Occlusal Dentin Outer Dentin Middle Dentin Inner Dentin 15,000/mm2 35,000/mm2 65,000/mm2 20,000/mm2 35,000/mm2 43,000/mm2 24,500/mm2 40,400/mm2 51,100/mm2 18,000/mm2 39,000/mm2 52,000/mm2 From data reported in Marshall GW. Dentin: microstructure and charac-terization. Quintessence Int. 1993;24:606–617. 11 2. The Oral Environment the treated dentin at the exposed surface after etch-ing (bottom). The two-dimensional network of colla-gen type I fibers is shown after treatment in Fig. 2.9A. Fig. 2.9B shows progressive demineralization of a dentin collagen fibril in which the external mineral and proteins are slowly removed to reveal the typical banded pattern of type I collagen. In Fig. 2.9C, this pattern is seen at high magnification of the treated dentin shown in Fig. 2.9A. If the demineralized dentin is dried, the remain-ing dentin matrix shrinks and the collagen fibrils become matted and difficult to penetrate by bonding agents. This is shown in Fig. 2.10, which compares demineralized and dried dentin with demineralized and hydrated dentin. Most restorative procedures involve dentin that has been altered in some way. Common alterations include formation of carious lesions that form vari-ous zones and include transparent dentin that forms under the caries-infected dentin layer. Transparent dentin results when the dentin tubules become filled with mineral, which changes the refractive index of the tubules and produces a translucent or transpar-ent zone. Fig. 2.11 shows a section through a tooth with a carious lesion, which has been stained to reveal its zones. The gray zone under the stained and severely demineralized dentin is the transparent layer (Fig. 2.11A). Fig. 2.11B shows the transparent dentin in which most of the tubule lumens are filled with min-eral. After etching, as shown in Fig. 2.11C, the peri-tubular dentin is etched away, but the tubules retain plugs of the precipitated mineral, which is more resistant to etching. This resistance to etching makes bonding more difficult. Several other forms of transparent dentin are formed as a result of different processes. A second form of transparent dentin results from bruxism. An additional form of transparent dentin results from aging as the root dentin gradually becomes transparent. In addition, noncarious cervical lesions, often called abfraction or notch lesions, form at the A B C SL S.P. FIG. 2.7 Smear layer formation. (A) Bur marks on dentin preparation. (B) Higher magnification showing smear layer surface and cutting debris. (C) Section showing smear layer (SL) and smear plugs (S.P.). (A and B, from Marshall GW, Marshall SJ, Bayne SC. Restorative dental materials: scanning electron microscopy and x-ray microanalysis. Scanning Microsc. 1988;2:2007– 2028; C, from Pashley DH, Tao L, Boyd L, et al. Scanning electron microscopy of the substructure of smear layers in human dentine. Arch Oral Biol. 1988;33(4):265–270.) 12 CRAIG’S RESTORATIVE DENTAL MATERIALS enamel-cementum or enamel-dentin junction, usu-ally on facial or buccal surfaces. Their etiology is not clear at this point; their formation has been attrib-uted to abrasion, tooth flexure, and erosion, or some combination of these processes. Nonetheless, these lesions occur with increasing frequency with age, and the exposed dentin becomes transparent as the tubules are filled. Fig. 2.12 shows examples of trans-parent dentin in which the tubule lumens are com-pletely filled. The properties of the transparent dentin may dif-fer from one to another depending on the processes that lead to deposit of the mineral in the tubules. Several studies have shown that elastic properties of the intertubular dentin are not altered by aging, although the structure may become more suscepti-ble to fracture. Similarly, arrested caries will contain transparent dentin and this has often been called scle-rotic dentin, a term that implies it may be harder than normal dentin. However, other studies have shown that the elastic properties of the intertubular dentin may actually be unaltered or lower than normal dentin. Physical and Mechanical Properties The marked variations in the structural elements of dentin when located within the tooth imply that the properties of dentin will vary considerably with location. That is, variable structure leads to variable properties. Because one major function of tooth structure is to resist deformation without fracture, it is useful to have knowledge of the forces that are experienced by teeth during mastication. Measurements have given values on cusp tips of about 77 kg distributed over the cusp tip area of 0.039 cm2, suggesting a stress of about 200 MPa. Difficulties in Testing In Table 2.2, values are presented for some important properties of enamel and dentin. The wide spread 5 10 15 5 10 15 5 10 15 C B D 20 s 60 s A FIG. 2.8 Stages of dentin demineralization. (A) Schematic showing progressive stages of dentin demineralization. (B–D) Atomic force microscopy images showing stages of etching. The etching leads to wider lumens as peritubular dentin is dissolved and funnel-shaped openings are formed. (B–D, from Marshall GW. Dentin: microstructure and characterization. Quintessence Int. 1993;24:606–617.) 13 2. The Oral Environment FIG. 2.9 Etching of dentin removes mineral from the intertubular dentin matrix leaving a collagen-rich layer and widening the dentin tubule orifices. (A) After etching, the tubule lumens are enlarged and the collagen network sur-rounding the tubules can be seen after fur-ther treatment. (B) Isolated dentin collagen fiber is slowly demineralized revealing the typical 67-nm repeat pattern of type I col-lagen. (C) High magnification view of col-lagen fibers in (A). (A and C, from Marshall GW, Yucel N, Balooch M, et al. Sodium hypo-cholorite alterations of dentin and dentin col-lagen. Surf Sci. 2001;491:444–455; B, modified from Balooch M, Habelitz S, Kinney JH, et al. Mechanical properties of mineralized collagen fibrils as influenced by demineralization. J Struct Biol. 2008;162:404–410.) A Unetched Treated B 484 s 360 s 0 s 100 nm C 600 400 200 A B FIG. 2.10 Demineralized dentin is sensitive to moisture and shrinks on drying. (A) Demineralized dentin undergoes shrinkage when air dried, forming a collapsed layer of collagen that is difficult to infiltrate with resin-bonding agents. (B) When kept moist, the collagen network is open and can be penetrated by bonding agents. (From Marshall GW, Marshall SJ, Kinney JH, et al. The dentin substrate: structure and properties related to bonding. J Dent. 1997;25:441–458.) 14 CRAIG’S RESTORATIVE DENTAL MATERIALS A Trans B 10 20 30 40 C 10 20 30 40 FIG. 2.11 Transparent dentin associated with carious lesions. (A) Carious lesion showing dentin carious zones revealed by staining, including the grayish transparent zone. (B) Atomic force microscopy of carious transparent dentin before etch-ing. (C) After etching, the tubule lumens remain filled even as the peritubular dentin is etched away. (A, from Zheng L, Hilton JF, Habelitz S, et al. Dentin caries activity status related to hardness and elasticity. Eur J Oral Sci. 2003;111(3):243–252; B and C, from Marshall GW, Chang JY, Gansky SA, et al. Demineralization of caries-affected transparent dentin by citric acid: an atomic force microscopy study. Dent Mater. 2001;17:45–52.) 15kv 2.0kx 523 5.00 A 15kv 2.00kx 519 5.0 B FIG. 2.12 Transparent dentin. (A) Viewed from the facial direction. (B) Viewed longitudinally. The transparent dentin results from filling of the tubules with mineral deposits that alter the optical properties of the tooth. (Courtesy G.W. Marshall.) 15 2. The Oral Environment of values reported in the literature is remarkable. Some of the reasons for these discrepancies should be appreciated and considered in practice or when reading the literature. First, human teeth are small, and therefore it is difficult to get large specimens and hold them, mak-ing the use of standard mechanical testing such as tensile, compressive, or shear tests difficult. When testing bonded teeth, the problem is even more com-plicated, and special tests have been developed to obtain insights into these properties. From the previ-ous discussion of structural variations, it is also clear that testing such small inhomogeneous specimens means that the properties will not be uniform. Another problem is the great variation in struc-ture in both tissues. Enamel prisms are aligned generally perpendicular to the DEJ, whereas dentin tubules change their number density with depth as they course toward the pulp chamber. Preparing a uniform sample with the structures running all in one direction for testing is challenging. In addition, properties generally vary with direction and loca-tion, and the material is not isotropic; therefore the best a single value can tell you is some average value for the material. Storage and time elapsed since extraction are also important considerations. Properties that exist in a natural situation or in situ or in vivo are of greatest interest. Clearly this condition is almost impossible to achieve in most routine testing, so changes that have occurred as a result of storage conditions prior to testing must be considered. It is also important to consider biological hazards because extracted teeth must be treated as potentially infective. How do you sterilize the teeth without altering their properties? Autoclaving undoubtedly alters the properties of proteins and is therefore not appropriate for dentin, and it might also affect enamel. Finally, the fluid content of these tissues must be considered. Moisture is a vital component of both tissues, and in vivo conditions cannot be replicated if the tissues have been desiccated (see Fig. 2.10). This becomes a critically important consideration in bonding to these tissues, as is discussed further in Chapter 13. In contrast to the importance of this issue is the issue of convenience. It is much more difficult to test the tissues in a fully hydrated condition than in a dry condition. All of these factors and a number of others, such as temperature of testing, will influ-ence the results and contribute to a spread in the val-ues reported for the properties. Despite these limitations, some generalizations about the properties of these tissues are useful (see Table 2.1). Root dentin is generally weaker and softer than coronal dentin. Enamel also appears to vary in its properties, with cuspal enamel being stronger and harder than other areas, presumably as an adaption to masticatory forces. Dentin is less stiff than enamel (i.e., has a lower elastic modulus) and has higher fracture toughness. This may be counterintuitive but will become clearer when we define these terms in Chapter 4. In addition, dentin is viscoelastic, which means that its mechanical deformation characteris-tics are time dependent, and elastic recovery is not instantaneous. Thus dentin may be sensitive to how rapidly it is strained, a phenomenon called strain rate sensitivity. Strain rate sensitivity is characteristic of polymeric materials; the collagen matrix imparts this property to tissues such as dentin. Under nor-mal circumstances, ceramic materials do not show this characteristic in their mechanical properties and are typically stiff, but brittle, and fracture without permanent deformation. Pure HA shows this typical characteristic, but when formed in enamel it exhib-its significant toughness (see Chapter 4) that is only slightly less than that of dentin. This toughness is associated with the microstructure and the small pro-tein component of enamel. The Dentin-Enamel Junction The DEJ is much more than the boundary between enamel and dentin. Because enamel is very hard and dentin is much softer and tougher, they need to be joined together to provide a biomechanically compatible system. Joining such dissimilar materi-als is a challenge, and it is not completely clear how nature has accomplished this. However, the DEJ not only joins these two tissues but also appears to resist cracks in the enamel from penetrating into dentin and leading to tooth fracture, as shown in Fig. 2.13A. Many such cracks exist in the enamel but do not TABLE 2.2 Properties of Enamel and Dentin Property Enamel Dentin Density (g/cm3) 2.96 2.1 Compressive Modulus of elasticity (GPa) 60–120 18–24 Proportional limit (MPa) 70–353 100–190 Strength (MPa) 94–450 230–370 Tensile Modulus of elasticity (GPa) 11–19 Strength (MPa) 8–35 30–65 Shear strength (MPa) 90 138 Flexural strength (MPa) 60–90 245–280 Hardness (GPa) 3–6 0.13–0.51 16 CRAIG’S RESTORATIVE DENTAL MATERIALS D 50 m B A Dentin DEJ Enamel Cracks C 50 m Enamel DEJ Dentin Apatite crystals E FIG. 2.13 Cracks in enamel appear to stop at the dentin-enamel junction (DEJ). (A) Low-magnification view of cracks in enamel. (B) Indentation-generated cracks stop near or at the scalloped DEJ (orange). (C) Large scallops in molars. (D) Smaller scallops in anterior teeth. (E) Crystals of the enamel are nearly in contact with dentin crystals at the DEJ forming an optically thin but functionally wide union. (A, C–E, from Marshall SJ, Balooch M, Habelitz S, et al. The dentin-enamel junction—a natural, multilevel interface. J Eur Ceram Soc. 2003;23:2897–2904; B, from Imbeni V, Kruzic JJ, Marshall GW, et al. The dentin-enamel junction and the fracture of human teeth. Nat Mater. 2005;4:229–232.) 17 2. The Oral Environment seem to propagate into the dentin. If the DEJ is intact, it is unusual to have tooth fracture except in the face of severe trauma. In Fig. 2.13B, microhardness inden-tations have been placed to drive cracks toward the DEJ (orange). The crack stops at or just past the inter-face. This image also shows that the DEJ is scalloped, with its concavity directed toward the enamel. This means that most cracks approach the DEJ at an angle, and this may lead to arrest of many of the cracks. The scalloped structure actually has three levels: scallops, microscallops within the scallops, and a finer struc-ture. Fig. 2.13C and D shows images of larger scal-lops in molars (∼24 μm across) and smaller scallops (∼15 μm across) in anterior teeth after the removal of the enamel. Finite element models suggest that the scallops reduce stress concentrations at the interface, but it is not known whether the larger scallop size in posterior teeth is an adaption to higher masticatory loads or a developmental variation. In Fig. 2.13E, the crystals of dentin are almost in contact with those of the enamel, so that the anatomical DEJ is said to be optically thin. However, measurements of property variations across the DEJ show that this is a graded interface with properties varying from those of the enamel to the adjacent mantle dentin over a consid-erable distance. This gradient, which is due in part to the scalloped nature of the DEJ, makes the functional width of the DEJ much larger than its anatomical appearance and further reduces stresses. In addition, although collagen is generally absent from enamel, collagen fibers cross the DEJ from dentin into enamel to further integrate the two tissues. Recent work sug-gests that other proteins that could be remnants of the basement membrane at the DEJ may include col-lagen types IV and VII and perhaps other proteins that could help stabilize the DEJ structure and con-tribute to its fracture resistance. ORAL BIOFILMS AND RESTORATIVE DENTAL MATERIALS Biofilms are complex, surface-adherent, spatially organized polymicrobial communities containing bacteria surrounded by a polysaccharide matrix. Oral biofilms that form on the surfaces of teeth and biomaterials in the oral cavity are also known as den-tal plaque. When the human diet is rich in ferment-able carbohydrates, the most prevalent organisms shown to be present in dental plaque are adherent acidogenic and aciduric bacteria such as streptococci and lactobacilli, which are primarily responsible for dental caries. Other consequences of long-term oral biofilm accumulation can also include periodontal diseases and periimplantitis (inflammation of the soft and hard tissues surrounding an implant), depend-ing on the location of attachment of the biofilm. Biofilm formation on hard surfaces in the oral cavity is a sequential process. A conditioning film from saliva (known as pellicle) containing adsorbed macromolecules such as phosphoproteins and gly-coproteins is deposited on tooth structure and bio-materials within minutes after a thorough cleaning. This stage is followed by the attachment of plank-tonic (free-floating) bacteria to the pellicle. Division of the attached initial colonizing bacterial species produces microcolonies, and subsequent attachment of later colonizing species results in the formation of matrix-embedded multispecies biofilms. These bio-films can mature over time if they are not detached by mechanical removal or intrinsic factors. Biofilm formation occurs via complicated physi-cochemical and cellular interactions between the substrate, pellicle, and bacteria. These interactions occur at several levels and can include physical prox-imity, metabolic exchange, signal molecule–medi-ated communication, exchange of genetic material, production of inhibitory factors, and coaggregation (“specific cell-to-cell recognition between geneti-cally distinct cell types,” as defined by Kolenbrander et al., 2006). The pellicle contains a variety of receptor mol-ecules that are recognized primarily by streptococci (Fig. 2.14). This is evident in healthy individuals, who typically have biofilms containing a thin layer of adherent gram-positive cocci. The ability to bind to nonshedding surfaces such as enamel gives strep-tococci a tremendous advantage and is consistent with the observation that streptococci constitute 60% to 90% of the initial bacterial flora on enamel in situ. Furthermore, the streptococci are less sensitive to exposure to air than most oral bacteria because they are facultatively anaerobic and can participate in modifying the biofilm environment to a more reduced state, a condition often considered to favor an ecological shift toward gram-negative anaerobes. Interactions among human oral bacteria are pivotal to the development of oral biofilms (see Fig. 2.14). In the first 4 hours of biofilm formation, gram-positive cocci appear to predominate, particularly mitis group streptococci. After 8 hours of growth, the majority of the bacterial population continues to be largely coc-coid, but rod-shaped organisms are also observed. By 24 to 48 hours, thick deposits of cells with vari-ous morphologies can be detected, including coccoid, coccobacillary, rod-shaped, and filamentous bacteria. Within 4 days of biofilm growth, an increase in the numbers of gram-negative anaerobes is observed, and particularly of Fusobacterium nucleatum. The lat-ter organism has the unique ability to coaggregate with a wide variety of bacteria and is believed to play a pivotal role in the maturation of biofilm because it forms coaggregation bridges with both early and late colonizers. As the biofilm matures, a shift is observed 18 CRAIG’S RESTORATIVE DENTAL MATERIALS toward a composition of largely gram-negative mor-photypes, including rods, filamentous organisms, vibrios, and spirochetes. These shifts in the microbial composition of biofilm are important because they correlate with the development of gingivitis (inflam-mation of gingival tissues). Even though biofilms accumulate on restorative, orthodontic, endodontic, and implant biomaterials, the remainder of this section focuses on biofilms that accumulate on the surfaces of restorative and implant materials only. The precise mechanisms of bacterial adhesion and biofilm formation on the sur-faces of dental materials have not yet been identified despite decades of research effort but are accepted to be complex processes that depend on a large num-ber of factors. In vitro studies have shown that the adhesion of salivary proteins and bacteria at small distances (5–100 nm) from the surfaces of biomateri-als is influenced by a combination of Lifshitz-van der Waals forces, electrostatic interactions, and acid-base Adhesin receptor Fusobacterium nucleatum Early colonizers S. flueggei Late colonizers V. atypica Statherin Sialylated mucins Proline-rich protein Salivary agglutinin Bacterial cell fragment Sialylated mucins Salivary agglutinin Alpha-amylase Proline-rich protein C. sputigena C. ochracea C. gingivalis H. parainfluenzae A. naeslundii A. israelii P . acnes P . loescheii P . denticola P . gingivalis T. denticola E. corrodens Eubacterium spp. P . intermedia A. actinomycetemcomitans S. oralis S. mitis S. gordonii Acquired pellicle Tooth surface S. gordonii S. oralis S. sanguis FIG. 2.14 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. 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. The bacterial strains shown are Actinobacillus actinomycetemcomitans, Actinomyces israelii, Actinomyces naeslundii, Capnocytophaga gingivalis, Capnocytophaga ochracea, Capnocytophaga sputigena, Eikenella cor-rodens, 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 sanguis, Treponema spp., and Veillonella atypica. (From Kolenbrander PE, Andersen RN, Blehert DS, et al. Communication among oral bacteria. Microbiol Mol Biol Rev. 2002;66(3):486–505.) 19 2. The Oral Environment bonding. Other properties such as substrate hydro-phobicity, surface free energy, surface charge, and surface roughness have commonly been investigated in vitro for correlation with the number of adhering bacteria. Many of the aforementioned surface prop-erties are described in later chapters. The role of surface roughness in biofilm formation has been widely investigated. Smooth surfaces have been shown to attract less biofilm in vivo than rough surfaces. It has also been observed that hydrophobic surfaces that are located supragingivally attract less biofilm in vivo than more hydrophilic surfaces over a 9-day period. An increase in the mean surface rough-ness parameter (Ra) above a threshold value of 0.2 μm or an increase in surface free energy were found to result in more biofilm accumulation on dental materi-als. When both of those surface properties interact with each other, surface roughness was observed to have a greater effect on biofilm accumulation. The creation of a rough restoration surface caused by abrasion, ero-sion, air polishing or ultrasonic instrumentation, or a lack of polishing after the fabrication of a restoration has also been associated with biofilm formation. Bacterial adhesion in vivo is considerably reduced by the formation of a pellicle, regardless of the com-position of the underlying substrate. Pellicle forma-tion has also been shown to have a masking effect on specific surface characteristics of biomaterials to a certain extent. Surfaces having a low surface energy were observed to retain the smallest amount of adherent biofilm because of the lower binding forces between bacteria and substrata even after several days of exposure in the human oral cav-ity. Reciprocally, the higher surface energy of many restorative materials compared with that of the tooth surface could result in a greater tendency for the sur-face and margins of the restoration to accumulate debris, saliva, and bacteria. This may in part account for the relatively high incidence of secondary (recur-rent) carious lesions seen in enamel at the margins of resin composite and amalgam restorations. Investigations of oral biofilms on restorative materials can generally be divided into in vivo, in situ, and in vitro studies, with the latter comprising monospecies or multispecies investigations. Biofilms that are formed on restorative materials can vary in thickness and viability. In vivo and in situ studies of biofilm formation on dental materials have produced inconsistent results, and a trend for accumulation on materials has not been determined so far. Levels of cariogenic organisms (capable of pro-ducing or promoting caries) such as Streptococcus mutans have been shown to be higher in biofilms adjacent to posterior resin restorations than in bio-films adjacent to amalgam or glass ionomer res-torations. The formation of oral biofilms has been associated with an increase in the surface roughness of resin composites, degradation of the material due to acid production by cariogenic organisms, hydroly-sis of the resin matrix, and a decrease in microhard-ness of the restoration’s surface. Esterases of salivary and bacterial origin have also been implicated as sources of degradation. In addition, it has been theo-rized that planktonic bacteria can enter the adhesive interface between the restorative material and the tooth, leading to secondary caries and pulp pathol-ogy. By contrast, trace amounts of unpolymerized resin, resin monomers, and the products of resin bio-degradation, such as 2,2-bis[4(2,3-hydroxypropoxy) phenyl]propane (BisHPPP), triethylene glycol mono-methacrylate (TEGMA), triethylene glycol (TEG), and methacrylic acid (MA), have been shown to modulate the growth of oral bacteria in the vicinity of resin restorations. All of these factors create a cycle of bacteria-surface interaction that further increases surface roughness and encourages bacterial attach-ment to the surface, thereby placing the adjacent enamel at greater risk for secondary caries. Bacterial adhesion to casting alloys and dental amalgams has received limited attention in recent times as dental amalgam is being discontinued in response to global concerns about mercury (Hg) in the environment. Biofilms on gold-based casting alloys are reported to be of low viability, possibly because of the bacteriostatic effect of gold. Biofilms on amalgam are also reported to have low viability, which could be attributed to the presence of the Hg(II) form of mercury in dental amalgam. Interestingly, amalgam restorations have been shown to promote the levels of Hg-resistant bacteria in vitro and in vivo. Resistance to antibiotics, and specifically tetracycline, was observed to be concurrent with Hg resistance in oral bacteria. However, it is worth noting that Hg-resistant bacteria were also found in children without amalgam fillings or previous exposure to amalgam. Information regarding the morphology of bio-films on ceramic restorations is limited, although it is generally accepted that ceramic crowns accumu-late less biofilm than adjacent tooth structure. The recent demonstration of increased surface roughness of zirconia surfaces in vitro after the use of hand and ultrasonic scaling instruments could be theorized to produce greater biofilm accumulation on zirco-nia restorations subsequent to dental prophylaxis procedures. Biofilms that adhere to denture base resins pre-dominantly contain Candida species of yeast. However, initial adhesion of bacteria such as streptococci to the denture base may have to occur before Candida species can form biofilms. This is attributed to the observa-tion of bacteria on dentures within hours and Candida species after days, and to the ability of Candida spe-cies to bind to the cell wall receptors in streptococci. Biofilms on dentures have commonly been associated 20 CRAIG’S RESTORATIVE DENTAL MATERIALS with denture stomatitis (chronic inflammation of the oral mucosa) in elderly and immunocompromised patients. Removal of biofilms from dentures typically requires mechanical and/or chemical means and is a significant clinical problem because of biofilm adher-ence to the denture base resins. The accumulation of biofilms on glass ionomer and resin-modified glass ionomer biomaterials is a factor that has been associated with an increase in the surface roughness of those biomaterials. Fluoride-releasing materials, and glass ionomers and compomers in particular, can neutralize acids pro-duced by bacteria in biofilms. Fluoride can provide cariostatic benefits and may affect bacterial metabo-lism under simulated cariogenic conditions in vitro. Although the large volume of saliva normally present in the oral cavity is hypothesized to result in fluoride concentrations that are too low for oral cavity–wide antibacterial protection, the amount of fluoride released could theoretically be sufficient to minimize demineralization in the tooth structure adjacent to glass ionomer and resin-modified glass ionomer res-torations. In addition, glass ionomer materials can be recharged by daily exposure to fluoride-containing dentifrices, thereby compensating for the signifi-cant decrease in fluoride release that occurs over time. Interestingly, more studies are needed because clinical studies have not clearly demonstrated that fluoride-releasing restorative materials significantly reduce the incidence of secondary caries compared with nonfluoride-releasing biomaterials. The accumulation of biofilms on titanium and titanium alloys that are used in dental implants has received much attention because biofilms play a significant role in determining the success of an implant. The sequence of microbial colonization and biofilm formation on dental implants has been shown to be similar to that on teeth, but differs in early colonization patterns. Several in vivo stud-ies have confirmed that a reduction in mean Ra of implant materials below the threshold value of 0.2 μm has no major effect on adhesion, colonization, or microbial composition. Compared with polished titanium surfaces, titanium implant surfaces that were modified with titanium nitride (TiN) showed significantly less bacterial adhesion and biofilm for-mation in vivo, thereby potentially minimizing bio-film accumulation and subsequent periimplantitis. Other contributing factors such as the hydrophobic-ity, surface chemistry, and surface free energy of the implant material have been found to play vital roles in bacterial adhesion to dental implant materials. In addition, the surface characteristics of the bacteria, the design of the implant and the abutment, and the microgap between the implant and abutment have also been shown to influence microbial colonization on dental implants. The most common reason for the replacement of dental restorations is secondary caries at the gingi-val tooth-restoration margin. It is estimated that 50% to 80% of resin restorations are replaced annually in the United States alone. The cost of replacing resto-rations is estimated to be in the billions of dollars worldwide, and the number and cost of replacing restorations is increasing annually. Although bacte-riological studies of secondary caries indicate that its etiology is similar to that of primary caries, the mechanisms by which secondary caries occur are a focus of ongoing investigations. The removal of tenaciously adherent oral bio-films from hard surfaces is crucial to caries control and is most effectively accomplished by mechanical brushing with toothpaste, especially in interproxi-mal regions and posterior teeth along with the use of adjunctive chemical agents. Although tooth brushing has been associated with increased surface roughness of restorations over time due to the process of wear, which could permit additional bacterial attachment on the surface, mechanical removal has been shown to be more effective than chemical intervention. This is because bacteria in biofilms are typically well pro-tected from the host immune response, antibiotics, and antibacterials when embedded within a complex biofilm matrix. 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Enamel organic matrix: potential structural role in enamel and relationship to residual basement mem-brane constituents at the dentin–enamel junction. Connect Tissue Res. 2014;55(suppl 1):33–37. Nazari A, Bajaj D, Zhang D, et al. Aging and the reduction in fracture toughness of human dentin. J Mech Behav Biomed Mater. 2009;2(5):550–559. Olsson S, Olio G, Adamczak E. The structure of dentin sur-faces exposed for bond strength measurements. Scand J Dent Res. 1993;101:180–184. Pashley DH. Dentin: a dynamic substrate—a review. Scanning Microsc. 1989;3:161–176. Pashley DH, Tao L, Boyd L, et al. Scanning electron micros-copy of the substructure of smear layers in human den-tine. Arch Oral Biol. 1988;33(4):265–270. Shimizu D, Macho GA. Functional significance of the microstructural detail of the primate dentino-enamel junction: a possible example of exaptation. J Hum Evol. 2007;52(1):103–111. Zheng L, Hilton JF, Habelitz S, et al. Dentin caries activity status related to hardness and elasticity. Eur J Oral Sci. 2003;111(3):243–252. Oral Biofilms Bernardo M, Luis H, Martin MD, et al. Survival and reasons for failure of amalgam versus composite posterior resto-rations placed in a randomized clinical trial. J Am Dent Assoc. 2007;138(6):775–783. Bollen CM, Lambrechts P, Quirynen M. Comparison of surface roughness of oral hard materials to the thresh-old surface roughness for bacterial plaque retention: a review of the literature. Dent Mater. 1997;13(4):258–269. Busscher HJ, Rinastiti M, Siswomihardjo W, et al. Biofilm formation on dental restorative and implant materials. J Dent Res. 2010;89(7):657–665. Drummond J. Degradation, fatigue, and failure of resin den-tal composite materials. J Dent Res. 2008;87(8):710–719. Ferracane JL. Resin-based composite performance: are there some things we can’t predict? Dent Mater. 2013;29(1):51–58. Hannig C, Hannig M. 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Oral bacteria resistant to mercury and to antibiotics are present in children with no previous exposure to amalgam restorative materials. FEMS Microbiol Lett. 2003;223(1):107–111. Spencer P, Ye Q, Misra A, et al. Proteins, pathogens, and failure at the composite–tooth interface. J Dent Res. 2014;93(12):1243–1249. Subramani K, Jung RE, Molenberg A, et al. Biofilm on dental implants: a review of the literature. Int J Oral Maxillofac Implants. 2009;24(4):616–626. Teughels W, Van Assche N, Sliepen I, et al. Effect of material characteristics and/or surface topography on biofilm devel-opment. Clin Oral Implants Res. 2006;17(suppl 2):68–81. von Fraunhofer JA, Loewy ZG. Factors involved in microbial colonization of oral prostheses. Gen Dent. 2009;57(2):136–143. quiz 44–45. Wiegand A, Buchalla W, Attin T. Review on fluoride-releasing restorative materials–fluoride release and uptake char-acteristics, antibacterial activity and influence on caries formation. Dent Mater. 2007;23(3):343–362. This page intentionally left blank 23 This section presents two concepts in dental treat-ment design: evidence-based dentistry and mate-rials-centered design. Both concepts are used to develop rational treatment plans that consider the patient’s needs and preferences, and materials char-acteristics appropriate for those needs. EVIDENCE-BASED DENTISTRY The American Dental Association (ADA) defines evidence-based dentistry as “an approach to oral healthcare that requires the judicious integration of systematic assessments of clinically relevant scientific evidence, relating to the patient’s oral and medical condition and history, with the den-tist’s clinical expertise and the patient’s treatment needs and preferences” ( This approach is patient centered and tailored to the patient’s needs and preferences. All three elements are used in the decision-making process for patient care (Fig. 3.1). Patient Evidence Patient needs, conditions, and preferences are con-sidered throughout the diagnostic and treatment planning process. Observation of patient needs and medical/dental history occurs first. In this phase, performance of prior and existing restorations, in terms of success or failure, should be noted. This is often a good indicator of conditions in the oral environment and the prognosis of success of similar materials in this environment. The patient’s facial profile and orofacial musculature is a good indica-tor of potential occlusal forces. Wear patterns on occlusal surfaces are indicators of bruxing, clench-ing, occlusal forces, and mandibular movements. Cervical abfractions may indicate heavy occlusal contact accompanied by bruxing or occlusal interfer-ences, and possibly in association with aggressive tooth brushing and acidic conditions. Erosion on anterior teeth typically suggests elevated levels of dietary acids, and generalized wear without occlu-sal trauma could involve a systemic disorder such as gastroesophageal reflux disease (GERD). Any of these conditions would compromise the longevity of restorative therapy. Unusually harsh environments require careful restoration design and selection of materials, sometimes different from the norm. Restorative material options then need to be con-sidered with the problems and needs of the patient. The integration of patient data and materials char-acteristics forms a more comprehensive plan for treatment. Scientific Evidence When searching for scientific evidence, the best avail-able evidence, usually compiled from a review of the scientific literature, provides objective information to inform the clinician and patient. The highest level of validity is chosen to minimize bias. These studies are typically meta-analyses of randomized controlled C H A P T E R 3 Materials-Centered Treatment Design Scientific evidence Clinician experience and expertise Patient needs, conditions, and preferences FIG. 3.1 The elements of evidence-based dentistry. 24 CRAIG’S RESTORATIVE DENTAL MATERIALS trials (RCTs), systematic reviews, or individual RCTs. Lower levels of evidence are found in case studies, cohort studies, and case reports. Laboratory studies are listed as “other evidence” because a clinical cor-relation can be made only as an extrapolation of the laboratory data. The listing of bench or laboratory research as “other evidence” should not be construed as meaning that bench research is not valid or useful. The hierarchy of evidence as presented for evidence-based data (EBD) is based on human clinical trials, for which laboratory tests are at best only a simulation. Because new material developments that are enhancements to existing products are not required to undergo clinical testing by the Food and Drug Administration (FDA), published laboratory or in vitro studies are often the only forms of scientific evidence available for specific materials. This does not mean that no evidence is available. However, the clinician must recognize the limitations of these data, despite their scientific validity, when translating them to the clinical situation and making treatment decisions for a patient (Table 3.1). Researchers in dental materials science have ana-lyzed the correlation between one or two physical or mechanical properties of materials and clinical per-formance. Although it is possible to use laboratory tests to rank the clinical performance of different for-mulations of the same class of material, the perfect clinical predictor remains to be found. Differences in test configuration, specimen geometry, speci-men processing, and environment conditions make direct comparison between laboratory tests difficult. However, understanding these tests and the informa-tion they provide can provide guidance for the selec-tion of a material for a specific situation. Tests and the properties they assess are discussed in Chapter 5. PLANNING FOR DENTAL TREATMENT Every patient is unique, including the patient’s oral envi-ronment and general physiology. This provides a unique set of circumstances and challenges for implementing successful materials choices in a treatment plan. In the next section, we present a rationale for selecting materi-als, based on the treatment design approach proposed by Spear and Kokich. They advocate a treatment plan-ning process that starts with an assessment of overall esthetics and proceeds to consider function, structure, and biology in that order. Decisions made at every stage directly affect the following stages. Treatment begins with the acute problems then progresses logically to facilitate a stepwise sequence that can be clearly defined and communicated among the clinicians involved in delivering care to the patient. Table 3.2 presents a TABLE 3.1 Assessing the Quality of Evidence Study Quality Diagnosis Treatment/Prevention/ Screening Prognosis Level 1: good-quality, patient-oriented evidence Validated clinical decision rule SR/meta-analysis of high-quality studies High-quality diagnostic cohort studya SR/meta-analysis or RCTs with consistent findings High-quality individual RCTb All-or-none studyc SR/meta-analysis of good-quality cohort studies Prospective cohort study with good follow-up Level 2: limited-quality patient-oriented evidence Unvalidated clinical decision rule SR/meta-analysis of lower quality studies or studies with inconsistent findings Lower quality diagnostic cohort study or diagnostic case-control study SR/meta-analysis of lower quality clinical trials or of studies with inconsistent findings Lower quality clinical trial Cohort study Case-control study SR/meta-analysis of lower quality cohort studies or with inconsistent results Retrospective cohort study or prospective cohort study with poor follow-up Case-control study Case series Level 3: other evidence Consensus guidelines, extrapolations from bench research, usual practice, opinion, disease-oriented evidence (intermediate or physiologic outcomes only), or case series for studies of diagnosis, treatment, prevention, or screening RCT, Randomized controlled trial; SR, systematic review. aHigh-quality diagnostic cohort study: cohort design, adequate size, adequate spectrum of patients, blinding, and a consistent, well-defined reference standard. bHigh-quality RCT: allocation concealed, blinding if possible, intention-to-treat analysis, adequate statistical power, adequate follow-up (greater than 80%). cIn an all-or-none study, the treatment causes a dramatic change in outcomes, such as antibiotics for meningitis or surgery for appendicitis, which precludes study in a controlled trial. From Newman MG, Weyant R, Hujoel P. JEBDP improves grading system and adopts strength of recommendation taxonomy grading (SORT) for guidelines and systematic reviews. J Evid Based Dent Pract. 2007;7:147–150. 25 3. Materials-Centered Treatment Design TABLE 3.2 Decision Matrix for Selecting Dental Materialsa Assessment and Factors Query Relevant Dental Materials and Properties (Chapter No.) ESTHETICS: MAXILLARY Central incisors relative to upper lip • Is the incisal edge display of the maxillary centrals sufficient? Surface characteristics (4) Light, reflection, color (4) Resin composites (9) Ceramics (11) Adhesives and cements (9, 13) Midline and inclination of incisors • Does the maxillary midline need correction? • Does the inclination of the maxillary incisors need correction? Surface characteristics (4) Light, reflection, color (4) Resin composites (9) Ceramics (11) Adhesives and cements (9, 13) Posterior occlusal plane • Does the maxillary posterior occlusal plane need correction? • Is sufficient tooth structure present? • What are the surface characteristics of the opposing dentition? Forces and wear (4) Core buildup (9) Provisional materials (9) Resin composites (9) Adhesives and cements (9, 13) Metals and alloys (10) Ceramics (11) Gingival levels • Do gingival margins need correction? Resin composites (9) Glass ionomers (9) Ceramics (11) Adhesives and cements (9, 13) ESTHETICS: MANDIBULAR Same factors as for maxillary: Midline, inclination, posterior occlusal plane, and gingival levels ESTHETICS AND FUNCTION Missing teeth • Are missing teeth in need of replacement? • Is a fixed or removable prosthesis preferred? • Should adjacent teeth be involved in the replacement? • What are the surface characteristics of the opposing dentition? Forces, stress, and wear (4) Provisional materials (9) Adhesives and cements (9, 13) Denture materials (9) Metals and alloys (10) Ceramics (11) Impression materials (12) Casting materials (12) Implants (15) FUNCTION Occlusion • Does the occlusal relationship need correction? • What are the surface characteristics of the opposing dentition? Forces, stress, and wear (4) Resin composites (9) Metals and alloys (10) Ceramics (11) Impression materials (12) Casting materials (12) Adhesives and cements (9, 13) Implants (15) Articulator BIOLOGIC Oral environment: enamel, dentin, pulp, and periodontal ligament • Is acute disease present? • Are conditions in the oral environment favorable (e.g., saliva pH, salivary flow, oral hygiene, diet, supporting bone structure, pulp, occlusal habits)? Oral environment (2) Forces, stress, and wear (4) Biocompatibility (6) Intermediary materials (8) Tissue engineering (16) aThis table augments the sequence and logic presented in the section “Planning for Dental Treatment” with factors, queries, and references to chapters in this textbook. 26 CRAIG’S RESTORATIVE DENTAL MATERIALS summary of the approach with queries for each stage, and relevant materials and properties to be considered. An esthetics appraisal analyzes the position of the midline and the length of the maxillary and mandibular incisors, which influence the position of the posterior occlusal plane, which in turn influ-ences function. The esthetics appraisal starts with an assessment of the position of the maxillary cen-tral incisors relative to the upper lip. If the incisal edge display is insufficient, lengthening of the inci-sal edges can be done surgically or by orthodontic treatment, or by restorative methods using dental materials. Most cultures would prefer materials that mimic natural dentition in color, texture, and reflectance. Ceramics and resin composites exhibit these properties. A number of options exist for these two classes of materials. Ceramics are discussed in Chapter 11. Resin composites are discussed in Chapter 9. The next consideration in the esthetics appraisal is position of the midline and inclination of the max-illary incisors. The labial surface characteristics and inclination influence the light reflectance of the inci-sors. Maximum light reflectance is achieved when the labial surface is perpendicular to the occlusal plane. Corrections to the midline and to the labial inclination can be done by orthodontics or restor-ative dentistry. Surface characteristics, light, reflec-tion, and color are discussed in Chapter 4. The next step assesses the maxillary posterior occlusal plane relative to an ideal position of the max-illary incisal edge. Corrections to the posterior occlu-sal plane can be achieved by surgery or restorative procedures. Materials for adjusting the posterior occlusion can be the same as for anterior restorations; however, the function of posterior teeth and occlusal relationships should be considered in the selection of materials. The wear of materials in contact as well as the resistance to occlusal forces are important consid-erations. Forces and wear are discussed in Chapter 4. Metals and alloys are discussed in Chapter 10. Gingival levels of the anterior teeth play a large role in esthetics. Similarly, the appearance of the gin-gival margin of anterior restorations will influence their overall esthetics. Ceramics can be used to fab-ricate restorations with an esthetic gingival margin. The combination of ceramics and metal at the gin-gival margin, as in ceramic-metal restorations, can make the esthetic gingival margin more difficult to achieve. Ceramic-metal materials are discussed in Chapters 10 and 11. After completing the assessment and plan for the maxillary anterior and posterior teeth, the mandibu-lar anterior and posterior teeth can be assessed and designed. Missing teeth can be restored by a fixed or removable dental prosthesis, or a dental implant. Materials for a fixed dental prosthesis include metals and ceramics. Removable prostheses or removable partial dentures can include these materials and polymers. Polymers for removable dentures are dis-cussed in Chapter 9. Single or multiple missing teeth can be restored by dental implants that mimic the shape and position of the tooth root onto which res-torations such as a crown or fixed dental prosthesis are secured. Implants are discussed in Chapter 15. Adhesives and cements for securing prostheses to tooth structure are discussed in Chapters 9 and 13. The esthetic plan is integrated with the functional occlusion by replicating the patient’s dentition and occlusal relationships, then positioning these casts on an articulator. Materials for replicating dentition and oral tissues are called impression materials. These materials form a negative replica or mold of the tissues into which a rigid-setting material, often gypsum, is poured to make a positive replica of the oral tissues. Impression and casting materials are dis-cussed in Chapter 12. The biological assessment wraps up the diagnos-tics and planning. In this phase, the health of the sup-porting periodontal tissues including the periodontal ligament is evaluated, along with the conditions of the oral environment, and condition of the enamel, dentin, and pulp. If acute disease such as dental car-ies is present, intermediary materials can be used to stabilize the condition before definitive materi-als are used. Intermediary materials are discussed in Chapter 8. The oral environment is discussed in Chapter 2. As mentioned at the start of this chapter, patient behaviors and preferences are also an important con-sideration. The patient may need instruction and coaching on prevention and maintenance of den-tal treatment. Preventive materials are discussed in Chapter 8. The performance of prior dental treatment is evaluated. Reactions to materials used in prior res-torations should be considered. Biocompatibility and tissue reactions are discussed in Chapter 6. Refer to Table 3.2 for questions to consider in each stage of treatment design along with relevant dental materials and properties. Chapter numbers are listed for the materials and properties for further informa-tion and review. Bibliography American Dental Association. ADA Center for Evidence-Based Dentistry. Accessed 03.10.17. Bader JD. Stumbling into the age of evidence. Dent Clin North Am. 2009;53(1):15. Forrest JL. Introduction to the basics of evidence-based dentistry: concepts and skills. J Evid Based Dent Pract. 2009;9(3):108. Forrest JL, Miller SA. Translating evidence-based decision making into practice: EBDM concepts and finding the evidence. J Evid Based Dent Pract. 2009;9(2):59. 27 3. Materials-Centered Treatment Design Miller SA, Forrest JL. Translating evidence-based decision making into practice: appraising and applying the evi-dence. J Evid Based Dent Pract. 2009;9(4):164. Newman MG, Weyant R, Hujoel P. JEBDP improves grad-ing system and adopts strength of recommendation tax-onomy grading (SORT) for guidelines and systematic reviews. J Evid Based Dent Pract. 2007;7:147–150. Sakaguchi RL. Evidence-based dentistry: achieving a bal-ance. J Am Dent Assoc. 2010;141(5):496–497. Spear FM, Kokich VG. A multidisciplinary approach to esthetic dentistry. Dent Clin N Am. 2007;51:487. Spear FM, Kokich VG, Mathews DP. Interdisciplinary man-agement of anterior dental esthetics. J Am Dent Assoc. 2006;137:160. This page intentionally left blank 29 Restorative dental materials are subjected to a very hostile environment, in which pH, salivary flow, and mechanical loading fluctuate constantly and often rapidly. These challenges have required substantial research and development to provide products for the clinician. Much of this is possible through the application of fundamental concepts of materials sci-ence. The understanding of properties of polymers, ceramics, and metals is crucial to their selection and design of dental restorations. No single property defines the quality of a mate-rial. Several properties, determined from standard-ized laboratory and clinical tests, are often used to describe quality. Clinical tests are expensive and inherently difficult to carry out, so laboratory tests are usually performed before clinical tests to provide standardized measures for comparing materials and guiding the interpretation of clinical trials. Standardization of laboratory tests is essential, however, to control quality and permit comparison of results between investigators. When possible, test specimens should mimic the size and shape of the structure in the clinical setting, using the same mix-ing and manipulating procedures as those used in routine clinical conditions. Although standardized laboratory tests are useful to compare values of properties of differ-ent restorative materials (e.g., different brands), they are also essential to know the characteris-tics of the supporting hard and soft tissues. Many restorations fail clinically because of fracture or deformation. This is a material property issue. Some well-constructed restorations become unser-viceable because the dentin or enamel fails. This is an interface or substrate failure. Consequently, when designing restorations and interpreting test results, it is important to remember that the suc-cess of a restoration depends not only on the phys-ical qualities of the restorative material, but also on the biophysical or physiological qualities of the supporting tissues. The physical properties described in this chapter include mechanical properties, thermal properties, electrical and electromechanical properties, color, and optical properties. MECHANICAL PROPERTIES In the oral environment, restorative materials are exposed to chemical, thermal, and mechanical chal-lenges. These challenges can cause deformation of the material. The science that studies how biological materials interact and deform is called biomechan-ics. This section introduces concepts of elastic, plas-tic, and viscoelastic deformation and mechanical quantities including force, stress, strain, strength, toughness, hardness, friction, and wear in terms of performance of materials in the oral environment. Force One body interacting with another generates force. Forces may be applied through actual contact of the bodies or at a distance (e.g., gravity). The result of an applied force on a body is translation or defor-mation of the body depending on whether the body is rigid or deformable and whether the body is con-strained or not. If the body is constrained (i.e., does not move), the force causes the body to deform or change its shape. If the body is free of constraints, an applied force results in movement. A force is defined by three characteristics: point of application, magnitude, and direction of application. The direction of a force is characteristic of the type of force. The International System of Units (SI) unit of force is the newton (N). One pound-force (lb-f) equals 4.4 newtons (N). Occlusal Forces Maximum occlusal forces range from 200 to 3500 N. Occlusal forces between adult teeth are highest in the C H A P T E R 4 Fundamentals of Materials Science 30 CRAIG’S RESTORATIVE DENTAL MATERIALS posterior region closest to the mandibular hinge axis and decrease from the molars to the incisors. Forces on the first and second molars vary from 400 to 800 N. The average force on the premolars, canines, and incisors is about 300, 200, and 150 N, respectively. A somewhat nonlinear but definite increase in force from 235 to 494 N occurs in growing children, with an average yearly increase of about 22 N. Forces on Restorations Patients with a partial removable denture gener-ate occlusal forces in the range of 65 to 235 N. For patients with a complete removable denture, the average force on posterior teeth is about 100 N; the forces on the incisors average 40 N. Age and gen-der variations in the patient populations, as well as facial form and muscle definition, contribute to the large variation in force values. When designing res-torations and selecting materials, it is important to consider the location in the arch, opposing dentition, and force-generating capacity of the patient. The suc-cess or failure of other restorations in the patient’s mouth should be an indication of how challenging those factors are for that specific individual. Stress When a force acts on a constrained body, the body resists the force. This internal reaction is equal in magnitude and opposite in direction to the applied external force, and is called stress, typically denoted as S or σ. Both the applied force and the internal resistance (stress) are distributed over an area of the body, so the stress in an object is defined as the force per area, or stress = force/area. Stress is difficult to measure directly, so the force and the area to which the force is applied are measured, and stress is cal-culated from the ratio of force per area. The unit of stress therefore is the unit of force (N) divided by a unit of area, and is commonly expressed in SI units as pascal (1 Pa = 1 N/m2 = 1 MN/mm2). It is common to report stress in units of megapascals (MPa) or mil-lions of pascals, 1 MPa = 106 Pa. Stress in a structure varies directly with the force and inversely with area, so the area over which the force acts is an important consideration. This is par-ticularly true in dental restorations in which the areas over which the forces are applied often are extremely small. For example, cusp areas of contact may have cross-sectional areas of only 0.16 to 0.016 cm2. Stresses of several hundred MPa occur in many types of restorations and of thousands of MPa when the contact area of a cusp or dental explorer is used to apply the force. This is one reason that premature contacts, in which small surface areas are support-ing large occlusal forces, are so damaging. When equilibrating the occlusion, multiple simultaneous occlusal contacts are desirable. Distributing occlu-sal forces over larger surface areas reduces the local occlusal stress. Types of Stress A force can be applied from any angle or direction. Several forces often combine to develop complex stresses in a structure. It is rare for forces and stresses to be isolated to a single axis. Individually applied forces can be defined as axial, shear, bending, or tor-sional. These directional forces are illustrated in a simplified manner in Fig. 4.1. All stresses, however, can be resolved into combinations of two basic types: axial and shear. Tension results from two sets of forces directed away from each other in the same straight line or when one end is constrained and the other end is subjected to a force directed away from the con-straint. Compression results from two sets of forces directed toward each other in the same straight line or when one surface is constrained and the other is subjected to a force directed toward the constraint. Shear occurs from two sets of forces directed par-allel to each other, but not along the same straight line. Torsion results from the twisting of a body, and bending or flexure results from an applied bending moment. When tension is applied, the molecules making up the body resist being pulled apart. When compression is applied, they resist being forced more closely together. As a result of a shear stress applica-tion, one portion of the body must resist sliding past another. These resistances of a material to deforma-tion represent the basic qualities of elasticity of solid bodies. An example of the complexity and varying direc-tion and magnitude of stresses in the oral cavity is shown in Fig. 4.2, in which a finite element model of Shear Twisting moment Bending moment Axial, tension Compression Axial, compression Bending Torsion Shear Elongation FORCE DEFORMATION FIG. 4.1 Schematic of the different types of stresses and their corresponding deformations. 31 4. Fundamentals of Materials Science a dental implant is loaded in compression. Fig. 4.2A shows the stresses on the shoulder of the implant resulting from occlusal forces. Fig. 4.2B shows the distribution of stresses in the implant abutment. Strain Each type of stress is capable of producing a corre-sponding deformation in a body (see Fig. 4.1). The deformation from a tensile force is an elongation in the axis of applied force, whereas a compressive force causes compression or shortening of the body in the axis of loading. Strain, ε, is described as the change in length (ΔL = L − Lo) per original length (Lo) of the body when it is subjected to a load. The units of measurement (length/length) cancel in the calculation of strain. Strain ε = Deformation/Original length = L −Lo /Lo = ∆L/Lo If a load is applied to a wire with an original length of 2 mm resulting in a new length of 2.02 mm, it has deformed 0.02 mm and the strain is 0.02/2 = 0.01, or 1%. Strain is often reported as a percentage. Although the length units cancel in the calculation of strain, it is best to report the units with the final result to specify the scale of the measurement (m/m; mm/mm; μm/μm). The amount of strain will differ with each type of material and with the magnitude of the load applied. Note that regardless of the com-position or nature of the material, and regardless of the magnitude and type of load applied to the mate-rial, deformation and strain result with each stress application. Strain is an important consideration in dental restorative materials, such as orthodontic wires or implant screws, in which a large amount of strain can occur before failure. Wires can be bent and adjusted without fracturing. Strain is also important in impression materials, where the material needs to recover without permanent distortion when remov-ing it from hard tissue retentive areas. Stress-Strain Curves If a bar of material is subjected to an applied force, F, the magnitude of the force and the resulting defor-mation (δ) can be measured. In another bar of the same material, but different dimensions, the same applied force produces different force-deformation characteristics (Fig. 4.3A). However, if the applied force is normalized by the cross-sectional area A of the bar (stress), and the deformation is normalized by the original length of the bar (strain), the resulting stress-strain curve is independent of the geometry of the bar (Fig. 4.3B). It is therefore preferred that the stress-strain relations of an object be reported rather than the force-deformation characteristics. The stress-strain relationship of a dental material can be studied by measuring the load and deformation and then calculating the corresponding stress and strain. When testing materials, loads should be applied at a uniform rate, and deformation should occur at a uniform rate. A typical universal testing machine can analyze materials in tension, compression, or shear. In the scheme illustrated in Fig. 4.4, a rod is clamped between two jaws and a tensile force is applied. The load is measured with a force trans-ducer and the deformation is measured with an extensometer clamped over a specified length of the specimen. A plot of load versus deformation is produced, which can be converted to a plot of stress versus strain (Fig. 4.5) by the simple calculations A B FIG. 4.2 Stress distribution in an implant-supported restoration. (A) Stresses on the shoulder of the implant body from an oblique occlusal load. (B) Stresses within the implant abutment and alveolar bone. (Courtesy Dr. Svenn Borgersen, Eagan, MN and Dr. Ronald Sakaguchi.) 32 CRAIG’S RESTORATIVE DENTAL MATERIALS described previously. By convention, strain is plot-ted on the x-axis as an independent variable because most tests are operated in strain control, where a constant strain is applied to the specimen and the resulting force is measured as the dependent, or y-axis, variable. In the calculation of stress, it is assumed that the cross-sectional area of the specimen remains con-stant during the test. Using this assumption, the stress-strain curve is called an engineering stress-strain curve, and stresses are calculated using the original cross-sectional area. When large loads are applied, or the object is tested in tension, the cross-sectional area might change dramatically during testing. In that case, the true stress, calculated with the actual cross-sectional area in the denominator, is very dif-ferent than the engineering stress, calculated with the original cross-sectional area. If the cross-sectional area decreases during the test, the true stress will be higher than the engineering stress because the denominator is smaller. In most mechanical tests, particularly those of small specimen dimensions, the original cross-sectional area is used for calculat-ing stress because it is often very difficult to measure the cross-sectional area as it changes throughout the experiment. Engineering stress is used in the presen-tation of stress-strain curves obtained in tension in this chapter. Proportional and Elastic Limits A stress-strain curve for a hypothetical material subjected to increasing tensile stress until failure is shown in Fig. 4.5. As the stress is increased, the strain is increased. In the initial portion of the curve, from 0 to A, the stress is linearly proportional to the strain. As the strain is doubled, the stress is also doubled. After point A, the stress is no longer linearly propor-tional to the strain. Hence the value of the stress at A is known as the proportional limit (SPL or σPL), defined as the highest stress at which the stress-strain curve is a straight line; that is, stress is linearly proportional to strain. Below the proportional limit, no permanent deformation occurs in a structure. When the force is Slope E ––– F/A /L F/A () /L () B 3 F F 2 1 A L FIG. 4.3 Force-deformation characteristics. (A) Force-deformation characteristics for the same material but having different dimensions. (B) Stress-strain characteristics of the same group of bars. The stress-strain curve is independent of the geometry of the bar. Load cell Extensometer Specimen Moving crosshead FIG. 4.4 Universal testing machine. 33 4. Fundamentals of Materials Science removed, the object will return to its original dimen-sions. Below the proportional limit, the material is elastic in nature. The region of the stress-strain curve before the proportional limit is called the elastic region. When an object experiences a stress greater than the pro-portional limit, permanent or irreversible strain occurs. The region of the stress-strain curve beyond the proportional limit is called the plastic region. This characterization refers to linearly elastic materials such as many metals in which the relation between stress and strain is linear up to the proportional limit, and nonlinear thereafter. There are exceptions to this general rule, however. Materials described as super-elastic exhibit nonlinear elastic behavior; that is, their relationship between stress and strain in the elastic region does not follow a straight line, but removal of the load results in a return to zero strain. The elastic limit (SEL or σEL) is defined as the maxi-mum stress that a material will withstand without permanent deformation. For linearly elastic materi-als, the proportional limit and elastic limit represent the same stress within the structure, and the terms are often used interchangeably in referring to the stress involved. An exception is when superelastic materials are considered. It is important to remem-ber, however, that the two terms differ in funda-mental concept; one deals with the proportionality of strain to stress in the structure, whereas the other describes the elastic behavior of the material. For the same material, values for proportional or elastic limit obtained in tension versus compression will differ. The concepts of elastic and plastic behavior can be illustrated with a simple schematic model of the deformation of atoms in a solid under stress (Figs. 4.6 and 4.7). The atoms are shown in Fig. 4.6A, without stress, and in Fig. 4.6B, with a resulting stress that is below the value of the proportional limit. When the stress shown in (B) is removed, the atoms return to their positions shown in (A), indicating that the deformation was reversible. When the stress is greater than the proportional limit, the atoms move to a position as shown in Fig. 4.7B, and on removal of the stress, the atoms remain in this new position, indicating an irreversible, permanent deformation. When the stress is less than the proportional or elastic limit, the strain is reversible, whereas when the stress is greater than the proportional or elastic limit, there is an irreversible or permanent strain in the object. Yield Strength It is often difficult to explicitly measure the propor-tional and elastic limits because the precise point of 0 Stress (MPa) Strain (mm/mm) 12 10 8 6 4 2 14 0 20 10 30 40 50 60 70 80 90 100 A B C D A B C D Stress (MPa) Strain (mm/mm) Plastic deformation Elastic deformation PL SF A B FIG. 4.5 Plotting stress-strain curves. (A) Stress-strain curve for a material subjected to tensile stress. Specimens illustrate amount of deformation at each point (A–D). (B) Elastic deformation is exhibited up to the proportional limit (PL) and plastic deformation is exhibited from PL to the fail-ure point, where we register the stress at failure (SF). Shear force Shear force Elastic shear strain Shear stress A B B Shear force Shear force d A–B interface A B A Shear stress FIG. 4.6 Sketch of an atomic model showing atoms in original position (A) and after elastic deformation (B). (Modified from Anusavice KJ. Phillips’ Science of Dental Materials. 11th ed. St. Louis: Saunders; 2003:79.) 34 CRAIG’S RESTORATIVE DENTAL MATERIALS deviation of the stress-strain curve from linearity is difficult to determine. The yield strength or yield stress or yield point (YS or σY) of a material is a property that can be determined readily and is often used to describe the stress at which the material begins to function in a plastic manner. At this point, a small, defined amount of permanent strain has occurred in the material. The yield strength is defined as the stress at which a material deforms plastically and there is a defined amount of permanent strain. The amount of permanent strain is arbitrarily selected for the material being examined and may be indicated as 0.1%, 0.2%, or 0.5% (0.001, 0.002, or 0.005) permanent strain. The amount of permanent strain is referred to as the percent offset. Many specifications use 0.2% as a convention, but this depends on the plastic behavior of the material tested. For stiff materials with small elongation, the calculation of yield stress will include greater offsets than those materials with larger elon-gation or deformation. The yield stress is determined by selecting the desired offset or strain on the x-axis and drawing a line parallel to the linear region of the stress-strain curve. The point at which the parallel line intersects the stress-strain curve is the yield stress. On the stress-strain curve shown in Fig. 4.5, for example, the yield strength is represented by the value B. This represents a stress of about 360 MPa at a 0.25% off-set. This yield stress is slightly higher than that for the proportional limit because it includes a speci-fied amount of permanent deformation. Note that when a structure is permanently deformed, even to a small degree (such as the amount of deformation at the yield strength), it does not return completely to its original dimensions when the stress is removed. For this reason, the elastic limit and yield strength of a material are among its most important proper-ties because they define the transition from elastic to plastic behavior. Any dental restoration that is permanently deformed through the forces of mastication usually loses its functionality to some extent. For example, a fixed partial dental prosthesis (such as a three-unit prosthesis) that is permanently deformed by exces-sive occlusal forces would exhibit altered occlusal contacts. The restoration is permanently deformed because a stress equal to or greater than the yield strength was generated. It is important to remember that dysfunctional occlusal loading also changes the stresses placed on a restoration. A deformed resto-ration may therefore be subjected to greater stresses than originally intended because the occlusion that was distributed over a larger number of occlusal con-tacts may now be concentrated on a smaller number of contacts. Under these conditions, fracture does not occur if the material is able to plastically deform. However, this permanent change in shape represents a destructive example of deformation. Permanent deformation and stresses in excess of the elastic limit are desirable when shaping an orthodontic arch wire or adjusting a clasp on a removable partial denture. In these examples, the stress must exceed the yield strength to permanently bend or adapt the wire or clasp. Elastic deformation occurs as the wire or clasp engages and disengages a retentive region in the cer-vical area of the tooth. Retention is achieved through small-scale elastic deformation. This elastic or revers-ible deformation describes the function of elastic bands, clasps, o-rings, and implant screws. Ultimate Strength In Fig. 4.5 the test specimen exhibits a maximum stress at point C. The ultimate tensile strength or stress (UTS) is defined as the maximum stress that a mate-rial can withstand before failure in tension, whereas the ultimate compressive strength or stress (UCS) is the maximum stress a material can withstand in com-pression. The ultimate engineering stress is deter-mined by dividing the maximum load in tension (or compression) by the original cross-sectional area of the test specimen. The ultimate tensile strength of the material in Fig. 4.5 is about 380 MPa. The ultimate strength of an alloy as used in den-tistry specifies the maximum load and minimum cross-sectional area when designing a restoration. Note that an alloy that has been stressed to near the ultimate strength will be permanently deformed, so a restoration receiving that amount of stress during function would be useless. A safety margin should be incorporated into the design of the restoration and choice of material to ensure that the ultimate strength is not approached in normal function. The yield strength is often of greater importance than ultimate Shear stress A B Shear force Shear force d A Plastic shear strain A B B FIG. 4.7 Sketch of an atomic model showing atoms in original position (A) and after plastic deformation (B). (Modified from Anusavice KJ. Phillips’ Science of Dental Materials. 11th ed. St. Louis: Saunders; 2003:79.) 35 4. Fundamentals of Materials Science strength in design and material selection because it is an estimate of when a material will start to deform permanently. Fracture Strength In Fig. 4.5 the test specimen fractured at point D. The stress at which a brittle material fractures is called the fracture strength or fracture stress (SF or σF). Note that a material does not necessarily fracture at the point at which the maximum stress occurs. After a maximum tensile force is applied to some materials, the speci-men begins to elongate excessively, resulting in “neck-ing” or a reduction of cross-sectional area (see Fig. 4.5). The stress calculated from the force and the origi-nal cross-sectional area may decrease dramatically before final fracture occurs because of the reduction in cross-sectional area. Accordingly, the stress at the end of the curve is less than that at some intermediate point on the curve. Therefore, in materials that exhibit necking, the ultimate and fracture strengths are dif-ferent. However, for the specific cases of many dental alloys and ceramics subjected to tension, the ultimate and fracture strengths are similar, as is shown later in this chapter. Note that the reduction in stress that is observed after the ultimate stress in materials that show necking is an artifact of using the original cross-sectional area in the calculation of stress. If the true cross-sectional area is used, the stress would increase. Elongation The deformation that results from the applica-tion of a tensile force is elongation. Elongation is extremely important because it gives an indica-tion of the possible manipulation of an alloy. As may be observed from Fig. 4.5, the elongation of a material during a tensile test can be divided conveniently into two parts: (1) the increase in length of the specimen below the proportional limit (from 0 to A), which is not permanent and is proportional to the stress; and (2) the elonga-tion beyond the proportional limit and up to the fracture strength (from A to D), which is perma-nent. The permanent deformation may be mea-sured with an extensometer while the material is being tested and calculated from the stress-strain curve. Total elongation is commonly expressed as a percentage. The percent elongation is calculated as follows: Elongation = Original length) × 100 (Increase in length/ Total elongation includes both the elastic elonga-tion and the plastic elongation. Plastic elongation is usually the greatest of the two, except in materials that are quite brittle or those with very low stiffness. A material that exhibits a 20% total elongation at the time of fracture has increased in length by one-fifth of its original length. Such a material, as in many dental gold alloys, has a high value for plastic or per-manent elongation and, in general, is a ductile type of alloy, whereas a material with only 1% elongation would possess little permanent elongation and be considered brittle. An alloy that has a high value for total elongation can be bent permanently without danger of frac-ture. Clasps can be adjusted, orthodontic wires can be adapted, and crowns or inlays can be burnished if alloys with high values for elongation are used. Elongation and yield strength are generally related in many materials, including dental gold alloys, where, generally, the higher the yield strength, the lower the elongation. Elastic Modulus The measure of elasticity of a material is described by the term elastic modulus, also referred to as modulus of elasticity or Young’s modulus, and denoted by the variable E. The word modulus means ratio and in this case, the ratio of stress to strain. The elastic modu-lus represents the stiffness of a material within the elastic range. The elastic modulus can be determined from a stress-strain curve (see Fig. 4.5) by calculating the ratio of stress to strain or the slope of the linear region of the curve. The modulus is calculated from the following equation: Elastic modulus = Stress/Strain or E = σ/ε This equation is also known as Hooke’s law. Because strain is unitless (length/length), the mod-ulus has the same units as stress and is usually reported in MPa or GPa (1 GPa = 1000 MPa). The elastic qualities of a material represent a fundamental property of the material. The inter-atomic or intermolecular forces of the material are responsible for the property of elasticity (see Fig. 4.6). The stronger the basic attraction forces, the greater the values of the elastic modulus and the more rigid or stiff the material. Because this property is related to the attraction forces within the material, it is usually the same when the mate-rial is subjected to either tension or compression. The property is generally independent of any heat treatment or mechanical treatment that a metal or alloy has received, but is quite dependent on the composition of the material. The elastic modulus is determined by the slope of the elastic portion of the stress-strain curve, which is calculated by choosing any two stress and strain coordinates in the elastic or linear range. As an example, for the curve in Fig. 4.5, the slope 36 CRAIG’S RESTORATIVE DENTAL MATERIALS can be calculated by choosing the following two coordinates: σ1 = 150 MPa ε1 = 0.005 and σ2 = 300 MPa ε2 = 0.010 The slope is therefore: σ2 −σ1 / ε2 −ε1 = 300 −150 / 0 010 −0 005 = 30 000 MPa = 30 GPa Stress-strain curves for two hypothetical materials, A and B, of different composition are shown in Fig. 4.8. Inspection of the curves shows that for a given stress, A is elastically deformed less than B, with the result that the elastic modulus for A is greater than for B. This difference can be demonstrated numeri-cally, by calculating the elastic moduli for the two materials subjected to the same stress of 300 MPa. At a stress of 300 MPa, material A is strained to 0.01 (1%) and the elastic modulus is as follows: E = 300 MPa/0 010 = 30 000 MPa = 30 GPa On the other hand, material B is strained to 0.02 (2%), or twice as much as material A for the same stress application. The equation for the elastic modu-lus for B is E = 300 MPa/0.020 = 15 000 MPa = 15 GPa The fact that material A has a steeper slope in the elastic range than material B means that a larger force is required to deform material A to a given amount than is required for material B. From the curves shown in Fig. 4.8, it can be seen that a stress of 300 MPa is required to deform A to the same amount elastically to which B is deformed by a stress of 150 MPa. Therefore A is stiffer or more rigid than B. Conversely, B is more flexible than A. Materials such as elastomers and other polymers have low values for elastic modulus, whereas many metals and ceramics have much higher values, as shown in Table 4.1. Poisson’s Ratio During axial loading in tension or compression there is a simultaneous strain in the axial and transverse, or lateral, directions. Under tensile loading, as a material elongates in the direction of load, there is a reduction in cross section, known as necking. Under compressive loading, there is an increase in the cross section. Within the elastic range, the ratio of the lateral to the axial strain is called Poisson’s ratio (ν). In tensile loading, the Poisson’s ratio indicates that the reduction in cross sec-tion is proportional to the elongation during the elastic deformation. The reduction in cross section continues until the material is fractured. Poisson’s ratio is a unit-less value because it is the ratio of two strains. Most rigid materials, such as enamel, dentin, amalgam, and dental composite, exhibit a Poisson’s ratio of about 0.3. Brittle substances such as hard gold alloys and dental amalgam show little permanent reduction in cross section during a tensile test. More ductile materials such as soft gold alloys, which are high in gold content, show a higher degree of reduc-tion in cross-sectional area and higher Poisson’s ratios. Rubber has a Poisson’s ratio of nearly 0.5. Cork exhibits little lateral expansion under compres-sion and has a Poisson’s ratio close to 0. This prop-erty has made cork a common material for sealing wine bottles. Ductility and Malleability Two significant properties of metals and alloys are ductility and malleability. The ductility of a material 60 55 50 45 B z' 40 35 30 25 20 A z x x' y' yN y 15 10 5 0 0 100 200 300 400 Strain (103) Stress (MPa) FIG. 4.8 Stress-strain curves of two hypothetical mate-rials subjected to tensile stress. TABLE 4.1 Elastic Modulus (GPa) of Selected Dental Materials Material Elastic Modulus (GPa) Enamel 84 Dentin 17 Gold (type IV) alloy 90–95 Amalgam 28–59 Cobalt-chromium removable partial denture alloy 218–224 Feldspathic porcelain 69–70 Resin composite with hybrid filler 17–21 Poly (methyl methacrylate) 2.4 Silicone elastomer for maxillofacial prosthesis 0.002–0.003 37 4. Fundamentals of Materials Science enables it to be drawn and shaped into wire by means of tension. When tensile forces are applied, the wire is formed by permanent deformation. The malleabil-ity of a material enables it to be hammered or rolled into thin sheets without fracturing. Malleability comes from the Latin malleus, or hammer. A high degree of elongation indicates good mal-leability and ductility, although some metals show some exception to this rule. The reduction in area in a specimen, together with the elongation at the break-ing point, is, however, a good indication of the rela-tive ductility of a metal or alloy. Ductility is a property that has been related to the workability of a material in the mouth (e.g., ability to adjust the margins of a casting). Although duc-tility is important, the amount of force necessary to cause permanent deformation during the adjustment process (also referred to as “burnishing”) must also be considered. A burnishing index has been used to rank the ease of burnishing alloys and is equal to the ductility (elongation) divided by the yield strength. Gold and silver, which are still used in dentistry, are the most malleable and ductile of the metals, but other metals do not follow the same order for both malleability and ductility. In general, metals tend to be ductile, whereas ceramics tend to be brittle. Resilience Resilience is the resistance of a material to perma-nent deformation. It indicates the amount of energy necessary to deform the material to the proportional limit. Resilience is therefore measured by the area under the elastic portion of the stress-strain curve, as illustrated in Fig. 4.9A. Resilience has particular importance in the evalu-ation of orthodontic wires. An example is the amount of work expected from a spring to move a tooth. The amount of stress and strain at the proportional limit is also of interest because these factors determine the magnitude of the force that can be applied to the tooth and how far the tooth can move before the spring is no longer effective. For example, Fig. 4.10 illustrates the load-deflection curve for a nickel-titanium (Ni-Ti) orthodontic wire. Note that the loading (activation) portion of the curve is different from the unloading (deactivation) portion. This difference is called hyster-esis. The units of resilience are mMN/m3 or mMPa/m. Resilience Strain Stress A Stress Strain Toughness B FIG. 4.9 Stress-strain curves showing (A) the area indi-cating the resilience and (B) the area representing the toughness of a material. D C Unload Stress (MPa) Load Martensite Austenite B M A max 8% Strain (%) T 37C FIG. 4.10 Load-deflection curve for Ni-Ti orthodontic wire. Note that the loading (activation) portion of the curve is different from the unloading (deactivation) portion, indicating hysteresis in the material. Ni-Ti, Nickel-titanium. 38 CRAIG’S RESTORATIVE DENTAL MATERIALS Toughness Toughness, which is the resistance of a material to fracture, is an indication of the amount of energy necessary to cause fracture. The area under the elastic and plastic portions of a stress-strain curve, as shown in Fig. 4.9B, represents the toughness of a material. The units of toughness are the same as the units of resilience: mMN/m3 or mMPa/m. Toughness repre-sents the energy required to stress the material to the point of fracture. Note that a material can be tough by having a combination of high yield and ultimate strength and moderately high strain at rupture, or by having moderately high yield and ultimate strength and a large strain at rupture. Brittle materials tend to have low toughness because little plastic defor-mation occurs before failure, thus the area under the elastic and plastic regions of the curve is not signifi-cantly different from the area under the elastic region alone. Fracture Toughness Concepts of fracture mechanics have been applied to a number of problems in dental materials. Fracture mechanics characterizes the behavior of materi-als with cracks or flaws. Flaws or cracks may arise naturally in a material or nucleate after a time in service. In either case, any defect generally weak-ens a material, and as a result, sudden fractures can arise at stresses below the yield stress. Sudden, cata-strophic fractures typically occur in brittle materials that do not have the ability to plastically deform and redistribute stresses. The field of fracture mechanics analyzes the material behavior during these types of failures. Two simple examples illustrate the significance of defects on the fracture of materials. Plates of glass or ceramic tiles are often scribed with a diamond or car-bide instrument. The purpose of the scribe is to cre-ate a defect that propagates when additional stresses are introduced. Both are difficult to break without a scribed line or defect. If the same experiment is per-formed on a ductile material, the small surface notch has no effect on the force required to break the plate, and the ductile plate can be bent without fracturing (Fig. 4.11). For a brittle material such as glass, no local plastic deformation occurs with fracture, whereas for a ductile material, plastic deformation, such as the ability to bend, occurs without fracture. The ability to be plastically deformed without fracture, or the amount of energy required for fracture, is the fracture toughness. In general, the larger a flaw, the lower the stress needed to cause fracture. This is because the stresses, which would normally be borne by a mass of mate-rial, are now concentrated at the tip of the flaw. The ability of a flaw to cause fracture depends on the frac-ture toughness of the material. Fracture toughness is a material property and is proportional to the energy consumed in plastic deformation. Fracture toughness (KIc) has been measured for a number of important restorative materials, including amalgam, acrylic denture base materials, composites, ceramics, orthodontic brackets, cements, and human enamel and dentin. Typical values for composites, ceramics, enamel, and dentin are listed in Table 4.2. The presence of fillers in polymers substantially increases fracture toughness. The mechanisms of toughening are presumed to be matrix-filler inter-actions, but these have not yet been established. Similarly, the addition of up to 50% by weight of zirconia to ceramic increases fracture toughness. As with other mechanical properties, aging or storage in a simulated oral environment or at elevated tem-peratures can decrease fracture toughness, but there is no agreement on this in the literature. Attempts to correlate fracture toughness with wear resistance Fracture Glass rod Grooves act as small notches Hardened steel file Copper rod Notch Plastic deformation FIG. 4.11 Schematic of different types of deformation in brittle (glass, steel file) and ductile (copper) materials of the same diameter and having a notch of the same dimen-sions. (From Flinn RA, Trojan PK. Engineering Materials and Their Applications. Boston: Houghton Mifflin; 1981:535.) TABLE 4.2 Fracture Toughness (KIC) of Selected Dental Materials Material KIC (MN·m−3/2) Enamel 0.7–1.3 Dentin 3.1 Amalgam 1.3–1.6 Ceramic 1.2–3.0 Resin composite 1.4–2.3 Porcelain 0.9–1.0 39 4. Fundamentals of Materials Science have had mixed results. Fracture toughness is not a reliable predictor of the wear of restorative materials. Properties and Stress-Strain Curves The shape of a stress-strain curve and the magni-tudes of the stress and strain allow classification of materials with respect to their general properties. The idealized stress-strain curves in Fig. 4.12 repre-sent materials with various combinations of physical properties. For example, materials 1 to 4 have high stiffness, materials 1, 2, 5, and 6 have high strength, and materials 1, 3, 5, and 7 have high ductility. If the only requirement for an application is stiff-ness, materials 1 to 4 are all satisfactory. However, if the requirements are both stiffness and strength, only materials 1 and 2 are acceptable. If the require-ments are to also include ductility, the choice would be limited to material 1. The properties of stiffness, strength, and ductility are independent, and materi-als may exhibit various combinations of these three properties. Tensile Properties of Brittle Materials Many restorative materials, including dental amal-gam, cements, ceramics, plaster, and stone, are much weaker in tension than in compression. This means cavity preparation design requirements for amalgams and ceramics, for example, are differ-ent than for ductile materials, such as metal alloys. One example is the amount of occlusal reduction necessary for ductile versus brittle materials. For brittle materials, such as ceramics, the occlusal reduction needs to be greater than for ductile mate-rials, such as gold alloys. This is because ceramics require a larger cross-sectional area to present the same resistance as metals. Also for that reason, the margins of a preparation can be beveled for metal restorations, but cannot be beveled for ceramic restorations. Viscoelasticity The mechanical properties of many dental materi-als, such as alginate, elastomeric impression mate-rials, waxes, amalgam, polymers, bone, dentin, oral mucosa, and periodontal ligaments, depend on how fast they are loaded. For these materials, increasing the loading (strain) rate produces a different stress-strain curve with higher rates giving higher values for the elastic modulus, proportional limit, and ulti-mate strength. Materials that have mechanical prop-erties independent of loading rate are termed elastic. In these materials, strain occurs when the load is applied. Other materials exhibit a lag in response when a load is applied. This time lag is referred to as a viscous response. Materials that have mechanical properties dependent on loading rate and exhibit both elastic and viscous behavior are termed visco-elastic. These materials have characteristics of an elastic solid and a viscous fluid. The properties of an elastic solid were previously discussed in detail. Before viscoelastic materials and their properties are presented, fluid behavior and viscosity are reviewed in the following section. Fluid Behavior and Viscosity In addition to the many solid dental materials that exhibit some fluid characteristics, many dental mate-rials, such as cements and impression materials, are in the fluid state when formed. Therefore fluid (vis-cous) phenomena are important. Viscosity (η) is the resistance of a fluid to flow and is equal to the shear stress divided by the shear strain rate, or: η =τ/ dε/dt When a cement or impression material sets, the viscosity increases, making it less viscous and more solidlike. The units of viscosity are poise, p (1 p = 0.1 Pa·s = 0.1 N·s/m2), but often data are reported in centipoise, cp (100 cp = 1 p). Rearranging the equation for viscosity, we see that fluid behavior can be described in terms of stress and strain, just like elastic solids. τ = η dε/dt In the case of an elastic solid, stress (σ) is pro-portional to strain (ε), with the constant of propor-tionality being the modulus of elasticity (E). The aforementioned equation indicates a similar situ-ation for a viscous fluid, where the stress (shear) is proportional to the strain rate and the constant of proportionality is the viscosity. The stress is therefore time dependent because it is a function of the strain rate, or rate of loading. To better comprehend the concept of strain rate dependence, consider two lim-iting cases: rapid and slow deformation. A material pulled extremely fast (dt → 0) results in an infinitely Strain - Strong Tough Stiff Ductile Stress - 1 Strong Stiff Brittle Strain - Flexible Ductile Strong Resilient Strong Resilient Ductile Weak Flexible Brittle Flexible Stress - 5 6 7 Flexible Brittle 8 2 Weak Stiff Ductile 3 Weak Stiff Brittle 4 Weak FIG. 4.12 Stress-strain curves for materials with vari-ous combinations of properties. 40 CRAIG’S RESTORATIVE DENTAL MATERIALS high stress, whereas a material pulled infinitesi-mally slow results in a stress of zero. This concept will be important in understanding stress relaxation and delayed gelation phenomena, explored later in this chapter. The behavior of elastic solids and vis-cous fluids can be understood from studying simple mechanical models. An elastic solid can be viewed as a spring (Fig. 4.13). When the spring is stretched by a force, F, it displaces a distance, x. The applied force and resultant displacement are proportional, and the constant of proportionality is the spring constant, k. Therefore, according to Hooke’s law: F = kx Note that this relation is equivalent to the equa-tion presented in the Stress-Strain Curves section of this chapter: σ = Eε Also note that the model of an elastic element does not involve time. The spring acts instantaneously when stretched. In other words, an elastic solid is independent of loading rate. A viscous fluid can be viewed as a dashpot, or a piston moving through a viscous fluid (Fig. 4.14). When the fluid-filled cylinder is pulled, the rate of strain (dε/dt) is proportional to the stress (τ) and the constant of proportionality is the viscosity of the fluid (π). Although the viscosity of a fluid is proportional to the shear rate, the proportionality differs for different fluids. Fluids may be classified as newtonian, pseudo-plastic, or dilatant depending on how their viscosity varies with shear rate, as shown in Fig. 4.15. The viscos-ity of a newtonian fluid is constant and independent of shear rate. Some dental cements and impression mate-rials are newtonian. The viscosity of a pseudoplastic fluid decreases with increasing shear rate. Monophase elastomeric impression materials are pseudoplastic. When subjected to low shear rates during spatulation or while an impression material is loaded in a tray in preparation of placing it into the mouth, these impres-sion materials have a high viscosity and stay in place without flowing. These materials, however, can also be used in a syringe, because at the higher shear rates encountered as they pass through the syringe tip, the viscosity decreases by as much as tenfold. This charac-teristic is sometimes referred to as thixotropy, although that term actually describes the change in viscosity of a material with time. The tomato-based food condiment ketchup is also pseudoplastic, which makes it difficult to remove from a bottle. Shaking the bottle or rapping the side of the bottle increases its shear rate, decreases its viscosity, and improves its pourability. The viscosity of a dilatant fluid increases with increasing shear rate. Examples of dilatant fluids in dentistry include the fluid denture base resins. Slope (k) x F Displacement (x) Force (F) F FIG. 4.13 Force versus displacement of a spring, which can be used to model the elastic response of a solid. (From Park JB. Biomaterials Science and Engineering. New York: Plenum Press; 1984:26.) x Slope () Newtonian fluid cylinder Strain rate (d/dt) Stress () F F FIG. 4.14 Stress versus strain rate for a dashpot, which can be used to model the response of a viscous fluid. (From Park JB. Biomaterials Science and Engineering. New York: Plenum Press; 1984:26.) Shear rate Shear stress Pseudoplastic Newtonian Dilatant FIG. 4.15 Shear diagrams of newtonian, pseudoplastic, and dilatant liquids. The viscosity is shown by the slope of the curve at a given shear rate. 41 4. Fundamentals of Materials Science Viscoelastic Materials For viscoelastic materials, the strain rate can alter the stress-strain properties. The tear strength of alginate impression material, for example, is increased about four times when the rate of loading is increased from 2.5 to 25 cm/min. Alginate impressions should there-fore be removed from the mouth quickly to improve their tear resistance. Another example of strain-rate dependence is the elastic modulus of dental amal-gam, which is 21 GPa at slow rates of loading and 62 GPa at high rates of loading. A viscoelastic mate-rial therefore may have widely different mechanical properties depending on the rate of load application, and for these materials, it is particularly important to specify the loading rate with the test results. Materials that have properties dependent on the strain rate are better characterized by relating stress or strain as a function of time. Two properties of importance to viscoelastic materials are stress relax-ation and creep. Stress relaxation is the reduction in stress in a material subjected to constant strain, whereas creep is the increase in strain in a material under constant stress. As an example of stress relaxation, consider how the load-time curves at constant deforma-tion are important in the evaluation of orthodontic elastic bands. The decrease in load (or force) with time for rubber and plastic bands of the same size at a constant extension of 95 mm is shown in Fig. 4.16. The initial force was much greater with the plastic band, but the decrease in force with time was much less for the rubber band. Therefore plastic bands are useful for applying high forces, although the force decreases rapidly with time, whereas rubber bands apply lower forces, but the force decreases slowly with time in the mouth; rubber bands are therefore useful for applying more sustained loads. The importance of creep can be seen by interpre-tation of the data in Fig. 4.17, which shows creep curves for low- and high-copper amalgam. For a given load at a given time, the low-copper amalgam has a greater strain. The implications and clinical importance of this are that the greater creep in the low-copper amalgam makes it more susceptible to strain accumulation and fracture, and also marginal breakdown, which can lead to secondary decay. The high creep behavior of low-copper amalgam contrib-uted to its decline in popularity. Creep Compliance A creep curve yields insight into the relative elas-tic, viscous, and inelastic response of a viscoelastic material; such curves can be interpreted in terms of the molecular structure of the associated materials, which have structures that function as elastic, vis-cous, and inelastic elements. Creep recovery curves are produced from data collected during removal of a load (Fig. 4.18). In such a curve, after the load 500 400 300 200 100 1 1 2 3 4 5 5 10 15 20 6 7 8 Hours Load (g) Days Latex Plastic FIG. 4.16 Decrease in load of latex rubber and plas-tic bands as a function of time at a constant extension of 95 mm. (From Craig RG, ed. Dental Materials: A Problem-Oriented Approach. St. Louis: Mosby; 1978.) Conventional alloy High-performance alloy 0.24 0.16 0.08 2 4 8 12 Time (hours) 16 20 24 Strain FIG. 4.17 Creep curves for conventional (low-copper) and high-performance (high-copper) amalgams. (From O’Brien WJ. Dental Materials: Properties and Selection. Chicago: Quintessence; 1989:25.) Remove load Apply load Time Strain A C B FIG. 4.18 Creep recovery curve showing (A) elastic, (B) anelastic, and (C) viscous strain. 42 CRAIG’S RESTORATIVE DENTAL MATERIALS is removed, there is an instantaneous drop in strain and slower strain decay to some steady-state strain value, which may be nonzero. The instantaneous drop in strain represents the recovery of elastic strain. The slower recovery represents the inelastic strain, and the remaining, permanent strain repre-sents the viscous strain. A family of creep curves can be determined by using different loads. A more use-ful way of presenting these data is by calculating the creep compliance. Creep compliance (Jt) is defined as strain divided by stress at a given time. Once a creep curve is obtained, a corresponding creep compliance curve can be calculated. The creep compliance curve shown in Fig. 4.19 is characterized by the following equation: Jt = J0 + JR + t/η where J0 is the instantaneous elastic compliance, JR is the retarded elastic (inelastic) compliance, and t/η represents the viscous response at time t for a viscosity η. The strain associated with J0 and JR is completely recoverable after the load is removed; however, the strain associated with JR is not recov-ered immediately but requires some finite time. The strain associated with t/η is not recovered and rep-resents a permanent deformation. If a single creep compliance curve is calculated from a family of creep curves determined at different loads, the material is said to be linearly viscoelastic. In this case, the vis-coelastic qualities can be described concisely by a single curve. The creep compliance curve therefore permits an estimate of the relative amount of elastic, inelastic, and viscous behavior of a material. J0 indicates the flexibility and initial recovery after deformation, JR the amount of delayed recovery that can be expected, and t/η the magnitude of permanent deformation to be expected. Creep compliance curves for elasto-meric impression materials are shown in Chapter 12, Fig. 12.17. Dynamic Mechanical Properties Although static properties can often be related to the function of a material under dynamic condi-tions, there are limitations to using static properties to estimate the properties of materials subjected to dynamic loading. Static testing refers to continuous application of force at slow rates of loading, whereas dynamic testing involves cyclic loading or loading at high rates (impact). Dynamic methods, includ-ing a forced oscillation technique used to determine dynamic modulus and a torsion pendulum used for impact testing, have been used to study viscoelas-tic materials such as dental polymers. Ultrasonic techniques have been used to determine elastic con-stants of viscoelastic materials such as dentin. Impact testing has been applied primarily to brittle dental materials. Dynamic Modulus The dynamic modulus (ED) is defined as the ratio of stress to strain for small cyclical deformations at a given frequency and at a particular point on the stress-strain curve. When measured in a dynamic oscillation instrument, the dynamic modulus is com-puted by: ED = mqp2 where m is the mass of the loading element, q is the height divided by twice the area of the cylindri-cal specimen, and p is the angular frequency of the vibrations. In general, elastic modulus calculated from dynamic testing is higher than when calculated from static testing. For ideal elastic materials subjected to an oscillatory strain, the sinusoidal wave of the resultant stress matches perfectly the strain wave; it is said then that stress and strain are “in phase” (Fig. 4.20A and B), or that there is no energy lost to the environment because all the energy is used to pro-vide a deformation. For newtonian fluids (ideal liq-uids), the strain response lags in time, and the phase lag equals the greatest possible angle (δ = 90 degrees) between stress and strain waves, for any given cycle (see Fig. 4.20A). As discussed earlier, from the stress-strain curves, a complex modulus (E) can be calcu-lated. The complex modulus, therefore, is the ratio of the stress amplitude to the strain amplitude and represents the stiffness of the material. Most real materials subjected to oscillatory strain behave somewhere in between a perfectly elastic and a perfectly plastic material, and in those cases, by resolv-ing the complex modulus (E) into an “in-phase” elas-tic component (called storage modulus, or E′) and an “out-of-phase” viscous component (called loss modu-lus, or E″), it is possible to gain insight into the elastic and viscous components, respectively (see Fig. 4.20B). Time Creep compliance JR t/ Jo FIG. 4.19 Creep compliance versus time for a viscoelas-tic material. (Modified from Duran RL, Powers JM, Craig RG. Viscoelastic and dynamic properties of soft liners and tissue con-ditioners. J Dent Res. 1979;58(8):1801.) 43 4. Fundamentals of Materials Science They correlate according to the mathematical relation-ship shown in Fig. 4.20C, where E′ = E sin δ and E″ = E cos δ. One useful concept that arises is the loss fac-tor tan δ (calculated as tan δ = E′/E″). This relationship allows us to determine whether a material presents a predominantly elastic or viscous response when sub-jected to load while in service. In conjunction with the dynamic modulus, val-ues of internal friction and dynamic resilience can be determined. For example, cyclical stretching or com-pression of an elastomer results in irreversibly lost energy that is exhibited as heat. The internal friction of an elastomer is comparable with the viscosity of a liquid. The value of internal friction is necessary to calculate the dynamic resilience, which is the ratio of energy lost to energy expended. The dynamic modulus and dynamic resilience of some dental elastomers are listed in Table 4.3. These properties are affected by temperature (−15°C to 37°C) for some maxillofacial elastomers. As shown in Table 4.3, the dynamic modulus decreases and the dynamic resilience increases as the temperature increases. As a tangible example, the dynamic resilience of a poly-mer used for an athletic mouth protector is a measure of the ability of the material to absorb energy from a blow and thereby protect the oral structures. Surface Mechanical Properties In our discussion so far, we have introduced and discussed mechanical properties that are mainly dependent on the bulk characteristics of a material. In this section, mechanical properties that are more a function of the surface condition of a material are presented. In particular, the concepts of hardness, friction, and wear are summarized. Hardness Hardness may be broadly defined as the resistance to permanent surface indentation or penetration. Formulating a more rigorous definition of hardness is difficult because any test method will, at a micro-scopic level, involve complex surface morphologies and stresses in the test material, thereby involving a variety of qualities in any single hardness test. Despite this condition, the most common concept of hard and soft substances is their relative resis-tance to indentation. Hardness is therefore a mea-sure of the resistance to plastic deformation and is measured as a force per unit area of indentation (Fig. 4.21). Based on this definition of hardness, it is clear why this property is so important to dentistry. Hardness influences ease of cutting, finishing, and polishing an object and its resistance to in-service scratch-ing. Finishing or polishing a structure is important for esthetic purposes and, as discussed previously, scratches can compromise fatigue strength and lead to premature failure. Some of the most common methods of test-ing the hardness of restorative materials are the Brinell, Knoop, Vickers, Rockwell, Barcol, and , t A A Stress E E E Strain , t A A Stress Strain A B C FIG. 4.20 Sinusoidal oscillation and response of (A) an ideal liquid and (B) a purely elastic mate-rial; δ is the phase angle. (C) Mathematical correlation of complex (E), storage (E′), and loss (E″) moduli. 44 CRAIG’S RESTORATIVE DENTAL MATERIALS Shore A hardness tests. Each of these tests differs slightly in the indenter used and in the calcula-tion of hardness. Each presents certain advantages and disadvantages, described in detail in Chapter 5. They have a common quality, however, in that each depends on the penetration of some small, symmetrically shaped indenter into the surface of the material being tested. The choice of a hard-ness test depends on the material of interest, the expected hardness range, and the desired degree of localization. Friction Friction is the resistance between contacting bodies when one moves relative to another (Fig. 4.22). A restraining force that resists movement is the (static) frictional force and results from the molecules of the two objects bonding where their surfaces are in close contact. The frictional force, Fs, is proportional to the normal force (Fn) between the surfaces and the (static) coefficient of friction (μs): FS = SFN µ The coefficient of friction varies between 0 and 1 and is a function of the two materials in contact, their composition, surface finish, and lubrication. Similar materials in contact have a greater coefficient of fric-tion, and if a lubricating medium exists at the inter-face, the coefficient of friction is reduced. Motion is possible when the applied force is greater than Fs. Once motion occurs, molecular bonds are made and broken, and microscopic pieces break off from the surfaces. With motion, a sliding or kinetic friction is produced, and the force of kinetic friction opposes the motion: Fk = kFN µ Frictional behavior therefore arises from surfaces that, because of microroughness, have a small real contact area (see Fig. 4.22). These small surface areas result in high contact stresses, which lead to local yielding, or permanent deformation. The resistance to shear failure of the junctions results in the frictional force. When static friction is overcome and relative motion takes place, it is accompanied by the modifica-tion of the interface through kinetic friction and wear. An example of the importance of friction in den-tistry lies in the concept of sliding mechanics used in orthodontics. A known and controlled frictional force is required when an orthodontic wire is slid through a bracket. Combinations of different materi-als result in different frictional forces. Friction is also an important consideration when dissimilar restor-ative materials contact and slide against each other in the oral cavity such as in protrusive or working movements of the mandible. TABLE 4.3 Values of Dynamic Modulus and Dynamic Resilience as a Function of Temperature for Some Dental Elastomers Material Temperature (°C) Dynamic Modulus (MPa) Dynamic Resilience (%) MAXILLOFACIAL MATERIALS Polyurethane −15 5.98 15.0 37 3.06 19.9 Polyvinylchloride −15 12.2 6.0 37 2.51 19.6 Silicone elastomer −15 2.84 16.0 37 2.36 23.2 POLYVINYLACETATE-POLYETHYLENE MOUTH PROTECTOR New 37 9.39 23.4 Worn 37 7.23 20.2 A Plastically displaced P Indenter FIG. 4.21 Schematic representation of surface changes from indenter in Rockwell hardness test. P, Normal load; A, area of plastic deformation. (From Park JB. Biomaterials Science and Engineering. New York: Plenum Press; 1984:18.) 45 4. Fundamentals of Materials Science Wear Wear is a loss of material resulting from removal and relocation of materials through the contact of two or more materials. When two solid materials are in con-tact, they touch only at the tips of their most protrud-ing asperities (Fig. 4.23). Wear is usually undesirable, but under controlled conditions during finishing and polishing, controlled wear can be very useful. Several factors make wear of biomaterials unique. Most important, wear can produce particles that can elicit an inflammatory response. The wear process can also produce shape changes in the object that can affect function. For example, wear of teeth and restorative materials is characterized by the loss of the original anatomical form of the material. Wear may result from mechanical, physiological, or patho-logical conditions. Normal mastication may cause attrition of tooth structure or materials. Bruxism is an example of a pathological form of wear in which clenching and grinding of teeth produces occlusal and incisal wear. Abrasive wear occurs when exces-sively abrasive toothpastes and hard toothbrush bristles are used when brushing teeth. Wear is a function of a number of material and environmental factors, including the characteristics of wearing surfaces (i.e., inhomogeneity, crystal orienta-tion, phases, and inclusions present); the microscopic contact; interaction between sliding surfaces (i.e., ele-vated stress, temperature, and flow at contact points, leading to localized yielding, melting, and hardening); lubrication; and different material combinations. In general, wear is a function of opposing materials and the interface between them. The presence of a lubri-cating film, such as saliva, separates surfaces during relative motion and reduces frictional forces and wear. In general, there are four types of wear: (1) adhe-sive wear; (2) corrosive wear; (3) surface fatigue wear; and (4) abrasive wear. Adhesive wear is char-acterized by the formation and disruption of micro-junctions. Microregions are pulled from one object and transferred to the other. Abrasive wear involves a harder material cutting or plowing into a softer material. There can be two types of abrasive wear: two- and three-body abrasive wear. This type of wear can be minimized if surfaces are smooth and hard and if third party particles are kept off the surfaces. Corrosive wear is secondary to physical removal of a protective layer and is therefore related to the chemi-cal activity of the wear surfaces. The sliding action of the surfaces accelerates corrosion. In surface fatigue wear, asperities or free particles with small areas of contact contribute to high localized stresses and pro-duce surface or subsurface cracks. Particles break off under cyclic loading and sliding. In general, metals are susceptible to adhesive, cor-rosive, and three-body wear, whereas polymers are susceptible to abrasive and fatigue wear. The Colloidal State The term colloid is used to describe a state of matter rather than a kind of matter. The main characteristic of colloidal materials is their high degree of microse-gmentation. These fine particles also have certain physical properties, such as electrical charges and surface energies that control the characteristics of the colloids. Particle size alone does not adequately define colloids. FIG. 4.22 Microscopic area of contact between two objects. The frictional force, which resists motion, is pro-portional to the normal force and the coefficient of friction. Mpa 50 40 30 20 10 0 NAT CER CAV_MOD ENDO_MOD FIG. 4.23 Stress distribution in a finite element model of a molar with a 100-N occlusal load. (From Magne P. Efficient 3D finite element analysis of dental restorative proce-dures using micro-CT data. Dent Mater 2007;23:539–548.) 46 CRAIG’S RESTORATIVE DENTAL MATERIALS Nature of Colloids Substances are called colloids when they consist of two or more phases, with the units of at least one of the phases having a dimension slightly greater than simple molecular size. Although the range of size is somewhat arbitrary, it is usually recognized as being approximately 1 to 500 nm in maximum dimension. Thus colloidal systems can be fine dispersions, gels, films, emulsions, or foams. In other words, the colloi-dal state represents a highly dispersed system of fine particles of one phase in another, and a characteristic property of the dispersed phase is an enormous surface area. This is true whether a dispersed phase of oil drop-lets in an emulsion or a finely divided solid suspended in a liquid is considered. This increase in surface area gives rise to a corresponding increase in surface energy and surface reactions. Not only is the surface energy important, but the interface between the two phases also imparts important and characteristic properties to the system. Except for a dispersion of a gas in a gas, which is a true solution, each of the three forms of matter—gas, liquid, and solid—may be dispersed as colloidal par-ticles in the other and in itself as well. The dispersed phase, which may be in the form of a gas, liquid, or solid, may also exist in a variety of conditions. Some examples of these dispersed phases are (1) colloidal silica as a filler in resin composites, (2) colloidal silica in water to be mixed with high-strength dental stone to improve abrasion resistance, (3) droplets of oil in water used during steam sterilization to prevent rusting of dental instruments, (4) fillers used in elas-tomeric impression materials to control such prop-erties as viscosity, and (5) agglomerates of detergent molecules in water that serve as wetting agents for wax patterns. Typical Colloid Systems The distinction between a sol and a gel is important because several of each are found in dental applica-tions. A sol resembles a solution, but it is made up of colloidal particles dispersed in a liquid. When a sol is chilled or caused to react by the addition of suitable chemicals, it may be transformed into a gel. In the gel form the system takes on a semisolid, or jellylike, quality. The liquid phase of either a sol or a gel is usu-ally water, but may be some organic liquid such as alcohol. Systems having water as one component are described as hydrosols or hydrogels. A more general term might be hydrocolloid, which is often used in dentistry to describe the alginate gels used as flex-ible impression materials. A general term to describe a system having an organic liquid as one component would be organosol or organogel. Gels possess an entangled framework of solid colloidal particles in which liquid is trapped in the interstices and held by capillarity. Such a gel has some degree of rigidity, depending on the extent of the structural solids present. One example is the algi-nate hydrocolloid impression material. Gels that are formed with water are hydrophilic (water loving) in character and tend to imbibe large quantities of water if allowed to stand submerged. The imbibition is accompanied by swelling and a change in physical dimensions. In dry air, the gel loses water to the atmosphere, with an accompany-ing shrinkage. Such changes may be observed read-ily in alginate gels. Diffusion Through Membranes and Osmotic Pressure Osmotic pressure is the pressure developed by dif-fusion of a liquid or solvent through a membrane. The solvent passes from the dilute to the more con-centrated solution through the membrane separating the two solutions. The presence of dissolved mate-rial in a solvent lowers the escaping tendency of the solvent molecules; the greater the concentration, the more the escaping tendency is lowered. Accordingly, the solvent will diffuse or pass through a membrane to a region of greater concentration, thus diluting the concentration of the solution. Osmotic pressure is a concept that has been used to explain the hypersensitivity of dentin. The change in pressure in carious, exposed dentin from contact with saliva or concentrated solutions causes diffusion throughout the structure that increases or decreases the pressure on the sensory system. Just as diffusion through membranes is impor-tant, so is the diffusion from a substance of a given concentration to that of another concentration, which is important in many materials in dentistry. Salts and dyes diffuse through human dentin. Stains and dis-coloring agents diffuse through polymeric restor-ative materials. Diffusion of salts and acids through some cavity liners is a potential problem. Adsorption, Absorption, and Sorption In the adsorption process, a liquid or gas adheres to the surface of the solid or liquid firmly by the attach-ment of molecules, thus reducing their surface free energy. In a physical sense, if the two substances are alike, as, for example, two pieces of the same metal in the solid state pressed closely together, the mass is said to cohere. When a dissimilar substance, such as a gas or liquid, is in intimate contact with the sur-face of the solid, it is said to adhere to the surface. The process of adsorption or adhesion to the surface of a substance is important in the wetting process, in which the substance is coated or wetted with a for-eign substance such as a liquid. The degree to which 47 4. Fundamentals of Materials Science saliva, for example, will wet or adhere to the enamel surface of a tooth depends on the tendency for sur-face adsorption. A substance that is readily wetted on the surface by water, as is glass or porcelain or tooth enamel, is considered to have adsorbed on its sur-face a layer of water molecules. When a wet, human enamel surface is desiccated, the first water to evapo-rate is bulk water, leaving physically and chemically adsorbed water. Considerable heat is required to remove physically adsorbed water, and even higher temperatures are needed to remove chemically adsorbed water. Thus any attempt to bond a restor-ative material to enamel must consider that adhesion will be to adsorbed water and not hydroxyapatite. High-energy surfaces such as metals will adsorb mol-ecules more readily than low-energy surfaces such as waxes; oxides have intermediate surface energies. The process of adsorption differs somewhat from the process of absorption. In the process of absorp-tion, the substance absorbed diffuses into the solid material by a diffusion process, and the process is characterized by concentration of molecules at the surface. In instances in which both adsorption and absorp-tion are known to exist and it is not clear which pro-cess predominates, the whole process is known as sorption. In measurement of the moisture content of dental resins, the process is described as one of sorp-tion of moisture by the resin. Numerous examples of these processes are found in the use of various restorative dental materials. The process of absorption of water by alginate impres-sion materials is particularly important to its sta-bility. When the quantity of liquid absorbed into a substance is relatively large, there is likely to be an accompanying swelling of the absorbent. Surface Tension and Wetting Surface tension is measured in terms of force (dynes) per centimeter of the surface of liquid. In the case of water at 20°C, the value is 72.8 dynes/cm. At the same temperature, benzene has a value of 29 dynes/ cm; alcohol, 22 dynes/cm; and ether, 17 dynes/cm. By contrast, mercury at 20°C has a surface tension of 465 dynes/cm. The values for each of these sub-stances are influenced by factors such as temperature and purity. In general, there is a reduction in surface tension of all liquids as the temperature is increased. For example, the surface tension of water (in dynes/ cm) is 76 at 0°C, 72 at 25°C, 68 at 50°C, and 59 at 100°C. The surface tension of liquids is also reduced by the presence of impurities, some of which are exceedingly effective. Detergents, such as sodium lauryl sulfate, or the ingredients of soaps, including sodium stearate or sodium oleate, which have long hydrocarbon chains attached to hydrophilic groups (such as COONa), are particularly effective in reduc-ing the surface tension of water. These surface-active agents affect the surface ten-sion by concentrating at the liquid-air interface or other interfaces or surfaces. As these molecules occupy surface positions in the water-air surface, they displace surface water molecules, thus reducing the cohesive force between water molecules over the surface area, because the cohesion between water and surface-active agent is less than that between water and water. This effect is demonstrated in Fig. 4.24, which represents two drops placed on wax, one of which is water and the other water with detergent. The presence of the sur-face-active agent molecules in the surface layer reduces the pull on the surface molecules toward the liquid mass. This reduces the surface tension to increase wetting. The soap molecules are oriented so that the hydrophilic end is in the water and the hydrophobic (hydrocarbon) end is oriented toward the wax or air. The increased wettability of solids with liquids of reduced surface tension is important in numerous dental applications. The wetting power of a liquid is represented by its tendency to spread on the surface of the solid. When pouring a hydrophobic, polymeric impression material with plaster or stone (gypsum), the gypsum wets the impression to reproduce the details recorded in the impression. Hydrophobic impressions are not well wetted by gypsum, so a dilute solution of some wetting agent (such as 0.01% aerosol) is sprayed on the impression in small quan-tities to aid in the spreading of the gypsum. Without adequate wetting, the gypsum will not flow over the surface of the impression and replicate fine detail. Water Wax Water Soap Wax Soap – Water FIG. 4.24 Spreading of pure water (top) and water con-taining soap molecules on wax (bottom). 48 CRAIG’S RESTORATIVE DENTAL MATERIALS Much can be learned about the spreading of liquids on solids, or the tendency for wetting surfaces, by mea-suring the angle of contact between the liquid and the solid surface. The angles of contact for different liquid droplets on a plane glass surface are illustrated in Fig. 4.25. The contact angle results from a balance of surface and interfacial energies. The greater the tendency to wet the surface, the lower the contact angle, until com-plete wetting occurs at an angle equal to zero. Contact angles of water and saliva in dental materials: The determination of contact angle is important in a number of clinically relevant situa-tions. For example, the contact angle of water and saliva on complete denture plastics relates to the retention of the denture. The contact angle and the tendency of a drop of water to spread on paraffin wax and methyl methacrylate are shown for compar-ison in Fig. 4.26. The contact angle of saliva freshly applied to an acrylic surface is similar to the one formed by water. This angle drops if saliva is allowed to stand overnight in contact with the plastic mate-rial, which indicates that the surface wetting is some-what improved. Table 4.4 gives contact angle values for water on selected materials. Contact angles can also provide important infor-mation regarding the wettability of dental elasto-meric materials, defining the ease of pouring a mix of dental stone and water to produce a model. The contact angles of water on various dental elastomeric impression materials are listed in Table 4.5, along with the castability of an impression of a very critical comblike model. Surfactants can be added to the sur-face to artificially decrease the contact angle. Contact angles between metals during casting, soldering, and amalgamation: The surface tension of metals is relatively high in comparison with that of other liquids, because of the greater cohesive forces between the liquid metal atoms in the liquid-air surface compared to water. The surface tension of most met-als, except mercury, cannot be measured at room tem-perature because of their high melting points. Typical values of a few metals are included in Table 4.6. This is important because it defines the ease of spreading of the molten metal or alloy on the investment material surface during casting, and determines the accuracy and reproduction of detail in the final restoration. The same applies to the spreading of molten flux on hot metal during melting or soldering operations. If the contact angle of the solder is too great, it will not pen-etrate into the fine detail of the structures to be joined. Adhesion Surface Considerations Atoms or molecules at the surfaces of solids or liq-uids differ greatly from those in the bulk of the solid or liquid, and neighboring atoms may be arranged anisotropically. In addition, some atoms or mol-ecules may accumulate at the surface and thus cause unusual physical and chemical properties. These solid surfaces have atoms of higher energy than bulk atoms because of the absence of some neighboring atoms and thus readily adsorb ambient atoms or molecules. To produce a clean solid surface, one with less than 1% of an adsorbed monolayer, a vacuum of 10−9 Torr or 1.33 × 10−7 Pa is required to keep a surface clean for about an hour. At a vacuum of about 3 × 10−6 Torr, a newly cleaned surface would FIG. 4.25 Relation of contact angle to the spreading or wetting of a liquid on a solid. A B D C FIG. 4.26 Diagrams show the contact angle formed by a drop of water or saliva on wax and acrylic plastic. (A) Water on wax. (B) Water on plastic. (C) Fresh saliva on plas-tic. (D) Saliva after remaining in contact with plastic. 49 4. Fundamentals of Materials Science be coated with ambient atoms or molecules in only a few seconds. Therefore, all dental materials and den-tal surfaces would be covered with a layer of ambi-ent atoms or molecules and thus adhesives would be bonding to these adsorbed monolayers. The energy involved in the adsorption of atoms or molecules onto the substrate may be at the level of a chemical reaction, or chemisorption, or may be at the level of van der Waals reaction, or physiosorp-tion. The former is irreversible, whereas the latter is reversible. Thus an important concept in surface chemistry is that critically important properties of a material may be more related to the chemistry of the surface layer and its composition than to the bulk properties. Such surface effects dominate the surface mechanical properties of adhesion and friction, the optical surface phenomena of the perception of color and texture, the tissue reaction to materials, the attachment of cells to materials, the wettability and capillarity of surfaces, the nucleation and growth of solids, and many other areas of crucial interest in biomaterials. Dental applications of surface chemistry can be seen in the elements chosen in metal alloys. Stainless steel used mainly in orthodontics is 72% to 74% iron, but has acceptable corrosion resistance in the mouth because the 18% chromium content forms an adher-ent oxide layer on the surface, which provides cor-rosion resistance. Titanium and its alloys, and noble alloys containing small amounts of indium and tin, have excellent biocompatibility properties as a result of oxides of titanium, indium, and tin on the surface. Penetration Coefficient The rate of penetration of a liquid into a crevice is an important aspect of capillary phenomena. An example is the penetration of a sealant into a fissure and the fine microscopic spaces created by etching of an enamel surface. The properties of the liquid affecting the rate of penetration may be related to the penetration coefficient (PC) where γ is the surface tension, η is the viscosity, and θ is the contact angle of the sealant on the enamel: PC = γcos/2η The penetration coefficients for sealants have been shown to vary from 0.6 to 12 cm/s. Narrow occlusal fissures can be filled almost completely if the penetration coefficient value is at least 1.30 cm/s, provided that no air bubbles trapped in the fissure are present. The same analysis applies to the penetra-tion of sealants into the etched surface of enamel to form tags, as shown in Fig. 4.27. TABLE 4.4 Contact Angles of Water on Solids at 27°C Solid Advancing Angle (degrees) Acrylic polymer 74 Teflon 110 Glass 14 Amalgam 77 Composite filling material 51 Modified from O’Brien WJ. Capillary Penetration of Liquids Between Dissimilar Solids, Doctoral Thesis, Ann Arbor, MI: University of Michigan; 1967:40. TABLE 4.5 Wettability and Castability of Stone Models in Flexible Impression Materials Advancing Contact Angle of Water (degrees) Castability of Water Mixes of High Strength Stone (%) Addition silicone-hydrophobic 98 30 Addition silicone-hydrophilic 53 72 TABLE 4.6 Surface Tension of Metals Metal Temperature (°C) Surface Tension (dynes/cm) Lead 327 452 Mercury 20 465 Zinc 419 758 Copper 1131 1103 Gold 1120 1128 25 µm E S FIG. 4.27 Scanning electron micrograph of the inter-face of sealant (S) and enamel (E) showing sealant tags that had penetrated into the etched enamel surface. (From O’Brien WJ, Fan PL, Apostolidis A. Penetrativity of sealants and glazes. The effectiveness of a sealant depends on its ability to pen-etrate into fissures. Oper Dent. 1978;3(2):51.) 50 CRAIG’S RESTORATIVE DENTAL MATERIALS OPTICAL PROPERTIES Color The perception of color is the result of a physiologi-cal response to a physical stimulus. The sensation is a subjective experience, whereas the beam of light, which is the physical stimulus that produces the sensation, is entirely objective. The perceived color response results from either a reflected or a transmit-ted beam of white light or a portion of that beam. According to one of Grassmann’s laws, the eye can distinguish differences in only three parameters of color. These parameters are dominant wavelength, luminous reflectance, and excitation purity. The dominant wavelength (λ) of a color is the wavelength of a monochromatic light that, when mixed in suitable proportions with an achromatic color (gray), will match the color perceived. Light having short wavelengths (400 nm) is violet in color, and light having long wavelengths (700 nm) is red. Between these two wavelengths are those corre-sponding to blue, green, yellow, and orange light. This attribute of color perception is also known as hue. Of all the visible colors and shades, there are only three primary colors: red, green, and blue (or violet). Any other color may be produced by the proper com-bination of these colors. For example, yellow light is a mixture of green and red lights. The luminous reflectance of a color classifies an object as equivalent to a member of a series of achro-matic, grayscale objects ranging from black to white for light-diffusing objects and from black to perfectly clear and colorless for transmitting objects. A black standard is assigned a luminous reflectance of 0, whereas a white standard is assigned 100. This attri-bute of color perception is described as value in one visual system of color measurement. The excitation purity or saturation of a color describes the degree of its difference from the achro-matic color perception most resembling it. Numbers representing excitation purity range from 0 to 1. This attribute of color perception is also known as chroma. Measurement of Color The color of dental restorative materials is most com-monly measured in reflected light using a color mea-suring instrument or a visual method. Color Measuring Instrument Curves of spectral reflectance versus wavelength can be obtained over the visible range (405 to 700 nm) with a recording spectrophotometer and integrating sphere. Typical curves for a resin composite before and after 300 hours of accelerated aging in a weathering chamber are shown in Fig. 4.28. From the reflectance values and tabulated color-matching functions, the tristimulus values (X, Y, Z) can be computed relative to a particular light source. These tristimulus values are related to the amounts of the three primary colors required to give, by additive mixture, a match with the color being considered. Typically, the tristimu-lus values are computed relative to the Commission Internationale de l’Eclairage (CIE) (International Commission on Illumination) source D55, D65, or C. The ratios of each tristimulus value of a color to their sum are called the chromaticity coordinates (x, y, z). Dominant wavelength and excitation purity of a color can be determined by referring its chromaticity coordi-nates to a chromaticity diagram such as the one shown in Fig. 4.29. The luminous reflectance is equal to the value of the second (Y) of the three tristimulus values. A diagram of the CIE Lab color space is shown in Fig. 4.30. The Lab color space is characterized by uniform chromaticities. Value (black to white) is denoted as L, whereas chroma (ab) is denoted as red (+a), green (−a), yellow (+b), and blue (−b). Ranges of CIE Lab values for bleaching shades of resin composites are listed in Table 4.7. Differences between two colors can be determined from a color difference formula. One such formula has the following form: ∆Eab ∗L ∗a ∗b ∗ = ∆L∗ 2 + ∆a∗ 2 + ∆b∗ 2 where L, a, and b depend on the tristimulus val-ues of the specimen and of a perfectly white object. A value of ΔE of 1 can be observed visually by half of the observers under standardized conditions. A value of ΔE of 3.3 is considered perceptible clinically. 400 Reflectance (%) 500 Wavelength (nm) 600 700 0 40 20 60 80 100 Before aging Black backing White backing After aging FIG. 4.28 Curves of spectral reflectance versus wave-length for a resin composite before and after exposure to conditions of accelerated aging. The specimen was exposed continuously for 300 hours to the radiation of a 2500-W xenon lamp and intermittently sprayed with water. The aging chamber was held at 43°C and 90% relative humidity. Spectral reflectance curves for translucent specimens often are obtained with both black and white backings. 51 4. Fundamentals of Materials Science Visual Method A popular system for the visual determination of color is the Munsell color system, the parameters of which are represented in three dimensions, as shown in Fig. 4.31. A large set of color tabs is used to determine the color. Value (lightness) is deter-mined first by the selection of a tab that most nearly corresponds with the lightness or darkness of the color. Value ranges from white (10/) to black (0/). Chroma is determined next with tabs that are close to the measured value but are of increasing satura-tion of color. Chroma ranges from achromatic or gray (/0) to a highly saturated color (/18). The hue of the color is determined last by matching with color tabs of the value and chroma already deter-mined. Hue is measured on a scale from 2.5 to 10 in increments of 2.5 for each of the 10 color families (red, R; yellow-red, YR; yellow, Y; green-yellow, GY; green, G; blue-green, BG; blue, B; purple-blue, PB; purple, P; red-purple, RP). For example, the color of the attached gingiva of a healthy patient has been measured as 5R 6/4 to indicate a hue of 5R, a value of 6, and a chroma of 4. Two similar colors also can be compared in the Munsell color system by a color difference formula such as the one derived by Nickerson: I = C/5 2∆H + 6∆V + 3∆C where C is the average chroma and ΔH, ΔV, and ΔC are differences in hue, value, and chroma of the two colors. For example, if the color of attached A B C 600 770 580 560 500 480 0.2 0.4 0.6 0.8 0 0 0.2 0.4 0.6 0.8 540 520 C.I.E. 1931 380 y x FIG. 4.29 Chromaticity diagram (x, y) according to the 1931 Internationale de l’Eclairage (CIE) Standard Observer and coordinate system. Values of dominant wavelength determine the spectrum locus. The excitation purity is the ratio of two lengths (AB/AC) on the chromaticity diagram, where A refers to the standard light source and B refers to the color being considered. The point C, the intersection of line AB with the spectrum locus, is the dominant wavelength. a green B R G Y YR Chroma Hue Value RY b yellow a red b blue FIG. 4.30 Internationale de l’Eclairage (CIE) Lab color arrangement. (From Seghi RR, Johnston WM, O’Brien WJ. Spectrophotometric analysis of color differences between por-celain systems. J Prosthet Dent. 1986;56:35.) TABLE 4.7 Ranges of CIE Lab (D55, 10 degrees, CIE 1964) Values for Bleaching Shades of Resin Composites Material L a b Microhybrid composites 56.3 to 82.4 −0.4 to −3.8 −4.1 to 3.3 Microfilled composites 62.1 to 77.8 −1.9 to −2.8 −2.9 to 1.7 Control shade 1M1 62.9 −0.8 2.9 Control shade B1 58.2 −0.8 1.5 CIE, Internationale de l’Eclairage. Modified from Paravina RD, Ontiveros JC, Powers JM. Accelerated aging effects on color and translucency of bleaching-shade composites. J Esthet Restor Dent. 2004;16:117. FIG. 4.31 Munsell scales of hue, value, and chroma in color space. (Image courtesy Munsell Color, Grand Rapids, MI.) 52 CRAIG’S RESTORATIVE DENTAL MATERIALS gingiva of a patient with periodontal disease was 2.5R 5/6, the color difference, I, between the dis-eased tissue and the aforementioned healthy tissue (5R 6/4) would be as follows: I = 5/5 2 2.5 + 6 1 + 3 2 = 17 A trained observer can detect a color difference, I, equal to 5. Surface Finish and Thickness When white light shines on a solid, some of the light is directly reflected from the surface and remains white light. This light mixes with the light reflected from the body of the material and dilutes the color. As a result, an extremely rough surface appears lighter than a smooth surface of the same material. This problem is associated with unpolished or worn glass ionomer and resin composite restorations. For example, as the resin matrix of a composite wears away, the restoration appears lighter and less chro-matic (grayer). The thickness of a restoration can affect its appearance. For example, as the thickness of a com-posite restoration placed against a white background increases, the lightness and the excitation purity decrease. This is observed as an increase in opacity as the thickness increases. Pigmentation Esthetic effects are sometimes produced in a resto-ration by incorporating colored pigments in non-metallic materials such as resin composites, denture acrylics, silicone maxillofacial materials, and den-tal ceramics. The perceived color results from the absorption of specific wavelengths of light by the pigments and the reflection of other wavelengths. Mercuric sulfide, or vermilion, is red because it absorbs all colors except red and it reflects red. The mixing of pigments therefore involves the process of subtracting colors. For example, a green color may be obtained by mixing a pigment such as cadmium sulfide, which absorbs blue and violet, with ultra-marine, which absorbs red, orange, and yellow. The only color reflected from such a mixture of pigments is green, which is the color observed. Inorganic pigments are often preferred to organic dyes because the pigments are more permanent and durable in their color qualities. When colors are combined with the proper translucency, restor-ative materials can be made to closely match the surrounding tooth structure or soft tissue. To match tooth tissue, various shades of yellow and gray are blended into the white base material, and occasion-ally some blue or green pigments are added. To match the pink gingival tissues, various blends of red and white are used, with occasional additions of blue, brown, and black in small quantities. The color and translucency of gingival tissues vary widely from patient to patient and from one area of the mouth to another. Metamerism Metameric colors are color stimuli of identical tris-timulus values under a particular light source but with different spectral energy distributions. The spectral reflectance curves of two such pairs would be complicated, with perhaps three or more crossing points. Under some lights the pairs would appear to match, but under other lights they would be different (Fig. 4.32). The quality and intensity of light are factors that must be controlled when matching colors in dental restorations. Because the light spectrum of incan-descent lamps, fluorescent lamps, and the sun differ from each other, a color match between a restorative material and tooth structure in one lighting condi-tion might not match in another. Whenever possible, shade matching should be done in conditions where most of the patient’s activities will occur. Fluorescence Fluorescence is the emission of luminous energy by a material when a beam of light is shone on it. The wavelength of the emitted light usually is longer than that of the exciting radiation. Typically, blue or ultraviolet light produces fluorescent light that is in the visible range. Light from most fluorescent substances is emitted in a single, broad, well-shaped curve, the width and peak depending on the fluo-rescing substance. Sound human teeth emit fluorescent light when excited by ultraviolet radiation (365 nm), the fluo-rescence being polychromatic with the greatest intensity in the blue region (450 nm) of the spec-trum. Some anterior restorative materials and FIG. 4.32 Example of metamerism: the apple changes color depending on the light source used to illuminate it. 53 4. Fundamentals of Materials Science dental porcelains are formulated with fluoresc-ing agents to reproduce the natural appearance of tooth structure. Opacity, Translucency, Transparency, and Opalescence The color of an object is modified not only by the intensity and shade of the pigment or coloring agent but also by the translucency or opacity of the object. Hard and soft tissues vary in their degree of opac-ity. Most exhibit some translucency. This is especially true of tooth enamel and the surrounding gingival tissues. Opacity is a property of materials that prevents the passage of light. When all of the colors of the spectrum from a white light source such as sunlight are reflected from an object with the same intensity as received, the object appears white. When all the spectrum colors are absorbed equally, the object appears black. An opaque material may absorb some of the light and reflect the remainder. If, for example, red, orange, yellow, blue, and violet are absorbed, the material appears green in reflected white light. Translucency is a property of substances that per-mits the passage of light but disperses the light, so objects cannot be seen through the material. Some translucent materials used in dentistry are ceramics, resin composites, and acrylics. Transparent materials allow the passage of light, so little distortion takes place and objects may be clearly seen through them. Transparent substances such as glass may be colored if they absorb certain wavelengths and transmit others. For example, if a piece of glass absorbed all wavelengths except red, it would appear red by transmitted light. If a light beam containing no red wavelengths were shone on the glass, it would appear opaque, because the remaining wavelengths would be absorbed. Opalescent materials, such as dental enamel, are able to scatter shorter wavelengths of light. Under transmitted light, they appear brown/yel-low, whereas shades of blue are perceptible under reflected light (Fig. 4.33). To produce highly esthetic restorations that truly mimic the natural appearance of the tooth, materials with opalescent properties should be used. This has popularized the use of por-celain veneering materials, as well as direct restor-ative composites. Index of Refraction The index of refraction (n) for any substance is the ratio of the velocity of light in a vacuum (or air) to its velocity in the medium. When light enters a medium, it slows from its speed in air (300,000 km/s) and may change direction. For example, when a beam of light traveling in air strikes the surface of water at an oblique angle, the light rays are bent toward the normal. The normal is a line drawn perpendicular to the water surface at the point where the light contacts the water surface. If the light is traveling through water and contacts a water-air surface at an oblique angle, the beam of light is bent or refracted away from the normal. The index of refraction is a characteristic property of the substance (Table 4.8) and is used extensively for identification. One of the most important appli-cations of refraction is the control of the refractive index of the dispersed and matrix phases in mate-rials such as resin composites and dental ceram-ics, designed to have the translucent appearance of tooth tissue. A perfect match in the refractive indi-ces results in a transparent solid, whereas large dif-ferences result in opaque materials. Optical Constants As light interacts with an object, several phenom-ena can be observed. Incident light can be reflected, absorbed, scattered (or backscattered), or transmit-ted. These parameters can all be calculated to more objectively characterize the optical properties of the material (Fig. 4.34). Esthetic dental materials such as ceramics, resin composites, and tooth structure Transmitted light Reflected light FIG. 4.33 Demonstration of opalescence in a ceramic restoration. The tooth appears brown under transmitted light and blue under reflected light. TABLE 4.8 Index of Refraction (n) of Various Materials Material Index of Refraction Feldspathic porcelain 1.504 Quartz 1.544 Synthetic hydroxyapatite 1.649 Tooth structure, enamel 1.655 Water 1.333 54 CRAIG’S RESTORATIVE DENTAL MATERIALS are turbid, or intensely light-scattering, materials. In a turbid material the intensity of incident light is diminished considerably when light passes through the specimen. These considerations are important not only for shade matching but also in situations where the restorative material is used to conceal imperfections in the tooth being restored, such as stains or other flaws. The optical properties of restor-ative materials are described by the Kubelka-Munk equations, which develop relations for monochro-matic light between the reflection of an infinitely thick layer of a material and its absorption and scat-tering coefficients. These equations can be solved algebraically by hyperbolic functions derived by Kubelka. Secondary optical constants (a and b) can be cal-culated as follows: a = [R (B) −R (W) −RB + RW −R (B) R (W) RB + R (B) R (W) RW + R (B) RBRW −R (W) RBRW −R (W) RBRW/{2 [R (B) RW −R (W) RB]} and b = (a2 −1) ½ where RB is the reflectance of a dark backing (the black standard), RW is reflectance of a light backing (the white standard), R(B) is the light reflectance of a specimen with the dark backing, and R(W) is the light reflectance of the specimen with the light backing. These equations are used under the assump-tions that (1) the material is turbid, dull, and of constant finite thickness; (2) edges are neglected; (3) optical inhomogeneities are much smaller than the thickness of the specimen and are distributed uniformly; and (4) illumination is homogeneous and diffused. Scattering Coefficient The scattering coefficient is the fraction of inci-dent light flux lost by reversal of direction in an elementary layer. The scattering coefficient, S, for a unit thickness of a material is defined as follows: S = 1/bX Arctgh 1 −a R + Rg + RRg/b R −Rg mm−1 where X is the actual thickness of the specimen, Ar ctgh is an inverse hyperbolic cotangent, and R is the light reflectance of the specimen with the backing of reflectance, Rg. The scattering coefficient varies with the wave-length of the incident light and the nature of the colorant layer, as shown in Fig. 4.35 for several shades of a resin composite. Composites with larger values of the scattering coefficient are more opaque. Absorption Coefficient The absorption coefficient is the fraction of incident light flux lost by absorption in an elementary layer. The absorption coefficient, K, for a unit thickness of a material is defined as follows: K = S(a −1) mm−1 The absorption coefficient also varies with the wavelength of the incident light and the nature of the colorant layer, as shown in Fig. 4.36 for several shades of a resin composite. Composites with larger values of the absorption coefficient are more opaque and more intensely colored. Incident light (Io) Superficial reflection Back scattering Transmission Scattering (S) Thickness Absorption (K) FIG. 4.34 Schematic of the possible interactions of light with a solid. CO 400 0 0.8 1.0 1.4 1.8 Scattering coefficient (mm1) 2.2 2.6 500 600 Wavelength (nm) 700 CL CU CY CDY CT CG FIG. 4.35 Scattering coefficient versus wavelength for shades of a composite, C. Shades are O, opaque; L, light; U, uni-versal; Y, yellow; DY, dark yellow; T, translucent; and G, gray. (From Yeh CL, Miyagawa Y, Powers JM. Optical properties of compos-ites of selected shades. J Dent Res. 1982;61(6):797–801.) 55 4. Fundamentals of Materials Science Light Reflectivity The light reflectivity, RI, is the light reflectance of a material of infinite thickness, and is defined as follows: RI = a −b This property also varies with the wavelength of the incident light and the nature of the colorant layer. The light reflectivity can be used to calculate a thickness, XI, at which the reflectance of a mate-rial with an ideal black background would attain 99.9% of its light reflectivity. The infinite optical thickness, XI, is defined for monochromatic light as follows: XI = (1/bS)Arctgh[(1 −0.999aRI)/0.999bRI] mm The variation of XI with wavelength is shown in Fig. 4.37 for a resin composite. It is interesting that composites are more opaque to blue than to red light, yet blue light is used to cure light-activated composites. Contrast Ratio Once a, b, and S are obtained, the light reflectance (R) for a specimen of any thickness (X) in contact with a backing of any reflectance (Rg) can be calculated using the following formula: R = [1 −Rg(a −bctghbSX)]/(a + bctghbSX −Rg) An estimate of the opacity of a 1-mm-thick speci-men can then be calculated from the contrast ratio (C) as follows: C = RO/R where R0 is the computed light reflectance of the specimen with a black backing. CU CT CL CG CY CO CDY 400 Absorption coefficient (mm1) 500 Wavelength (nm) 600 700 0.0 0.5 1.0 1.5 2.0 FIG. 4.36 Absorption coefficient versus wavelength for shades of a composite, C. Shades are DY, dark yellow; O, opaque; Y, yellow; G, gray; L, light; T, translucent; and U, universal. (From Yeh CL, Miyagawa Y, Powers JM. Optical properties of com-posites of selected shades. J Dent Res. 1982;61(6):797–801.) 400 Infinite optical thickness (mm) 500 Wavelength (nm) 600 700 0.0 2.5 5.0 7.5 10.0 CO CDY CG CY CL CT CU FIG. 4.37 Infinite optical thickness versus wavelength for shades of a composite, C. Shades are U, universal; T, translucent; L, light; Y, yellow; G, gray; DY, dark yellow; and O, opaque. (From Yeh CL, Miyagawa Y, Powers JM. Optical properties of composites of selected shades. J Dent Res. 1982;61(6):797–801.) 56 CRAIG’S RESTORATIVE DENTAL MATERIALS Masking Ability Dental restorations are often used to resolve esthetic problems, even when carious lesions are not pres-ent. This is the case in patients presenting staining due to intrinsic or extrinsic factors (examples of which are staining by antibiotics and smoking hab-its, respectively) or in restorations where an opaque reinforcing structure is required, as in the case of metallic or highly crystalline ceramic posts. The masking ability of restorative materials depends on their optical constants, as previously described, and on their thickness. In Fig. 4.34 examples of materials with the same thickness but different optical prop-erties are shown against a black and white back-ground to demonstrate variations in the masking ability. THERMAL PROPERTIES Temperature The temperature of a substance can be measured with a thermometer or a thermocouple. An impor-tant application of temperature assessment in dentistry is the measurement of heat during cav-ity preparation or during light activation of resin composites. Examples of the effect of heat genera-tion by the handpiece while on rotation and cool-ants on temperature in tooth structure during cavity preparation are shown in Fig. 4.38. The temperature was measured by a thermocouple inserted into a small opening that extended into the dentoenamel junction. The tooth was then cut in the direction of the thermocouple and the maximum temperature recorded. Transition Temperatures The arrangement of atoms and molecules in materi-als is influenced by the temperature; as a result, ther-mal techniques are important in understanding the properties of dental materials. Differential thermal analysis (DTA) has been applied to study the components of dental waxes. The DTA curve of a mixture of paraffin and carnauba wax is shown in Fig. 4.39. The thermogram was obtained when the difference in temperature between the wax and a standard was recorded under the same heating conditions in which thermocouples were used. The difference in temperature was recorded as a function of the temperature of the surroundings. A decrease in the value of ΔT indicated an endothermic process in the specimen. The endotherms at 31.5°C and 35°C are solid-solid transitions occurring in the paraffin wax as the result of a change of crystal structure. The endotherm at 52°C represents the solid-liquid transition of paraffin wax, whereas the endotherms at 68.7°C and 80.2°C result from the melting of car-nauba wax. The heat of transition of the two solid-solid transitions is about 8 cal/g, and the melting transition of paraffin and carnauba wax is approxi-mately 39 and 11 cal/g, respectively. These and other thermograms show that 25% carnauba wax added to paraffin wax has no effect on the melting point 25 50 75 Rotating speed (rpm 1000) 100 125 150 175 200 0 Temperature rise (C) 11.1 22.2 33.3 44.4 55.5 66.6 37C H2O - Air spray 8.5 cc/min 1.1N 25C H2O - Air spray 8.5 cc/min 2.2N Air coolant 2.2N No coolant 2.2N # 37 CARBIDE BUR 25C H2O - Air spray 8.5 cc/min 1.1N 25C H2O Stream 125 cc/min 1.1N 0 FIG. 4.38 Temperature rises developed by carbide burs during cutting of tooth tissue, operated at different speeds and with and without coolants. (Modified from Peyton FA. Effectiveness of water coolants with rotary cutting instruments. J Am Dent Assoc. 1958;56(5):664.) 57 4. Fundamentals of Materials Science of paraffin wax but increases the melting range by about 28°C. Thermomechanical analysis (TMA) of the car-nauba-paraffin wax mixture is also shown in Fig. 4.39. The percent penetration of the wax mixture by a cylindrical probe is shown for two stresses of 0.013 and 0.26 MPa. The penetration of the wax at the lower stress was controlled by the melting transition of the carnauba wax component, whereas the pen-etration at the higher stress was dominated by the solid-solid and solid-liquid transitions of the paraffin wax components. About 44% penetration, which is related to flow, occurred before the melting point of the paraffin wax was reached. Other properties correlate with thermograms. The coefficient of thermal expansion of paraffin wax increases from about 300 × 10−6/C to 1400 × 10−6/C just before the solid-solid transition, and the flow increases greatly in this temperature range. Dynamic mechanical analysis (DMA) of a dimeth-acrylate copolymer is shown in Fig. 4.40. A thin film of the copolymer was subjected to a sinusoidal ten-sile strain at a frequency of 11 Hz. As temperature was increased, values of modulus of elasticity (E′) and loss tangent (tan δ) were obtained. The glass transition temperature (Tg) was determined from identification of the beginning of a rapid decrease in E′ with temperature. The value of Tg identifies the temperature at which a glassy polymer transforms to a softer, rubbery state upon heating, which in turn relates to the increase in the number of degrees of freedom given to the molecules by the increased entropy. A lower value of Tg can result from a lower degree of conversion of double bonds, less cross-linked, more flexible networks, or from saturation by water. As discussed later, the value of the coefficient of thermal expansion of a polymer changes at Tg. Heat of Fusion The heat of fusion, L, is the heat in calories, or joules, J, required to convert 1 g of a material from solid to liquid state at the melting temperature. The equation for the calculation of heat of fusion is L = Q/m, where Q is the total heat absorbed and m is the mass of the substance melted. Therefore in practical applica-tions it is apparent that the larger the mass of mate-rial being melted, the more heat required to change the total mass to liquid. The heat of fusion is closely related to the melting or freezing point of the sub-stance, because when the change in state occurs, it is always necessary to apply additional heat to the mass to cause liquefaction, and as long as the mass remains molten, the heat of fusion is retained by the liquid. When the mass is frozen, or solidified, the heat that was retained in the liquid state is liberated. The difference in energy content is necessary to maintain 80.2 68.7 31.5 35 52 20 40 60 80 100 100 75 50 Penetration (%) 25 0 120 0 .5 T, C 1.0 1.5 2.0 2.5 C DTA TMA 0.013 MN/m2 TMA 0.26 MN/m2 FIG. 4.39 Thermograms of a 75% paraffin and 25% carnauba wax mixture. Tg 25C 48C 100 4 3 2 1 0 Log tan Log E' (dynes/cm2) Tan 1 2 3 4 50 0 50 Temperature (C) 100 150 200 250 6 7 8 9 10 11 E' FIG. 4.40 Dynamic mechanical properties of a 75 wt% bisphenol A-glycidyl methacrylate (Bis-GMA)/25 wt% triethylene glycol dimethacrylate (TEGDM) copolymer. (From Wilson TW, Turner DT. Characterization of polydimeth-acrylates and their composites by dynamic mechanical analysis. J Dent Res. 1987;66:1032.) 58 CRAIG’S RESTORATIVE DENTAL MATERIALS the kinetic molecular motion, which is characteristic of the liquid state. The values for heat of fusion of some common substances (given in round numbers) are listed in Table 4.9. It may be seen that the values for heat of fusion of gold and the metals used for dental gold alloys (silver and copper) are below those of many other metals and compounds. This is true also for the specific heat of gold and its alloys. Thermal Conductivity The thermal conductivity, K, of a substance is the quantity of heat in calories, or joules, per second passing through a body 1 cm thick with a cross sec-tion of 1 cm2 when the temperature difference is 1°C. The units are cal/s/cm2/(°C/cm). The conductivity of a material changes slightly as the surrounding temperature is altered, but generally the difference resulting from temperature changes is much less than the difference that exists between different types of materials. Several important applications of thermal con-ductivity exist in dental materials. For example, a large amalgam filling or gold crown in proximity to the pulp may cause the patient considerable dis-comfort when hot or cold foods produce temperature changes; this effect is mitigated when adequate tooth tissue remains or cavity liners are placed between the tooth and filling for insulation. Cavity liners are relatively poor thermal conductors and insulate the pulp area. A better understanding of the conductivities of various restorative materials is desirable to develop an appropriate degree of insulation for the pulp tis-sue, comparable with that in the natural tooth. The conductivity of certain dental materials is listed in Table 4.10. Nonmetallic materials have lower ther-mal conductivity than metals, and are therefore good insulators. Dental cements have a thermal conduc-tivity similar to that of dentin and enamel. Note that the thermal conductivity of a liner or base is impor-tant in reducing the thermal transfer to the pulp, and that the temperature difference across an insu-lator depends on the extent of the heating or cool-ing period and the magnitude of the temperature difference. Specific Heat The specific heat, Cp, of a substance is the quan-tity of heat needed to raise the temperature of 1 g of the substance by 1°C. Water is usually chosen as the standard substance and 1 g as the standard mass. The heat required to raise the temperature of 1 g of water from 15°C to 16°C is 1 cal, which is used as the basis for the definition of the heat unit. Most substances are more readily heated, gram for gram, than water. TABLE 4.9 Heat of Fusion (L) of Some Materials Materials Temperature (°C) Heat of Fusion (cal/g [J/g]) METALS Mercury −39 3 Gold 1063 16 Silver 960 26 Platinum 1773 27 Copper 1083 49 Cobalt 1495 58 Chromium 1890 75 Aluminum compounds 660 94 Alcohol −114 25 Paraffin 52 35 Beeswax 62 42 Glycerin 18 47 Ice 0 80 TABLE 4.10 Thermal Conductivity (K) of Various Materials Material Thermal Conductivity cal/s/cm2/(°C/cm) J/s/cm2(°C/cm) METALS Silver 1.006 4.21 Copper 0.918 3.84 Gold 0.710 2.97 Platinum 0.167 0.698 Dental amalgam 0.055 0.23 Mercury 0.020 0.084 NONMETALS Gypsum 0.0031 0.013 Resin composite 0.0026 0.011 Porcelain 0.0025 0.010 Enamel 0.0022 0.0092 Dentin 0.0015 0.0063 Acrylic resin 0.0005 0.0021 Beeswax 0.00009 0.0004 59 4. Fundamentals of Materials Science Obviously, the total heat required to raise the temperature of a substance by 1°C depends on the total mass and the specific heat. For example, 100 g of water requires more calories than 50 g of water to raise the temperature by 1°C. Likewise, because of the difference in specific heat of water and alco-hol, 100 g of water requires more heat than 100 g of alcohol to raise the temperature the same amount. In general, the specific heat of liquids is higher than those of solids. Some metals have specific heat values of less than 10% that of water. During the melting and casting process, the spe-cific heat of the metal or alloy is important because of the total amount of heat that must be applied to the mass to raise the temperature to the melting point. Fortunately, the specific heat of gold and the metals used in gold alloys is low, so prolonged heating is unnecessary. The specific heat of both enamel and dentin is higher than that of metals used for fillings, as shown in Table 4.11. Thermal Diffusivity The thermal diffusivity, Δ, is a measure of transient heat flow and is defined as the thermal conductiv-ity, K, divided by the product of the specific heat, Cp, times the density, ρ: ∆= K/(Cpρ) The units of thermal diffusivity are mm2/s. The thermal diffusivity describes the rate at which a body with a nonuniform temperature approaches equilibrium. For a gold crown or a dental amalgam, the low specific heat combined with the high thermal conductivity creates a thermal shock more readily than normal tooth structure does. Values of thermal diffusivity of some materials are listed in Table 4.12. These values may vary somewhat with composition of the particular restorative material. As mentioned in the discussion of thermal con-ductivity, thickness of the material is important. A parameter governing lining efficiency (Z) is related to thickness (T) and thermal diffusivity (Δ) as follows: Z = T/(Δ)½ Coefficient of Thermal Expansion The change in length (lfinal − loriginal) per unit length of a material for a 1°C change in temperature is called the linear coefficient of thermal expansion, α, and is cal-culated as follows: (lﬁnal −loriginal)/[loriginal × ( °Cﬁnal −°Coriginal)] = α The units are represented by the notation /°C, and because the values are usually small they are expressed in exponential form such as 22 × 10−6/°C. A less common practice is to report the change in parts per million (ppm) and the previous number would be expressed as 22 ppm. The linear coefficients of thermal expansion for some materials important in restorative dentistry are given in Table 4.13. Although the coefficient is a material constant, it does not remain constant over wide temperature ranges. For example, the linear coefficient of thermal expansion of a dental wax may have an average value of 300 × 10−6/°C up to TABLE 4.11 Specific Heat (Cp) of Various Materials Material Specific Heat (cal/g/°C [J/g/°C]) SOLIDS Gold 0.031 [0.13] Platinum 0.032 [0.13] Silver 0.056 [0.23] Copper 0.092 [0.38] Enamel 0.18 [0.75] Quartz 0.19 [0.79] Aluminum 0.21 [0.88] Porcelain 0.26 [1.09] Dentin 0.28 [1.17] Acrylic resin 0.35 [1.46] LIQUIDS Water 1.000 [4.18] Paraffin 0.69 [2.88] Glycerin 0.58 [2.42] Alcohol (ethyl) 0.547 [2.29] Mercury 0.033 [0.14] TABLE 4.12 Thermal Diffusivity (Δ) of Various Materials Material Thermal Diffusivity (mm2/s) Pure gold (calculated) 119.0 Amalgam 9.6 Resin composite 0.675 Porcelain 0.64 Enamel 0.469 Glass ionomer cement 0.198 Dentin 0.183 Acrylic resin 0.123 60 CRAIG’S RESTORATIVE DENTAL MATERIALS 40°C, whereas it may have an average value of 500 × 10−6/°C from 40 to 50°C. The coefficient of thermal expansion of a polymer changes as the polymer goes from a glassy state to a softer, rubbery material. This change in the coefficient corresponds to the glass transition temperature (Tg). Either the linear or volumetric coefficient of ther-mal expansion may be measured, and for most mate-rials that function as isotropic solids, the volumetric thermal coefficient may be considered to be three times the linear thermal coefficient. Both linear expansion and volume expansion are important in restorative materials and processes. It is obvious that with a reduction of temperature, or cooling, there is a contraction of the substance that is equal to the expansion that results from heating. Accordingly, tooth structure and restorative mate-rials in the mouth will expand when warmed by hot foods and beverages but will contract when exposed to cold substances. Such expansions and contractions may break the marginal seal of a filling in the tooth, particularly if the difference between the coefficient of expansion of the tooth and the restorative material is large. The high coefficient of expansion of pattern waxes is an important factor in the construction of properly fitting restorations. The change in volume as a result of cooling is responsible for the shrinkage spots or surface cracks that often develop in gold alloy castings during solidification. Compensation for the contraction that occurs during the cooling of gold alloys must be made if accurate gold castings are to result. The values in Table 4.13 show that with comparable temperature changes, materials such as acrylic resin and amalgam expand more than tooth tissue, whereas ceramic expands less. The coefficient of inlay pattern wax is excep-tionally high when compared with that of other materials. Of particular importance in casting investments is the property of thermal expansion of three crys-talline polymorphic forms of silica. As a princi-pal ingredient in dental investments that are to be heated before a metal casting is made, the amount of expansion at various temperatures is critical and important. This quality of silica compounds in rela-tion to use in casting investments was described in 1932. Curves in Fig. 4.41 illustrate the relative per-centage of thermal expansion of the four forms of silica at different temperatures below about 800°C. Of the crystalline forms, cristobalite shows the great-est expansion at the lowest temperature and quartz requires a higher temperature to develop an equal amount of expansion as cristobalite. Fused silica has long been recognized as having an exceedingly low thermal expansion. ELECTRICAL PROPERTIES Electrical Conductivity and Resistivity The ability of a material to conduct an electric current may be stated as either specific conductance or con-ductivity, or conversely, as the specific resistance or resistivity. Resistivity is the more common term. The resistance of a homogeneous conductor of uniform cross section at a constant temperature varies directly with the length and inversely with the cross-sectional area of the specimen, according to the equation: R = ρl/A TABLE 4.13 Linear Coefficient (α) of Thermal Expansion of Various Materials Material Coefficient (×10−6/°C) Inlay waxes 350–450 Silicone impression material 210 Pit and fissure sealants 71–94 Acrylic resin 76.0 Mercury 60.6 Resin composites 14.50 Amalgam 22–28 Silver 19.2 Copper 16.8 Gold 14.4 Porcelain 12.0 Tooth (crown portion) 11.4 Glass ionomer (type 2) 10.2–11.4 0 100 200 300 400 500 Temperature (C) 600 700 800 900 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Expansion (%) Fused silica Quartz Tridymite Cristobalite FIG. 4.41 Thermal expansion curves for four types of silica. (Modified from Volland RH, Paffenbarger GC. Cast gold inlay technic as worked out in the cooperative research at the National Bureau of Standards and applied by a group of practic-ing dentists. J Am Dent Assoc. 1932;19(2):185.) 61 4. Fundamentals of Materials Science where R is the resistance in ohms, ρ (rho) is the resis-tivity, l is the length, and A is the section area. The resistivity depends on the nature of the material. If a unit cube of 1-cm edge length is employed, the l and A are equal to unity, and in this case R = ρ. The resistivity is expressed as ohm-centimeters, where R is in ohms, l is in centimeters, and A is in square centimeters. The change in electrical resistance has been used to study the alteration in internal structure of various alloys as a result of heat treatment. An early investi-gation of the gold-copper alloy system by electrical conductivity methods revealed a change in internal crystal structure with an accompanying change in conductivity. The correlation of these conductiv-ity studies with related changes in other proper-ties established the fundamental basis of structural changes associated with heat-treatment operations on dental gold alloys. Values for the resistivity of human tooth struc-ture are shown in Table 4.14. Resistivity is impor-tant in the investigation of the pain perception threshold resulting from applied electrical stimuli and of displacement of fluid in teeth caused by ionic movements. The electrical resistance of nor-mal and carious teeth has been observed to differ, with less resistance offered by the carious tissue. Sound enamel is a relatively poor conductor of electricity, whereas dentin is somewhat better (see Table 4.14). The conductivity of materials used to replace tooth tissue is of concern in restorative dentistry. The effectiveness of insulating cement bases and other nonmetallic restorative materials is not yet estab-lished. Several studies have measured the resistiv-ity of dental cements (see Table 4.14). Glass ionomer cements are the most conductive of the cements and have values most similar to dentin. Dielectric Constant A material that provides electrical insulation is known as a dielectric. Values of the dielectric con-stant for human dentin and several dental cements are listed in Table 4.15. The dielectric constant of a dental cement generally decreases as the material hardens. This decrease reflects a change from a paste that is relatively ionic and polar to one that is less so. As shown by the high values of permittivity of glass ionomer cements in Table 4.15, these cements have a high ionic content and are quite polar compared with human dentin. The problem of electrical insulation is made more complex by the presence of galvanic currents in the mouth, resulting from cells formed from metallic restorations. Recent studies indicate that a cement base does not effectively insulate the pulp from the electric current developed in a metallic restoration in the mouth. How much insulation is essential or how to effectively restore the tooth to its original status of equilibrium is currently not known. Electromotive Force Working with metals and alloys for dental resto-rations or with instruments that are susceptible to corrosion necessitates some understanding of the relative position of the metal in the electromotive force series. The electromotive series is a listing of electrode potentials of metals according to the order of their decreasing tendency to oxidize in solu-tion. This serves as the basis of comparison of the tendency of metals to oxidize in air. Those metals with a large negative electrode potential are more resistant to tarnish than those with a high positive electrode potential. In general, the metals above copper in the series, such as aluminum, zinc, and nickel, tend to oxidize relatively easily, whereas those below copper, such as silver, platinum, and gold, resist oxidation. A list of oxidation-reduction potentials for some common corrosion reactions in water and in salt water is given in Table 4.16. The values of electrode potential and the order of the series change when measured in a saline solution rather than water. The electrode potentials of some dental alloys measured in artificial saliva at 35°C are listed in Table 4.17. TABLE 4.14 Values of Resistivity (r) of Human Tooth Structure and Glass Ionomer Cement Material Resistivity (ohm·cm) HUMAN ENAMEL Bjorn (1946) 2.9–3.6 × 106 Mumford (1967) 2.6–6.9 × 106 HUMAN DENTIN Bjorn (1946) 0.7–6.0 × 104 Mumford (1967) 1.1–5.2 × 104 DENTAL CEMENT Glass ionomer 0.8–2.5 × 104 TABLE 4.15 Dielectric Constant (εr) for Human Dentin and Glass Ionomer Cement Material Dielectric Constant Human dentin 8.6 Glass ionomer 2 to 7 × 105 62 CRAIG’S RESTORATIVE DENTAL MATERIALS Likewise, it is possible to determine from the elec-tromotive force series that the reduction of the oxides of gold, platinum, and silver to pure metal can be accomplished more readily than with those metals that have a higher electromotive force value. Galvanism The presence of metallic restorations in the mouth may cause a phenomenon called galvanic action, or galvanism. This results from a difference in potential between dissimilar fillings in opposing or adjacent teeth. These fillings, in conjunction with saliva or bone fluids such as electrolytes, make up an electric cell. When two opposing fillings contact each other, the cell is short-circuited, and if the flow of current occurs through the pulp, the patient experiences pain and the more anodic restoration may corrode. A single filling plus the saliva and bone fluid may also constitute a cell of liquid junction type. As shown in Fig. 4.42, ions capable of conducting electricity can easily migrate through dentin and around the mar-gins of a restoration. Studies have indicated that relatively large cur-rents will flow through metallic fillings when they are brought into contact. The current rapidly falls off if the fillings are maintained in contact, probably as a result of polarization of the cell. The magnitude of the voltage, however, is not of primary importance, because indications support the fact that the sensitiv-ity of the patient to the current has a greater influence on whether pain is felt. Although most patients feel pain at a value between 20 and 50 μamp, some may TABLE 4.16 Oxidation-Reduction Potentials for Corrosion Reactions in Water and Salt Water Metal Corrosion Reaction In Water, Electrode Potential at 25°C (Volts vs. Normal Hydrogen Electrode) In Salt Water, Electrode Potential at 25°C (Volts vs. 0.1 N Calomel Scale) Aluminum Al → Al3+ + 3e +1.662a +0.83 Zinc Zn → Zn2+ + 2e +0.763 +1.10 Chromium Cr → Cr3+ + 3e +0.744 +0.4 to −0.18 Iron Fe → Fe2+ + 2e +0.440 +0.58 Cobalt Co → Co2+ + 2e +0.277 — Nickel Ni → Ni2+ + 2e +0.250 +0.07 Tin Sn → Sn2++ 2e +0.136 +0.49 Hydrogen H2 → 2H+ + 2e 0.000 — Copper Cu → Cu2+ + 2e −0.337 +0.20 4(OH−) → O2 + 2H2O + 4e −0.401 — Mercury 2Hg → Hg22+ + 2e −0.788 — Silver Ag → Ag+ + e −0.799 +0.08 Palladium Pd → Pd2+ + 2e −0.987 — Platinum Pt → Pt2+ + 2e −1.200 — 2H2O → O2 + 4H+ + 4e −1.229 — Gold Au →Au3+ + 3e −1.498 — aA positive value indicates a strong tendency for the metal to go into solution. Higher positive values are more anodic, whereas higher negative values are more cathodic. Modified from Flinn RA, Trojan PK. Engineering Materials and Their Applications. 4th ed. Boston, MA: Houghton Mifflin; 1990. TABLE 4.17 Galvanic Series of Some Dental Alloys in Artificial Saliva at 35°C Material Voltsa Hydrogen/H 0.000 Amalgam Conventional spherical −0.023 Dispersed high-copper −0.108 Nickel-chromium alloy −0.126 to 0.240 Cobalt-chromium alloy −0.292 Gold Alloy Au-Cu-Ag −0.345 Au-Pt-Pd-Ag −0.358 to -0.455 aHigh positive sign indicates a strong tendency for the metal to go into solution. Modified from Arvidson K, Johansson EG. Galvanic series of some dental alloys. Scand J Dent Res. 1977;85:485. 63 4. Fundamentals of Materials Science feel pain at 10 μamp, whereas others do not experi-ence it until 110 μamp is developed. This is a possible explanation for the fact that some patients are both-ered by galvanic action and others are not, despite similar conditions in the mouth. The galvanic currents developed from the con-tact of two metallic restorations depend on their composition and surface area. An alloy of stainless steel develops a higher current density than either gold or cobalt-chromium alloys when in contact with an amalgam restoration. As the size of the cathode (such as a gold alloy) increases relative to that of the anode (such as an amalgam), the current density may increase. The larger cathode, likewise, can enhance the corrosion of the smaller anode. Current densities associated with non-γ2-containing amalgams appear to be less than those associated with the γ2-containing amalgams. Electrochemical Corrosion The corrosion and electrochemical behavior of restor-ative materials have received new interest with the study of multiphase systems such as gold alloys and amalgam. For example, the corrosion of γ, γ1, and γ2 phases in amalgam has been studied by electrochem-ical analysis. Anodic and cathodic polarization mea-surements indicated no strongly passive behavior of these phases in artificial saliva. The dental amalgam specimens became pitted at the boundaries between the phases or in γ2 phase. Other studies, however, indicate that amalgam alloys exhibit decreasing electrochemical potentials, resulting in noble val-ues when stored in neutral solutions. The addition of copper to amalgam alloys to form copper-tin compounds during hardening has improved the resistance of amalgam to chloride and galvanic cor-rosion. As shown in Fig. 4.43, the anodic activity of AgSn amalgam is quite different from AgSn + AgCu amalgams. The AgSn + AgCu amalgam remains pas-sive under the testing conditions, whereas the AgSn amalgam does not. Studies of corrosion of surgical stainless steel and stainless steel orthodontic brackets have been reported. Corrosion of these alloys and others can result in decreased mechanical properties and the formation of corrosion products, which in some instances accumulate in the human organs. As shown previously in Table 4.16, corrosion can be affected by the environment, and certain metals such as cobalt and copper corrode more rapidly in a saline solution containing serum albumin and fibrinogen proteins. Zeta-Potential A charged particle suspended in an electrolytic solution attracts ions of opposite charge to those at its surface. The layer formed by these ions is called the Stern layer. To maintain the electrical balance of the suspending fluid, ions of opposite charge are attracted to the Stern layer. The potential at the sur-face of that part of the diffuse double layer of ions is called the electrokinetic or zeta-potential. Electrophoresis may be used to increase the sta-bility of colloids, stimulate adsorption of ions, and characterize particle surfaces. Effects of pH, surface-active agents, and enzymes on zeta-potential are important. Zeta-potential may affect the near-surface mechanical properties (such as wear) of a material. The zeta-potentials of some materials are listed in Table 4.18. OTHER PROPERTIES Certain properties often are highly important in the selection and manipulation of materials for use either in the mouth or for laboratory applications. Five such properties are tarnish and discoloration, water sorp-tion, solubility and disintegration, setting time, and shelf life. Tarnish and Discoloration Discoloration of a restorative material from any cause is a very troublesome quality. The tarnish of metal restorations from oxide, sulfide, or any other materi-als causing a surface reaction is a critical quality of FIG. 4.42 Human pulp capped with calcium hydroxide cement. Observation period: 70 days. A thin bond of hard tissue lined by cells is covering most of the exposure site (rank B). Calcified tissue in relation to displaced calcium hydroxide cement particles (arrow; hematoxylin-eosin, orig-inal magnification ×100). (From Hörsted-Bindslev P, Vilkinis V, Sidlauskas A. Direct capping of human pulps with a dentin bond-ing system or with calcium hydroxide cement. Oral Surg Oral Med Oral Pathol Oral Radiol Endod. 2003;96(5):591–600.) 64 CRAIG’S RESTORATIVE DENTAL MATERIALS metal restorations in the mouth and of laboratory and clinical instruments. The process of steam ster-ilization of surgical instruments has long presented a serious problem of tarnish and corrosion. Many nonmetallic materials such as cements and compos-ite restorations have displayed a tendency to discolor in service because colored substances penetrate the materials and continue chemical reactions in the composites. Various in vitro tests have been proposed to study tarnish, particularly that of crown and bridge and partial denture alloys. Testing generally relies on controlled exposure of the alloy to a solution rich in sulfides, chlorides, and phosphates. Most recently the discoloration of alloys exposed to such solutions has been evaluated by spectrophotometric methods to determine a color-difference parameter discussed earlier in this chapter. Water Sorption Water sorption of a material represents the amount of water adsorbed on the surface and absorbed into the body of the material during fabrication or while the restoration is in service. Water sorption of denture acrylic, for example, is measured gravimetrically in μg/mm3 after 7 days in water. The tendency of plas-tic denture base materials to have a high degree of water sorption is the reason this quality was included in American National Standards Institute/American Dental Association (ANSI/ADA) specification No. 12 for this type of material. Usually a serious warpage and dimensional change in the material are associ-ated with a high percentage of water sorption. The tendency of alginate impression materials to imbibe water if allowed to remain immersed and then to change dimensions requires careful disinfection pro-cedures and pouring within the manufacturer’s rec-ommended time. Setting Time Setting time characteristics are associated with the reaction rates and affect the practical applications of many materials in restorative dentistry. Materials such as cements, impression materials, dental plaster, stone, and casting investments depend on a critical AgSn AgCu amalgam AgSn amalgam Sn oxidation Cu oxidation Breakdown of passivity 7 6 5 4 Log current density (A/cm2) 3 2 0.8 0.6 0.4 0.2 0 0.2 Potential, V(SCE) FIG. 4.43 Anodic polarization curves of two types of amalgam in synthetic saliva. (Modified from Fairhurst CW, Marek M, Butts MB, et al. New information on high copper amalgam corrosion. J Dent Res. 1978;57:725.) TABLE 4.18 Zeta-Potential (ζ) of Some Dental Materials Material Zeta-Potential (mV) Hydroxyapatite −9.0 to −10.9 Tooth structurea Calculus −15.3 Cementum Exposed −6.96 Unexposed −9.34 Dentin −6.23 Enamel −9.04 to −10.3 aMeasured in Hanks’ balanced salt solution at 30°C. Modified from O’Brien WJ, ed. Dental Materials: Properties and Selection. 2nd ed. Chicago, IL: Quintessence; 1997. 65 4. Fundamentals of Materials Science reaction time and hardening rate for their successful application. From the practical standpoint of manip-ulation and successful application, the time required for a material to set or harden from a plastic or fluid state may be its most important quality. The setting time does not indicate the completion of the reaction, which may continue for much longer times. The time varies for different materials, depending on the par-ticular application, but duplication of results from one lot to another or from one trade brand of mate-rial to another is highly desirable. The influence of manipulative procedures on the setting time of vari-ous types of materials is important to the dentist and the assistant. Shelf Life Shelf life is a term applied to the general deterioration and change in quality of materials during shipment and storage. The temperature, humidity, and time of storage, as well as the bulk of material involved and the type of storage container, are significant fac-tors that vary greatly from one material to another. A material that has exceptionally good properties when first produced may be quite impractical if it deteriorates badly after a few days or weeks. These qualities are discussed in chapters dealing with gyp-sum materials and impression materials. Some stud-ies of these qualities of various materials have been made in recent years, and through accelerated aging tests, improvements in quality can sometimes be made. Anesthetics, dental adhesives, and a few other products carry dates of expiration beyond which the product should not be expected to be service-able. This practice assures the user that the material is not deteriorated because of age. Most materials that meet the requirements of the American Dental Association specifications carry a date of produc-tion as a part of the serial number or as a separate notation. SUMMARY The physical properties of oral restorations must adequately withstand the stresses of mastication. Several methods may be used to ensure proper per-formance of a restoration. With a constant force, the stress is inversely proportional to the contact area; therefore stresses may be reduced by increasing the area over which the force is distributed. In areas of high stress, materials having high elastic moduli and strength properties should be used if possible. If a weaker material has desirable properties, such as esthetic qualities, one may minimize the stress by increasing the bulk of the material when possible or ensuring proper occlusion on the restoration. Restorations and appliances should be designed so the resulting forces of mastication are distributed as uniformly as possible. In addition, sharp line angles, nonuniform areas, and notched, scratched, or pitted surfaces should be avoided to minimize stress concentrations. For example, joints between abut-ments and pontics of fixed partial dental prostheses should be properly radiused to distribute stress dur-ing function. Implant screws should not be scratched or notched when inserted. Restorative materials are generally weaker in ten-sion than in compression. Restorations should be designed to minimize areas of high tension. Material flaws can further contribute to areas prone to fail-ure. Fatigue is also an important consideration. For example, repeated flexure of an improperly loaded implant-supported restoration can concentrate stresses in the abutment screw or implant body, lead-ing to fatigue fracture. The dentist is often concerned not so much with the fracture of an appliance as with the deflection that occurs when a force is applied. This is the case with a fixed partial dental prosthesis, which may be cast as a single unit or may consist of soldered units. As discussed earlier in this chapter, the deflection of a beam, or in this case a fixed partial dental pros-thesis, supported on each end with a concentrated load in the center depends directly on the cube of the beam length and indirectly on the cube of the beam thickness. Doubling the length of the beam, there-fore, increases the deflection by eight times. This also indicates that decreasing the thickness of the beam by one-half increases the deflection by eight times. If too much bulk were required to develop the stiffness desired, changing to a material with a higher elastic modulus, or stiffness, would be beneficial. If repeated failures occur, consider increasing the occlusogingi-val dimension of the proximal connectors, balancing the occlusion over a larger surface area, and narrow-ing the occlusal table. These isolated examples of applied knowledge of biting forces and stresses in dental structures indi-cate why an understanding of this subject is neces-sary to the practicing dentist. In summary, three interrelated factors are impor-tant in the long-term function of dental restorative materials: (1) material choice, (2) component geom-etry (e.g., to minimize stress concentrations), and (3) component design (e.g., to distribute stresses as uni-formly as possible). It should be noted that failures can and do occur. In such instances, a failure analysis should be performed by answering several questions: (1) Why did it fail? (2) How did it fail? (3) Did the material or design fail? and (4) How can this failure be prevented in the future? Lastly, remember that dental material behavior depends on interrelated physical, chemical, optical, mechanical, thermal, electrical, and 66 CRAIG’S RESTORATIVE DENTAL MATERIALS biological properties, and improvement of one spe-cific property often leads to a reduction in another property. Bibliography Mechanical Properties Forces on Dental Structures Anusavice KJ. Phillips’ Science of Dental Materials. 11th ed. St. Louis: Saunders; 2003. Bujtár P, Sándor GK, Bojtos A, Szucs A, Barabás J. Finite element analysis of the human mandible at 3 different stages of life. Oral Surg Oral Med Oral Pathol Oral Radiol Endod. 2010;110(3):301. Castelo PM, Pereira LJ, Bonjardim LR, Gavião MB. Changes in bite force, masticatory muscle thickness, and facial morphology between primary and mixed dentition in preschool children with normal occlusion. Ann Anat. 2010;192(1):23. Koolstra JH, van Euden TM. 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Lee JK, Choi JY, Lim BS, et al. Change of properties dur-ing storage of a UDMA/TEGDMA dental resin. J Biomed Mater Res B Appl Biomater. 2004;68:216. O’Brien WJ. Dental Materials: Properties and Selection. Chicago: Quintessence; 1989. Dynamic Properties Graessley WW. Linear viscoelasticity. In: Polymeric Liquids and Networks: Dynamics and Rheology. New York: Taylor and Francis Group; 2008. 67 4. Fundamentals of Materials Science Impact resistance of plastics and electrical insulating material, D 256–92. ASTM Standards 1993. Vol. 8.01. Phil-adelphia: American Society for Testing and Materials; 1993. Rubinstein M, Colby RH. Networks and gelation. In: Polymer Physics. New York: Oxford University Press; 2008. Sakaguchi RL, Shah NC, Lim BS, et al. Dynamic mechani-cal analysis of storage modulus development in light-activated polymer matrix composites. Dent Mater. 2002;18:197. Properties of Composite Materials Choi KK, Condon JR, Ferracane JL. The effects of adhesive thickness on polymerization contraction stress of com-posite. J Dent Res. 2000;79:812. Condon JR, Ferracane JL. Reduction of composite contrac-tion stress through non-bonded microfiller particles. Dent Mater. 1998;14:256. Ferracane JL, Berge HX, Condon JR. In vitro aging of den-tal composites in water—effect of degree of conversion, filler volume, and filler/matrix coupling. J Biomed Mater Res. 1998;42:465. Ferracane JL, Condon JR. In vitro evaluation of the mar-ginal degradation of dental composites under simulated occlusal loading. Dent Mater. 1999;15:262. Peutzfeldt A. Resin composites in dentistry: the monomer systems. Eur J Oral Sci. 1997;105:97. Sakaguchi RL, Wiltbank BD, Murchison CF. Prediction of com-posite elastic modulus and polymerization shrinkage by computational micromechanics. Dent Mater. 2004;20:397. Urabe I, Nakajima M, Sano H, et al. Physical proper-ties of the dentin-enamel junction region. Am J Dent. 2000;13:129. Tear Strength and Tear Energy Strength of conventional vulcanized rubber and thermo-plastic elastomers, D 624–91. ASTM Standards 1994. Vol. 9.01. Philadelphia: American Society for Testing and Materials; 1994. Hardness, Friction, and Wear Abe Y, Sato Y, Akagawa Y, Ohkawa S. An in vitro study of high-strength resin posterior denture tooth wear. Int J Prosthodont. 1997;10:28. Condon JR, Ferracane JL. Factors effecting dental composite wear in vitro. J Biomed Mater Res. 1997;38:303. Condon JR, Ferracane JL. In vitro wear of composite with varied cure, filler level, and filler treatment. J Dent Res. 1997;76:1405. Ferracane JL, Mitchem JC, Condon JR, Todd R. Wear and marginal breakdown of composites with various degrees of cure. J Dent Res. 1997;76:1508. Hu X, Harrington E, Marquis PM, et al. The influence of cyclic loading on the wear of a dental composite. Biomaterials. 1999;20:907. Hu X, Marquis PM, Shortall AC. Two-body in vitro wear study of some current dental composites and amalgams. J Prosthet Dent. 1999;82:214. Koczorowski R, Wloch S. Evaluation of wear of selected prosthetic materials in contact with enamel and dentin. J Prosthet Dent. 1999;81:453. Teoh SH, Ong LF, Yap AU, et al. Bruxing-type dental wear simulator for ranking of dental restorative materials. J Biomed Mater Res. 1998;43:175. Turssi C, Purquerio B, Serra M. Wear of dental resin com-posites: insights into underlying processes and assess-ment methods. A review. J Biomed Mater Res B Appl Biomater. 2003;65B:280. Xu HH, Smith DT, Jahanmir S, et al. Indentation damage and mechanical properties of human enamel and den-tin. J Dent Res. 1998;77:472. Yap AU, Ong LF, Teoh SH, et al. Comparative wear ranking of dental restoratives with the BIOMAT wear simulator. J Oral Rehabil. 1999;26:228. Colloidal State, Surface Properties, Adhesion Iler RK. 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Hardness and Young’s modulus determined by nanoindentation technique of filler particles of dental restorative materi-als compared with human enamel. J Biomed Mater Res. 1993;27:747. Yoshida Y, van Meerbeek B, Nakayama Y, et al. Evidence of chemical bonding at biomaterial-hard tissue interfaces. J Dent Res. 2000;79:709. Yoshida Y, van Meerbeek B, Snowwaert J, et al. A novel approach to AFM characterization of adhesive tooth-biomaterials interfaces. J Biomed Mater Res. 1999;47:85. Color and Optical Properties Cho MS, Yu B, Lee YK. Opalescence of all-ceramic core and veneer materials. Dent Mater. 2009;25:695. Corciolani G, Vichi A, Louca C, Ferrari M. Influence of layering thickness on the color parameters of a ceramic system. Dent Mater. 2010;26:737. Heffernan MJ, Aquilino SA, Diaz-Arnold AM, Haselton DR, Stansford CM, Vargas MA. Relative translucency of six all ceramics. Part I: core materials. J Prosthet Dent. 2000;88:4. Heffernan MJ, Aquilino SA, Diaz-Arnold AM, Haselton DR, Stansford CM, Vargas MA. Relative translucency of six all ceramics. Part II: core and veneer materials. J Prosthet Dent. 2000;88:10. Johnston WM, Ma T, Kienle BH. Translucency parameter of colorants for maxillofacial prostheses. Int J Prosthodont. 1995;8:79. 68 CRAIG’S RESTORATIVE DENTAL MATERIALS Judd DB, Wyszecki G. Color in Business, Science, and Industry. 3rd ed. New York: John Wiley & Sons; 1975. Kiat-Amnuay S, Lemon JC, Powers JM. Effects of opaci-fiers on color stability of pigmented maxillofacial sili-cone A-2186 subjected to artificial aging. J Prosthodont. 2002;11:109. Kubelka P. New contributions to the optics of intensely light-scattering materials, Part I. Opt Soc Am J. 1948;38:448. Lee Y-K, Lim B-S, Powers JM. Color changes of dental resin composites by a salivary enzyme. J Biomed Mater Res. 2004;70B:66. Noie F, O’Keefe KL, Powers JM. Color stability of resin cements after accelerated aging. Int J Prosthodont. 1995;8:51. O’Keefe KL, Powers JM, Noie F. Effect of dissolution on color of extrinsic porcelain colorants. Int J Prosthodont. 1993;6:558. Paravina RD, Ontiveros JC, Powers JM. Curing-dependent changes in color and translucency parameter of compos-ite bleach shades. J Esthet Restor Dent. 2002;14:158. Paravina RD, Ontiveros JC, Powers JM. Accelerated aging effects on color and translucency of bleaching-shade composites. J Esthet Restor Dent. 2004;16:117. Paravina RD, Powers JM, eds. Esthetic Color Training in Dentistry. St. Louis: Mosby; 2004. Ragain JC, Johnston WM. Accuracy of Kubelka-Munk reflectance theory applied to human dentin and enamel. J Dent Res. 2001;80:449. Seghi RR, Johnston WM, O’Brien WJ. Spectrophotometric analysis of color differences between porcelain systems. J Prosthet Dent. 1986;56:35. Specifying color by the Munsell system, D1535–D68 (1974). ASTM Standards, 1975, Part 20. Philadelphia: American Society for Testing and Materials; 1975. Vichi A, Ferrari M, Davidson CL. Influence of ceramic and cement thickness on the masking of various types of opaque posts. J Prosthet Dent. 2000;83:412. Yeh CL, Miyagawa Y, Powers JM. Color of selected shades of composites by reflection spectrophotometry. J Dent Res. 1982;61(1):1176. Thermal Properties Antonucci JM, Toth EE. Extent of polymerization of dental resins by differential scanning calorimetry. J Dent Res. 1983;62:121. Craig RG, Peyton FA. Thermal conductivity of tooth structure, dental cements, and amalgam. J Dent Res. 1961;40:411. de Vree JH, Spierings TA, Plasschaert AJ. A simulation model for transient thermal analysis of restored teeth. J Dent Res. 1983;62:756. Murayama T. Dynamic Mechanical Analysis of Polymeric Materials. New York: Elsevier Science; 1978. Peyton FA. Effectiveness of water coolants with rotary cut-ting instruments. J Am Dent Assoc. 1958;56(5):664. Volland RH, Paffenbarger GC. Cast gold inlay technic as worked out in the cooperative research at the National Bureau of Standards and applied by a group of practic-ing dentists. J Am Dent Assoc. 1932;19(2):185. Wilson TW, Turner DT. Characterization of polydimeth-acrylates and their composites by dynamic mechanical analysis. J Dent Res. 1987;66:1032. Electrical and Electrochemical Properties Arvidson K, Johansson EG. Galvanic series of some dental alloys. Scand J Dent Res. 1977;85:485. Bergman M, Ginstrup O, Nilner K. Potential and polariza-tion measurements in vivo of oral galvanism. Scand J Dent Res. 1978;86:135. Fairhurst CW, Marek M, Butts MB, et al. New informa-tion on high copper amalgam corrosion. J Dent Res. 1978;57:725. Gjerdet NR, Brune D. Measurements of currents between dissimilar alloys in the oral cavity. Scand J Dent Res. 1977;85:500. Holland RI. Galvanic currents between gold and amalgam. Scand J Dent Res. 1980;88:269. Hörsted-Bindslev P, Vilkinis V, Sidlauskas A. Direct cap-ping of human pulps with a dentin bonding system or with calcium hydroxide cement. Oral Surg Oral Med Oral Pathol Oral Radiol Endod. 2003;96(5):591. Maijer R, Smith DC. Corrosion of orthodontic bracket bases. Am J Orthod. 1982;81:43. Mohsen NM, Craig RG, Filisko FE. The effects of different additives on the dielectric relaxation and the dynamic mechanical properties of urethane dimethacrylate. J Oral Rehabil. 2000;27:250. Mumford JM. Electrolytic action in the mouth and its rela-tionship to pain. J Dent Res. 1957;36:632. Mumford JM. Resistivity of human enamel and dentin. Arch Oral Biol. 1957;12:925. Phillips LJ, Schnell RJ, Phillips RW. Measurement of the elec-tric conductivity of dental cement. IV. Extracted human teeth; in vivo tests; summary. J Dent Res. 1955;34:839. Tay WM, Braden M. Dielectric properties of glass ionomer cements. J Dent Res. 1981;60:1311. Other Properties Raptis CM, Powers JM, Fan PL, et al. Staining of composite resins by cigarette smoke. J Oral Rehabil. 1982;9:367. 69 In Chapter 4, we introduced fundamental concepts in biomechanics and physical properties of dental materials. The data presented were collected with a variety of test instruments. In this chapter we describe the individual tests in more detail. COMPRESSIVE STRENGTH When an object is tested in compression, complex stresses are created in the object. In compression, forces are resolved into forces of shear in a cone-shaped area at each end and, as a result of the action of the two cones on the cylinder, into tensile forces in the central portion of the object. Because of these com-plex forces, standard sizes and dimensions are used to obtain reproducible test results. If a test specimen is too short (Fig. 5.1), the force distributions are more complicated because the cones overlap in the ends of the cylinder. If the specimen is too long, buckling may occur. Therefore for the most satisfactory results, the cylinder’s length should be twice the diameter. Compressive strength is most useful for compar-ing materials that are brittle and generally weak in tension. Compressive strength is therefore used in the comparison of dental amalgam, resin compos-ites, and cements, and other materials such as dental stone and investments. Typical values of compres-sive strength of some restorative dental materials are given in Table 5.1. FLEXURE The bending, or flexural, properties of many mate-rials are often more important than their tensile or compressive properties because of the way they are used. For example, the flexural properties of stainless steel wires, endodontic files and reamers, and hypo-dermic needles are important because of the bend-ing that happens in function. American National Standards Institute/American Dental Association (ANSI/ADA) specification No. 28 for endodontic files and reamers requires flexure tests. Flexural properties are measured by bending a beam-shaped specimen. In a single cantilever beam test, the beam is fixed at one end and a force is applied at a prescribed distance from the fixed end. In a dual cantilever beam test, both ends of the beam are fixed and a load is placed on the center of the beam. In a three-point or four-point flexural test, the beam is supported on two rollers and a load is applied to the top of the beam at one location (three-point) or two locations (four-point). Specimens are subjected to conditions that resemble pure bend-ing, and beam theory is used to analyze the data. As the force is increased and the specimen is bent, corresponding values for the angle of bending and the bending moment (force × distance) are recorded. Graphic plots of the bending moment versus the angle of bending are similar in appearance to stress-strain curves. As an example, a series of plots for various sizes of endodontic reamers is shown in Fig. 5.2. An instrument will be permanently bent if the bending angle exceeds the value at the end of the lin-ear portion of the curve. Instruments that are larger in diameter are stiffer, as shown by the initial steeper slope. The initial linear portion of the curve is shorter for larger instruments and thus the deviation from linearity occurs at lower angular bends. FLEXURAL STRENGTH Flexural strength is measured by applying a load in the middle of a beam that is simply supported (not fixed) at each end (Figs. 5.3 and 5.4). This test is called a three-point bending or flexure test and the maximum stress measured in the test is called flexural strength. The flexural strengths for several dental materials are shown in Table 5.2. This test determines not only the strength of the material C H A P T E R 5 Testing of Dental Materials and Biomechanics 70 CRAIG’S RESTORATIVE DENTAL MATERIALS but also the amount of deflection expected. Flexural strength and the accompanying deflection are important in long spans such as in a fixed dental prosthesis or removable partial dental prosthesis where occlusal stresses may be severe. Maximum stress in a rectangular beam loaded in the center of the span is: Stress = 3 × Load × Length/ ( 2 × Width × Thickness2) or σ = 3Pl/2bd2 The deformation or displacement in this loaded beam is: Deformation = Load × Length3/4 × Elastic modulus × Width × Thickness3 Or δ = Pl/4Ebd3 Four-point bending is often preferred to three-point bending when measuring flexural modulus and flexural strength. If an easily deformed material is tested with inadequately rounded loading and sup-port elements, localized deformation can occur at the loading and supporting points. This is undesirable because the beam theory used to calculate deflec-tion assumes uniform beam deformation without localized stresses and constraints. A four-point bend fixture uses two loading elements instead of the one used in a three-point bend fixture. The two loading elements apply a more uniform load to the beam that prevents V-shaped buckling of the beam, and stress concentrations in the midline when a single loading element is used. In this configuration, a larger, more representative area of the specimen is tested. SS ST SC FIG. 5.1 Complex stress pattern developed in cylinder subjected to compressive stress. SC, Compressive stress; SS, shear stress; ST, tensile stress. TABLE 5.1 Compressive Strength of Selected Dental Materials Material Compressive Strength (MPa) Enamel 384 Dentin 297 Amalgam 189 Calcium hydroxide liner 8 Feldspathic porcelain 149 High-strength stone 81 Resin composite 225 Zinc phosphate cement 110 60 40 20 0 5 10 15 20 25 30 20 30 40 50 60 70 35 40 45 Angular deflection (degrees) Bending moment (N-mm) FIG. 5.2 Bending moment-angular deflection curves for endodontic reamers of sizes 20 through 70. Neutral axis Compression Tension FIG. 5.3 Schematic of a three-point bending test. The three points are the two supports at the bottom and the cen-tral loading point on the top. 71 5. Testing of Dental Materials and Biomechanics PERMANENT BENDING Many dental restorations are subjected to permanent bending during fabrication. The adjustment of the clasps of a removable partial dental prosthesis and the shaping of orthodontic wires are two examples of permanent bending. Comparisons of wires and needles of different compositions and diameters sub-jected to repeated 90-degree bends are often made. The number of bends a specimen will withstand is influenced by its composition and dimensions, as well as its chemical and temperature treatment in fabrication. Cyclic tests are important because a material’s performance is not always easily related to standard mechanical test data such as tensile prop-erties or hardness. Severe tensile and compressive stresses can be induced into a material that is sub-jected to permanent bending. It is partly for this reason that tensile and compressive test data for a material are so important. DIAMETRAL TENSILE STRENGTH An alternative method of testing brittle materials, described in the literature as the diametral compres-sion test for tension or the Brazilian method, is popular because of its relative simplicity and reproducibility. In this test, a cylindrical disk is compressed in a test-ing machine transversely or diametrally until frac-ture occurs, as shown in Fig. 5.5. The compressive stress applied to the specimen introduces a tensile stress in the material in the plane of the force applica-tion of the test machine because of the Poisson effect. The tensile stress (σx) is directly proportional to the load (P) applied in compression through the follow-ing formula σx = 2P/πDT Note that this test is designed for brittle materials. If the specimen deforms significantly before failure or fractures into more than two equal pieces, the data may not be valid. Some materials exhibit different diametral tensile strengths when tested at different rates of load-ing and are described as being strain-rate sensitive. The diametral tensile test is not valid for these materi-als. Values of diametral and ultimate tensile strengths for some dental materials are listed in Table 5.3. SHEAR STRENGTH Shear strength is the maximum stress that a material can withstand before failure in a shear mode of load-ing. It is particularly important in the study of inter-faces between two materials, such as ceramic-metal or implant-bone. One method of testing the shear strength of dental materials is the punch or push-out method, where an axial load is applied to push one material through another. The shear strength (τ) is calculated by the following formula: Shear strength (τ) = F/πdh where F is the compressive force applied to the specimen, d is the diameter of the punch, and h is the thickness of the specimen. Note that the stress distribution caused by this method is not pure shear. Results often vary because of differences in specimen dimensions, surface geometry, composition and prep-aration, and mechanical testing parameters. Despite these variations, it is a simple test to perform and has been used extensively. Alternatively, shear properties 666 N NA Tension Compression A 666 N 0 1 3 3 2 2 4 4 4 4 4 4 3 3 3 2 2 2 1 1 0 5 5 5 5 6 6 6 15 12 12 5 11 7 6 B FIG. 5.4 Photoelastic analysis of flexural strength test. (A) Photoelastic model with isochromatic fringes. (B) Drawing to illustrate isochromatic fringe order. NA, Neutral axis. TABLE 5.2 Flexural Strength of Selected Dental Materials Material Flexural Strength (MPa) Resin composite 139 Lathe-cut amalgam 124 Feldspathic porcelain 65 High-strength stone 17 Resin-modified glass ionomer 42–68 Resin cement 66–121 72 CRAIG’S RESTORATIVE DENTAL MATERIALS may be determined by subjecting a specimen to tor-sional loading. Shear strengths of some dental materi-als are listed in Table 5.4. The specifics of shear testing for adhesive interfaces are discussed in detail in the bond strength methods section of this chapter. TORSION Another mode of loading that is relevant in den-tistry is torsion or twisting. For example, endodon-tic files and reamers are rotated in the root canal during endodontic treatment, and so their proper-ties in torsion are of particular interest. In this situ-ation, the endodontic file is effectively clamped at the tip where the file engages dentin. As the handle is rotated, the file is subjected to torsion. ANSI/ ADA specification No. 28 for endodontic files and reamers describes a test to measure resistance to fracture by twisting with a torque meter. Torsion results in a shear stress and a rotation of the speci-men. In these types of applications, we are inter-ested in the relation between torsional moment (Mt = shear force × distance) and angular rotation, π. Fig. 5.6 shows a series of graphs in which the tor-sional moment was measured as a function of angu-lar rotation. In this example, the instruments were twisted clockwise, which results in an unwinding of the instrument. As was the case with bending, the curves are similar to stress-strain curves, with an initial linear section followed by a nonlinear sec-tion. Instruments should be used clinically so they are not subjected to permanent angular rotation. Rotation should be limited to stay within the linear portion of the torsional moment-angular rotation curve. Larger instruments are stiffer in torsion than smaller ones, and the linear section of the curve is less. The irregular shape of the curves at high angular rotation results from the unwinding of the instrument. Torsion is also an important consider-ation for threaded fasteners. A torque gauge should be used when tightening screws to prevent possible torsional failure in the shank of the screw that can result from overloading the screw. TABLE 5.3 Tensile Strength of Selected Dental Materials Material Diametral Tensile Strength (MPa) Ultimate Tensile Strength (MPa) Enamel — 10 Dentin — 106 Amalgam 54 32 Calcium hydroxide liner 1 2.3 Feldspathic porcelain — 25 High-strength stone 8 6 TABLE 5.4 Values of Shear Strength Tested by the Punch Method for Some Restorative Dental Materials Material Shear Strength (MPa) Enamel 90 Dentin 138 Acrylic denture resin 122 Amalgam 188 Porcelain 111 Zinc phosphate cement 13 0 0 20 40 30 60 90 120 150 180 Torsional moment (N-mm) Angular rotation (degrees) 30 40 45 50 55 60 15 FIG. 5.6 Torsional moment-angular rotation curves for endodontic files of sizes 15 through 60. Thickness Diameter D Load P Compression support T Tensile stress x FIG. 5.5 How a compressive force develops tensile stress in brittle materials. 73 5. Testing of Dental Materials and Biomechanics FATIGUE STRENGTH Based on the earlier discussion of elasticity, an object subjected to a stress less than its yield stress and then relieved of this stress should return to its original form without permanent change in its inter-nal structure or properties. A few cycles of loading and unloading do not appreciably affect a material. When this stress is repeated many times, the strength of the material may be drastically reduced and the object may fail. The progressive fracture that occurs with repeated loading is called fatigue. Fatigue tests are performed by cyclically loading and unloading a specimen below the yield strength until failure. Fatigue tests can be done in tensile, compressive, shear, bending, and torsional modes of testing. Fatigue strength is the stress at which a material fails under repeated loading. Failure under repeated or cyclic loading is dependent on the magnitude of the load and the number of loading cycles. Fatigue data are often represented by an S-N curve (Fig. 5.7), which shows the stress (or strain) (S) where a mate-rial will fail as a function of the number of loading cycles (N). When the stress is sufficiently high, the specimen will fracture at a relatively low number of cycles. As the stress is reduced, the number of cycles required for failure increases. Therefore the num-ber of cycles must also be specified when defining fatigue strength. For some materials, a stress that can be cycled an infinite number of times without failure can be defined. This is called the endurance limit. Dental restorations are subjected to cyclic forces during mastication that can result in 300,000 cycles per year. It is important in the design of a den-tal restoration or prosthesis to know the fatigue strength of the restorative material at a high num-ber of cycles. Restorations should be designed with appropriate geometry and dimensions to prevent fatigue failure. Fatigue fractures develop from microscopic cracks that coalesce during load cycling. This can ultimately create a macroscopic crack that results in catastrophic failure. Areas of stress concentration, such as surface defects and sharp tipped notches, are particularly prone to catastrophic failure. Fatigue properties are mostly dependent on the microstructure of the mate-rial and the history of fabrication and treatment. They do not always correlate well with other mechanical properties. The environment around the object also plays a role. Elevated temperatures, humidity, flu-ids, biological substances, and higher or lower pH can all affect fatigue properties. Fatigue data that are typically based on tests in a laboratory at room tem-perature are not always relevant to the conditions in the oral cavity. The higher temperature, humidity, saline environment with proteins, and fluctuating pH reduce fatigue strength of dental materials from levels measured in a laboratory. FRACTURE TOUGHNESS A fracture toughness test is usually performed using flexure bars that include a notch with a nanometer-sized crack. With this test, materials can be charac-terized by the energy release rate, G, and the stress intensity factor, K. The energy release rate is a func-tion of the energy used in crack propagation. The stress intensity factor describes the stresses at the tip of a crack. The stress intensity factor changes with crack length and stress by: K = Yσa1/2 where Y is a function that is dependent on crack size and geometry. A material fractures when the stress intensity reaches a critical value, Kc. The value of stress intensity at fracture is called fracture toughness. Fracture toughness is a relative value of a material’s ability to resist crack propagation. The units of Kc are units of stress (force/length2) × units of length1 ⁄ 2, or force × length−3 ⁄ 2, and are typically reported as MN·m−3 ⁄ 2 or MPa·m1 ⁄ 2. FRACTOGRAPHIC ANALYSIS Fractographic analysis helps define the cause of fail-ures and aids in structural design and improvement of existing materials. Advances in the field have helped identify the role of residual stresses, tempera-ture, and preexisting flaws on the longevity of dental restorations. Fractography is effective in analyzing brittle materials because they typically fail catastrophically. In fractographic analysis, typical features of crack propagation (Fig. 5.8) are assessed that identify the origin of the fracture. The origin of fracture is the point at which the worst combination of flaw sever-ity (determined by flaw size and shape) and stress magnitudes is present. Variation in ceramic process-ing, for example, may lead to significantly different structures, as shown in Fig. 5.9. A homogenous struc-ture is produced by proper processing. Flaws grow 10 1 100 750 1500 Cycles 106 Stress (MPa) FIG. 5.7 Flexural fatigue curve for a cobalt-chromium-nickel alloy used for partial dentures. 74 CRAIG’S RESTORATIVE DENTAL MATERIALS during cumulative processing errors. Flaws larger than the ones observed in Fig. 5.9B are considered critical. In Fig. 5.9D a very sharp flaw concentrates stresses that can lead to failure. Improper prosthesis design can also lead to failure even without a preexisting flaw. In this case fracto-graphic analysis can identify the origin, but fracture patterns are much more complex. In Fig. 5.10 a small A Hackle lines Mirror Origin ac 200 m B FIG. 5.8 Typical features of a brittle fracture surface. (A) Drawing of a fracture surface. (B) The photograph shows a fracture surface in a quartz rod that failed catastrophically. It is possible to identify a mirrorlike region, with hackle lines pointing to the origin of fracture. (B From Quinn GD. Fractography of Ceramics and Glasses (NIST Special Publication 960-16), Washington, DC: NIST/US Department of Commerce; 2007.) A B 5 µm 15 µm 5 x 6 µm C D FIG. 5.9 Scanning electron micrographs of ceramic materials. (A) A well-processed material, with little to no flaws pres-ent. The sequence from (B) to (D) shows materials with increasingly bigger/sharper flaws, resulting from poor processing. (Courtesy S.S. Scherrer, University of Geneva.) 75 5. Testing of Dental Materials and Biomechanics crack caused a catastrophic failure at a margin where the porcelain structure was too thin. TEAR STRENGTH AND TEAR ENERGY Tear strength is the resistance of a material to tearing forces. Tear strength is an important consideration where flexible materials are thin, such as impression materials in interproximal areas and edges of maxil-lofacial prostheses. Specimens for tear strength test-ing are usually crescent shaped and notched. Tear strength of the notched specimen is calculated by dividing the maximum load by the thickness of the specimen. The unit of tear strength is N/m. Tear strength depends on the rate of loading because of the viscoelastic characteristics of the flex-ible materials tested. High loading rates result in higher values of tear strength and lower permanent deformation. Alginate impression material has low tear strength at slow loading rates, but if removed (loaded) quickly, the tear strength can be increased. This reduces the possibility of tearing the impression and also reduces the amount of permanent deforma-tion (distortion). Typical values of tear strength are listed in Table 5.5 for some dental materials. Tear energy (T) is the energy per unit area of a newly torn surface. It is calculated from the load (F) required to propagate a tear in a trouser-shaped specimen: T = (F/t)(λ + 1) where t is the specimen thickness and λ is an extension ratio. Tear energy values for dental impres-sion materials and maxillofacial materials are listed in Table 5.6. HARDNESS Hardness is measured by indenting a test specimen with a standard force or weight. The symmetrically shaped indentation is measured under a microscope for depth, area, or width of the indentation. The indentation dimensions are then related to tabulated A 5 core 3 4 2 1 B 3 4 2 5 1 FIG. 5.10 Determination of origin of fracture in a ceramic restoration. Sketched illustration of the stereo findings (A) as well as a summary image of scanning electron microscopic mapping the general direction of crack propagation of the recovered broken Procera AllCeram crown part (B). (From Scherrer SS, Quinn GD, Quinn JB. Fractographic failure analysis of a Procera AllCeram crown using stereo and scanning electron microscopy. Dent Mater. 2008;24(8):1107–1113.) TABLE 5.5 Tear Strength of Selected Dental Materials Material Tear Strength (kN/m) Denture liners 2.6–45 Impression materials Alginate 0.47 Polyvinylacetate-polyethylene mouth protectors 114 TABLE 5.6 Tear Energya (T) of Some Dental Materials Material Tear Energy (J/m2 [Mergs/cm2]) IMPRESSION MATERIALS Addition silicone 390–1150 [0.39–1.15] Alginate 66 [0.066] MAXILLOFACIAL MATERIALS Polyurethane 1800 [1.8] Polyvinylchloride 11,000 Silicone 660 [0.66] aCrosshead speed, 2 cm/min. 76 CRAIG’S RESTORATIVE DENTAL MATERIALS hardness values. Dimensions of the indentation vary inversely with the resistance to penetration. Smaller loads are used for softer materials. Brinell Hardness Test The Brinell hardness test is used to test metals and alloys used in dentistry. The method uses a small spherical steel or tungsten carbide indenter, typically 1.6 mm in diameter, and a 123 N load. The load is applied for 30 seconds and then removed, after which the indentation diameter is carefully measured. Fig. 5.11 shows the principle of Brinell hardness testing with a microscopic view of the indentations into a gold alloy. The Brinell hardness test produces a rela-tively large indentation area, making the test good for determining average hardness values in a speci-men and poor for determining very localized values. Knoop Hardness Test The Knoop hardness test is a microindentation test for materials that vary in hardness over an area of interest. The method is suitable for thin plastic or metal sheets or brittle materials where the applied load does not exceed 3.6 kgf (35 N). Materials with a large range of hardness can be tested simply by varying the test load. The resulting indentation area varies by the applied load and characteristics of the material. Light loads with the Knoop hardness test produce extremely delicate microindentations, mak-ing this method useful for testing materials that vary in hardness in a small region. The Knoop method requires a highly polished and flat test specimen. The time to complete the test is considerably greater than that of other less precisely controlled methods. The Knoop hardness number values of some dental materials are listed in Table 5.7. Vickers Hardness Test The Vickers hardness test uses a diamond indenter that produces a square indentation (Fig. 5.12). While similar in principle to the Knoop and Brinell tests, the Vickers test uses a 136-degree pyramid-shaped indenter. Rockwell Hardness Test The Rockwell hardness test is a rapid method for hardness measurement. A ball or cone produces the indentation and a sensitive dial micrometer mea-sures the depth of penetration. Hardness is deter-mined by the depth of penetration under a large load compared to the penetration from a small preload. Various diameters of balls or cones are used with a range loads [60 to 150 kgf (588 to 1470 N)]. Each combination is defined as a specific Rockwell scale, Rockwell A to G, denoted RA, RB, and so on. Plastics used in dentistry have been tested using a revised Rockwell test called the superficial Rockwell method. This method uses a relatively light (30 kgf [294 N]) load and a larger diameter (12.7 mm) ball than standard Rockwell methods. A small preload of 3 kgf (29.4 N) is first applied. Then a major load of 30 kgf (294 N) is applied for 10 minutes after which W A W B C FIG. 5.11 Brinell hardness test. (A) Indentation in soft material. (B) Indentation in harder material. (C) Microscopic view of indentations. 77 5. Testing of Dental Materials and Biomechanics a reading is taken. Recovery from the indentation occurs after the major load is removed. The percent recovery is calculated by: Percent recovery = [(A −B)/A] × 100 where A is the depth of the indentation from the major load applied for 10 minutes, and B is the depth of the indentation 10 minutes after the major load is removed. Values of indentation depth and percent recovery for some dental plastics are listed in Table 5.8. Barcol Hardness Test The Barcol hardness test uses a 1-mm diameter spring-loaded needle (Barcol impressor) that is pressed against the surface to be tested. The reading on the instrument dial decreases as the impressor penetrates the surface. Depth of cure of a resin com-posite is tested by preparing specimens varying in thickness from 0.5 to 6.0 mm or more in increments of 0.5 mm. After the top surface of the specimen is irra-diated by a dental curing light, the Barcol hardness of the top surface is compared to that of the bottom. Depth of cure is defined as the maximum thickness at which the Barcol reading of the bottom surface dif-fers from the top by less than 10%. A 10% decrease in Barcol hardness of a resin composite results in a 20% decrease in the flexural strength. Shore A Hardness Test Hardness methods that use an indenter are not suit-able for elastomers because the indentation disap-pears after the load is removed. A Shore A durometer is used in the rubber industry to determine the relative hardness of elastomers where hardness is measured in terms of material elasticity. The instrument consists of a 0.8-mm diameter blunt-pointed indenter that tapers to a 1.6-mm cylinder. The indenter is attached by a lever to a scale. If the indenter completely penetrates the specimen, a reading of 0 is obtained. If no penetra-tion occurs, a reading of 100 units results. An accurate reading is difficult on viscoelastic elastomers because the indenter continues to penetrate the elastomer as a function of time. In this case the indenter is pressed firmly and quickly with the maximum reading recorded as the Shore A hardness. The test has been used to evaluate soft denture liners, mouth protectors, and maxillofacial elastomers (Table 5.9). NANOINDENTATION Traditional indentation tests use loads as high as several kilograms that result in indentations as large as 100 μm. Although these tests are valu-able for screening materials and determining rela-tive values among different materials, they are not TABLE 5.7 Knoop Hardness Number (KHN) of Selected Dental Materials Material KHN (kg/mm2) Enamel 343 Dentin 68 Cementum 40 Cobalt-chromium partial denture alloy 391 Denture acrylic 21 Feldspathic porcelain 460 Silicon carbide abrasive 2480 Zinc phosphate cement 38 W A W B FIG. 5.12 (A) Principle of the Knoop hardness measure-ment. (B) The diamond pyramid (Vickers) indentation test. TABLE 5.8 Indentation Depth and Percent Recovery of Some Dental Polymers Material Indentation Depth (μm) % Recovery Acrylic denture teeth 93 88 Pit and fissure sealants 85–158 74–86 Resin composite 56–72 70–83 TABLE 5.9 Values of Shore A Hardness for Selected Dental Polymers Material Shore A Hardness Resilient denture liners 48–85 Polyvinylacetate-polyethylene mouth protector 67 Silicone maxillofacial elastomer 25 78 CRAIG’S RESTORATIVE DENTAL MATERIALS suitable for materials with constituents or phases that are smaller than the indenter. Microfilled resin composites are an example where the filler phase is substantially smaller than the dimensions of the indenter. To accurately measure the properties of these microphases, smaller indentations and pre-cise spatial control of the indentations are required. Techniques commonly referred to as nanoindenta-tion apply loads in the range of 0.1 to 5000 mg-f (milligram-force) that result in 1 μm indentations. Indentation depth is continuously monitored, elimi-nating the need to image the indentation to calculate mechanical properties. Although nanoindentation is most commonly used to measure hardness of micrometer-sized phases, the technique is also use-ful for measuring elastic modulus. For brittle mate-rials, yield strength and fracture toughness can also be determined. The nanohardness, dynamic hardness, and elastic moduli of human enamel and dentin are listed in Table 5.10, along with the nanohardness and elastic modulus for the region of the dentin-enamel junction. The nanohardness of dentin of 71 kg/mm2 (696 MPa) agrees well with the Knoop value of 68 kg/mm2 (666 MPa) reported in Table 5.7; however, the nanohardness of 457 kg/mm2 (4.48 GPa) for enamel is considerably higher than the Knoop value of 343 kg/mm2 (3.36 GPa). This difference may result from the small nanoindenta-tion dimension relative to the size of enamel rods. Dynamic hardness values are calculated from maximum displacement and result in lower val-ues than for corresponding nanohardness methods because nanohardness values are calculated from permanent deformation. The elastic moduli of 87.7 and 24.0 GPa for enamel and dentin by nanoinden-tation are similar to values from compressive test specimens of 84.1 and 18.3 GPa. Of special inter-est is the elastic modulus for the dentin-enamel junction, which at 53.2 GPa is intermediate to the values for enamel and dentin. The nanoindenta-tion test is especially useful in studying this small region, which is not possible with older, traditional compressive or tensile tests. Nanoindenters can also measure storage and loss modulus in viscoelastic materials by measur-ing the resistance to the indentation force dur-ing force removal. This feature, called dynamic mechanical analysis, is described more fully later in this chapter. WEAR Wear has been studied by (1) clinical testing, (2) clini-cal simulations, (3) model systems using wear test-ing devices, (4) measurements of related mechanical properties such as hardness, and (5) examination of surface failure from a single or low number of slid-ing strokes. Wear resistance of restorative materials has been evaluated by abrasion tests. Two-body abra-sion tests include the restorative material and an enamel or simulated enamel antagonist. Three-body abrasion adds an additional substance such as toothpaste or prophylaxis paste that intervenes between the restorative material and enamel. As shown in Table 5.11, the resistance of composite res-ins to abrasion depends on the nature of the filler particles (glass or quartz) and on silanation of the filler. Enamel is about 5 to 20 times more abrasion resistant than dentin. Of the natural dental hard tissues, cementum is the least resistant to abrasion. Measurements of enamel loss during a 30-second prophylaxis have shown enamel loss of 0.6 to 4 μm with fluoride removed from the enamel surface, depending on the abrasive. Unfortunately, a 1:1 ratio between wear observed clinically and that measured in the laboratory sel-dom exists. Thus most tests strive to rank materials in an order that is seen clinically. Traditional wear tests measure the volume of material lost but do not explain mechanisms of wear. A single-pass sliding technique may characterize modes of surface fail-ure. In general, wear data do not correlate well with other mechanical property data, making it difficult to infer wear properties from other simpler labora-tory tests. TABLE 5.10 Properties of Tooth Tissues from Nanoindentation Tests Tissue Nanohardness Dynamic Hardness Elastic Modulus GPa kg/mm2 GPa kg/mm2 GPa Enamel 4.48 (0.44)a 457 (45) 2.90 (0.23) 295 (23) 87.7 (5.9) Dentin-enamel junction 2.37 242 53.2 Dentin 0.70 (0.12) 71 (12) 0.55 (0.09) 56 (9) 24.0 (3.9) aNumbers in parentheses represent standard deviations. Modified from Urabe I, Nakajima M, Sano H, Tagami J. Physical properties of the dentin-enamel junction region. Am J Dent. 2000;13:129–135. 79 5. Testing of Dental Materials and Biomechanics SETTING TIME Final setting time is the time required for a reaction to be completed. If the reaction rate is too rapid or if the material has a short setting time, the mixed mass may harden before it can be properly manipulated. By contrast, if the reaction rate is too slow, an excessively long time is required to complete the procedure. An appropriate setting time is one of the most important characteristics of materials such as gypsum. Working time is the time after which the material cannot be manipulated without causing distortion in the final product. An example from gypsum is time after which the semifluid mass can no longer flow easily into the fine details of an impression. An example from impression materials is the time after which the paste does not flow to record the details of the hard and soft tissues. Final setting time is the time at which a material such as alginate can be withdrawn without distor-tion or tearing. For gypsum, it is the time when it can be separated from the impression without fracture. The initial setting time is the time at which a particular stage of firmness is reached in the setting process. Measurement The initial setting time is usually measured by a penetration test, although other test methods can be used. For example, the loss of gloss from the surface of dental stone is an indication of the initial set of the mass. Similarly, the setting time of gypsum may be measured by the temperature rise because the chemi-cal reaction is exothermic. The Vicat apparatus shown in Fig. 5.13 is com-monly used to measure the initial setting time of gypsum products. It consists of a 300-g rod with a 1-mm diameter needle. Gypsum is poured into a shallow cylinder then, after a period of time, the rod is lowered until it contacts the surface of the material. The needle is released and allowed to penetrate the mix. When the needle fails to penetrate to the bottom of the container, the material has reached the Vicat or the initial setting time. Other types of instruments, such as Gillmore needles, can be used to obtain the initial and final setting times of gypsum materials. DYNAMIC MECHANICAL ANALYSIS Through dynamic mechanical analysis, some very useful properties of materials can be measured, such as the dynamic elastic modulus (E’) and the glass tran-sition temperature (Tg) in polymers. Testing standard ASTM D-4092 (American Society for Testing and Materials [ASTM] International) describes the calcu-lation of these values. The test can be carried out in several modes: tensile, flexure in single or dual can-tilever, three-point bending, compression, or shear. The test is suitable for liquids or solids (in the form of bars or powder), increasing the scope of applica-tion to many different materials. A sinusoidal strain is applied to the material at a given frequency, while the temperature is ramped up or down over time through a range, typically between −50°C and 220°C for most polymers, between 25°C and 600°C for most glasses and ceramics, and between 50°C and TABLE 5.11 Two-Body Abrasion of Restorative Dental Materials Material Two-Body Abrasion (10–4 mm3/mm of travel) AMALGAM Spherical 7.0 AgSn/AgCu 5.6 COMPOSITE RESIN Glass filled 7.7 Glass filled: no silane 13.8 Quartz filled 3.8 Quartz filled: no silane 5.6 Microfilled 12.0 Diacrylate resin 17.0 Pit and fissure sealant 21.5 Unfilled acrylic resin 13.3 FIG. 5.13 Vicat penetrometer used to determine initial setting time of gypsum products. 80 CRAIG’S RESTORATIVE DENTAL MATERIALS 600°C for metals. As the test progresses, the resulting force is registered by a transducer and a stress-strain plot is generated. The complex modulus (E) is cal-culated from the slope of this curve. Storage (E′) and loss (E″) moduli are resolved from E, as explained in Chapter 4. The ratio between E′ and E″ provides the loss factor, tan δ. In an increasing temperature ramp, the typical evolution of properties is as follows: as molecular motion is favored by the increase in tem-perature, loss or viscous modulus increases and storage or elastic modulus decreases. The tempera-ture at which the maximum in the tan delta peak is observed is the Tg. This defines the point at which the material transitions from an elastic to a rubbery state. Through analysis of the breadth of the tan delta peak, it is also possible to gain insight into the degree of homogeneity of the material’s structure. Broader tan delta peaks indicate more heterogeneous materi-als, and the presence of two tan delta peaks is strong evidence for the presence of two phases within the structure. Even though virtually all materials used in dentistry have Tg values well above room or body temperatures, a good correlation between other mechanical properties and Tg makes it a useful pre-dictor of the strength and structure of materials. RHEOLOGY Rheology is the study of deformation and flow of materials. Similar to dynamic mechanical analysis, this test involves the application of an oscillatory shear deformation (strain) to the material, placed between circular plates (parallel or in a cone-plate configuration), at a determined frequency, usually under isothermal conditions. In this case, the com-plex shear modulus (G) is calculated and resolved into storage (G′) and loss (G″) shear moduli. As discussed in Chapter 4, viscosity is the relation-ship between shear modulus and shear rate (or fre-quency). Viscometers are a very simple version of a rheometer. Working and setting times in cements and direct filling composites are determined through rheology, which monitors increasing viscosity as the material sets. Rheology has been used recently to determine gel point in polymers. Gel point defines the point in conversion at which the material transitions from a viscous liquid into a viscoelastic solid. This point is correlated to the crossover between G′ and G″ devel-opment curves during polymerization. At the cross-over, elastic properties start to predominate over the viscous response. That is a reflection of polymeric network development. This is especially important during the polymerization of dental composites that are restrained by adhesion to the cavity walls. For conventional dimethacrylates found in most com-mercial formulations, vitrification follows shortly after gelation as shown in a reaction kinetics plot. At this point, stresses at the bonded interface become more significant, and therefore materials with delayed gelation are desirable. This technique is very useful for the design of new materials. DIFFERENTIAL SCANNING CALORIMETRY Differential scanning calorimetry is another tool for measuring a series of temperature transitions in materials, such as the Tg and melting tempera-ture (Tm). A calorimeter measures the difference in heat flow between the sample and a blank refer-ence, either during a temperature sweep or during a nonisothermal phenomenon, such as polymer-ization (Tg) or the melting of metals (Tm). During a temperature sweep experiment, endotherm peaks are observed as the material goes through its glass transition and melting. The endotherm is from the sudden increase in the number of molecular degrees of freedom at those transitions, which require energy gain from the environment. For dynamic exothermic reactions, as is the case for active polymerizations, the heat released by the material during isothermal experiments is correlated to the amount of reacted vinyl double bonds and the degree of conversion in real time. This method measures an indirect charac-teristic of the reaction (enthalpy) and is therefore not accurate in evaluating chemical structure. SPECTROMETRIC TECHNIQUES Fourier-transformed infrared (IR) spectroscopy is a very useful tool for characterizing molecules and for monitoring chemical reactions. Each chemical bond between atoms of a material has one specific vibrational characteristic. This produces interference in electromagnetic waves at highly specific wave-lengths. As light is transmitted through a sample, an IR bench detector identifies chemical bonds. The Fourier transform algorithm produces a spectrum with characteristic bands over a wavelength range, revealing a very accurate picture of molecular struc-ture. Using this method, newly synthesized materials can be characterized and reactions can be followed through the appearance or disappearance of deter-mined bands. This is of particular interest for polym-erization reactions, such as those of vinyl monomers, in which the C–H stretch vibration of the carbon dou-ble bond can be monitored. Fig. 5.14A and B shows the mid- and near-IR spectra of bisphenol A-glycidyl methacrylate (Bis-GMA), a very commonly used 81 5. Testing of Dental Materials and Biomechanics monomer in dental restorative materials. This bond has peaks both in the mid-IR (400 to 4000 cm−1) and in the near-IR regions (4000 to 7000 cm−1). Other peaks of interest include the C-H stretch vibration of aromatic rings. Sampling in the mid-IR region is somewhat complicated because absorptions are usu-ally very high, requiring the use of thin samples. Another concern is the strong absorption of water and carbon dioxide in this region, which requires the system to be purged with an inert gas to allow accu-rate measurements. For dental composites, another drawback is a very broad band from glass particles that shadows many bands of interest in mid-IR. This requires the use of salt plates as substrates. In the near-IR region, absorptions are relatively weaker, so relatively thick samples can be used. Glass and carbon dioxide show no absorption in the near-IR region, eliminating the need for purging and allow-ing the use of samples sandwiched between glass slides for more convenient specimen preparation. That also allows the use of fiber optics for remote monitoring of double-bond conversion. Spectroscopic techniques can be combined with other test instruments to monitor conversion or molecular characterization simultaneously with the development of other properties. For example, near-IR spectroscopy can be combined with rheometry to determine the exact polymer conversion at the onset of gelation. The same is true for volumetric shrink-age and shrinkage stress measurements, described in the section on Methods for Measuring Shrinkage and Stress During the Cure of Resin Composites. PYCNOMETRY Pycnometry is used to determine material densi-ties. Water pycnometry relies on the buoyancy of a material in water, the Archimedes principle. This method underestimates density because small pores entrapped in the material cannot be accessed by the water molecules, and dissolved oxygen is not purged from the sample. Gas pycnometry, on the other hand, uses the difference between a known volume of helium gas molecules and the volume occupied by the specimen (V). Knowing the material’s mass (m), density (d) is calculated by: d = m/V Because helium molecules are much smaller than water, they can occupy voids in the material and also displace some of the dissolved oxygen and moisture. This provides an accurate measurement of density. Volumetric shrinkage in polymerizations can be cal-culated with gas pycnometry by equating the densi-ties of the material in the monomeric and polymeric states. BOND STRENGTH TEST METHODS Bond strength tests are relatively easy to perform and can be done without expensive equipment. They are some important considerations, however, when using bond strength data to select materials in clini-cal practice. Stresses at the interface are not uniformly distrib-uted: Bond strength is reported as the nominal stress value (in MPa), which is the failure load (in new-tons) divided by the total bonded area (in mm2). Averaging stress over the total bonded area does not accurately represent the typically heteroge-neous stress distribution at the interface. A void at the interface (critical size flaw) causes stress concen-tration and crack propagation that leads to localized debonding. The actual stress magnitude that initi-ates crack propagation can be several times higher than the nominal (or average) value. Therefore nominal bond strength does not represent failure stress (Fig. 5.15). 4000 3000 2000 1000 Wavenumbers (cm1) 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 A B 0.2 Absorption (A.U.) 7000 6000 5000 4000 Wavenumbers (cm1) 2.2 1.8 2.0 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 Absorption (A.U.) FIG. 5.14 Infrared spectra of bisphenol A-glycidyl methacrylate (Bis-GMA) in the (A) mid-infrared (IR) and in the (B) near-IR regions. 82 CRAIG’S RESTORATIVE DENTAL MATERIALS High incidence of mixed and cohesive failures: Loads on a tooth create concentrations of tensile stress that can cause a crack to propagate into dentin or enamel. This prevents an accurate assessment of interfacial strength. Results of different studies are not comparable: Bond strength values for a specific material can vary con-siderably because of differences in the bonding sub-strate, specimen preparation, storage conditions, and loading method. There is very little standardization across research laboratories, so comparisons of data from different labs should be done very carefully. Bond strength tests lack clinical significance: Based on these limitations of bone strength tests, it is not possible to define a threshold bond strength value that is associated with good clinical performance. Nevertheless, we can see trends in the laboratory literature for some adhesive systems. Systems that perform poorly in vitro generally perform poorly in clinical situations. A variety of methods are available for testing interfacial bond strength. Methods are categorized by the dimensions of the bonded area: macro (4 to 28 mm2) or micro (approximately 1 mm2). The interface is loaded either in tension or shear. Macroshear Bond Strength Tests A macroshear bond strength test consists of a com-posite cylinder that is attached to a bonding substrate. After a predetermined storage time, the specimen is placed in a universal testing machine where a single-edged chisel, a flat-end rod, or a wire loop is used to dislodge the composite cylinder from the substrate in the plane of the interface. It is important to note that although this is referred to a shear test, it is a tensile stress that actually causes debonding of the composite cylinder from the sub-strate. The term shear in this test refers to the mode of loading rather than the stress that causes inter-facial failure. As the distance between the load and interface increases, a bending moment is created in the composite cylinder that results in larger tensile stresses. The location and geometry of the loading device influences the distribution of stresses at the bonded interface thereby altering the bond strength. For example, a chisel with a nominal stress of 15 MPa creates a 178-MPa tensile stress at the interface ver-sus 69 MPa with a wire loop, as shown by computer simulation using finite element analysis. The higher the stress concentration at the load application area, the lower the bond strength. Therefore a knife-edge chisel results in lower bond strength values than a wire loop, where the load is distributed over the entire contact area between the loop and cylinder. Macroshear tests report typical dentin bond strength values between 10 and 50 MPa. Cohesive and mixed failures are very frequent, and may affect up to 55% of the specimens. Another aspect of interest is the elastic modulus of the composite used for the specimen cylinder. The max: 20 MPa min: 0 MPa 100 90 80 70 60 50 40 30 20 10 B A τ max σ max τ max σ max B A –10 (% max) 0 max: 6 MPa min: 0 MPa max: 105 MPa min: 0 MPa max: 178 MPa min: –8 MPa FIG. 5.15 Stress distributions (maximum principal stress, σmax, and maximum shear stress, τmax) at the dentin side of dentin-composite interfaces loaded in tension (left) or shear, using a 0.2-mm chisel applied at 0.2 mm from the interface (right). Line A–B indicates the diameter of the bonding area. (From Braga RR, Meira JB, Boaro LC, Xavier TA. Adhesion to tooth structure: a critical review of “macro” test methods. Dent Mater. 2010;26(2):e38–e49.) 83 5. Testing of Dental Materials and Biomechanics larger the mismatch between the elastic modulus of the composite and the elastic modulus of the sub-strate, the higher the stress concentration at the inter-face. This results in a lower measured bond strength. Macrotensile Bond Strength Tests Stress distribution in tensile tests is much more uni-form than in shear tests. Macrotensile bond strength tests apply loads in an axis that is perpendicular to the interface. This provides a truer estimate of the stress level that initiated debonding. The loading axis must be perpendicular to the interface plane to prevent bending stresses. Specimen preparation and test configuration are thus more difficult for tensile bond strength tests than shear bond tests. As for the shear test, a mismatch between the elastic moduli of the composite and the substrate also influences bond strength. With this method, typical dentin bond strengths are about 10 MPa. Cohesive and mixed failures may occur in 35% of the specimens. Microtensile Bond Strength Tests Microtensile tests use beam-shaped or hourglass-shaped specimens with a cross-sectional area of approximately 1 mm2. This method provides a much lower incidence of mixed and cohesive failures com-pared to other methods (less than 20%). Specimen preparation is more challenging and precise than with macro tests because it requires the fabrication of thin slices from a large bonded interface using dia-mond disks. The slices are trimmed to create hour-glass specimens or further sectioned to create beams. A large number of specimen failures may occur just in setting up the test. Researchers have not agreed on how these pretest failures should be addressed in the experiment data set. Several testing fixtures are available for microten-sile testing. The specimen can either be glued using cyanoacrylate adhesive or attached to the testing fix-ture actively or passively with grips. The grip method interferes with the stress distribution in the speci-men. Dentin bond strength values vary between 30 and 50 MPa with the microtensile method. Values are much higher than those found with macrotensile tests because the critical size for flaws is smaller in a micro-interface. Fracture mechanics theory shows that the size of the critical flaw is inversely related to the inten-sity of the stress required to initiate crack propagation. Defects can be created at the periphery of the bonded interface when sectioning and trimming the specimen with diamond disks. These defects concen-trate stress and initiate debonding at relatively low loads. This can contribute to an artificially low bond strength. Microshear Bond Strength Tests Microshear tests are similar to macroshear tests in the mode of testing, but use much smaller cylinders of a resin composite. Silicone tubes 0.5 mm in height and 0.7 mm in diameter are used to create the composite cylinders. Typically, up to six tube segments are bonded to a surface and filled with composite. Microshear and macroshear share the same issues related to stress dis-tribution. Bond strength values are about 20 MPa and the incidence of mixed and cohesive failures is 50%. Push-Out Tests Another option for testing bond strength is the push-out test. When testing the bond strength of adhesives to dentin, a 1- to 2-mm thick dentin slice is bored to create a tapered conical hole. The internal surface of the hole is treated with an adhesive and the hole is filled with a resin composite. After storage, the com-posite cone is pushed though the dentin from the smaller diameter side. Bond strength is calculated by dividing the extrusion force by the area of the wall of the cone. This method simulates the clinical condi-tion more closely than in shear/tensile tests because the composite is placed into a cavity. This adds the factors of constraint of the curing composite in a cav-ity and the associated polymerization stress from the constraint. Some authors refer to this method as a micro push-out test when disks of radicular dentin are used and the root canal is the cavity that is filled. METHODS FOR MEASURING SHRINKAGE AND STRESS DURING THE CURE OF RESIN COMPOSITES Several methods are described in the literature for measuring the contraction that accompanies the cure of resin composite restorative materials. Some of them record the total change in volume during cure, whereas others measure specific phases of cure. In resin composites, shrinkage that occurs after development of a measurable stiffness of the paste is referred to as postgel shrinkage. Some methods are also affected by the constraint imposed on the specimen, which defines the shrinkage force vectors. Some methods record linear shrinkage and others record volumetric shrinkage, which is three times the linear value if the material is isotropic. Data from dif-ferent methods cannot be directly compared because of these factors, although dimensional change dur-ing cure is a basic material characteristic. Mercury Dilatometer This method uses the change in height of a column of mercury caused by shrinkage of a resin composite 84 CRAIG’S RESTORATIVE DENTAL MATERIALS specimen to calculate total volumetric shrinkage. A composite specimen is placed on a glass slide and immersed in mercury that fills a glass capil-lary tube. A linear variable differential transformer (LVDT) probe floats on the surface of the mercury in the column. After the LVDT probe is stabilized, the resin composite specimen is light activated and cured from below through the glass slide while the change in height of the column is monitored by the LVDT in real time. Because the mercury in the col-umn is affected by heat from the curing light, a ther-mocouple is used to monitor the temperature of the mercury. Thermal expansion of the mercury is sub-tracted from the change in height in the column that results from shrinkage of the composite specimen. Shrinkage values are calculated using the initial mass of the composite specimen and its specific gravity. Bonded Disk A disk of resin composite, 8 × 1.5 mm, is placed within a brass ring (16 mm in diameter and 1.5 mm in height) that is bonded to a glass slide (Fig. 5.16). The composite specimen does not touch the brass ring. A microscope cover slip (approximately 0.1 mm thick) contacts the composite specimen and rests on the brass ring. An LVDT probe contacts the center of the cover slip. The composite specimen is light acti-vated from below the specimen through the glass slide. As the composite cures and shrinks, it pulls the cover slip down and its deflection is monitored by the LVDT probe. Output of the transducer (mV) is converted to displacement (μm) using a calibration curve. Shrinkage is calculated by dividing the mea-sured deflection of the cover slip by the initial height of the composite. This method likely measures post-gel shrinkage because the composite specimen must exhibit some stiffness to deflect the cover slip. The values of shrinkage from the bonded disk method are usually higher than those from other postgel shrinkage methods. AcuVol AcuVol is a video-imaging device that uses a cam-era to capture and analyze profiles of the specimen. A 12-μL composite specimen is shaped into a hemi-sphere and positioned on a Teflon pedestal. The tip of a curing light source is placed 1 mm above the specimen. Lateral profiles of the composite specimen during cure are used to create shrinkage-time curves. The measured values express the total volumetric shrinkage of the composite and are quite similar to those obtained with a mercury dilatometer. Managing Accurate Resin Curing Test The Managing Accurate Resin Curing (MARC) test measures composite shrinkage in a constrained con-figuration (Fig. 5.17). The internal walls of a glass ring (5 mm in diameter, 2 mm in height) are etched with hydrofluoric acid. The volume and density of the ring are measured then coated with ceramic primer and a layer of unfilled resin. The ring is filled with composite and, after curing, the specimen is again measured for volume and density. The volume of the cured composite is calculated from the dif-ference between the volumes of the glass ring filled with composite and the empty ring. Polymerization shrinkage is calculated as the variation between the volume of the cured composite and the internal vol-ume of the glass ring. Cavity Configuration Factor (C-Factor) When a resin composite or glass ionomer cement cures while bonded to the walls of a tooth cavity, stresses develop in the material, at the tooth-restoration interface and in the enamel and dentin of the tooth. The stresses result from volumetric shrinkage of the composite or cement, and their developing stiff-ness (elastic modulus). Constraint from the cavity A B C D E F G FIG. 5.16 Schematic cross section of the shrinkage test assembly. A, Transducer; B, test specimen; C, cover slip; D, brass support ring; E, rigid glass plate; F, light optic; and G, height adjustment screw. (From Watts DC, Cash AJ. Determination of polymerization shrinkage kinetics in visible-light-cured materials: methods development. Dent Mater. 1991;7:281–287) 85 5. Testing of Dental Materials and Biomechanics walls at the bonded interface creates these stress conditions. Without the constraint, fewer stresses occur. These stresses are of clinical relevance because they may create interfacial gaps or, if the bond is sufficiently strong, cause deformation of the tooth. The stresses depend on the anatomy of the tooth and the geometry of the cavity prepara-tion, the quality of the bonded interface, and the restorative technique used (bulk or incremental filling and curing method). The cavity configura-tion factor (C-factor), defined as the ratio of bonded- to-unbonded areas of the restoration, describes the constraint imposed on the shrinking restorative material (Fig. 5.18). For a given material and labo-ratory test parameters, the higher the specimen’s C-factor, the higher the calculated nominal stress. Although it seems reasonable to conclude that a class I restoration should exhibit more stress than a class II and saucer-shaped class V restoration because of its high bonded-to-nonbonded surface area, the clinical condition is complex. C-factor alone does not accurately predict stresses or clini-cal longevity in resin composite or glass ionomer restorations. STRESS ANALYSIS AND DESIGN OF DENTAL STRUCTURES The design of dental restorations is as important as the selection of the appropriate material. Restoration designs must not result in stresses or strains that Light tip Detector 4 mm Light tip Detector 2 mm Class I Class V FIG. 5.17 MARC (Managing Accurate Resin Curing). Schematics of the location of the light detectors placed in simu-lated class I and class V preparation sites. The teeth were placed inside a mannequin simulation head. (From Price RBT, Felix CM, Whalen JM. Factors affecting the energy delivered to simulated class I and class V preparations. J Can Dent Assoc. 2010;76:a94.) 0.2 Low Stress Class VI C-factor = 1 Bonded Surface 5 Unbonded Surfaces MO Class II Class I and V 5.0 High Stress 1.0 C-Factor 0.5 Unbonded Bonded 2.0 C-factor = 4 Bonded Surfaces 2 Unbonded Surfaces C-factor = 5 Bonded Surfaces 1 Unbonded Surface FIG. 5.18 C-factor. Relation between model rectangular preparations, corresponding C-values, standard cavity prepa-rations, and cylindrical test specimens. (Modified from Feilzer AJ, De Gee AJ, Davidson CL. Setting stress in composite resin in relation to configuration of the restoration. J Dent Res. 1987;66(11):1636–1639, 1987.) 86 CRAIG’S RESTORATIVE DENTAL MATERIALS exceed the mechanical limits of a material under clinical conditions. Stresses in dental structures have been studied by brittle coating analysis, strain gauges, holography, two- and three-dimensional photoelasticity, finite ele-ment analysis, and other numerical methods. Many studies have been published on the stress analysis of dental prostheses and tooth and bone biomechanics. Descriptions of the various methods and results can be found in the articles listed in the Bibliography. POLYMERIZATION STRESS TEST The in vitro polymerization stress test evaluates the stresses at the bonded interface due to resin compos-ite polymerization. The basic principle is common to all tests: the resin composite is bonded to two surfaces, under variable degrees of constraint, and cured. Shrinkage of the resin composite pulls the two bonded surfaces together, as it does in a cavity preparation. Load and/or displacement is applied to the bonding substrate and stress is calculated using the initial cross-sectional area of the specimen. Overall stiffness of the test instrument must be much higher than the stresses being measured to prevent the instrument from deforming during the test. Even though all tests are useful for ranking materials by the stress developed, they do not simulate the clini-cal condition. Direct correlations with in vivo obser-vations should be made carefully. Tensilometer In this instrument (Fig. 5.19), the test material is bonded between two rods made of steel, glass, or polymethyl methacrylate (in decreasing order of elastic modulus). The rods are connected to a uni-versal testing machine or system with closed loop feedback control, where one rod is connected to the crosshead and the other rod is fixed. An extensome-ter is attached to the specimen to maintain a constant distance between the two bonded interfaces during the test through closed loop feedback control of the crosshead position. This minimizes the compliance in the test system. Stress is calculated by dividing the load exerted by the shrinkage of the specimen by the initial cross-sectional area of the specimen. A C B FIG. 5.19 Tensilometer for measuring polymerization stress during cure of composites. (A) Overview of test configu-ration. (B) Detail of test specimen and extensometer. (C) Detail as composite is photoactivated. 87 5. Testing of Dental Materials and Biomechanics Tensometer In the tensometer (Fig. 5.20) the test material is bonded between two glass rods with one rod fixed to the base of the instrument, and the second attached to a canti-lever beam. As the material cures, the beam deflects, which is monitored by an LVDT probe. Using a cali-bration curve of force × displacement and deflecting beam theory, stress is calculated and corrected for by the cross-sectional area of the specimen. An extensom-eter is not used in this instrument. System compliance is controlled by the elastic modulus of the cantilever beam and position of the glass rod relative to the ful-crum of the beam. Fiber-optic cables provide remote monitoring of degree of conversion through near-IR spectrometric techniques, described earlier in this chapter, for measuring the extent of polymerization and stress development in real time. Crack Analysis Localized contraction stresses can be calculated by analyzing the propagation of initial indentations made in a brittle material. Using an indenter, initial cracks are made adjacent to a hole in a brittle mate-rial that simulates dental enamel, such as a glass or ceramic. As the bonded composite in the hole is polymerized, tensile stresses develop and the crack lengthens. The lengths of the cracks are measured before and after polymerization, and the resulting stress is calculated from the changes in crack length and the known fracture toughness of the brittle substrate. SPECIFICATIONS FOR RESTORATIVE MATERIALS The properties described in this and other chapters serve as the basis for a series of specifications that have been developed for restorative materials, instru-ments, and equipment. One group is the ANSI/ ADA Standards Committee on Dental Products. Standards developed and approved by this commit-tee are reviewed by the Council on Scientific Affairs Cantilever compliance Sample Sleeve Silanized quartz rod/light guide B C A FIG. 5.20 American Dental Association Foundation (ADAF) Tensometer for measuring polymerization stress during cure of composites. Test configuration before light exposure (A); during light exposure (C); illustration of test device (B) and enlargement of region shown in parts (A) and (C). 88 CRAIG’S RESTORATIVE DENTAL MATERIALS of the ADA, which has responsibility for adopting specifications. Presently, 68 specifications have been adopted. A larger group called Federal Specifications and Standards is designed to regulate requirements of federal government service agencies for the pur-chase and use of materials. Specifications of this type have been available for the past half century, and additional specifications continue to be added in each group. A series of similar specifications is available for products in Australia, Japan, and sev-eral other countries. In 1963, a program for interna-tional specifications was established that combined the efforts of the FDI World Dental Federation and the International Organization for Standardization (ISO). The practice of using physical test controls through methods of applied specifications is well established and will likely continue. Both the dental student and the practitioner must not only recognize that specifications for certain materials are available but also learn to some extent the qualities that are controlled by each specification. Through the specifi-cations the quality of each product is maintained and improved. American Dental Association Specifications The first of the ADA Specifications was for amalgam alloy, formulated and reported in 1930. Since that time other specifications have been or are being for-mulated, as indicated in Appendix Table 1. Copies of the specifications and worksheets to assist in the recording of the required data are avail-able from the Council on Scientific Affairs of the ADA in Chicago. The website of the Council lists the trade names and manufacturers of accepted dental products. This publication can also be obtained from the ADA. An examination of each specification reveals a general pattern of standardization common to each material. 1. These features include an item on the scope and classification of the material, which defines the application and general nature of each material. 2. Each specification includes information on other applicable specifications. 3. The requirements of each material consider such factors as uniformity, color, or general working characteristics of the material, as well as the general limitations of test values. 4. The methods of sampling, inspection, and testing procedures include details of specimen preparation and physical tests to be performed. 5. Each specification includes information on preparation for delivery, with instructions concerning packaging, instructions for use, and marking with lot numbers and the date of manufacture. 6. Each specification includes notes that provide additional information on intended uses, and references to the literature or other special items. The important features of each of these specifica-tions are described appropriately in later chapters. American Dental Association Acceptance Program The ADA, through the Council on Scientific Affairs, maintains an acceptance program for consumer products, such as denture adherents, dental floss, and toothbrushes. Index of Federal Specifications and Standards The Index of Federal Specifications and Standards includes specifications for a number of restorative dental materials not described elsewhere. These specifications are used primarily by the federal services to maintain some quality control of den-tal products and are valuable for suppliers of these materials. In a few instances, reference is made to specific federal specifications and standards in later chapters. Bibliography Dynamic Mechanical Analysis and Rheology Botella A, Dupuy J, Roche AA, et al. Photo-rheometry/NIR spectrometry: an in situ technique for monitoring con-version and viscoelastic properties during photopoly-merization. Macr Rapid Comm. 2004;25:1155. Chiou BS, Khan SA. Real-time FTIR and in situ rheological studies on the UV curing kinetics of thiol-ene polymers. Macromolecules. 1997;30(23):7322–7328. Graessley WW. Linear viscoelasticity. In: Polymeric Liquids and Networks: Dynamics and Rheology. New York: Taylor and Francis Group; 2008. Macosko CW. Linear viscoelasticity. In: Rheology: Principles, Measurements and Applications. New York: Wiley-VCH; 1994. Odian G. Principles of Polymerization. New York: Wiley-Interscience; 2004:11–114. Rubinstein M, Colby RH. Networks and Gelation, Polymer Physics. New York: Oxford University Press; 2008. Urabe I, Nakajima S, Sano H, Tagami J. Physical properties of the dentin-enamel junction region. Am J Dent. 2000; 13(3):129–135. Spectrometric Techniques Silverstein R, Webster F, Kiemle D. Spectrometric Identification of Organic Compounds. Hoboken, NJ: John Wiley & Sons; 2005:72–79. Stansbury JW, Dickens SH. Determination of double bond conversion in dental resins by near infrared spectros-copy. Dent Mater. 2001;17(1):71–79. 89 5. Testing of Dental Materials and Biomechanics Wells-Gray EM, Kirkpatrick SJ, Sakaguchi RL. A dynamic light scattering approach for monitoring dental compos-ite curing kinetics. Dent Mater. 2010;26(7):634–642. Pycnometry Viana M, Jouannin P, Pontier C, Chulia D. About pycnomet-ric density measurements. Talanta. 2002;57:583. Polymerization Stress Tests Condon JR, Ferracane JL. Assessing the effect of composite formulation on polymerization stress. J Am Dent Assoc. 2000;131(4):497–503. Feilzer AJ, De Gee AJ, Davidson CL. Setting stress in com-posite resin in relation to configuration of the restora-tion. J Dent Res. 1987;66(11):1636–1639. Lu H, Stansbury JW, Dickens SH, et al. Probing the origins and control of shrinkage stress in dental resin-composites: I. Shrinkage stress characterization technique. J Mater Sci Mater Med. 2004;15(10):1097–1103. Lu H, Stansbury JW, Dickens SH, et al. Probing the origins and control of shrinkage stress in dental resin compos-ites. II. Novel method of simultaneous measurement of polymerization shrinkage stress and conversion. J Biomed Mater Res B Appl Biomater. 2004;71(1):206–213. Pfeifer CS, Ferracane JL, Sakaguchi RL, Braga RR. Factors affecting photopolymerization stress in dental compos-ites. J Dent Res. 2008;87(11):1043–1047. Sakaguchi RL, Wiltbank BD, Murchison CF. Contraction force rate of polymer composites is linearly correlated with irradiance. Dent Mater. 2004;20(4):402–407. Sakaguchi RL, Wiltbank BD, Murchison CF. Prediction of composite elastic modulus and polymerization shrink-age by computational micromechanics. Dent Mater. 2004;20(4):397–401. Sakaguchi RL, Wiltbank BD, Murchison CF. Cure induced stresses and damage in particulate reinforced polymer matrix composites: a review of the scientific literature. Dent Mater. 2005;21(1):43–46. Stansbury JW, Trujillo-Lemon M, Lu H, et al. Conversion-dependent shrinkage stress and strain in dental resins and composites. Dent Mater. 2005;21(1):56–67. Yamamoto T, Ferracane JL, Sakaguchi RL, Swain MV. Calculation of contraction stresses in dental composites by analysis of crack propagation in the matrix surround-ing a cavity. Dent Mater. 2009;25(4):543–550. Fracture Toughness and Fractographic Analysis Lohbauer U, Amberger G, Quinn GD, Scherrer SS. Fractographic analysis of a dental zirconia framework: a case study on design issues. J Mech Behav Biomed Mater. 2010;3(8):623–629. Quinn GD. Fractographic Analysis of Ceramics and Glasses: NIST Recommended Practice Guide. Special Publication 950-16. Gaithersburg, MD: National Institute of Standards and Technology; 2007. Quinn JB, Quinn GD, Kelly JR, Scherrer SS. Fractographic analyses of three ceramic whole crown restoration fail-ures. Dent Mater. 2005;21(10):920–929. Scherrer SS, Kelly JR, Quinn GD, Xu K. Fracture toughness (KIc) of a dental porcelain determined by fractographic analysis. Dent Mater. 1999;15(5):342–348. Scherrer SS, Quinn GD, Quinn JB. Fractographic failure analysis of a Procera AllCeram crown using stereo and scanning electron microscopy. Dent Mater. 2008; 24(8):1107–1113. Scherrer SS, Quinn JB, Quinn GD, Wiskott HW. Fractographic ceramic failure analysis using the replica technique. Dent Mater. 2007;23(11):1397–1404. Bond Strength Methods, Volumetric Shrinkage Methods, C-factor Armstrong A, Geraldeli S, Maia R, et al. Adhesion to tooth structure: a critical review of “micro” bond strength test methods. Dent Mater. 2010;26:e50–e62. Braga RR, Boaro LC, Kuroe T, et al. Influence of cavity dimensions and their derivatives (volume and ‘C’ fac-tor) on shrinkage stress development and microleakage of composite restorations. Dent Mater. 2006;22:818–823. Braga RR, Meira JB, Boaro LC, Xavier TA. Adhesion to tooth structure: a critical review of “macro” test methods. Dent Mater. 2010;26:e38–e49. Choi KK, Ryu GJ, Choi SM, Lee MJ, et al. Effects of cav-ity configuration on composite restoration. Oper Dent. 2004;29:462–469. Price RBT, Felix CM, Whalen JM. Factors affecting the energy delivered to simulated class I and class V prepa-rations. J Can Dent Assoc. 2010;76:a94. Price RB, Riskalla AS, Hall GC. Effect of stepped light expo-sure on the volumetric polymerization shrinkage and bulk modulus of dental composites and an unfilled resin. Amer J Dent. 2000;13:176–180. Sakaguchi RL, Wiltbank BD, Shah NC. Critical configura-tion analysis of four methods for measuring polym-erization shrinkage strain of composites. Dent Mater. 2004;20:388–396. Sharp LJ, Choi IB, Lee TE, et al. Volumetric shrinkage of composites using video-imaging. J Dent. 2003;31:97–103. van Dijken JW. Durability of resin composite restorations in high C-factor cavities: a 12-year follow-up. J Dent. 2010;38:469–474. Van Meerbeek B, Peumans M, Poitevin A, et al. Relationship between bond-strength tests and clinical outcomes. Dent Mater. 2010;26:e100–e121. Versluis A, Tantbirojn D, Pintado MR, et al. Residual shrink-age stress distributions in molars after composite resto-ration. Dent Mater. 2004;20:554–564. Watts DC, Cash AJ. Determination of polymerization shrinkage kinetics in visible-light-cured materials: methods development. Dent Mater. 1991;7:281–287. Witzel MF, Ballester RY, Meira JB, et al. Composite shrinkage stress as a function of specimen dimensions and compli-ance of the testing system. Dent Mater. 2007;23:204–210. This page intentionally left blank 91 Biocompatibility is formally defined as the ability of a material to elicit an appropriate biological response in a given application in the body. Inherent in this definition is the idea that a single material may not be biologically acceptable in all applications. For example, a material that is acceptable as a full cast crown may not be acceptable as a dental implant. Also implicit in this definition is an expectation for the biological performance of the material. In a bone implant, the expectation is that the material will allow the bone to integrate with the implant. Thus an appropriate biological response for the implant is osseointegration. In a full cast crown, the expecta-tion is that the material will not cause inflammation of pulpal or periodontal tissues, but osseointegra-tion is not an expectation. Whether or not a material is biocompatible therefore depends on the physical function for which the material will be used and the biological response that will be required from it. Using this definition, it makes little sense to say that any given material is or is not biocompatible, and so how the material will be used must be defined before that can be assessed. In that regard, biocompatibility is much like color. Color is a property of a material interacting with its environment (light), and the color of a material depends on the light source and the observer of the light. Similarly, biocompatibility is a property of a material interacting with its environment. The bio-logical response will change if changes occur in the host, the application of the material, or the material itself (Fig. 6.1). In the development of any biomaterial, one must consider the strength, esthetics, and functional aspects of the material, as well as its biocompatibil-ity. Furthermore, demands for appropriate biological responses are increasing as materials are expected to perform more sophisticated functions in the body for longer time periods. Thus considerations of biocompatibility are important to manufacturers, practitioners, scientists, and patients. The field of biocompatibility is interdisciplinary and draws on knowledge from materials science, bioengineering, biochemistry, molecular biology, tissue engineering, and other fields. This chapter briefly surveys the tests used for evaluating biocompatibility of dental materials and how well they correlate with one another, overviews the specifications that govern such testing, and describes the strengths and weaknesses of the test-ing methods. The majority of the chapter is devoted to a discussion of the biocompatibility of the various materials used in dentistry within the framework of these principles. MEASURING BIOCOMPATIBILITY Measuring biocompatibility continues to evolve as more is known about the interactions between C H A P T E R 6 Biocompatibility and Tissue Reaction to Biomaterials Light source Material Observer FIG. 6.1 Biocompatibility. Like color, biocompatibility is not a property of just a material, but rather a property of how a material interacts with its environment. A material’s color depends on the character of the light source, how the light interacts with the material, and how the observer interprets the reflected light. In this sense, the material’s color depends on its environment. The biocompatibility of a material is similar in the sense that it depends on its envi-ronment as well as the nature of the material. 92 CRAIG’S RESTORATIVE DENTAL MATERIALS dental materials and oral tissues and as technolo-gies for testing improve. New materials must be extensively screened to ensure that they are biologically acceptable before they are used in humans. Several varieties of tests are used for this purpose, and are classified as in vitro, animal, and usage tests, the latter including clinical tri-als. This section discusses examples of each type of test, their advantages and disadvantages, how the tests are used together, and standards that rely on these tests to regulate the use of materials in dentistry. In Vitro Tests In vitro tests for biocompatibility require place-ment of a material or a component of a material in contact with a cell, enzyme, or some other iso-lated biological system. The contact can be either direct, when the material contacts the cell system without barriers, or indirect, when there is a bar-rier of some sort between the material and the cell system. Direct tests can be further subdivided into those in which the material is physically present with the cells and those in which some extract from the material contacts the cell system. In vitro tests can be roughly subdivided into those that mea-sure cytotoxicity or cell growth, those that measure some metabolic or other cell function, and those that measure an effect on the genetic material in a cell (mutagenesis assays). Often there is overlap in what a test measures. In vitro tests have a number of significant advantages over other types of bio-compatibility tests (Table 6.1). They are relatively quick, generally cost less than animal or usage tests, can be standardized, are well suited to large-scale screening, and can be tightly controlled to address specific scientific questions. The overriding disad-vantage of in vitro tests is their questionable rel-evance to the final in vivo use of the material (see the section on Correlation Among In Vitro, Animal, and Usage Tests). Other significant disadvantages include the lack of inflammatory and other tissue-protective mechanisms in the in vitro environment. It should be emphasized that in vitro tests alone cannot entirely predict the overall biocompatibility of a material. Standardization of in vitro tests is a primary concern. Two types of cells can be used for in vitro assays. Primary cells are those cells taken directly from an animal and cultured. These cells will grow for only a limited time in culture but usually retain many of the characteristics of cells in vivo. Continuously grown cells or cell lines are cells that have been transformed previously to allow them to grow more or less indefinitely in culture. Because of this transformation, these cells do not retain all in vivo characteristics, but they do consistently exhibit those features that they do retain. Primary cell cultures seem to be more relevant than con-tinuous cell lines for measuring cytotoxicity of materials. However, primary cells, being from a single individual, have limited genetic variabil-ity, may harbor viral or bacterial agents that alter their behavior, and often rapidly lose their in vivo functionality once placed in culture. Furthermore, the genetic and metabolic stability of continuous cell lines contributes significantly toward stan-dardizing assay methods. In the end, both pri-mary and continuous cells play important roles in TABLE 6.1 Advantages and Disadvantages of Biocompatibility Tests Test Advantages Disadvantages In vitro tests Quick to perform Least expensive Can be standardized Large-scale screening Good experimental control Excellence for mechanisms of interactions Relevance to in vivo is questionable In vivo tests Allows complex systemic interactions Response more comprehensive than in vitro tests More relevant than in vitro tests Relevance to use of material is questionable Expensive Time consuming Legal/ethical concerns Difficult to control Difficult to interpret and quantify Usage tests Relevance to use of material is assured Very expensive Very time consuming Major legal/ethical issues Can be difficult to control Difficult to interpret and quantify 93 6. Biocompatibility and Tissue Reaction to Biomaterials in vitro testing, and both should be used to assess materials. Cytotoxicity Tests Cytotoxicity tests assess cell death caused by a mate-rial by measuring cell number or growth before and after exposure to that material. Control materials should be well defined and commercially available to facilitate comparisons among other testing labo-ratories. Membrane permeability tests are used to mea-sure cytotoxicity by the ease with which a dye can pass through a cell membrane, because membrane permeability is equivalent to or very nearly equiva-lent to cell death (Figs. 6.2 and 6.3). Tests for Cell Metabolism or Cell Function Some in vitro tests for biocompatibility use the bio-synthetic or enzymatic activity of cells to assess cyto-toxic response. Tests that measure DNA synthesis or protein synthesis are common examples of this type of test. A commonly used enzymatic test for cytotoxicity is the 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyl tetra-zolium bromide (MTT) test; other tests include the nitroblue tetrazolium (NBT), 2,3-Bis-(2-methoxy-4-nitro-5-sulfophenyl)-2H-tetrazolium-5-carboxanilide salt (XTT), and a water-soluble tetrazolium (WST) assays, all being colorimetric assays based on differ-ent tetrazolium salts. alamarBlue tests quantitatively measure cell proliferation using a fluorescent indica-tor that allows continuous monitoring of cells over time. Tests That Use Barriers (Indirect Tests) Because direct contact often does not exist between cells and materials during in vivo use, several in vitro barrier tests have been developed to mimic in vivo conditions. These tests include an agar overlay method, which uses agar to form a barrier between the cells and the material, and the Millipore filter assay, in which a monolayer of cells is grown on a filter that is turned over so that test materials are placed on the filter and leachable diffusion products are allowed to interact with the cells. The agar diffu-sion and Millipore filter tests can provide, at best, a qualitative cytotoxic ranking among materials (Fig. 6.4). For many materials, dentin is a barrier through which toxic components must diffuse to reach pulp tissue, with the thickness of the dentin directly corre-lating with the protection offered to the pulp. These assays, which incorporate dentin disks between the test sample and the cell assay system, have the added advantage of directional diffusion between the restorative material and the culture medium (Fig. 6.5). Other Assays for Cell Function In vitro assays to measure immune function or other tissue reactions have also been used. These assays FIG. 6.2 Noncytotoxic interaction. Light microscopic view of a noncytotoxic interaction between a material (dark image at bottom of the picture) and periodontal ligament fibro-blasts in a cell culture (in vitro) test. The morphology of the fibroblasts indicates that they are alive and are not suffering from a toxic response (see Fig. 6.3 for contrast). The material in this case was a calcium hydroxide pulp-capping agent. FIG. 6.3 Cytotoxic interaction. Light microscopic view of a cytotoxic interaction between a material (dark image at the bottom of the picture) and periodontal ligament fibro-blasts in a cell culture test. The fibroblasts are rounded and detached (see Fig. 6.2 for contrast), indicating that they are either dead or dying. The material is a type of calcium hydroxide pulp-capping agent, different from the one shown in Fig. 6.2. NR-stained cell layer A Sample Control Control FIG. 6.4 Agar overlay method. The agar overlay method has been used to evaluate the cytotoxicity of dental materi-als. The cell layer, which has been previously stained with neutral red (NR), is covered with a thin layer of agar (A). Samples are placed on top of the agar for a time. If the mate-rial is cytotoxic, it will injure the cells and the neutral red will be released, leaving a zone of inhibition. 94 CRAIG’S RESTORATIVE DENTAL MATERIALS measure cytokine production by lymphocytes and macrophages, lymphocyte proliferation, chemotaxis, or T-cell rosetting to sheep red blood cells. Other tests measure the ability of a material to alter the cell cycle or activate complement. The in vivo significance of these assays is yet to be ascertained, but many show promise for being able to reduce the number of ani-mal tests required to assess the biocompatibility of a material. Mutagenesis Assays Mutagenesis assays assess the effect of a biomaterial on a cell’s genetic material. There are a wide range of mechanisms by which a material can affect a cell’s genes. Genotoxic mutagens directly alter cell DNA through various types of mutations. Each chemical may be associated with a specific type of DNA muta-tion. Genotoxic chemicals may be mutagens in their native states, or may require activation or biotrans-formation to be mutagens, in which case they are called promutagens. Epigenetic mutagens do not alter the DNA themselves, but support tumor growth by altering the cell’s biochemistry, altering the immune system, acting as hormones, or by other mechanisms. Carcinogenesis is the ability to cause cancer in vivo. Mutagens may or may not be carcinogens, and carcin-ogens may or may not be mutagens. Thus quantita-tion and relevance of tests that measure mutagenesis and carcinogenesis are extremely complex. The Ames test is the most widely used short-term mutagenesis test and the only one that is considered thoroughly validated. It looks at the conversion of a mutant stock of Salmonella typhimurium back to a native strain, because chemicals that increase the fre-quency of reversion back to the native state have a high probability of being carcinogenic in mammals. A second test for mutagenesis is the Styles’ cell trans-formation test. This test on mammalian cells offers an alternative to bacterial tests (Ames test), which may not be relevant to mammalian systems. However, because the Ames test is widely used, extensively described in the literature, and technically easier to conduct, it is most often conducted in a screening program. Animal Tests Animal tests for biocompatibility, usually involving mammals such as mice, rats, hamsters, or guinea pigs, are distinct from usage tests (which are also often done in animals) in that the material is not placed in the animal with regard to its final use. The use of an animal allows for the complex interactions between the material and a functioning, complete biological system to occur. This is extremely difficult to mimic in a cell-culture system. Thus the biological responses in animal tests are more comprehensive and may be more relevant than in vitro tests, and these features are the major advantages of these tests (see Table 6.1). The main disadvantages of animal tests are that they can be difficult to interpret and control, are expensive, time consuming, and often involve significant ethical concerns and oversight. Furthermore, the relevance of the test to the in vivo use of a material is often unclear, especially in esti-mating the appropriateness of an animal species to represent a human. A variety of animal tests have been used to assess biocompatibility. The mucous membrane irritation test determines whether a material causes inflammation to mucous membranes or abraded skin. In a skin sensitization test, materials are injected intradermally to test for development of skin hypersensitivity reactions, fol-lowed by secondary treatment with adhesive patches containing the test substance. Implantation tests are used to evaluate materials that will contact subcuta-neous tissue or bone. The location of the implantation site is determined by the use of the material and may include connective tissue, bone, or muscle. Although restorative materials are tested because the margins often contact the gingiva, most subcutaneous tests are used for materials that will directly contact soft tissue during implantation, as well as endodontic and periodontal treatment materials. Usage Tests Usage tests may be done in animals or in human study participants. They are distinct from other ani-mal tests because they require that the material be placed in a situation identical to its intended clinical use. The usefulness for predicting biocompatibility is directly proportional to the fidelity with which the test mimics the clinical use of the material, includ-ing time, location, environment, and placement technique. For this reason, usage tests in animals C A Out In B FIG. 6.5 Dentin disk barrier test method. A dentin disk is used as a barrier in cytotoxicity tests that attempt to predict the toxicity of materials placed on dentin in vivo. The material is placed on one side (A) of the dentin disk (B) in the device used to hold the dentin disk. Collection fluid (cell culture medium or saline) is on the other side of the disk (C). Cells can also be grown on the collection side. Components of the material may diffuse through the dentin and the effect of the medium on cell metabolism can then be measured. To assess the rate of diffusion, the collection fluid can be circulated into and out of the collection chamber (C). 95 6. Biocompatibility and Tissue Reaction to Biomaterials usually employ larger animals that have similar oral environments to humans, such as dogs, mini-swine, or monkeys. When humans are used, the usage test is termed a clinical trial. The overwhelming advan-tage for usage tests is their relevance (see Table 6.1). These tests are the gold standard, in that they give the ultimate answer to whether or not a material will be biocompatible and clinically useful. One might ask, then, why bother with in vitro or animal tests at all. The answer is in the significant disadvantages of the usage test. These tests are extremely expensive, last for long periods, involve many ethical and often legal concerns, are exceptionally difficult to control and interpret accurately, and may harm the test par-ticipants. In addition, statistical analysis of these tests is often a daunting process. In dentistry, dental pulp, periodontium, and gingival or mucosal tissues are the main targets of usage tests. Dental Pulp Irritation Tests In general, materials to be tested on the dental pulp are placed in class 5 cavity preparations in intact teeth without caries. At the conclusion of the study, the teeth are removed and sectioned for microscopic examina-tion, with tissue necrotic and inflammatory reactions classified according to the intensity of the response. Although most dental-pulp irritation tests have involved teeth without inflamed pulps, there has been increased concern that inflamed dental pulp tissue may respond differently than healthy pulps to liners, cements, and restorative agents. Thus usage tests on teeth with induced pulpitis, which allow evaluation of the type and amount of reparative dentin formed, will likely continue to be developed and refined. Dental Implants in Bone At present, the best predictors for success of implants are careful patient selection and ideal clinical condi-tions. The following terms are used to define various degrees of success: early implant success for implants surviving 1 to 3 years, intermediate implant success for implants surviving 3 to 7 years, and long-term suc-cess for implants surviving more than 7 years. As such, there are three commonly used tests to predict implant success: (1) penetration of a periodontal probe along the side of the implant, (2) mobility of the implant, and (3) radiographs indicating either osseous integration or radiolucency around the implant. A bone implant is considered successful if it exhibits no mobility and no radiographic evidence of periimplant radiolucency, has minimal vertical bone loss and is completely encased in bone, and has an absence of persistent periimplant soft-tissue compli-cations. Any fibrous capsule formation is a sign of irritation and chronic inflammation, which is likely to lead to micromotion of the implant and ultimately to loosening and failure. Mucosa and Gingival Usage Tests Tissue response to materials with direct contact of gingival and mucosal tissues is assessed by place-ment in cavity preparations with subgingival exten-sions. The material’s effect on gingival tissues is observed and responses are categorized as slight, moderate, or severe, depending on the number of mononuclear inflammatory cells (mainly lympho-cytes and neutrophils) in the epithelium and adja-cent connective tissues. A difficulty with this type of study is the frequent presence of some degree of preexisting inflammation in gingival tissue due to the presence of bacterial plaque, surface roughness of the restorative material, open or overhanging mar-gins, and overcontouring or undercontouring of the restoration. Correlation Among In Vitro, Animal, and Usage Tests In the field of biocompatibility, some scientists ques-tion the usefulness of in vitro and animal tests in light of the apparent lack of correlation with usage tests and the clinical history of materials. However, lack of correlation is not surprising in light of differences among these tests, in that in vitro and animal tests often measure aspects of biological response that are more subtle or less prominent than those observed during a material’s clinical use. Furthermore, barriers between the material and tissues may exist in usage tests or clinical use, but may not exist in in vitro or animal tests. Thus it is important to remember that each type of test has been designed to measure differ-ent aspects of biological response to a material, and correlation is not always to be expected. The best example of a barrier that occurs in use but not during in vitro testing is the dentin barrier. When restorative materials are placed in teeth, den-tin will generally be interposed between the material and the pulp. The dentin barrier, although possibly only a fraction of a millimeter thick, is effective in modulating the toxic effect of a dental material. This dentin barrier effect is illustrated by the following classic study (Table 6.2). Three methods were used to evaluate the following materials: zinc oxide–eugenol (ZOE) cement, resin composite, and silicate cement. The evaluation methods included (1) four different cell culture tests, (2) an implantation test, and (3) a usage test in class 5 cavity preparations in monkey teeth. The results of the four cell culture tests were relatively consistent, with silicate having only a slight effect on cultured cells, composite a moderate effect, and ZOE a severe effect. These three materi-als were also embedded subcutaneously in connec-tive tissue in polyethylene tubes (secondary test), and observations were made at 7, 30, and 90 days. Reactions at 7 days could not be determined because 96 CRAIG’S RESTORATIVE DENTAL MATERIALS of inflammation caused by the operative procedure. At 30 days, ZOE caused a more severe reaction than silicate cement. The inflammatory reactions at 90 days caused by ZOE and silicate were slight, whereas the reaction to resin composites was moderate. When the three materials were evaluated in class 5 cavity preparations under prescribed conditions of cavity size and depth (usage test), the results were quite dif-ferent from those obtained by the other methods. The silicate was found to have the most severe inflamma-tory reaction, the composite had a moderate-to-slight reaction, and the ZOE had little or no effect. Apparent contradictions in this study are explained by considering the components that were released from the materials and the environments into which they were released. The silicate cement released hydrogen ions that were probably buffered in the cell culture and implantation tests but were not adequately buffered by the dentin in the usage tests. Microleakage of bacteria or bacterial products may have added to the inflammatory reaction in those usage tests. Thus this material appeared to be the most toxic in the usage test. The composites released low-molecular-weight resins, and the ZOE released eugenol and zinc ions. In the cell culture tests, these compounds had direct access to cells and probably caused the moderate-to-severe cytotoxicity. In the implantation tests, the released components may have caused some cytotoxicity, but the severity may have been reduced because of the capacity of the sur-rounding tissue to disperse the toxins. In usage tests, these materials probably were less toxic because the diffusion gradient of the dentin barrier reduced con-centrations of the released molecules to low levels. The slight reaction observed with the composites may also have been caused in part by microleakage around these restorations. The ZOE did not show this reaction, however, because the eugenol and zinc probably killed bacteria in the cavity, and the ZOE may have reduced microleakage. Another example of the lack of correlation of usage tests with implantation tests is the inflamma-tory response of the gingiva at the gingival and proxi-mal margins of restorations that accumulate bacterial plaque and calculus. Plaque and calculus cannot accumulate on implanted materials and therefore the implantation test cannot hope to duplicate the usage test. However, connective tissue implantation tests are of great value in demonstrating the cyto-toxic effects of materials and evaluating materials that will be used in contact with alveolar bone and apical periodontal connective tissues. In these cases, the implant site and the usage sites are sufficiently similar to compare the test results of the two sites. Using In Vitro, Animal, and Usage Tests Together For about 25 years, scientists, industry, and the gov-ernment have recognized that the most accurate and cost-effective means to assess biocompatibility of a new material is a combination of in vitro, animal, and usage tests. Implicit in this philosophy is the concept that no single test will be adequate to completely characterize biocompatibility of a material. The ways in which these tests are used together, however, are controversial and have evolved over many years as knowledge has increased and new technologies were developed. Early combination schemes proposed a pyramid testing protocol, in which all materials were tested at the bottom of the pyramid and materials were “weeded out” as the testing continued toward the top of the pyramid (Fig. 6.6). Tests at the bottom of the pyramid were “unspecific toxicity” tests of any type (in vitro or animal) with conditions that did not nec-essarily reflect those of the material’s use. The next tier shows specific toxicity tests that presumably dealt with conditions more relevant to the use of the mate-rial. The final tier was a clinical trial of the material. Later, another pyramid scheme was proposed that divided tests into initial, secondary, and usage tests. The philosophy was similar to that used in the first scheme, except that the types of tests were broadened to encompass biological reactions other than toxic-ity, such as immunogenicity and mutagenicity. The concept of a usage test in an animal was also added (versus a clinical trial in a human). There are several important features of these early schemes. First, only materials that “passed” the first tier of tests were grad-uated to the second tier, and only those that passed the second tier were graduated to the clinical trials. Presumably, then, this scheme funneled safer materials into the clinical trials area and eliminated unsafe materials. This strategy was appreciated because clinical trials are the most expensive and time-consuming aspect of biocompatibility testing. TABLE 6.2 Comparison of Reactions of Three Materials by Screening and Usage Tests Material Cell Culture Implantation in Connective Tissue Pulp Response Silicate + + + + Resin composite + + + + + ZOE + + + + 0 + + +, Severe; + +, moderate; +, slight; 0, no reaction. ZOE, Zinc oxide–eugenol. From Mjör IA, Hensten-Pettersen A, Skogedal O. Biologic evaluation of filling materials. A comparison of results using cell culture techniques, implantation tests and pulp studies. Int Dent J. 1977;27(2):124–129. 97 6. Biocompatibility and Tissue Reaction to Biomaterials Second, any material that survived all three tiers of tests was deemed acceptable for clinical use. Third, each tier of the system put a great deal of weight on the tests used to accurately screen in or out a material. Although still used in principle today, the inability of in vitro and animal tests to unequivocally screen materials in or out has led to development of newer schemes in biocompatibility testing. Two newer testing schemes have evolved in the past 5 years with regard to using combinations of biocom-patibility tests to evaluate materials (Fig. 6.7). In both of these schemes, all tests (in vitro, animal, and usage) continue to be of value in assessing biocompatibil-ity of a material during its development and even in its clinical service. For example, tests of inflammatory response in animals may be useful not only during the development of a material, but also if a problem is noted with the material after it has been on the market for a time. These new schemes also recognize the inability of current testing methods to accurately and absolutely screen in or out a material. In addition, both incorpo-rate the philosophy that assessing the biocompatibility of a material is an ongoing process. Undoubtedly, we will see still newer strategies in the use of combinations of biocompatibility tests as the roles of materials change and the technologies for testing improve. Standards That Regulate the Measurement of Biocompatibility The first efforts of the American Dental Association (ADA) to establish guidelines for dental materials Clinical trials Specific toxicity Unspecific toxicity Number of tests Number of tests Primary Secondary Usage Progress of testing A B FIG. 6.6 Early and contemporary strategies for the use of biocompatibility tests to assess the safety of materials. Testing begins at the bottom of the pyramid and works up. The number of tests needed decreases with the progress of testing because unacceptable materials are theoretically eliminated in the early testing stages. (A) The earliest strategy, in which the testing strategy is focused on toxicity only. Unspecific toxicity refers to tests not necessarily related to the use of the material, whereas tests under specific toxicity are more relevant. Clinical trials are equivalent to usage tests in this scheme. (B) The contemporary strategy used in most standards documents. Primary Secondary Usage Secondary Usage Progress of testing Primary A B FIG. 6.7 Two suggested future strategies for biocompatibility testing of materials. (A) The pyramid scheme of Fig. 6.6 is retained, but it is acknowledged that primary and secondary tests will play a continuing (but decreased) role as the progress of the testing continues. (B) The usage test has the most stature and the most common progression of tests is from primary to secondary to usage, but the need to go through several iterations between testing types is acknowledged. Furthermore, the ongoing nature of biocompatibility is recognized by the need to use primary and secondary tests after clinical evaluation of a material. In this scheme the order of testing is ultimately determined as the testing and clinical use of the material continues to provide new data. 98 CRAIG’S RESTORATIVE DENTAL MATERIALS came in 1926 when scientists at the National Bureau of Standards (NBS), now the National Institute of Science and Technology (NIST), developed specifica-tions for dental amalgam. Unfortunately, recommen-dations on materials and conditions for biological compatibility have not kept pace with the techno-logical development of dental materials. Reasons for this are (1) the fast advance of cellular and molecular biology, (2) the variety of tests available for assess-ing biocompatibility of materials, and (3) the lack of standardization of these tests. Standardization is a difficult and lengthy process, made more difficult by disagreement on the appro-priateness and significance of particular tests. In early attempts to develop a uniform test for toxicity of den-tal materials, small, standard-sized pieces of gold, amalgam, gutta-percha, silicates, and copper amal-gam were sterilized and placed in uniformly sized pockets within skeletal muscle tissue. Biopsy speci-mens were evaluated microscopically after 6 months. Somewhat later came attempts to standardize tech-niques by placing materials within connective tissue and tooth pulp. Not until the passage of the Medical Device Bill by Congress in 1976 was biological test-ing for all medical devices (including dental materi-als) given a high priority. In 1972 the ADA Council on Dental Materials, Instruments, and Equipment (now the Council on Scientific Affairs) approved specifica-tion No. 41 for Recommended Standard Practices for Biological Evaluation of Dental Materials. The com-mittee that developed this document recognized the need for standardized methods of testing and for sequential testing of materials to reduce the number of compounds that would need to be tested clinically. In 1982, an addendum was made to this document, and it was further updated in 2005. ANSI/ADA Specification 41 Three categories of tests are described in the 2005 American National Standards Institute (ANSI)/ ADA specification: initial, secondary, and usage tests. This document uses the testing scheme shown in Fig. 6.6B. The initial tests include in vitro assays for cytotoxicity, red blood cell membrane lysis (hemolysis), mutagenesis and carcinogenesis at the cellular level, and in vivo acute physiological dis-tress and death at the level of the organism. Based on the results of these initial tests, promising materi-als are evaluated by one or more secondary tests in small animals (in vivo) for inflammatory or immu-nogenic potential (e.g., dermal irritation, subcuta-neous and bony implantation, and hypersensitivity tests). Finally, materials that pass secondary tests are subjected to one or more in vivo usage tests, first in larger animals, often primates, and finally, with Food and Drug Administration approval, in humans. The ANSI/ADA specification No. 41, 1982 addendum, added two assays for mutagenesis: the Ames test and the Styles’ cell transformation test. The standard was most recently revised to conform to International Organization for Standardization (ISO) 10993, and was released as ANSI/ADA specification No. 41, Recommended Standard Practices for Biological Evaluation of Dental Materials (2005). ISO 10993 In the 1980s, international efforts were initiated by several organizations to develop international stan-dards for biomedical materials and devices. Several multinational working groups, including scientists from ANSI and the ISO, were formed to develop standard ISO 10993, published in 1992. Revision of the dental components of this document resulted in ISO 7405:2008 “Preclinical evaluation of biocompat-ibility of medical devices used in dentistry—Test methods for dental materials.” This is the most recent ISO standard available for biocompatibility testing of dental materials. The standard divides tests into initial and sup-plementary tests to assess the biological reaction to materials. Initial tests are tests for cytotoxicity, sen-sitization, and systemic toxicity. Some of these tests are done in vitro, others in animals in nonusage situ-ations. Most of the supplementary tests for assessing chronic toxicity, carcinogenicity, and biodegradation are done in animal systems, many in usage situa-tions. Significantly, although guidelines for the selec-tion of tests are given in part 1 of the standard and are based on how long the material will be present; whether it will contact body surface only, blood, or bone; and whether the device communicates exter-nally from the body, the ultimate selection of tests for a specific material is left up to the manufacturer, who must present and defend the testing results. BIOCOMPATIBILITY OF DENTAL MATERIALS Reactions of Pulp Microleakage There is evidence that restorative materials may not adequately bond to or seal enamel or dentin. In this case, bacteria, food debris, or saliva may be drawn into the gap between the restoration and the tooth by capillary action. This effect has been termed microle-akage, and its influence on pulpal irritation has been extensively studied. Several early studies reported that various dental restorative materials irritated pulp tissue in animal tests. However, several other studies hypothesized that the products of microleak-age, not the restorative materials, caused the irrita-tion. Subsequently, numerous studies suggested that bacteria present under restorations and in dentinal 99 6. Biocompatibility and Tissue Reaction to Biomaterials tubules might be responsible for pulpal irritation. Other studies showed that bacteria or bacterial prod-ucts such as lipopolysaccharides could cause pulp irritation within hours of being applied to dentin. Finally, a classic animal study shed light on the roles of restorative materials and microleakage on pulpal irritation. Amalgam, composite, zinc phos-phate cement, and silicate cement were used as restorative materials in class 5 cavity preparations in monkey teeth. The materials were placed directly on pulp tissues. Half of the restorations were sur-face sealed with ZOE cement. Although some irrita-tion was evident in all restorations at 7 days, after 21 days, the sealed restorations showed less pulpal irritation than those not sealed, presumably because microleakage had been eliminated. Only zinc phos-phate cement elicited a long-term inflammatory response. Furthermore, the sealed teeth exhibited a much higher rate of new dentin formation, termed dentin bridging, under the material. Only amalgam seemed to prevent bridging. This study suggests that microleakage plays a significant role in pulpal irritation, but that the materials can also alter normal pulpal and dentinal repair. Recently, the concept of nanoleakage has been put forward. Like microleakage, nanoleakage refers to the leakage of saliva, bacteria, or material com-ponents through the interface between a material and tooth structure. However, nanoleakage refers specifically to dentin bonding, and may occur between mineralized dentin and a bonded mate-rial in the very small spaces of demineralized col-lagen matrix into which the bonded material did not penetrate. Thus nanoleakage can occur even when the overall bond between the material and dentin is intact. It is not known how significant a role nanoleakage plays in the biological response to materials, but it is suspected of contributing to the hydrolytic degradation of the dentin-material bond, leading ultimately to much more serious microleakage. The full biological effects of restorative materials on the pulp are still not clear. Restorative materials may directly affect pulpal tissues, or may play an auxiliary role by causing sublethal changes in pulpal cells that make them more susceptible to bacteria or neutrophils. It is clear, however, that the design of tests measuring pulpal irritation to materials must include provisions for eliminating bacteria, bacterial products, and other microleakage. Furthermore, the role of dentin in mitigating the effects of microleak-age remains to be fully understood. Recent research has focused on the effects that resin components have on the ability of odontoblasts to form repara-tive dentin. Other research has established the rates at which these components traverse the dentin (see the next section on dentin bonding). Although it is true that the majority of studies in this arena have in the past focused on the damag-ing effects of materials on the cells of the pulp and dentin, more recent evidence suggests that there are potentially beneficial effects that may derive from these interactions. Subtoxic exposure to certain den-tal materials, such as acid etchants, bonding resins, liners and bases, cements, and restorative materi-als, may solubilize molecules sequestered within the dentin during tooth development. These mol-ecules include growth factors and other proteins and enzymes capable of stimulating existing odon-toblasts or signaling undifferentiated cells to migrate to the site and begin the process of dentinal regen-eration. These events may occur whether or not the material produces a sealed margin with the tooth, and are likely moderated by the health of the tooth in terms of the level of inflammation and the presence of bacterial infection. The exciting aspect of acquir-ing this new knowledge is the potential to design dental materials capable of initiating the tooth repair process in a systematic rather than random way. This is discussed at greater length in Chapter 16, Tissue Engineering. Dentin Bonding Traditionally, bond strengths to enamel have been higher than those to dentin. Bonding to dentin has proved more difficult because of its composition (being both organic and inorganic), wetness, and lower mineral content. The wettability of demineral-ized dentin collagen matrix has also been problem-atic. Because the dentinal tubules and their resident odontoblasts are extensions of the pulp, bonding to dentin also involves biocompatibility issues. After being cut, such as in a cavity preparation, the dentin surface that remains is covered by a 1- to 2-μm layer of organic and inorganic debris. This layer has been named the smear layer (Fig. 6.8). In addition to covering the surface of the dentin, the smear layer debris is also deposited into the tubules to form dentinal plugs. The smear layer and dentinal plugs, which appear impermeable when viewed by electron microscopy, reduce the flow of fluid (con-vective transport) significantly. However, research has shown that diffusion of molecules as large as albumin (66 kDa) will occur through the smear layer. Numerous studies have shown that removing the smear layer improves the strength of the bond between dentin and restorative materials with con-temporary dentin-bonding agents. A variety of agents have been used to remove the smear layer, including acids, chelating agents such as ethylene-diaminetetraacetic acid (EDTA), sodium hypochlo-rite, and proteolytic enzymes. Removing the smear layer increases the wetness of the dentin and requires that the bonding agent be able to wet dentin and 100 CRAIG’S RESTORATIVE DENTAL MATERIALS displace dentinal fluid. The precise mechanism by which bonding occurs remains unclear. However, it appears that the most successful bonding agents are able to penetrate into the layer of collagen fibrils that remains after acid etching removes the mineral com-ponent. There, they create a hybrid layer of resin and collagen in intimate contact with dentin and dentinal tubules. The strength of the collagen itself has also been shown to be important to bond strengths. From the standpoint of biocompatibility, the removal of the smear layer may pose a threat to the pulp for three reasons. First, its removal juxta-poses resin materials and dentin without a barrier, and therefore increases the risk that these materials can diffuse and cause pulpal irritation. Second, the removal of the smear layer makes any microleakage more significant because a significant barrier to the diffusion of bacteria or bacterial products toward the pulp is removed. Third, the acids used to remove the smear layer are a potential source of irritation themselves. Nevertheless, removal of the smear layer is now a routine procedure because superior bond strengths are achieved. Numerous acids, including phosphoric, hydro-chloric, citric, and lactic acids, have been used to remove the smear layer. The effect of these acids on pulp tissues depends on a number of factors, includ-ing thickness of dentin between the restoration and the pulp, strength of the acid, and degree of etching. Most studies have shown that dentin is a very effi-cient buffer of protons, and that most of the acid never reaches the pulp if sufficient dentin remains. A den-tin thickness of 0.5 mm has proved adequate in this regard. Citric or lactic acids are not as well buffered, probably because these weak acids do not dissociate as efficiently. Usage tests that have studied the effects of acids have shown that phosphoric, pyruvic, and citric acids produce moderate pulpal inflammatory responses, but this resolves after 8 weeks. Recent research has shown that in most cases the penetra-tion depth of acid into the dentin is less than 100 μm. However, the possibility of adverse effects of these acids cannot be ruled out, because odontoblastic pro-cesses in the tubules may be affected even though the acids do not reach the pulp itself. The more positive aspect of this dissolution of the dentin by acids used in dentin-bonding agents may be the release of potentially bioactive molecules entrapped during development. Significant research has shown that extracted dentin matrix proteins, which contain a large variety of phosphorylated and nonphosphorylated proteins, proteoglycans, metal-loproteinases, and a variety of growth factors, may be released from intact dentin by basic and acidic chemicals, including acid etchants used in dental adhesives. Studies have shown that many of these molecules may serve as cell signaling agents to recruit undifferentiated cells or as direct stimulants to upregulate the production of extracellular matrix as a step in the process of dentin remineralization. The specific role for each of the molecules in this pro-cess is not currently known, nor is it known what the desirable concentration of a specific protein or com-bination of molecules is to produce optimal results. However, the fact that these naturally present mol-ecules may be released by routine dental restorative procedures and serve as participants in the repair process provides an opportunity for the develop-ment and design of future materials. Bonding Agents There have been a number of studies of biocompatibil-ity of dentin-bonding systems. Many of these reagents are cytotoxic to cells in vitro if tested alone. However, when placed on dentin and rinsed with water between applications of subsequent reagents as pre-scribed by the manufacturer, cytotoxicity is reduced. Longer-term in vitro studies suggest, however, that S P T FIG. 6.8 Scanning electron micrograph of cut dentin. When a dentin surface is cut with a bur, a layer of debris, called the smear layer (S), remains on the surface. The smear layer consists of organic and inorganic debris that covers the dentinal surface and the tubules (T). Often, the debris fills the distal part of the tubules in a smear plug (P). (From Brännström M. Dentin and Pulp in Restorative Dentistry. London: Wolfe Medical Publications; 1982.) 101 6. Biocompatibility and Tissue Reaction to Biomaterials components of the bonding agents may penetrate up to 0.5 mm of dentin and cause significant suppression of cellular metabolism for up to 4 weeks after applica-tion. This suggests that residual unbound constituents may cause adverse reactions. Hydroxyethyl methacrylate (HEMA), a hydro-philic resin contained in several bonding systems, is at least 100 times less cytotoxic in tissue culture than bisphenol A-glycidyl methacrylate (Bis-GMA). Studies using long-term in vitro systems have shown, however, that adverse effects of resins occur at much lower concentrations (by a factor of 100 or more) when exposure times are increased to 4 to 6 weeks. Many cytotoxic effects of resin components are reduced significantly by the presence of a den-tin barrier. However, if the dentin in the floor of the cavity preparation is thin (<0.1 mm), there is some evidence that HEMA is cytotoxic in vivo. Further, studies have shown that HEMA is capable of dif-fusing through dentin, presumably via the dentinal tubules, even in opposition to an outward flow of fluid driven by normal pulpal pressure. What effect HEMA may then have on the pulp cells in situ is not known, but HEMA has been shown to stimulate the expression of growth factors in mouse odontoblast-like cells. Other studies have established the in vitro cyto-toxicity of most of the common resins in bonding agents, such as Bis-GMA, triethylene glycol dimeth-acrylate, and urethane dimethacrylate (UDMA). Combinations of HEMA and other resins found in dentin-bonding agents may act synergistically to cause cytotoxic effects in vitro. There have been very few clinical studies of diffusion of hydrophilic and hydrophobic resin components through dentin. These studies indicated that some diffusion of these components occurs in vivo as well. Interestingly, there has been one report that some resin compo-nents enhance the growth of oral bacteria. If substan-tiated, this would cause concern about the ability of resin-based materials to increase plaque formation. Finally, studies have also shown that the release of matrix metalloproteinases (MMPs) from dentin by virtue of its interaction with the acid components in dentin adhesives may cause degradation of the adhesive bond by enzymatic action on the exposed collagen within the hybrid layer. The application of an MMP inhibitor, such as chlorhexidine, has been shown to minimize this effect, and has been recom-mended for maintaining the clinical durability of the dentin bond. However, the overall effect of chlorhex-idine on pulp cells has yet to be determined. Resin-Based Materials Resin-based materials have been used as dental cements and restorative materials. Because they are a combination of organic and inorganic phases, these materials are called resin composites. In vitro, freshly set chemically cured and light-cured resins often cause moderate cytotoxic reactions in cultured cells over 24 to 72 hours of exposure, although several newer systems seem to have minimal toxicity. The cytotoxicity is significantly reduced 24 to 48 hours after setting and by the presence of a dentin barrier. Several studies have shown that some materials are persistently cytotoxic in vitro even up to 4 weeks, whereas others gradually improve, and a few newer systems show little toxicity even initially. In all cases, cytotoxicity is thought to be mediated by resin com-ponents released from the materials. Evidence indi-cates that the light-cured resins are less cytotoxic than chemically cured systems, but this effect is highly dependent on the curing efficiency of the light and the type of resin system. In vivo, usage tests have been used to assess the biological response to resin composites. The pulpal inflammatory response to chemically and light-activated resin composites was low to moderate after 3 days when they were placed in cavities with approximately 0.5 mm of remaining dentin. Any reaction diminished as the postoperative periods increased to 5 to 8 weeks and was accom-panied by an increase in reparative dentin (Fig. 6.9). With a protective liner or a bonding agent, the reac-tion of the pulp to resin composite materials is mini-mal. The longer-term effects of resins placed directly on pulpal tissue are not known, but are suspected to be less favorable. Amalgam and Casting Alloys Biocompatibility of amalgam as a dental restor-ative material is thought to be determined largely FIG. 6.9 Light micrograph of the dentinal and pulpal response to unlined composite at 5 to 8 weeks in a mon-key. The primary dentin is the lighter layer seen at the top. The tubules are evident. Secondary dentin is occurring (the dark, wide middle layer), and it is closely approximated by intact odontoblasts in the pulp. Few inflammatory cells are present. The response seen in this micrograph is indicative of a favorable response to the material. (Courtesy A.K. Avery, Ann Arbor, Michigan.) 102 CRAIG’S RESTORATIVE DENTAL MATERIALS by the corrosion products released while in ser-vice. Amalgam is a complex metallic material com-posed of multiple phases, and its corrosion, in turn, depends on the type of amalgam, whether it contains the tin-mercury γ2 phase, and its composition. In cell culture screening tests, free or nonreacted mercury from amalgam is toxic. With the addition of copper, amalgams become toxic to cells in culture, but low-copper amalgam that has set for 24 hours does not inhibit cell growth. Implantation tests show that traditional low-copper amalgams were well tolerated, but the more modern high-copper amalgams caused severe reactions when in direct contact with tissue. Unreacted mercury or cop-per leaching out from these high-copper alloys has usu-ally been the constituent leading to adverse response. An in vitro study of the effects of particulate amalgams and their individual phases on macrophages showed that all particles except γ2 are effectively phagocytized by macrophages. Cell damage was seen in treated cultures exposed to particulate γ1, the silver-mercury matrix phase of amalgams. In usage tests, the response of the pulp to amalgam in shallow cavities or in deeper but lined cavities is minimal, and amalgam rarely causes irreversible damage to the pulp. However, pain results from using amalgams in deep, unlined cavity preparations (0.5 mm or less remaining dentin), with an inflammatory response occurring after 3 days. This pain may be related to the high thermal and electrical conductivity of the material, which is sig-nificantly mitigated by the presence of a barrier of remaining dentin or an insulating material. Thus in cavities with less than 0.5 to 1.0 mm of dentin remain-ing in the floor, a base should be placed on the floor of the cavity preparation for two reasons. First, the transfer of hot and cold stimuli, primarily from food and drink, through the amalgam may be substantial. Second, margins of newly placed amalgam restora-tions show significant microleakage. Marginal leak-age of salivary and microbial products is probably enhanced by the natural daily thermal cycle in the oral cavity, which may expand and contract the mar-ginal gap leading to a percolation of fluids. Although long-term sealing of the margins occurs through the buildup of corrosion products, the timeframe over which this occurs is somewhat a function of the com-position of the amalgam, being longer for the high-copper amalgams in use today. Usage tests reported that after 3 days, the pulpal response to high-copper amalgams appears similar to that elicited by low-copper amalgams in deep, unlined cavities. At 5 weeks they provoked only slight pulpal response. At 8 weeks the inflammatory response was reduced. Bacterial tests on the high-copper amalgam pellets have revealed little inhibi-tory effect on serotypes of Streptococcus mutans, thus suggesting that metallic elements were not released in amounts necessary to kill these microorganisms. Although the high-copper amalgams seem biologi-cally acceptable in usage tests, liners are suggested for all deep cavities. Again, this may be related more to a need for thermal and electrical insulation than a concern over toxicity. Further, the diffusion of released metallic elements into the tooth structure produces discoloration, and may be minimized by the presence of an intervening liner. There are also reports of inflammatory reactions of the dentin and pulp, similar to the reactions to many other restor-ative materials. Mercury has been found in the lysosomes of macrophages and fibroblasts in some patients with lesions. Cast alloys have been used for single restora-tions, fixed partial dentures, ceramic-metal crowns, and removable partial dentures. The gold content in these alloys ranges from 0 wt% to 85 wt%. These alloys contain several other noble and nonnoble metals that may have an adverse effect on cells if they are released from the alloys. However, metal ions released from these materials are most likely in contact with gingival and mucosal tissues, whereas the pulp is more likely to be affected by the cement retaining the restoration. Glass Ionomers Glass ionomer has been used as a cement (luting agent), liner, base, and restorative material. Light-cured ionomer systems use HEMA or other mono-mers or oligomers as additives or as pendant chains on the polyacrylic acid main chain. In screening tests, freshly prepared ionomer is mildly cytotoxic, but this effect is reduced over time. The fluoride release from these materials, which may have some therapeutic value, has been implicated in this cytotoxicity in vitro. Some researchers have reported that certain systems are more cytotoxic than others, and though the rea-sons for this are not clear, presumably it is related to the composition of the glasses used in the material, which may contain aluminum, calcium, manganese, zinc, strontium, and other metallic elements. The overall pulpal biocompatibility of glass iono-mer materials has been attributed to the weak acidic nature of the polyacrylic acid, as well as to its high molecular weight. Thus polyacrylic acid is unable to diffuse through dentin due to its large size. In usage tests the pulp reaction to these cements is mild, and histological studies show that any inflammatory infiltrate from ionomer is minimal or absent after 1 month. There have been several reports of pulpal hyperalgesia for short periods (days) after placing glass ionomers in cervical cavities. This effect is prob-ably the result of increased dentin permeability after acid etching. In any case, glass ionomer has not been shown to be well tolerated when placed directly upon living pulp tissue as a direct pulp-capping agent. 103 6. Biocompatibility and Tissue Reaction to Biomaterials As previously discussed with dentin-bonding agents, acidic dental materials have the capacity for demineralizing dentin and therefore releasing bioac-tive molecules present within this tissue. Although this effect has not been shown specifically for glass ionomers to date, it seems reasonable to assume that it does occur clinically. In a recent study in nonhu-man primates, dentin matrix proteins were shown to enhance the formation of reactionary dentin over exposed pulps, compared with calcium hydroxide or resin-modified glass ionomer. Although the response to resin-modified glass ionomer was less consis-tent than calcium hydroxide, in many cases it did result in new dentin formation, even when directly exposed to the pulp. It is important to note that the natural tooth repair process producing reactionary dentin does occur, following an initial inflamma-tory reaction, under glass ionomer when the material is placed over an existing dentin surface. Thus it is possible that the repair process is again aided by the presence of the bioactive molecules released from the dentin by the mild demineralization produced by the material under these conditions. Liners, Varnishes, and Nonresin Cements Calcium hydroxide cavity liners come in many forms, typically as pastes with a very alkaline pH (>12). Resin-containing preparations also exist and are capable of light-activated polymerization. The high pH of calcium hydroxide in suspension leads to extreme cytotoxicity in screening tests. Calcium hydroxide cements containing resins cause mild-to-moderate cytotoxic effects in tissue culture in both the freshly set and long-term set conditions. Inhibition of cell metabolism is reversible in tissue culture by high levels of serum proteins, suggesting that pro-tein binding or buffering in inflamed pulp tissue may play an important role in detoxifying these materi-als in vivo. The initial response after exposing pulp tissue to these highly alkaline aqueous pulp-capping agents is necrosis to a depth of 1 mm or more. The alkaline pH also helps to coagulate any hemorrhagic exudate of the superficial pulp. Shortly after necrosis occurs, neutrophils infiltrate into the subnecrotic zone. After 5 to 8 weeks, only a slight inflammatory response remains. Within weeks to months, however, the necrotic zone undergoes dystrophic calcification, which appears to be a stimu-lus for dentin bridge formation. When resins are incorporated into the compound, these calcium hydroxide compounds become less irritating and are able to stimulate dentin bridge formation more quickly than the Ca(OH)2 suspen-sion alone. Significantly, this occurs with no zone of necrosis, and reparative dentin is laid down adjacent to the liner (Fig. 6.10). This indicates that replace-ment odontoblasts form the dentin bridge in contact with the liner. However, some of these materials evidently break down with time and create a gap between the restoration and the cavity wall. Resin-containing calcium hydroxide pulp-capping agents are the most effective liners now available for treat-ing pulp exposures, and after treatment, the unin-fected pulp undergoes a relatively uncomplicated wound-healing process. Recent evidence suggests that calcium hydroxide placed on residual dentin in a tooth preparation may also have a stimulating effect on dentin remineral-ization through the solubilization of noncollagenous proteins, including growth factors such as trans-forming growth factor-beta-1 (TGF-β1), and glycos-aminoglycans from the dentin. Mineral trioxide aggregate (MTA) has the same effect, and possibly to an even greater degree. This is perhaps not surpris-ing because the main soluble component from MTA has been shown to be calcium hydroxide. Thus when FIG. 6.10 Light micrograph of a dentin bridge that has formed between a material and the pulp in a monkey. Initially, the pulp of the tooth was purposely exposed (top right) with a bur. The exposure was covered with a calcium hydroxide pulp-capping agent for 5 weeks before histologi-cal evaluation. A layer of secondary dentin has formed at the site of the pulp exposure, forming a dentin bridge. Some inflammatory cells are evident under the bridge, but the pulpal response is generally favorable. (Courtesy D.R. Heys, Ann Arbor, Michigan.) 104 CRAIG’S RESTORATIVE DENTAL MATERIALS placed in contact with dentin, these materials may cause the release of these bioactive molecules, which then serve as signaling agents to recruit undifferenti-ated cells to the wound site. These cells may then differentiate to odontoblast-like cells that begin the process of dentin bridge for-mation described earlier. Evidence exists both in cell culture and in situ that pulp cells exposed to MTA undergo proliferation and migration, followed by differentiation to odontoblast-like cells. Further, studies have shown that MTA-derived products can stimulate osteoblast-like cells and fibroblasts to express proteins, such as osteonectin, osteocalcin, and osteopontin, which are involved with extracel-lular matrix formation and mineralization. Thus the mode of dentin bridge formation under materials such as calcium hydroxide and MTA may be more complex than simply a reaction to an elevated pH stimulus. Numerous investigators have analyzed the effects of applying thin liners such as resin-based copal var-nishes and polystyrenes under restorations. These materials are not generally used under resin-based materials, because resin components dissolve the thin film of varnish. Because liners are used in such thin layers, they do not provide thermal insulation, but initially isolate the dentinal tubule contents from the cavity preparation. They may also reduce pen-etration of bacteria or chemical substances for a time. However, because of the thinness of the film and for-mation of pinpoint holes, the integrity of these mate-rials is not as reliable as that of other cavity liners applied in a greater thickness. Zinc phosphate has been widely used as a cement for seating castings and fixing orthodontic bands, and as a thermal insulating base under metallic den-tal restorations, because the thermal conductivity of this cement is approximately equal to that of enamel and is considerably less than that of metals. In vitro screening tests indicate that zinc phosphate cement elicits strong-to-moderate cytotoxic reactions that decrease with time. Leaching of zinc ions and a low pH may explain these effects. The dilution of leached cement products by dentin filtration has been shown to protect the pulp from most of these cytotoxic effects. Focal necrosis, observed in implantation tests with zinc phosphate cements injected into rat pulp, confirms the cytotoxic effects of this cement when it contacts pulp tissue. In usage tests in deep cavity preparations, moderate-to-severe localized pulpal damage is produced within 3 days, probably because of the initial low pH (4.2 at 3 minutes). However, the pH of the set cement approaches neutrality after 48 hours. By 5 to 8 weeks, only mild chronic inflam-mation is present, and reparative dentin has usually formed. Because of the initially painful and damag-ing effects on the pulp by this cement when placed in deep cavity preparations, the placement of a protec-tive layer of a dentin-bonding agent, ZOE, varnish, or calcium hydroxide, is recommended in prepara-tions with minimal remaining dentin covering the pulp. Zinc polyacrylate cements (polycarboxylate cements) were developed as biocompatible and cements chemi-cally adhesive to tooth structure. In short-term tissue culture tests, cytotoxicity of freshly set and completely set cements has correlated with both the release of zinc and fluoride ions into the culture medium and with a reduced pH. Some researchers suggest that this cytotoxicity is an artifact of tissue culture because the phosphate buffers in the culture medium facilitate zinc ion leaching from the cement. Supporting this theory, cell growth inhibition can be reversed if EDTA, which chelates zinc, is added to the culture medium. Further-more, inhibition of cells decreases as the cement sets. The polymer component of the cement may also be of concern, because concentrations of polyacrylic acid above 1% appear to be cytotoxic in tissue culture tests. On the other hand, subcutaneous and bone implant tests over a 1-year period have not indicated long-term cytotoxicity of these cements. Thus other mechanisms such as buffering and protein binding of these mate-rials may neutralize these effects in vivo over time. Polyacrylate cements evoke a pulpal response simi-lar to that caused by ZOE, with a slight-to-moderate response after 3 days and only mild, chronic inflam-mation after 5 weeks. Reparative dentin formation is minimal with these cements, and thus they are recom-mended only in cavities with intact dentin in the floors of the cavity preparations. ZOE cements have been used in dentistry for many years. In vitro, eugenol from ZOE fixes cells, depresses cell respiration, and reduces nerve transmission with direct contact. Surprisingly, it is relatively innocuous in usage tests with class 5 cavity preparations. This is not contradictory for a number of reasons. The effects of eugenol are dose dependent and diffusion through dentin dilutes eugenol by several orders of magni-tude. Thus although the concentration of eugenol in the cavity preparations just below the ZOE has been reported to be 10−2 M (bactericidal), the concentration on the pulpal side of the dentin may be 10−4 M or less. This lower concentration reportedly suppresses nerve transmission and inhibits synthesis of prostaglandins and leukotrienes (antiinflammatory). In addition and as described before, ZOE may form a temporary seal against bacterial invasion. In cavity preparations in pri-mate teeth (usage tests), ZOE caused only a slight-to-moderate inflammatory reaction within the first week. This was reduced to a mild, chronic inflammatory reac-tion, with some reparative dentin formation (within 5 to 8 weeks), when cavities were deep. For this rea-son, it has been used as a negative control substance for comparison with restorative procedures in usage tests. 105 6. Biocompatibility and Tissue Reaction to Biomaterials Bleaching Agents The use of bleaching agents on vital teeth has become commonplace. These agents usually contain some form of peroxide (generally carbamide or hydrogen peroxide) in a gel that can be applied to the teeth either by a dentist or at home by a patient. The agents may be in contact with teeth for several minutes to several hours depending on the formulation of the material. Home bleaching agents may be applied for weeks to even months in some cases. In vitro studies have shown that peroxides can rapidly (within min-utes) traverse the dentin in sufficient concentrations to be cytotoxic. The cytotoxicity depends to a large extent on the concentration of the peroxide in the bleaching agent. Other studies have even shown that peroxides can rapidly penetrate intact enamel and reach the pulp in a few minutes. In vivo studies have demonstrated adverse pulpal effects from bleach-ing, and most reports agree that a legitimate concern exists about the long-term use of these products on vital teeth. In clinical studies, the occurrence of tooth sensitivity is very common with the use of these agents, although the cause of these reactions is not known. Bleaching agents will also chemically burn the gingiva if the agent is not sequestered adequately in the bleaching tray. This is not a problem with a properly constructed tray, but long-term, low-dose effects of peroxides on the gingival and periodontal tissues have not been completely elucidated. Reaction of Other Oral Soft Tissues to Restorative Materials Restorative materials may cause reactions in the oral soft tissues such as the gingiva. It is not clear how much of the in vivo cytotoxicity observed is caused by the restorative materials and how much is caused by products of bacterial plaque that accu-mulate on teeth and restorations. In general, con-ditions that promote retention of plaque, such as rough surfaces or open margins, increase inflam-matory reactions around these materials. However, released products from restorative materials also contribute either directly or indirectly to this inflam-mation. This is particularly true in areas where the washing effects of saliva are minimal, such as in interproximal areas, in deep gingival pockets, or under removable appliances. Several studies have documented increased inflammation or recession of gingiva adjacent to restorations where plaque indi-ces are low. In these studies, released products from materials could cause inflammation in the absence of plaque or could inhibit formation of plaque and cause inflammation in gingiva. In vitro research has shown that components from dental materials and plaque may synergize to enhance inflammatory reactions. Cements exhibit some soft-tissue cytotoxicity in the freshly set state, but this decreases substantially over time. The buffering and protein-binding effects of saliva appear to mitigate these cytotoxic effects. Resin composites in direct contact with fibroblasts are initially very cytotoxic in vitro. This cytotoxicity most likely results from unpolymerized components in the air-inhibited layer that leach out from the mate-rials. Other in vitro studies, in which the composites were aged in artificial saliva for up to 6 weeks, have shown that toxicity diminishes with some materials but remains high for others. Some composites with non-Bis-GMA and non-UDMA matrices have sig-nificantly lower cytotoxicity in vitro, presumably because of lower amounts of leached components. Polished composites show markedly less cytotoxic-ity in vitro, although some materials are persistently toxic even in the polished state. Recently, there has been significant controversy about the ability of bisphenol A and bisphenol A dimethacrylate to cause estrogen-like responses in vitro. These compounds are basic components of many commercial composites. However, there is no evidence that xenoestrogenic effects are a con-cern in vivo from any commercial resin. Relatively little is known about other in vivo effects of released components of composites on soft tissues, although the concerns are similar to those regarding denture base resin and soft liners (see later discussion in this section). There is some evidence that methacrylate-based composite components may cause significant rates of hypersensitivity, although few clinical trials exist. Amalgams have been extensively used for 150 years. In spite of its substantial history, however, periodically concern arises about the biocompatibility of amalgam. Allergic reactions to amalgam restorations are rare, although there are case reports of allergic contact der-matitis, gingivitis, stomatitis, and remote cutaneous reactions. Such responses usually disappear in a few days or, if not, on removal of the amalgam or with use of a cavity liner. Other local or systemic effects from mercury contained in dental amalgam have not been demonstrated. No well-conducted scientific study has conclusively shown that dental amalgam, placed and used correctly, produces any ill effects. Despite this, a global consensus has been reached to phase down the use of mercury in all industries, dentistry included. Thus amalgam use continues to decline throughout the world, and this in large part is due to environmen-tal concerns over mercury contamination in the air, water, and soil. In patients with oral lesions near amalgam sites, positive patch tests have been reported. However, the appropriate patch test has still not been determined. Amalgam restorations carried into the gingival crev-ice may cause inflammation of the gingiva because 106 CRAIG’S RESTORATIVE DENTAL MATERIALS of products of corrosion or bacterial plaque. Seven days after placing an amalgam, a few inflammatory cells appear in the gingival connective tissue, and hydropic degeneration of some epithelial cells may be seen. Some proliferation of epithelial cells into the connective tissue may also occur by 30 days, and chronic mononuclear cell infiltration of connective tissue is evident. Increased vascularity persists, with more epithelial cells invaginating into the connec-tive tissue. Some of these changes may be a chronic response of the gingiva to plaque on the margins of the amalgam. Nevertheless, corrosion products from amalgam cannot be ruled out at this time because implanted amalgams produce similar responses in connective tissues in animals. In addition, although copper enhances the physical properties of amalgam and is bactericidal, it is also toxic to host cells and causes severe tissue reactions in implantation tests. There is literature that shows that amalgam and resin composites release cytotoxic materials that cause tissue responses, at least at sites of implanta-tion. However, in general, implantation tests show that the material is fairly well tolerated in soft and hard tissues. For materials that are placed where they are rinsed in saliva, these cytotoxic agents are prob-ably washed away before they harm the gingiva. However, rough surfaces on these types of resto-rations have been associated with increased inflam-mation in vivo. Usage tests in which restorations were extended into the gingival crevice have shown that finished materials gave a much milder inflam-matory response than unfinished materials. The detrimental effect of surface roughness has been attributed to the increased plaque retention on these surfaces. However, rough surfaces on alloy restora-tions have also been shown to cause increased cyto-toxic effects in vitro, where plaque was absent. This and other in vitro studies would again suggest that the cytotoxic response to alloys may be associated with release of elements from the alloys, and that the increased surface area of a rough surface may enhance release of these elements. In another series of studies, low- and high-copper amalgam powders and various phases of amalgam were implanted subcutaneously in guinea pigs. After 1.5 to 3 months, fine secondary particles con-taining silver and tin were distributed throughout the lesions. These gave rise to macroscopic tattooing of the skin. Secondary material and small, degrad-ing, primary particles from both types of amalgam were detected in the submandibular lymph nodes. Elevated mercury levels were detected in the blood, bile, kidneys, liver, spleen, and lungs, with the highest concentrations found in the renal cortex. In another study, primates received occlusal amalgam fillings or maxillary bone implants of amalgam for 1 year. Amalgam fillings caused deposition of mercury in the spinal ganglia, anterior pituitary, adrenal, medulla, liver, kidneys, lungs, and intestinal lymph glands. Maxillary amalgam implants released mer-cury into the same organs, except for the liver, lungs, and intestinal lymph glands. Organs from control animals were devoid of precipitate. However, neither of these studies, nor any other, has demonstrated any changes in biochemical function of any of the laden organs. Note that studies using powdered amalgam likely overestimate the amount of breakdown products, and therefore biological response, because the sur-face area of powders can be 5 to 10 times the surface area of a solid component. It must also be empha-sized that any reaction to amalgam, whether in cell culture, local tissue response, or systemic response, does not necessarily imply a reaction to mercury. Such reactions could be in response to some other constituent of the amalgam or corrosion product. For example, in vitro cell culture testing that measured fibroblasts affected by various elements and phases of amalgams has shown that pure copper and zinc show greater cytotoxicity than pure silver and mer-cury. Pure tin has not been shown to be cytotoxic (Fig. 6.11). The γ1 phase is moderately cytotoxic. Cytotoxicity is decreased by the addition of 1.5% and 5% tin (Fig. 6.12). However, the addition of 1.5% zinc to γ1 containing 1.5% tin increases cytotoxicity to the same level as that of pure zinc. Whenever zinc is present, higher cytotoxicity is revealed. High-copper amalgams show the same cytotoxicity as a zinc-free, low-copper amalgam. The addition of selenium does not reduce amalgam cytotoxicity, and excessive additions of selenium increase cytotoxicity. The cyto-toxicity of amalgams decreases after 24 hours, pos-sibly from the combined effects of surface oxidation and further amalgamation. The results of this study 300 250 200 150 Ag Affected area (mm2) 100 50 0 Cu Sn Zn Hg Element FIG. 6.11 Quantitative representation of the affected areas of fibroblasts reveals the magnitude of cytotoxicity of amalgam elements. Standard deviations are represented by vertical bars. Ag, Silver; Cu, copper; Hg, mercury; Sn, tin; Zn, zinc. (From Kaga M, Seale NS, Hanawa T, et al. Cytotoxicity of amalgams, alloys, and their elements and phases. Dent Mater. 1991;7(1):68–72.) 107 6. Biocompatibility and Tissue Reaction to Biomaterials suggest that the major contributor to the cytotoxic-ity of amalgam alloy powders is probably copper, whereas that for amalgam is zinc. Casting alloys have a long history of in vivo use with a generally good record of biocompatibility. Some questions about the biological liability of ele-mental release from many of the formulations devel-oped in the past 10 years have arisen, but there is no clinical evidence that elemental release is a problem, aside from hypersensitivity. Nickel allergy is a rela-tively common problem, occurring in 10% to 20% of females. It is a significant risk from nickel-based alloys, because release of nickel ions from these alloys is generally higher than for noble or high-noble alloys. Stainless steels, commonly used in pre-formed pediatric crowns and orthodontic appliances, also contain a significant concentration of Ni in their composition. Palladium sensitivity has also been a concern in some countries, although the incidence of true palladium allergy is one-third that of nickel allergy. While it has been clinically documented that patients with palladium allergy are virtually always allergic to nickel, the converse is not true. Numerous in vitro studies have examined the effects of metal ions on cells in the gingival tissues, such as epithelial cells, fibroblasts, and macrophages. For the most part, the concentrations of metal ions required to cause problems with these cells in vitro are greater than those released from most casting alloys. However, some recent research has shown that extended exposures to low doses of metal ions may also have biological liabilities. This is notewor-thy because the low-dose concentrations approach those known to be released from some alloys. The clinical significance of this research, however, is not known. Denture base materials, especially methacrylates, have been associated with immune hypersensitivity reactions of gingiva and mucosa more than any other dental material. The greatest potential for hypersen-sitization is for dental and laboratory personnel who are exposed repeatedly to a variety of unreacted components. Hypersensitivity has been documented to the acrylic and diacrylic monomers, certain cur-ing agents, antioxidants, amines, and formaldehyde. For patients, however, most of these materials have undergone the polymerization reaction, and the inci-dence of hypersensitization is quite low. Screening tests for sensitization potential include testing the unreacted ingredients, the polymeric substance after reaction, and oil, saline, or aqueous extracts of the polymer using the in vitro tests previously described. In addition to hypersensitivity, visible light-cured denture base resins and denture base resin sealants have been shown to be cytotoxic to epithelial cells in culture. Soft-tissue responses to soft denture liners and denture adhesives are of concern because these mate-rials are used in intimate contact with the gingiva. Plasticizers, incorporated into some materials to make them soft and flexible, are released in vivo and in vitro. Cell culture tests have shown that some of these materials are extremely cytotoxic and affect a number of cellular metabolic reactions. In animal tests, several of these materials have caused signifi-cant epithelial changes, presumably from the released plasticizers. In usage, the effects of the released plas-ticizers are probably often masked by the inflamma-tion already present in the tissues onto which these materials are placed. Denture adhesives have been evaluated in vitro and show severe cytotoxic reac-tions. Several had substantial formaldehyde content. The adhesives also allowed significant microbial growth. Newer formulations that add antifungal or antibacterial agents have not yet been shown to be clinically effective. Reaction of Bone and Soft Tissues to Implant Materials Interest in the biocompatibility of implant materi-als has grown because the use of implants in clini-cal practice has increased dramatically. Successful dental implant materials either promote osseointe-gration or biointegration (see Dental and Orofacial Implants, Chapter 15). Reactions to Ceramic Implant Materials Ceramic materials may be conveniently divided into two groups: bioactive materials and nonbioactive ceramics. Most ceramic implant materials have very low toxic effects on tissues, because they are already in an oxidized state and are highly corrosion resis-tant. As a group, not only are they minimally toxic but they also are nonimmunogenic and noncarci-nogenic. Nonbioactive ceramic materials generally 300 250 A: 1 B: 1 1.5%Sn C: 1 5%Sn D: 1 1.5%Sn 1.5%Zn E: 2 F: Y 200 150 Affected area (mm2) 100 50 0 A B C E F D Amalgam phase FIG. 6.12 Quantitative representation of the affected areas of fibroblasts reveals the magnitude of cytotoxicity of amalgam phases. Standard deviations are represented by vertical bars. (From Kaga M, Seale NS, Hanawa T, et al. Cytotoxicity of amalgams, alloys, and their elements and phases. Dent Mater. 1991;7(1):68–72.) 108 CRAIG’S RESTORATIVE DENTAL MATERIALS invoke fibrous encapsulation when implanted, as mentioned earlier. Reactions to Implant Metals and Alloys Pure metals and alloys are the oldest type of oral implant materials. Initially, metallic implant materi-als were selected based on strength and ease of fab-rication. Over time, however, biocompatibility with bone and soft tissue and the longevity of the implant have become more important. Although a variety of implant materials have previously been used (includ-ing stainless steel and chromium-cobalt-molybde-num), the only metallic dental implant materials in common use today are titanium-based alloys. Titanium is a pure metal when initially cast. However, in less than a second the surface forms a thin conformal layer of various titanium oxides. This oxide layer is corrosion resistant and allows bone to osseointegrate. A major disadvantage of this metal is that it is difficult to cast. It has been wrought into various forms, but this process introduces metallic impurities into the surface that may adversely affect bone cell response unless extreme care is taken dur-ing manufacturing. Titanium implants have been used with success as root forms to support a pros-thesis. With frequent recall and good oral hygiene, implants have been maintained in healthy tissue for longer than three decades. Titanium-aluminum-vanadium alloys (Ti-6Al-4V) have been used success-fully in this regard as well. This alloy is significantly stronger than commercially pure titanium, and has better fatigue resistance, but has the same desirable stiffness and thermal properties as the commercially pure (CP) metal. Although titanium and titanium alloy implants have corrosion rates that are markedly less than other metallic implants, they do release tita-nium into the body. Currently, there is no evidence that released titanium ions are a problem locally or systemically. However, questions remain about the liability of released aluminum and vanadium from alloys. In soft tissue, the bond epithelium forms with titanium is morphologically similar to that formed with the tooth, but this interface has not been fully characterized. Connective tissue apparently does not bond to the titanium, but does form a tight seal that seems to limit ingress of bacteria and bacterial products. Techniques are being developed to limit down-growth of the epithelium and loss of bone height around the implant, because this will ulti-mately cause implant failure. Periimplantitis is now a documented disease around implants and involves many of the same bacteria as periodontitis. The role of the implant material or its released components in the progression of periimplantitis is not known, but this disease is considered to be a major contributor to implant failure and the subject of much investigation. Reactions to Resorbable Materials With the survival of implanted materials for decades or more, the predominant thought began to shift in emphasis from achieving a benign (or tolerated) tis-sue response to instead producing bioactive materi-als that could elicit a controlled action and reaction in the physiological environment. Continuing in this vein was the development of resorbable bio-materials that exhibit clinically appropriate, con-trolled chemical breakdown and resorption. In these materials, the problem of a tissue-material interface is resolved, because the materials provoke a physiologic response to replace the material with regenerated tissues. One of the earliest examples of these materials was the development of resorbable sutures. These materials were composed of a copo-lymer of polylactic acid (PLA) and polyglycolic acid (PGA). When implanted in the body, they undergo a hydrolytic decomposition into CO2 and H2O. By the mid-1980s, clinical use of resorbable polymeric sutures was commonplace. Resorbable fracture fixa-tion plates and screws, guided tissue membranes, and controlled drug-release systems have rapidly followed. Although generally well tolerated by tis-sues in vivo, the resorbability of these materials depends on the volume of material implanted and because these materials degrade into acidic by-prod-ucts, the subsequent drop in pH in the surrounding tissues may invoke an inflammatory response. Other polymeric materials such as polycaprolactone, and hyaluronan derivatives, as well as natural polymers such as cross-linked collagen, starch, and cellulose are currently being investigated for their ability to resorb in vivo after serving their function as an implant. SUMMARY Biocompatibility of a dental material depends on its composition, location, and interactions with the oral cavity. Metal, ceramic, and polymer materials elicit different biological responses because of differences in composition. Furthermore, diverse biological responses to these materials depend on whether they release their components and whether those compo-nents are toxic, immunogenic, or mutagenic at the released concentrations. The location of a material in the oral cavity partially determines its biocompat-ibility. Materials that are biocompatible in contact with the oral mucosal surface may cause adverse reactions if they are implanted beneath it. Materials that are toxic in direct contact with the pulp may be essentially innocuous if placed on dentin or enamel. Finally, interactions between the material and the body influence the biocompatibility of the material. A material’s response to changes in pH, application 109 6. Biocompatibility and Tissue Reaction to Biomaterials of force, or the effect of biological fluids can alter its biocompatibility. 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Initial biological testing of root canal sealing materials—a critical review. J Dent. 1992;20: 259. Whitford GM. The physiological and toxicological charac-teristics of fluoride. J Dent Res. 1990;69:539. Williams DF. Toxicology of ceramics. In: Williams DF, ed. Fundamental Aspects of Biocompatibility. vol. 2. Boca Raton, FL: CRC Press; 1981. This page intentionally left blank 113 Dental biomaterials are generally categorized into four classes: metals, polymers, ceramics, and com-posites. The four classes are distinctly different from each other in terms of density, stiffness, trans-lucency, processing method, application, and cost. One class, composites, is a combination of two or more classes that produces materials that can be engineered for specific applications. For some appli-cations, such as intracoronal and extracoronal resto-rations, several classes offer suitable materials. For other applications, such as removable partial dental denture frameworks, only one class is appropriate. Requirements such as esthetics, hardness, stiffness, and bioactivity dictate the choice of material class. Restoration design and material class are always coordinated to achieve the best patient outcome. This chapter is organized into four sections by the class of material. Fundamental concepts of each class are presented here. Additional detail is pro-vided in other chapters when specific applications are discussed. METALS AND ALLOYS Metals and alloys are used in almost all aspects of dental practice, including the dental laboratory, direct and indirect dental restorations, implants, and instruments used to prepare and clean teeth. Metals and alloys have optical, physical, chemical, thermal, and electrical properties that are unique among the basic types of materials and suitable for many den-tal applications. Although tooth-colored materials are often desired for restorations, metals provide strength, stiffness, fracture resistance, and longevity for long-term dental applications that are often not achievable with other classes of materials. Evidence in the scientific literature of clinical performance is the most extensive for this material class. As a class, metals are ductile and malleable and therefore exhibit elastic and plastic behavior; they are good electrical and thermal conductors, are higher in density than other classes, exhibit good fracture resis-tance, are opaque, and can be polished to a luster. Metals may be cast, drawn into wires, or machined to create dental restorations and instruments. CHEMICAL AND ATOMIC STRUCTURE OF METALS A metal is any element that ionizes positively in solu-tion. As a group, metals constitute nearly two-thirds of the periodic table (Fig. 7.1). During ionization, metals release electrons. This ability to exist as free, positively charged, stable ions is a key factor in the behavior of metals and is responsible for many metal-lic properties that are important in dentistry. Another important group of elements shown in Fig. 7.1 are the metalloids, including carbon, silicon, and boron. Although metalloids do not always form free positive ions, their conductive and electronic properties make them important components of many dental alloys. Atomic Structure At the atomic level, pure metals exist as crystalline arrays (Fig. 7.2) that are continuous in three dimen-sions. In these arrays, the nuclei and core electrons occupy the atomic center with the ionizable elec-trons floating freely among the atomic positions. The mobility of the valence electrons is responsible for many properties of metals, such as electrical con-ductivity. It is important to note that the positively charged atomic centers are held together by the elec-trons and their positive charge is simultaneously neutralized by the negative electrons. Thus pure metals have no net charge. The relationships between the atomic centers in a metallic crystalline array are not always uniform in all directions. The distances in the x, y (horizontal), and z (vertical) axes may be the same or different, C H A P T E R 7 General Classes of Biomaterials 114 CRAIG’S RESTORATIVE DENTAL MATERIALS and the angles between these axes may or may not be 90 degrees. In all, six crystal systems occur (Fig. 7.3), and they can be further divided into 14 crystal-line arrays. Metallic nuclei may occur at the center of faces or vertices of the crystal. Within each array, the smallest repeating unit that captures all the rela-tionships among atomic centers is called a unit cell (see Fig. 7.2). The unit cells for the most common arrays in dental metals are shown in Fig. 7.4. In the body-centered cubic (BCC) array, all angles are 90 degrees and all atoms are equidistant from one another in the horizontal and vertical directions. Metallic atoms are located at the corners of the unit cell, and one atom is at the center of the unit cell (hence the name body-centered cubic). This is the crystal structure of iron and is common for many iron alloys. The face-centered cubic (FCC) array has 90-degree angles and atomic centers that are equidistant horizontally and vertically (as does the BCC), but atoms are located in FIG. 7.2 A typical metallic crystal lattice, in this case a body-centered cubic lattice. Every lattice has a unit cell (shown in bold) that extends (repeats) in three dimensions for large distances. Electrons are only relatively loosely bound to atomic nuclei and core electrons. The nuclei occupy spe-cific sites (shown as dots in the unit cell) in the lattice, whereas the electrons are relatively free to move about the lattice. In reality, the metal atoms are large enough to touch each other. Cubic Simple Body-centered Face-centered Triclinic Tetragonal Simple Body-centered Rhombohedric Orthorhombic Simple ∗Body-centered ∗Face-centered Base-centered ∗Hexagonal Monoclinic Simple Base-centered FIG. 7.3 Lattice structures. All metals occur in one of the lattice structures shown. There are six families of lattices, four of which can be subdivided. Each family is defined by the distances between vertices and the angles at the ver-tices. The body-centered cubic, face-centered cubic, and hexagonal lattices (asterisks) are the most common in dental alloys and pure metals. H Li Na K Rb Cs Fr Ra Ba Sr Ca Ac La Y Sc Hf Zr Nb Ti Mg Be W Mo Re Tc Cr V Os Ru Fe Mn Ir Rh Pt Pd Co Au Ag Cu Ni Hg Cd Tl In Zn Pb Sn Ge Ga Bi Sb Po Te As At I Br Rn Xe Kr Se Th Ce Pa Pr U Np Nd Pu Am Sm Pm Cm Gd Eu Bk Cf Tb Es Ho Dy Fm Md Er No Yb Tm Lr Lu Si Al P Cl Ar S C B N F Ne O He Ta FIG. 7.1 Periodic table of elements. The periodic table of the elements can be subdivided into metals (blue backgrounds), metalloids (purple backgrounds), and nonmetals (yellow backgrounds). Elements in nonbolded type are used in dental alloys or as pure metals. The metals are elements that ionize positively in solution and comprise the majority of elements in the periodic table. Note that not all elements are shown. Hydrogen is often included in group IA (left column) because it forms compounds with oxidation numbers of both +1 and −1. In addition, under very high pressures, hydrogen exhibits the prop-erties of a metal. The single asterisk indicates the insertion point in the table for the lanthanide series of elements, whereas the double asterisk indicates the insertion point for the actinide series of elements. (From The American Chemical Society.) 115 7. General Classes of Biomaterials the centers of the faces with no atom in the center of the unit cell (hence the name face-centered cubic). Most pure metals and alloys of gold, palladium, cobalt, and nickel exhibit the FCC array. Titanium exhibits the more complex hexagonal close-pack array. In this array, the atoms are equidistant from each other in the horizontal plane, but not in the vertical direction. In a metallic crystal, the atomic centers are posi-tively charged because the free valence electrons float in the crystal. Although we might expect the atomic centers to repel each other, the freely floating elec-trons bind the centers together and create a strong force between the atomic centers. This is known as the metallic bond and is a fundamentally important type of primary bond. The metallic bond is funda-mentally different from other primary bonds, such as covalent bonds that occur in organic compounds, and ionic bonds that occur in ceramics. Physical Properties of Metals All properties of metals result from the metallic crystal structure and metallic bonds. In general, metals have high densities that result from the efficient packing of atomic centers in the crystal lattice. Metals are electri-cally and thermally conductive because of the mobility of the valence electrons in the crystal lattice. The opacity and reflective nature of metals result from the ability of the valence electrons to absorb and emit light. Melting occurs as the metallic bond energy is overcome by the applied heat. Interestingly, the number of valence electrons per atomic center influences the melting point somewhat. As the number of valence electrons increases, the metallic bond develops some covalent character that contributes to higher melting points. This phenomenon occurs for iron (Fe3+) and nickel (Ni2+). The corrosion properties of metals depend on the ability of atomic centers and electrons to be released in exchange for energy. The amount of energy required depends on the strength of the metallic force, which is related to the freedom of the valence electron, and the energy that the released ion can gain by solvating in solution. For metals such as sodium and potassium, the metallic bond is weaker because the valence electrons are loosely held, and the energy of solvation is high. Thus these metals corrode into water with explosive energy release. For metals such as gold and platinum, the metallic bond is stronger; valence electrons are more tightly held, and solvation energies are relatively low. Thus gold and platinum are far less likely to corrode. The corrosion of met-als always involves oxidation and reduction. The released ion is oxidized because the electrons are given up, and the electrons (that cannot exist alone) are gained by some molecules in the solution (that are therefore reduced). Because the distances between metal atoms in a crystal lattice may be different in the horizontal and vertical directions (see Fig. 7.4), properties such as conductivity of electricity and heat, magnetism, and strength may also vary by direction if a single crystal is observed. These directional properties of metals and metalloids have been exploited in the semicon-ductor industry to fabricate microchips for comput-ers. However, in dentistry, a single crystal is rarely observed. Rather, a collection of randomly oriented crystals, each called a grain, generally make up a dental alloy. In this case, the directional properties are averaged across the material. In general, a fine-grained structure is desirable to encourage alloys with uniform properties in any direction. Nonuniformity of directional properties is termed anisotropy. Like the physical properties, the mechanical prop-erties of metals are also a result of the metallic crystal structure and metallic bonds. Metals generally have good ductility (ability to be drawn into a wire) and mal-leability (ability to be hammered into a thin sheet) rela-tive to polymers and ceramics. To a large extent, these properties result from the ability of the atomic centers to slide against each other into new positions within the same crystal lattice. Because the metallic bonds are essentially nondirectional, such sliding is possible. If the metallic crystals were perfect, calculations have shown that the force required to slide the atoms in the lattice would be hundreds of times greater than experiments indicate. Less force is necessary because the crystals are not perfect; they have flaws called dislocations. Dislocations allow the atomic centers to A B C FIG. 7.4 The three most common crystal lattice unit cells in dental metals and alloys. (A) Body-centered cubic cell; (B) face-centered cubic cell; and (C) hexagonal close-packed cell. The atoms (circles) in all three cases would be larger and touching each other. They were drawn smaller to make the structures easier to visualize. 116 CRAIG’S RESTORATIVE DENTAL MATERIALS slide past each other one plane at a time (Fig. 7.5). Because movement can occur one plane at a time, the force required is much less than if the forces of all the planes have to be overcome simultaneously. An analogy is moving a large heavy rug by forming a small fold or kink in the rug and pushing the fold from one end of the rug to the other. Dislocations are of several types, but all serve to allow the relatively easy deformation of metals. All methods for increas-ing the strength of metals act by impeding the move-ment of dislocations. Metals fracture when the atomic centers cannot slide past one another freely. For example, this fail-ure can happen when impurities block the flow of dislocations (Fig. 7.6). The inability of the dislocation to be moved through the solid results in the lattice rupturing locally. Once this small crack is started, it takes little force to propagate the crack through the lattice. An example illustrates this idea. Consider a plate of steel 15 cm wide and 6 mm thick. Suppose it has a 5-cm crack running into one side. The force required to make the crack run the remaining 10 cm would be about 1800 newtons (N). Without the aid of the crack, 2.2 million newtons (MN) would be required if the steel were the best commercial grade available. If the steel were a single, flawless crystal, 44 MN would be necessary! The fracture of metals depends heavily on dislocations and the local rup-ture of the crystal lattice. POLYMERS Polymers are commonly used for applications such as tooth restoratives, sealants, cements, orthodontic space maintainers and elastics, obturators for cleft pal-ates, impressions, provisional restorations, root canal filling materials, denture bases, and athletic mouth protectors. In addition, polymers are typically one of the components of the fourth class of material, com-posites, which are discussed later in this chapter. As a class, polymers are formable, can be made translucent or opaque, are low in density and hardness compared with metals, and are poor conductors of temperature and electricity. Of the four classes of materials pre-sented, polymers have the lowest stiffness, lowest long-term stability in an aqueous environment, and the lowest melting or glass transition point. Basic Nature of Polymers Chemical Composition The term polymer denotes a molecule that is made up of many (poly) parts (mers). The mer ending rep-resents the simplest repeating chemical structural unit from which the polymer is composed. Thus poly(methyl methacrylate) is a polymer having chemical structural units derived from methyl meth-acrylate, as indicated by the simplified reaction and structural formula I. A C B D FIG. 7.5 Sketches representing a crystal and slip mechanisms resulting from movement of a dislocation. By the dis-location moving through the metal one plane at a time (A to B to C to D), far less energy is necessary to deform the metal. Furthermore, the movement occurs without fracture or failure of the crystal lattice. CH3 O CH3 C O n or CH2 C I C n CH2 CH2 CH2 Methyl methacrylate Poly(methyl methacrylate) C O O CH3 CH3 C O CH3 CH3 C O CH2 C O CH3 CH3 C O C O CH3 CH3 C O 117 7. General Classes of Biomaterials The molecules from which the polymer is con-structed are called monomers (one part). Polymer molecules may be prepared from a mixture of differ-ent types of monomers. They are called copolymers if they contain two or more different chemical units and terpolymers if they contain three different units, as indicated by the structural formulas II and III. Methyl methacrylate–ethyl methacrylate copolymer II C CH2 C O n O CH3 CH3 CH2 C O CH3 CH2CH3 C O m C CH2 C O n O CH3 CH3 CH2 C O CH3 CH2CH3 C O m CH2 C O CH3 CH2CH2CH3 C O p Methyl-, ethyl-, propyl methacrylate copolymer or terpolymer III As a convenience in expressing the structural formulas of polymers, the mer units are enclosed in brackets, and subscripts such as n, m, and p represent the average number of the various mer units that make up the polymer molecules. Notice that in nor-mal polymers the mer units are spaced in a random Load A C Load E Load B Load D F FIG. 7.6 Sketches showing plastic shearing with crack formation at the site of an impurity (orange circles). Without the impurity (A, B, C), the load forces the dislocations completely through the lattice without fracture (note the progression of red circles from left to right). However, when the impurity is present (D, E, F), it stops the progress of the dislocation. As other dislocations build up, the lattice below them cannot accommodate and a crack forms in the lattice (E). In (E) and (F), note the broken bonds between atoms. Once formed, a crack can grow rapidly and relatively easily and lead to catastrophic failure. 118 CRAIG’S RESTORATIVE DENTAL MATERIALS orientation along the polymer chain. It is possible, however, to produce copolymers with mer units arranged so that a large number of one mer type are connected to a large number of another mer type. This special type of polymer is called a block polymer. It also is possible to produce polymers having mer units with a special spatial arrangement with respect to the adjacent units; these are called stereospecific polymers. The mers of the polymers are joined through covalent, C–C, bonds. Typically, during the polymer-ization process, C=C double bonds are converted to C–C single bonds and a mer is attached to one of the carbon atoms that was part of the C=C double bond. The next section describes various network configu-rations for mers, including cross-linking, in which chains are linked in a nonlinear configuration. Molecular Weight The molecular weight of the polymer molecule, which equals the molecular weight of the various mers multiplied by the number of the mers, may range from thousands to millions of molecular weight units, depending on the preparation condi-tions. The higher the molecular weight of the poly-mer made from a single monomer, the higher the degree of polymerization. The term polymerization is often used in a qualitative sense, but the degree of polymerization is defined as the total number of mers in a polymer molecule. In general, the molecu-lar weight of a polymer is reported as the average molecular weight because the number of repeating units may vary greatly from one molecule to another. As would be expected, the fraction of low-, medium-, and high-molecular-weight molecules in a material, or in other words, the molecular weight distribution, has as pronounced an effect on the physical proper-ties as does the average molecular weight. Therefore two poly(methyl methacrylate) specimens can have the same chemical composition but greatly different physical properties because one of the specimens has a high percentage of low-molecular-weight mol-ecules, whereas the other has a high percentage of high-molecular-weight molecules. Variation in the molecular weight distribution may be obtained by altering the polymerization procedure. These materi-als therefore do not possess any precise physical con-stants, such as melting point, as do ordinary small molecules. For example, the higher the molecular weight, the higher the softening and melting points and the stiffer the polymer. Spatial Structure In addition to chemical composition and molecular weight, the physical or spatial structure of the poly-mer molecules is also important in determining the properties of the polymer. There are three basic types of structures: linear, branched, and cross-linked. They are illustrated in Fig. 7.7 as segments of linear, branched, and cross-linked polymers. The linear homopolymer has mer units of the same type, and the random copolymer of the linear type has the two mer units randomly distributed along the chain. The linear block copolymer has segments, or blocks, along the chain, whereas the mer units are the same. The branched homopolymer again consists of the same mer units, whereas the graft-branched copolymer consists of one type of mer unit on the main chain and another mer for the branches. The cross-linked polymer shown in Fig. 7.7 is made up of a homopoly-mer cross-linked with a single cross-linking agent. The linear and branched molecules are separate and discrete, whereas the cross-linked molecules are a network structure that may result in the creation of one giant polymeric molecule. The spatial struc-ture of polymers affects their flow properties, but generalizations are difficult to make because either the interaction between linear polymer molecules or the length of the branches on the branched molecules may be more important in a particular example. In general, however, the cross-linked polymers flow at higher temperatures than linear or branched poly-mers. Another distinguishing feature of some cross-linked polymers is that they do not absorb liquids as readily as either the linear or branched materials. Thermoplastics and Thermosets An additional method of classifying polymers other than by their spatial structure is according to whether they are thermoplastic or thermosetting. The term thermoplastic refers to polymers that may be softened by heating and solidify on cooling, the pro-cess being repeatable. Typical examples of polymers of this type are poly(methyl methacrylate) and poly-ethylene-polyvinylacetate. The term thermosetting or thermoset refers to polymers that solidify during fab-rication but cannot be softened by reheating. These polymers generally become nonfusible because of a cross-linking reaction and the formation of a spatial structure. Typical dental examples are cross-linked poly(methyl methacrylate), silicones, cis-polyisoprene, and dimethacrylates. Polymers as a class have unique properties, and by varying the chemical composition, molecular weight, molecular-weight distribution, or spatial arrange-ment of the mer units, the physical and mechanical properties of polymers may be altered. Additional discussion of polymers is included in Chapter 9. CERAMICS The term ceramic refers to any product made essen-tially from a nonmetallic inorganic material usu-ally processed by firing at a high temperature to 119 7. General Classes of Biomaterials achieve desirable properties. They are oxides of metals. As a class, ceramics are hard, low in tough-ness compared to metals, stiff, poor thermal and electrical conductors, and can be cast or machined to fabricate dental restorations. The translucency and opacity of a dental ceramic can be modified for applications where color and translucency are critical. Ceramics generally demonstrate little plas-tic behavior and are thus considered brittle when compared to metals or polymers. Their stress-strain curves are generally linear with no plastic strain. Ceramics are used in restorative dentistry as full- and partial-coverage crowns, denture teeth, and as particulate fillers for resin matrix composite filling materials. The more restrictive term porcelain refers to a spe-cific compositional range of ceramic materials made by mixing kaolin, quartz, and feldspar, and firing at high temperature. Dental ceramics for ceramic-metal restorations belong to this compositional range and are commonly referred to as dental porcelains. Dental porcelain is used as veneers on metal frameworks (metal ceramic restoration) and on minimally pre-pared anterior teeth, and for denture teeth. The laboratory portion of a ceramic restoration is usually made in a commercial dental laboratory by a skilled technician working with specialized equip-ment to the shape and shade specifications provided by the dentist. Computer-aided design and manu-facturing or milling (CAD-CAM) is the basis for the Copolymer, random Homopolymer Homopolymer Block Graft Cross-Linked Polymer BRANCHED LINEAR Copolymer, random FIG. 7.7 Linear, branched, and cross-linked homopolymers and copolymers. Red circles, One type of mer unit; blue circles, another type of mer unit; dashed lines, continuation of the polymer segment. 120 CRAIG’S RESTORATIVE DENTAL MATERIALS acquisition of digital images of tooth preparations and computer-aided design of restorations. Portable milling machines under digital control mill machine-able ceramic blanks to create final restorations. Additional discussion of digital impressioning can be found in Chapter 14. The properties of dental ceramics depend on their composition, microstructure, and flaw population. The nature and amount of reinforcing crystalline phase present dictate the material’s strength and resistance to crack propagation as well as its optical properties. Ceramics are brittle and contain at least two populations of flaws: fabrication defects and sur-face cracks. The fracture mechanisms involve crack propagation from these flaws. Fabrication defects are created during processing and consist of inclusions at the condensation stage or voids generated during sintering. Inclusions are often linked to improper cleaning of the metal framework or use of unclean instruments. Porosity on the internal side of clini-cally failed glass-ceramic restorations has been iden-tified as the fracture initiation site. Microcracks also develop upon cooling in feldspathic porcelains and can be due to thermal contraction mismatch between the leucite crystals and the glassy matrix or to ther-mal shock if the porcelain is cooled too rapidly. Surface cracks are induced by machining or grind-ing. The average natural flaw size varies from 20 to 50 μm. Usually, failure of the ceramic originates from the most severe flaw. Dental ceramics are subjected to repeated (cyclic) loading in a humid environment (chewing), condi-tions that are ideal for the extension of the preexist-ing defects or cracks. This phenomenon, called slow crack growth, can contribute to a severe reduction of the survival probability of ceramic restorations. COMPOSITES Composites are a combination of two or more classes of materials. In dentistry, the most common compos-ite is a combination of a polymer and ceramic, where the polymer is used to bind ceramic particles. The polymer functions as the matrix in dental composites and the particles are reinforcing materials. Polymer matrix composites, also known as resin composites, are used as sealants, intracoronal and extracoronal restorations, provisional restorations, veneers, den-ture teeth, cements, and core buildups. As a class, dental composites are formable, can be made to be machineable, opaque or translucent, moderate in stiffness and hardness, thermal and electrical insu-lators, and sparingly soluble. Many advances have been made in particle technology and are discussed in Chapter 9. In a composite the properties are intermediate between the two compositional materials. A benefit of combining two material classes is the ability to fabricate a new material that has desirable handling properties that are not achievable with one material alone. For example, individual ceramic particles do not adhere to each other, but the addition of a poly-mer to bind them enables the composite to be used as a paste. Use of a polymer alone will not achieve suffi-cient stiffness and stability, which are properties con-tributed by the ceramic particles. The polymer used in many dental composites, bisphenol A-glycidyl methacrylate (Bis-GMA), has shown no significant health risks when used in dental resin composites. In industries and professions other than dentistry, other classes are combined to form composites, such as metal-ceramic composites used in aerospace. A commonly used material in the construction indus-try, concrete, is a composite of sand, gravel, and portland cement. As with dental resin composites, the cement in concrete is the binder for the sand and gravel particles. Composites differ from alloys in that, at the microscopic level, the individual compo-nents of the composite are visible. In the case of concrete, a limiting factor is the adhesion between the portland cement and sand-gravel particles. At the surface, the cement washes away with use, leaving the particles incompletely surrounded by cement. These particles are then eas-ily dislodged, leaving a void in the surface of the con-crete. In dental resin composites, coupling agents are used to enhance the adhesion between the ceramic particles and polymer matrix, thereby increasing its wear resistance and long-term surface integrity. During polymerization of resin composites, a volumetric contraction of the polymer matrix occurs that results in strain within the matrix. This contrac-tion strain is coupled with the increase in elastic modulus as the composite cures. The combination of contraction strain and development of elastic modu-lus produces stress within the composite because the periphery of the restoration is constrained by adhe-sion to the enamel and dentin cavity walls. Methods to reduce residual stress include the development of polymers with reduced shrinkage during cure and modifications to the clinical placement technique. More detail on the measurement of polymerization shrinkage can be found in Chapter 5 and the mecha-nism for polymerization can be found in Chapter 9. Bibliography Anusavice KJ, Shen C, Rawls HR. Phillips’ Science of Dental Materials. 12th ed. St. Louis: Saunders; 2012. Denry I, Holloway JA. Ceramics for dental applications: a review. Materials. 2010;3(1):351. Denry I, Kelly JR. State of art of zirconia for dental applica-tions. Dent Mater. 2008;24(3):299. 121 7. General Classes of Biomaterials Dieter G. Mechanical Metallurgy. 3rd ed. New York: McGraw-Hill; 1986. Flinn RA, Trojan PK. Engineering Materials and Their Applications. 4th ed. New York: John Wiley & Sons; 1990. Gettleman L. Noble alloys in dentistry. Current Opinion Dent. 1991;2:218. Höland W, Beall G. Glass-Ceramic Technology. Westerville, OH: The American Ceramic Society; 2002. Imazato S, Ma S, Chen J, Xu HK. Therapeutic polymers for dental adhesives: loading resins with bio-active compo-nents. Dent Mater. 2014;30(1):97. Kelly JR, Nishimura I, Campbell SD. Ceramics in dentistry: historical roots and current perspectives. J Prosthet Dent. 1996;75:18. Khvostenko D, Mitchell JC, Hilton TJ, Ferracane JL, Kruzic JJ. Mechanical performance of novel bioactive glass containing dental restorative composites. Dent Mater. 2013;29(11):1139. Kingery WD, Bowen HK, Uhlmann DR. Introduction to Ceramics. 2nd ed. New York: John Wiley & Sons; 1976. Lawn BR, Pajares A, Zhang Y, et al. Materials design in the performance of all-ceramic crowns. Biomaterials. 2004;25(14):2885. Malhotra ML. Dental gold casting alloys: a review. Trends Tech Contemp Dent Lab. 1991;8:73. O’Brien WJ. Recent developments in materials and pro-cesses for ceramic crowns. J Am Dent Assoc. 1985;110:547. Paravina RD, Powers JM, eds. Esthetic Color Training in Dentistry. St. Louis: Mosby; 2004. Powers JM, Wataha JC. Dental Materials: Foundations and Applications. 11th ed. St. Louis: Mosby; 2017. Rekow ED. A review of the developments in dental CAD/ CAM systems. Curr Opin Dent. 1992;2:25. Zhang Y, Lawn BR. Long-term strength of ceramics for bio-medical applications. J Biomed Mater Res. 2004;69B(2):166. This page intentionally left blank 123 Prevention is a foundation of dentistry. Low-level flu-orides in water supplies have provided tremendous benefit in reducing the incidence of dental caries in children. Fluorides can be introduced into community water supplies to ensure systemic ingestion during early life, when the teeth are forming. Fluoride can also be provided as a dietary supplement to inhibit caries where drinking water is not fluoridated. Patients who are at high risk for developing caries in spite of receiv-ing systemic fluoride can be given additional fluoride via topical application in toothpastes, mouth rinses, gels, and varnishes. A combination of systemic and topical fluoride applications has contributed to a dra-matic reduction in the prevalence of smooth surface caries since the 1960s. Pits and fissures on the occlusal surfaces of posterior teeth, however, are more resistant to fluoride uptake because of the irregular morphol-ogy of the occlusal surface. This, combined with the retention of food and the difficulty of proper brushing in the posterior segment, can lead to the start of a cari-ous lesion. A preventive therapy consisting of a sealant to fill in the occlusal irregularities can reduce the risk of caries by creating a smoother surface that is easier to clean and less likely to retain food and harbor bacteria. PIT AND FISSURE SEALANTS The most common sealants are based on bisphenol A-glycidyl methacrylate (Bis-GMA) resin and are light-cured, although some self-cured products are also available. The chemistry of Bis-GMA sealants is the same as that described for resin composites in Chapter 9. The principal difference is that sealants are much more fluid to enable them to penetrate the pits, fissures, and etched areas on the enamel, which promotes reten-tion of the sealant. The viscous Bis-GMA resin is mixed with a diluent, such as triethylene glycol dimethacry-late, to produce a reasonably low-viscosity, flowable resin. An alternative but similar oligomer base is ure-thane dimethacrylate; some materials are formulated from a combination of the two base resins. To provide stiffness to the material and improve wear resistance, filler particles of fumed silica or silanated inorganic glasses can be added to form low-viscosity composites. Light-Cured Sealants The polymerization of light-cured sealants is initi-ated by a photosensitive diketone in conjunction with a tertiary amine. The complete reactions for similar resin composites are given in Chapter 9. Light-cured sealants are supplied in light-proof containers and should have a shelf life of more than 12 months. The sealant is applied to the pit and fissure with an appropriate applicator and is cured by exposing it to light for 10 to 20 seconds, with the end of the light source positioned about 1 to 2 mm from the surface. Sealants are applied in thin layers, so depth of cure should be adequate with 10- to 20-second exposure times, even for opaque materials. The advantage in using a light-cured sealant is that the working time can be completely controlled by the operator. Air Inhibition of Polymerization Owing to air inhibition of resin curing, a surface layer of uncured resin that varies in depth with different commercial products remains on the sealant surface after light curing. Sufficient material must be applied to completely coat all pits and fissures with a layer thick enough to ensure complete polymerization after removal of the tacky surface layer. The uncured, air-inhibited layer can be easily removed after curing using an abrasive slurry of pumice, applied on a cot-ton pellet or with a prophylaxis cup in a rotary hand-piece. This is more effective than wiping or rinsing. Properties of Sealants Because sealants are completely circumscribed by enamel and should not be subjected to heavy C H A P T E R 8 Preventive and Intermediary Materials 124 CRAIG’S RESTORATIVE DENTAL MATERIALS occlusal stresses without support of the underlying enamel, the mechanical properties of sealants are less important than those of resin composite restoratives that must support occlusal loads in bulk. By adding ceramic or glass filler particles up to 40% by weight, most properties show improvement as compared to unfilled resins. The modulus of elasticity shows the most dramatic improvement, and the increased rigid-ity makes the filled material less subject to deflection under occlusal stress. Filler is also added with the hope of improving wear resistance and making the material more visible on clinical inspection (Fig. 8.1). Optimal adhesion of the sealant to enamel occurs when the sealant has a low surface tension, good wetting, and a low viscosity. These properties per-mit the sealant to flow and spread easily along the enamel surface. The surface wettability is demon-strated by the contact angle of a drop of liquid on the enamel surface. A drop that spreads readily pro-duces a low contact angle. This highly wetted sur-face is conducive to a strong adhesive bond because it increases the amount of surface area in contact. Polymer tags form when the resin flows into the surface irregularities created by acid etching and are responsible for the mechanical bond that retains the sealant to enamel. Functional durability of the seal-ant bond is related to stresses induced by shrinkage of the resin during curing, thermal cycling, deflec-tion from occlusal forces, water sorption, and abra-sion, with total failure manifested by the clinical loss of material. Sealant materials have a variety of features that must be selected carefully by the health care pro-vider. Most current materials are light-cured rather than self-cured because of the ease of use and con-trolled rate of cure. Tooth-colored or clear resins are available that are very natural looking on the tooth surface, but they are also available in opaque or tinted materials to make the recall examination process easier (Fig. 8.2). Color-reversible, photosen-sitive sealants include photosensitive pigments that are normally colorless but change to green or pink when exposed to the dental curing light to help determine whether the sealant adequately covers the pit and fissures. The color change lasts for about 5 to 10 minutes after exposure but can be repeated at recall visits with another exposure to a dental curing light. An increasing number of resin sealants are mar-keted with the claim that they release fluoride. The release is highest in the first 24 hours after placement and then tapers to a low maintenance level, which to A B FIG. 8.1 Typical molar with stained fissures and no diagnosable caries. (A) Before sealing and (B) after sealing with a natural-colored sealant material. (From Hatrick CD, Eakle WS, Bird WF. Dental Materials: Clinical Applications for Dental Assistants and Dental Hygienists. 2nd ed. St. Louis: Saunders; 2011.) FIG. 8.2 Maxillary molar tooth with opaque sealant that has been in place for 5 years. 125 8. Preventive and Intermediary Materials date has not been proven to provide any significant improvement in clinical protection against caries. Clinical Studies Many clinical studies using Bis-GMA-based resins have been documented. In earlier studies on effec-tiveness of treatment with sealant in newly erupting teeth, a light-cured sealant demonstrated a reten-tion rate of 42% and an effectiveness of 35% in car-ies reduction after 5 years. In a similar study, a filled resin sealant showed a retention rate of 53% and a clinical effectiveness of 54% after 4 years. Results involving a quicker-setting unfilled resin sealant with very good penetration showed a retention rate of 80% and an effectiveness of 69% after 3 years. The longest published study on sealant effectiveness is a 15-year evaluation of a self-cured unfilled material, which showed 27.6% complete retention and 35.4% partial retention. In pairwise comparisons, the treated first molars had 31.3 decayed and filled primary tooth surfaces (dfs) and the untreated controls had 82.8 dfs. In a more current 4-year study comparing a fluoride-releasing sealant with one that did not have fluoride, retention rates were 91% for the fluoride material (77% complete and 14% partial) and 95% for the nonfluoride sealant (89% complete and 6% partial). Although the retention was somewhat lower in the fluoride-containing sealant, the caries incidence for both groups was identical (10%). In a study conducted in private practice, the 2-year retention rates for two newer fluoride-containing resins were greater than 90%, and no caries was detected on the test teeth. In a continuing study with retreatment of all defective sealant surfaces at 6-month recalls, the teeth were maintained caries free for a 5-year period. The retreatment rate was highest (18%) at 6 months, and then diminished as time progressed, but at each recall period at least two teeth (about 4%) required reapplication. Almost all studies show a direct correlation between sealant retention and caries protection. Therefore it is important to use materials that are retentive to enamel, resistant against occlusal wear, and easily applied with minimal opportunities for surface contamination. Current evidence indicates that sealants are most effective on occlusal surfaces where pits and fissures are well defined and reten-tive to food and in patients with elevated risk for pit and fissure caries. Application of Sealants The handling characteristics of a sealant depend on the composition of the material and the surface to which it is applied. Optimal preparation of the surface will lead to close adaptation of the sealant to the tooth enamel, a strong seal against the ingress of oral fluids and debris, and long-term material retention. The penetration of any of the sealants to the bot-tom of the pits and fissures and filling them without voids is important. Air or debris can be trapped in the bottom of the fissure that prevents it from being completely filled, as shown in Fig. 8.3. Control of the viscosity of the sealant is important to obtain opti-mum results, and sealants that are too thick and vis-cous will not penetrate the pits and fissures, or the etched enamel itself as well. Penetration of sealant into etched enamel, forming tags to a depth of 25 to 50 μm, is shown in Fig. 8.4. Etching the pit and fissure surface for a speci-fied time (15 to 30 seconds is adequate for enamel with a normal mineral and fluoride content) with a A µ 20 m µ 100 m B FIG. 8.3 Section showing a fissure incompletely filled with sealant as a result of (A) air and (B) debris. (From Gwinnett AJ. The bonding of sealants to enamel. J Am Soc Prevent Dent. 1973;3:21–29.) 126 CRAIG’S RESTORATIVE DENTAL MATERIALS solution or a gel of 35% to 40% phosphoric acid is recommended. Afterward, the acid etchant should be flushed thoroughly with water and the entire area extensively dried with air. Inadequate rinsing per-mits phosphate salts to remain on the surface as a contaminant, interfering with bond formation. The enamel surface should not be rubbed during etching and drying because the roughness developed can easily be destroyed. Isolation of the site is impera-tive throughout the procedure to achieve optimum tag formation and clinical success. If salivary con-tamination occurs during the treatment, the surface should be rinsed and the etchant reapplied. On clini-cal inspection, acid-etched enamel should appear white (frosty) and dull with an obviously rough tex-ture. If the appearance is not uniform, an additional 30 seconds of etching should be done. The etched area should extend beyond the anticipated area for sealant application to secure optimum bonding along the margin and reduce the potential for early leakage, but without extensive overcoverage. A light-cured bonding agent (see Chapter 13) placed on the freshly etched enamel before placing the sealant will improve retention. Single step etching and priming systems appear to provide a weaker bond to uncut enamel than to cut enamel walls and bevels, likely due to their reduced acidity. Depending on its viscosity and setting time, the sealant may best be applied with a thin brush, a ball applicator, or a syringe. A buildup of excess mate-rial should be avoided because it could interfere with the occlusion. A sufficient amount of material should be placed to completely cover all exposed pits and provide a smooth transition along the inclines of the enamel cusps. Excessive manipulation of even the light-cured sealants on the tooth surface during application can introduce air voids that appear later as surface defects. The air-inhibited surface layer should be wiped away immediately after curing and the coating inspected carefully for voids or areas of incomplete coverage. Defects can be covered at this time by repeating the entire application procedure, includ-ing the acid etch, and applying fresh sealant only to those areas with insufficient coverage. After the seal-ant is applied and fully cured, the occlusion should be checked and adjusted if necessary, to eliminate premature occlusal contacts with the opposing tooth. Glass Ionomers as Sealants Because of their demonstrated ability to release fluo-ride and provide some caries protection on tooth surfaces at risk, glass ionomers have been suggested and tested for their ability to function as a fissure sealant. Glass ionomers are generally viscous, and it is difficult to gain penetration to the depth of a fissure. Their lack of penetration also makes it dif-ficult to obtain mechanical retention to the enamel surface to the same degree as with resins. They are also more brittle and less resistant to occlusal wear. Clinical studies using various formulations of glass ionomers have shown significantly lower retention rates than resin sealants but greater fluoride deposi-tion in the enamel surfaces. Thus there is a greater potential for latent caries protection after sealant loss. Thus although glass ionomer retention appears to be poorer than for resins, clinical results have been relatively favorable. In areas where high-risk children do not have access to definitive treatment, a conservative caries management technique can seal remaining caries in a fluoride-rich environment and establish some degree of remineralization. Atraumatic restorative treat-ments (ARTs) involve opening a lesion, removing soft surface decay, and filling or sealing the surface with highly filled glass ionomer with a fast setting time. Two-year survival rates of single- and multiple-surface ART restorations in primary teeth have been reported as 93% and 62%, respectively. Five-year sur-vival rate of single-surface ART restorations in per-manent teeth was reported as 80%. Flowable Composites as Sealants Low-viscosity composites referred to as flowable com-posites are marketed for a wide variety of applica-tions, such as preventive resin restorations, cavity liners, restoration repairs, and cervical restorations. The properties of flowable composites are described in Chapter 9. Flowable composites are usually packaged in syringes or in capsules (Fig. 8.5) for direct application µ 100 m FIG. 8.4 Penetration of sealant into etched enamel. These tags are responsible for the bonding to enamel. (From Gwinnett AJ. The bonding of sealants to enamel. J Am Soc Prevent Dent. 1973;3:21–29.) 127 8. Preventive and Intermediary Materials to the pit or fissure. As with lower-viscosity resin seal-ants, trapping of air in the sealant must be avoided. Because they have higher filler content than most resin sealants, flowable composites should have bet-ter wear resistance. Flowable composites appear to provide good retention and caries resistance after 24 months. When flowable composites are used as preventive restorations, their low viscosity is a benefit in extend-ing the restoration into adjacent fissures as a sealant. A 24-month study showed the retention and caries incidence of a flowable composite to be equivalent to that of a fluoride-containing fissure sealant. GLASS IONOMERS TO PREVENT THE PROGRESSION OF CARIES The final materials that need to be considered for caries control and prevention are glass ionomers and resin-modified glass ionomers (RMGIs). Because of their documented slow release of fluoride, glass ionomers are used in cervical restorations when the highest esthetics is not critical. They are specifi-cally recommended for patients with high caries risk (Table 8.1). A detailed description of glass ionomer chemistry can be found in Chapter 9. Composition and Reaction Glass ionomers are supplied as various shaded pow-ders and a liquid. The powder is an ion-leachable aluminosilicate glass, and the liquid is a water solu-tion of polymers and copolymers of acrylic acid. The material sets as a result of the metallic salt bridges between the Al3+ and Ca2+ ions leached from the glass and the negatively charged acid groups (COO–) on the polymers. The reaction progresses slowly, with the formation of a cross-linked gel matrix mainly from the calcium in the initial set and an alu-minum ion exchange strengthening the cross-linking in the final set. A similar ionic interaction called “chelation” takes place between the negatively charged polymer and the calcium on the exposed tooth surface, creating an adhesive bond. The sur-faces of new restorations should be protected from saliva during the initial set with a protective coating of varnish or light-cured resin. Properties The properties of glass ionomers are compared quali-tatively with other restorative materials in Table 8.2. Significant properties are (1) elastic modulus that is A B FIG. 8.5 Selection of flowable composite resins in syringe delivery system (A) and syringe and capsule delivery systems (B). (A, Courtesy Pentron Clinical, Orange, CA. B, Courtesy 3M Company, St. Paul, MN.) TABLE 8.1 Uses of Composites, Compomers, Resin-Modified Glass Ionomers, and Glass Ionomers Type Uses Hybrid/microfilled/ multipurpose composite Classes 1, 2, 3, 4, 5, low caries– risk patient Classes 1, 3, 4, medium caries– risk patients Compomer Primary teeth, classes 1, 2 restorations in children Cervical lesions, classes 3, 5, medium caries–risk patients Resin-modified glass ionomer Cervical lesions, classes 3, 5, primary teeth, sandwich technique, class 5, high caries– risk patients, root caries Glass ionomer Cervical lesions, class 5 restorations in adults where esthetics are less important, root caries 128 CRAIG’S RESTORATIVE DENTAL MATERIALS similar to dentin, (2) bond strength to dentin of 2 to 3 MPa, (3) expansion coefficient comparable to tooth structure, (4) low solubility, and (5) fairly high opac-ity. Fluoride in the glass releases slowly to provide a potentially anticariogenic effect on adjacent dental plaque and tooth structure. Although the bond strength of glass ionomers to dentin is lower than that of resin composites, clinical studies have shown that the retention of glass iono-mers in areas of cervical erosion is considerably better than for composites. When the dentin is conditioned (etched) using a dilute solution (15% to 25%) of poly-acrylic acid, the glass ionomer may be applied without a cavity preparation. Four-year clinical data showed a retention rate for glass ionomer cervical restorations of 75%. The surfaces of the restorations seen in the studies were noticeably rough, and some shade mis-matches were present. Pulp reaction to glass ionomers is mild; if the thickness of dentin is less than 1 mm, a calcium hydroxide liner is recommended. Although the surface remains slightly rough, cervical restora-tions did not contribute to inflammation of gingival tissues. In fact, gingival response to glass ionomers is typically very good. Fewer Streptococcus mutans organisms exist in plaque adjacent to glass ionomer restorations than in controls without glass ionomers. Glass ionomers are packaged in bottles and in vac-uum capsules for mixing in a mechanical mixer. When supplied in bulk, the powder and liquid are dispensed in proper amounts on a paper pad and half the pow-der is initially incorporated to produce a homogeneous milky consistency. The remainder of the powder is then added for a total mixing time of 30 to 40 seconds. The typical initial setting time is about 4 minutes. After placing the restorative and developing the correct con-tour, the surface should be protected from contamina-tion by applying a protective barrier. Trimming and finishing should be done after 24 hours due to the rather slow maturation of the material’s structure. For preencapsulated systems, the liquid in the unit-dose capsule is forced into the powder by a handpress and is mixed by a mechanical mixer, essentially the same as that used to mix dental amalgam. The mixture is injected directly into the cavity preparation with a special syringe. Working time is short and critical, so it is imperative to place the material with a minimum of manipulation. If the gel stage of the reaction is dis-rupted during the early phase of the reaction, the physi-cal properties will be very low and adhesion can be lost. Optimum results are achieved if the manufacturer’s instructions are followed carefully: maintaining isola-tion, using adequate etching procedures, protecting the restoration from saliva after placement, and delaying final finishing for a day or longer if possible. RESIN-MODIFIED GLASS IONOMERS RMGIs, at one time known as hybrid ionomers, are used for restorations in low stress–bearing areas and are recommended for patients with high caries risk (see Table 8.2). These restorations are more esthetic than glass ionomers because of their resin content. Examples of RMGIs in cervical erosions, abfractions, and other restorations are shown in Fig. 8.6. TABLE 8.2 Ranking of Selected Properties of Resin-Modified Glass Ionomers and Glass Ionomers Property Resin-Modified Glass Ionomer Glass Ionomer Compressive strength Med Low–Med Flexural strength Med Low–Med Flexural modulus Med Med–High Wear resistance Med Low Fluoride release Med–High High Fluoride rechargability Med–High High Esthetics Good Acceptable A B FIG. 8.6 Restoration of root surface lesions. (A) Abrasion/erosion lesions on the facial surface of mandibular premolars. (B) Restorations with resin-modified glass ionomer cement and composite. (Courtesy Dr. Thomas J. Hilton, Portland, OR.) 129 8. Preventive and Intermediary Materials Composition and Reaction The powder of RMGI is similar to that used in the conventional glass ionomers. The liquid contains monomers, polyacids, and water. RMGIs set by a combined acid-base ionomer reaction and light-cured resin polymerization of monomers, typically 2-hydroxyethyl methacrylate. RMGIs are typically light-cured like dental composites for 10 to 20 sec-onds, depending on the manufacturer’s instructions. Properties RMGIs bond to tooth structure without the use of a bonding agent, and because they are somewhat stronger than conventional glass ionomers, tend to have higher bond strength to tooth structure than conventional glass ionomers. Typically, the tooth is conditioned (etched) with polyacrylic acid or another primer before placing the material. The flexural strength of an RMGI is almost double that of a con-ventional glass ionomer. RMGIs release more fluoride than compomers and composites but almost the same as conventional glass ionomers. Fig. 8.7 illustrates the release of fluoride ions from a glass ionomer and RMGI over a 30-day period. There is an early period of high release, which tapers after about 10 days to 1 ppm. Both ionomer materials recharge when exposed to fluoride treatments or fluoride dentifrices. Fig. 8.8 illustrates this recharge capability with a similar time-dependent release curve. In evaluating the effective-ness of this release, fluoride has been measured in plaque samples immediately adjacent to glass ionomer- based restorations (Fig. 8.9). For these two materials from the same manufacturer, plaque adjacent to the F– Release in ppm 6 5 4 3 0 1 2 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 2 1 Days Photac Fil Ketac Fil Tetric Enamel FIG. 8.7 Fluoride release from glass ionomer cements and composite resin in distilled water over 30 days. (Modified from Strother JM, Kohn DH, Dennison JB, et al. Fluoride release and re-uptake in direct tooth colored restorative materials. Dent Mater. 1998;14:129–136.) F– Release in ppm 6 5 4 3 0 1 2 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 2 1 Days Photac Fil Ketac Fil Control FIG. 8.8 Fluoride reuptake and rerelease from glass ionomer cements after recharging the material with 1.1% neutral sodium fluoride gel. (Modified from Strother JM, Kohn DH, Dennison JB, et al. Fluoride release and re-uptake in direct tooth colored restorative materials. Dent Mater. 1998;14:129–136.) 130 CRAIG’S RESTORATIVE DENTAL MATERIALS RMGI had significantly higher fluoride content than plaque adjacent to compomer restorations at 2 and 21 days after insertion of the restorations. Manipulation An example of an RMGI packaged in capsules is shown in Fig. 8.10. For RMGI packaged in bulk as powder-liquids, manipulation is like that of conven-tional glass ionomers. Mechanical mixing of the unit-dose capsules provides a uniform mix that has much fewer of the larger air voids than can be introduced during hand spatulation. Optimum powder-to- liquid ratio is critical to the long-term maintenance of physical properties and the clinical success of res-torations. Unlike conventional glass ionomer restora-tions, RMGIs set immediately when light-cured and can be finished 5 to 10 minutes after initial set. Color can be maintained and surface texture improved by finishing the restorations in a wet environment (water spray or water-soluble lubricant) and then recoating with a protective varnish or light-cured resin. Glass ionomer materials are an increasingly important material in operative dentistry for both an aging population with high incidence of root caries, patients with xerostomia and reduced salivary flow, and children who have high caries risk factors. RESIN-MODIFIED GLASS IONOMERS AS CAVITY LINERS RMGIs can also be used to line the dentin walls of a deep cavity. When used as a cavity liner, these materials provide thermal insulation. A sandwich technique uses an RMGI as a liner to seal the den-tin and provide the benefit of fluoride release, fol-lowed by a surface layer of resin composite to fill the remainder of the cavity. Some advocate the use of the glass ionomer as a liner under class I and II composite restorations to relieve stresses that result from shrinkage of the composite dur-ing cure. Glass ionomer lining materials bond to dentin with bond strengths varying from 2.0 to 4.9 MPa. These materials also adhere to composite restorative materials, by mechanical retention for conventional glass ionomer and mechanical and chemical bonding for RMGI. Glass ionomer lining materials release fluoride ions and are radiopaque. More discussion of glass ionomers as cements can be found in Chapter 13. CALCIUM HYDROXIDE CAVITY LINERS Calcium hydroxide cements are used for lining spe-cific areas of deep cavities or for direct pulp capping. The antibacterial action of calcium hydroxide makes these cements useful in indirect pulp-capping proce-dures involving carious dentin. Calcium hydroxide cavity liners are provided as pastes that set to a hard mass when mixed. The base paste of a typical product contains calcium tungstate, tribasic calcium phosphate, and zinc oxide powders suspended in a glycol salicylate liquid. The catalyst paste contains calcium hydroxide, zinc oxide, and zinc stearate powders in ethylene toluene sulfon-amide liquid. The ingredients responsible for setting are calcium hydroxide and a salicylate, which react to form an amorphous calcium disalicylate. Fillers such as calcium tungstate or barium sulfate provide radiopacity. A light-cured calcium hydroxide liner consists of calcium hydroxide and barium sulfate dispersed in a urethane dimethacrylate resin, similar to what F– 1.4 1 1.2 0.8 0.6 0.4 0.2 0 PF 2 days PF 21 days Hytac 2 days Hytac 21 days Test Control FIG. 8.9 Total fluoride concentration in plaque (micro-gram fluoride per milligram plaque) adjacent to resin-modified glass ionomer and compomer restorations over 21 days; restored test teeth versus nonrestored control teeth. FIG. 8.10 Resin-modified glass ionomer materials available for hand mixing or encapsulated for mechanical mixing. (Courtesy 3M ESPE Dental Products, St. Paul, MN.) 131 8. Preventive and Intermediary Materials is used in some dental composites. The impor-tant properties of calcium hydroxide cements are mechanical and thermal properties, solubility, and pH. Research has shown that these cements can stimulate the formation of protective secondary dentin bridges when applied to direct pulp expo-sures. Calcium hydroxide (self-cured) liners have low values of tensile strength, compressive strength, and elastic modulus, compared with high-strength bases. Although setting times vary between 2.5 and 5.5 minutes, strength of these cements continues to increase over a 24-hour period. For a group of five commercial products, compressive strengths ranged from 6.5 to 14.3 MPa at 10 minutes to from 9.8 to 26.8 MPa at 24 hours. The low elastic modu-lus of calcium hydroxide cavity liners restricts their usage to specific areas not critical to the support of restorations. The solubility of calcium hydroxide bases has been measured in several solvents for various peri-ods of immersion and has been found to be sig-nificant. Some solubility of the calcium hydroxide is necessary to achieve its therapeutic properties, although an optimum value is not known. Clearly the use of acid-etching procedures and varnish in the presence of calcium hydroxide liners must be done with care. The pH of commercial products has been measured at between 9.2 and 11.7. Free calcium hydroxide in excess of that necessary to form the calcium disalicylate stimulates secondary dentin in proximity to the pulp and shows antibacterial activ-ity. Calcium hydroxide liners are mostly used in direct pulp capping and specifically in deep areas of a cavity preparation, but not for general lining of an entire pulpal flow. RMGI liners are a better choice for general lining of cavities because of their fluoride release, decreased solubility, and superior mechani-cal properties. MINERAL TRIOXIDE AGGREGATE Another material that is used in similar situations as calcium hydroxide, such as pulp capping and as an endodontic root end filling material, is min-eral trioxide aggregate (MTA). This material is composed of tricalcium silicate, dicalcium silicate, tricalcium aluminate, and bismuth oxide, the lat-ter being added to make the material radiopaque. MTA is basically similar to Portland cement. The main reaction product from the mixture of MTA and water is calcium hydroxide. MTA is slower setting than calcium hydroxide, requiring hours to days to be completely hardened. It is also much more expensive, but studies have shown that it produces a more ideal outcome as a pulp-capping agent than calcium hydroxide. FLUORIDE VARNISHES Fluoride-containing varnishes deliver fluoride topi-cally to the surfaces of teeth in patients at risk for caries. The varnishes are usually used after a pro-phylaxis. Products contain either 5% sodium fluo-ride (2.26% F− or 22,600 ppm) or 1% difluorosilane (0.1% F− or 1000 ppm). The fluoride is dissolved in an organic solvent that evaporates when applied or sets when exposed to moisture, leaving a thin film of material covering all exposed tooth surfaces. The mechanism of action for a fluoride varnish is similar to that of a fluoride mouthwash. Calcium fluoride is deposited on the tooth surface and later converted through a remineralization reaction to fluorapatite. One advantage of fluoride varnish is the extended time of exposure for the active fluoride ingredient against the tooth surface. Instead of seconds, as with a mouthwash, it may be hours before a varnish wears off. One RMGI-based varnish has been reported to release fluoride for up to 6 months. Clinical trials have documented the efficacy of varnish in treating young children at risk for caries, with reductions reported as high as 70%. Another potential use for this type of material is in the prevention of root caries in an older population having exposed root surfaces. Semiannual application of fluoride varnishes seems to provide optimum efficacy. More research is neces-sary to fully document the value of using these mate-rials in patients with moderate to high caries risk. REMINERALIZATION Remineralization is a natural repair process for cari-ous lesions. Elevated levels of fluoride in toothpaste have been shown to be effective in rehardening root caries lesions that are cavitated. A 5000-ppm-F tooth-paste rehardened 76% of lesions compared with 35% in a 1100-ppm-F group. The concept of the caries balance proposed by Featherstone describes three pathological factors and three protective factors for dental caries. The pathological factors are (1) acid-producing bacteria, (2) frequent consumption of fermentable carbohydrates, and (3) below normal salivary flow and function. The three protective fac-tors are (1) a normal salivary flow and components, (2) fluoride, and (3) antibacterials. Two salivary com-ponents required for remineralization are calcium and phosphate. Fluoride enhances remineralization. Calcium phosphate formulations have been developed for addition to toothpaste, varnishes, and gum (Fig. 8.11). A calcium phosphate remineraliza-tion technology based on casein phosphopeptide-amorphous calcium phosphate (CPP-ACP) was effective in remineralizing enamel subsurface lesions by stabilizing high levels of calcium and phosphate 132 CRAIG’S RESTORATIVE DENTAL MATERIALS ions. When added to sugar-free gum in a random-ized controlled clinical trial, an 18% reduction in car-ies progression after 24 months was demonstrated. In paste form, the CPP-ACP complexes have been shown to be effective in reversing early caries lesions and stabilizing the progression of caries. A bioactive glass (calcium sodium phosphosili-cate) originally developed as a bone-regenerative material has been shown to deposit onto dentin surfaces and mechanically occlude dentinal tubules when delivered in a dentifrice. When combined with therapeutic levels of fluoride, this material increases the remineralization of caries lesions in situ. There are many new calcium silicate–based mate-rials that have been developed for tooth lining with the main objectives being the protection of the pulp and the potential remineralization of overlying den-tin. Many of these materials are light-cured and therefore have reasonable mechanical properties and solubility resistance. They are the subject of many research studies, specifically looking at the effect the materials have on nearby odontoblast cells, which may be stimulated to form extracellular matrix as the initiation of the mineralization process, or to cause undifferentiated cells to differentiate into odonto-blast-like cells. The ultimate success of such materi-als and strategies is not yet known. One final material that also has been suggested to cause tooth remineralization, especially of frank car-ies lesions, as well as having a strong antibacterial effect is silver diamine fluoride. Silver diamine fluo-ride (SDF) is solution of about 30% silver diamine fluoride (of which approximately 25% is silver and 5% is fluoride) in water with a pH of approximately 10. The high pH makes it a strong neutralizer of acids, but perhaps more important is its strong anti-bacterial effect, predominantly due to the presence of silver, a known antimicrobial. The material was preceded by silver nitrate used in a similar way, that is, the application of the colorless liquid to frank car-ies. There is growing evidence that caries is arrested in the presence of the material, and this has great advantages for use in children and geriatric popula-tions especially. The problem with the material is that it stains tooth structure, as well as other objects such as skin or clothing. Therefore while it may be ben-eficial for arresting lesions, it requires being covered by an esthetic material to block out its black- staining effect on the tooth. The material was originally approved as a dentin desensitizer, but it is acceptable now to use it for arresting caries. Bibliography Fluoride Varnishes and Silver Diamine Fluoride Banting DW, Papas A, Clark DC, et al. The effectiveness of 10% chlorhexidine varnish treatment on dental caries inci-dence in adults with dry mouth. Gerodontology. 2000;17:67. Beltran-Aguilar ED, Goldstein JW. Fluoride varnishes: a review of their clinical use, cariostatic mechanism, effi-cacy and safety. J Am Dent Assoc. 2000;131:589. Horst JA, Ellenikiotis H, Milgrom PL. UCSF protocol for caries arrest using silver diamine fluoride: ratio-nale, indications and consent. J Calif Dent Assoc. 2016; 44(1):16. Peng JJ, Botelho MG, Matinlinna JP. Silver compounds used in dentistry for caries management: a review. J Dent. 2012;40(7):531. Petersson LG, Twetman S, Pakhomov GN. The efficiency of semiannual silane fluoride varnish applications: a two-year clinical study in preschool children. J Public Health Dent. 1998;58:57. Pit and Fissure Sealants Arenholt-Bindslev D, Breinholt V, Preiss A, et al. Time-related bisphenol-A content and estrogenic activity in saliva samples collected in relation to placement of fis-sure sealants. Clinical Oral Invest. 1999;3:120. Boksman L, Carson B. Two-year retention and caries rates of UltraSeal XT and FluoroShield light-cured pit and fis-sure sealants. General Dent. 1998;46:184. De Amorim RG, Leal SC, Frencken JE. Survival of atrau-matic restorative treatment (ART) sealants and restora-tions: a meta-analysis. Clin Oral Invest. 2012;16:429. Feigal RJ, Quelhas I. Clinical trial of a self-etching adhe-sive for sealant application: success at 24 months with Prompt-L-Pop. Am J Dent. 2003;16:249. Folke BD, Walton JL, Feigal RJ. Occlusal sealant success over ten years in a private practice: comparing longevity of sealants placed by dentists, hygienists and assistants. Pediatr Dent. 2004;26:426. Frencken JE, Leal SC, Navarro MF. Twenty-five year atrau-matic restorative treatment (ART) approach: a compre-hensive overview. Clin Oral Invest. 2012;16:1337. FIG. 8.11 Paste for remineralizing enamel. (Courtesy GC America, Alsip, IL.) 133 8. Preventive and Intermediary Materials Gungor HC, Altay N, Alpar R. Clinical evaluation of a poly-acid-modified resin composite-based fissure sealant: two year results. Oper Dent. 2004;29:254. Gwinnett AJ. The bonding of sealants to enamel. J Am Soc Prevent Dent. 1973;3:21. Hannig M, Grafe A, Atalay S, et al. Microleakage and SEM evaluation of fissure sealants placed by use of self-etching priming agents. J Dent. 2004;32:75. Hatrick CD, Eakle WS, Bird WF. Dental Materials: Clinical Applications for Dental Assistants and Dental Hygienists. 2nd ed. St. Louis: Saunders; 2011. Hori M, Yoshida E, Hashimoto M, et al. In vitro testing of all-in-one adhesives as sealants. Am J Dent. 2004; 17:177. Manabe A, Kaneko S, Numazawa S, et al. Detection of Bisphenol-A in dental materials by gas chromatography-mass spectrometry. Dent Mater. 2000;19:75. Myers CL, Rossi F, Cartz F. Adhesive taglike extensions into acid-etched tooth enamel. J Dent Res. 1974;53:435. O’Brien WJ, Fan PL, Apostolidis A. Penetrativity of sealants and glazes. Oper Dent. 1978;3:51. Pahlavan A, Dennison JB, Charbeneau GT. Penetration of restorative resins into acid-etched human enamel. J Am Dent Assoc. 1976;93:1170. Pardi V, Pereira AC, Mialhe FL, et al. Six-year clinical evalu-ation of polyacid-modified composite resin used as fis-sure sealant. J Clin Pediatr Dent. 2004;28:257. Pereira AC, Pardi V, Mialhe FL, et al. A 3-year clinical evalu-ation of glass ionomer cements used as fissure sealants. Am J Dent. 2003;16:23. Tarumi H, Imazato S, Narimatsu M, et al. Estrogenicity of fissure sealants and adhesive resins determined by reporter gene assay. J Dent Res. 1838;79:2000. Taylor CL, Gwinnett AJ. A study of the penetration of seal-ants into pits and fissures. J Am Dent Assoc. 1973;87:1181. Flowable Composites Erdemir U, Sancakli HS, Yaman BC, Ozel S, Yucel T, Yildiz E. Clinical comparison of a flowable composite and fis-sure sealant: A 24-month split-mouth, randomized, and controlled study. J Dent. 2014;42(2):149. Fortin D, Vargas MA. The spectrum of composites: new techniques and materials. J Am Dent Assoc. 2000;131: 26S. Unterbrink GL, Liebenberg WH. Flowable resin composites as “filled adhesives”: literature review and clinical rec-ommendations. Quint Int. 1999;30:249. Glass Ionomers and Resin Modified Glass Ionomers Cattani-Lorente MA, Dupuis V, Moya F, et al. Comparative study of the physical properties of a polyacid-modified composite resin and a resin-modified glass ionomer. Dent Mater. 1999;15:21. Farah JW, Powers JM. Fluoride-releasing restorative mate-rials. Dent Advis. 1998;15:p 2. Fleming GJ, Faroog AA, Barralet JE. Influence of powder/ liquid mixing ratio on the performance of a restorative glass-ionomer dental cement. Biomaterials. 2003;24:4173. Forss H. Release of fluoride and other elements from light-cured glass ionomer in neutral and acidic conditions. J Dent Res. 1993;72:1257. Holmgren CJ, Roux D, Domejean S. Minimal interven-tion dentistry: part 5. Atraumatic restorative treatment (ART) – a minimum intervention and minimally inva-sive approach for the management of dental caries. British Dental J. 2013;214:1. Müller J, Brucker G, Kraft E, et al. Reaction of cultured pulp cells to eight different cements based on glass ionomers. Dent Mater. 1990;6:172. Quackenbush BM, Donly KJ, Croll TP. Solubility of a resin-modified glass ionomer cement. J Dent Child. 1998;65:310. Ribeiro AP, Serra MC, Paulillo LA, et al. Effectiveness of surface protection for resin-modified glass-ionomer materials. Quint Int. 1999;30:427. Strother JM, Kohn DH, Dennison JB, et al. Fluoride release and re-uptake in direct tooth colored restorative materi-als. Dent Mater. 1998;14:129. Weidlich P, Miranda LA, Maltz M, et al. Fluoride release and uptake from glass ionomer cements and composite resins. Braz Dent J. 2000;11:89. Wellbury RR, Shaw AJ, Murray JJ, et al. Clinical evaluation of paired compomer and glass ionomer restorations in primary teeth. Br Dent J. 2000;189:93. Ylp HK, Smales RJ. Fluoride release and uptake by aged resin-modified glass ionomers and a polyacid-modified resin composite. Int Dent J. 1999;49:217. Remineralization and Lining Baysan A, Lynch E, Ellwood R, et al. Reversal of primary root caries using dentifrices containing 5,000 and 1,100 ppm fluoride. Caries Res. 2001;35:41–46. Burwell AK, Litkowski LJ, Greenspan DC. Calcium sodium phosphosilicate (NovaMin): remineralization potential. Adv Dent Res. 2009;21(1):35. Camilleri J. Characterization of hydration products of min-eral trioxide aggregate. Int Endod J. 2008;41(5):408. Featherstone JD. Prevention and reversal of dental car-ies: role of low level fluoride. Community Dent Oral Epidemiol. 1999;27:31–40. Featherstone JD. The caries balance: the basis for caries management by risk assessment. Oral Health Prev Dent. 2004;2(suppl 1):259–264. Featherstone JDB. Remineralization, the natural caries repair process: the need for new approaches. Adv Dent Res. 2009;21(1):4. Hilton TJ, Ferracane JL, Mancl L. Northwest Practice-based Research Collaborative in Evidence-based Dentistry (NWP). Comparison of CaOH with MTA for direct pulp capping: a PBRN randomized clinical trial. J Dent Res. 2013;92(suppl 7):16S. Niu LN, Jiao K, Wang TD, et al. A review of the bioactivity of hydraulic calcium silicate cements. J Dent. 2014;42(5):517. Prati C, Gandolfi MG. Calcium silicate bioactive cements: biological perspectives and clinical applications. Dent Mater. 2015;31(4):351. Reynolds EC. Casein phosphopeptide-amorphous cal-cium phosphate: the scientific evidence. Adv Dent Res. 2009;21(1):25. ten Cate JM. The need for antibacterial approaches to improve caries control. Adv Dent Res. 2009;21:8–12. Weintraub JA, Ramos-Gomez FR, Shain SG, et al. Fluoride varnish efficacy in preventing early childhood caries. J Dent Res. 2006;85:172–176. This page intentionally left blank 135 The concept of a composite biomaterial, introduced in Chapter 4, can be described as a solid that contains two or more distinct constituent materials or phases when considered at greater than an atomic scale. In these materials, mechanical properties such as elastic modulus are significantly altered in comparison with a homogenous material consisting of either of the phases alone. Enamel, dentin, bone, and reinforced polymers are considered composites, but alloys such as brass are not. The ability to change properties of the macroscale object based on control of the indi-vidual constituents is a significant advantage for the use of composite materials. In dentistry, the term “resin composite” generally refers to a reinforced polymer system used for restoring hard tissues, such as enamel and dentin. The proper materials science term is “polymer matrix composite” or for those composites with filler particles often used as direct-placed restorative composites, “particulate-rein-forced polymer matrix composite.” In this chapter, the term “resin composite” will refer to the reinforced polymer matrix materials used as restorative materi-als. The class of materials called conventional glass ionomers (GIs) and resin-modified glass ionomers (RMGIs) also fall in the scientific class of composite materials but because these are water-based mate-rials and have a distinct acid-base setting reaction, they have been traditionally categorized as a class of their own. It is important to remember, however, that most biological materials including enamel, dentin, bone, connective tissue, muscle, and even cells are classified as composites within the broad range of biological engineering materials. Resin composites are used to replace missing tooth structure and modify tooth color and contour, thus enhancing esthetics. A number of commercial resin composites are available for various applications. Traditionally, some have been optimized for esthetics and others were designed for higher stress bearing areas. More recently, nanocomposites have become available, which are optimized for both excellent esthetics and high mechanical properties for stress bearing areas. GIs and RMGIs are used selectively as filling materials usually for small lesions, especially where one or more margins are in dentin and in areas of caries activity. Resin-based composites were first developed in the early 1960s and provided materials with higher mechanical properties than acrylics and silicates, lower thermal coefficient of expansion, lower dimen-sional change on setting, and higher resistance to wear, thereby improving clinical performance. Early composites were chemically activated followed by photoactivated composites initiated with ultravio-let (UV) wavelengths. These were later replaced by composites activated in the visible wavelengths. Continued improvements in composite technology have resulted in the modern materials with excellent durability, wear resistance, and esthetics mimicking the natural teeth. In particular, the incorporation of nanotechnology in controlling the filler architecture has made dramatic improvements in these materials. Moreover, the development of bonding agents for bonding composites to tooth structure (see Chapter 13) has also improved the longevity and perfor-mance of composite restorations. A classification of preparation type and recom-mended composite category is listed in Table 9.1. Characteristics of these composite categories are summarized in Table 9.2. GIs were developed in the 1960s and are based on an acid-base cement-forming reaction between fluoroaluminosilicate (FAS) glass powder similar to those used in silicate cements and aqueous solution of polycarboxylic acids. These were less prone to dis-solution than silicates but the early materials suffered from difficulty of manipulation, technique sensitivity, and poor esthetics. Advances in these materials have continued and the modern materials have improved properties. RMGIs were invented in the late 1980s to C H A P T E R 9 Restorative Materials: Resin Composites and Polymers 136 CRAIG’S RESTORATIVE DENTAL MATERIALS preserve the advantages of fluoride release and clini-cal adhesion of the conventional GIs yet provide the ease of light curing and good esthetics of resin-based materials. The use of nanotechnology in RMGI has resulted in enhanced esthetics of these materials. MULTIPURPOSE RESIN COMPOSITES Composition A resin composite is composed of four major compo-nents: organic polymer matrix, inorganic filler par-ticles, coupling agent, and the initiator-accelerator system. The organic polymer matrix in most commer-cial resin composites today is a cross-linked matrix of dimethacrylate monomers. The most common monomers are aromatic dimethacrylates. The double bonds at each end of these molecules undergo addi-tion polymerization by free-radical initiation. While these monomers can provide an optimum of optical, mechanical, and clinical properties, they are rather viscous and have to be blended with low-molecular-weight diluent monomers so that a clinically workable consistency may be obtained upon incorporation of the fillers. More recently, low-shrink composites have been introduced that contain, for example, monomers with epoxy (also known as oxirane) functional groups at the ends. The polymerization of these monomers is initiated by cations. Other commercial resin compos-ites utilize various monomers and filler technology to reduce polymerization shrinkage or stress. The dispersed inorganic filler particles may con-sist of one or more inorganic materials such as finely ground quartz or glass, sol-gel-derived ceramics, microfine silica, or more recently, nanoparticles. Two-dimensional diagrams of fine and microfine particles surrounded by polymer matrix are shown in Fig. 9.1. TABLE 9.1 Types of Restorations and Recommended Resin Composites Type of Restoration Recommended Resin Composite Class 1 Multipurpose, nanocomposite, bulk filled, microfilled (posterior),a compomer (posterior)a Class 2 Multipurpose, nanocomposite, bulk filled, laboratory, microfilled (posterior),a compomer (posterior)a Class 3 Multipurpose, nanocomposite, microfilled, compomer Class 4 Multipurpose, nanocomposite Class 5 Multipurpose, nanocomposite, microfilled, resin-modified glass ionomer, compomer Class 6 (MOD) Bulk filled, nanocomposite Cervical lesions Flowable, resin-modified glass ionomer, compomer Pediatric restorations Flowable, resin-modified glass ionomer, compomer 3-unit bridge or crown Laboratory (with fiber reinforcement) Alloy substructure Laboratory (bonded) Core build-up Core Temporary restoration Provisional High caries-risk patients Glass ionomers, resin-modified glass ionomer aSpecial microfilled composites and compomers are available for posterior use. MOD, Mesial-occlusal-distal. TABLE 9.2 Characteristics of Various Types of Resin Composites Type of Composite Size of Filler Particles (mm) Volume of Inorganic Filler (%) Handling Characteristics and Properties Advantages Disadvantages Multipurpose 0.04, 0.2–3.0 60–70 High strength, high modulus Nanocomposite 0.002–0.075 72–79 High polish, high strength, high modulus, polish retention Microfilled 0.04 32–50 Best polish, best esthetics Higher shrinkage, lower strength Bulk filled 0.04, 0.2–20 59–80 Deep cure, reduced step Questionable marginal adaptation Flowable 0.04, 0.2–3.0 42–62 Syringeable, lower modulus Higher wear Laboratory 0.04, 0.2–3.0 60–70 Best anatomy and contacts, lower wear Laboratory cost, special equipment, requires resin cement 137 9. Restorative Materials: Resin Composites and Polymers The coupling agent, an organosilane (often referred to as “silane”), is applied to the inorganic particles by the manufacturer to surface treat the fillers before being mixed with the unreacted monomer mixture. Silanes are called coupling agents, because they form a bond between the inor-ganic and organic phases of the composite. One end of the molecule contains functional groups (such as methoxy), which hydrolyze and react with the inorganic filler, whereas the other end has a meth-acrylate double bond that copolymerizes with the monomers. The role of the initiator-accelerator system is to polymerize and cross-link the system into a hard-ened mass. The polymerization reaction can be triggered by light activation, self-curing (chemical activation), and dual curing (chemical and light curing). Resin Matrix METHACRYLATE MONOMERS The vast majority of monomers used for the resin matrix are dimethacrylate compounds. Two mono-mers that have been commonly used are 2,2-bis[4(2-hydroxy-3-methacryloxypropyloxy)-phenyl] propane [bisphenol A-glycidyl methacrylate (Bis-GMA)] and urethane dimethacrylate (UDMA). Both contain reactive carbon double bonds at each end that can undergo addition polymerization initi-ated by free-radical initiators. The use of aromatic groups affords a good match of refractive index with the radiopaque glasses and thus provides better overall optical properties of the composites. A few products use both Bis-GMA and UDMA monomers. A B FIG. 9.1 Two-dimensional diagrams of composites with (A) fine and (B) microfine particles. (From Powers JM, Wataha JC. Dental Materials: Foundations and Applications. 11th ed. St. Louis: Elsevier, 2017.) O O O O O O OH Structure of Bis-GMA OH Structure of UDMA O O O O O O O O H N H N The viscosity of the monomers, especially Bis-GMA, is rather high and diluents must be added, so a clinical consistency can be reached when the resin mixture is compounded with the filler. Low-molecular-weight compounds with difunctional car-bon double bonds, for example, triethylene glycol dimethacrylate (TEGDMA), or bisphenol A ethox-ylate dimethacrylate (Bis-EMA6), are added by the manufacturer to reduce and control the viscosity of the compounded composite. O O O Structure of TEGDMA O O O 138 CRAIG’S RESTORATIVE DENTAL MATERIALS O O O O O Structure of Bis-EMA6 O O O O O LOW-SHRINK METHACRYLATE MONOMERS A variety of other methacrylate monomers have been used in the newer commercial products intro-duced since 2008 for controlling the volumetric shrinkage and polymerization stress of compos-ites. The general approach relies on increasing the distance between the methacrylate groups resulting in lower cross-link density or increasing the stiff-ness of the monomers. Some examples include the use of dimer acids, incorporation of cycloaliphatic units, and photocleavable units to relieve stress after polymerization. O O O O O O O O Structure of a Monomer with Cycloaliphatic Units O O O O O n O O O N H N H N H N H n O O O O O O O Structure of Monomer with Photocleavable Units O O O O O O O The bonding agents widely used with these com-posites are also prepared from similar organic mono-mers so that they are compatible with the composites. LOW-SHRINK SILORANE MONOMER A new monomer system called “silorane” has been developed to reduce shrinkage and internal stress build-up resulting from polymerization. The name silorane was coined from its chemical building blocks siloxane and oxirane (also known as epoxy). The siloxane functionality provides hydrophobicity to the composite. The oxirane functionalities undergo ring-opening cross-linking via cationic polymeriza-tion. Special initiator systems are required for the polymerization of the siloranes (described in the sec-tion Initiators and Accelerators). Care has to be taken in choosing the filler system. If the filler surface has any residual basicity (as with some glasses and sol-gel-derived systems), the composite may become unstable. Furthermore, specific adhesive system has to be used for bonding these materials during clinical placement. O O O O O O O O O O O O Si Si Si Si Si Si Si Siloxane Silorane Structure of Silorane Oxirane 139 9. Restorative Materials: Resin Composites and Polymers Fillers and Classification of Composites Fillers make up a major portion by volume or weight of the composite. The function of the filler is to rein-force the resin matrix, provide the appropriate degree of translucency, and control the volume shrinkage of the composite during polymerization. Fillers have been traditionally obtained by grinding minerals such as quartz, glasses, or sol-gel-derived ceramics. Most glasses contain heavy-metal oxides such as barium or zinc so that they provide radiopacity for visualization when exposed to x-rays. It is advantageous to have a distribution of filler diameters so that smaller par-ticles fit in the spaces between larger particles and pro-vide more efficient packing. Recently, nanofillers have been introduced into composites. These are described in the section Nanofillers and Nanocomposites. A helpful method of classifying dental composites is by the particle size, shape, and the particle-size dis-tribution of the filler. This classification is presented in the following section. MACROFILLS The early composites were macrofills. These com-posites contained large spherical or irregular-shaped particles of average filler diameter of 20 to 30 μm. The resultant composites were rather opaque and had low resistance to wear. HYBRID AND MICROHYBRID COMPOSITES In hybrid composites two types of fillers are blended together: fine particles of average particle size 2 to 4 μm and 5% to 15% of microfine particles, usually silica, of particle size 0.04 to 0.2 μm. In microhybrid compos-ites the fine particles of a lower average particle size (0.04 to 1 μm) are blended with microfine silica. The fine particles may be obtained by grinding glass (e.g., borosilicate glass, lithium or barium aluminum sili-cate glass, strontium, or zinc glass), quartz, or ceramic materials and have irregular shapes. The distribution of filler particles provides efficient packing so that high filler loading is possible while maintaining good handling of the composite for clinical placement. Microhybrid composites may contain 60% to 70% filler by volume, which, depending on the density of the filler, translates into 77% to 84% by weight in the composite. Most manufacturers report filler concen-tration in weight percent (wt%). A micrograph of a typical, fine glass filler is shown in Fig. 9.2A. Hybrids and microhybrids have good clinical wear resistance and mechanical properties and are suitable for stress-bearing applications. However, they lose their surface polish with time and become rough and dull. NANOCOMPOSITES Recently, the incorporation of nanotechnology in designing and manufacturing composites has greatly improved their properties. Nanocomposites describe this class of composites. The nanofiller technology is described in the next section. Nanofillers and Nanocomposites The latest advancement in composite technol-ogy has been the utilization of nanotechnology in A C 1 m µ 1 m µ 1 m µ B FIG. 9.2 Scanning electron micrographs of types of filler. (A) Fine inorganic filler; (B) microfine silica filler; (C) microfine silica in organic polymer filler. 140 CRAIG’S RESTORATIVE DENTAL MATERIALS development of fillers. Nanotechnology is the pro-duction of functional materials and structures in the range of 1 to 100 nm—the nanoscale—by various physical and chemical methods. Nanotechnology requires devices and systems to create structures that have novel properties and functions because of their small sizes. Thus it implies the ability to con-trol and manipulate structures at the atomic and/ or molecular scale. Although true nanocomposites should have all filler particles in the nanometer size, the term nanotechnology has some hype associated with it and it is sometimes misused in describing a material. To date, oxide nanoparticles have been the most prevalent types of nanomaterials used in dental composites. At present, there are two dis-tinct types of resin composites available that contain nanoparticles: 1. Nanofills: These contain nanometer-sized particles (1 to 100 nm) throughout the resin matrix. Larger primary particles are not present. 2. Nanohybrids: These consist of large particles (0.4 to 5 μm) with added nanometer-sized particles. Thus they are hybrid materials, not true nanofilled composites. NANOFILL COMPOSITES All filler particles of true nanofilled composites are in the nanometer range. There are several purposes for incorporating nanofillers in dental composites. First, the size of nanomeric particles is below that of visible light (400 to 800 nm), which provides the opportunity of creating highly translucent materials. In addition, the surface area-to-volume ratio of the nanoparticles is quite large. The sizes of the smallest nanoparticles approach those of polymer molecules so they can form a molecular-scale interaction with the host resin matrix. Two types of nanoparticles have been synthe-sized and utilized for preparing this class of com-posite. The first type consists of nanomeric particles that are essentially monodispersed nonaggregates and nonagglomerated particles of silica or zirco-nia. The surface of the nanoparticles is treated with silane coupling agents that allow them to be bonded to the resin matrix when the composite is cured after placement. Nanomers are synthesized from sols, creating particles of the same size. Because of this, if nanomeric particles alone are used to make highly filled composites, the rheological properties are rather poor. To overcome this disadvantage, one manufacturer has designed a second type of nano-filler, which is called nanocluster. The nanoclusters are made by lightly sintering nanomeric oxides to form clusters of a controlled particle size distribu-tion. Nanoclusters have been synthesized from sil-ica sols alone as well as from mixed oxides of silica and zirconia. The primary particle size of the nano-mers used to prepare the clusters ranges from 5 to 75 nm. It is important to remember that in a nanocluster, the nanoparticles still maintain their individual form, much as in a cluster of grapes. The clusters can be made to have a wide size distribution ranging from 100 nm to submicron level and have an average size of 0.6 μm. Fig. 9.3A shows a scanning electron micro-graph (SEM) image of a nanocluster of silica in the composite in a commercial composite after the resin matrix was removed by washing with acetone. In this material, the surface of the nanoclusters is treated with a silane coupling agent to provide compatibil-ity and chemical bonding with the resin system. Fig. 9.3B shows the micrograph image of a nanocluster composed of silica and zirconia. The differences in A Supreme 6.0kV 16.1mm x20.0k SE[M] 2.00um HV 15.00 kV mag 1 832 x HFW 81.4 µm Det ETD WD 14.0 mm vac mode High vacuum B 20µm Quanta 200 FIG. 9.3 (A) Scanning electron micrograph image of a nanocluster of silica in a commercial composite 3M ESPE Filtek Supreme. (B) Image of a nanocluster of zirconia- silica in Filtek Supreme Ultra. (A, Courtesy Dr. Jorge Perdigao, University of Minnesota. B, From Rodrigues Jr SA, Scherrer SS, Ferracane JL, Della Bona A. Microstructural characterization and fracture behavior of a microhybrid and a nanofill composite. Dent Mater. 2008;24(9):1281–1288.) 141 9. Restorative Materials: Resin Composites and Polymers particle architecture of nanomers, nanoclusters, and conventional microhybrid fillers are readily appar-ent from transmission electron micrographs (TEMs) of composites prepared from these fillers. Fig. 9.4A shows the TEM image of a nanocomposite filled with 75-nm diameter nanoparticles only; Fig. 9.4B is that of a nanocomposite filled with a mixture of nanoclusters alone; and Fig. 9.4C is of a conventional microhybrid composite. To date, there is only one true nanofilled dental composite available. In this manufactured composite, a combination of nano-meric particles and nanoclusters is used in optimum combinations. Fig. 9.5A shows a schematic diagram of this nanocomposite containing a blend of nanoclu-ster and nanomeric fillers, whereas Fig. 9.5B shows a TEM of the nanocomposite showing the presence of the two types of nanofillers. The uniqueness of the nanofilled composite is that it has the mechanical strength of a microhybrid but at the same time retains smoothness during service like a microfill. The initial gloss of many restoratives is quite good but in hybrid composites (microhybrids, nanohybrids) plucking of the larger fillers causes loss of gloss. By contrast, in the nanofilled composite, the nanoclusters shear at a rate similar to the surround-ing matrix during abrasion. This allows the restora-tion to maintain a smoother surface for long-term polish retention. Optical analysis of the polish reten-tion can be done using atomic force microscopy after extended toothbrush abrasion. Nanofillers also offer advantages in optical prop-erties. In general, it is desirable to provide low visual opacity in unpigmented dental composites. This allows for the creation of a wide range of shades and A B C FIG. 9.4 (A) Transmission electron micrograph (TEM) image of composite with nanomeric particles (×60,000 magnifica-tion). (B) TEM image of composite with nanocluster particles (×300,000 magnification). (C) TEM image of composite with hybrid fillers (×300,000 magnification). (A, B, and C From Mitra SB, Wu D, Holmes BN. An application of nanotechnology in advanced dental materials. J Am Dent Assoc. 2003;134(10):1382–1390.) B Nanomers Nanoclusters Nanocluster Nanomer A FIG. 9.5 (A) Schematic diagram of a nanofilled compos-ite containing nanoclusters and nanomers. (B) Transmission electron micrograph image of a nanocomposite with nanocluster and nanomeric fillers in Filtek Supreme Plus. (Courtesy 3M Company, St. Paul, MN.) 142 CRAIG’S RESTORATIVE DENTAL MATERIALS opacities so the clinician can design a highly esthetic restoration. In hybrid types of composites, the filler particles are 0.4 to 3.0 μm in size. When particles and resin are mismatched in the refractive index, which measures the ability of the material to transmit light, the particles will scatter light and produce opaque materials. Nanomeric fillers particles are far smaller than the wavelength of light, making them unmea-surable by refractive index. When light enters, long wavelength light passes directly through and mate-rials show high translucency. As shown by Fig. 9.6, the discs made with hybrid and microfill fillers are rather opaque. The nanofill composite sample made predominantly with the nanomeric filler is quite clear, as the background can be easily seen through the composite. In addition, when placed on a black background, the nanomeric and nanocluster parti-cles preferentially scatter blue light, giving the com-posite an opalescent effect. This gives a more lifelike appearance because natural enamel also exhibits the same effect. The ability to create a nanocomposite with very low opacity provides the ability to formulate a vast range of shade and opacity options from the very translucent shades needed for the incisal edge and for the final layer in multilayered restorations to the more opaque shades desired in the enamel, body, and dentin shades. This allows the clinician the flexibility of choosing a single shade or a multi-shade layering technique depending on the esthetic needs. The wear resistance of this material after 3 and 5 years of clinical use was found to be similar to human enamel. NANOHYBRID COMPOSITE Several manufacturers have placed nano-sized particles in their microhybrids. These composites have been described as nanohybrids. Because the smoothness and wear of any composite is often determined by the size of its largest filler particles as with microhybrids, the surface of nanohybrids becomes gradually dull after a few years of clinical service. Interfacial Phase and Coupling Agents For a composite to have successful clinical perfor-mance, a good bond must form between the inor-ganic filler particles and the organic resin matrix during setting. This is achieved through the use of compounds called coupling agents, the most com-mon of which are organic silicon compounds called silane coupling agents. The surface of the filler is treated with a coupling agent during the manufac-ture of the composite. A typical silane coupling agent is 3-methacryloxypropyltrimethoxysilane, the chem-ical structure of which is shown below. O O O Structure of 3-Methacryloxypropyltrimethoxysilane O O Si In the low-shrink silorane composite, an epoxy functionalized coupling agent, 3-glycidoxypropyltri-methoxysilane, is used to bond the filler to the oxi-rane matrix. O Si O O Structure of 3-Glycidoxypropyltrimethoxysilane O O During the filler treatment process, the methoxy groups hydrolyze to generate hydroxyl groups through an acid-or base-catalyzed reaction. These hydroxyl groups then undergo condensation with the hydroxyl groups on the surface of the filler and become attached by covalent bonds (see the follow-ing schematic sketch). Condensation is also possible with the adjacent –OH groups of the hydrolyzed silanes or with water absorbed on the surface of the filler. This results in the formation of a very thin monolayer or multilayer polymeric film on the sur-face of the filler with unreacted double bonds. During the curing of the composite, the double bonds of the methacryloxy groups of the treated surface coreact with the monomer resins. The coupling agent plays a critical role in the composite. Its functions are as follows: • It forms an interfacial bridge that strongly binds the filler to the resin matrix. • It enhances the mechanical properties of the composite and minimizes the plucking of the fillers from the matrix during clinical wear. Hybrid Microfill Nanocomposite FIG. 9.6 Translucency of a hybrid composite, microfill composite, and a nanocomposite. (From Mitra SB, Wu D, Holmes BN. An application of nanotechnology in advanced den-tal materials. J Am Dent Assoc. 2003;134(10):1382–1390.) 143 9. Restorative Materials: Resin Composites and Polymers • The resulting interfacial phase provides a medium for stress distribution between adjacent particles and the polymer matrix. • It provides a hydrophobic environment that minimizes water absorption of the composite. R OCH3 R Matrix Filler R R R O O O OH nCH3O-Si-OCH3 nHO-Si-OH Si-O-Si-O-Si Initiators and Accelerators The curing of composites is triggered by light or a chemical reaction, with the former being more com-mon. Light activation is accomplished with blue light at a peak wavelength of about 465 nm, which is absorbed usually by a photosensitizer, such as cam-phorquinone, added to the monomer mixture during the manufacturing process in amounts varying from 0.1% to 1.0%. In methacrylate composites, free radicals are generated upon activation. The reaction is acceler-ated by the presence of an organic amine. Various amines have been used, both aromatic and aliphatic. Examples of two such amines are shown below. The amine and the camphorquinone are stable in the pres-ence of the oligomer at room temperature, as long as the composite is not exposed to light. Although cam-phorquinone is the most common photosensitizer, others are sometimes used to accommodate special esthetic considerations. Camphorquinone adds a slight yellow tint to the uncured composite paste. Although the color bleaches during cure, sometimes clinicians find shade matching difficult with the color shift. O O O O N Camphorquinone A typical amine Chemical activation is accomplished at room tem-perature by an organic amine (catalyst paste) reacting with an organic peroxide (universal paste) to produce free radicals, which in turn attack the carbon double bonds, causing polymerization. Once the two pastes are mixed, the polymerization reaction proceeds rapidly. Some composites, such as core and provisional products, are dual-cured. These formulations contain initiators and accelerators that allow light activation followed by self-curing or self-curing alone. In the silorane composite, the initiator system generates cations when irradiated with light. One of the components is the camphorquinone pho-tosensitizer enabling the composite to be cured by a dental curing unit. Other components of the initiation system are iodonium salts and electron donors, which generate the reactive cationic spe-cies that start the ring-opening polymerization process. I + O O + + Electron-Donor A-Reactive cationic species Pigments and Other Components Inorganic oxides are usually added in small amounts to provide shades that match the majority of tooth shades. The most common pigments are oxides of iron. Numerous shades are supplied, ranging from very light shades to yellow to gray. Various color scales are used to characterize the shades of the com-posites. A UV absorber may be added to minimize color changes caused by oxidation. Darker and more opaque shades of composites cannot be cured to the same depth as the lighter translucent shades. Fluorescent agents are sometimes added to enhance the optical vitality of the composite and mimic the appearance of natural teeth. These are dyes or pigments that absorb light in the UV and vio-let region (usually 340 to 370 nm) of the electromag-netic spectrum, and reemit light in the blue region (typically 420 to 470 nm). These additives are often used to enhance the appearance of color causing a perceived “whitening” effect, making materials look less yellow by increasing the overall amount of blue light reflected. 144 CRAIG’S RESTORATIVE DENTAL MATERIALS 2 Initiation Stage Example: Benzoyl peroxide Free radical ( R ·) Camphorquinone Amine Light Free radical Free radical Monomer Propagation Stage C O O O C O C O O O O N O R · O· C R C · Initiator or chemical reaction light, heat Free radical R · R · CH3 CH3 + + Growing chain R C · C R C C · CO2CH3 + CH3 CH2 CO2CH3 CO2CH3 CO2CH3 CO2CH3 CO2CH3 CH2 CH2 CH2 CH2 CH3 CH3 CH3 CH3 CH2 CH3 CH2 H3C Polymerization Reactions Polymerization of Methacrylate Composites Methacrylate composites form the workhorse of direct restorative materials. The polymer network of these composites is formed by a process called free-radical addition polymerization of the corre-sponding methacrylate monomers. The polymeriza-tion reaction takes place in three stages: initiation, propagation, and termination, and is shown in the following scheme: 145 9. Restorative Materials: Resin Composites and Polymers Transfer reaction: R C· C C C· CH3 CH3 CH3 CH3 CH3 CO2R CO2R CO2R CO2R CH2 CH2 RCH + + Disproportionation reaction: . R C· C C CH3 CH3 CH3 CH3 CH2 CO2CH3 CH2R CH2R HC RCH + + CO2R CO2CH3 CO2CH3 Polymer free radical Termination Stage Combination reaction: n n+1 R C C· CH3 CH3 R· R C R CH2 CO2CH3 CH2 CH2 + CO2CH3 CO2CH3 CH3 The polymerization reaction of self-cured com-posites is chemically initiated at room temperature with a peroxide initiator and an amine accelerator. Polymerization of light-cured composites is triggered by visible blue light. The photoinitiators used are described in the section Initiators and Accelerators. Dual-cured products use a combination of chemical and light activation to carry out the polymerization reaction. At this stage an active free radical species, designated as R% in the foregoing scheme, is first formed as the initiating species. This free radical adds to a monomer species generating an active cen-ter monomer radical. The initiation stage is followed by the propagation stage during which rapid addition of other monomers molecules to the active center occurs to provide the growing polymer chain. The propagation reaction con-tinues to build molecular weight and cross-link density until the growing free radical is terminated. The termi-nation stage may take place in several ways as indi-cated, where “n” represents the number of mer units. The polymerized resin is highly cross-linked because of the presence of difunctional carbon double bonds. The degree of polymerization varies, depend-ing on whether it is in the bulk or in the air-inhibited layer of the restoration. Polymerization of light-cured composites varies by the distance of the light from the restoration and the duration of light exposure. The percentage of double bonds that react may vary from 35% to 80%. The degree of polymerization is higher for laboratory composites that are postcured at elevated temperatures and light intensities. During polymerization, molecules have to approach their “neighbors” to form chemical bonds with them. Reduction of volume, or shrinkage, is gen-erally observed during polymerization because two factors are reduced: the van der Waals volume and the free volume. The van der Waals volume is the volume of molecule itself derived from the atoms and bond lengths. Reduction in the van der Waals volume takes place during polymerization because of a change in the bond lengths (conversion of double bonds to 146 CRAIG’S RESTORATIVE DENTAL MATERIALS single bonds). The free volume of a molecular species, whether a monomer or a polymer, is the volume occu-pied by it due to its random rotational and thermal movement. When monomers are converted to poly-mers, reduction of the free volume occurs because the rotation of the polymer chain is more restricted than in unpolymerized monomer molecules. A schematic illustration of the polymerization of methacrylate resin resulting in shrinkage is shown in Fig. 9.7. Manufacturers have taken several steps to mini-mize the polymerization contraction in methacrylate composites by adopting one or more of the following methods: • filling the monomer resins with prepolymerized resins • maximizing the amount of inorganic filler • using high molecular mass methacrylate monomers In addition, incremental placement of methacry-late composites in the tooth cavity, necessitated by their limited depth of cure, controls shrinkage stress so that clinical success of the modern-day methacry-late composite is quite excellent. Polymerization of Silorane Composites Polymerization of the silorane molecule takes place through a cationic initiation process during which the oxirane segments undergo ring opening to form covalent single bonds with their neighbors. The chemistry of the polymerization is shown below: Methacrylate-volumetric shrinkage FIG. 9.7 Schematic illustration of the polymerization of methacrylate resin and resulting volumetric shrinkage. O H H+ O H+ O H O O H O H O O H O O H O O O H O O O Cationic Photoinitiator Blue light + + + + + + + Ring Opening Expansion Bond Forming Contraction Proton Initiation Propagation Expansion Expansion Contraction Contraction.... The ring-opening chemistry of the siloranes starts with the cleavage and opening of the oxirane ring. This process gains space and counteracts some of the reduction in volume when chemical bonds are established to form the polymer. A schematic diagram to depict the polymerization is shown in Fig. 9.8. The silorane composites generate lower volume shrinkage and stress upon polymerization. It is still 147 9. Restorative Materials: Resin Composites and Polymers important to place these composites in increments due to limited depth of cure. In addition, special adhesives are needed. Packaging of Composites Composites as supplied from the manufacturer are in their precured state and hence have to be pack-aged with adequate protection against inadvertent setting. The primary package is made from a plastic material that allows the diffusion of oxygen (which works as an inhibitor for methacrylate polymer-ization) and also prevents moisture absorption in humid environments. Light-Cured Composites Because the setting of light-cured composite is triggered by visible light, these materials have to be protected from premature curing when sup-plied from the manufacturer and stored in the dental office. Hence they are packaged in opaque, most often black, plastic syringes or unit-dose capsules, sometimes referred to as compules. In the latter case, a delivery gun for direct intraoral placement is provided. An advantage of the cap-sule delivery is the lower risk of cross-infection. Composite packaging and delivery systems are shown in Fig. 9.9. The composites are supplied in a variety of shades and opacities. Some manufactur-ers color code their capsule caps or syringe plung-ers for ease of identification of the shades and/or opacities. Self-Cured and Dual-Cured Composites These materials are supplied in two syringes. Two pastes are mixed to initiate the chemical cure. An example of a two-paste core build-up composite is shown in Fig. 9.10. It is advisable to store these materials in a cool temperature to prolong their shelf-life. PROPERTIES OF COMPOSITES To have good clinical service life, composites have to meet certain performance criteria. Important physi-cal, mechanical, and clinical properties are described in this section. Selected properties of various types of composites are listed in Table 9.3. Values of proper-ties for polymer-based filling and restorative mate-rials based on ISO 4049 (ANSI/ADA No. 27) are summarized in Table 9.4. Physical Properties Working and Setting Times For light-cured composites, curing is considered to be “on demand.” Polymerization is initiated when the composite is first exposed to the curing light. Stiffening takes place within seconds after light exposure by a high-intensity curing light source. A B FIG. 9.9 Single-paste, visible light–initiated composite in syringe (A) and capsules (B). (Courtesy 3M Company, St. Paul, MN.) Silorane-volumetric shrinkage FIG. 9.8 Schematic illustration of the polymeriza-tion of silorane composite and resulting volumetric shrinkage. 148 CRAIG’S RESTORATIVE DENTAL MATERIALS Although the composite restoration appears hard and fully cured after exposure to the curing light source, the setting reaction continues for a period of 24 hours. All of the available unsaturated carbon double bonds of methacrylate-based composites do not react; studies report that about 25% remain unreacted in the bulk of the restoration. A thin layer of air-inhibited, unpolymerized material remains on the surface of the polymerized layer, which is advantageous for subsequent incremental place-ment during layering. It is useful to protect the sur-face of the contoured restoration with a transparent matrix, to minimize the amount of unpolymerized resin in the final restoration. Although for some composites the final physical properties may not be reached until about 24 hours after the reaction is initiated, enough of the mechanical strength is attained immediately after curing, so the restoration can be finished and polished with abrasives and is functional. For most composites that are initiated by visible light, bright operatory lights can initiate cure prema-turely if the composite is left unprotected on a mix-ing pad. Within 60 to 90 seconds after exposure to ambient light, the surface of the composite may lose its capability to flow readily against the tooth, and further work with the material becomes difficult. The dispensed paste can be covered with an opaque or orange cover to present premature exposure to light. The setting times for chemically activated com-posites range from 3 to 5 minutes. These short set-ting times have been accomplished by controlling the concentration of initiator and accelerator. Polymerization Shrinkage and Stress As explained in the section Polymerization Reactions, all composites undergo volumetric shrinkage upon setting. Typical shrinkage values are listed in Table 9.3. Volumetric shrinkage results in the development of contraction stresses as high as 13 MPa between the composite and the tooth structure. These stresses severely strain the interfacial bond between the com-posite and the tooth, leading to a very small gap that can allow marginal leakage of saliva and microor-ganisms. Recurrent caries and marginal staining may result. This stress can exceed the tensile strength of enamel and result in stress cracking and enamel frac-tures along the interfaces. Because the development of shrinkage stress depends on the volumetric shrink-age strain and the stiffness of the composite at the time of shrinkage, low-shrinkage composites might exhibit high stress if the composite has a high elastic modulus. Adding the composite in 2-mm increments and polymerizing each increment independently can reduce the net effect of polymerization shrinkage. Net shrinkage stress is less because a smaller volume of composite is allowed to shrink before successive additions. A recent paper has reviewed the clinical and laboratory properties of several low-shrink/ low-stress composites. Most of these products are universal composites but two products are described as flowable composites. The shrinkage values are dependent on the method used. Volumetric polym-erization shrinkage for low-shrink universal com-posites using pycnometer varies from 0.9% to 1.8%, whereas that of low-shrink flowables is 2.4% to 2.5%. When the ACTA linometer was used, the values were 1.0% to 1.4% and 2.6% to 2.9%, respectively. The polymerization stress was measured from 1.2 to 1.6 MPa. In comparison, traditional universal compos-ites have been reported to have polymerization stress of 0.8 to 2.4 MPa, whereas flowables were reported to have stress values ranging from 1.3% to 3.2%. Thermal Properties The linear coefficient of thermal expansion (α) of composites ranges from 25 to 38 × 10−6/°C for com-posites with fine particles to 55 to 68 × 10−6/°C for composites with microfine particles. The α values for composites are less than the mean of the constituents added together; however, the values are higher than those for dentin (8.3 × 10−6/°C) and enamel (11.4 × 10−6/°C). The higher values for the microfilled com-posites are related mostly to the greater amount of polymer present. Certain glasses may be more FIG. 9.10 Dual-curing composite for core build-ups. (Courtesy DMG Chemisch-Pharmazeutische Fabrik GmbH, Hamburg, Germany.) 149 9. Restorative Materials: Resin Composites and Polymers TABLE 9.3 Properties of Various Types of Resin Composites, Compomers, Conventional Glass Ionomers, and Resin-Modified Glass Ionomers Property Nanocompositea Multipurpose Composite Microfill Composite Packable Composite Flowable Composite Laboratory Composite Core Composite Conventional Glass Ionomer Resin-Modified Glass Ionomer Flexural strength (MPa) 180 80–160 60–120 85–110 70–120 90–150b ― 7–15 50–60 Flexural modulus (GPa) ― 8.8–13 4.0–6.9 9.0–12 2.6–5.6 4.7–15b ― ― ― Flexural fatigue limit (MPa) ― 60–110 ― ― ― ― ― ― ― Compressive strength (MPa) 460 240–290 240–300 220–300 210–300 210–280 210–250 10–15 200–250 Compressive modulus (GPa) ― 5.5–8.3 2.6–4.8 5.8–9.0 2.6–5.9 ― 7.5–22 7.2–10.3 3.2–6.9 Diametral tensile strength (MPa) 81 30–55 25–40 ― 33–48 ― 40–50 7–15 30–40 Linear polymerization shrinkage (%) ― 0.7–1.4 2–3 0.6–0.9 ― ― ― ― ― Color stability, accelerated aging: 450 kJ/m2 (ΔE)c ― 1.5 ― ― 15 1.1–2.3 ― ― ― Color stability, stained by juice/tea (ΔE)c ― 4.3 ― ― ― 1.7–3.9 ― ― ― aFrom Mitra SB, Wu D, Holmes BN. An application of nanotechnology in advanced dental materials. J Am Dent Assoc. 2003;134(10):1382–1390. bWithout fiber reinforcement. cΔE < 3.3 is considered not clinically perceptible. 150 CRAIG’S RESTORATIVE DENTAL MATERIALS effective in reducing the effect of thermal change than are others, and some resins have more than one type of filler to compensate for differential rates. Thermal stresses place an additional strain on the bond to tooth structure, which adds to the detrimen-tal effect of the polymerization shrinkage. Thermal changes are also cyclic in nature, and although the entire restoration may never reach thermal equi-librium during the application of either hot or cold stimuli, the cyclic effect can lead to material fatigue and early bond failure. If a gap forms, the differ-ence between the thermal coefficient of expansion of composites and teeth could permit percolation of oral fluids. The thermal conductivity of composites with fine particles [25 to 30 × 10−4 cal/s/cm2 (°C/cm)] is greater than that of composites with microfine par-ticles [12 to 15 × 10−4 cal/s/cm2 (°C/cm)] because of the higher conductivity of the inorganic fill-ers compared with the polymer matrix. However, for highly transient temperatures, the composites do not change temperature as fast as tooth struc-ture and this difference does not present a clinical problem. Water Sorption The water sorption of composites with hybrid particles (5 to 17 μg/mm3) is lower than that of composites with microfine particles (26 to 30 μg/ mm3) because of the lower volume fraction of polymer in the composites with fine particles. The quality and stability of the silane coupling agent are important in minimizing the deteriora-tion of the bond between the filler and polymer and the amount of water sorption. Expansion associated with the uptake of water from oral fluids could relieve some polymerization stress, but water sorption is a slow process when com-pared to polymerization shrinkage and stress development. In the measurement of hygroscopic expansion starting 15 minutes after the initial polymerization, most resins required 7 days to reach equilibrium and about 4 days to show the majority of expansion. Because composites with fine particles have lower values of water sorp-tion than composites with microfine particles, they exhibit less expansion when exposed to water. Solubility The water solubility of composites varies from 0.25 to 2.5 mg/mm3. Inadequate light intensity and dura-tion can result in insufficient polymerization, particu-larly at greater depths from the surface. Inadequately polymerized composites have greater water sorption and solubility, possibly manifested clinically with early color instability. During the storage of microhybrid compos-ites in water, the leaching of inorganic ions can be detected; such ions are associated with a break-down in interfacial bonding. Silicon leaches in the greatest quantity (15 to 17 μg/mL) during the first 30 days of storage in water and decreases with time of exposure. Microfilled composites leach silicon more slowly and show a 100% increase in amount during the second 30-day period (14.2 μg/mL). Boron, barium, and strontium, which are present in glass fillers, are leached to various degrees (6 to 19 μg/mL) from the various resin-filler systems. Breakdown and leakage can be a contributing fac-tor to the reduced resistance to wear and abrasion of composites. Color and Color Stability The color and blending of shades for the clinical match of esthetic restorations are important. The characteristics of color are discussed in Chapter 4, and these principles can be applied specifically to composites for determining appropriate shades for clinical use. Universal shades vary in color among currently marketed products. Modern-day compos-ites are often supplied by the manufacturer in multi-ple opacities. This allows for better esthetic outcome using multiple shades of different opacities to con-struct the restoration. Change of color and loss of shade match with surrounding tooth structure are reasons for replac-ing restorations. Stress cracks within the polymer matrix and partial debonding of the filler to the TABLE 9.4 Requirements for Polymer-Based Filling and Restorative Materials Based on ISO 4049 Property Class 1 Class 2 Class 3 Working time (min, seconds) 90 — 90 Setting time (max, min) 5 — 10 DEPTH OF CURE (MIN, MM) Opaque shades — 1.0 — Other shades — 1.5 — Water sorption (max, μg/mm3) 40 40 40 Solubility (max, μg/mm3) 7.5 7.5 7.5 FLEXURAL STRENGTH (MPA) Type 1 80 80a 100b 80 Type 2 50 50a 50 aGroup 1: cured intraorally. bGroup 2: cured extraorally. 151 9. Restorative Materials: Resin Composites and Polymers resin as a result of hydrolysis tend to increase opac-ity and alter appearance. Discoloration can also occur by oxidation and result from water exchange within the polymer matrix and its interaction with unreacted polymer sites and unused initiator or accelerator. Color stability of current composites has been studied by artificial aging in a weathering chamber (exposure to UV light and elevated temperatures of 70 °C) and by immersion in various stains (coffee/ tea, cranberry/grape juice, red wine, and sesame oil). As shown in Table 9.3, composites are resistant to color changes caused by oxidation but are suscep-tible to staining. Mechanical Properties Although composites take advantage of selected properties of each constituent material, the physical and mechanical properties of the composites are dif-ferent from those of the separate phases. Factors that affect the properties of compos-ites include (1) the state of matter of the second (dispersed) phase; (2) the geometry of the second phase; (3) the orientation of the second phase; (4) the composition of the dispersed and continuous phases; (5) the ratio of the phases; and (6) bond-ing of the phases. Examples of properties that can be changed (improved if the composites are judi-ciously developed) are (1) modulus, (2) strength, (3) fracture toughness, (4) wear resistance, (5) thermal expansion, and (6) chemical and corrosion resistance. Strength and Modulus Values of compressive, tensile (tested by the diam-etral method), and flexural strengths and modu-lus for dental composites are listed in Table 9.3. Compressive strength is of importance because of the chewing forces. The flexural and compressive mod-uli of microfilled and flowable composites are about 50% lower than values for multipurpose hybrids and packable composites, which reflects the lower volume percent filler present in the microfilled and flowable composites (see Table 9.2). For comparison, the modulus of elasticity in compression is about 62 GPa for amalgam, 19 GPa for dentin, and 83 GPa for enamel. Knoop Hardness Knoop hardness for composites (22 to 80 kg/mm2) is lower than enamel (343 kg/mm2) or dental amalgam (110 kg/mm2). The Knoop hardness of composites with fine particles is somewhat greater than values for composites with microfine particles because of the hardness and volume fraction of the filler par-ticles. These values indicate a moderate resistance to indentation under functional stresses for more highly filled composites, but this difference does not appear to be a major factor in resisting functional wear. A microhardness measurement such as Knoop can be misleading on composites with large filler particles (>10 μm in diameter), in which the small indentation could be made solely on the organic or the inorganic phase. However, with most current products, filler particle sizes are much smaller (<1 μm), and the micro-hardness values appear more reliable. Bond Strength to Dental Substrates Bonding of composites to tooth structure and other dental substrates is discussed in detail in Chapter 13. A brief overview of bonding dental composites to various substrates is presented here. ENAMEL AND DENTIN The bond strength of composites to etched enamel and primed dentin is typically between 20 and 30 MPa. Bonding is principally a result of microme-chanical retention of the bonding agent into the etched surfaces of enamel and primed dentin. In dentin, a hybrid layer of bonding resin and collagen is often formed, and the bonding adhesive penetrates the dentinal tubules (Fig. 9.11). OTHER SUBSTRATES Composite can be bonded to existing composite res-torations, ceramics, and alloys when the substrate is roughened and appropriately primed (see Chapter 13). In general, the surface to be bonded is sand-blasted (microetched) with 50-μm alumina and then treated with a resin-silane primer for composite, a silane primer for silica-based ceramics, an acidic phosphate monomer for zirconia, or a special alloy primer. Bond strengths to treated surfaces are typi-cally greater than 20 MPa. 10.0 µm C A H T FIG. 9.11 Transverse section of composite bonded to dentin showing composite (C), adhesive layer (A), hybrid layer (H), and resin tags (T). 152 CRAIG’S RESTORATIVE DENTAL MATERIALS Clinical Properties Clinical requirements for composites accepted for unre-stricted use, including cuspal replacement in posterior teeth, as defined by American Dental Association (Proposed) Guidelines for Resin-based Composites for Posterior Restorations, are listed in Table 9.5. Depth of Cure (Light-Cured Composites) Light intensity decreases as the light source is moved away from the surface of an object. Furthermore, as the light travels through a scattering medium like a composite with filler particles, the light intensity is reduced. The depth of light penetration into a com-posite restoration depends on the wavelength of light, its irradiance, and the scattering that takes place within the restoration. A number of factors influence the degree of polymerization at given depths from the surface after light curing. The concentration of pho-toinitiator or light absorber in the composite must be such that it will react at the proper wavelength and be present in sufficient concentration. Both filler con-tent and particle size are critical to dispersion of the light beam. For this reason, microfilled composites with smaller and more numerous particles scatter more light than microhybrid composites with larger and fewer glass particles. Longer exposure times are needed to obtain adequate polymerization of micro-filled composites. Another important consideration is the particu-lar shade and opacity of the composite used. Many shades are intentionally opacified and have more pigments to mask discolored tooth after removal of carious tissue. These materials have higher concen-tration of opacifying agents and pigments that scat-ter more light and hence have lower depth of cure. In such cases longer exposure times and smaller incre-ments are essential for clinical success. Light intensity at the surface is a critical factor in completeness of cure at the surface and within the material. The tip of the light source should be held within 1 mm of the surface to provide optimum exposure. More opaque shades reduce light trans-mission and cure only to minimal depths (1 mm). A standard exposure time using most dental curing lights is 20 seconds. In general, this is sufficient to cure a light shade of resin to a depth of 2 or 2.5 mm, assuming that the light guide is immediately adja-cent to the restoration surface. The anatomy of the tooth often precludes the positioning of the light guide close to the restoration surface. A 40-second exposure improves the degree of cure at all depths, and is required to obtain sufficient cure with the darker shades. Because the light beam is partially col-limated and does not spread sufficiently beyond the diameter of the tip at the emitting surface, it is nec-essary to “step” the light across the surface of large restorations, so the entire surface receives a complete exposure. Larger tips have been manufactured for placement on most light-curing units. However, as the light beam is distributed over a larger surface area, the intensity at a given point is reduced. A lon-ger exposure time of up to 60 seconds should be used when larger emitting tips are used. Radiopacity It is rather difficult to locate enamel-composite margins radiographically because of the relatively low radiopacity of composites. Modern com-posites include glasses having atoms with high atomic numbers, such as barium, strontium, and zirconium. Some fillers, such as quartz, lithium-aluminum glasses, and silica, are not radiopaque and must be blended with other fillers to produce a radiopaque composite. Even at the highest vol-ume fraction of filler, the amount of radiopacity is noticeably less than that exhibited by a metallic restorative like amalgam. Some microhybrid com-posites achieve some radiopacity by incorporating finely divided heavy-metal glass particles. Others use ceramic particles containing heavy metal oxides. In the nanofilled composite, radiopacity is achieved by using nanomeric zirconia (5 to 7 nm) or by incorporating the zirconia in the nanoclus-ters along with silica. TABLE 9.5 Clinical Requirements for Resin Composites Accepted for Unrestricted Use, Including Cuspal Replacement, in Posterior Teeth Property Criteria Maintenance of color (18 months) No more than 10% Marginal discol oration (18 months) No more than 10% Marginal integrity (18 months) No more than 5% Caries: recurrent or marginal (18 months) No more than 5% Maintenance of interproximal contact (18 months) 95% showing no observable broadening of contacts Postoperative sensitivity Thorough history of adverse sensitivity to hot, cold, and biting stimuli Failure (18 months) No more than 5% Wear between 6 and 18 months No more than 50 μm Proposed American Dental Association guidelines for resin-based compos-ites for posterior restorations. 153 9. Restorative Materials: Resin Composites and Polymers Wear Rates Under clinical conditions, a composite restoration comes in contact with other surfaces such as the opposing tooth, food particles, and oral fluids, which can result in surface wear and degradation. The extent of wear is a complex phenomenon and depends on several intrinsic and extrinsic factors that are elabo-rated in Chapters 4 and 5. Many in vitro wear stud-ies have been reported but because there are many different methodologies used, standardization and direct comparison of these results with actual clinical performance are not available. It is advisable to look at controlled clinical studies when choosing a com-posite, particularly for posterior restorations. Clinical studies have shown that composites are ideal for anterior restorations in which esthetics is essential and occlusal forces are low. Wear rates are a larger concern in the posterior segments where occlusal forces and lateral excursive contacts are higher than in the anterior segment. Although ear-lier generations of composites exhibited attrition and abrasion wear, newer formulations minimize the problem. Marginal degradation is still evident and is attributed to improper preparation design, inadequate adhesion, polymerization contraction of the composite, and marginal microcracks. Marginal degradation and stain are sometimes interpreted as recurrent caries, although this is not always the case. Currently accepted composites for posterior applica-tions require clinical studies that demonstrate, over an 18-month period, a loss of surface contour less than 50 μm. Several clinical studies have been pub-lished showing that the newest generation of filled composite (nanocomposite) has excellent wear resis-tance. The nanofilled composite has been shown to exhibit wear resistance similar to that of natural human enamel in a 3-year and 5-year clinical study. Biocompatibility Details about the biocompatibility of composites are discussed in Chapter 6, but some of the central issues are discussed here. Nearly all of the major components of composites (Bis-GMA, TEGDMA, and UDMA, among others) are cytotoxic in vitro if tested as the bulk monomer, but the biological liabil-ity of a cured composite depends on the extent of release of these components from the composite. Although composites may release some low levels of components for weeks after curing, there is con-siderable controversy about the biological effects of these components. The amount of release depends on the type of composite and the method and effi-ciency of the cure of the composite. A dentin barrier markedly reduces the ability of components to reach pulpal tissues, but these components can traverse dentin barriers, albeit at reduced concentrations. The effects of low-dose, long-term exposures of cells to resin components are not generally known. By contrast, the use of composite materials as direct pulp-capping agents poses a higher risk for adverse biological responses, because no dentin barrier exists to limit exposure of the pulp to the released components. The effects of released components from com-posites on oral or other tissues are not known with certainty, although no studies have documented any adverse biological effects. The ISO standard for test-ing of toxicity of dental materials requires the testing of composites after immersion in various aqueous and organic elution media followed by the testing of the eluants for adverse biological response. The tis-sue at highest risk from this type of release would appear to be the mucosa in close, long-term contact with composites. Components of composites are known allergens, and there has been some docu-mentation of contact allergy to composites. Most of these reactions occur with dentists or dental person-nel who regularly handle uncured composite and, therefore, have the greatest exposure. There are no good studies documenting the frequency of allergy to composites in the general population. Finally, there has been some controversy about the ability of components of composites to act as xenoestrogens. Studies have proved that bisphenol A is estrogenic in in vitro tests that measure this effect using breast cancer cell growth. Trace levels of these components have been identified in some commer-cial uncured composites; however, estrogenicity from cured commercial composites has not been demon-strated. Furthermore, there is considerable contro-versy about the accuracy and utility of in vitro tests using breast cancer cells to measure a true estrogenic effect. An early study in this area, which claimed that dental sealants and composites were estrogenic in children, has since been discredited. Manipulation of composites can be found on the book’s website at uchi/restorative. COMPOSITES FOR SPECIAL APPLICATIONS Microfilled Composites These composites are recommended for low stress bearing class 3 and class 5 restorations, in which a high polish and esthetics are most important. One product has been used successfully in posterior restorations. They are composed of light-activated, dimethacrylate resins with 0.04-μm colloidal sil-ica fillers and prepolymerized resins, which are sometimes filled with colloidal silica. The total 154 CRAIG’S RESTORATIVE DENTAL MATERIALS inorganic filler loading is 32% to 50% by volume (see Table 9.2). Typical properties of microfilled composites are listed in Table 9.3. Because they are less highly filled, microfilled composites exhibit more water sorption and thermal expansion than microhybrid compos-ites or nanocomposites. Depending on the amount of prepolymerized resin, the shrinkage can be more than microhybrids or nanocomposites. Bulk Fill Composites Bulk fill composites (Fig. 9.12) have been developed to enable the restoration to be built up in thick layers of up to 4 mm and are recommended by manufactur-ers to simplify clinical technique and save time com-pared to traditional incremental placement. Although the idea of bulk fill is not new, and several materials have been available over the years, recently there has been a surge of interest in these materials. A host of new products including both flowable and high-viscosity pastes have become available from various manufacturers. The newer materials have increased translucency thus allowing for greater light transmis-sion and consequently increased depth of cure. One product incorporates a new germanium initiator to enable greater cure depths. Because of the translu-cency limitation, these materials are available only in a limited range of shades. These composites are rec-ommended for use primarily in classes 1 and 2 cavity preparations although their use is not contraindicated for other classes as long as there is adequate shade match with the surrounding tooth (see Table 9.1). A number of approaches have been taken to con-trol polymerization shrinkage stress as well as pro-vide good marginal adaptation to the axial walls and floor of the cavity due to bulk filling. In one approach, a rheology modifier that responds to sonic energy has been incorporated into the composite paste. This allows for a decrease in viscosity of the initially thick paste to provide good adaptation to the cavity sur-faces. In other approaches materials have been for-mulated to include special components to modulate the polymerization reaction and thus relieve shrink-age stress. These include the incorporation of special stress-relieving monomer, the addition of addition-fragmentation monomer, and the addition of special fillers with low elastic modulus to absorb stresses during polymerization. The flowable bulk fill composites appear to have better curing efficiency than the high-viscosity ones. Typical physical properties are listed in Table 9.3. In general, mechanical and physical properties cured in larger depths appear to be within normal range of incrementally placed traditional composites. In addi-tion, important properties include greater depth of cure compared to traditional composites. In several cases the measured volumetric shrinkage may be similar to traditional composites but the shrinkage stress is lower. There is a paucity of clinical perfor-mance data on the recent bulk fill composites and most reported evaluations are from in vitro studies. The quality of marginal adaptation seems to be com-parable to incrementally placed composites although a few studies have shown equivocal results for the bulk fill materials. Once the results of long-term clinical studies become available, the ultimate clini-cal effectiveness of these newer bulk fill composite materials will become apparent. Syringeable Composites These light-activated, low-viscosity composites are recommended for cervical lesions, restorations in deciduous teeth, and other small, low- or nonstress-bearing restorations (see Table 9.1). In much of the older dental literature these are also referred to as flowable composites. Typically, they are delivered through a needle tip attached to the head of the syringe. In some instances, they are also used as pit and fissure sealants. These composites contain dimethacrylate resin and inorganic fillers with a par-ticle size of 0.4 to 3.0 μm and filler loading of 42% to 53% by volume (see Table 9.2). These low-viscosity composite materials typically show shear thin-ning (pseudoplasticity). When expressed through a syringe tip there is a reversible structural breakdown due to disruption of the hydrogen bonds between the polymer and filler. After the material has been placed FIG. 9.12 A bulk fill composite. (Filtek, Courtesy 3M Company, St. Paul, MN.) 155 9. Restorative Materials: Resin Composites and Polymers the hydrogen bonds reform very quickly so that the material does not slump. The newest generation of syringeable compos-ites contains nanofiller particles at a volume load-ing somewhat lower than universal or multipurpose composites. Recently, self-adhesive syringeable com-posites (commonly referred to as self-adhesive flow-ables) have become available. Dual-cured syringeable composites in conjunction with bonding agents have been used in the treatment of internal resorption. This technique seals the dentinal tubules and strengthens the remaining tooth structure. Typical properties of these composites are listed in Table 9.3. Flowable composites have a low modu-lus of elasticity, which may make them useful in cer-vical abfraction areas. Because of their lower filler content, they exhibit higher polymerization shrink-age and lower wear resistance than universal com-posites. The viscosity of these composites allows them to be dispensed by a syringe with a needle tip for easy handling. Gentle heating of higher-viscosity composites can improve their flow and enable them to be placed as flowable composites. Laboratory Composites Laboratory composites are used to fabricate den-tal prosthetic devices extraorally and then affixed to the tooth preparation with the aid of adhesives. Although the newest generations of direct compos-ites have excellent properties, their use can still be a challenge for large cavities with high C-factors due to concerns of polymerization stress leading to microleakage, postoperative sensitivity, poor interproximal margins, and recurrent caries. In such cases a prefabricated and indirectly placed laboratory composite is clinically preferred. The basic composition of the laboratory composites is similar to the new generation of direct composites prior to the polymerization step. Crowns, inlays, and veneers bonded to metal copings can be pre-pared with composites processed in the laboratory (see Table 9.1), using various combinations of light, heat, pressure, and vacuum to increase the degree of polymerization, density, mechanical properties, and wear resistance. Typical properties of laboratory composites are listed in Table 9.3. Although their ultimate mechani-cal properties are not as high as ceramic restorations, due to their lower modulus and stress absorption capacity these polymeric composites are often the materials of choice for certain clinical situations where a considerable amount of masticatory force is transmitted to the restoration (e.g., coronal restora-tion on a dental implant). For increased strength and rigidity, laboratory composites can be combined with fiber reinforcement. Restorations are usually bonded with resin cements. Core Build-Up Composites If sufficient tooth structure remains to retain and support a full-coverage restoration, but extensive regions of dentin have been lost to disease, the core of the tooth can be restored before final preparation and impression. Composites are commonly used in this application. Core composites are available as self-cured, light-cured, and dual-cured products. Core composites are usually tinted (blue, white, or opaque) to provide a contrasting color with the tooth struc-ture. Some products release fluoride. An example of a composite core build-up is shown in Fig. 9.13. Typical properties of core composites are listed in Table 9.3. Composite cores have the following advantages as compared with amalgam: they can be bonded to dentin, can be finished immediately, are easy to contour, and can have a more natural color under ceramic restorations. Composite cores are bonded to remaining enamel and dentin using bonding agents. A bonding agent recommended by the manufacturer of the core material should be used because some self-cured composite core materials are incompatible with some light-cured bonding agents. Retention of the final restoration should not rely on the composite structure alone because adhesion of the composite core to remaining dentin alone is insufficient to resist rotation and dislodgement of the crown. Provisional Composites Provisional restorations maintain the position of the prepared tooth, seal and insulate the prepa-ration and protect the margins, establish proper vertical dimension, aid in diagnosis and treatment planning, and help to evaluate candidates for FIG. 9.13 A reconstructed composite resin core pre-pared for a cast metal crown. (Courtesy Dr. Charles Mark Malloy, Portland, OR.) 156 CRAIG’S RESTORATIVE DENTAL MATERIALS esthetic replacements. Provisional inlays, crowns, and fixed partial dentures are usually fabricated from acrylic resins or composites. Provisional res-torations fabricated from composites are generally harder, stiffer, and more color stable than those made from acrylics. GLASS IONOMERS GIs are water-based, self-adhesive restorative mate-rials in which the filler is a reactive glass called FAS glass and the matrix is polymer or copolymer of car-boxylic acids. The setting reaction of these materials involves an acid-base reaction. They are used as fill-ing materials in clinical situations where isolation is a problem and fluoride release is desirable for the patient. There are two main types of GIs: • Conventional GI • RMGI Components and Setting Reaction of Conventional Glass Ionomer GIs, invented in the 1970s, combine the technologies and chemistry of silicate and zinc polycarboxylate materials to incorporate the desirable characteristics of both. Thus they contain finely ground FAS glass filler that is ion leachable but avoids the suscepti-bility to dissolution (a disadvantage in silicates) by substituting phosphoric acid with the polymeric carboxylic acids of zinc polycarboxylate materials. The materials are supplied as two-part powder-liquid systems that require mixing. The original systems have undergone several modifications but all conventional GIs have the following essential components: • Polycarboxylic acid • FAS glass • Water • Tartaric acid The polymeric matrix of most GIs is a copolymer of acrylic acid and itaconic acid or maleic acid. In most cases this is formulated as a concentrated aque-ous liquid. Tartaric acid is added to control the work-ing and setting characteristics of the material. The powder consists of an acid-reactive comminuted FAS glass and has ions such as calcium, strontium, and lanthanum. When heavy-metal ions are used the set material is radiopaque to x-rays. When the powder and liquid are mixed, an acid-base setting reaction begins between the FAS glass and the polycarboxylic acid. An initial set is achieved within 3 to 4 minutes of mixing but the ionic reaction continues for at least 24 hours or more so that maturation is achieved much later. Maturation time has been improved in newer formulations to allow finishing after 15 min-utes of placement of the mix. The actual process of ion extraction and complex formation is quite elabo-rate; however, the essential steps are described in the scheme shown. All carboxylic acids have a common organic functional group denoted by COOH. In presence of water the COOH group undergoes partial ion-ization to yield a carboxylate anion COO− and a hydrated proton, H+3O (see below, reaction 1). The hydrated proton attacks the surface of the glass par-ticles releasing calcium and aluminum ions. The carboxylate ions from the polymer react with these metallic ions to form a salt bridge, resulting in gela-tion and setting. During the initial setting, calcium ions are more rapidly bound to the polyacrylate chains; binding to the aluminum ions occurs at a later stage. The strength of the cement builds with time. Silicic acid is initially formed when the glass breaks down, but rapidly polymerizes to form silica hydrogel (see below, reaction 4). A very important by-product of the setting reaction is the release of fluoride ions from the glass matrix. This fluo-ride release process is sustained and occurs over a long period. It is important to understand that this fluoride ion release is a result of the setting reac-tion and the ion-exchange process in the cement. In this process the fluoride from the glass is being replaced by carboxylates and water. Hence if prop-erly formulated, there is little chance of the cement losing its strength with time. Considerable research has shown no loss of strength of the cement during years of storage in water. 157 9. Restorative Materials: Resin Composites and Polymers CO2H CO2H CO2H CO2-F-M+n M+n where M+n denotes metal ion CO2-CO2-CO2-COO COO COO COO COO COO + + + (1) (2) (3) (4) + + FAS glass CO2-AIF2 +, AIF+2, AI+3, Ca+2, Sr+2 etc. AIF2 +, AIF+2, AI+3, Ca+2, Sr+2 CO2-H2O H2O H3O+ Si(OH)4 Si(OH)4 Silica hydrogel Setting Mechanism of Conventional Glass Ionomers H3O+ Water plays several important roles in the over-all setting. First, it provides for the ion transport needed for the acid-base setting reaction and fluoride release. Second, a portion of the water is also chemi-cally bound in the set complex and provides stability to the restorative material. Water also provides plas-ticity during the manipulative stages. The set cement is constituted by a hydrogel of cal-cium, aluminum, and fluoroaluminum polyacrylates involving the unreacted glass particles sheathed by a weakly bonded siliceous hydrogel layer. About 20% to 30% of the glass is dissolved in the reaction. Smaller glass particles may be entirely dissolved and replaced by siliceous hydrogel particles contain-ing fluorite crystallites. The stability of the matrix is given by an association of chain entanglement, weak ionic cross-linking, and hydrogen bonding. Significant advances have been made in formula-tion of conventional GIs in recent years to improve their manipulation and mechanical properties. Fast hardening has been achieved by altering the particle size and particle size distribution of the glass pow-der. One manufacturer coats the powder particles with a polymeric material for easy mixing. Cermets The early conventional GIs were not very strong mechanically, so the glasses were fused with metals such as gold, silver, titanium, and silver to improve their strength. These materials are called cermets. The commercial systems are made from silver fused to the glass. Although the wear resistance is better than the conventional materials, the flexural strength and abrasion resistance are not significantly better while the fluoride release is diminished. Because of the presence of metallic phase, the cermet cements are gray in color. 158 CRAIG’S RESTORATIVE DENTAL MATERIALS Components and Setting Reactions of Resin-Modified Glass Ionomers To create a longer working time yet quick setting time so that immediate finishing can take place, the con-cept of RMGI was introduced in the late 1980s. The essential components are similar to those in conven-tional GIs in which an aqueous polycarboxylic acid undergoes an acid-base setting reaction with FAS glass. To this methacrylate components are added in limited amounts so a photoinitiated and/or redox curing reaction of the double bonds can also occur. Although commercial materials vary widely in com-position, the essential components of true RMGIs are: • Polycarboxylic acid polymer: one manufacturer uses a polycarboxylic acid in which some pendant methacrylate groups are provided • FAS glass • Water • Hydrophilic methacrylate monomer • Free radical initiators The RMGIs contain some methacrylate com-ponents common in resin composites. There are two ways in which methacrylate components can be introduced. In the first type the polycarboxylic acid polymer chain is modified to contain a pen-dant methacrylate group. A common way of doing this is to react some of the carboxylic acid groups of the polycarboxylic acid with isocyanatoethyl meth-acrylate to provide pendant methacrylate groups connected through the hydrolytically stable amide linkages. The first commercial GI was introduced using this type of chemistry. In addition to the methacrylate-modified carbox-ylic acid, the liquid portion contains a water-miscible methacrylate monomer; for example, hydroxy ethyl methacrylate or glycerol dimethacrylate. In another type of RMGI system, the polymer is unmodified polycarboxylic acid. In this case the liquid is formu-lated with a mixture of hydrophilic methacrylate monomers and water. Generally, the water content of these materials is lower and the monomer content higher than for the first type. As a result, the coeffi-cient of thermal expansion of these GIs is high. Free radical initiators are added to trigger the curing of the methacrylate groups. Visible light initiators and/ or self-cure redox initiators are employed to effect this curing and covalent cross-linking reaction. The FAS glass of the RMGI systems is similar in composition to the glasses described for conventional GIs, although some variations are made in order to match the refractive index of the glass with that of the matrix. It is also common to treat the surface of the glass with an organic modifier. Two distinct types of curing reactions take place in a true light-cure GI: the traditional acid-base GI cure and the free-radical methacrylate polymeriza-tion. In the laboratory the former can be followed by infrared spectroscopy through the appearance of carboxylate ion peaks. This is shown in the following reaction scheme. The methacrylate reaction, being a chain polymerization, proceeds at a rate that is sev-eral orders of magnitude higher than the acid-base reaction. In practice, the extent to which each of these two reactions occurs is very dependent on a partic-ular system. If the system is low in water and high in the methacrylate components, the ionization of HOOC HOOC HOOC OC O Polymeric Component of Some Popular Commercial Resin-Modified Glass Ionomers O n NH HOOC COOH 159 9. Restorative Materials: Resin Composites and Polymers the polycarboxylic acid will be severely suppressed resulting in little acid-base reaction. The extent of acid-base reaction is easily detected by chemical techniques such as Fourier transform infrared spec-troscopy and electron spectroscopy for chemical analyses (ESCAs). (1) (2) (3) (4) (5) Setting Reaction of Resin-Modified Glass Ionomer (Light-Cure Type) + + + FAS glass AI+3, AIF+2, AIF2+ etc. AI+3, AIF+2, AIF2+ etc. H2O H2O Si(OH)4 H+ COO COO COO COO COO COO COO COO COO AI AI AI AI COO COO COO COO COOH COOH COOH COOH COO COO COO COO COO COO hv HEMA AI AI AI AI COO COO-COO-COO-COO-COO-COO-COO-COO-Tri-Cure Glass Ionomer System These are RMGIs with an additional curing mode. If only photoinitiators are used for cross-linking of the methacrylate groups, the RMGI has to be cured in layers because penetration of visible light can occur only to a limited depth. This is not a disadvantage in applications where thin layers of materials are to be placed; for example, for lining 160 CRAIG’S RESTORATIVE DENTAL MATERIALS or basing. However, for restorative and core build-up application, the need for incremental filling is a drawback. This problem has been overcome in the so-called tri-cure GI system. Here, in addition to the photoinitiators, self-cure redox imitators are added so that the methacrylate polymerization can proceed in the absence of light. The three curing reactions are as follows: 1. Acid-base GI reaction 2. Light-activated polymerization 3. Chemically activated polymerization CO2H Functionalized polyacid Setting Reactions in Tri-Cure Glass Ionomer System Light Redox Catalysts HEMA HEMA + + F 1 2 3 Acid-Base Reaction Free radical light cure Oxidation-Reduction dark cure Fluoroaluminosilicate Glass CO2H CO2H CO2H CO2 O2C O2C O2C Al+3 CO2H CO2 O2C Al+3 O2C CO2H CO2 O2C Al+3 H2O CO2H Reactions 2 and 3 are chemically similar but dif-fer in the mode of initiation. Reactions 1 and 3 take place spontaneously when the powder and liquid are mixed. Reaction 2 occurs only when initiated by light. The introduction of tri-cure technology has allowed RMGIs to be used as bulk-cured materials, thus saving time for the practitioner. In one com-mercial system, the redox initiators are microencap-sulated separately in polymers and added to the powder. The spatulation and mixing of the powder and liquid trigger the release of the catalysts from the microcapsules resulting in the autocuring. Although several commercial products claim to have the tri-cure chemistry, it is important to become familiar with the instructions for use and realize that there are very important differences between them. In a true tri-cure, the redox cure is quite rapid to allow the material to be placed in bulk, if desired. Nanoionomer The latest advancement in RMGIs is the nanoiono-mer available commercially since 2007. This mate-rial is a RMGI in which some nanoparticles such as nanomers and nanoclusters (see the section Nanofillers and Nanocomposites) are added to the FAS glass. Like all RMGIs, it has an aqueous compo-nent with a polycarboxylic acid and water-miscible methacrylate monomers. The addition of nanopar-ticles improves the polishability and the optical characteristics of the cured ionomer. The FAS of 161 9. Restorative Materials: Resin Composites and Polymers this material has very high surface area so that the fluoride release is not compromised. Infrared and ESCAs have confirmed the presence of significant acid-base reaction. Packaging of Glass Ionomers GIs are two-part systems. Until recently all GIs con-sisted of a powder component and a liquid compo-nent. The powder is commonly provided in a jar and is dispensed with a measuring spoon while the liquid is provided in a vial with a dropper tip for use of dis-pensing. After dispensing the recommended ratio of powder and liquid according to the manufacturers’ directions, the components are hand spatulated. In some cases it is recommended that the mixed mate-rial be transferred to a syringe and injected into the tooth preparation. To aid in the dispensing and mixing the GIs are also supplied in single-unit encapsulated version. The powder and liquid are kept separated in the capsule for shelf-stability. Prior to clinical use the capsule is activated and then triturated in an amal-gamator to mix the two components. An applicator is provided which pushes the mixed material through a narrow tip so that it can be directly placed in the oral preparation. Recently, the RMGIs have been formulated in paste-liquid or two-paste systems. During manu-facture the FAS powder component is mixed with a small amount of resin to provide a pastelike con-sistency. The liquid may be left as such or alterna-tively formulated with a nonreactive glass and also provided as a paste. The manufacturer provides the two components in a dual-barrel syringe type of con-struction (Fig. 9.14). During use the two components are extruded by a lever in a predetermined ratio in the amount needed for the clinical preparation. The variability in dispensing is expected to be less in these types of dispensers. Furthermore, mixing by spatulation is more facile than with powder-liquid materials. The latest advancement in dispensing of two-paste systems is an automixable, single-unit direct deliv-ery device (Fig. 9.15). In this device, the two pastes are placed in two side-by-side compartments. The nozzle of the capsule contains a ministatic mixer. In use, the nozzle is lifted and positioned parallel to the barrels. An applicator then pushes out the two pastes into the nozzle where mechanical mixing occurs and the paste is extruded through the tip directly into the tooth preparation. The system is said to produce less microbubbles in the restoration, a condition that could potentially arise during trituration. Manipulation of GIs can be found on the book’s website at restorative. Clinical Applications of Glass Ionomers Clinically, both conventional and RMGIs are used for a variety of restorative applications, particularly in situations of high caries activity or where caries is likely to recur. The main clinical indications are for small lesions (long-term nonstress bearing res-torations in permanent teeth, interim restoration in permanent teeth, and in the atraumatic restoration technique) especially where one or more margins are on dentin. They make an excellent liner or base in all deep lesions where demineralized dentin remains on the cavity floor to be remineralized. They are also advocated for a technique known as “sandwich-ing”, “layering,” or “stratification,” where a resin composite is bonded over a base of the GI. Because of their low modulus, they are often advocated for class V restorations and abfraction lesions where tooth flexure is more pronounced. RMGIs are often the material of choice for pediatric restorations and preventive applications (direct filling as well as core build-up), because they are one-step procedures and require minimal isolation during placement. Some products are indicated for erupting permanent first and second molars with partially exposed grooves that are not yet able to be sealed with conventional resin sealant. Properties of Glass Ionomers Like many two-part systems the properties of GIs, both conventional type and resin-modified, are quite dependent on the ratio of polycarboxylic acid and FAS glass components dispensed. Particular care has to be exercised for powder-liquid hand-mixed systems to ensure accurate proportions. The ISO standard 9917 for water-based cements provides some require-ments of GIs as restorative materials, whereas the ISO standard 9917-2 covers the properties of RMGIs. Comparative properties are shown in Table 9.3. Physical, Mechanical, and Thermal Properties The physical and mechanical properties of GIs are lower than those of composite resins and hence these materials are indicated for conservative restorations. The physical properties of the RMGIs, including wear resistance and dimensional stability, are improved over the conventional counterparts (Table 9.3). The additional covalent cross-linking in the matrix due to the polymerization of the methacrylate groups con-tributes toward this improvement. The modulus of the RMGIs is low during the initial set by light acti-vation but increases over time as the acid-base reac-tion completes. This unique characteristic makes the RMGI particularly attractive when used as liner or as the base in sandwich restorations under resin com-posites because it can relieve the stress associated with the polymerization shrinkage of the latter. 162 CRAIG’S RESTORATIVE DENTAL MATERIALS A B FIG. 9.14 Paste-liquid resin-modified glass ionomer dispensers. (A) Paste-Pak; (B) Clicker. (A, Courtesy GC America, Alsip, IL; B, Courtesy 3M Company, St. Paul, MN.) FIG. 9.15 Single-unit automix dispensing “Quick Mix” Capsule for a two-paste resin-modified glass ionomer. The dispensing tip contains a ministatic mixer for automixing when expressed by a delivery gun device. (Courtesy 3M Company, St. Paul, MN.) The thermal diffusivity and coefficient of thermal expansion of several conventional and RMGIs have been shown to be closer to tooth structure (dentin) than resin composites. Such materials should, there-fore, serve as good insulation against thermal shock particularly when used as liners and bases. However, because products from different manufacturers vary widely in their thermal expansion coefficient values, it is advisable to check the values of individual mate-rials. In general, the products that have the smallest proportion of resin component exhibit the lowest coefficient of thermal expansion values. Fluoride Ion Release and Uptake A particularly beneficial characteristic of GIs, con-ventional or resin modified, is that these materials act as a reservoir of fluoride ions. The fluoride is released by an ion-exchange mechanism from these materials. Research has shown that the released fluo-ride ions are taken up by the associated enamel and dentin, rendering those tooth structures less suscep-tible to acid challenge by a combination of decreased solubility and disruption of the activity of cariogenic bacteria. The release of fluoride ion is sustained over prolonged periods (Fig. 9.16). These materials also have been shown to act as fluoride reservoirs in the oral environment by taking up salivary fluoride from dentifrices, mouthwashes, and topical fluoride solu-tions. Fluoride has been measured in plaque samples immediately adjacent to RMGI restorations (see Fig. 8.9). Fluoride ion dynamics is particularly advanta-geous for those with high susceptibility to dental 163 9. Restorative Materials: Resin Composites and Polymers Time (days) 0 60 120 180 240 300 360 420 480 0 500 1000 1500 2000 2500 3000 3500 4000 Cumulative fluoride release, ppm Vitremer Fuji II LC Ketac nano Fuji IX FIG. 9.16 Fluoride release from typical glass ionomers. (From Mitra SB, Oxman JD, Falsafi A, Ton TT. Fluoride release and recharge behavior of a nano-filled resin-modified glass ionomer compared with that of other fluoride releasing materials. Am J Dent. 2011;24(6):372–378.) caries. A vast amount of in vitro and in situ research and a limited number of clinical studies have been carried out to assess the clinical benefit of the fluo-ride. Most of these studies have shown the utility of these materials when medium to high caries activity is present. Adhesion GI materials have good clinical adhesion to tooth structure. Unlike the resin-based composite materi-als, etching of the enamel or dentin surface by phos-phoric acid is not needed. Hence these materials are sometimes referred to as being “self-adhesive.” Preconditioning of the tooth surface is recom-mended for some products, especially those with high powder-to-liquid ratio to ensure good wetting. One of the following procedures is used for the pretreatment: • The cavity surface is conditioned using 10% to 20% polyacrylic acid for 10 seconds, washed well to remove the conditioner and surface debris, and dried. • For some RMGI restoratives (identified by manufacturers as primer or self-conditioner), a dilute polycarboxylic acid-based solution is applied on the cavity surface and set through light. This ensures good contact of the viscous mix of the GI with the tooth while not impeding ion-exchange reactions. The mechanism of adhesion to the tooth structure is mostly chemical in nature and proceeds through an exchange of ions arising from both the tooth and restoration. Calcium-polyacrylate bonds have been shown by some products by in vitro ESCA studies. A small amount of micromechanical bonding has been exhibited by some RMGIs. Laboratory measurements of bond strengths of conventional and RMGIs to tooth structure have generally yielded lower values than with the com-bination of resin adhesives and composites. The fail-ure is usually cohesive in the GI, hence it is doubtful if these laboratory measurements reflect the actual interfacial adhesion. However, retrospective clinical analyses of in vivo studies have shown RMGIs to provide excellent retention and sealing of the tooth. One of the reasons for this is due to the relief of exter-nal stress provided by the dual-curing reactions of this class of materials. RMGIs have been recognized as one of the best treatments for minimizing postoperative sensitivity in restored teeth. There are two reasons for this. First, because prior etching is not needed during placement, the collagen fibrils are not demineralized and collapse of the denuded layers cannot occur. Second, the dual-setting mechanism and gradual build-up of modulus allow the material to absorb considerable amount of shrinkage stresses thus minimizing the effect of con-traction forces at the tooth-restoration interfaces. COMPOMERS Compomers or poly acid–modified composites are used for restorations in low stress–bearing areas, although a recent product is recommended by the manufacturer for class 1 and class 2 restorations in adults (see Table 9.1). Compomers are recommended for patients at medium risk of developing caries. Composition and Setting Reaction Compomers contain poly acid–modified monomers with fluoride-releasing silicate glasses and are for-mulated without water. Some compomers have 164 CRAIG’S RESTORATIVE DENTAL MATERIALS modified monomers that provide additional fluoride release. The volume percent filler ranges from 42% to 67% and the average filler particle size ranges from 0.8 to 5.0 μm. Compomers are packaged as single-paste formulations in compules and syringes. Setting occurs primarily by light-cured polymer-ization, but an acid-base reaction also occurs as the compomer absorbs water after placement and upon contact with saliva. Water uptake is also important for fluoride transfer. Properties Typical properties of compomers are listed in Table 9.3. Compomers release fluoride by a mechanism similar to that of glass and hybrid ionomers. Because of the lower amount of GI present in compomers, the amount of fluoride release and its duration are lower than those of glass and hybrid ionomers. In addition, compomers do not recharge from fluoride treatment or brushing with fluoride dentifrices as much as glass and hybrid ionomers. Manipulation Compomers are packaged in unit-dose compules. They require a bonding agent to bond to tooth struc-ture. The material is to be cured by light in incre-ments of 2 to 2.5 mm. LIGHT-CURING UNITS The most common light sources used in dentistry to photoactivate composites are quartz-tungsten-halogen (QTH) and blue light-emitting diode (LED). Defini-tions of terms that describe light sources used to acti-vate dental resins are listed in Table 9.6. Quartz-Tungsten-Halogen Light-Curing Units QTH light-curing units can be used to activate polym-erization of composites. The peak wavelength varies among units from about 450 to 490 nm. Typically, the irradiance ranges from 400 to 800 mW/cm2, but higher-intensity QTH units are available. Some units can be controlled to provide two or three different intensities (step cure) or at a continuously increas-ing (ramp cure) intensity. A typical 2-mm-thick resin composite restoration requires a radiant exposure of 8 J/cm2 (400 mW/cm2 × 20 seconds = 8000 mW s/cm2) for proper polymerization. A QTH light source consists of a broad-spectrum light bulb (typically 75 W), several filters, a reflector, a fan, a power supply, and a light guide. The broad-spectrum output of the QTH bulb is clipped by a blue bandpass filter that only allows a narrow band of wavelengths centered around 470 to 480 nm (blue wavelengths) to be transferred to the light guide. A UV filter blocks passage of UV wavelengths. A dichroic reflector focuses the light on the end of the light guide. The reflector also enables infrared wave-lengths to dissipate as heat through the back of the housing. Because substantial heat is generated by the 75 W bulb, a fan is necessary to cool the bulb and assembly. Bulb life ranges from 50 to 75 hours. Because of the high intensity of the light, the operator should not look directly at the tip or the reflected light from the teeth. A number of devices are marketed to filter the visible-light beam so the operator can directly observe the curing procedure and to protect the patient and staff. Some lamps produce considerable heat at the curing tip, which may produce pulpal irritation. Maintenance of QTH lights must be provided on a regular basis, as sum-marized in Table 9.7. Blue Light-Emitting Diodes Solid-state LEDs use junctions of doped semicon-ductors (p-n junctions) based on gallium nitride to emit blue light. The spectral output of blue LEDs falls between 450 and 490 nm, so these units are effective for curing materials with camphorquinone photoinitiators. LED units (Fig. 9.17) do not require a filter, have a long life span, and do not produce as much heat as QTH devices. Heat becomes a concern even with LED sources, when large arrays are used. Because the output spectrum of blue LEDs matches the absorption spectrum of camphorquinone more closely than QTH sources, it is thought that blue LED sources are more efficient. For QTH sources, most of the light energy is discarded because QTH is a broad-spectrum source and only the wavelengths absorbed by camphorquinone are desired. For LED sources, the emission is not filtered. This, however, does not make LED sources more efficient in activating the camphorquinone photoinitiator than QTH. Creation of photons is dependent only on the energy applied in the absorbable wavelengths. Unlike the halogen lights, the heat generated from LED curing lights is much less, which means it does not require a fan to cool it; however, the heat at the tip of the light can be high. Thus these are lighter in weight and smaller than the halogen units. Because LEDs inherently have low consumption of power, they can use rechargeable batteries, making them por-table. The newer generation of LED lights has dramat-ically decreased size and is lighter, more ergonomic, and easier to use. They are also high powered and emit light intensity of 1000 to 1400 mW/cm2. This fea-ture allows more efficient and deeper curing depths. Composites cured with LED units have flexural properties similar to those cured with QTH units. Depth of cure with LED units appears to be higher. 165 9. Restorative Materials: Resin Composites and Polymers PROSTHETIC APPLICATIONS OF POLYMERS Acrylic polymers have a wide variety of applications in restorative dentistry as denture bases, artificial teeth, denture repair materials, impression trays, provisional restorations, and maxillofacial appli-ances for skeletal defects. The vast majority of dentures made today are fabricated from heat-cured poly(methyl methacry-late) and rubber reinforced poly(methyl methacry-late). Fractures of dentures still occur, but are usually associated with carelessness or unreasonable use by the patient. Considering functional stresses, the oral environment, and expected service life, denture base materials perform remarkably well. Physical Form and Composition Denture base plastics are commonly supplied in a powder-liquid or a gel form. The powder-liquid type may contain the materials listed in Box 9.1. Powder Most commercial materials contain poly(methyl methacrylate), modified with small amounts of ethyl, butyl, or other alkyl methacrylates to produce a polymer somewhat more resistant to fracture by impact. The powder also contains an initiator such as benzoyl peroxide or diisobutylazonitrile to initi-ate the polymerization of the monomer liquid after being added to the powder. The peroxide initiator may be added to the poly-mer or be present as a residual from the polymeriza-tion reaction and is present in amounts from 0.5% to 1.5%. Pure polymers, such as poly(methyl methacry-late), are clear and are adaptable to a wide range of pigmentation. Colorants are added to obtain the various tissuelike shades and zinc or titanium oxides are used as opacifiers. Dyed synthetic fibers made from nylon or acrylic are usually added to simulate the small capillaries of the oral mucosa. Plasticizers such as dibutyl phthalate may be incorporated in the powder or the monomer. Adding glass fibers and alumina (sapphire) whis-kers increases the stiffness, decreases the thermal coefficient of expansion, and increases thermal diffusivity. Polyethylene-woven yarn and polyara-mid fabric have also been used to reinforce acrylic polymers. TABLE 9.6 Definitions of Terms Used to Describe Light Sources for Polymerization of Dental Resins Term Unit Definition Spectral emission nm Effective bandwidth of wavelengths emitted by light source Spectral requirement nm Bandwidth of wavelengths required to activate photoinitiator(s) of dental resin Flux mW Number of photons per second emitted by light source Irradiance or radiant exitance mW/cm2 Number of photons per second emitted by light source per unit area of curing tip Energy Ja Flux × time Energy density J/cm2 Radiant exitance ×time aJoule (J) = 1000 mW × s TABLE 9.7 Factors Causing Decrease in Intensity of Light from Quartz-Tungsten-Halogen Light-Curing Units and Maintenance Hints Factors Maintenance Hints Dust or deterioration of reflector Clean or replace reflector Burn-out of bulb filament Replace bulb Darkening/frosting of bulb Replace bulb Age of components Monitor intensity, replace unit Chipping of light tip Replace light tip Resin deposit on light tip Clean or replace light tip Change in line voltage Get built-in voltage regulator Lack of uniformity across light tip Overlap curing on larger surface Increased distance of tip from material to be cured Keep light tip close to material FIG. 9.17 LED source for photoinitiation. (Espe Elipar S10, Courtesy 3M Company, St. Paul, MN.) 166 CRAIG’S RESTORATIVE DENTAL MATERIALS Liquid The liquid component of the powder-liquid type acrylic resin is methyl methacrylate, but it may be modified by the addition of other monomers. Because these monomers may be polymerized by heat, light, or traces of oxygen, inhibitors are added to give the liquid adequate shelf life. The inhibitor most commonly used to prevent premature polym-erization is hydroquinone, which may be present in concentrations of 0.003% to 0.1%. When a chemical accelerator rather than heat is used to speed up the peroxide decomposition and enable the polymerization of the monomer at room temperature, an accelerator is included in the liquid. Common accelerators are amines such as N,N-dimethyl-para-toluidine and N,N-dihydroxyethyl-para-toluidine. These systems are referred to as self-curing, cold-curing, or autopolymeriz-ing resins. The pour type of denture resin is included in this category. Plasticizers are sometimes added to produce a softer, more resilient polymer. They are generally relatively low-molecular-weight esters, such as dibu-tyl phthalate. Plasticizer molecules do not enter the polymerization reaction but do interfere with the interaction between polymer molecules, making the plasticized polymer softer than the pure poly-mer. One disadvantage in using plasticizers is that they gradually leach out of the plastic into oral flu-ids, resulting in hardening of the denture base. A polymer also may be plasticized by the addition of some higher ester such as butyl or octyl methacry-late to methyl methacrylate. The esters polymerize and form a more flexible plastic. This type of internal plasticizing does not leach out in the oral fluids, and the material remains flexible. If a cross-linked polymer is desired, organic com-pounds such as glycol dimethacrylate are added to the monomer. Cross-linking compounds are char-acterized by reactive –CR=CH– groups at opposite ends of the molecules and serve to link long poly-mer molecules together. Using cross-linking agents provides greater resistance to minute surface crack-ing, termed crazing, and may decrease solubility and water sorption. Cross-linking materials may be pres-ent in amounts of 2% to 14%, but have little effect on the tensile strength, flexural properties, or hardness of acrylic plastics. A discussion of the properties of denture plastics for dental bases, other properties of dental polymers, and denture teeth can be found on the book’s web-site at ative. ATHLETIC MOUTH PROTECTORS Polymers are used in fabricating mouth protectors because they can be formed to fit the occlusal sur-faces, they are light weight, and they are resilient. Mouth protectors are routinely used in football, soc-cer, ice hockey, basketball, wrestling, field hockey, softball, and other sports. As a result of the possi-bilities of orofacial injury, high-school athletes are required to wear internal mouth protectors, and the National Collegiate Athletic Association (NCAA) has adopted a mouth protector rule. As a result of these actions, more professional athletes are wear-ing mouth protectors. Because of the increased use of mouth protectors, it is estimated that 50,000 orofacial injuries are prevented each year. The rationale for the use of mouth protectors is that the mouth protector acts like a shock absorber when the athlete receives a blow to the mouth or chin. The mouth protector absorbs 80% to 90% of the energy of the blow and distributes the remaining energy uniformly to the entire arch, resulting in less trauma to the oral structures. Stock, mouth-formed (boil-and-bite), and custom mouth protectors are the three types available and all provide some protection to the athlete. Custom-made mouth protectors are usually vacuum formed from sheets of flexible, thermoplastic polymers about 14 cm2 in area and 1.6 to 3 mm in thickness; they may be clear or colored. In most instances the sheets are of a single material, but they may be laminates of two or more thermoplastic polymers. Laminated mouth BOX 9.1 P R I N C I PA L I N G R E D I E N T S O F A C R Y L I C D E N T U R E B A S E : P O W D E R A N D L I Q U I D Powder Acrylic polymer (or copolymer) beads Initiator Pigments Dyes Opacifier Plasticizer Dyed organic fibers Inorganic particles Liquid Monomer Inhibitor Accelerator Plasticizer Cross-linking agent 167 9. Restorative Materials: Resin Composites and Polymers protectors are fabricated so that the softer of the two layers contacts the teeth and soft tissue. Most sheets for custom mouth protectors are vinyl acetate-ethylene copolymers. 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J Am Dent Assoc. 1939;135(10):1471–1479. 2004. Provisional Materials Chung K, Lin T, Wang F. Flexural strength of a provi-sional resin material with fibre addition. J Oral Rehabil. 1998;25:214. Doray PG, Eldiwany MS, Powers JM. Effect of resin sur-face sealers on improvement of stain resistance for a composite provisional material. J Esthet Restor Dent. 2003;15:244. Doray PG, Li D, Powers JM. Color stability of provi-sional restorative materials after accelerated aging. J Prosthodont. 2001;10:212. 170 CRAIG’S RESTORATIVE DENTAL MATERIALS Farah JW, Powers JM, eds. Provisional composites and liq-uid polishes. Dent Advis. 2010;27(4):1. Grajower R, Shaharbani S, Kaufman E. Temperature rise in pulp chamber during fabrication of temporary self-curing resin crowns. J Prosthet Dent. 1979;41:535. Ireland MF, Dixon DL, Breeding LC, et al. In vitro mechani-cal property comparison of four resins used for fabri-cation of provisional fixed restorations. J Prosthet Dent. 1998;80:158. Lepe X, Bales DJ, Johnson GH. Retention of provisional crowns fabricated from two materials with the use of four temporary cements. J Prosthet Dent. 1999;81:469. Lui JL. Hypersensitivity to a temporary crown and bridge material. J Dent. 1979;7:22. Robinson FB, Hovijitra S. Marginal fit of direct temporary crowns. J Prosthet Dent. 1982;47:390. 171 Various metallic materials are used in dentistry to restore or repair individual teeth, and to replace sin-gle or multiple missing teeth, as well as entire den-tal arches. The metals used for direct restoration of tooth structure lost due to caries or fracture include dental amalgam and direct gold, though the latter is used on a very limited basis in contemporary restor-ative dentistry. Many metals are used for the indi-rect replacement of lost or damaged teeth or parts of teeth, including high-noble metals, noble metals, and predominantly base metals. The designation of these types of dental metals is based on their composition. A variety of base metals are used in dental pros-thetics, such as partial dentures, and as implants to restore lost tooth roots. These materials vary widely in terms of their composition, structures, and prop-erties, and thus are indicated for specific applica-tions based on the requirements of the given clinical situation. METALS FOR DIRECT PLACEMENT: AMALGAM An amalgam is an alloy (mixture of metallic ele-ments) of mercury and one or more other met-als. Dental amalgam is produced by mixing liquid mercury with solid particles of an alloy containing predominantly silver, tin, and copper. Zinc and pal-ladium may also be present in small amounts. It is important to differentiate between dental amalgam and the amalgam alloy, the latter being the commer-cially produced and marketed small filings, spheroid particles, or a combination of these, which are suit-able for mixing with liquid mercury to produce the dental amalgam through a chemical reaction. Once amalgam alloy is freshly mixed with liquid mercury, it has the plasticity that permits it to be conveniently packed or condensed into a prepared tooth cavity. After condensing, the dental amalgam is carved to generate the required anatomical features and then further hardens with time. Amalgam can be used for direct, permanent, posterior restorations and for large foundation restorations, or cores, which restore large areas of lost tooth structure prior to plac-ing crowns. Dental amalgam restorations are reason-ably easy to insert, are not overly technique sensitive, maintain anatomical form, have reasonably adequate resistance to fracture, prevent marginal leakage after a period in the mouth, can be used in stress-bearing areas, and have a relatively long service life. The principal disadvantage of dental amalgam is that its silver color does not match tooth structure. In addition, amalgam restorations are somewhat brittle, are subject to corrosion and galvanic action, may demonstrate a degree of breakdown at the mar-gins of tooth and amalgam, and do not help retain weakened tooth structure. Finally, there are regula-tory concerns about amalgam being disposed of in the wastewater. Despite these shortcomings, dental amalgam has a long history as a cost-effective and successful restorative material. In this chapter, the composition and morphol-ogy of the different dental amalgams are presented, followed by a discussion of low- and high-copper amalgams, the chemical reactions that occur during amalgamation, and the resultant microstructures. Various physical and mechanical properties are cov-ered in the next section, as well as factors related to the manipulation of amalgam. Composition and Morphology American National Standards Institute/American Dental Association (ANSI/ADA) specification No. 1 [International Organization for Standardization (ISO) standard 24234] for amalgam alloy includes a requirement for composition, stating that it shall con-sist primarily of silver, tin, and copper, and indium, palladium, platinum, zinc, or mercury may also be C H A P T E R 10 Restorative Materials: Metals 172 CRAIG’S RESTORATIVE DENTAL MATERIALS included in lesser amounts. This specification does prescribe a specific composition for the alloys. The ANSI/ADA specification also includes a notation about the presence of zinc in amalgam alloys, with more than 0.01% zinc classified as zinc containing and those with less than 0.01% as non-zinc alloys. Zinc has been included in amalgam alloys as an aid in manufacturing; it helps produce clean, sound castings of the ingots used for produc-ing lathe-cut alloys. The presence of contamination within the amalgam must be avoided because it can degrade the integrity of the restoration. The approxi-mate composition of commercial amalgam alloys is shown in Table 10.1. The alloys are broadly classified as low-copper (5% or less copper) and high-copper alloys (13% to 30% copper). In modern dentistry, the low-copper formulations have been essentially totally replaced by the high-copper formulations due to the improved strength, corrosion resistance, marginal integrity, and overall clinically proven better performance, as exem-plified in Fig. 10.1, where a low-copper amalgam dem-onstrates dramatically more marginal breakdown at 3 years than a high-copper amalgam in adjacent teeth. The remainder of the discussion in this chapter will therefore focus on the high-copper amalgam. The powdered amalgam alloy is composed of irregularly shaped particles produced by grinding an alloy ingot on a lathe, microspheres of various sizes produced by special hot spraying techniques, or a combination of the two (so-called admix, where the composition of the two types of particles may or may not be similar). Scanning electron micrographs of the particles are shown in Fig. 10.2. The irregular lathe-cut particles are made from an alloy of silver and tin where the ratio of the two elements approxi-mates the intermetallic compound Ag3Sn. These are typically used in the admix alloys. The spherical par-ticles may contain either mostly silver and copper, and be used as the second component in the admix alloy, or may be more similar to the lathe-cut parti-cles in composition and contain silver, tin, and cop-per (unicompositional). The compositional ranges of the different types of particles are shown in Table 10.1. The admixed regu-lar alloy contains 33% to 60% spherical particles that have a composition close to the eutectic composi-tion of Ag3Cu2 (see Fig. 10.2); the balance is irregular particles. The silver content of the unicompositional spherical alloys varies from 40% to 60%, copper con-tent varies from 13% to 30%, and tin content varies from 22% to 30%. A high-copper admixed alloy is also available, in which both spherical and irregular particles have the same composition and the copper content is between 29% and 30%. Admixed alloys are overall more popular than spherical alloys for amalgams. In general, alloy composition—particle size, shape, and distribution—and heat treatment con-trol the characteristic properties of the amalgam. The following sections describing the amalgama-tion reaction and properties of amalgam will be devoted to the high-copper amalgams currently in use in dentistry. Amalgamation Processes: Admixed Alloys All dental amalgam alloys have Ag3Sn as their pri-mary component, which reacts with mercury to form Ag2Hg3, the major matrix phase of the set amalgam. The amalgam alloy is intimately mixed with liquid TABLE 10.1 Approximate Composition of Low- and High-Copper Amalgam Alloys Alloy Particle Shape Element (wt%) Ag Sn Cu Zn In Pd Admixed regular Irregular Spherical 40–70 40–65 26–30 0–30 2–30 20–40 0–2 0–1 0 0 0 0–1 Admixed unicomposition Irregular Spherical 52–53 52–53 17–18 17–18 29–30 29–30 0 0 0 0 0.3 0.3 Unicompositional Spherical 40–60 22–30 13–30 0 0–5 0–1 FIG. 10.1 Amalgam restorations from a low-copper lathe cut alloy (left) and a high-copper admix alloy (right) after 3 years of clinical service. (Courtesy David B. Mahler, OHSU School of Dentistry, Portland, OR.) 173 10. Restorative Materials: Metals mercury in a process called trituration to wet the surface of the particles and facilitate their reaction with mercury. During this process, mercury diffuses into the alloy particles and reacts with the silver and tin portions of the particles to form predominantly a silver-mercury compound, Ag2Hg3, known as the gamma one (γ1) phase. This phase forms act as a matrix to hold the unreacted amalgam alloy together. While crystals of the γ1 phase are being formed, the amalgam is relatively soft and easily condensable and carvable. As time progresses, more crystals of γ1 are formed; the amalgam becomes harder and stron-ger and is no longer condensable or carvable. The lapse of time between the end of the trituration and when the amalgam hardens and is no longer work-able is called working time. Completion of the reac-tion may take several days to several weeks, which is reflected by the change in mechanical proper-ties over this time. Patients are typically advised to avoid chewing directly on amalgam restorations for the first 24 hours after placement to be safe, though considerable strength has been achieved within the first few hours. The amount of liquid mercury used to amalgam-ate the alloy particles is not sufficient to react with the particles completely. Therefore the set mass of amal-gam contains about 27% unreacted particles, which actually enhance the strength of the final material. In high-copper admix alloys, additional copper has typically been supplied by adding spherical particles of the silver-copper eutectic alloy to the silver-tin alloy. The solubility of silver, tin, and cop-per in mercury differs considerably. Approximately 1 mg of copper, 10 mg of silver, and 170 mg of tin can dissolve in mercury, all at the same tempera-ture. Therefore while mercury is dissolving mainly the silver and tin in Ag3Sn, as described earlier, very little of the silver-copper eutectic particles are dis-solved. However, some of the tin and copper that are dissolved by the mercury react to form a copper-tin compound, Cu6Sn5, referred to as the eta prime (η′) phase. It is the presence of this tin-copper compound, A B C FIG. 10.2 Scanning electron micrographs. (A) Lathe-cut; (B) spherical; and (C) admixed amalgam alloys. 174 CRAIG’S RESTORATIVE DENTAL MATERIALS rather than the formation of a weak, corrosion-prone tin-mercury compound, that gives the high-copper amalgams their superior performance as compared with the older low-copper amalgams. The amalgamation reaction may be simplified as follows: γ (Ag3Sn) + Ag-Cu (eutectic) + Hg → γ1 (Ag2Hg3) + η (Cu6Sn5) + unreacted γ (Ag3Sn) + unreacted Ag-Cu (eutectic) Reaction of Mercury in a Unicompositional Alloy In high-copper unicompositional alloys, the alloy particles, typically spherical, contain both Ag3Sn (γ) and Cu3Sn (ε). When liquid mercury is mixed with these alloys, it diffuses into the surface of these par-ticles and Ag2Hg3 and Cu6Sn5 are formed, as in the admixed alloy. The difference is that because all of the copper is present within the single particles, the reaction of copper and tin occurs in a ring around the spherical particles, which become surrounded by the silver-mercury matrix. Microstructure of Amalgam Color-coded images of the microstructures of the set amalgams of the high-copper admix and the high-copper unicompositional types are shown in Fig. 10.3. The blue/black matrix phase is A2Hg3 (γ1). The tangerine color is for the Cu6Sn5 (η′) phase, which is very evident around spherical particles. Physical and Mechanical Properties ANSI/ADA Specification for Amalgam Alloy ANSI/ADA specification No. 1 (ISO 24234) for amal-gam alloy contains requirements that help control the qualities of commercially available dental amalgam. The specification lists three physical properties as a measure of amalgam quality: compressive strength, creep, and dimensional change. The minimum allowable com-pressive strength is 80 MPa for 1 hour after setting and 300 MPa for 24 hours after setting, the maximum allow-able creep is 1%, and the dimensional change between 5 minutes and 24 hours must fall within the range of −15 to +20 μm/cm. The physical properties for several amalgams are shown in Table 10.2. A B C FIG. 10.3 Microstructures of the set amalgams of the (A) low-copper, lathe-cut; (B) the high-copper, admix; and (C) the high-copper, unicompositional types. These photographs were made by superimposing microprobe x-ray scans of the ele-ments through colored filters: blue for silver, red for copper, and green for tin. The blue/black matrix phase is A2Hg3 (γ1) for all amalgams. The green-colored Sn7–8Hg (γ2) phase is only present in the low-copper alloy (A). The tangerine-colored Cu6Sn5 (η′) phase is minimal in alloy (A) but substantial in alloys (B) and (C). In alloy (B), the source of the increased copper is in the spherical silver-copper eutectic phase where the η′ surrounds this spherical particle. In alloy (C), the source of the increased copper is in the additional Cu3Sn added to the spherical Ag3Sn particle and Cu6Sn5 (ηʹ) phases are present around this spherical particle. (Courtesy David B. Mahler, OHSU School of Dentistry, Portland, OR.) 175 10. Restorative Materials: Metals TABLE 10.2 Mercury in Mix, Compressive Strength, Tensile Strength, Creep, and Dimensional Change Mercury in Mix (%) Compressive Strength (MPa) Tensile Strength (MPa) Creep (%) Dimensional Change (mm/cm) 1 h 7 days 15 min 7 days LOW COPPER Alloys Lathe-cut Caulk 20th century 53.7 45 302 3.2 51 6.3 −19.7 Spherical Caulk spherical 46.2 141 366 4.7 55 1.5 −10.6 HIGH COPPER Alloys Admixed Dispersalloy 50.0 118 387 3.8 43 0.45 −1.9 Unicompositional Sybraloy 46.0 252 455 8.5 49 0.05 −8.8 Tytin 43.0 292 516 8.1 56 0.09 −8.1 Modified from Malhotra ML, Asgar K. Physical properties of dental silver-tin amalgams with high and low copper contents. J Am Dent Assoc. 1978;96:444–450. Mercury in Mix In general, irregular particles have higher surface areas than spherical particles, and therefore require more mercury to wet their surfaces. In turn, higher percentages of mercury in the mix will result in higher mercury contents and lower strengths of the hardened amalgams. This effect is clearly shown in Table 10.2. Compressive Strength Resistance to compression forces is an important strength characteristic of amalgam. Because amal-gam is strongest in compression and much weaker in tension and shear, the prepared cavity design should maximize compressive stresses in service and minimize tensile or shear stresses. When sub-jected to a rapid application of force either in ten-sion or in compression, a dental amalgam does not exhibit significant deformation or elongation and, as a result, functions as a brittle material. Therefore a sudden application of excessive force to amalgam may lead to fracture of the amalgam restoration. The early compressive strengths after 1 hour of setting for several low- and high-copper alloys are listed in Table 10.2. The high-copper unicomposi-tional materials have the highest early compressive strengths of more than 250 MPa. High values for early compressive strength are an advantage for an amalgam, because they reduce the possibility of frac-ture by the application of prematurely high occlu-sal forces by the patient before the final strength is reached. The compressive strengths at 7 days are again highest for the high-copper unicompositional alloys, with only modest differences in the other alloys. Tensile Strength The tensile strengths of various amalgams after 15 minutes and 7 days are also listed in Table 10.2. The tensile strengths at 7 days for low- and high-copper amalgams are about the same. The tensile strengths are only a fraction of their compressive strengths; therefore cavity designs should be constructed to reduce tensile stresses resulting from biting forces. The tensile strengths at 15 minutes for the high- copper unicompositional alloys are significantly higher than for the other alloys. Elastic Modulus The elastic modulus, or the stiffness, for dental amal-gam is in the range of 40 to 60 GPa. As a comparison, the elastic modulus of resin composites is only 5 to 15 GPa, which can be of significance when consid-ering amalgam versus composites in certain clinical applications. 176 CRAIG’S RESTORATIVE DENTAL MATERIALS Creep Creep is the time-dependent inelastic deformation of materials that are used at temperatures that are close to their melting points. Expressed in absolute temperatures, the melting point of the major matrix phase (γ1) in dental amalgam is 400 K, whereas it is used at the mouth temperature of 310 K for a ratio of 0.8. In metals, ratios that exceed 0.5 are considered to be a forerunner for examining creep behavior. Therefore dental amalgam is an appropriate candi-date for this examination. The creep test in the specifications is conducted by applying a compressive stress of 36 MPa on a 7-day-old cylindrical specimen in a 37°C environ-ment. Creep is measured by the shortening of the test specimen between 1 and 4 hours of testing, and the specification sets the acceptable limit for creep of 1.0%. However, amalgams whose creep values vary within the range of less than 1.0% do not show differ-ences in clinical performance. For example, referring to Table 10.2, unicompositional alloys with creep val-ues of 0.05 and 0.09 do not show superior clinical per-formance compared to the admix alloy with a creep value of 0.45. Therefore physical properties are help-ful in predicting clinical performance but care should be exercised in the limits of their interpretation. The ability of creep to demonstrate the permanent deformation of dental amalgam in the clinical envi-ronment is shown to be of significance in Fig. 10.1. Dimensional Change The dimensional change during the setting of amal-gam is one of its most significant properties. Modern amalgams mixed with mechanical amalgamators usu-ally have negative dimensional changes. The initial contraction after a short time (the first 20 minutes) is believed to be associated with the solution of the alloy particles in mercury. After this period, an expansion occurs that is believed to be a result of the reaction of mercury with silver mainly and the formation of the matrix phase. The dimensions become nearly constant after 6 to 8 hours, and thus the values after 24 hours are final values. The only exception to this statement is the excessive delayed dimensional change seen clinically when some older zinc-containing alloys were contaminated with water-based fluids during trituration or condensation. Dimensional change is measured by the change in length of an 8-mm cylindrical specimen between 5 minutes and 24 hours after trituration. The change in length can be determined continuously, although ANSI/ADA specification No. 1 requires only the value at 24 hours. The dimensional changes in micrometers per cen-timeter for various alloys are listed in Table 10.2. The lowest dimensional change of −1.9 μm/cm was for the high-copper admixed alloy. All the amalgams meet the requirements of ANSI/ADA specification No. 1 of −15 to +20 μm/cm but are susceptible to influence from various manipulative factors. An additional clinical significance of dimen-sional change is related to the occasional occur-rence of postoperative sensitivity associated with newly placed amalgam restorations. Amalgam does not adhere to tooth structure; therefore a negative dimensional change would result in the presence of an interfacial gap between the amalgam restoration and tooth structure. When a cavity is prepared that cuts through dentin in a tooth requiring restoration, pulpal fluid in the tubules can flow outward into the interfacial gap. Changes in pressure of this fluid are considered to be one of the major causes of postoper-ative sensitivity. Apparently, the size of the interfacial gap is a key factor in determining whether sensitivity will occur, with teeth with restorations having larger gaps being more prone to being sensitive. Although most alloys that pass ANSI/ADA speci-fication No. 1 for negative dimensional changes of −15 μm/cm or less have not been shown to have an uncommon amount of postoperative sensitiv-ity, some high-copper amalgams consisting of only spherical particles have been reported to show a propensity for this sensitivity. The reason for this anomaly was found by in vitro microleakage stud-ies that showed that spherical particle alloys leaked more than lathe-cut particle alloys, even though their respective dimensional changes were not sig-nificantly different. Examination showed that the surfaces of these amalgams next to the cavity walls exhibited a relatively uneven texture for the spheri-cal particle alloys compared to a smoother texture for the lathe-cut alloys. Thus the interfacial space filled by pulpal fluid was greater for the spherical particle alloys. In Fig. 10.4, the microleakage of a number of dental amalgams is shown where spherical particle alloys are marked with a capital S. It is clear that the presence of higher microleakage values is associated with the spherical alloys. Bars that are shaded refer to alloys in which data were available to indicate an unusual propensity for postoperative sensitivity. The use of film-forming agents such as dentin bonding agents to seal the dentinal tubules before placement of an amalgam restoration has proven to be an effective solution to the problem of postop-erative sensitivity of spherical particle amalgams. However, this practice has not been widely adopted by the profession. Corrosion In general, corrosion is the progressive destruction of a metal by chemical or electrochemical reaction with its environment. Excessive corrosion can lead to increased porosity, reduced marginal integrity, loss 177 10. Restorative Materials: Metals of strength, and the release of metallic products into the oral environment. Corrosion products identified in dental amalgams include tin oxides, tin hydroxychlorides, copper oxides, copper chlorides, and other more complex compounds. The formation of oxides and chlorides is not surprising considering that the amalgams operate in an aerated environment containing salt solutions. Because of their different chemical compositions, the different phases of an amalgam have different cor-rosion potentials. Electrochemical measurements on pure phases have shown that the Ag2Hg3 (γ1) phase has the highest corrosion resistance, followed by Ag3Sn (γ), Ag3Cu2, Cu3Sn (ε), Cu6Sn5 (η′), and Sn7–8Hg (γ2). However, the presence of small amounts of tin, silver, and copper that may dissolve in various amalgam phases has a great influence on their cor-rosion resistance. For example, in the γ1 phase, the silver-mercury phase always has some tin dissolved within it, and the higher the tin concentration, the lower is the corrosion resistance. The average depth of corrosion for most amalgam alloys is 100 to 500 μm, measured from the amalgam/tooth margin. Phosphate buffer solutions inhibit the corrosion process, as do the formation of protein pellicles on the amalgam surface; thus saliva may provide some protection of dental amalgams from corrosion. A study of amalgams that had been in service for 2 to 25 years revealed that the bulk elemental com-positions were similar to newly prepared amalgams, except for the presence of a small amount of chloride and other contaminants. The compositions of the phases were also similar to new amalgams, except for internal amalgamation of the γ particles. The dis-tribution of phases in the clinically aged amalgams, however, differed from that of new amalgams, veri-fying that dental amalgam is a dynamic material that changes with time. Surface tarnish in high-copper amalgams is related to the copper-rich phases. Bonding of Amalgam Although amalgam has been a highly successful restorative material when used as an intercoronal restoration, it does not bond to tooth structure and therefore does not restore the original strength of the clinical crown. For large restorations, features such as pins, slots, holes, and grooves must be supplied to provide retention for large restorations, but they do not reinforce the amalgam or increase its strength. With the development of adhesive systems for dental composites came the opportunity to attempt to bond amalgams to tooth structure. Bonding agents containing 4-META, an acronym for 4-meth-acryloxyethyl trimellitic anhydride (see Chapter 13), have been the most successful products. Shear bond strengths of amalgam to dentin as high as 10 MPa have been reported using these adhesives, whereas comparable values for the shear bond strength of microfilled composites to dentin using these same adhesives have been 20 to 22 MPa. A B C D E F Alloys G H I J K L M N O P S S S S S S S Note scale change S - Spherical alloys Postoperative sensitivity S S S S S S S S S Q R S T U V W X Y Z 0 1.0 2.0 3.0 Leakage (mL/min) 5.0 10.0 15.0 20.0 25.0 FIG. 10.4 In vitro microleakage of various commercial amalgams. (From Mahler DB, Nelson LW. Sensitivity answers sought in amalgam alloy microleakage study. J Am Dent Assoc. 1994;125:282–288.) 178 CRAIG’S RESTORATIVE DENTAL MATERIALS There is no true adhesion between amalgam and tooth structure. Bonding that has been shown by shear bond tests is strictly produced by the com-mingling of the bonding agent and the amalgam at their common interface. The technique for placing a bonded amalgam consists of initially placing the bonding agent into the cavity and before the bond-ing agent has completely polymerized, the amalgam is condensed into the cavity. This represents the tech-nical challenge of filling the retentive features of the preparation with amalgam mixed together with the bonding agent. The fracture resistance of teeth restored with amalgam-bonded mesio-occlusal-distal (MOD) res-torations was more than twice that of restorations containing unbonded amalgams. In addition, in spite of the lower shear-bond strength of amalgam bonded to dentin as compared to that for composites, the fracture strength of MODs in teeth restored with bonded amalgams was as high as that for compos-ites, although neither was as high (45% to 80%) as values for the intact tooth. As expected, amalgam-bonded MODs with narrow preparations had higher strengths than those with wide preparations. Other studies showed that the retention of amalgam-bonded MODs with proximal boxes was as great as pin-retained amalgams. In addition, amalgam-bonded restorations decreased marginal leakage in class 5 restorations compared with unbonded amalgams. Finally, the bonding agents for amalgam have not been successful in increasing the amalgam-to-amalgam bond strength for the repair of amalgam restorations. The history of dental amalgam and its manipula-tion can be found on the website ier.com/sakaguchi/restorative. DENTAL CASTING ALLOYS This section is divided into noble alloys and base-metal alloys. Fluctuations in the price of gold, plati-num, and palladium influence the selection of alloys for cast dental restorations. Each alloy has specific physical and mechanical properties that affect its manipulation and application. Tooth preparation and restoration design will determine the required physical and mechanical properties of the alloy, so all factors should be kept in mind during the process of treatment planning. Types and Composition The ADA specification for dental casting alloys clas-sifies alloys by composition, dividing alloys into three groups: (1) high noble, with a noble-metal con-tent of at least 60 wt% and a gold content of at least 40%; (2) noble, with a noble-metal content at least 25% (no stipulation for gold); and (3) predominately base metal, with a noble-metal content less than 25% (Table 10.3). It is important to keep in mind that the percentages used as boundaries in the specification are somewhat arbitrary. ANSI/ADA specification No. 5 (ISO 1562) uses a type I through IV classification system with each alloy type recommended for specific applications, in addition to the compositional classification previ-ously described (Table 10.4). Thus a high-noble alloy might be type I or type IV, depending on its mechani-cal properties. This situation is somewhat confusing, because in the old specification the alloy type was related to its composition and virtually all alloys were gold based. In the current system, each type of alloy is recommended for intraoral use based on the amount of force the restoration is likely to receive. Alloy types I and II have high elongation and are therefore eas-ily burnished, but are appropriate only in low-stress environments, such as inlays that experience low occlusal forces. Type IV alloys are to be used in clini-cal situations where very high stresses are involved, such as long-span, fixed dental prostheses. Type III alloys are the most commonly used in dental prac-tices for crowns and shorter fixed-partial dentures. Although the number of casting alloys is immense, it is possible to subdivide each ADA compositional group into several classes (Table 10.5). These classes are simply a convenient way of organizing the diverse strategies that have been used to formulate casting alloys. For each class of alloy shown in Table 10.5, there are many variations; the compositions shown are meant only to be representative. Note that both the wt% (weight percent) and at% (atomic percent) compositions of the alloys are shown in Table 10.5. Weight percentages of the alloys are most commonly used by manufacturers in the production and sales of the alloys. However, the physical, chemical, and biological properties are best understood in terms TABLE 10.3 Revised American Dental Association Classification of Prosthodontic Alloys Class Required Noble Content (%) Required Gold Content (%) Required Titanium Content (%) High-noble alloys ≥60 ≥40 Titanium and titanium alloys ≥85 Noble alloys ≥25 Predominantly base materials ≥25 179 10. Restorative Materials: Metals TABLE 10.4 ANSI/ADA Specification No. 5, Mechanical Properties of Dental Casting Alloys Alloy Type Description Use Yield Strength (annealed, MPa) Elongated (annealed, %) I Soft Restorations subjected to low stress: some inlays <140 18 II Medium Restorations subjected to moderate stress: inlays and onlays 140–200 18 III Hard Restorations subjected to high stress: crowns, thick-veneer crowns, short-span fixed dental prostheses 201–340 12 IV Extra-hard Restorations subjected to very high stress: thin-veneer crowns, long-span fixed dental prostheses, removable dental prostheses >340 10 ANSI/ADA, American National Standards Institute/American Dental Association. TABLE 10.5 Typical Compositions (wt%/at%) of Noble Dental Casting Alloys Alloy Type Ag Au Cu Pd Pt Zn Other HIGH NOBLE Au-Ag-Pt 11.5/19.3 78.1/71.4 — — 9.9/9.2 — Ir (trace) Au-Cu-Ag-Pd-I 10.0/13.6 76.0/56.5 10.5/24.2 2.4/3.4 0.1/0.1 1.0/2.0 Ru (trace) Au-Cu-Ag-Pd-II 25.0/30.0 56.0/36.6 11.8/23.9 5.0/6.1 0.4/0.3 1.7/3.4 Ir (trace) NOBLE Au-Cu-Ag-Pd-III 47.0/53.3 40.0/24.8 7.5/14.4 4.0/4.7 — 1.5/2.8 Ir (trace) Au-Ag-Pd-In 38.7/36.1 20.0/10.3 — 21.0/33.3 — 3.8/5.8 In 16.5 Pd-Cu-Ga — 2.0/1.0 10.0/15.8 77.0/73.1 — — Ga 7.0/10.1 Ag-Pd 70.0/69.0 — — 25.0/25.0 — 2.0/3.3 In 3/2.3 of atomic percentages. For the sake of simplicity, the following discussion will be in terms of wt% com-position. Most of the alloys contain some zinc as a deoxidizer and either iridium (Ir) or ruthenium (Ru) as grain refiners. Some of these compositions are used for both full metal castings and ceramic-metal restorations. There are three classes of high-noble alloys: the Au-Ag-Pt alloys; the Au-Cu-Ag-Pd alloys with a gold content greater than 70 wt% (Au-Cu-Ag-Pd-I in Table 10.5); and the Au-Cu-Ag-Pd alloys with a gold content of about 50% to 65% (Au-Cu-Ag-Pd-II). The Au-Ag-Pt alloys typically consist of 78 wt% gold with roughly equal amounts of silver and platinum. These alloys have been used as casting alloys and porcelain-metal alloys. The Au-Cu-Ag-Pd-I alloys are typically 75 wt% gold with approximately 10 wt% each of silver and copper and 2 to 3 wt% palladium. The Au-Cu-Ag-Pd-II alloys typically have less than 60 wt% gold, with the silver content increased to accommodate the reduced gold content. Occasionally, these alloys will have slightly higher palladium and lower silver percentages. There are four classes of noble alloys: the Au-Cu-Ag-Pd alloys (Au-Cu-Ag-Pd-III in Table 10.5); Au-Ag-Pd-In alloys; Pd-Cu-Ga alloys; and Ag-Pd alloys. The Au-Cu-Ag-Pd-III alloys typically have a gold content of 40 wt%. The reduced gold is com-pensated primarily with silver, thus the copper and palladium contents are not changed much from the Au-Cu-Ag-Pd-II alloys. The Au-Ag-Pd-In alloys have a gold content of only 20 wt% and have about 40 wt% silver, 20 wt% palladium, and 15 wt% indium. The Pd-Cu-Ga alloys have little or no gold, with about 75 wt% palladium and roughly equal amounts of copper and gallium. Finally, the Ag-Pd alloys have no gold, but have 70 wt% silver and 25 wt% palla-dium. By the ADA specification, these alloys are con-sidered noble because of their palladium content. The compositions of casting alloys determine their color. In general, if the palladium content is over 10 wt%, the alloy will be white. Thus the Pd-Cu-Ga and Ag-Pd alloys in Table 10.5 are white, whereas the other alloys are yellow (gold). The Au-Ag-Pd-In alloys are an exception because they have palladium content over 20% and retain a light yellow color. The 180 CRAIG’S RESTORATIVE DENTAL MATERIALS color of this alloy results from interactions of the indium with the palladium in the alloy. Among the yellow alloys, the composition will modify the shade of yellow. In general, copper adds a reddish color and silver lightens either the red or yellow color of the alloys. Metallic Elements Used in Dental Alloys For dental restorations, various elements are com-bined to produce alloys with adequate properties for dental applications because none of the elements by themselves have properties that are suitable. These alloys may be used for dental restorations as cast alloys or may be manipulated into wire or other wrought forms. The metallic elements that make up dental alloys can be divided into two major groups, the noble metals and the base metals. Noble Metals Noble metals are elements with a good metallic sur-face that retain their surface in dry air. They react easily with sulfur to form sulfides, but their resis-tance to oxidation, tarnish, and corrosion during heating, casting, soldering, and use in the mouth is very good. The noble metals are gold, platinum, palladium, iridium, rhodium, osmium, and ruthe-nium (Table 10.6). These metals can be subdivided into two groups. The metals of the first group, con-sisting of ruthenium, rhodium, and palladium, have atomic weights of approximately 100 and densities of 12 to 13 g/cm3. The metals of the second group, TABLE 10.6 Properties of Elements in Dental Casting Alloys Element Symbol Atomic Number Atomic Mass Density (g/cm3) Melting Temperature (°C) Color Comments NOBLE Ruthenium Ru 44 101.07 12.48 2310.0 White Grain refiner, hard Rhodium Rh 45 102.91 12.41 1966.0 Silver-white Grain refiner, soft, ductile Palladium Pd 46 106.42 12.02 1554.0 White Hard, malleable, ductile Osmium Os 76 190.20 22.61 3045.0 Bluish-white Not used in dentistry Iridium Ir 77 192.22 22.65 2410.0 Silver-white Grain refiner, very hard Platinum Pt 78 195.08 21.45 1772.0 Bluish-white Tough, ductile, malleable Gold Au 79 196.97 19.32 1064.4 Yellow Ductile, malleable, soft, conductive BASE Nickel Ni 28 58.69 8.91 1453.0 White Hard Copper Cu 29 63.55 8.92 1083.4 Reddish Malleable, ductile, conductive Zinc Zn 30 65.39 7.14 419.6 Bluish-white Soft, brittle, oxidizes Gallium Ga 31 69.72 5.91 29.8 Grayish-white Low melting Silver Ag 47 107.87 10.49 961.9 Soft, malleable, ductile, conductive Tin Sn 50 118.71 7.29 232.0 White Soft Indium In 49 114.82 7.31 156.6 Gray-white Soft 181 10. Restorative Materials: Metals TABLE 10.7 Physical and Mechanical Properties of Cast Pure Gold and Gold Alloys Material Density (g/cm3) Hardness (VHN/BHN) (kg/mm2) Tensile Strength (MPa) Elongation (%) Cast 24k gold 19.3 28 (VHN) 105 30 Cast 22k gold — 60 (VHN) 240 22 Coin gold — 85 (BHN) 395 30 Typical Au-based casting alloy (70 wt% Au)a 15.6 135/195 (VHN) 425/525 30/12 aValues are for softened/hardened condition. BHN, Brinell hardness number; VHN, Vickers hardness number. Modified from Rule RW. A further report on physical properties and clinical values of platinum-centered gold foil as compared to pure gold filling materi-als. J Am Dent Assoc. 1937;24:583–595. consisting of osmium, iridium, platinum, and gold, have atomic weights of about 190 and densities of 19 to 23 g/cm3. The melting points of members of each group decrease with increasing atomic weight. Thus ruthenium melts at 2310°C, rhodium at 1966°C, and palladium at 1554°C. In the second group the melting points range from 3045°C for osmium to 1064°C for gold. The melting point and density are important properties when composing alloys, because they affect the casting process, which affects the overall accuracy and quality of the final product. The noble metals, together with silver, are sometimes called precious metals. The term precious comes from the relatively high cost of these metals and their trading on the commodities market. Some metallurgists consider silver a noble metal, but it is not considered a noble metal in dentistry because it corrodes considerably in the oral cavity. Thus the terms noble and precious are not synonymous in dentistry. GOLD (AU) Pure gold is a soft, malleable, ductile metal that has a rich yellow color with a strong metallic luster. Although pure gold is the most ductile and mal-leable of all metals, it is relatively low in strength. The density of gold depends somewhat on the condi-tion of the metal, whether it is cast, rolled, or drawn into wire. Small amounts of impurities have a pro-nounced effect on the mechanical properties of gold and its alloys. The presence of less than 0.2% lead causes gold to be extremely brittle. Mercury in small quantities also has a harmful effect. Therefore scrap of other dental alloys should not be mixed with gold used for dental restorations. Air or water at any temperature does not affect or tarnish gold. Gold is not soluble in sulfuric, nitric, or hydrochloric acids. However, it readily dissolves in combinations of nitric and hydrochloric acids (aqua regia, 18 vol% nitric and 82 vol% hydrochloric acids) to form the trichloride of gold (AuCl3). It is also dissolved by a few other chemicals, such as potas-sium cyanide and solutions of bromine or chlorine. Because gold is nearly as soft as lead, it must be alloyed with copper, silver, platinum, and other metals to develop the hardness, durability, and elasticity necessary in dental alloys, coins, and jew-elry (Table 10.7). Through appropriate refining and purification, gold with an extremely high degree of purity may be produced. Gold can be work hard-ened to improve its physical properties. Without the improvement, cast gold would lack sufficient strength and hardness. CARAT AND FINENESS OF GOLD-BASED ALLOYS For many years the gold content of gold-containing alloys has been described on the basis of the carat, or in terms of fineness, rather than by weight percentage. The term carat refers only to the gold content of the alloy; a carat represents a one-twenty-fourth part of the whole. Thus 24 carat indi-cates pure gold. The carat of an alloy is designated by a small letter k, for example, 18k or 22k gold. The use of the term carat to designate the gold content of dental alloy is less common now. It is not unusual to find the weight percentage of gold listed or to have the alloy described in terms of fineness. Fineness also refers only to the gold content, and represents the number of parts of gold in each 1000 parts of alloy. Thus 24k gold is the same as 100% gold or 1000 fineness (i.e., 1000 fine). An 18k gold would be designated as 750 fine, or, when the decimal sys-tem is used, it would be 0.750 fine; this indicates that 750/1000 of the total is gold. A comparison of the carat, fineness, and weight percentage of gold is given in Table 10.8. Both the whole number and the decimal system are in common use, especially for noble dental solders. The fineness system is some-what less relevant today because of the introduction of alloys that are not gold based. It is important to emphasize that the terms carat and fineness refer only to gold content, not noble-metal content. 182 CRAIG’S RESTORATIVE DENTAL MATERIALS PLATINUM (Pt) Platinum is a bluish-white metal; is tough, ductile, and malleable; and can be produced as foil or fine-drawn wire. Platinum has hardness similar to that of copper. Pure platinum has numerous applica-tions in dentistry because of its high fusing point and resistance to oral conditions and elevated temperatures. Platinum increases the hardness and elastic quali-ties of gold, and some dental casting alloys and wires contain quantities of platinum up to 8% combined with other metals. Platinum tends to lighten the color of yellow gold-based alloys. PALLADIUM (Pd) Palladium is a white metal somewhat darker than platinum. Its density is a little more than half that of platinum and gold. Palladium is not used in the pure state in dentistry, but is used extensively in dental alloys. Palladium can be combined with gold, silver, copper, cobalt, tin, indium, or gallium for dental alloys. Alloys are read-ily formed between gold and palladium, and palla-dium quantities of as low as 5% by weight have a pronounced effect on whitening yellow gold-based alloys. Palladium-gold alloys with a palladium con-tent of 10% or more by weight are white. Alloys of pal-ladium and the other elements previously mentioned are available as substitutes for yellow-gold alloys, and the mechanical properties of the palladium- based alloys may be as good as or better than many traditional gold-based alloys. Although many of the palladium-based alloys are white, some, such as palladium-indium-silver alloys, are yellow. IRIDIUM (IR), RUTHENIUM (RU), AND RHODIUM (RH) Iridium and ruthenium are used in small amounts in dental alloys as grain refiners to keep the grain size small. A small grain size is desirable because it improves the mechanical properties and uniformity of properties within an alloy. As little as 0.005% (50 ppm) of iridium is effective in reducing the grain size. Ruthenium has a similar effect. The grain-refining properties of these elements are largely due to their extremely high melting points. Iridium melts at 2410°C and ruthenium at 2310°C. Thus these elements do not melt during the casting of the alloy and serve as nucle-ating centers for the melt as it cools, resulting in a fine-grained alloy. Rhodium also has a high melting point (1966°C) and has been used in alloys with platinum to form wire for thermocouples. These thermocouples help measure the temperature in porcelain furnaces used to make dental restorations. Base Metals Several base metals are combined with noble metals to develop alloys with properties suitable for den-tal restorations. Base metals used in dental alloys include silver, copper, zinc, indium, tin, gallium, and nickel (see Table 10.6). SILVER (Ag) Silver is a malleable, ductile white metal. It is the best-known conductor of heat and electricity and is stron-ger and harder than gold but softer than copper. At 961.9°C, the melting point of silver is below the melt-ing points of both copper and gold. It is unaltered in clean, dry air at any temperature, but combines with sulfur, chlorine, phosphorus, and vapors containing these elements or their compounds. Foods contain-ing sulfur compounds cause severe tarnish on silver, and for this reason silver is not considered a noble metal in dentistry. Pure silver is not used in dental restorations because of the black sulfide that forms on the metal in the mouth. Adding small amounts of palladium to silver-containing alloys prevents the rapid corrosion of such alloys in the oral environment. Silver forms a series of solid solutions with pal-ladium (see Fig. 10.5D) and gold (see Fig. 10.5C), and is therefore common in gold- and palladium-based dental alloys. In gold-based alloys, silver is effective in neutralizing the reddish color of alloys containing appreciable quantities of copper. Silver also hardens the gold-based alloys via a solid-solution harden-ing mechanism. In palladium-based alloys, silver is TABLE 10.8 Comparison of Carat, Fineness, and Weight Percentage of Gold in Gold Alloys Carat Amount of Gold by Carats Weight (%) of Gold Fineness Parts/1000 Decimal 24 24 24 100.0 1000.00 1.000 22 22 24 91.7 916.66 0.916 20 20 24 83.3 833.33 0.833 18 18 24 75.0 750.00 0.750 16 16 24 66.7 666.66 0.666 14 14 24 58.3 583.33 0.583 9 9 24 37.5 374.99 0.375 183 10. Restorative Materials: Metals important in developing the white color of the alloy. Although silver is soluble in palladium, the addition of other elements to these alloys, such as copper or indium, may cause the formation of multiple phases and increased corrosion. COPPER (Cu) Copper is a malleable and ductile metal with high thermal and electrical conductivity and a characteris-tic red color. When added to gold-based alloys, cop-per imparts a reddish color to the gold and hardens A Composition (wt.% Au) 25 AuCu3 396 Cu Temperature (C) 50 AuCu 424 884 1064 1083 75 Au 900 600 300 1200 25 50 75 L S Composition (at.% Au) B 1554 1600 1200 800 400 25 PdCu3 500 Cu Temperature (C) 50 PdCu 600 1083 75 Pd 25 50 75 L S at.% Pd 1600 1200 25 50 L S 962 D 75 800 400 1555 25 Ag 50 75 Pd at.% Pd E 1064 1600 1200 25 50 L S 1554 75 800 400 25 Pd 50 75 Au at.% Au L 975 1250 1772 PtAu3 1064 F 2000 1500 25 50 S 75 1000 500 25 Au 50 75 Pt at.% Pt 40 962 C 25 Ag Temperature (C) 50 1064 75 Au 900 600 300 1200 25 50 75 L S at.% Au AgAu FIG. 10.5 Phase diagrams for binary combinations. (A) Copper (Cu) and gold (Au); (B) copper and palladium (Pd); (C) silver and gold; (D) silver and palladium; (E) palladium and gold; and (F) gold and platinum (Pt). Atomic percent-ages are shown along the bottom of each graph; weight percentages are shown along the top. L, Liquidus; S, solidus. (Modified from Hansen M. Constitution of Binary Alloys. New York: McGraw Hill; 1958.) 184 CRAIG’S RESTORATIVE DENTAL MATERIALS the alloy via a solid-solution or ordered-solution mechanism. The presence of copper in gold-based alloys in quantities between approximately 40% and 88% by weight allows the formation of an ordered phase. Copper is also commonly used in palla-dium-based alloys, where it can be used to reduce the melting point and strengthen the alloy through solid-solution hardening and formation of ordered phases when Cu is between 15 and 55 wt%. The ratio of silver and copper must be carefully balanced in gold- and palladium-based alloys, because silver and copper are not miscible. Copper is also a common component of most hard dental solders. ZINC (Zn) Zinc is a blue-white metal with a tendency to tar-nish in moist air. In its pure form, it is a soft, brittle metal with low strength. When heated in air, zinc oxidizes readily to form a white oxide of relatively low density. This oxidizing property is exploited in dental alloys. Although zinc may be present in quantities of only 1% to 2% by weight, it acts as a scavenger of oxygen when the alloy is melted. Thus zinc is referred to as a deoxidizing agent. Because of its low density, the resulting zinc oxide lags behind the denser molten mass during casting and is there-fore excluded from the casting. If too much zinc is present, it will markedly increase the brittleness of the alloy. INDIUM (In) Indium is a soft, gray-white metal with a low melt-ing point of 156.6°C. Indium is not tarnished by air or water. It is used in some gold-based alloys as a replace-ment for zinc and is a common minor component of some noble ceramic dental alloys. Recently, indium has been used in greater amounts (up to 30% by weight) to impart a yellow color to palladium-silver alloys. TIN (Sn) Tin is a lustrous, soft, white metal that is not subject to tarnish in normal air. Some gold-based alloys con-tain limited quantities of tin, usually less than 5% by weight. Tin is also an ingredient in gold-based dental solders. It combines with platinum and palladium to produce a hardening effect, but also increases brittleness. GALLIUM (Ga) Gallium is a grayish metal that is stable in dry air but tarnishes in moist air. It has a very low melting point of 29.8°C and a density of only 5.91 g/cm3. Gallium is not used in its pure form in dentistry, but is used as a component of some gold- and palladium-based dental alloys, especially ceramic alloys. The oxides of gallium are important to the bonding of the ceramic to the metal. NICKEL (Ni) Nickel has limited application in gold- and palladium-based dental alloys, but is a common component in base-metal dental alloys. Nickel has a melting point of 1453°C and a density of 8.91 g/cm3. When used in small quantities in gold-based alloys, nickel whitens the alloy and increases its strength and hardness. Noble Alloys Phase Structure of Noble Alloys The structure of noble alloys can consist of solid solu-tions, in which the elements are completely soluble in one another at all temperatures and compositions; ordered solutions, in which the elements in the alloy assume specific and regular positions in the crystal lattice of the alloy; or multiple individual phases, formed because the elements are not capable of totally dissolving in one another at all compositions and temperatures. The presence of a second phase is important because it significantly changes the corrosion proper-ties of an alloy. Fig. 10.6 shows electron micrographs of single- and multiple-phase alloys. The single-phase alloy has little visible microstructure because its composition is more or less homogeneous. In the multiple-phase alloy, areas that have distinct compo-sitions are clearly visible. These areas correspond to the different phases that formed during the solidi-fication process because the elements were no lon-ger completely able to be dissolved in one another to form a single phase as the alloy cooled. Because the different phases may interact electrochemically, the corrosion of multiple-phase alloys may be higher than for a single-phase alloy. Hardening of Noble Alloys The use of pure cast gold is not practical for dental res-torations because cast gold lacks sufficient strength and hardness. Solid-solution and ordered-solution hardening are two common ways of strengthening noble dental alloys sufficiently for use in the mouth. By mixing two elements in the crystal lattice ran-domly (forming a solid solution), the force needed to distort the lattice may be significantly increased. For example, adding just 10% by weight of copper to gold, the tensile strength increases from 105 to 395 MPa and the Brinell hardness increases from 28 to 85 (see Table 10.7). If the positions of the two elements become ordered (forming an ordered solu-tion), the properties of the alloy are improved further (see Table 10.7). For a typical gold-based casting alloy, the formation of an ordered solution may increase yield strength by 50%, tensile strength by 25%, and hardness by at least 10%. It is important to note that the elongation of an alloy is reduced by the formation of the ordered solution. For the typical gold-based 185 10. Restorative Materials: Metals alloy, the percentage elongation will decrease from 30% to about 12%. The formation of ordered solutions has been commonly used to strengthen cast dental restora-tions, particularly in gold-based alloys. The process requires precise control of the cooling rate. For the correct composition capable of forming the ordered state, slow cooling will result in a harder, stronger alloy due to the formation of the ordered crystals. However, rapid cooling of the cast metal, such as by plunging it into cold water soon after the casting pro-cess, leaves the metal in the softer, disordered state because there is simply not enough time during cool-ing for the atoms to arrange correctly on the crystal lattice. The conversion between the ordered solu-tion and solid solution is reversible in the solid state. Thus it is possible to heat an alloy that exists in a dis-ordered state under appropriate conditions and tem-peratures to provide time for the ordered structure to form. An example of how this process can be utilized for dental castings is as follows. An alloy is cooled rapidly after casting, leaving the alloy in the softer, disordered state, and thus allowing it to be more eas-ily ground and burnished at the margins to fit the die, and ultimately the prepared tooth. However, because it is beneficial for the alloy to be in a hard-ened state once placed in the mouth, the casting that has been worked in the laboratory is reheated to cause the formation of the harder, ordered structure, and this is the material that is ultimately cemented on the patient’s prepared tooth. Formulation of Noble Alloys The desired qualities of noble dental casting alloys determine the selection of elements that will be used to formulate the alloys. The ideal noble casting alloy should have (1) a low melting range; (2) ade-quate strength, hardness, and elongation; (3) a low tendency to corrode in the oral environment; and (4) low cost, among other properties. Traditionally, the noble elements gold and palladium have gener-ally been the foundation to which other elements are added to formulate dental casting alloys. Gold and palladium are preferable to other noble ele-ments because they have relatively low melting points, low corrosion, and form solid solutions with other alloy elements, such as copper or silver. Solid-solution systems are desirable for the formulation of alloys because they are generally easier to man-ufacture and manipulate, have a lower tendency to corrode than multiple phase systems, and pro-vide increased strength through solid-solution or ordered-solution hardening. Thus it is not surpris-ing that combinations of these elements have been extensively used in the formulation of noble dental casting alloys. GRAIN SIZE Studies have shown that minute quantities of various elements can influence the grain size of dental casting alloys. With the addition of small amounts (0.005% or 50 ppm) of elements such as iridium and ruthenium, fine-grained castings are produced. Adding one of these elements to the alloy is believed to develop centers for nucleating grains throughout the alloy. Most alloy manufac-turers use grain refinement in present-day prod-ucts. The mechanical properties of tensile strength and elongation are improved significantly (30%) by the fine grain structure in castings, which con-tributes to uniformity of properties from one cast-ing to another. Other properties, however, such as A Magn 1000x Deguplus #1,Trip/Rouge Polish Magn 1000x Rex #6, lac acid, 4 h, pH 4 20 µm 20 µm B FIG. 10.6 Electron micrographs of single-phase (A) and multiple-phase (B) alloys. (A) Few distinguishing microstructure characteristics are seen because the alloy is nearly homogeneous. Only a few scratches from polishing and some debris on the surface are visible. (B) A rich microstructure is evident, reflecting the several phases present. Each phase has a different composition. 186 CRAIG’S RESTORATIVE DENTAL MATERIALS hardness and yield strength, show less effect from the grain refinement. Properties MELTING RANGE Dental casting alloys do not have melting points, but rather melting ranges, because they are combinations of elements rather than pure elements. It is desirable for the dental casting alloy to have a relatively nar-row melting range, because if the alloy spends a long time in the partially molten state during cast-ing, there is increased opportunity for the formation of oxides and contamination. Therefore alloys with wide melting ranges are more difficult to cast with-out problems. The melting range of the alloys determines the burnout temperature, type of investment, and type of heat source that must be used during casting. In general, the burnout temperature must be about 500°C below the bottom temperature of the melting range. For the Au-Cu-Ag-Pd-I alloys, therefore, a burnout temperature of about 450°C to 475°C should be used. If the burnout temperature approaches 700°C, a gypsum-bonded investment cannot be used because the calcium sulfate will decompose and embrittle the alloys. At temperatures near 700°C or greater, a phosphate-bonded investment is used. As shown in Table 10.9, a gypsum-bonded investment may be used with the Au-Cu-Ag-Pd-I, II, and III and the Au-Ag-Pd-In alloys, but a phosphate-bonded investment is advisable for the other alloys. The gas-air torch will adequately heat alloys with liquidus temperatures below 1100°C. Above this temperature, a gas-oxygen torch or electrical induction method must be used. Again, from Table 10.9, a gas-air torch would be acceptable only for the Au-Cu-Ag-Pd-I, II, and III and the Au-Ag-Pd-In alloys. The maximum temperature of the melting range is important to soldering and formation of ordered phases, because during both of these operations, the shape of the alloys is to be retained. Therefore dur-ing soldering or hardening-softening, the alloy may be heated only to 50°C below the maximum of the melting range to avoid local melting or distortion of the casting. DENSITY Density is important during the acceleration of the molten alloy into the mold during casting. Alloys with high densities will generally accelerate faster and tend to form complete castings more easily. Among the alloys shown in Table 10.9, all have densities sufficient for convenient casting. Lower densities (7 to 8 g/cm3) seen in the predominantly base-metal alloys are more difficult to cast. Alloys in Table 10.6 with high densities generally contain higher amounts of denser elements such as gold or platinum. Thus the Au-Ag-Pt alloys and Au-Cu-Ag-Pd-I alloys are among the densest of the casting alloys. STRENGTH Strength of alloys can be measured by either the yield strength or tensile strength. Although tensile strength represents the maximum strength of the alloy, the yield strength is more useful in dental applications because it is the stress at which permanent defor-mation of the alloys occurs (see Chapter 4). Because permanent deformation of dental castings is gener-ally undesirable, the yield strength is a reasonable TABLE 10.9 Physical and Mechanical Properties of Several Types of Noble Dental Casting Alloys Alloy Property Solidus (°C) Liquidus (°C) Color Density (g/cm3) Yield Strength at 0.2% Offset (Soft/Hard) (MPa) Elongation (Soft/Hard) (%) Vickers Hardness (Soft/ Hard) (kg/mm2) HIGH NOBLE Au-Ag-Pt 1045 1140 Yellow 18.4 420/470 15/9 175/195 Au-Cu-Ag-Pd-I 910 965 Yellow 15.6 270/400 30/12 135/195 Au-Cu-Ag-Pd-II 870 920 Yellow 13.8 350/600 30/10 175/260 NOBLE Au-Cu-Ag-Pd-III 865 925 Yellow 12.4 325/520 27.5/10 125/215 Au-Ag-Pd-In 875 1035 Light yellow 11.4 300/370 12/8 135/190 Pd-Cu-Ga 1100 1190 White 10.6 1145 8 425 Ag-Pd 1020 1100 White 10.6 260/320 10/8 140/155 187 10. Restorative Materials: Metals practical maximum strength for dental applications. The yield strengths for the different classes of alloys are shown in Table 10.6. Where applicable, the hard and soft conditions, resulting from the formation of ordered solutions, are shown. For several alloys, such as Au-Cu-Ag-Pd-I, II, and III, the formation of the ordered phase increases the yield strength signifi-cantly. For example, the yield strength of the Au-Cu-Ag-Pd-II alloys increases from 350 to 600 MPa with the formation of an ordered phase. For other alloys, such as the Au-Ag-Pt and Ag-Pd alloys, the increase in yield strength is more modest in the hardened condition. The Pd-Cu-Ga alloys do not support the formation of ordered phase because the ratio of pal-ladium and copper is not in the correct range for ordered phase formation (see Table 10.9). The yield strengths of these alloys range from 320 to 1145 MPa (hard condition). The strongest alloy is Pd-Cu-Ga, with a yield strength of 1145 MPa. The other alloys range in strength from 320 to 600 MPa. These latter yield strengths are adequate for dental applications and are generally in the same range as those for the base-metal alloys, which range from 495 to 600 MPa. The effect of solid-solution hardening by the addition of copper and silver to the gold or palladium base is significant for these alloys. Pure cast gold has a tensile strength of 105 MPa (see Table 10.7). As mentioned earlier, with the addition of 10 wt% copper (coin gold), solid-solution hardening increases the tensile strength to 395 MPa. With the further addition of 10 wt% silver and 3 wt% palladium (Au-Cu-Ag-Pd-I), the tensile strength increases to about 450 and 550 MPa in the hard condition. HARDNESS Hardness is a good indicator of the ability of an alloy to resist local permanent deformation under occlusal load. Although the relationships are complex, hard-ness is related to yield strength and gives some indi-cation of the difficulty in polishing the alloy. Alloys with high hardness will usually have high yield strengths and are more difficult to polish. As Table 10.9 shows, the values for hardness generally paral-lel those for yield strength. In the hard condition, the hardness of these alloys ranges from 155 kg/mm2 for the Ag-Pd alloys to 425 kg/mm2 for the Pd-Cu-Ga alloys. More typically, the hardness of the noble cast-ing alloys is around 200 kg/mm2. The Ag-Pd alloys are particularly soft because of the high concentra-tion of silver, which is a soft metal. The Pd-Cu-Ga alloys are particularly hard because of the high con-centration of Pd, which is a hard metal. The hard-ness of most noble casting alloys is less than that of enamel (343 kg/mm2), and typically less than that of base-metal alloys. If the hardness of an alloy is greater than enamel, it may wear the enamel of the teeth opposing the restoration. ELONGATION Elongation is a measure of the ductility of the alloy. For crown and bridge applications, a low value of elongation for an alloy is generally not a big concern, because permanent deformation of the alloys is gen-erally not desirable. However, the elongation will indicate whether the alloy can be burnished. Alloys with high elongation can be burnished without fracture. Elongation is sensitive to the presence or absence of an ordered phase, as shown in Table 10.9. In the hardened condition, the elongation will drop significantly. For example, for the Au-Cu-Ag-Pd-II alloys, the elongation is 30% in the soft condition ver-sus only 10% in the hard condition. In the soft con-dition, the elongation of noble dental casting alloys ranges from 8% to 30%. These alloys are substantially more ductile than the base-metal alloys, which have elongation on the order of 1% to 2%. BIOCOMPATIBILITY The biocompatibility of noble dental alloys is equally important as other physical or chemical properties. A detailed discussion about the principles of bio-compatibility can be found in Chapter 6, but a few general principles are mentioned here. The biocom-patibility of noble dental alloys is primarily related to elemental release from these alloys (i.e., their cor-rosion). Thus any toxic, allergic, or other adverse bio-logical response is primarily influenced by elements released from these alloys into the oral cavity. The biological response is also influenced significantly by exactly which elements are released, their con-centrations, and duration of exposure to oral tissues. For example, the short-term (more than 1 to 2 days) release of zinc may not be significant biologically, but longer-term (more than 2 to 3 years) release might have more significant effects. Similarly, equivalent amounts (in moles) of zinc, copper, or silver will have quite different biological effects, because each of the elements is unique in its interactions with tissues. Unfortunately, there is currently no way of com-pletely assessing the biocompatibility of noble alloys (or any other material), because the effects of elemen-tal release on tissues are not completely understood. However, in general, several principles apply to alloy biocompatibility. The elemental release from noble alloys is not proportional to alloy composition, but rather is influenced by the numbers and types of phases in the alloy microstructure and the composi-tion of the phases. In general, multiple-phase alloys release more atoms than single-phase alloys. Some elements, such as copper, zinc, silver, cadmium, and nickel, are inherently more prone to be released from dental alloys than others, such as gold, palladium, platinum, and indium. Alloys with high noble-metal content generally release less atoms than alloys with little or no noble-metal content. However, the only reliable way to assess elemental release is by direct 188 CRAIG’S RESTORATIVE DENTAL MATERIALS measurement, because there are exceptions to each of the generalizations just mentioned. Similarly, it is difficult to predict, even knowing the elemental release from an alloy, what the biological response to the alloy will be. Thus the only reliable way is to measure the biological response directly, either in vitro, in animals, or in humans (see Chapter 6). It is important to also remember that combinations of alloys used in the mouth may alter their corrosion and biocompatibility. The IdentAlloy certification program was devel-oped to make dentists and patients more aware of the composition of dental alloys. Under this program, each alloy has a certificate (Fig. 10.7) that lists the complete composition, its manufacturer, name, and the ADA compositional classification (high noble, noble, or predominantly base metal). When the dental prosthesis is delivered by the laboratory to the dental office, a certificate is placed in the patient’s chart. In this manner, all parties know the exact composition of the material used. This information can be invalu-able later if there are problems with the restoration; for example, if the patient develops an allergic reac-tion. This information is also useful when planning additional restorations that may contact the existing restoration, or if some modification (such as occlusal adjustment or contouring) becomes necessary. Composition and Properties of Noble-Metal Alloys for Ceramic-Metal Restorations Ceramic-metal restorations consist of a cast metallic framework (or core) on which at least two layers of ceramic are baked. It is essential that the coefficient of thermal expansion of the alloy be slightly higher than that of the veneering ceramic to ensure that the ceramic is in slight compression after cooling. This will establish a better resistance to crack propagation of the ceramic-metal restoration. There are several requirements for the alloy in a ceramic-metal system (a complete list of requirements for both the alloy and ceramic can be found in Chapter 11): 1. The alloy must have a high melting temperature. The melting range must be substantially higher (greater than 100°C) than the firing temperature of the ceramic and solders used to join segments of a bridge. 2. A good bond between the ceramic and metal is essential and is achieved by the interactions of the ceramic with metal oxides on the surface of metal (Fig. 10.8) and by the roughness of the metal coping. 3. Coefficients of thermal expansion of the ceramic and metal must be compatible so that the ceramic does not crack during fabrication. The system is designed so the value for the metal is slightly higher than for the ceramic, thus putting the ceramic in compression (where it is stronger) following cooling (Fig. 10.9). 4. Adequate stiffness and strength of the alloy core are especially important for fixed bridges and posterior crowns. High stiffness in the alloy reduces stresses in the ceramic by reducing deflection and strain. High strength is essential in the interproximal regions in fixed bridges. 5. High sag resistance is essential. The alloy copings are relatively thin; no distortion should occur during firing of the ceramic, or the fit of the restoration will be compromised. 6. An accurate casting of the metal coping is required even with the higher melting range of the alloy. FIG. 10.7 An example of an IdentAlloy certificate showing the alloy name, manufacturer, composition, and American Dental Association (ADA) classification. This section of the certificate is for the dentist’s records. A duplicate retained by the laboratory is not shown here. Many dentists will give this information to the patient upon delivery of the prosthesis. FIG. 10.8 Electron micrograph of replicated oxidized surface of an Au-Pt-Pd (gold-platinum-palladium) alloy (×8000). (From Kelly M, Asgar K, O’Brien WJ. Tensile strength determination of the interface between porcelain fused to gold. J Biomed Mater Res. 1969;3:403–408.) 189 10. Restorative Materials: Metals 7. Adequate design of the restoration is critical. The preparation should provide for adequate thickness of alloy as well as enough space for an adequate thickness of ceramic to yield an esthetic restoration. The composition ranges and colors of five types of noble alloys for ceramic-metal restorations are listed in Table 10.10. The properties of these alloys are given in Table 10.11. AU-PT-PD ALLOYS The Au-Pt-Pd alloys contain very high noble-metal content, mainly gold with platinum and palladium to increase the melting range. The high noble con-tent provides good corrosion resistance. Indium, tin, and iron (Fe) are present and form oxides to produce a ceramic-metal bond. Rhenium (Re) is added as a grain refiner. Hardening of Au-Pt-Pd alloys results from solid-solution hardening and the formation of an FePt3 precipitate. Optimum heat treatment for hardening is 30 minutes at 550°C, but practically the hardening occurs during firing of the ceramic. From Table 10.11 it is seen that these alloys have high stiffness (elastic modulus), strength, and hard-ness and reasonable elongation; however, they have somewhat low sag resistance. The alloys are very costly because of their high noble-metal content and high density. The casting temperature is reasonably high, and although reasonably easy to solder, care must be taken because the soldering temperature is only about 50°C below the melting range of the alloys. Finally, although considerable platinum and palladium are present, these alloys are still yellow, which makes producing pleasing esthetics with the ceramic easier than with white alloys. AU-PD ALLOYS The Au-Pd high-noble alloys with good corrosion resistance have decreased gold but increased palla-dium content. These alloys contain no platinum or P M P M P M P M CTE 14.0 106/C CTE 13.5 106/C No bond Bond Firing temperature Room temperature FIG. 10.9 Diagram of the ceramic-metal bond. Shown at the firing temperature and at room temperature, when the thermal coefficient of expansion of the metal is 0.5 × 10−6/°C greater than the ceramic, thus placing the ceramic in compression at room temperature. CTE, Coefficient of thermal expansion; M, metal; P, porcelain. (From Powers JM, Wataha JC. Dental Materials: Foundations and Applications. 11th ed. St. Louis: Elsevier; 2017.) TABLE 10.10 Composition Ranges and Color of Noble Alloys for Ceramic-Metal Restorations (wt%) Type Au (%) Pt (%) Pd (%) Ag (%) Cu (%) Other (%) Total Noble-Metal Content (%) Color Au-Pt-Pd 84–86 4–10 5–7 0–2 — Fe, In, Re, Sn 2–5 96–98 Yellow Au-Pd 45–52 — 38–45 0 — Ru, Re, In 8.5, Ga 1.5 89–90 White Au-Pd-Ag 51–52 — 26–31 14–16 — Ru, Re, In 1.5, Sn 3–7 78–83 White Pd-Ag — — 53–88 30–37 — Ru, In 1–5, Sn 4–8 49–62 White Pd-Cu 0–2 — 74–79 — 10–15 In, Ga 9 76–81 White TABLE 10.11 Properties and Casting Temperatures of Noble Alloys Used in Ceramic-Metal Restorations Type Ultimate Tensile Strength (MPa) Yield Strength at 0.2% Offset (MPa) Elastic Modulus (GPa) Elongation (%) VHN (kg/ mm2) Density (g/cm3) Casting Temperature (°C) Au-Pt-Pd 480–500 400–420 81–96 3–10 175–180 17.4–18.6 1150 Au-Pd 700–730 550–575 100–117 8–16 210–230 13.5–13.7 1320–1330 Au-Pd-Ag 650–680 475–525 100–113 8–18 210–230 13.6–13.8 1320–1350 Pd-Ag 550–730 400–525 95–117 10–14 185–235 10.7–11.1 1310–1350 Pd-Cu 690–1300 550–1100 94–97 8–15 350–400 10.6–10.7 1170–1190 VHN, Vickers hardness number. 190 CRAIG’S RESTORATIVE DENTAL MATERIALS iron and thus are solution hardened rather than pre-cipitation hardened. They contain indium for bond-ing, gallium (Ga) to decrease the fusion temperature, rhenium for grain refining, and ruthenium (Ru) for enhancing castability. Because of their high palla-dium content, the alloys are white (some call it gray) rather than yellow, even though they contain about 50% gold. This color causes increased difficulty in producing esthetic restorations. These alloys are stronger, stiffer, and harder than the Au-Pt-Pd alloys and have higher elongation (more ductile) and casting temperatures (easier to solder). They have lower densities and this means more care should be taken during casting because of the decrease in the force with which the alloy enters the casting ring. However, these alloys remain relatively easy to cast, and soldering is easy because of the higher cast-ing temperature. AU-PD-AG ALLOYS The Au-Pd-Ag alloys contain less palladium and more silver than the Au-Pd alloys. However, they still have good corrosion resistance. Again, indium and tin are added for bonding with the ceramics, ruthe-nium for castability, and rhenium for grain refining. Hardening results from solution hardening. As seen in Table 10.11, the properties of the Au-Pd-Ag alloys are similar to those of the Au-Pd alloys. PD-AG ALLOYS The Pd-Ag alloys, which contain no gold and have a moderately high silver content, have the lowest noble-metal content of the five noble alloys. They contain indium and tin for bonding and ruthenium for enhanced castability. Their properties are similar to those of the Au-Pd-Ag alloys, except that they are less dense (≈11 g/cm3 vs. 14 g/cm3). Some ceramics used with these high-gold alloys resulted in what was called “greening” relating to a color shift toward yellow. Furnace contamination and technique were blamed to some extent for this problem. PD-CU ALLOYS The Pd-Cu alloys contain very high palladium con-tent with 10% to 15% copper. They contain indium for bonding with porcelain and gallium for control-ling casting temperature. These alloys have high strength and hardness, moderate stiffness and elon-gation, and low density. However, they have low sag resistance and form dark oxides. They are white alloys, like all the other metals except the yellow Au-Pt-Pd alloys. Base-Metal Alloys Base-metal alloys are used extensively in dentistry for a variety of restorations and instruments, as shown in Box 10.1. Cast cobalt-chromium alloys have been used for many years for fabricating removable den-tal prosthesis frameworks and have replaced type IV gold alloys almost completely for this application. Nickel-chromium and cobalt-chromium alloys are used in ceramic-metal restorations. The addition of beryllium to base-metal alloys improves castability by lowering the melting tem-perature and surface tension and increasing the strength of the porcelain-metal bond. However, beryllium, in vapor or particulate form, is asso-ciated with several diseases, including contact dermatitis, chronic lung disease, lung carcinoma, and osteosarcoma. Laboratory personnel are at greatest risk for beryllium exposure when per-forming melting, grinding, polishing, and fin-ishing procedures. Efficient local exhaust and filtration systems as well as adequate general ven-tilation should be used when casting, finishing, and polishing these beryllium-containing alloys. The ADA Council on Scientific Affairs recom-mends that, where possible, beryllium-containing alloys should not be used in the fabrication of dental restorations. If alloys containing beryl-lium must be used, the Occupational Safety and BOX 10.1 D E N TA L A P P L I C AT I O N S O F C A S T A N D W R O U G H T B A S E – M E TA L A L L O Y S Cast cobalt-chromium alloys Removable dental prosthesis framework Ceramic-metal restorations Cast nickel-chromium alloys Ceramic-metal restorations Cast titanium and titanium alloys Crowns Fixed partial prosthesis Removable dental prosthesis framework Implants Wrought titanium and titanium alloys Implants Crowns Fixed partial prosthesis Wrought stainless steel alloys Endodontic instruments Orthodontic wires and brackets Preformed crowns Wrought cobalt-chromium-nickel alloys: orthodontic wires and endodontic files Wrought nickel-titanium alloys: orthodontic wires and endodontic files 191 10. Restorative Materials: Metals Health Administration (OSHA) guideline (OSHA Hazard Information Bulletin 02-04-19) must be followed. Several manufacturers have eliminated beryllium in their alloys. The ISO standard limits beryllium content to 0.02 wt%. The Food and Drug Administration (FDA) has accepted the ISO stan-dard but has “grandfathered” beryllium- containing alloys on the market before 1976. The presence of nickel in nickel-chromium alloys and stainless steel is of significant importance because nickel is a known allergen. The incidence of sensitivity to nickel has been reported to be from 5 to 10 times higher for females than for males, with 5% to 8% of females showing sensitivity. However, no correlation has been found between the pres-ence of intraoral nickel-based restorations and sen-sitivity. A cobalt-chromium alloy without nickel or other nonnickel-containing alloy should be used on patients with a medical history indicating an allergic response to nickel. The amount of nickel in base-metal alloys used in direct soft tissue contact, such as in removable dental prosthesis frameworks, is diminishing. Nickel is mostly found in alloys for ceramic-metal restorations and for wrought applications such as wires. To minimize exposure of patients to metallic dust containing nickel or beryllium, intraoral finishing should be done with a high-speed evacuation system and preferably in a wet environment. The use of titanium and titanium alloys is rapidly increasing for implants, orthodontic wires, and end-odontic files. Stainless steel alloys are used princi-pally for orthodontic wires, in fabricating endodontic instruments, and for preformed crowns. General Requirements of a Dental Base-Metal Alloy The metals and alloys used as substitutes for noble alloys in dental restorations must possess certain minimal fundamental characteristics: 1. The alloy’s chemical nature should not produce toxicologic or allergic effects in the patient or the operator. 2. The chemical properties of the prosthesis should provide resistance to corrosion and physical changes when in the oral fluids. 3. The physical and mechanical properties, such as thermal conductivity, melting temperature, coefficient of thermal expansion, and strength, should all be satisfactory, meeting certain minimum values for various prostheses’ designs. 4. The technical expertise needed for fabrication and use should be feasible for the average dentist and skilled technician. 5. The metals, alloys, and companion materials for fabrication should be plentiful, relatively inexpensive, and readily available, even in periods of emergency. When base-metal alloys are used in ceramic-metal systems, the same requirements as listed for noble alloys apply. This list of requirements for the ideal substitute for noble alloys suggests that a combination of chem-ical, physical, mechanical, and biological qualities is involved in the evaluation of each alloy. The proper-ties of the alloys depend on material, compositional, and processing factors. Cast and wrought base-metal alloys, including cobalt-chromium-nickel, nickel-chromium-iron, com-mercially pure titanium (CP Ti), titanium-aluminum- vanadium, stainless steel, nickel-titanium, and titanium-molybdenum (beta-titanium) alloys are dis-cussed in this section. The discussion is based on the synergistic relationship between processing, composi-tion, structure, and properties of the materials. Cobalt-Chromium and Nickel-Chromium Casting Alloys for Removable Dental Prostheses Almost all metal frameworks of removable dental prostheses are made from cobalt-chromium alloys. ANSI/ADA SPECIFICATION NO. 14 (ISO 6871) According to ANSI/ADA specification No. 14, the weight of chromium should be no less than 20%, and the total weight of chromium, cobalt, and nickel should be no less than 85%. Alloys having other com-positions may also be accepted by the ADA, provided the alloys comply satisfactorily with requirements on toxicity, hypersensitivity, and corrosion. Elemental composition to the nearest 0.5% must be marked on the package, along with the presence and percentage of hazardous elements and recommendations for pro-cessing the materials. The specification also requires minimum values for elongation (1.5%), yield strength (500 MPa), and elastic modulus (170 GPa). COMPOSITION PRINCIPAL ELEMENTS The principal elements present in cast base metals for removable dental prostheses are chromium, cobalt, and nickel, which together account for 82 to 92 wt% of most alloys used. Representative compositions of five commer-cial dental casting alloys, including three that are used for ceramic-metal restorations, are listed in Table 10.12. Chromium, cobalt, and nickel compose about 85% of the total weight of these alloys, yet their effect on the physical properties is rather lim-ited, because the physical properties of these alloys are more controlled by the presence of minor alloy-ing elements such as carbon, molybdenum, tung-sten, manganese, nitrogen, tantalum, gallium, and aluminum. 192 CRAIG’S RESTORATIVE DENTAL MATERIALS FUNCTION OF VARIOUS ALLOYING ELE-MENTS Chromium is responsible for the tarnish and corrosion resistance of these alloys. When the chromium content of an alloy is higher than 30%, the alloy is more difficult to cast and becomes more brit-tle. Therefore cast base-metal dental alloys should not contain more than 28% or 29% chromium. In general, cobalt and nickel, up to a certain percentage, are interchangeable elements. Cobalt increases the elastic modulus, strength, and hardness of the alloy more than nickel. The effect of other alloying elements on the properties of these alloys is much more pronounced. One of the most effective ways of increasing the hardness of cobalt-based alloys is by increasing their carbon content. A change in the carbon content of approximately 0.2% changes the properties to such an extent that the alloy becomes too hard and brittle and should not be used for making any dental prostheses. Conversely, a reduction of 0.2% in the carbon content would reduce the alloy’s yield and ultimate tensile strengths to such low values that the alloy would also not be usable in dentistry. Furthermore, almost all elements in these alloys, such as chromium, silicon, molybdenum, cobalt, and nickel, react with carbon to form carbides, which change the properties of the alloys. Note that, as shown in Table 10.12, the nickel-chromium alloys used with ceramic contain signifi-cantly less carbon than the alloys used for removable dental prostheses. The presence of 3% to 6% molyb-denum contributes to the strength of the alloys. Microstructure of Cast Base-Metal Alloys The microstructure of a material controls its proper-ties. In other words, a change in the physical prop-erties of a material is a strong indication that there must have been some alteration in its microstructure. Sometimes this variation in microstructure cannot be distinguished by ordinary means. The micro-structures of cobalt-chromium and nickel-chromium alloys are complex and change with slight alterations of manipulative conditions. Many elements present in cast base-metal alloys, such as chromium, cobalt, and molybdenum, are car-bide-forming elements. Depending on the composition of the alloy and its manipulative condition, it may form many types of carbide in various types of arrangement. The microstructure of a commercial cobalt- chromium alloy is illustrated in Fig. 10.10. In Fig. 10.10A, the carbides are continuous along the grain boundaries. Such a structure is obtained when the metal is quickly cast as soon as it is completely melted. TABLE 10.12 Composition of Major Cast Base-Metal Alloys Used in Dentistry Elements Alloy (wt%) Vitalliuma Ticoniuma Ni-Cr Alloy with Beb Ni-Cr Alloy without Beb Co-Cr Alloyb Co-Cr with Some Noble Metalsc Chromium (Cr) 30 17 13 22 26 20 Cobalt (Co) Balance — — — Balance Balance Nickel (Ni) — Balance Balance Balance — — Molybdenum (Mo) 5 5 5.5 9 6 4 Tungsten (W) — — — — 5 — Niobium (Nb) — — — 3.5 — — Aluminum (Al) — 5 2.5 0.25 — 2 Iron (Fe) 1 0.5 — 1.75 0.5 — Carbon (C) 0.5 0.1 <0.1 <0.1 <0.1 <0.1 Beryllium (Be) — 1.0 1.9 — — — Silicon (Si) 0.6 0.5 — 0.6 1 — Manganese (Mn) 0.5 5 — 0.3 — 4 Gold (Au) — — — — — 2 Gallium (Ga) — — — — — 6 Rare earth — — — — 0.5 <0.25 aData from Asgar K. An overall study of partial dentures. USPHS Research Grant DE-02017. Washington, DC: National Institutes of Health (NIH); 1965, and from Baran G. The metallurgy of Ni-Cr alloys for fixed prosthodontics. J Prosthet Dent. 1983;50:639–650. bTypical alloy compositions for ceramic-metal restorations with conventional porcelains. cAlloy suitable for high-expansion porcelain. 193 10. Restorative Materials: Metals In this condition, the cast alloy possesses low elonga-tion values with a clean surface. Carbides that are spherical and discontinuous, like islands, are shown in Fig. 10.10B. Such a structure can be obtained if the alloy is heated more than 100°C above its normal melting temperature; this results in a casting with good elongation values but with a very poor surface because of an increased reaction with the investment material, and thus is not useful in dentistry. An alloy with dark areas having a distinct lamellar structure is shown in Fig. 10.10C. Such a structure is respon-sible for very low elongation values but a good and clean casting. From these three examples, it is clear that microstructure can strongly affect physical and mechanical properties. The microstructure of Ni-Cr alloys is strongly dependent on alloy composition. Alloys that do and do not contain Be have complicated, multiphase micro-structures such as those shown in Fig. 10.10D and E. The precipitates dispersed within the matrix include complex carbides, and these precipitates are relatively unaffected by the short heat-treatment cycles that the alloys are subjected to during ceramic firing procedures when used for porcelain-fused-to-metal restorations. B C D E A FIG. 10.10 Microstructure of alloys. (A) Cast cobalt-chromium alloy, where the carbides are continuous around the grain boundaries. (B) The islandlike structures are carbides, which are dispersed throughout the entire area. (C) The dark areas are eutectoid, which are lamellar in nature. (D) The microstructure of a beryllium-containing nickel-chromium alloy. (E) The microstructure of a boron- and silicon-containing nickel-chromium alloy. (A, B, and C from Asgar K, Peyton FA. Effect of microstructure on the physical properties of cobalt-base alloys. J Dent Res. 1961;40:63–72; D and E, Courtesy G. Baran, Temple University, Philadelphia, PA.) 194 CRAIG’S RESTORATIVE DENTAL MATERIALS Heat Treatment of Base-Metal Alloys The early base-metal alloys used in removable den-tal prostheses were primarily cobalt-chromium and were relatively simple. Heat treating these alloys up to 1 hour at 1000°C did not appreciably change their mechanical properties. Base-metal alloys available today for removable dental prostheses, however, are more complex. Presently, complex cobalt-chromium alloys, nickel-chromium alloys, and iron-chromium alloys are used for this purpose. Studies have shown that many heat treatments of cobalt-based alloys reduce both the yield strength and elongation. If for any reason some soldering or weld-ing must be performed on these removable dental prostheses, the lowest possible temperature should be used with the shortest possible heating time. Physical Properties MELTING TEMPERATURE Compared with cast gold alloy types I to IV, which have a melting range of 800°C to 1050°C, the melt-ing temperature of base-metal alloys is much higher, with a range of 1150°C to 1500°C. DENSITY The average density of cast base-metal alloys is between 7 and 8 g/cm3, which is about half the den-sity of most dental gold alloys. Density is of some importance in bulky maxillary prostheses, in which the force of gravity causes the relative weight of the casting to place additional forces on the supporting teeth. With certain prostheses, therefore, the reduction of weight resulting from the lower density of the cast base-metal alloys can be considered an advantage. Mechanical Properties Typical mechanical properties of the alloys for removable dental prostheses listed in Table 10.12 have been assembled in Table 10.13, together with a representative range of values for type IV casting gold alloys subjected to a hardening heat treatment. YIELD STRENGTH The yield strength gives an indication of when a per-manent deformation of a device or part of a device, such as a partial denture clasp, will occur. As such, it is one of the important properties of alloys intended for removable dental prostheses. It is believed that dental alloys should have yield strengths of at least 415 MPa to withstand permanent deformation when used as removable prosthesis clasps. It may be seen from Table 10.13 that base-metal dental alloys have yield strengths greater than 600 MPa. TENSILE STRENGTH The ultimate tensile strength of cast base-metal alloys is less influenced by variations in specimen preparation and test conditions than are some other properties, such as elongation. Table 10.13 shows that the ultimate tensile strength of cast base-metal dental alloys is greater than 800 MPa. Table 10.13 also shows that hardened removable dental pros-thesis gold alloys can have ultimate tensile strengths almost equal to those of cast base-metal alloys. ELONGATION The percent elongation of an alloy is important as an indication of the relative brittleness or ductility a restoration will exhibit. There are many occasions, therefore when elongation is an important property for comparison of alloys for removable dental pros-theses. For example, as described in Chapter 4, the combined effect of elongation and ultimate tensile strength is an indication of toughness of a material. Because of their toughness, removable dental pros-thesis clasps cast of alloys with a high elongation and tensile strength do not fracture in service as often as do those with low elongation. TABLE 10.13 Mechanical Properties of Alloys Used in Removable Dental Prostheses Yield Strength at 0.2% Offset (MPa) Tensile Strength (MPa) Elongation (%) Elastic Modulus (GPa) Vickers Hardness Number (kg/mm2) CAST BASE-METAL ALLOYSa Vitallium 644 870 1.5 218 380 Ticonium 710 807 2.4 186 340 Hardened removable dental prosthesis gold alloysb 480–510 700–760 5–7 90–100 220–250 aData from Asgar K, Techow BO, Jacobson JM. A new alloy for partial dentures. J Prosthet Dent. 1970;23:36–43; Morris HF, Asgar K. Physical proper-ties and microstructure of four new commercial partial denture alloys. J Prosthet Dent. 1975;33:36–46; Moffa JP, Lugassy AA, Guckes AD, Gettlemen L. An evaluation of non-precious alloys for use with porcelain veneers. Part I. Physical properties. J Prosthet Dent. 1973;30:424–431. bData from Oilo G, Gjerdet NR. Dental casting alloys with a low content of noble metals: physical properties. Acta Odontol Scand. 1983;41(2):111–116. 195 10. Restorative Materials: Metals A small amount of microporosity will decrease the elongation of a cast metal prosthesis considerably, whereas its effect on yield strength, elastic modu-lus, and tensile strength is rather limited. One can therefore assume that practical castings may exhibit similar variations in elongation from one casting to another. To some degree this is borne out in practice, with some castings from the same product showing a greater tendency toward brittleness than others. This observation indicates that control of the melting and casting variables is of extreme importance if repro-ducible results are to be obtained. Although nickel and cobalt are interchangeable in cobalt-nickel-chromium alloys, increasing the nickel content with a corresponding reduction in cobalt generally increases the ductility and elongation. High values of elongation are obtained by casting at the normal melting temperature and by not heating the alloy more than 100°C above its normal casting temperature. High elongation is achieved without sacrificing strength and is the result of the precise and proper combination of carbon, nitrogen, silicon, manganese, and molybdenum content. ELASTIC MODULUS The higher the elastic modulus, the more rigid is the structure. Some dental professionals recommend the use of a well-designed, rigid prosthesis because it properly distributes forces on the supporting tis-sues when in service. With a greater elastic modulus, one can design the restoration with slightly reduced dimensions. From Table 10.13, it can be seen that the elastic modulus of base-metal alloys is approxi-mately double the modulus of type IV cast dental gold alloys. HARDNESS Differences in composition of the cast base-metal alloys have some effect on their hardness, as indi-cated by the values given in Table 10.13. In general, cast base-metal alloys have hardness values about one-third greater than gold alloys used for the same purpose. Hardness is an indication of the ease of finish-ing the structure and its resistance to scratching in service. The higher hardness of the cast base-metal alloys as compared with gold alloys requires the use of different polishing equipment and compounds, but the finishing operation can be completed without difficulty by experienced operators. FATIGUE The importance of the fatigue resistance of alloys used for removable dental prostheses is obvious when one considers that these prostheses are placed and removed daily. At these times, the clasps are strained as they slide around the retaining tooth, and the alloy undergoes fatigue. Comparisons among cobalt-chromium, titanium, and gold alloys show that cobalt-chromium alloys possess superior fatigue resistance, as indicated by a higher number of cycles (putting on and taking off) required to fracture a clasp. Any procedures that result in increasing the porosity or carbide content of the alloy will reduce fatigue resistance. In addition, soldered joints, which often contain inclusions or pores, represent weak links in the fatigue resistance of the prosthesis. CORROSION In vitro corrosion tests have evaluated a number of important variables, including effects of electrolytic media and artificial saliva, alloy composition, alloy microstructure, and surface state of the metal. These variables account for 2 to 4 orders of magnitude variation in the amount of metal ions released. The surface state of the metal is an extremely important factor influencing corrosion, because the surface com-position is almost always different from that of the bulk alloy. Another important consideration is corro-sion coupled with wear. Up to three times the mass of metal ions, such as nickel (Ni), is released during occlusal rubbing in combination with corrosion than during corrosion alone for nickel- chromium (Ni-Cr) alloys. No long-term studies have been performed to monitor the impact of the release of such large concentrations of metal ions on the overall health of patients. Base-Metal Casting Alloys for Fixed Prosthodontics Most of the nickel-chromium alloys contain 60% to 80% nickel, 10% to 27% chromium, and 2% to 14% molybdenum. As a comparison, cobalt-chromium alloys contain 53% to 67% cobalt, 25% to 32% chro-mium, and 2% to 6% molybdenum. They may also contain small amounts of aluminum, carbon, cobalt, copper, cerium, gallium, iron, manganese, niobium, silicon, tin, titanium, and zirconium. The range of compositions of base-metal alloys for ceramic-metal restorations is given in Table 10.14, and typical prop-erties of these alloys are listed in Table 10.15. Base-metal casting alloys exhibit a higher hard-ness and elastic modulus than do noble-metal alloys, but they require a slightly different approach in casting and soldering to accommodate their higher solidification shrinkage and generally lower densi-ties than noble alloys. NICKEL-CHROMIUM (NI-CR) ALLOYS Chromium provides tarnish and corrosion resis-tance, whereas alloys containing aluminum (Al) are strengthened by the formation of coherent pre-cipitates of Ni3Al. Molybdenum (Mo) is added to decrease the thermal coefficient of expansion. Note 196 CRAIG’S RESTORATIVE DENTAL MATERIALS TABLE 10.14 Composition Ranges of Base Metals for Ceramic-Metal Restorations (wt%) Type Ni Cr Co Ti Mo Al V Fe Be Ga Mn Nb W B Ru Ni-Cr 69–77 13–16 — — 4–14 0–4 — 0–1 0–2 0–2 0–1 — — — — Co-Cr — 15–25 55–58 — 0–4 0–2 — 0–1 — 0–7 — 0–3 0–5 0–1 0–6 Ti — — — 90–100 — 0–6 0–4 0–0.3 — — — — — — — TABLE 10.15 Properties of Base-Metal Alloys for Ceramic-Metal Restorations Type Ultimate Tensile Strength (MPa) Yield Strength at 0.2% Offset (MPa) Elastic Modulus (GPa) Elongation (%) VHN (kg/mm2) Density (g/cm3) Casting Temperature (°C) Ni-Cr 400–1000 255–730 150–210 8–20 210–380 7.5–7.7 1300–1450 Co-Cr 520–820 460–640 145–220 6–15 330–465 7.5–7.6 1350–1450 Ti 240–890 170–830 103–114 10–20 125–350 4.4–4.5 1760–1860 VHN, Vickers hardness number. that because of the wide differences in atomic weight of nickel and chromium, 2 wt% is roughly equal to 6 at%. These alloys are harder than noble alloys but usually have lower yield strengths. They also have higher elastic moduli, in some cases allowing for the use of thinner copings and frameworks. They have much lower densities (7 to 8 g/cm3) and generally higher casting temperatures. Adequate casting com-pensation is at times a problem, as is the fit of the coping. COBALT-CHROMIUM (CO-CR) ALLOYS Again, chromium provides tarnish and corrosion resistance. Unlike Co-Cr removable dental prosthe-sis alloys, the alloys for ceramic-metal restorations are strengthened by solution hardening rather than carbide formation. Molybdenum helps lower the coefficient of expansion, and ruthenium improves castability. Co-Cr alloys are stronger and harder than noble and Ni-Cr alloys and have roughly the same densities and casting temperature as Ni-Cr alloys. Casting and soldering of these alloys are more dif-ficult than for noble alloys, as is obtaining a high degree of accuracy in the castings. TITANIUM (TI) AND TITANIUM ALLOYS Pure titanium (Ti) and titanium alloyed with alumi-num and vanadium (Ti-6Al-4V) have been attempted for cast restorations, but they are mainly important in implant and orthodontic wire applications. They have superior biocompatibility compared with the other base-metal alloys, but Ti and Ti-6Al-4V pres-ent processing difficulties, as indicated by their high casting temperatures (1760°C to 1860°C), low densi-ties, and ease of oxidation. Other processing meth-ods, such as computer-assisted machining and spark erosion to fabricate copings, may increase the use of these metals. Additional discussion of titanium and titanium alloys appears in the following sections. Other Applications of Cast Base-Metal Alloys Cast cobalt-chromium alloys are also used in ortho-pedics in the surgical repair of bone fractures, spe-cifically for bone plates, screws, various fracture appliances, and splints. Metallic obturators and implants for various purposes can be formed from cast base-metal alloys. The use of cobalt-chromium alloys for surgical purposes is well established, and these alloys have numerous oral surgical uses. They can be implanted directly into the bone structure for long periods without harmful reactions. This favor-able response of the tissue is probably attributable to the low solubility and electrogalvanic action of the alloy; the metal is inert and produces no inflam-matory response. The product known as surgical Vitallium has been used extensively for this purpose. However, the primary metal used in dental implants today is titanium (see Chapter 15). Advanced rapid manufacturing technology called direct metal laser sintering is being used to create pure cobalt-chrome crowns and fixed dental prosthesis frameworks. This method uses a high-power laser to fuse successive 0.02-mm-thick lay-ers of powdered metal. After all layers are built, the solid copings and frameworks are removed from the machine, sand blasted, polished, and cleaned, ready for ceramic application. Cobalt-chrome can also be machined using computer-aided design and manufacturing processes. High-speed milling machines under numerical control reproduce geom-etries created in software originating from scanners or other dental computer-aided design systems. These devices process zirconium, cobalt-chromium, 197 10. Restorative Materials: Metals titanium, and plastics. Five-axis machining enables the creation of embrasures, undercuts, and other intricate geometries without the need for manual trimming and adjustment. TITANIUM AND TITANIUM ALLOYS Titanium’s resistance to electrochemical degrada-tion; benign biological response elicited; relatively light weight; and low density, low modulus, and high strength make titanium-based materials attrac-tive for use in dentistry. Titanium forms a very stable oxide layer with a thickness on the order of ang-stroms, and it repassivates in a time on the order of nanoseconds (10–9 second). This oxide formation is the basis for the corrosion resistance and biocompat-ibility of titanium. Titanium has therefore been called the material of choice in dentistry. CP Ti is used for dental implants, surface coat-ings, and more recently, for crowns, partial remov-able dental prostheses, and orthodontic wires. Several titanium alloys are also used. Of these alloys, Ti-6Al-4V is the most widely used. Wrought alloys of titanium and nickel and titanium and molybdenum are used for orthodontic wires. The term titanium is often used to include all types of pure and alloyed titanium. However, it should be noted that the pro-cessing, composition, structure, and properties of the various titanium alloys are quite different, and also that differences exist between the wrought and cast forms of a given type of titanium. COMMERCIALLY PURE TITANIUM CP Ti is available in four grades, which vary according to the oxygen (0.18 to 0.40 wt%) and iron (0.20 to 0.50 wt%) content (Table 10.16). These seemingly slight concen-tration differences have a substantial effect on the physical and mechanical properties. At room temperature, CP Ti has a hexagonal close-packed crystal lattice, which is denoted as the alpha (α) phase. On heating, a phase transforma-tion occurs. At 883°C, a body-centered cubic phase, which is denoted as the beta (β) phase, forms. A component with predominantly β phase is stron-ger but more brittle than a component with α-phase microstructure. As with other metals, the tempera-ture and time of processing and heat treatment dic-tate the amount, ratio, and distribution of phases, overall composition and microstructure, and resul-tant properties. As a result, casting temperature and cooling procedure are critical factors in ensuring a successful casting. The density of CP Ti (4.5 g/cm3) and its elastic modulus (100 GPa) are about half the value of many of the other base metals. The yield and ultimate strengths vary, respectively, from 170 to 480 MPa and 240 to 550 MPa, depending on the grade of titanium. Table 10.17 lists the mechanical properties for CP grades 1 and 4 Ti for comparison with noble alloys and other base-metal alloys. TITANIUM ALLOYS: GENERAL Alloying ele-ments are added to stabilize either the α or the β phase, by changing the β-transformation tempera-ture. For example, in Ti-6Al-4V, aluminum is an α stabilizer, whereas vanadium, as well as copper and palladium, are β stabilizers. In general, alpha-titanium is weldable, but diffi-cult to form or work with at room temperature. Beta-titanium, however, is malleable at room temperature and is thus used in orthodontics to make wires. The (α + β) TABLE 10.16 Composition of CP Titanium and Alloy (wt%) Titanium N C H Fe O Al V Ti CP grade I 0.03 0.10 0.015 0.02 0.18 Balance CP grade II 0.03 0.10 0.015 0.03 0.25 Balance CP grade III 0.03 0.10 0.015 0.03 0.35 Balance CP grade IV 0.03 0.10 0.015 0.05 0.40 Balance Ti-6Al-4V alloy 0.05 0.08 0.012 0.25 0.13 5.50–6.50 3.50–4.50 Balance CP, Commercially pure. TABLE 10.17 Mechanical Properties of Titanium and Other Selected Materials Material Elastic Modulus (GPa) Ultimate Tensile Strength (MPa) Yield Strength (MPa) 316L SS 200 965 690 Co-Cr-Mo 240 700 450 Type IV gold 90 770 >340 CP grade 1 Ti 102 240 170 CP grade 4 Ti 104 550 483 Ti-6Al-4V 113 930 860 CP, Commercially pure; SS, stainless steel. 198 CRAIG’S RESTORATIVE DENTAL MATERIALS alloys are strong and formable but difficult to weld. Thermal and thermochemical treatments can refine the postcast microstructures and improve properties. TI-6AL-4V At room temperature, Ti-6Al-4V is a two-phase (α + β) alloy. At about 975°C, a phase trans-formation takes place, transforming the microstruc-ture to a single-phase body-centered cubic β alloy. Thermal treatments dictate the relative amounts of the α and β phases and the phase morphologies and yield a variety of microstructures and a range of mechanical properties. Microstructural variations depend on whether working and heat treatments were performed above or below the β-transition tem-perature and on the cooling rate. Following forging (i.e., mechanically deforming) at temperatures in the range of 700°C to 950°C, ther-mal treatments below the β-transition temperature (typically performed at approximately 700°C) produce recrystallized microstructures having fine equiaxed α grains (Fig. 10.11). Equiaxed microstructures are char-acterized by small (3 to 10 μm), rounded grains that have aspect ratios near unity. This class of microstruc-ture is recommended for Ti-6Al-4V surgical implants. The mechanical properties of (α + β) titanium alloys are dictated by the amount, size, shape, and morphology of the α phase and the density of α/β interfaces. The tensile and fatigue proper-ties of Ti-6Al-4V have been studied extensively. Microstructures with a small (less than 20 μm) α-grain size, a well-dispersed β phase, and a small α/β interface area, such as in equiaxed microstruc-tures, resist fatigue crack initiation best and have the best high-cycle fatigue strength (approximately 500 to 700 MPa). Lamellar microstructures, which have a greater α/β surface area and more oriented colo-nies, have lower fatigue strengths (approximately 300 to 500 MPa) than do equiaxed microstructures. MACHINED TITANIUM FOR DENTAL IMPLANTS Endosseus dental implants are ma chined from billets of titanium. Typical materials are CP Ti or the Ti-6Al-4V alloy. Studies have been published on the potential for replacing vanadium with niobium, which might improve cell attach-ment. Recent research has focused on engineering specific surface textures on machined titanium to improve both the degree of osseointegration and the adaptation of soft tissue to the collar of the implant. To increase surface area for contact by bone cells, machined titanium can be grit blasted with metal oxide or hydroxyapatite particles. The surface can also be plasma sprayed with titanium or coated with hydroxyapatite. More discussion of implant surface modifications can be found in Chapter 15. CAST TITANIUM Based on the attributes, extensive knowledge, and clinical success of wrought titanium implants, interest has developed in cast titanium for dental applications. Although titanium has been cast for more than 50 years, only recently have nearly precision castings been attain-able. For aerospace and medical components, hot isostatic pressing and specific finishing techniques are routinely practiced. However, these techniques are beyond the capabilities and affordability of most dental laboratories. The two most important factors in casting titanium-based materials are their high melting point (1700°C for CP Ti) and chemical reactivity. Because of the high melting point, special melting procedures, cooling cycles, mold material, and casting equip-ment to prevent metal contamination are required. Titanium readily reacts with gaseous elements such as hydrogen, oxygen, and nitrogen, particularly at elevated temperatures (greater than 600°C). As a result, any manipulation of titanium at elevated tem-peratures must be performed in a well-controlled vacuum or inert atmosphere. Without such con-trols, titanium surfaces will be contaminated by an oxygen-enriched and hardened surface layer, which can be as thick as 100 μm, and can reduce strength and ductility and promote cracking because of the embrittling effect of the oxygen. The technology required to overcome these factors is what makes casting titanium relatively more expensive. Because of the high affinity titanium has for hydrogen, oxygen, and nitrogen, standard cru-cibles and investment materials cannot be used. Investment materials or face coats for the wax pat-terns must have oxides that are more stable than the very stable titanium oxide, and must also be able to withstand a temperature sufficient to melt titanium. If this is not the case, oxygen is likely to diffuse into the molten metal. Investment materials using a com-bination of ZrO2-type face coat that is backed up by FIG. 10.11 Microstructure of equiaxed Ti-6Al-4V (×200). Equiaxed microstructures are characterized by small, rounded α-grains, with aspect ratios near unity. 199 10. Restorative Materials: Metals a phosphate-bonded silica investment or phosphate investment materials involving inert fillers (ZrO2, Al2O3, MgO) achieve this goal. Because of the low density of titanium, it is difficult to cast in conventional, centrifugal-force casting machines. In the last 20 years, advanced casting techniques, which combine centrifugal, vacuum, pressure, and gravity casting, new invest-ment materials, and advanced melting techniques (e.g., electric arc melting) have been developed. These advances have improved the feasibility of casting titanium-based materials in the dental laboratory. Pure titanium and Ti-alloys such as Ti-6Al-4V have been cast into crowns, and removable dental prosthesis frameworks. Titanium alloys have a lower melting point than pure titanium. By alloying tita-nium, the melting temperature can be lowered to the same temperature as that of nickel-chromium and cobalt-chromium alloys. For example, the Ti-Pd and Ti-Cu alloys have melting points of 1350°C. Lower casting temperatures may also reduce the reactivity of titanium with oxygen and other gases. Microstructures of cast titanium materials are similar to those described previously, namely, coarse lamellar grains, a result of slow cooling through the β to α or β to (α + β) transformation temperature (Fig. 10.12). The mechanical properties of cast CP Ti are sim-ilar to those of types III and IV gold alloy, whereas cast Ti-6Al-4V and Ti-15V exhibit properties, except for modulus, similar to those of nickel-chromium and cobalt-chromium alloys. Recently, cast Ti-6Al-4V microstructures have been refined by temporary alloying with hydrogen. The resulting microstructures (Fig. 10.13) can have α-grain sizes less than 1 μm, aspect ratios near unity, and discontinuous grain boundary α, microstructural attributes that increase tensile and fatigue strength. These changes in microstructural form and structure result in significant increases in yield strength (974 to 1119 MPa), ultimate strength (1025 to 1152 MPa), and fatigue strength (643 to 669 MPa) as compared with respective values for lamellar (902, 994, and 497 MPa) and equiaxed microstructures (914, 1000, and 590 MPa). Pure titanium has been cast with a pressure-vacuum casting machine. Other manufacturers have developed centrifugal casting machines that use an electric arc to melt the titanium in an argon or helium atmosphere. Melting is performed in a cop-per crucible, followed by centrifugal casting into a mold that uses investment. Such machines provide a relatively oxygen-free environment and, with the use of a tungsten arc, can reach temperatures of 2000°C. This latter casting regime has been used to cast CP Ti crowns. Crowns cast in this manner have been evaluated clinically, and results revealed that, although the fit was inferior to that of silver-palla-dium alloy, it was superior to that of nickel-chro-mium. Occlusal adjustment was no more difficult than with conventional crowns, and discoloration, occlusal wear, and plaque retention were similar to other metals. Observations of randomly chosen cast crowns using old machines and silica-containing invest-ments have revealed gross surface porosities, to a depth of 75 μm, on both the inside and outside of the surfaces. Mechanical polishing is insufficient to remove this porosity. Internal porosities, sometimes measuring up to 30% of the cross-sectional area, are also readily observed. Surfaces of castings can also be contaminated, probably due to poor atmo-sphere control or contamination from crucible and mold materials. For optimum functionality of the final casting, the surface layer must be removed during finishing. However, internal oxidation can remain and compromise the mechanical properties of the final prosthesis. Further examination of such FIG. 10.12 Microstructure of as-cast Ti-6Al-4V. FIG. 10.13 Microstructure of hydrogen-alloy-treated Ti-6Al-4V (×200). 200 CRAIG’S RESTORATIVE DENTAL MATERIALS castings has also revealed multiple microcracks at the edges of the margins. Some cracks are as long as 100 μm. Cracks of this length are catastrophic to a notch-sensitive material such as titanium. As outlined, the difficulties with cast titanium for dental purposes include high melting point and high reactivity, low casting efficiency, inadequate expansion of investment, casting porosity, and diffi-culty in finishing this metal. From a technical stand-point, titanium is difficult to weld, solder, machine, finish, and adjust. Casting titanium requires expen-sive equipment. WROUGHT ALLOYS Alloys that are worked and adapted into prefab-ricated forms for use in dental restorations are described as wrought alloys. A wrought form is one that has been worked or shaped and fashioned into a serviceable form for a prosthesis (Fig. 10.14). The work done to the alloy is usually at a temperature far below the melting range and is therefore referred to as cold work. Wrought forms may include precision attachments, backings for artificial teeth, and wire in various cross-sectional shapes. Wrought alloys are used in two ways in dental prostheses. First, they can be soldered to a previously cast restoration. An example is a wrought wire clasp on a removable dental prosthesis framework. Second, they can be embedded into a cast framework by casting to the alloy, as a precision attachment is cast to the retainer of a crown, bridge, or removable prosthesis. The physical properties required of the wrought alloy will depend on the technique used and the composi-tion of the alloy in the existing prosthesis. Microstructure The microstructure of wrought alloys is fibrous. This fibrous structure results from the cold work applied during the operations that shape the alloy into its final form. Wires or other wrought forms normally have a measurable increase in tensile strength and hardness when compared with corresponding cast structures. The increase in these properties results from the entangled, fibrous internal structure created by the cold work. Wrought forms will recrystallize during heating operations unless caution is exercised. During recrys-tallization, the fibrous microstructure is converted to a grained structure similar to the structure of a cast form. In general, the amount of recrystallization increases as both the heating time and temperature become excessive. For example, in most noble den-tal wires, a short heating cycle during the soldering operation is not sufficient to appreciably recrystallize the wire, even though the temperature approaches the fusion temperature. However, a prolonged heat-ing period of 30 to 60 seconds or longer may cause recrystallization, depending on the time, tempera-ture, alloy composition, and manner in which the wire was fabricated. Recrystallization results in a reduction in mechanical properties in proportion to the amount of recrystallization. Severe recrystalliza-tion can cause wrought forms to become brittle in the area of recrystallization. Therefore heating operations must be minimized when working with wrought forms. Composition By the current ADA definitions, all alloys used for wrought forms are high-noble alloys except one, which is a noble alloy (Table 10.18). As with the casting alloys, several strategies have been used to formulate alloys with appropriate properties. The compositions in Table 10.18 are not inclusive of all available wrought alloys, but are intended to demon-strate typical alloys. These compositions are designed to provide a range of melting ranges and mechani-cal properties that are appropriate for wrought alloy applications. The Pt-Au-Pd alloys contain primar-ily platinum with equal amounts (27 wt%) of pal-ladium and gold. These platinum-gold-palladium alloys have been commonly used as clasping wires on removable dental prostheses. The Au-Pt-Pd alloys are primarily gold with platinum and palladium. The Au-Pt-Cu-Ag, Au-Pt-Ag-Cu, and Au-Ag-Cu-Pd alloys contain approximately 60 wt% gold, but have Wrought Cast Mechanical work FIG. 10.14 Diagram of the process of mechanical work that transforms cast structures into wrought structures. The microstructure and mechanical properties of cast and wrought forms are fundamentally different. 201 10. Restorative Materials: Metals adopted different strategies for the remaining 40% of the mass. The first two of these alloys contain about 15 wt% platinum with the balance in silver, copper, and palladium, whereas the third of these alloys con-tains no platinum and higher amounts of silver. The last alloy shown in Table 10.18 contains no apprecia-ble gold or platinum, but consists of palladium and silver in approximately equal amounts with about 16 wt% copper. The Au-Ag-Cu-Pd wrought alloy (see Table 10.18) is similar to the Au-Cu-Ag-Pd-II casting alloy (see Table 10.5). These alloys differ only slightly in the gold/silver ratio. Other wrought alloys differ from the casting alloys primarily in their higher plat-inum contents and absence of iridium or ruthenium grain refiners. Platinum is added to increase the melting temperature of the alloys. The grain refine-ment is not necessary because these alloys are cold-worked into their final forms. Properties The properties of alloys used for wrought applications are shown in Table 10.19. The solidus (temperature at which the alloy is completely frozen) of these alloys ranges from 875°C for Au-Ag-Cu-Pd to 1500°C for Pt-Au-Pd. If the wrought form is to be cast to or sol-dered to, the solidus must be sufficiently high so the form does not melt or lose its fibrous structure during burnout or casting operations. The solidus required will depend on the metals to be joined, the solder, and the burnout and casting temperatures to be used. In gen-eral, alloys with high solidus temperatures also have higher recrystallization temperatures. These alloys are mostly white because of the high platinum and palladium contents. Exceptions are the Au-Pt-Ag-Cu and Au-Ag-Cu-Pd alloys, which are light yellow and yellow, respectively. Yield strength, elongation, and hardness are properties relevant to wrought alloys (see Table 10.19). The wrought form must generally have yield strength low enough to allow for adjustment (of a clasp or attachment), but be high enough that perma-nent distortion does not occur in service. Furthermore, the elongation must be sufficient to allow for adjust-ment without fracture. Three of the wrought alloys shown in Table 10.19 can be hardened by formation of ordered phases. The Au-Pt-Ag-Cu and Au-Ag-Cu-Pd alloys are hardened by an Au-Cu ordered phase, whereas the Pd-Ag-Cu alloys are hardened by a Pd-Cu ordered phase. As with the casting alloys, the ordered phase imparts significantly more strength and hard-ness to the alloy and lower elongation. Wrought Stainless Steel Alloys Steel is an iron-carbon alloy. The term stainless steel is applied to alloys of iron and carbon that contain TABLE 10.18 Composition of Typical Wrought Dental Alloys (wt%) Alloy Ag Au Cu Pd Pt Other Pt-Au-Pd — 27 — 27 45 Au-Pt-Pd — 60 — 15 24 Ir 1.0 Au-Pt-Cu-Ag 8.5 60 10 5.5 16 Au-Pt-Ag-Cu 14 63 9 — 14 Au-Ag-Cu-Pd 18.5 63 12 5 — Zn 1.5 Pd-Ag-Cu 39 — 16 43 1 TABLE 10.19 Properties of Typical Wrought Dental Alloys Alloy Property Solidus (°C) Color 0.2% Yield (Soft/ Hard) (MPa) Elongation (Soft/ Hard) (%) Vickers Hardness (Soft/ Hard) (kg/mm2) Pt-Au-Pd 1500 White 750 14 270 Au-Pt-Pd 1400 White 450 20 180 Au-Pt-Cu-Ag 1045 White 400 35 190 Au-Pt-Ag-Cu 935 Light yellow 450/700 30/10 190/285 Au-Ag-Cu-Pd 875 Yellow 400/750 35/8 170/260 Pd-Ag-Cu 1060 White 515/810 20/12 210/300 202 CRAIG’S RESTORATIVE DENTAL MATERIALS chromium, nickel, manganese, and perhaps other metals to improve properties and give the stainless quality to the steel. Usually, stainless steel alloys are not cast, but instead are used in the wrought form in dentistry. As a result, the types of prostheses formed from these two materials differ. The most common applications of stainless steel for dental purposes at present are in the preparation of orthodontic appli-ances and fabrication of endodontic instruments, such as files and reamers. Some specialized appli-cations of stainless steel exist for temporary space maintainers, prefabricated crowns, or other prosthe-ses placed in the mouth, and for various clinical and laboratory instruments. Composition The various classes of stainless steel alloys are referred to as ferritic, martensitic, and austenitic, and they have different compositions, properties, and applications. The ferritic stainless steels are chro-mium steels employed in the manufacture of instru-ments or equipment parts in which some degree of tarnish resistance is desirable. A wide range of com-positions is available in this group, in which chro-mium, the principal element contributing to stainless qualities, may vary from 15% to 25%. Elements such as carbon, silicon, and molybdenum are included but are all held within narrow limits. The martensitic steels also are primarily chro-mium steels with a lower chromium content (about 12% to 18%). These steels can be hardened to some degree by heat treatment, and they have a moder-ate resistance to tarnish. They are used chiefly in the manufacture of instruments and, to a limited degree, for orthodontic appliances. The austenitic steels represent the alloys used most extensively for dental prostheses. The most common austenitic steel used in dentistry is 18–8 stainless steel, so named because it contains approximately 18% chromium and 8% nickel. The carbon content is between 0.08% and 0.20%, and titanium, manganese, silicon, molybdenum, niobium, and tantalum are present in minor amounts to give important modifi-cations to the properties. The balance (≈72%) is iron. Function of Alloying Elements and Chemical Resistance The corrosion resistance of stainless steel is attrib-uted largely to the presence of chromium in the alloy. Iron cannot be used without chromium additions because iron oxide (Fe2O3), or rust, is not adherent to the bulk metal. About 11% chromium is needed to produce corrosion resistance in pure iron, and the necessary proportion is increased with the addition of carbon to form steel. Chromium resists corrosion well because of the formation of a strongly adher-ent coating of oxide on the surface, which prevents further reaction with the metal below the surface. The formation of such an oxide layer is called pas-sivation. The surface coating is not visible, even at high magnification, but the film adds to the metallic luster of the metal. The degree of passivity is influ-enced by a number of factors, such as alloy com-position, heat treatment, surface condition, stress in the prosthesis, and the environment in which the prosthesis is placed. In dental applications, the stainless characteristics of the alloys can there-fore be altered or lost by excessive heating during assembly or adaptation; using abrasives or reactive cleaning agents (specifically those containing chlo-rine), which can alter the surface conditions of the prosthesis; and even by poor oral hygiene practices over prolonged periods. Of the stainless steel alloys in general use, the aus-tenitic type of 18–8 stainless steel shows the greatest resistance to corrosion and tarnish. The chromium composition in these alloys must be between 13% and 28% for optimal corrosion resistance. If the chro-mium content is less than 13%, the adherent chro-mium oxide layer does not form. If there is more than 28% chromium, chromium carbides form at the grain boundaries, embrittling the steel. The amount of carbon must also be tightly controlled. If not, car-bon will react with chromium, forming chromium carbides in the grain-boundaries, which leads to depletion of chromium in the individual grains and decreases corrosion resistance in a process known as sensitization. Molybdenum increases the resistance to pitting corrosion. The elements present in small amounts tend to prevent the formation of carbides between the car-bon present in the alloy and the iron or chromium and, as a result, often are described as stabilizing ele-ments. Some steels, termed stabilized stainless steels, contain titanium, niobium, or tantalum, so the car-bides that do form are titanium carbides rather than chromium carbides. The chemical resistance of stainless steel alloys is improved if the surface is clean, smooth, and pol-ished. Irregularities promote electrochemical action on the surface of the alloy. Soldering operations on stainless steel with gold and silver solder may con-tribute to a reduction in stainless qualities because of electrogalvanic action between dissimilar metals or because of localized, improper composition of the stainless steel wire. Stress-Relieving Treatments The 18–8 alloys are not subject to an increase in properties by heat treatment, but they do respond to strain hardening as a result of cold work during adjustment or adaptation of the alloy to form the prosthesis. Heat treatment above 650°C results in recrystallization of the microstructure, compositional 203 10. Restorative Materials: Metals changes, and formation of chromium carbides, three factors that can reduce mechanical properties and corrosion resistance. Prostheses formed from these alloys may, how-ever, be subjected to a stress-relieving operation to remove the effects of cold working during fabrica-tion, increase ductility, or produce some degree of hardening with some alloys. If heat treatment is to be performed, it should be held to temperatures between 400°C and 500°C for 5 to 120 seconds, depending on the temperature, type of prosthesis, and alloy being heated. A time of 1 minute at 450°C would represent an average treatment to be used on an orthodontic appliance. Keep in mind that temperatures above 650°C will soften or anneal the alloy, and the prop-erties cannot be restored by further treatment. The main advantage of a low-temperature heat-treating operation is that it establishes a uniformity of prop-erties throughout the prosthesis after adaptation and fabrication, which may reduce the tendency toward breakage in service. Factors affecting an alloy’s abil-ity to be heat treated and stress relieved include alloy composition, working history (i.e., fabrication pro-cedure), and the duration, temperature, and atmo-sphere of the heat treatment. A description of stainless steel orthodontic wires, wrought cobalt-chromium-nickel alloy, and other orthodontic wires can be found on the website http:// evolve.elsevier.com/sakaguchi/restorative. Wrought Nickel-Titanium Alloy A wrought nickel-titanium alloy known as Nitinol is used as a wire for orthodontic appliances. Nitinol is characterized by its high resiliency, limited form-ability, and thermal memory. Other nickel-titanium alloys contain copper in small amounts to modify the temperature of the shape-memory effect described in the next section. Composition and Shape-Memory Effect The industrial alloy is 55% nickel and 45% titanium and possesses a temperature transition range (TTR). At temperatures below the TTR, the alloy can be deformed plastically. When the alloy is then heated from below to above the TTR, a temperature-induced crystallographic transformation from a martensitic to an austenitic microstructure occurs and the alloy will return to its original shape. Hence nickel-tita-nium is called a shape-memory alloy. The orthodon-tic alloy contains several percent cobalt to lower the TTR. A number of variations of the Ni-Ti alloy have been developed in dentistry. Compositional varia-tions lead to changes in the martensitic and austen-itic start and finish temperatures and mechanical properties. Only those wires with austenitic finish temperatures less than 37°C exhibit the property known as super-elasticity, where the wire can be deformed dramatically without becoming strain hardened. Properties and Manipulation Mechanical properties of an orthodontic nickel-titanium alloy are compared with those of stainless steel and a beta-titanium alloy in tension, bending, and torsion in Table 10.20. The nickel-titanium alloy has the lowest elastic modulus and yield strength but the highest springback (maximum elastic deflection). As shown in Figs. 10.15 and 10.16, nickel-titanium has the lowest spring rate but the highest resiliency in bending and torsion of the three alloys used for orthodontic wires. Clinically, the low elastic modu-lus and high resiliency mean that lower and more constant forces can be applied with activations and an increased working range. The high springback is important if large deflections are needed, such as with poorly aligned teeth. Nitinol wire requires special bending techniques and cannot be bent over a sharp edge or into a complete loop; thus the wire is more suited for use with pretorqued, preangu-lated brackets. The alloy is brittle and therefore can-not be soldered or welded, so wires must be joined mechanically. TABLE 10.20 Properties of Orthodontic Wires in Tension, Bending, and Torsion Property 18-8 Stainless Steel Nickel-Titanium Beta-Titanium TENSION Yield strength, 0.1% offset, MPa 1200 343 960 Elastic modulus, GPa 134 28.4 68.6 Springback (σs/E), 10−2 0.89 1.40 1.22 BENDING Yield strength, 2.9-degree offset, MPa 1590 490 1080 Elastic modulus, GPa 122 32.3 59.8 Spring rate, mm-N/degree 0.80 0.17 0.37 TORSION Spring rate, mm-N/degree 0.078 0.020 0.035 Values are for a 0.43 × 0.64-mm2 rectangular wire. Modified from Drake SR, Wayne DM, Powers JM, Asgar K. Mechanical properties of orthodontic wires in tension, bending, and torsion. Am J Orthod. 1982;82:206–210. 204 CRAIG’S RESTORATIVE DENTAL MATERIALS A description of nickel-titanium endodontic instru-ments can be found on the website elsevier.com/sakaguchi/restorative. Wrought Beta-Titanium Alloy Composition and Microstructure A titanium-molybdenum alloy known as beta-titanium is used as a wrought orthodontic wire. As discussed previously, CP Ti exists in a hexagonal, close-packed crystal lattice at temperatures below 883°C and in a body-centered cubic crystal lattice at higher temperatures. These structures are referred to as alpha-titanium and beta-titanium, respectively. The beta form of Ti can be stabilized at room tempera-ture by alloying with certain elements. Beta-titanium alloy for dental use has the composition 78% tita-nium, 11.5% molybdenum, 6% zirconium, and 4.5% tin and is supplied as wrought wire. Properties Compared with stainless steel wires, beta-titanium wire has lower force magnitudes, a lower elas-tic modulus, higher springback (maximum elastic deflection), a lower yield strength, and good ductility, weldability, and corrosion resistance. The mechani-cal properties of beta-titanium alloy in tension, bend-ing, and torsion are compared with stainless steel and nickel-titanium alloys in Table 10.20 and Figs. 10.15 and 10.16. 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In vitro tarnish mea-surement on fixed prosthodontic alloys. J Prosthet Dent. 1982;47:399. Gettleman L. Noble alloys in dentistry. Curr Opin Dent. 1991;2:218. Givan DA. Precious metals in dentistry. Dent Clin N Am. 2007;51:591. Glantz PO. Intraoral behaviour and biocompatibility of gold versus non precious alloys. J Biol Buccale. 1984; 12:3. Johansson BI, Lemons JE, Hao SQ. Corrosion of dental cop-per, nickel, and gold alloys in artificial saliva and saline solutions. Dent Mater. 1989;5:324. Keller JC, Lautenschlager EP. Metals and alloys. In: von Recum AF, ed. Handbook of Biomaterials Evaluation. New York: Macmillan; 1986. Leinfelder KF. An evaluation of casting alloys used for restorative procedures. J Am Dent Assoc. 1997;128:37. Leinfelder KF, Price WG, Gurley WH. Low-gold alloys: a laboratory and clinical evaluation. Quint Dent Technol. 1981;5:483. Malhotra ML. Dental gold casting alloys: a review. Trends Tech Contemp Dent Lab. 1991;8:73. Malhotra ML. New generation of palladium-indium-silver dental cast alloys: a review. Trends Tech Contemp Dent Lab. 1992;9:65. Mezger PR, Stols AL, Vrijhoel MM, et al. Metallurgical aspects and corrosion behavior of yellow low-gold alloys. Dent Mater. 1989;5:350. Moffa JP. Alternative dental casting alloys. Dent Clin North Am. 1983;27:733. Morris HF, Manz M, Stoffer W, et al. Casting alloys: the materials and “The Clinical Effects”. Adv Dent Res. 1992;6:28. Powers JM, Wataha JC. Dental Materials: Foundations and Applications. 11th ed. St. Louis: Elsevier; 2017. Roberts HW, Berzins DW, Moore BK, Charlton DG. Metal-ceramic alloys in dentistry, a review. J Pros. 2009; 18:188. Stub JR, Eyer CS, Sarkar NK. Heat treatment, microstruc-ture and corrosion of a low-gold casting alloy. J Oral Rehabil. 1986;13:521. Vermilyea SG, Cai Z, Brantley WA, et al. Metallurgical structure and microhardness of four new palladium-based alloys. J Prosthodont. 1996;5:288. Wataha JC. 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A new dental super alloy system, I, II, III. J Dent Res. 1973;52:136. 145, 151. Morris HF, Asgar K. Physical properties and microstructure of four new commercial partial denture alloys. J Prosthet Dent. 1975;33:36. Morris HF, Asgar K, Rowe AP, et al. The influence of heat treatments on several types of base-metal removable partial denture alloys. J Prosthet Dent. 1979;41:388. Roach M. Base metal alloys used for dental restorations and implants. Dent Clin N Am. 2007;51:603. Rowe AP, Bigelow WC, Asgar K. Effect of tantalum addi-tion to a cobalt-chromium-nickel base alloy. J Dent Res. 1974;53:325. Smith DC. Tissue reaction to noble and base metal alloys. In: Smith DC, William DF, eds. Biocompatibility of Dental Materials. Vol. 4. Boca Raton, FL: CRC Press; 1982. Vallittu PK, Kokkonen M. Deflection fatigue of cobalt- chromium, titanium, and gold alloy cast denture clasps. J Prosthet Dent. 1995;74:412. Wakasa K, Yamaki M. Corrosive properties in experimen-tal Ni-Cu-Mn based alloy systems for dental purposes. J Mater Sci: Mater Med. 1990;1:171. Wakasa K, Yamaki M. Dental application of the 30Ni-30Cu-40Mn ternary alloy system. J Mater Sci Mater Med. 1990;1:44. Wakasa K, Yamaki M. Tensile behaviour in 30Ni-30Cu-30Mn based alloys for a dental application. J Mater Sci Mater Med. 1991;2:71. Wataha JC, Craig RG, Hanks CT. The release of elements of dental casting alloys into cell-culture medium. J Dent Res. 1991;70:1014. Wataha JC, Craig RG, Hanks CT. The effects of cleaning on the kinetics of in vitro metal release from dental casting alloys. J Dent Res. 1992;71:1417. Waterstrat RM. New alloys. J Am Dent Assoc. 1992;123:33. Yong T, De Long B, Goodkind RJ, et al. Leaching of Ni, Cr and Be ions from base metal alloys in an artificial oral environment. J Prosthet Dent. 1992;68:692. Wrought Base–Metal Alloys Alapati SB, Brantley WA, Svec TA, et al. Scanning electron microscope observations of new and used nickel-titanium rotary files. J Endod. 2003;29:667. Alapati SB, Brantley WA, Svec TA, et al. Observations of nickel-titanium rotary endodontic instruments that frac-tured during clinical use. J Endod. 2005;31:40. Andreasen GF, Barrett RD. An evaluation of cobalt-substituted Nitinol wire in orthodontics. Am J Orthod. 1973;63:462. Andreasen GF, Bigelow H, Andrews JG. 55 Nitinol wire: force developed as a function of “elastic memory”. Aust Dent J. 1979;24:146. Andreasen GF, Brady PR. A use hypothesis for 55 Nitinol wire for orthodontics. Angle Orthod. 1972;42:172. Andreasen GF, Morrow RE. Laboratory and clinical analy-ses of Nitinol wire. Am J Orthod. 1978;73:142. Brantley WA, Augat WS, Myers CL, et al. Bending deforma-tion studies of orthodontic wires. J Dent Res. 1978;57:609. Brantley WA, Svec TA, Iijima M, et al. Differential scanning calorimetric studies of nickel titanium rotary endodon-tic instruments. J Endod. 2002;28:567. Brantley WA, Svec TA, Iijima M, et al. Differential scanning calorimetric studies of nickel-titanium rotary endodon-tic instruments after simulated clinical use. J Endod. 2002;28:774. Burstone CJ, Goldberg AJ. Beta titanium: a new orthodontic alloy. Am J Orthod. 1980;77:121. Chen R, Zhi YF, Arvystas MG. Advanced Chinese NiTi alloy wire and clinical observations. Angle Orthod. 1992; 62:15. Dolan DW, Craig RG. Bending and torsion of endodontic files with rhombus cross sections. J Endod. 1982;8:260. Drake SR, Wayne DM, Powers JM, et al. Mechanical proper-ties of orthodontic wires in tension, bending, and tor-sion. Am J Orthod. 1982;82:206. Goldberg AJ, Burstone CJ, Hadjinikolaoa I, et al. Screening of matrices and fibers for reinforced thermoplastics intended for dental applications. J Biomed Mater Res. 1994;28:167. Goldberg J, Burstone CJ. An evaluation of beta titanium alloys for use in orthodontic appliances. J Dent Res. 1979;58:593. Ha’kel Y, Serfaty R, Bateman G, et al. 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Clinical application of pure titanium for cast plate dentures. Dent Mater J. 1988;7:39. 209 The term ceramic refers to any product made from a nonmetallic inorganic material usually processed by firing at a high temperature to achieve desirable properties. The more restrictive term porcelain refers to a specific compositional range of ceramic mate-rials originally made by mixing kaolin (hydrated aluminosilicate), quartz (silica), and feldspars (potas-sium and sodium aluminosilicates), and firing at high temperature. Dental ceramics for metal-ceramic restorations belong to this compositional range and are commonly referred to as dental porcelains. The laboratory portion of ceramic restorations is usually made in a commercial dental laboratory by skilled technicians working with specialized equip-ment to shape and tint the restoration to the specifi-cations provided by the dentist. Skilled technicians and artisans are also employed by the manufacturers of artificial denture teeth to produce the many forms, types, and shades necessary in this application of porcelain. However, a variety of machinable ceram-ics are also available for chair-side fabrication of all-ceramic restorations by computer-aided design/ computer-aided manufacturing (CAD/CAM). A discussion of CAD/CAM systems is presented in Chapter 14. CLASSIFICATION OF DENTAL CERAMICS Dental ceramics can be classified according to their applications, fabrication method, or crystalline phase (Table 11.1). Classification by Application Ceramics have two major applications in dentistry: (1) ceramics for metal-ceramic crowns (Fig. 11.1, right) and fixed dental prostheses (FDPs), (2) all-ceramic materials for crowns (Fig. 11.1, left), inlays, onlays, veneers, and FDPs. In addition, ceramic orthodontic brackets, dental implant abutments, and ceramic denture teeth are available. Classification by Fabrication Method The classification by fabrication method is summa-rized in Table 11.1, which also includes examples of commercial ceramics and their manufacturers. The most common fabrication technique for metal-ceramic restorations is called sintering. Sintering is the process of firing the compacted ceramic powder at high temperature to ensure optimal densification. This occurs by progressive pore elimination and vis-cous flow when the firing temperature is reached. All-ceramic restorations can also be produced by sintering, but they encompass a wider range of processing techniques, including slip casting, heat pressing, and CAD/CAM machining. Some of these techniques, such as machining and heat pressing, can also be combined to produce the final restoration. Classification by Crystalline Phase Regardless of their applications or fabrication tech-nique, after firing, dental ceramics are composed of a glassy (or vitreous) phase and one or more crys-talline phases, together with various amounts of porosity. Depending on the nature and amount of crystalline phase and porosity present, the mechanical and optical properties of dental ceramics vary widely. Increasing the amount of crystalline phase may lead to crystalline reinforcement and increase the resistance to crack propagation but also can decrease translucency. Materials for all-ceramic restorations have increased amounts of crystalline phase (between 35% for leucite-reinforced ceramics and up to 99% for polycrystalline zirconia ceramics such as 3Y-TZP) for better mechani-cal properties, but they are usually more opaque than dental porcelains for metal-ceramic restorations with C H A P T E R 11 Restorative Materials: Ceramics 210 CRAIG’S RESTORATIVE DENTAL MATERIALS low crystallinity. Table 11.1 lists the various combina-tions of fabrication techniques and crystalline phases found in dental ceramics. GENERAL APPLICATIONS OF CERAMICS IN PROSTHETIC DENTISTRY Ceramics represent the best material available for matching the esthetics of a complex human tooth structure. Their applications in dentistry are steadily expanding as new materials and manufacturing tech-niques are being introduced. As mentioned earlier, they are used in single and multiunit metal-ceramic restorations. The applications of all-ceramic mate-rials include inlays, onlays, veneers, and crowns. The development of high-strength zirconia-based systems has made possible the fabrication of dental implant abutments and FDPs. In addition, ceramics are still used to fabricate denture teeth. However, ceramics are brittle, weak in tension, and their per-formance is highly dependent on both their micro-structure and the quality of the processing from the raw components to the final staining or glazing step. Metal-Ceramic Crowns and Fixed Dental Prostheses Ceramic is widely used as the veneering material in metal-ceramic crowns and FDPs. This development was the result of successfully matching the coeffi-cients of thermal expansion of porcelain with that of metal alloys and achieving a proper metal-ceramic bond. The finished glazed restoration is color sta-ble, tissue friendly, biologically inert, and chemi-cally durable. Although progressively replaced with TABLE 11.1 Classification of Dental Ceramic Materials with Examples of Products and Their Manufacturers Application Fabrication Crystalline Phase Products Manufacturers All-ceramic Soft machined Zirconia (3Y-TZP) Cercon Dentsply International Lava 3M Company IPS e.max ZirCAD Ivoclar Vivadent In-Ceram YZ Vident Zirconia (cubic & tetragonal) Zpex Smile Tosoh Corporation Hard machined Lithium disilicate (Li2Si2O5) IPS e.max CAD Ivoclar Vivadent Lithium silicate (Li2Si2O5 and Li2SiO3) Vita Suprinity Celtra Duo Vident Dentsply Feldspar [(Na, K)AlSi3O8] Vita Mark II Vident Leucite (KAlSi2O6) IPS Empress CAD Ivoclar Vivadent Heat pressed Leucite (KAlSi2O6) IPS Empress Ivoclar Vivadent Lithium disilicate (Li2Si2O5) IPS e.max Press Ivoclar Vivadent Fluorapatite [Ca5(PO4)3F] IPS e.max ZirPress Ivoclar Vivadent Sintered Leucite (KAlSi2O6) IPS Empress layering ceramic Ivoclar Vivadent Alumina (Al2O3) Procera AllCeram Nobel Biocare Fluorapatite [Ca5(PO4)3F] IPS e.max Ceram layering ceramic Ivoclar Vivadent Metal-ceramic Sintered Leucite (KAlSi2O6) VMK-95 Vident Denture teeth Manufactured Feldspar TruByte Dentsply International Feldspar VITA LUMIN Vacuum Vident FIG. 11.1 Cutaways of all-ceramic crown (left) and por-celain fused to metal crown (right). (Courtesy Dr. Charles Mark Malloy, Portland, OR.) 211 11. Restorative Materials: Ceramics all-ceramic materials, metal-ceramic restorations are still widely used. However, although the survival rate of most all-ceramic crown compares favorably to that of metal-ceramic crowns for single restorations, the long-term survival rate of multiunit all-ceramic FDPs remains lower. All-Ceramic Crowns, Inlays, Onlays, and Veneers Ceramics have been used to fabricate jacket crowns since the early 1900s. At that time feldspathic porce-lains were the material of choice used in jacket crown fabrication. Alumina-reinforced ceramics with improved mechanical properties were developed in the early 1960s. In the past 50 years, numerous novel materials and techniques for fabricating all-ceramic restorations have been introduced. As mentioned earlier in this chapter, they include heat-pressed, slip-cast, and machined all-ceramic materials. These new materials and techniques have widened the range of applications of ceramics, and in general, made their processing easier and more reliable. Meanwhile, as technologies are constantly evolving, some tech-niques, such as slip casting, have been replaced by others, with increasing popularity for machined ceramics. Ceramic inlays and onlays are becoming increas-ingly popular as an alternative to posterior resin composites. They have better abrasion resistance than posterior resin composites and therefore are more durable. However, occlusal adjustments are more difficult and can lead to subsequent wear of the opposing tooth if not properly polished. The marginal gap is clinically acceptable, yet greater than with gold inlays or onlays. A ceramic esthetic veneer (laminate veneer) is a layer of ceramic bonded to the facial surface of a prepared tooth often for cosmetic reasons. Ceramic veneers are custom made and are fabricated in a den-tal laboratory. Initially, ceramic veneers were made of feldspathic porcelain and sintered. Currently, most ceramic veneers are fabricated by heat-pressing or machining, using either a leucite-reinforced or lithium disilicate ceramic. To obtain sufficient adhesion, the tooth enamel is etched with phosphoric acid and the bonding surface of the ceramic is etched with 5% to 9% hydrofluoric acid gel and treated with a silane cou-pling agent. Resin composites specifically formulated for bonding to ceramic are used as the adhesive. MECHANICAL AND THERMAL PROPERTIES OF DENTAL CERAMICS Toughening Mechanisms Toughening mechanisms for glasses and ceramics are either “built-in” (intrinsic) to the material, relying on chemical composition or crystalline phases, or introduced by extrinsic processing steps. Crystalline reinforcement and transformation toughening are examples of “built-in” toughening mechanisms. Extrinsic processing steps, such as tempering, chemi-cal strengthening, or glaze application have also been used in the past to achieve strengthening. The principle of toughening by crystalline rein-forcement is to increase the resistance of the ceramic to crack propagation by introducing a dispersed crystalline phase with high toughness. Crystals can also act as crack deflectors when their coefficient of thermal expansion (CTE) is greater than that of the surrounding glassy matrix, placing them under tan-gential compressive stresses after the ceramic has been cooled to room temperature, as they contract more than the surrounding glassy matrix. Stress-induced transformation toughening is obtained, for example, in ceramics consisting of partially stabilized tetragonal zirconia. Zirconia (ZrO2) exists under several crystallographic forms. The monoclinic form is stable at all temperatures below 1170°C. The tetragonal form is stable between 1170° and up to 2370°C. The transformation from the tetragonal to the monoclinic form upon cool-ing is associated with a volume increase of the unit cell. This is the reason why compacts of pure unal-loyed zirconia cannot be obtained at room tem-perature; the compact would spontaneously shatter upon cooling due to the transformation and volume increase. The tetragonal form can be partially stabi-lized to room temperature by doping with various oxides, such as yttrium oxide (Y2O3) or cerium oxide (CeO2). Zirconia-based dental ceramics produced by machining followed by sintering at high temperature consist of tetragonal zirconia polycrystals, partially stabilized with 3 mole percent yttrium (3Y-TZP). This partial stabilization or metastability of the tetragonal phase allows the transformation from tetragonal to monoclinic to occur under external applied stresses. The transformation is also called stress induced and is accompanied by a volume increase with associated compressive stresses in the vicinity of the crack tip, eventually leading to closing and arrest of the crack in the transformed zone (Fig. 11.2). Transformation toughening is responsible for the excellent mechani-cal properties of 3Y-TZP. Fig. 11.3 shows a Vickers indentation in a 3Y-TZP dental ceramic under a 98.1-N load. Only one short crack can be seen ema-nating from one corner of the indentation, indicative of an excellent resistance to crack propagation. Tempering and chemical strengthening are extrin-sic strengthening techniques based on the creation of a compressive stress layer at the surface of a glass or a ceramic. Tempering is obtained by using rapid but controlled cooling rates, whereas chemical strengthening applies to glasses and ceramics with a large proportion of glassy matrix and relies on the 212 CRAIG’S RESTORATIVE DENTAL MATERIALS replacement of small ions with larger ions within the matrix and above the glass transition temperature by diffusion from a molten salt bath in which the ceramic or glass is immersed. Although widely used in the glass industry, these techniques are no longer used for dental ceramics due to controllability issues, as well as potential elimination and benefit loss from grinding adjustments. Glazing is the final step in the fabrication of metal-ceramic restorations. This standard technique, also called self-glazing, does not significantly improve the flexural strength of feldspathic dental porcelains. However, a low-expansion glass called glaze can also be applied to the surface of the ceramic, then fired to high temperature. Upon cooling, this glaze layer is placed under compression from the greater con-traction of the underlying ceramic. This layer is also known to reduce depth and width of the surface flaws, thereby improving the overall resistance of the ceramic to crack propagation. Test Methods Numerous test methods are available to evaluate the mechanical properties of ceramics. Studies of the influence of test method on the failure stress of brittle dental materials have shown that important test parameters are the specimen thickness, contact zone at loading, homogeneity and porosity of the material, and loading rate. For this reason, discrep-ancies exist among the published values of mechani-cal properties for a given ceramic. Manufacturers evaluate dental ceramics using a standard (ISO 6872) published and regularly revised by the International Organization for Standardization. Set protocols are proposed to quantify radioactivity, flexural strength, linear CTE, glass transition temperature, and chemi-cal solubility. Sometimes, researchers use testing protocols and fixtures aimed at simulating dental morphol-ogy. However, the experimental variables can become extremely complex and difficult to repro-duce in this type of testing. Finite element analysis constitutes another approach to the simulation of clinical conditions. Failure predictions for ceramic inlays by the finite element analysis technique have successfully matched fractographic analyses of clinically failed restorations. Fractography is well established as a failure-analysis technique for glasses and ceramics. It has been recognized as a powerful analytical tool in dentistry. The in vivo failure stress of clinically failed all-ceramic crowns can be determined using fractography (see more discussion in Chapter 5). Transformed monoclinic zirconia Direction of crack propagation Partially stabilized tetragonal zirconia FIG. 11.2 Schematic of transformation toughening mechanism in partially stabilized zirconia. FIG. 11.3 Vickers indentation under a 98.1-N load on a zirconia-based dental ceramic. 213 11. Restorative Materials: Ceramics Comparative Data Representative flexural strength data for dental ceramics are summarized in Table 11.2. Feldspathic porcelains for metal-ceramic restorations have a mean flexural strength between 60 and 80 MPa. This value is lower than those listed for all-ceramic mate-rials; however, because metal-ceramic restorations are supported by a metallic framework, their long-term probability of survival is usually higher than that of leucite-reinforced or lithium disilicate–based glass-ceramics. Among the currently available all-ceramic mate-rials, tetragonal zirconia (3Y-TZP) ceramics exhibit the highest values (900 to 1500 MPa), followed by recently introduced translucent cubic zirconia ceramics (600 to 700 MPa), and lithium disilicate– reinforced ceramics (262 to 420 MPa). The flexural strength of leucite-reinforced ceramics is around 120 MPa. As mentioned previously, the nature and amount of the crystalline phase present in the ceramic material strongly influences the mechanical properties of the final product. The shear strength of feldspathic porcelain is 110 MPa, and the diametral tensile strength is lower at 34 MPa. The compressive strength is about 172 MPa, and the Knoop hardness is 460 kg/mm2. Fracture toughness is another important prop-erty of ceramics; it measures the resistance to brittle fracture when a crack is present. The fracture tough-ness of conventional feldspathic porcelains is very similar to that of soda lime glass (0.78 MPa·m0.5). Leucite-reinforced ceramics exhibit slightly higher fracture toughness values (1.2 MPa·m0.5), followed by lithium disilicate–reinforced ceramics (2.75 MPa·m0.5). 3Y-TZP ceramics have the highest fracture toughness of all-ceramic materials (greater than 6.0 MPa·m0.5). The elastic constants of dental ceramics are needed in the calculations of both flexural strength and frac-ture toughness. Poisson’s ratio ranges between 0.21 and 0.30 for dental ceramics. The modulus of elas-ticity is about 70 GPa for feldspathic porcelain, 110 GPa for lithium disilicate heat-pressed ceramics, and 210 GPa for 3Y-TZP ceramics and reaches 350 GPa for alumina-based ceramics. Sintering of structural ceramics is associated with shrinkage as porosity is eliminated by firing at high temperature. Shrinkage remains an issue for all-ceramic materials with the exception of machined ceramics from fully sintered ceramic blocks and heat-pressed ceramics. Shrinkage of the veneering ceram-ics applied on all-ceramic cores has to be carefully compensated for during porcelain buildup. The large shrinkage of machined zirconia restorations (about 25%) during sintering at high temperature is com-pensated for at the design stage by computerized enlargement of the restorations. The density of fully sintered feldspathic porcelain is around 2.45 g/cm3 and decreases as the amount of porosity increases. The density of ceramic materials also depends on the amount and nature of crystal-line phase present. The theoretical density of 3Y-TZP TABLE 11.2 Flexural Strength of Selected Dental Ceramics Processing Technique Crystalline Phase Flexural Strength (MPa) Percent Crystallinity Soft machined Zirconia (3Y-TZP) 1087 ± 173 Highly crystalline Zirconia (cubic + tetragonal) ≈700a Highly crystalline Hard machined Feldspar ([Na, K]AlSi3O8) 122 ± 13 ≈30 Lithium disilicate (Li2Si2O5) 262 ± 88 65 Lithium silicate (Li2Si2O5 and Li2SiO3) ≈420a >50 Leucite (KAlSi2O6) ≈160a ≈35 Heat pressed Leucite (KAlSi2O6) 106 ± 17 35 Lithium disilicate (Li2Si2O5) 306 ± 29 65 Sintered Leucite (KAlSi2O6) 104 35–40 Fluorapatite (Ca5[PO4]3F) ≈80a 10 Sintered metal-ceramic Leucite (KAlSi2O6) 61 ± 5 15–25 aData from manufacturer. Data from Guazzato M, Albakry M, Ringer SP, Swain MV. Strength, fracture toughness and microstructure of a selection of all-ceramic materials. Part I. Pressable and alumina glass-infiltrated ceramics. Dent Mater. 2004;20:441–448; Guazzato M, Albakry M, Ringer SP, Swain MV. Strength, fracture toughness and microstructure of a selection of all-ceramic materials. Part II. Zirconia-based dental ceramics. Dent Mater. 2004;20:449–456; Denry IL, Holloway JA, Tarr LA. Effect of heat treatment on microcrack healing behavior of a machinable dental ceramic. J Biomed Mater Res. 1999;48:791–796; Della Bona A, Mecholsky Jr JJ, Anusavice KJ. Fracture behavior of lithia disilicate- and leucite-based ceramics. Dent Mater. 2004;20:956–962; Höland W, Beall G. Glass-Ceramic Technology. Westerville: The American Ceramic Society; 2002. 214 CRAIG’S RESTORATIVE DENTAL MATERIALS dental ceramics is 6.08 g/cm3, assuming that the material is pore free. A density greater than 98.7% of the theoretical density is required for medical-grade 3Y-TZP ceramics. All currently used 3Y-TZP dental ceramics have a density that meets this standard requirement. The thermal properties of feldspathic porcelain include a conductivity of 0.0030 cal/s/cm2 (°C/cm), a diffusivity of 0.64 mm2/s, and a linear CTE of about 12.0 × 10−6/°C between 25° and 500°C. The CTE is about 10 × 10−6/°C for aluminous ceramics and lith-ium disilicate ceramics, 10.5 × 10−6/°C for zirconia-based ceramics (3Y-TZP), and 14 to 18 × 10−6/°C for leucite-reinforced ceramics. The low thermal con-ductivity of zirconia-based ceramics was responsible for early issues of delamination of the veneering por-celain when fast heating and cooling rates were used. These issues have been addressed by strict recom-mendations regarding firing schedules for veneering porcelains on zirconia, including slower heating and cooling rates. OPTICAL PROPERTIES OF DENTAL CERAMICS Shade matching is a critical problem in replacing natural teeth. In addition, porcelain, being mostly amorphous in structure, cannot match the opti-cal properties of crystalline enamel completely. As a result, ultraviolet (UV) and visible light rays are reflected, refracted, and absorbed unevenly by the combination dentin/enamel, compared with porce-lain. As a consequence, restorations viewed from one incidence angle may not appear the same as they do when viewed from a different incidence angle. The cementing medium is an important factor in the final appearance of an all-ceramic restoration. Zirconia-based all-ceramic materials are not etchable due to the absence of glassy phase but their opacity may permit cementation with various luting agents with-out the need for specific shade matching. However, more translucent all-ceramic restorations such as leucite-reinforced heat-pressed or machined inlays, crowns, or veneers, or a machined inlay or veneer, usually require the use of color-matched resin luting agents that are available in different shades. The shades of commercial premixed dental porce-lain powders are in the yellow to yellow-red range. Because the range of shades existing in natural teeth is much greater than the range available in a kit of premixed porcelains, modifier porcelains are also available for precise shade adjustments. These modifiers are strongly pigmented porcelains usually supplied in blue, yellow, pink, orange, brown, and gray. The dental technician may add the modifier porcelain to the opaque and body porcelains during the building of the crown. Extrinsic surface stain-ing is another way of changing the appearance of a ceramic crown. It involves the application of highly pigmented glazes. The main disadvantages of sur-face staining compared with intrinsic staining are a limited durability (a result of solubility) and the reduction of translucency. Translucency is another critical property of dental ceramics. The translucency of opaque, dentin (body), and enamel (incisal) porcelains differs considerably. By design, opaque porcelains have very low trans-lucency, allowing them to efficiently mask metal substructure surfaces. Tin oxide (SnO2) and titanium oxide (TiO2) are important opacifying oxides for opaque porcelains. Dentin porcelain translucency values range between 18% and 38% (Table 11.3). Enamel porcelains have the highest values of trans-lucency, ranging between 45% and 50%. The translu-cency of materials for all-ceramic restorations varies with the nature and amount of the reinforcing crystal-line phase. Alumina- and zirconia-based ceramics are opaque, whereas leucite-reinforced and lithium disil-icate–based ceramics are more translucent. Recently, zirconia ceramics with increased translucency have become available. Greater translucency is obtained by either decreasing the amount of alumina additive in the 3Y-TZP composition or using higher amounts of yttrium oxide stabilizer to increase the amount of cubic phase that has greater translucency. To mimic the optical properties of human enamel, opalescence is also a desirable optical property. Opalescence is a TABLE 11.3 Percent Light Transmission of 1-mm Thick Dentin Porcelains Shade Ceramco Vita Neydium Will-Ceram Steeles 59 29.97 22.66 31.93 26.06 27.23 62 27.85 — — 27.88 — 65 23.31 20.39 35.39 33.50 22.10 67 26.32 18.04 23.58 19.03 23.42 91 31.81 — 38.41 — — Modified from Brodbelt RHW, O’Brien WJ, Fan PL. Translucency of dental porcelains. J Dent Res. 1980;59:70–75. 215 11. Restorative Materials: Ceramics form of light scattering and occurs when the size of crystalline phase particles is equal to or shorter than the wavelength of light. An opalescent glass appears reddish orange in transmitted light and blue in reflected or scattered light. Both zirconium oxide and yttrium oxide have been shown to increase opales-cence in base dentin ceramics due to their light scat-tering effect. Dental enamel also exhibits fluorescence. This characteristic is achieved in dental porcelains by add-ing rare earth oxides (such as cerium oxide). Because the outer layers of a ceramic crown are translucent, the apparent color is affected by reflectance from the inner opaque or core ceramic. For metal-ceramic restorations, shade mixing results from combining the light reflected from the inner, opaque porcelain surface and the light transmitted through the body porcelain. The thickness of the body porcelain layer determines the final shade obtained with a given opaque porcelain. ALL-CERAMIC RESTORATIONS Materials for all-ceramic restorations use a wide variety of crystalline phases as reinforcing agents and contain up to 99% by volume of crystalline phase. The nature, amount, and particle size distri-bution of the crystalline phase directly influence the mechanical, thermal and optical properties of the ceramic material. The match between the refractive indexes of the crystalline phase and glassy matrix is an important factor for controlling the translucency of porcelain and glass ceramics, and polycrystalline ceramics such as zirconia. As mentioned earlier, several processing tech-niques are available for fabricating all-ceramic res-torations: sintering, heat pressing, slip casting, and CAD/CAM. Fig. 11.1, left, illustrates the cross section of an all-ceramic crown. Sintered All-Ceramic Materials Mainly due to the success of machined and heat-pressed restorations, sintered all-ceramic systems are now mostly obsolete. Two main types of all-ceramic materials were available for the sintering tech-nique: alumina-based ceramic and leucite-reinforced ceramic. Alumina-Based Ceramic The aluminous core ceramic used in the aluminous porcelain crown developed by McLean in 1965 is a typical example of strengthening by dispersion of a crystalline phase. Alumina has a high modu-lus of elasticity (350 GPa) and relatively high frac-ture toughness (3.5 to 4 MPa·m0.5), compared with feldspathic porcelains. Its dispersion in a glassy matrix of similar thermal expansion coefficient leads to a significant strengthening effect. It has been proposed that the excellent bond between the alumina and the glass phase is responsible for this increase in strength compared with leucite- containing ceramics. The first aluminous core ceramics contained 40% to 50% alumina by weight, dispersed in a low-fusing glassy matrix. The core was baked on a platinum foil and later veneered with matched-expansion porcelain. Aluminous core ceramic can also be sintered directly on a refractory die. Aluminous core porcelains have flexural strengths approxi-mately twice that of feldspathic porcelains (139 to 145 MPa). Densely sintered alumina-based ceramics were also produced by dry pressing, followed by sinter-ing. To compensate for sintering shrinkage (12% to 20% linear), an enlarged die was generated by CAD. A high-purity alumina-based ceramic was fabricated by dry pressing and sintering at high temperature (1550°C). The final product was a highly crystalline ceramic with a mean grain size of about 4 μm and a flexural strength of about 600 MPa. The entire process had to be carefully controlled by the manufacturer. The last steps consist of veneering with translucent porcelain, staining, and glazing. The clinical perfor-mance of this ceramic in vivo at 15 years was con-sidered excellent. Zirconia-based core ceramics have slowly replaced alumina-based ceramics. A similar technology is available for their fabrication. Leucite-Reinforced Ceramic Leucite-reinforced ceramics containing up to 45% by volume of tetragonal leucite were used for the fab-rication of all-ceramic sintered restorations. Leucite acts as a reinforcing phase; the greater leucite content (compared with conventional feldspathic porcelain for metal-ceramic restorations) leads to higher flex-ural strength (104 MPa) and compressive strength. The large amount of leucite in the material also con-tributes to a high thermal contraction coefficient. In addition, the large mismatch in thermal contraction between leucite (20 to 25 × 10−6/°C) and the glassy matrix (8 × 10−6/°C) results in the development of tangential compressive stresses in the glassy matrix surrounding the leucite crystals upon cooling, because the crystals contract more than the sur-rounding glassy matrix. These stresses can act as crack deflectors and contribute to increased resis-tance of the ceramic to crack propagation (fracture toughness). As mentioned earlier, both sintered and slip-cast all-ceramic restorations have now been replaced by heat-pressed or machined all-ceramic restorations containing similar crystalline phases but with better-controlled processing steps. 216 CRAIG’S RESTORATIVE DENTAL MATERIALS Heat-Pressed All-Ceramic Materials Heat pressing relies on the application of external pressure at high temperature to sinter and shape the ceramic. Heat pressing is used in dentistry to pro-duce all-ceramic crowns, inlays, onlays, veneers, and more recently, FDPs. During heat pressing, ceramic ingots are brought to high temperature in a phos-phate-bonded investment mold produced by the lost wax technique. The heat-pressing temperature is chosen near the softening point of the ceramic. A pressure of 0.3 to 0.4 MPa is then applied through a refractory plunger. This allows filling of the mold with the softened ceramic. The high temperature is held for durations between 10 and 20 minutes. Heat-pressing requires a specially designed automated pressing furnace (Fig. 11.4) and classically promotes a good dispersion of the crystalline phase within the glassy matrix. The mechanical properties of heat-pressed ceramics are therefore maximized in addi-tion to higher crystallinity, and smaller crystal size, compared with sintered all-ceramics. Leucite-Based Ceramic First-generation heat-pressed ceramics contain tetragonal leucite (KAlSi2O6 or K2O·Al2O3·4SiO2) as a reinforcing phase, in amounts varying from 35% to 55% by volume. Heat-pressing temperatures for this system are between 1150° and 1180°C with a dwell at temperature of about 20 minutes. The ceramic ingots are available in a variety of shades. The final micro-structure of these heat-pressed ceramics consists of leucite crystals, 1 to 5 μm, dispersed in a glassy matrix (Fig. 11.5A). The amount of porosity in the heat-pressed ceramic is 9 vol%. Two techniques are available: a staining technique and a layering tech-nique involving the application of veneering ceramic. The two techniques lead to comparable mean flex-ural strength values for the resulting ceramic. To ensure compatibility with the thermal expansion coefficient of the veneering ceramic, the thermal expansion coefficient of the core material for the veneering technique (14.9 × 10−6/°C) is lower than that of the core material for the staining technique (18 × 10−6/°C). The flexural strength of these ceram-ics (120 MPa) is almost double that of conventional feldspathic porcelains. This increase in strength can be explained by the fact that these ceramics possess a higher crystallinity and that the heat-pressing pro-cess generates an excellent dispersion of these fine leucite crystals. In addition, as mentioned earlier, residual thermal stresses around the leucite crystals promote crack deflection and contribute to improved mechanical performance. The main advantages of leucite-reinforced ceramics are their excellent esthet-ics and translucency, whereas their limitations lie in their modest mechanical properties restricting their use to anterior single-unit restorations. Lithium Disilicate–Based Materials The second generation of heat-pressed ceramics con-tain lithium disilicate (Li2Si2O5) as a major crystalline phase. Heat pressing takes place in the 910° to 920°C temperature range, using the same equipment as for the leucite-based ceramics. Heat-pressed restorations are later veneered with ceramics of matching ther-mal expansion, or stained. The final microstructure consists of about 65% by volume of highly interlock-ing prismatic lithium disilicate crystals (2 to 5 μm in length, 0.8 μm in diameter) dispersed in a glassy matrix (Fig. 11.5B). The amount of porosity after heat pressing is about 1 vol%. Compared with first-generation leucite-based ceramics, the main advan-tage of the lithium disilicate–based ceramics is their enhanced flexural strength (350 MPa) and fracture toughness (2.75 MPa·m0.5). This can be explained by a higher crystallinity and a house of cards micro-structure consisting of elongated, highly interlocked, needle-shaped lithium disilicate crystals. In addition, the thermal expansion mismatch between the lith-ium disilicate crystals and the glassy matrix leads to compressive residual stresses which, combined with multiple crystal orientations, is efficient in promot-ing multiple crack deflections, thereby increasing the resistance to crack propagation. Finally, several stud-ies have reported that heat pressing promotes crystal alignment along the direction of pressing because of the high aspect ratio of the crystals. This leads to an even higher resistance to crack propagation in the direction perpendicular to crystal alignment. The enhanced mechanical properties of these second-generation heat-pressed ceramics have extended their range of dental applications, making possible the fabrication of multiunit FDPs. FIG. 11.4 Porcelain furnace. (Modified from Whip Mix Corporation, Louisville, KY.) 217 11. Restorative Materials: Ceramics For a discussion of slip-cast all-ceramic materials please go to the website sakaguchi/restorative. Machinable All-Ceramic Materials All-ceramic materials can be machined in the fully sintered state. This is termed hard machining and restorations produced in this way are machined directly to final size. Some all-ceramic materials can also be machined in a soft, partially sintered state and later fully sintered. This is called soft machining. The latter technique requires milling of enlarged restora-tions to compensate for sintering shrinkage, and is well adapted to ceramics that are difficult to machine in the fully sintered state, such as alumina and zirconia. Acc.V Spot Magn Det WD 15.0kV 4.0 2000x SE 5.2 VNA MKII-17NOV09-1.DENRY 10 µm Acc.V Magn Det WD 10.0kV 4000x SE 9.9 OPC pressed 1150C 1B-I.DENRY 5 µm Acc.V Magn Det WD 15.0kV 8000x SE 10.8 Empress 2-17 AUG 99-I. DENRY DENRY-UI x20.0k l. DENRY-UI 2.00um 2.00um 2 µm A B C D E F FIG. 11.5 Scanning electron micrographs showing the microstructure of selected all-ceramic materials (polished and etched surfaces). (A) Leucite-reinforced heat-pressed ceramic; (B) lithium disilicate heat-pressed ceramic; (C) feldspar-based machinable ceramic; (D) zirconia lithium silicate machinable ceramic; (E) soft-machined sintered zirconia ceramic (3Y-TZP); (F) soft-machined sintered high-translucency zirconia ceramic (cubic and tetragonal). 218 CRAIG’S RESTORATIVE DENTAL MATERIALS Hard Machining Machinable ceramics can be milled to form inlays, onlays, veneers, and crowns using the CAD/CAM technology to produce restorations in one office visit. After the tooth is prepared, the preparation is optically scanned and the image is computer-ized. The restoration is designed with the aid of a computer, as shown in Fig. 11.6. The restoration is then machined from ceramic blocks by a computer-controlled milling machine. The milling process takes only a few minutes. Restorations are bonded to the tooth preparation with resin cements. The most recent versions of oral scanners combined with digital impression reconstruction software (3M True Definition Scanner, 3M Company; CEREC AC, Sirona Dental Systems, LLC; PlanScan Restorative System, Planmeca; iTero Intra Oral Digital Scanner, Align Technologies) allow complete tridimensional visualization of the projected restoration with vir-tual seating capabilities. The various surfaces of the virtual restoration can be modified in all three dimensions prior to machining. Further informa-tion on digital impression systems can be found in Chapter 14. Several machinable glass-ceramics are presently available for hard machining: feldspar-, leucite-, and lithium disilicate–based. The feldspar-based glass-ceramic contains approximately 30 vol% feldspar [(Na,K) AlSi3O8] as a major crystalline phase, dis-persed in a glassy matrix (see Fig. 11.5C). Its flexural strength is ranked as moderate (120 MPa). Leucite-reinforced and lithium disilicate glass-ceramic blocks are also available for hard machining by CAD/ CAM. The leucite-reinforced ceramic blocks are simi-lar in microstructure and mechanical properties to the first-generation heat-pressed, leucite-reinforced ceramics. The lithium disilicate glass-ceramic blocks are machined in a partially crystallized state, which corresponds to a softer and easier-to-machine state compared with the fully crystallized state. In the par-tially crystallized (nucleated) state, the glass-ceramic contains crystal nuclei of both lithium metasilicate (Li2SiO3) and lithium disilicate (Li2Si2O5). By con-trolling the nucleation and crystallization heat treat-ment, the number of nucleation sites, crystal size, and nature of the crystalline phases can be adjusted to modulate the translucency of this glass ceramic. Low-, medium-, and high-translucency blocks are proposed for CAD/CAM machining. After the restorations are machined, a heat treatment at 850°C for 10 minutes is performed to complete the crystallization process, and therefore ensure that the glass ceramic possesses optimized mechanical properties prior to glazing and cementation. Depending on the translucency, the microstructure will be slightly different, with the high-translucency glass-ceramic exhibiting lithium disili-cate crystals (1.5 × 0.8 μm) in a glassy matrix, and the low-translucency ceramic exhibiting a larger number of smaller (0.8 × 0.2 μm) interlocked lithium disilicate crystals. The flexural strength after completion of the crystallization heat treatment is between 360 and 400 MPa, according to manufacturer’s data. Another lithium silicate–based glass ceramic was recently introduced, in which about 10 wt% zirco-nium dioxide was added to a lithium silicate glass composition and remains in solution in the glassy matrix. This modification leads to a larger amount of glassy matrix in the precrystallized (nucleated) state, with ease of machining due to the presence of lith-ium metasilicate crystals. The final microstructure after completion of the crystallization heat treatment (840°C for 8 minutes) consists of lithium metasilicate (0.1 to 0.2-μm platelets) interlocked with lithium dis-ilicate crystals (0.5 to 0.8 μm-long prisms), leading to a glass ceramic with excellent translucency and mechanical properties comparable to those of lith-ium disilicate glass ceramics (see Fig. 11.5D). Soft Machining Followed by Sintering In 2002, the first zirconia-based ceramic for soft machining was introduced on the dental market. The FIG. 11.6 Chair-side computer-aided design/computer-aided manufacturing system for all-ceramic restorations fabrication. (Courtesy Sirona Dental Systems, LLC, Charlotte, NC.) 219 11. Restorative Materials: Ceramics material consists of tetragonal zirconia polycrystals partially stabilized by addition of 3 mole percent yttrium (3Y-TZP). Single or multiunit restorations are produced by direct ceramic machining (DCM) of presintered 3Y-TZP blocks. These blocks are soft and easy to mill, thus leading to substantial savings in time and tool wear, compared with fully sintered zirconia. The process involved the fabrication of a full contour wax-up of the restoration, later digitized with a laser scanner. Restorations were oversized at the design and machining stages, to compensate for the large shrinkage (20% to 25%) that occurs during the sintering process at high temperature (1350°C for 2 hours). Since the introduction of the DCM technique, a wide variety of partially sintered 3Y-TZP blocks have become available for soft machining by CAD/CAM. In this case, the wax-up step is eliminated, a digital impression of the preparation is made, and the resto-ration design is accomplished by computer. Similar to the DCM technique, machined restorations are fully sintered at high temperature. The microstructure of these polycrystalline 3Y-TZP ceramics consists of densely packed tetrago-nal zirconia grains with a mean grain size of 0.2 to 1.0 μm, depending on sintering temperature and duration (Fig. 11.5E), which can vary from 1350° to 1600°C and 2 to 6 hours, respectively, depending on the manufacturer. Zirconia ceramics exhibit the high-est flexural strength (900 to 1500 MPa) and highest fracture toughness (greater than 6 MPa·m0.5) of all currently available dental ceramics. They can serve as core ceramics that are veneered with porcelain of matched thermal expansion. Early clinical issues consisting of cracking and delamination at the inter-face between veneering porcelain and zirconia core were reported. These findings have been explained by the fact that both veneering porcelain and zirco-nia core exhibit low thermal conductivity and that thermal gradients may develop when fast heating or cooling rates are used, leading to transient stresses and microcracking. The metastability of 3Y-TZP ceramics should be kept in mind when surface-altering treatments such as grinding or air abrasion are performed. Given the fact that transformability increases with grain size, such treatments have the potential to trigger the tetragonal to monoclinic transforma-tion with the immediate beneficial consequence of producing surface compressive stresses. However, long-term effects may be detrimental due to the combination of defects produced by the surface treatment and the presence of underlying ten-sile stresses. This is why extreme care should be taken to follow manufacturer’s instructions when working with partially stabilized zirconia-based ceramics. Hard-machining techniques make it possible to fabricate the restoration chair side in one office visit. However, all-ceramic materials available with these techniques exhibit only low to moderate strength, restricting the applications to single-unit restora-tions, or short-span FDPs. The benefit of fabricating the restoration in one office visit is lost with soft-machining techniques, because restorations require sintering at high tem-perature for several hours after they are machined. This disadvantage is counterbalanced by the excel-lent mechanical properties of 3Y-TZP, making pos-sible the realization of both single and multiunit anterior and posterior restorations. Initially a con-cern, marginal accuracy is currently clinically accept-able with these techniques. The negative impact of the high opacity of zirconia is attenuated by the abil-ity to decrease coping thickness to 0.4 to 0.5 mm. In addition, more translucent zirconia compositions have been recently introduced. The increase in trans-lucency is obtained either by decreasing the amount of alumina present to 0.05 wt% or less, or by adding higher amounts of yttria (up to 5.3 mol.%) to stabilize the cubic polymorph of zirconia as a major crystal-line phase. Cubic zirconia is more translucent due to its isotropic crystal symmetry, compared with tetrag-onal zirconia, which is anisotropic and birefringent. The retention of cubic zirconia at room temperature is also accompanied with a substantial increase in grain size (see Fig. 11.5F). The cubic form of zirco-nia is not transformable and exhibits lower fracture toughness. This is reflected in the lower mechani-cal properties of cubic zirconia formulations, with a reported flexural strength of 609 MPa and a fracture toughness of 2.4 MPa·m0.5. METAL-CERAMIC RESTORATIONS Metal-ceramic restorations consist of a cast metallic framework on which at least two layers of ceramic are baked (Fig. 11.7). The first layer applied is a thin opaque layer, consisting of porcelain modified with opacifying oxides. Its role is to mask the dark-gray appearance of the oxidized metal framework to permit the achievement of adequate esthetics. This thin opaque layer also establishes the metal-ceramic bond. The next step is the buildup of dentin and enamel (most translucent) porcelains to obtain an esthetic appearance similar to that of a natural tooth. Dentin and enamel porcelain powders are mixed with modeling liquid (mainly distilled water) to a creamy consistency and applied on the opaque layer. The porcelain is then condensed by vibration and removal of the excess water with absorbent tis-sue. The porcelain buildup has to be oversized to compensate for the large shrinkage (25% to 30%) 220 CRAIG’S RESTORATIVE DENTAL MATERIALS associated with the sintering process. After building up of the porcelain powders, metal-ceramic restora-tions are slowly dried to allow for adequate water diffusion and evaporation, and sintered under vac-uum in a porcelain furnace. Sintering under vacuum helps eliminate pores. As the furnace door closes, the pressure is lowered to 0.01 MPa (0.1 atmo-sphere). The temperature is raised until the sintering temperature is reached, the vacuum is then released, and the furnace pressure returns to 0.1 MPa (1 atmo-sphere). In combination with viscous flow at high temperature, the increase in pressure helps close residual pores. The result is a dense, relatively pore-free porcelain, as illustrated in Fig. 11.8. Studies have shown that sintering under vacuum reduces the amount of porosity from 5.6% in air-fired porce-lains to 0.56%. This decrease in porosity is noticeable by the associated increase in translucency. Opaque, dentin, and enamel porcelains are available in vari-ous shades. Fig. 11.9 shows two three-unit metal-ceramic FDPs. When fabricated by skilled technicians, these restorations provide excellent esthetics, along with adequate strength because of the metal framework support. The alloys used for casting the substructure are usually gold-based containing tin and indium. It is essential that the CTE of the veneering por-celain be slightly lower than that of the alloy to ensure that the ceramic is in slight compression after cooling. This will prevent microcrack forma-tion in the porcelain and enhance long-term clinical performance. Requirements for a Metal-Ceramic System 1. The alloy must have a high melting temperature. The melting range must be substantially higher (greater than 100°C) than the firing temperature of the veneering porcelain and solders used to join segments of an FDP. 2. The veneering porcelain must have a low fusing temperature so that no creep, sag, or distortion of the framework takes place during sintering. 3. The porcelain must wet the alloy readily when applied as a slurry to prevent voids forming at the metal-ceramic interface. In general, the contact angle should be 60 degrees or less. 4. A strong bond between the ceramic and metal is essential and is achieved by chemical reaction of the opaque porcelain with metal oxides on the surface of metal (Fig. 11.10) and by mechanical interlocking made possible by roughening of the metal coping. Metal coping Opaque porcelain Dentin porcelain Enamel FIG. 11.7 Cross section of a metal-ceramic crown show-ing metal coping, opaque porcelain layer, dentin, and enamel porcelain layers. A B FIG. 11.8 Air-fired and vacuum-fired porcelain. (A) Optical micrograph of air-fired porcelain, showing porosity. (B) Optical micrograph of vacuum-fired porcelain showing minimal porosity. (Courtesy J.O. Semmelman, York, PA, 1959, Dentsply International.) 221 11. Restorative Materials: Ceramics 5. CTEs of the porcelain and metal must be compatible so that the veneering porcelain never undergoes tensile stresses, which would lead to cracking. Metal-ceramic systems are therefore designed so that the CTE of the metal is slightly higher than that of the porcelain, thus placing the veneering porcelain in compression (where it is stronger) following cooling (see Fig. 10.9). This is assuming that linear coefficients of thermal expansion of both porcelain and metal are identical to linear coefficients of thermal contraction. 6. Adequate stiffness and strength of the metal framework are especially important for FDPs and posterior crowns. High stiffness of the metal reduces tensile stresses in the porcelain by limiting deflection amplitude and deformation (strain). High strength is essential in the interproximal connector areas of FDPs. 7. High resistance to deformation at high temperature is essential. Metal copings are relatively thin (0.4 to 0.5 mm); no distortion should occur during firing of the porcelain, or the fit of the restorations would be compromised. 8. Adequate design of the restoration is critical. The preparation should provide for adequate thickness of the metal coping, as well as enough space for an adequate thickness of the porcelain to yield an esthetic restoration. During preparation of the metal framework, prior to porcelain application, it is important that all sharp angles be eliminated and rounded to later avoid stress concentration in the porcelain. If full porcelain coverage is not used (e.g., a metal occlusal surface), the position of the metal-ceramic junction should be located at least 1.5 mm from all centric occlusal contacts. Metal-Ceramic Bonding The bond strength between porcelain and metal is an important requirement for good long-term performance of metal-ceramic restorations. In gen-eral, the bond is a result of chemisorption by diffu-sion between the surface oxide layer on the alloy and the porcelain. For metal alloys that do not oxidize easily, this oxide layer is formed during a special fir-ing cycle prior to opaque porcelain application. For metal alloys that do oxidize easily, the oxide layer is formed during wetting of the alloy by the porce-lain and subsequent firing cycle. The most common mechanical failure for metal-ceramic restorations is debonding of the porcelain from the metal. Many factors control metal-ceramic adhesion: the forma-tion of strong chemical bond, mechanical interlock-ing between the two materials, and thermal residual stresses. In addition, as noted earlier, the porcelain must wet and fuse to the surface to form a uniform interface with no voids. These factors are also impor-tant for ceramic coatings on metallic implants. From a practical standpoint, the surface roughness at the metal-ceramic interface has a large effect on the quality of the metal-ceramic bond. Airborne particle abrasion is routinely used on metal frameworks for metal-ceramic restorations to produce a clean surface with controlled roughness. During the firing cycle, the porcelain softens, its viscosity decreases, and the porcelain first wets the metal surface before the inter-locking between porcelain and metal is created. The increased area of the rough metal surface also permits the formation of a greater density of chemical bonds. The contact angle between the porcelain and metal is a measure of the wetting and, to some extent, the quality of the bond that forms. Low contact angles indicate good wetting. The contact angle of porcelain on a gold (Au) alloy is about 60 degrees. A scanning electron micrograph of the oxidized surface of a gold (Au)-platinum (Pt)-palladium (Pd) 98% noble alloy is shown in Fig. 10.8. However, rough surfaces can reduce adhesion if the porcelain does not wet the surface and voids are present at the interface. The formation of an oxide layer at the surface of the metal has been shown to be the key to an ade-quate metal-ceramic bond. Noble metal alloys, which are resistant to oxidizing, usually have other more easily oxidized elements added, such as indium (In) and tin (Sn), to form an oxide layer and improve the bond. The oxide layer is formed during a special fir-ing cycle prior to porcelain application. Some noble alloys containing silver have been shown to lead to porcelain discoloration or greening, explained by ionic diffusion of silver in the porcelain. Base-metal alloys contain elements, such as nickel (Ni) and chromium (Cr), that oxidize easily, and care must be taken to avoid the formation of too thick an oxide layer. Manufacturers specify firing conditions for the formation of an optimal oxide layer and often indi-cate the color of the oxide. Oxides rich in nickel (NiO) tend to be dark gray, whereas those rich in chromium FIG. 11.9 View of metal-ceramic fixed dental prostheses. (Courtesy Dr. Charles Mark Malloy, Portland, OR.) 222 CRAIG’S RESTORATIVE DENTAL MATERIALS (Cr2O3) are greenish. If firing recommendations are not followed, these oxides may dissolve in the por-celain during firing, leading to discoloration visible in areas where the porcelain is thinnest; for example, near the gingival margin of the restoration. Some alloys form oxide layers rich in Cr2O3, which do not bond or adhere well to the alloy. These alloys typi-cally require the application of a bonding agent to the alloy surface to modify the type of oxide formed. In some cases, manufacturers recommend an oxidation firing under reduced pressure to limit the thickness of the oxide layer. An oxidation firing in air may lead to a thicker oxide layer. High thermal residual stresses between the metal and porcelain can lead to failure. If the metal and ceramic have largely different thermal expansion coefficients, the two materials will contract at differ-ent rates during cooling and large thermal residual stresses will form along the metal-ceramic inter-face. If these stresses are very high (whether tensile or compressive), the porcelain will crack and/or delaminate from the metal. Even if these stresses do not cause immediate failure, they can still weaken the bond, and lead to delayed failure. To avoid these problems, porcelains and alloys are formulated to have adequately matched thermal expansion coef-ficients. Most porcelains have coefficients of ther-mal expansion between 13.0 and 14.0 × 10−6/°C, and metals between 13.5 and 14.5 × 10−6/°C. The difference of 0.5 × 10−6/°C in thermal contraction between metal and porcelain causes the metal to contract slightly more than does the ceramic during cooling. This condition places the porcelain under slight residual compression, which makes it less sen-sitive to the tensile stresses induced by mechanical loading. A metal-ceramic bond may fail in any of three possible locations (see Fig. 11.10). Knowing the location of failure provides considerable informa-tion on the quality of the bond. The highest bond strength leads to failure within the porcelain when tested (see Fig. 11.10C); this is observed with some alloys that were properly prepared with excellent wetting by the porcelain and is also called a cohe-sive failure. Testing these high-strength specimens using the push-through shear test shows that the bond strength is approximately the same as the shear strength of the porcelain. Another possible cohesive failure is within the oxide layer (see Fig. 11.10B). Failures occurring at the interface between metal and oxide layer (see Fig. 11.10A) are called adhesive failures and are commonly observed with metal alloys that are resistant to forming surface oxides, such as pure gold or plati-num, and exhibit poor bonding. Base-metal alloys commonly exhibit failures within the oxide layer if an excessively thick oxide layer is present. Ceramics for Metal-Ceramic Restorations Ceramics for metal-ceramic restorations must fulfill five requirements: (1) they must simulate the appear-ance of natural teeth, (2) they must fuse at relatively low temperatures, (3) they must have thermal expan-sion coefficients compatible with alloys used for metal frameworks, (4) they must age well in the oral environment, and (5) they must have low abrasive-ness. Porcelains are carefully formulated to achieve these requirements. These ceramics are composed of a crystalline phase (leucite) dispersed in a glassy (amorphous) matrix. Their chemical composition includes silica (SiO2), alumina (Al2O3), sodium oxide (Na2O), and potassium oxide (K2O) (Table 11.4). Opacifiers (TiO2, ZrO2, SnO2), various heat-stable coloring oxides, and small amounts of fluorescing oxides (CeO2) are added to match the appearance of the dentin-enamel complex structure. The presence of a large amount of glassy phase in dental porce-lains (80 to 90 vol%) permits a translucency similar to that of enamel. Coloring oxides and opacifiers allow fine tuning of the final appearance and shade control. Porcelain is supplied as a fine powder of controlled granulometry. Dental Porcelain COMPOSITION The quality of any ceramic depends on the choice of components, correct proportioning of each compo-nent, and control of the firing procedure. High-purity components are used in the manufacture of dental porcelains because of the stringent requirements of Ceramic A B C Oxide Metal Failure Failure Failure FIG. 11.10 Diagram showing three observed types of bond failure in metal-ceramic systems. (A) Metal-metal oxide (adhesive); (B) metal oxide-metal oxide (cohesive); and (C) ceramic-ceramic (cohesive). note: The dimensions of the layers are not to scale. 223 11. Restorative Materials: Ceramics optical properties and chemical inertness, combined with adequate strength, toughness, and thermal expansion. In its mineral state, feldspar, the main raw com-ponent of dental porcelains for metal-ceramic resto-rations, is crystalline and opaque. Chemically, it is designated as potassium aluminosilicate, with a com-position of KAlSi3O8 or K2O·Al2O3·6SiO2. Feldspar melts incongruently at about 1150°C, forming leucite (KAlSi2O6 or K2O·Al2O3·4SiO2) and molten glass. MANUFACTURE Many dental porcelain manufacturers buy feld-spar as powder already screened and cleaned from impurities to their specifications. Other raw materi-als used in the manufacture of dental porcelains are various types of silica (SiO2) in the form of fine pow-der, alumina (Al2O3), as well as alkali and alkaline earth carbonates as fluxes. During the manufacturing process, the ground components are carefully mixed together and heated to about 1200°C in large cruci-bles. As mentioned earlier, feldspar melts incongru-ently at about 1150°C to form a glassy phase with an amorphous structure, as illustrated in Fig. 11.11, and a crystalline phase consisting of leucite, a potassium aluminosilicate (KAlSi2O6). The mix of leucite and glassy phase is then cooled very rapidly (quenched) in water that causes the mass to shatter in small fragments. The prod-uct obtained, called a frit, is ball milled to achieve proper particle size distribution. Coloring pigments in small quantities are added at this stage to obtain the delicate shades necessary to mimic natural teeth. The metallic pigments include titanium oxide for yellow-brown shades, manganese oxide for laven-der, iron oxide for brown, cobalt oxide for blue, cop-per or chromium oxides for green, and nickel oxide for brown. In the past, uranium oxide was used to TABLE 11.4 Composition of Dental Ceramics for Fusing to High-Temperature Alloys Compound Biodent Opaque BG 2 (%) Ceramco Opaque 60 (%) V.M.K. Opaque 131 (%) Biodent Dentin BD 27 (%) Ceramco Dentin T 69 (%) SiO2 52.0 55.0 52.4 56.9 62.2 Al2O3 13.55 11.65 15.15 11.80 13.40 CaO — — — 0.61 0.98 K2O 11.05 9.6 9.9 10.0 11.3 Na2O 5.28 4.75 6.58 5.42 5.37 TiO2 3.01 — 2.59 0.61 — ZrO2 3.22 0.16 5.16 1.46 0.34 SnO2 6.4 15.0 4.9 — 0.5 Rb2O 0.09 0.04 0.08 0.10 0.06 BaO 1.09 — — 3.52 — ZnO — 0.26 — — — UO3 — — — — — B2O3, CO2, and H2O 4.31 3.54 3.24 9.58 5.85 From Nally JN, Meyer JM. Experimental study on the nature of the ceramic-metallic bonding. SSO Schweiz Monatsschr Zahnheilkd. 1970;80(3):250–278. [Article in French] Si O Na FIG. 11.11 Two-dimensional structure of sodium sili-cate glass. Na, Sodium; O, oxygen; Si, silicon. (Modified from Warren BE, Biscoe J. Fourier analysis of x-ray patterns of soda-silica glass. J Am Ceram Soc. 1938;21(7):259–265.) 224 CRAIG’S RESTORATIVE DENTAL MATERIALS provide fluorescence; however, because of the small amount of radioactivity, lanthanide oxides (such as cerium oxide) have been substituted for this pur-pose. Tin, titanium, and zirconium oxides are used as opacifiers. After the manufacturing process is completed, feldspathic dental porcelain consists of a glassy (or amorphous) phase and leucite (KAlSi2O6) as a crys-talline phase. The glassy phase formed during the manufacturing process has properties typical of glass, such low toughness and strength, and high translucency. The crystalline structure of leucite is tetragonal at room temperature (Fig. 11.12). Leucite undergoes a reversible crystallographic phase trans-formation at 625°C, temperature above which its structure becomes cubic. This transformation is accompanied by a thermal expansion resulting in a 1.2 vol% increase of the unit cell. This explains the high thermal expansion coefficient associated with tetragonal leucite (greater than 20 × 10−6/°C). As a result, the amount of leucite present (10 to 20 vol%) controls the thermal expansion coefficient of the por-celain so that it is adequately matched to that of den-tal alloys. The microstructure of conventional feldspathic porcelain is shown in Fig. 11.13; the glassy phase has been lightly acid-etched to reveal the leucite crystals. Typical compositions for opaque and dentin porce-lain powders are given in Table 11.4. Feldspathic porcelains have other qualities that make them well suited for metal-ceramic restora-tions. They fuse at lower temperatures than do many other ceramic materials, lessening the potential for distortion of the metal coping. This is made possible by the presence of alkali oxides (Na2O and K2O) in the glassy matrix; these oxides are responsible for the creation of nonbridging oxygens in the glass net-work, thereby lowering the fusing temperatures to the range 930° to 980°C. Porcelains having an even lower fusing temperature (760° to 780°C) and high CTE (15.8 × 10−6/°C) are also available. These por-celains are designed to be compatible for bonding to yellow high-Au alloys, which have coefficients of thermal expansion between 16.1 and 16.8 × 10−6/°C. They can, however, be abrasive to opposing teeth because of their hardness; this becomes a significant problem if the porcelain surface is roughened by occlusal adjustments or sensitivity to aging in the oral environment. Effect of Design on Metal-Ceramic Restorations Because ceramics are weak in tension and can with-stand very little strain before fracturing, the metal framework must be rigid to minimize deformation of the porcelain. However, copings should be as thin as possible to allow space for the porcelain to mask the metal framework without overcontouring the porce-lain. This consideration is especially true for alloys that appear gray. This might lead to the conclusion that nickel-chromium (Ni-Cr) or cobalt-chromium (Co-Cr) alloys would be superior to the noble alloys because their moduli of elasticity (stiffness) are 1.5 to 2 times greater and the thickness of the coping could be halved. However, loading the restoration places it in bending, and the bending deflection is a function of only the first power of the modulus, whereas it is a function of the cube of the thickness. It can be shown that for a typical dental metal-ceramic restoration, the thickness of a base-metal coping can be reduced only about 7% because of the higher modulus of elas-ticity. Thus the advantage of the higher modulus for the base-metal alloys is minimal. The labial margin of metal-ceramic prostheses is a critical area regarding design because there is little porcelain thickness at the margin to mask the appearance of the metal coping and to resist fracture. K (Si, AI) O4 FIG. 11.12 Three-dimensional structure of leucite (KAl-Si2O6). Al, Aluminum; K, potassium; O, oxygen; Si, silicon. GM Acc.V Spot Magn Det WD 10.0kV 4.0 4000x SE 10.1 IPS Classic-I. DENRY 5 µm LC FIG. 11.13 Scanning electron micrograph showing the microstructure of feldspathic porcelain for metal-ceramic restorations. GM, Glassy matrix; LC, leucite crystal. 225 11. Restorative Materials: Ceramics Recommended margin designs include a 90-degree shoulder, a 120-degree shoulder, or a shoulder bevel. Provided that the shoulder depth is at least 1.2 mm, these designs should all provide for sufficient por-celain thickness to minimize the risk of porcelain fracture. When using partial porcelain coverage, such as when a metal occlusal surface is desired, the posi-tion of the metal-ceramic joint is critical. Because of the large difference in modulus of elasticity between porcelain and metal, stresses occur at the interface when the restoration is loaded. These stresses should be minimized by placing the metal-ceramic junction at least 1.5 mm from centric occlusal contacts. The geometry of the interproximal connector area between abutment crown and pontic is critical in the design of a metal-ceramic FDP. The incisocervical thickness of the connector should be large enough to prevent deformation or fracture because deflec-tion is decreased as the cube of the thickness; greater thickness will minimize deflection of the framework, which may lead to debonding or fracture of the por-celain. It should be noted that an FDP is not a uniform beam; maximum deflection on loading will occur at the thinnest cross section, which is the interproximal connector area. However, connector thickness cannot impinge on gingival tissues or restrict access for oral hygiene procedures. Failure and Repair of Metal-Ceramic Restorations Metal-ceramic restorations remain the most popular material combination selected for crown and bridge applications and have a 10-year success rate of about 95%. The majority of retreatments are due to biologi-cal failures, such as tooth fracture, periodontal dis-ease, and secondary caries. Prosthesis fracture and esthetic failures account for only 20% of retreatment cases for single-unit restorations. For metal-ceramic FDPs, prosthesis fracture is the most common reason for retreatment, with long-span FDPs (five or more units) having approximately twice the incidence of failure compared with short-span FDPs. When metal-ceramic prosthesis fails, it is often due to adhesive failure between porcelain and metal or cohesive failure within the ceramic near the metal-ceramic interface. Ideally, the prosthe-sis should be retrieved, metal surfaces should be cleaned, and a new oxide layer should be formed on the exposed area of metal prior to porcelain application and firing. However, this cannot be achieved intraorally, and removal of the prosthesis is both unpleasant for the patient and time con-suming. Thus a variety of techniques have been developed for porcelain repair using resin compos-ites. All of these techniques present the challenge of bonding chemically dissimilar materials. When porcelain fragments are available and no functional loading is exerted on the fracture site, silane cou-pling agents can be used to achieve good adhesion between the composite and porcelain; however, metal alloys have no such bonding agent and this type of repair is considered only temporary. Systems are available for coating the metal sur-face with silica particles through airborne particle abrasion. The particles are embedded in the metal surface upon impact, then a silane coupling agent can be applied. Alternatively, base metal alloys can be coated with tin followed by the application of an acidic primer. Both methods achieve adequate bond strength and may delay the eventual need for remaking the prosthesis. For a discussion of porcelain application and properties of porcelain denture teeth please go to the website restorative. Bibliography Albakry M, Guazzato M, Swain MV. Influence of hot press-ing on the microstructure and fracture toughness of two pressable dental glass–ceramics. J Biomed Mater Res. 2004;71B:99–107. Ban S. Reliability and properties of core materials for all-ceramic dental restorations. Japan Dent Sci Rev. 2008; 44:3–21. Baran GR, O’Brien WJ, Tien TY. Colored emission of rare-earth ions in a potassium feldspar glass. J Dent Res. 1977;56:1323–1329. 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Schweiz Monatsschr Zahnheilked. 1970;80:25. Nâpânkangas R, Salonen-Kemppi MA, Raustia AM. Longevity of fixed metal ceramic bridge prostheses: a clinical follow-up study. J Oral Rehabil. 2002;29:140. O’Brien WJ. Ceramics. Dent Clin North Am. 1985;29:851. Özcan M, Niedermeier W. Clinical study on the reasons for and location of failures of metal-ceramic restorations and survival of repairs. Int J Prosthodont. 2002;15:299. Ringle RD, Fairhurst CW, Anusavice KJ. Microstructures in non-precious alloys near the porcelain-metal interaction zone. J Dent Res. 1979;58:1987. Robin C, Scherrer SS, Wiskott HWA, et al. Weibull parameters of composite resin bond strengths to porcelain and noble alloy using the Rocatec system. Dent Mater. 2002;18:389. Shell JS, Nielsen JP. Study of the bond between gold alloys and porcelain. J Dent Res. 1962;41:1424. Shimoe S, Tanoue N, Yanagida H, et al. Comparative strength of metal-ceramic and metal-composite bonds after extended thermocycling. J Oral Rehabil. 2004;31:689. Walton TR. A 10-year longitudinal study of fixed prosth-odontics: clinical characteristics and outcome of single-unit metal-ceramic crowns. Int J Prosthodont. 1999;12:519. Zarone F, Russo S, Sorrentino R. From porcelain-fused-to-metal to zirconia: clinical and experimental consid-erations. Dent Mater. 2011;27:83. This page intentionally left blank 229 Impression materials are used to register or repro-duce the form and relationship of the teeth and oral tissues. Hydrocolloids and synthetic elastomeric polymers are among the materials most commonly used to make impressions of various areas of the den-tal arch. Each of these classes of materials has certain advantages and disadvantages. An understanding of the physical characteristics and the limitations of each material is necessary for their successful use in clinical dentistry. Digital impressions are described in Chapter 14. Impression materials and techniques are discussed on the website .com/sakaguchi/restorative. PURPOSE OF IMPRESSION MATERIALS Impression materials are used to make an accurate replica or mold of the hard and soft oral tissues. The area involved may vary from a single tooth to the whole dentition, or an impression may be made of an edentulous mouth. The impression is a nega-tive reproduction of the tissues, and by filling the impression with dental stone or other model mate-rial, a positive cast is made that can be removed after the model material has set. An impression and a stone cast made from the impression are shown in Fig. 12.1. Casts of the mouth are used to evaluate the dentition when orthodontic, occlusal, or other prob-lems are involved, and in the laboratory fabrication of restorations and prostheses. Usually the impression material is carried to the mouth in an unset (flowable) condition in a tray and applied to the area under treatment. When the impres-sion material has set, it is removed from the mouth with the tray. The cast is made by filling the impres-sion with dental stone or other model material or by scanning the impression and printing a plastic model from the digital impression (see Chapter 14). The accuracy, detail, and quality of this final replica are of greatest importance. When the positive reproduction takes the form of the tissues of the upper or lower jaw and serves for the construction of dentures, crowns, fixed dental prostheses, and other restorations, it is described as a cast. The positive reproduction of the form of a prepared tooth constitutes a die for the preparation of inlays or fixed dental prostheses. When a positive likeness of the arch or certain teeth is reproduced for orthodontic treatment, it is some-times described as a model, although cast is the more proper term. On other occasions and in other branches of dentistry, these terms are used interchangeably. Sometimes impression materials are used to duplicate a cast or model that has been formed when more than one positive reproduction is required. Such impres-sion materials are referred to as duplicating materials (for additional information refer to website http:// evolve.elsevier.com/sakaguchi/restorative). A variety of impression trays are used to make impressions. Examples of typical impression trays are shown in Fig. 12.2. The tray is placed so the material is supported and brought into contact with the oral tissues, and then held without movement until the impression material has set. The tray with the impression material is then removed from the mouth, and the impression is ready for disinfection and pouring with a cast material to make a positive replica. The clinical impression technique and the production of the cast vary with each impression material. The properties of custom trays are dis-cussed later in this chapter. DESIRABLE QUALITIES Affording safe contact with tissues in the mouth and having the ability to fulfill the needs of clinical proce-dures are critical requirements that dictate the physi-cal properties of dental impression materials. No C H A P T E R 12 Replicating Materials: Impression and Casting 230 CRAIG’S RESTORATIVE DENTAL MATERIALS impression material fulfills every requirement, and selection of the material best suited for a particular clinical situation and technique rests with the den-tist. The desirable properties of an impression can be summarized briefly as follows: 1. A pleasant odor, taste, and acceptable color 2. Absence of toxic or irritant constituents 3. Adequate shelf life for requirements of storage and distribution 4. Economically commensurate with the results obtained 5. Easy to use with the minimum of equipment 6. Setting characteristics that meet clinical requirements 7. Satisfactory consistency and texture 8. Readily wets oral tissues 9. Elastic properties that allow easy removal of the set material from the mouth and good elastic recovery 10. Adequate strength to avoid breaking or tearing upon removal from the mouth 11. Dimensional stability over temperature and humidity ranges normally found in clinical and laboratory procedures for a period long enough to permit the production of a cast or die 12. Compatibility with cast and die materials 13. Accuracy in clinical use 14. Readily disinfected without loss of accuracy 15. No release of gas or other by-products during the setting of the impression or cast and die materials A B FIG. 12.1 Alginate impression (A) and gypsum stone cast (B). (Courtesy Dr. Charles Mark Malloy and Dr. Kyle Malloy, Portland, OR.) B A FIG. 12.2 (A) Mandibular and maxillary rim-lock impression trays. (B) Custom impression tray. (Courtesy Dr. Charles Mark Malloy, Portland, OR.) 231 12. Replicating Materials: Impression and Casting TYPES OF IMPRESSION MATERIALS Alginate hydrocolloid and elastomeric impression materials are the most widely used today, and the properties of these materials are examined first. Elastomeric impression materials have replaced rigid setting materials such as plaster, impression compound, and zinc oxide-eugenol for recording soft-tissue and occlusal relationships. Information on plaster, impression compound, and zinc oxide-eugenol impression materials can be found on the website orative. Alginate Hydrocolloids Dental alginate impression materials change from the sol phase to the gel phase because of a chemi-cal reaction. Once gelation is completed, the material cannot be reliquefied to a sol. These hydrocolloids are called irreversible to distinguish them from the agar reversible hydrocolloids. Agar impression materials are described on the website com/sakaguchi/restorative. Alginate impressions are widely used to form study casts used to plan treatment, monitor changes, and fabricate provi-sional restorations and removable dental prostheses. Alginate impression products have acceptable elastic properties. Preparation for use requires only the mixing of measured quantities of powder and water. The resulting paste flows well and registers acceptable anatomical detail. Gypsum casts and models are made by pouring dental plaster or stone into the impression; no separating medium is nec-essary. The powder is supplied in bulk containers along with suitable measures for dispensing the cor-rect quantities of powder and water. The powder is also available in small sealed packets containing a quantity suitable for a single impression and ready for mixing with a measured quantity of water. These methods of packaging, together with the measuring devices supplied by the manufacturer, are shown in Fig. 12.3. Composition and Chemistry Potassium and sodium salts of alginic acid have properties that make them suitable for compound-ing a dental impression material. Alginic acid, which is prepared from a marine plant, is a high-molecular-weight block copolymer of anhydro- β-d-mannuronic acid and anhydro-β-d-guluronic acid, as shown in the top part of the formula for alginate below. The properties of alginate raw mate-rial depend largely on the degree of polymeriza-tion and the ratio of guluronan and mannuronan blocks in the polymeric molecules. The mannuronan regions are stretched and flat, whereas the guluro-nan regions contribute less flexibility. In addition, mainly guluronan blocks bind with Ca2+. Therefore alginates rich in guluronan form strong, brittle gels, whereas those rich in mannuronan form weaker and more flexible gels. A B FIG. 12.3 Alginate impression products. (A) imprESSIX (Courtesy DENTSPLY Raintree Essix, Bradenton, FL); (B) Kromafaze (Courtesy DUX Dental, Oxnard, CA.) 232 CRAIG’S RESTORATIVE DENTAL MATERIALS C C C C O O O C C O H H H H H OH HO HO Alginic Acid Sol (Chains) C C C O C O C C H H H H H OH HO HO C C C C O O O C C O O H H H H OH HO HO C C C O C O C C H H H H H H OH HO HO C C C C O O O O O C C O H H H H H OH Na Na HO Na-/Ca-Alginate Gel (Cross-Linked Chains) C Ca C C O C O O Ca O C C H H H H H OH HO C C C C O O O O C C O O H H H H OH HO C C C O C O O C C H H H H H Na Na H OH HO O H C C C O C O O O C C H H H H OH HO C C C C O O O O Ca O C C O O H H H H OH HO C C C O C O O C C H H H H H Na Na H C C C C O O O O C C H H H H OH HO H OH HO 233 12. Replicating Materials: Impression and Casting O COONa O O HO OH HO OH O O O NaOOC Mannuronate Guluronate 2H2O(s) CaSO4 Na4P2O7(s) P2O7 (aq) Ca2P2O7(s) P2O7 (aq) SO4 (aq) (retarder) 2Ca2(aq) Ca2(aq) Na(aq) Alginate(s) Alginate(aq) Na sol 4Na(aq) gel network Ca2(aq) Alginate(aq) Alginate Ca 4 4 2 Solutions of these soluble salts, when reacted with a calcium salt, produce an insoluble flexible gel commonly called calcium alginate; the structures are shown above. Upon mixing with water, the alginate impression material first forms a sol. Following the chemical reaction described above, a gel is formed to create the set impression material. The gel-forming ability of alginates is mainly related to the proportion of l-guluronan blocks. The concept of sols and gels is presented in the discussion of colloids in Chapter 4. The nature of this chemical reaction is shown above for the sodium salt. The equally common potassium salt reacts similarly. In an alginate impres-sion compound, the calcium sulfate dihydrate, sol-uble alginate, and sodium phosphate are included in the powder. When water is added to the powder, compounds disassociate as shown. Calcium ions from the calcium sulfate dihydrate react preferen-tially with phosphate ions from the sodium phos-phate and pyrophosphate to form insoluble calcium phosphate. Calcium phosphate is formed rather than calcium alginate because it has a lower solubility; thus the sodium phosphate is called a retarder and provides working time for the mixed alginate. After the phosphate ions are depleted, the cal-cium ions react with the soluble alginate to form the insoluble calcium alginate, which together with water forms the irreversible calcium alginate gel. The calcium alginate is insoluble in water, and its forma-tion causes the mixed material to gel. This reaction is irreversible; it is not possible to convert the calcium alginate to a sol after it has set. To meet the critical requirements of a dental impression material, this reaction must be controlled to attain the desirable properties of consistency, working time, setting time, strength, flexibility, elas-tic quality, and smooth, hard surfaces on gypsum casts. These requirements are achieved by adding agents to control the rate of the reaction, develop strength and elasticity in the gel, and counteract the delaying effect of alginate on the setting of gypsum products. The use of suitable fillers in correct quanti-ties produces a consistency that is suitable for vari-ous clinical uses. The composition of a typical alginate impres-sion material and the function of its ingredients are shown in Table 12.1. Manufacturers adjust the concentration of sodium phosphate to produce regular- and fast-set alginates. They also adjust the concentration of filler to control the flexibility of the set impression material from soft-set to hard-set. Although alginate impressions are usually made in a tray, injection types are much more fluid after mix-ing and more flexible after setting. Manufacturers add organic glycols to the alginate powder to reduce dust. Diatomaceous earth or fine siliceous particles are used as fillers. Because these particles can be a respiratory irritant, inhalation of the dust should be minimized. Impressions should be disin-fected with a spray solution after removal from the mouth and before pouring with a casting material. Other ingredients in some products include antimi-crobials agents and pH indicators that change color when setting has occurred. New alginates have been formulated to have increased dimensional sta-bility on storage, allowing orthodontic impressions, for example, to be sent to an orthodontic laboratory for production of the model. 234 CRAIG’S RESTORATIVE DENTAL MATERIALS Proportioning and Mixing The proportioning of the powder and water before mixing is critical to obtaining consistent results. Changes in the water-to-powder (W/P) ratio will alter the consistency and setting times of the mixed mate-rial and also the strength and quality of the impression. Usually the manufacturers provide suitable containers for proportioning the powder and water by volume, and these are sufficiently accurate for clinical use. The mixing time for regular alginate is 1 min-ute; the time should be carefully measured, because both undermixing and overmixing are detrimental to the strength of the set impression. Fast-set algi-nates should be mixed with water for 45 seconds. The powder and water are best mixed vigorously in a flexible rubber bowl with an alginate spatula or a spatula of the type used for mixing plaster and stone. Mechanical mixing devices are also available. Properties Some typical properties of a tray-type alginate impres-sion material are listed in Table 12.2. WORKING TIME The fast-set materials have working times of 1.25 to 2 minutes, whereas time of the regular-set materials is usually 3 minutes, but may be as long as 4.5 min-utes. With a mixing time of 45 seconds for the fast-set types, 30 to 75 seconds of working time remain before the impression needs to be completely seated. For the regular-set materials, a mixing time of 60 seconds leaves 2 to 3.5 minutes of working time for materials that set at 3.5 to 5 minutes. In both cases, the mixed alginate must be loaded into the tray and the impression made promptly. SETTING TIME Setting times range from 1 to 5 minutes. The American National Standards Institute/American Dental Association (ANSI/ADA) specification No. 18 [International Organization for Standardization (ISO) 1563] requires that it be at least that value listed by the manufacturer and at least 15 seconds longer than the stated working time. Lengthening the setting time is better accomplished by reduc-ing the temperature of the water used with the mix than by reducing the proportion of powder. Reducing the ratio of powder to water reduces the strength and accuracy of the alginate. Selecting an alginate with a different setting time is a better alternative than changing the W/P ratio. The setting reaction is a typical chemical reac-tion, and the rate can be approximately doubled by a temperature increase of 10°C. However, using water that is cooler than 18°C or warmer than 24°C is not advisable, as the temperature of the water also affects the comfort of the patient. The clinical setting time is detected by a loss of surface tackiness. If possible, the impression should be left in place 2 to 3 minutes after the loss of tackiness, because the tear strength and elastic recovery (recovery from deformation) increase significantly during this period. Color-changing alginates provide a visual indica-tion of working time and setting time. The mechanism of the color change is a pH-related change of a dye. One such alginate changes its color from light pink to white. TABLE 12.1 Ingredients in an Alginate Impression Powder and Their Functions Ingredient Weight (%) Function Potassium alginate 18 To dissolve in water and react with calcium ions Calcium sulfate dihydrate 14 To react with potassium alginate to form an insoluble calcium alginate gel Potassium sulfate, potassium zinc 10 To counteract the inhibiting effect of the hydrocolloid on the fluoride, silicates, or borates setting of gypsum, giving a high-quality surface to the die Sodium phosphate 2 To react preferentially with calcium ions to provide working time before gelation Diatomaceous earth or silicate 56 To control the consistency of the mixed alginate and the powder flexibility of the set impression Organic glycols Small To make the powder dustless Wintergreen, peppermint, anise Trace To produce a pleasant taste Pigments Trace To provide color Disinfectants (e.g., quaternary ammonium salts and chlorhexidine) 1–2 To help in the disinfection of viable organisms 235 12. Replicating Materials: Impression and Casting ELASTIC RECOVERY A typical alginate impression is compressed about 10% in areas of undercuts during removal. The actual magnitude depends on the extent of the undercuts and the space between the tray and the teeth. The ANSI/ADA specification requires that the elastic recovery be more than 95% when the material is compressed 20% for 5 seconds at the time it would normally be removed from the mouth. As indicated in Table 12.2, a typical value for elastic recovery is 98.2%. The corresponding permanent deformation is 1.8%. The permanent deformation (or lack of elastic recovery), indicated as percent compression set, is a function of percent compression, time under com-pression, and time after removal of the compressive load, as illustrated in Fig. 12.4. Note that permanent deformation is a time-dependent property. Lower permanent deformation (higher elastic recovery) occurs (1) when the percent compression is lower, (2) when the impression is under compression a shorter time, and (3) when the recovery time is longer, up to about 8 minutes after the release of the load. Clinically these factors translate into requirements for a reasonable bulk of alginate between the tray and the teeth, appropriate retention of the alginate in the tray, and a rapid removal of the impression from the mouth. The usual procedures followed to disin-fect the impression and produce a gypsum model provide adequate time for any recovery that might occur. FLEXIBILITY The ANSI/ADA specification permits a range of 5% to 20% at a stress of 0.1 MPa, and most alginates have a typical value of 14%. However, some of the hard-set materials have values from 5% to 8%. A reasonable amount of flexibility is required for ease of removal of the impression. STRENGTH The compressive and tear strengths of alginates are listed in Table 12.2. Both properties are time dependent, with higher values obtained at higher rates of loading. Compressive strengths range from approximately 0.5 to 0.9 MPa. The ANSI/ADA specification requires that certified products have a compressive strength of at least 0.35 MPa. Tear strengths vary from 0.4 to 0.7 kN/m, and this prop-erty is probably more important than the compres-sive strength. The tear strength is a measure of the force-to-thickness ratio needed to initiate and con-tinue tearing and is often determined on a specimen of the shape shown in Fig. 12.5. Tearing occurs in the thin sections of the impression, and the probability of tearing decreases with increasing rates of removal. The effect of loading rate on the tear strength of sev-eral alginates is shown in Fig. 12.6. Values for tray TABLE 12.2 Typical Properties of Alginate and Heavy-Bodied Agar Hydrocolloid Impression Materials Working Time (min) Setting Time (min) Gelation (°C) Recoverya (%) Flexibilityb (%) Compressive Strengthc (MPa) Tear Strengthd (kN/m) Alginate 1.25–4.5 1.5–5.0 — 98.2 8–15 0.49–0.88 0.4–0.7 Agar — — 37–45 99.0 4–15 0.78 0.8–0.9 aAt 10% compression for 30 seconds. bAt a stress of 1000 g/cm2. cAt a loading rate of 10 kg/min. dASTM Tear Die C at 25 cm/min. 0 5 10 Time (min) → 10% 10% 5 sec. 10 sec. 20% 5 sec. 20% 10 sec. 30% 5 sec. 30% 10 sec. 15 0 1 2 3 4 5 6 7 Percent compression set → FIG. 12.4 Variation of compression set with time of an alginate impression material at strains of 10%, 20%, and 30% applied for 5 and 10 seconds. (Modified from Wilson HJ. Elastomeric impression materials. 1. The setting material. Br Dent J. 1966;121(6):277–283.) 236 CRAIG’S RESTORATIVE DENTAL MATERIALS materials range from 0.38 to 0.48 N/mm at 20 mm/ min to 0.6 to 0.7 N/mm at 500 mm/min. The lower tear strength at corresponding rates for the syringe materials reflects the decreased alginate in the syringe material. COMPATIBILITY WITH GYPSUM The selection of an alginate-gypsum combination that produces good surface quality and detail is highly important. The surface quality and ability of alginate-gypsum combinations to reproduce fine V-shaped grooves are shown in Fig. 12.7A and B. A type III model plaster was poured against an alginate in Fig. 12.7A, and type IV dental stone was poured against the same alginate in Fig. 12.7B. The finest groove was 0.025 mm wide in each instance. The combination in Fig. 12.7B was not as compat-ible as the one in Fig. 12.7A with respect to either surface quality or detail. For purposes of compari-son, in Fig. 12.7C, the same type IV dental stone used in Fig. 12.7B was poured against a polysulfide impression. The impression must be rinsed well in cold water to remove saliva and any blood, and then disinfected. Next, all free surface water should be removed before preparing a gypsum model. Saliva and blood interfere with the setting of gyp-sum, and if free water accumulates, it tends to collect in the deeper parts of the impression and dilute the gypsum model material, yielding a soft, chalky surface. The excess surface water has been removed when the reflective surface becomes dull. If the alginate impression is stored for 30 minutes B C D 50 40 30 20 10 Loading rate (cm/min) 1.0 2.0 3.0 Tear strength (N/cm) 4.0 5.0 6.0 7.0 A FIG. 12.6 Tear strength (N/cm) of alginate impression materials as a function of rate of loading (cm/min). Materials A, B, and C are designed to be used in a tray; D is a syringe material. (Modified from MacPherson GW, Craig RG, Peyton FA. Mechanical properties of hydrocolloid and rubber impression materi-als. J Dent Res. 1967;46(4):714–721.) B A C FIG. 12.7 Surface quality and reproduction using model plaster and dental stone. (A) Model plaster poured against alginate; (B) dental stone poured against the same alginate; and (C) the same dental stone poured against polysulfide. It should be emphasized that another alginate with the same plaster and stone could yield opposite results. (From Craig RG, MacPherson GW. Ann Arbor: University of Michigan School of Dentistry; 1965.) FIG. 12.5 Sketch of tear strength specimen with load applied in the directions of the arrows; the specimen tears at the V-notch. 237 12. Replicating Materials: Impression and Casting or more before preparing the model, it should be rinsed with cool water to remove any exudate on the surface caused by syneresis of the alginate gel; exudate will retard the setting of the gypsum. Thereafter, it should be wrapped loosely in a moist paper towel and sealed in a plastic bag to avoid moisture loss. The set gypsum model should not remain in con-tact with the alginate impression for periods of several hours because contact of the slightly soluble calcium sulfate dihydrate with the alginate gel containing a great deal of water is detrimental to the surface quality of the model. DIMENSIONAL STABILITY Alginate impressions lose water by evaporation and shrink when standing in air. Impressions left on the bench for as short a time as 30 minutes may become inaccurate enough to require remaking the impression. Even if the impression stored for more than 30 minutes in air were immersed in water, it would not be feasible to determine when the cor-rect amount of water had been absorbed, and in any case the previous dimensions would not be repro-duced. For maximum accuracy, the model material should be poured into the alginate impression as soon as possible. If for some reason the models can-not be prepared directly, the impressions should be stored in 100% relative humidity in a plastic bag or wrapped in a damp (but not wringing-wet) paper towel. There is a greater chance for distortion the longer the impression is stored (Fig. 12.8). New alginates have improved long-term storage ranging from 48 to 120 hours when stored in a plastic bag. Now, orthodontists routinely send alginate impres-sions to companies that offer digital fabrication of appliances. DISINFECTION Disinfection of impressions is a concern with respect to viral diseases such as hepatitis B, acquired immu-nodeficiency syndrome, and herpes simplex, because the viruses may be transferred to gypsum models and present a risk to dental laboratory and operating personnel. All alginate impressions should be disinfected before pouring with gypsum to form a cast. The most common form of disinfection is spraying, but studies have shown that alginate impressions can be immersed in disinfectant also. The effect of disinfection in 1% sodium hypochlorite or 2% potentiated glutaraldehyde solutions on accuracy and surface quality has been measured after 10- to 30-minute immersion. Statistically significant dimensional changes were observed; however, the changes were on the order of 0.1% and the qual-ity of the surface was not impaired. Such changes would be insignificant for clinical applications such as the preparation of study models and work-ing casts. In another study, immersion disinfection of alginates demonstrated little effect on accuracy and surface quality, but it was shown that one alginate product was best immersed in iodophor and another brand in glyoxal glutaraldehyde. The effect of disinfection on agar impression materials has not been reported, but considering the similar-ity of the two hydrocolloids, similar recommenda-tions are reasonable. Elastomeric Impression Materials Four types of synthetic elastomeric impression mate-rials are available to record dental impressions: poly-sulfides, condensation silicones, addition silicones (polyvinylsiloxanes), and polyethers. Polysulfides were the first synthetic elastomeric impression mate-rial introduced (1950). Condensation silicones were made available to dentists in 1955, polyether in 1965, and addition silicones in 1975. Polysulfide and con-densation silicone impression materials are described on the website chi/restorative. Polyvinylsiloxanes and polyethers form the vast majority of elastomeric impressions used worldwide today. Changes in recent years have provided greater choice of consistency and new mix-ing techniques. Consistencies Elastomeric impression materials are typically sup-plied in several consistencies (viscosities) to accom-modate a range of impression techniques. Addition silicones are available: extra-low, low (syringe or wash), medium (regular), monophase, high (tray), and putty (extra-high) consistencies. Polyether impression materials are available in low, medium, and high consistencies. Dimensional stability of alginates stored in 100% relative humidity 3.50 3.00 2.50 2.00 1.50 1.00 0.50 0.00 0 24 48 72 100 Time, hours Dimensional change,% ID JL KP FIG. 12.8 Dimensional change of alginate impression materials stored in 100% relative humidity. (Modified from Lu H, Frey GN, Powers JM, unpublished data.) 238 CRAIG’S RESTORATIVE DENTAL MATERIALS Mixing Systems Two types of systems are available to mix the catalyst and base thoroughly before taking the impression: static automixing and dynamic mechanical mixing. A very popular means of mixing the catalyst and base is with a so-called automixing system. The base and catalyst are in separate cylinders of the plastic car-tridge. The cartridge is placed in a mixing gun con-taining two plungers that are advanced by a ratchet mechanism to extrude equal quantities of base and catalyst. The base and catalyst are forced through the static-mixing tip containing a stationary plastic internal spiral; the two components are folded over each other many times as they are pushed through the spiral, resulting in a uniform mix at the tip end. Because one cylinder may be filled slightly more than the other, the first part of the mix from a new cartridge should be discarded. In addition, be sure that the cartridge tips are not occluded before attach-ing the mixing tip. The mixed material can be extruded directly into an injection syringe or into the impression tray. Intraoral delivery tips can be placed on the end of the static mixing tip, and the mixed material can be injected into and around the cavity preparation. The tip can be removed, and additional mixed material can be extruded into the impression tray. The auto-mixing systems have been shown to result in mixes with many fewer voids than hand mixes. Although for each mix the material left in the mixing tip is wasted, the average loss is only 1 to 2 mL, depend-ing on the manufacturer’s tip, whereas three to four times this much is wasted in a hand mix as a result of overestimating the amount needed. Initially, automixing was used for low consistencies, but new designs of guns and mixing tips allow all con-sistencies except putty to be used with this system. Addition silicones and polyethers are available with this means of mixing. The second and newest system is a dynamic, mechanical mixer, illustrated in Fig. 12.9. The cata-lyst and base are supplied in large foil bags housed in a cartridge, which is inserted into the top of the mixing machine. A new, plastic mixing tip is placed on the front of the machine, and when the button is depressed, parallel plungers push against the col-lapsible foil bags, thereby opening the bags and forc-ing material into the dynamic mixing tip. This mixing tip differs from automixing in that the internal spiral is motor driven so it rotates. Thus mixing is accom-plished by this rotation plus forward motion of the material through the spiral. In this manner, thorough mixing can be ensured and higher viscosity mate-rial can be mixed with ease. The advantage of this system is ease of use, speed, and thoroughness of mixing, but more must be invested in the purchase of the system compared with hand and automixing. In addition, there is slightly more material retained in the mixing tip than with automixing, but less than that wasted when mixed by hand. Polyether and addition-silicone impression materials are available for mixing with a dynamic, mechanical mixer. One variation in mixing is with the two-putty addition-silicone systems mixed by hand. Scoops are supplied by the manufacturer for dispensing, and the putties are most often kneaded with fingers until free from streaks. The putty materials that have a liq-uid catalyst are initially mixed with a spatula until the catalyst is reasonably incorporated, and mixing is completed by hand. It should be noted that latex gloves may interfere with setting of addition-silicone impression materials, as discussed later. Impression Techniques Three common methods for making impressions for fixed restorations are a simultaneous, dual-viscosity technique, a single-viscosity or monophase tech-nique, and a putty-wash technique. In nearly all cases, impression material is injected directly on and into the prepared teeth and a tray containing the bulk of the impression material is placed thereafter. After the impression is set, the tray is removed. The simultaneous, dual-viscosity technique is one in which low-consistency material is injected with a syringe into critical areas and the high-consistency material is mixed and placed in an impression tray. After injecting the low-viscosity material, the tray containing the higher-viscosity material is placed in the mouth. In this manner, the more viscous tray impression material forces the lower-viscosity mate-rial to flow into fine aspects of the areas of interest. Because they are both mixed at nearly the same time, the materials join, bond, and set together. After the materials have set, the tray and the impression are removed. An example of an impression using this procedure is shown in Fig. 12.10. In the single-viscosity or monophase technique, impressions are often taken with a medium-viscosity FIG. 12.9 Addition-silicone impression materials pack-aged with automixed cartridges, mixing gun, and static mixing tips, and dynamic mechanical mixer. (Courtesy 3M Company, St. Paul, MN.) 239 12. Replicating Materials: Impression and Casting impression material. Addition-silicone and poly-ether impression materials are well suited for this technique because both have a capacity for shear thinning. As described in Chapter 4, pseudoplastic materials demonstrate a decreased viscosity when subjected to high shear rates such as those occurring during mixing and syringing. When the medium viscosity material is forced through an impres-sion syringe, the viscosity is reduced, whereas the viscosity of the same material residing in the tray is unaffected. In this manner, such materials can be used for syringing and for trays, as previously described for the simultaneous, dual-viscosity technique. The mechanism for shear thinning is discussed in the later section on the viscosity of impression materials. The putty-wash technique is a two-step impression procedure whereby a preliminary impression is taken in high- or putty-consistency material before the cav-ity preparation is made. Space is provided for a low-consistency material by a variety of techniques, and after cavity preparation, a low-consistency material is syringed into the area and the preliminary impression reinserted. The low- and high-consistency materials bond, and after the low-consistency material sets, the impression is removed. This procedure is sometimes called a wash technique. The putty-consistency mate-rial and this technique were developed for condensa-tion silicones to minimize the effects of dimensional change during polymerization. Most of the shrink-age during polymerization takes place in the putty material when the preliminary impression is made, confining final shrinkage to the thin wash portion of the impression. Care must be taken so the wash mate-rial can freely escape via vents in the putty material when the wash impression is made. If not, the wash material can compress the putty in the second-stage impression, inducing permanent distortion and inac-curacies to the impression. The putty-wash technique was extended to addition silicones after their intro-duction, even though their polymerization shrinkage is significantly lower. Manufacturers add coloring agents to the accel-erator or base as an aid in determining the thorough-ness of the mix. Normally a different color is used for each consistency of a particular product line so one can distinguish the wash (low) consistency from the tray consistency in the set impression. Retarders may be added as well to control working and setting time of the products. Some manufacturers have added fla-vors to addition silicones. Composition and Reactions The next two sections describe the general compo-sition and setting reactions of addition-silicone and polyether impression materials. The following sec-tion describes their physical properties, permitting a more direct comparison of the various types and their properties. ADDITION SILICONE Addition silicone (also called polyvinylsiloxane) is available in extra low, low, medium, heavy, and very heavy (putty) consistencies. A representative prod-uct line of addition silicones is shown in Fig. 12.11. The base paste of this class of impression materials contains a moderately low-molecular-weight poly-mer (polymethylhydrosiloxane) with more than three and up to ten pendant or terminal hydrosi-lane groups per molecule [see formulas below and addition-silicone formula 1 (AS1)]. The base also contains filler. Pendant hydrosilane groups O O Si H CH3 Terminal hydrosilane groups O H Si CH3 CH3 FIG. 12.10 An elastomeric addition-silicone impression. Turquoise material is of a low or injection consistency, and maroon material of a high or tray consistency. (Courtesy Dr. Charles Mark Malloy, Portland, OR.) FIG. 12.11 Various consistencies and types of packag-ing of an addition-silicone impression material. (Courtesy Coltene/Whaledent Inc, Cuyahoga Falls, OH.) 240 CRAIG’S RESTORATIVE DENTAL MATERIALS The accelerator (catalyst) and the base paste contain a dimethylsiloxane polymer with vinyl terminal groups, plus filler. The accelerator also contains a platinum catalyst of the so-called Karstedt type, which is a complex compound consisting of platinum and 1,3-divinyltetramethyldisiloxane. Unlike the condensation type, the addition reaction does not normally produce a low-molecular-weight by-product, as indicated in the reaction shown below (AS2). Platinum Catalyst Si O H CH3 CH2 CH3 Si CH3 O H Si CH3 O H Si CH3 CH Si O CH3 CH2 CH3 CH Platinum Catalyst Platinum Catalyst Si O CH3 CH2 CH3 CH Si O CH3 CH2 CH2 CH3 Si CH3 O Si CH3 O Si CH3 Si O CH3 CH2 CH2 CH3 Si O CH3 CH2 CH2 CH3 AS2 Platinum Catalyst Si O O CH3 Si OH CH3 H2 O O O H Si CH3 O H H H O Si O O CH3 H2 CH3 Si O O Si O O CH3 H Platinum Catalyst AS3 Polymethylhydrosiloxane Si O O CH3 CH3 CH3 Si CH3 CH3 Si CH3 CH3 CH3 Si CH3 H x y Vinylpolysiloxane AS1 Si O CH3 CH3 CH CH CH2 CH2 Si CH3 CH3 n 241 12. Replicating Materials: Impression and Casting A secondary reaction can occur, however, with the production of hydrogen gas if –OH groups are present. The most important source of –OH groups is water (H–OH), the reaction of which under con-sumption of Si–H units is illustrated above (AS3). Another possible source of hydrogen gas is a side reaction of the Si–H units of the polymethylhydro-siloxane with each other, under the influence of the platinum catalyst, also shown above (AS3). Not all addition-silicone impression materials release hydrogen gas, and because it is not known which do, it is recommended that one wait at least 30 minutes for the setting reaction to be completed before the gypsum models and dies are poured. Epoxy dies should not be poured until the impres-sion has stood overnight. The difference in the delay with gypsum and epoxy is that gypsum products have much shorter setting times than epoxy die mate-rials. Some products contain a hydrogen absorber such as palladium, and gypsum and epoxy die mate-rials can be poured against them as soon as practi-cal. Examples of high-strength stone poured after 15 minutes against addition silicone, with and without a hydrogen absorber, are shown in Fig. 12.12. Latex gloves have been shown to adversely affect the setting of addition-silicone impressions. Sulfur compounds that are used in the vulcanization of latex rubber gloves can migrate to the surface of stored gloves. These compounds can be transferred onto the prepared teeth and adjacent soft tissues dur-ing tooth preparation and when placing tissue retrac-tion cord. They can also be incorporated directly into the impression material when mixing two putties by hand. These compounds can poison the platinum-containing catalyst, which results in retarded or no polymerization in the contaminated area of the impression. Thorough washing of the gloves with detergent and water just before mixing sometimes minimizes this effect, and some brands of gloves interfere with the setting more than others. Vinyl and nitrile gloves do not have such an effect. Residual monomer in acrylic provisional restorations and resin composite cores has a similar inhibiting effect on the set of addition-silicone materials. The prepa-ration and adjacent soft tissues can also be cleaned with 2% chlorhexidine to remove contaminants. POLYETHER Polyethers are supplied in low-, medium-, and heavy-body consistency. The base paste consists of a long-chain polyether copolymer with alternating oxygen atoms and methylene groups (O–[CH2]n) and reactive terminal groups [see polyether 1 (PE1)]. Also incorporated are a silica filler, compatible plasticiz-ers of a nonphthalate type, and triglycerides. In the catalyst paste, the former 2,5-dichlorobenzene sulfo-nate was replaced by an aliphatic cationic starter as a cross-linking agent. The catalyst also includes silica filler and plasticizers. Coloring agents are added to base and catalyst to aid in the recognition of different material types. Examples of polyether impression materials are shown in Fig. 12.9. The reaction mechanism is shown (PE2) in a sim-plified form. The elastomer is formed by cationic polymerization by opening of the reactive terminal rings. The backbone of the polymer is believed to be a copolymer of ethylene oxide and tetramethylene oxide units. The reactive terminal rings open under the influence of the cationic initiator of the catalyst paste and can then, as a cation itself, attack and open additional rings. Whenever a ring is opened, the cat-ion function remains attached, thus lengthening the chain (see PE3). Because of the identical chemical base, all polyether consistencies can be freely com-bined with each other. A chemical bond between all materials develops during curing. A B FIG. 12.12 Addition-silicone impressions poured in high-strength stone at 15 minutes. (A) Bubbles are caused by the release of hydrogen. (B) No bubbles are apparent because palladium hydrogen absorber is included in the impression material. 242 CRAIG’S RESTORATIVE DENTAL MATERIALS CH R' O O R CH3 CH R" CH R' R (CH2)n R" HC CH3 O (CH2)n m PE1 Cationic Starter R Reactive terminal ring PE2 Copolymer Copolymer Copolymer Copolymer PE3 Setting Properties Typical values of the setting properties of elastomeric impression materials are presented in Table 12.3. The temperature rise in typical mixes of impression materials was pointed out in the previous section, but Table 12.3 illustrates that the temperature rise is small and of no clinical concern. VISCOSITY The viscosity of materials 45 seconds after mixing is listed in Table 12.3. As expected, the viscosity increases for the same type of material from low to high consistencies. Viscosity is a function of time after the start of mixing. A shearing force can affect the viscosity of poly-ether and addition-silicone impression materials, as was mentioned in the section on impression tech-niques. This effect is called shear thinning or pseu-doplasticity. For impression materials possessing this characteristic, the viscosity of the unset mate-rial diminishes with an increasing outside force or shearing speed. When the influence is discontinued, the viscosity immediately increases. This property is very important for the use of monophase impression materials, and is illustrated for polyether in Fig. 12.13. In the case of polyether, shear-thinning properties are influenced by a weak network of triglyceride crys-tals. The crystals align when the impression material is sheared, as occurs when mixed or flowing through a syringe tip. The microcrystalline triglyceride net-work ensures that the polyether remains viscous in the tray or on the tooth but flows under pressure. This allows a single or monophase material to be used as a low- and medium-consistency material. Cooling of the pastes results in substantial viscosity increase. Before using, pastes have to be brought to room temperature. The effect of shear rate (rotational speed of the viscometer) on the viscosity of single-consistency (monophase) addition silicones is shown in Fig. 12.14. Although all products showed a decrease in viscosity with increasing shear rate, the effect was much more 243 12. Replicating Materials: Impression and Casting TABLE 12.3 Setting Properties of Elastomeric Impression Materials Material Consistency Temperature Rise (°C) Viscosity 45 s after Mixing (cp) Working Time (min) Setting Time (min) Dimensional Change at 24 h (%) POLYSULFIDES Low 3.4 60,000 4–7 7–10 −0.40 Medium 110,000 3–6 6–8 −0.45 High 450,000 3–6 6–8 −0.44 SILICONES Condensation Low 1.1 70,000 2.5–4 6–8 −0.60 Very high 2–2.5 3–6 −0.38 Addition Low 2–4 4–6.5 −0.15 Medium 150,000 2–4 4–6.5 −0.17 High 2.5–4 4–6.5 −0.15 Very high 1–4 3–5 −0.14 POLYETHERS Low 4.2 3 6 −0.23 Medium 130,000 2.5–3 6 −0.24 High 2.5 5.5 −0.19 B A C FIG. 12.13 Demonstration of the mechanism for the property of shear thinning or pseudoplasticity in polyethers. The trigliceride network (A) within the impression material aligns when sheared as with syringing, and (B) to achieve a lower viscosity. Once the shear force is removed, the viscosity increases with randomization of the triglyceride network (C). pronounced for two products, Ba and Hy, with about an eightfold to eleven-fold decrease from the lowest to the highest shear rate. The substantial decrease in viscosity at high shear stress, which is comparable with the decrease during syringing, permits the use of a single mix of material, with a portion to be used as syringe material and another portion to be used as tray material in the syringe-tray technique. WORKING AND SETTING TIMES The working and setting times of addition-silicone and polyether impression materials are listed in Table 12.3. In general, for a given class of elastomeric impression materials by a specific manufacturer, the working and setting times decrease as the viscos-ity increases from low to high. Polyethers show a clearly defined working time with a sharp transition 244 CRAIG’S RESTORATIVE DENTAL MATERIALS into the setting phase. This behavior is often called snap-set. This transition from plastic condition into elastic properties is rather short compared with older addition silicones, which was shown in inves-tigations of rheological properties of setting materi-als (Fig. 12.15). Note that the working and setting times of the elastomeric impression materials are shortened by increases in temperature and humidity; on hot, humid days this effect should be considered in the clinical application of these materials. The initial (or working) and final setting times can be determined fairly accurately by using a pen-etrometer with a needle and weight selected to suit these materials. The Vicat penetrometer, as shown in Fig. 12.16, with a 3-mm diameter needle and a total weight of 300 g, has been used by a number of investigators. A metal ring, 8 mm high and 16 mm in diameter, is filled with freshly mixed material and placed on the penetrometer base. The needle is applied to the surface of the impression material for 10 seconds, and a reading is taken. This is repeated every 30 seconds. The initial set is that time at which the needle no longer completely penetrates the speci-men to the bottom of the ring. The final set is the time of the first of three identical nonmaximum penetra-tion readings. When the material has set, the elastic-ity still allows penetration of the needle, but it is the same at each application. DIMENSIONAL CHANGE ON SETTING The impression material undergoes a dimensional change on setting. The major factor for contrac-tion during setting is cross-linking and rearrange-ment of bonds within and between polymer chains. FIG. 12.16 Vicat penetrometer used to determine set-ting time of impression materials and other restorative materials. 0.0 2.0 Gr Im Hy Ba Om 4.0 6.0 8.0 10.0 Rotational speed (rpm) 0 100 Viscosity ( 104 cp) 200 300 FIG. 12.14 Viscosity in centipoise as a function of shear rate (rotational speed of the viscometer) for five single-consistency addition-silicone impression materials. A rotational speed of 0.5 rpm would represent a shear rate comparable with that observed when placing the material in a tray, and a speed of 10 rpm would represent a shear rate comparable with that experienced when syringing the mate-rial. (Data from Kim KN, Craig RG, Koran A 3rd. Viscosity of monophase addition silicones as a function of shear rate. J Prosthet Dent. 1992;67(6):794–798.) 6 3 (working time) Weak network Viscosity (arb. units) (setting time) Time (min) Strong network Strong network: polymerization of the polyether copolymer chains Weak network: Interaction of glycerides, crystallization effects Strong network: polymerization of the polyether copolymer chains Weak network: Interaction of glycerides, crystallization effects FIG. 12.15 Illustration of the snap-set of polyether. The initial viscosity of the unset material is influenced by the structural triglycerides, whereas the polymerization of copo-lymer chains thereafter provides the quick increase in viscos-ity as the material sets. 245 12. Replicating Materials: Impression and Casting Impressions can expand if water sorption takes place and an impression can be distorted if seated after the material has set to any degree. Finally, distortion or creep will occur if the material does not recover elastically when the set impression is removed from undercuts. Imbibition is discussed in the section on disinfecting impressions, and creep-induced distor-tion is discussed under elastic recovery. Addition-silicone and polyether impression materi-als undergo shrinkage due to polymerization. The linear dimensional change between a die and the impression after 24 hours is listed in Table 12.3. The addition sili-cones have the smallest change, about −0.15%, followed by the polyethers at about −0.2%. The contraction is low for these two products because there is no loss of by-products. The rate of shrinkage of elastomeric impression materials is not uniform during the 24 hours after removal from the mouth. In general, about half the shrinkage observed at 24 hours occurs during the first hour after removal; for greatest accuracy, therefore, the models and dies should be prepared promptly, although in air the elastomeric impression materials are much more stable than hydrocolloid products. Mechanical Properties Typical mechanical properties of elastomeric impres-sion materials are listed in Table 12.4. The permanent deformation (in the current specification, elastic recovery, which is 100% minus the permanent defor-mation), strain in compression, and dimensional change are properties used in ANSI/ADA specifica-tion No. 19 (ISO 4823) to classify elastomeric impres-sion materials as low, medium, high, or very high viscosity types. The requirements for these proper-ties are given in Table 12.5. Further requirements of the specification for elastomeric impression mate-rials are indicated in Table 12.6. The consistency diameter is used to classify viscosity by measuring the diameter of the disk formed when 0.5 mL of mixed material is subjected to a 5.6-N weight at 1.5 minutes after mixing for 12 minutes. Because the setting times of elastomeric impression materials vary, the consistency diameter is affected not only by the viscosity but also by the setting time. The classification of a material by the consistency diam-eter may be different from that by a true viscosity measurement. ELASTIC RECOVERY The order in which the permanent deformation of the elastomeric impression materials is listed in Table 12.4 demonstrates that addition silicones have the best elastic recovery during removal from the mouth, followed by polyethers. A material with a permanent deformation of 1% has an elastic recovery of 99%. TABLE 12.4 Mechanical Properties of Elastomeric Impression Materials Material Consistency Permanent Deformationa (%) Strain in Compression (%) Flow (%) Shore A Hardness Tear Strength (kN/m) POLYSULFIDES Low 3–4 14–17 0.5–2 20 2.5–7.0 Medium 3–5 11–15 0.5–1 30 3.0–7.0 High 3–6 9–12 0.5–1 35 — SILICONES Condensation Low 1–2 4–9 0.05–0.1 15–30 2.3–2.6 Very high 2–3 2–5 0.02–0.05 50–65 — Addition Low 0.05–0.4 3–6 0.01–0.03 35–55 1.5–3.0 Medium 0.05–0.3 2–5 0.01–0.03 50–60 2.2–3.5 High 0.1–0.3 2–3 0.01–0.03 60–70 2.5–4.3 Very high 0.2–0.5 1–2 0.01–0.1 50–75 — POLYETHERS Low 1.5 3 0.03 35–40 1.8 Medium 1–2 2–3 0.02 40–60 2.8–4.8 High 2 3 0.02 40–50 3.0 aElastic recovery from deformation is 100% minus the percent permanent deformation. 246 CRAIG’S RESTORATIVE DENTAL MATERIALS STRAIN IN COMPRESSION The strain in compression under a stress of 0.1 MPa is a measure of the flexibility of the material. Table 12.4 illustrates that, in general, the low-consistency mate-rials of each type are more flexible than the high-consistency elastomeric impressions. For a given consistency, polyethers are generally the stiffest, fol-lowed by addition silicones. FLOW Flow is measured on a cylindrical specimen 1 hour old, and the percent flow is determined 15 minutes after a load of 1 N is applied. As seen in Table 12.4, silicones and polyethers have low values of flow. Typical elastomeric impression materials appar-ently have no difficulty meeting the mechanical property requirements of ANSI/ADA specification No. 19 (see Table 12.6). Although the flow, hard-ness, and the tear strengths of elastomeric impres-sion materials are not mentioned in the specification, these are important properties; they are also listed in Table 12.4. HARDNESS The Shore A hardness increases from low to high con-sistency. When two numbers are given, the first rep-resents the hardness 1.5 minutes after removal from the mouth, and the second number is the hardness after 2 hours. The low-, medium-, and high-viscosity addition silicones do not change hardness signifi-cantly with time, whereas the hardness of polyethers does increase with time. In addition, the hardness and strain in compression affect the force necessary to remove the impression from the mouth. Low flex-ibility and high hardness can be compensated for clinically by providing more space for the impression material between the tray and the teeth. This can be accomplished with additional block-out for custom trays or by selecting a larger tray when using dispos-able trays. A new variation in polyether provides less resis-tance to deformation during removal of the impres-sion from the mouth and the gypsum cast from the impression. To achieve this, the filler content was reduced from 14 to 6 parts per unit, thereby reduc-ing the Shore A hardness from 46 to 40 after 15 min-utes, and from 61 to 50 after 24 hours. The ratio of high-viscous softener to low-viscous softener was changed to achieve a consistency similar to that of the conventional monophase polyether. TEAR STRENGTH Tear strength is important because it indicates the abil-ity of a material to withstand tearing in thin interproxi-mal areas and margins of periodontally involved teeth. The tear strengths listed in Table 12.4 are a measure TABLE 12.5 Elastic Recovery, Strain in Compression, and Dimensional Change Requirements for Elastomeric Impression Materials Viscosity Type Minimum Elastic Recovery (%) Strain in Compression (%) Minimum Maximum Maximum Dimensional Change in 24 h (%) Low 96.5 2.0 20 1.5 Medium 96.5 2.0 20 1.5 High 96.5 0.8 20 1.5 Very high 96.5 0.8 20 1.5 TABLE 12.6 Requirements by ANSI/ADA Specification No. 19 (ISO 4823) for the Various Viscosities of Elastomeric Impression Materials Viscosity Maximum Mixing Time (min) Minimum Working Time (min) Diameter of Consistency Disk (mm) Reproduction of Detail Minimum Maximum Line Width in Impression (mm) Line Width in Gypsum (mm) Low 1 2 36 — 0.020 0.020 Medium 1 2 31 41 0.020 0.020 High 1 2 — 35 0.050 0.050 Very High 1 2 — 35 0.075 0.075 ADA, American Dental Association; ANSI, American National Standards Institute; ISO, International Organization for Standardization. 247 12. Replicating Materials: Impression and Casting of the force needed to initiate and continue tearing a specimen of unit thickness. As the consistency of the impression type increases, tear strength undergoes a small increase, but most of the values are between 2.0 and 3.9 kN/m. Values for very high consistency types are not listed because this property is not important for these materials. Higher tear strengths for elastomeric impression materials are desirable, but compared with the values for hydrocolloid impression materials of 0.3 to 0.7 kN/m, they are a major improvement. CREEP COMPLIANCE Elastomeric impression materials are viscoelastic, and their mechanical properties are time dependent. For example, the higher the rate of deformation, the higher the tear strength; and the longer the impres-sions are deformed, the higher the permanent defor-mation. As a result, plots of creep compliance versus time describe the properties of these materials bet-ter than stress-strain curves. Creep-compliance time curves for low-consistency polysulfide, condensation silicone, addition silicone, and medium-consistency polyether are shown in Fig. 12.17. The initial creep compliance illustrates polysulfide is the most flexible and polyether is the least flexible. The flatness or par-allelism of the curves with respect to the time axis indicates low permanent deformation and excellent recovery from deformation during the removal of an impression material; addition silicones and poly-ethers have the best elastic recovery. The recoverable viscoelastic quality of the materi-als is indicated by differences between the initial creep compliance and the creep compliance value obtained by extrapolation of the linear portion of the curve to zero time. As a result, addition silicones have the low-est viscoelastic quality and require less time to recover viscoelastic deformation, followed by the polyethers. DETAIL REPRODUCTION The requirements of elastomeric impression materi-als are listed in Table 12.6. Except for the very high-viscosity products, all should reproduce a V-shaped groove and a 0.02-mm wide line in the elastomeric. The impression should be compatible with gypsum products so the 0.02-mm line is transferred to gyp-sum die materials. Low-, medium-, and high-vis-cosity elastomeric impression materials have little difficulty meeting this requirement. Wettability of Elastomeric Impression Materials Wettability may be assessed by measuring the advanc-ing contact angle of water on the surface of the set impression material or by using a tensiometer to mea-sure forces as the material is immersed and removed (Wilhelmy technique). The advancing contact angles for elastomeric impression materials are listed in Table 12.7. Of all the impression materials discussed in this chapter, only alginates can be considered truly hydro-philic. All of the elastomeric impression materials pos-sess advancing and receding contact angles greater than 45 degrees. There are, however, differences in wetting among and within types of elastomeric impression materials. Traditional addition silicone is not as wettable as polyether. When mixes of gyp-sum products are poured into hydrophobic addition silicone, high contact angles are formed, making the preparation of bubble-free models difficult. Surfactants have been added to addition sili-cones by manufacturers to reduce the contact angle, 3.5 3.0 2.5 2.0 1.5 1.0 Creep compliance, Jt (MPa1) 0.6 0 0.2 0.4 0.8 1 2 3 5 7 6 8 9 11 10 12 4 Time (min) FIG. 12.17 Creep compliance of elastomeric impres-sion materials at the time recommended for removal from the mouth. Curves from top to bottom: polysulfide, con-densation silicone, addition silicone, and polyether. (Data from Tolley LG, Craig RG. Viscoelastic properties of elastomeric impression materials: polysulphide, silicone and polyether rub-bers. J Oral Rehabil. 1978;5:121–128.) TABLE 12.7 Wettability of Elastomeric Impression Materials Material Advancing Contact Angle of Water (degrees) Castability of High-Strength Dental Stone (%) Polysulfide 82 44 Condensation silicone 98 30 Addition silicone Hydrophobic 98 30 Hydrophilic 53 72 Polyether 49 70 248 CRAIG’S RESTORATIVE DENTAL MATERIALS improve wettability, and simplify the pouring of gypsum models. This class with improved wetting characteristics is most accurately called hydrophilized addition silicone. Most commonly, nonionic surfactants have gained importance in this area. These molecules consist of an oligoether or polyether substructure as the hydrophilic part and a silicone-compatible hydrophobic part (Fig. 12.18A). The mode of action of these wetting agents is believed to be a diffusion-controlled transfer of surfactant molecules from the polyvinylsiloxane into the aqueous phase, as shown, thereby altering the surface tension of the surround-ing liquid. As a result, a reduction in surface tension and therefore greater wettability of the polyvinyl-siloxane is observed (Fig. 12.18B). This mechanism differs from polyethers, which possess a high degree of wettability because their molecular structure con-tains polar oxygen atoms, which have an affinity for water. Because of this affinity, polyether materials flow onto hydrated intraoral surfaces and are there-fore cast with gypsum more easily than are addition silicones. This affinity also allows polyether impres-sions to adhere quite strongly to soft and hard tissues. By observing water droplets on impression sur-faces, it has been shown that hydrophilized addition silicones and polyethers are wetted the best, and con-densation silicones and conventional addition silicones the least. Wettability was directly correlated to the ease of pouring high-strength stone models of an extremely critical die, as shown in Table 12.7. Using a tensiometer to record forces of immersed impression specimens (Wilhelmy method), polyether was shown to wet sig-nificantly better than hydrophilized addition silicones for both advancing (74 degrees vs. 108 degrees) and receding contact angles (50 degrees vs. 81 degrees). To evaluate the ability of impression materials to reproduce detail under wet and dry surface condi-tions, impressions were made of a standard wave pattern used to calibrate surface analyzers. The surfaces of impressions were scanned for average roughness (Ra) after setting to determine their abil-ity to reproduce the detail of the standard, the value of which is shown with a double line in Fig. 12.19. From a clinical standpoint, most impression mate-rials produced acceptable detail under wet and dry conditions. Polyethers produced slightly better detail than did addition silicones, and were generally unaf-fected by the presence of moisture, whereas detail decreased for some addition silicones under wet con-ditions, even if hydrophilized. Disinfection of Elastomeric Impressions All impressions should be disinfected upon removal from the mouth to prevent transmission of organisms Water PVS Water Air PVS Advancing droplet B Lens Micelle Hydrophilic Lipophilic Surfactant PVS Water Micelle A FIG. 12.18 Hydrophilization of addition silicones. (A) The hydrophilization of addition silicones is gained with the incor-poration of nonionic surfactants shown as micelles. These molecules consist of a hydrophilic part and a silicone-compatible hydrophobic part. The mode of action of these surfactants is thought to be a diffusion-controlled transfer of surfactant mol-ecules from the polyvinylsiloxane into the aqueous phase, as shown. In this manner, the surface tension of the surrounding liquid is altered. (B) This increased wettability allows the addition silicone to spread more freely along the surface. PVS, Polyvinylsiloxane. 249 12. Replicating Materials: Impression and Casting to gypsum casts and to laboratory personnel. Several studies confirm that addition-silicone and polyether impressions can be disinfected by immersion in sev-eral different disinfectants for up to 18 hours without a loss of surface quality and accuracy. Relationship of Properties and Clinical Application Accuracy, the ability to record detail, ease of han-dling, and setting characteristics are of prime impor-tance in dental impressions. Silicones generally have shorter working times than polysulfides but somewhat longer times than polyethers. Single-mix materials have some advantage in that, as a result of shear thinning, they have low viscosities when mixed or syringed but higher viscosities when inserted in a tray. The time of placement of an elastomeric impression material is critical, because viscosity increases rapidly with time as a result of the polymeriza-tion reaction. If the material is placed in the mouth after the consistency or viscosity has increased via polymerization, internal stresses induced in the impression are released after the impression is removed from the mouth, resulting in an inaccu-rate impression. Thorough mixing is essential; otherwise portions of the mix could contain insufficient accelerator to polymerize thoroughly or may not set at the same rate as other portions of the impression. In this event, removal of the impression would cause less elastic recovery and result in an inaccurate impression. Automixing and mechanical mixing systems pro-duce mixes with fewer bubbles than hand mixing, save time in mixing, and result in a more bubble-free impression. Polymerization of elastomeric impression mate-rials continues after the material has set, and the mechanical properties improve with time. Removal too early may result in high permanent deformation; however, excessively long times in the mouth are unacceptable to the patient. The manufacturer usu-ally recommends a minimum time for leaving the impression in the mouth, and this minimum is used for testing the materials according to ANSI/ADA specification No. 19. Dimensional changes on setting can be compen-sated for by use of a double-impression or putty-wash technique. When using a double-impression tech-nique, a preliminary impression is taken in the high- or puttylike-consistency material, providing some space for the final impression in a low-consistency material. The preliminary impression is removed, the cavity prepared, and the final impression taken with the low-consistency material, using the prelim-inary impression as a tray. In this way, the dimen-sional change in the high consistency or puttylike consistency is negligible, and although the percent dimensional change of the low-consistency material is still large, the thickness is so small that the actual dimensional change is small. The double-impression technique is suitable for use with a stock impression tray, because the preliminary impression serves as a custom tray. With the monophase and simultaneous dual-viscosity technique, a slight improvement in accuracy results when a custom-made tray is used because it provides a uniform thickness of impres-sion material. Several studies have shown, however, that relatively stiff stock plastic or metal trays yield nearly the same accuracy. Clinical studies have shown that the viscosity of the impression material is the most important fac-tor in producing impressions and dies with mini-mal bubbles and maximum detail. As a result, the syringe-tray technique produced superior clinical results in the reproduction of fine internal detail of proximal boxes or grooves. The accuracy of the impression may be affected when the percentage of deformation and the time involved in removing the impression are increased. In both instances, permanent deformation increases, the amount depending on the type of elastomeric impression material. Because elastomeric impressions recover from deformation for a period after their removal, some increase in accuracy can be expected during this time. However, polymerization shrinkage is also occurring, and the overall accuracy is determined by a combination of these two effects. Insignificant elastic recovery occurs after 20 to 30 minutes; there-fore dies should be prepared promptly after that time for greatest accuracy. Addition silicones that release hydrogen are an exception to this guideline. Polyether Addition silicone Standard Ra (µm) 0 0.5 1 1.5 2 3 2.5 Dry Wet FIG. 12.19 Ability of polyether and hydrophilized addition-silicone materials to reproduce detail under dry and wet conditions. The average roughness, Ra, of the standard from which impressions were made is shown (double line). Polyethers produced the best detail and were unaffected by moisture. The detail captured by addition silicones decreased slightly in the presence of moisture. (Data from Johnson GH, Lepe X, Berg JC. Effect of moisture on the quality of crown and bridge impressions. J Dent Res. 1998;77(Spec Issue B);798.) 250 CRAIG’S RESTORATIVE DENTAL MATERIALS Second pours of gypsum products into addition-silicone impressions produce dies that are not quite as accurate as the first, because the impression can be deformed during the removal of the first die; how-ever, they are usually sufficiently accurate to be used as a working die. OCCLUSAL REGISTRATION MATERIALS Addition silicones and polyethers have been formu-lated for use as occlusal registration materials. Most of the products are addition silicones and most are supplied in automix cartridges. Properties of these occlusal registration materials are listed in Table 12.8. These materials are characterized by short working times and the length of time left in the mouth com-pared with typical elastomeric impression materials. They are also noted for their high stiffness, indicated by the low percent strain in compression, and for their low flow and dimensional change even after 7 days. The property that distinguishes addition silicones from polyethers is their lower dimensional change after removal; however, either is superior to the stability of waxes for making occlusal records. IMPRESSION TRAYS Custom impression trays provide a nearly constant distance between the tray and the tissues, allowing a more even distribution of the impression material during the impression procedure, and improved accuracy. Light-activated and vacuum-formed poly-mers are now used more frequently than chemically accelerated acrylic to produce custom impression trays because of the volatility of the acrylic monomer and sensitivity to the monomer reported by dental staff. Vacuum-formed polystyrene is popular with commercial laboratories because the trays can be made rapidly. These trays must be handled carefully because they are more flexible than acrylic trays and can be deformed easily by the application of heat. Prefabricated impression trays are very popular. These stock trays vary considerably between manu-facturers. When a stock tray is chosen, care must be taken to ensure that the tray is well adapted to the tissues and is adequately reinforced to prevent flexing during impression fabrication and removal. All trays require the use of a tray adhesive, which must be allowed to dry before placing the impression material in the tray. Light-activated tray materials have many advan-tages over chemically accelerated acrylic. They are similar to light-activated denture base materials but are of a different color. The trays are strong, easy to make, contain no methyl methacrylate, and have negligible polymerization shrinkage in the light chamber. They can be used soon after processing because there is no clinically significant dimensional change after polymerization. DIE, CAST, AND MODEL MATERIALS Dental stones, plaster, epoxy resin, and refractory materials are some of the materials used to make casts or dies from dental impressions. The selec-tion of one of these is determined by the particular impression material in use and by the purpose for which the die or cast is to be used. Impressions in alginate hydrocolloid can be used only with a gypsum material, such as plaster, stone, or casting investment. Various elastomeric impres-sion materials can be used to prepare gypsum or epoxy dies. Impression materials can also be digitally scanned to produce printed plastic casts or dies (see Chapter 14). Desirable Qualities of a Cast or Die Material Cast and die materials must reproduce an impres-sion accurately and remain dimensionally stable under normal conditions of use and storage. Setting expansion, contraction, and dimensional variations in response to changes in temperature must be held to a minimum. Not only should the cast be accu-rate, but it should also satisfactorily reproduce fine detail and have a smooth, hard surface. Such an TABLE 12.8 Properties of Elastomeric Impression Materials Used for Occlusal Registrations Material Mixing Type Working Time (min) Time in Mouth (min) Strain in Compression (%) Dimensional Change Flow (%) 1 Day (%) 7 Days (%) Addition silicone Automix 0.5–3.0 1.0–3.0 1.0–2.9 0.0–0.01 0.0 to −0.15 −0.04 to −0.20 Addition silicone Hand mix 1.4 2.5 0.92 0.0 −0.06 −0.08 Polyether Hand mix 2.1 3.0 1.97 0.0 −0.29 −0.32 251 12. Replicating Materials: Impression and Casting accurate cast or die must also be strong and durable and withstand the subsequent manipulative proce-dures without fracture or abrasion of the surface. Qualities of strength, resistance to shearing forces or edge strength, and abrasion resistance are there-fore important and are required in varying degrees, according to the purpose for which the cast or die is to be used. For example, because it will not be subjected to much stress in use, a satisfactory study cast might be formed from dental model plaster in which the aforementioned qualities are at a mini-mum. However, an elastomeric impression used to produce an indirect inlay could be poured in high-strength stone or epoxy, thereby producing a die in which these qualities are sufficient to withstand the carving and finishing procedures that are a part of this technique. The color of a cast or die can facilitate manipu-lative procedures, such as waxing inlay patterns, by presenting a contrast in color to the inlay wax. The ease with which the material can be adapted to the impression and the time required before the cast or die is ready for use are of considerable practical significance. Dental Plaster and Stone The chemistry and physical properties of dental plas-ter, stone, and high-strength stone are discussed later in this chapter. Gypsum materials are used exten-sively to make casts and dies from dental impres-sions and can be used with any impression material. Stone casts, which are stronger and resist abrasion better than plaster casts, are used whenever a resto-ration or appliance is to be made on the cast. Plaster may be used for study casts, which are for record purposes only. Hardening solutions, usually about 30% silica sols in water, are mixed with stone. The increase in hardness of stone dies poured against impressions varies from 2% for silicones to 110% for polyether. The dimensional change on setting of stones mixed with hardener is slightly greater than when mixes are made with water, 0.07% versus 0.05%. In most instances the abrasion or scraping resistance of mixes of stone made with hardening solutions is higher than comparable mixes made with water. A range of effects in the abrasion resistance of surface treatments of stone has been reported. Model and die sprays gener-ally increase the resistance to scraping, whereas lubri-cants can decrease surface hardness and resistance to scraping. High-strength dental stones make excellent casts or dies, readily reproduce the fine detail of a den-tal impression, and are ready for use after approxi-mately 1 hour. The resulting cast is dimensionally stable over long periods and withstands most of the manipulative procedures involved in the production of appliances and restorations. When wax patterns constructed on high-strength stone dies are to be removed, some separating agent or die lubricant is necessary to prevent the wax from adhering. The lubricant is applied liberally to the high-strength stone die and allowed to soak in; usually several applications can be made before any excess accumulates on the surface. The excess is blown off with an air blast before proceeding to make the wax pattern. Epoxy Die Materials Until recently, epoxy materials were supplied in the form of a paste to which a liquid activator (amine) was added to initiate hardening. Because the acti-vators are toxic, they should not come into contact with the skin during mixing and manipulation of the unset material. Shrinkage of 0.1% has occurred during hardening, which may take up to 24 hours. The hardened resin is more resistant to abrasion and stronger than a high-strength stone die. The viscous paste is not as readily introduced into the details of a large impression as high-strength dental stone is; a centrifugal casting machine has been developed to assist in the pouring of epoxy resins. Fast-setting epoxy materials have been supplied in automixing systems similar to those described for automixing addition silicones. The epoxy resin is in one cartridge, and the catalyst in the other. Forcing the two pastes through the static mixing tip thoroughly mixes the epoxy material, which can be directly injected into a rubber impression. A small intraoral delivery tip may be attached to the static mixing tip if desired for injecting into detailed areas of the impression. The fast-setting epoxy hardens rapidly, so dies can be waxed 30 minutes after injecting into the impression. Because water retards the polymerization of resin, epoxy resins cannot be used with water-containing agar and alginate impression materials, and thus are limited to use with elastomeric impression materials. Comparison of Impression and Die Materials High-strength stone dies may be from 0.35% larger to 0.25% smaller than the master, depending on the location of the measurement and the impression material used. In general, occlusogingival (vertical) changes are greater than buccolingual or mesiodistal (horizontal) changes. The shrinkage of the impression material toward the surfaces of the tray in the hori-zontal direction usually results in dimensions larger than the master. In the vertical direction, shrinkage is away from the free surface of the impression and toward the tray, and dimensions smaller than the master are obtained. 252 CRAIG’S RESTORATIVE DENTAL MATERIALS The accuracy of elastomeric impression materials is in the following order from best to worst, regard-less of whether stone or metal dies are used: addition silicone and polyether. Epoxy dies all exhibit some polymerization shrink-age, with values ranging from 0.1% to 0.3%, and as a result the dies are undersized. Ranking materials by the ability of an impression- die combination to reproduce surface detail pro-duces different results than does ranking by values for dimensional change. If a release agent is not needed on the surface of the impression, epoxy dies are best for reproducing detail (10 μm), followed by high-strength stone dies (170 μm). The silicone-epoxy combination produces the sharpest detail, although not all epoxy die materials are compatible with all silicone impression materials. Resistance to abrasion and scraping should also be considered. Epoxy dies have good resistance and high-strength stone dies have the least resistance. GYPSUM PRODUCTS Gypsum products probably serve the dental pro-fession more adequately than any other materials. Dental plaster, stone, high-strength/high-expansion stone, and casting investment constitute this group of closely related products. With slight modifica-tion, gypsum products are used for several different purposes. For example, impression plaster is used to make impressions of edentulous mouths or to mount casts, whereas dental stone is used to form a die that duplicates the oral anatomy when poured into any type of impression. Gypsum products are also used as a binder for silica in gold alloy casting investment, sol-dering investment, and investment for low- melting-point nickel-chromium alloys. These products are also used as a mold material for processing complete dentures. The main reason for such diversified use is that the properties of gypsum materials can be easily modified by physical and chemical means. The dihydrate form of calcium sulfate, called gyp-sum, usually appears white to milky yellowish and is found in a compact mass in nature. The mineral gypsum has commercial importance as a source of plaster of Paris. The term plaster of Paris was given this product because it was obtained by burning the gypsum from deposits near Paris, France. Deposits of gypsum, however, are found in most countries. Chemical and Physical Nature of Gypsum Products Most gypsum products are obtained from natural gypsum rock. Because gypsum is the dihydrate form of calcium sulfate (CaSO4·2H2O), on heating, it loses 1.5 g mol of its 2 g mol of H2O and is converted to calcium sulfate hemihydrate (CaSO4·½H2O), some-times written (CaSO4)2·H2O. When calcium sulfate hemihydrate is mixed with water, the reverse reac-tion takes place, and the calcium sulfate hemihy-drate is converted back to calcium sulfate dihydrate. Therefore partial dehydration of gypsum rock and rehydration of calcium sulfate hemihydrate consti-tute a reversible reaction. Chemically, the reaction is expressed as follows: CaSO4 · H2O + 1½ ½ H2O → CaSO4 · 2H2O + 3900 cal/g mol Gypsum Water Plaster of Paris The reaction is exothermic, and whenever 1 g mol of calcium sulfate hemihydrate is reacted with 1.5 g mol of water, 1 g mol of calcium sulfate dihydrate is formed, and 3900 calories of heat are developed. This chemical reaction takes place regardless of whether the gypsum material is used as an impres-sion material, a die material, or a binder in casting investment. Manufacture of Dental Plaster, Stone, and High-Strength Stone Three types of base raw materials are derived from partial dehydration of gypsum rock, depending on the nature of the dehydration process. Plasters are fluffy, porous, and least dense, whereas the hydrocal variety has a higher density and is more crystalline. Densite is the densest of the raw materials. These three types of raw materials are used to formulate the four types of relatively pure gypsum products used in dentistry. They are classified as plasters (model and laboratory), low- to moderate-strength dental stones, high-strength/low-expansion dental stones, and high-strength/high-expansion dental stones, or alternatively as types 2, 3, 4, and 5 in ANSI/ADA specification No. 25 (ISO 6873). Although these types have identical chemical for-mulas of calcium sulfate hemihydrate, CaSO4·½H2O, they possess different physical properties, which makes each of them suitable for a different dental purpose. All four forms are derived from natural gypsum deposits, with the main difference being the manner of driving off part of the water of the calcium sulfate dihydrate. Synthetic gypsum can also be used to formulate some products, but is less popular because of higher manufacturing costs. Mineral gypsum dehydration by heat or other means Plasters formulation Model plaster Lab plaster Dental stone High-strength dental stone Hydrocal Densite 253 12. Replicating Materials: Impression and Casting Plasters are produced when the gypsum mineral is heated in an open kettle at a temperature of about 110 to 120°C. The hemihydrate produced is called β-calcium sulfate hemihydrate. Such a powder is known to have a somewhat irregular shape and is porous in nature. These plasters are used in formulating model and lab plasters. Crystals of model plaster are shown in Fig. 12.20. If gypsum is dehydrated under pressure and in the presence of water vapor at about 125°C, the prod-uct is called hydrocal. The powder particles of this product are more uniform in shape and denser than the particles of plaster. Crystals of a dental stone are shown in Fig. 12.21. The calcium sulfate hemihydrate produced in this manner is designated as α-calcium sulfate hemihydrate. Hydrocal is used in making low- to moderate-strength dental stones. Types 4 and 5 high-strength dental stones are manufactured with a high-density raw material called densite. This variety is made by boiling gypsum rock in a 30% calcium chloride solution, after which the chloride is washed away with hot water (100°C) and the material is ground to the desired fineness. The powder obtained by this process is the densest of the types. These materials are generally formulated as high-strength/low-expansion dental stone or high-strength/high-expansion dental stone. Gypsum products may be formulated with chem-icals that modify their handling characteristics and properties. Potassium sulfate, K2SO4, and terra alba (set calcium sulfate dihydrate) are effective accelera-tors. Sodium chloride in small amounts shortens the setting reaction but increases the setting expansion of the gypsum mass. Sodium citrate is a depend-able retarder. Borax, Na2B4O7, is both a retarder and accelerator. A mixture of calcium oxide (0.1%) and gum arabic (1%) reduces the amount of water neces-sary to mix gypsum products, resulting in improved properties. Type 4 gypsum differs from type 5 in that type 4 contains extra salts to reduce its setting expansion. Chemical Reaction The chemical reaction that takes place during the set-ting of gypsum products determines the quantity of H2O needed for the reaction. The reaction of 1 g mol of plaster with 1.5 g mol of water produces 1 g mol of gypsum material. In other words, 145 g of plas-ter requires 27 g of water to react and form 172 g of gypsum or 100 g of plaster requires 18.6 g of water to form 118 g of calcium sulfate dihydrate. As seen in practice, however, model plaster cannot be mixed with such a small amount of water and still develop a mass suitable for manipulation. Table 12.9 shows the recommended mixing water, required water, and excess water for model plaster, dental stone, and high-strength dental stone. For example, to mix 100 g of model plaster to a usable flowable consistency, use 45 g of water. Note that only 18.6 g of 45 g of water reacts with the 100 g of model plaster; the excess (45 g − 18.6 g = 26.4 g) is distributed as free water in the set mass with-out taking part in the chemical reaction. When the set material is dried, the excess water evaporates and leaves porosity in the structure, weakening it. Therefore set model plaster is weaker than dental FIG. 12.21 Crystal structure typical of dental stone. FIG. 12.20 Crystals of model plaster. 254 CRAIG’S RESTORATIVE DENTAL MATERIALS stone, which in turn is weaker than high-strength dental stone. If 100 g of model plaster is mixed with 50 g of water, the resultant mass is thinner and mixes and pours easily into a mold, but the quality of the set gypsum is inferior and weaker than when 45 g of water is used. When model plaster is mixed with a lesser amount of water, the mixed mass is thicker, is more difficult to handle, and traps air bubbles easily when it is poured into a mold, but the set gypsum is usually stronger. Thus careful control of the proper amount of water in the mix is necessary for proper manipulation and quality of the set mass. Water-to-Powder Ratio of Dental Stone and High-Strength Dental Stone The reason for the differences among the recom-mended amounts of mixing water for model plaster, dental stone, and high-strength dental stone is in the shape and form of the calcium sulfate hemihydrate crystals. Some calcium sulfate hemihydrate crystals are comparatively irregular in shape and porous in nature, as are the crystals in model plaster, whereas the crystals of dental stone and the two high-strength dental stones are dense and more regular in shape, as shown in Figs. 12.20 and 12.21. This difference in the physical shape and nature of the crystals makes it possible to obtain the same consistency with less excess water with dental stone and high-strength dental stones than with model plaster. When mixed with water, model plaster, dental stone, or high-strength dental stones set to a hard mass of gypsum. The gypsum products known as high-strength dental stones (types 4 and 5) are the strongest, the mass produced as model plaster is the weakest, and dental stone produces an intermediate strength mate-rial. Note, however, that all gypsum products have the same chemical formula, and that the chemical nature of the masses produced by mixing them with water is also identical; the differences among them are primarily in their physical properties. Mechanism of Setting The most important and well-recognized theory for the mechanism of the setting is the crystalline theory. It was originated in 1887 by Henry Louis Le Chatelier, a French chemist. The theory received the full support of Jacobus Henricus van ’t Hoff, a famous Dutch chemist in Berlin at the turn of the century. According to the explanation of van ’t Hoff, the setting reaction of water with calcium sulfate hemihydrate to from calcium sulfate dihydrate is caused by the difference in solubility between these two components. Calcium sulfate dihydrate is less soluble than the hemihydrate form. When the hemi-hydrate dissolves in water, the dihydrate, being of lower solubility, is then supersaturated and precipi-tates out of solution from points of nucleation in the form of needlelike crystals. Bonding between con-tacting crystals results in the final cohesive structure. Volumetric Contraction Theoretically, calcium sulfate hemihydrate should contract volumetrically during the setting process. However, experiments have determined that all gypsum products expand linearly during setting. As indicated earlier, when 145.15 g of calcium sulfate hemihydrate reacts with 27.02 g of water, the result is the production of 172.17 g of calcium sulfate dihy-drate. However, if the volume rather than the weight of calcium sulfate hemihydrate is added to the vol-ume of water, the sum of the volumes will be about 7% less than the volume of calcium sulfate dihydrate. In practice about 0.2% to 0.4% linear expansion is obtained. According to the crystalline theory of Le Chatelier and van ’t Hoff, the expansion results from the thrusting action of gypsum crystals, CaSO4·2H2O, during their growth from a supersaturated solution. The fact that the contraction of gypsum is not vis-ible does not invalidate its existence, and when the volumetric contraction is measured by a dilatometer, it is determined to be about 7%. Because of the linear expansion of the outer dimensions, which is caused by the growth of calcium sulfate dihydrate, with a simultaneous true volumetric contraction of calcium sulfate dihydrate, these materials are porous when set. Effect of Spatulation The mixing process, called spatulation, has a definite effect on the setting time and setting expansion of the material. Within practical limits an increase in the amount of spatulation (either speed of spatulation TABLE 12.9 Required and Excess Water for Gypsum Materialsa Gypsum Mixing Water (mL/100 g of Powder) Required Water (mL/100 g of Powder) Excess Water (mL/100 g of Powder) Model plaster 37–50 18.6 18–31 Dental stone 28–32 18.6 9–13 High-strength dental stone 19–24 18.6 0–5 aWater-to-powder ratio varies with each product. 255 12. Replicating Materials: Impression and Casting or time or both) shortens the setting time. Obviously when the powder is placed in water, the chemical reaction starts, and some calcium sulfate dihydrate is formed. During spatulation the newly formed calcium sulfate dihydrate breaks down to smaller crystals and starts new centers of nucleation, from which the calcium sulfate dihydrate can be precipi-tated. Because an increased amount of spatulation causes more nuclei centers to be formed, the conver-sion of calcium sulfate hemihydrate to dihydrate is accelerated. Effect of Temperature The temperature of the water used for mixing, as well as the temperature of the environment, has an effect on the setting reaction of gypsum products. The set-ting time probably is affected more by a change in temperature than by any other physical property. Evidently the temperature has two main effects on the setting reaction of gypsum products. The first effect of increasing temperature is a change in the relative solubilities of calcium sulfate hemihydrate and calcium sulfate dihydrate, which alters the rate of the reaction. The ratio of the solubili-ties of calcium sulfate dihydrate and calcium sulfate hemihydrate at 20°C is about 4.5. As the temperature increases, the solubility ratios decrease, until 100°C is reached and the ratio becomes 1. As the ratio of the solubilities becomes lower, the reaction is slowed, and the setting time is increased. The solubilities of calcium sulfate hemihydrate and calcium sulfate dihydrate are shown in Table 12.10. The second effect is the change in ion mobility with temperature. In general, as the temperature increases, the mobility of the calcium and sulfate ions increases, which tends to increase the rate of the reac-tion and shorten the setting time. Practically, the effects of these two phenomena are superimposed, and the total effect is observed. Thus by increasing the temperature from 20 to 30°C, the solubility ratio decreases from 0.90/0.200 = 4.5 to 0.72/0.209 = 3.4, which ordinarily should retard the reaction. At the same time, however, the mobil-ity of the ions increases, which should accelerate the setting reaction. Thus according to the solubil-ity values, the reaction should be retarded, whereas according to the mobility of the ions, the reaction should be accelerated. Experimentation has shown that increasing the temperature from room tempera-ture of 20°C to body temperature of 37°C increases the rate of the reaction slightly and shortens the set-ting time. However, as the temperature is raised over 37°C, the rate of the reaction decreases, and the set-ting time is lengthened. At 100°C the solubilities of dihydrate and hemihydrate are equal, in which case no reaction occurs, and plaster does not set. Effect of Humidity When the relative humidity increases to 70% and above, moisture in the air can cause some conversion of hemihydrate to dihydrate. Because dihydrate crys-tals can accelerate the reaction by providing more nuclei for crystallization, the initial result is accel-eration of setting. However, further contamination by moisture can reduce the amount of hemihydrate remaining to form gypsum and retardation of setting will occur. Therefore all gypsum products should be kept in a closed container and well protected from moisture in the air. Effect of Colloidal Systems and pH Colloidal systems such as agar and alginate retard the setting of gypsum products. If these materials are in contact with CaSO4·½H2O during setting, a soft, easily abraded surface is obtained. Accelerators such as potassium sulfate are added to improve the sur-face quality of the set CaSO4·2H2O against agar or alginate. These colloids do not retard the setting by altering the solubility ratio of the hemihydrate and dihydrate forms, but rather by being adsorbed on the hemihy-drate and dihydrate nucleation sites, thus interfering in the hydration reaction. The adsorption of these materials on the nucleating sites retards the setting reaction more effectively than adsorption on the cal-cium sulfate hemihydrate. Liquids with low pH, such as saliva, retard the set-ting reaction. Liquids with high pH accelerate setting. Properties The important properties of gypsum products include quality, fluidity at pouring time, setting time, linear set-ting expansion, compressive strength, hardness and abrasion resistance, and reproduction of detail. Some of these property requirements, described by ANSI/ ADA specification No. 25 (ISO 6873), are summarized in Table 12.11. TABLE 12.10 Solubility of Calcium Sulfate Hemihydrate and Calcium Sulfate Dihydrate at Different Temperatures Temperature (°C) CaSO4·1/2H2O (g/100 g Water) CaSO4·2H2O (g/100 g Water) 20 0.90 0.200 25 0.80 0.205 30 0.72 0.209 40 0.61 0.210 50 0.50 0.205 100 0.17 0.170 256 CRAIG’S RESTORATIVE DENTAL MATERIALS Setting Time DEFINITION AND IMPORTANCE The time required for the reaction to be completed is called the final setting time. If the rate of the reac-tion is too fast or the material has a short setting time, the mixed mass may harden before the operator can manipulate it properly. By contrast, if the rate of reac-tion is too slow, an excessively long time is required to complete the operation. Therefore a proper setting time is one of the most important characteristics of gypsum materials. The chemical reaction is initiated at the moment the powder is mixed with water, but at the early stage only a small portion of the hemihydrate is converted to gypsum. The freshly mixed mass has a semifluid consistency and can be poured into a mold of any shape. As the reaction proceeds, however, more and more calcium sulfate dihydrate crystals are produced. The viscosity of the mixed mass increases, and the mass can no longer flow easily into the fine details of the mold. This time is called the working time. The final setting time is defined as the time at which the material can be separated from the impres-sion without distortion or fracture. The initial setting time is the time required for gypsum products to reach a certain arbitrary stage of firmness in their set-ting process. In the normal case, this arbitrary stage is represented by a semihard mass that has passed the working stage but is not yet completely set. At final setting, the conversion of calcium sulfate hemi-hydrate to calcium sulfate dihydrate is virtually completed. MEASUREMENT The initial setting time is usually measured arbitrarily by some form of penetration test, although occasion-ally other types of test methods have been designed. For example, the loss of gloss from the surface of the mixed mass of model plaster or dental stone is an indication of this stage in the chemical reaction and is sometimes used to indicate the initial set of the mass. Similarly, the setting time may be measured by the temperature rise of the mass, because the chemical reaction is exothermic. The Vicat apparatus shown in Fig. 12.16 is com-monly used to measure the initial setting time of gypsum products. It consists of a rod weighing 300 g with a needle of 1-mm diameter. A ring container is filled with the mix, the setting time of which is to be measured. The rod is lowered until it contacts the surface of the material, then the needle is released and allowed to penetrate the mix. When the needle fails to penetrate to the bottom of the container, the material has reached the Vicat or the initial setting time. Other types of instruments, such as Gillmore needles, can be used to obtain the initial and final set-ting times of gypsum materials. CONTROL OF SETTING TIME Methods for controlling setting time have been dis-cussed previously. Initially the manufacturer can add various components that act as either accelera-tors or retarders. The operator can alter setting time by changing the temperature of the mix water and by changing the degree of spatulation. The W/P ratio can also affect setting time; using more water in the mix can prolong the setting time as shown in Table 12.12. The easiest and most reliable way to change the setting time is to add different chemicals. Potassium sulfate, K2SO4, is known as an effective accelerator, and the use of a 2% aqueous solution of this salt rather than water reduces the setting time of model plaster from approximately 10 minutes to about 4 minutes. By contrast, sodium citrate is a dependable TABLE 12.11 Property Requirements for Gypsum Materials Type Setting Time (min) Setting Expansion Range (%) Compressive Strength (MPa) Reproduction of Detail (µm) Minimum Maximum 1. Impression plaster 2.5–5.0 0–0.15 4.0 8.0 75 ± 8 2. Model plaster ±20%a 0–0.30 9.0 — 75 ± 8 3. Dental stone ±20% 0–0.20 20.0 — 50 ± 8 4. High-strength/ low-expansion dental stone ±20% 0–0.15 35.0 — 50 ± 8 5. High-strength/ high-expansion dental stone ±20% 0.16–0.30 35.0 — 50 ± 8 aSetting time shall be within 20% of value claimed by manufacturer. 257 12. Replicating Materials: Impression and Casting retarder. The use of a 2% aqueous solution of borax to mix with the powder may prolong the setting time of some gypsum products to a few hours. If a small amount of set calcium sulfate dihydrate is ground and mixed with model plaster, it provides nuclei of crystallization and acts as an accelerator. The set gypsum used as an accelerator is called terra alba, and it has a pronounced effect at lower concen-trations. The setting time changes significantly if the amount of terra alba present in the mix is changed from 0.5% to 1%. However, terra alba concentra-tions above 1% have less effect on the setting time. Manufacturers usually take advantage of this fact and add about 1% terra alba to plaster. Thus the set-ting time of model plaster is altered less in normal use because of opening and closing the container. The W/P ratio has a pronounced effect on the set-ting time. The more water in the mix of model plas-ter, dental stone, or high-strength dental stone, the longer the setting time, as shown in Table 12.12. The effect of spatulation on setting time of model plaster and dental stone is shown in Table 12.13. Increased spatulation shortens the setting time. Properties of a high-strength dental stone mixed by hand and by a power-driven mixer with vacuum are shown in Table 12.14. The setting time is usually shortened for power mixing compared with hand mixing. Viscosity The viscosities of several high-strength dental stones and impression plaster are listed in Table 12.15. A range of viscosities from 21,000 to 101,000 centipoises (cp) was observed for five different high-strength stones. More voids were observed in casts made from the stones with the higher viscosities. Impression plaster is used infrequently, but it has a low viscos-ity, which makes it possible to take impressions with a minimum of force on the soft tissues (mucostatic technique). Compressive Strength When set, gypsum products show relatively high values of compressive strength. The compressive strength is inversely related to the W/P ratio of the mix. The more water used to make the mix, the lower the compressive strength. TABLE 12.12 Effect of Water-to-Powder Ratio on Setting Time Material W/P Ratio (mL/g) Spatulation Turns Initial (Vicat) Setting Time (min) Model plaster 0.45 8 0.50 100 11 0.55 14 Dental stone 0.27 4 0.30 100 7 0.33 8 High-strength dental stone 0.22 5 0.24 100 7 0.26 9 W/P ratio, Water-to-powder ratio. TABLE 12.13 Effect of Spatulation on Setting Time Material W/P Ratio (mL/g) Spatulation Turns Setting Time (min) Model plaster 0.50 20 14 0.50 100 11 0.50 200 8 Dental stone 0.30 20 10 0.30 100 8 TABLE 12.14 Properties of a High-Strength Dental Stone Mixed by Hand and by a Power-Driven Mixer with Vacuum Hand Mix Power-Driven Mix with Vacuum Setting time 8.0 7.3 Compressive strength at 24 h (MPa) 43.1 45.5 Setting expansion at 2 h (%) 0.045 0.037 Viscosity, centipoise (cp) 54,000 43,000 TABLE 12.15 Viscosity of Several High-Strength Dental Stones and Impression Plaster Material Viscosity (cp)b HIGH-STRENGTH DENTAL STONEa A 21,000 B 29,000 C 50,000 D 54,000 E 101,000 Impression plaster 23,000 aStones were mixed with 1% sodium citrate solution to retard setting. bViscosity was measured 4 minutes from the start of mixing. 258 CRAIG’S RESTORATIVE DENTAL MATERIALS Model plaster has the greatest quantity of excess water, whereas high-strength dental stone contains the least excess water. The excess water is uniformly distributed in the mix and contributes to the volume but not to the strength of the material. Set model plaster is more porous than set dental stone, caus-ing the apparent density of model plaster to be lower. Because high-strength dental stone is the densest, it shows the highest compressive strength, with model plaster being the most porous and thus the weakest. The 1-hour compressive strength values are about 12.5 MPa for model plaster, 31 MPa for dental stone, and 45 MPa for high-strength dental stones. These values are representative for the normal mixes, but they vary as the W/P ratio is increased or decreased. The effect of the W/P ratio on the compressive strength of these materials is given in Table 12.16. As shown in Table 12.14, the compressive strength of a high-strength dental stone is improved slightly by vacuum mixing. Evidently, when stone is mixed with the same W/P ratio as model plaster, the com-pressive strength of dental stone is almost the same as that of model plaster. Similarly, the compressive strength of high-strength dental stone with W/P ratios of 0.3 and 0.5 is similar to the normal compres-sive strength of dental stone and model plaster. At 1 or 2 hours after the final setting time, the hardened gypsum material appears dry and seems to have reached its maximum strength. Actually, this is not the case. The wet strength is the strength of gypsum materials with some or all of the excess water present in the specimen. The dry strength is the strength of the gypsum material with all of its excess water driven out. The dry compressive strength is usually about twice that of the wet strength. Notice that as the hardened mass slowly loses its excess water, the compressive strength of the material does not increase uniformly. The effect of drying on the compressive strength of dental stone is shown in Fig. 12.22. Theoretically, about 8.8% of excess water is in the hardened mass of the stone. As the mass loses up to 7% of the water, no appreciable change develops in the compressive strength of the material. When the mass loses 7.5% of the excess water, however, the strength increases sharply, and when all of the excess (8.8%) is lost, the strength of the material is over 55 MPa. The drying time for gypsum materials varies according to the size of the gypsum mass and the temperature and humidity of the storage atmo-sphere. At room temperature and average humidity, about 7 days are necessary for an average denture flask filled with gypsum materials to lose the excess water. Surface Hardness and Abrasion Resistance The surface hardness of unmodified gypsum mate-rials is related in a general way to their compres-sive strength. A high compressive strength of the hardened mass corresponds to a high surface hard-ness. After the final setting occurs, the surface hard-ness remains practically constant until most excess water is evaporated from the surface, after which its increase is similar to the increase in compressive TABLE 12.16 Effect of Water-to-Powder Ratio on the Compressive Strength of Model Plaster, Dental Stone, and High-Strength Dental Stonea Material W/P Ratio (mL/g) Compressive Strength (MPa) Model plaster 0.45 12.5 0.50 11.0 0.55 9.0 Dental stone 0.27 31.0 0.30 20.5 0.50 10.5 High-strength dental stone 0.24 38.0 0.30 21.5 0.50 10.5 aAll mixes spatulated 100 turns and tested 1 hour after the start of mixing. 60 50 40 Compressive strength (MPa) 30 20 0 2 4 6 8 10 Weight loss (%) FIG. 12.22 Effect of loss of excess water on compressive strength of dental stone. 259 12. Replicating Materials: Impression and Casting strength. The surface hardness increases at a faster rate than the compressive strength, because the sur-face of the hardened mass reaches a dry state earlier than the inner portion of the mass. Attempts have been made to increase the hardness of gypsum products by impregnating the set gypsum with epoxy or methyl methacrylate monomer that is allowed to polymerize. Increases in hardness were obtained for model plaster but not for dental stone or high-strength dental stone. Increases in scratch resis-tance of 15% to 41% were observed for a high-strength dental stone impregnated with epoxy resins or a light-cured dimethacrylate resin. In general, impregnating set gypsum with resin increases abrasion resistance, but decreases compressive strength and surface hardness. The idea of drying molds, casts, or dies in an oven to obtain a quick, dry compressive strength and dry surface hardness of a material is not practical, because the gypsum would be dehydrated, which would reduce the strength instead of increasing it. Soaking the gypsum dies or casts in glycerin or dif-ferent oils does not improve the surface hardness but rather makes the surface smoother, so that a wax carver or other instrument will not cut the stone as it slides over the surface. Mixing high-strength dental stone with a commercial hardening solution contain-ing colloidal silica (about 30%) improves the surface hardness of the set gypsum. The Knoop hardness of two commercial high-strength dental stones was 54 and 77 kg/mm2 when mixed with water. When the hardening solution was used, these values increased to 62 and 79 kg/mm2, respectively. Increased surface hardness does not necessarily mean improved abra-sion resistance because hardness is only one of many factors that can affect wear resistance. Two-body abrasion studies suggest that the commercial harden-ing solutions do not improve the abrasion resistance of high-strength dental stones. However, the clinical relevancy of the two-body abrasion test on gypsum has not been established. Further studies of abrasion resistance and methods of measurement are needed. As discussed in the chapter on impression materials, gypsum dies abrade more readily than epoxy dies, even though the gypsum dies are harder. Although the use of disinfectant chemicals on gypsum dies effectively destroys potentially danger-ous organisms, some can damage the surface of a die. Surfaces can be eroded, and the surface hardness can be adversely affected by treatment with some commonly used disinfectants. Other disinfectants, including sodium hypochlorite solutions, have very little effect on the surfaces of gypsum dies. Reproduction of Detail ANSI/ADA specification No. 25 requires that types 1 and 2 reproduce a groove 75 μm in width, whereas types 3, 4, and 5 reproduce a groove 50 μm in width (see Table 12.11). Gypsum dies do not reproduce surface detail as well as electroformed or epoxy dies because the surface of the set gypsum is porous on a microscopic level (Fig. 12.23). Air bubbles are often formed at the interface of the impression and gyp-sum cast because freshly mixed gypsum does not wet some elastomeric impression materials (conden-sation silicones) well. The incorporation of nonionic surfactants in silicone impression materials improves the wetting of the impression by slurry water. The use of vibration during the pouring of a cast reduces the presence of air bubbles. Contamination of the impression in which the gypsum die is poured by saliva or blood can also affect the detail reproduc-tion. Rinsing the impression and blowing away excess water can improve the detail recorded by the gypsum die material. Setting Expansion When set, all gypsum products show a measurable linear expansion. The percentage of setting expansion, however, varies from one type of gypsum material to another. Under ordinary conditions, plasters have 0.2% to 0.3% setting expansion, low- to moderate- strength dental stone about 0.15% to 0.25%, and high-strength dental stone only 0.08% to 0.10%. The setting expansion of high-strength/high-expansion dental stone ranges from 0.10% to 0.20%. Typically, over 75% of the expansion observed at 24 hours occurs during the first hour of setting. The setting expansion may be controlled by dif-ferent manipulative conditions and by the addition of some chemicals. Mechanical mixing decreases set-ting expansion. As shown in Table 12.14, a vacuum-mixed high-strength stone expands less at 2 hours than when mixed by hand. Power mixing appears to cause a greater initial volumetric contraction than is 20 µm FIG. 12.23 Scanning electron photomicrograph of the surface of a set high-strength stone die. (From Powers JM, Wataha JC. Dental Materials: Foundations and Applications. 11th ed. St. Louis: Elsevier; 2017.) 260 CRAIG’S RESTORATIVE DENTAL MATERIALS observed for hand mixing. The W/P ratio of the mix also has an effect, with an increase in the ratio reduc-ing the setting expansion. The addition of different chemicals affects not only the setting expansion of gypsum products, but may also change other prop-erties. For example, the addition by the manufacturer of sodium chloride (NaCl) in a small concentration increases the setting expansion of the mass and shortens the setting time. The addition of 1% potas-sium sulfate, by contrast, decreases the setting time but has no effect on the setting expansion. If during the setting process, the gypsum mate-rials are immersed in water, the setting expansion increases. This is called hygroscopic expansion. A typi-cal, high-strength dental stone has a setting expan-sion of about 0.08%. If during the setting process the mass is immersed in water, it expands about 0.10%. Increased expansion is observed when dental stone hardens as it comes in contact with a hydrocolloid impression. A more detailed explanation of hygro-scopic expansion is presented later under casting investments with a gypsum binder. Manipulation When any of the gypsum products is mixed with water, it should be spatulated properly to obtain a smooth mix. Water is dispensed into a mixing bowl of an appropriate size and design (Fig. 12.24). The powder is added and allowed to settle into the water for about 30 seconds. This technique minimizes the amount of air incorporated into the mix during ini-tial spatulation by hand. Spatulation can be contin-ued by hand using a spatula with a stiff blade (Fig. 12.25) with the bowl on a vibrator (see Fig. 12.25) or a power-driven mechanical spatulator (Fig. 12.26). A summary of the effect of various manipulative vari-ables on the properties of gypsum products is pre-sented in Table 12.17. Spatulation by hand involves stirring the mixture vigorously while wiping the inside surfaces of the bowl with the spatula. Spatulation to wet and mix the powder uniformly with the water requires about 1 minute at 2 revolutions per second. Spatulation with a power-driven mechanical spatu-lator requires that the powder initially be wet by the water as with hand mixing. The mix is then spatulated for 20 seconds on the low-speed drive of the mixer. Vacuuming during mixing reduces the air entrapped in the mix. Vibration immediately after mixing and dur-ing pouring of the gypsum minimizes air bubbles in the set mass. Pouring an impression with gypsum requires care to avoid trapping air in critical areas. The mixed gyp-sum should be poured slowly or added to the impres-sion with a small instrument such as a wax spatula. The mass should run into the rinsed impression under vibration in such a manner that it pushes air ahead of itself as it fills the impressions of the teeth. Commonly, the teeth of a cast are poured in dental stone or high-strength dental stone, whereas the base is poured in model plaster for easier trimming. Once poured, the gypsum material should be allowed to harden for 45 to 60 minutes before the impression and cast are separated and disinfected. Models can be disinfected by immersion in 1:10 dilution of sodium hypochlorite for 30 minutes or with a spray of iodophor following manufacturer’s instructions. CASTING INVESTMENTS The adoption of the casting practice in dentistry for making gold alloy inlays, crowns, bridges, and other restorations represents one of the major advances in restorative dentistry. In recent years, alloys with higher melting points, the palladium and base-metal FIG. 12.24 Flexible rubber mixing bowl and metal spatula with a stiff blade. (Courtesy Whip Mix Corporation, Louisville, KY.) FIG. 12.25 A vibrator is designed to promote the release of bubbles in the gypsum mix and to facilitate pouring of the impression. (Courtesy Whip Mix Corporation, Louisville, KY.) 261 12. Replicating Materials: Impression and Casting alloys, have been cast into crowns, and fixed and removable dental prostheses by using basically the same lost-wax technique used for dental gold alloys. All such casting operations involve (1) a wax pattern of the object to be reproduced; (2) a suitable mold material, known as investment, which is placed around the pattern and permitted to harden; (3) suit-able furnaces for burning out the wax patterns and heating the investment mold; and (4) proper facili-ties to melt and cast the alloy. An investment can be described as a ceramic material that is suitable for forming a mold into which a metal or alloy is cast. The operation of forming the mold is described as investing. Details of the casting technique are described on the website sakaguchi/restorative. Properties Required of an Investment 1. Easily manipulated: Not only should it be possible to mix and manipulate the mass readily and to paint the wax pattern easily, but the investment should also harden within a relatively short time. 2. Sufficient strength at room temperature: The investment should permit ease in handling and provide enough strength at higher temperatures to withstand the impact force of the molten metal. The inner surface of the mold should not break down at a high temperature. 3. Stability at higher temperatures: Investment must not decompose to give off gases that could damage the surface of the alloy. 4. Sufficient expansion: It must expand enough to compensate for shrinkage of the wax pattern and metal that takes place during the casting procedure. 5. Beneficial casting temperatures: Preferably the thermal expansion versus temperature curve should have a plateau of the thermal expansion over a range of casting temperatures. 6. Porosity: It should be porous enough to permit the air or other gases in the mold cavity to escape easily during the casting procedure. 7. Smooth surface: Fine detail and margins on the casting should be preserved. 8. Ease of divestment: The investment should break away readily from the surface of the metal and should not have reacted chemically with it. 9. Inexpensive. These requirements describe an ideal investment. No single material is known that completely fulfills all these requirements. However, by blending differ-ent ingredients, one can develop an investment that possesses most of the required qualities. These ideal qualities are the basis for considering the behavior and characteristics of casting investments. Composition In general, an investment is a mixture of three dis-tinct types of materials: refractory material, binder material, and other chemicals. FIG. 12.26 Power-driven mechanical spatulator with a vacuum attachment. (Courtesy Whip Mix Corporation, Louisville, KY.) TABLE 12.17 Summary of Effect of Manipulative Variables on Properties of Gypsum Products Manipulative Variable Setting Time Consistency Setting Expansion Compressive Strength Increase water-to-powder ratio Increase Increase Decrease Decrease Increase rate of spatulation Decrease Decrease Increase No effect Increase temperature of mixing water from 23° to 30°C Decrease Decrease Increase No effect 262 CRAIG’S RESTORATIVE DENTAL MATERIALS Refractory Material Refractory material is usually a form of silicon diox-ide, such as quartz, tridymite, or cristobalite, or a mixture of these. Refractory materials are contained in all dental investments, whether for casting gold or high-melting-point alloys. Binder Material Because the refractory materials alone do not form a coherent solid mass, some kind of binder is needed. The common binder used for dental casting gold alloy is α-calcium sulfate hemihydrate. Phosphate, ethyl silicate, and other similar materials also serve as binders for high-temperature casting investments. These latter investments are described later in con-junction with investment for casting high-melting-point alloys. Other Chemicals Usually a mixture of refractory materials and a binder alone is not enough to produce all the desirable prop-erties required of an investment. Other chemicals, such as sodium chloride, boric acid, potassium sul-fate, graphite, copper powder, or magnesium oxide, are often added in small quantities to modify various physical properties. For example, small amounts of chlorides or boric acid enhance the thermal expan-sion of investments bonded by calcium sulfate. Calcium Sulfate–Bonded Investments The dental literature and patent references describe the quantity and purpose of each of a variety of ingre-dients in dental casting investments. In general, the investments suitable for casting gold alloys contain 65% to 75% quartz or cristobalite, or a blend of the two, in varying proportions; 25% to 35% of α-calcium sulfate hemihydrate; and about 2% to 3% chemical modifiers. With the proper blending of these basic ingredients, the manufacturer is able to develop an investment with an established group of physical properties that are adequate for dental gold casting practices. A list of specific compositions is of little value, however, because the final product’s proper-ties are influenced by both the ingredients present in the investment and the manner in which the mass is manipulated and used in making the mold. Investments with calcium sulfate hemihydrate as a binder are relatively easy to manipulate, and more information about the effect of different additives, as well as various manipulative conditions, is available for this type than for other types, such as those that use silicates or phosphates as binders. The calcium sulfate–bonded investment is usually limited to gold castings and is not heated above 700°C. The calcium sulfate portion of the investment decomposes into sulfur dioxide and sulfur trioxide at temperatures over 700°C, tending to embrittle the casting metal. Therefore the calcium sulfate type of binder is usu-ally not used in investments for making castings of high-melting-point metals such as palladium or base-metal alloys. Properties of Calcium Sulfate–Bonded Investments ANSI/ADA specification No. 126 (ISO 7490) for gypsum-bonded casting investments applies to two different types of investments suitable for casting dental restorations of gold alloys: Type 1: For casting inlays and crowns Type 2: For casting complete denture and removable partial denture frameworks Both types have calcium sulfate as a binder mate-rial. The physical properties included in this specifi-cation are appearance of powder, fluidity at working time, setting time, compressive strength, linear set-ting expansion, and linear thermal expansion. The values allowed for these properties are summarized in the specification. The manipulation of investments in the inlay casting procedure is discussed in detail on the website hi/restorative. Effect of Temperature on Investment In casting with the lost-wax process, the wax pattern is invested and placed in an oven at a temperature that melts and removes the pattern from the invest-ment, thereby leaving a mold cavity into which the molten metal is cast. This oven temperature varies from one technique to another, but in no case is it lower than 550°C or higher than 700°C for calcium sulfate–bonded investments. During the heating pro-cess, the refractory material is affected differently by the thermal changes than is the gypsum binder. Effect of Temperature on Silicon Dioxide Refractories Each of the polymorphic forms of silica (quartz, trid-ymite, and cristobalite) expands when heated, but the percentage of expansion varies from one type to another. Pure cristobalite expands to 1.6% at 250°C, whereas quartz expands about 1.4% at 600°C, and the thermal expansion of tridymite at 600°C is less than 1%. The percentage of expansion of the three types of silica versus temperature is shown in Fig. 4.41. As seen in Fig. 4.41, none of the three forms of silica expands uniformly; instead they all show a break (nonlinearity) in their thermal expansion curves. In the case of cristobalite, the expansion is somewhat uniform up to about 200°C. At this temperature its expansion increases sharply from 0.5% to 1.2%, and 263 12. Replicating Materials: Impression and Casting then above 250°C it again becomes more uniform. At 573°C quartz also shows a break in the expansion curve, and tridymite shows a similar break at a much lower temperature. The breaks on the expansion versus temperature curves indicate that cristobalite and quartz each exist in two polymorphic forms, one of which is more sta-ble at a higher temperature and the other at a lower temperature. The form that is more stable at room temperature is called the α-form, and the more stable form at higher temperatures is designated as the β-form. Tridymite has three stable polymorphic forms. Thus the temperatures of 220°C for cristobalite, 573°C for quartz, and 105° and 160°C for tridymite are displacive transition temperatures. A displacive change involves expansion or contraction in the volume of the mass without breaking any bonds. In changing from the α-form (which is the more stable form at room temperature) to the β-form (which is stable at higher temperatures), all three forms of silica expand. The amount of expansion is highest for cristobalite and lowest for tridymite. The quartz form of silica is found abundantly in nature, and it can be converted to cristobalite and tridymite by being heated through a reconstruc-tive transition during which bonds are broken and a new crystal structure is formed. The α-quartz is converted to β-quartz at a temperature of 573°C. If the β-quartz is heated to 870°C and maintained at that temperature, it is converted to β-tridymite. From β-tridymite, it is possible to obtain either α-tridymite or β-cristobalite. If β-tridymite is cooled rapidly to 120°C and held at that temperature, it is changed to α-tridymite, which is stable at room temperature. By contrast, if β-tridymite is heated to 1475°C and held at that temperature, it is converted to β-cristobalite. Further heating of β-cristobalite produces fused sil-ica, but if it is cooled to 220°C and held at that tem-perature, α-cristobalite is formed. These transitions are shown in the following equation. β-quartz 573° C 870° C 220° C 160° C β-tridymite Middle tridymite 1475° C β-cristobalite α-cristobalite Fused silica 1700° C α-quartz 105° C α-tridymite All forms of silica are in their α-forms in the investment, and during the heating process they are converted completely or in part to their correspond-ing β-forms. This transition involves an expansion of the mass, which helps to compensate for the casting shrinkages. Effect of Temperature on Calcium Sulfate Binders The binder used for gold alloy casting investments in dentistry is α-calcium sulfate hemihydrate. During the investing process, some of the water mixed with the investment reacts with the hemihydrate and is converted to calcium sulfate dihydrate, whereas the remainder of the water is uniformly distributed in the mix as excess water. During the early stages of heat-ing, the excess water evaporates. As the temperature rises to about 105°C, calcium sulfate dihydrate starts losing water. The investment mass is then heated still further to the proper temperature for casting the metal. In this way, anhydrous calcium sulfate, silica, and certain chemical additives remain to form the mold into which the gold alloy is cast. It has been observed experimentally that invest-ment expands when it is first heated from room tem-perature to about 105°C, then contracts slightly or remains unchanged up to about 200°C, and registers varying degrees of expansion, depending on the sil-ica composition of the investment, between 200° and 700°C. These properties are explained as follows. Up to about 105°C, ordinary thermal expansion occurs. Above 105°C, the calcium sulfate dihydrate is con-verted to anhydrous calcium sulfate. Dehydration of the dihydrate and a phase change of the calcium sulfate anhydrite cause a contraction. However, the α-form of tridymite (which might be present as an impurity) is expanding and compensates for the contraction of the calcium sulfate sufficiently to prevent the investment from registering a serious degree of contraction. At elevated temperatures, the α-forms of silica present in the investment are con-verted to the β-forms, which cause some additional expansion. The thermal expansion curves for a currently available hygroscopic type of investment contain-ing quartz (A) and a thermal expansion type of investment containing cristobalite (B) are shown in Fig. 12.27, which illustrates the expected degree of expansion at different temperatures. The expansion of the silica content of the investment must not only be sufficiently high to overcome all the contraction, but should also take place at temperatures close to the temperature at which contraction of the hemihy-drate occurs. 264 CRAIG’S RESTORATIVE DENTAL MATERIALS Cooling of the Investment When the investment cools, the refractory and binder contract according to a thermal contraction curve that is different from the thermal expansion curve of the investment (Fig. 12.28). On cooling to room tem-perature, the investment exhibits an overall contrac-tion compared with its dimensions before heating. On reheating to the temperature previously attained, the investment does not expand thermally to the previous level; moreover, the process of cooling and reheating causes internal cracks in the investment that can affect the quality of the casting. Setting Expansion of Calcium Sulfate–Bonded Investment All the calcium sulfate–bonded investments cur-rently available for casting gold alloys have both set-ting and thermal expansion. The sum of these two expansions results in a total dimensional change that is an essential property of dental casting investments because it provides compensation for the casting shrinkage of the casting alloys. The setting expansion of an investment, like that of other gypsum products discussed earlier in this chapter, is the linear expan-sion that takes place during the setting of the invest-ment. If the investment is setting surrounded by air, the expansion is referred to as normal setting expan-sion. On the other hand, if the mixed investment is setting in contact with water, the expansion is sub-stantially greater and is called hygroscopic setting expansion. Such contact with water can be achieved in the commonly used casting techniques of (1) placing a wet liner inside the casting ring in which the invest-ment is poured, or (2) if after investing, the casting ring is placed in a water bath. The presently accepted mechanism for hygroscopic setting expansion also relates to the normal setting expansion that occurs when the investment mix sets in contact with air. The basis for this mechanism lies in the role played by the surface tension of the mix water and can be described as follows. After the investment is mixed, water sur-rounds the components of the setting investment. As the reaction of the calcium sulfate binder progresses, the surrounding water is reduced and growing gyp-sum crystals impinge on the surface of the remaining water whose surface tension inhibits outward crys-tal growth. When the water needed for the reaction is used up and the reaction is virtually completed, the growth of gypsum crystals stops in its inhibited form. If the investment is poured into a casting ring having a water-filled liner, the gypsum crystals can grow further, but only until the new water sur-face provided by the additional water in the liner is reached; surface tension then inhibits further growth. If water is supplied to the mixed investment mass by immersing the invested ring in a water bath, no new surface is close enough to provide inhibition of crystal growth. The resulting hygroscopic setting expansion for complete immersion as measured in an unconfined trough (ANSI/ADA specification No. 126) is more than twice that of normal expansion. However, when the investment is setting in a con-fined ring, hygroscopic expansion is limited by the confinement of the ring. For hygroscopic expansion, the additional water provided must be presented to 0.6 0.4 0.2 0.0 Dimensional change (%) 0.2 0 200 400 Temperature ( C) 1 3 2 600 0.4 0.6 1.0 0.8 FIG. 12.28 Thermal expansion and contraction curves for calcium sulfate–bonded investment (thermal expansion type). Curve 1 is first heating, curve 2 is cooling, and curve 3 is reheating. 1.4 1.2 1.0 0.8 A 0 200 400 600 B 0.6 Expansion (%) 0.4 0.2 0 Temperature (C) FIG. 12.27 Thermal expansion curves for calcium sul-fate–bonded investments. (A) Hygroscopic type; (B) thermal expansion type. (Modified from Asgar K. Casting restorations. In: Clark JW, ed. Clinical Dentistry. Vol. 4. New York: Harper & Row; 1976.) 265 12. Replicating Materials: Impression and Casting the investment during setting. This is significantly different than adding more water to the premixture components (i.e., increasing the W/P ratio). Another requirement for hygroscopic expansion is that the additional water be presented before the observed loss of gloss, which is when the setting reaction is not complete and the mix water can still be observed on the surface of the setting investment. This allows the additional water to join the remaining mix water and extend the water surface so that the action of surface tension is either delayed or inactive. PARTICLE SIZE OF SILICA The particle size of calcium sulfate hemihydrate has little effect on hygroscopic expansion, whereas the particle size of silica has a significant effect. Finer silica produces higher setting and hygroscopic expansions. SILICA-TO-BINDER RATIO Investments usually contain 65% to 75% silica, 25% to 35% calcium sulfate hemihydrate, and about 2% to 3% of some additive chemicals to control the differ-ent physical properties and to color the investments. If the silica/stone ratio is increased, the hygroscopic expansion of the investment also increases, but the strength of the investment decreases. WATER-TO-POWDER RATIO As with the setting expansion of gypsum products, the more water in the mix (the thinner the mix or the higher the W/P ratio), the less the normal and hygro-scopic setting expansions. Less thermal expansion is also obtained with a thinner mix. SPATULATION The effect of spatulation on the setting and hygro-scopic expansion of the investment is similar to that on the setting expansion of all gypsum products. AGE OF INVESTMENT Investments that are 2 or 3 years old do not expand as much as freshly prepared investments. For this reason, the containers of investment must be kept closed as much as possible, especially if the invest-ment is stored in a humid atmosphere. WATER-BATH TEMPERATURE For the water-bath immersion technique, the tem-perature of the water bath has a measurable effect on the wax pattern. At higher water-bath temperatures, the wax pattern expands, requiring less expansion of the investment to compensate for the total casting shrinkage. In addition, higher water-bath tempera-tures soften the wax. The softened wax then provides less resistance to the expansion of the investment, thus making the setting expansion more effective. The net effect is higher expansion of the mold with higher water-bath temperatures. Thermal and Hygroscopic Casting Investment Casting techniques involving gypsum-bonded invest-ments are often classified as thermal or hygroscopic techniques. The thermal technique directs placing the invested ring after setting into the burnout oven set for a relatively high temperature (649°C), whereas the hygroscopic technique directs immersing the invested ring before setting in a water bath and then, after set-ting, placing the ring into the burnout oven set for relatively low temperature (482°C). Although all gyp-sum-bonded investments exhibit both thermal and hygroscopic setting expansion, the relative proportion of these two expansions can vary. Investments used in the thermal technique usually contain cristobalite as the refractory ingredient, which has a high thermal expansion. Investments used in the hygroscopic tech-nique usually contain quartz or tridymite, which have lower thermal expansions but higher hygroscopic set-ting expansions. Hygroscopic-Thermal Gold Casting Investment There is one gold casting investment on the market that was designed for use with either hygroscopic or thermal type of casting techniques. Fig. 12.29 shows the high thermal expansion of this investment in the range between 482° and 649°C. This expansion is high enough to use the investment with the ther-mal casting technique, without water immersion. However, when immersed in a water bath, the invest-ment expands hygroscopically (Fig. 12.30). With the 1.2 1.0 0.8 Percent expansion 0.6 0.4 0.2 0 100 0 200 300 400 Hygroscopic casting temperature High heat casting temperature 500 600 700 Temperature (C) FIG. 12.29 Thermal expansion of mixed hygroscopic-thermal gold casting investment. (Courtesy Whip Mix Corporation, Louisville, KY.) 266 CRAIG’S RESTORATIVE DENTAL MATERIALS hygroscopic technique, the investment needs to be heated to only 482°C to provide the appropriate expansion. Investment for Casting High-Melting-Point Alloys Most palladium and base-metal alloys used for removable partial denture frameworks and ceramic-metal restorations have high melting temperatures. They should be cast at a mold temperature greater than 700°C. For this reason, calcium sulfate–bonded investments are usually not used for casting these alloys. Only one base-metal alloy for dental applica-tions possesses a low enough melting point to be cast into a mold at 700°C with a calcium sulfate binder. This alloy is an exception, because base-metal alloys are usually cast into molds at 850° to 110°C. To with-stand these high temperatures, the molds require different types of binders, such as silicate and phos-phate compounds. This type of investment usually has less than 20% binder, and the remainder of the investment is quartz or another form of silica. PHOSPHATE-BONDED INVESTMENT The most common type of investment for casting high-melting point alloys is the phosphate-bonded investment. This type of investment consists of three different components. One component contains a water-soluble phosphate ion. The second component reacts with phosphate ions at room temperature. The third component is a refractory, such as silica. Different materials can be used in each component to develop different physical properties. The binding system of a typical phosphate-bonded investment undergoes an acid-base reaction between acid monoammonium phosphate (NH4H2PO4) and basic magnesia (MgO). The soluble phosphate in water reacts with the sparingly soluble magnesia at its surface, forming a binding medium with filler particles embedded in the matrix. The chemical reac-tion at room temperature can be expressed simply as follows: NH4H2PO4 + MgO + H2O → NH4MgPO4 · 6H2O + H2O The water produced by this reaction at room tem-perature lowers the viscosity of the mix as spatula-tion continues. As the reaction takes place, colloidal particles are formed with a strong interaction among the particles. During setting and burnout, the sequence of chemical and thermal reactions causes vari-ous phase changes, providing room-temperature strength (green strength) and high-temperature strength that enable the investment to withstand the impact of high-melting-point alloys. Phases formed at high temperatures include Mg2P2O7 and subse-quently Mg3(PO4)2. To produce higher expansion, a combination of different particle sizes of silica is used. These investments can be mixed with water or with a special liquid supplied by the manufacturer. The special liquid is a form of silica sol in water. As shown in Fig. 12.31, phosphate-bonded investments possess higher setting expansion when they are mixed with the silica sol than when mixed with water. With a mix containing silica sol, the investment mass is capable of expanding hygroscopically, whereas if the mix is only water, the hygroscopic expansion of such an investment is negligible. Not all phosphate-bonded investments, however, can expand hygroscopically. Using silica sol instead of water with phosphate-bonded investment also increases its strength con-siderably. Fig. 12.32 shows thermal expansion curves of two commercial phosphate-bonded investments mixed according to the manufacturers’ recommended liquid-to-powder ratio. Both the setting and thermal expansions must be considered in selecting these investments. ANSI/ADA specification No. 126 (ISO 9694) for dental phosphate-bonded casting investments speci-fies two types of investments for alloys having a soli-dus temperature above 1080°C: Type 1: For inlays, crowns, and other fixed restorations Type 2: For removable partial denture frameworks The following properties and their specified val-ues are described by the specification: fluidity, initial setting time, compressive strength, and linear thermal expansion. The setting time must not differ by more than 30% from the time stated by the manufacturer. 1.4 0 0 15 30 45 60 75 90 105 120 0.2 0.4 0.6 0.8 Percent expansion 1.0 1.2 Time in minutes Normal setting expansion Hygroscopic expansion (under water) FIG. 12.30 Setting and hygroscopic expansion of mixed hygroscopic-thermal gold casting investment. (Courtesy Whip Mix Corporation, Louisville, KY.) 267 12. Replicating Materials: Impression and Casting The compressive strength at room temperature shall not be less than 2.5 MPa for type 1 investments and 3.0 MPa for type 2 investments. The linear thermal expansion must not differ by more than 15% from the time stated by the manufacturer. SILICA-BONDED INVESTMENT Another type of binding material for investments used with casting high-melting-point alloys is a silica-bonding ingredient. This type of invest-ment may derive its silica bond from ethyl silicate, an aqueous dispersion of colloidal silica, or from sodium silicate. One such investment consists of silica refractory, which is bonded by the hydrolysis of ethyl silicate in the presence of hydrochloric acid. The product of the hydrolysis is a colloidal solution of silicic acid and ethyl alcohol, which can be writ-ten as follows: Si(OC2H5)4 4H2O 4C2H5OH Si(OH)4 HCl In practice, however, the reaction is more com-plicated, and instead of tetrasilicic acid, which is converted into SiO2–2H2O, a polymerized compound of silicon is formed with the following structure: O Si Si O O O Si Si O O O Si Si This material has an even higher silica content and better refractory properties than the SiO2·2H2O. Ethyl silicate has the disadvantage of giving off flammable components during processing, and the method is expensive; thus other techniques and methods have been developed to reduce the use of this material. Sodium silicate and colloidal silica are more common binders of the silica type. Today this investment is usually supplied with two bottles of special liquid, instead of water, with which the investment powder should be mixed. In one of the 0 0.2 0.4 0.6 Expansion (%) 0.8 A A 25 0 50 75 100 B B 1.0 1.2 Concentration of sol (%) FIG. 12.31 Effect of silica sol concentration on thermal expansion (solid lines) at 800°C and setting expansion (dotted lines) of two phosphate-bonded investments. A, Thermal expansion type; B, hygroscopic expansion type. (Data from Zarb GA, Bergman G, Clayton JA, MacKay HF, eds. Prosthodontic Treatment for Partially Edentulous Patients. St. Louis: Mosby; 1978.) 1.2 1.0 0.8 0.6 0.4 A B Expansion (%) 0.2 0 0 200 400 600 800 Temperature (C) FIG. 12.32 Thermal expansion curves of two phos-phate-bonded investments mixed at recommended liquid-to-powder ratios. A, Thermal expansion type; B, hygroscopic expansion type. (Data from Zarb GA, Bergman G, Clayton JA, MacKay HF, eds. Prosthodontic Treatment for Partially Edentulous Patients. St. Louis: Mosby; 1978.) 268 CRAIG’S RESTORATIVE DENTAL MATERIALS bottles the manufacturer usually supplies a properly diluted water-soluble silicate solution. The other bottle usually contains a properly diluted acid solution, such as a solution of hydrochloric acid. The contents of each bottle can be stored almost indefinitely. Before use, mix an equal volume from each bottle and allow the mixed liquids to stand for a prescribed time, accord-ing to the manufacturer’s instructions, so hydrolysis can take place and freshly prepared silicic acid forms. ANSI/ADA specification No. 126 (ISO 11246) for ethyl silicate casting investments specifies setting time, compressive strength, and linear thermal expan-sion. The setting time must not differ by more than 30% from the time stated by the manufacturer. The compressive strength at room temperature shall not be less than 1.5 MPa. The linear thermal expansion must not differ by more than 15% from the time stated by the manufacturer. Brazing Investment When brazing (soldering) the parts of a restoration, such as clasps on a removable partial denture frame-work, the parts must be surrounded with a suitable ceramic or investment material before the heating operation. The assembled parts are temporarily held together with sticky wax until they are surrounded with the appropriate investment material, after which the wax is softened and removed. The portion to be soldered is left exposed and free from invest-ment to permit wax removal and effective heating before it is joined with solder. ANSI/ADA specification No. 126 (ISO 11244) for dental brazing investments defines two types of investment: Type 1: Gypsum-bonded dental brazing investments Type 2: Phosphate-bonded dental brazing investments The specification specifies quality, fluidity, setting time, compressive strength, linear thermal expan-sion, and linear setting expansion. The setting time must not differ by more than 30% from the time stated by the manufacturer. The compressive strength shall be in the range of 2.0 to 10 MPa. The linear setting and thermal expansions must not differ by more than 15% from the time stated by the manufacturer. The investment for soldering of low-melting-point alloys is similar to casting investments contain-ing quartz and a calcium sulfate hemihydrate binder. For high-melting-point alloys, a phosphate-bonded investment is used. Soldering investments are designed to have lower setting and thermal expansions than casting invest-ments, a feature that is desirable so the assembled parts do not shift in position during the setting and heating of the investment. Soldering investments are often made of ingredients that do not have as fine a particle size as the casting investment, because the smoothness of the mass is less important. Relatively little information is available in the dental literature on the properties of soldering investments. Investment for All-Ceramic Restorations Two types of investment materials have been devel-oped recently for producing all-ceramic restorations. The first type is used for the cast glass technique. This investment is provided by the manufacturer of the glass casting equipment and is composed of phosphate-bonded refractories. The second type of investment for making all-ceramic restorations is the refractory die type of material, which is used for all-ceramic veneers, inlays, and crowns. Refractory dies are made by pouring the investment into impres-sions. When the investment is set, the die is removed, and is heated to remove gases that may be detrimen-tal to the ceramic (degassing). A refractory die spacer may be added to the surface. Next, porcelain or other ceramic powders are added to the die surface and fired. These materials must accurately reproduce the impression, remain undamaged during the por-celain firing, and have a thermal expansion compat-ible with that of the ceramic (otherwise the ceramic could crack during cooling). These materials are also phosphate-bonded, and they generally contain fine-grained refractory fillers to allow accurate reproduc-tion of detail. ANSI/ADA specification No. 126 (ISO 11245) for phosphate-bonded refractory die materi-als describes the required properties. Bibliography Review Articles: Impression Materials Allen EP, Bayne SC, Becker IM, et al. Annual review of selected dental literature: report of the committee on scientific investigation of the American Academy of Restorative Dentistry. J Prosthet Dent. 1999;82:50. Allen EP, Bayne SC, Donovan TE, et al. Annual review of selected dental literature. J Prosthet Dent. 1996;76:75. Craig RG. Review of dental impression materials. Adv Dent Res. 1988;2:51. Donovan TE, Chee WW. 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Docking AR, Chong MP, Donnison JA. The hygroscopic set-ting expansion of dental casting investments. II. Aust J Dent. 1948;52:160. Docking AR, Donnison JA, Chong MP. The hygroscopic set-ting expansion of dental casting investments. III. Aust J Dent. 1948;52:320. Eames WB, Edwards Jr CR, Buck Jr WH. Scraping resis-tance of dental die materials: a comparison of brands. Oper Dent. 1978;3:66. Earnshaw R. The effect of restrictive stress on the thermal expansion of gypsum-bonded investments. I. Inlay cast-ing investments, “thermal expansion” type. Aust Dent J. 1966;11:345. Earnshaw R. The effects of additives on the thermal behav-iour of gypsum-bonded casting investments. I. Aust Dent J. 1975;20:27. Earnshaw R, Morey EF, Edelman DC. The effect of potential investment expansion and hot strength on the fit of full crown castings made with phosphate-bonded invest-ment. J Oral Rehabil. 1997;24:532. Higuchi T. Study of thermal decomposition of gypsum bonded investment. I. Gas analysis, differential ther-mal analysis, thermobalance analysis, x-ray diffraction. Kokubyo Gakkai Zasshi. 1967;34:217. Jones DW. Thermal analysis and stability of refractory investments. J Prosthet Dent. 1967;18:234. Jones DW, Wilson HJ. Setting and hygroscopic expansion of investments. Br Dent J. 1970;129:22. Luk HW-K, Darvell BW. Strength of phosphate-bonded investments at high temperature. Dent Mater. 1991;7:99. Luk HW-K, Darvell BW. Effect of burnout temperature on strength of phosphate-bonded investments. J Dent. 1997;25:153. Luk HW-K, Darvell BW. Effect of burnout temperature on strength of phosphate-bonded investments—part II: effect of metal temperature. J Dent. 1997;25:423. Lyon HW, Dickson G, Schoonover IC. Effectiveness of vac-uum investing in the elimination of surface defects in gold castings. J Am Dent Assoc. 1953;46:197. Lyon HW, Dickson G, Schoonover IC. The mechanism of hygroscopic expansion in dental casting investments. J Dent Res. 1955;34:44. Mahler DB, Ady AB. An explanation for the hygroscopic expansion of dental gypsum products. J Dent Res. 1960;39:578. Mahler DB, Ady AB. The influence of various factors on the effective setting expansion of casting investments. J Prosthet Dent. 1963;13:365. Matsuya S, Yamane M. Thermal analysis of the reaction between II-CaSO4 and quartz in nitrogen flow. Gypsum Lime. 1980;164:3. Miyaji T, Utsumi K, Suzuki E, et al. Deterioration of phos-phate-bonded investment on exposure to 100% rela-tive humidity atmosphere. Bull Tokyo Med Dent Univ. 1982;29:53. Moore TE. Method of making dental castings and composi-tion employed in said method. U.S. Patent. 1933;1:924. 874. Mori T. Thermal behavior of the gypsum binder in dental casting investments. J Dent Res. 1986;65:877. Neiman R, Sarma AC. Setting and thermal reactions of phosphate investments. J Dent Res. 1980;59:1478. Norling BK, Reisbick MH. Wetting of elastomeric impres-sion materials modified by nonionic surfactant addi-tions. J Dent Res. 1977;56B(abstr):148. O’Brien WJ, Nielsen JP. Decomposition of gypsum invest-ment in the presence of carbon. J Dent Res. 1959;38:541. Phillips RW. Relative merits of vacuum investing of small castings as compared to conventional methods. J Dent Res. 1947;26:343. Ryge G, Fairhurst CW. Hygroscopic expansion. J Dent Res. 1956;35:499. Schilling ER, Miller BH, Woody RD, et al. Marginal gap of crowns made with a phosphate-bonded investment and accelerated casting method. J Prosthet Dent. 1999;81: 129. Schnell RJ, Mumford G, Phillips RW. An evaluation of phosphate bonded investments used with a high fusing gold alloy. J Prosthet Dent. 1963;13:324. Shell JS, Dootz ER. Permeability of investments at the cast-ing temperature. J Dent Res. 1961;40:999. Shell JS, Hollenback GM. Setting and thermal investment expansion in longitudinal and transverse directions. J Calif Dent Assoc. 1965;41:511. Tiara M, Okazaki M, Takahashi J, et al. Effects of four mixing methods on setting expansion and compressive strength of six commercial phosphate-bonded silica investments. J Oral Rehabil. 2000;27:306. Weinstein LJ. Composition for dental molds. U.S. Patent. 1929;1:708. 436. Zarb GA, Bergman B, Clayton JA, MacKay HF, eds. Prosthodontic Treatment for Partially Edentulous Patients. St. Louis: Mosby; 1978. 273 A large factor in the clinical success of modern esthetic dentistry has been the development of den-tal adhesives and luting agents. Tooth-colored resin-based direct and indirect composites, metal-ceramic and all-ceramic dental prostheses (e.g., inlays, onlays, veneers, crowns, and bridges), endodontic posts, and resin cores must all be bonded to the remaining tooth structure to function adequately. Advancements in dental adhesive materials have facilitated the growth of conservative dentistry, strengthening and sup-porting the remaining tooth structure without the need to remove healthy tooth tissue. Cementation is one of the final steps in the sequence of clinical procedures for indirect restora-tions. There are two objectives for the cementation, or luting, procedure: to help retain the restoration in place and to maintain the integrity of the remain-ing tooth structure. Retention may be achieved by friction (or micromechanical interlocking) or by an adhesive joint consisting of the prepared tooth, the cement, and the restoration, or a combination of both mechanisms. An effective interfacial seal depends on the ability of the cement to fill the irreg-ularities between the tooth and the restoration and to resist the solubilizing action of the oral environ-ment, short and long term. Adhesion is also impor-tant in this context, because a strong bond between the luting agent and the dental substrates may help prevent bacteria from colonizing the interface and minimizing the transit of fluids that may cause den-tin hypersensitivity. This chapter presents the basic aspects of the application of adhesion science to dentistry and describes the composition, properties, and indica-tions for use of acid-base and resin-based cements. Acid-base cements are easy to use and, when cor-rectly indicated, provide good long-term clini-cal service. Some release fluoride and bond to tooth structures. Resin cements have a chemistry based on resin composites. They show high bond strengths to tooth structures. Some products also contain monomers or are compatible with primers that enable bonding to metal alloys and ceramics. In general, resin cements have better mechanical prop-erties than acid-base cements, but the cementation process is more technique sensitive. The fundamental technologies and chemistries used to formulate the various types of adhesives and luting cements are derived from their corresponding restorative materials. However, in most cases modi-fications have been made to create formulations suit-able for a particular clinical application in terms of viscosity and handling characteristics. Different clinical situations require different lut-ing agents and no one material is indicated for every case. Therefore it is important to differentiate luting cements based on their mechanical properties and overall characteristics to identify the best options available for each clinical situation. PRINCIPLES OF ADHESION The creation of a strong, durable, and bonded interface with enamel or dentin provides impor-tant benefits. It significantly protects the restora-tion’s interface against penetration of bacteria that may cause secondary caries. It reduces the need for retentive areas in the preparation that would require removal of sound tooth structure. In some cases, bonding may help strengthen the remaining tooth structure. The development of adhesive luting techniques also broadened the application of mate-rials such as low-strength ceramics and indirect composites for crowns, inlays, and onlays as they reduce the risk of crack propagation within the bulk of the restoration, which ultimately may lead to its catastrophic failure. The term adhesion refers to the establishment of molecular interactions between a substrate (adher-end) and an adhesive brought into close contact, cre-ating an adhesive joint (Fig. 13.1). Cohesion is used C H A P T E R 13 Materials for Adhesion and Luting 274 CRAIG’S RESTORATIVE DENTAL MATERIALS to describe the interaction of similar atoms and molecules within a material, involving primary (i.e., covalent or ionic) or strong secondary forces (i.e., hydrogen bonding). In dentistry, true chemical bonding between the tooth structure and restorative or luting materials is very difficult to achieve, because of the complex composition of some substrates such as dentin, the presence of contaminants, and the presence of water. Zinc polycarboxylate, glass ionomer, resin-modified glass ionomer, calcium aluminate/glass ionomer, and self-adhesive resin cements are examples of den-tal materials capable of establishing chemical interac-tion with hydroxyapatite. However, in daily practice, adhesion is accomplished by micromechanical inter-locking between the adhesive and the substrate. It is important to point out that when two materials are in close contact, physical bonding is always present (e.g., van der Waals dipoles); however, it is weak, especially in a wet environment, and does not really contribute significantly to the integrity of the adhe-sive joint. A dental sealant attached to enamel is an example of a simple adhesive joint with one interface. Often, however, adhesive joints involve more than one interface (e.g., tooth/adhesive and adhesive/restor-ative or luting material), which presents an extra challenge because an adhesive does not necessarily bond equally well to different substrates. The most basic aspect to be observed in creating any adhesive joint is the cleanliness of the substrate. Saliva, biofilm, and other organic debris are always present on the tooth surface. The walls of a cavity preparation are covered with a smear layer. All of these contaminants reduce the surface energy of the bonding substrate and, consequently, its wet-tability. Therefore it is very important for the sur-face that will contact the adhesive to be thoroughly clean and, in some cases, for the smear layer to be removed by acid etching. Indirect restorations also need to have their internal surface cleaned and free from films that may impede the penetration of the adhesive. Wettability is the result of molecular interactions between the adhesive and the substrate, as well as the cohesion forces of the adhesive, particularly its surface tension. Liquids tend to form spheres when placed on a surface because that is the shape with the lowest surface area and, therefore, the minimum sur-face energy (Fig. 13.2). Wetting is usually evaluated by the contact angle (θ), that is, the internal angle between the liquid and the substrate. Generally, small contact angles are achieved when a low surface tension liquid is placed on a high-energy surface sub-strate. Contact angles less than 90 degrees indicate a favorable wetting of the surface. Ideal wetting occurs when the liquid spreads over the surface with θ ≈ 0 degrees. Surface roughness increases the wettability of the surface by liquids. Viscosity influences the contact of the adhesive with the substrate. It should be low enough to allow the adhesive to flow readily and penetrate into the details of the substrate surface, without leaving porosities at the interface. Finally, the adhesive must set sufficiently to create strong interlocks with the substrate microstructure to achieve micromechanical retention. Dental Adhesion Adhesive Interface 2 Adherend 2 Interface 1 Interface 1 Adherend 1 Adhesive system or luting cement Dental Joint FIG. 13.1 Definitions of the terminology associated with adhesive systems (adhesives, adherends or sub-strates, and interfaces). Most dental joints involve at least one adhesive, two substrates, and two interfaces. FIG. 13.2 Relation of contact angle to the spreading or wetting of a liquid on a solid. 275 13. Materials for Adhesion and Luting Adhesive Systems Classification and Basic Components Adhesive systems can rely on different approaches to obtain a strong and durable bond to dentin and enamel. They are classified according to the etching strategy as etch-and-rinse or self-etch. Additionally, universal systems (or multimode systems) can be applied following either etching approach. Etch-and-rinse (also referred to as total-etch) systems can be presented as three-step systems, that is, etching, priming, and bonding in separate application steps. Alternatively, two-step systems present primer and bonding resin mixed in a single component. Etching uses 30% to 40% phosphoric acid gels to demineral-ize the tooth structure. Originally, etching solutions were free-flowing liquids and were difficult to con-trol during placement. Gel etchants were developed by adding small amounts of microfiller or cellulose-thickening agents. These gels flow under slight pres-sure but not under their own weight. Primers are hydrophilic monomers, oligomers, or polymers, usually carried in a solvent. The solvents used in primers are acetone, ethanol-water, or pri-marily water. In some primers, the solvent levels can be as high as 90%. Therefore primers have different evaporation rates, drying patterns, and penetration characteristics, all of which can influence the result-ing bond strength. Dimethacrylate oligomers and lower-molecular-weight monomers can be added to the primer in two-step etch-and-rinse systems, or presented as a separate step in three-step systems or in self-etch two-step systems. Self-etch systems contain ester monomers with grafted carboxylic or phosphate acid groups dis-solved in water. According to their aggressiveness, these systems can be divided into strong (pH of 1 or less), moderate (pH between 1 and 2), or mild (pH of 2 or greater). They can be presented as two-step sys-tems, with a hydrophobic bonding resin in a separate bottle (also known as self-etching primers) or single-component systems (all-in-one systems). Universal systems are so called because they can be used following either an etch-and-rinse, two-step technique or a self-etch (one step) approach, depend-ing on the practitioner’s preference. When used as self-etch systems, universal adhesives can be clas-sified as mild, based on the micromorphology of the bonded interface. These versatile systems were developed to be used with other bonding substrates and contain components such as silanes and acidic monomers to mediate bonding to ceramics and metals. Most bonding agents are light cured and contain an activator such as camphorquinone and an organic amine. Dual-cured bonding agents include a cata-lyst to promote self-curing. Although most bonding agents are unfilled, some products contain nano-fillers and submicron glasses ranging from 0.5% to 40% by weight. Fillers are described in more detail in Chapter 9. Filled bonding agents may be easier to place on the tooth and may produce higher in vitro bond strengths. Bonding agents may contain fluo-ride, antimicrobial ingredients, or desensitizers, such as glutaraldehyde. The effectiveness of fluoride and antimicrobial release from a bonding agent has not been demonstrated. In Vitro Evaluation of Bond Performance Laboratory tests have been extensively used to com-pare the bond performance of adhesive systems. Although clinical relevance of in vitro evaluations is questionable, they certainly represent a valuable “screening” tool. In addition, different than clinical studies, laboratory evaluations allow isolation of specific variables that may interfere with bond per-formance, for example, substrate conditions, con-taminants, application procedures, and thermal and mechanical cycling. Bond strength tests are, by far, the most popu-lar among in vitro methods. ISO/TS11405 (2003) describes test protocols for both shear and tensile bond strength tests (Fig. 13.3). Both tests use rela-tively large bonding areas (3 to 6 mm in diameter, 7 to 28 mm2). Nominal (average) bond strength A B FIG. 13.3 Bond strength tests. (A) Diagram of the ten-sile test apparatus; (B) diagram of the shear test apparatus. (From Cardoso PE, Braga RR, Carrilho MR. Evaluation of micro-tensile, shear and tensile tests determining the bond strength of three adhesive systems. Dent Mater. 1998;14(6):394–398.) 276 CRAIG’S RESTORATIVE DENTAL MATERIALS is calculated by dividing the failure load by the specimen cross-sectional area. The high incidence of cohesive failures of the substrate observed with these tests prompted the development of micro bond strength tests (Fig. 13.4), using specimens with much smaller bonding areas (1 mm2). The main limitation of bond strength tests, despite their great popular-ity, is that results from different studies cannot be directly compared because of the lack of standard-ization among research groups. In addition, because of the heterogeneous stress distribution along the bonded interface, the nominal bond strength value is far from representative of the true stress that initiated debonding. The quality of the marginal seal obtained with adhesive systems can be estimated by different meth-ods. Interfacial gaps can be measured under a scan-ning electron microscope (Fig. 13.5). Microleakage tests use the immersion of a restored tooth in a tracer or dye solution (e.g., methylene blue or silver nitrate). The tooth is sectioned and the extent of dye penetra-tion is evaluated, either qualitatively (using scores) or quantitatively (Fig. 13.6). The term nanoleakage applies to a method in which specimens previously immersed in silver nitrate are observed under a transmission electron microscope. The presence of silver deposits demonstrates the presence of gaps and voids at the bonded interface. Other in vitro methods for evaluating the perfor-mance of bonding systems are fracture toughness tests that quantify the critical stress level responsible for initiating debonding, and fatigue testing in which the cyclic fatigue resistance after a predetermined number of loading cycles (usually 105 cycles) is calculated. Biocompatibility Solvents and monomers in bonding agents are typi-cally skin irritants. For example, 2-hydroxyethyl methacrylate (HEMA) may produce local and sys-temic reactions in dentists and dental assistants sufficient to preclude their further use in the den-tal office. It is critical that dental personnel protect themselves from recurring exposure. Protective techniques include wearing gloves, immediately replacing contaminated gloves, using high-speed suction, keeping all bottles tightly closed or using unit-dose systems, and disposing of materials in such a way that the monomers cannot evaporate into the office air. Even with double gloves, con-tact with aggressive solvents and monomers will produce actual skin contact in a few minutes. All reasonable precautions should be followed, and if unwanted contact occurs, affected areas should be flushed immediately with copious amounts of water and soap. Once the materials are polymer-ized, there is very little risk of side effects. Although patients should be protected during bonding opera-tions, properly polymerized materials have not been shown to be hazardous to the patient. A B C D E FIG. 13.4 Microtensile bond strength test. (A) Enamel specimen’s preparation involved the removal of a portion of superficial tissue without exposing the underlying den-tin. (B) Tooth prepared for dentin test: the occlusal third was removed with a diamond disc, creating a flat surface. (C) Resin buildup over the enamel and the dentin surface. (D) Cutting of the tooth along the x- and y-axis and the result-ing sticks. (E) Procedure for the preparation of hourglass-shaped specimens: the bonded tooth is sectioned in multiple slabs. On each slab the narrowest cross section is created at the interface by trimming with a bur. (From Goracci C, Sadek FT, Monticelli F, et al. Influence of substrate, shape, and thickness on microtensile specimens’ structural integrity and their mea-sured bond strengths. Dent Mater. 2004;20(7):643–654.) 277 13. Materials for Adhesion and Luting Clinical Performance American Dental Association guidelines require adhesives to be tested in restorations for nonretentive class 5 lesions. The lesions, which may be saucer or notch shaped, have enamel along the coronal margin and dentin along the apical margin. The success of a bonding agent is evaluated indirectly by examining the performance of the restorations for (1) postopera-tive sensitivity, (2) interfacial staining, (3) secondary caries, and (4) retention or fracture followed for 18 months. These clinical trials test short-term retention and initial sealing. Most commercial adhesive systems are successful in clinical trials. However, these clinical trials gener-ally combine enamel and dentin bonding. There is no acceptable clinical regimen for critically testing only dentin bonding in nonretentive preparations. Because clinical trials are usually highly controlled, they are often not predictive of routine clinical use in general practice. Longevity of the bond in general practice may be only 40% of that achieved in clini-cal trials. While long-term clinical performance is not known for all bonding systems, there are reports of studies of longer than 10-year duration showing excellent results for some two-step self-etch and three-step etch-and-rinse materials. Sites of failure for most bonded restorations occur along cervical margins where the bonding is primar-ily to dentin. Studies of bonded composites in class 2 restorations have shown that 95% of all secondary caries associated with the composite restoration is in the interproximal area. These margins are the most difficult to seal during placement of the restoration because they are typically bonded to dentin and cementum rather than enamel, and are hard to access with a light guide for adequate polymerization. Based on the most extensive clinical evidence, the three-step etch-and-rinse systems as a group remain the “gold standard” for adhesive systems, in both laboratory and clinical evaluations. Enamel Bonding Bonding to enamel occurs by micromechanical reten-tion after acid etching is used to preferentially dissolve hydroxyapatite crystals in the enamel outer surface (Fig. 13.7). Fluid adhesive constituents penetrate into the newly produced surface irregularities and become locked into place after polymerization of the adhesive. Gel etchants (typically phosphoric acid) are dis-pensed from a syringe onto tooth surfaces. Etching times for enamel vary depending on the type and quality of enamel. Generally, a 15-second etch with 30% to 40% phosphoric acid is sufficient to reach the characteristic clinical endpoint of a frosty enamel appearance. Deciduous unground enamel gener-ally contains some prismless enamel that has not yet worn away and requires longer etching times (20 to 30 seconds) to create a retentive pattern. Enamel may have been rendered more insoluble as a result of fluorosis. In those cases, extended etching times (15 to 30 seconds) are required to ensure that suffi-cient micromechanical bonding can occur. The only caution is that dentin should not be etched for the same extended time because fluorotic dentin is more susceptible to acid than regular dentin and extensive dentin demineralization should be avoided. After the intended etching time, the acid gel is rinsed away and the tooth structure is dried to receive the bonding resin. If a hydrophilic primer or a two-step etch-and-rinse system is used, the surface can be left moist for the next stage of bonding. Then, primer can be flowed onto the surface to penetrate into the available surface irregularities. After cur-ing, primer and adhesive produce resin macrotags 10 KV X 750 10 µm 000001 FIG. 13.5 Scanning electron micrograph of the epoxy replica showing a contraction gap between enamel (right) and resin cement (left). (From Braga RR, Ferracane JL, Condon JR. Polymerization contraction stress in dual-cure cements and its effect on interfacial integrity of bonded inlays. J Dent. 2002;30(7–8):333–340.) FIG. 13.6 Section of restored tooth showing microle-akage at the composite-enamel interface. (Courtesy Dr. Fernanda C. Calheiros, São Paulo, Brazil.) 278 CRAIG’S RESTORATIVE DENTAL MATERIALS by penetrating the space surrounding the enamel prisms. Microtags form where adhesive flows into the etched prisms involving individual hydroxyapa-tite crystals. Microtags are much more numerous and contribute to most of the micromechanical retention. Strong self-etch adhesives produce a similar pat-tern on enamel as that obtained with phosphoric acid. Mild self-etch systems present lower bond strength to enamel compared to etch-and-rinse systems, prob-ably because of a shallower etching pattern. Dentin Bonding The high water content in dentin represents an extra challenge for the establishment of an interdiffusion zone. To manage this problem, primers have hydro-philic components, such as HEMA, that wet dentin and penetrate its structure. In etch-and-rinse systems, etching with phosphoric acid removes the mineral content, creating microporosities within the collagen network. Once the hydroxyapatite component of the outer layer of dentin is removed, dentin contains about 50% unfilled space and about 20% remaining water. After acid is rinsed, drying of dentin must be done cautiously. Even a short air blast from an air-water spray can inadvertently dehydrate the outer surface and cause the remaining collagen scaffold to collapse onto itself. Once this happens, the collagen mesh read-ily excludes the penetration of primer and bonding will fail. However, excess moisture tends to dilute the primer and interfere with resin interpenetration. The ideal dentin moisture level varies according to the sol-vent present in the adhesive. One advantage of self-etch systems is the elimination of this rather subjective step of the bonding procedure. The infiltration of resin within the collagen scaf-fold is termed hybridization (Fig. 13.8). The result of this diffusion process is called resin-interpenetration zone or resin-interdiffusion zone or simply hybrid layer. Concurrent with hybrid layer formation is the penetration of primer into the fluid-filled dentinal tubules. This may generate long resin tags, though these appear to be of little value to overall bonding. This material is generally undercured and behaves as soft flexible tags. If dentin is dehydrated before priming and bonding, these resin tags are more likely to penetrate even deeper. Primers contain solvents to displace the water and carry the monomers into the microporosities in the collagen network. During application of the primer, most of the solvent evaporates quickly. Thus several layers usually must be applied to ensure a complete impregnation. The rule of thumb is that one should apply as many layers as are necessary to produce a persisting glistening appearance on dentin. The thickness of a hybrid layer is not a critical requirement for success. Dentin bond strength is prob-ably proportional to the interlocking between resin and collagen, as well as to the “quality” of the hybrid layer, not to its thickness. Effective etching of dentin does not require long times to produce acceptable dentin bond strengths. Usually 15 seconds is employed. If etch-ing time is too long and the etched zone is too deep, the decalcified dentin may not be fully impregnated. The etched but not impregnated space may reside as a mechanically weak zone and promote nanoleakage. Although this zone has been detected in laboratory experiments, the clinical results of this process have never been demonstrated to be a problem. After priming the surface, an adhesive is applied and light cured. Surfaces of the cured bonding agents are initially air inhibited and do not immediately react. However, as composite is placed against the surface, much of the air is displaced and copolymer-ization occurs. A 40%PA-carb 5.0kV 12.0mm x7.00k SE(M) 5.00µm PA 5.0kV 12.0mm x5.00k SE(M) 10.0µm B FIG. 13.7 Scanning electron micrograph (SEM) of etched enamel and dentin. (A) Field emission SEM of den-tin etched with 40% phosphoric acid for 15 seconds. Note the collagen fibers deprived from hydroxyapatite crys-tals as a result of acid demineralization. The more intense decalcification around the peritubular area may be a result of both the high mineral content of the peritubular region and the easier penetration of the acid through the tubular lumen. (B) Enamel etched with 38% phosphoric acid for 15 seconds. (From Perdigão J. New developments in dental adhe-sion. Dent Clin N Am. 2007;51(2):333–357, viii.) 279 13. Materials for Adhesion and Luting Self-etch systems have the great advantages of eliminating the risk of incomplete primer/adhesive penetration into the collagen scaffold and also elimi-nating the subjectivity when determining the ideal amount of moisture on the dentin surface for primer diffusion. With these systems, the smear layer is dis-solved and incorporated into the hybrid layer. The bonding mechanism for strong self-etch adhesives is very similar to that of etch-and-rinse systems. Their bond strength, particularly for all-in-one sys-tems, is relatively low, probably because of their high initial acidity and high water content. Mild self-etch systems demineralize dentin only superficially (a few micrometers) and leave residual hydroxyapa-tite attached to collagen fibrils. Although the main bonding mechanism is the interlocking between col-lagen fibrils and the polymerized resin, monomers such as 4-methacryloxyethyl trimellitic anhydride (4-META) and 10-methacryloyloxydecyl dihydrogen phosphate (10-MDP) may bond chemically to this residual hydroxyapatite. In addition, the presence of hydroxyapatite may help protect the collagen against A H RC T 1.5 KV 1 u 5 mm A Macrotag HYBRID LAYER: resin microtags that are within intertubular dentin and surround collagen fibers. Collagen fibers Microtag Composite Bonding Priming Conditioning Dentinal tubule Peritubular dentin Intertubular dentin Residual smear layer particles Residual smear plug particles B FIG. 13.8 Adhesion to dentin. (A) Scanning electron micrograph of interface bonded with a dental adhesive (final mag-nification: ×4000). Note the visible thickness of the adhesive layer (A, arrowheads) beneath the resin composite (RC). The hybrid layer (H, arrowheads) is 2 μm thick. The tubular resin tags (T) show lateral branches (asterisks). (B) Schematic showing that etching removes hydroxyapatite crystals within intertubular dentin and along peritubular dentin. Primer penetrates intertubular spaces and fluid-filled tubular spaces. Cured primer forms microtags within intertubular dentin and macrotags within tubules. (A, From Frankenberger R, Perdigão J, Rosa BT, et al. “No-bottle” vs “multi-bottle” dentin adhesives—a microtensile bond strength and morphological study. Dent Mater. 2001;17(5):373–380.) 280 CRAIG’S RESTORATIVE DENTAL MATERIALS degradation, which weakens the bonded interface. Mild self-etch systems may present relatively low bond strength values when applied to sclerotic den-tin. Another drawback associated with all-in-one systems is that, due to their high water content, the polymers formed from these adhesives behave as semipermeable membranes, which increases degra-dation by hydrolysis. Universal Bonding Universal adhesives have been designed by man-ufacturers to be a single adhesive system, which can be used for bonding to all surfaces relevant to restorative dentistry. Ideally a universal adhe-sive should be a single-bottle no-mix adhesive that can be used reliably in total-etch, self-etch, and selective-etch (i.e., phosphoric etch of enamel only) modes according to the clinicians’ needs for all direct and indirect restorations. Thus it should bond to tooth surfaces (enamel and dentin), direct restoratives (methacrylate resin-based and glass ionomer or resin-modified glass ionomer), and indirect restoratives (e.g., metals, glass-ceramics, and high-strength alumina and zirconia without the need for an extra primer step). Furthermore, it should be compatible with self-cure, light-cure, and dual-cure resin-based cements. Care should be taken in the choice and use of such adhesives because in actuality, many commercial universal adhesives still require an additional component or step. Thus certain products require a separate “activator” to be used for self-cure or dual-cure resin cements. Others may need two components to be mixed prior to use, whereas for some sequen-tial application of two separate components is essential. The key to the successful performance of a univer-sal adhesive is to have the right hydrophilic-hydro-phobic balance in the formulation. Hydrophilicity is needed to properly wet the dentin while hydro-phobicity is essential after polymerization of the adhesive to minimize hydrolysis and water absorp-tion with time. The adhesive should have adequate acidity to be effective in etching all substrates yet not be so acidic that it deactivates the initiators needed for the polymerization of self-cured and dual-cured cements. The best performance is seen for such adhe-sives when they are in the pH range of 2.2 to 3.2. Optimal cohesive strength is also necessary to with-stand the stresses due to polymerization shrinkage of resin restoratives. Most universal adhesives contain a polymerizable phosphate ester as the primary functional monomer. The acidic phosphate group can etch tooth and other substrates and at the same time bond to hydroxy-apatite through the formation of soluble Ca2+ salts. Most modern universal adhesives use 10-MDP as the acidic monomer. One commonly used commercial product uses a proprietary methacrylate-function-alized polycarboxylic acid copolymer (also used in some popular resin-modified glass ionomers, see Chapter 9) in the formulation to provide consistent adhesive strength under the varying humidity condi-tions often encountered in clinical situations. Like the other types of adhesives these materials also contain common monomers such as bisphenol A-glycidyl methacrylate (Bis-GMA), urethane dimethacrylate (UDMA), and HEMA to control the hydrophilic-hydrophobic balance. Photoinitiators and stabilizers are used as with other materials. Water and alcohol are used as carrier solvents. Some universal adhe-sives also contain silanes to provide bonding to sil-ica-based ceramic restorations; however, the use of zirconia primers (see later) is advisable for zirconia-based restorations. Bonding to Other Substrates Cast Alloys Sandblasting with aluminum oxide is the most com-monly used method to prepare metal substrates for receiving bonding resins or resin cements. It creates a microretentive, high-energy surface. Electrolytic etching can be used with base metal alloys, but is not as effective with noble alloys because of its more homogeneous microstructure. Tin plating can be used to improve the retention of noble alloys to resin cements. Commercial systems using silica coating at high temperatures or tribochemical appli-cation of a silica layer using aluminum oxide modi-fied by silicic acid have also been available for many years. In both cases, a silane solution is applied to the treated metal to create a surface capable of bonding to dimethacrylate-based resins. Monomers such as 10-MDP and 4-META are used in formulations of resin cements to improve reten-tion of cast alloy restorations. They seem to be more effective with base-metal alloys, compared to noble alloys. Metal primers developed for improving the bond strength between alloy and resin cements are also available. However, research results are inconsistent. Silica-based Ceramics Silica-based ceramics have been successfully bonded to resin cements by etching the restoration’s inner surface with a hydrofluoric acid solution, fol-lowed by the application of a silane primer (Fig. 13.9). Different acid concentrations are commer-cially available, from 2.5% to 10%, in liquid or gel forms, and recommended etching times vary from 1 to 4 minutes. Hydrofluoric acid attacks the glass phase of ceramics, to the point where crystals are removed, leaving a microretentive honeycomb-like, 281 13. Materials for Adhesion and Luting high-energy surface. Silane application improves the wettability of the resin cement on the ceramic surface and establishes covalent bonds with both the ceramic surface (via siloxane bonds, –Si–O– Si–) and the resin cement (by carbon double bond polymerization). Hydrolysis of the silane molecule is necessary to convert the methoxy groups (– OCH3) to silanol (–Si–OH). Silanes are presented in a nonhydrolyzed form (two bottles) or prehydro-lyzed (one bottle). Zirconia Ceramics The clinical success of indirect ceramic restorations is highly dependent on the cementation procedure employed. In recent years there has been an increase in the popularity of zirconia-based prosthetics such as crowns and bridges due to the material’s superior mechanical strength, esthetic properties, versatility of clinical indications, and ability to be used in digital procedures involving computer-aided design/computer-aided manufacturing mill-ing. However, conventional adhesive cementation procedures involving hydrofluoric acid treatment and application of silane primers do not work for zirconia restorations. This is because zirconia is a polycrystalline material with no amorphous silica glass component, thus making it resistant to acid etching by hydrofluoric acid and also unreactive toward silane primers. Several strategies have been employed for for-mulating commercial zirconia primers. The pri-mary approach has been to roughen the bonding surface of the zirconia by sandblasting and then use a specially formulated zirconia primer con-taining phosphate or phosphonate monomers as the key reactive ingredient. These acidic groups are believed to form a stable Zr–O–P bond with the surface of the zirconia. In addition to the phosphate or phosphonate functionality, these monomers contain a hydrophobic backbone and a methacrylate group that can copolymerize with the adhesive resin cement upon initiation to build up cohesive strength. The most widely used mono-mer in zirconia primers is 10-MDP. It has also been reported that combining phosphate/dithione and phosphate/carboxyl monomers produces a syner-gistic effect in bonding. Some manufacturers also incorporate a silane component in addition to the organophosphate monomer in the primer in order to expand their use to both zirconia and porce-lain surfaces. However, the shelf stability of the silanes in the acidic environment of these prim-ers has been questioned and refrigerated storage of the primers is indicated. In another approach, laboratory or chair-side air abrasion with 110- and 30-μm silica-coated aluminum particles have been used on the interior surface of the zirconia device to create a siliceous surface followed by the treat-ment with conventional silane-based primer (tri-bochemical bonding). This technique has given mixed results. Bonding glass-infiltrated or densely sintered alumina, as well as yttria-stabilized tetragonal zir-conia polycrystalline (Y-TZP) ceramics, remains a subject of debate among clinicians and researchers. Hydrofluoric acid etching is not efficient in highly crystalline ceramics. Therefore other methods such as airborne particle abrasion with 35 to 110 μm alu-mina are indicated to increase surface roughness. Tribochemical coating of Y-TZP surfaces using silica-modified alumina particles followed by silanization is also efficient. Organophosphate monomers such as 10-MDP, present in primers developed specifically for zirconia bonding, universal adhesive systems, Ceramic Inlay Enamel B HF etched surface Acid-etched enamel Enamel bonding system Composite inlay cement Silanated/bonded surface A Mag = 1.00 K X EHT = 15.00 kV Detector = SE1 Date :15 Dec 2010 20µm FIG. 13.9 Etched porcelain. (A) Scanning electron micro-graph of etched porcelain. (B) Schematic of materials and interfaces involved in bonding all-ceramic restorations to tooth structure. HF, Hydrofluoric acid. (A, From Cesar PF, Yoshimura HN, Miranda Júnior WG, et al. Correlation between fracture toughness and leucite content in dental porcelains. J Dent. 2005;33:721–729.) 282 CRAIG’S RESTORATIVE DENTAL MATERIALS and self-adhesive resin cements, were shown to form stable Zr–O–P bonds on the zirconia surface and improve its bond strength to other substrates, partic-ularly when the surfaces were previously modified by air abrasion with alumina. Indirect (Laboratory) Composites A microretentive bonding surface is obtained with alumina sandblasting. Etching with 37% phosphoric acid is used to clean debris from the surface prior to the application of the resin cement. Etching with hydrofluoric acid is not recommended, because it causes degradation of the composite surface by etch-ing away the silica glass and leaving a weak and porous polymer matrix. Amalgam Adhesive systems, filled adhesives, and resin cements can be used in association with amalgam in the so-called bonded amalgam restoration. The purpose of this technique is to reduce the need for macromechanical retention, which would save tooth structure, and reinforce the remaining structure by creating a bonded interface between the restorative material and the cavity walls. The bonding between the adhesive and the amalgam is achieved by the establishment of an interpenetration zone. Although laboratorial studies show better results for bonded amalgams compared to conventional, nonbonded amalgam in terms of bond strength, microleakage, and retention, these findings are not supported by clinical data, which show no difference between bonded restorations and those retained by mechani-cal undercuts. Fiber Posts Bonding fiber-reinforced resin posts to dentin is one of the most challenging situations faced by the cli-nician. Adhesive application is critical, because it is virtually impossible to control moisture inside the root canal. The use of self-etching adhesives systems is not indicated, because their acidity would impede the chemical activation of the resin cement. The use of self-adhesive resin cements (see later) has shown promising results in laboratory evaluations. The surface treatment of the post has also been debated. Silanization, sandblasting, or the association of both treatments are often quoted as being effective pro-cedures to improve the bonding between the resin cement and the fiber post. Repair of Composite, Ceramic, and Ceramic-Metal Restorations Repair of fractured restorations is indicated when the extent of the fracture is not severe enough to war-rant the replacement of the restoration or when there are other factors taken into consideration, such as conservation of the tooth structure, cost, time, or in case of fixed prostheses, the replacement of multiple units. Aging of composite restorations in the oral environment severely decreases the composite-to-composite bond strength. Therefore the use of adhesive systems to mediate the bond between the aged and the fresh composite is recommended. The surface can be roughened with the use of intra-oral sandblasters or a diamond bur, followed by phosphoric acid application for cleaning, prior to adhesive application. The repair of chipped ceramic restorations includes conditioning with hydrofluoric acid, silani-zation, application of a bonding resin, and restoration with a resin composite. Intraoral use of hydrofluoric acid gel must be performed with rubber dam isola-tion because of its caustic effect on soft tissues. Repair of metal-ceramic restorations includes bonding to different substrates. When there is a large area of the metal infrastructure exposed, sandblast-ing with alumina or alumina modified with silicic acid is recommended, followed by the application of silane and adhesive resin, prior to composite applica-tion. Fractured porcelain surfaces can be sandblasted and etched with hydrofluoric acid gel prior to silani-zation, adhesive application, and restoration with composite. CLASSIFICATION AND CHARACTERISTICS OF LUTING AGENTS Classification Luting agents can be classified according to the length of time they are expected to stay in function as provi-sional or definitive. Provisional (temporary) cements are indicated for fixation of temporary restorations used between the clinical appointments necessary to finish the definitive restoration. Because temporary restorations often need to be removed during treat-ment, provisional cements must have a relatively low strength and be easily handled. In addition, they must not irritate the pulp. Examples of tempo-rary luting agents are zinc oxide-eugenol (ZOE) and noneugenol cements and calcium hydroxide pastes. Definitive cements are supposed to remain in func-tion for the longest time possible and therefore must have sufficient properties. According to setting mechanism, luting agents are divided into those presenting an acid-base reac-tion (which include glass ionomer, resin-modified glass ionomer, ZOE, zinc polycarboxylate, and zinc phosphate), those that set by dissolution and repre-cipitation in aqueous medium (calcium aluminate 283 13. Materials for Adhesion and Luting cements), and those setting by polymerization (resin cements, compomers, and self-adhesive resin cements). In some cases, this classification refers to the predominant setting mechanism because resin-modified glass ionomers contain polymerizable groups, whereas compomers and self-adhesive resin cements may have an acid-base reaction. The physical requirements of luting cements are described in the following standards from the International Association for Standardization: ISO 3107:2004 (ZOE and noneugenol cements), ISO 9917-1:2007 (powder/liquid acid-base cements), ISO 9917-2:2010 (resin-modified cements), and ISO 4049:2009 (polymer-based cements) standards (Box 13.1). Those requirements, along with other important characteristics, are described below. Biocompatibility Luting agents are often placed in contact with large areas of exposed dentin. Also, remaining dentin thickness can be insufficient to protect the pulp tis-sue from external stimuli. The majority of the luting agents show cytotoxicity in vitro to different degrees. Histological studies also show an early inflamma-tory reaction to cements placed close to connective tissue. Such responses are usually associated to the initial low pH of some acid-base cements and self-etch resin cements or monomers present in resin-modified glass ionomers and resin cements. Interfacial Sealing and Anticariogenic Activity The perfect sealing of the tooth/restoration inter-face is important to prevent bacterial penetration that may lead to secondary caries and also, when dentin is involved, prevent excessive fluid move-ment in the dentinal tubules that may cause hyper-sensitivity. Sealing is related to the ability of the cement to penetrate in the irregularities of both substrates and establish an intimate contact with them. Ideally, luting cements should not shrink upon setting, or voids may develop at the interface. Adhesion also contributes for a good interfacial sealing. Fluoride-containing cements are supposed to inhibit bacterial activity, however, the clinical sig-nificance of fluoride release from luting cements is yet to be confirmed. Adhesion Lack of retention is a common cause of failure of indi-rect restorations. The use of adhesive materials may reduce the risk of displacement. In some instances (e.g., porcelain crowns), bonding may reduce the risk of restoration fracture. Adhesion may also help improve interfacial sealing. Adhesion may occur by chemical or physical bonding, micromechanical interlocking, or friction. Some acid-base cements and self-adhesive resin cements bond to dental tissues by chelation involving metal ions and carboxylic or phosphate groups. Resin cements require the use of adhesive systems to establish a strong bond to dentin and enamel. Mechanical Properties Mechanically, luting cements are described in terms of strength (usually in compression or in flexural mode), elastic modulus, fatigue resistance, fracture toughness, and wear. Wear is less of a problem when the cement line is not exposed to masticatory forces (e.g., a full crown). Fatigue strength is usually con-sidered more representative of the type of loading cements must endure in the clinic. However, fatigue tests are much more time consuming than static strength tests. Elastic modulus expresses the amount of elastic (recoverable) deformation the cement presents relative to a stress state caused by external loading. Fracture toughness describes the resistance to unstable crack propagation that will cause cata-strophic failure of the material. Permanent luting cements must have high strength (both static and fatigue) and fracture tough-ness and good wear resistance. Ideal values for elastic modulus are debatable, and values can vary substan-tially even among permanent cements. Temporary cements, by contrast, must have a relatively low strength, or removal of temporary restoration can become a difficult task. Handling Properties and Radiopacity Ease of use, long working time, and short setting time are desirable characteristics of luting cements. Along with powder and liquid materials, recent products are encapsulated or presented as two-paste, self-dispensing systems, which makes pro-portioning and mixing faster and less prone to error. BOX 13.1 I S O S TA N D A R D S F O R D E N TA L C E M E N T S ISO 3107:2004 (zinc oxide-eugenol and noneugenol cements) ISO 9917-1:2007 (powder:liquid acid-base cements) ISO 9917-2:2010 (resin-modified cements) ISO 4049:2009 (polymer-based cements) 284 CRAIG’S RESTORATIVE DENTAL MATERIALS A long working time is important to make sure the cement presents low viscosity while the restoration is seated. Otherwise, adaptation may be compromised. For some materials (e.g., resin cements), removal of excess cement also needs to be done before set-ting. Radiopacity is important to allow radiographic diagnostic. Viscosity and Film Thickness A low film thickness is important to allow for the correct seating of the restoration. Film thickness is usually determined by the cement average particle size and its viscosity. Some cements are pseudoplas-tic, looking excessively thick at the end of the mix-ing period, but flowing well under seating pressure. Overall, if handled properly and applied within the recommended working time, all currently avail-able materials are able to reach a thickness below that required by the ISO standards. However, some cements may show a sudden increase in viscosity and film thickness in short intervals after the end of the recommended working time. Solubility Solubility refers to the resistance to disintegration and dissolution when the cement is immersed in water or other solutions. It affects the marginal integ-rity of the indirect restoration, which may increase plaque accumulation. Resin-based cements present much lower solubility than acid-base cements. Esthetics When used with translucent materials or when resto-ration margins are exposed, shade and translucency of the cement are important aspects to be considered because they may affect the final esthetic result of the restoration. It is particularly critical with porce-lain laminate veneers. Resin cements are the most esthetic luting materials available. Glass ionomer, resin-modified glass ionomer, compomer, and self-adhesive resin cements also have good esthetics. Zinc polycarboxylate, ZOE, and zinc phosphate are opaque. ACID-BASE CEMENTS Zinc Oxide-Eugenol and Noneugenol Cements The reaction between zinc oxide and eugenol has several applications in dentistry, such as endodon-tic sealers and root-end filling materials, periodontal dressings, inelastic impression materials, cavity bases, and temporary restorations. For luting purposes, different formulations of ZOE cements are avail-able for both temporary cementation and permanent fixation of metallic and metalloceramic crowns and bridges. Due to an inhibitory effect of eugenol on polymerization of methacrylate-based resins and lut-ing composites, temporary cements using nonpheno-lic components are often preferred over conventional formulations. Their popularity is justified by their ease of use, antibacterial action, and anodyne effect on dental pulp. Composition The powder is basically zinc oxide, with up to 8% of other zinc salts (acetate, propionate, or succinate) as accelerators. Rosin (abietic acid) is added to reduce brittleness and increase working time and strength. The liquid contains eugenol (4-allyl-2-methoxy phe-nol), a weak acid. Acetic acid (up to 2%) is added as accelerator. In two-paste materials used for tem-porary cementation, one paste contains zinc oxide mixed with mineral or vegetable oils, whereas fill-ers are incorporated into eugenol to form the other paste. Noneugenol materials use long-chain aliphatic acids or aryl-substituted butyric acid to react with zinc oxide particles. Other oils can be added to adjust paste consistency. An important improvement of ZOE cements was the development of materials in which the liquid is a mixture of 2-ethoxybenzoic acid (EBA) and eugenol, roughly in a 2:1 proportion. Rather than forming a stronger matrix, the addition of EBA allows for the use of very high powder-to-liquid ratios (6:1) which, per se, increases the strength of the set cement. In these materials, alumina (30%) was added to the powder as a reinforcing agent. The incorporation of 20% poly(methyl methacrylate) particles is also used to improve mechanical properties in some products. Setting Reaction and Structure The reaction of zinc oxide with eugenol results in the formation of a zinc eugenolate chelate, that is, a complex in which one zinc (Zn) atom binds to two eugenolate molecules. In addition, as mentioned earlier, the dissociation constant of eugenol is small. Therefore reaction rate is increased with the use of more reactive oxides, along with the presence of accelerators. The acid-base reaction does not take place in an aqueous medium; however, water plays a very important role in the reaction, because it reacts with zinc oxide forming ZnOH+ ions that dissociate in Zn2+ and OH–. The zinc cations then react with the eugenolate, whereas the hydroxyl anions react with the H+ forming water. Because water is present as reagent and final product, the reaction is autocata-lytic. The presence of acetic acid eliminates the need of water to initiate the reaction. 285 13. Materials for Adhesion and Luting The structure of the set cement is represented by zinc oxide particles bound together by an amor-phous zinc eugenolate matrix. EBA also forms a chelate with zinc oxide, and crystalline phases have been identified within the matrix of EBA-eugenol cements. Manipulation, dispensing, and mixing con-siderations can be found on the book’s website Properties ZOE cements are considered biocompatible because of their neutral pH, antibacterial action, and anodyne effect on hyperemic pulpal tissue. Their antibacterial activity in vitro was shown to be more efficient than those displayed by conventional and resin-modified glass ionomers. That characteristic associated with a good marginal seal favors the recovery of the pulp. Eugenol released from the salt matrix may contrib-ute to pain relief in preparations with little remaining dentin thickness. However, in high concentrations or when placed directly in contact with connective tissue, it may increase the inflammatory response because of its cytotoxicity. The low strength displayed by ZOE cements makes them a suitable material for temporary cementation. The ISO 3107 standard (2004) estab-lishes a maximum 24-hour compressive strength of 35 MPa for type 1 materials (i.e., intended for tem-porary cementation). An important aspect related to the mechanical behavior of ZOE cements is that their properties are very sensitive to temperature. For example, compressive strength at 37°C may represent only 20% of what was found at 23°C. EBA-eugenol cements can be several times stronger than the basic formulation (72 MPa vs. 26 MPa, in compression at room temperature). EBA-alumina cements can present 20% higher strength compared to EBA-eugenol materials. Even though these val-ues are above the minimum compressive strength required for type 2 materials (i.e., permanent luting cements) of 35 MPa, both reinforced ZOE cements are the weakest among luting agents used for per-manent cementation. The elastic modulus of EBA-eugenol cements (determined at room temperature) is 3 GPa. ZOE cements present increased plasticity even after set and flow under load. Plastic strain at frac-ture was shown to be above 15% at 37°C, against a maximum value of 4% presented by other acid-base and resin cements. Creep behavior may explain the good marginal seal achieved with these materials, even considering their setting shrinkage. Linear shrinkage values of wet samples after 24 hours were shown to be 0.31% for the basic ZOE formulation, 0.38% for EBA-eugenol, and 0.12% for EBA-eugenol/ alumina cements. Film thickness measured according to the ISO standard ranges between 16 and 28 μm for EBA/alu-mina materials; therefore it is close to the maximum value allowed. Simulated crowns cemented with a basic formulation and EBA-eugenol cement showed similar film thicknesses at the occlusal surface (20 to 25 μm), whereas for the EBA-alumina cement, film thickness was higher (57 μm). The zinc-eugenolate matrix chelate is very unsta-ble in water. Its hydrolysis forms eugenol and zinc hydroxide, releasing the zinc oxide particles exposed in the process. In vitro studies showed that zinc 2-ethoxybenzoate matrix formed in EBA-eugenol cements is even more prone to hydrolysis than the zinc eugenolate. In vivo, material loss after 6 months was three to seven times higher for an EBA-alumina cement compared to other acid-base cements. Clinically, fixed prostheses cemented with EBA-alumina cement showed a success rate of 92% after 2.5 years, whereas for zinc polycarboxylate, it was 95%. Zinc phosphate, for many decades the “gold standard” for permanent luting agents, showed a success rate of 98%. The inhibitory effect of methoxyphenols such as eugenol on the polymerization of methacrylate res-ins is of clinical importance. Eugenol is considered a free-radical scavenger, due to the presence of the allyl group in its structure acting as a degradative chain-transfer agent (i.e., when activated, it prefer-ably undergoes primary radical termination, rather than propagation). Temporary cements containing eugenol may negatively affect the polymerization of methyl methacrylate used in provisional resto-rations. If the final restoration will be bonded to the prepared tooth, the polymerization of both the adhesive system and the resin cement may be inhib-ited, increasing the risk of debonding, or even frac-ture in case of low-strength, silica-based ceramics or indirect composite restorations. In fact, in ZOE cement/composite interfaces, composite mechani-cal properties were reduced up to a 100 μm away from the interface, which may be relevant if the resin cement is applied to a eugenol-contaminated surface. However, several in vitro investigations have shown that bond strength to dentin is not adversely affected if the surface is thoroughly cleaned prior to adhesive application. Glass Ionomer Glass ionomer (or glass polyalkenoate) cement is arguably one of the most popular materials for permanent cementation used in the clinic, along with resin cements. The chemistry that is the basis for these cements is similar to that in glass iono-mer restorative, lining, and preventive materials (see Chapter 9), although there are some important 286 CRAIG’S RESTORATIVE DENTAL MATERIALS differences in working and setting behavior to fit the needs of luting agents. Besides good physi-cal properties, glass ionomers adhere to the tooth structure and metals and, most importantly, release significant amounts of fluoride, which increase the resistance of enamel and dentin to acid dissolution and act as a bacteriostatic agent. Fluoride release makes this material the first choice for cementation of orthodontic bands. It is indicated for cementation of metallic and metal-ceramic restorations, as well as high-strength ceramic crowns and fixed prostheses. Its setting reaction is sensitive to moisture condi-tions, and for this reason, it is extremely important to protect the cement against gain and loss of water during the first 24 hours. Composition Details of chemical composition and setting reac-tion are provided in Chapter 9. The powder is a calcium fluoroaluminosilicate glass with maxi-mum particle size of 15 μm. Other glasses can be formulated in which calcium is replaced by strontium or lanthanum to increase radiopacity. The basic character of the glass is defined by its alumina-to-silica ratio and, in order to react with acids, it must exceed 1:2 by mass. Large amounts of fluoride are incorporated in the glass by adding calcium and sodium fluoride to the other oxides. Fluoride is an important component, because it lowers the melting point and enhances the trans-lucency of the powder and improves the consis-tency of the mixing paste and the strength of the set material. The presence of electropositive ions, such as Ca2+ and Na+, is important to balance the ionic charges in the basic aluminosilicate lattice. Zinc oxide and barium glasses can be added to the powder to increase radiopacity. The liquid contains homopolymers of acrylic acid or copolymers of acrylic, itaconic, maleic, and tricarboxylic acids. Overall, high molecular weights and increased acid concentrations improve physical properties of the set cement, but they also increase the viscosity of the liquid. Therefore commercial materials usually employ polyacids with average molecular weight of 10,000 g/mol and concentra-tions around 45% by mass. Tartaric acid (around 5% by mass) is an important component of the liquid, because it accelerates the setting without shortening working time. Its presence increases cement strength and allows for the use of glasses with higher fluoride content and, therefore, higher translucency. To avoid the increase in viscosity of the liquid after prolonged storage, some products contain the polyacid in a freeze-dried form added to the pow-der. In this case, the powder is mixed with distilled water or a tartaric acid solution. Such presentation adds the advantage of allowing the use of polyacids with higher molecular weight and in higher con-centrations, which increases the strength of the set material. Setting Reaction and Structure When the powder is brought in contact with the acid solution, H+ from the acid attacks the glass, releasing metal ions (Al3+, Ca2+, Na+, and F–) and silicic acid (general formula: [SiOx(OH)4-2x]n) (see Chapter 9). The silicic acid condenses on the ion-depleted outer layer of the particle forming a layer of silica gel. Calcium ions are preferentially released from the glass. As the concentration of ions in the solu-tion increases, the pH rises and metal ions begin to condense among the poly(acrylic acid) chains pre-cipitating the polyacrylate salts, initially in a sol state (initial set) and latter turning into a gel. The precipitation of aluminum salts initiates after a few hours into the reaction because it is released from the glass as a strong complex with fluoride. The reaction continues until all the ions are bound to the polyacrylate. From a clinical standpoint, the fact that ions remain in solution for extended periods before reacting with the polyanions, even after the initial set, is critical. If ions are washed out from the cement, the structure of the polysalt matrix is irre-versibly compromised. In addition, calcium poly-acrylate is more vulnerable to dissolution in water than the aluminum polyacrylate formed at later stages. By contrast, water plays a very important role in the reaction and in the set cement, because it remains tightly bound to the cement structure, hydrating the silica gel layer and involving the cation-polyacrylate bonds. Therefore a high relative humidity (approximately 80%) is the ideal condi-tion for the setting reaction to take place. The tartaric acid is stronger than poly(acrylic acid) and therefore reacts first with the glass and can form complexes with metal cations at lower pH. Its presence extends working time by delaying the for-mation of calcium polyacrylate, and upon gelation it accelerates setting by increasing the deposition rate of aluminum polyacrylate. The set cement is constituted by a hydrogel of cal-cium, aluminum, and fluoroaluminum polyacrylates involving the unreacted glass particles sheathed by a weakly bonded siliceous hydrogel layer. About 20% to 30% of the glass is dissolved in the reaction. Smaller glass particles may be entirely dissolved and replaced by siliceous hydrogel particles contain-ing fluorite crystallites. The stability of the matrix is given by an association of chain entanglement, weak ionic cross-linking, and hydrogen bonding. Manipulation considerations can be found on the book’s website /restorative. 287 13. Materials for Adhesion and Luting Properties Glass ionomer cements are considered mild to the pulp compared to their predecessors, which used phosphoric acid solutions. However, inflammatory response is more intense than that associated with ZOE cements. In fact, the biocompatibility of glass ionomers is controversial, and in vitro results seem to vary according to the commercial brand tested. In general, there is some consensus regarding the fact that freshly mixed cements may present differ-ent degrees of cytotoxicity and cause a mild tran-sient inflammatory response when placed in contact with pulpal connective tissue, but such response is greatly attenuated if at least 1-mm thickness of den-tin is present. Besides a low remaining dentin thick-ness, the risk of postoperative sensitivity increases if a faulty technique is used. Thin mixtures seem to increase the risk of sensitivity. Rather than pulpal irritation, it is possible that postoperative pain may be related to the hydrostatic pressure exerted by the cement through the dentin tubules. Glass ionomer cements release significant amounts of fluoride, both in the short and long term, which was shown to have an important anticariogenic effect. Fluoride release increases the resistance of enamel to acid dissolution, by inhibiting bacterial growth and interfering with the metabolism of the dental plaque. The use of glass ionomer for orthodontic bonding reduced the risk of white spots formation almost by half compared to a resin cement. However, when patients were exposed to fluoride-containing tooth-paste, no differences in enamel or dentin deminer-alization under accumulated plaque were observed in the short term between an ionomeric and a resin cement. It must be emphasized that the surface area of the luting cement exposed to the oral environment is small. Therefore the amount of fluoride released to the adjacent structures, as well as the fluoride recharging ability of the cement layer, may be less clinically relevant compared to direct glass ionomer restorations. Bonding to tooth structures is one of the main characteristics of glass ionomers. It helps to enhance the marginal sealing of the restoration compared to nonadhesive cements, but is not high enough to significantly increase retention. The proposed adhesion mechanism is twofold: it occurs by the displacement of phosphate and calcium ions from the hydroxyapatite by carboxylate ions pendant from the polyacid chains and the incorporation of these carboxylate groups into the hydroxyapatite structure, and also by micromechanical interlocking achieved by a shallow hybridization of the partially demineralized dentin. Dentin surface treatment with 10% to 20% polyacrylic acid for 5 to 20 sec-onds (shorter times for higher concentrations) sig-nificantly increases bond strength by removing the smear layer, partially demineralizing the surface-creating microporosities for micromechanical inter-locking, and enhancing the chemical interaction of poly(alkenoic acid) with the hydroxyapatite. A solu-tion containing 3% to 10% citric acid is also effective because Fe3+ ions deposited on the dentin surface increase the interaction with the cement. Bond strength of glass ionomer to dentin and enamel varies according to commercial product tested, but when loaded in shear it is around 2 to 5 MPa. Glass ionomer cements bond well to stainless steel, noble, and nonnoble alloys and titanium, but not to high-strength core ceramics. Its mechanical properties are superior to other acid-base cements and increase significantly over long periods. Compressive strength is between 100 and 150 MPa; therefore it is far beyond the minimum of 70 MPa specified in the ISO 9917 standard. These cements are much weaker in tension because of their brittle nature, with diametral tensile strengths of about 6 MPa. Elastic modulus is around 15 GPa. Film thickness is below the maximum allowed by the ISO standard (25 μm) and should not prevent the correct seating of the restoration, if the cement is properly handled. Erosion tests in vitro using citric acid showed that the fully set glass ionomers are more resistant than nonadhesive acid-base luting cements and erode at levels similar to those shown by enamel and dentin. Such behavior may be related to the silica gel layer that envelops the glass particles. Resin-Modified Glass Ionomer Resin-modified (or hybrid) glass ionomers set by both an acid-base and a polymerization reaction. The technology was originally developed for direct restoratives, but as with resin cements, the chem-istry was adapted to formulate materials for luting cements. Although details of chemistry and setting reactions of resin-modified glass ionomer systems are provided in Chapter 9, this section gives a brief overview pertinent to luting cements. This class of cements does not show the early sensitivity to mois-ture conditions presented by conventional glass ionomers because of the presence of a polymeric phase, which prevents the loss of water and metal ions from the immature polysalt matrix. Available as powder-liquid, capsules, and paste-paste hand-mix and automix systems, resin-modified glass ionomer luting cements are indicated for permanent cemen-tation of ceramic-metal crowns and fixed prostheses (e.g., metal inlays, onlays, and crowns; prefabri-cated or cast posts; porcelain fused to metal crowns and bridges, high-strength core zirconia all-ceramic crowns, and bridges; and luting of orthodontic appli-ances). Traditionally, these cements were self-cure 288 CRAIG’S RESTORATIVE DENTAL MATERIALS only but the more recent versions have a photoini-tiator so that they can be briefly light activated (i.e., “tack cured”) to speed up the placement. Composition The chemistry of resin-modified glass ionomers is more complex than that of conventional glass ionomers (see Chapter 9). In powder-liquid systems, the powder con-tains fluoroaluminosilicate glass particles similar in composition to those found in conventional glass ion-omers. Catalysts for the self-cure (redox) polymeriza-tion are added to the powder. The liquid may contain poly(acrylic acids) modified with pendant methacrylate groups replacing a small part of the carboxylic radicals, HEMA, water, and tartaric acid. HEMA replaces part of the water and is a small molecule (molecular weight: 130 g/mol) soluble in water due to the presence of a hydroxyl group in its structure. Another liquid formu-lation contains similar concentrations (around 25% to 30% each) of a copolymer of poly(acrylic acid), HEMA, and water, and smaller amounts of low-viscosity dimethacrylate resins (such as urethane or triethylene glycol dimethacrylates). Initiators for the light-cured polymerization, if present, are found in the liquid. Formulations of paste-paste materials are brand specific. Basically, one of the pastes contains the glass particles, HEMA, and a dispersing agent. Water and the reducing agent of the self-cure activation may be present, or a UDMA. The other paste contains the modified poly(acrylic acid), water, the oxidizing agent of the activation system, and fillers, and may present HEMA or a high-viscosity dimethacrylate monomer, such as Bis-GMA. Setting Reaction and Structure The setting reaction of resin-modified glass ionomer cement comprises two different mechanisms. The ini-tial set is the result of either a light-cured or self-cured polymerization reaction of the methacrylate groups, present as pendant groups in the poly(acrylic acid) chain, in the HEMA molecule, or in the dimethacry-late monomers. Refer to reactions in Chapter 9. The acid-base reaction, described in the previous section, is slower than in conventional glass ionomers because of the lower water content. The HEMA polymer and the polysalt are linked by hydrogen bonds. However, phase separation between the two matrices formed may occur. The use of a modified poly(acrylic acid) prevents phase separation, because the carbon double bond in the HEMA structure may polymerize with the pendant methacrylate from the polyacid chain. As a result, the cement matrix is formed by both ionic and covalent crosslinks. For further discussion, refer to Chapter 9. Manipulation considerations can be found on the book’s website /restorative. Properties Resin-modified glass ionomers are probably the most popular type of luting cements used clinically due to several beneficial properties, which include very low postoperative sensitivity; convenient proce-dure, especially ease of cleanup; minimal solubility; good bond to tooth structure; and extended fluoride release. This category is considered less biocompat-ible than conventional glass ionomers because of the presence of HEMA. Besides its already mentioned allergenic effect, it is a potential source for adverse reactions in the pulp. The largest amounts of HEMA are released in the first 24 hours, but release con-tinues for several days. The release of free HEMA from the cement is higher in undercured materials. Therefore a correct mixing technique must be used to optimize the polymerization. In light-cured mate-rials, the recommended exposure must be followed. In general, clinical results with these materials that have been reported to date are generally positive and this class of cements is by far the most popular class of luting cements preferred by clinicians. In vitro fluoride release by conventional and resin-modified luting glass ionomers was found to be similar over a 180-day period, ranging from 99 to 198 ppm. Mineral loss and lesion depth around orth-odontic brackets in vitro were significantly lower with resin-modified glass ionomers, compared to one resin cement and one luting compomer. Fluoride release is higher after 24 hours, stabilizing after 2 weeks. Resin-modified glass ionomer cements show shear bond strength to conditioned dentin (10% cit-ric acid, 2% ferric chloride for 20 seconds) or enamel (10% polyacrylic acid solution for 20 seconds) in the range of 8 to 12 MPa, although the popular products are self-adhesive and do not require additional den-tin treatment. The bonding mechanisms are the same as described for conventional glass ionomers. The lower bond strength to enamel compared to resin cements may actually facilitate orthodontic bracket debonding. They bond to metal alloys and high-strength ceramics, with initial shear bond strengths of 2 to 5 MPa. Bond strength to metal alloy is sig-nificantly increased with the use of metal primers. Because of the presence of methacrylate groups, these cements bond well to resin composites. Retention of metal-ceramic crowns to prepared teeth may vary significantly between the two-paste and the powder:liquid versions of the same product, and it is usually higher in the latter. In terms of mechanical properties, resin-modified glass ionomer cements show compressive strength similar to conventional glass ionomers, between 90 and 140 MPa, and lower elastic modulus (3 to 6 GPa). Flexural strength may vary between 15 and 30 MPa. Film thickness determined at room temperature 2 minutes after the start of mixing may vary between 289 13. Materials for Adhesion and Luting 9 and 25 μm. However, film thickness may increase substantially if the restoration is not placed within the recommended working time. The presence of HEMA increases the water sorp-tion of resin-modified glass ionomers, compared to conventional glass ionomers and resin cements. In fact, some manufacturers do not recommend its use for luting low-strength, silica-based ceramic crowns because of the risk of fracture caused by swell-ing of the cement. Water uptake after 7 days mea-sured according to ISO 4049 may be three to nine times higher compared to resin cements. Solubility in water is also higher compared to resin cements, about two to four times. In lactic acid (pH = 4), the solubility of some resin-modified glass ionomers is about 10 times higher than resin cements. Calcium Aluminate/Glass Ionomer Cement This material contains a mixture of monocalcium aluminate (CaOAl2O3), inert glasses and, in some cases, glass ionomer particles. The liquid can be either a neutral polycarboxylic acid solution or a mixture of polyacrylic, tartaric, and neutral poly-carboxylic acids. This material does not set solely by acid-base reaction, but also by dissolution and reprecipitation of the monocalcium aluminate parti-cles. In contact with water, the monocalcium alumi-nate dissolves and reprecipitates as katoite [Ca3Al2 (SiO4)1.5(OH)6] and aluminum hydroxide [Al(OH)3, or gibbsite]. The new crystals attach to the tooth structure, which associated to its alkaline pH could reduce the risk of postoperative sensitivity. Because of its calcium content and high pH, these cements were shown to be bioactive, promoting hydroxyapa-tite precipitation in vitro. Its performance in terms of mechanical properties and crown retention (metal and ceramic) is similar to self-adhesive cements. Because the aluminum hydroxide initially forms as an amorphous gel, excess removal is facilitated. A description of zinc polycarbonate (or zinc poly-acrylate) and zinc phosphate, materials that are no longer commonly used in the United States, can be found on the book’s website com/sakaguchi/restorative. RESIN-BASED CEMENTS Resin Cements Overview Resin cements are low-viscosity composite materials with filler distribution and initiator content adjusted to allow for a low film thickness and suitable work-ing and setting times. They have a wide range of applications, from inlays to fixed bridges, prefabri-cated posts, and orthodontic appliances. They are mandatory materials for luting low-strength ceramic and laboratory-processed composite restorations, but can also be used with cast restorations, particu-larly in cases where extra retention is needed. The ISO specification 4049 (2009) classifies resin cements according to curing mode as class 1 (self-cured), class 2 (light-cured), or class 3 (dual-cured). Most of the commercial products are dual-cured, combining chemical- and light-activation mechanisms. These materials show a comfortable working time and cure on command characteristic of light-cured compos-ites, and also the security of high degrees of conver-sion even in areas not reached by the light. Class 1 and class 3 materials are typically hand-mixed or automixed two-paste systems (base and catalyst). Self-cured and dual-cured materials can be opaque or translucent, and those indicated for cementa-tion of ceramic restorations are usually provided in several shades. Light-cured materials are indicated for bonding of laminated ceramic veneers (esthetic cements) or orthodontic brackets. Some esthetic resin cements used for cementation of veneers include glycerin-based, water-soluble “try-in” pastes to help with shade selection. Composition Most resin cements share a very similar composi-tion to that of restorative composites, which are described in Chapter 9. The organic matrix contains dimethacrylate monomers and oligomers. High-molecular-weight molecules such as Bis-GMA (Mw = 512 g/ mol), UDMA (Mw = 480 g/mol), and eth-oxylated Bis-GMA (Bis-EMA, Mw = 540 g/mol) are combined with smaller molecules usually derived from ethylene glycol dimethacrylates (diethylene glycol dimethacrylate, Mw = 242 g/mol, and tri-ethylene glycol dimethacrylate, Mw = 286 g/mol) to achieve a high degree of conversion with a rela-tively low volumetric shrinkage. The filler fraction may vary between 30% and 66% by volume and con-tains silanated radiopaque glasses such as barium, strontium, or zirconia, along with silica particles. Average filler size may vary between 0.5 and 8.0 μm. Microfilled cements are also available, containing silica with an average filler size of 40 nm. Pigments and opacifiers are also present in both pastes. Some adhesive resin cements contain proprietary monomers. One example combines MDP, a polymer-izable phosphoric acid ester, with Bis-GMA. Another product contains 4-META and methyl methacrylate in the liquid, poly(methyl methacrylate) in the pow-der, and tri-n-butylborane as catalyst. Camphorquinone and a tertiary amine are pres-ent in one of the pastes to initiate the light-activated reaction. Benzoyl peroxide, the self-cure activator, is present in the catalyst paste. The amine functions as proton donor and is considered an accelerator 290 CRAIG’S RESTORATIVE DENTAL MATERIALS of free-radical production. Aromatic amines (such as ethyl 4-dimethylaminobenzoate) are consid-ered more efficient than aliphatic amines [such as 2-(dimethylamino)ethyl methacrylate]. The presence of amine in the composite matrix poses some clini-cally relevant concerns. First, amines are known to degrade over time, altering the shade of the cement. Second, they become inactive when in contact with acidic adhesive systems, and when cement polym-erization takes place in the absence of light activa-tion, the deleterious effect on degree of conversion may increase the risk of restoration debonding. It is important to point out that the relative amounts of self-cure and light-cure initiators vary significantly among commercial brands. Consequently, some materials are more dependent on light activation to achieve a high degree of conversion. Likewise, some commercial materials cure more promptly in the absence of light than others. Setting Reaction and Structure Resin cements set by free-radical polymerization, resulting in the formation of a densely cross-linked polymer structure surrounding the filler particles. Free radicals are generated by light activation, in which camphorquinone in the excited state combines with an amine molecule to generate a free radical. In the absence of light, free radicals are formed by redox reaction of the amine-peroxide system. A crosslink is formed when a propagating chain encounters an unreacted carbon double bond in a different poly-mer chain. Polymerization proceeds until the mobil-ity of the reactive species becomes restricted by the increasing viscosity of the material and free radicals cannot propagate further, becoming entrapped in the polymer. Final degree of conversion is around 70% and depends on matrix formulation, initial viscos-ity, and curing mode. Conversion is usually higher in cases where the cement is dual-cured, compared to self-cured. Manipulation considerations can be found on the book’s website /restorative. Properties Monomers released from resin cements are known to produce cytotoxic effects on mammalian cells. Dual-cured resin cements show higher cytotoxicity at early setting stages when tested in self-cure mode, com-pared to specimens exposed to light curing. After 7 days of incubation, Bis-GMA-based dual-cured cements are less cytotoxic than zinc polyacrylate, resin-modified glass ionomer, and a resin cement containing MDP monomer. Mechanical properties of resin cements are defined by their filler content and degree of con-version reached by the organic matrix. As a rule of thumb, higher filler levels and higher conver-sion correspond to higher mechanical properties. Degrees of conversion of dual-cured cements are between 50% and 73% in the self-cure mode and 67% and 85% when light-cured. Compressive strengths of dual- and light-cured resin com-posite cements have been reported from 180 to 300 MPa, therefore much superior to acid-base cements. Flexural strength is between 80 and 100 MPa, higher than the minimum value required by the ISO 4049 standard (50 MPa). Elastic modulus may vary significantly among commercial brands, being between 4 and 10 GPa, values comparable to other cements. For dual-cured cements, mechani-cal properties are slightly higher when the cement is light-cured. Film thicknesses measured according to ISO stan-dards are between 13 and 20 μm, therefore within the maximum of 50 μm required by the ISO 4049. Water sorption and solubility of resin cements are much lower than those of resin-modified glass iono-mer cements. However, the cement line may become apparent after a prolonged period of clinical use because of discoloration. Shrinkage of resin cements varies between 2% and 5%. Immediate shear bond strength of resin cements to dentin varies between 12 and 18 MPa. MDP can bond to tooth structures, ceramics, and cast alloys by the reaction between its phosphate groups and calcium or with metal oxides. The integrity of the bonded interface is challenged by polymerization stress development. Polymerization stresses arise because of resin cement polymerization shrinkage, associ-ated with the development of elastic behavior. In general, dual-cured cements develop higher polym-erization stress values when light-cured because the curing reaction is faster than the self-cure reaction, allowing less time for viscous flow to accommodate the shrinkage before the resin composite reaches the vitrification stage. After the resin cement reaches the degree of conversion corresponding to the vitrifica-tion point of the organic matrix, all the shrinkage will contribute to stress buildup. When stresses at the interface surpass the bond strength of the adhesive layer to dentin or enamel, debonding and the forma-tion of a contraction gap may occur. Compomers (polyacid-modified resin composites) can be found on the book’s website elsevier.com/sakaguchi/restorative. Self-Adhesive Resin Cements Self-adhesive resin cement is a class of resin-based cements that incorporates the etching, priming, and bonding chemistry in a single material. This should obviate the need for separate etching and bonding steps (and products), thus greatly simplifying the 291 13. Materials for Adhesion and Luting placement of indirect restorations. The first gen-eration of this class of products was supplied as powder-liquid formulations that had to be mixed either by hand or via triturable capsules. The newer generations are provided as two-paste systems that can be automixed through a static mixer. The mixed materials provide some initial fluoride release and produce low postoperative sensitivity. These materi-als are indicated for cementation of cast alloy single restorations and bridges, ceramic-metal crowns and bridges, ceramic (except veneers), and indirect com-posite restorations. Good results are also obtained with luting of prefabricated posts and high-strength ceramics. Composition The distinguishing feature of these two-part self-adhesive resin-cements over the classical resin cements is the inclusion in one of the parts of one or more acid-functional monomer whose role is to etch the tooth tissue while bonding to other mono-mers to build up cohesive strength. Most commercial products contain polymerizable monomers based on phosphates and phosphonates. Examples are 2-methacryloxyethyl phenyl hydrogen phosphate (Phenyl-P), 10-MDP, Bis(2-methacryloxyethyl) acid phosphate, and dipentaerythritol pentaacrylate monophosphate (Penta-P)(meth)acrylate. In addi-tion, monomers with carboxylic acid groups such as 4-META and pyromellitic glycerol dimethacrylate are used by some manufacturers. In addition, common methacrylate monomers such as Bis-GMA, glycerol dimethacrylate, UDMA, and HEMA are present in varying proportions. Inert filler is included along with photoinitiators. The other part contains nonacidic polymerizable resins, and a small amount of an acid-neutralizing filler such as fluoroaluminosilicate glass (found in glass ionomers). Nonreactive fillers and photoini-tiators may also be included depending on the par-ticular product. The total filler content of the mixed cement is about 70% by mass (approximately 50% by volume), which is significantly lower than in com-posite restoratives. Setting Reaction and Structure The primary curing mechanism is via free-radical polymerization, either self-activated or dual-cured. The initial pH of the mixed cement is about 2 so that it can provide etching of the tooth mineral. In vitro studies have also shown that the acidic groups (phos-phate and carboxylate) can bind with calcium in the hydroxyapatite to form a stabilizing attachment between the methacrylate network and the tooth. At later stages, the remaining acidity is neutralized in some cements by the reaction between phosphoric and carboxylic acid groups and the alkaline glass. The structure of the set material is mainly a cross-linked polymer, covalently bonded to filler particles by the silane layer. Some ionic bridging between car-boxylic groups and ions released by the glass may also be present. Manipulation considerations can be found on the book’s website /restorative. Properties In terms of biocompatibility, self-adhesive resin cements present higher cytotoxicity than resin cements and acid-base cements. Cytotoxicity is reduced when cements are used in dual-cure mode. Their mechanical properties vary among commercial materials but, in general, are somewhat lower than those of conventional resin cements. A significant advantage clinically while using the self-adhesive cements is the low incidence of postop-erative sensitivity reported with these products. This is thought to be due to the fact that the dentin does not need to be etched with phosphoric acid. The overall examination of the strength, hardness, and wear of several popular resin cements reported in studies suggests that their resistance to fracture and wear may be similar to, or perhaps slightly lower than, that of conventional resin cements. Flexural strength is in the 50 to 100 MPa range and compressive strength is between 200 and 240 MPa. Values in the lower range are usually associated with the cement tested in self-cure mode, whereas higher values are obtained with light activation. Film thick-ness is between 15 and 20 μm. Bonding to the tooth structures are supposed to occur by micromechanical interlocking and chemical interaction between the acidic groups and the hydroxyapatite. Initial shear bond strength to enamel varies from 3 to 15 MPa, intermediate between resin cements and glass iono-mers. On dentin, some products have bond strengths comparable to resin cements. The self-adhesive resin cements were designed specifically to interact with the dentin substrate with minimal additional surface preparation. However, the bond to enamel is not as strong as with the use of phosphoric acid etchants. If substantial enamel margins are present, it is often recommended to etch with phosphoric acid even while using these cements. They show good bond strength values to metal alloys and high-strength ceramics. The presence of unreacted acid groups increases water sorption, in comparison to conventional resin cements. Their fluoride content is low (around 10%) and, unlike the glass ionomer and resin-modified glass ionomer cements, the release of fluoride ions decreases rapidly with time. The beneficial effects of fluoride in the self-adhesive resin cements have not been clinically proven. 292 CRAIG’S RESTORATIVE DENTAL MATERIALS Resin Cements for Provisional Restorations These provisional cements are paste-paste systems, which can be dual- or light-cured. 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Mechanism of adhesion of polyelectrolyte cements to hydroxyapatite. J Dent Res. 1983;62(5):590–592. 295 DENTAL CAD/CAM SYSTEMS CAD/CAM, the abbreviation for computer-aided design/computer-aided manufacturing, describes a process in which digital images or models of objects are created and used for the design and fabrication of prototypes or final products using computer numeri-cal control (CNC) or other fabrication methods such as three-dimensional (3D) printing. This process has been used for decades in a variety of industries and has become a popular method in restorative den-tistry for creating impressions, cast and dies, and provisional and final restorations. Reports of 10-year follow-up studies for one system have shown good outcomes that are improving with each technological enhancement. Dental CAD/CAM systems consist of three components: 1. A scanner or digitizing instrument that transforms physical geometry into digital data. 2. Software that processes the scanned data and creates images of the digitized object. Some systems then enable restorations to be designed for the digitized object. 3. Fabrication technology that transforms the digital data of the restoration into a physical product. Different systems place the fabrication technology in the dental office, dental laboratory, or centralized facility. The two types of CAD/CAM systems for dental offices are acquisition (digital impression) only, and scan and mill. Acquisition-only systems create digi-tal impressions by capturing images of the prepa-ration and then sending the digital file to a center where either (1) a model is made upon which a laboratory technician can fabricate the final resto-ration or (2) the digital file is used to fabricate the restoration without a model. A scan and mill sys-tem adds an in-office restoration fabrication device to the digital impression instrument, enabling a restoration to be designed, fabricated, and deliv-ered in one appointment. For the acquisition-only system, multiple appointments are required as in conventional indirect restorative care, and a provi-sional restoration is placed in the interim while the restoration is being fabricated by a laboratory tech-nician. Scan and mill systems offer the convenience of one appointment preparation, impression, fabri-cation, and delivery, but include a waiting period while the restoration is milled and the additional cost of the milling machine. Dental CAD/CAM systems have the following benefits: • Provide improved precision and consistency • Allow the clinician to visualize the preparation on a computer display from many perspectives • Allow the clinician to design the restoration on a computer while visualizing the opposing dentition • Provide a clean and streamlined impression method without the complexity of the many materials required for conventional elastomeric impressions • Offer instant display and feedback for making corrections immediately • Reduce the environmental impact of disposing the materials required for conventional impressions. There are several digital impression systems cur-rently on the market (Table 14.1). These systems (iTero, Fig. 14.1A; 3M True Definition Scanner, Fig. 14.1B; and TRIOS) produce digital impressions that require design and milling at a dental laboratory or milling center. C H A P T E R 14 Digital Imaging and Processing for Restorations 296 CRAIG’S RESTORATIVE DENTAL MATERIALS TABLE 14.1 Digital Impression Systems Without In-Office Milling Option Scanner Manufacturer Powder Required Ortho and Implant Integration 3M True Definition Scanner (compatible with TS 150 and PlanMill 40 milling machines) 3M Company (St. Paul, MN) Yes Yes TRIOS and TRIOS Color 3Shape (Stoneham, MA) No Yes iTero Align Technologies (San Jose, CA) No Yes Modified from Bunek SS. Digitizing dental impressions. Dent Advis. 2014;31(8):1. FIG. 14.1 Digital impression sys-tems. (A) iTero Element scanner. (B) 3M True Definition Scanner. (A, Courtesy Align Technology, Inc., San Jose, CA; B, Courtesy 3M Company, St. Paul, MN.) A B TABLE 14.2 Digital Impression Systems With In-Office Milling Option Scanner Mill Manufacturer PlanScan Restorative System PlanMill 40 Planmeca (Roselle, IL) CEREC AC and CEREC Omnicam CEREC MC, MCX, MCXL DENTSPLY/ Sirona (Charlotte, NC) CS 3500 CS 3000 Carestream Dental (Atlanta, GA) Modified from Bunek SS. Digitizing dental impressions. Dent Advis. 2014;31(8):1. There are several dental CAD/CAM systems currently on the market (Table 14.2). These systems (CEREC AC, Fig. 14.2A, and PlanScan, Fig. 14.2B) offer the option of in-office design and milling but also allow design and milling by dental technicians. All of these systems can produce models from their digital files and may have the option for in-office design. DIGITAL IMPRESSIONS After the tooth preparation is complete and the tis-sues are retracted to visualize the tooth margins, the tooth is dried and readied for scanning. Some scan-ning systems require the use of an oxide powder on the tooth to remove optical highlights from the surface of the preparation and to enhance the scan 297 14. Digital Imaging and Processing for Restorations quality. Scanners use either a series of static images or a stream of video images to capture the geometry of the tooth preparation. CEREC AC with the CEREC Bluecam has a blue light-emitting diode (LED) and camera system, and uses active triangulation to create images of the tooth surface. Static images of the tooth are stitched together to create a single 3D model. The PlanScan uses a high-speed swept laser beam com-bined with a camera to obtain a series of 3D scans of the tooth using the principle of laser triangula-tion. Laser utilization allows scanning of a variety of different surface types and colors without the need for a contrast agent (powder). These scans are registered together to form a single 3D model. The iTero Element uses confocal imaging with 6000 frames per second and approximately 32,000 con-focal spots to produce a single height-map. Over 20 such height-maps are produced per second, whereby a total series of a several hundreds of such height-maps record the preparation and the occlusal relationship. DESIGN SOFTWARE Each system includes proprietary software for the visualization of the scanned data and design of restorations (Fig. 14.3). A wide variety of restora-tions can be designed, including inlays, onlays, crowns, veneers, customized implant scanbodies, and fixed dental prostheses. The digital cast and dies can be visualized from any perspective, with or without the opposing dentition. Restorations are designed interactively by the clinician and computer, adapting the contours to harmonize with the adjacent and opposing teeth. A virtual “clay” is used to mold the restoration to the cor-rect emergence profile, interproximal contact, and occlusal scheme. The opposing dentition can be moved through excursive paths to further develop a functional occlusal profile. Some systems allow for pre-preparation scanning. A B FIG. 14.2 In-office CAD/CAM systems. (A) CEREC AC. (B) PlanScan. (A, Courtesy Sirona Dental Systems LLC, Charlotte, NC; B, Courtesy Planmeca, Roselle, IL.) FIG. 14.3 Software (PlanCAD) for the visualization of the scanned data and design of restorations. (Courtesy Planmeca, Roselle, IL.) 298 CRAIG’S RESTORATIVE DENTAL MATERIALS PROCESSING DEVICES Milling centers and dental laboratories produce res-torations directly from the digital impression and restoration design data. Restorations can be milled from a variety of materials such as resin composites, acrylic polymers, leucite-reinforced ceramic, lithium silicate and lithium disilicate ceramics, and zirconia (Table 14.3). Wax patterns and acrylic provisional res-torations can also be milled. The digitally produced models can be used to produce restorations by tradi-tional methods in the dental laboratory. Milling devices are distinguished by the number of milling axes. The quality of the final product does not necessarily depend on the number of milling axes, but it does affect the level of geometric complexity that can be produced. Three-axis devices are capable of move-ment in three spatial directions. They are not capable of milling axis divergences and convergences. Three-axis devices can turn the material block used for milling by 180 degrees during processing. Four-axis devices add the ability to rotate the material block infinitely. This enables the fabrication of a fixed prosthesis with a large vertical height difference. Five-axis devices add the abil-ity to rotate the milling spindle so complex geometries can be milled in sections. This enables geometries such as converging abutment teeth to be accommodated. Metals, resins, composites, and ceramics can be milled by the processing devices. Commercially pure titanium, titanium alloys, and cobalt-chromium alloys are metals commonly used in the devices. Resins can be milled to create lost wax frames for casting and also for long-term provisional prosthe-ses. Composite blanks that are prefabricated to mimic enamel and dentin in their translucency and color can be milled to create final anterior restorations. Zirconia, described in Chapter 11, is a high- performance ceramic with excellent mechanical characteristics. It is used in milling devices for crowns, fixed partial prostheses, and implant abutments. CLINICAL OUTCOMES The performance of restorations produced in CAD/ CAM systems has improved dramatically in the last decade. An older perception of poor marginal integrity associated with CAD/CAM restorations is no longer true. Enhancements in image capture, design software, and milling technology along with improvements in materials have all contributed to superior clinical outcomes. Patient selection and attention to margin design and tissue retraction are important factors, as they should be for all restor-ative procedures. In recent studies of zirconia-based restorations, digital impressions resulted in better quality of contacts, better fit, and better occlusion than elasto-meric impressions (Table 14.4). Digital impressions typically result in 33% shorter seating/adjustment time and fewer incidents of remakes when com-pared to elastomeric impressions. In a 10-year study of 308 ceramic restorations placed in 74 patients between 1991 and 1994, the restoration survival rate was 94.7% after 5 years and 85.7% after 10 years, which is comparable to the survival rates of cast gold restorations. A systematic review of four stud-ies that reported on implant-supported CAD/CAM fabricated restorations found a cumulative 5-year survival rate of all-ceramic single crowns of 100% (95% confidence interval [CI]: 92.4% to 100%). A systematic review of studies that reported on sin-gle-tooth restorations fabricated with CAD/CAM technology from 1985 to 2007 revealed a failure rate of 1.75% per year, calculated per 100 restoration years from a total of 1957 restorations and a mean exposure time of 7.9 years. The review estimated a total 5-year survival rate of 91.6% (95% CI: 88.2% to 94.1%). The long-term survival rates for CAD/ CAM single-tooth restorations were found to be similar to restorations fabricated with conventional methods. TABLE 14.3 In-Office Mills: Choice of Materials Mill Resin Composite Acrylic Polymer Resin Ceramic Lithium Disilicate Leucite-Reinforced Glass Ceramic Zirconia CEREC Yes Yes Yes Yes Yes Yes (via CEREC Connect) PlanMill No Yes Yes Yes Yes Yes (via PlanScan) TS-150 (Glidewell Laboratories) No No Yes Lithium Silicate No Yes (open .stl file) CS 3000 No No Yes No Yes (via CS Connect) Modified from Bunek SS. Digitizing dental impressions. Dent Advis. 2014;31(8):1. 299 14. Digital Imaging and Processing for Restorations Bibliography Anderson S. E4D Dentist, E4D Studio and E4D Labworks along the digital skyway. Dent Advis Clin Case Rpt. 2010;17:1–3. Beuer F, Schweiger J, Edelhoff D. Digital dentistry: an over-view of recent development for CAD/CAM generated restorations. Br Dent J. 2008;204(9):505–511. Bunek SS. Digitizing dental impressions. Dent Advis. 2014;31(8):1. Farah JW, Brown L. Comparison of the fit of crowns: 3M ESPE Lava Chairside Oral Scanner C.O.S. vs. traditional impressions. Dent Advis Res Rpt. 2009;22:1–3. TABLE 14.4 Comparison of Restorations Made by Digital Impression Versus Elastomeric Impressions Parameter Digital Impression (% Perfect) Elastomeric Impression (% Perfect) Quality of contacts 62 46 Fit 92 71 Occlusion 74 48 Modified from Farah JW, Brown L. Comparison of the fit of crowns: 3M ESPE Lava Chairside Oral Scanner C.O.S. vs. traditional impressions. Dent Advis Res Rpt. 2009;22:1–3. Farah JW, Brown L. Integrating iTero into a busy dental practice. Dent Advis Clin Case Rpt. 2009;16:1–3. Farah JW, Brown L. Integrating the 3M ESPE Lava Chairside Oral Scanner C.O.S. into daily clinical practice. Dent Advis Clin Case Rpt. 2009;12:1–4. Farah JW, Powers JM. CAD/CAM update. Dent Advis. 2009;26(7):1. Farah JW, Powers JM. Digital impressions. Dent Advis. 2010;27(6):1. Fasbinder DJ. Digital dentistry: innovation for restor-ative treatment. Compendium of Continuing Education in Dentistry. 2010;31(Spec Iss 4):2–11. Giannetopoulos S, van Noort R, Tsitrou E. Evaluation of the marginal integrity of ceramic copings with different marginal angles using two different CAD/CAM sys-tems. J Dent. 2010;38(12):980–986. Harder S, Kern M. Survival and complications of computer aided-designing and computer-aided manufacturing vs. conventionally fabricated implant-supported recon-structions: a systematic review. Clin Oral Implants Res. 2009;4:48–54. Schroder BK, Brown C. Use of selective open architecture in digital restoration fabrication. Compend Contin Educ Dent. 2010;31 Spec No 4:15–22. Wittneben J-G, Wright RF, Weber H-P, Gallucci GO. A sys-tematic review of the clinical performance of CAD/CAM single-tooth restorations. Int J Prosthodont. 2009;22:466–471. Zimmer G, Gohlich O, Ruttemann S, Lang H, Raab WH, Barthel CR. Long-term survival of Cerec restorations: a 10-year study. Oper Dent. 2008;33(5):484–487. This page intentionally left blank 301 C H A P T E R 15 Dental and Orofacial Implants The practice of restorative dentistry seeks to replace the form and function of missing tooth structure. It was therefore expected that dentistry would fol-low orthopedic medicine in the use of implants to anchor prosthetic devices and as expected, that has happened. Global dental implant sales are expected to reach over $4.5 billion by 2022 at a compounded annual growth rate of 6.1%. In 2017 Europe exhibited the largest market share, followed by North America and the Asia-Pacific region. The Asia-Pacific region is expected to see the highest growth rate between 2017 and 2022. Dental implants are fixtures that serve as replace-ments for the root of a missing natural tooth. Implants may be placed in the mandible or maxilla. When properly designed and placed, dental implants bond with bone over time and serve as an anchor for den-tal prostheses. Dental implants are used to replace a single missing tooth or many teeth, or to support a complete removable denture. Worldwide, modern single-tooth implants have a success rate of nearly 95% survival at 15 years. Implants are permanent devices, surgically anchored in the oral cavity, that often provide significant advan-tages over other fixed or removable prosthodontic options. Implants are often more conservative than tra-ditional fixed partial dentures because they conserve tooth structure by eliminating the need for reduction of adjacent abutment teeth and they support the mainte-nance of healthy bone in the region. CLASSIFICATION Historically, dental implants have been classi-fied according to their design. This design was in turn based on the way in which they are surgically implanted. The three types of implants commonly used for the past 40 years are the subperiosteal implant, the transosteal implant, and the endosseous implant (Table 15.1). Endosseous Implant Endosseous implants are by far the most common type of implant placed today. Implants are placed directly into the mandible or maxilla (Fig. 15.1). A pilot hole is drilled into the alveolar or basal bone beneath (in cases in which the alveolar bone has been partially or completely resorbed), and the implant body is inserted into this site. The top of the implant is positioned so that it either protrudes slightly through the cortical plate or is flush with the surface of the bone. Typically a superstructure containing a prosthetic tooth or teeth connects to the implant body through an abutment that is screwed into the body directly through the mucosa. OSSEOINTEGRATION AND BIOINTEGRATION A major issue for implant design is the develop-ment of materials that are physically and biologi-cally compatible with alveolar bone. Ideally, bone should integrate with the material, substance, or device and remodel the bone structure around it, rather than responding to the material as a foreign substance by encapsulating it with fibrous tissue. Under optimum circumstances, bone differentiation occurs directly adjacent to the material (osseointe-gration). Ideally, this osseointegration provides a stable bone-implant connection that can support a dental prosthesis and transfer applied loads without concentrating stresses at the interface between bone and the implant. Osseointegration is formally defined as the close approximation of bone to an implant material (Fig. 15.2). To achieve osseointegration, the bone must be viable, the space between the bone and implant must be less than 10 nm and contain no fibrous tissue, and the bone-implant interface must be able to survive loading by a dental prosthesis. In current practice, osseointegration is an absolute requirement for the 302 CRAIG’S RESTORATIVE DENTAL MATERIALS successful implant-supported dental prosthesis. To achieve osseointegration between an implant and bone, a number of factors must be correct. The bone must be prepared in a way that does not cause necro-sis or inflammation. The implant must be allowed to heal for a time without a load. Finally, the proper material must be implanted, because not all materi-als will promote osseointegration. In recent years, various surface configurations have been proposed as means of improving the cohe-siveness of the implant-tissue interface, maximizing load transfer, minimizing relative motion between the implant and tissue, minimizing fibrous integra-tion and loosening, and lengthening the service life of the construct. Because of the necessity of devel-oping a stable interface before loading, effort has been placed on developing materials and methods to accelerate tissue apposition to the implant sur-face. Surface-roughened implants and ceramic coat-ings have been implemented into clinical practice. Other, more experimental techniques include electri-cal stimulation, bone grafting, and the use of growth factors and other tissue engineering approaches described in Chapter 16. The application of bioactive ceramics as implant materials was traditionally limited to their use as bone bonding and augmentation materials. There has been interest in coating titanium alloys with bio-active materials to promote an implant bone connec-tion. Bioactive ceramic materials are more than just biocompatible. The use of the term bioactive implies that they have the ability to elicit a favorable tissue response when implanted in vivo. These ceramics form a direct chemical bond with natural tissues and are most often designed to bioresorb or biodegrade, having high solubility. Commonly implanted den-tal ceramics include the calcium phosphates with various calcium-to-phosphorus ratios [e.g., hydroxy-apatite (HA) and tricalcium phosphate], bioactive glasses (mixtures of SiO2, CaO, P2O5, and sometimes Na2O, and MgO), and glass ceramics. Important examples of bioactive glasses and glass ceramics include Bioglass (a glass contain-ing a mixture of silica, phosphate, calcia, and soda); Ceravital (which has a different alkali oxide con-centration compared to Bioglass); Biogran (which has a different physical conformation compared to Bioglass); and glass ceramic A-W (a glass ceramic– containing crystalline oxyapatite and fluorapatite [Ca10{PO4}6{O,F2}] and β-wollastonite [SiO2CaO] in a MgO-CaO-SiO2 glassy matrix). In addition, many other glass and glass-ceramic compositions, based on recently developed sol-gel synthesis methods, are being developed. Calcium phosphate ceramics vary in composition, depending on processing-induced physical and chemical changes. Among this group are the apatite ceramics, and of particular interest is HA. This is the synthetic version of the inorganic phase found in tooth and bone and is the bioactive ceramic material that has been most extensively investigated. The impetus for using synthetic HA as a bioma-terial stems from the perceived advantage of using a material similar to the mineral phase in natural TABLE 15.1 Implant Design Classification Scheme Implant Design Contact With Bone Composition Location Used Subperiosteal Directly on bone surface under the gingival tissues; no bone penetration Co-Cr-Mo (Vitallium) Maxilla and mandible Transosteal Completely through the bone, penetrating the cortical wall twice Titanium or Ti alloy Mandible only Endosteal Within the bone, penetrating the cortical wall once Titanium or Ti alloy Maxilla and mandible Lower jawbone (mandible) ENDOSSEOUS IMPLANTS Blade Cylinder Implants are placed inside jawbone Screw FIG. 15.1 Endosteal implant design. Shown here are three different endosseous implant designs. Notice that all of the designs are implanted directly within the bone. Although the blade design has fallen out of use, the cyl-inder and screw-shaped versions continue to be the most widely placed implant designs in use today. 303 15. Dental and Orofacial Implants tissues for replacing these materials. Because of this similarity, better tissue bonding is expected. Additional perceived advantages of HA and other bioactive ceramics include low thermal and electri-cal conductivity, elastic properties similar to those of bone, control of in vivo degradation rates through control of material properties, and the possibility of the ceramic functioning as a barrier to metallic corrosion products when it is coated onto a metal substrate. However, temperature-induced phase transfor-mations while processing HA provoke considerable changes in its in vitro dissolution behavior, and the altered structure changes the biological reaction to the material. Given the multitude of chemical com-positions and structures resulting from processing bioactive ceramics and the resultant fact that pure HA is rarely used, the broader term calcium phosphate ceramics has been proposed in lieu of the more spe-cific term hydroxyapatite. Each individual calcium phosphate ceramic is then defined by its own unique set of chemical and physical properties. Although calcium phosphate ceramics are too brittle and too stiff to serve as stand-alone dental implants for prosthetic tooth replacement, there has been continuing interest in using a thin (50 to 75 μm) layer of ceramic materials to coat the surface of metallic implants. This provides the beneficial osseo-integration characteristics of the ceramic combined with the high strength of the metallic alloy. Most manufacturers provide implants coated with calcium phosphate ceramic for use in sites where poor bone quality exists. A major limitation in using this con-cept in all clinical situations, however, has revolved around the inability to predict and maintain the bond strength of the coating to the metal. When the bioac-tive ceramic material resorbs in vivo, an unpredict-able change occurs in the implant-bone interface, and implant micromotion and loosening may occur. This makes the long-term stability of these implants uncertain. If successful, the ceramic coating becomes com-pletely fused with the surrounding bone. In this case, the interface is called biointegration rather than osseointegration, and there is no intervening space between the bone and the implant (see Fig. 15.2). A number of ceramic coatings have been used in this manner. Typically, these coatings have been applied to the surface of an implant via a plasma-spray depo-sition process. This results in a complex mixture of HA, tricalcium phosphate, and tetracalcium phos-phate in the coating, rather than a recapitulation of the starting powder mixture. Physical properties of importance to the functionality of calcium phosphate ceramics include powder particle size, particle shape, pore size, pore shape, pore-size distribution, specific surface area, phases present, crystal structure, crystal size, grain size, density, coating thickness, hardness, and surface roughness. The long-term integrity of the ceramic coating in vivo is not known, but evidence indicates that these coatings will resorb over time. In addition, results of ex vivo push-out tests indicate that the B A FIG. 15.2 Osseointegration and biointegration. (A) In osseointegration, the implant material (left) and the bone (right) closely approximate one another. This approximation must be closer than 10 nm (arrows). In the intervening space, there can be no fibrous tissue. (B) In biointegration, the implant and bone are fused and continuous with one another. Osseointegration commonly occurs with titanium alloys, whereas biointegration occurs with ceramics and ceramic-coated metallic implants. 304 CRAIG’S RESTORATIVE DENTAL MATERIALS ceramic-metal bond fails before the ceramic-tissue bond and is the weak link in the system. Thus the weak ceramic-metal bond and the integrity of that interface over a lengthy service life of functional loading is reason for concern. FACTORS AFFECTING THE ENDOSTEAL IMPLANT Geometry Two primary objectives influence a patient’s decision to pursue dental implant treatment: aesthetics and function. To fulfill these objectives over an extended period, a dental implant must be capable of with-standing the occlusal stresses generated in the oral environment and in turn transfer this load to the sup-porting tissues. Not only must loads be transferred, they should also be of an appropriate direction and magnitude so tissue viability is maintained. In this respect, the implant principally acts to minimize and distribute the biomechanical forces. The forces are characterized by their magnitude, duration, and type. The ability to transfer force largely depends on attaining interfacial fixation. The interface between the implant and bone must stabilize in as short a time as possible postoperatively, and once stable, must remain stable throughout its service life. Designing an “optimal” implant that meets all the foregoing objectives requires the integration of material, physi-cal, chemical, mechanical, biological, and economic factors. Magnitude of the Force The amount of load applied during normal chewing varies greatly, depending on location and state of the patient’s dentition. Bite force values reported in the literature range from about 40 to 1250 N. The magni-tude of force is greatest in the molar region because this area acts like the hinge of a lever (Fig. 15.3). The incisor region, in comparison, experiences about 10% of the magnitude seen in the posterior segment. This difference in load borne by the teeth and supporting bone dictates differences in mechanical requirements between anterior and posterior implants. Because stress depends not only on the applied load, but also on the area over which this load is distributed, the loss of some teeth by a patient will greatly increase the stresses applied to the remaining teeth and implants in partially edentulous patients. A prime requirement for any dental implant is adequate supporting bone height, width, and den-sity. It is well established that bone grows in response to strain, and the presence of an increasing magni-tude of stress applied to the bone will result in an increasing magnitude of resorption or loss of bone. However, in the absence of a critical level of strain for normal bone maintenance, the bone will also resorb. Therefore if the patient has been edentulous for a prolonged time, the underlying bone will have resorbed and become less dense. It is common to place implants preferentially in the anterior man-dible, because this region has the greatest trabecu-lar bone density when compared with the premolar or molar regions in both dentate and edentulous patients. When planning implant treatment, careful consideration must be given to the load distribution. A great majority of the materials considered to be biocompatible are not suitable for use as implants, because their ultimate strength is not high enough to withstand the forces to which they are subjected during normal function. However, in order to sur-vive and continue to function effectively, it is not only the ultimate strength, but also the modulus of elasticity (or stiffness) of the material that must be considered. Unless the bone experiences at least 50 microstrain on a routine basis, it will begin to resorb. Most ceramic materials are extremely stiff; for exam-ple, polycrystalline aluminum oxide has a modulus of elasticity ≈372 GPa. This stiffness is too high to transfer an adequate amount of an applied force to the bone. Instead, the stiffer implant material will carry a disproportionate amount of the load, causing stress shielding of the bone. By contrast, titanium has a modulus of elasticity ≈100 GPa; still too high to be ideal, but much closer to that of bone (≈20 GPa). It will permit normal physiological loading of the bone. Duration of the Force When considering repetitive loading such as that occurring during mastication, it is more appropriate to consider the endurance limit of a material rather than its ultimate strength. The endurance limit is the highest 100 80 60 40 20 A B C D E Bite position Right Left Male Group Female Pounds force FIG. 15.3 Mean adult bite force at different posi-tions in the jaw. (From Rugh SD, Solberg WK. The measure-ment of human oral forces. Behav Res Methods Instrum. 1972;4(3):125–128.) 305 15. Dental and Orofacial Implants amount of stress to which a material may be repeatedly subjected without failing. This limit is typically only about half of the ultimate strength for the material. The tooth root-form implant is designed to be loaded parallel to the long axis and is vulnerable to fatigue failure from cyclic bending loads. These bending loads often result from premature contact, bruxism, inappropriate occlusal schemes, and the use of angled abutments. Off-axis loading should be avoided in design of the implant superstructure. Type of Force An implant experiences three types of loads in func-tion: tensile forces, compressive forces, and shear forces. As discussed, a well-designed implant trans-fers and distributes these forces to the support-ing bone. Bone is composed of both inorganic and organic constituents, and the inorganic components render it strongest when loaded in compression. Bone is about 30% weaker when placed in tension, and nearly 70% weaker when subjected to shear forces. Therefore occlusion is a crucial consideration in designing the implant loading. Smooth-sided cylindrical implant designs place the interface between the implant and the bone in nearly pure shear, the weakest possible loading sce-nario. These implant designs rely either on micro-scopic texturing of the implant body to offer some mechanical interlocking and provide retention, or on a coating. If the coating on these fails or resorbs, bone loss usually results from the lack of load transfer. By contrast, screw-shaped implants have threads to engage the bone in compression and transfer the applied load. The thread designs have been exten-sively researched to provide a minimum of shear forces and maximal compression to the bone. This allows for the most favorable bone response. A num-ber of recent thread designs have been introduced that use rounded thread tips (to reduce shear forces at the tip), changes in the thread angle (to maximize compression), two or more thread profiles on the same implant (which will cut at different locations in the osteotomy, thereby increasing the contact area), and/or a reduced thread height accompanied by an increased thread pitch (spreading the implant load-ing over a greater contact area while simultaneously increasing the strength of the implant body). The concept of osseointegration around cylin-drical or screw-shaped implants represents a situ-ation of bone ongrowth. An alternative method of implant fixation is based on bone tissue ingrowth into roughened or three-dimensional porous surface layers. Such designs incorporating sintered beads or a sintered wire mesh are typical of orthopedic implants. Recently, implants with porous metal bod-ies have been developed and marketed. These new designs incorporate macroscale porosity or porous cellular structures, resembling cancellous bone. This results in a modulus of elasticity close to that of bone, thereby reducing the resulting stress shielding. Such retention systems have been shown to have higher bone/metal shear strength than other types of fixa-tion. Increased interfacial shear strength results in a better stress transfer from the implant to the sur-rounding bone, a more uniform stress distribution between the implant and bone, and lower stresses in the implant. In principle, the result of a stronger interfacial bond is a decreased propensity for implant loosening. The theoretical progression of macro-scale surface effects from the lowest implant/tissue shear strength to the highest is as follows: smooth, tex-tured, screw threaded, plasma sprayed, and porous coated, porous body design. Implant Diameter An increase in implant length or diameter increases the total surface area of the implant. As a conse-quence, the area for distribution of the occlusal forces is increased and the stress on the bone is decreased. The bending fracture resistance (and hence rigidity) of the implant increases greatly as the implant width increases and is related to the implant radius raised to the fourth power. This dramatic increase can be deleterious if the diameter chosen causes stress shielding by reducing bone strain to subphysiologi-cal levels. Implant Length As with increases in the width, increases in implant length also increase the surface area and reduce the bone stress. However, a careful consideration of the bone quality is advised. In the highly dense type of bone usually found in the anterior mandible, over-heating of the bone while drilling is a major cause of future failure. Preparation of an extra-long implant site tends to increase heating in this type of bone. Any immediate stability advantages provided by this long implant are transitory, because once the implant osseointegrates, the apical region of the implant receives minimal stress transfer. Most of the stresses are still concentrated around the upper cortical plate through which the implant emerges. Conversely, in regions of poor bone quality, typically found in the posterior mandible and maxilla, anatomical consid-erations dictate the length of implant placed. SURFACES AND BIOCOMPATIBILITY In analyzing an implant/tissue system, three aspects are important: (1) the individual constituents, namely 306 CRAIG’S RESTORATIVE DENTAL MATERIALS the implant materials and tissues; (2) the effect of the implant and its breakdown products on the local and systemic tissues; and (3) the interfacial zone between the implant and tissue. Regarding the ultrastructure of the implant-tissue interface, it is important to understand that, although this zone is relatively thin (on the order of 0.1 nm), the constituents of the zone (heterogeneous metallic oxide, proteinaceous layer, and connective tissue) have a substantial effect on the maintenance of interfacial integrity. Furthermore, interfacial integrity depends on material, mechani-cal, chemical, surface, biological, and local environ-mental factors, all of which change as functions of time in vivo. Thus implant success is a function of biomaterial and biomechanical factors, as well as of surgical techniques, tissue healing, and a patient’s overall medical and dental status. Ion Release Implant materials may corrode or wear, leading to the generation of particulate debris, which may in turn elicit both local and systemic biological responses. Metals are more susceptible to electrochemical deg-radation than are ceramics. Therefore a fundamental criterion when choosing a metallic implant material is that it must not elicit significant adverse biological response. Titanium alloys are well tolerated by the body because of their passive oxide layers. The main elemental ingredients, as well as the minor alloy-ing constituents, are endured by the body in trace amounts. However, larger amounts of any metal cannot be tolerated. Therefore minimizing mechani-cal and chemical breakdown of implant materials is a primary objective. Titanium and other implant metals are in their passive state under typical physiological conditions, and breakdown of passivity should not occur. Both commercially pure titanium (CP Ti) and the titanium alloy Ti-6Al-4V possess excellent corrosion resistance for a full range of oxide states and pH levels. It is the extremely coherent, conformal oxide layer and the fact that titanium repassivates almost instan-taneously through surface-controlled oxidation kinetics that renders titanium so corrosion resistant. The low dissolution rate and near chemical inert-ness of titanium dissolution products allow bone to thrive and therefore osseointegrate with titanium. However, even in its passive condition, titanium is not inert. Titanium ion release does occur as a result of the chemical dissolution of titanium oxide. Surfaces Analysis of the implant surface is necessary to ensure a twofold requirement. First, implant materials can-not adversely affect local tissues, organ systems, or organ functions. Second, the in vivo environ-ment cannot degrade the implant and compromise its long-term function. The interface zone between an implant and the surrounding tissue is therefore the most important entity in defining the biologi-cal response to the implant and the response of the implant to the body. The success of any implant depends on its bulk and surface properties, the site of implantation, tissue trauma during surgery, and motion at the implant-tissue interface. Surface analysis in implan-tology therefore aids in material characterization, determining structural and composition changes occurring during processing, identifying biologically induced surface reactions, and analyzing environ-mental effects on the interfaces. The surface of a material is always different in chemical composition, form, and structure from the bulk material, because the atoms at the surface are fundamentally different from those in the bulk of the implant metal. The surface of a metal can be consid-ered as an abrupt cessation of the orderly stacking of atoms below. As such, the coordination number of these atoms differs and hence their physical and chem-ical properties are different from atoms deeper in the bulk, arising from their molecular arrangement, sur-face reactions, and potential contamination with other species. These differences may lead to changes in the interaction of the implant with the biological system. In this regard, interface chemistry is primarily determined by the properties of the metal oxide and not as much by the metal itself. Little or no similar-ity is found between the properties of the metal and the properties of the oxide, but the adsorption and desorption phenomena can still be influenced by the properties of the underlying metal. Therefore char-acterization of surface composition, binding state, form, and function are important in the analysis of implant surfaces and implant-tissue interfaces. Surface Alterations In efforts to improve the in vivo performance of den-tal implants, considerable research has been, and continues to be, conducted to investigate the effects of macro-, micro-, and nano-scale surface features on osseointegration. Many of these research reports are contradictory; for example, Ti and hydroxylapatite surfaces are highly cyto-compatible, yet particles of these materials of a certain size cause cell death in culture. Therefore few absolutes have been identified, but some overarching guiding principles have been slowly emerging. The first of these is that cells in vitro (and possibly in vivo) undergo contact guidance on the implant surface. In other words, cells grow pref-erentially in and along nanometer- to micrometer-sized groove and ridge patterns on the surface of an 307 15. Dental and Orofacial Implants implant. These minute grooves influence cell behavior by causing the cells to align themselves in the direc-tion of the groove and migrate guided by the surface grooves (Fig. 15.4). Interestingly, very deep nano-scale grooves enhance cell guidance, while increasingly wider grooves decrease this effect. Furthermore, mod-ification of the implant surface to incorporate these micro- and nano-scale surface features on top of mac-rotexturing increases the bone-implant contact area and the biomechanical interaction between implant and anchoring bone, especially in the immediate term, after implantation. Cell shape, proliferation rate, and differentiation rate also depend on the texture of the implant surface to a great extent. Nanometer-scale surface textures, smaller than the cell itself, particularly influence nonguided cell adhesion, migration, and proliferation on the surface of implants. This scale of feature is simi-lar to the size and topography of proteins nor-mally found in the extracellular matrix of bone. It is likely that it is the influence of these features on serum protein adsorption that facilitates cell interaction with the implant surface. An adsorbed protein layer on the surface permits effective cell integrin interaction with the underlining topogra-phy. Those proteins that have dimensions similar to the nano-scale textural features will not have their three-dimensional conformation changed by adsorption to the surface, while surface features smaller or larger than the proteins tend to alter protein conformation and activity during adsorp-tion. However, conclusive evidence of the mecha-nism by which topographic effects are recognized by focal adhesions, and how this information is transferred and interpreted by the cells, remains an area of intense investigation. A second principle is that varying the macro-scale surface texture of an implant material significantly affects the interface between the implant and bone in vivo. In general, rough-surfaced implants exhibit greater shear bond strengths to bone than corre-sponding smooth-surfaced implants. Upon micro-scopic examination, rough implants exhibit apparent direct bone apposition, whereas smooth implants exhibit various degrees of fibrous tissue encapsu-lation. Because this direct bone apposition is the method by which dental implants are retained in the jaw, they appear to be significantly affected by mac-roscale surface texture. Not all surface roughness, however, has the same desirable effects. The exact dimensions or degree of roughness that is optimal remains ambiguous at this time. A third defining principle is that the molecular events which occur in cells when they encounter the surface of a material likely dominate all subsequent cell interactions with that material. These interac-tions are highly specific, mediated by proteins at the surface of the material and the cell, and are extremely dynamic in nature. Osteoblasts use integrin recep-tors to bind to specific surface-adsorbed proteins, and these proteins change over time and maturity of the cell. These attachment proteins may be present in physiologic serum, or they may be expressed directly by the cells themselves. As a result of these interac-tions, transmembrane integrin receptors will alert the cell of the nature of its substrate and modify its attachment to the material. Therefore fundamental properties of materials such as pH, pI, surface charge, zeta potential, wettability, and van der Waal’s forces may play significant roles in cell-material interaction. As a result of these observations, during the last 30 years, implant surfaces have changed dramati-cally. Once, machined surfaces were the norm. Now, surfaces that are prepared by grit blasting, followed by either acid etching or coating to enhance the topography and/or remove embedded grit particles, dominate the marketplace. The resulting micro-scale retentive features not only roughen the implant sur-face, creating a greater implant-bone contact area, but also play a role in activation of key biochemical sequences that ultimately accelerate the wound heal-ing process and encourage osteogenesis. It is quite clear that the chemistry of the implant surface plays a significant role in osseointegration and anchorage of the implant within the bone. This remains an area of intense commercial research. Recently, a surface modification technique that incor-porates grit blasting, followed by acid etching with a solution that results in fluoride ions on the implant surface, has been brought to the market. This prep-aration procedure results in a surface with varied chemical formulae within the surface oxide layer. This fluoride-containing surface has been shown FIG. 15.4 Light microscope image of cells grown on a patterned surface. Notice the contact guidance of the cells provided by the surface texture. (Courtesy John C. Mitchell, Midwestern University College of Dental Medicine-Arizona, Glendale, AZ.) 308 CRAIG’S RESTORATIVE DENTAL MATERIALS to enhance gene expression and lead to enhanced osteogenesis. Other new technologies to alter surfaces are also emerging on the market. These methods hold the promise to simultaneously alter an implant oxide layer thickness, chemistry, and/or structure. Additional surface treatments being explored include chemical surface hydroxylation to enhance the hydrophilicity of the implant surface and laser micromachining to create micro- and nano-structured surface roughness in hard-to-reach areas such as inside implant threads. Finally, other techniques such as electrochemical anodization processes can grow thick porous oxide layers with varied chemistries while creating micro-scale open pores on the surface. Integrating phos-phorus into the growing anodization oxide layer has even been shown to promote early molecular adhesion on the implant surface. There is a grow-ing awareness that the type of metallic oxide at the implant surface dictates cellular and protein binding onto that surface. Comprehension of this phenom-enon is moving these surface technologies rapidly forward. However, these new surface oxides are con-tinually altered by the inward diffusion of oxygen, and by hydroxide formation and the outward diffu-sion of metallic ions. Thus an ideal, single-oxide stoi-chiometry rarely exists. Surface Coatings The use of an additional surface coating treatment warrants additional discussion. Calcium phos-phate–based coatings have traditionally been the most heavily investigated. These materials are com-monly applied to the implant surface as a plasma-spray coating. In this high-temperature process, a 25- to 50-μm thick layer of material is deposited onto the roughened implant surface and allowed to cool. These coatings rely on relatively weak mechanical interlocking between the coating and the roughened surface to maintain adhesion to the metallic surface. Furthermore, the rapid cooling of the molten ceramic sprayed onto the surface produces uncontrollable crystallinity changes within the material and results in large-scale cracking of the coating. Although research studies have noted enhanced bioactiv-ity with these types of coatings, their use has been limited in the dental profession because the coating ultimately provides additional interfaces that may undergo stress-induced failure that leads to uncer-tainty as to their service life, as discussed previously. Another coating approach under investigation involves the attachment of biological mediators to the implant surface. In particular, the immobilization of short peptide sequences onto the implant surface has been demonstrated to influence cell response in vitro. Cell integrins, which bind to specific short peptide sequences, are responsible for these cell responses. In particular, the tripeptide sequence l-arginine, glycine, and l-aspartic acid (RGD) plays an impor-tant role in cell adhesion. This sequence is present in many extracellular matrix proteins, including fibrin, collagen, vitronectin, fibronectin, and osteopontin, and helps to mediate cell adhesion to surfaces. The covalent bonding of recombinant forms of these sequences, via silane chemistry, onto an implant surface may stimulate mesenchymal cell attachment and provoke osteoblast proliferation and differentia-tion at the site. Additional peptide sequences under investigation include the following: YIGSR, IKVAV, and KRSR (to improve cell adhesion), and FHRRIKA (to increase osteoblast mineralization). In addition to small peptide sequences, the use of entire recombinant proteins on the implant surface has been investigated. The use of immobilized cytokine growth factors such as bone morphogenetic protein, transforming growth factor-β, fibroblast growth fac-tor, vascular endothelial growth factor, and platelet- derived growth factor has been shown to posi-tively increase the regeneration of tissues around an implant. However, homogeneous coating of the implant surfaces and the release of these proteins into the surrounding tissues are rather unpredictable and uncontrolled with respect to both duration and dosage. Although further research is needed to illu-minate these unresolved issues, this treatment holds promise as a future therapy. IMPLANT MATERIALS AND PROCESSING In general, two basic classes of materials (ceramics and metals) are used as implants, either alone or in hybrid fashion. Metallic implant materials are largely titanium based: either CP Ti or Ti-6Al-4V. However, it is essential to note that synergistic relationships between processing, composition, structure, and properties of the bulk metals and their surface oxides effectively leave more than two metals. Casting, forging, and machining, to form near-net-shaped end products, alter the bulk microstructure, surface chemistry, and properties. Similarly, densification of ceramics and deposition of ceramic and metal coat-ings by hot isostatic pressing or sintering can change bulk and surface composition, structure, and prop-erties. Thus the many material processing sequences necessary to yield the end-stage dental implant have a strong influence on the properties and functionality of the implant, primarily through temperature and pressure effects. Metallic dental implants are almost exclusively titanium-based alloys, although cobalt-based alloys have been used historically and experimentally in 309 15. Dental and Orofacial Implants dentistry. The attributes of titanium, namely, corro-sion resistance and high strength, are discussed in Chapter 10. The initial rationale for using ceramics in den-tistry was based on the relative biological inert-ness of ceramics as compared with that of metals. Ceramics are fully oxidized materials and therefore chemically stable. Thus ceramics are less likely to elicit an adverse biological response than are metals, which oxidize only at their surface. As discussed pre-viously, a greater emphasis has been placed recently on bioactive and bioresorbable ceramics, materials that not only elicit normal tissue formation, but that may also form an intimate bond with bone tissue and even be replaced by tissue over time. CHALLENGES AND THE FUTURE Although there is no consensus regarding methods of evaluating dental implants and what criteria are most important, clinical evaluations have generally shown that dental implants are successful in about 95% of cases, 5 years after implantation. Despite advances in synthesis and processing of materials, surgical technique, and clinical protocols, clinical failures occur at rates of approximately 2% to 5% per year. Causes of failure and current problems with dental implants include (1) early loosening from a lack of initial osseointegration; (2) late loosening, or loss of osseointegration; (3) bone resorption; (4) infec-tion; (5) fracture of the implant or abutment; and (6) delamination of the coating from the bulk implant in the case of coated implants. The most common failure mechanism is alveolar crest resorption due to overloading. This inevitably leads to progressive periodontal lesions, decreased areas of supporting tissues, and ultimately to implant loosening. Aseptic failures are most often the cumulative result of more than one of the aforementioned factors. Changes in implant materials and design will be accomplished by groups composed of dental researchers and the implant manufacturers them-selves. They will continue to perform careful, mul-tiinstitutional clinical trials and prospective studies of compatibility, stress shielding, and bone loading among other factors. These three areas in particular present a major motivation for change in implant materials. Although very biocompatible, the current alloys suffer from a large elastic modulus mismatch with the supporting bone. Research work is under way to create composite materials that are biologi-cally compatible and have the same modulus of elas-ticity as bone. Similar moduli will result in a stress distribution that more closely mimics that seen phys-iologically. In addition, the work being performed to investigate implant texture effects is sure to reveal additional fundamental principles that will incre-mentally improve implant designs. However, in spite of these new research direc-tions, the future of implant dentistry lies in the hands of the restorative dentist. 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Dent Clin North Am. 1991;35:585. Wennerberg A, Albrektsson T. On implant surfaces: a review of current knowledge and opinions. Int J Oral Maxillofac Implants. 2010;25(1):63. Yang JY, Ting YC, Lai JY, et al. Quantitative analysis of osteo-blast-like cells (MG63) morphology on nanogrooved substrata with various groove and ridge dimensions. J Biomed Mater Res A. 2009;90(3):629. 313 Tissue engineering is a term coined at a meeting spon-sored by the National Institutes of Health in 1987. This discipline is a rapidly developing multidisci-plinary branch of science that combines many of the basic principles of biology, medicine, and engineer-ing. The primary goal of tissue engineering is the res-toration, maintenance, or enhancement of tissue and organ function. In addition to having therapeutic applications, in which a particular organ is custom grown to replace a failing or missing body part, tissue engineering has diagnostic applications in which tissues are fabri-cated in vitro and used for in vitro biocompatibility testing of compounds. Examples include application in drug metabolism and uptake, toxicity, or pathoge-nicity. Tissue engineering research, therefore, trans-lates fundamental knowledge in physics, chemistry, and biology into materials, devices, and strategies. It also integrates biomaterials, cell biology, and stem cell research; engineering characteristics of three-dimensional structures and mass transport issues; biomechanical characteristics of native and replace-ment tissues, biomolecules, and growth factors; and bioinformatics to support gene/protein expression and analysis. Tissue engineering as a discipline grew out of the pressing need for replacement tissues and organs. During 2016, in the United States alone, over 33,500 solid organs (heart, lung, intestine, kidney, pancreas, and liver) were transplanted. More than three quar-ters of those organs came from deceased donors. Meanwhile, during this same period, 58,851 new potential recipients were added to the waiting list and nearly 6200 patients died while waiting for a transplant (Box 16.1). Clearly, the demand for organs greatly exceeds the supply. Enthusiasm for tissue engineering comes from the promise of making transplants easier and more common. In dentistry, the disciplines of periodontology and oral and max-illofacial surgery often use bone tissue transplant materials to repair defects. Today, there are four primary classes of tissue/ organ transplants: autograft, allograft, xenograft, and alloplast (Box 16.2). AUTOGRAFT An autograft is a tissue or organ that is transferred from one location to another within a single individ-ual (Fig. 16.1). It is common to transplant tissues such as hair, blood, and even limited amounts of skin and bone. These tissues regenerate to some extent, repair-ing the void left after their removal. This method of transplantation avoids immunologic complications and is considered the “gold standard” for success. ALLOGRAFT Allografts are tissues or organs that are transplanted from one individual to another within the same spe-cies (Fig. 16.2). Routinely, tissues and organs are removed from deceased individuals (as well as liv-ing donors) and transferred to a different individual. Blood, bone, skin, corneas, ligaments, and tendons are collected in banks and frozen, to be used in future surgical procedures. XENOGRAFT The Center for Biologics Evaluation and Research (CBER) is the Food and Drug Administration (FDA) branch that oversees and regulates human tissue transplants. They define xenotransplants as “trans-plantation, implantation, or infusion into a human recipient of either (a) live cells, tissues, or organs from a nonhuman animal source or (b) human body fluids, cells, tissues, or organs that have had ex vivo contact with live nonhuman animal cells, tissues, or organs.” This therapeutic regimen has been used C H A P T E R 16 Tissue Engineering 314 CRAIG’S RESTORATIVE DENTAL MATERIALS experimentally to treat neurodegenerative disorders, liver failure, and diabetes, when compatible human materials are not widely available. Xenografts are now common in dentistry. One example is Bio-Oss (a product derived from cow bone) that is used to augment defects in the maxilla and mandible (Fig. 16.3). ALLOPLASTS Alloplasts are the newest type of grafting procedure materials. These grafts are fabricated completely from synthetic materials, making them quite different from the other three types of grafts, because no liv-ing component is used. Alloplastic materials, such as dental implants, are becoming increasingly common in dentistry. Dental implants fabricated from metals and ceramics are considered routine restorative treat-ment in many countries. These materials integrate with bone and help restore function for the patient, with excellent long-term success. Bone grafting alloplasts are also common (Figs. 16.4 and 16.5). Autograft bone placed in the recon-struction of craniofacial structures can be augmented with ceramic and bioactive glasses. These alloplasts are available in nearly unlimited quantity with no adverse immunological reaction. An important ben-efit is that they do not pose the risk of transmitting disease from one individual to another. STRATEGIES FOR TISSUE ENGINEERING Tissue engineering began with the concept of using bio-materials and cells to assist the body in healing itself. As the discipline matured, its goal shifted to developing logical strategies for optimizing new tissue formation through the judicious selection of conditions that will enhance the performance of tissue progenitors in a graft site, ultimately encouraging the production of a desired tissue or organ. Several strategies are now available for developing new organs and tissues (Box 16.3). Injection of Cells With the cell injection method, disaggregated cells at an undifferentiated stage of development are injected into the recipient. Considerable research had been conducted into the use of this method to combat sys-temic diseases such as Alzheimer’s and Parkinson’s disease, as well as juvenile-onset diabetes and multi-ple sclerosis. It also holds potential for treating dam-aged nerve and muscle sites. Commonly referred to as stem cells, the injected cells are more appropriately termed undifferentiated or progenitor cells (see later discussion in the section on Stem Cells). These cells BOX 16.1 S U M M A R Y O F T R A N S P L A N T D ATA , U N I T E D S TAT E S CANDIDATE WAITING LIST AS OF NOVEMBER 10, 2017a All 116,446 All—added in 2016 58,851 Kidney 104,243 Pancreas 938 Kidney/pancreas 1,748 Liver 14,524 Intestine 258 Heart 4,034 Lung 1,403 Heart/lung 46 Removed from list due to death, 2016 6175 TRANSPLANTS PERFORMED IN 2016a Total 33,646 Deceased donor 27,610 Living donor 6036 MEDIAN WAITING TIMES FOR KIDNEY TRANSPLANT Type O blood 1999–2000 1763 days (4.8 years) Type O blood 2001–2002 1833 days (5.0 years) Type O blood 2003–2004 1852 days (5.1 years) aBased on data from the Organ Procurement and Transplantation Network, U.S. Department of Health & Human Services ( BOX 16.2 S O U R C E S O F T I S S U E F O R G R A F T I N G Autograft: The patient’s own tissue Allograft: Human source other than the patient (could be cadaveric) Xenograft: Tissue from a different species Alloplast: Synthetic origin 315 16. Tissue Engineering are capable of forming new tissue with one or more phenotypes. As a therapeutic regimen, the cells are injected into the vicinity of the site in which they are intended to propagate, and they migrate to the area of injury and begin to replicate and replace the lost tissue, or produce a desired compound such as insulin (Fig. 16.6). This strategy has already been successful in regenerating small areas of cartilage in temporomandibular joints. Guided Tissue Regeneration Guided tissue regeneration (GTR) is a surgical pro-cedure for regenerating tissue by enhancing the opportunity for one cell type to populate an area while providing contact guidance to the develop-ing cells. The desired cell types can then populate an area without competition because unwanted cell types are excluded. In the laboratory, the method has been successful in creating a biodegradable polymer conduit through which nerve cell regeneration and reconnection can occur. GTR is commonly used in periodontal treatment to regenerate lost periodontal tissues such as the bone, periodontal ligament (PDL), and connective tissue attachment that support the teeth. The procedure involves placement of a mem-brane under the mucosa and over the residual bone (Fig. 16.7). The barrier helps to exclude the faster-growing epithelium and gingival connective tissues during the postsurgical healing phase, allowing the slower-growing PDL and bone cells to migrate into the protected areas. Cell Induction In the last decade, there has been explosive growth in understanding the role of cytokines, developmental A B FIG. 16.1 Autograft bone (B) is harvested (A) from the patient into whom it will be reimplanted. (From Newman MG, Takei HH, Klokkevold PR, et al. Carranza’s Clinical Periodontology. 11th ed. St. Louis: Saunders; 2012.) FIG. 16.2 Freeze-dried bone allograft is harvested from humans and sold in sterilized vials in both demineralized and nondemineralized form (original magnification ×100 for inset image). (Courtesy Lydia P. Mitchell, Midwestern University College of Dental Medicine-Arizona, Glendale, AZ.) FIG. 16.3 Bio-Oss is a porous bone mineral matrix xenograft prepared from bovine sources that has been sterilized by gamma ionizing radiation. Note the large pores visible (original magnification ×25 for inset image). (Courtesy John C. Mitchell, Midwestern University College of Dental Medicine-Arizona, Glendale, AZ.) 316 CRAIG’S RESTORATIVE DENTAL MATERIALS proteins, and growth factors in molecular biology. Many of these growth factors are available as recom-binant human lyophilized proteins. There have been tremendous advances in administering various mixtures of these growth factors directly to tissues to force them down a particular differentiation lin-eage. Often these growth and differentiation factors can be simply injected into the site. This technique, FIG. 16.4 OsteoGen (left) is a highly crystalline osteoconductive, bioactive, and resorbable bone graft material that is a biphasic mixture of β-tricalcium phosphate and hydroxylapatite. The Ca:P ratio is designed to mimic that of human bone (original magnification x50 for inset image); SynthoGraft (right) is a popular pure, single-phase β-tricalcium phosphate alloplast that is resorbable and has nanometer-scale porosity (original magnification ×100 for inset image). (Courtesy John C. Mitchell, Midwestern University College of Dental Medicine-Arizona, Glendale, AZ.) FIG. 16.5 Bioactive glasses are receiving increased attention because of their surface bioactivity. Shown here is PerioGlas (original magnification ×75 for inset image). (Courtesy John C. Mitchell, Midwestern University College of Dental Medicine-Arizona, Glendale, AZ.) BOX 16.3 S T R AT E G I E S F O R T I S S U E E N G I N E E R I N G Injection of cells: Undifferentiated cells (usually not from the patient) are injected directly into the vicinity of injury. Guided tissue regeneration: Undesired cells are excluded from repopulating a defect or injury site by placing a physical barrier to prevent their migration. Desirable cells are able to enter the site from the surrounding tissue. Cell induction: Growth and differentiation factors are injected (or implanted with a time-release substrate) within the injury or defect site. Circulating cells are induced to differentiate and populate the site with a desirable phenotype. Alternatively, gene vectors are injected and cause the growth/ differentiation factors to be produced endogenously. Cells in a scaffold matrix: Preformed scaffolds are seeded with cells from a patient. This construct is grown in vitro to expand the number of cells and to allow the cells to begin to produce a matrix. After a suitable growth interval, the construct is implanted back into the patient. As the cells grow and develop into tissues, the scaffold slowly resorbs, leaving no trace of its former presence. 317 16. Tissue Engineering as a tissue-engineering regimen, targets local connec-tive tissue progenitors already present in the region where new tissues are desired and induces those cells to generate the desired tissue. Some of the injected proteins may serve as mitogens in recruiting cells to migrate into the area, where other growth factors cause them to differentiate. Alternatively, they can be delivered by a substrate that releases them over time. Gene therapy can be used with cell induction meth-ods. In this application, a gene sequence that encodes for production of a specific growth factor or therapeutic compound is inserted wholly into the genome of the recipient cell. Insertion is achieved by a carrier, called a vector, to deliver the therapeutic gene to the patient’s target cells. The most common vector is a genetically altered virus that has been modified to carry human DNA. Because viruses have evolved a way of encap-sulating and delivering their genes to human cells, they can be manipulated to insert these therapeutic genes into the recipient cells. Therefore vectors are injected into a site along with an initial bolus of the therapeu-tic compound, and the vectors then upload their genes into resident cells. After incorporating this DNA into their genome, the newly transfected cells begin to rep-licate the desired growth factor endogenously. This method promotes continuous protein production at the site long after the initially injected growth factors dif-fuse from their target tissues or degrade enzymatically. Cells Within Scaffold Matrices Three-dimensional porous scaffolds can be used with cells to provide many of the advantages of the afore-mentioned methods. These preformed scaffolds are usually made of bioresorbable materials. The scaffolds promote new tissue formation by providing a surface and void volume that encourages attachment, migra-tion, proliferation, and the desired differentiation of connective tissue progenitors throughout the region where new tissue is required. Typically, the scaffold is seeded with progenitor cells that are allowed to attach and proliferate in vitro. The cell constructs are often grown in a nutrient media supplemented with Patient (tissue biopsy) Cell suspension Expand cells in culture Seed cells onto scaffold Implant cells OR scaffold into patient FIG. 16.6 Cell injection therapy. May involve the use of scaffold into which the cells are expanded, or they may be directly injected into their target site without a substrate. FIG. 16.7 Guided bone regeneration (GBR). GBR is being used to isolate the site being regenerated from the overlying tissues by means of a titanium-reinforced membrane barrier (arrowheads). The newly forming bone may be augmented by the addition of particulate grafting material. The barrier is securely attached to the margins of the defect to prevent displacement during healing. Notice that decortication of the underlying bone bed allows invasion of the site by osteogenic precursor cells from the bloodstream and surrounding bone. 318 CRAIG’S RESTORATIVE DENTAL MATERIALS growth factors necessary for cell and tissue develop-ment. During the growth phase, a static or dynamic mechanical load may be applied to the construct, to align the cells in response to the load. The aligned cells tend to produce a highly organized extracellular matrix that results in improved tissue structure and function. After a suitable time in vitro, the entire con-struct is then implanted in vivo, where the tissue must continue to develop while forming a connection with the existing vascular system. The scaffold gradually degrades until it is completely replaced by new tis-sues. As the scaffold degrades, the developing tissues gradually experience higher fractions of the loads on the tissue and begin to function as native tissues. The scaffold can therefore serve a dual function, as both a rigid substrate for cell growth and as a delivery vehicle for the release of therapeutic regulatory com-pounds in vivo. Release of bioactive molecules that are attached to the scaffold surface or encapsulated within the scaffold matrix can change the function of connective tissue progenitor cells (activation, prolifera-tion, migration, differentiation, or survival) to create new or enhanced tissues (Fig. 16.8). There are several critical variables in design and function of the scaffold design. Variables include the composition of the scaf-fold; its three-dimensional architecture; surface chemis-try; mechanical properties; and the physical, chemical, and biological environment in the area surrounding the scaffold during its functional lifetime, which is often determined by its degradation characteristic. All cells require access to metabolic molecules (oxygen, glucose, and amino acids) and removal of cellular waste prod-ucts (carbon dioxide, nitrogen compounds, and salts). There also must be a balance between consumption and delivery of these molecules if cells are to survive. Design of the scaffold must accommodate these issues. Eventually a rich blood supply will perform these tasks, but such a circulatory system takes time to mature. Patients who receive allogeneous tissue and organ transplants are often treated with immunosuppressive drugs for their lifetime to prevent rejection of the grafted tissue. These drugs can have severe side effects. The ideal source of cells for tissue engineering therapies is the patient. Autograft tissue eliminates the potential for adverse immunological reaction. However, autograft tissues usually require an additional surgical site and the associated expense, discomfort, and healing time. STEM CELLS Stem cells are particular cells within the body that are unspecialized, and capable of division and self-renewal prior to differentiation into a specialized cell type. They are commonly used in tissue engineer-ing therapies because they are not terminally dif-ferentiated and can migrate within the body to sites requiring repair or replacement. Stem cells are able to produce progeny cells with multiple phenotypes. There are different types of stem cells within the body: totipotent cells are single cells that can divide to generate any cell type, including extraembryonic tissues; pluripotent cells can become any of the over 200 types of cells in the body, but they lack the capa-bility to generate extraembryonic tissues such as a placenta; multipotent cells are capable of forming Polymer Polymer Pore PDGF Porous matrix VEGF FIG. 16.8 Scaffold systems. These systems may serve as delivery substrates for various therapeutic compounds, in addition to providing the cells with a suitable surface on which to grow. Multiple factors may even be delivered with dif-ferent release profiles by varying the method in which they are incorporated into the substrate. In this example, vascular endothelial growth factor (VEGF) is incorporated largely near the surface of the scaffold, and is subject to rapid release in vivo. In contrast, the preencapsulated platelet-derived growth factor (PDGF) is more uniformly incorporated throughout the scaffold and is subject to release regulated by the degradation of the matrix polymer. (Modified from Richardson TP, Peters MC, Ennett AB, et al. Polymeric system for dual growth factor delivery. Nat. Biotechnol. 2001;19(11):1029–1034.) 319 16. Tissue Engineering one of a number of specific tissue types; oligopotent cells can take on only two or at most three different functions; and finally a unipotent cell can divide and migrate, but is restricted to forming only a single cell or tissue type. Until very recently, most stem cell researchers worked with only two types of cells: embryonic stem cells (which are pluripotent) and somatic or “adult” stem cells (usually considered to be multipo-tent progenitor cells). Besides their origin, there are important differences between these stem cell types. For example, adult mesenchymal (or stromal) stem cells have been shown to only be capable of trans-differentiation into neural tissue, cartilage, bone, and fat. Therefore these “adult” cells were thought to be restricted to developing into one of only a limited number of cell types. Mesenchymal cells are found in small numbers in bone marrow and are also found circulating in the bloodstream. Isolating these cells from mature tissues is difficult, and routine methods to multiply them in vitro have not yet been perfected. Embryonic stem cells, by contrast, can be grown rela-tively easily in culture. Because a large number of cells are needed for successful stem cell replacement therapy, the choice of cell type is important. Despite being easier to culture, embryonic stem cells are prone to immunogenic rejection. This is a significant drawback. By contrast, adult stem cells, and tissues derived from them, are less likely to induce rejection because the origin of the cells is the patient. In that case, the patient’s own cells could be multiplied in culture, induced to differentiate into the specific cell type needed, and then reimplanted. Recently, additional stem cell types have been investigated. One previously unknown type has been isolated from the pulp of normally lost decidu-ous teeth. These cells have been termed stem cells from human exfoliated deciduous teeth, or SHED cells. SHED cells appear to have greater proliferative capabilities than adult stem cells and they also main-tain the ability to produce the same range of prog-eny as mesenchymal stem cells (Fig. 16.9). Stem cells can also be obtained as the mesenchymal-derived cells inside permanent teeth. These cells have proven to be multipotent and provide for regeneration of osteoblasts, chondrocytes, myocytes, neurons, and adipocytes. They are frequently referred to, in gen-eral, as dental pulp stem cells (DPSCs). Additional types of tooth-derived stem cells include periodontal ligament stem cells (which have been shown to differentiate into osteoblasts, cementoblasts, adipocytes, and chondrocytes), stem cells from the apical papilla (which can differentiate into osteoblasts, adipo-cytes, chondrocytes, and neurons), and dental follicle progenitor cells (which differentiate into osteoblasts, adipocytes, neuronal cells, and chondrocytes). Even more recently, culture conditions and viral vectors were found in which differentiated adult cells can be “re-programmed” to take on an embry-onic stem cell-like state. The development of these technological advances led to receipt of the 2012 Noble Prize for Physiology or Medicine “for the dis-covery that mature cells can be reprogrammed to become pluripotent”. These new types of stem cells are called induced pluripotent stem cells (iPSCs). They are capable of generating cells that have the charac-teristics of all three germ layers and can differentiate into many different tissue types; for example, neu-ral tissues, cardiac tissues, liver tissues, pancreatic tissues, or even blood cells. Because these cells and tissues are patient derived, immunogenic rejection is unlikely. To reduce the potential of cancer develop-ment from viral vectors during reprogramming, non-viral delivery methods are being heavily researched, mostly involving various types of material nanopar-ticles as the new delivery systems. Mesenchymal stem cell Proliferation Commitment Differentiation and maturation Osteogenesis Chondrogenesis Myogenesis Marrow stroma Tenogenesis/ ligamentogenesis Fibroblasts Stroma cells Fused myoblasts Chondrocyte Osteoblasts FIG. 16.9 Differentiation pathways of mesenchymal cells. A circulating mesenchymal cell may become one of any of the cell types shown here. The pathway down which it travels is influenced by both local and systemic factors. 320 CRAIG’S RESTORATIVE DENTAL MATERIALS Compared to other tissues, cells from dental-derived tissues are readily obtainable and easy to harvest. They can be obtained from gingival tissues and the oral mucosa by swiping with a cotton swab, or by removal of pulpal tissues from extracted permanent or deciduous teeth. Thus these iPSC types currently hold the greatest promise for future success with stem cell therapies. An interesting facet of iPSC technology has emerged in the last few years: epigenetic memory of these cells seems to preferentially differentiate them back to their original cell type. This might provide an advantage in the differentiation of cells into hard tissues, but could also be a shortcoming in the ability to repair other tissues. For this reason, DPSC-derived iPSCs have been mainly chosen as the starting cells for most oral tissue repair (bone, blood vessel, peri-odontium, nerve, and teeth). Research into stem cell differentiation has led to significant discoveries, but the ultimate cause of dif-ferentiation remains unclear. Left in a cell culture plate alone, several tissue types will result from a single group of stem cells. However, with suitably timed administration of the appropriate growth fac-tors, a single cell type emerges and begins to orga-nize into a tissue. The fate of a cell is also controlled by changes in the migration, proliferation, differen-tiation, or survival of their progeny. Transplanted stem cells may even fuse with existing cells in a body and assume the characteristics of that tissue. Tactile stimulus or other factors to upregulate or downregu-late genes to initiate these changes are being studied. BIOMATERIALS AND SCAFFOLDS Three types of biomaterials have been studied as scaffolds and carrier systems: (1) natural (or biologi-cal) materials, (2) ceramic or glass materials, and (3) polymeric materials. Each type has advantages and disadvantages in particular locations and tissues to be regenerated. All scaffolds must be nontoxic and nonimmunogenic, biodegradable, sterilizable, able to withstand mechanical loads, sufficiently porous to permit migration and growth of cells into their interior, and be supportive of a new fractal circulatory system to promote the exchange of metabolic constituents. Biological Materials Natural materials such as collagen, lyophilized bone (both allogenous and xenogenous), and coral have been used as tissue engineering substrates. Collagen has been extensively tested as a scaffold for bone regeneration. One of the first materials used for bone tissue engineering was the insoluble collagenous matrix obtained after extraction of the bone matrix with various chemical agents. This collagenous matrix, with freeze-dried bone, formed new endochondral bone when used with growth factors in vivo. Coral, based on calcium carbonate, is strikingly similar to the structure of alveolar bone. When coral is treated with phosphoric acids, the resulting calcium phosphate is very strong and biocompatible. Many patients prefer nonbiological implantable substrates because of the high potential for viral, prion, and disease transmis-sion from these biological materials. Ceramic and Glass Materials Three decades of research have shown that certain types of glasses, glass-ceramics, and pure ceramics can bond tightly with living bone tissue. Hydroxylapatite, the major inorganic (ceramic) constituent of bone, was one of the first alloplastic materials used as a bone augmentation scaffold. Ceramic and glass-ceramic materials are generally biocompatible and perform adequately when biomechanical loads are applied. Their use as scaffolds is limited because of their long degradation times in vivo and lack of native porosity. Some of these limitations might be overcome in the near future with recent advances in sol-gel synthesis methods for nanoporous and nanoparticulate glasses. These newer materials are more bioactive and resorb-able than materials fabricated by “melt-derived” pro-cesses. In general, the sol-gel process converts a colloidal liquid, sol, into a solid gel of particles with entrapped pore liquids. The starting precursors are usually metal organic compounds, or alkoxides M(OR)n, in which M is a metal network former and R is an alkyl group. These liquid precursors are mixed and hydrolyzed. This forms silanol groups that condense to create an inter-connected network of siloxane bonds, with water and alcohols as by-products. Precise control of the synthesis and drying steps results in a final glassy solid with a very large degree of interconnected mesoporosity (pore diameters in the range of 2 to 50 nm) and high specific surface area. This nanoporous glass is an outstanding matrix for entrapping and adsorbing cytokines and drugs, for example. As the glassy matrix resorbs, these compounds are released in an activated form. In addition, these bioactive glasses chemically bond to both hard and soft tissues, and they stimu late the for-mation of new bone in vivo. Bioactive glasses exchange ions with surrounding fluids within seconds of immer-sion into the body or media. In brief, the processes on the glass surface are characterized by this rapid ion exchange, followed by dissolution of the glass net-work and reprecipitation and growth of a silica gel layer on the surface, which in turn precipitates a cal-cium-deficient carbonate apatite [hydroxyl carbonate apatite (HCA)] layer onto its surface. This layer reor-ganizes and quickly results in the formation of a crys-talline HCA layer on the glass surface. As these layers are forming and growing outward from the surface, 321 16. Tissue Engineering extracellular proteins become entrapped in the grow-ing layers and invoke subsequent cellular reactions including cell attachment and colonization, prolifera-tion, and differentiation into relevant progenitor cells (Fig. 16.10). The interaction of bioactive glasses with living tis-sue, in particular forming strong chemical bonds to a tissue, is called bioreactivity or bioactivity. It is now believed that a biologically induced active apatite surface layer must form at the interface between the material and the bone to create a material bond with bone. In addition, the ionic species released from the reacting glasses upregulate at least seven families of genes found in mesenchymal cells and osteoblasts. Polymeric Materials Polymers are by far the most common materials used for tissue-engineering scaffolds. Polylactic acid and polyglycolic acid (and copolymers of these two) as well as polycaprolactone are common examples. These polymers are metabolized in vivo, and their acidic deg-radation products are easily removed from the body. They can easily be cast into a mesh or other desired 0 Initial bioactive glass model... replaced by silicate model Distance from the surface of the Bioactive Glass (nm) Weeks Time Ca P Extracellular proteins become entrapped and result in cellular involvement. Ions diffuse out of superficial bioactive glass layers. As ions leave a silicate lattice, Ca and P ions begin to model on the “skeleton”. Cells, in this case osteoblasts, migrate into area to further model the “skeleton”. FIG. 16.10 The in vivo reactions that occur when a bioactive glass is implanted. Ca, Calcium (green); P, phosphorus (purple). 322 CRAIG’S RESTORATIVE DENTAL MATERIALS shape or can simply be extruded as fibers, which are used to loosely pack an anatomically designed mold. The same material from which the scaffold is designed can be used to encapsulate growth factors to provide a timed release of the protein as the capsule degrades. Polymers release acidic and toxic products when they degrade that create inflammation around the implan-tation site. Their survival time in the body is difficult to control, and they become stiff as they degrade. CELL CULTURE METHODS Cells can be grown as a monolayer (or sheet) on a polystyrene growth plate treated to optimize cell attachment and proliferation. Culturing cells on three-dimensional scaffolds for later implantation is more difficult. Scaffolds thicker than 1 mm often produce a shell of viable cells and new extracellular matrix surrounding a necrotic core. Some type of perfusion bioreactor system (Fig. 16.11) must be used to more closely mimic the mass transport in vivo environment. Alternatively, the tissues can be fabricated in a well-vascularized region, in vivo. This allows a circulatory system to develop along with the cells. Optimal culture conditions for tissue-engineering scaffolds require high seeding efficiency to minimize growth time and a homogeneous cell distribution in the scaffolds to ensure a uniform, organized tissue. Mechanical loads can improve tissue organization if they are applied to the developing cells as the cells begin to embed themselves within their extracellular matrix. Physiological loads are continually applied to natural tissues during development and use, so some loads applied in vitro begin to prepare the cells and tissues for implantation. Early loading aligns the cells into a stronger, more organized matrix, which in turn creates improved tissue function. TISSUE-ENGINEERED DENTAL TISSUES A great amount of research has been done to develop methods for regenerating tooth structure and its sup-porting tissues. The FDA has already approved two tissue-engineered living skin products and these are commercially available. It is probable that tissue-engineered bone and cartilage will soon follow. Two approaches are being used to fabricate PDL. The first harvests existing PDL cells from the patient. The cells are grown and expanded in vitro (Fig. 16.12). They are then cultured as a monolayer without any substrate. Once the layer is continuous, with tight intercellular junctions, the sheet of cells is released from the culture plate and placed in situ on the tooth surface to repair the periodontal defect. FIG. 16.11 Image of National Aeronautics and Space Administration (NASA) bioreactor. (Courtesy NASA/ Johnson Space Center, Houston, TX.) Periodontal ligament Cell sheet transplantation Periodontal ligament cell Temperature-responsive dish Periodontal ligament cell sheet FIG. 16.12 One method of periodontal ligament engineering under development. Periodontal cells are extracted from a patient’s tooth and grown on temperature-responsive culture plates in vitro. Upon lowering the temperature on these cultures, the confluent layer of cells spontaneously lifts off of the plate as a sheet of cells with intact cell junctions. These sheets are then implanted with various treatments to attempt regeneration of the periodontal tissues. (Modified from Yamato M, Okano T. Cell sheet engineering. Mater. Today. 2004;7(5):42–47.) 323 16. Tissue Engineering The second approach is a cell and scaffold method in which cells are again harvested from the PDL of the patient. The cells are then seeded onto a three-dimensional polymer matrix. This is grown in vitro and eventually implanted back into the patient’s periodontal defect (Fig. 16.13). Another oral tissue being targeted by considerable research is a tissue-engineered salivary gland. The technique uses human parotid cells grown in vitro to develop an orally implantable, functioning, fluid-secreting tissue. Finally, several research groups announced in 2004 that they had succeeded in growing primitive teeth using tissue-engineering methods. They cre-ated a tooth-shaped porous scaffold of bioresorbable polymer and seeded it with individual cells taken Scaffold or Matrix for Cell Culture A Cells Seeded into Scaffold or Matrix B New Matrix Produced by Cells in Scaffold (Engineered Matrix) C Periodontal Defect Pocket Loss of attachment Bone loss D Periodontal Defect Filled with Engineered Matrix Epithelial seal Engineered matrix E Regenerated Defect F New epithelial attachment New cementum New alveolar bone New PDL FIG. 16.13 A more classical approach to periodontal tissue regeneration being developed. (A) The support scaffold is developed and shaped to the desired geometry. (B) In this method, cells are again harvested from the patient’s peri-odontal ligament (PDL) and seeded into a scaffold, where they are expanded in vitro. (C) The cells are allowed to grow for a time to allow synthesis of an appropriate matrix for implantation. (D) A periodontal defect is shown. (E) The tissue- engineered matrix is implanted into the defect site, leading to a regenerative response. (F) In this method the fully regener-ated periodontal defect is expected to be indistinguishable from other sites in the patient’s mouth. (Modified from Bartold PM, McCulloch CA, Narayanan AS, et al. Tissue engineering: a new paradigm for periodontal regeneration based on molecular and cell biology. Periodontol 2000. 2000;24:253–269.) 324 CRAIG’S RESTORATIVE DENTAL MATERIALS from a tooth bud. This cell-seeded construct was implanted into the omentum of a rat to provide the fluid and nutrient transfer during growth and devel-opment. A mixture of cell types from the tooth bud migrated to the appropriate region during growth, and differentiated to form pulp tissue, dentin, and enamel in the correct anatomical relationships and ratios. 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US Department of Health and Human Services. Organ procure-ment and transplantation network. hrsa.gov/; Accessed 15.11.17. US Food and Drug Administration. Vaccines, blood and bio-logics: tissue and tissue products. BiologicsBloodVaccines/TissueTissueProducts/default. htm; 2016 Accessed 15.11.17. 327 Conversion of Units A P P E N D I X This appendix presents several tables that will assist the reader in converting units. TABLE OF WEIGHTS AND MEASURES LENGTHS 1 millimeter (mm) = 0.001 meter = 0.03937 inch 1 centimeter (cm) = 0.01 meter = 0.3937 inch 1 meter (m) = 39.37 inches 1 yard (yd) = 0.9144 meter = 36 inches 1 inch (in) = 2.54 centimeters = 25.4 millimeters 1 micrometer (μm) = 0.001 millimeter = 0.00003937 inch 1 micrometer (μm) = 10,000 Angstrom units 1 Angstrom unit (Å) = 0.1 nanometer = 3.937 × 10−9 inch 1 nanometer (nm) = 0.001 micrometer = 10 Angstrom units WEIGHTS 1 milligram (mg) = 0.001 gram = 0.015 grain 1 gram (g) = 0.0022 pound = 15.432 grains 1 gram (g) = 0.035 ounce 1 kilogram (kg) = 1000 grams = 2.2046 pounds 1 ounce (oz) = 28.35 grams 1 pound (lb) = 453.59 grams = 16 ounces 1 pennyweight (Troy dwt) = 1.555 grams = 24 grains 1 grain (gr) = 0.0648 gram FORCES 1 newton (N) = 0.2248 pound force = 0.102 kilogram force = 100,000 dynes 1 dyne (d) = 0.00102 gram force A 328 APPENDIX A CONVERSION OF UNITS CAPACITY (LIQUID) 1 milliliter (mL) = 1 cubic centimeter = 0.0021 pint 1 liter (L) = 1000 cubic centimeters = 1.057 quarts 1 quart (qt) = 0.946 liter = 32 ounces 1 ounce (oz) = 29.6 milliliters 1 cubic foot (cu ft) = 28.32 liters AREA sq in (in2) sq ft (ft2) sq mm (mm2) sq cm (cm2) 1 0.00694 645.16 6.4516 144 1 92,903 929.03 0.00155 0.000011 1 0.01 0.155 0.0011 100 1 VOLUME cu in (in3) cu mm (mm3) cu cm (cc, cm3) 1 16,387 16.387 0.0000610 1 0.001 0.0610 1000 1 CONVERSION TABLES CONVERSION FACTORS (LINEAR) Millimeters (mm) Centimeters (cm) Inches (in) 1 Angstrom unit (Å) 0.0000001 0.00000001 0.000000003937 1 nanometer (nm) 0.000001 0.0000001 0.00000003937 1 micrometer (μm) 0.001 0.0001 0.00003937 CONVERSION FACTORS (FORCE PER AREA) To change kilograms force per square centimeter (kgf/cm2) to pounds force per square inch (lbf/in2), multiply by 14.223 (1 kgf/cm2 = 14.223 lbf/in2). To change kilograms force per square centimeter (kgf/cm2) to megapascals (MPa), multiply by 0.0981 (1 kgf/cm2 = 0.0981 MPa). note: 1 MN/m2 = 1 MPa. To change kilograms force per square millimeters (kgf/mm2) to gigapascals (GPa), multiply by 0.00981. To change pounds force per square inch (lbf/in2) to megapascals (MPa), multiply by 0.00689. To change meganewtons force per square meter (MN/m2) to pounds force per square inch (lbf/in2), multiply by 145 (1 MN/m2 = 145 lb/m2). To change meganewtons per square meter (MN/m2) to gigapascals (GPa), divide by 1000. CONVERSION OF THERMOMETER SCALES Temperature Fahrenheit (°F) = (9/5 temperature Celsius) + 32° Temperature Celsius (°C) = 5/9 (temperature Fahrenheit − 32°) 329 APPENDIX A CONVERSION OF UNITS CONVERSION FACTORS (MISCELLANEOUS) 1 foot-pound (ft-lb) = 13,826 gram-centimeters = 1.356 newton-meters 1 radian = 57.3 degrees 1 watt = 14.3 calories/minute CONVERSION OF EXPONENTIALS TO DECIMALS Exponential no. Decimal no. 1 × 10−5 (or 10−5) 0.00001 1 × 10−3 0.001 1 × 10−1 0.1 1 × 100 (or 100) 1 1 × 101 10 1 × 104 10,000 1 × 107 (or 107) 10,000,000 COMPARATIVE TABLE OF TROY, AVOIRDUPOIS, AND METRIC WEIGHTS Grain Troy dwt Troy oz Avoirdupois oz Avoirdupois lb Gram g 1 0.042 0.002 0.00228 0.00014 0.065 24 1 0.05 0.0548 0.0034 1.555 480 20 1 1.097 0.0686 31.10 437.5 18.23 0.91 1 0.063 28.35 7000 291.67 14.58 16 1 453.59 15.43 0.64 0.032 0.035 0.0022 1 PREFIXES AND SYMBOLS FOR EXPONENTIAL NUMBERS Factor Prefix Symbol 1018 exa E 1015 peta P 1012 tera T 109 giga G 106 mega M 103 kilo k 102 hecto h 10 deca da 10−1 deci d 10−2 centi c 10−3 milli m 10−6 micro μ 10−9 nano n 10−12 pico p 10−15 femto f 10−18 atto a This page intentionally left blank 331 Index A Abfraction lesions, 11–12 Abrasion resistance, gypsum materials, 258–259 Absorption, 46–47 Absorption coefficient, 54 for composite shades, 55f Accelerator, addition silicone impression material, 240 Acid-base cements, 284–289 composition of, 284 properties of, 285 setting reaction and structure of, 284–285 Acid etching of dentin, 10, 13f of enamel, 7f AcuVol, 84 Addition silicone impression material, 239f–241f accelerator, 240 composition and reactions, 239–242 consistencies and types of, 239f dimensional change, 244–245 viscosity, 244f working and setting times, 243–244 Adhesion, 48–49 to dentin, 279f materials for, 273–294 principles of, 273–282 surface considerations, 48–49 Adhesive systems, 275–280 biocompatibility, 276 classification and basic components, 275 clinical performance of, 277 definitions of terms, 274f enamel bonding, 277–278 universal, 280 Admixed alloys, 172–174, 173f Adsorption, 46–47 Agar overlay method, 93, 93f Alginate, properties of, 235t Alginate hydrocolloids, 231–237 Alginate impression, 230f dental stone, 236f dimensional change, 237f dimensional stability, 237 disinfection, 237 elastic recovery, 235 flexibility, 235 gypsum compatibility, 236–237 Alginate impression (Continued) products, 231, 231f properties, 234–237 setting time, 234 strength, 235–236 working time, 234 Alginate impression powder, ingredients and functions, 234t Alginic acid, 231, 232f–233f Alkoxide, 320 All-ceramic crowns, 210f, 211 All-ceramic materials, microstructure, 217f All-ceramic restorations, investment for, 268 Allograft, 313, 314b, 315f Alloplasts, 314, 314b Alloys in artificial saliva, galvanic series of, 62t cast, 280 crystal lattice unit cells in, 115f elongation, 35 flexural fatigue curve, 73f fracture strength, 35 gold-based, carat and fineness of, 181, 182t metallic elements used, 180–184 ultimate strength, 33f, 34–35 wrought, 200–204, 200f Alumina, 214–215 Alumina-based ceramic, 215 Amalgam, 282 corrosion products, 105–106 corrosion-resistant, 107–108 creep-curves, 41f phases physical and mechanical properties, 174–177 strength of, 174 Amalgam alloys, 63, 101–102, 106–107, 171 anodic polarization curves, in synthetic saliva, 64f bonding of, 177–178 composition and morphology of, 171–172, 172f, 172t cytotoxicity, 106–107, 106f–107f microstructure of, 174, 174f oral lesions, 105–106 Amalgam-bonded MOD restorations, 178 American Dental Association Acceptance Program, 88 American Dental Association Classification of Prosthodontic Alloys, 178t American Dental Association Foundation (ADAF) tensometer, 87f American Dental Association Specifications, 88 Ames test, 94 Animal study, pulpal irritation and, 99 Animal tests, 94 tests correlation, 95–96 Anisotropy, 115 ANSI/ADA specification, 178, 235 for amalgam alloy, 174 brazing investment, 268 calcium sulfate-bonded investments, 262 dental casting alloys, mechanical properties, 179t dental phosphate-bonded casting investments, 266 elastomeric addition silicone impression, 245, 246t gypsum products, 259 ANSI/ADA specification 41, 98 Anticariogenic activity, of luting agents, 283 Apatite, 5, 8 Area, 328t Athletic mouth protectors, 166–167 Atomic model, after plastic deformation, 33f–34f Atomic structure, metals, 113–115, 114f AU-PD alloys, 189–190 AU-PD-AG alloys, 189t, 190 AU-PT-PD alloys, 189, 189t Austenitic steels, 202 Autograft, 313, 315f bone, 315f Automixing system, 238, 238f Axial stress, 30 B Barcol hardness test, 77 Base metals, 180t, 182–184 Base-metal alloys, 190–200, 190b application of, 196–200 corrosion, 195 Page number followed by t, f, or b indicates table, figure, or box, respectively. 332 INDEX Base-metal alloys (Continued) density, 194 elastic modulus, 194t, 195 elongation, 194–195 fatigue, 195 for fixed prosthodontics, 195–196, 196t hardness, 194t, 195 heat treatment of, 194 mechanical properties, 192t, 194–195, 194t melting temperature, 194 physical properties, 194 tensile strength, 194, 194t yield strength, 194, 194t Bending moment-angular deflection curves, 70f Benzoyl peroxide, 289–290 Binder material, casting investments, 262 Bioactive, defined, 302 Bioactive ceramics, 302 Bioactive glasses, 132, 302, 316f, 320–321 with living tissue, 321 Biocompatibility, 91–112, 91f, 276 casting alloy, 187–188 composites, 153 of dental materials, 98–108 implant/tissue system, 305–306 measurement, regulation standards, 97–98 measuring, 91–98 summary, 108–109 tests, 92t, 97f in vitro tests, 92–94 standardization of, 92–93 Biofabrication methods, 3 Biofilms, 17–20 formation of, 17 restorative materials and, 19 on titanium, 20 Bioglass, 302 BioGran, 302 Biointegration, 301–304, 303f Biomaterials future developments in, 2–3 general classes of, 113–122 scaffolds and, 320–322 as tissue engineering substrates, 320 Bio-Oss, 315f Bioprinting methods, 3 Bioreactor, 322f Bis EMA6, structure of, 138f Bis-GMA. see Bisphenol A-glycidyl methacrylate Bisphenol A-glycidyl methacrylate (Bis-GMA), 101, 105, 120, 123 infrared spectra of, 81f resins, 125 structure of, 137f Bite force, jaw position and, 304f Bleaching agents, 105 Block polymer, 117–118 Blue light-emitting diodes, 164, 165f Body-centered cubic (BCC) array, 113–115 Bond, strength, 81–83 Bonded amalgam, 282 Bonded disk method, 84 Bonding agents, 100–101, 275 biocompatibility, 276 composites, 135 dentin, 278–280 enamel, 277–278 failure, 222f performance, in vitro evaluation, 275–276 of resin cements, 290 strength test, 275–276, 275f–276f universal, 280 Bone, reaction of, implant materials, 107 Bone grafting alloplasts, 314 Bone tissue, living, ceramic implant materials, 320 Brazing investment, 268 Brinell hardness test, 76, 76f Brittle materials fractography, 73–74, 74f tensile properties of, 39 tensile stress in, 72f Bruxism, 11–12, 45 Bulk fill composites, 154, 154f Bur cutting marks, 10, 11f C CAD-CAM technology (computer aided design/computer-aided manufacturing), 119–120, 295–296 all-ceramic restorations fabrications, 218f benefits, 295 clinical outcomes, 298 components, 295 in-office, 297f Calcium alginate, 233 Calcium aluminate, 289 Calcium hydroxide bases, 131 cavity liners, 103–104, 130–131 Calcium phosphate ceramics, 303 Calcium phosphate formulations, 131–132, 132f Calcium sulfate binders, temperature effects on, 263 Calcium sulfate-bonded investments, 262 properties, 262 setting expansion of, 264–265, 264f thermal expansion, 264f–265f Calcium sulfate dihydrate, 255, 255t Calcium sulfate hemihydrate, 252, 255, 255t, 262 Camphorquinone, 289–290 Candida species, 19–20 Capacity, 328, 328t Carat, 181 Carcinogenesis, 94 Caries formation, 19 glass ionomers and, 127–128 remineralization treatments and, 10 Cariogenic organisms, 19 Carious lesions, 14f Carnauba wax mixture, 57f Casein phosphopeptide-amorphous calcium phosphate (CPP-ACP), 131–132 Cast alloys, 280 Cast base-metal alloys, microstructure of, 192–193, 193f Cast titanium, 198–200 Casting alloys, 101–102, 107 replicating materials, 229–272 Casting investments composition, 261–262 gypsum products, 260–268 properties required, 261 Casting materials, 250–252 biocompatibility, 187–188 density, 180t, 186, 186t desirable qualities of, 250–251 elements in, 180–184 elongation, 186t, 187 grain size, 185–186 hardness, 186t, 187 mechanical properties of ANSI/ADA specification, 179t types and composition of, 178–180, 179t melting range, 186, 186t properties, 186–188 strength, 180t, 186–187, 186t Cavity configuration factor (C-factor), 84–85, 85f Cavity liners, 103–104, 130–131 calcium hydroxide, 103, 130–131 resin-modified glass ionomers, 130 thermal conductivity, 58 C-C bonds, 118 Cell culture methods, 322, 322f death, 93 function tests, 93 induction, 315–317 lines, 92–93 metabolism tests, 93 in vitro assays, 92–93 Cell injection method, 317f gene therapy, 317 tissue engineering, 314–315 Cell integrins, 308 Cementation, 273 333 INDEX Cements calcium hydroxide, 63f dielectric constant, 61t nonresin, 103–104 soft-tissue cytotoxicity, 105 thermal conductivity, 58 values for electrical resistivity, 61t zinc polyacrylate, 104 Cementum, 5, 78 Ceramic-metal restorations, composition and properties of, noble-metal alloys, 188–190, 188f–189f, 189t Ceramic restorations fracture determination in, 75f origin of fracture in, 73–74 scanning electron micrographs, 74f Ceramics, 26, 118–120 classification of, 209–210 by application, 209, 210f, 210t by crystalline phase, 209–210, 210t by fabrication method, 209, 210t comparative data, 213–214 composition of, 223t flexural strength of, 213t inlays, 209 mechanical properties, 211–214 test methods, 212 optical properties of, 214–215 properties of, 120 in prosthetic dentistry, 210–211 restorations, 215–219 silica-based, 280–281 thermal properties of, 211–214 veneers, 211 zirconia, 281–282 Ceravital, 302 CEREC AC with CEREC Bluecam, 297 Cermets, 157 C-factor. see Cavity configuration factor Chemical strengthening, 211–212 Chemicals, casting investments, 262 Chromaticity coordinates, 50, 51f CIE Lab color space, 51f, 51t Clinical trial, 94–95 Cobalt-Chromium (CO-CR) alloys, 196 Coefficient of thermal expansion (CTE), 211 Cohesion, 273–274 Cold work, 200 Collagen, 320 Colloidal state, 45–46 Colloidal systems gypsum products, 255 restorative materials and, 46 Colloids, nature of, 45 Color, 91 composite restoration, 150–151 dental materials, 50 measurement of, 50–52 Color (Continued) measuring instrument, 50 stability, composite restoration, 150–151 visual method of, 51–52 Commercial adhesive systems, 277 Commercially pure titanium, 197, 197t Compomers, 136t, 163–164, 290 composition and setting reaction, 163–164 properties of, 149t use of, 127t Composites, 120 bond strength, to dental substrates, 151 classification of, 139 clinical properties, 152–153 dentin and, 151, 151f enamel, 151 fine/microfine particles, 137f initiators and accelerators, 143 Knoop hardness, 151 mechanical properties, 151 other substrates, 151 packaging of, 147, 147f physical properties of, 147–151 working and setting times, 147–148 pigments, 143 polymerization stress, 86–87 properties of, 147–153, 149t–150t overview of, 147 resin core, 155f restoration biocompatibility, 153 color, 150–151 radiopacity, 152 solubility, 150 thermal properties, 161–162 water sorption, 150 wear rates, 153 as sealants, 129 for special applications, 153–156 strength and modulus, 151 uses of, 127t Compression, 30 Compressive strength, 69, 175t amalgam alloys, 175 of dental stone, 258f, 258t plaster products, 257–258 of selected dental materials, 70t water-to-powder ratio and, 258t Compressive stress (CS), 70f Concrete, 120 Continuously grown cells, 92–93 Contraction gap, 277f Contrast ratio, 55 Conventional glass ionomers, 135 components and setting reaction, 156–157 properties of, 149t setting mechanism of, 157f Conversion factors force per area, 328 linear, 328, 328t miscellaneous, 329 Copolymers, 117, 117f, 119f Copper (Cu), 183–184 Copper amalgam powders, 106 Copper-tin compound, 173–174 Coral, 320 Core build-up composites, 155 Corrosion, 177 products, from amalgam, 105–106 Coupling agents functions, 142 nanohybrid composite, 142 CPP-ACP. see Casein phosphopeptide-amorphous calcium phosphate Crack analysis, 87 in enamel, 16f formation, plastic shearing with, 117f growth, slow, 120 surface, 120 Creep, 175t, 176 Creep compliance (Jt), 41–42, 247, 247f curves, 42f Creep curves, amalgams, 41, 41f Creep recovery curve, 41f Creep test, 176 Crown, metal ceramic, 210–211, 210f, 220f Crystal lattice unit cells, in dental metals and alloys, 115f CS. see Compressive stress CTE. see Coefficient of thermal expansion Cubic zirconia ceramics, 213 Custom impression tray, 230f Cytotoxicity, 105 amalgam, 106–107, 106f–107f plasticizers, 107 tests, 93, 93f D Decussation, 5–6 Deformation, 30f strain and, 31 types of, 38f DEJ. see Dentin-enamel junction Demineralized freeze-dried bone allograft (DFDBA), 315f Density, casting alloy, 180t, 186, 186t Dental base-metal alloy, requirements of, 191 Dental caries. see Caries Dental implant, 301–312. see also Implants Dental materials decision matrix for, 25t discoloration, 63–64 334 INDEX Dental materials (Continued) dynamic mechanical properties, 42–43 elastic modulus of, 36t electrical properties, 60–63 fracture toughness of, 31f, 38–39 hardness of, 43–44 heat of fusion of, 58t optical properties, 50–56 properties, 63–65 resilience, 37 saliva, contact angles of, 48 specific heat, 59t surface mechanical properties, 43–45 tarnish, 63–64 testing of, 69–90 thermal conductivity, 58, 58t toughness of, 38 transition temperatures, 56–57 water on, contact angles of, 48, 49t wear, 45, 45f, 78 Dental pulp irritation tests, 95 Dental restorations digital imaging, and processing, for restorations, 295–300 masking ability, 56 physical properties of, 65 replacement of, 20 surface finish, 52–53 surface thickness, 52–53 thermal properties, 56–60 yield strength, 34 Dental stone alginate impression material, 236f chemistry and physical properties, 251 compressive strength of, 258f, 258t crystal structure, 253f manufacture of, 252–253, 252f–253f water-to-powder ratio of, 254 Dental structure design, stress analysis and, 85–86 Dentin, 5, 5f, 9–17 acid etching of, 10, 13f adhesion to, 279f barrier effect, 95–96 bonding, 99–100, 278–280 bonding agents, 100–101, 101f composites and, 151, 151f cut, 100f demineralized, 11, 12f–13f dielectric constant, 61t difficulties in testing, 12–15 formation, 104 fracture surface, 10f intratubular, 9 physical and mechanical properties of, 12–15 primary, 9 properties of, 15t remineralization, 103–104 Dentin (Continued) scanning electron microscopy image of, 9f sclerotic, 12 transparent, 14f Dentin bridge, 103f Dentin disk barrier test method, 94f Dentin-enamel junction (DEJ), 5, 9, 15–17, 16f Dentures adhesive, soft-tissue responses to, 107 base materials, immune hypersensitivity reactions, 107 biofilms and, 19–20 Deoxidizing agent, 184 Design software, 297, 297f Detergents, surface tension and, 47, 47f Diametral compression test, 71 Diametral tensile strength, 71 Diametral tensile test, 71 Die materials, 250–252 desirable qualities of, 250–251 impression materials compared to, 251–252 Dielectric constant, 61, 61t Differential scanning calorimetry (DSC), 80 Differential thermal analysis (DTA), 56–57, 57f Diffusion, 46 Digital imaging, and processing, for restorations, 295–300 Digital impression systems, 296–297, 296f, 296t compared to elastomeric impressions, 299t in-office milling option, 296t processing devices, 298 Dilatant fluid, 40, 40f Dimensional change, 175t, 176 elastomeric impression materials, 246t Dimensional stability, alginate impression material, 237 Direct metal laser sintering, 196–197 Disinfection alginate impression, 237 elastomeric impressions, 248–249 Dislocations, 115–116, 116f DMA. see Dynamic mechanical analysis DNA synthesis, 93 DSC. see Differential scanning calorimetry DTA. see Differential thermal analysis Dual-curing composite, 148f Ductility (of dental material), 36–37 Duplicating materials, 229 Durometer, 77 Dynamic elastic modulus (E’), 79–80 Dynamic mechanical analysis (DMA), 57, 57f, 78–80 Dynamic mechanical mixing, 238 Dynamic modulus (ED), 42–43, 44t Dynamic resilience, 43, 44t E EDTA. see Ethylenediaminetetraacetic acid Elastic behavior concepts of, 33 of solid, 40f Elastic deformation, 34 Elastic limit, 33 Elastic modulus, 35–36, 189, 195 of dental materials, 36t Elastic recovery, 235, 245, 246t Elastic region, 33 Elastomeric addition-silicone impression, 239f creep compliance, 247, 247f detail reproduction, 246t, 247 dimensional change, 246t elastic recovery, 245, 246t hydrophilization, 247–248, 248f mechanical properties, 245–247, 245t clinical application and, 249–250 strain in compression, 245t, 246 wettability, 247–248, 247t Elastomeric impressions digital impression systems compared to, 299t disinfection of, 248–249 materials, 237–250 consistencies, 237 impression techniques, 238–239 mixing systems, 238 setting properties, 242–245, 243t viscosity, 242–243, 243f Electrical conductivity, 60–61 Electrical resistivity, 60–61 Electrochemical corrosion, 63 Electrolyte etching, 280 Electromotive force, 61–62 Electrophoresis, 63 Elements, in casting alloy, 180–184, 180t Elongation, 33f, 35 casting alloy, 186t, 187 Embryonic stem cells, 319 Enamel, 5–8, 5f acid etching, 6f, 7–8 apatites, carbonate contents, 8–9 bonding, 277–278 composites and, 151 cracks in, 16f difficulties in, 12–15 nanoindentation mapping, 8f prisms, 5 properties of, 15t rods, 5 335 INDEX Enamel (Continued) sealant adhesion to, 124 structural variations of, 8 surface, for sealant preparation, 125, 125f Endodontology, advances in, 2 Endosseous implant, 301, 302f Endosteal implant diameter of, 305 factors affecting, 304–305 force duration, 304 length of, 305 Epoxy die materials, 251 Epoxy dies, 251 Esthetics, 2, 26, 284 Etched enamel for sealant, 126f sealant penetration of, 126f Etched porcelain, 281f Ethyl silicate casting investments, 267f, 268 Ethylenediaminetetraacetic acid (EDTA), 104 Evidence-based dentistry, 23–24, 23f hierarchy of, 23–24 integration of, 23 patient evidence, 23 scientific evidence, 23–24 Exponential numbers, prefixes and symbols for, 329, 329t Exponentials to decimals, conversion of, 329, 329t F Fabrication, permanent bending, 71 Face-centered cubic (FCC) array, 113–115 Fatigue strength, 73 Federal Specifications and Standards, 87–88 Feldspar, 223 Feldspathic porcelain, microstructure of, 224, 224f Ferritic stainless steels, 202 Fiber posts, bonding of, 282 Fillers, 139 types of, 139f Final setting time, 79, 256 Fineness, 181 Finite element analysis, 86, 212 Fissure incompletely filled, 125f stained, 124f Fixed dental prostheses, 210–211 Fixed prosthodontics, base-metal alloys for, 195–196, 196t Flexibility, alginate impression material, 235 Flexural fatigue curve, alloy, 73f Flexural strength, 69–70 of dental ceramics, 213t of selected dental materials, 71t test, photo-elastic analysis, 71f Flexure, 69 Flow, elastomeric addition silicone impression, 246 Flowable composites, 155 as sealants, 126–127, 127f Fluids, 40f behavior, 39–40 classification of, 40 pseudoplastic, 40f shear rate, 40f Fluorescence, 215 dental restoration, 52–53 Fluoride, 2 in plaque, 130f release, 129f reuptake and rerelease, 129f varnishes, 131 Fluoride ion release, 162–163, 163f Fluoride-releasing materials, 20 Fluorine ion, 8 Focal necrosis, 104 Force, 29–30 duration of, 304–305 geometry, 304 magnitude of, 304, 304f Force-deformation, characteristics of, 32f Forces, 327, 327t and wear, 26 Fourier-transformed infrared spectroscopy, 80–81 Fractography, 73–74, 74f, 212 Fracture determination, in ceramic restoration, 75f Fracture strength, 35 Fracture stress, 35 Fracture toughness, 73, 213 of dental materials, 38–39, 38t stress-strain curves, 38f Free-radical addition polymerization of corresponding methacrylate monomers, 144 Free-radical scavenger, 285 Friction, 44 Frictional force Fs, 44, 45f Frit, 223–224 Fusobacterium nucleatum, 17–18 G Gallium (Ga), 184 Galvanism, 62–63 Gel etchants, 275, 277 Gel point, 80 Gels, 46 Gene therapy, cell injection method, 317 Geometry, endosteal implant, 304 Gingival usage tests, 95 Glass ceramic A-W, 302 Glass ionomers, 102–103, 156–163, 285–287 caries and, 127–128 Glass ionomers (Continued) cement, 289 fluoride release from, 129f fluoride reuptake and rerelease from, 129f clinical applications, 161 composition of, 286 and reaction, 127 erosion tests of, 287 materials, 20 packaging of, 161, 162f properties of, 127–128, 287 ranking of, 128t resin-modified, 287–289 setting reaction and structure of, 286 uses of, 127t Glass materials, living bone tissue, 320–321, 321f Glass transition temperature, 79–80 Glazing, 212 3-Glycidoxypropyltrimethoxysilane, structure of, 142f Gold (Au), 181, 181t Gold alloys, 63 Grafted tissue, immunosuppressive drugs and, 318 Grafting, tissue sources for, 314b Grain size, casting alloy, 185–186 GTR. see Guided tissue regeneration Guided tissue regeneration (GTR), 315, 317f Gypsum casts, 231 compatibility, alginate impression material, 236–237, 236f materials abrasion resistance, 258–259 surface hardness, 258–259 pH, 255 products, 252–260 casting investments, 260–268 chemical and physical nature, 252–255 chemical reaction, 253–254 effect of spatulation, 254–255 effect of temperature, 255 manipulation, 260, 260f measurement, 256 mechanism of setting, 254 properties, 255–260 manipulative variables, 261t property requirements, 256t reproduction of detail, 259 required and excess water from, 254t setting expansion, 259–260 setting time, 256–257 volumetric contraction, 254 Gypsum stone cast, 230f 336 INDEX H Hardening solutions, 251 Hardness casting alloy, 186t, 187 elastomeric addition silicone impression, 246 test, 44f Heat of fusion, 57–58, 58t Heat-pressed all-ceramic materials, 216–217 Heavy-bodied agar hydrocolloid impression materials, properties of, 235t HEMA. see Hydroxyethyl methacrylate High-copper alloy, composition, 172t High-melting-point alloys, casting, investing for, 266–268 High-strength dental stone chemistry and physical properties, 251 compressive strength of, 258t manufacture of, 252–253, 252f–253f properties of, 257t scanning electron photomicrograph, 259f viscosity, 257, 257t water-to-powder ratio, 254 High-strength stone dies, 251 High temperature alloys, 223t Homopolymers, 119f Hooke’s law, 35 Humidity, gypsum products, 255 Hybrid composites, 139, 139f Hybridization, 278, 279f Hydrated aluminosilicate, 209 Hydrocal, 252 Hydrofluoric acid, 280–281 Hydrophilicity, 280 Hydrophilization, elastomeric addition-silicone impression, 247–248, 248f–249f Hydroxyapatite, 303, 320 formula, 8 Hydroxyethyl methacrylate (HEMA), 101 Hygroscopic casting investment, 265–268 Hygroscopic setting expansion, 264 Hygroscopic-thermal gold casting investment, 265–266 setting and hygroscopic expansion, 266f thermal expansion, 265f I IdentAlloy certification program, 188, 188f Immune hypersensitivity reactions, 107 Immunosuppressive drugs, grafted tissue and, 318 Implant supported restoration, stress distribution, 31f Implantation tests, 94, 102 Implants alloys, reactions to, 108 in bone, 95 ceramic materials, bone tissue and, 320 challenges and future, 309 design biointegration, 301–304 classification, 301, 302t osseointegration, 301–304 materials bone reaction, 107 ceramic, reaction to, 107–108 processing, 308–309 soft tissue, 107 metals, reactions to, 108 screw-shaped, 305 surface, 305–308 alterations, 306–308 coatings, 308 diameter, 305 length, 305 patterned, 307f titanium and, 20 Implant/tissue system, surfaces and biocompatibility, 305–306 Impression materials chemistry, 231–233 compared to die materials, 251–252 composition, 231–233 desirable qualities, 229–230 flexible, stone models, wettability and castability of, 49t proportioning and mixing, 234 purpose of, 229 types of, 231–250 Impression plaster, viscosity, 257 Impression trays, 229, 230f, 250 In vitro, animal, and usage tests, together, 96–97 In vitro assays tests correlation, 95–96 types of cells, 92–93 Index of Federal Specifications and Standards, 88 Index of refraction, 53, 53t Indirect composites, bonding of, 282 Indirect tests, 93 Indium (In), 184 Induced pluripotent stem cells (iPSCs), 319 In-office mills, choice of materials, 298t Inorganic oxides, 143 Interfacial bond strength, 82 Interfacial sealing, of luting agents, 283 Intermediary dental materials, 123–134 Intratubular dentin, 9 Investment age of, 265 cooling of, 264 Ion release, implant materials and, 306 iPSCs. see Induced pluripotent stem cells Iridium (Ir), 182 Irreversible hydrocolloids, 231 ISO 10993, 98 ISO standards, for dental cements, 283b J Jaw position, bite force and, 304f K Kaolin, 209 Karstedt type, 240 Kinetic friction, 44 Knoop hardness composites, 151 test, 76, 77f, 77t L Laboratory composites, 155 Lactobacilli, 17 Laminate veneer, 211 Latex gloves, addition silicone impressions and, 241 Lathe-cut alloys, 176 Lattice structures, 114f Lengths, 327, 327t Leucite-based ceramic, 216 structures of, 224f Leucite-reinforced ceramic, 215 Light contact angle of, 48f interactions with solid, 54f reflectivity, 55 transmission, of porcelains, 214t Light-activated tray materials, 250 Light-cured composites, 147, 152 Light-curing units, 164, 165t Linear coefficient of thermal expansion, 59, 60t Liners, 103–104, 103f Liquid, 166 surface tension of, 47, 47f Lithium disilicate-based materials, 216–217 Load-deflection curve, for Ni-Ti orthodontic wire, 37f Lost-wax process, temperature effect on, 262 Low-copper alloy, composition, 172t Low-shrink methacrylate monomers, 138 Low-shrink silorane composite, 142 Luting agents adhesion of, 283 anticariogenic activity of, 283 biocompatibility of, 283 337 INDEX Luting agents (Continued) classification of, 282–283 handling properties and radiopacity of, 283–284 interfacial sealing of, 283 materials for adhesion, 273–294 mechanical properties of, 283 physical requirements of, 283 solubility of, 284 viscosity and film thickness of, 284 M Machinable all-ceramic materials, 217–219 hard machining, 218 soft machining, and sintering, 218–219 Machined titanium, for dental implants, 198 Macrofills, 139 Macroscopic tattooing, 106 Macroshear bond strength test, 82–83 Macrotags, 277–278 Macrotensile bond strength test, 83 Malleability, 36–37 Managing accurate resin curing (MARC) test, 84, 85f Martensitic steels, 202 Materials science, fundamentals of, 29–68 Maximum light reflectance, 26 Mechanism of setting, gypsum products, 254 Melting range, casting alloy, 186 Membrane permeability tests, 93 Mer units, 117–118 Mercury in mix, 175, 175t reaction, uncompositional alloy, 174 Mercury dilatometer, 83–84 Mesenchymal cells, differentiation pathways, 319f Metal ceramic bonding, 221–222 Metal ceramic crown ceramics for, 209 cross-section, 220f and fixed dental prostheses, 210–211 Metal ceramic restorations, 209, 219–225 ceramics for, 222–224 design effect on, 224–225 failure and repair of, 225 Metal ceramic systems failure in, 222f requirements for, 220–221 Metallic crystalline array, 113–115 Metalloids, 113 Metals, 113, 171–208 and alloys, 26 atomic structure, 113–115, 114f Metals (Continued) chemical and atomic structure of, 113–116 corrosion properties of, 115 crystal lattice unit cells in, 115f heat fusion of, 58t physical properties of, 115–116 restorative materials, 171–208 surface tension of, 49t Metamerism, 52, 52f Methacrylate composites, 143 polymerization of, 144–146 Methacrylate resin, polymerization contraction of, 145–146, 146f 3-Methacryloxypropyltrimethoxysi-lane, structure of, 142f Methyl methacrylate, 117f Microbond strength tests, 276f Microcracks, 120 Microfill composite, 142f Microhybrid composites, 139 Microleakage, 98–99, 176, 177f specimen, slot, composite-enamel interface, 277f tests, 276 Microshear bond strength tests, 83 Millipore filter tests, 93 Mineral, of calcified tissues, 8–9 Mineral trioxide aggregate (MTA), 103–104 Model, 229 materials, 250–252 plaster, crystals of, 253f Molar, 124f Molecular weight, 118 Monomers, 117, 280 methacrylate, 137–138 structure of, 138f MTA. see Mineral trioxide aggregate Mucosa usage tests, 95 Mucous membrane irritation test, 94 Multipurpose resin composite, 136–147 composition, 136–143 Munsell color system, 51, 51f Mutagenesis assays, 94 N Nanocluster, 140, 140f particles, 141f Nanocomposite, 139 Nanofill composites, 140–142, 140f Nanofillers, 139–142 Nanohybrid composite, 142 coupling agents, 142–143 interfacial phase, 142–143 Nanoindentation mapping, of enamel, 8f Nanoindentation test, 77–78, 78t Nanoionomer, 160–161 Nanoleakage, 99, 276 Nanomeric particles, 141f Nanomers, 141f Nanometer-scale surface textures, 307 Nanotechnology, 3 Newton (N), 116 Newtonian fluid, 42 viscosity, 40, 40f Nickel (Ni), 184 Nickel-chromium (NI-CR) alloys, 195–196 Ni-Ti orthodontic wire, load deflection curve for, 37f Noble alloys, 184–190 formulation of, 185–186 hardening of, 181t, 184–185 phase structure of, 184, 185f Noble dental casting alloys, compositions, 186t Noble metals, 180–182 classes of, 180–181 Noncarious cervical lesions, 11–12 Noneugenol cements, 284–285 Nonresin cements, 103–104, 103f Normal setting expansion, 264 Notch lesions, 11–12 O Occlusal forces, 29–30 Occlusal registration materials, 250 properties used, 250t Opacity, 53 Opalescence, 53, 53f, 214–215 Optical constants, 53–56, 55f Optical properties, of dental ceramics, 214–215 Oral bacterial colonization, 18f Oral environment, 5–22 Oral lesions, amalgam sites, 105–106 Oral soft tissues, restorative materials and, 105–108 Orofacial implants, 301–312 Osmotic pressure, 46 Osseointegration, 301–304, 303f OsteoGen, 316f Oxidation-reduction potentials, for corrosion reactions, water and salt water, 62t P Packable composites, 151 Pain, amalgams and, 102 Palladium (Pd), 182 allergy, 107 Paraffin mixture, thermograms of, 56–57, 57f Particulate-reinforced polymer composite, 135 Passivation, 202 Patient evidence, 23, 23f PD-AG alloys, 190 PD-CU alloys, 190 Pellicle, 17, 18f Penetration coefficient, 49 338 INDEX Percent recovery, 76–77 dental polymers, 77t Periodic table of elements, 114f Periodontal ligament (PDL) engineering, 323f Periodontology, advances in, 2 PerioGlas, 316f Permanent bending, during fabrication, 71 PGA. see Polyglycolic acid pH, gypsum products, 255 Phosphate buffer solutions, corrosion and, 177 Phosphate-bonded investment, 266–267 ANSI/ADA specification, 266 thermal expansion curves, 267f Phosphoric acid, etching of enamel with, 6f, 7–8 Photo-elastic analysis, flexural strength test, 71f Photoinitiation, LED source for, 165f Photosensitizer, 143 Pigmentation, 52 PLA. see Polylactic acid Plaque, 17 fluoride in, 130f Plaster of Paris, 252 Plaster products alginate impression, 236f chemistry and physical properties, 251 compressive strength, 257–258 impression plaster, viscosity, 257, 257t manufacture of, 252–253, 252f–253f model plaster alginate impression material, 236f compressive strength of, 258t viscosity, 257, 257t Plastic behavior, 33 Plastic deformation, 33f Plasticizers, 166 cytotoxicity, 107 Platinum (Pt), 182 Platinum catalyst, 240f–241f Poisson’s ratio, 36 Poly (methyl methacrylate), 116f Polyether, 241–242, 242f ability of, 249f impression materials, composition and reactions, 239–242 pseudoplasticity in, 243f Polyglycolic acid (PGA), 108 Polylactic acid (PLA), 108 Polymer matrix composite, 135 Polymer-based filling, requirements for, 150t Polymeric materials, tissue engineering scaffolds, 321–322 Polymerization, 118 air inhibition of, 123 chemistry of, 146f reactions, 144–147 shrinkage and stress, 148 stress test, 86–87 Polymers, 116–118, 135–170 basic nature of, 116–118 chemical composition, 116–118 glass transition temperature, 79–80 indentation depth, 77t prosthetic application of, 165–166 toxic products, 321–322 Polymethylhydrosiloxane, 239 Porcelain, 119, 209 air-fired, 220f composition, 222–223 etched, 281f feldspathic, 214, 224f furnace, 216f manufacture of, 223–224 percent light transmission of, 214t vacuum-fired, 220f Power-driven mechanical spatulator, 261f Precious metals, 180–181 Preventive dental materials, 123–134 Primary cells, 92–93 Primers, 275, 278 Prism sheaths, 6–7 Prismless enamel, 8 Processing devices, 298 Promutagens, 94 Proportional limits, 32–33 Prostheses fixed dental, metal-ceramic crowns and, 210–211 metal ceramic fixed dental, 221f labial margin of, 224–225 Prosthetic dentistry, ceramics in, 210–211 Provisional composites, 155–156 Pseudoplastic fluid, 40, 40f Pseudoplasticity, in polyethers, 243f Pulpal irritation animal study, 99 tests, 95 Punch method, 72t Pure cast gold, 181t, 187 Push-out tests, 83 Putty-wash technique, 239 Pycnometry, 81 Q Quality of evidence, 24t Quartz, 209 Quartz-tungsten-halogen light-curing units, 164, 165t R Radiopacity, composite restoration, 152 Randomized controlled trials (RCTs), 23–24 RCTs. see Randomized controlled trials Refractory material, 262 Remineralization, 103–104, 131–132 caries and, 10 of enamel, paste for, 132f Removable dental prostheses, 191–192 ANSI/ADA specification No. 14, 191 composition, 191–192, 192t Replicating materials, impression and casting, 229–272 Resilience dental materials, 37 stress-strain curves, 37f Resin-based cements, 289–292 composition of, 289–290 mechanical properties of, 290 overview of, 289 properties of, 290 for provisional restorations, 292 setting reaction and structure of, 290 Resin-based materials, 101 Resin composite, 26, 101, 120, 135–170 clinical requirements for, 152t curves, 50 restoration types, 136t shrinkage and stress, 83–85 spectral reflectance curves, 50f types of, characteristics, 136t Resin-interpenetration zone, 278 Resin matrix, 137–138 Resin-modified glass ionomers, 128–130, 135, 287–289 as cavity liners, 130 commercialized, polymeric component, 158f components and setting reaction, 158–159, 159f composition and reaction, 129 composition of, 288 manipulation, 130 materials, 130f properties of, 128t, 129–130, 288–289 restoration of, 128f setting reaction and structure of, 288 uses of, 127t Resorbable materials, 108 Restorations, forces on, 30 Restorative dental materials, 17–20 requirements for, 150t role and significance of, 1–4 Restorative dentistry, scope of, 1 Restorative materials, 135–170 ceramics, 209–228 hypothetical, stress-strain curves for, 36f mechanical properties of, 29–49 metals, 171–208 339 INDEX Restorative materials (Continued) oral soft tissues and, 105–108 specifications for, 87–88 Restorative procedures, dentin alteration and, 11 Retarder, 233 Retention, 273 Rheology, 80 Rhodium (Rh), 182 Rockwell hardness test, 76–77 Root dentin, 15 Ruthenium (Ru), 182 S Saliva contact angles of, 48, 48f synthetic, 64f Sandblasting, with aluminum oxide, 280 Scaffold matrices with cells, tissue engineering, 317–318, 318f Scaffold systems, 318f Scanning electron microscope, 276, 277f–278f Scanning electron microscopy image (SEM image), 74f Scattering coefficient, 54, 54f Sciences, various, application of, 2 Scientific evidence, 23–24, 23f Screening tests, 96t SDF. see Silver diamine fluoride Sealant tags, 49f Sealants, 124f application of, 125–126 clinical studies, 125 into etched enamel, 126f fissure, 123–127, 125f flowable composites as, 126–127 fluoride-releasing, 125 glass ionomers as, 126 light-cured, 123 opaque, 124f pit, 123–127 properties of, 123–125 Secondary optical constants, calculated, 54 Self-adhesive resin cements, 282, 290–291 composition of, 291 properties of, 291 setting reaction and structure of, 291 Self-cured composites, 147 polymerization reaction, 145 Self-etch systems, 275, 279–280 Self-etching primers, 275 Self-glazing, 212 Sensitization, 202 Setting time, 64–65, 79 alginate impression material, 234 control of, 256–257 gypsum products, 256–257 measurement, 79 Setting time (Continued) spatulation and, 257t, 265 water-to-powder ratio, 257t, 265 Shade matching, 214 Shape-memory alloy, 203 Shear force, 30 Shear rate addition silicones, 242–243, 244f fluids, 40f Shear strength, 71–72 values of, by punch method, 72t Shear stress (SS), 70f Shear test, 83 SHED stem cells, 319 differentiation research, 320 Shelf life, 65 Shore A hardness test, 77 dental polymers, 77t Shrinkage, 245 measuring, 83–85 silorane-volumetric, 147f test assembly, 84f Silane, 137, 280–281 Silane coupling agents, 142 Silica, 60, 209 particle size of, 265 sol concentration, thermal expansion, 267f thermal expansion of, 60f Silica-based ceramics, 280–281 Silica-bonded investment, 267–268 Silica-to-binder ratio, 265 Silicon dioxide refractories, temperature effects on, 262–263, 263f Silorane, 138 structure of, 138f Silorane composites, polymerization of, 146–147, 146f Silver (Ag), 182–183, 183f Silver diamine fluoride (SDF), 132 Sintered all-ceramic materials, 215 Sintering, 209 Sinusoidal oscillation, 43f Slip-cast all-ceramic materials, 217 Smear layer formation of, 11f removal of, 100 Snap-set, of polyether, 244f Sodium silicate glass, structure of, 223f Soft denture liners, soft-tissue responses to, 107 Soft tissues cytotoxicity, 105 reaction of, implant materials, 107 Soldering investments, 268 Solids interactions with light, 54f water on, contact angles of, 49t Solubility composite restoration, 150 temperature and, 255t Sorption, 46–47 Spatial structure, 118 Spatiotemporal model, of oral bacterial colonization, 18f Spatulation, 254–255, 260, 265 setting time and, 257t, 265 Specific heat, 58–59, 59t Spectral reflectance curves, 50f Spectrometric techniques, 80–81 Spherical particles, 172 SS. see Shear stress Static automixing, 238 Static testing, 42 Stem cells, 318–320 types, 318–319 Stereospecific polymers, 117–118 Stern layer, 63 Storage modulus, 42–43 Strain calculation of, 31 in compression, 235f, 245t, 246 rate sensitivity, 15 Strength, casting alloy, 180t, 186–187, 186t Streptococci, 17 Streptococcus mutans, 19 organisms, glass ionomer and, 128 Stress, 30–31 analysis, 85–86 calculation of, 32 distribution of, 31f, 82f measuring, 83–85 plotting, 33f relaxation, 41, 41f types of, 30–31, 30f Stress-induced transformation toughening, 211 Stress-strain curves, 31–39 fracture toughness, 38f material properties and, 39f resilience, 37f Substrates, bonding to, 280–282 Superelastic materials, 33 Superficial Rockwell method, 76–77 Surface hardness, gypsum materials, 258–259 Surface oxides, 308 Surface tension detergents and, 47f liquids, 47, 47f of metals, 49t wetting and, 47–48 Syringeable composites, 136t, 154–155 T Tear energy, 75 of some dental materials, 75t Tear strength, 75 alginate impression material, 236f elastomeric addition silicone impression, 246–247 of some dental materials, 75t 340 INDEX TEGDMA, structure of, 137f Temperature calcium sulfate dihydrate, 255, 255t dental restorations, 56, 56f effects, calcium sulfate binders, 263 investment and, 262–265 silicon dioxide refractories, 262–263, 263f solubility calcium sulfate dihydrate, 255t calcium sulfate hemihydrate, 255t Tempering, 211–212 Tensile strength, 175, 175t of selected dental materials, 72t Tensile stress (TS), 70f, 82 brittle materials, 72f Tensilometer, 86, 86f Tension, 30 Tensometer, 87, 87f Terpolymers, 117, 117f Thermal casting investment, 265–268 Thermal conductivity amalgam alloys, 58 of dental materials, 58t Thermal diffusivity, 59, 59t Thermal properties, composite restoration, 161–162 Thermomechanical analysis (TMA), 57 Thermometer scales, conversion of, 328 Thermoplastics, 118 Thermosets, 118 Thixotropy, 40 3Y-TZP blocks, 213, 219 Three-point bending test, 69–70, 70f TI-6AL-4V microstructure of, 199, 199f room temperature, 198, 198f Tin (Sn), 184 Tin oxide, 214–215 Tin plating, 280 Tissue-engineered dental tissues, 322–324, 322f Tissue engineering, 313–326 scaffolds culture conditions for, 322 polymeric materials, 321–322 strategies, 314–318, 316b Tissue reaction, restorative dental materials, 2 Titanium, 196–200 biofilm and, 20 ion release, 306 reactions to, 108 Titanium alloys, 197–200, 198f Titanium oxide, 214–215 TMA. see Thermomechanical analysis Tooth calcified tissues in, 5, 5f pulp, 63f, 99 reactions of, 98–105 pulp chamber, 5f Torsion, 30, 72, 72f Torsional moment angular rotation curves, 72f Toughening mechanisms, 211–212 Toughness, 38 Toxicity, 2 Transformation toughening, 211, 212f Translucency, 53, 214–215 Transparency, 53 Transparent dentin, 11, 14f Transplant performed, 314b waiting list for, 314b waiting time for, 314b Tri-Cure glass ionomer system, 159–160 setting reactions, 159f–160f Troy, avoirdupois, and metric weights, comparative table of, 329, 329t TS. see Tensile stress Tubule density, 9 comparison of, 10t Two-body abrasion tests, 78, 79t Two-paste systems, 161, 162f Two-putty addition-silicone systems, 238 U UCS. see Ultimate compressive strength Ultimate compressive strength (UCS), 34 Ultimate tensile strength (UTS), 34 Unicompositional alloy, 174 Units, conversion of, 327 Universal bonding, 280 Universal systems, 275 Universal testing machine, 31–32, 32f Urethane dimethacrylate (UDMA), structure of, 137f Usage tests, 94–95, 96t, 102, 106 UTS. see Ultimate tensile strength V Values for electrical resistivity, human tooth structure, 61t Van der Waals volume, 145–146 Varnishes, 103–104, 103f Veneers, 211 Vicat penetrometer, 79f, 244f Vickers hardness test, 76 Vickers indentation, 77f, 211, 212f Viscoelastic materials, 41 Viscoelasticity, 39–42 Viscosity, 274 addition-silicone impression materials, 244f fluid behavior and, 39–40 impression plaster, 257, 257t Newtonian fluid, 40, 40f Viscous response, 39 Visual method, color, 51–52 Volume, 328, 328t Volumetric shrinkage, 146f W Wash technique, 239 Water contact angles of, in dental materials, 48 GIs, 156 Water-bath temperature, 265 Water-to-powder ratio, 265 compressive strength and, 258t setting time and, 257t, 265 Water sorption, 64 composite restoration, 150 Wear, 45, 45f of dental materials, 78 rates, 153 tests, traditional, 78 Weights, 327, 327t and measures, table of, 327–328 Wettability, 274, 274f impression materials, 49t Wetting, surface tension and, 47–48 Working time alginate impression material, 234 silicones, 249 Wrought alloys, 200–204, 200f composition of, 200–201, 201t microstructure of, 200 properties of, 201, 201t Wrought beta-titanium alloy, 203t, 204, 204f Wrought nickel-titanium alloy, 203–204 composition and shape-memory effect, 203 properties and manipulation, 203–204, 203t, 204f Wrought stainless steel alloys, 201–203 composition of, 202 function of alloying elements and chemical resistance, 202 stress-relieving treatments, 202–203 X Xenoestrogens, 153 Xenograft, 313–314, 314b, 315f Y Yield point, 33–34 Yield strength, 33–34 Z Zeta-potential, 63, 64t Zinc (Zn), 171, 184 Zinc oxide-eugenol (ZOE), 284–285 cement, 95–96, 104 Zinc phosphate, 104 Zirconia, 211 based dental ceramics, 211, 212f ceramics, 281–282 toughening mechanism, 212f Zirconia-based restorations, digital impressions and, 298
13217	https://www.youtube.com/watch?v=q0PxCQWG3ic	Step and Delta Functions \| MIT 18.03SC Differential Equations, Fall 2011 MIT OpenCourseWare 813 likes 70500 views 4 Jan 2012 Step and Delta Functions: Integration and Generalized Derivatives Instructor: Lydia Bourouiba View the complete course: License: Creative Commons BY-NC-SA More information at More courses at
13218	https://pmc.ncbi.nlm.nih.gov/articles/PMC6168365/	RNA-seq: Basic Bioinformatics Analysis - PMC Skip to main content An official website of the United States government Here's how you know Here's how you know Official websites use .gov A .gov website belongs to an official government organization in the United States. Secure .gov websites use HTTPS A lock ( ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites. Search Log in Dashboard Publications Account settings Log out Search… Search NCBI Primary site navigation Search Logged in as: Dashboard Publications Account settings Log in Search PMC Full-Text Archive Search in PMC Journal List User Guide View on publisher site Download PDF Add to Collections Cite Permalink PERMALINK Copy As a library, NLM provides access to scientific literature. Inclusion in an NLM database does not imply endorsement of, or agreement with, the contents by NLM or the National Institutes of Health. Learn more: PMC Disclaimer \| PMC Copyright Notice Curr Protoc Mol Biol . Author manuscript; available in PMC: 2019 Oct 1. Published in final edited form as: Curr Protoc Mol Biol. 2018 Sep 17;124(1):e68. doi: 10.1002/cpmb.68 Search in PMC Search in PubMed View in NLM Catalog Add to search RNA-seq: Basic Bioinformatics Analysis Fei Ji Fei Ji 1 Department of Molecular Biology, Massachusetts General Hospital, Boston, Massachusetts 2 Department of Genetics, Harvard Medical School, Boston, Massachusetts Find articles by Fei Ji 1,2, Ruslan I Sadreyev Ruslan I Sadreyev 1 Department of Molecular Biology, Massachusetts General Hospital, Boston, Massachusetts 3 Department of Pathology, Massachusetts General Hospital and Harvard Medical School, Boston, Massachusetts Find articles by Ruslan I Sadreyev 1,3, Author information Article notes Copyright and License information 1 Department of Molecular Biology, Massachusetts General Hospital, Boston, Massachusetts 2 Department of Genetics, Harvard Medical School, Boston, Massachusetts 3 Department of Pathology, Massachusetts General Hospital and Harvard Medical School, Boston, Massachusetts Corresponding Author, sadreyev@molbio.mgh.harvard.edu Issue date 2018 Oct. PMC Copyright notice PMCID: PMC6168365 NIHMSID: NIHMS977214 PMID: 30222249 The publisher's version of this article is available at Curr Protoc Mol Biol Abstract Quantitative analysis of gene expression is crucial for understanding the molecular mechanisms underlying genome regulation. RNA-seq is a powerful platform for comprehensive investigation of the transcriptome. In this Unit, we present a general bioinformatics workflow for the quantitative analysis of RNA-seq data and describe a few current publicly available computational tools applicable at various steps of this workflow. These tools comprise a pipeline for quality assessment and quantitation of RNA-seq data that starts from raw sequencing files and is focused on the identification and analysis of genes that are differentially expressed between biological conditions. Keywords: RNA-seq, bioinformatics, quantitative analysis of gene expression, differentially expressed genes INTRODUCTION Quantifying gene expression and identifying transcripts that are differentially expressed between two conditions in a cell, tissue, or organism is an important approach to deciphering the molecular physiology of the cell. RNA-seq analysis based on next-generation sequencing (NGS) data has recently become the de facto standard for the analysis of gene expression at the level of the whole transcriptome. This analysis is often crucial for the generation of mechanistic hypotheses about molecular events in cells and tissues. Examples include cellular responses to physiological stimuli, effects of experimental perturbations on specific genes and pathways, or the malfunction of gene regulation in disease. RNA-seq involves isolation of total RNA from tissues or cells of interest followed by the construction of DNA libraries and sequencing of these libraries using a next-generation sequencing instrument. This Unit covers a basic computational workflow of bioinformatics analysis of RNA-seq data. The focus is on basic computational analysis of traditional RNA-seq data, and does not cover single-cell RNA-seq, small RNA-seq, GRO-seq, or other specialized RNA-seq applications. The workflow described below requires installation of and basic familiarity with Unix/Linux and R command-line interfaces. The workflow includes three parts: (a) mapping sequencing reads to a reference genome or transcriptome; (b) quantifying expression levels of individual genes and transcripts; and (c) identifying specific genes and transcripts that are differentially expressed between samples. The resulting sets of differentially expressed genes can be further analyzed, either manually or automatically, for example, for the presence of relevant genes of interest, enrichment of functional gene categories, or overlap with sets of genes or regulatory genomic elements identified in other experiments. STRATEGIC PLANNING Meaningful experimental design is essential for successful RNA-seq analysis. A key recommendation is to include at least three biological replicates per condition/group, which is crucial for robust estimates of statistical significance in the analysis of differential gene expression. In addition, the samples should be sequenced to sufficient depth. For a basic RNA-seq experiment in a mammalian model with sequencing performed on an Illumina HiSeq, NovaSeq, NextSeq or MiSeq instrument, the recommended number of reads is at least 10 million per sample, and optimally, 20–30 million reads per sample. Lower sequencing depths yield statistically insufficient numbers of reads per transcript and effectively limit statistical analyses to highly expressed genes. Another key issue concerns whether the goal is to quantify expression levels at loci, or to go to greater depth and compare splicing patterns on genes. Paired-end (PE) Illumina sequencing is better suited for capturing splicing events than single-end (SE) sequencing, but is more costly. Finally, 50 bp Illumina reads are typically sufficient for the unique mapping of a mammalian RNA to the genome, but longer reads increase the likelihood of directly capturing splice sites within the reads, thereby improving the analysis of potential alternative splice forms. BASIC PROTOCOL Raw RNA-seq data are typically formatted as FASTQ files. FASTQ is a text-based format storing the sequences of the reads as well as their sequencing quality. The file is organized in groups of four lines per read as shown below: @NB500929:247:HL2TYBGX3:1:11101:25163:1060 GATTTGGGGTTCAAAGCAGTATCGATCAAATAGTAAATCCATTTGTTCAACTCACAGTTT + !’’((((+))%%%++)(%%%%).1-+’’))55CCF>>>>>>CCCCCCC65 The first line starts with “@” and is followed by a unique sequence identifier, which includes instrument ID (NB500929), run number (247), and flow cell ID (HL2TYBGX3), followed by the numbers specifying the location of the DNA fragment on the flowcell. In the case of paired-end sequencing, two FASTQ files for read 1 and read 2 include the same sequence identifiers plus the read number (1 or 2), which indicates whether the sequence comes from read 1 or read 2 of the DNA fragment. The second line contains the read sequence. The third line starts with a “+” character and can optionally be followed by the same sequence identifier and any additional description. The fourth line encodes the sequencing quality scores for each base, which are coded as individual symbols according to a coding scheme (see Alignment is the computational process of mapping the sequence of each read to a reference genome using a specific annotation of genes and other genomic elements generated, for example, by the ENSEMBL project (Zerbino et al., 2017). Compared to the alignment performed in whole-genome sequencing and other applications, a challenge of mapping short-read RNA-seq data comes from the non-contiguous structure of eukaryotic transcripts along genomic coordinates. This challenge requires special algorithmic treatment of the cases when the 5’ and 3’ parts of a read sequence correspond to two different exons, or when reads from two ends of the same library fragment are mapped to non-adjacent exons in the reference transcript. In this protocol, we describe the use of the STAR alignment tool (Dobin et al., 2013) as it provides relatively high alignment speed and lower mapping error rates. After mapping reads to the genome, it is important to survey the quality of the RNA-seq data in more depth. This can be accomplished using standard software tools, for example Picard ( Qualimap2 (Okonechnikov et al. 2016), RNASeQC (DeLuca et al. 2012), or SAMTools (Li et al. 2009). The workflow described in this UNIT uses Picard ( Picard generates various “conglomerate” metrics of the mapped reads in a given sample. These metrics include the fractions of total nucleotide bases in the reads that map to annotated exons, introns, UTRs, and intergenic regions bases aligned to mRNA regions, the rate of read duplication (fraction of redundant reads mapping to the same genomic coordinates) etc. This step is essential for assessing the quality of sequencing libraries and diagnosing potential issues with RNA extraction, library construction, or sequencing. After resolving potential quality issues and removing low-quality samples, the workflow proceeds to the quantitation of reads mapped to individual transcripts and identification of differentially expressed genes. Necessary Resources Download and install the required tools: STAR: Picard: HTseq: R: HARDWARE: Computer with Unix, Linux, or Mac OS X operating systems. RAM requirements are at least 10 × genome size bytes for STAR alignment. A human genome of ~3 gigabases (Gbp) will require ~30 gigabytes (GB) of RAM. 32 GB is recommended for human genome alignments. Consecutive STAR jobs with the same reference genome can be run using shared memory using –genomeLoad LoadAndKeep command option, which saves the time required to load the reference index for each job. It is also necessary to have sufficient storage space (>100Gb) for output files Download the reference genome as a DNA FASTA file and the gene annotation GTF file from the Ensembl database: Open a Unix/Linux command line environment (“Terminal” application in a Linux operating system or macOS). Create the alignment index of the reference genome using the STAR index utility as described at the following website: using the following command: STAR --runMode genomeGenerate --genomeDir --genomeFastaFiles --sjdbGTFfile --sjdbOverhang 49 For example, for genome reference fasta file “Homo_sapiens.GRCh38.dna.fa” and gene annotation file “Homo_sapiens.GRCh38.92.gtf” downloaded in step 1, use the following command to create the reference STAR index: STAR --runMode genomeGenerate --genomeDir human_GRCh38 --genomeFastaFiles Homo_sapiens.GRCh38.dna.fa --sjdbGTFfile Homo_sapiens.GRCh38.92.gtf --sjdbOverhang 49 A more detailed protocol for STAR usage is described in Dobin and Gingeras, 2015. Download the set of custom wrapper scripts from This set includes three Perl scripts (RNAseq_align.pl, RNAseq_qc.pl, and RNAseq_count.pl) and two examples of input files with local configuration of required computational tools (configure.txt) and the list of input samples (sample_list.txt). Edit the tab-delimited configuration file (configure.txt), which was downloaded at step 3. This file contains a tab-delimited table (Table 1) that indicates the names and locations on the user’s machine (full local file paths) of the three required tools, STAR, Picard, and HTseq installed before starting the protocol; the GTF file with genome annotation downloaded at step 1; the directory with the STAR reference files generated at step 2; and the directory with the input FASTQ files. To determine the full path to a standard pre-installed package in a Unix/Linux environment, one can use the “which” command, for example: $ which STAR /usr/local/bin/STAR 5. Edit the tab-delimited input list in file sample.list, which was downloaded at step 3. This file contains a tab-delimited table (Table 2) that indicates the group assignment, the name of the sample, and the name of the corresponding FASTQ file for each experimental sample. In the example shown in Table 2, there is a total of 6 RNA samples that form two groups of biological triplicates: samples from wild-type (marked WT) and mutant cells (marked mut). The gene expression in the “WT” group will be compared to the gene expression in the “mut” group, and differentially expressed genes will be identified at the later steps of the workflow. Specific group names (the first column) and sample names (the second column) can be arbitrary, whereas file names (the third column) should be the exact names of the input FASTQ files that are located in the directory whose full path is listed as FASTQ_DIR in the configuration file (Table 1). In the case of paired-end sequencing when two FASTQ files are produced for each sample, this table should be extended into four columns, with the fourth column indicating the name of the second FASTQ file for each sample. From the directory that contains the downloaded scripts (step 3) and edited files confirgure.txt (step 4) and sample_list.txt (step 5), use the following command to run the alignment: ./RNAseq_align.pl sample_list.txt configure.txt This step will map the reads from the input FASTQ files to the reference genome using the STAR aligner. Once it is completed, this step will generate several subdirectories that correspond to each individual sample and are named by sample names listed in the file sample_list.txt (Table 2), for example “WT.RNA.rep1”. Each subdirectory will contain the generated STAR alignments as BAM formatted files. The completion of this command may take several hours. This time will depend on the number of samples, the number of reads, genome size, and the CPU capacity of the particular machine. Table 1. Example of the configuration table (file configure.txt) STAR/usr/local/bin/STAR Picard/home/ji/tools/picard-tools/picard-tools-1.100 HTseq/home/ji/.local/bin/htseq-count GTF/home/ji/data/CPMB/pipeline_RNA/ref/gtf STAR_REF/home/ji/data/CPMB/pipeline_RNA/ref FASTQ_DIR/home/ji/data/CPMB/pipeline_RNA/fastq Open in a new tab The first column includes the identifiers of tools and data files, and should be kept intact. The second column includes the full paths to these files at the user’s computer and should be edited by the user. Table 2. Example of the table with the list of group names, sample names, and corresponding input FASTQ files for the RNA samples in the specific study (file sample.list) WT WT.RNA.rep1 WT.RNA.rep1.fastq WT WT.RNA.rep2 WT.RNA.rep2.fastq WT WT.RNA.rep3 WT.RNA.rep3.fastq mut mut.RNA.rep1 mut.RNA.rep1.fastq mut mut.RNA.rep2 mut.RNA.rep2.fastq mut mut.RNA.rep3 mut.RNA.rep3.fastq Open in a new tab For each RNA sample, the first column indicates group assignment (e.g., whether the RNA is from a wild-type or mutant organism or is a control or a treatment sample; arbitrary alphanumeric string), the second column indicates the name of the sample (arbitrary alphanumeric string), and the third column indicates the name of the FASTQ file located in the directory that is listed as FASTQ_DIR in the configuration file. In the case of paired-end sequencing, the name of the FASTQ file for the second read should be indicated in the additional fourth column. Initial quality assessment Use the following command to produce data quality metrics from the alignments generated at the previous step: ./RNAseq_qc.pl sample_list.txt confirgure.txt This step uses the Picard tools to generate a table of quality control metrics written in the file RNA.qc.xls. This table includes alignment rate, duplication rate, and fractions of ribosomal RNA, UTR, Exon, Intron and intergenic nucleotide bases among the mapped reads (Table 3). Before proceeding to the next steps, it is important to closely examine these metrics as described below. Fraction of mapped reads (“Mapped read percentage”). For most RNA-seq libraries of high quality, this fraction is greater that 80–90%. A lower mapping rate may indicate contamination of foreign DNA/RNA species, issues with library construction (e.g. high level of adapter dimers), or other issues. Unmapped reads can be found in the file “Unmapped.out” in each run subfolder. A first approach to analyzing potential sources of unmapped reads is to manually inspect a few randomly selected read sequences and to run BLAST (website with the unmapped reads as queries against a non-redundant (NR) nucleotide database from NCBI. This will indicate whether the samples have been contaminated by DNA/RNA from other species (e.g. bacteria) or by artifacts of library construction. Fraction of ribosomal RNA (“Ribosomal RNA percentage”). In a typical high-quality RNA-seq library, the amount of ribosomal RNA, which originally accounts for >90% of all RNA in the cell, is significantly reduced by polyA selection or rRNA depletion strategies and usually accounts for <5% of mapped nucleotide bases. A higher rRNA fraction may indicate potential issues with library quality and will reduce the representation of mRNA in the sample. Duplication rate. Duplication rate is the fraction of duplicate reads that map to exactly the same location in the genome. Overly high duplication rates may suggest over-amplification by PCR during library construction, which may create bias in the representation of particular transcripts and regions over others. In some cases, over-amplification may stem from low complexity within the original RNA sample. RNA-seq alignments can have a higher duplication rate than many other NGS applications, including whole-genome sequencing, ChIP-seq, ATAC-seq, etc. Typical duplication rates range from 30% to 90%, often depending on sequencing depth and transcriptome size. Extremely high duplication rates (>90%) may, however, suggest potential PCR over-amplification. Over-amplification is often apparent when BAM alignment files are manually inspected in a genome browser, for example in IGV (Robinson et al., 2011). Multiple identical reads aligned to the same genomic position form characteristic “stacking” patterns, suggesting over-amplification of a single fragment, especially when immediately adjacent flanking regions have much lower numbers of aligned reads. These measures are the most important among the set of quality metrics produced by Picard. Similar metrics can also be calculated by other packages, e.g. Qualimap2 (Okonechnikov et al. 2016), RNASeQC (DeLuca et al. 2012), SAMTools (Li et al. 2009). Table 3. The table of quality control metrics generated by Picard tools (example) ID Total read #Uniquely Mapped %Multi Mapped %Unmapped %Duplication %rRNA %Coding Reads %UTR Reads %Intronic %Intergenic % WT.RNA.rep1 37,764,610 78.21%16.03%5.76%43.0%1%48%45%4%1% WT.RNA.rep2 38,522,082 78.39%16.13%5.48%43.4%1%49%45%4%1% mut.RNA.rep1 38,899,392 80.63%13.93%5.44%38.7%1%50%41%6%1% mut.RNA.rep2 39,984,549 81.58%12.99%5.43%36.8%1%48%45%5%1% Open in a new tab The first column (“ID”) indicates the name of sample as listed in the sample list (Table 2), the second column (“Total read #”) indicates the total number of input reads in the submitted FASTQ file. The subsequent columns indicate various metrics of data quality based on the alignments produced at step 6. The names of these metrics are indicated in the header of the table. Quantitation of mapped reads The numbers of reads mapped to individual reference transcripts are counted using the HTseq package, which generates a tab delimited table of read counts for each transcript. Use the following command to run HTSeq on all samples: ./htseq-count_table.pl sample_list.txt configure.txt This command runs HTseq to quantify sequencing reads mapped to each gene and generates a tab-delimited table of read counts, count.xls, with genes as rows and samples as columns. This table contains the raw read count for each gene according to the genomic coordinates annotated in the input GTF file whose location should be listed as “GTF” in file configure.txt (Table 1). These raw counts are used at further steps of the workflow to: (a) identify genes that are differentially expressed between conditions (sample groups), and (b) derive gene expression values for each individual transcript, which can be calculated by normalizing the raw counts by the total number of reads in the dataset and by the length of individual transcripts. A few commonly used approaches for normalization include CPM (counts per million reads), RPKM (reads per kilobase per million reads), FPKM (fragments per kilobase per million reads), and TPM (transcripts per million reads). Analysis of differential gene expression There are multiple computational tools to identify genes that are differentially expressed between sample groups: EdgeR (Robinson et al., 2010), DESeq2 (Love et al. 2014), CuffDiff2 (Trapnell et al. 2013) etc. These tools use counts of next-generation sequencing reads over individual genes and transcripts across the genome to infer genes or transcripts that show statistically significant differences in gene expression between the samples that are being compared, which usually represent different biological conditions. As an example, the particular workflow described in this UNIT uses edgeR (Robinson et al., 2010) as a statistically robust and relatively user-friendly R package with an extensive manual. The edgeR package is included in the Bioconductor collection of R libraries and should be used within the R environment. To start using edgeR, the user should install and open R, and then, within the R environment, download and install the edgeR package using the following commands: source(“ biocLite(“edgeR”) Load the count table produced by HTseq at step 8 and the group assignments (e.g., wild-type or mutant or non-treated or treated sample) for each individual sample (column 1 of Table 2) defined at step 5 in file sample_list.txt : counts <- as.matrix(read.table(“htseq.count.txt”,sep=“\t”,header = T,row.names = 1)) group <- as.character(read.table(“sample_list.txt”)[,1]) Load the counts and group assignments from step 10 into a single computational object of the DGEList class, i.e. a specially designed combination of variables, data structures, and functional operations for the manipulation of these data as a single entity, in edgeR: library(edgeR) cds <- DGEList( counts, group = group ) Filter the genes that have low expression values in the majority of samples. For these genes, the number of reads is too low for a robust statistical analysis of differential expression between samples. A generally recommended cutoff of read number for a low-expressed transcript is CPM of 1. In the case of a typical sequencing depth of a total 10–30 million reads per sample, this cutoff corresponds to 10–30 reads mapped to the transcript. For example, only keep the genes whose CPM value is higher than 1 in at least two samples: cds <- cds[rowSums(1e+06 (cds$counts/expandAsMatrix(cds$samples$lib.size, dim(cds)))> 1) >= 2, ] cds <- calcNormFactors( cds ) For the genes retained after filtering at step 12, generate a tab-delimited table of CPM values in all samples as file “CPM.txt”: CPM <- cpm(cds) write.table(CPM,”CPM.txt”,sep=“\t”,quote=F) An important initial way of visualizing relationships between the compared samples is to represent each sample as a point in a multi-dimensional space of expression values. This multi-dimensional space is based on a system of coordinates where each coordinate axis is the level of expression of an individual gene. In this system, an RNA-seq sample can be represented by a point whose coordinates correspond to the levels of expression of all genes. If two samples have similar patterns of gene expression, they will be represented by points that are close to each other in this space. To produce a convenient view of samples in this space, one can use various computational techniques for dimensionality reduction, which effectively collapse multiple dimensions of the original space of gene expression into two or three artificial dimensions that achieve a strong degree of separation between samples as two or three-dimensional points. A popular example of a computational algorithm for dimensionality reduction based on linear transformations is principal component analysis (PCA). EdgeR implements a different, non-linear algorithm of multi-dimensional scaling (MDS). Use this command to generate a two-dimensional MDS in order to inspect the similarity between individual samples as points in a multi-dimensional space of expression values: plotMDS(cds) The resulting two- or three-dimensional plots allow the researcher to quickly inspect the consistency of expression patterns within a group of biological replicates and the separation between two or more compared groups of replicates (Fig. 1). These plots may also help identify potential outlier samples, i.e., individual samples whose expression patterns are strongly dissimilar from other replicates in the same group. Since consistency between individual replicates is important for a robust statistical comparison between groups of replicates from different biological conditions, the expression patterns of outlier samples can skew the comparison and bias the final results. Therefore, potential outliers (e.g. WT. rep3 in Fig. 1) should be examined for data quality (e.g. basic quality metrics generated at step 7) and for possible deviations in the experimental conditions used to produce the RNA samples. It is important to carefully consider the possibility of removing these outlier samples, especially if their quality is suspect. On the other hand, removing a replicate from further analysis may have negative effect on the downstream results due to the reduction of statistical sample size. This potential possibility highlights the importance of advance planning and having a robust experimental design that includes a sufficient number of biological replicates even after removing possible outliers. This removal can be performed using simple commands. For example, use the following commands to remove sample A_Rep1 (replicate 1 of group A) and sample B_Rep3 (replicate 1 of group B) as outliers: outliers <- c(“A_Rep1”, “B_Rep3”) counts <- counts[,-outliers] group <- group[-outliers] After removing outlier samples, repeat steps 10–14 and visually examine the new MDS plot. Calculate fold change and statistical significance of expression differences between sample groups for all individual genes: cds <- estimateCommonDisp(cds) de.poi <- exactTest( cds, pair = c( “WT”,”mut” )) resultsByFC.poi <- topTags( de.poi, n = nrow( de.poi$table ), sort.by = “logFC” )$table These commands generate a tab-delimited table that contains the estimate of absolute difference in gene expression between two groups of replicate samples, “WT” and “mut”, and the estimate of statistical significance of this difference for each individual gene or transcript. Both estimates are based on the analysis of read counts for individual genes or transcripts across two groups of biological replicates. The estimate of absolute expression difference is calculated for each gene as log2 of fold change (logFC) of average expression in the two compared sample groups. The estimate of statistical significance of this difference is calculated as the false discovery rate (FDR). As opposed to the unadjusted P-values, which are based on statistical comparisons for a single gene, FDR is a more conservative estimate of statistical significance adjusted for multiple statistical tests performed among the large population of all genes and therefore is preferable for the accurate identification of differentially expressed genes. Identify differentially expressed genes and create a file with a separate tab-delimited table for these genes. In the example below, differential gene expression is defined by the cutoffs of at least a 2-fold change in expression value (absolute value of logFC > 1) and FDR less than 0.01. The following two commands identify differentially expressed genes and create an Excel file (DE.gene.logFC.xls) with quantitative expression metrics for each gene: de.gene.logFC <- resultsByFC.poi[abs(resultsByFC.poi[,”logFC”])>1 & resultsByFC.poi[,”FDR”]<0.01, ] write.table(de.gene.logFC,”DE.gene.logFC.xls”,sep=“\t”,quote=F) As the result, the output file DE.gene.logFC.xls contains for each gene (i.e., gene name), the log fold change and the statistical significance of differential expression. To simultaneously visualize both expression changes and their statistical significance across the whole gene set, a Volcano plot (Fig. 2) shows each gene as a point in a two-dimensional space of statistical significance (P-value or FDR) vs log fold change. Differentially expressed genes identified at step 16 are highlighted in color. Use the following commands to generate a Volcano plot: png(“Volcano.png”,5,5,units = “in”,res=300) plot(resultsByFC.poi[,1],-log10(resultsByFC.poi[,”FDR”]),xlab=“logFC”,ylab=“-log(P-value)”,pch=20,cex=0.3) points(de.gene.logFC[,1],-log10(de.gene.logFC[,”FDR”]),col=“red”,pch=1,cex=0.3) dev.off() For a more detailed visualization of expression patterns, a heatmap of the expression values of differentially expressed genes across all individual samples can be generated (Fig. 3). To highlight grouping among samples and recurrent expression patterns among genes, heatmaps are typically clustered both by columns (samples) and rows (genes), often using a hierarchical clustering method. The degree of inferred similarity between individual samples and between individual genes can be represented as dendrograms of columns and rows, respectively (Fig. 3). Inspection of these heatmaps can provide more detailed information about similarities and differences of expression patterns between samples and between conditions, as well as about groups of genes whose expression behaves in a similar way. Below is an example of R commands using the R package gplots to produce an expression heatmap, as a graphic PNG file, from the table of differentially expressed genes produced at step 16. library(gplots) de.genes = rownames(de.gene.logFC) rpkm = rpkm(cds,gene.length) de.gene.RPKM.mtx = log10(rpkm[de.genes,]+0.1) colfunc <- colorRampPalette(brewer.pal(9,”Blues”)) png(“DE.gene.heatmap.png”,5,7,units = “in”,res=300) heatmap.2(de.gene.RPKM.mtx,col=colfunc(100),trace=“none”,labRow=““,cexRow=1,cexCol=1.5,lhei=c(1,5), lwid=c(1, 3), density.info=“none”,margins = c(5,1),srtCol=45,key.title = ““,key.xlab = “logRPKM”) dev.off() These commands generate the file DE.gene.heatmap.png that contains the expression heatmap with samples and genes clustered using a basic hierarchical clustering method (Fig. 3). Since this clustering is non-supervised, the grouping of samples by the patterns of gene expression can serve as an additional verification of consistency between experimental replicates and provide a more detailed view of inconsistencies between potential outlier samples and the rest of the group (sample WT.rep3 in Fig. 3), in addition to a more general view of samples as points in the MDS or PCA plots (step 14). Most importantly, these heatmaps provide a detailed visual summary of expression differences between compared experimental conditions at the level of individual genes and groups of genes. The tables of differentially expressed genes (Table 4) can be further inspected manually and analyzed computationally. Among various ways that the data can be further analyzed, the list of differentially expressed genes can be used to detect the enrichment of functional gene sets using a variety of computational methods such as DAVID (Huang et al., 2018) ( or EnrichR (Kuleshov et al., 2016) ( among many others. As an alternative approach, the enrichment of functional gene sets can also be analyzed using the full tables of expression and fold change values across all genes in the genome (product of step 15), for example by submitting these ranked whole-genome tables to the GSEA tool (Subramanian et al., 2005). Figure 1. Open in a new tab Example of MDS plot of six RNA-seq samples. Each sample is shown as a two-dimensional point represented by text (sample name) and colored by group (condition). In this particular case, the group of three biological replicates from mutant samples (mut, shown in red) is well separated from the group of three biological replicates from wild-type samples (WT, shown in black). In the WT group, replicate 3 (WT.rep3) is separated from other replicates of the same group and may be a potential outlier. Figure 2. Open in a new tab Example of a Volcano plot. Each gene is represented as a point in the space of absolute difference in expression value between two compared groups of replicates (log2 of fold change, logFC) as the x axis and the statistical significance of this difference (-log10 of FDR or P-value) as the y-axis. The plot has a characteristic shape reflecting a general relationship between fold change and statistical significance. The overall distribution of points is usually symmetrical between up-regulated genes (points to the right of x=0) and down-regulated genes (points to the left of x=0), with the majority of points located near the origin, which corresponds to small and statistically insignificant differences. Differentially expressed genes (highlighted in red) are defined here by the cutoffs of 2-fold change (logFC > 1 or logFC < −1) and statistical significance < 0.01. Figure 3. Open in a new tab Heatmap of expression values of differentially expressed genes across individual samples. Clustering of expression patterns of samples (columns) and genes (rows) is represented by the dendrograms on top and on the left, respectively. Color indicates expression value (log10 of RPKM). Table 4. The table of differentially expressed genes (example) Gene Name logFC logCPM PValue FDR Rbmxl2−12.2 2.5 3.2E-72 3.7E-70 Dppa3−12.2 2.5 3.7E-72 4.3E-70 Utf1−12.1 2.5 2.8E-71 3.1E-69 Neto1 11.9 2.3 1.0E-67 9.9E-66 Elf3−11.1 1.5 1.1E-54 6.1E-53 Vrtn−11.1 1.5 4.4E-54 2.3E-52 Tdh−11.1 1.5 1.8E-53 9.2E-52 Fgf4−11.0 4.5 6.6E-106 4.9E-103 EU599041−10.9 1.3 1.6E-51 7.5E-50 Open in a new tab For each identified gene, the table indicates gene name (column 1), log2 fold change of absolute expression (logFC), average expression (CPM) value across all compared samples in the log2 scale (logCPM), P-value, and false discovery rate (FDR) as an estimate of statistical significance of differential expression. COMMENTARY Background Information The STAR aligner described in this UNIT and similar methods represent an approach to mapping reads to a whole genome as well as attempting to identify splicing events across non-contiguous exons and UTRs whose genomic coordinates come from the reference genome annotation supplied by the user. This is a computationally intensive but comprehensive and precise whole-genome approach to mapping. Another example of a similar but less computationally intensive approach is the BWA-MEM algorithm of the popular BWA aligner, which is able to map a chimeric sequencing read that is comprised of parts from separate regions of the genome (Li and Durbin, 2009). There are also various methods that can be used as alternatives to the HTSeq package at the stage of quantitating reads mapped to each transcript, for example RSEM (Li and Dewey, 2011). A few alternative computational methods (Roberts and Pachter, 2013, Patro et al, 2014, Bray et al, 2016, Patro et al, 2017) bypass the stage of precise mapping of a read to the reference transcriptome and proceed directly to quantification of transcript abundance using more indirect but faster algorithmic approaches, for example quantitating the representation of short k-mer strings within the reads and the reference transcripts. Many of these methods are focused on assigning reads to the fully spliced mRNA (cDNA) sequences, which additionally increases speed by concentrating on a small fraction of the total genome, albeit at the potential price of being confined to identifying only the transcript isoforms included in the reference cDNA set. These approaches are faster and more lightweight than traditional aligners. As an example, Salmon (Patro et al, 2017) is a relatively fast and user-friendly method for both mapping and quantitation of RNA-seq reads and may be attractive especially for an entry-level user. The edgeR package used in this pipeline is conceptually similar to other popular tools for statistical analysis of differential expression, DEseq (Anders et al., 2012), DESeq2 (Love et al. 2014), DEXseq (Li et al., 2015). Critical Parameters and Troubleshooting Quality assessment is essential to ensure robust and reproducible results. Although the quality and relevance of the intermediate results should be assessed throughout the workflow, two steps are the most important and informative. Picard or similar analytical tools produce metrics that indicate the quality of RNA extraction, library construction, and, to a lesser extent, sequencing (step 5). A high-quality RNA-seq library corresponds to a > 90% read mapping rate, a high level of “usable” nucleotide bases, and contains less than 5% ribosomal RNA reads. PCR over-amplification can be evaluated by the duplication rate and, in more detail, by visual examination of BAM files as tracks in a genome viewer. At the step of differential expression analysis, sample-centric MDS plots can reveal potential outlier samples that may bias downstream identification of differentially expressed genes. Gene-centric Volcano or other conceptually similar plots can help verify the general distribution and relationships between metrics of differential expression for individual genes. Two important parameters for calling differentially expressed genes are the cutoffs of fold change and statistical significance (typically FDR), which are most often set to 2-fold and 0.01 or 0.05, respectively. In a typical RNA-seq experiment in mammalian cells or tissues, one would usually expect to identify between a few hundred and a few thousand differentially expressed genes, depending on the experimental design. Anticipated Results This protocol is expected to generate a table of expression values for all genes in all samples, a list of candidate differentially expressed genes between compared sample groups, an MDS plot with relative positioning of samples as points in multi-dimensional space, and a volcano plot that shows expression fold changes and their statistical significance for individual genes. At the earlier stages, this protocol generates a table of quality metrics for input RNA-seq datasets. Time Considerations The timing depends on the number of samples, number of reads per sample, number of comparisons between sample groups, and the available computational resources. Minimal hardware requirements for a basic analysis in a mammalian genome include Unix, Linux or MacOS operating system, 30 GB of RAM, and 50 GB of disk space for storing reference genome and output files. Alignment of sequencing reads typically takes the largest amount of time. As a very rough estimate, STAR can align 10–100 million reads per hour to a mammalian reference genome. Picard, HTseq, edgeR analyses and data inspection may take a few hours each. After installation of all required packages, the full comparison of two sample groups with three biological replicates in each group usually takes 1–2 days. Acknowledgements This work was supported in part by National Institutes of Health grant P30 DK040561. Footnotes Conflicts of Interest The authors have declared no conflicts of interest for this article. Literature Cited Anders S, Pyl PT and Huber W, 2015. HTSeq a Python framework to work with high-throughput sequencing data. Bioinformatics, 31(2), pp.166–169. 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[DOI] [PMC free article] [PubMed] [Google Scholar] ACTIONS View on publisher site PDF (582.3 KB) Cite Collections Permalink PERMALINK Copy RESOURCES Similar articles Cited by other articles Links to NCBI Databases On this page Abstract INTRODUCTION STRATEGIC PLANNING BASIC PROTOCOL Necessary Resources Initial quality assessment Quantitation of mapped reads Analysis of differential gene expression COMMENTARY Acknowledgements Footnotes Literature Cited Cite Copy Download .nbib.nbib Format: Add to Collections Create a new collection Add to an existing collection Name your collection Choose a collection Unable to load your collection due to an error Please try again Add Cancel Follow NCBI NCBI on X (formerly known as Twitter)NCBI on FacebookNCBI on LinkedInNCBI on GitHubNCBI RSS feed Connect with NLM NLM on X (formerly known as Twitter)NLM on FacebookNLM on YouTube National Library of Medicine 8600 Rockville Pike Bethesda, MD 20894 Web Policies FOIA HHS Vulnerability Disclosure Help Accessibility Careers NLM NIH HHS USA.gov Back to Top
13219	https://www.yahoo.com/news/articles/military-junta-rebranding-itself-hold-001737328.html	This military junta is rebranding itself to hold elections. But a UN probe has found evidence of intensifying atrocities Search query Search the web Skip to main News Finance Sports More MailSign in Search the web Advertisement Return to Homepage Top Stories: Michigan church shooting and fire N.C. mass shooting Tropical Storm Imelda Trump's economic priorities Shutdown deadline looms More Epstein files released 4 dead in Arizona flooding Child vaccination timeline City troop deployment update ICE arrests schools superintendent This military junta is rebranding itself to hold elections. But a UN probe has found evidence of intensifying atrocities Helen Regan, CNN Sun, August 17, 2025 at 12:17 AM UTC 10 min read Add Yahoo on Google 3 Senior Gen. Min Aung Hlaing, head of the military council, inspects officers during a parade to commemorate Myanmar's 80th Armed Forces Day, in Naypyidaw, Myanmar, on March 27, 2025. - Aung Shine Oo/AP More As evidence mounts of intensifying atrocities, including the torture of children, being committed in Myanmar, the country’s military generals are rebranding their junta regime and planning stage-managed elections in a nation they only control parts of. They’ve rescinded a four-year state of emergency order, imposed during their 2021 military coup, and formed a caretaker administration to govern the war-torn Southeast Asian country until a new parliament is assembled following a national vote. But it is merely a cosmetic change, analysts say — designed to give the appearance that it’s playing by the democratic playbook while remaining firmly in power, something Myanmar’s military have a long and notorious history of doing. Advertisement Advertisement Advertisement The election, to be held in stages over December 2025 and January 2026, is resoundingly regarded as a sham and a tool used by the junta to give it a veneer of legitimacy as it seeks to entrench its rule and gain international recognition. The junta’s notoriety, though, is only growing. UN investigators have gathered evidence of systemic torture against those detained by the military, summary executions of captured combatants or civilians accused of being informers, children as young as two being detained in place of their parents, and aerial attacks on schools, homes and hospitals. Here’s what to know: How we got here For more than four years, Myanmar’s military rulers have waged a brutal civil war across the country, sending columns of troops on bloody rampages, torching and bombing villages, massacring residents, jailing opponentsand forcing young men and women to join the army. Advertisement Advertisement Advertisement The United Nations and other rights groups have accused the military of war crimes as it battles democracy fighters and longstanding ethnic armed groups to cling to power. Military officers march during a parade to commemorate Myanmar's 80th Armed Forces Day in Naypyidaw, Myanmar, on March 27, 2025. - Aung Shine Oo/AP At the head of this junta is Sen. Gen. Min Aung Hlaing, the army chief who seized power in 2021, overthrowing the democratically elected government of Nobel laureate Aung San Suu Kyi and installed himself as leader. The military, which had previously ruled Myanmar with an iron fist for decades, sought to justify its takeover by alleging widespread voter fraud in the 2020 election, which was won in a landslide by Suu Kyi’s National League for Democracy Party. The claims were never substantiated. Min Aung Hlaing has been sanctioned and spurned by the West, the country’s economy is in tatters, and his military has lost significant territory in its grinding, multi-front civil war. Evidence of ‘systemic torture’ The UN’s Independent Investigative Mechanism for Myanmar has said that the “frequency and intensity” of atrocities in the country has only escalated over the past year. Advertisement Advertisement Advertisement Children as young as two years old were often detained in place of their parents and some were also abused and tortured, the group found. It has collected evidence of “systemic torture” in the military-run detention facilities, including rape and other forms of sexual violence. Some detainees died as a result of the torture, according to the IIMM. Protesters sit in the middle of the street during the demonstration to protest against the military coup on February 1, 2021 in Yangon, Myanmar. - Santosh Krl/SOPA Images/LightRocket/Getty Inmages/File More Those responsible include specific members and units of security forces involved in operations as well as high-ranking commanders, according to the group. The military has repeatedly denied committing atrocities and says it is targeting “terrorists.” The junta has not responded to media requests for comment. ‘A sham election’ The junta said its election objectives are for a “genuine, disciplined multiparty democratic system and the building of a union based on democracy and federalism.” Advertisement Advertisement Advertisement But with most of the country’s pro-democracy lawmakers in exile or jail, and the military’s widespread repression and attacks on the people, such a vote would never be considered free or fair, observers say. “It’s a sham election… It’s not inclusive, it’s not legitimate,” Mi Kun Chan Non, a women’s activist working with Myanmar’s Mon ethnic minority, told CNN. Many observers have warned that Min Aung Hlaing is seeking to legitimize his power grab through the ballot box and rule through proxy political parties. “He needs to make himself legitimate … He thought that the election is the only way (to do that.),” said Mi Kun Chan Non. Advertisement Advertisement Advertisement The United States and most Western countries have never recognized the junta as the legitimate government of Myanmar, and the election has been denounced by several governments in the region - including Japan and Malaysia. A soldier from the Karenni Nationalities Defence Force (KNDF), a main armed group fighting the military, walks to a reconnaissance mission. - Thierry Falise/LightRocket//Getty Images A collective of international election experts said a genuine election in Myanmar “is impossible under the current conditions,” in a joint statement released by the umbrella organization International Idea. The experts pointed to “draconian legislation banning opposition political parties, the arrest and detention of political leaders and democracy activists, severe restrictions of the media, and the organization of an unreliable census by the junta as a basis for the voter list.” Others say they cannot trust the military when it continues its campaign of violence, and when its history is littered with false promises of reform. Voting in a war zone Details on the election process are thin, but many citizens could be casting their votes in an active conflict zone or under the eyes of armed soldiers – a terrifying prospect that some say could lead to more violence. Advertisement Advertisement Advertisement Junta bombs have destroyed homes, schools, markets, places of worship and hospitals, and are a primary cause of the displacement of more than 3.5 million people across the country since the coup. There are fears that those in junta-controlled areas will be threatened or coerced into voting. And some townships may never get to vote, given the junta’s lack of control over large swathes of the country outside its heartland and major cities. One of the country’s most powerful ethnic armed groups, the Arakan Army, has said it will not allow elections to be held in territories it controls, which includes most of western Rakhine state. unknown content item Advertisement Advertisement Advertisement - And the National Unity Government, an exiled administration which considers itself the legitimate government of Myanmar, has urged the people to “oppose and resist” participating in the poll, saying the junta “does not have the right or authority to conduct elections.” There are also signs the military is moving to consolidate its power in those parts of the country it does not control. As it rescinded the nationwide state of emergency, it also imposed martial law in more than 60 townships – giving the military increased powers in resistance strongholds. “The military has been pushing hard to reclaim the territories it has lost, but regaining consolidated control — especially in the lead-up to the elections — will be a near impossibility within such a short timeframe,” said Ye Myo Hein, a senior fellow at the Southeast Asia Peace Institute, based in Washington DC. Advertisement Advertisement Advertisement “Instead, holding elections amid this perilous context is likely to trigger even greater violence and escalate conflict nationwide.” Already, there are moves to further quash dissent ahead of the poll. A new law criminalizes criticism of the election, threatening long prison sentences for those opposing or disrupting the vote. And a new cybercrime law expands the regime’s online surveillance powers, banning unauthorized use of VPNs and targeting users who access or share content from prohibited social media sites. Like ‘putting old wine in a new bottle’ Min Aung Hlaing recently formed a new governing body, the National Security and Peace Commission (NSPC), replacing the previous State Administration Council. Advertisement Advertisement Advertisement The junta chief also has added chairman of the new regime to the roster of titles he now holds, which includes acting President and chief of the armed forces. And the new interim administration is stacked with loyalists and active military officers. The move was “nothing more than an old trick — putting old wine in a new bottle,” said Ye Myo Hein. “The military has used such tactics many times throughout its history to create the illusion of change… The military junta, led by Min Aung Hlaing, remains firmly in the driver’s seat.” It has been here before. Myanmar has been governed by successive military regimes since 1962, turning a once prosperous nation into an impoverished pariah state home to some of the world’s longest running insurgencies. A military soldier (L) stands in front of a pile of seized illegal drugs during a destruction ceremony in Yangon on June 26, 2025. - Sai Aung Main/AFP/Getty Images In 2008, the military regime pushed ahead with constitutional reform that paved the way for a semi-civilian government to take power, while preserving its significant influence on the country’s politics. What followed was a decade of limited democratic reform and freedoms that brought greater foreign investment –- including the return of global brands like Coca-cola – and engagement with western nations. A generation of young Myanmar nationals began to dream of a different future to their parents and grandparents, as investment and opportunities poured in. But the military never really gave up political power. When state counselor Aung San Suu Kyi’s party stormed to a second term victory in the 2020 election, it came as a surprise to some military figures, who had hoped their own proxy party might take power democratically. The former democracy icon was detained during a coup the following year, tried by a military court and sentenced to 27 years in prison. The 80-year-old’s exact whereabouts is still a tightly guarded secret, and the junta has sought to ensure Suu Kyi and her popular, but now dissolved, NLD party would be politically wiped out. International recognition By presenting itself as a civilian government, analysts say the military will also try to convince some countries to normalize ties. Russia and China are two of Myanmar’s biggest backers, and Thailand and India have pushed for more engagement with the junta to end the crisis on their borders. China’s foreign ministry last Thursday said it “supports Myanmar’s development path in line with its national conditions and Myanmar’s steady advancement of its domestic political agenda.” In recent weeks, Min Aung Hlaing had unexpectedly good news from the US. A letter from the Trump administration detailing its new tariff rates was spun domestically by the junta leader as increased engagement. Then, the Trump administration dropped sanctions on several companies and individuals responsible for supplying weapons to Myanmar, prompting outcry from the UN Special Rapporteur for Myanmar Tom Andrews who called the moved “unconscionable and a major step backward for efforts to save innocent lives.” Members of Ta'ang National Liberation Army (TNLA) receive military equipment after getting special combat training in a secret jungle near Namhkam, Myanmar's northern Shan State on November 9, 2024. - Stringer/AFP/Getty Images More Myanmar’s Ministry of Information has also signed a $3 million a year deal with Washington lobbying firm DCI Group to help rebuild relations with the US, Reuters news agency recently reported. The group, as well as the US Treasury Department, the US State Department, and Myanmar’s Washington embassy did not immediately respond to Reuters’ requests for comment. Democracy supporters opposed to the junta have warned the international community against falling for the military’s election plan, and say such a poll will never be accepted by the people. Min Aung Hlaing and his junta “have sucked all the resources and money than can and the country has nothing left,” said Mi Kun Chan Non, the women’s activist. “Everything has fallen apart … The education system has collapsed; the healthcare system has collapsed. Business is just for the cronies.” So, any future peace negotiations that follow the elections, “we can never trust,” she said. “And the situation of the people on the ground will not change.” For more CNN news and newsletters create an account at CNN.com View comments(3) Terms and Privacy Policy Privacy Dashboard About Our Ads Play Daily Sudoku Together New Release: Unlimited puzzles across 14 levels!New Release: Unlimited puzzles across 14 levels! 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13220	https://www.cuemath.com/algebra/partial-fractions/	Partial Fraction Partial Fractions are the fractions that are formed when a complex rational expression is split into two or more simpler fractions. Generally, fractions with algebraic expressions are difficult to solve and hence we use the concepts of partial fractions to split the fractions into numerous subfractions. While decomposition, generally, the denominator is an algebraic expression, and this expression is factorized to facilitate the process of generating partial fractions. A partial fraction is a reverse of the process of the addition of rational expressions. In the normal process, we perform arithmetic operations across algebraic fractions to obtain a single rational expression. This rational expression, on splitting in the reverse direction involved the process of decomposition of partial fractions and results in the two partial fractions. Let us learn more about partial fractions in the following sections. \| \| \| --- \| \| 1. \| What are Partial Fractions? \| \| 2. \| Partial Fractions Formulas \| \| 3. \| Partial Fraction Decomposition \| \| 4. \| Partial Fractions of Improper Fraction \| \| 5. \| FAQs on Partial Fractions \| What are Partial Fractions? When a rational expression is split into the sum of two or more rational expressions, the rational expressions that are a part of the sum are called partial fractions. This is referred to as splitting the given algebraic fraction into partial fractions. The denominator of the given algebraic expression has to be factorized to obtain the set of partial fractions. Every factor of the denominator of a rational expression corresponds to a partial fraction. For example, in the above figure, (4x + 1)/[(x + 1)(x - 2)] has two factors in the denominator, and hence there are two partial fractions, one with the denominator (x + 1) and the other with the denominator (x - 2). Partial Fractions Formulas In the above example, the numerators of partial fractions are 1 and 3. The numerator of a partial fraction is not always a constant. If the denominator is a linear function, the numerator is constant. And, if the denominator is a quadratic equation, then the numerator is linear. It means, the numerator's degree of a partial fraction is always one less than the denominator's degree. Further, the rational expression needs to be a proper fraction to be decomposed into a partial fraction. Listed below in the table are partial fraction formulas (here, all variables apart from x are constants). \| Type \| Form of Rational Fraction \| Partial Fraction Decomposition \| --- \| Non-repeated Linear Factor \| (px + q)/(ax + b) \| A/(ax + b) \| \| Repeated Linear Factor \| (px + q)/(ax + b)n \| A1/(ax + b) + A2/(ax + b)2 + .......... An/(ax + b)n \| \| Non-repeated Quadratic Factor \| (px2 + qx + r)/(ax2 + bx + c) \| (Ax + B)/(ax2 + bx + c) \| \| Repeated Quadratic Factor \| (px2 + qx + r)/(ax2 + bx + c)n \| (A1x + B1)/(ax2 + bx + c) + (A2x + B2)/(ax2 + bx + c)2 + ...(Anx + Bn)/(ax2 + bx + c)n \| Let us look at a few examples of partial fractions. In all these examples, A, B, and C are constants to be determined. Let's learn how to find these constants. Partial Fraction Decomposition The partial fraction decomposition is writing a rational expression as the sum of two or more partial fractions. The following steps are helpful to understand the process to decompose a fraction into partial fractions. Let us learn this process of decomposing a given fraction into partial fractions by an example. Example: Find the partial fraction expansion of the expression(4x + 12)/(x2 + 4x) Solution: Always remember to factor the denominator as much as possible before doing the partial fraction decomposition. (4x + 12)/(x2 + 4x) = (4x + 12)/[x(x + 4)] ; The denominator has non-repeated linear factors. So, every factor corresponds to a constant in the numerator while writing the partial fractions. Let us assume that: (4x + 12)/[(x)(x + 4)] = [A/x] + [B/(x + 4)] → (1) The LCD (Least Common Denominator) of the sum (on the right side) is x(x + 4). Multiplying both sides by x(x + 4), 4x + 12 = A(x + 4) + Bx → (2) Now we have to solve it for A and B. For that, we set each linear factor to zero. Substitute x + 4 = 0 , or x = -4 in (2): 4(-4) + 12 = A(0) + B(-4); -4 = -4B; B = 1. Substitute x = 0 in (2): 4(0) + 12 = A(0 + 4) + B(0); 12 = 4A; A = 3. Substitute the values of A and B in (1), we get the partial fractions decomposition of the given expression: (4x + 12)/[x(x + 4)] = [3/x] + [1/(x + 4)] Tips & Tricks on Partial Fractions Decomposition The following tips are helpful to decompose a fraction into its partial fractions. Partial Fractions of Improper Fraction When we have to decompose an improper fraction into partial fractions, we first should do the long division. The long division is helpful to give a whole number and a proper fraction. The whole number is the quotient in the long division, and the remainder forms the numerator of the proper fraction, and the denominator is the divisor. The format of the result of the long division would be Quotient + Remainder/Divisor. Let us understand more of this with the help of the below example. Example: Find the partial fraction decomposition of the expression (x3 +4x2 - 2x - 5)/(x2 - 4x + 4) Solution: Here, the degree of the numerator (3) is greater than the degree of the denominator (2). So the given fraction is improper. So we have to do the long division first. Then write the given fraction as Quotient + Remainder/Divisor. Then we get: (x3 + 4x2 - 2x - 5)/(x2 - 4x + 4) = x + 8 + (26x - 37)/(x2- 4x + 4). Here, the fraction on the right side is a proper fraction and hence it can be split into partial fractions. (26x - 37)/(x2 - 4x + 4) = (26x - 37)/(x - 2)2 = A/(x - 2)+ B/(x - 2)2 Now let us try to solve for A and B. Hint: Set each of (x - 2) and x one by one to zero to get A and B. You should get A = 26 and B = 15. Substituting these values in we have: (26x-37)/(x2 - 4x + 4) = [26/(x-2)] + [15/(x-2)2] Further we have: (x3+ 4x2 - 2x - 5)/(x2- 4x + 4) = x + 8 + [26/(x - 2)] + [15/(x - 2)2 ] Important Notes on Partial Fractions The following points would help in gaining a more clear understanding of partial fractions. ☛ Related Topics: Solved Examples on Partial Fraction Example 1: Find the partial fraction decomposition of (x + 2) / [ (x + 1) (x - 2) ]. Solution: Since the denominator has non-repeating linear factors, by the partial fraction formulas, assume that: (x + 2) / [ (x + 1) (x - 2) ] = A / (x + 1) + B / (x - 2) ... (1) Multiply both sides by (x + 1) (x - 2), (x + 2) = A (x - 2) + B (x + 1) Substitute x = -1: 1 = A (-3) ⇒ A = -1/3 Substitute x = 2: 4 = B (3) ⇒ B = 4/3 Substituting A and B values in (1): (x + 2) / [ (x + 1) (x - 2) ] = -1 / [3(x + 1)] + 4 / [3(x - 2)] Answer: -1 / [3(x + 1)] + 4 / [3(x - 2)] Example 2: Decompose the following expression into partial fractions. (x4 + x3 + x2 + 1)/(x2 + x - 2) Solution: When we factorize the denominator, we get: x2 + x - 2 = (x + 2)(x - 1). The degree of the numerator (4) is greater than that of the denominator (2). So it is an improper fraction. We need to first do the long division. So the given fraction can be written as: (x4 + x3 + x2 + 1)/(x2 + x - 2) = x2 + 3 + (-3x + 7)/[(x + 2)(x - 1)]; Now we will decompose (-3x + 7)/[(x + 2)(x - 1)] into partial fractions using: (-3x + 7)/[(x + 2)(x - 1)] = A/(x + 2) + B/(x - 1) ... (1) Multiplying both sides by the LCD (x + 2)(x - 1); -3x + 7 = A(x - 1) + B(x + 2). Substitute x - 1 = 0, or x = 1 we have -3 + 7 = 3B ;B = 4/3. Substitute x + 2 = 0, or x = -2 we have 6 + 7 = -3A ; A= -13/3. Substitute the values of A and B in the equation (1) we have:(-3x + 7)/[(x + 2)(x - 1)] = -13/[3(x + 2)]+ 4/[3(x - 1)]. Answer: Therefore the partial fractions decomposition of the given expression is: x2 + 3 - 13/[3(x + 2)]+ 4/[3(x - 1)] Example 3: Decompose the following rational expression into partial fractions. (4x3 + x + 2)/[x2(x2 + 1)] Solution: Look at the denominator. We have x2. It means the linear factor x is repeating. (x2 + 1) is an irreducible (can't be factorized) quadratic factor. So the given fraction can be decomposed as follows: (4x3 + x + 2)/[x2(x2 + 1)] = [A/x] + [B/x2] + [(Cx + D)/(x2 + 1)] ... (1) Multiplying both sides by the LCD x2(x2 + 1); 4x3 + x + 2 = Ax3 + Ax + Bx2 + B + Cx3 + Dx2 Setting the linear factor x to 0, i.e., x = 0, we get: 2 = B. Now we do not have any other linear factors to set to zero. So we will expand the right-hand side expression. Then we will compare the coefficients of x3, x2, x, and constant. By comparing the coefficients of x3, we get 4 = A + C. By comparing the coefficients of x2, we get 0 = B + D. By comparing the coefficients of x, we get 1 = A. By comparing the constants, we get 2 = B. By solving these equations, we get: A = 1, B = 2, C = 3, D = -2 . Further, substitute all these values in (1), the given expression becomes: [1/x] + [2/x2] + [(3x - 2)/(x2 + 1)] Answer: Therefore we have the resultant partial fractions as (4x3 + x + 2)/[x2(x2 + 1)] = [1/x] + [2/x2] + [(3x - 2)/(x2 + 1)]. go to slidego to slidego to slide Book a Free Trial Class Practice Questions on Partial Fractions go to slidego to slidego to slide FAQs on Partial Fractions What is the Partial Fraction Method? The partial fraction is the result of writing a rational expression as the sum of two or more fractions. First simplify the rational expression by breaking it down into the possible factors for the numerator, and the denominator. Further, split the expression into partial fractions based on the formulas. The formulas for partial fractions depend on the number of factors and the degree of the denominator of the rational expression. Further, find the value of the required constants to solve the partial fractions. What is the Procedure for Partial Fraction Decomposition? The decomposition of partial fractions is across the following three simple steps. What Is Meant by A Partial Fraction? The word "partial" means a "part" and hence a partial fraction is one of the fractions when a given fraction is decomposed into the sum of multiple fractions. The input for the process of the partial fractions is a rational expression, and the result is the sum of two or more proper fractions. What Are the Different Denominator Types In the Partial Fractions? The different denominator types in partial fractions are based on the number of factors of the denominator expression, and the degree of the terms in the denominator. The different denominator types of a partial P/(ax + b), P/[(ax + b)(cx + d)], P/(ax + b)2, P/(ax + b)3, P/(ax + b)n. How Do you Know How To Add Partial Fractions? While writing an expression as the sum of partial fractions, keep the following points in mind: For more information, go to "What are General Formulas of Partial Fractions?" section of this page. To add to partial fractions, we just make their denominators the same and add. For example: 3/x + 1/(x + 4) = 3/x · (x + 4)/(x + 4) + 1/(x + 4) · x/x = (3x + 12)/(x2 + 4x) + x/(x2 + 4x) = (3x + 12 + x)/(x2 + 4x)= (4x + 12)/(x2 + 4x) How Do you Solve a Repeated Root Partial Fraction? When a partial fraction has repeated factors of the form (ax+b)n or (ax2+bx+c)n, they correspond to n different partial fractions where the denominators of the partial fractions have exponents 1, 2, 3, ..., n. For example, if the denominator is of the form (ax+b)n, then the corresponding partial fractions should be of the form A1/(ax + b) + A2/(ax + b)2 + .......... An/(ax + b)n. How Do you Know When to Use Partial Fraction Decomposition? The partial fraction decomposition is to be used when the denominator of the fraction is an algebraic expression, and when there is a need to split the fraction. Also, there should be a possibility of getting at least two factors for the algebraic expression in the denominator. What are Formulas for Solving Different Types of Partial Fractions are there? The types of partial fractions depend on the number of possible factors of the denominator, and the degree of the factors of the denominator. Broadly there are about three types of partial fractions. The following three types of partial fractions are as follows. Is Partial Fraction a Proper Fraction? For the process of getting partial fractions, the given fraction needs to be a proper fraction. If the given fraction is an improper fraction, the numerator is divided by the denominator to obtain a quotient and a remainder. And the fraction that is used to split into partial fractions in this case would be the remainder/denominator. How Do you Decompose Partial Fraction with 3 Terms? Decomposing a partial fraction with 3 terms is the same as the solving of partial fractions with 2 terms. Further, the two formulas for partial fractions with 3 terms are as follows.
13221	https://www.degreeforum.net/mybb/Thread-Intersection-and-union-of-sets-so-confused	Intersection and union of sets....so confused Portal Search Member List Calendar Help Hello There, Guest! LoginRegister Login Username: Password:Lost Password? - [x] Remember me Online Degrees and CLEP and DSST Exam Prep Discussion › Miscellaneous › Off Topic › What does this Flashcard mean or Do this math problem for me « Previous1234Next » Intersection and union of sets....so confused Thread Rating: 0 Vote(s) - 0 Average 1 2 3 4 5 Thread Modes Intersection and union of sets....so confused ironheadjack Senior Member Posts: 587 Threads: 28 Likes Received: 2 in 2 posts Likes Given: 0 Joined: Jun 2013 #1 08-22-2013, 10:46 PM So I'm going through Aleks College algebra doing good, but then I get to this problem, and I have been stumped, perplexed, confused, and lost for the past 3 days trying to figure this out. I have read every article Bing gave me, tried using purplemath, mathway, and I am still lost. Something is just not clicking for me. Could someone please walk me through this problem, before I pull all of my hair out. Sets C and D are defined as: C={y \|y≥2} D={y \|y>6} Write C∪D and C∩D, using interval notation. If set is empty, write Ã. Any help is much appreciated. BA in Social Science-TESC Arnold Fletcher Award [h=1]âOpportunity is missed by most people because it is dressed in overalls and looks like work.â ~Thomas Edison[/h] • Find Reply Lindagerr Posting Freak Posts: 2,403 Threads: 88 Likes Received: 13 in 10 posts Likes Given: 3 Joined: Mar 2007 #2 08-22-2013, 11:27 PM The union of two or more sets is a set containing all of the numbers in those sets So {1,2,3)u{3,4,5} ={1,2,3,4,5} The intersection of two or more sets is a set containing only the members contained in every set. So {1,2,3}(intersection) {3,4,5}= {3} Sorry too lazy to find symbols So you set would have union y= or more then 2 and intersection y = or more then 7 I hope this makes sense Linda Start by doing what is necessary: then do the possible; and suddenly you are doing the impossible St Francis of Assisi Now a retired substitute Teacher in NY, & SC AA Liberal Studies TESC '08 BA in Natural Science/Mathematics TESC Sept '10 AAS Environmental safety and Security Technology TESC Dec '12 • Find Reply ironheadjack Senior Member Posts: 587 Threads: 28 Likes Received: 2 in 2 posts Likes Given: 0 Joined: Jun 2013 #3 08-23-2013, 02:52 PM Thank you but I'm still not getting it. So your saying the union is y≥2 and the intersection is y≥7 Where did the 7 come from? Is the above answer written using interval notation? :confused: BA in Social Science-TESC Arnold Fletcher Award [h=1]âOpportunity is missed by most people because it is dressed in overalls and looks like work.â ~Thomas Edison[/h] • Find Reply Lindagerr Posting Freak Posts: 2,403 Threads: 88 Likes Received: 13 in 10 posts Likes Given: 3 Joined: Mar 2007 #4 08-23-2013, 04:26 PM Set C ={y (The straight line means such that) y≥2} so the set C =y such that y≥ 2 so that set includes all numbers from 2 up Set D= {y such that y>6} so the set D = includes all numbers above 6 ( I used seven but that does not account for intergers so it should be >6) So CUD = {y≥2} because that set includes all of the numbers in C and all of the numbers that are in D but each number is only listed once no matter how many sets you have . So C∩D ={y>6} because that set includes only the numbers that are in both sets. If we had C= {y such that y≥2 and y≤9} that set would be {2,3,4,5,6,7,8,9} Assuming we are using only whole numbers. If we had D= {y such that y>6 and y≤10} that set would be {7,8,9,10} So with those C and D the CUD would be {y=2,3,4,5,6,7,8,9,10} because this is all the numbers that are in either set just written once. and C∩D would be {y=7,8,9} because those numbers are in both sets I hope this explains it better I found most of the keystroke shortcuts Linda Start by doing what is necessary: then do the possible; and suddenly you are doing the impossible St Francis of Assisi Now a retired substitute Teacher in NY, & SC AA Liberal Studies TESC '08 BA in Natural Science/Mathematics TESC Sept '10 AAS Environmental safety and Security Technology TESC Dec '12 • Find Reply « Next Oldest \| Next Newest » View a Printable Version Forum Jump: Users browsing this thread: 1 Guest(s) Contact Us DegreeForum.net Return to Top Mobile Version Mark All Forums Read RSS Syndication Current time: 09-28-2025, 07:41 PM Powered By MyBB, © 2002-2025 MyBB Group. Linear Mode Threaded Mode
13222	https://www.kenhub.com/en/library/anatomy/inguinal-region	Connection lost. Please refresh the page. #1 platform for learning anatomy Login Register Success stories Anatomy Basics Upper limb Lower limb Spine and back Thorax Abdomen Pelvis and perineum Head and neck Neuroanatomy Cross sections Radiological anatomy+ Histology Types of tissues Body systems+ Physiology Introduction Muscular system Nervous system Anatomy Basics Upper limb Lower limb Spine and back Thorax Abdomen Pelvis and perineum Head and neck Neuroanatomy Cross sections Radiological anatomy+ Histology Types of tissues+ Physiology Nervous system Get help How to study What's new? Kenhub in... Deutsch Português Español Français What's new? Get help How to study English English Deutsch Português Español Français Login Register #1 platform for learning anatomy Courses Anatomy Basics Upper limb Lower limb Spine and back Thorax Abdomen Pelvis and perineum Head and neck Neuroanatomy Cross sections Radiological anatomy Histology Types of tissues Body systems Physiology Introduction Muscular system Nervous system Articles Anatomy Basics Upper limb Lower limb Spine and back Thorax Abdomen Pelvis and perineum Head and neck Neuroanatomy Cross sections Radiological anatomy Histology Types of tissues Physiology Nervous system The #1 platform to learn anatomy 6,332,346 users worldwide Exam success since 2011 Serving healthcare students globally Reviewed by medical experts 2,907 articles, quizzes and videos ArticlesAnatomyAbdomenInguinal region Table of contents Ready to learn? Pick your favorite study tool Videos Quizzes Both Register now and grab your free ultimate anatomy study guide! ArticlesAnatomyAbdomenInguinal region Inguinal region Author: Christina Loukopoulou, MSc • Reviewer: Dimitrios Mytilinaios, MD, PhD Last reviewed: October 30, 2023 Reading time: 3 minutes Recommended video: Regions of the abdomen [11:41] Regions of the abdomen seen anteriorly. Inguinal region Regio inguinalis 1/5 Synonyms: Iliac region, Groin , show more... The inguinal region, also known as the groin, is an anatomical space in the lower portion of the anterior abdominal wall, located superior to the thigh, lateral to the pubic tubercle, and inferomedial to the anterior superior iliac spine (ASIS). Based on the nine region (quadrant) scheme, there are two inguinal regions on each side of the abdomen: left and right. The left inguinal region contains part of the small intestine, the descending colon, the sigmoid colon and, in females, the left ovary and the left fallopian tube. In contrast, the right inguinal region contains the small intestine, the cecum and appendix, the ascending colon and, in females, the right ovary and right fallopian tube. The inguinal region also houses the inguinal lymph nodes which receive lymphatic drainage from the lower extremity, genitals, dorsal perineum and the inferior most aspect of the anterior abdominal wall. These range from approximately 12-14 lymph nodes and are divided into superficial and deep groups. The superficial inguinal lymph nodes and the great saphenous vein are enclosed by the superficial fascia of the hip and thigh. A clinically important structure, the inguinal canal, is also located in the inguinal region. It is an oblique intramuscular slit running inferomedially, which serves as a conduit transmitting structures from the pelvis to the perineum. There are two openings to the inguinal canal: The deep inguinal ring is found approximately 1cm above the midpoint of the inguinal ligament and lateral to the epigastric vessels. It is formed by the transversalis fascia which provides the posterior wall of the inguinal canal. The superficial inguinal ring is a triangular aperture in the aponeurosis of the external oblique. It is located about 1 cm superolateral to the pubic tubercle and bordered medially by the inferolateral border of rectus abdominis, laterally by the inferior epigastric vessels and inferiorly by the medial third of the inguinal ligament. These three borders are often referred to as Hesselbach's (inguinal) triangle and serve as an important landmark for the superficial ring. The contents of the inguinal canal vary between males and females. In males, it contains the spermatic cord and its contents, while in females it contains the round ligament of uterus. Two nerves also traverse the inguinal canal in both males and females: these are the ilioinguinal nerve (T12, L1) and the genital branch of the genitofemoral nerve (L2). \| \| \| --- \| \| Terminology \| English: Inguinal region; Synonym: GroinLatin: Regio inguinalis \| \| Definition \| The inguinal region is an anatomical space in the lower portion of the anterior abdominal wall, located superior to the thigh, lateral to the pubic tubercle, and inferomedial to the anterior superior iliac spine (ASIS). \| Learn more about the inguinal region and the other regions of the abdomen in the following study unit: Learn faster Regions of the abdomen Explore study unit Sources All content published on Kenhub is reviewed by medical and anatomy experts. The information we provide is grounded on academic literature and peer-reviewed research. Kenhub does not provide medical advice. You can learn more about our content creation and review standards by reading our content quality guidelines. Moore, K. L., Dalley, A. F., & Agur, A. (2017). Clinically oriented anatomy (8th ed.). Lippincott Williams and Wilkins.Standring, S. (2016). Gray's Anatomy (41st ed.). Edinburgh: Elsevier Churchill Livingstone. Tuma, F., Lopez, R., Varacallo, M. (2022). Anatomy, Abdomen and Pelvis: Inguinal Region (Inguinal Canal). In: StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing. Inguinal region: want to learn more about it? Our engaging videos, interactive quizzes, in-depth articles and HD atlas are here to get you top results faster. What do you prefer to learn with? Videos Quizzes Both “I would honestly say that Kenhub cut my study time in half.” – Read more. Kim Bengochea, Regis University, Denver © Unless stated otherwise, all content, including illustrations are exclusive property of Kenhub GmbH, and are protected by German and international copyright laws. All rights reserved. Register now and grab your free ultimate anatomy study guide! Learning anatomy isn't impossible.We're here to help. Learning anatomy is a massive undertaking, and we're here to help you pass with flying colours. Create your free account ➞ Want access to this video? Get instant access to this video, plus: Curated learning paths created by our anatomy experts 1000s of high quality anatomy illustrations and articles Free 60 minute trial of Kenhub Premium! Create your free account ➞ ...it takes less than 60 seconds! Want access to this quiz? Get instant access to this quiz, plus: Curated learning paths created by our anatomy experts 1000s of high quality anatomy illustrations and articles Free 60 minute trial of Kenhub Premium! Create your free account ➞ ...it takes less than 60 seconds! Want access to this gallery? Get instant access to this gallery, plus: Curated learning paths created by our anatomy experts 1000s of high quality anatomy illustrations and articles Free 60 minute trial of Kenhub Premium! 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13223	https://www.gauthmath.com/solution/1811995635841093/Find-the-tangent-equation-a-to-the-ellipse-frac-x24-frac-y29-1-which-is-perpendi	Question Solution Flash Burn. Step 1: The description provided indicates a burn injury caused by poor contact and resistance of dry skin, resulting in a pricked appearance with a central white zone (parchment) and surrounding hyperemia. Step 2: Based on the characteristics described, the type of burn injury being referred to is a Flash Burn. contact@gauthmath.com
13224	https://www.merckvetmanual.com/multimedia/table/clinical-signs-associated-with-hypercalcemia	Table: Clinical Signs Associated with Hypercalcemia-Merck Veterinary Manual honeypot link skip to main content ENGLISH MERCK MANUAL Veterinary Manual VETERINARY PROFESSIONALSPET OWNERSRESOURCESQUIZZESABOUT VETERINARY PROFESSIONALSPET OWNERSRESOURCESQUIZZES Veterinary/ Tables/ Clinical Signs Associated with Hypercalcemia/ Clinical Signs Associated with Hypercalcemia Clinical Signs Associated with Hypercalcemia\| Body System \| Descriptions \| --- \| \| Nervous \| Weakness, lethargy, difficulty rising, trembling \| \| Gastrointestinal \| Hyporexia, nausea, vomiting, constipation \| \| Urinary \| Polydipsia, polyuria, urolithiasis, urinary tract infection \| \| Cardiovascular \| Hypertension, arrhythmia \| In these topics Hypercalcemia in Dogs and Cats> Merck & Co., Inc., Rahway, NJ, USA(known as MSD outside of the US and Canada) is dedicated to using leading-edge science to save and improve lives around the world. The Veterinary Manual was first published in 1955 as a service to the community. The legacy of this great resource continues in the online and mobile app versions today. About Disclaimer Permissions Privacy Cookie Preferences Terms Of Use Partnerships Contact Us Human Health Manuals Consumer Health Data Privacy Policy Your Privacy Choices © 2025 Merck & Co., Inc., Rahway, NJ, USA and its affiliates. All rights reserved. Find In Topic This Site Uses Cookies and Your Privacy Choice Is Important to Us. Choose Customize My Settings to make your privacy choices. Choose Accept All Cookies to accept third-party cookies.See our Privacy Policy Customize My Settings Accept All Cookies
13225	https://en.wikipedia.org/wiki/Terminal_Velocity_(film)	Jump to content Terminal Velocity (film) Cymraeg Deutsch فارسی Français 한국어 Italiano עברית 日本語 Português Русский Svenska Edit links From Wikipedia, the free encyclopedia 1994 American film \| Terminal Velocity \| \| --- \| \| Film poster \| \| \| Directed by \| Deran Sarafian \| \| Written by \| David Twohy \| \| Produced by \| Ron Booth Tom Engelman Scott Kroopf \| \| Starring \| Charlie Sheen Nastassja Kinski James Gandolfini Christopher McDonald \| \| Cinematography \| Oliver Wood \| \| Edited by \| Frank J. Urioste \| \| Music by \| Joel McNeely \| \| Production companies \| Hollywood Pictures Interscope Communications PolyGram Filmed Entertainment Nomura Babcock & Brown \| \| Distributed by \| Buena Vista Pictures Distribution \| \| Release date \| September 23, 1994 (1994-09-23) \| \| Running time \| 102 minutes \| \| Country \| United States \| \| Language \| English \| \| Budget \| $50 million \| \| Box office \| $47 million \| Terminal Velocity is a 1994 American action film directed by Deran Sarafian, written by David Twohy, and starring Charlie Sheen, Nastassja Kinski, James Gandolfini, and Christopher McDonald. It follows a daredevil skydiver (Sheen) who is caught up in a criminal plot by Russian mobsters (Gandolfini and McDonald), forcing him to team up with a freelance secret agent (Kinski) in order to survive. It was one of two skydiving-themed action films released in the fourth quarter of 1994 (the other being Paramount Pictures' Drop Zone), and received mostly negative reviews from critics. Plot [edit] About to leave the country, a young Russian woman was ambushed in her Tucson apartment after calling her contact about a Boeing 747 she witnessed landing in the desert. The lead assailant, Kerr, tortures her for information about her roommate before drowning her in an aquarium. Former Olympic gymnast-turned-daredevil skydiver Richard "Ditch" Brodie participates in an illegal BASE jump off a skyscraper, despite his jump school being under tight scrutiny by the FAA. Upon returning to his school, he's approached by a beautiful but nervous woman named Chris Morrow, who insists on performing a static jump from cruising altitude immediately. Playing along due to her flirtatious attitude, Ditch agrees to take her himself. During the flight, Chris briefly spots another aircraft below. When Ditch checks to see if his pilot has noticed it, Chris cuts ties with Ditch and jumps on her own. Ditch spots Chris tumbling uncontrollably below him, and is unable to save her before she hits the ground at terminal velocity. An investigation ensues, and the school is closed down indefinitely. Feeling guilty and confused, Ditch rifles through Chris' personal belongings, and finds her apartment key. There he finds a photograph of Chris performing a jump, thus contradicting her earlier claim of inexperience. Ditch is attacked by Kerr, but fends him off and escapes. At the flight school, Ditch is approached by Assistant District Attorney Ben Pinkwater, who tells Ditch he may be charged with manslaughter for Chris' death. Later, Ditch sees the same plane that had been following him during the jump, and follows it to a shack where he finds Chris alive, having faked her death using her roommate's body. She then takes Ditch on an unexplained nighttime jump at an aeronautics plant, promising to clear his name if he co-operates. Chris has Ditch infiltrate the plant via a smokestack and disable the security system before stealing a hidden optical disc. Kerr and his men arrive, forcing Ditch to flee from gunfire back to his school. Wanting his name cleared, he arranges a meeting with Chris and Pinkwater at a scrapyard, but upon arriving Pinkwater kills Chris' partner Lex, revealing himself to be a cohort of Kerr's. A firefight ensues, and Chris and Ditch escape using a makeshift rocket car. Taking shelter in the desert, Chris reveals that her real name is Krista Moldova, and that she and her pursuers are former KGB operatives left unemployed due to the collapse of the Soviet Union. "Pinkwater" and his men have fallen in with the Russian mob, and have hijacked a shipment of gold bullion intended for the Moscow reserve, and intend to use it to finance a coup d'état against the democratic Russian government. Using the optical disc retrieved by Ditch, Chris determines the location of the missing Boeing 747 carrying the shipment. She and Ditch get on board and find the gold, but are discovered by Pinkwater's men. The two barely escape, and Ditch decides to quit while Chris heads off to face Pinkwater alone. As Ditch is about to leave on a bus, he finds a picture taken by Chris holding up a sign reading "Ditch Did Not Kill Me", thereby exonerating him. Having a change of heart, Ditch drives off to the airfield just as Pinkwater and his men take off, having kidnapped Chris. Posing as an FAA agent, Ditch convinces a biplane stunt pilot to fly him up and onto the 747. Ditch gets on board just as Chris is stuffed in the trunk of Kerr's sports car to be killed. Ditch and Kerr get into a fight, driving the car out of the cargo hold and plummeting toward the ground below. Ditch manages to force Kerr off sending him falling several thousands of feet to his death, and gets Chris out of the trunk before it hits the ground. The two land in a nearby wind farm, and the plane, damaged in the fight, is forced to land. As police swarm the runway, Chris and Ditch are attacked by a parachuting Pinkwater, and Chris is stabbed in the back. Ditch pulls Pinkwater's back-up chute, sucking him into a nearby turbine and killing him. Some time later, Ditch and Chris receive official commendations at the Kremlin for their actions in preventing the coup. Cast [edit] Charlie Sheen as Richard 'Ditch' Brodie Nastassja Kinski as Agent Krista Moldova / Chris Morrow James Gandolfini as Stefan / Ben Pinkwater Christopher McDonald as Kerr Suli McCullough as 'Robocam' Hans R. Howes as Sam Melvin Van Peebles as Noble Gary Bullock as Agent Lex Margaret Colin as Joline Cathryn de Prume as Agent Karen Rance Howard as Chuck Sofia Shinas as Maxine 'Broken Legs Max' Production [edit] Based on David Twohy’s original spec script which sold to Hollywood Pictures for over $500,000 Kevin Reynolds and Tom Cruise were initially slated as director and star, but commitments prevented this. The final stunt, which features Sheen at the wheel of a Cadillac Allanté falling to earth, was a mixture of bluescreen and camera work, as a real car was suspended beneath a helicopter and then a reverse zoom made it seem as if it were in free-fall. Portions of the film were shot in Palm Springs, California. Other filming locations were Alabama Hills (Lone Pine, California); a windfarm near Tehachapi, California; Douglas, Arizona; Flagstaff, Arizona; Little Colorado River Canyon, Arizona; Moscow, Russia; Phoenix, Arizona; San Bernardino, California and Tucson, Arizona, where a cameo appearance by Martha Vasquez of its station KVOA was filmed. Reception [edit] The film debuted at number 2 at the US box office behind Timecop in its second week with an opening weekend gross of $5.5 million. It eventually grossed $16.5 million in the United States and Canada and over $31 million internationally, for a worldwide total of over $47 million compared to its $50 million budget. It received mostly negative reviews by critics; it has a 19% positive scale on the ratings aggregator website Rotten Tomatoes, based on 26 reviews. Owen Gleiberman opined that "Terminal Velocity is the kind of movie in which the hero keeps sneaking into rooms to peek into some file and you wait, with glum certitude, for yet another 'surprise' thug to leap out of the shadows. It's fun to hear Charlie Sheen deliver quips like, 'I'm not just a walking penis — I'm a flying penis!' But for most of the movie, Sheen, lowering his voice to a basso he-man growl, gives a boringly flat, square-jawed performance, as if he thought he were doing Hot Shots! Part Quatre." Roger Ebert suggested that "Sheen's behavior in this and other scenes is so close to the self-parody of his work in the Hot Shots! movies that he almost seems to be telling us something — such as, that he takes the movie with less than perfect seriousness. No wonder. It's based on such a goofy premise that with just a nudge here and a pun there it could easily have become 'Hot Shots Part Cinq' and taken advantage of the franchise. It's not so much that Sheen can keep a straight face in any situation, as that he always seems to be testing himself with the situations he gets himself into." Year-end lists [edit] Honorable mention – David Elliott, The San Diego Union-Tribune References [edit] ^ Jump up to: a b "Sarafian signed to direct Interscope's 'Terminal'". Variety. Retrieved July 23, 2021. ^ Niemann, Greg (2006). Palm Springs Legends: creation of a desert oasis. San Diego: Sunbelt Publications. pp. 168–171. ISBN 978-0-932653-74-1. OCLC 61211290. (for Table of Contents) ^ "Eyewitness News Team". KVOA.com. 1997. Archived from the original on February 21, 1997. Retrieved November 22, 2016. ^ "Filming Locations for Terminal Velocity". IMDb.com. Retrieved November 22, 2016. ^ Strauss, Bob (October 3, 1994). "'Timecop' Puts Brakes On 'Velocity'". Sun Sentinel. Los Angeles Daily News. Archived from the original on May 24, 2012. Retrieved November 2, 2010. ^ "Terminal Velocity". BoxOfficeMojo.com. Internet Movie Database. Retrieved November 22, 2016. ^ Klady, Leonard (February 19, 1996). "B.O. with a vengeance: $9.1 billion worldwide". Variety. p. 1. ^ "Terminal Velocity (1994)". Rotten Tomatoes. Retrieved November 22, 2016. ^ Gleiberman, Owen (October 7, 1994). "Terminal Velocity". Entertainment Weekly. Retrieved November 2, 2010. ^ Ebert, Roger (September 23, 1994). "Terminal Velocity". Chicago Sun Times. Retrieved November 2, 2010. ^ Elliott, David (December 25, 1994). "On the big screen, color it a satisfying time". The San Diego Union-Tribune (1, 2 ed.). p. E=8. External links [edit] Terminal Velocity at the AFI Catalog of Feature Films Terminal Velocity at IMDb Terminal Velocity at Rotten Tomatoes Terminal Velocity at Box Office Mojo \| Films directed by Deran Sarafian \| \| --- \| \| The Falling (1986) Interzone (1987) To Die For (1989) Death Warrant (1990) Back in the USSR (1992) Gunmen (1994) The Road Killers (1994) Terminal Velocity (1994) Road Rage (1999) Trapped (2001) \| \| \| v t e Films by David Twohy \| \| --- \| \| Written and directed \| Timescape (1992) The Arrival (1996) Pitch Black (2000) Below (2002) The Chronicles of Riddick (2004) A Perfect Getaway (2009) Riddick (2013) Riddick: Furya (TBA) \| \| Written only \| Critters 2: The Main Course (1988) Warlock (1989) The Fugitive (1993) Terminal Velocity (1994) Waterworld (1995) G.I. Jane (1997) Impostor (2001) The Chronicles of Riddick: Dark Fury (2004, short) \| Retrieved from " Categories: 1994 films 1994 action films 1990s American films 1990s English-language films American action films American aviation films English-language action films Films directed by Deran Sarafian Films produced by Scott Kroopf Films scored by Joel McNeely Films set in Moscow Films set in Tucson, Arizona Films shot in Lone Pine, California Films shot in Palm Springs, California Films shot in Tucson, Arizona Films with screenplays by David Twohy Hollywood Pictures films Interscope Communications films PolyGram Filmed Entertainment films Skydiving in fiction Hidden categories: Use American English from October 2019 All Wikipedia articles written in American English Use mdy dates from October 2019 Articles with short description Short description is different from Wikidata Template film date with 1 release date Rotten Tomatoes ID same as Wikidata Rotten Tomatoes template using name parameter
13226	https://artofproblemsolving.com/wiki/index.php/2016_AMC_10A_Problems/Problem_10?srsltid=AfmBOopbyz-f1ClLboIh1xKScZL6N6WLbk6noj8QKQz4FO2Aao_kL67l	Art of Problem Solving 2016 AMC 10A Problems/Problem 10 - AoPS Wiki Art of Problem Solving AoPS Online Math texts, online classes, and more for students in grades 5-12. Visit AoPS Online ‚ Books for Grades 5-12Online Courses Beast Academy Engaging math books and online learning for students ages 6-13. Visit Beast Academy ‚ Books for Ages 6-13Beast Academy Online AoPS Academy Small live classes for advanced math and language arts learners in grades 2-12. Visit AoPS Academy ‚ Find a Physical CampusVisit the Virtual Campus Sign In Register online school Class ScheduleRecommendationsOlympiad CoursesFree Sessions books tore AoPS CurriculumBeast AcademyOnline BooksRecommendationsOther Books & GearAll ProductsGift Certificates community ForumsContestsSearchHelp resources math training & toolsAlcumusVideosFor the Win!MATHCOUNTS TrainerAoPS Practice ContestsAoPS WikiLaTeX TeXeRMIT PRIMES/CrowdMathKeep LearningAll Ten contests on aopsPractice Math ContestsUSABO newsAoPS BlogWebinars view all 0 Sign In Register AoPS Wiki ResourcesAops Wiki 2016 AMC 10A Problems/Problem 10 Page ArticleDiscussionView sourceHistory Toolbox Recent changesRandom pageHelpWhat links hereSpecial pages Search 2016 AMC 10A Problems/Problem 10 Contents [hide] 1 Problem 2 Solution 3 Video Solutions 4 See Also Problem A rug is made with three different colors as shown. The areas of the three differently colored regions form an arithmetic progression. The inner rectangle is one foot wide, and each of the two shaded regions is foot wide on all four sides. What is the length in feet of the inner rectangle? Solution Let the length of the inner rectangle be . Then the area of that rectangle is . The second largest rectangle has dimensions of and , making its area . The area of the second shaded area, therefore, is . The largest rectangle has dimensions of and , making its area . The area of the largest shaded region is the largest rectangle minus the second largest rectangle, which is . The problem states that is an arithmetic progression, meaning that the terms in the sequence increase by the same amount each term. Therefore, Video Solutions i) (Creative Thinking) ~Education, the Study of Everything ii) ~IceMatrix iii) ~savannahsolver See Also 2016 AMC 10A (Problems • Answer Key • Resources) Preceded by Problem 9Followed by Problem 11 1•2•3•4•5•6•7•8•9•10•11•12•13•14•15•16•17•18•19•20•21•22•23•24•25 All AMC 10 Problems and Solutions These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Retrieved from " Art of Problem Solving is an ACS WASC Accredited School aops programs AoPS Online Beast Academy AoPS Academy About About AoPS Our Team Our History Jobs AoPS Blog Site Info Terms Privacy Contact Us follow us Subscribe for news and updates © 2025 AoPS Incorporated © 2025 Art of Problem Solving About Us•Contact Us•Terms•Privacy Copyright © 2025 Art of Problem Solving Something appears to not have loaded correctly. Click to refresh.
13227	https://www.suburbandiagnostics.com/blog/laboratory-diagnosis-of-hemoglobinopathies/?srsltid=AfmBOooM9z43DTcUUN_Woj_ieHdAXk3mCoXyQbqUNvtWkRl0OzjB0eVs	Hemoglobinopathies : Laboratory Diagnosis \| Suburban Diagnostics Suburban Menu Home About Us Tests & Packages Services Health Check-Ups Diagnostic Services Home Helthcare Corporate Wellness Hospital Lab Management Blog Partner With Us Home>For Doctors>Hemoglobinopathies : Laboratory Diagnosis (Suburban Medical Journal) Hemoglobinopathies : Laboratory Diagnosis (Suburban Medical Journal) 6 Dec, 2024 Suburban Hemoglobinopathies are a group of inherited disorders in which there is abnormal production or structure of the globin moiety of the hemoglobin molecule. Hemoglobinopathies, which include the thalassemias and structural hemoglobin (Hb) variants, are the most common group of autosomal recessively inherited monogenic disorders of Hb production and pose a significant health burden in India.(1,2) There are thousands of genetic abnormalities possible in the globin genes, many of which are asymptomatic. Proper and timely diagnosis is imperative to ensure optimal treatment and also to offer genetic counselling to those who may be carriers. Hemoglobinopathies can be broadly classified into: Variant hemoglobins Thalassemias Variant Hemoglobins These are caused by a qualitative defect in the genetic code that leads to structural change in the hemoglobin molecule. Most alpha and beta globin chain variants are clinically silent and are discovered incidentally or during screening of family members of a patient.(3) A few variant hemoglobins are capable of causing severe disease, especially in homozygous state (e.g. HbS) or when inherited in conjunction with another variant or a thalassemia mutation. Common examples of variant hemoglobins in India include HbS, HbE and HbD. These hemoglobinopathies are prevalent in certain geographies and communities, e.g. HbE in the north eastern states of India.(4) Change in oxygen affinity – variant hemoglobins can have either decreased or increased affinity to hemoglobin. Low affinity hemoglobins can cause cyanosis (eg: Hb Titusville, Hb Kansas, Hb Beth Israel) and high affinity hemoglobins can cause polycythemia (eg: Hb Olympia, Hb Chesapeake).(5) Reduced stability – some variant hemoglobins can cause the hemoglobin molecule to precipitate and form Heinz bodies (eg: Hb Zurich, Hb Koln) when exposed to oxidative stress.(4) Change in physical properties – variant hemoglobins can have altered solubility leading to crystallization/polymerization of the hemoglobin (eg: HbS – polymerization, HbC – crystallization).(4) Oxidation of the heme iron – mutations which affect the heme binding site can cause oxidation of the heme iron from a ferrous to a ferric state causing resultant methemoglobinemia (eg: HbM).(4) Thalassemias These are quantitative defects of Hb resulting in reduced levels of a globin chain in red cells. As a result, one or the other globin chains will accumulate, form aggregates and then precipitate, leading to premature intramedullary or intravascular destruction of RBCs. Beta thalassemia – These cases have reduced levels of beta globin chains caused by point mutations that disrupt regulatory elements of beta globin gene expression. The mutations are expressed as β+ if some amount of beta globin is produced and as β0 if there is no beta globin production.(4) Alpha thalassemia– These cases have reduced levels of alpha globin chains caused by deletions of one or both alpha globin genes.(4) Mutations in gamma and delta globin genes can also cause thalassemic disorders ranging from clinically silent (Hereditary persistence of fetal hemoglobin – HPFH) to symptomatic (delta-beta thalassemia). Rarely, thalassemic mutations can result in altered hemoglobin structure (eg: Hb Lepore). An example of delta globin chain mutation not uncommonly seen in India is HbA2 Saurashtra.(6) Diagnosis of Hemoglobinopathies The laboratory diagnosis of hemoglobinopathies has evolved quite a bit over the years, progressing from gel electrophoresis all the way to next generation sequencing. “In most cases, a well elicited family history and parental testing in combination with HPLC is sufficient for definitive diagnosis of common Hb variants.”(4) There are 2 broad categories of tests for diagnosis/screening of hemoglobinopathies:(4) Protein-based methods DNA-based methods Protein-based methods These are the methods of choice in the present day, with more advanced DNA based tests being used only for cases which cannot be resolved using protein-based methods. The routinely used protein-based methods are as follows:(4) HPLC (High performance liquid chromatography) IEF (Isoelectric focusing) CE (Capillary electrophoresis) Gel electrophoresis Cellulose acetate electrophoresis Table 1 – Comparison of Protein-Based Methods(4) Advantages(4)Disadvantages(4) High performance liquid chromatography (HPLC) Fully automated High precision Rapid, high throughput Only a very small sample is required Can identify and quantify many variant hemoglobins as well as normal hemoglobins. Information from the pattern gives the possible diagnosis of variant peaks and guides further testing Interpretation of results requires technical skill, experience Interference /interpretation of results affected by prematurity (in newborn), recent transfusion Decreased resolution and increase in P3 peak with sample age due to Hb degradation Cannot distinguish Hb E and Hb Korle-Bu from Hb A2 due to overlapping retention times Isoelectric focusing (IEF) Excellent resolution of common Hb vari- ants and Hb Barts Distinguishes Hb E from Hb O and Hb S from Hb D and Hb G Hb A and Hb F are clearly resolved Requires only small sample Cannot precisely quantify Hb variants Cost per test is higher Methemoglobin and glycosylated Hb appear as separate bands. Bands on gel are less sharp with automat- ed compared with manual IEF Capillary electrophoresis Fully automated High-throughput Identifies common Hb variants Separates Hb A2 from Hb E (unlike HPLC) Precise quantification of hemoglobins Information from zone pattern of variants guides further testing Complementary to HPLC Capital cost (equipment, reagents) Requires technical skill, expertise Poor separation of Hb S from Hb D Electrophoresis zones are shifted in the absence of Hb A Decreased resolution with sample age Minimal sample required (1 mL), but if sample is <1 mL, dilution of other sam- ples is required, adding labor Electrophoresis (cellulose acetate, citrate agar) Low cost Separation of major Hbs (Hb A, Hb F, Hb S/D, Hb C/E/O-Arab) and several less common Hb variants Acid pH (citrate agar) resolves Hb S and Hb C, and Hb E and Hb D Iran Poor separation of Hbs other than HbS A, F, S, C Cannot distinguish Hb E from Hb O, or Hb D from Hb G Labor intensive DNA-based methods These are almost never used as first-line tests. They do have immense significance and potential in prenatal and newborn screening. The commonly used methods are:(4) Gap polymerase chain reaction Traditional DNA sequencing (Sanger) Multiplex ligation-dependent probe amplification (MLPA) Next-generation sequencing (NGS) Table 2 – Comparison of DNA-Based Methods(4) Advantages(4)Disadvantages(4) Gap polymerase chain reaction (PCR) Identification of common alpha thalassemia deletions Identification of beta thalassemia and HPFH deletions Identification of alpha globin gene duplications Can be multiplexed to test several deletions in single assay Specific probes required for known deletional lesions of globin chains Testing is limited to selected/pre-defined deletions (cannot detect unknown deletions) Traditional DNA sequenc- ing (Sanger) Identifies a spectrum of point mutations and small insertions and deletions (in-dels) that result in a hemoglobinopathy (thalassemia, Hb variants) Cannot identify large deletions or duplications Only one DNA sequence (up to 1 kb can be obtained at a time Multiplex ligation-dependent probe amplification(MLPA) Detects large deletions and duplications (alpha or beta genes) Capital cost, kits, reagents, software Requires technical skill, expertise Requires additional DNA sequencing to define deletion breakpoints (to characterize deletion) Next-generation DNA sequencing (NGS) Simultaneous identification of complete spectrum of deletions, duplications, point mutations in alpha and beta globin genes (single parallel assay) Requires very small sample (less than that for Sanger sequencing) Rapid High accuracy, reliability Capital cost, reagents (but less expensive than Sanger sequencing) Who should be screened for Hemoglobinopathies? It is recommended that screening for hemoglobinopathies should be done in the following situations with the method of choice being HPLC:(1) Premarital screening Antenatal screening Preconception screening Neonatal screening Preoperative/pre-anesthesia screening References: Ghosh K, Colah R, Choudhry V, Das R, Manglani M, Madan N, et al. Guidelines for screening, diagnosis and management of hemoglobinopathies. Indian J Hum Genet. 2014;20(2):101. Centers for Disease Control and Prevention (CDC), Asscoiation of Public Health Laboratories (APHL). Hemoglobinopathies: Current Practices for Screening, Confirmation and Follow-up [Internet]. Centers for Disease Control (CDC); 2015. Available from: Gupta AD, Nadkarni A, Mehta P, Goriwale M, Ramani M, Chaudhary P, et al. Phenotypic expression of HbO Indonesia in two Indian families and its interaction with sickle hemoglobin. Indian J Pathol Microbiol. 2017 Mar;60(1):79–83. Hoppe C, Mentzer WC, Tirnauer JS. Methods for hemoglobin analysis and hemoglobinopathy testing. In: UpToDate. 2.0. Wolters Kluwer Health; 2018. Das Gupta A, Hariharan P, Daruwalla M, Sidhwa K, Pawar R, Nadkarni A. Hemoglobin Titusville [α2 Codon 94 G>A]: A Rare Alpha Globin Chain Variant Causing Low Oxygen Saturation. Indian J Hematol Blood Transfus. 2019 Jul;35(3):593–5. Das Gupta A, Ramani M, Sidhwa K, Pawar R, Nadkarni A. Hemoglobin A2 Saurashtra – a Delta Globin Chain Variant That Can Mask the Diagnosis of Beta Thalassemia Trait. (Unpublished). [post_date] [Sassy_Social_Share] Search Search Search Related Posts MPox: Everything you need to know What is Mpox? Mpox is an illness caused by the monkeypox virus, which is a… Migraine – Treatment, Types & Symptoms Introduction: Migraine headaches are characterized by throbbing pain, typically on one side of the head.… The importance of Mammogram The importance of Mammogram Breast cancer (BC) is the most common malignancy among women worldwide,… Categories GENERAL FOR DOCTOR Have a Query? Speak with our experts now. 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13228	https://www.khanacademy.org/python-program/payroll/5236384742686720	Khan Academy \| Khan Academy Skip to main content If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains .kastatic.org and .kasandbox.org are unblocked. Explore Search DonateLog inSign up Search for courses, skills, and videos Our mission is to provide a free, world-class education to anyone, anywhere. Khan Academy is a 501(c)(3) nonprofit organization. Donate or volunteer today! Site Navigation About News Impact Our team Our interns Our content specialists Our leadership Our supporters Our contributors Our finances Careers Internships Cookie Preferences Contact Help center Support community Share your story Press Download our apps Courses Language en CountryU.S.IndiaMexicoBrazil © 2025 Khan Academy Terms of use Privacy Policy Cookie Notice Accessibility Statement
13229	https://www.studocu.com/en-us/document/rensselaer-polytechnic-institute/fluid-mechanics/lecture-03-hydrostatic-forces-on-submerged-plane-surfaces/139336739	Lecture 03: Hydrostatic Forces on Submerged Plane Surfaces - Studocu Skip to document Teachers University High School Discovery Sign in Welcome to Studocu Sign in to access study resources Sign in Register Guest user Add your university or school 0 followers 0 Uploads 0 upvotes New Home My Library AI Notes Ask AI AI Quiz Chats Recent You don't have any recent items yet. My Library Courses You don't have any courses yet. Add Courses Books You don't have any books yet. Studylists You don't have any Studylists yet. Create a Studylist Home My Library Discovery Discovery Universities High Schools High School Levels Teaching resources Lesson plan generator Test generator Live quiz generator Ask AI Lecture 03: Hydrostatic Forces on Submerged Plane Surfaces The content explores the hydrostatic forces acting on submerged plane surfaces,...such as those found in dam gates and storage tanks. It delves into the calculation of fluid pressures and resultant forces, providing methodologies for determining the center of pressure. Key concepts include the relationship between atmospheric pressure and hydrostatic forces, the significance of the centroid in fluid mechanics, and practical applications, including in-class problems that involve calculating forces and pressures on submerged surfaces. View more Course Fluid Mechanics (MANE-2720) 30 documents University Rensselaer Polytechnic Institute Academic year:2025/2026 Comments Please sign in or register to post comments. Report Document Preview text Lecture 03 Forces on Submerged Plane Surfaces A plate (such as a gate valve in a dam, the wall of a liquid storage tank, or the hull of a ship at rest) is subjected to fluid pressure distributed over its surface when exposed to a liquid. On a plane surface, the hydrostatic forces form a system of parallel forces, and we often need to determine the magnitude of the force and its point of application, which is called the center of pressure. Consider the top surface of a flat plate of arbitrary shape completely submerged in a liquid, with a free surface open to atmospheric conditions. (Cengel, Yunus A., et al. Fundamentals of thermal-fluid sciences. New York: McGraw-Hill, 2008) The plane of this surface (normal to the page) intersects the horizontal free surface at angle ƨ; the line of intersection to be the x-axis (out of the page). Considering just the case with atmospheric pressure P atm at the surface, then the absolute pressure at any point on the plate is P(h) = Patm + Ʊgh P(y) = Patm + Ʊgysinƨ where h is the vertical distance of the point from the free surface and y is the distance of the point from the x-axis (from point O) The resultant force F R acting on the surface is determined by integrating the force P dA acting on a differential area dA over the entire surface area But the first moment of area A y dA is related to the y-coordinate of the centroid (or center) of the surface by Plh ) = Paton tsgh ply ) = Paton tggysiuoocou " - " If faut Pata mummy .fEmmwr¥ sin ) •\z Fr v ' i , Y FR - - la PDA = fnfpatmtggysiuo ) da ¥¥¥÷÷÷÷÷÷÷ ' g. a , " ← . Fn = Patin At ggsi.no/n ' n , I centroid , C P ' :¥hItIh. ceu-eq.t.ar: To . " \| Cp ) place surface of aaea , A . Ye tafaydtt Lecture 03 The locations of centroids for many common shapes are listed in Table 4-1. This is the magnitude of the resultant force. Next we need to determine the line of action of the resultant force FR. The line of action of the resultant hydrostatic force, in general, does not pass through the centroid of the surface³it lies underneath where the pressure is higher. To find the center of pressure take the moment of the resultant force about the x-axis (point O) and equate to the moment caused by the distributed pressure: I xx,O = A y 2 dA -- second moment of area or area moment of inertia -- about the x-axis (O). It is more common to report I xx,C passing through the centroid of the area. The second moments of area about two parallel axes are related to each other by the parallel axis theorem: Ixx,O = Ixx,C + y 2 C A Fr -_PatmA-ggsin0ycA warm he - vertical distance to centroid of area " %EF:7?geyfI. che - - smog , Urfa lay PDA =P, = pane [ centroid of surface = Ja, y ( Paton tggy she DA Patula. 4 da t ggsiuofy DA Fr = ( Patmtgghc) A - - = IKAT & III:L : " . " , ". A /PaneA Yp FR = Patin Yc t g g sino Ixx , o n#..:m::::::::::::.m:.h:: Lecture 03 In-Class problem 2 : A submerged gate separates water from a pressurized tank which contains air. The water reservoir is open to atmospheric pressure, Zhich iV 101 kPa, aV VhRZQ iQ Whe ÀgXUe beORZ. The gaWe iV rectangular, 8 m wide (out of page) and hinged along its bottom edge. What is the minimum absolute pressure of the tank, P, required to keep the gate closed? Density of water may be assumed to be 996 kg/m 3. [ k9a → N ] V Fr - ( 996k¥, )( 9%2 )sinl6o ) ( 4 )( 3)( 8ms) = 9× 105 N The point of application : yp= yet Ix Yc A by Ixx ,c= aqza Maa- Yp y. + ages 4 kycaqae yet Nyc Yp = g. 04mi 13 1214 - 04M ) Yp = 4 - since the tank contains a gas , Assertions gravity effects are negligible and hence pressure →;§mm] acts uniformly across lower surface of gate with a resultant force through centroid . → Uniform pressure in tank where Ff=Pgage A Path - - 101 O Fr BBB ' ar # I a . - army. Fr i ' ' ' ' n , OT , # T¥- 93=2.314-13.46-4 , If I as - - i. 4am ' ' n.. - a , I -# ' i i ' t Fr Taking moments around n r '. 8× 10 ' N Absolute pressure in tank ' y , - are Tatem " " ° " ' hinge Pgage = TAI = is F- gm , Patmtpgage. ' y ' ¥ Since Paton acts on both sides ¥, Fa ( AI ) =Fr( as ) Pgage = 29237 Ng Fr - - gg sino yc A Fg -_ ZFR as where Az P = 101 t 29 kPa ye = a , t II ( the centroid of a rectangle is at the center of plate) Fg = 2(%46×N5N)(t48m# -1p=13o€ a 3- 46in , = Im = 3 Sinko ) Fg = 8× 10 ' N ^ ' = ZITO, = 2 , m } Yc = 404ns sin Lecture 03: Hydrostatic Forces on Submerged Plane Surfaces Download Download AI Tools Ask AI Multiple Choice Flashcards Quiz Video Audio Lesson 0 0 Save Lecture 03: Hydrostatic Forces on Submerged Plane Surfaces Course: Fluid Mechanics (MANE-2720) 30 documents University: Rensselaer Polytechnic Institute Info More info Download Download AI Tools Ask AI Multiple Choice Flashcards Quiz Video Audio Lesson 0 0 Save Lecture 03 Forces on Submerged Plane Surfaces A plate (such as a gate valve in a dam, the wall of a liqu id storage tank, or the hull of a ship at rest) is subjected to fluid pressure distributed over its surface when exposed to a liquid. On a plane surface, t he h ydr os t atic forces form a system of parallel forces, and we often need to determi ne th e m agnitu de o f the force and its poin t o f application, w hich i s ca lled t he cen ter of pre s sure. Consider the top surface of a flat plate of arbitrary shape completely submerged in a liquid, with a free surface o pen t o atmospheric conditions. (Cengel, Yunus A., et al. Fundamentals of thermal-fluid scienc es. New York: McGraw-H ill, 2008) The plane of this surface (normal to the page) intersect s the horizonta l free surface at angle ; t he lin e of intersection to be the x-axis (out of the page). Considering just the case with atmospheric p ressure P atm at the surface,then the absolute pressure at any point on the plate is P(h) = P atm + g h P(y) = P atm +gy sin where h is t h e v ertic a l dis t a n ce o f t h e p o in t f ro m t h e f r ee s u rf a ce an d y is th e di s ta n ce o f th e p o i n t f r o m th e x-a xis(f ro m p o i nt O) The resultant force F R acting on the su r fa ce is determined by integrating the force P d A acting on a di ff ere ntial area d A over the entire surface area But the first moment of area A y d A i s rela ted t o th e y-c oordina te of the c en tr o id(o r ce n ter)o f th e s u r f a ce b y Plh ) = Pa t o n ts g h ply ) = Pa t o n t g g y s i u o o co u.g s " - " If fa u t Pa t a m um m y .fEmmwr¥ ↳ sin ) •\z Fr v ' i , Y FR - - la PD A = fnfp at m t g g y s iuo ) da ¥¥¥÷÷÷÷÷÷÷ ' g. a , " ← . Fn = Pa t i n At ggsi.n o/n.y d A ' n , I ce n t r oi d , C P ' :¥hItIh . ce u-e q.t.ar.i e : To . " \| Cp ) pl a c e su r f a c e of aae a , A . Ye - ta f a y d t t Lecture 03 The locations of centroids for many common shapes a re listed in Table 4-1. This is the magnitude of the resultant force. Next we need to determine the line of action of the resultant force F R. The line of action of the resultant hydrosta tic force, in general, does not pass through the centroid of the surfaceit lies underneath where the pressure is higher. To find the center o f pressure take th e m oment of the resultant force about the x-axis (po i nt O) and equate to the moment caus ed by the distributed pressure: I xx,O= A y 2 d A -- second moment of area or ar ea moment of inertia -- about the x-axis (O). It is more common to report I xx,C passing through t he centroid of the area. Th e second moments of area about two parallel axes are related to each other by the parall el axis theorem: I xx,O= I xx,C+ y 2 C A Fr -_P atmA-ggsin0ycA war m he - ver ti ca l distance to centroid of area " %EF.in:7?geyfI . che - - smog , Ur f a lay PD A =P , = pane • [ centroid of sur face = Ja , y ( Pat on tgg y she DA = Pa t u l a . 4 da t ggsiuofy - DA Fr = ( Pa t m t g g h c ) A - - = IKA T & III :L : " . " , " . - A = /P aneA 7 Yp FR = Pa ti n Yc t g g sino Ixx , o - 󲰛 n.io#..:m::::::::::::.m:.h:: Lecture 03 I xx,C is the s econd moment of area ab out the x-ax i s passing through the cen troid of the area It follows P atm acts on both sides of the plate. Subtract P atm and work with P gage = g h. In-Class problem 1: A tank is filled with water to a depth of 11 ft.An op e ning in the bottom of the tank is covered by a rectangular gate 3 ft high and 2 ft wide. The gate is hinged at the bottom and held in place at the top by a wire cable, as shown. Calculate the tension in the cable. Solu tion: Because atmospheric pressure a ct s on both sides of the gate, the resultant force on the gate is: To find the point of application of this force, use Ixx.co = Ixx , at ya ? A w/ Some ne anna - Gheg → Yo - - ya t Ix# 5=62-3 ¥7 [ yet ] A Gg sin O ) Putin acts on both sides . Pat on on both sides Pat in cancels out . Imre Pato n = it :€÷f . " s ::÷÷ : ni :÷i:÷ : :c : : : . . . . ( tes t - - Fr = 3551 lbf 32.2 lbmjft ) - - w - fou r Figure 3.2 8 patient Sgh ) path ggk The point of application : Yp = yet I× - ya A Fn=ggsiu0y yp= g - sft + Htt ' yp-ay.ttxx.CI/w!Ihs!7Is . " Ti HEE Ix . g. = g. soft Etta Ya A Tkz = Fn x , T = ( 3551lb f) ( H - 9 - 581ft lT=l682lbfT - - 3ft Too long to read on your phone? Save to read later on your computer Save to a Studylist Lecture 03 In-Class problem 2: A submerg ed gate separates water from a pressurized t ank which contains air. The water reservoir is open to atmospheri c pres sure, hich i 101.3 kPa, a h i he ge be. Th e gae i rectangular, 8 m wide (out of page) and hinged along it s bottom edge. What is the minimum absolute pressure of the tank, P, required to keep the gate closed? Density of water may be assumed to be 996 kg/m 3. [ k9a → N ] V Fr - ( 996k¥ , )( 9.8 1%2 )sinl6o ) ( 4.04 i n )( 3.4 6m s )( 8ms ) = 9.4 6×1 0 5 N The point of application : yp= yet Ix Yc A by Ixx ,c= aqza Ma a - Yp - y . + ages 4 kycaqae = yet Nyc Yp = g. 04mi 13.46in 1214 - 04M ) Yp = 4.2 9 M - since the tank contains a gas , gra vity eff ects are negligible Asser t ion s and hence pressur e →;§mm] acts unif ormly across low er surface of gate with a resultant for ce through centroid . → Uniform pressure in tank where Ff=Pgage A Pat h - - 101.3kt O Fr BBB ' ar I a . - army . Fr i ' ' ' ' n , OT , - T¥- 93=2.314-13.4 6-4.04 , If I as - - i. 4am ' ' n . . - a , I - -# i ' i t Fr Ta k i n g moments around ' n r ' . 8.09×10 ' N Absolute pressur e in tank ' y , - are Ta t e m " " ° " ' hinge Pga ge = TA I = gm , is F- Pat m tp ga g e . ' y ' ¥ ¥ , Fa ( AI ) =Fr( as ) Since Pato n acts on both sides Pga g e = 29237.5 Ng Fr - - gg sino yc A Fg -_ ZFR as - P = 101.3hPa t 29.24 kPa where Az ye = a , t II ( the centroid -1 of a rec ta ng le is at the center of plate ) Fg = 2(%46×N5N)(t 48m# p=13o.5kp€ 3- 46in a , = Im = 3.4 6 M Sinko ) Fg = 8.09×1 0 ' N ^ ' = ZIT O , = 2.3 , m } Yc = 404ns sin 1 out of 4 Share Download Download More from:Fluid Mechanics(MANE-2720) More from: Fluid MechanicsMANE-2720Rensselaer Polytechnic Institute 30 documents Go to course 6 Homework 04 Answers Fluid Mechanics Assignments 100% (1) 9 Fluid Kinematics: Lecture 05 on Motion Characteristics and Velocity Fluid Mechanics Lecture notes None 32 Comprehensive Fluid Mechanics (ENGR 301): Principles and Applications Fluid Mechanics Coursework None 47 Fluid Mechanics (ENG 101): Comprehensive Overview of Principles and Applications Fluid Mechanics Other None More from: Fluid MechanicsMANE-2720Rensselaer Polytechnic Institute30 documents Go to course 6 Homework 04 Answers Fluid Mechanics 100% (1) 9 Fluid Kinematics: Lecture 05 on Motion Characteristics and Velocity Fluid Mechanics None 32 Comprehensive Fluid Mechanics (ENGR 301): Principles and Applications Fluid Mechanics None 47 Fluid Mechanics (ENG 101): Comprehensive Overview of Principles and Applications Fluid Mechanics None 8 Lecture 08: Bernoulli Equation Derivation & Fluid Dynamics Problems Fluid Mechanics None 4 Fluid Mechanics: Lecture 6 - Conservation of Mass Principles Fluid Mechanics None Recommended for you 6 Homework 04 Answers Fluid Mechanics Assignments 100% (1) 6 Homework 04 Answers Fluid Mechanics 100% (1) Get homework AI help with the Studocu App Open the App English United States Company About us Studocu Premium Academic Integrity Jobs Blog Dutch Website Study Tools All Tools Ask AI AI Notes AI Quiz Generator Notes to Quiz Videos Notes to Audio Infographic Generator Contact & Help F.A.Q. 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13230	https://physics.stackexchange.com/questions/318135/the-converse-of-newtons-shell-theorem	Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Visit Stack Exchange Teams Q&A for work Connect and share knowledge within a single location that is structured and easy to search. Learn more about Teams The converse of Newton's shell theorem Ask Question Asked Modified 4 years, 2 months ago Viewed 1k times $\begingroup$ The shell theorem states that a spherically symmetric body $S$ of mass $m$ has a gravitational field identical to that of a point particle $P$ of mass $m$ located at the center of $S$. We can ask the converse question: suppose there is a force $F$ between masses $M$ and $m$, separated by a distance $r$ of the form $$F = M m f ( r )$$ such that any spherically symmetric body affects external bodies as if its mass were concentrated at its center. Then what form can the function $f$ take? According to Wikipedia: the general solution is $$f(r)=a/r^2+br$$ where $a$ and $b$ are constants. I attempted to demonstrate this. Replacing the gravitational force with the general force $F=Mmf(r)$ in the calculations to prove the shell theorem, I got that for all distances $r \ge R > 0$, $f$ satisfies: $$\int_{r-R}^{R+r} (r^2-R^2 +s^2) f(s)\ ds = 4r^2Rf(r).$$ We can take the second derivative of both sides with respect to $r$ to get rid of the integral (we'll need to differentiate inside the integral), and we get the following nasty differential equation: $$2Rrf''(r)+6Rf'(r)=f'(r+R)(r+R)+2f(r+R)-f'(r-R)(r-R)-2f(r-R).$$ I don't think this really helps. We can easily verify that $f=ar^2+br$ is a solution of this equation, so I didn't make any mistakes thus far (note the equation is linear so it suffices to check it for $f=r$ and $f=1/r^2$). So how can we demonstrate the result? forces classical-mechanics newtonian-gravity symmetry potential-energy Share Improve this question edited Jul 22, 2018 at 8:30 Qmechanic♦ 222k5252 gold badges635635 silver badges2.5k2.5k bronze badges asked Mar 11, 2017 at 22:50 math_lovermath_lover 4,7461111 gold badges5151 silver badges9898 bronze badges $\endgroup$ 0 Add a comment \| 4 Answers 4 Reset to default 11 $\begingroup$ Converse shell theorem for an exterior point mass: Assume that the force ${\bf F}_{12}$ between two point masses $m_1$ and $m_2$ is collinear with the difference in positions ${\bf r}_{12}:={\bf r}_1-{\bf r}_2$, is central, and the magnitude $$\|{\bf F}_{12}\|=m_1m_2 f(\|{\bf r}_{12}\|)\tag{}$$ is proportional to both the two point masses. We call the function $f(\|{\bf r}_{12}\|)$ the specific force. Assume furthermore that the magnitude of the total force between an extended spherically symmetric mass $M$ and an exterior point mass $m$ is of the same form $$\|{\bf F}\|=mM f(r),\tag{}$$ where $r\equiv \|{\bf r}\|$ is the distance between $m$ and the center of $M$. Then the specific force $f$ is a linear combination of a linear/Hooke force, an inverse square/Newtonian gravity force. Sketched proof: Let us use the same notation as the Wikipedia page. We consider the outside of a thin shell, i.e. $r\geq R$. Let us for simplicity work in terms of potential energy (rather than force), because it is easier to work with a scalar (rather than a vector) quantity. We may assume that the contribution $dU$ to the potential energy of the mass $m$ and $dM$ with distance $s$ is of the form $$ dU~=~m~dM~u(s),\tag{1.1}$$ where $s\mapsto u(s)$ is an unknown specific potential. Define for later convenience the antiderivative $$V(s)~:=~\int^s! ds^{\prime}~s^{\prime}~ u(s^{\prime}), \tag{1.2}$$ so that $$V^{\prime}(s)~\stackrel{(1.2)}{=}~s~u(s).\tag{1.3}$$ From geometry we have the cosine relation $$ \cos\theta ~=~\frac{r^2+R^2-s^2}{2rR},\tag{1.4} $$ and therefore $$dM ~=~ \frac{M}{2}\sin\theta~ d\theta ~=~-\frac{M}{2}~d\cos(\theta) ~\stackrel{(1.4)}{=}~\frac{M}{2}\frac{s~ds}{rR}.\tag{1.5}$$ In the last equality of eq.(1.5) we varied $s$ and $\theta$ while holding $r$ and $R$ fixed. Then we have $$dU~\stackrel{(1.1)+(1.5)}{=}~\frac{mM}{2}\frac{s~ds}{rR}~u(s) ~\stackrel{(1.3)}{=}~\frac{mM}{2rR}ds~V^{\prime}(s).\tag{1.6}$$ So the total potential energy is $$U(r,R)~=~\int dU ~\stackrel{(1.6)}{=}~mM\frac{V(r+R)-V(r-R)}{2rR}$$ $$~\stackrel{(1.8)}{=}~\frac{mM}{r}\left(V^{\prime}(r)+ \frac{R^2}{6}V^{\prime\prime\prime}(r)+ {\cal O}(R^5)\right).\tag{1.7}$$ In the last equality of eq. (1.7), we Taylor-expanded the potential $$V(r\pm R)~=~V(r) \pm RV^{\prime}(r) + \frac{R^2}{2}V^{\prime\prime}(r) \pm \frac{R^3}{6}V^{\prime\prime\prime}(r)+ {\cal O}(R^4). \tag{1.8}$$ Let us now implement the main converse shell assumption: We assume that the potential energy $U(r,R)$ up to an ambiguity in the choice of zero-point energy $U_0(R)$ does not depend on the radius $R$ of the thin shell, i.e. $U(r,R)$ is of the form $$U(r,R)~=~U_1(r)+U_0(R) .\tag{1.9} $$ We see that the only way that eq. (1.7) could be of the form (1.9) is iff $$ V^{\prime\prime\prime}(r)~\stackrel{(1.7)+(1.9)}{\propto}~r,\tag{1.10} $$ i.e. $V^{\prime}$ is a 3rd-order polynomial with a missing 2nd-order term: $$ V^{\prime}(r)~\stackrel{(1.10)}{=}~Ar^3+Br^2+Cr+D\tag{1.11}, \qquad B~=~0. $$ Or in terms of the specific potential $$ u(r)~\stackrel{(1.3)+(1.11)}{=}~Ar^2+C+\frac{D}{r}\tag{1.12}. $$ Or in terms of the specific force $$ -f(r)~=~u^{\prime}(r)~\stackrel{(1.12)}{=}~2Ar-\frac{D}{r^2}\tag{1.13}. $$ $\Box$ Share Improve this answer edited Jun 29, 2021 at 21:05 answered Mar 12, 2017 at 18:34 Qmechanic♦Qmechanic 222k5252 gold badges635635 silver badges2.5k2.5k bronze badges $\endgroup$ 2 $\begingroup$ Future project: Generalize to $n$ spatial dimensions: $f(r)~=~ a/r^{1-n} +b r $. $\endgroup$ Qmechanic – Qmechanic ♦ 2018-07-24 08:39:46 +00:00 Commented Jul 24, 2018 at 8:39 $\begingroup$ Is this $n$-dimensional generalization solved? Can you direct me to the proof @Qmechanic $\endgroup$ Hyakutake – Hyakutake 2025-05-05 14:35:00 +00:00 Commented May 5 at 14:35 Add a comment \| 3 $\begingroup$ This follows from Gauss's law. The $1/r^2$ part would be for a Gaussian sphere of radius greater the radius if the source, while the $r$ part follows from having a Gaussian sphere with radius inside the source, assuming uniform mass density. The best way to show this is to start from the differential equation for the potential in spherical coordinates assuming spherical symmetry; this would be the Laplace equation outside and the Poisson equation with a constant term on the right inside the source. Once you have the potential you can get the force through the gradient. Edit. Start from \begin{align} \nabla^2V(r)&=0\, ,\ \frac{1}{r^2}\frac{d}{dr}\left(r^2\frac{dV}{dr}\right)&=0\, ,\ r^2\frac{dV}{dr}&=-a\, , \end{align} for some constant $a$. This is enough to give you the force as $\sim 1/r^2$ outside the source since $F_r=-\frac{dV}{dr}$. Inside, you need to find a particular solution to $$ \nabla^2V=4\pi G\,\rho_m $$ where $\rho_m$ is the mass density. By inspection $dV/dr=4\pi G\rho_m\,r/3$ will work; this entails $F_r=br$ inside the source. The general solution with $\rho_m\ne 0$ is then the sum of the particular solution and the sum of the homogenous problem. Share Improve this answer edited Mar 12, 2017 at 17:34 answered Mar 12, 2017 at 0:23 ZeroTheHeroZeroTheHero 49.4k2121 gold badges7272 silver badges149149 bronze badges $\endgroup$ 4 $\begingroup$ I guess I'll have to revisit this answer when I've done some higher level physics because I don't understand why the statement that a spherically symmetric body acts as if all its mass is concentrated at its center is equivalent to the condition you gave with the Laplace and Poisson equations. $\endgroup$ math_lover – math_lover 2017-03-12 17:18:16 +00:00 Commented Mar 12, 2017 at 17:18 $\begingroup$ @JoshuaBenabou The key points are: 1. the spherical symmetry and 2. the potential, which must satisfy $\nabla^2V(r)=4\pi G\rho_m$ as per en.wikipedia.org/wiki/… (I corrected missing $4\pi G$ factors in my answer). $\endgroup$ ZeroTheHero – ZeroTheHero 2017-03-12 18:09:34 +00:00 Commented Mar 12, 2017 at 18:09 $\begingroup$ how come the total force is the sum when inside and outside follow different equations? $\endgroup$ user86425 – user86425 2017-03-17 12:53:19 +00:00 Commented Mar 17, 2017 at 12:53 $\begingroup$ @rpfphysics the coefficients $a$ and $b$ that appear in the general solution need to be adjusted for particular solutions. $\endgroup$ ZeroTheHero – ZeroTheHero 2017-03-17 13:02:46 +00:00 Commented Mar 17, 2017 at 13:02 Add a comment \| 2 $\begingroup$ In this answer, we give a proof of the converse shell theorem for an exterior point mass summing over forces rather than potentials, in the spirit of OP's calculation. Sketched proof: We use the same notation as the Wikipedia page and my other Phys.SE answer. We consider the outside of a thin shell, i.e. $r\geq R$. Define for later convenience the antiderivative $$W(s)~:=~-\int^s! ds^{\prime}~(s^{\prime})^2~ f(s^{\prime}), \tag{2.1}$$ so that $$W^{\prime}(s)~\stackrel{(2.1)}{=}~- s^2~f(s).\tag{2.2}$$ The cosine relation yields $$ \cos\phi ~=~\frac{s^2+r^2-R^2}{2sr}.\tag{2.3} $$ The radial contribution $dF_r$ to the force on the mass $m$ from the ring $dM$ with distance $s$ is of the form $$ \begin{align}dF_r~=~& -m~dM~f(s)~\cos\phi\cr ~\stackrel{(1.5)}{=}& -m~\frac{M}{2}\frac{s~ds}{rR}~f(s)~\cos\phi \cr ~\stackrel{(2.3)}{=}&-\frac{mM}{4r^2R}~ds~f(s)~(s^2+r^2-R^2)\cr ~\stackrel{(2.2)}{=}&\frac{mM}{4r^2R}~ds\left[W^{\prime}(s)+(r^2-R^2)u^{\prime}(s)\right].\end{align}\tag{2.4}$$ The total radial force should be independent of $R$: $$ \begin{align}F_r(r)~=~&\int ! dF_r\cr ~\stackrel{(2.4)}{=}&\frac{mM}{4r^2R}~\int_{r-R}^{r+R} ! ds\left[W^{\prime}(s)+(r^2-R^2)u^{\prime}(s)\right] \cr ~=~&\frac{mM}{4r^2R}\left[W(r!+!R)-W(r!-!R)+(r^2-R^2)\left(u(r!+!R)-u(r!-!R)\right)\right] \cr ~=~&\frac{mM}{2r^2}\left[W^{\prime}(r)+\frac{R^2}{6}W^{\prime\prime\prime}(r)+(r^2-R^2)\left(u^{\prime}(r)+\frac{R^2}{6}u^{\prime\prime\prime}(r)\right)+{\cal O}(R^4)\right]\cr ~=~&\frac{mM}{2}\left[\underbrace{r^{-2}W^{\prime}(r)+u^{\prime}(r)}_{=~-2f(r)}+R^2 (\ldots)+{\cal O}(R^4)\right].\end{align} \tag{2.5}$$ Therefore the ellipses $(\ldots)$ in eq. (2.5) must vanish: $$ \begin{align}0~=~&(\ldots) \cr ~\stackrel{(2.5)}{=}& \frac{W^{\prime\prime\prime}(r)}{6r^2}- \frac{u^{\prime}(r)}{r^2} +\frac{u^{\prime\prime\prime}(r)}{6} \cr ~\stackrel{(2.2)}{=}& -\frac{1}{6r^2}\frac{d^2(r^2f(r))}{dr^2}+ \frac{f(r)}{r^2} -\frac{f^{\prime\prime}(r)}{6} \cr ~=~& \frac{1}{3}\left( \frac{2f(r)}{r^2}-\frac{2f^{\prime}(r)}{r} -f^{\prime\prime}(r)\right)\cr ~=~& -\frac{d}{dr}\left(\frac{1}{3r^2} \frac{d(r^2f(r))}{dr}\right)\cr ~\stackrel{(2.2)}{=}& \frac{d}{dr}\left(\frac{W^{\prime\prime}(r)}{3r^2}\right).\end{align} \tag{2.6}$$ Hence $$ W^{\prime\prime}(r)~\stackrel{(2.6)}{\propto}~r^2 ,\tag{2.7}$$ so that $$ W^{\prime}(r)~\stackrel{(2.7)}{=}~\alpha r^3+\beta. \tag{2.8}$$ Or in terms of the specific force $$ -f(r)~\stackrel{(2.2)}{=}~\frac{W^{\prime}(r)}{r^2}~\stackrel{(2.8)}{=}~\alpha r+\frac{\beta}{r^2}. \tag{2.9}$$ $\Box$ So can we understand this result (2.9) intuitively? Yes: The Coulomb law comes from Gauss' law. The Hooke's law $\vec{f}(\vec{r})=-k\vec{r}$ works for every extended mass $M$ (not necessarily a spherically symmetric shell) that is invariant under spatial point reflection $\vec{R}\to -\vec{R}$. This follows from linearity: Two antipodes $\vec{f}(\vec{r}!+!\vec{R})+\vec{f}(\vec{r}!-!\vec{R})=2\vec{f}(\vec{r})$ contribute as much as twice the midpoint(=center). Share Improve this answer edited Jun 29, 2021 at 21:05 answered Jul 21, 2018 at 20:08 Qmechanic♦Qmechanic 222k5252 gold badges635635 silver badges2.5k2.5k bronze badges $\endgroup$ 0 Add a comment \| 2 $\begingroup$ Converse shell theorem for an interior point mass: Assume that the force ${\bf F}_{12}$ between two point masses $m_1$ and $m_2$ is collinear with the difference in positions ${\bf r}_{12}:={\bf r}_1-{\bf r}_2$, is central, and the magnitude $$\|{\bf F}_{12}\|=m_1m_2 f(\|{\bf r}_{12}\|)\tag{}$$ is proportional to both the two point masses. We call the function $f(\|{\bf r}_{12}\|)$ the specific force. Assume furthermore that the total force between an extended spherically symmetric mass $M$ and an interior point mass $m$ vanish. Then the specific force $f$ is an inverse square/Newtonian gravity force. Sketched proof: We use the same notation as the Wikipedia page and my other Phys.SE answer. We consider the inside of a thin shell, i.e. $r\leq R$. The total radial force should be zero: $$\begin{align} 0~=~&F_r(r)\cr ~=~&\int ! dF_r\cr \stackrel{(2.4)}{=}&\frac{mM}{4r^2R}~\int_{R-r}^{R+r} ! ds\left[W^{\prime}(s)+(r^2-R^2)u^{\prime}(s)\right]\cr ~=~&\frac{mM}{4r^2R}\left[W(R!+!r)-W(R!-!r)+(r^2-R^2)\left(u(R!+!r)-u(R!-!r)\right)\right] \cr ~=~&\frac{mM}{2rR}\left[W^{\prime}(R)+\frac{r^2}{6}W^{\prime\prime\prime}(R)+(r^2-R^2)\left(u^{\prime}(R)+\frac{r^2}{6}u^{\prime\prime\prime}(R)\right)+{\cal O}(r^4)\right]\cr ~=~&\frac{mM}{2rR}\left[\underbrace{W^{\prime}(R)-R^2u^{\prime}(R)}_{=~0}+r^2 (\ldots)+{\cal O}(r^4)\right].\end{align}\tag{3.1}$$ In particular the ellipsis $(\ldots)$ in eq. (3.1) must vanish: $$\begin{align} 0~=~&(\ldots) \cr ~\stackrel{(3.1)}{=}& \frac{W^{\prime\prime\prime}(R)}{6}+ u^{\prime}(R) -R^2\frac{u^{\prime\prime\prime}(R)}{6} \cr ~\stackrel{(2.2)}{=}&-\frac{1}{6}\frac{d^2(R^2f(R))}{dR^2}-f(R)+R^2\frac{f^{\prime\prime}(R)}{6}\cr ~=~&-\frac{2}{3}\left(2f(R) +Rf^{\prime}(R)\right)\cr ~=~&-\frac{2}{3R}\frac{d(R^2f(R))}{dR}\cr ~\stackrel{(2.2)}{=}&\frac{2W^{\prime\prime}(R)}{3R}.\end{align}\tag{3.2}$$ Hence $$W^{\prime}(R)~\stackrel{(3.2)}{=}~ {\rm constant},\tag{3.3}$$ and therefore the specific force $$f(R)~\stackrel{(2.2)}{=}~-\frac{W^{\prime}(R)}{R^2}~\stackrel{(3.3)}{\propto}~ R^{-2}\tag{3.4}$$ is an inverse square force. $\Box$ Share Improve this answer edited Jun 29, 2021 at 21:05 answered Jul 21, 2018 at 20:47 Qmechanic♦Qmechanic 222k5252 gold badges635635 silver badges2.5k2.5k bronze badges $\endgroup$ 5 $\begingroup$ Thank you Qmechanic for helping me this far. Now how shall we logically prove that $f(R)=kR^{-2}$ is the only solution, i.e. there are no other solutions. Have you proved in your answer. I do not think so. Am I right or wrong? Please have a look at math.stackexchange.com/q/3612111 $\endgroup$ Joe – Joe 2020-04-06 10:16:55 +00:00 Commented Apr 6, 2020 at 10:16 $\begingroup$ Yes, this answer proves that $f(r)=kr^{-2}$ is the only solution. $\endgroup$ Qmechanic – Qmechanic ♦ 2020-04-07 06:40:25 +00:00 Commented Apr 7, 2020 at 6:40 $\begingroup$ Qmechanic : I think the logic goes as follows: (Please point out if I am wrong) $$\text{Suppose there exists $n$ solutions ${f_1(R)=kR^{-2}, f_2(R), f_3(R),......,f_n(R)} $}$$ $$\text{You have only proved that $f_1(R)=kR^{-2}$ }$$ $$\text{So next we have to prove $n=1$, i.e. there exists only one $f(R)=kR^{-2}$} $$ $\endgroup$ Joe – Joe 2020-04-07 09:22:58 +00:00 Commented Apr 7, 2020 at 9:22 $\begingroup$ $f(r)=kr^{-2}$ is not an assumption in my proof; it is a conclusion. $\endgroup$ Qmechanic – Qmechanic ♦ 2020-04-07 10:57:53 +00:00 Commented Apr 7, 2020 at 10:57 $\begingroup$ You started from $F=0$ and reached $f(r)=kr^{-2}$. Now what if we start from $F=0$ and by a different approach, we reach $f(r)=f_2(r)$. Then $f(r)=kr^{-2}$ and $f(r)=f_2(r)$ will both be solutions. How can we eliminate the possibility that we may get $f(r)$ other than $kr^{-2}$? $\endgroup$ Joe – Joe 2020-04-07 11:11:53 +00:00 Commented Apr 7, 2020 at 11:11 Add a comment \| Start asking to get answers Find the answer to your question by asking. Ask question Explore related questions forces classical-mechanics newtonian-gravity symmetry potential-energy See similar questions with these tags. Featured on Meta Introducing a new proactive anti-spam measure Spevacus has joined us as a Community Manager stackoverflow.ai - rebuilt for attribution Community Asks Sprint Announcement - September 2025 Linked 2 How is Newtonian gravity derived from the converse of shell theorem? 2 What kind of forces would follow only the second part of shell theorem? What is the connection between Newton's Shell Theorem and Bertrand's Theorem? 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13231	https://ajkdblog.org/2025/03/01/nephmadness-2025-minimal-change-dz-region/	# AJKD Blog Official Blog of the American Journal of Kidney Diseases #NephMadness 2025: Minimal Change Disease Region Posted on March 1, 2025 by AJKDblog in NephMadness // 0 Comments Submit your picks! \| @NephMadness \| @nephmadness.bsky.social \| NephMadness 2025 Selection Committee Member: Susan Samuel @drsusansamuel Susan Samuel is a Clinician Scientist and Pediatric Nephrologist at the BC Children’s Hospital, in Vancouver, Canada. She received her undergraduate medical degree from the University of British Columbia, completed her postgraduate medical training in pediatrics and nephrology at SickKids Hospital in Toronto, and completed her MSc degree with specialization in Clinical Epidemiology at the University of Toronto. Her research goals are to improve care and outcomes of children with kidney disease and kidney failure. She leads the multi-centre Canadian Childhood Nephrotic Syndrome Project, a multi-centre initiative to improve care of children with nephrotic syndrome. She is passionate about mentoring and training individuals to pursue careers in health research, and serves as the Director of the ENRICH program. Writer: Mallory Downie @mallorydownie Mallory Downie is an Assistant Professor of Pediatrics in the Division of Nephrology at McGill University and Junior Scientist at the Research Institute of the McGill University Health Centre. She has trained in genetics, pediatrics, and nephrology. She is currently the principal investigator of a bioinformatics lab working to identify new genes and genetic risk factors in childhood kidney disease. Writer: Robert Myette @RobertMyette Robert Myette is a pediatric nephrologist-scientist pursuing fundamental and translational basic science research work at the Children’s Hospital of Eastern Ontario Research Institute. His work is targeted at understanding the molecular underpinnings of pediatric nephrotic syndrome. Competitors for the Minimal Change Disease Region Team 1: Minimal Change Disease Diagnosis and Pathogenesis versus Team 2: Minimal Change Disease Relapse Image generated by Evan Zeitler using DALLE-E 3, accessed via ChatGPT at February 2025. After using the tool to generate the image, Zeitler and the NephMadness Executive Team reviewed and take full responsibility for the final graphic image. Team 1: Minimal Change Disease Diagnosis and Pathogenesis Copyright: Mateusz Lachowski Photo / Shutterstock Introduction Minimal change disease (MCD) is characterized by injury to podocytes and features massive proteinuria, hypoalbuminemia, and edema. Though MCD is diagnosed by kidney biopsy in adults, children with steroid sensitive nephrotic syndrome (SSNS) are infrequently biopsied because they are presumed to have MCD; thus, MCD and SSNS are often considered synonymous. The pathogenesis of MCD/SSNS is yet unknown. Childhood nephrotic syndrome is the most common glomerulopathy in children, and its clinical classification is primarily based on the response to glucocorticoid treatment within the first year following diagnosis. SSNS is defined as complete remission after four weeks of treatment with the recommended dose of steroids. Patients are classified as infrequent relapsers if they experience fewer than two relapses within six months or fewer than four relapses within twelve months. Frequent relapsing nephrotic syndrome (FRNS) are those with more than two relapses within six months or greater than or equal to three relapses within twelve months. Steroid-dependent nephrotic syndrome (SDNS) is characterized by two consecutive relapses while on glucocorticoid therapy or within 14 days of discontinuing glucocorticoid treatment. Patients who fail to achieve complete remission after four weeks of the recommended glucocorticoid dose are classified as steroid-resistant nephrotic syndrome (SRNS). MCD is a puzzling disease. The disease shows no apparent sign of inflammation in the kidney, yet MCD responds to immunosuppressive drugs such as corticosteroids, strongly suggesting an immune pathogenesis. Moreover, the onset of the disease is typically associated with an environmental exposure to another immune-activating process, such as infection, vaccination, allergy, systemic autoimmunity, or cancer. Genome-wide association studies (GWAS) in MCD and SSNS also show the strongest genetic risk loci to be at the human leukocyte antigen (HLA), which encodes cell-surface proteins responsible for regulation of the immune system. For more than 30 years, MCD was considered a T cell-mediated process in that T cells were thought to secrete a circulating permeability factor that injured the podocytes. However, this circulating factor has never been identified. Evidence from the last several years points more and more toward the role of B cells and auto-antibody formation in the pathogenesis of the disease. B cells in MCD A potential role of B cells in the pathobiology of MCD first emerged due to the therapeutic effect of B cell-depleting anti-CD20 antibodies (rituximab, ofatumumab, and most recently, obinutuzumab) in inducing and maintaining remission in children with SSNS. Moreover, the association of MCD occurrence with non-Hodgkin and Hodgkin lymphoma where tumor cells derive from mature B cells, and with Epstein Barr Virus infection (EBV), which mainly targets B cells, provides further compelling evidence. The role of B cells in the pathophysiology of MCD was recently substantiated with the discovery of anti-nephrin antibodies in children and adults with active MCD and atypical B cells in children with active SSNS. Anti-nephrin antibodies Nephrin is an important component of the slit diaphragm, the specialized cell junctions between mature podocytes and the site of injury in MCD. Rare monogenic mutations (minor allele frequency <1%) in NPHS1, that cause lack of nephrin localization to the cell surface, cause what is termed Finnish type congenital nephrotic syndrome, and common genetic variants (minor allele frequency >1%) in NPHS1 have more recently been associated with SSNS in genome-wide association studies. In a recent study by Watts et al, authors used a custom-developed indirect enzyme-linked immunosorbent assay (ELISA) to demonstrate that 18 of 62 (29%) of patients with MCD and active disease had anti-nephrin antibodies in their serum. Interestingly, anti-nephrin antibodies were reduced or completely absent in patients with MCD during complete or partial remission. The authors also identified IgG colocalizing with nephrin, which they speculated to represent in situ nephrin antibody binding in patients with circulating anti-nephrin antibodies. These results were expanded across other podocytopathies and centers in a more recent study by Hengel et al, which found anti-nephrin antibodies in 46 of 105 (44%) of adults with MCD and 94 of 182 (52%) of children with SSNS. Antibody measurements were as high as 69% and 90% in adults and children, respectively, who had active disease, some on no immunosuppression, therefore correlating with disease activity. Anti-nephrin antibodies were either absent or found in much smaller proportions of patients with other immune-mediated glomerulopathies. Overall, the possibility of anti-nephrin antibodies as a novel glomerular biomarker for a subset of MCD is very promising and may pave the way for use of anti-nephrin antibodies, not only for diagnosis of MCD but also as a potential marker of response to therapy or for predicting an impending relapse or recurrence post-transplantation – much like is done with anti-PLA2R antibodies in membranous nephropathy. Atypical B cells B cells generate antibodies, like the anti-nephrin antibodies mentioned above. Building on the hypothesis that MCD is an autoimmune disease caused by antibodies, Al-Aubodah et al demonstrated a distinct B cell signature in children with active SSNS. Through the use of single-cell RNA sequencing (scRNA-seq), the authors demonstrated that the expansion of two specific B cell populations in the extrafollicular B cell pathway – atypical memory B cells (atBCs) and short-lived antibody-secreting cells (ASCs) – was evident in children with active disease. They further demonstrated that treatment of disease with corticosteroids and rituximab targeted these specific SSNS-associated B cell populations (ASCs only), with rituximab providing more specific and extensive coverage. This work provides further support in the use and development of B cell-targeting therapies in the treatment of SSNS/MCD. Moreover, the future investigation of ASCs as biomarkers for disease activity is also very promising. Summary Taken together, the discovery of anti-nephrin antibodies and the characterization of the distinct B cell signature of active MCD and SSNS confirms that B cells play an important role in the pathogenesis of this disease. These discoveries provide valuable insight into the etiology of a disease that has been poorly understood for decades. These findings provide a mechanistic rationale for further development of B cell-targeted therapies and for further characterization of these potential biomarkers in predicting disease activity and treatment response. COMMENTARY BY NASIM WIEGLEY: Anti-Nephrin Antibodies – The Breakthrough That Will Transform Minimal Change Disease Management COMMENTARY BY GABRIEL MIGUEL CARA FUENTES: Beyond “Idiopathic” – Redefining Nephrotic Syndrome for the Modern Era In this episode of The Kidney Chronicles, host Emily Zangla is joined by NephMadness Exec Ana Catalina Alvarez-Elías and pediatric nephrologist Mallory Downie: Episode 36: NephMadness 2025 Minimal Change Disease in Kids Team 2: Minimal Change Disease Relapse Copyright: Tanasan Sungkaew / Shutterstock Nephrotic syndrome (NS) is a podocytopathy characterized by proteinuria, hypoalbuminemia, and edema. Podocyte effacement on histology is a unifying feature. Both pediatric and adult patients with MCD are treated initially with steroids with escalation to steroid-sparing, second-line agents as required. The approach to relapses also usually involves steroids. Adult Nephrotic Syndrome In adults, the approach to treatment during the initial episode of MCD includes high-dose oral steroids, usually prednisone, at a dose of 2 mg/kg/day, with a maximum dose of 80 mg for 4-16 weeks, followed by a taper [KDIGO 2021]. For those patients unable to tolerate steroids, steroid-sparing agents are offered and include cyclophosphamide, calcineurin inhibitors such as tacrolimus, mycophenolate mofetil (MMF), and B cell-depleting therapies such as rituximab [KDIGO 2021]. Steroid response is the cornerstone for both the prognosis of the disease and its clinical classification. Recently, the Nephrotic Syndrome Study Network (NEPTUNE) externally validated a promising urinary biomarker risk ‘score’ which incorporates the following five biomarkers: vitamin D binding protein (VDB), fetuin-A (FetA), transthyretin (TTR), alpha-1 acid glycoprotein 2 (AGP2) and neutrophil gelatinase-associated lipocalin (NGAL). The biomarker ‘score’ was measured in 34 adults with SSNS, and was compared to 24 patients with SRNS. The biomarker ‘score’ was able to predict development of steroid resistance with both a sensitivity and specificity of 0.74 and a receiver operating characteristic (ROC) area under the curve (AUC) of 0.79. Though this AUC implies that this biomarker score is not reliable enough to distinguish disease etiology in an individual patient, if other biomarkers (such as genetic variants or serological tests) become available to clinicians in the future, the clinical utility of this score might be re-examined. Despite these advances, there is still no reliable biomarker available to determine initial steroid responsiveness or frequency of relapse after remission in adults. This is an important consideration given that relapses occur in approximately two-thirds of adults with MCD. Predictive factors for relapse include a younger age of onset, not initially using cyclophosphamide, and shorter glucocorticoid treatment duration. In the event of infrequent relapses of MCD, adults are typically treated with high-dose steroids, followed by rapid taper. For those with frequent relapses or steroid dependence, steroid-sparing therapies such as cyclophosphamide, tacrolimus, MMF, or rituximab are initiated. A study by Heybeli et al suggested that treatment with rituximab may increase the likelihood of discontinuing immunosuppressive agents. This finding contributed to the initiation of the TURING trial, a two-arm, randomized, placebo controlled, phase III clinical trial in the United Kingdom, currently recruiting, which assesses the effectiveness and cost-effectiveness of rituximab. In patients who are steroid-resistant, second-line medications will also be trialed, with calcineurin inhibitors like tacrolimus being the preferred agents. Pediatric Nephrotic Syndrome In children, the initial approach differs in that steroids are the first line agent in all cases. The current International Pediatric Nephrology Association (IPNA) and KDIGO guidelines recommend using 60 mg/m2/day or 2 mg/kg/day for 4-6 weeks (with a maximum dose of 60 mg/day) and 40 mg/m2/ every other day or 1.5 mg/kg/ every other day for 4-6 weeks, for a total duration of 8-12 weeks for initial treatment (2022 IPNA SSNS Guidelines). Overall, recent trials showed no significant benefit in prolonging treatment past 12 weeks with respect to delaying time to first relapse and reducing relapse frequency. Though the older guidelines recommended a longer steroid taper, longer duration and higher cumulative exposure to steroids do not provide significant benefit. Because the pathophysiology of childhood NS is unclear, clinicians often provide prognostic information based on the response to steroid treatment. Using response as a metric helps guide classification, and sometimes clinical decision-making for subsequent treatments including the use of glucocorticoid-sparing agents. Knowledge gaps in the underlying pathogenesis of disease creates variability in clinical practice where clinicians – together with patients and caregivers – choose which steroid-sparing drug may work best in order to reduce relapse frequency and/or maintain remission. Genome-wide association studies have revealed nine genetic risk loci associated with the development of SSNS in children. Each study found the strongest genetic risk locus to be at the HLA (which encodes the proteins of the human immune system). In these studies, there are observed ancestral differences in the genetic risk variants for SSNS among South Asian, East Asian, African, and European children, particularly at the HLA locus. In African populations, APOL1 was found to be specifically associated with SRNS. Urinary biomarkers have also been extensively investigated. For example, a proteomic study comparing pediatric patients with SSNS and SRNS over a two-year follow up period demonstrated that a urine panel including ten different urinary biomarkers predicted steroid resistance more effectively than a single biomarker with a ROC AUC of 0.92. Up to 80% of children with initially steroid-responsive NS will experience relapse. Furthermore, 30-50% will have frequent relapses or become steroid-dependent. The risk for relapse persists even after transitioning from childhood to adulthood. A large population-based study conducted in Israel using health administrative data found that the average age at which children reached long-standing remission was 11 years (411/524 patients). A significant proportion of participants (22%) continued to experience relapse once they reached adulthood (113/524 patients). Predictive factors for relapse in pediatric patients Clinical characteristics and common laboratory biomarkers have been described as potential predictors of prognosis, including younger age at presentation, time to relapse, infections, increased dyslipidemia, microhematuria, and lower albumin levels. However, to date, there are no reliable predictive markers for relapse in children. Specifically, demographic factors, kidney histology, and the presence of initial steroid sensitivity are not useful in predicting relapse rates or the likelihood of long-term remission. The relapse rate varies by ancestry. For instance, children of East/Southeast Asian ancestry exhibit up to six times higher incidence of NS compared to those of European ancestry. Nevertheless, children of East/Southeast Asian ancestry have a lower rate of relapse than children of European descent. Substantial efforts are underway to identify a non-invasive, dependable, measurable predictor of relapses. It is currently debated whether MCD and focal segmental glomerulosclerosis (FSGS) are a continuum of the same immune-mediated disease. Given this, we have been able to apply evidence from FSGS research to MCD, as it pertains to the elusive circulating factor. First hypothesized by Gentil et al many years ago, a serum ‘factor’ was thought to play a role in relapse. This hypothesis is supported by evidence from animal models, which show proteinuria when rats are exposed to plasma from patients with NS. Further, case reports of women with FSGS showing increased fetal kidney echogenicity have suggested transplacental exposure of the circulating factor from the mother to the fetus. Perhaps the most convincing insights were from isolated cases reporting the need for kidney allograft removal due to massive proteinuria recurrence and severe kidney function decline in patients with FSGS. Subsequently, there was recovery of kidney function after re-transplanting the allograft to a patient without FSGS. Given the evidence around a presumed circulating factor, many studies are now trying to determine if biomarkers in the serum or urine can be identified as the circulating factor, or at least as a mechanism to predict relapse. Several urinary biomarkers have been studied in the past in both adults and children, and some of them have shown promising performance as markers of steroid sensitivity, including VDBP, NGAL, alpha 1-B glycoprotein (A1BG), and CD80 (also known as B7-1). However, these biomarkers have not been studied in terms of relapse prediction. Regarding serum biomarkers, hemopexin has been studied as a putative circulating factor and marker of relapse. More recently, anti-nephrin antibodies have been identified in the serum during relapse (as discussed by Team 1), and might represent both a biomarker of relapse, as well as the circulating factor in some cases of MCD. Relapse treatment in pediatrics The approach to relapse includes treating again with prednisone 60 mg/m2 daily (maximum 60 mg/day) until the urine is negative for 3 days consecutively. Thereafter, 40 mg/m2/every other day for 4 weeks is prescribed, and then stopped. Importantly, there was a historic treatment approach to preventing relapse by giving low dose prednisone to children with NS who were experiencing an upper respiratory tract infection (URTI). The PREDNOS2 trial revealed that administering 6 days of daily low dose prednisone at the time of URTI did not reduce the risk of relapse. Though the 2021 KDIGO guidelines still recommend administering low dose prednisone during URTI, the up-to-date IPNA guidelines for managing children with steroid sensitive NS do not recommend the use of low-dose prednisone at the onset of upper respiratory tract infection; however, they do suggest considering a short course of low dose daily prednisone when children are already in a relapse and are on alternate-day steroids when challenged with an upper respiratory tract infection. Currently, there is no conclusive evidence to help with selection of a second line agent in the context of steroid resistance or frequent relapse. Common strategies include attempting to switch to low dose alternate day prednisone, maintaining low dose daily prednisone, adding calcineurin inhibitors, cyclophosphamide, levamisole, MMF, and rituximab. The choice is made through shared decision making with the family, and/or patient, and balancing the risks and benefits while attempting to control the disease and minimize the exposure to prednisone. Ongoing research is dedicated to determining which agent would be best; however, no single clinical trial has yet compared all available options head to head. In recent years, at least six clinical trials involving the pediatric population with NS have been published, proving some evidence on the efficacy of rituximab compared to either placebo or other steroid-sparing therapies. Although the interventional studies have been small, rituximab is increasingly used as a steroid-sparing agent in various clinical presentations of NS. This is based on the assumption that its effectiveness stems from its ability to deplete B cells. This trend has been most prominent in high-resourced countries where access to the drug is more readily available. However, from a global perspective, the cost and availability of medication significantly influences treatment decisions made by healthcare providers and families. One of the more affordable alternatives, although not available for human use in the United States or Canada (where its use is restricted to livestock), is levamisole. Levamisole, an antiparasitic agent listed on the World Health Organization’s (WHO) Essential Medicines List, is widely used in the UK and Europe, as well as South American, African, and other low- and middle-income countries as a steroid-sparing option following relapse. A multicenter, international, randomized, double-blind, placebo-controlled trial conducted in patients with SSNS across five European countries and India found that, during the first 100 days post-diagnosis, the time to relapse was similar between the levamisole and placebo groups. However, the risk of relapse between days 100 and 365 (12 months) was 78% lower in the levamisole group (HR 0.22, 95%CI 0.11-0.43). A second non-inferiority trial showed that levamisole use in frequently relapsing NS resulted in a lower relapse frequency (22.5%) compared to prednisolone (40%). Both groups demonstrated similar rates of sustained remission, with levamisole showing a lower frequency of adverse events. Conclusion The unresolved pathophysiology of MCD and SSNS presents significant challenges in identifying reliable biomarkers for predicting relapse risk, treatment response, and long-term prognosis. Ongoing investigations are focusing on various urinary and serum biomarkers linked to immune response pathways, and ancestry. The development of non-invasive tools to assist healthcare providers in clinical decision-making is crucial, particularly in the pediatric population. Relapses are primarily treated with steroids in pediatric patients, which increases the risk of adverse effects including delayed growth and bone health impairment. Numerous glucocorticoid-sparing therapies are currently being studied to identify the most effective treatment options based on clinical presentation, individual risk factors, and affordability of the drug. The KDIGO 2021 and IPNA guidelines offer robust and reliable recommendations to the international community, providing evidence-based treatment options. However, larger, multicenter, international randomized controlled trials comparing these therapies side by side are essential for refining treatment recommendations. – Executive Team Members for this region: Ana Catalina Alvarez-Elías@catochita–@catochita.bsky.social and Matthew Sparks @Nephro_Sparks – @nephrosparks.bsky.social \| Meet the Gamemakers How to Claim CME and MOC US-based physicians can earn 1.0 CME credit and 1.0 MOC per region through NKF PERC (detailed instructions here). The CME and MOC activity will expire on June 1, 2025. 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Alvarez Autoimmunity cancer corticosteroids edema FirstRound 2025 GWAS HLA infection MalloryDownie MCD minimal change disease NephMadness NephMadness 2025 NephMadness2025 nephrotic syndrome NM25 NM25MCD proteinuria relapse rituximab RobertMyette serum biomarkers Sparks SusanSamuel vaccination Privacy & Cookies: This site uses cookies. By continuing to use this website, you agree to their use. To find out more, including how to control cookies, see here: Cookie Policy Leave a ReplyCancel reply Copyright © 2025 Powered by WordPress.com. Discover more from AJKD Blog Subscribe now to keep reading and get access to the full archive. Continue reading Loading Comments...
13232	https://www.gradesaver.com/textbooks/science/chemistry/chemistry-the-central-science-13th-edition/chapter-16-acid-base-equilibria-exercises-page-715/16-1a	Chemistry: The Central Science (13th Edition) by Brown, Theodore E.; LeMay, H. Eugene; Bursten, Bruce E.; Murphy, Catherine; Woodward, Patrick; Stoltzfus, Matthew E. Chapter 16 - Acid-Base Equilibria - Exercises - Page 715: 16.1a Answer Work Step by Step Update this answer! You can help us out by revising, improving and updating this answer. After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
13233	https://artofproblemsolving.com/wiki/index.php/Modular_arithmetic/Introduction?srsltid=AfmBOorDB2sIQJLyFwkfPzZOvSrZ_ZzgGKgRedlTD_TJKi509-Q5gh9b	Art of Problem Solving Modular arithmetic/Introduction - AoPS Wiki Art of Problem Solving AoPS Online Math texts, online classes, and more for students in grades 5-12. Visit AoPS Online ‚ Books for Grades 5-12Online Courses Beast Academy Engaging math books and online learning for students ages 6-13. Visit Beast Academy ‚ Books for Ages 6-13Beast Academy Online AoPS Academy Small live classes for advanced math and language arts learners in grades 2-12. Visit AoPS Academy ‚ Find a Physical CampusVisit the Virtual Campus Sign In Register online school Class ScheduleRecommendationsOlympiad CoursesFree Sessions books tore AoPS CurriculumBeast AcademyOnline BooksRecommendationsOther Books & GearAll ProductsGift Certificates community ForumsContestsSearchHelp resources math training & toolsAlcumusVideosFor the Win!MATHCOUNTS TrainerAoPS Practice ContestsAoPS WikiLaTeX TeXeRMIT PRIMES/CrowdMathKeep LearningAll Ten contests on aopsPractice Math ContestsUSABO newsAoPS BlogWebinars view all 0 Sign In Register AoPS Wiki ResourcesAops Wiki Modular arithmetic/Introduction Page ArticleDiscussionView sourceHistory Toolbox Recent changesRandom pageHelpWhat links hereSpecial pages Search Modular arithmetic/Introduction Modular arithmetic is a special type of arithmetic that involves only integers. This goal of this article is to explain the basics of modular arithmetic while presenting a progression of more difficult and more interesting problems that are easily solved using modular arithmetic. Contents [hide] 1 Introductory Video 2 Understand Modular Arithmetic 3 Residue 4 Congruence 4.1 Examples 4.2 Sample Problem 4.2.1 Solution: 4.2.2 Another Solution: 4.2.3 Another Solution: 5 Making Computation Easier 5.1 Addition 5.1.1 Problem 5.1.2 Solution 5.1.3 Why we only need to use remainders 5.1.4 Solution using modular arithmetic 5.1.5 Addition rule 5.1.6 Proof of the addition rule 5.2 Subtraction 5.2.1 Problem 5.2.2 Solution 5.2.3 Subtraction rule 5.3 Multiplication 5.3.1 Problem 5.3.2 Solution 5.3.3 Solution using modular arithmetic 5.3.4 Multiplication rule 5.4 Exponentiation 5.4.1 Problem #1 5.4.2 Problem #2 5.4.3 Problem #3 6 Summary of Useful Facts 7 Problem Applications 8 Applications of Modular Arithmetic 9 Resources 10 See also Introductory Video Understand Modular Arithmetic Let's use a clock as an example, except let's replace the at the top of the clock with a . This is the way in which we count in modulo 12. When we add to , we arrive back at . The same is true in any other modulus (modular arithmetic system). In modulo , we count We can also count backwards in modulo 5. Any time we subtract 1 from 0, we get 4. So, the integers from to , when written in modulo 5, are where is the same as in modulo 5. Because all integers can be expressed as , , , , or in modulo 5, we give these integers their own name: the residue classes modulo 5. In general, for a natural number that is greater than 1, the modulo residues are the integers that are whole numbers less than : This just relates each integer to its remainder from the Division Theorem. While this may not seem all that useful at first, counting in this way can help us solve an enormous array of number theory problems much more easily! Residue We say that is the modulo-residue of when , and . Congruence There is a mathematical way of saying that all of the integers are the same as one of the modulo 5 residues. For instance, we say that 7 and 2 are congruent modulo 5. We write this using the symbol : In other words, this means in base 5, these integers have the same residue modulo 5: The (mod 5) part just tells us that we are working with the integers modulo 5. In modulo 5, two integers are congruent when their difference is a multiple of 5. In general, two integers and are congruent modulo when is a multiple of . In other words, when is an integer. Otherwise, , which means that and are not congruent modulo . Examples because is a multiple of . because , which is an integer. because , which is not a multiple of . because , which is not an integer. Sample Problem Find the modulo residue of . Solution: Since R , we know that and is the modulo residue of . Another Solution: Since , we know that We can now solve it easily and is the modulo residue of Another Solution: We know is a multiple of since is a multiple of . Thus, and is the modulo residue of . Making Computation Easier We don't always need to perform tedious computations to discover solutions to interesting problems. If all we need to know about are remainders when integers are divided by , then we can work directly with those remainders in modulo . This can be more easily understood with a few examples. Addition Problem Suppose we want to find the units digit of the following sum: We could find their sum, which is , and note that the units digit is . However, we could find the units digit with far less calculation. Solution We can simply add the units digits of the addends: The units digit of this sum is , which must be the same as the units digit of the four-digit sum we computed earlier. Why we only need to use remainders We can rewrite each of the integers in terms of multiples of and remainders: . When we add all four integers, we get At this point, we already see the units digits grouped apart and added to a multiple of (which will not affect the units digit of the sum): . Solution using modular arithmetic Now let's look back at this solution, using modular arithmetic from the start. Note that Because we only need the modulo residue of the sum, we add just the residues of the summands: so the units digit of the sum is just . Addition rule In general, when , and are integers and is a positive integer such that the following is always true: . And as we did in the problem above, we can apply more pairs of equivalent integers to both sides, just repeating this simple principle. Proof of the addition rule Let , and where and are integers. Adding the two equations we get: Which is equivalent to saying Subtraction The same shortcut that works with addition of remainders works also with subtraction. Problem Find the remainder when the difference between and is divided by . Solution Note that and . So, Thus, so 1 is the remainder when the difference is divided by . (Perform the subtraction yourself, divide by , and see!) Subtraction rule When , and are integers and is a positive integer such that the following is always true: Multiplication Modular arithmetic provides an even larger advantage when multiplying than when adding or subtracting. Let's take a look at a problem that demonstrates the point. Problem Jerry has boxes of soda in his truck. The cans of soda in each box are packed oddly so that there are cans of soda in each box. Jerry plans to pack the sodas into cases of cans to sell. After making as many complete cases as possible, how many sodas will Jerry have leftover? Solution First, we note that this word problem is asking us to find the remainder when the product is divided by . Now, we can write each and in terms of multiples of and remainders: This gives us a nice way to view their product: Using FOIL, we get that this equals We can already see that each part of the product is a multiple of , except the product of the remainders when each and are divided by 12. That part of the product is , which leaves a remainder of when divided by . So, Jerry has sodas leftover after making as many cases of as possible. Solution using modular arithmetic First, we note that Thus, meaning there are sodas leftover. Yeah, that was much easier. Multiplication rule When , and are integers and is a positive integer such that The following is always true: . Exponentiation Since exponentiation is just repeated multiplication, it makes sense that modular arithmetic would make many problems involving exponents easier. In fact, the advantage in computation is even larger and we explore it a great deal more in the intermediate modular arithmetic article. Note to everybody: Exponentiation is very useful as in the following problem: Problem #1 What is the last digit of if there are 1000 7s as exponents and only one 7 in the middle? We can solve this problem using mods. This can also be stated as . After that, we see that 7 is congruent to -1 in mod 4, so we can use this fact to replace the 7s with -1s, because 7 has a pattern of repetitive period 4 for the units digit. is simply 1, so therefore , which really is the last digit. Problem #2 What are the tens and units digits of ? We could (in theory) solve this problem by trying to compute , but this would be extremely time-consuming. Moreover, it would give us much more information than we need. Since we want only the tens and units digits of the number in question, it suffices to find the remainder when the number is divided by . In other words, all of the information we need can be found using arithmetic mod . We begin by writing down the first few powers of mod : A pattern emerges! We see that So for any positive integer , we have (mod ). In particular, we can write . By the "multiplication" property above, then, it follows that (mod ). Therefore, by the definition of congruence, differs from by a multiple of . Since both integers are positive, this means that they share the same tens and units digits. Those digits are and , respectively. Problem #3 Can you find a number that is both a multiple of but not a multiple of and a perfect square? No, you cannot. Rewriting the question, we see that it asks us to find an integer that satisfies . Taking mod on both sides, we find that . Now, all we are missing is proof that no matter what is, will never be a multiple of plus , so we work with cases: This assures us that it is impossible to find such a number. Summary of Useful Facts Consider four integers and a positive integer such that and . In modular arithmetic, the following identities hold: Addition: . Subtraction: . Multiplication: . Division: , where is a positive integer that divides and . Exponentiation: where is a positive integer. Problem Applications Applications of Modular Arithmetic Modular arithmetic is an extremely flexible problem solving tool. The following topics are just a few applications and extensions of its use: Divisibility rules Linear congruences Resources The AoPS Introduction to Number Theory by Mathew Crawford. The AoPS Introduction to Number Theory Course. Thousands of students have learned more about modular arithmetic and problem solving from this 12 week class. 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13234	https://www.windings.com/post/innovations-in-magnet-retention-for-electric-motors-in-advanced-air-mobility/	Skip to content Windings Inc. August 29, 2024 Innovations in Magnet Retention for Electric Motors in Advanced Air Mobility Introduction As the advanced air mobility (AAM) industry rapidly evolves, the demand for lightweight, high-performance electric motors has never been greater. These motors are at the heart of electric vertical take-off and landing (VTOL) aircraft, air taxis, and drones that promise to redefine transportation in urban environments. One of the most critical aspects of electric motor design, particularly for the extreme demands of AAM applications, is magnet retention. The ability to securely fasten permanent magnets to the rotor while maintaining minimal weight and maximizing performance is a key challenge that engineers face in this burgeoning industry. This article delves into the latest innovations in magnet retention systems, focusing on how these advancements are enabling the development of lighter, more efficient, and more reliable electric motors for AAM vehicles. By exploring the materials, technologies, and design approaches that are shaping the future of magnet retention, we can better understand the pivotal role these innovations play in advancing air mobility. The Importance of Magnet Retention in AAM Electric Motors Permanent magnets are a core component of many electric motor designs, particularly in brushless DC (BLDC) motors and permanent magnet synchronous motors (PMSMs), which are commonly used in AAM applications. These magnets generate the magnetic fields that interact with the motor windings to produce torque, driving the rotation of the motor’s rotor. In high-speed, high-power applications like AAM, the forces acting on these magnets are substantial. Centrifugal forces, coupled with rapid acceleration and deceleration, create significant stress on the magnets, which must remain securely attached to the rotor to ensure continuous operation. Failure of magnet retention can lead to catastrophic motor failure, resulting in potential safety risks, especially in flight-critical systems like those used in AAM vehicles. Moreover, the need for weight reduction in AAM adds another layer of complexity to magnet retention. Traditional methods that might add significant weight to the motor are no longer viable. Engineers must innovate to develop retention systems that are both lightweight and robust, capable of withstanding the extreme conditions of AAM operations without compromising performance. Traditional Magnet Retention Methods Historically, magnet retention in electric motors has been achieved through a variety of methods, including adhesives, mechanical fastening, and metal sleeves. Each of these approaches has its advantages and limitations, particularly in the context of AAM. Adhesives Adhesive bonding is one of the most common methods for securing magnets to the rotor. High-strength adhesives, often epoxy-based, are applied between the magnet and the rotor surface, creating a bond that holds the magnet in place. Adhesives are favored for their simplicity and minimal impact on the motor’s weight and size. However, adhesive bonding has its drawbacks. The bond strength can degrade over time, especially when exposed to high temperatures, which are common in high-speed electric motors. Additionally, adhesives can suffer from fatigue under the constant cycling of mechanical stresses, leading to potential failure in critical applications. While suitable for many lower-stress environments, adhesives alone may not provide the reliability needed for AAM applications. 2. Mechanical Fastening Mechanical retention methods involve physically securing the magnets to the rotor using clips, slots, or other fastening mechanisms. These methods can provide a more reliable attachment than adhesives alone, as they are less susceptible to environmental factors like temperature and humidity. However, mechanical fastening typically adds weight to the motor and can increase the complexity of the rotor design. The additional components required for mechanical retention can also increase the overall size of the motor, which is a significant disadvantage in weight-sensitive AAM applications. Furthermore, the precision required to implement these methods can drive up manufacturing costs. 3. Metal Sleeves Metal sleeves are another traditional approach to magnet retention. In this method, a metal sleeve is placed around the rotor, encasing the magnets and holding them in place through mechanical compression. This method is effective in high-speed applications, as the sleeve provides a strong, durable barrier that prevents the magnets from becoming dislodged. The primary disadvantage of metal sleeves is their weight. Metal, even in thin layers, adds significant mass to the motor, which is particularly detrimental in AAM applications where weight is critical. Additionally, the conductive nature of metals can introduce eddy current losses, reducing the efficiency of the motor. Innovations in Lightweight Magnet Retention Given the limitations of traditional methods, the AAM industry has driven the development of innovative magnet retention techniques that address the dual challenges of weight reduction and reliability. These advancements are critical in enabling the next generation of electric motors for AAM applications. Carbon Fiber Roving One of the most promising innovations in magnet retention is the use of carbon fiber roving. Carbon fiber is renowned for its high strength-to-weight ratio, making it an ideal material for applications where both durability and weight savings are paramount. In the context of magnet retention, carbon fiber roving involves wrapping high-tension carbon fiber strands around the rotor, securing the magnets in place. Advantages of Carbon Fiber Roving: Lightweight: Carbon fiber is significantly lighter than metal, which helps reduce the overall weight of the motor. High Strength: The tensile strength of carbon fiber is exceptionally high, providing a secure hold on the magnets even at high rotational speeds. Thermal Stability: Carbon fiber can withstand high temperatures, maintaining its mechanical properties under the extreme conditions of AAM operations. Low Eddy Current Losses: Unlike metal, carbon fiber is non-conductive, which minimizes eddy current losses and improves motor efficiency. Challenges and Considerations: Manufacturing Complexity: The process of winding carbon fiber roving onto a rotor requires precise control of tension and alignment, making it a more complex and potentially costly manufacturing process. Material Costs: Carbon fiber is more expensive than traditional materials like steel or aluminum, which can increase the cost of the motor. Despite these challenges, carbon fiber roving represents a significant step forward in magnet retention technology, particularly for applications where weight reduction is critical. As manufacturing techniques improve and costs decrease, it is likely to become a standard solution in high-performance electric motors for AAM. Advanced Composite Materials Beyond carbon fiber, other advanced composite materials are being explored for use in magnet retention. These materials, which often combine multiple types of fibers with resin matrices, offer unique properties that can be tailored to specific application needs. For example, composites that incorporate aramid fibers (such as Kevlar) can provide exceptional impact resistance, which is valuable in applications where the motor may be subject to sudden shocks or vibrations. Additionally, composites that integrate ceramic fibers can offer enhanced thermal resistance, making them suitable for motors that operate at extremely high temperatures. Advantages of Advanced Composites: Customizability: Composite materials can be engineered to meet specific performance requirements, offering a high degree of flexibility in motor design. Strength and Durability: Composites can match or exceed the strength of traditional materials while being significantly lighter. Resistance to Environmental Degradation: Many composites are resistant to corrosion, moisture, and other environmental factors that can affect the longevity of motor components. Challenges and Considerations: Cost and Availability: Advanced composites can be costly to produce, and their availability may be limited depending on the specific materials and manufacturing processes required. Processing Requirements: The curing and molding processes for composites can be time-consuming and require specialized equipment, which may increase production time and costs. The use of advanced composites in magnet retention is still an emerging field, but the potential benefits make it a compelling area of research and development for AAM applications. Additive Manufacturing (3D Printing) of Retention Systems Additive manufacturing, commonly known as 3D printing, has opened up new possibilities for magnet retention systems by enabling the creation of highly complex and customized components that would be difficult or impossible to produce using traditional manufacturing methods. Advantages of Additive Manufacturing: Challenges and Considerations: 3D printing allows for the creation of intricate retention systems that optimize the distribution of material around the magnets, minimizing weight while maximizing strength. Material Efficiency: Additive manufacturing can reduce material waste by building components layer by layer, using only the necessary amount of material. Rapid Prototyping: The ability to quickly produce and test different designs using 3D printing accelerates the development process, allowing engineers to optimize retention systems more effectively. Challenges and Considerations: Material Limitations: While 3D printing is highly versatile, not all materials are suitable for additive manufacturing. The selection of materials that offer the necessary strength and thermal properties for magnet retention is currently limited. Surface Finish and Precision: Depending on the printing technology used, the surface finish of 3D-printed components may require additional processing to achieve the required tolerances for high-performance motors. Additive manufacturing is an exciting area of innovation that holds great promise for the future of magnet retention. As the technology advances and more materials become available, it is likely to play an increasingly important role in the production of lightweight, high-performance electric motors. Hybrid Retention Systems Hybrid retention systems combine multiple retention methods to leverage the strengths of each while mitigating their respective weaknesses. For example, a hybrid system might use adhesive bonding in conjunction with a lightweight composite sleeve or carbon fiber roving. This approach can provide a more secure and reliable attachment than any single method alone, while still achieving the desired weight reduction. Advantages of Hybrid Systems: Enhanced Reliability: By combining different retention methods, hybrid systems can offer multiple layers of security, reducing the risk of magnet detachment. Optimized Performance: Hybrid systems can be tailored to balance weight, strength, and thermal properties, resulting in a motor that is optimized for the specific demands of AAM applications. Challenges and Considerations: Complexity: Hybrid systems can be more complex to design and manufacture, requiring careful coordination of different materials and processes. Cost: The use of multiple materials and methods can increase the overall cost of the motor, particularly if advanced composites or specialized adhesives are involved. Hybrid retention systems are an area of active research and development, offering the potential to create motors that meet the rigorous demands of AAM while maintaining a lightweight and efficient design. Conclusion As the advanced air mobility industry continues to grow, the need for lightweight, reliable electric motors becomes increasingly critical. Innovations in magnet retention systems are at the forefront of this effort, enabling the development of motors that can withstand the extreme conditions of AAM while minimizing weight. From carbon fiber roving and advanced composites to additive manufacturing and hybrid systems, these innovations represent the cutting edge of electric motor design. By embracing these advancements, engineers can create motors that not only meet the current demands of AAM but also push the boundaries of what is possible in the future. As technology continues to evolve, the motors powering the next generation of air mobility vehicles will be lighter, stronger, and more efficient than ever before, driving the industry toward new heights. Stay Up To Date Join Our Newsletter "" indicates required fields
13235	https://www.youtube.com/watch?v=Z3cxk13kqnY	5.1: Finding a formula for the nth partial sum \| Wellesley College Calc. 2 Professor Fernandez' Math Videos 311 subscribers 21 likes Description 3025 views Posted: 4 Jan 2023 This video works through several examples of finding the formula for the nth partial sum of an infinite series. BOOKS: If you liked this video, you might enjoy my books published by Princeton University Press: - Everyday Calculus ( - The Calculus of Happiness ( - Calculus Simplified ( - Calculus 2 Simplified ( Learn more about all these books on my site ( ADDITIONAL RESOURCES: Visit my site ( for interactive graphs, practice problems, and additional resources for helping you learn calculus. 2 comments Transcript: Introduction hi this is Professor Fernandez in this video we're going to work out an example on finding partial sums for Series this is an example from lesson five in the calculus two notes and if you want to read those notes or download other resources head over to the site and you'll find all these other things there Example so let me zoom into the example and we can get started so what does it say it says find a formula for the nth partial sum of the series below okay great so let me just remind you really quickly what the partial sum of a series is we're talking here about infinite Series so here is the definition down here again from the lesson five notes so the nth partial sum denoted S Sub n capital N of the infinite series a sub n from 1 to Infinity is literally the sum of its first n terms so S Sub n is the sum from n equals 1 to capital N of A7 so it's A1 Plus A2 plus all the way up to a n okay time for a quick example right so what if the infinite series looks like uh 1 over n right what would be S Sub n well would be just the sum of the first n terms of this so This Series starts at one so one plugging in there for n and then plug in the next n value in here so one-half and then add plug in the next value one-third all the way up to the last one over capital n and this over here down here should be a capital N okay um that's S Sub n right most of the time what you want to do is you want to find a closed form formula for S Sub n in other words we would like to be able to say that this equals maybe something over something I don't know rather than leave it as a sum why because you may remember this is also in the lesson five notes by the way if you want to take a look that if the limit as n goes to Infinity of s of n equals l then that's the same as saying that this series a sub n converges to l right so in other words if we can show that the sum the partial of the S partial sum tends to limit right L some number then that is literally what we mean by this particular series converging so partial sums are really at the core of infinite series and convergence of infinite series and then clearly if you want to find the limit as n goes to Infinity of anything it would be nice if you have a formula for it not if it's left in some you know version where there's a bunch of terms that are just being added right so it does pay to find some closed formula for S Sub n okay so we're going to do that in this example that is the point of this example to help you develop that skill to find closed SMN closed form SMN formulas so I'm going to zoom in here let's take a look at the first one so a this infinite series is a really silly infinite Series right but sometimes it's really nice to start with the silly examples first so how do I write out the terms in the series well it's just one plus one plus one plus one all the way forever so how would I find an nth partial sum for this well the way you do this is usually thinking about the sequences right because we can think about the nth partial sums as a sequence the first partial sum would be just the quote sum of the first term right it's just the first term uh the second partial sum is the sum of the first two terms right so that's two the third partial sum is the sum of the first three terms so that's three and so on the fourth partial sum sum of the first four terms that's four and then now we're back to sequences right so we're back to some of the earlier lessons in the course we would like to try to find a pattern for this sequence so that I can therefore down here say oh S Sub n is something what is the pattern and you can see now perhaps why I've started with this really simple series because the pattern is fairly simple right it's just n so whatever this number is is exactly the same as what's on the right hand side so S Sub n is n so this is the answer for part A this is the nth partial sum for this particular series all right great so we started simple let's ratchet up the complexity a little bit um let's take a look at this one so we'll do the same thing we'll write out the terms in the sequence uh n is starting at one so it's minus one to the first minus 1 squared minus 1 cubed so on simplifying a little bit this is minus one plus one and this is minus one and then we can kind of see the alternating nature of this sequence so we'll do the same thing S Sub 1 is the first term S Sub 2 is the sum of the first two that's zero S Sub 3 is the sum of the first three that's negative one S Sub 4 sum of the first four that's zero oops equals zero equals zero all right and so to find the pattern here we're going to have to do a little bit of thinking because looking at again the sequence of partial sums um what do we notice right so first we have negative numbers every odd term and then we have zero every even term so this is a sequence that's doing different things depending on whether the index is even or odd and the numbers themselves are always the same right all the e odd number terms are negative one all the even number terms are zero so that's useful information right so if we just start trying to come up with a SQL a formula for S Sub n we might want to have you know half the sequence be negative one half a sequence be zero how do we do that right so one way you might want to try to do it to do that is to build negative one to the N into here that's going to alternate between plus and minus one and there are lots of zeros here right so plus and minus one one way to get it to be zero is to either add or subtract one you can play around with adding or subtracting if you make n uh something like n plus 1 or n minus 1. so what would this generate right here so if n equals one I would have 1 minus negative one so that would be two so that doesn't give me negative one right so I want to multiply it by a negative sign so that would then give me negative two and then I want to divide it by 2 because then that would then give me negative 1. so that gives me the first term question does this work for the next term let's try it so S2 right negative 1 minus negative 1 squared divided by 2. so I get minus 1 minus negative 1 squared that's 1. divided by two that's zero so yes it does work for the second term so again this is a trickier example like I foreshadowed earlier right this is we started simple with one over here which is very quick and now we ratcheted up the complexity and so we've now found a formula for S of n so we're technically done with this second example but I do want to point one thing out right as has been the case uh with earlier videos in this course with each example I'm trying to teach you something new with this example what I wanted to teach you is trial and error right so it's not always going to be so cut and dry and clear as it was in this example what your S Sub n patterns are and how to quantify those patterns to come up with a formula right trial and error is always a good thing to keep in the back of your mind try things right like we did we started off trying this and we said it doesn't quite work let's modify it this way it almost Works let's modify it that way okay that works right so keep trial and error in the back of your mind as a really useful and totally legitimate way to find S7 formulas um you know and do other things as well we'll talk about that as the course progresses okay how about part C right Part C so we want to find an S of n formula here we'll do the same thing we'll write out the first term that's S1 so when n equals one I get 1 over 1 minus one over one plus one so that's one minus one half okay how about S Sub 2. so S Sub 2 is the sum of the first two terms that one and then notice what this series does right now when n equals two it's one half minus one third okay so this series basically as the terms progress you know whatever was here becomes the the positive uh part of the next term uh and then this numerator is one more this denominator is one more than that one and then the pattern is going to repeat so S3 is going to be all of this minus 1 3 plus and then now we write over this one here and then minus 1 4. again I'm doing this you know explicitly talking it over to build in some more pattern recognition for you sequences in series as I'm sure you've noticed by now is a lot about pattern recognition and really does help to develop that skill okay um so finding a formula for the nth partial sum of this uh series okay uh uh so of you know the SNS that we have so far so how are we going to do this right um one thing you might want to do is you know talking about options here right maybe try to simplify this so this is one half okay so this one is one half plus one half minus one-third right because this is one-half so this is one minus one third okay which is two-thirds all right so then that that's the you know that's S2 right so this is S2 here so that is two thirds so this is two-thirds plus one-third minus one-fourth so this gives us one minus one fourth so that is um uh three-fourths all right so now we've done enough that we can kind of start seeing a pattern one half two thirds three-fourths this is actually a sequence that we worked on in one of the videos in lesson three so if I write over the S uh S Sub n patterns I have one half for S1 I have two thirds for S2 and I have three fourths for S three you could probably predict S4 because we can detect the pattern now right the numerator is the same as the index so this should be a four and the denominators are one more than the numerator so this should be a five and then just writing out the pattern that I just talked about here if the numerator is n then the denominator is n plus one okay so that's my S Sub n formula all right so what I did just now is I showed you how to get this pattern by really just calculating each one of the terms in the sequence of partial sums what if I you know to close out the video give you another way to think about this particular series what if I do something different right I don't calculate is there a way to find the pattern of the partial sums for this particular sequence without calculating the partial sums themselves because you know as you can see that took a lot of time it's taken me all this stalling in the video so I can erase stuff so of course that must have taken a lot of time to write all that stuff in the first place okay so how do I do all of that without writing out doing all those calculations here's another thing you might notice about the sequence here's a minus one half here's a plus one half those terms cancel so 1 minus one third here's a minus one half plus one half cancel minus one third plus one third cancel so one minus a quarter right so you can predict S4 one one so it's going to have a one minus minus minus is going to have a minus and then one over something two here is one more than one three is one more than two four is one more than three so four five so this is leading us to a quote different version of the S Sub n formula right one more than the index so n plus one um which we found through a radically different way we did not have to calculate I mean sure we have to cancel things here that is a version of calculation but you can see the utility of this other way of thinking about the sequence of partial sums in this case okay I said earlier a quote difference you know formula for S of n the one that we derived earlier was n Over N plus one if I go here and find a common denominator right I would make this n plus 1. so I would also make this n plus one then I have n plus 1 minus 1 coming from here which is these cancel n Over N plus one right same one that I got earlier so we have two algebraically equivalent representations of the S Sub n formula for this example example uh C I think it was yep but we got to them in radically different ways right so we will later learn that this particular series that we are talking about this is we're going to learn this in the next lesson this is an example of a telescoping series right as you write out the terms the kind of inner terms quote unquote right the last portion of the previous term and the first portion of the next term you know intuitively speaking those cancel as they did here as they did here leaving you with the first term in the series minus the last term whatever term it is you're writing out the partialism for okay so that's a nice property of this particular type of series called the telescoping series and it's another way that you can as we did here come up with a partial sun thanks for watching
13236	https://www.tuitionkenneth.com/h2-maths-plane-foot-perpendicular	Foot of perpendicular from point to plane Kenneth's page full-time tutor × H2 Maths Formulas, Techniques & Graphs >> Vectors >> 3D Vector Geometry >> Planes >> Foot of perpendicular from point to plane Verify if point lies on plane p:r⋅(−102)=3 p:r⋅⎛⎝⎜−102⎞⎠⎟=3 Any point that lies on the plane must satisfy the equation of the plane. Checking if the point (-1, 1, 1) lies on the plane: (−111)⋅(−102)=1+0+2=3∴(−1,1,1) lies on plane p ⎛⎝⎜−111⎞⎠⎟⋅⎛⎝⎜−102⎞⎠⎟∴(−1,1,1)=1+0+2=3 lies on plane p Checking if the point (1, 1, 1) lies on the plane: (111)⋅(−102)=−1+0+2=1∴(1,1,1) does not lie on plane p ⎛⎝⎜111⎞⎠⎟⋅⎛⎝⎜−102⎞⎠⎟∴(1,1,1)=−1+0+2=1 does not lie on plane p Foot of perpendicular from point to plane In the diagram above, the foot of perpendicular from point QQ to the plane pp is denoted by the point FF. There are two ways to find the coordinates of FF. Given Q(1,1,1) and p:r⋅(−102)=3 Q(1,1,1) and p:r⋅⎛⎝⎜−102⎞⎠⎟=3 Method 1: Point F as intersection between line & plane Form the vector equation of line QFQF, which is parallel to the normal vector and passes through Q: lQF:r=(111)+λ(−102),λ∈RSince F lies on lQF,→OF=(1−λ11+2λ) lQF:rSince FOF−→−=⎛⎝⎜111⎞⎠⎟+λ⎛⎝⎜−102⎞⎠⎟,λ∈R lies on lQF,=⎛⎝⎜1−λ11+2λ⎞⎠⎟ Since FF is a point on the plane, it must satisfy the equation of the plane: Since F lies on p,→OF⋅(−102)=3(1−λ11+2λ)⋅(−102)=3−1+λ+0+2+4λ=31+5λ=35λ=2λ=25→OF=(1−2511+2(25))=(35195)∴.F(35,1,95) Method 2: Projection vector Find a point that satisfies the equation of the plane: (−300)⋅(−102)=3+0+0=3Let A denote the point (-3, 0, 0) on the plane Find the projection vector, →QF →QF=(→QA⋅ˆn)ˆn→QA=→OA−→OQ=(−300)−(111)=(−4−1−1)ˆn=1\|n\|n=1√(−1)2+02+22(−102)=1√5(−102)→QF=[(−4−1−1)⋅1√5(−102)]1√5(−102)=15(−4−1−1)⋅(−102)=154+0+(−2)=25(−102)→OF=→OQ+→QF=(111)+25(−102)=(35195)∴.F(35,1,95)
13237	https://www.chegg.com/homework-help/questions-and-answers/364-find-th-venin-equivalent-circuit-terminals-b-circuit-fig-p364-402-figure-p364-circuit--q40823808	Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on. Question: 3.64 Find the Thévenin equivalent circuit at terminals (a, b) for the circuit in Fig. P3.64. 402 Figure P3.64: Circuit for Problem 3.64. Not the question you’re looking for? Post any question and get expert help quickly. Chegg Products & Services CompanyCompany Company Chegg NetworkChegg Network Chegg Network Customer ServiceCustomer Service Customer Service EducatorsEducators Educators
13238	https://gesicap.com/ebook/wp-content/uploads/2024/05/Libro_Deflexiones_en_Vigas.pdf	1 DEFLEXIONES EN VIGAS TEORÍA Y EJERCICIOS RODGER SALAZAR LOOR DEFLEXIONES EN VIGAS TEORÍA Y EJERCICIOS RODGER SALAZAR LOOR TODOS LOS DERECHOS RESERVADOS: Se autoriza la reproducción de esta obra con fines educativos y otros que no sean comerciales sin permiso escrito previo detentar el derecho de autor, siempre y cuando se mencione la cita de los autores de esta obra. © Salazar Loor, Rodger Benjamin © Ediciones Gesicap. El Carmen, Manabí, Ecuador www.gesicap.com ISBN: 978-9942-626-20-2. Deposito legal: 1ra Edición: Ediciones Gesicap, Calle 24 de julio y Ave 3 de julio, El Carmen, Manabí Ecuador. Copyright © Diciembre 2023. COMO CITAR ESTE LIBRO: Salazar Loor, R. B. (2023). Deflexiones en vigas: teoría y ejercicios. Ediciones GESICAP. 152 pp. EQUIPO EDITORIAL: Edición y Diagramación: Sergio Alejandro Rodríguez Hernández Revisión y Corrección: Xenia Pedraza González. Cubierta y diseño: Sergio Alejandro Rodríguez Hernández Imagen de Cubierta: Rodger Salazar Loor. 2 Índice CAPÍTULO I Método de doble integración ........................................................................... 4 1.1. Deflexión en vigas .................................................................................................... 7 1.2. Condiciones de frontera .......................................................................................... 10 1.3. Convenciones de signos ......................................................................................... 10 1.4. Método de doble integración (M.D.I.) ................................................................... 11 1.4.1. Viga empotrada con carga puntual en el extremo .................................................. 11 1.4.2. Viga empotrada con carga puntual ubicada en un punto determinado ................... 16 1.4.3. Viga empotrada con carga distribuida rectangular completa ................................. 21 1.4.4. Viga empotrada con carga distribuida rectangular parcial desde empotramiento .. 26 1.4.5. Viga empotrada con carga distribuida rectangular parcial desde extremo libre .... 31 1.4.6. Viga empotrada con momento en el extremo ......................................................... 37 1.4.7. Viga empotrada con carga distribuida triangular decreciente total ........................ 41 1.4.8. Viga empotrada con carga distribuida triangular creciente total ............................ 46 1.4.9. Viga apoyada en los extremos con carga puntual ubicada en el centro ................. 50 1.4.10. Viga apoyada en los extremos con carga distribuida rectangular completa ........... 56 1.5. Método de Macaulay .............................................................................................. 62 1.5.1. Pasos de aplicación del método de Macaulay ........................................................ 62 1.6. Problemas ............................................................................................................... 69 CAPÍTULO II Método de superposición ............................................................................. 71 2.1. Método de superposición ........................................................................................ 72 2.2. Problemas ............................................................................................................... 88 CAPÍTULO III Método de Momento de Área ..................................................................... 89 3 3.1. Generalidades ......................................................................................................... 90 3.2. Teorema 1 ............................................................................................................... 91 3.2.1. Criterios de aplicación del Teorema 1 .................................................................... 92 3.3. Teorema 2 ............................................................................................................... 92 3.3.1. Criterios de aplicación del Teorema 2 .................................................................... 93 3.4. Diagrama de momentos por partes ......................................................................... 93 3.5. Problemas ............................................................................................................. 115 CAPÍTULO IV Método de la viga conjugada .................................................................... 117 4.1. Generalidades ....................................................................................................... 118 4.2. Teorema 1 ............................................................................................................. 120 4.3. Teorema 2 ............................................................................................................. 120 4.4. Convención de signos. .......................................................................................... 120 4.5. Problemas ............................................................................................................. 136 CAPÍTULO V Vigas indeterminadas ................................................................................. 138 5.1. Generalidades ....................................................................................................... 139 5.2. Ventajas ................................................................................................................ 140 5.3. Doble integración ................................................................................................. 140 5.4. Superposición ....................................................................................................... 144 5.5. Momento de área .................................................................................................. 146 4 Acerca del autor Ha recibido el título de Ingeniero Mecánico de la Universidad Técnica Estatal de Quevedo en 2015; de Master en Magíster en Diseño mecánico mención en fabricación de autopartes de vehículos de la Universidad Internacional SEK. Ha realizado varias publicaciones de artículos y libros en revistas y repositorios científicos de medio y alto impacto. Sus campos de investigación son el Diseño mecánico, Diseño y simulación computacional, Métodos de análisis multicriterio y Selección de materiales. Actualmente trabaja como docente de la Universidad Técnica Estatal de Quevedo donde ha impartido asignaturas como: Neumática e Hidráulica, Sistema de Flujo de Fluidos, Dinámica de Fluidos, Resistencia de Materiales, Esfuerzos y Deformaciones, Mecánica de los Materiales Básica, Mecánica de los Materiales Avanzada, Cálculo Vectorial, Diseño de Máquinas, Termodinámica Aplicada, Termodinámica y Ondas Mecánicas. Rodger Salazar Loor 5 PREFACIO La ingeniería mecánica es el arte de dar vida a las máquinas, donde cada pieza y cada componente se convierten en los cimientos de la funcionalidad y la eficiencia. Dentro de este mundo de precisión y movimiento, el estudio de las deflexiones en vigas emerge como un pilar fundamental, delineando la resistencia y la estabilidad de estructuras cruciales para la ingeniería moderna. Este libro surge de la necesidad por comprender la mecánica subyacente que dicta cómo las vigas soportan cargas y resisten las fuerzas que moldean nuestro entorno. Se ha diseñado específicamente para estudiantes, ingenieros y entusiastas de la ingeniería mecánica que buscan profundizar en la esencia de cómo las vigas, elementos aparentemente simples, sostienen la complejidad de máquinas y estructuras robustas. Es necesario tener conocimientos preliminares de física, estática y ecuaciones diferenciales para su entendimiento y comprensión. A lo largo de estas páginas, se abordará las teorías y principios fundamentales que rigen las deflexiones en vigas. Desde los conceptos básicos hasta los desafíos más avanzados, este libro ofrece un enfoque exhaustivo para comprender, calcular y aplicar las deflexiones en vigas en el diseño y la optimización de componentes mecánicos. Asimismo, se presenta una serie meticulosa de ejercicios diseñados para desafiar y consolidar su comprensión de los conceptos presentados. 1 CAPÍTULO I MÉTODO DE DOBLE INTEGRACIÓN 7 Objetivos • Comprender los fundamentos teóricos del análisis de vigas mediante el método de doble integración, explorando las condiciones de contorno y las ecuaciones diferenciales asociadas a la flexión de vigas. • Dominar el proceso de resolución paso a paso para aplicar el método de doble integración en el cálculo preciso de las deflexiones en vigas, desde la obtención de las ecuaciones de la línea elástica hasta la interpretación de cómo las vigas se deforman bajo cargas específicas. • Aplicar activamente el método de doble integración en una variedad de problemas y ejemplos prácticos, permitiendo a los lectores una experiencia directa en la resolución de situaciones reales y diversas en ingeniería mecánica. • Desarrollar habilidades para evaluar y validar los resultados obtenidos mediante el método de doble integración, comprendiendo la importancia de la verificación de cálculos y la comprensión de la precisión y limitaciones inherentes a este método en distintos contextos de análisis estructural. 8 1.1. Deflexión en vigas Considérese una viga apoyada en sus extremos que se encuentra sometida a una carga en el centro como se muestra en la Figura 1.1, de manera que al actuar directamente sobre la viga se produce un desplazamiento vertical que la deforma y modifica su geometría original. La forma adoptada por el eje neutro de la viga se convierte en una línea curva denominada curva elástica, mientras que la deformación en el eje y se conoce como deflexión (Rajput, 2018). Figura 1.1. Deflexión en viga Si para la curva generada por la deflexión se toman dos puntos arbitrarios A y B, se puede relacionar la longitud del arco con un ángulo de posición dθ denominado pendiente mediante la Ecuación 1.1. ds = dθρ (Ec. 1.1) Suponiendo que el valor de la longitud del arco es pequeño se podría asumir que ds ≈dx, y sustituyendo esta expresión y expresando el ángulo dθ en términos de dx se obtiene la Ecuación 1.2. dθ dx = 1 ρ (Ec. 1.2) Por otro lado, se puede observar que la tangente entre los puntos A y B y el eje X, produce un ángulo dθ, que al relacionarlo con los desplazamientos en x e y se obtiene la Ecuación 1.3. 9 tan dθ = dy dx (Ec. 1.3) Suponiendo que el valor del ángulo es pequeño se podría asumir que dθ ≈tan dθ, y sustituyendo esta expresión se obtiene la Ecuación 1.4. dθ = dy dx (Ec. 1.4) Derivando la Ecuación 1.4 con respecto a x, se obtiene la Ecuación 1.5. dθ dx = d2y dx2 (Ec. 1.5) Igualando las Ecuaciones 1.2 y 1.5, se obtiene Ecuación 1.6. d2y dx2 = 1 ρ (Ec. 1.6) Aplicando la teoría de vigas en flexión se tiene que la relación momento curvatura se representa mediante la Ecuación 1.7. κ = 1 ρ = M EI (Ec. 1.7) Igualando las Ecuaciones 1.6 y 1.7, se obtiene Ecuación 1.8 que se conoce como la ecuación de la viga elástica. d2y dx2 = M EI (Ec. 1.8) Es posible expresar la ecuación de la viga elástica en dos formas alternativas, derivando con respecto a x, y considerando que V = dM dx y q = dV dx, se obtienen las Ecuaciones 1.9 y 1.10. d3y dx3 = V EI (Ec. 1.9) 10 d4y dx4 = −q EI (Ec. 1.10) 1.2. Condiciones de frontera Se representan como valores conocidos de las deflexiones y pendientes en particulares localizaciones a lo largo de una viga (Philpot, 2017a). Se puede identificar en la Figura 1.2 que las condiciones de frontera localizadas en apoyos fijos y móviles no presentan deflexiones, sin embargo, son susceptibles a rotaciones. Por otro lado, en la ubicación de empotramientos no se producen ni deflexiones ni rotaciones. Por último, en los extremos libres no se producen fuerzas cortantes ni momentos internos. Figura 1.2. Condiciones de frontera en vigas 1.3. Convenciones de signos Para encontrar la pendiente y la deflexión de una viga en cualquier localización se deberá considerar ciertas convenciones de signos (Singh, 2021), que se indican a continuación: • Las posiciones de x e y son positivas cuando se recorre hacia la derecha y hacia arriba. • La deflexión es negativa cuando la viga se deforma hacia abajo de su posición original. • La pendiente es positiva se mide en sentido antihorario con respecto al eje x, y negativa cuando se mide en sentido horario. • El momento flector es positivo cuando se produce compresión en la parte superior de la viga, y negativa cuando se produce tracción en la parte superior. 11 1.4. Método de doble integración (M.D.I.) El método consiste en una resolución algebraica de la Ecuación 1.8, empleando la integración doble del momento flector en términos de x. Es importante indicar que este método presenta ciertas limitaciones a casos específicos de carga individual, por lo que los casos abordados a continuación familiarizaran al lector con el procedimiento de cálculo. 1.4.1. Viga empotrada con carga puntual en el extremo Se considera una viga empotrada en donde actúa una carga puntual en su extremo como se muestra en la Figura 1.3, al realizar un corte a una distancia x se puede determinar estáticamente su momento interno. ΣMx = 0 Mx −P(L −x) = 0 Mx = P(L −x) Figura 1.3. Viga empotrada con carga puntual en el extremo Observando que la viga al deformarse se produce tracción en la parte superior, se considera que el momento Mx es negativo. Sustituyendo este momento en la Ecuación 1.8, se obtiene la expresión [I]: EI d2y dx2 = −P(L −x) [I] Integrando la expresión [I] con respecto a x, se tiene que: EI නd2y dx2 dx = −P න(L −x)dx EI dy dx = −P ቆLx −x2 2 ቇ+ C1 [II] 12 En la condición de frontera para el empotramiento del punto A, sustituyendo cuando x = 0, dy dx = 0 en la expresión [II] se tiene: EI(0) = −P ቆL(0) −(0)2 2 ቇ+ C1 0 = 0 + C1 C1 = 0 En la condición de frontera para el extremo libre en el punto B, sustituyendo cuando x = L, θB = dy dx, C1 = 0 en la expresión [II] se obtiene la Ecuación 1.11: EIθB = −P ቆL(L) −L2 2 ቇ+ 0 EIθB = −P ቆL2 −L2 2 ቇ EIθB = −PL2 2 θB = −PL2 2EI (Ec. 1.11) Integrando la expresión [II] con respecto a x, se tiene que: EI නdy dx dx = −P නቆLx −x2 2 ቇdx + C1 නdx EIy = −P ቆLx2 2 −x3 6 ቇ+ C1x + C2 [III] En la condición de frontera para el empotramiento del punto A, sustituyendo cuando x = 0, y = 0 en la expresión [III] EI(0) = −P ቆL(0)2 2 −(0)3 6 ቇ+ C1(0) + C2 0 = 0 + 0 + C2 13 C2 = 0 En la condición de frontera para el extremo libre en el punto B, sustituyendo cuando x = L, y = yB, C1 = 0, C2 = 0 en la expresión [III] se obtiene la Ecuación 1.12: EIyB = −P ቆL(L)2 2 −L3 6 ቇ+ (0)L + 0 EIyB = −P ቆL3 2 −L3 6 ቇ+ 0 + 0 EIyB = −P ቆL3 3 ቇ yB = ymax = −PL3 3EI (Ec. 1.12) Ejemplo 1.1. Una viga empotrada tiene una longitud de 4 m y una carga de 8 kN que actúa en su extremo, como se muestra en la Figura 1.4. Determine la deflexión máxima producida, considere que 𝐄𝐄𝐄𝐄= 𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐 𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆 y 𝐈𝐈𝐈𝐈= 𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟐𝟐𝟐𝟐𝟔𝟔𝟔𝟔 𝐦𝐦𝐦𝐦𝐦𝐦𝐦𝐦𝟒𝟒𝟒𝟒. Figura 1.4. Aplicación de M.D.I. en viga empotrada con carga puntual en el extremo. Datos I = 65x106 mm4 = 65x10−6 m4 E = 200 GPa = 200x106 kN m2 L = 4 m P = 8 kN 14 Resolución Realizando un corte en el punto x hacia la derecha se puede obtener el momento interno de la siguiente manera: ΣMx = 0 Mx −8(4 −x) = 0 Mx = 8(4 −x) Observando que la viga al deformarse se produce tracción en la parte superior, se considera que el momento Mx es negativo, sustituyendo el momento encontrado en la Ecuación 1.8 se obtiene: EI d2y dx2 = −8(4 −x) [I] Integrando dos veces la expresión [I] se obtiene: EI dy dx = 4(4 −x)2 + C1 [II] EIy = −4 3 (4 −x)3 + C1x + C2 [III] En la condición de frontera para el empotramiento del punto A, sustituyendo cuando x = 0, dy dx = 0 en la expresión [II] se tiene: EI(0) = 4(4 −0)2 + C1 0 = 64 + C1 C1 = −64 En la condición de frontera para el empotramiento del punto A, sustituyendo cuando x = 0, y = 0 en la expresión [III] se tiene: EI(0) = −4 3 (4 −0)3 + C1(0) + C2 0 = −256 3 + 0 + C2 15 C2 = 256 3 Substituyendo x = 4, C1 = −64, C2 = 256 3 , E = 200x106, I = 65x10−6 en la expresión [III] se obtiene: (200x106)(65x10−6)y = −4 3 (4 −4)3 −64(4) + 256 3 13000y = 0 −256 + 256 3 13000y = −512 3 y = − 512 3(13000) = −0.01313 m = −13.13 mm Comprobando el resultado obtenido con la Ecuación 1.12 se determina que el procedimiento esta correctamente realizado. ymax = − 8 (4 )3 3(200x106 )(65x10−6) = −0.01313 m = −13.13 mm Adicionalmente se emplea el software MDSolids para validar este resultado como se observa en la Figura 1.5, siendo el valor de la deflexión coincidente con lo calculado. Figura 1.5. Comprobación mediante MDSolids de viga empotrada con carga puntual en el extremo. 16 1.4.2. Viga empotrada con carga puntual ubicada en un punto determinado Se considera una viga empotrada en donde actúa una carga puntual en un punto determinado como se muestra en la Figura 1.6, al realizar un corte a una distancia x se puede analizar estáticamente su momento interno. ΣMx = 0 Mx −P(a −x) = 0 Mx = P(a −x) Figura 1.6. Viga empotrada con carga puntual ubicada en un punto determinado Observando que la viga al deformarse se produce tracción en la parte superior, se considera que el momento Mx es negativo. Sustituyendo este momento en la Ecuación 1.8, se obtiene la expresión [I]: EI d2y dx2 = −P(a −x) [I] Integrando la expresión [I] con respecto a x, se tiene que: EI නd2y dx2 dx = −P න(a −x)dx EI dy dx = −P ቆax −x2 2 ቇ+ C1 [II] En la condición de frontera para el empotramiento del punto A, sustituyendo cuando x = 0, dy dx = 0 en la expresión [II] se tiene: EI(0) = −P ቆa(0) −(0)2 2 ቇ+ C1 17 0 = 0 + C1 C1 = 0 En la condición de frontera donde se aplica la carga en el punto C, sustituyendo cuando x = a, θC = dy dx, C1 = 0 en la expresión [II] se obtiene la Ecuación 1.13. EIθC = −P ቆa(a) −a2 2 ቇ+ 0 EIθC = −P ቆa2 −a2 2 ቇ EIθC = −Pa2 2 θC = −Pa2 2EI (Ec. 1.13) Cuando se aplica la carga en algún punto de la viga, desde esa ubicación en adelante la pendiente se mantendrá constante, de manera que la pendiente de C a B se expresa con la Ecuación 1.14. θB = θC = −Pa2 2EI (Ec. 1.14) Integrando la expresión [II] con respecto a x, se tiene que: EI නdy dx dx = −P නቆax −x2 2 ቇdx + C1 නdx EIy = −P ቆax2 2 −x3 6 ቇ+ C1x + C2 [III] En la condición de frontera para el empotramiento del punto A, sustituyendo cuando x = 0, y = 0 en la expresión [III] EI(0) = −P ቆa(0)2 2 −(0)2 6 ቇ+ C1(0) + C2 0 = 0 + 0 + C2 18 C2 = 0 En la condición de frontera donde se aplica la carga en el punto C, sustituyendo cuando x = a, y = yC, C1 = 0, C2 = 0 en la expresión [III] se obtiene la Ecuación 1.15: EIyC = −P ቆa(a)2 2 −a3 6 ቇ+ (0)a + 0 EIyC = −P ቆa3 2 −a3 6 ቇ+ 0 + 0 EIyC = −Pa3 3 yC = −Pa3 3EI (Ec. 1.15) Para determinar la deflexión en el punto B se debe considerar el tramo ΔyBC, mediante la siguiente expresión: tan θC = ΔyBC L −a tan θC (L −a) = ΔyBC ΔyBC = tan θC (L −a) Considerando que el ángulo θC es pequeño se puede considerar que tan θC ≈θC ΔyBC = θC(L −a) [IV] Reemplazando la Ecuación 1.14 en la expresión [IV]. ΔyBC = −Pa2 2EI (L −a) [V] La deflexión en B se determina mediante la suma de la deflexión en C con la expresión [V], mediante la Ecuación 1.16. yB = yC + ΔyBC 19 yB = ymax = −Pa3 3EI −Pa2 2EI (L −a) (Ec. 1.16) Ejemplo 1.2. Una viga empotrada tiene una longitud de 6 m y una carga de 30 kN que actúa en la mitad de ella, como se muestra en la Figura 1.7. Determine la deflexión en la mitad de la viga, considere que la constante de rigidez 𝐄𝐄𝐄𝐄𝐈𝐈𝐈𝐈= 𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟐𝟐𝟐𝟐𝟒𝟒𝟒𝟒 𝐤𝐤𝐤𝐤𝐤𝐤𝐤𝐤 𝐦𝐦𝐦𝐦𝟐𝟐𝟐𝟐. Figura 1.7. Aplicación de M.D.I. en viga empotrada con carga puntual ubicada en un punto determinado. Datos EI = 6x104 kN m2 L = 6 m P = 30 kN Resolución Realizando un corte en el punto x hacia la derecha se puede obtener el momento interno de la siguiente manera: ΣMx = 0 Mx −30(3 −x) = 0 Mx = 30(3 −x) Observando que la viga al deformarse se produce tracción en la parte superior, se considera que el momento Mx es negativo, sustituyendo el momento encontrado en la Ecuación 1.8 se obtiene: 20 EI d2y dx2 = −30(3 −x) [I] Integrando dos veces la expresión [I] se obtiene: EI dy dx = 15(3 −x)2 + C1 [II] EIy = −5(3 −x)3 + C1x + C2 [III] En la condición de frontera para el empotramiento del punto A, sustituyendo cuando x = 0, dy dx = 0 en la expresión [II] se tiene: EI(0) = 15(3 −0)2 + C1 0 = 135 + C1 C1 = −135 En la condición de frontera para el empotramiento del punto A, sustituyendo cuando x = 0, y = 0, C1 = −135 en la expresión [III] se tiene: EI(0) = −5(3 −0)3 −135(0) + C2 0 = −135 + 0 + C2 C2 = 135 Substituyendo x = 3, y = yC, C1 = −135, C2 = 135, EI = 6x104 en la expresión [III] se obtiene: 6x104yC = −5(3 −3)3 −135(3) + 135 6x104yC = 0 −405 + 135 6x104yC = −270 yC = −270 6x104 = −0.0045 m = −4.5 mm Comprobando el resultado obtenido con la Ecuación 1.15 se determina que el procedimiento esta correctamente realizado. 21 yC = −30(3)3 3(6x104) = −0.0045 m = −4.5 mm Adicionalmente se emplea el software MDSolids para validar este resultado como se observa en la Figura 1.8, siendo el valor de la deflexión coincidente con lo calculado. Figura 1.8. Comprobación mediante MDSolids de viga empotrada con carga puntual ubicada en un punto determinado. 1.4.3. Viga empotrada con carga distribuida rectangular completa Se considera una viga empotrada en donde actúa una carga distribuida rectangular a lo largo de su longitud como se muestra en la Figura 1.9, al realizar un corte a una distancia x se puede determinar estáticamente su momento interno. Figura 1.9. Viga empotrada con carga distribuida rectangular completa ΣMx = 0 Mx −q(L −x) (L −x) 2 = 0 22 Mx −q 2 (L −x)2 = 0 Mx = q 2 (L −x)2 Observando que la viga al deformarse se produce tracción en la parte superior, se considera que el momento Mx es negativo. Sustituyendo este momento en la Ecuación 1.8, se obtiene la expresión [I]: EI d2y dx2 = −q 2 (L −x)2 [I] Integrando la expresión [I] con respecto a x, se tiene que: EI නd2y dx2 dx = −q 2 න(L −x)2dx EI dy dx = q 6 (L −x)3 + C1 [II] En la condición de frontera para el empotramiento del punto A, sustituyendo cuando x = 0, dy dx = 0 en la expresión [II] se tiene: EI(0) = q 6 (L −0)3 + C1 0 = qL3 6 + C1 C1 = −qL3 6 En la condición de frontera para el extremo libre en el punto B, sustituyendo cuando x = L, θB = dy dx, C1 = − qL3 6 en la expresión [II] se obtiene la Ecuación 1.17: EIθB = q 6 (L −L)3 −qL3 6 EIθB = −qL3 6 23 θB = −qL3 6EI (Ec. 1.17) Integrando la expresión [II] con respecto a x, se tiene que: EI නdy dx dx = q 6 න(L −x)3 dx + C1 EIy = −q 24 (L −x)4 + C1x + C2 [III] En la condición de frontera para el empotramiento del punto A, sustituyendo cuando x = 0, y = 0, C1 = − qL3 6 en la expresión [III] EI(0) = −q 24 (L −0)4 −qL3 6 (0) + C2 0 = −qL4 24 + C2 C2 = qL4 24 En la condición de frontera para el extremo libre en el punto B, sustituyendo cuando x = L, y = yB, C1 = − qL3 6 , C2 = qL4 24 en la expresión [III] se obtiene la Ecuación 1.18: EIyB = −q 24 (L −L)4 −qL3 6 (L) + qL4 24 EIyB = −qL4 6 + qL4 24 EIyB = −qL4 8 yB = −qL4 8EI (Ec. 1.18) 24 Ejemplo 1.3. Una viga empotrada tiene una longitud de 3 m y una carga distribuida de 𝟑𝟑𝟑𝟑 𝐤𝐤𝐤𝐤𝐤𝐤𝐤𝐤 𝐦𝐦𝐦𝐦 que actúa sobre ella, como se muestra en la Figura 1.10. Determine la pendiente en el extremo libre de la viga, considere que 𝐄𝐄𝐄𝐄= 𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐 𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆 y 𝐈𝐈𝐈𝐈= 𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟐𝟐𝟐𝟐𝟔𝟔𝟔𝟔 𝐦𝐦𝐦𝐦𝐦𝐦𝐦𝐦𝟒𝟒𝟒𝟒. Figura 1.10. Aplicación de M.D.I. en viga empotrada con carga distribuida rectangular completa. Datos I = 65x106 mm4 = 65x10−6 m4 E = 200 GPa = 200x106 kN m2 L = 3 m q = 3 kN m Resolución Realizando un corte en el punto x hacia la derecha se puede obtener el momento interno de la siguiente manera: ΣMx = 0 Mx −3 (3 −x) (3 −x) 2 = 0 Mx = 3 2 (3 −x)2 25 Observando que la viga al deformarse se produce tracción en la parte superior, se considera que el momento Mx es negativo, sustituyendo el momento encontrado en la Ecuación 1.8 se obtiene: EI d2y dx2 = −3 2 (3 −x)2 [I] Integrando la expresión [I] se obtiene: EI dy dx = 1 2 (3 −x)3 + C1 [II] En la condición de frontera para el empotramiento del punto A, sustituyendo cuando x = 0, dy dx = 0 en la expresión [II] se tiene: EI(0) = 1 2 (3 −0)3 + C1 0 = 27 2 + C1 C1 = −27 2 Substituyendo x = 3, C1 = − 27 2 , E = 200x106, I = 65x10−6, dy dx = θB en la expresión [II] se obtiene: (200x106)(65x10−6 ) θB = 1 2 (3 −3)3 −27 2 13000 θB = 0 −27 2 θB = − 27 2(13000) = −0.001038 rad Comprobando el resultado obtenido con la Ecuación 1.17 se determina que el procedimiento esta correctamente realizado. θB = − 3 (3)3 6(200x106)(65x10−6) = −0.001039 rad 26 Adicionalmente se emplea el software MDSolids para validar este resultado como se observa en la Figura 1.11, siendo el valor de la pendiente coincidente con lo calculado. Figura 1.11. Comprobación mediante MDSolids de viga empotrada con carga distribuida rectangular completa. 1.4.4. Viga empotrada con carga distribuida rectangular parcial desde empotramiento Se considera una viga empotrada en donde actúa una carga distribuida rectangular hasta una determinada distancia como se muestra en la Figura 1.12, al realizar un corte a una distancia x se puede determinar estáticamente su momento interno. Figura 1.12. Viga empotrada con carga distribuida rectangular parcial desde empotramiento ΣMx = 0 Mx −q(a −x) (a −x) 2 = 0 Mx −q(a −x)2 2 = 0 27 Mx = q(a −x)2 2 Observando que la viga al deformarse se produce tracción en la parte superior, se considera que el momento Mx es negativo. Sustituyendo este momento en la Ecuación 1.8, se obtiene la expresión [I]: EI d2y dx2 = −q 2 (a −x)2 [I] Integrando la expresión [I] con respecto a x, se tiene que: EI නd2y dx2 dx = −q 2 න(a −x)2dx EI dy dx = q 6 (a −x)3 + C1 [II] En la condición de frontera para el empotramiento del punto A, sustituyendo cuando x = 0, dy dx = 0 en la expresión [II] se tiene: EI(0) = q 6 (a −0)3 + C1 0 = qa3 6 + C1 C1 = −qa3 6 En la condición de frontera donde se aplica la carga distribuida hasta el punto C, sustituyendo cuando x = a, θC = dy dx, C1 = − qa3 6 en la expresión [II] se obtiene la Ecuación 1.19: EIθC = q 6 (a −a)3 −qa3 6 EIθC = −qa3 6 θC = −qa3 6EI (Ec. 1.19) 28 Para los casos donde se aplica la carga en algún punto de la viga, desde esa ubicación en adelante la pendiente se mantendrá constante, de manera que la pendiente de C a B se expresa con la Ecuación 1.20. θB = θC = −qa3 6EI (Ec. 1.20) Integrando la expresión [II] con respecto a x, se tiene que: EI නdy dx dx = q 6 න(a −x)3 dx + C1 EIy = −q 24 (a −x)4 + C1x + C2 [III] En la condición de frontera para el empotramiento del punto A, sustituyendo cuando x = 0, y = 0, C1 = − qa3 6 en la expresión [III] EI(0) = −q 24 (a −0)4 −qa3 6 (0) + C2 0 = −qa4 24 + C2 C2 = qa4 24 En la condición de frontera donde se extiende la carga distribuida en el punto C, sustituyendo cuando x = a, y = yC, C1 = − qa3 6 , C2 = qa4 24 en la expresión [III] se obtiene la Ecuación 1.21: EIyC = −q 24 (a −a)4 −qa3 6 (a) + qa4 24 EIyC = −qa4 6 + qa4 24 EIyC = −qa4 8 yC = −qa4 8EI (Ec. 1.21) 29 Para determinar la deflexión en el punto B se debe considerar el tramo ΔyBC, empleando las condiciones indicadas en el caso de viga empotrada con carga puntual en un punto determinado, obteniéndose: ΔyBC = θC(L −a) [IV] Reemplazando la Ecuación 1.17 en la expresión [IV]. ΔyBC = −qa3 6EI (L −a) [V] La deflexión en B se determina mediante la suma de la deflexión en C con la expresión [V], obteniéndose la Ecuación 1.22. yB = yC + ΔyBC yB = −qa4 8EI −qa3 6EI (L −a) (Ec. 1.22) Ejemplo 1.4. Una viga empotrada tiene una longitud de 9 m y una carga distribuida de 𝟖𝟖𝟖𝟖 𝐤𝐤𝐤𝐤𝐤𝐤𝐤𝐤 𝐦𝐦𝐦𝐦 que actúa hasta 5 m del lado empotrado, como se muestra en la Figura 1.13. Determine la pendiente en el punto C, considere que la constante de rigidez EI es constante. Figura 1.13. Aplicación de M.D.I. en viga empotrada con carga distribuida rectangular parcial desde empotramiento. 30 Datos L = 9 m q = 8 kN m Resolución Realizando un corte en el punto x hacia la derecha se puede obtener el momento interno de la siguiente manera: ΣMx = 0 Mx −8 (5 −x) (5 −x) 2 = 0 Mx = 4(5 −x)2 Observando que la viga al deformarse se produce tracción en la parte superior, se considera que el momento Mx es negativo, sustituyendo el momento encontrado en la Ecuación 1.8 se obtiene: EI d2y dx2 = −4(5 −x)2 [I] Integrando la expresión [I] se obtiene: EI dy dx = 4 3 (5 −x)3 + C1 [II] En la condición de frontera para el empotramiento del punto A, sustituyendo cuando x = 0, dy dx = 0 en la expresión [II] se tiene: EI(0) = 4 3 (5 −0)3 + C1 0 = 500 3 + C1 C1 = −500 3 31 Substituyendo x = 5, C1 = − 500 3 , dy dx = θC en la expresión [II] se obtiene: EIθC = 4 3 (5 −5)3 −500 3 EIθC = −500 3 θC = −500 3EI = −166.67 EI Comprobando el resultado obtenido con la Ecuación 1.20 se determina que el procedimiento esta correctamente realizado. θC = −(8)(5)3 6EI = −166.67 EI Adicionalmente se emplea el software MDSolids para validar este resultado como se observa en la Figura 1.14, siendo el valor de la pendiente coincidente con lo calculado. Figura 1.14. Comprobación mediante MDSolids de viga empotrada con carga distribuida rectangular parcial desde empotramiento. 1.4.5. Viga empotrada con carga distribuida rectangular parcial desde extremo libre Se considera una viga empotrada en donde actúa una carga distribuida rectangular desde cierta ubicación de la viga hasta el extremo libre como se muestra en la Figura 1.15, es relevante destacar que relacionando los casos que se han abordado anteriormente es posible determinar los parámetros de deflexiones y pendientes. 32 Figura 1.15. Viga empotrada con carga distribuida rectangular parcial desde extremo libre Este caso puede ser formulado de las diferencias de las deflexiones y pendientes de los apartados 1.4.3 y 1.4.4. La pendiente en el punto B se expresa mediante la Ecuación 1.23. θB = −qL3 6EI −ቆ−qa3 6EIቇ θB = −qL3 6EI + qa3 6EI θB = −q 6EI (L3 −a3) (Ec. 1.23) Mientras que la deflexión en el punto B se determina mediante la Ecuación 24. yB = −qL4 8EI −൭−qa4 8EI −qa3 6EI (L −a)൱ yB = −qL4 8EI −ቆ−qa4 8EI −qa3L 6EI + qa4 6EIቇ yB = −qL4 8EI + qa4 8EI + qa3L 6EI −qa4 6EI yB = −3qL4 + 3qa4 + 4a3L −4qa4 24EI 33 yB = −3qL4 + 4a3L −qa4 24EI yB = − q 24EI (3L4 −4a3L + a4) (Ec. 1.24) Ejemplo 1.5. Una viga empotrada tiene una longitud de 9 m y una carga distribuida de 𝟖𝟖𝟖𝟖 𝐤𝐤𝐤𝐤𝐤𝐤𝐤𝐤 𝐦𝐦𝐦𝐦 que actúa desde los 5 m del lado empotrado hasta el extremo libre, como se muestra en la Figura 1.16. Determine la deflexión y la pendiente en el punto C, considere que EI es constante. Figura 1.16. Aplicación de M.D.I. en viga empotrada con carga distribuida rectangular parcial desde extremo libre. Datos L = 9 m q = 8 kN m Resolución En este caso particular es necesario aplicar un ajuste a la condición de carga distribuida para que el corte en el punto x hacia la derecha pueda permitir completarse de manera que sea continua la carga. Para esto se añaden dos condiciones de cargas distribuidas opuestas y equivalentes a la original en el tramo faltante como se muestra en la Figura 1.17. 34 Figura 1.17. Arreglo de carga en viga empotrada con carga distribuida rectangular parcial desde extremo libre. Realizando un corte en el punto x hacia la derecha se puede obtener el momento interno de la siguiente manera: ΣMx = 0 Mx −8 (9 −x) (9 −x) 2 + 8 (5 −x) (5 −x) 2 = 0 Mx −4 (9 −x)2 + 4 (5 −x)2 = 0 Mx = 4 (9 −x)2 −4 (5 −x)2 Observando que la viga al deformarse se produce tracción en la parte superior, se considera que el momento Mx es negativo, sustituyendo el momento encontrado en la Ecuación 1.8 se obtiene la expresión [I]: EI d2y dx2 = −4 (9 −x)2 + 4 (5 −x)2 [I] Integrando dos veces la expresión [I] se obtiene: EI dy dx = 4 3 (9 −x)3 −4 3 (5 −x)3 + C1 [II] EIy = −1 3 (9 −x)4 + 1 3 (5 −x)4 + C1x + C2 [III] 35 En la condición de frontera para el empotramiento del punto A, sustituyendo cuando x = 0, dy dx = 0 en la expresión [II] se tiene: EI(0) = 4 3 (9 −0)3 −4 3 (5 −0)3 + C1 0 = 972 −500 3 + C1 0 = 2416 3 + C1 C1 = −2416 3 En la condición de frontera para el empotramiento del punto A, sustituyendo cuando x = 0, y = 0 en la expresión [III] se tiene: EI(0) = −1 3 (9 −0)4 + 1 3 (5 −0)4 + C1(0) + C2 0 = −2187 + 625 3 + C2 0 = −5936 3 + C2 C2 = 5936 3 Substituyendo C1 = − 2416 3 , dy dx = θC, x = 5 en la expresión [II] se obtiene: EIθC = 4 3 (9 −5)3 −4 3 (5 −5)3 −2416 3 EIθC = 256 3 −0 −2416 3 EIθC = −720 θC = −720 EI Substituyendo x = 5, C1 = − 2416 3 , C2 = 5936 3 en la expresión [III] se obtiene: 36 EIy = −1 3 (9 −5)4 + 1 3 (5 −5)4 −2416 3 (5) + 5936 3 EIy = −256 3 + 0 −12080 3 + 5936 3 EIy = −6400 3 y = −6400 3EI = −2133.33 m EI = −2133333.33 mm EI Para la comprobación del resultado se emplea el software MDSolids para validar el procedimiento como se observa en la Figura 1.18 y 1.19, siendo el valor de la pendiente coincidente con lo calculado. Figura 1.18. Comprobación mediante MDSolids de viga empotrada con carga distribuida rectangular parcial desde extremo libre (pendiente). Figura 1.19. Comprobación mediante MDSolids de viga empotrada con carga distribuida rectangular parcial desde extremo libre (deflexión). 37 1.4.6. Viga empotrada con momento en el extremo Se considera una viga empotrada en donde actúa un momento en su extremo como se muestra en la Figura 1.20, al realizar un corte a una distancia x se puede determinar estáticamente su momento interno. Figura 1.20. Viga empotrada con momento en el extremo ΣMx = 0 Mx −M = 0 Mx = M Observando que la viga al deformarse se produce tracción en la parte superior, se considera que el momento Mx es negativo. Sustituyendo este momento en la Ecuación 1.8, se obtiene la expresión [I]: EI d2y dx2 = −M [I] Integrando la expresión [I] con respecto a x, se tiene que: EI නd2y dx2 dx = −නMdx EI dy dx = −Mx + C1 [II] En la condición de frontera para el empotramiento del punto A, sustituyendo cuando x = 0, dy dx = 0 en la expresión [II] se tiene: EI(0) = −M(0) + C1 0 = 0 + C1 38 C1 = 0 En la condición de frontera para el extremo libre en el punto B, sustituyendo cuando x = L, dy dx = θB, C1 = 0 en la expresión [II] se obtiene la Ecuación 1.25: EIθB = −M(L) + 0 EIθB = −ML θB = −ML EI (Ec. 1.25) Integrando la expresión [II] con respecto a x, se tiene que: EI නdy dx dx = −M නx dx + C1 නdx EIy = −Mx2 2 + C1x + C2 [III] En la condición de frontera para el empotramiento del punto A, sustituyendo cuando x = 0, y = 0 en la expresión [III] EI(0) = −M(0)2 2 + C1(0) + C2 0 = 0 + 0 + C2 C2 = 0 En la condición de frontera para el extremo libre en el punto B, sustituyendo cuando x = L, y = yB, C1 = 0, C2 = 0 en la expresión [III] se obtiene la Ecuación 1.26: EIyB = −ML2 2 + (0)L + 0 EIyB = −ML2 2 yB = −ML2 2EI (Ec. 1.26) 39 Ejemplo 1.6. Una viga empotrada tiene una longitud de 3 m y un momento de 30 kN m que actúa en su extremo, como se muestra en la Figura 1.21. Determine la deflexión máxima, considere que 𝐄𝐄𝐄𝐄= 𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐 𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆 y 𝐈𝐈𝐈𝐈= 𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟐𝟐𝟐𝟐𝟔𝟔𝟔𝟔 𝐦𝐦𝐦𝐦𝐦𝐦𝐦𝐦𝟒𝟒𝟒𝟒. Figura 1.21. Aplicación de M.D.I. en viga empotrada con momento en el extremo. Datos I = 65x106 mm4 = 65x10−6 m4 E = 200 GPa = 200x106 kN m2 L = 3 m M = 30 kN m Resolución Realizando un corte en el punto x hacia la derecha se puede obtener el momento interno de la siguiente manera: ΣMx = 0 Mx −30 = 0 Mx = 30 Observando que la viga al deformarse se produce tracción en la parte superior, se considera que el momento Mx es negativo, sustituyendo el momento encontrado en la Ecuación 1.8 se obtiene: EI d2y dx2 = −30 Integrando dos veces la expresión [I] se obtiene: 40 EI dy dx = −30x + C1 [II] EIy = −15x2 + C1x + C2 [III] En la condición de frontera para el empotramiento del punto A, sustituyendo cuando x = 0, dy dx = 0 en la expresión [II] se tiene: EI(0) = −30(0) + C1 0 = 0 + C1 C1 = 0 En la condición de frontera para el empotramiento del punto A, sustituyendo cuando x = 0, y = 0 en la expresión [III] se tiene: EI(0) = −15(0)2 + C1(0) + C2 0 = 0 + 0 + C2 C2 = 0 Substituyendo x = 3, C1 = 0, C2 = 0, E = 200x106, I = 65x10−6 en la expresión [III] se obtiene: (200x106)(65x10−6)y = −15(3)2 + 0(3) + 0 13000y = −135 y = −135 13000 = 0.01038 m = −10.38 mm Comprobando el resultado obtenido con la Ecuación 1.12 se determina que el procedimiento esta correctamente realizado. yB = − 30(3)2 2(200x106)(65x10−6) = −0.01038 m = −10.38 mm Adicionalmente se emplea el software MDSolids para validar este resultado como se observa en la Figura 1.22, siendo el valor de la deflexión coincidente con lo calculado. 41 Figura 1.22. Comprobación mediante MDSolids de viga empotrada con momento en el extremo 1.4.7. Viga empotrada con carga distribuida triangular decreciente total Se considera una viga en voladizo con carga distribuida triangular decreciente ubicada a lo largo de su longitud como se muestra en la Figura 1.23, la relación geométrica de la carga triangular se puede identificar la siguiente igualdad en función de su pendiente. (tan α)triángulo menor = (tan α)triángulo mayor qx L −x = q L qx = q(L −x) L Analizando mediante la estática el momento en el punto x se tiene: ΣMx = 0 Mx −q(L −x) L ൬L −x 2 ൰൬L −x 3 ൰= 0 Mx = q(L −x)3 6L 42 Figura 1.23. Viga empotrada con carga distribuida triangular decreciente total Observando que la viga al deformarse se produce tracción en la parte superior, se considera que el momento Mx es negativo. Sustituyendo este momento en la Ecuación 1.8, se obtiene la expresión [I]: EI d2y dx2 = −q 6L (L −x)3 [I] Integrando la expresión [I] con respecto a x, se tiene que: EI නd2y dx2 dx = −q 6L න(L −x)3dx EI dy dx = q 24L (L −x)4 + C1 [II] En la condición de frontera para el empotramiento del punto A, sustituyendo cuando x = 0, dy dx = 0 en la expresión [II] se tiene: EI(0) = q 24L (L −0)4 + C1 0 = qL4 24L + C1 C1 = −qL3 24 43 En la condición de frontera para el extremo libre en el punto B, sustituyendo cuando x = L, dy dx = θB, C1 = − qL3 24 en la expresión [II] se obtiene la Ecuación 1.27: EIθB = q 24L (L −L)4 −qL3 24 EIθB = 0 −qL3 24 θB = −qL3 24EI (Ec. 1.27) Integrando la expresión [II] con respecto a x, se tiene que: EI නdy dx dx = q 24L න(L −x)4 dx + C1 EIy = − q 120L (L −x)5 + C1x + C2 [III] En la condición de frontera para el empotramiento del punto A, sustituyendo cuando x = 0, y = 0, C1 = − qL3 24 en la expresión [III] EI(0) = − q 120L (L −0)5 −qL3 24 (0) + C2 0 = −qL5 120L + C2 0 = −qL4 120 + C2 C2 = qL4 120 En la condición de frontera para el extremo libre en el punto B, sustituyendo cuando x = L, y = yB, C1 = − qL3 24 , C2 = qL4 120 en la expresión [III] se obtiene la Ecuación 1.28: EIyB = −q(L −L)5 120L −qL3 24 (L) + qL4 120 44 EIyB = −qL4 24 + qL4 120 EIyB = −qL4 30 yB = −qL4 30EI (Ec. 1.28) Ejemplo 1.7. Una viga empotrada tiene una longitud de 3 m y una carga triangular decreciente de 𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔 𝐤𝐤𝐤𝐤𝐤𝐤𝐤𝐤 𝐦𝐦𝐦𝐦 que actúa sobre ella, como se muestra en la Figura 1.24. Determine la pendiente en el extremo libre, considere que 𝐄𝐄𝐄𝐄𝐈𝐈𝐈𝐈 es constante. Figura 1.24. Aplicación de M.D.I. en viga empotrada con carga distribuida triangular decreciente total. Datos L = 3 m q = 12 kN m Resolución Relacionando geométricamente la distribución de cargas triangulares se tiene: (tan α)triángulo menor = (tan α)triángulo mayor qx 3 −x = 12 3 qx = 4(3 −x) 45 Realizando un corte en el punto x hacia la derecha se puede obtener el momento interno de la siguiente manera: ΣMx = 0 Mx −4(3 −x) ൬3 −x 2 ൰൬3 −x 3 ൰= 0 Mx = 2 3 (3 −x)3 Observando que la viga al deformarse se produce tracción en la parte superior, se considera que el momento Mx es negativo, sustituyendo el momento encontrado en la Ecuación 1.8 se obtiene: EI d2y dx2 = −2 3 (3 −x)3 [I] Integrando la expresión [I] se obtiene: EI dy dx = 1 6 (3 −x)4 + C1 [II] En la condición de frontera para el empotramiento del punto A, sustituyendo cuando x = 0, dy dx = 0 en la expresión [II] se tiene: EI(0) = 1 6 (3 −0)4 + C1 0 = 27 2 + C1 C1 = −27 2 Substituyendo x = 3, C1 = − 27 2 , dy dx = θB en la expresión [II] se obtiene: EIθB = 1 6 (3 −3)4 −27 2 EIθB = 0 −27 2 46 θB = −27 2 = −13.5 EI Comprobando el resultado obtenido con la Ecuación 1.27 se determina que el procedimiento esta correctamente realizado. θB = −qL3 24EI = −12(3)3 24EI = −13.5 EI Adicionalmente se emplea el software MDSolids para validar este resultado como se observa en la Figura 1.25, siendo el valor de la pendiente coincidente con lo calculado. Figura 1.25. Comprobación mediante MDSolids de viga empotrada con carga distribuida triangular decreciente total. 1.4.8. Viga empotrada con carga distribuida triangular creciente total Se considera una viga en voladizo con carga distribuida triangular creciente ubicada a lo largo de su longitud como se muestra en la Figura 1.26, es relevante destacar que relacionando los casos que se han abordado anteriormente es posible determinar los parámetros de deflexiones y pendientes. Figura 1.26. Viga empotrada con carga distribuida triangular creciente total 47 Este caso puede ser formulado de las diferencias de las deflexiones del apartado 1.4.3 y 1.4.7 (carga invertida). La deflexión en el punto B se expresa mediante la Ecuación 1.29. yB = −qL4 8EI −ቆ−qL4 30EIቇ yB = −qL4 8EI + qL4 30EI yB = −11qL4 120EI (Ec. 1.29) Ejemplo 1.8. Una viga empotrada tiene una longitud de 3 m y una carga triangular creciente de 𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔 𝐤𝐤𝐤𝐤𝐤𝐤𝐤𝐤 𝐦𝐦𝐦𝐦 que actúa sobre ella, como se muestra en la Figura 1.27. Determine la deflexión en el extremo libre, considere que la constante de rigidez 𝐄𝐄𝐄𝐄𝐈𝐈𝐈𝐈. Figura 1.27. Aplicación de M.D.I. en viga empotrada con carga distribuida triangular creciente total. En este caso particular es necesario aplicar un ajuste a la condición de carga distribuida equivalente, se considera una carga distribuida hacia abajo y una carga decreciente hacia arriba, de manera que corresponda al caso original de la viga del ejercicio como se muestra en la Figura 1.28. Figura 1.28. Arreglo de carga en viga empotrada con carga distribuida triangular creciente total. 48 Relacionando geométricamente la distribución de cargas triangulares hacia arriba se tiene: (tan α)triángulo menor = (tan α)triángulo mayor qx 3 −x = 12 3 qx = 4(3 −x) Realizando un corte en el punto x hacia la derecha se puede obtener el momento interno de la siguiente manera: ΣMx = 0 Mx −12(3 −x) (3 −x) 2 + 4(3 −x) ൬3 −x 2 ൰൬3 −x 3 ൰= 0 Mx −6(3 −x)2 + 2 3 (3 −x)3 = 0 Mx = 6(3 −x)2 −2 3 (3 −x)3 Observando que la viga al deformarse se produce tracción en la parte superior, se considera que el momento Mx es negativo, sustituyendo el momento encontrado en la Ecuación 1.8 se obtiene la expresión [I]: EI d2y dx2 = −6(3 −x)2 + 2 3 (3 −x)3 [I] Integrando dos veces la expresión [I] se obtiene: EI dy dx = 2(3 −x)3 −1 6 (3 −x)4 + C1 [II] EIy = −1 2 (3 −x)4 + 1 30 (3 −x)5 + C1x + C2 [III] En la condición de frontera para el empotramiento del punto A, sustituyendo cuando x = 0, dy dx = 0 en la expresión [II] se tiene: EI(0) = 2(3 −0)3 −1 6 (3 −0)4 + C1 49 0 = 54 −27 2 + C1 0 = 81 2 + C1 C1 = −81 2 En la condición de frontera para el empotramiento del punto A, sustituyendo cuando x = 0, y = 0 en la expresión [III] se tiene: EI(0) = −1 2 (3 −0)4 + 1 30 (3 −0)5 + C1(0) + C2 0 = −81 2 + 81 10 + C2 0 = −162 5 + C2 C2 = 162 5 Substituyendo x = 3, C1 = − 81 2 , C2 = 162 5 en la expresión [III] se obtiene: EIy = −1 2 (3 −3)4 + 1 30 (3 −3)5 −81 2 (3) + 162 5 EIy = −243 2 + 162 5 y = −891 10EI = −89.1 EI Multiplicando el valor por 1000 para convertirlo en mm. y = −89.1 EI (1000) = −89100 EI Comprobando el resultado obtenido con la Ecuación 1.29 y multiplicándolo para 1000 para convertirlo en mm, se determina que el procedimiento esta correctamente realizado. yB = −11(12)(3)4 120EI = −89.1 EI (1000) = −89100 EI 50 Adicionalmente se emplea el software MDSolids para validar este resultado como se observa en la Figura 1.29, siendo el valor de la deflexión coincidente con lo calculado. Figura 1.29. Comprobación mediante MDSolids de viga empotrada con carga distribuida triangular creciente total. 1.4.9. Viga apoyada en los extremos con carga puntual ubicada en el centro Se considera una viga apoyada en los extremos en donde actúa una carga puntual en la mitad de su longitud como se muestra en la Figura 1.30, siendo correspondiente a este caso que las reacciones en cada apoyo son iguales a la mitad de la carga aplicada. RA = RB = P 2 Figura 1.30. Viga apoyada en los extremos con carga puntual ubicada en el centro Por lo que al realizar un corte a una distancia x se puede determinar estáticamente su momento interno. 51 ΣMx = 0 Mx −Px 2 = 0 Mx = Px 2 Observando que la viga al deformarse se produce compresión en la parte superior, se considera que el momento Mx es positivo. Sustituyendo este momento en la Ecuación 1.8, se obtiene la expresión [I]: EI d2y dx2 = Px 2 [I] Integrando la expresión [I] con respecto a x, se tiene que: EI නd2y dx2 dx = P 2 නxdx EI dy dx = Px2 4 + C1 [II] En las vigas apoyadas en los extremos cuando se produce la condición de deflexión máxima la pendiente es nula, sustituyendo cuando x = L 2, dy dx = 0 en la expresión [II] se tiene: EI(0) = P ቀL 2ቁ 2 4 + C1 0 = PL2 16 + C1 C1 = −PL2 16 En la condición de frontera en el apoyo del punto A, sustituyendo cuando x = 0, dy dx = θA, C1 = − PL2 16 en la expresión [II] se obtiene la Ecuación 1.30: EIθA = P(0)2 4 −PL2 16 52 EIθA = 0 −PL2 16 θA = −PL2 16EI (Ec. 1.30) Integrando la expresión [II] con respecto a x, se tiene que: EI නdy dx dx = P 4 නx2 dx + C1 නdx EIy = Px3 12 + C1x + C2 [III] En la condición de frontera en el apoyo del punto A, sustituyendo cuando x = 0, y = 0, C1 = − PL2 16 en la expresión [III] EI(0) = P(0)3 12 −PL2 16 (0) + C2 0 = 0 + 0 + C2 C2 = 0 En la condición de frontera en la mitad de la viga, sustituyendo cuando x = L 2, y = yC, C1 = − PL2 16 , C2 = 0 en la expresión [III] se obtiene la Ecuación 31: EIyC = P ቀL 2ቁ 3 12 −PL2 16 ൬L 2൰+ 0 EIyC = PL3 96 −PL3 32 EIyC = −PL3 48 yC = ymax = −PL3 48EI (Ec. 1.31) 53 Ejemplo 1. 9. Determine la pendiente en el punto A de una viga apoyada en los extremos que tiene una longitud de 2 m y una carga puntual de 𝟐𝟐𝟐𝟐 𝐤𝐤𝐤𝐤𝐤𝐤𝐤𝐤 que actúa sobre ella, como se muestra en la Figura 1.31. Considere que el material de la viga es de acero (𝐄𝐄𝐄𝐄= 𝟐𝟐𝟐𝟐𝟔𝟔𝟔𝟔𝟐𝟐𝟐𝟐 𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆), con una sección cuadrada de 45 mm por cada lado. Figura 1.31. Aplicación de M.D.I. en viga apoyada en los extremos con carga puntual ubicada en el centro. Datos E = 210 GPa = 210x106 kN m2 b = h = 45 mm = 0.045 m L = 2 m P = 2 kN Resolución Se calcula el momento de inercia de la sección cuadrada mediante la siguiente expresión: I = bh3 12 = (0.045 m)(0.045 m)3 12 = 3.417x10−7m4 Realizando momento desde el punto A: ΣMA = 0 54 −2 kN(1 m) + RB(2 m) = 0 −2 kN m + RB(2 m) = 0 RB(2 m) = 2 kN m RB = 2 kNm 2 m = 1 kN Realizando un corte en el punto x hacia la derecha se puede obtener el momento interno de la siguiente manera: ΣMx = 0 Mx −2 (1 −x) + 1(2 −x) = 0 Mx = 2 (1 −x) −(2 −x) Observando que la viga al deformarse se produce compresión en la parte superior, se considera que el momento Mx es positivo, sustituyendo el momento encontrado en la Ecuación 1.8 se obtiene la expresión [I]: EI d2y dx2 = 2 (1 −x) −(2 −x) [I] Integrando la expresión [I] se obtiene: EI dy dx = − (1 −x)2 + 1 2 (2 −x)2 + C1 [II] En la condición de frontera en el centro de la viga, sustituyendo cuando x = 1, dy dx = 0 en la expresión [II] se tiene: EI(0) = − (1 −1)2 + 1 2 (2 −1)2 + C1 0 = 0 + 1 2 + C1 C1 = −1 2 55 Substituyendo cuando x = 0, dy dx = θA, C1 = − 1 2, E = 210x106, I = 3.417x10−7 en la expresión [II] se obtiene: EIθA = − (1 −0)2 + 1 2 (2 −0)2 −1 2 (210x106)(3.417x10−7)θA = −1 + 2 −1 2 71.76θA = 1 2 θA = 1 2(71.76) = 0.00697 rad Como la pendiente se mide en sentido horario desde el eje x la pendiente en A es negativa siendo: θA = −0.00697 rad Comprobando el resultado obtenido con la Ecuación 1.30 se determina que el procedimiento esta correctamente realizado. θA = − 2(2)2 16(210x106)(3.417x10−7) = 0.00697 rad Adicionalmente se emplea el software MDSolids para validar este resultado como se observa en la Figura 1.32, siendo el valor de la pendiente coincidente con lo calculado. Figura 1.32. Comprobación mediante MDSolids de viga apoyada en los extremos con carga puntual ubicada en el centro. 56 1.4.10. Viga apoyada en los extremos con carga distribuida rectangular completa Se considera una viga apoyada en los extremos en donde actúa una carga distribuida a lo largo de su longitud como se muestra en la Figura 1.33, siendo correspondiente a este caso que las reacciones en cada apoyo son iguales a la mitad del producto de la carga distribuida por su longitud. RA = RB = qL 2 Figura 1.33. Viga apoyada en los extremos con carga distribuida rectangular completa Por lo que al realizar un corte a una distancia x se puede determinar estáticamente su momento interno. ΣMx = 0 Mx −qL 2 (x) + qx ቀx 2ቁ= 0 Mx = qLx 2 −qx2 2 Observando que la viga al deformarse se produce compresión en la parte superior, se considera que el momento Mx es positivo. Sustituyendo este momento en la Ecuación 1.8, se obtiene la expresión [I]: EI d2y dx2 = qLx 2 −qx2 2 [I] Integrando la expresión [I] con respecto a x, se tiene que: EI නd2y dx2 dx = qL 2 නxdx −q 2 නx2dx 57 EI dy dx = qLx2 4 −qx3 6 + C1 [II] En las vigas apoyadas en los extremos cuando se produce la condición de deflexión máxima la pendiente es nula, sustituyendo cuando x = L 2, dy dx = 0 en la expresión [II] se tiene: EI(0) = qL ቀL 2ቁ 2 4 − q ቀL 2ቁ 3 6 + C1 0 = qL3 16 −qL3 48 + C1 0 = qL3 24 + C1 C1 = −qL3 24 En la condición de frontera en el apoyo del punto A, sustituyendo cuando x = 0, dy dx = θA, C1 = − qL3 24 en la expresión [II] se obtiene la Ecuación 1.32: EIθA = qL(0)2 4 −q(0)3 6 −qL3 24 EIθA = −qL3 24 θA = −qL3 24EI (Ec. 1.32) Integrando la expresión [II] con respecto a x, se tiene que: EI නdy dx dx = qL 4 නx2dx −q 6 නx3dx + C1 නdx EIy = qLx3 12 −qx4 24 + C1x + C2 [III] En la condición de frontera en el apoyo del punto A, sustituyendo cuando x = 0, y = 0 en la expresión [III] 58 EI(0) = qL(0)3 12 −q(0)4 24 + C1(0) + C2 0 = 0 −0 + 0 + C2 C2 = 0 En la condición de frontera en la mitad de la viga, sustituyendo cuando x = L 2, y = yB, C1 = − qL3 24 , C2 = 0 en la expresión [III] se obtiene la Ecuación 1.33: EIyB = qL ቀL 2ቁ 3 12 − q ቀL 2ቁ 4 24 −qL3 24 ൬L 2൰+ 0 EIyB = qL4 96 −qL4 384 −qL4 48 EIyB = −5qL4 384 yB = ymax = −5qL4 384EI (Ec. 1.33) Ejemplo 1.10. Determine la deflexión máxima de una viga apoyada en los extremos que tiene una longitud de 2 m y una carga distribuida de 𝟐𝟐𝟐𝟐 𝐤𝐤𝐤𝐤𝐤𝐤𝐤𝐤 𝐦𝐦𝐦𝐦 que actúa sobre ella, como se muestra en la Figura 1.34. Considere que el material de la viga es de acero (𝐄𝐄𝐄𝐄= 𝟐𝟐𝟐𝟐𝟔𝟔𝟔𝟔𝟐𝟐𝟐𝟐 𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆), con una sección cuadrada de 45 mm por cada lado. Figura 1.34. Aplicación de M.D.I. en viga apoyada en los extremos con carga distribuida rectangular completa. 59 Datos E = 210 GPa = 210x106 kN m2 b = h = 45 mm = 0.045 m L = 2 m q = 2 kN m Resolución Se calcula el momento de inercia de la sección cuadrada mediante la siguiente expresión: I = bh3 12 = (0.045 m)(0.045 m)3 12 = 3.417x10−7m4 En este ejercicio se empleará la forma alternativa para condiciones de carga distribuida, por lo que aplicando la Ecuación 1.10 se obtiene: EI d4y dx4 = −2 [I] Integrando dos veces la expresión [I] se obtiene: EI d3y dx3 = −2x + C1 [II] EI d2y dx2 = −x2 + C1x + C2 [III] En la condición de frontera para el apoyo del punto A, sustituyendo cuando x = 0, M = EI d2y dx2 = 0 en la expresión [III] se tiene: 0 = −(0)2 + C1(0) + C2 0 = 0 + 0 + C2 C2 = 0 60 En la condición de frontera para el apoyo del punto B, sustituyendo cuando x = 2, M = EI d2y dx2 = 0, C2 = 0 en la expresión [III] se tiene: 0 = −(2)2 + C1(2) + 0 0 = −4 + 2C1 + 0 4 = 2C1 4 2 = C1 C1 = 2 Substituyendo C1 = 2, C2 = 0 en la expresión [III] se obtiene la ecuación de la viga elástica del ejercicio, que se expresa con la expresión [IV]: EI d2y dx2 = −x2 + 2x + 0 EI d2y dx2 = −x2 + 2x [IV] Integrando dos veces la expresión [IV] se obtiene la expresión [V]: EI dy dx = −x3 3 + x2 + C3 EIy = −x4 12 + x3 3 + C3x + C4 [V] En la condición de frontera para el apoyo del punto A, sustituyendo cuando x = 0, y = 0 en la expresión [V] se tiene: EI(0) = −(0)4 12 + (0)3 3 + C3(0) + C4 C4 = 0 En la condición de frontera para el apoyo del punto B, sustituyendo cuando x = 2, y = 0, C4 = 0 en la expresión [V] se tiene: 61 EI(0) = −(2)4 12 + (2)3 3 + C3(2) + 0 EI(0) = −4 3 + 8 3 + C3(2) + 0 0 = 4 3 + 2C3 −4 3 = 2C3 C3 = − 4 3(2) = −2 3 Substituyendo cuando x = 1, C3 = − 2 3, C4 = 0, E = 210x106, I = 3.417x10−7 en la expresión [V] se obtiene: (210x106)(3.417x10−7)y = −14 12 + 13 3 −2 3 (1) + 0 71.76y = −1 12 + 1 3 −2 3 71.76y = −5 12 y = − 5 12(71.76) = −0.00581 m = −5.81 mm Comprobando el resultado obtenido con la Ecuación 1.33 se determina que el procedimiento esta correctamente realizado. ymax = −5qL4 384EI = − 5(2)(2)4 384(210x106)(3.417x10−7) = −0.0581 m = −5.81 mm Adicionalmente se emplea el software MDSolids para validar este resultado como se observa en la Figura 1.35, siendo el valor de la deflexión coincidente con lo calculado. 62 Figura 1.35. Comprobación mediante MDSolids con carga distribuida rectangular completa. 1.5. Método de Macaulay Este método consiste en establecer una ecuación general que satisfaga todas las condiciones de frontera, que mediante el método de doble integración resultaría una tarea compleja (Singh, 2021). Para ello se emplean dos tipos funciones: las funciones de Macaulay, que se utilizan para describir las cargas distribuidas y las funciones de singularidad que se utilizan para representar las fuerzas y los momentos concentrados, denominadas como funciones de discontinuidad (Philpot, 2017a). Su uso se base en la definición de restricciones para funciones ordinarias, expresándose mediante el uso de corchetes angulares en la forma 〈x −a〉n, que se denomina como corchetes de Macaulay. Las funciones de Macaulay se expresan mediante la Ecuación 1.34, es importante indicar que al cumplirse la primera condición en ambas expresiones el valor definido para ese tramo es igual a 0, eso implica que al realizar un corte en determinado tramo las demás cargas no se consideran o no existen para dicha función. 〈x −a〉n = ൜ 0, x < a (x −a)n, x ≥a (Ec. 1.34) 1.5.1. Pasos de aplicación del método de Macaulay Los pasos para aplicar el método de Macaulay (Srivastava & Gope, 2012), se presentan a continuación: 63 1. Se calculan las reacciones en los apoyos de una viga simplemente apoyada mediante el método tradicional. 2. Realizar un corte en el extremo más alejado del inicio de coordenadas en x, escribiendo una única ecuación de momentos, diferenciando cada expresión por tramo. 3. Al integrar las expresiones se integran como un todo manteniéndose entre paréntesis. Ejemplo 1.11. Una viga apoyada en los extremos tiene una longitud de 6 m con una carga distribuida de 𝟑𝟑𝟑𝟑 𝐤𝐤𝐤𝐤𝐤𝐤𝐤𝐤 𝐦𝐦𝐦𝐦 y una carga puntual de 5 kN, como se muestra en la Figura 1.36. Considere que el material de la viga es de acero (𝐄𝐄𝐄𝐄= 𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐 𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆), con una sección circular de 30 mm. Determine la deflexión y pendiente a 1 m, 3 m y 5 m. Figura 1.36. Aplicación del método de Macaulay en viga apoyada en los extremos en combinación de carga distribuida rectangular parcial y carga puntual. Datos E = 200 GPa = 200x106 kN m2 d = 30 mm ൬ 1 m 1000 mm൰= 0.030 m L = 6 m q = 3 kN m P = 5 kN 64 Resolución Se calcula el momento de inercia de la sección cuadrada mediante la siguiente expresión: I = πd4 64 = π(0.030 m)4 64 = 3.976x10−8m4 Calculando la constante de rigidez se tiene: EI = 200x106 kN m2 (3.976x10−8m4) = 7.952 kN m2 Realizando momento desde el punto B: ΣMB = 0 −RA(6 m) + 3 kN m (4 m)(2 m) + 5 kN(2 m) = 0 −RA(6 m) + 24 kN m + 10 kN m = 0 −RA(6 m) + 34 kN m = 0 −RA(6 m) = −34 kN m RA = −34 kN m −6 m = 17 3 kN Para la aplicación del método de Macaulay se debe realizar un corte en el punto más alejado hacia la derecha donde se pueda obtener el momento interno, como se realiza a continuación: ΣMx = 0 −17 3 x + 3 (x −2) (x −2) 2 + 5 (x −4) + Mx = 0 −17 3 x + 3 2 (x −2)2 + 5 (x −4) + Mx = 0 Mx = 17 3 x −3 2 (x −2)2 −5 (x −4) Observando que la viga al deformarse se produce compresión en la parte superior, se considera que el momento Mx es positivo, sustituyendo el momento encontrado en la Ecuación 1.8 se obtiene la expresión [I]: 65 EI d2y dx2 = 17 3 x −3 2 (x −2)2 −5 (x −4) [I] Integrando dos veces la expresión [I] se obtiene: EI dy dx = 17 6 x2 −1 2 〈x −2〉3 −5 2 (x −4)2 + C1 [II] EIy = 17 18 x3 −1 8 〈x −2〉4 −5 6 (x −4)3 + C1x + C2 [III] En la condición de frontera del apoyo izquierdo, cuando x = 0, y = 0, se observa que en el segundo y tercer término se cumple la primera condición de la Ecuación 1.34 que indica que cuando x < a se sustituye todas las expresiones en paréntesis por cero. Reemplazando estos elementos en la expresión [III] se tiene: EI(0) = 17 18 (0)3 −1 8 〈0〉4 −5 6 〈0〉3 + C1(0) + C2 0 = 0 −0 −0 + 0 + C2 C2 = 0 En la condición de frontera en el extremo de la viga, cuando x = 6, y = 0, C2 = 0 se observa que todos los términos en paréntesis cumplen la segunda condición de la Ecuación 1.34 que indica que cuando x > a se consideran todas las expresiones involucradas. Reemplazando estos elementos en la expresión [III] se tiene: EI(0) = 17 18 (6)3 −1 8 〈6 −2〉4 −5 6 〈6 −4〉3 + C1(6) + 0 0 = 204 −32 − 20 3 + 6C1 0 = 496 3 + 6C1 6C1 = −496 3 C1 = −496 3(6) = −248 9 66 Substituyendo cuando C1 = − 248 9 , C2 = 0, EI = 7.952 en las expresiones [II] y [III] se obtiene: 7.952 dy dx = 17 6 x2 −1 2 〈x −2〉3 −5 2 〈x −4〉2 −248 9 [IV] 7.952y = 17 18 x3 −1 8 〈x −2〉4 −5 6 〈x −4〉3 −248 9 x [V] Substituyendo cuando x = 1, y = y1, dy dx = θ1 se observa que en el segundo y tercer término se cumple la primera condición de la Ecuación 1.34 que indica que cuando x < a se sustituye todas las expresiones en paréntesis por cero. Reemplazando estos elementos en las expresiones [IV] y [V] se tiene: 7.952θ1 = 17 6 (1)2 −1 2 〈0〉3 −5 2 〈0〉2 −248 9 7.952θ1 = 17 6 −0 −0 −248 9 7.952θ1 = −445 18 θ1 = − 445 18(7.952) = −3.109 rad 7.952y1 = 17 18 (1)3 −1 8 〈0〉4 −5 6 〈0〉3 −248 9 (1) 7.952y1 = 17 18 −0 −0 −248 9 7.952y1 = −479 18 y1 = − 479 18(7.952) = −3.346 m = −3346 mm Substituyendo cuando x = 3, y = y2, dy dx = θ2 se observa que en el segundo término se cumple la primera condición de la Ecuación 1.34 que indica que cuando x < a se sustituye todas las expresiones en paréntesis por cero. Reemplazando estos elementos en las expresiones [IV] y [V] se tiene: 67 7.952θ2 = 17 6 (3)2 −1 2 〈3 −2〉3 −5 2 〈0〉2 −248 9 7.952θ2 = 51 2 −1 2 −0 −248 9 7.952θ2 = −23 9 θ2 = − 23 9(7.952) = −0.321 rad 7.952y2 = 17 18 (3)3 −1 8 〈3 −2〉4 −5 6 〈0〉3 −248 9 (3) 7.952y2 = 51 2 −1 8 −0 −248 3 7.952y2 = −1375 24 y2 = − 1375 24(7.952) = −7.205 m = −7205 mm Substituyendo cuando x = 5, y = y3, dy dx = θ3 se observa que todos los términos en paréntesis cumplen la segunda condición de la Ecuación 1.34 que indica que cuando x > a se consideran todas las expresiones involucradas. Reemplazando estos elementos en las expresiones [IV] y [V] se tiene: 7.952θ3 = 17 6 (5)2 −1 2 〈5 −2〉3 −5 2 〈5 −4〉2 −248 9 7.952θ3 = 425 6 −27 2 −5 2 −248 9 7.952θ3 = 491 18 θ3 = 491 18(7.952) = 3.43 rad 7.952y3 = 17 18 (5)3 −1 8 〈5 −2〉4 −5 6 〈5 −4〉3 −248 9 (5) 7.952y3 = 2125 18 −81 8 −5 6 −1240 9 68 7.952y3 = −2209 72 y3 = − 2209 72(7.952) = −3.858 m = −3858 mm Se emplea el software MDSolids para validar estos resultados como se observa en las Figuras 1.37 y 1.38, siendo coincidentes con lo calculado. Figura 1.37. Comprobación mediante MDSolids del método de Macaulay (pendiente). Figura 1.38. Comprobación mediante MDSolids del método de Macaulay (deflexión). 69 1.6. Problemas 1. En los problemas 1.1 a 1.10 aplique el método de doble integración para determinar la deflexión y pendiente a 1 m a la derecha del punto A para los casos individuales de carga. Ejercicio 1.1 Ejercicio 1.2 Ejercicio 1.3 Ejercicio 1.4 Ejercicio 1.5 Ejercicio 1.6 Ejercicio 1.7 Ejercicio 1.8 Ejercicio 1.9 Ejercicio 1.10 70 2. Aplique el método de Macaulay para determinar la deflexión y pendiente a 0 m, 1 m, 2 m, 3 m y 4 m con las combinaciones de las cargas de los ejercicios 1.1 a 1.8 para los dos casos de vigas que se detallan a continuación: Combinaciones de carga de ejercicios 1.1 + 1.2 1.2 + 1.3 1.3 + 1.4 1.4 + 1.5 1.5 + 1.6 1.6 + 1.7 1.7 + 1.8 1.1 + 1.3 1.2 + 1.4 1.3 + 1.5 1.4 + 1.6 1.5 + 1.7 1.6 + 1.8 1.1 + 1.4 1.2 + 1.5 1.3 + 1.6 1.4 + 1.7 1.5 + 1.8 1.1 + 1.5 1.2 + 1.6 1.3 + 1.7 1.4 + 1.8 1.1 + 1.6 1.2 + 1.7 1.3 + 1.8 1.1 + 1.7 1.2 + 1.8 1.1 + 1.8 1 CAPÍTULO I MÉTODO DE SUPERPOSICIÓN 72 Objetivos • Explorar en profundidad el método de superposición aplicado al análisis de deflexiones en vigas, con el propósito de proporcionar a los lectores una comprensión integral y práctica de esta técnica avanzada. • Detallar los fundamentos teóricos que sustentan el método de superposición en el análisis de vigas, abordando conceptos clave como las condiciones de contorno, la linealidad del comportamiento estructural y la aplicación de cargas combinadas. • Guiar a los lectores a través del proceso paso a paso para aplicar el método de superposición en el cálculo preciso de las deflexiones en vigas, destacando la resolución de problemas complejos mediante la descomposición de cargas y la combinación de soluciones individuales. • Presentar ejemplos prácticos y problemas diversos que permitan a los lectores aplicar el método de superposición en situaciones concretas de ingeniería mecánica, demostrando su versatilidad y aplicabilidad en diferentes contextos estructurales. • Fomentar la habilidad para evaluar la validez de los resultados obtenidos mediante el método de superposición, haciendo hincapié en la verificación de cálculos y en la comprensión de las limitaciones y precisión del método en diversos escenarios de análisis de vigas. 2.1. Método de superposición Cuando una viga está sometida a varias cargas, suele ser conveniente determinar la pendiente o deflexión combinado de las cargas superponiendo (sumando algebraicamente) las pendientes o deflexiones debidas a cada actúan individualmente sobre la viga, a este procedimiento se lo conoce como método de superposición (Kassima la combinación de los casos de los apartados 1.4.1 y 1.4.3 se podría determinar la deflexión total en el extremo su 1.12 y 1.18 que corresponden a las deflexiones individuales de cada caso como se muestra en la Figura 2.1. Figura 2.1 Demostración del método de superposición La determinación de las deflexiones y pendientes en las vigas es un proceso que requiere mucho tiempo, incluso relativamente sencillas. Para facilitar el proceso de obtención se han definido tablas para caso de apoyos típicos simplificar el proceso de resolución de vigas (Bedford & Liechti, 2020). A continuación, se muestra una reco casos aplicativos de este método en la Tabla 2.1. Tabla 2.1. Deflexiones y pendientes de casos típicos de vigas. Tipo de viga Pendiente Deflexió 1 yAC = −Px 48EI (3L2 −4x2) yCB = − P 48EI (−L3 + 9L2x −12Lx2 + 4x3) ymax = yC = −PL3 48EI θAC = − P 16EI (L2 −4x2) θCB = − P 16EI (3L2 −8Lx + 4x2) θmax = θA = −θB = −PL2 16EI 2 yAC = −Pbx 6EIL (L2 −b2 −x2) yCB = −Pa(L −x) 6EIL (2Lx −a2 −x2), yC = −Pa2b2 3EIL Si a ≥b, ymax = −Pb(L2−b2) 3 2 9EIL√3 , cuando x = ඨL2 −b2 3 Si a ≤b, ymax = −Pa(L2−b2) 3 2 9EIL√3 , cuando x = ඨL2 −a2 3 θAC = −Pb 6EIL (L2 −b2 −3x2) θCB = −Pa 6EIL (a2 + 2L2 −6Lx + 3x2) θA = −Pb(L2 −b2) 6EIL θB = Pa(L2 −a2) 6EIL 3 yAC = −Px 6EI (3aL −3a2 −x2) yCD = −Pa 6EI (3Lx −a2 −3x2) yDB = −P(L −x) 6EI (3aL −3a2 −(L −x)2) yC = yD = −Pa 6EI (3L −4a) ymax = −Pa 24EI (3L2 −4a2), cuando x = L 2 θAC = −P 2EI (aL −a2 −x2) θCD = −Pa 2EI (L −2x) θDB = −P 2EI (aL −a2 −(L −x)2) θmax = θA = −θB = −Pa(L −a) 2EI 4 yAB = −qx 24EI (L3 −2Lx2 + x3) ymax = −5qL4 384EI , cuando x = L 2 θAB = − q 24EI (L3 −6Lx2 + 4x3) θmax = θA = −θB = −qL3 24EI 5 yAC = − qx 384EI (16x3 −24Lx2 + 9L3) yCB = − qL 384EI (8x3 −24Lx2 + 17L2x−L3) yC = −5qL4 768EI ymax = −0.006563 qL4 EI , cuando x = 0.4598L θAC = − q 384EI (64x3 −72Lx2 + 9L3) θCB = − qL 384EI (24x2 −48Lx + 17L2 θA = −3qL3 128EI θB = 7qL3 384EI 6 yAC = − qx 24EIL (a4 −4a3L + 4a2L2 + 2a2x2 −4aLx2 + Lx3) yCB = −qa2 24EIL (−a2L + 4L2x + a2x −6Lx2 + 2x3) θAC = − q 24EIL (a4 −4a3L + 4a2L2 + θCB = −qa2 24EIL (4L2 + a2 −12Lx + 6 θA = −qa2 24EIL (2L −a)2, θB 7 yAB = − qx 360EIL (7L4 −10L2x2 + 3x4) ymax = −0.00652 qL4 EI , cuando x = 0.5193L θAB = − qx 360EIL (7L4 −30L2x2 + 15x θA = −7qL3 360EI, θB 8 yAC = − qx 960EIL (5L2 −4x2)2 yCB = −q(L −x) 960EIL (5L2 −4(L −x)2)2 ymax = yC = −qL4 120EI , cuando x = L 2 θAC = − q 192EIL (5L2 −4x2)(L2 −4x θCB = − q 192EIL (5L2 −4(L −x)2)(L2 θA = −θB = −5qL3 192EI 9 yAB = −qoL4 π4EI sin πx L ymax = yC = −qoL4 π4EI , cuando x = L 2 θAB = −qoL3 π3EI cos πx L θA = −θB = −qoL3 π3EI 10 yAB = −Mx 6EIL (2L2 −3Lx + x2) ymax = −ML2 9EI√3 , cuando x = L ቆ1 −√3 3 ቇ θAB = −M 6EIL (2L2 −6Lx + 3x2) θA = −ML 3EI , θB = ML 6EI 11 yAC = Mx 24EIL (L2 −4x2) yCB = M(L −x) 24EIL (L2 −4(L −x)2), yC = 0 θAC = − M 24EIL (L2 −12x2), θCB = θA = θB = M 6EIL (L2 −3b2) 12 yAC = Mx 6EIL (6aL −3a2 −2L2 −x2) yCB = M 6EIL (3a2L −3a2x −2L2x + 3Lx2 −x3) yC = Mab 3EIL (2a −L) ymax = −ML2 9√3EI , cuando x = L ቆ1 −√3 3 ቇ θAC = M 6EIL (L2 −3b2 −3x2) θCB = −M 6EIL (L2 −3a2 −3(L −x)2) θA = −M 6EIL (3b2 −L2) θC = M 3EIL (3aL −3a2 −L2), θ 13 yAB = −Mx 6EIL (x2 −L2) ymax = −ML2 9√3EI , cuando x = L √3 θAB = M 6EIL (L2 −3x2) θA = ML 6EI , θ 14 yAB = −x(L −x) 6EIL [(M1 −M2)x −(2M1 + M2)L] θAB = 1 6EIL [(M1 −M2)(3x2 −2Lx) −( 15 yAB = −x(L −x) 6EIL [(M1 + M2)x −(2M1 −M2)L] θAB = − 1 6EIL [(M1 + M2)(3x2 −2Lx) − 16 yAB = −Mx 2EI (L −x) ymax = −ML2 8EI , cuando x = L 2 θAB = −M 2EI (L −2x) θA = −θB = −ML 2EI 17 y = −PL2a 8EI , cuando x = L 2 yA = yB = −Pa2 3EI ൬a + 3 2 L൰ 18 y = −w(L −2a)3 384EI ቈ5 L (L −2a) −24 L ቆ a2 L −2aቇ቉, cuando x = L 2 yA = yB = −wa(L −2a)3 24EIL ൤−1 + 6 ቀ a L −2aቁ 2 + 3 ቀ a L −2aቁ 3 ൨ 19 yAC = −Pbx 6EIL (L2 −b2 −x2) yCB = −Pa(L −x) 6EIL (2Lx −a2 −x2), yBD = Pabx 6EIL (L + a) ymax = −Pab(L + b)ඥ3a(L + b) 27EIL , cuando x = ඨa(L + b) 3 θAC = −Pb 6EIL (L2 −b2 −3x2) θCB = −Pa 6EIL (2L2 −6Lx + a2 + 3x2) θBD = Pab(L + a) 6EIL 20 yAB = Pax 6EIL (L2 −x2) yBC = Px 6EI (2aL −3ax −x2) θAB = Pa 6EIL (L2 −3x2) θBC = −P 6EI (2aL + 6ax −3x2) 21 yAB = − qx 24EIL (L4 −2L2x2 + Lx3 −2a2L2 + 2a2x2) θAB = − q 24EIL (L4 −6L2x2 + 4Lx3 − 22 Desde A hasta L 2 , y = − qx 24EIL (L3 −2Lx2 + x3) Desde B hasta L 2 , y es simétrica la deformación ymax = −5qL4 384EI , cuando x = L 2 yC = qL3a 24EI 23 yAB = qa2x 12EIL (L2 −x2) yBC = −qx 24EI (4a2L + 6a2x −4ax2 + x3) θAB = qa2 12EIL (L2 −3x2) θBC = −q 6EI (a2L + 3a2x −3ax2 + x3 24 yAB = −Px2 6EI (3L −x) yB = ymax = −PL3 3EI θAB = −Px 2EI (2L −x) θmax = θB = −PL2 2EI 25 yAC = −Px2 12EI (3L −2x) yCB = −PL2 48EI (6x −L) ymax = yB = −5PL3 48EI θB = θmax = −PL2 2EI θC = θB = −PL2 2EI 26 yAC = −Px2 6EI (3a −x) yCB = −Pa2 6EI (3x −a), yC = −Pa3 3EI ymax = yB = −Pa2 6EI (3L −a) θAC = −Px 2EI (2a −x) θmax = θCB = −Pa2 2EI 27 yAB = −qx2 24EI (6L2 −4Lx + x2) ymax = yB = −qL4 8EI θAB = −qx 6EI (3L2 −3Lx + x2) θmax = θB = −qL3 6EI 28 yAC = −qx2 24EI ൬3 2 L2 −2Lx + x2൰ yCB = −qL3 384EI (8x −L), ymax = yB = −7qL4 384EI θmax = θB = −qL3 48EI 29 yAC = −qx2 24EI (6a2 −4ax + x2) yCB = −qa3 24EI (4x −a) ymax = yB = −qa3 24EI (4L −a) θAC = −qx 6EI (3a2 −3ax + x2) θmax = θCB = −qa3 6EI 30 yAC = −qbx2 12EI (3L + 3a −2x) yCB = − q 24EI (x4 −4Lx3 + 6L2x2 −4a3x + a4) yC = −qa2b 12EI (3L + a) ymax = yB = − q 24EI (3L4 −4a3L + a4) θAC = −qbx 2EI (L + a −x) θCB = −q 6EI (x3 −3Lx2 + 3L2x −a3) θC = −qabL 2EI θmax = θB = −q 6EI (L3 −a3) 31 yAC = −qbx2 12EI (6a + 3b −2x) yCD = − q 24EI [x4 −4(a + b)x3 + 6(a + b)2x2 −4a3x + a4] yDB = − q 24EI (4x[(a + b)3 −a3] −(a + b)4 + a4) θAC = −qbx 2EI (2a + b −x) θCD = −q 6EI (x3 −3(a + b)x2 + 3(a θDB = −q 6EI [(a + b)3 −a3] 32 yAB = − qx2 120EIL (20L3 −10L2x + x3) ymax = yB = −11qL4 120EI θAB = − qx 24EIL (8L3 −6L2x + x3) θmax = θB = −qL3 8EI 33 yAB = − qx2 120EIL (10L3 −10L2x + 5Lx2 −x3) ymax = yB = −qL4 30EI θAB = − qx 24EIL (4L3 −6L2x + 4Lx2 − θmax = θB = −qL3 24EI 34 yAB = − q 12EI ቆx6 30L2 −L3 5 x + L4 6 ቇ ymax = yB = −qL4 72EI θmax = θB = −qL3 60EI 35 yAB = −Mx2 2EI , ymax = yB = −ML2 2EI θAB = −Mx EI θmax = θB = −ML EI 36 yAC = −Mx2 2EI , yCB = −Ma 2EI (2x −a) yC = −Ma2 2EI , ymax = yB = −Ma 2EI (2L −a) θAC = −Mx EI θmax = θCB = −Ma EI 37 yAB = − qL 3π4EI ቀ48L3 cos πx 2L −48L3 + 3π3Lx2 −π3x3ቁ ymax = yB = −2qL4 3π4EI (π3 −24) θAB = −qL π3EI ቀ2π2Lx −π2x2 −8L2 s θmax = θB = −qL3 π3EI (π2 −8) 81 Ejemplo 2.1. Determine la deflexión y la pendiente en el punto C de la viga mostrada en la Figura 2.2. Considere la constante de rigidez 𝐄𝐄𝐄𝐄𝐈𝐈𝐈𝐈= 𝟔𝟔𝟔𝟔 𝐌𝐌𝐌𝐌𝐤𝐤𝐤𝐤 𝐦𝐦𝐦𝐦𝟐𝟐𝟐𝟐. Figura 2.2 Aplicación del método de superposición en viga simplemente apoyada con extremo libre. Datos EI = 1 MN m2 = 1000 kN m2 L = 6 m q = 3 kN m P = 10 kN Resolución Se procede a dividir las cargas aplicadas en la viga según los casos 19, 20 y 21 indicados en la Tabla 2.1 como se muestra en la Figura 2.3. De manera que se empleen las ecuaciones correspondientes para determinar las deflexiones y pendientes individuales en el punto C. Figura 2.3 Aplicación de división de cargas según el método de superposición en viga simplemente apoyada con extremo libre. 82 Caso 19 yC1 = yAC = −Pbx 6EIL (L2 −b2 −x2) = −10(2)(2) 6(1000)(4) (42 −22 −22) = −1 75 θC1 = θAC = −Pb 6EIL (L2 −b2 −3x2) = − 10(2) 6(1000)(4) (42 −22 −3(2)2) = 0 Caso 20 yC2 = yAB = Pax 6EIL (L2 −x2) = 10(2)(2) 6(1000)(4) (42 −22) = 1 50 θC2 = θAB = Pa 6EIL (L2 −3x2) = 10(2) 6(1000)(4) (42 −3(2)2) = 1 300 Caso 21 yC3 = yAB = − qx 24EIL (L4 −2L2x2 + Lx3 −2a2L2 + 2a2x2) yC3 = − 3(2) 24(1000)(4) (44 −2(4)2(2)2 + 4(2)3 −2(2)2(4)2 + 2(2)2(2)2) = −1 250 θC3 = θAB = − q 24EIL (L4 −6L2x2 + 4Lx3 −2a2L2 + 6a2x2) θC3 = − 3 24(1000)(4) (44 −6(4)2(2)2 + 4(4)(2)3 −2(2)2(4)2 + 6(2)2(2)2) = 1 1000 Se determina la deformación y pendiente total en C sumando cada una de las deformaciones y pendientes individuales en ese punto. yC = yC1 + yC2 + yC3 = −1 75 + 1 50 −1 250 = 1 375 = 0.0026 m = 2.67 mm θC = θC1 + θC2 + θC3 = 0 + 1 300 + 1 1000 = 13 3000 = 0.00433 rad Se emplea el software MDSolids para validar este resultado como se observa en las Figuras 2.4 y 2.5, siendo coincidentes con lo calculado. 83 Figura 2.4. Comprobación mediante MDSolids del método de superposición en viga simplemente apoyada con extremo libre (deflexión). Figura 2.5. Comprobación mediante MDSolids del método de superposición en viga simplemente apoyada con extremo libre (pendiente). Ejemplo 2.2. Determine la deflexión y la pendiente en el punto B de la viga mostrada en la Figura 2.6. Considere que 𝐄𝐄𝐄𝐄= 𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐 𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆 y 𝐈𝐈𝐈𝐈= 𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔 𝐦𝐦𝐦𝐦𝐦𝐦𝐦𝐦𝟒𝟒𝟒𝟒. Figura 2.6 Aplicación del método de superposición en viga empotrada. 84 Datos E = 200 GPa = 200x106 kN m2 I = 1665x106 mm4 = 1.665x10−3 m4 L = 9 m q = 45 kN m P = 270 kN Resolución Se procede a dividir las cargas aplicadas en la viga según los casos 26 y 30 indicados en la Tabla 2.1 como se muestra en la Figura 2.7. De manera que se empleen las ecuaciones correspondientes para determinar las deflexiones y pendientes individuales en el punto B. Figura 2.7 Aplicación de división de cargas según el método de superposición en viga empotrada. Caso 26 yB1 = yB = −Pa2 6EI (3L −a) = − 270(3)2 6(200x106)(1.665x10−3) (3(9) −3) = −0.0292 θB1 = θCB = −Pa2 2EI = − 270(3)2 2(200x106)(1.665x10−3) = −0.003649 Caso 30 yB2 = yB = − q 24EI (3L4 −4a3L + a4) yB2 = − 45 24(200x106)(1.665x10−3) (3(9)4 −4(6)3(9) + 64) = −0.0743 85 θB2 = θB = −q 6EI (L3 −a3) θB2 = − 45 6(200x106)(1.665x10−3) (93 −63) = −0.011554 Se determina la deformación y pendiente total en B sumando cada una de las deformaciones y pendientes individuales en ese punto. yB = yB1 + yB2 = −0.0292 −0.0743 = −0.1035 m = −103.5 mm θB = θB1 + θB2 = −0.003649 −0.011554 = −0.015203 rad Se emplea el software MDSolids para validar este resultado como se observa en las Figuras 2.8 y 2.9, siendo coincidentes con lo calculado. Figura 2.8. Comprobación mediante MDSolids del método de superposición en viga simplemente apoyada con extremo libre (deflexión). Figura 2.9. Comprobación mediante MDSolids del método de superposición en viga simplemente apoyada con extremo libre (pendiente). 86 Ejemplo 2.3. Determine la deflexión y la pendiente de la viga a 3 m del apoyo A como se muestra en la Figura 2.10. Considere que 𝐄𝐄𝐄𝐄𝐈𝐈𝐈𝐈 como constante. Figura 2.10 Aplicación del método de superposición en viga apoyada en sus extremos. Datos L = 4 m q = 40 kN m M = 10 kN m Resolución Se procede a dividir las cargas aplicadas en la viga según los casos 14 y 6 indicados en la Tabla 2.1 como se muestra en la Figura 2.11. De manera que se empleen las ecuaciones correspondientes para determinar las deflexiones y pendientes individuales a 3 m del apoyo. Figura 2.11 Aplicación de división de cargas según el método de superposición en viga apoyada en sus extremos. Caso 14 y1 = yAB = −x(L −x) 6EIL [(M1 −M2)x −(2M1 + M2)L] y1 = −3(4 −3) 6EI(4) [(10 −10)(3) −(2(10) + 10)(4)] = 15 EI 87 θ1 = θAB = 1 6EIL [(M1 −M2)(3x2 −2Lx) −(2M1 + M2)(2Lx −L2)] θ1 = 1 6EI(4) ൣ(10 −10)൫3(3)2 −2(4)(3)൯−(2(10) + 10)(2(4)(3) −42)൧= −10 EI Caso 6 y2 = yCB = −qa2 24EIL (−a2L + 4L2x + a2x −6Lx2 + 2x3) y2 = −40(3)2 24EI(4) (−32(4) + 4(4)2(3) + 32(3) −6(4)(3)2 + 2(3)3) = −315 4EI θ2 = −qa2 24EIL (4L2 + a2 −12Lx + 6x2) = −40(3)2 24EI(4) (4(4)2 + 32 −12(4)(3) + 6(3)2) = 255 4EI Se determina la deformación y pendiente cuando x = 3 m sumando cada una de las deformaciones y pendientes individuales en ese punto. y = y1 + y2 = 15 EI −315 4EI = −255 4EI = −63.75 EI θ = θ1 + θ2 = −10 EI + 255 4EI = −215 4EI = 53.75 EI Se emplea el software MDSolids para validar este resultado como se observa en las Figuras 2.12 y 2.13, siendo coincidentes con lo calculado. Figura 2.12. Comprobación mediante MDSolids del método de superposición viga apoyada en sus extremos (deflexión). 88 Figura 2.13. Comprobación mediante MDSolids del método de superposición viga apoyada en sus extremos (pendiente). 2.2. Problemas En los problemas 2.1 a 2.6 aplique el método de superposición para determinar la deflexión y pendiente a 3 m del apoyo A (viga apoyada en los extremos) y en el extremo (viga empotrada). Considere EI constante. Ejercicio 2.1 Ejercicio 2.2 Ejercicio 2.3 Ejercicio 2.4 Ejercicio 2.5 Ejercicio 2.6 1 CAPÍTULO III MÉTODO DE MOMENTO DE ÁREA 90 Objetivos • Comprender y aplicar los principios fundamentales del momento de área en el análisis de deflexiones en vigas, ofreciendo a los lectores una comprensión detallada y práctica de esta técnica matemática. • Explorar en profundidad los conceptos teóricos del momento de área y su relación con el comportamiento de las vigas bajo cargas, centrándose en la interpretación geométrica de la rigidez de una sección transversal. • Guiar a los lectores en el proceso de cálculo de momentos de área para secciones transversales simples y compuestas, capacitándolos para determinar las propiedades geométricas necesarias en el análisis de deflexiones. • Demostrar la aplicación práctica del momento de área en el cálculo de deflexiones en vigas, empleando ejemplos variados que ilustren su utilidad en situaciones reales de ingeniería mecánica. • Desarrollar la capacidad de los lectores para evaluar y validar los resultados obtenidos a través del uso del momento de área en el análisis de deflexiones, destacando la importancia de la precisión y la verificación de los cálculos realizados. 91 3.1. Generalidades El método se basa en dos teoremas, denominados teoremas del momento de área, que fueron desarrollados por Otto Mohr y posteriormente expuestos formalmente por Charles E. Greene en 1873 (Hibbeler, 2020), estos relacionan la geometría de la curva elástica de una viga con su diagrama de momento flector, expresando soluciones de la ecuación de la viga elástica gráficamente mediante las áreas del diagrama (Kassimali, 2020a). Al analizar el diagrama de momentos producido en una condición de cargas en una viga, es posible determinar la pendiente y deflexión de la viga. Esto se debe a que, al integrar la Ecuación 1.8, como se sabe por conocimientos de cálculo, la expresión de la integral corresponde al área bajo la curva como se observa en la Figura 3.1. Figura 3.1. Representación del área bajo la curva del diagrama de momentos Tomando dos puntos arbitrarios A y B de una viga el área bajo la curva quedaría definida por estos límites, de manera que la integral se expresaría mediante la Ecuación 3.1. θB/A = θB −θA = ൬dy dx൰ B −൬dy dx൰ A = නM EI B A dx (Ec. 3.1) 3.2. Teorema 1 El primer teorema expresa que “la diferencia de pendientes entre dos puntos cualesquiera de una viga es igual al área neta del diagrama de momentos flectores entre esos puntos, dividida por la constante de rigidez (EI) de la viga” (R.K. Kaushik, 2019). Esto se ejemplifica mediante la Figura 3.2, en donde se identifican los dos ángulos formados con respecto a los puntos A y B por las rectas tangentes que se han trazado, cuya diferencia es equivalente al área producida del área bajo la curva como se indicó en el apartado 3.1. Esto se expresa empleando la Ecuación 3.2. θB/A = Área bajo el diagrama de M/EI de A a B (Ec. 3.2) 92 Figura 3.2. Identificación de rectas tangentes para pendientes según el Teorema 1 del método de Momento de Área 3.2.1. Criterios de aplicación del Teorema 1 Para la aplicación del teorema 1 es importante realizar ciertas convenciones de signos (Goodno, Barry J. & Gere James, 2018), que se indican a continuación: • Los ángulos θA y θB son positivos cuando son antihorarios. • El ángulo θB/A entre las tangentes es positivo cuando el ángulo θB es algebraicamente mayor que el ángulo θA. Además, nótese que el punto B debe estar a la derecha del punto A; es decir, debe estar más a lo largo del eje de la viga a medida que nos movemos en la dirección x. • El momento flector M es positivo según la convención de signos habitual, es decir, M es positivo cuando produce compresión en la parte superior de la viga. • El área del diagrama M EI recibe un signo positivo o negativo según que el momento flector sea positivo o negativo. Si una parte del diagrama de momentos flectores es positiva y otra negativa, las partes correspondientes del diagrama M EI reciben esos mismos signos. 3.3. Teorema 2 El segundo teorema expresa que “el desplazamiento vertical de un punto de la curva elástica desde una tangente a la curva elástica en un segundo punto es igual al momento del área del diagrama de momentos que se encuentra entre los dos puntos, tomado alrededor del primer punto, dividido por la constante de rigidez (EI)” (Limbrunner & D'Allaird, 2016). Esto se ejemplifica mediante la Figura 3.3, en donde se identifican las dos rectas tangentes que se han trazado en los dos puntos centrales, cuya extensión hasta el punto A y medición vertical es equivalente a la deflexión alcanzada en términos diferenciales, como se indica en la Ecuación 3.3. Figura 3.3. Identificación de rectas tangentes para deflexiones según el Teorema 2 del método de Momento de Área 93 yB/A = yB −yA = නMx EI B A dx = Área(x) (Ec. 3.3) 3.3.1. Criterios de aplicación del Teorema 2 Para la aplicación de este teorema es importante realizar ciertas convenciones de signos, que se indican a continuación (Goodno, Barry J. & Gere James, 2018): • Si el momento flector es positivo, entonces el primer momento del diagrama M EI es también positivo, siempre que el punto B esté a la derecha del punto A. En estas condiciones, la desviación tangencial tB/A es positiva y el punto B está por encima de la tangente en A. • Si, al moverse de A hacia B en la dirección x, el área del diagrama M EI es negativa, entonces el primer momento es también negativo y la desviación tangencial es negativa, lo que significa que el punto B está por debajo de la tangente en A. • El primer momento del área del diagrama M EI puede obtenerse tomando el producto del área del diagrama y la distancia x desde el punto B al centroide C del área. 3.4. Diagrama de momentos por partes A modo de facilitar el procedimiento de resolución del método de momento de área, se recomienda analizar individualmente el efecto de cada carga en una viga. Para ello, se dibuja el diagrama de momento reducido para cada carga, y se obtiene el ángulo θB/A mediante la suma algebraica de cada área. Mientras que la desviación tangencial yB/A se obtiene con la suma de los primeros momentos de área respecto al eje vertical de B (Beer et al., 2020). En la Tabla 3.1 se observa una representación de las áreas y centroides de las geometrías más comunes para el área de los diagramas de momentos. Tabla 3.1. Representación de áreas y centroides comunes. Área bh bh 2 bh 3 bh 4 bh n + 1 c b 2 b 3 b 4 b 5 b n + 2 94 Ejemplo 3.1. Determine la deflexión y pendiente en el punto B de la viga mostrada en la Figura 3.4 empleando el método de momento de área. Considere que 𝐄𝐄𝐄𝐄𝐈𝐈𝐈𝐈= 𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔 𝐌𝐌𝐌𝐌𝐤𝐤𝐤𝐤 𝐦𝐦𝐦𝐦𝟒𝟒𝟒𝟒. Figura 3.4 Aplicación del método de momento de área en viga empotrada. Datos EI = 10 MN m2 = 10000 kN m2 L = 3 m P = 90 kN m M = 180 kN Resolución Realizando momento desde el punto A: ΣMA = 0 −50 kN(3 m) + 90 kN m + MA = 0 −60 kN m + MA = 0 MA = 60 kN m Aplicando sumatoria de Fuerzas en y se tiene: ΣFy = 0 RA −50 kN = 0 RA = 50 kN 95 Realizando un corte en el punto B y analizando el momento hacia la izquierda: ΣMB = 0 −50 kN(3 m) + 90 kN m −MB = 0 −60 kN m + MB = 0 MB = 60 kN m Con los valores de momentos encontrados se procede a realizar el diagrama de momentos, para ello se emplea MDSolids y se dividen en áreas como se muestra en la Figura 3.5. Figura 3.5. Obtención del diagrama de momentos MDSolids para método de momento de área en viga empotrada. Para determinar la distancia cuando el momento se vuelve cero se considera la relación geométrica de la pendiente del diagrama, de manera que: tan ∝= 60 x = 90 3 −x 60(3 −x) = 90x 180 −60x = 90x 180 = 90x + 60x 180 = 150x 96 x = 180 150 = 1.2 m Pendiente y deflexión en B Empleando la Ecuación 3.2 y 3.3, y reemplazando los valores de las áreas correspondientes del tramo AB según la Tabla 3.1 se tiene: θB/A = 1 EI (A1 + A2) = 1 EI ቈ−1.2(60) 2 + 1.8(90) 2 ቉= 45 EI = 45 10000 = 0.0045 rad yB/A = 1 EI (A1x1 + A2x2) = 1 EI ቈ−1.2(60) 2 ቆ1.8 + 2(1.2) 3 ቇ+ 1.8(90) 2 ൬1.8 3 ൰቉= −45 EI yB/A = − 45 10000 = −0.0045 m Se debe recordar que en los empotramientos la condición de frontera para la pendiente y deflexión son cero, por lo que θA = 0 y yA = 0. Considerando que θB/A = θB−θA se puede despejar θB. θB = θB/A + θA = 0.0045 + 0 = 0.0045 rad Considerando que yB/A = yB−yA se puede despejar yB. yB = yB/A + yA = −0.0045 + 0 = −0.0045 m = −4.5 mm Se emplea el software MDSolids para validar este resultado como se observa en las Figuras 3.6 y 3.7, siendo coincidentes con lo calculado. Figura 3.6. Comprobación mediante MDSolids del método de momento de área en viga empotrada (deflexión). 97 Figura 3.7. Comprobación mediante MDSolids del método de momento de área en viga empotrada (pendiente). Ejemplo 3.2. Determine la pendiente en los puntos A y B, y la deflexión en los puntos C y D de la viga mostrada en la Figura 3.8 empleando el método de momento de área. Considere que 𝐄𝐄𝐄𝐄= 𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔. 𝟔𝟔𝟔𝟔 𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆 y 𝐈𝐈𝐈𝐈= 𝟔𝟔𝟔𝟔𝟏𝟏𝟏𝟏𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔 𝐦𝐦𝐦𝐦𝐦𝐦𝐦𝐦𝟒𝟒𝟒𝟒. Figura 3.8 Aplicación del método de momento de área en viga apoyada en los extremos. Datos E = 12.5 GPa = 12.5x106 kN m2 I = 19200x106 mm4 = 0.0192 m4 L = 12 m P 1 = 270 kN P 2 = 180 kN 98 Resolución Realizando momento desde el punto B: ΣMB = 0 −RA(12 m) + 270 kN(6 m) + 180 kN(3 m) = 0 −RA(12 m) + 1620 kN m + 540 kN m = 0 −RA(12 m) + 2160 kN m = 0 −RA(12 m) = −2160 kN m RA = −2160 kN m −12 m = 180 kN Aplicando sumatoria de Fuerzas en y se tiene: ΣFy = 0 RA −270 kN −180 kN + RB = 0 180 kN −270 kN −180 kN + RB = 0 −270 kN + RB = 0 RB = 270 kN Realizando un corte en el punto C y analizando el momento hacia la izquierda: ΣMC = 0 −RA(6 m) + MC = 0 −180 kN(6 m) + MC = 0 −1080 kN m + MC = 0 MC = 1080 kN m Realizando un corte en el punto D y analizando el momento hacia la derecha: ΣMD = 0 99 RB(3 m) −MD = 0 270 kN(3 m) −MD = 0 810 kN m −MD = 0 MD = 810 kN m Con los valores de momentos encontrados se procede a realizar el diagrama de momentos, para ello se emplea MDSolids y se dividen en áreas como se muestra en la Figura 3.9. Figura 3.9. Obtención del diagrama de momentos MDSolids para método de momento de área en viga apoyada en los extremos. Pendiente A y B Empleando la Ecuación 3.2 y 3.3, y reemplazando los valores de las áreas correspondientes del tramo AB según la Tabla 3.1 se tiene: θB/A = 1 EI (A1 + A2 + A3 + A4) = 1 EI ቈ6(1080) 2 + 3(1080 −810) 2 + 3(810) + 3(810) 2 ቉ θB/A = 7290 EI yB/A = 1 EI (A1x1 + A2x2 + A3x3 + A4x4) yB/A = 1 EI ቈ6(1080) 2 ൬6 + 6 3൰+ 3(1080 −810) 2 ቆ3 + 2(3) 3 ቇ+ 3(810) ൬3 + 3 2൰+ 3(810) 2 ൬6 3൰቉ 100 yB/A = 41310 EI Considerando que la pendiente en A se forma hasta la desviación vertical en B como se muestra en la Figura 3.10 se represente mediante la expresión: tan θA = yB/A L Figura 3.10. Representación de desviación vertical y pendiente de tramo AB en viga apoyada en los extremos. Si la pendiente es pequeña tan θA ≈θA, entonces θA = yB/A L = 41310 EI 12 = 3442.50 EI = 3442.50 12.5x106(0.0192) = 0.01434 rad Como θA está ubicado en sentido horario se considera negativo. θA = −0.01434 rad Considerando que θB/A = θB−θA se puede despejar θB. θB = θB/A + θA = 7290 EI + (−0.01434) = 7290 12.5x106(0.0192) −0.01434 = 0.016035 rad Deflexión C Empleando la Ecuación 3.3, y reemplazando los valores de las áreas correspondientes del tramo AC según la Tabla 3.1 se tiene: yC/A = 1 EI (A1x1) = 1 EI ቈ6(1080) 2 ൬6 3൰቉= 6480 EI 101 Considerando que la pendiente en A se forma hasta la desviación vertical en C como se muestra en la Figura 3.11 se represente mediante la expresión: tan θA = yC + yC/A 6 Figura 3.11. Representación de desviación vertical y pendiente de tramo AC en viga apoyada en los extremos. Si la pendiente es pequeña tan θA ≈θA, entonces θA = yC + yC/A 6 6θA = yC + yC/A yC = 6θA −yC/A yC = 6(0.01434) − 6480 12.5x106(0.0192) = 0.05904 m = 59.04 mm Como la deflexión va hacia abajo yC se considera negativo. yC = −59.04 mm Deflexión D Empleando la Ecuación 3.3, y reemplazando los valores de las áreas correspondientes del tramo BD según la Tabla 3.1 se tiene: yD/B = 1 EI (A4x4) = 1 EI ቈ3(810) 2 ൬3 3൰቉= 1215 EI Considerando que la pendiente en B se forma hasta la desviación vertical en D como se muestra en la Figura 3.12 se represente mediante la expresión: tan θB = yD + yD/B 3 102 Figura 3.12. Representación de desviación vertical y pendiente de tramo BD en viga apoyada en los extremos. Si la pendiente es pequeña tan θB ≈θB, entonces θB = yD + yD/B 3 3θB = yD + yD/B yD = 3θB −yD/B yD = 3(0.016035) − 1215 12.5x106(0.0192) = 0.04304 m = 43.04 mm Como la deflexión va hacia abajo yD se considera negativo. yD = −43.04 mm Se emplea el software MDSolids para validar este resultado como se observa en las Figuras 3.13 y 3.14, siendo coincidentes con lo calculado. Figura 3.13. Comprobación mediante MDSolids del método de momento de área en viga apoyada en sus extremos (deflexión). 103 Figura 3.14. Comprobación mediante MDSolids del método de momento de área en viga apoyada en sus extremos (pendiente). Ejemplo 3.3. Determine la deflexión máxima mediante el método de momento de área en la viga mostrada en la Figura 3.15. Considere que 𝐄𝐄𝐄𝐄𝐈𝐈𝐈𝐈= 𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔 𝐤𝐤𝐤𝐤𝐤𝐤𝐤𝐤 𝐦𝐦𝐦𝐦𝟐𝟐𝟐𝟐. Figura 3.15 Aplicación del método de momento de área en viga apoyada en los extremos (simétrica). Datos EI = 50 kN m2 L = 6 m P = 2 kN Resolución Realizando momento desde el punto B: ΣMB = 0 −RA(6 m) + 2 kN(4 m) + 2 kN(2 m) = 0 104 −RA(6 m) + 8 kN m + 4 kN m = 0 −RA(6 m) + 12 kN m = 0 −RA(6 m) = −12 kN m RA = −12 kN m −6 m = 2 kN Por simetría de la viga se deduce: RB = RA = 2 kN Realizando un corte en el punto C y analizando el momento hacia la izquierda: ΣMC = 0 −RA(2 m) + MC = 0 −2 kN(2 m) + MC = 0 −4 kN m + MC = 0 MC = 4 kN m Si se realiza un corte en el punto C hacia la derecha por simetría de la viga se deduce: MD = 4 kN m Con los valores de momentos encontrados se procede a realizar el diagrama de momentos, para ello se emplea MDSolids y se dividen en áreas como se muestra en la Figura 3.16. Figura 3.16. Obtención del diagrama de momentos MDSolids para método de momento de área en viga apoyada en los extremos (viga simétrica). 105 Empleando la Ecuación 3.3, y reemplazando los valores de las áreas correspondientes del tramo desde la mitad al punto A según la Tabla 3.1 se tiene: yL 2/A = 1 EI (A1x1 + A2x2) = 1 EI ൭2(4) 2 ቆ2(2) 3 ቇ+ 1(4) ൬2 + 1 2൰൱= 46 3EI Considerando que la pendiente en la mitad de la viga es cero la desviación vertical es igual a la deflexión obtenida en ese punto como se muestra en la Figura 3.17, se representa mediante la expresión: yL 2/A = yL 2 = 22 3EI = 22 3(50) = 0.3067 m = 306.7 mm Figura 3.17. Representación de desviación vertical y pendiente de tramo AB en viga apoyada en los extremos (viga simétrica). Como la deflexión en la mitad de la viga va hacia abajo se considera negativa. yL 2 = −306.7 mm Se emplea el software MDSolids para validar este resultado como se observa en la Figura 3.18, siendo coincidentes con lo calculado. Figura 3.18. Comprobación mediante MDSolids del método de momento de área en viga apoyada en sus extremos (deflexión en viga simétrica). 106 Ejemplo 3.4. Determine la deflexión en el punto C mediante el método de momento de área de la Figura 19. Considere que 𝐄𝐄𝐄𝐄𝐈𝐈𝐈𝐈= 𝟐𝟐𝟐𝟐𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔 𝐤𝐤𝐤𝐤𝐤𝐤𝐤𝐤 𝐦𝐦𝐦𝐦𝟐𝟐𝟐𝟐 Figura 3.19 Aplicación del método de momento de área en viga apoyada en los extremos (proporcionalidad geométrica). Datos EI = 215 kN m2 L = 2 m P = 5 kN Realizando momento desde el punto B: ΣMB = 0 −RA(2 m) + 5 kN(0.8 m) = 0 −RA(2 m) + 4 kN m = 0 −RA(2 m) = −4 kN m RA = −4 kN m −2 m = 2 kN Aplicando sumatoria de Fuerzas en y se tiene: ΣFy = 0 RA −5 kN + RB = 0 2 kN −5 kN + RB = 0 107 −3 kN + RB = 0 RB = 3 kN Realizando un corte en el punto D y analizando el momento hacia la derecha: ΣMD = 0 RB(0.8 m) −MD = 0 3 kN(0.8 m) −MD = 0 2.4 kN m −MD = 0 MD = 2.4 kN m Con los valores de momentos encontrados se procede a realizar el diagrama de momentos, para ello se emplea MDSolids y se dividen en áreas como se muestra en la Figura 3.20. Figura 3.20. Obtención del diagrama de momentos MDSolids para método de momento de área en viga apoyada en los extremos (proporcionalidad geométrica). El momento en el punto C se puede determinar mediante la proporcionalidad de la pendiente de manera que: tan θ = 2.4 1.2 = MC 1 MC = 2 kN m 108 Empleando la Ecuación 3.3, y reemplazando los valores de las áreas correspondientes del tramo AB según la Tabla 3.1 se tiene: yB/A = 1 EI (A1x1 + A2x2) = 1 EI ቈ1.2(2.4) 2 ൬0.8 + 1.2 3 ൰+ 0.8(2.4) 2 ቆ2(0.8) 3 ቇ቉= 2.24 EI Considerando que la pendiente en A se forma hasta la desviación vertical en B y a 1 m como se muestra en la Figura 3.21 se represente la proporcionalidad geométrica mediante la expresión: tan θA = yB/A L = y 1 2.24 EI 2 = y 1 y = 2.24 EI 2 = 1.12 EI Figura 3.21. Representación de desviación vertical y pendiente de tramo AB en viga apoyada en los extremos (proporcionalidad geométrica). Empleando la Ecuación 3.3, y reemplazando los valores de las áreas correspondientes del tramo AC según la Tabla 3.1 se tiene: yC/A = 1 EI (A) = 1 EI ቈ1(2) 2 ൬1 3൰቉= 1 3EI Considerando que yC/A = y −yC se puede despejar yC. yC = y −yC/A = 1.12 EI −1 3EI = 0.7867 EI = 0.7867 215 = 0.003659 m = 3.66 mm 109 Se emplea el software MDSolids para validar este resultado como se observa en la Figura 3.22, siendo coincidente con lo calculado. Figura 3.22. Comprobación mediante MDSolids del método de momento de área en viga apoyada en sus extremos por proporcionalidad geométrica (deflexión). Ejemplo 3.5. Determine la deflexión en el punto C mediante el método de momento de área por partes de la Figura 23. Considere que 𝐄𝐄𝐄𝐄= 𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐 𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆 y 𝐈𝐈𝐈𝐈= 𝟖𝟖𝟖𝟖𝟑𝟑𝟑𝟑𝟑𝟑𝟑𝟑𝟑𝟑𝟑𝟑𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔 𝐦𝐦𝐦𝐦𝐦𝐦𝐦𝐦𝟒𝟒𝟒𝟒. Figura 3.23 Aplicación del método de momento de área en viga apoyada en los extremos (método por partes). Datos E = 200 GPa = 200x106 kN m2 I = 830x106 mm4 = 0.00083 m4 L = 12 m 110 P = 55 kN q = 30 kN m Resolución Se procede a dividir las condiciones de carga para realizar los diagramas de momentos individuales como se muestra en la Figura 3.24. Figura 3.24. Representación de división de cargas para aplicación de método de momento de área por partes. Caso 1 Realizando momento desde el punto A: ΣMA = 0 −30 kN m (9 m) ൬9 m 2 ൰+ RB(9 m) = 0 −1215 kN m + RB(9 m) = 0 RB(9 m) = 1215 kN m RB = 1215 kN m 9 m = 135 kN Aplicando sumatoria de Fuerzas en y se tiene: ΣFy = 0 RA −135 kN = 0 RA = 135 kN 111 Realizando un corte en la mitad del tramo AB y analizando el momento hacia la izquierda: ΣMx = 0 −135 kN(4.5 m) + 30 kN m (4.5 m) ൬4.5 m 2 ൰+ Mx = 0 −303.75 kN m + Mx = 0 Mx = 303.75 kN m Con el valor del momento encontrado y conociendo que existe simetría del tramo AB se procede a realizar el diagrama de momentos, para ello se emplea MDSolids como se muestra en la Figura 3.25. Figura 3.25. Obtención del diagrama de momentos MDSolids para el método de momento de área por partes (Caso 1). Caso 2 Realizando momento desde el punto A: ΣMA = 0 RB(9 m) −55 kN(12 m) = 0 RB(9 m) −660 kN m = 0 RB(9 m) = 660 kN m 112 RB = 660 kN m 9 m = 220 3 kN Aplicando sumatoria de Fuerzas en y se tiene: ΣFy = 0 RA + 220 3 kN −55 kN = 0 RA + 55 3 kN = 0 RA = −55 3 kN Realizando un corte en el punto B y analizando el momento hacia la izquierda: ΣMB = 0 55 3 kN(9 m) −MB = 0 165 kN m −MB = 0 MB = 165 kN m Con el valor del momento encontrado se procede a realizar el diagrama de momentos, para ello se emplea MDSolids como se muestra en la Figura 3.26. Figura 3.26. Obtención del diagrama de momentos MDSolids para el método de momento de área por partes (Caso 2). 113 Se unifican los diagramas de momentos obtenidos y se dividen en áreas como se muestra en la Figura 3.27. Figura 3.27. Obtención del diagrama de momentos MDSolids para el método de momento de área por partes (Agrupación). Empleando la Ecuación 3.3, y reemplazando los valores de las áreas correspondientes del tramo AB según la Tabla 3.1 se tiene: yA/B = 1 EI (A1x1 + A2x2 + A3x3 + A4x4 + A5x5) yA/B = 1 EI ቈ−4.5(303.75) 3 ൬4.5 4 ൰+ 4.5(303.75) ൬4.5 2 ൰−4.5(303.75) 3 ቆ4.5 + 3(4.5) 4 ቇ + 4.5(303.75) ൬4.5 + 4.5 2 ൰−9(165) 2 ቆ2(9) 3 ቇ቉= 3746.25 EI Empleando la Ecuación 3.3, y reemplazando los valores del área correspondiente del tramo BC según la Tabla 3.1 se tiene: yC/B = 1 EI (A6x6) = 1 EI ቈ3(165) 2 ቆ2(3) 3 ቇ቉= 495 EI Considerando que la pendiente en B se forma hasta la desviación vertical en A como se muestra en la Figura 3.28 se represente mediante la expresión: Figura 3.28. Representación de desviación vertical y pendiente de tramo AC en viga empleando método de momento de área por partes. 114 tan θB = yA/B 9 Si la pendiente es pequeña tan θB ≈θB, entonces θB = yA/B 9 = 3746.25 EI 9 = 416.25 EI Considerando que la pendiente en B se forma hasta la desviación vertical en C como se muestra en la Figura 3.11 se represente mediante la expresión: tan θB = yC/B + yC 3 Si la pendiente es pequeña tan θB ≈θB, entonces θB = yC/B + yC 3 3θB = yC/B + yC yC = 3θB −yC/B = 3 ൬416.25 EI ൰−495 EI = 753.75 EI = 753.75 (200x106)(0.00083) yC = 0.004541 m = 4.54 mm Se emplea el software MDSolids para validar este resultado como se observa en la Figura 3.29, siendo coincidente con lo calculado. Figura 3.29. Comprobación mediante MDSolids del método de momento de área por partes (deflexión). 115 3.5. Problemas En los problemas 3.1 a 3.10 aplique el método de momento de área tradicional y por partes para determinar la deflexión y pendiente según se solicite. Considere EI constante. Ejercicio 3.1 Encuentre la deflexión y pendiente en la mitad de la viga Ejercicio 3.2 Encuentre la deflexión y pendiente en la mitad de la viga Ejercicio 3.3 Encuentre la deflexión y pendiente en la mitad de la viga Ejercicio 3.4 Encuentre la deflexión en cada carga de la viga Ejercicio 3.5 Encuentre la deflexión máxima en la viga Ejercicio 3.6 Encuentre la deflexión y pendiente máxima en la viga Ejercicio 3.7 Encuentre la deflexión y pendiente máxima en la viga Ejercicio 3.8 Encuentre la deflexión y pendiente máxima en la viga 116 Ejercicio 3.9 Encuentre la deflexión y pendiente en la mitad de la viga Ejercicio 3.10 Encuentre la deflexión y pendiente en los extremos de la viga 1 CAPÍTULO IV MÉTODO DE VIGA CONJUGADA 118 Objetivos • Profundizar en el estudio de la viga conjugada como herramienta fundamental en el análisis de deflexiones, proporcionando a los lectores una comprensión exhaustiva y práctica de esta técnica avanzada en ingeniería estructural. • Explorar los fundamentos teóricos de la viga conjugada, centrándose en la relación entre el esfuerzo cortante y la pendiente de la línea elástica, y su aplicación en la determinación de las deflexiones en vigas. • Guiar a los lectores a través del proceso para el cálculo de la viga conjugada y su aplicación en el análisis de deflexiones en vigas sometidas a cargas variables y distribuidas, destacando la simplificación de cálculos mediante esta técnica. • Demostrar la aplicabilidad práctica de la viga conjugada en el análisis de deflexiones mediante ejemplos diversos y problemas representativos, permitiendo a los lectores comprender su utilidad en situaciones reales de ingeniería mecánica. • Fomentar la capacidad de los lectores para evaluar y validar los resultados obtenidos a través del uso de la viga conjugada en el análisis de deflexiones, enfatizando la importancia de verificar los cálculos y comprender la precisión y las limitaciones inherentes a esta técnica. 119 4.1. Generalidades La base de este método depende de la modificación del método momento de área, resultando conveniente emplearlo para las vigas de EI variable, a diferencia del método precedente que se recomienda para las vigas de EI constante, complementándose en dos teoremas principales (R.K. Kaushik, 2019). Este método fue desarrollado por Otto Mohr en 1868, el cual consiste en crear una viga ficticia, denominada viga conjugada, que posee la misma longitud que la viga real, pero apoyada exteriormente y conectada interiormente de tal forma que si la viga conjugada se carga con el diagrama M EI de la viga real, el cortante y el momento flector en cualquier punto de la viga conjugada son iguales, respectivamente, a la pendiente y la flecha en el punto correspondiente de la viga real (Kassimali, 2020a). Para realizar la conversión de una viga real a ficticia, se debe emplear las configuraciones con sus condiciones de carga y frontera que se muestran en la Tabla 4.1 Algunos ejemplos de conversiones de viga real a ficticia se ilustran en la Figura 4.1 a modo de guía para la aplicación del método para el lector. Tabla 4.1. Representación de casos de viga real y conjugada. Viga real Pendiente y deformación Fuerza cortante y momento flector Viga ficticia θ ≠0, y = 0 V ≠0, M = 0 θ = 0, y = 0 V = 0, M = 0 θ ≠0, y ≠0 V ≠0, M ≠0 θ ≠0 además, es continua, y ≠0 V ≠0 además, es continua, M ≠0 θ ≠0 además, es discontinua, y ≠0 V ≠0 además, es discontinua, M ≠0 120 Figura 4.1. Aplicación de casos de viga normal a ficticia 4.2. Teorema 1 El primer teorema expresa que "la pendiente en cualquier sección de una viga cargada respecto al eje original de la viga es igual al cortante en la viga conjugada en la sección correspondiente" (Rajput, 2018). Esta relación se puede expresar mediante la Ecuación 4.1 y 4.2. wconj = M EI (Ec. 4.1) Vconj = නwdx = නM EI dx = dy dx = θ (Ec. 4.2) 4.3. Teorema 2 El segundo teorema expresa que "la deflexión en una sección cualquiera de una viga cargada, respecto a la posición original, es igual al momento flector en la sección correspondiente de la viga conjugada" (Rajput, 2018). Esta relación se puede expresar mediante la Ecuación 4.3 y 4.4. Vconj = නM EI dx (Ec. 4.3) Mconj = නනM EI dx = y (Ec. 4.4) 4.4. Convención de signos. Para la aplicación del método de la viga conjugada deben emplearse ciertas convenciones y criterios (Gamio, 2014). • Si el diagrama de momentos es positivo, la carga de la viga conjugada se considera hacia abajo. • Si el diagrama de momentos es negativo, la carga de la viga conjugada se considera hacia arriba. • Si la fuerza cortante y el momento flector de la viga conjugada son positivos, la rotación se realiza en sentido horario y la deflexión va hacia abajo respectivamente. 121 • Si la fuerza cortante y el momento flector de la viga conjugada son negativos, la rotación se realiza en sentido antihorario y la deflexión va hacia arriba respectivamente. Ejemplo 4.1. Determine la deflexión y pendiente en los puntos C y D de la viga mostrada en la Figura 4.2 empleando el método de la viga conjugada. Considere que 𝐄𝐄𝐄𝐄= 𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐 𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆 y 𝐈𝐈𝐈𝐈= 𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔 𝐦𝐦𝐦𝐦𝐦𝐦𝐦𝐦𝟒𝟒𝟒𝟒. Figura 4.2 Aplicación del método de la viga conjugada en viga apoyada en los extremos Datos E = 200 GPa = 200x106 kN m2 I = 150x106 mm4 = 1.5x10−4 m4 L = 10 m P 1 = 80 kN P 2 = 60 kN Resolución Realizando momento desde el punto B: ΣMB = 0 −RA(10 m) + 80 kN(8 m) + 60 kN(3 m) = 0 −RA(10 m) + 640 kN m + 180 kN m = 0 −RA(10 m) + 820 kN m = 0 122 −RA(10 m) = −820 kN m RA = −820 kN m −10 m = 82 kN Aplicando sumatoria de Fuerzas en y se tiene: ΣFy = 0 RA −80 kN −60 kN + RB = 0 82 kN −80 kN −60 kN + RB = 0 −58 kN + RB = 0 RB = 58 kN Realizando un corte en el punto C y analizando el momento hacia la izquierda: ΣMC = 0 −82 kN(2 m) + MC = 0 −164 kN m + MC = 0 MC = 164 kN m Realizando un corte en el punto D y analizando el momento hacia la derecha: ΣMD = 0 58 kN(3 m) −MD = 0 174 kN m −MD = 0 MD = 174 kN m Con los valores de momentos encontrados se procede a realizar el diagrama de momentos, para ello se emplea MDSolids y se dividen en áreas como se muestra en la Figura 4.3. 123 Figura 4.3. Obtención del diagrama de momentos MDSolids para método de viga conjugada en viga apoyada en los extremos. Se puede identificar que el diagrama de momentos tiene signo positivo por lo que la carga de la viga conjugada actuaría hacia abajo, distribuyéndose uniformemente sobre toda el área proyectada (color verde) como se muestra en la Figura 4.4. Además, al convertir la viga, en el caso de los apoyos en los extremos, se mantienen los apoyos y actúan fuerzas hacia abajo como se indica en la Tabla 4.1, que se han denominado como RA′ y RB′. Figura 4.4. Representación de cargas para viga conjugada en viga apoyada en los extremos. Una vez obtenida la viga conjugada con su distribución de cargas se procede analizar estáticamente, identificando las reacciones en los apoyos. Realizando momento desde el punto B: ΣMB = 0 124 −RA′(10) −2(164) 2 ൬8 + 2 3൰−5(164) ൬3 + 5 2൰−5(174 −164) 2 ൬3 + 5 3൰ −3(174) 2 ቆ2(3) 3 ቇ= 0 −10RA′ −4264 3 −4510 −350 3 −522 = 0 −6570 −10RA′ = 0 −10RA′ = 6570 RA′ = −6570 10 = −657 kN m2 (↑) Realizando sumatoria de fuerzas en y: ΣFy = 0 RA′ −2(164) 2 −5(164) −5(174 −164) 2 −3(174) 2 −RB′ = 0 657 −164 −820 −25 −261 −RB′ = 0 −613 −RB′ = 0 RB′ = −613 kN m2 (↑) Realizando un corte en el punto C en la viga conjugada y analizando la fuerza cortante hacia la izquierda: ΣFy = 0 RA′ −2(164) 2 −VC = 0 657 −164 −VC = 0 493 −VC = 0 VC = 493 kN m2 Realizando un corte en el punto D en la viga conjugada y analizando la fuerza cortante hacia la derecha: 125 ΣFy = 0 −3(174) 2 + RB′ −VD = 0 −261 + 613 −VD = 0 352 −VD = 0 VD = 352 kN m2 Realizando un corte en el punto C en la viga conjugada y analizando el momento hacia la izquierda: ΣMC = 0 −RA′(2) + 2(164) 2 ൬2 3൰+ MC = 0 −2(657) + 328 3 + MC = 0 −3614 3 + MC = 0 MC = 3614 3 = 1204.67 kN m3 Realizando un corte en el punto D en la viga conjugada y analizando el momento hacia la derecha: ΣMD = 0 −3(174) 2 ൬3 3൰+ RB′(3) −MD = 0 −261 + 613(3) −MD = 0 1578 −MD = 0 MD = 1578 kN m3 Empleando la Ecuación 4.1 se tiene obtienen las pendientes en C y D: 126 θC = Vconj−C EI = 493 200x106(1.5x10−4) = 0.01643 rad θD = Vconj−D EI = 352 200x106(1.5x10−4) = 0.01173 rad Empleando la Ecuación 4.2 se tiene obtienen las deflexiones en C y D: yC = Mconj−C EI = 1204.67 200x106(1.5x10−4) = 0.04016 m = 40.16 mm yD = Mconj−D EI = 1578 200x106(1.5x10−4) = 0.0526 m = 52.26 mm Se emplea el software MDSolids para validar este resultado como se observa en las Figuras 4.5 y 4.6, siendo coincidente con lo calculado. Figura 4.5. Comprobación mediante MDSolids del método de la viga conjugada para viga apoyada en los extremos (pendiente). Figura 4.6. Comprobación mediante MDSolids del método de la viga conjugada para viga apoyada en los extremos (deflexión). 127 Ejemplo 4.2. Determine la deflexión y pendiente en el punto B de la viga mostrada en la Figura 4.7 empleando el método de la viga conjugada. Considere que 𝐄𝐄𝐄𝐄𝐈𝐈𝐈𝐈 como constante. Figura 4.7 Aplicación del método de la viga conjugada en viga empotrada Datos L = 4 m P = 8 kN Resolución Realizando momento desde el punto A: ΣMA = 0 MA −8 kN(2 m) −8 kN(4 m) = 0 MA −16 kN m −32 kN m = 0 MA −48 kN m = 0 MA = 48 kN m Realizando momento desde la mitad de la viga hacia la derecha: ΣMx = 0 Mx −8 kN(2 m) = 0 Mx −16 kN m = 0 Mx = 16 kN m 128 Con los valores de momentos encontrados se procede a realizar el diagrama de momentos, para ello se emplea MDSolids y se dividen en áreas como se muestra en la Figura 4.8. Figura 4.8. Obtención del diagrama de momentos MDSolids para método de viga conjugada en viga empotrada. Se puede identificar que el diagrama de momentos tiene signo negativo por lo que la carga de la viga conjugada actuaría hacia arriba, distribuyéndose uniformemente sobre toda el área proyectada (color verde) como se muestra en la Figura 4.9. Además, al convertir la viga, en el caso del empotramiento, se sustituye por un segmento libre, y el extremo libre por un empotramiento se indica en la Tabla 4.1. Figura 4.9. Representación de cargas para viga conjugada en viga empotrada. Una vez obtenida la viga conjugada con su distribución de cargas se procede analizar estáticamente, identificando las reacciones en los apoyos. Realizando momento desde el punto B: ΣMB = 0 −2(48 −16) 2 ቆ2 + 2(2) 3 ቇ−2(16) ൬2 + 3 2൰−2(16) 2 ቆ2(2) 3 ቇ+ MB′ = 0 −320 3 −112 −64 3 + MB′ = 0 129 −240 + MB′ = 0 MB ′ = 240 kNm3 Realizando un corte en el punto B en la viga conjugada y analizando la fuerza cortante hacia la izquierda: ΣFy = 0 −2(48 −16) 2 −2(16) −2(16) 2 + VB = 0 −32 −32 −16 + VB = 0 −80 + VB = 0 VB = 80 kN m2 Empleando la Ecuación 4.1 se tiene obtiene la pendiente en B: θB = Vconj−B EI = 80 EI Empleando la Ecuación 4.2 se tiene obtiene la deflexión en B: yB = Mconj−B EI = 240 m EI = 240000 mm EI Se emplea el software MDSolids para validar este resultado como se observa en las Figuras 4.10 y 4.11, siendo coincidente con lo calculado. Figura 4.10. Comprobación mediante MDSolids del método de la viga conjugada para viga empotrada (pendiente). 130 Figura 4.11. Comprobación mediante MDSolids del método de la viga conjugada para viga empotrada (deflexión). Ejemplo 4.3. Determine la deflexión y pendiente en los puntos C y D de la viga mostrada en la Figura 4.12 empleando el método de la viga conjugada. Considere que 𝐄𝐄𝐄𝐄= 𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐 𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆𝐆 e 𝐈𝐈𝐈𝐈= 𝟒𝟒𝟒𝟒𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔 𝐦𝐦𝐦𝐦𝐦𝐦𝐦𝐦𝟒𝟒𝟒𝟒 Figura 4.12 Aplicación del método de la viga conjugada en viga apoyada con extremo libre. Datos L = 12 m P 1 = 180 kN P 2 = 45 kN E = 200 GPa = 200x106 kN m2 131 I = 415x106 mm4 = 4.15x10−4 mm4 Resolución Realizando momento desde el punto A: ΣMA = 0 −180 kN(4.5 m) + RB(9 m) −45 kN(12 m) = 0 −810 kN m + RB(9 m) −540 kN m = 0 RB(9 m) −1350 kN m = 0 RB(9 m) = 1350 kN m RB = 1350 kN m 9 m = 150 kN Realizando sumatoria de fuerzas en y: ΣFy = 0 RA −180 kN + RB −45 kN = 0 RA −180 kN + 150 kN −45 kN = 0 RA −75 kN = 0 RA = 75 kN Realizando momento desde el punto C hacia la izquierda ΣMC = 0 MC −75 kN(4.5 m) = 0 MC −337.5 kN m = 0 MC = 337.5 kN m Realizando momento desde el punto B hacia la derecha ΣMB = 0 132 MB −45 kN(3 m) = 0 MB −135 kN m = 0 MB = 135 kN m Realizando momento entre el punto B y C hacia la izquierda para determinar cuando Mx = 0 ΣMx = 0 −RAx + 180(x −4.5) + Mx = 0 −75x + 180x −810 + 0 = 0 105x −810 = 0 x = 810 105 = 54 7 = 7.71 mm Con los valores de momentos encontrados se procede a realizar el diagrama de momentos, para ello se emplea MDSolids y se dividen en áreas como se muestra en la Figura 4.13. Figura 4.13. Obtención del diagrama de momentos MDSolids para método de viga conjugada en viga apoyada con extremo libre. Se puede identificar que el diagrama de momentos tiene signo positivo hasta los 9 m por lo que la carga de la viga conjugada actuaría hacia abajo, y de 9 a 12 m tiene signo negativo por lo que actuaría hacia arriba distribuyéndose uniformemente sobre toda el área proyectada (color verde) como se muestra en la Figura 4.14. Además, al convertir la viga, en el caso del apoyo B, se sustituye por un apoyo interno y el extremo libre por un empotramiento se indica en la Tabla 4.1. 133 Figura 4.14. Representación de cargas para viga conjugada en viga apoyada con extremo libre. Como se posee un apoyo interno se puede dividir la estructura en dos segmentos AB y BC como se muestra en la Figura 4.15 para resolverlo mediante estática. Figura 4.15. Representación de cargas para viga conjugada en viga apoyada con extremo libre (división en apoyos internos). Realizando momento en el punto B del tramo AB: ΣMB = 0 RA′(9) + 4.5(337.5) 2 ൬4.5 + 4.5 3 ൰+ (7.71 −4.5)(337.5) 2 ൬4.5 −7.71 −4.5 3 ൰ −(9 −7.71)(135) 2 ൬9 −7.71 3 ൰= 0 9RA′ + 4556.25 + 1857.99 −37.44 = 0 9RA′ + 6376.80 = 0 9RA′ = −6376.80 134 RA′ = −6376.80 9 = 708.54 kN m2 (↑) Realizando sumatoria de fuerzas en y para la viga completa: ΣFy = 0 RA′ −4.5(337.5) 2 −(7.71 −4.5)(337.5) 2 + (9 −7.71)(135) 2 + 3(135) 2 + RC′ = 0 708.54 −759.38 −541.68 + 87.08 + 202.5 + RC′ = 0 −302.94 + RC′ = 0 RC′ = 302.94 kN m2 Como la fuerza cortante en C corresponde a la reacción, se tiene: VC = RC′ = 302.94 kN m2 Realizando un corte en el punto D en la viga conjugada y analizando la fuerza cortante hacia la izquierda: RA′ −4.5(337.5) 2 + VD = 0 708.54 −759.38 + VD = 0 −50.84 + VD = 0 VD = 50.84 kN m2 Realizando un corte en el punto D en la viga conjugada y analizando el momento hacia la izquierda: −708.54(4.5) + 4.5(337.5) 2 ൬4.5 3 ൰+ MD = 0 −3188.43 + 1139.06 + MD = 0 −2049.37 + MD = 0 MD = 2049.37 kN m3 Realizando un corte en el punto C en la viga conjugada y analizando el momento 135 −708.54(12) + 4.5(337.5) 2 ൬7.5 + 4.5 3 ൰+ (7.71 −4.5)(337.5) 2 ൬7.5 −7.71 −4.5 3 ൰ −(9 −7.71)(135) 2 ൬3 + 9 −7.71 3 ൰−3(135) 2 ቆ2(3) 3 ቇ−MC = 0 −8502.48 + 6834.38 + 3483.05 −298.67 −405 −MC = 0 1111.28 −MC = 0 MC = 1111.28 kN m3 Empleando la Ecuación 4.1 se tiene obtiene las pendientes en C y D: θC = Vconj−C EI = 302.94 200x106(4.15x10−4) = 0.003650 rad θD = Vconj−D EI = 50.84 200x106(4.15x10−4) = 0.000613 rad Empleando la Ecuación 4.2 se tiene obtiene las deflexiones en C y D: yC = Mconj−C EI = 1111.28 m 200x106(4.15x10−4) = 0.01339 m = 13.39 mm yD = Mconj−D EI = 2049.37 m 200x106(4.15x10−4) = 0.02469 m = 24.69 mm Se emplea el software MDSolids para validar este resultado como se observa en las Figuras 4.16 y 4.17, siendo coincidente con lo calculado. Figura 4.16. Comprobación mediante MDSolids del método de la viga conjugada para viga empotrada con extremo libre (pendiente). 136 Figura 4.17. Comprobación mediante MDSolids del método de la viga conjugada para viga empotrada con extremo libre (deflexión). 4.5. Problemas En los problemas 4.1 a 4.10 aplique el método de momento de la viga conjugada para determinar la deflexión y pendiente según se solicite. Considere EI constante. Ejercicio 4.1 Encuentre la deflexión en D y pendiente en C Ejercicio 4.2 Encuentre la deflexión y pendiente en D Ejercicio 4.3 Encuentre la deflexión en C y D, pendiente en A y B Ejercicio 4.4 Encuentre la pendiente y deflexión en C y D 137 Ejercicio 4.5 Encuentre la deflexión y pendiente en C Ejercicio 4.6 Encuentre la deflexión y pendiente en A Ejercicio 4.7 Encuentre la deflexión y pendiente en A Ejercicio 4.8 Encuentre la deflexión y pendiente en A Ejercicio 4.9 Encuentre la deflexión y pendiente en A Ejercicio 3.10 Encuentre la deflexión y pendiente en A y B 1 CAPÍTULO V VIGAS INDETERMINADAS 139 Objetivos • Abordar el análisis de vigas indeterminadas utilizando métodos avanzados para el cálculo de deflexiones, proporcionando a los lectores una comprensión profunda y práctica de técnicas especializadas en ingeniería estructural. • Explorar y aplicar métodos como el de las fuerzas conjugadas, las ecuaciones diferenciales, la energía de deformación y otros métodos avanzados en el análisis de vigas indeterminadas, focalizándose en la determinación precisa de las deflexiones. • Guiar a los lectores a través de la aplicación de estos métodos en el análisis de vigas con condiciones de contorno complejas, cargas variables y restricciones estructurales, demostrando la versatilidad y efectividad de cada método en situaciones desafiantes. • Demostrar la aplicabilidad práctica de estos métodos mediante ejemplos detallados y problemas representativos que aborden situaciones realistas de ingeniería mecánica, permitiendo a los lectores desarrollar habilidades para resolver problemas complejos de deflexión en vigas indeterminadas. • Fomentar la capacidad de los lectores para evaluar y validar los resultados obtenidos mediante el uso de estos métodos en el análisis de vigas indeterminadas, resaltando la importancia de la verificación de cálculos y la comprensión de la precisión y las limitaciones inherentes a cada técnica. 140 5.1. Generalidades Una viga es estáticamente indeterminada si el número de reacciones en los apoyos es superior al número de ecuaciones de equilibrio independientes (B. Raghu Kumar, 2022). Refiriéndose a vigas con sujeciones adicionales, redundantes, más allá de las esenciales para detener los movimientos del cuerpo rígido como lo son: las vigas empotradas apoyadas, doble empotramiento y vigas continuas con tres o más apoyos (Bhaskar & Varadan, 2023). El enfoque general utilizado para resolver vigas estáticamente indeterminadas consiste en seleccionar las reacciones redundantes y desarrollar una ecuación pertinente para cada redundante a partir de la configuración deformada de la viga cargada. Para desarrollar estas ecuaciones geométricas, se seleccionan las reacciones redundantes y se eliminan de la viga. La viga que queda se denomina viga liberada. La viga liberada debe ser estable (es decir, capaz de soportar las cargas) y estáticamente determinada, de modo que las reacciones de la viga liberada puedan determinarse mediante consideraciones de equilibrio. El efecto de las reacciones redundantes se aborda por separado, mediante el conocimiento de las deflexiones o rotaciones que deben producirse en el apoyo redundante (Philpot, 2017b) 5.2. Ventajas Existen algunas ventajas de las estructuras estáticamente indeterminadas frente a las estructuras determinadas (Kassimali, 2020b), se detallan a continuación: • Los esfuerzos máximos en estructuras estáticamente indeterminadas suelen ser inferiores a las de estructuras determinadas comparables. • Las estructuras estáticamente indeterminadas suelen tener rigideces mayores (es decir, deformaciones menores) que las de estructuras determinadas comparables. • Las estructuras indeterminadas tienen más miembros o reacciones de apoyo de las necesarias para la estabilidad estática, por lo que si una parte (o miembro o apoyo) de una estructura de este tipo falla, no necesariamente se derrumbará toda la estructura, y las cargas se redistribuirán a las partes adyacentes de la estructura. 5.3. Doble integración El procedimiento es esencialmente el mismo que para una viga estáticamente determinada, consiste en escribir la ecuación diferencial, integrarla para obtener su solución general y, a continuación, aplicar las condiciones de contorno y otras condiciones para evaluar las incógnitas. Las incógnitas consisten en las reacciones redundantes, así como las constantes de integración (Goodno, Barry & Gere, 2018). 141 Ejemplo 5.1. Determine las reacciones en los apoyos para la viga que se muestra en la Figura 5.1, considere que 𝐄𝐄𝐄𝐄𝐈𝐈𝐈𝐈= 𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐 𝐊𝐊𝐊𝐊𝐤𝐤𝐤𝐤 𝐦𝐦𝐦𝐦𝟐𝟐𝟐𝟐. Desprecie los efectos de la carga axial. Figura 5.1 Aplicación del método de doble integración en viga indeterminada. Datos EI = 200000 kN m2 L = 7 m q = 120 kN m Resolución Realizando sumatoria de fuerzas en y se tiene la expresión I: ΣFy = 0 Ay + By + Cy −120 (6) = 0 Ay + By + Cy −720 = 0 Ay + By + Cy = 720 [I] Realizando sumatoria de momentos en el punto A se tiene la expresión II: ΣMA = 0 −120 (6) ൬6 2൰+ By(6) + Cy(10) = 0 142 −2160 + 6By + 10Cy = 0 [II] Se completa la carga distribuida para el análisis del momento interno como se muestra en la Figura 5.2. Figura 5.2 Aplicación del método de doble integración en viga indeterminada (completar carga). Para la aplicación del método de Macaulay se debe realizar un corte en el punto más alejado hacia la derecha donde se pueda obtener el momento interno, como se realiza a continuación: ΣMx = 0 −Ayx + 120 (x) ቀx 2ቁ−By(x −6) −120 (x −6) ൬x −6 2 ൰+ M = 0 −Ayx + 60 x2 −By(x −6) −60 (x −6)2 + M = 0 M = Ayx −60 x2 + By(x −6) + 60 (x −6)2 Observando que la viga al deformarse se produce compresión en la parte superior, se considera que el momento Mx es positivo, sustituyendo el momento encontrado en la Ecuación 1.8 se obtiene la expresión [III]: EI d2y dx2 = Ayx −60 x2 + By(x −6) + 60 (x −6)2 [III] Integrando dos veces la expresión [III] se obtiene: EI dy dx = Ay 2 x2 −60 3 x3 + By 2 (x −6)2 + 60 3 (x −6)3 + C1 [IV] EIy = Ay 6 x3 −5 x4 + By 6 (x −6)3 + 5 (x −6)4 + C1x + C2 [V] 143 En la condición de frontera del apoyo izquierdo, cuando x = 0, y = 0, se observa que en el segundo y tercer término se cumple la primera condición de la Ecuación 1.34 que indica que cuando x < a se sustituye todas las expresiones en paréntesis por cero. Reemplazando estos elementos en la expresión [V] se tiene: EI(0) = Ay 6 (0)3 −5 (0)4 + By 6 (0)3 + 5 (0)4 + C1(0) + C2 0 = 0 −0 + 0 + 0 + 0 + C2 C2 = 0 En la condición de frontera en el extremo de la viga, cuando x = 6, y = 0, C2 = 0 se observa que todos los términos en paréntesis cumplen la segunda condición de la Ecuación 1.34 que indica que cuando x > a se consideran todas las expresiones involucradas. Reemplazando estos elementos en la expresión [VI] se tiene la expresión: EI(0) = Ay 6 (6)3 −5 (6)4 + By 6 (6 −6)3 + 5 (6 −6)4 + C1(6) + 0 0 = 36Ay −5 (6)4 + By 6 (0)3 + 5 (0)4 + C1(6) + 0 0 = 36Ay −6480 + 6C1 [VI] En la condición de frontera en el extremo de la viga, cuando x = 10, y = 0, C2 = 0 se observa que todos los términos en paréntesis cumplen la segunda condición de la Ecuación 1.34 que indica que cuando x > a se consideran todas las expresiones involucradas. Reemplazando estos elementos en la expresión [VII] se tiene: EI(0) = Ay 6 (10)3 −5 (10)4 + By 6 (10 −6)3 + 5 (10 −6)4 + C1(10) + 0 0 = 500Ay 3 −50000 + 32 3 By + 1280 + 10C1 + 0 0 = 500Ay 3 −48720 + 32 3 By + 10C1 [VII] Resolviendo las ecuaciones [I], [II], [VI] y [VII] se obtiene que: C1 = −756 kN mm2 144 Ay = 306 kN By = 495 kN Cy = −81 kN Adicionalmente se emplea el software Ftool para validar este resultado como se observa en la Figura 5.3, siendo el valor de las reacciones coincidentes con lo calculado. Figura 5.3. Comprobación mediante Ftool de viga indeterminada para el método de doble integración. 5.4. Superposición En una viga estáticamente indeterminada dada, se utiliza el método de superposición para satisfacer las condiciones de contorno que existen en los apoyos de la viga. Este procedimiento conduce a una o más relaciones entre las cantidades desconocidas que complementan las ecuaciones de equilibrio disponibles (Muvdi & Elhouar, 2016). Ejemplo 5.2. Determine las reacciones en el punto B para la viga que se muestra en la Figura 5.4, EI es constante. Desprecie los efectos de la carga axial. Figura 5.4 Aplicación del método de superposición en viga indeterminada. Datos L = 4 m 145 q = 9 kN m Resolución Se procede a dividir las cargas aplicadas en la viga según los casos 28, 24 y 35 indicados en la Tabla 2.1 como se muestra en la Figura 2.5. De manera que se empleen las ecuaciones correspondientes para determinar las deflexiones y pendientes individuales en el punto B. Figura 5.5 Aplicación de división de cargas según el método de superposición en viga indeterminada. Caso 28 yB1 = −7qL4 384EI = −7(9)(4)4 384EI = −42 EI θB1 = −qL3 48EI = −9(4)3 48EI = −12 EI Caso 24 yB2 = −PL3 3EI = −RB(4)3 3EI = −64RB 3EI θB2 = −PL2 2EI = −RB(4)2 2EI = −8RB EI Caso 35 yB3 = −ML2 2EI = −MB(4)2 2EI = −8MB EI θB3 = −ML EI = −MB(4) EI = −4MB EI Se determina la deformación y pendiente total en B sumando cada una de las deformaciones y pendientes individuales en ese punto, como detalle importante se debe recordar que inicialmente el punto B estaba restringido, por lo que la deformación y pendiente en ese punto es igual a cero. 146 yB = yB1 + yB2 + yB3 = 0 −42 EI −64RB 3EI −8MB EI = 0 −42 −64RB 3 −8MB = 0 42 + 64RB 3 + 8MB = 0 [I] θB = θB1 + θB2 + θB3 = 0 −12 EI −8RB EI −4MB EI = 0 −12 −8RB −4MB = 0 12 + 8RB + 4MB = 0 [II] Resolviendo el sistema de ecuaciones [I] y [II] se obtiene que: RB = 3.375 kN MB = −3.75 kN m Adicionalmente se emplea el software Ftool para validar este resultado como se observa en la Figura 5.6, siendo el valor del momento en B coincidentes con lo calculado. Figura 5.6. Comprobación mediante Ftool de viga indeterminada para el método de superposición. 5.5. Momento de área Para una viga indeterminada en primer grado, una de las reacciones se designa como redundante, y el apoyo correspondiente se elimina o modifica en consecuencia. La reacción redundante se trata entonces como una carga desconocida que, junto con las otras cargas, debe producir deformaciones compatibles con los apoyos originales. Esta condición de 147 compatibilidad suele expresarse escribiendo que la desviación tangencial de un apoyo con respecto a otro es cero o tiene un valor predeterminado (Beer et al., 2020). Ejemplo 5.3. Determine la reacción en el punto A para la viga que se muestra en la Figura 5.7, EI es constante. Desprecie los efectos de la carga axial. Figura 5.7 Aplicación del método de momento de área en viga indeterminada (método por partes). Datos L = 4.5 m P 1 = 60 kN P 2 = 40 kN m Resolución Se procede a mover el apoyo del punto A y convertirlo en redundante, con lo cual se puede dividir las condiciones de carga para realizar los diagramas de momentos individuales como se muestra en la Figura 5.8. Figura 5.8 Representación de división de cargas para aplicación de método de momento de área por partes. 148 Caso 1 Realizando momento desde el punto B: ΣMB = 0 60(3) −MB1 = 0 180 −MB1 = 0 MB1 = 180 kN m Con el valor del momento encontrado se procede a realizar el diagrama de momentos, para ello se emplea MDSolids como se muestra en la Figura 5.9. Figura 5.9. Obtención del diagrama de momentos MDSolids para el método de momento de área por partes en viga indeterminada (Caso 1). Caso 2 Realizando momento desde el punto B: ΣMB = 0 RA(4.5) −MB2 = 0 MB2 = 4.5RA Con el valor del momento encontrado se procede a realizar el diagrama de momentos, para ello se emplea MDSolids como se muestra en la Figura 5.10. 149 Figura 5.10. Obtención del diagrama de momentos MDSolids para el método de momento de área por partes en viga indeterminada (Caso 2). Caso 3 Realizando momento desde el punto B: ΣMB = 0 40(1.5) −MB3 = 0 MB3 = 60 kN m Con el valor del momento encontrado se procede a realizar el diagrama de momentos, para ello se emplea MDSolids como se muestra en la Figura 5.11. Figura 5.11. Obtención del diagrama de momentos MDSolids para el método de momento de área por partes en viga indeterminada (Caso 3). 150 Se considera que la deformación alcanzada entre AB es cero, debido a los apoyos en los extremos. Empleando la Ecuación 3.3, y reemplazando los valores de las áreas correspondientes del tramo AB según la Tabla 3.1 se tiene: yA/B = 1 EI (A1x1 + A2x2 + A3x3) = 0 1 EI ቈ(180)(3) 2 ቆ1.5 + 2(3) 3 ቇ−4.5RA(4.5) 2 ቆ2(4.5) 3 ቇ+ 60(1.5) 2 ቆ3 + 2(1.5) 3 ቇ቉= 0 1 EI [1125 −30.375RA] = 0 1125 −30.375RA = 0 30.375RA = 1125 RA = 1125 30.375 = 37.037 kN 151 Bibliografía B. Raghu Kumar. (2022). Statically indeterminate beams. Strength of materials (pp. 120-152). CRC Press. 10.1201/9781003298748 Bedford and Liechti. (2020). Deflections of beams. In A. Bedford, & K. M. Liechti (Eds.), Mechanics of materials (pp. 671-728). Springer International Publishing. 10.1007/978-3-030-22082-2_9 Beer, et al. (2020). Deflections of beams. In , (Ed.), Mechanics of materials (8th ed., pp. 599-689). McGraw-Hill Education. Bhaskar and Varadan. (2023). Beams–Deflections. In K. Bhaskar, & T. K. Varadan (Eds.), Strength of materials: A concise textbook (pp. 61-90). Springer International Publishing. 10.1007/978-3-031-06377-0_7 Gamio. (2014). Método viga conjugada. In E. Macro (Ed.), (1; 1 ed., pp. 377-394). Macro. Goodno and Gere James. (2018). Deflections of beams. Mechanics of materials (pp. 811-908). Cengage learning. Goodno and Gere. (2018). Statically indeterminate beams. In , (Ed.), Mechanics of materials (9th ed., pp. 909-962). Cengage Learning. Hibbeler. (2020). Deflections. Structural analysis (pp. 294-337). Pearson Education. Kassimali. (2020a). Deflections of beams: Geometric methods. Structural analysis (pp. 224-288). Cengage Learning. 152 Kassimali. (2020b). Introduction to statically indeterminate structures. Structural analysis (pp. 441-470). Cengage Learning. Limbrunner and D'Allaird. (2016). Deflection of beams. Applied statics and strength of materials (pp. 334-365). Pearson. Muvdi and Elhouar. (2016). Bending loads: Deflections under symmetric loading . In , (Ed.), Mechanics of materials : With applications in excel (pp. 391-472). Taylor & Francis. Philpot. (2017a). Beam deflections. In , (Ed.), (4th ed., pp. 391-444). John Wiley & Sons. Philpot. (2017b). Statically indeterminate beams. In , (Ed.), (4th ed., pp. 469-506). John Wiley & Sons. R.K. Kaushik. (2019). Deflection of beams. Strength of materials (pp. 234-290). Dreamtech Press. Rajput. (2018). Deflection of beams. A textbook of strength of materials (pp. 331-455). S. Chand Publishing. Singh. (2021). Deflections of beams. In D. K. Singh (Ed.), Strength of materials (pp. 251-318). Springer International Publishing. 10.1007/978-3-030-59667-5_6 Srivastava and Gope. (2012). Deflection of beams. Strength of materials (pp. 158-209). PHI Learning Private Limited. 1 ESTE LIBRO SURGE DE LA NECESIDAD POR COMPRENDER LA MECÁNICA SUBYACENTE QUE DICTA CÓMO LAS VIGAS SOPORTAN CARGAS Y RESISTEN LAS FUERZAS QUE MOLDEAN NUESTRO ENTORNO. SE HA DISEÑADO ESPECÍFICAMENTE PARA ESTUDIANTES, INGENIEROS Y ENTUSIASTAS DE LA INGENIERÍA MECÁNICA QUE BUSCAN PROFUNDIZAR EN LA ESENCIA DE CÓMO LAS VIGAS, ELEMENTOS APARENTEMENTE SIMPLES, SOSTIENEN LA COMPLEJIDAD DE MÁQUINAS Y ESTRUCTURAS ROBUSTAS.
13239	https://askfilo.com/user-question-answers-smart-solutions/6-the-number-of-non-empty-subsets-of-the-setis-1-2-3-4-is-a-3239343336313130	Question asked by Filo student Views: 5,123 students Updated on: Mar 11, 2025 Text SolutionText solutionverified iconVerified Concepts: Set theory, Subsets Explanation: To find the number of non-empty subsets of a set, we first calculate the total number of subsets of the set. For a set with n elements, the total number of subsets is given by 2n. Then, we subtract 1 to exclude the empty subset. Step by Step Solution: Step 1 Identify the number of elements in the set {1, 2, 3, 4}. The set has 4 elements. Step 2 Calculate the total number of subsets using the formula 2n. Here, n = 4, so the total number of subsets is 24=16. Step 3 Subtract 1 to exclude the empty subset. Therefore, the number of non-empty subsets is 16−1=15. Final Answer: The number of non-empty subsets of the set {1, 2, 3, 4} is 15. Students who ask this question also asked Views: 5,614 Topic: Smart Solutions View solution Views: 5,668 Topic: Smart Solutions View solution Views: 5,651 Topic: Smart Solutions View solution Views: 5,657 Topic: Smart Solutions View solution Stuck on the question or explanation? Connect with our tutors online and get step by step solution of this question. \| \| \| --- \| \| Question Text \| 6. The number of non-empty subsets of the setis {1,2,3,4} is a. 14 {1,2,3,4) fem a zid dich zukkaat aan 16 c. 17 \| \| Updated On \| Mar 11, 2025 \| \| Topic \| All topics \| \| Subject \| Smart Solutions \| \| Class \| Class 11 \| \| Answer Type \| Text solution:1 \| Are you ready to take control of your learning? Download Filo and start learning with your favorite tutors right away! Questions from top courses Explore Tutors by Cities Blog Knowledge © Copyright Filo EdTech INC. 2025
13240	https://brainly.com/question/43488287	[FREE] Proof of cosine half-angle identity: 1. \cos(2θ) = 2\cos^2(θ) - 1 (given) 2. 1 + \cos(2θ) = 2\cos^2(θ) - brainly.com Search Learning Mode Cancel Log in / Join for free Browser ExtensionTest PrepBrainly App Brainly TutorFor StudentsFor TeachersFor ParentsHonor CodeTextbook Solutions Log in Join for free Tutoring Session +23,8k Smart guidance, rooted in what you’re studying Get Guidance Test Prep +37,2k Ace exams faster, with practice that adapts to you Practice Worksheets +7,7k Guided help for every grade, topic or textbook Complete See more / Mathematics Expert-Verified Expert-Verified Proof of cosine half-angle identity: cos(2 θ)=2 cos 2(θ)−1 (given) 1+cos(2 θ)=2 cos 2(θ) (add 1 to both sides) cos 2(2 θ)=2 1+c o s(2(2 θ)) (divide by 2) cos 2(2 θ)=2 1+c o s(θ) cos(2 θ)=±2 1+c o s(θ) Analyze the proof. Use the drop-down boxes to complete the sentences. The third line of this proof is known as the _____ identity of cosine. The justification for the fourth line is ____. 2 See answers Explain with Learning Companion NEW Asked by LacrosseGator4029 • 11/27/2023 0:02 / 0:15 Read More Community by Students Brainly by Experts ChatGPT by OpenAI Gemini Google AI Community Answer This answer helped 246272607 people 246M 4.8 4 Upload your school material for a more relevant answer The third line of this proof is known as the power reducing. identity of cosine. The justification for the fourth line is substitution. In Mathematics and Geometry, a trigonometric equation is a type of mathematical equation that comprises one or more of the six trigonometric expression cotangent, sine, secant, cosine, tangent, and cosecant. A two-column proof of cosine half-angle identity should be completed as follows; Statements Reasons_____ cos(2 θ)=2 co s 2 θ−1 Given 1+cos(2 θ)=2 co s 2 θ Add 1 to both sides co s 2 θ=2 1+cos(2 θ)Divide by 2 co s 2(2 θ)=2 1+cos(2(2 θ))Power reducing co s 2(2 θ)=2 1+cos θMultiplication cos(2 θ)=±2 1+cos θ Square root Missing information; Analyze the proof. Use the drop-down boxes to complete the sentences. The third line of this proof is known as the . identity of cosine. The justification for the fourth line is . Answered by Lanuel •38K answers•246.3M people helped Thanks 4 4.8 (4 votes) Expert-Verified⬈(opens in a new tab) This answer helped 246272607 people 246M 4.8 3 Upload your school material for a more relevant answer The third line of the proof is known as the power reducing identity of cosine, while the justification for the fourth line is substitution. The proof illustrates the relationship between the cosine of an angle and its half-angle. Understanding this relationship is essential in trigonometry and its applications. Explanation To analyze the proof given for the cosine half-angle identity, let's fill in the blanks in the provided statements. The third line of this proof is known as the power reducing identity of cosine. This identity allows us to express the cosine of a doubled angle in terms of the cosine of a single angle. The justification for the fourth line is substitution. In this step, we substitute the argument for cosine in the power reducing identity with the specific argument given, which is 2(2 θ)=θ, thereby simplifying our equation to reflect this substitution. This proof ultimately demonstrates that cos 2(2 θ) indeed equals 2 1+cos(θ). This relationship is useful in various applications of trigonometry, especially in integrating or simplifying trigonometric functions. Examples & Evidence For instance, if θ=6 0∘, we can use the half-angle identity to find cos(3 0∘). By substituting into the formula, we find that ( \cos(30^\circ) = \pm \sqrt{\frac{1 + \cos(60^\circ)}{2}} = \pm \sqrt{\frac{1 + \frac{1}{2}}{2}} = \pm \sqrt{\frac{3}{4}} = \pm \frac{\sqrt{3}}{2}. Since 3 0∘ is in the first quadrant, we accept the positive value, confirming that (\cos(30^\circ) = \frac{\sqrt{3}}{2}. The power reducing identity cos 2 x=2 1+c o s(2 x) is a well-established trigonometric identity derived from the general definition of cosine and can be verified by substituting specific angle values in any standard trigonometric reference. Thanks 3 4.8 (4 votes) Advertisement Community Answer This answer helped 3455829 people 3M 3.0 0 The third line of this proof is known as the "double angle" identity of cosine. The justification for the fourth line is "applying the algebraic operation of adding 1 to both sides of the equation." How is it so? Given: cos(2 θ)=2 cos 2(θ)−1 Add 1 to both sides: 1+cos(2 θ)=2 cos 2(θ) Divide by 2: 2 1+c o s(2 θ)=cos 2(2 θ) This follows from dividing both sides of the equation by 2. Apply double angle identity: cos 2(2 θ)=cos(2 2(2 θ)) Substituting 2 θ for θ in the double angle identity cos(2 θ)=2 cos 2(θ)−1.[/tex] Simplify the expression: [tex]cos 2(2 θ)=2 1+c o s(θ) This simplification follows from the double angle identity \cos(2\theta) = 2\cos^2(\theta) - 1 \ So, the third line is the application of the double angle identity of cosine, and the justification for the fourth line is applying algebraic operations to simplify the expression. Answered by Yormex •7.1K answers•3.5M people helped Thanks 0 3.0 (1 vote) Advertisement ### Free Mathematics solutions and answers Community Answer Review the proof. A 2-column table with 8 rows. Column 1 is labeled Step with entries 1, 2, 3, 4, 5, 6, 7, 8. Column 2 is labeled Statement with entries cosine (2 x) = 1 minus 2 sine squared (x), let 2 x = theta, then x = StartFraction theta Over 2 EndFraction, cosine (theta) = 1 minus 2 sine squared (StartFraction theta Over 2 EndFraction), negative 1 + cosine (theta) = negative 2 sine squared (StartFraction theta Over 2 EndFraction), 1 + cosine (theta) = 2 sine squared (StartFraction theta Over 2 EndFraction), StartFraction 1 minus cosine (theta) Over 2 EndFraction = sine squared (StartFraction theta Over 2 EndFraction), sine (StartFraction theta Over 2 EndFraction) = plus-or-minus StartRoot StartFraction 1 minus cosine (theta) Over 2 EndFraction EndRoot. Which step contains an error? Community Answer 5.0 1 A 2-column table with 3 rows. column 1 is labeled statements with entries 1. sine squared (t) = startfraction 1 minus cosine (2 t) over 2 endfraction, 2. sine squared (startfraction t over 2 endfraction) = startstartfraction 1 minus cosine (startfraction t over 2 endfraction) overover 2 endendfraction, 3. sine (startfraction t over 2 endfraction) = plus-or-minus startroot startstartfraction 1 minus cosine (startfraction t over 2 endfraction) overover 2 endendfraction endroot. column 2 is labeled justification with entries power reducing identity, substitution of half angle, square root. select the place in which an error first occurs in the proof of sine (startfraction t over 2 endfraction). statement 1 statement 2 justification 1 justification 3 Community Answer Review the proof (not in order) of the identity tangent (startfraction theta over 2 endfraction) = plus-or-minus startroot startfraction 1 minus cosine (theta) over 1 cosine (theta) endfraction endroot.. a 2-column table with 5 rows. column 1 is labeled step with entries 1, 2, 3, 4, 5. column 2 is labeled statement with entries tangent (startfraction theta over 2 endfraction) = startstartfraction sine (startfraction theta over 2 endfraction) overover cosine (startfraction theta over 2 endfraction) endendfraction, tangent (startfraction theta over 2 endfraction) = startroot startfraction (1 minus cosine (theta) over 2 endfraction) (startfraction 2 over 1 cosine (theta) endfraction endroot, tangent (startfraction theta over 2 endfraction) = startstartfraction startroot startfraction 1 minus cosine (theta) over 2 endfraction endroot overover startroot startfraction 1 cosine (theta) over 2 endfraction endroot endendfraction, tangent (startfraction theta over 2 endfraction) = startroot startstartfraction startfraction 1 minus cosine (theta) over 2 endfraction overover startfraction 1 cosine (theta) over 2 endfraction endendfraction endroot, tangent (startfraction theta over 2 endfraction) = plus-or-minus startroot startfraction 1 minus cosine (theta) over 1 cosine (theta) endfraction endroot. what is the correct sequence of steps? 1-3-2-4-5 1-3-4-2-5 1-4-2-3-5 1-4-3-2-5 Community Answer Which equation can be used to prove 1 + tan2(x) = sec2(x)? StartFraction cosine squared (x) Over secant squared (x) EndFraction + StartFraction sine squared (x) Over secant squared (x) EndFraction = StartFraction 1 Over secant squared (x) EndFraction StartFraction cosine squared (x) Over sine squared (x) EndFraction + StartFraction sine squared (x) Over sine squared (x) EndFraction = StartFraction 1 Over tangent squared (x) EndFraction StartFraction cosine squared (x) Over tangent squared (x) EndFraction + StartFraction sine squared (x) Over tangent squared (x) EndFraction = StartFraction 1 Over tangent squared (x) EndFraction StartFraction cosine squared (x) Over cosine squared (x) EndFraction + StartFraction sine squared (x) Over cosine squared (x) EndFraction = StartFraction 1 Over cosine squared (x) EndFraction Community Answer 5.0 1 Use the drop-down menus to complete the solution to the equation cosine (startfraction pi over 2 endfraction minus x) = startfraction startroot 3 endroot over 2 endfraction for all possible values of x on the interval [0, 2pi]. cosine (x minus startfraction pi over 2 endfraction) = startfraction startroot 3 endroot over 2 endfraction cosine (x) cosine (startfraction pi over 2 endfraction) sine (x) sine (startfraction pi over 2 endfraction) = startfraction startroot 3 endroot over 2 endfraction cos(x) ( ) + sin(x) ( ) = startfraction startroot 3 endroot over 2 endfraction _(x) =startfraction startroot 3 endroot over 2 endfraction thus, x = pi/_ ,2pi/_____. Community Answer 4.8 21 URGENT PLS HELP - This proof shows the first five steps for verifying Cotangent squared (StartFraction x Over 2 EndFraction) = StartFraction cosine x + 1 Over cosine x minus 1 EndFraction Use the drop-down boxes to complete the steps of the proof. Community Answer 5.0 1 For what value of θ is inverse of cosine (startfraction startroot 2 endroot over 2 endfraction) = theta? a. startfraction pi over 6 endfraction b. startfraction pi over 4 endfraction c. startfraction pi over 3 endfraction d. startfraction pi over 2 endfraction Community Answer 4.6 12 Jonathan and his sister Jennifer have a combined age of 48. If Jonathan is twice as old as his sister, how old is Jennifer Community Answer 11 What is the present value of a cash inflow of 1250 four years from now if the required rate of return is 8% (Rounded to 2 decimal places)? Community Answer 13 Where can you find your state-specific Lottery information to sell Lottery tickets and redeem winning Lottery tickets? (Select all that apply.) 1. Barcode and Quick Reference Guide 2. Lottery Terminal Handbook 3. Lottery vending machine 4. OneWalmart using Handheld/BYOD New questions in Mathematics The power 3−3 equals 27 1. Which expression is equivalent to 3−3?A. 3 2 1B. 3 3 1C. 9 3 1D. 3 9 1 89.5×5 6 Write your answer as a decimal. Compare the average rate of change for f(x)=3 x and g(x)=3 x+5 for 0≤x≤4. A. The average rate of change of g(x) is greater than that of f(x). B. The average rate of change of f(x) is greater than that of g(x). C. The average rates of change of f(x) and g(x) are the same. Which graph represents the function f(x)=−∣x−3∣+1 ? Select all of the non-real complex numbers in the given table. \| 5−4 9 \| \| 1+−3 \| \| 4−3−16 \| \| 5 2−12 \| \| 7 3+2−9 \| \| 9−5 7 \| Previous questionNext question Learn Practice Test Open in Learning Companion Company Copyright Policy Privacy Policy Cookie Preferences Insights: The Brainly Blog Advertise with us Careers Homework Questions & Answers Help Terms of Use Help Center Safety Center Responsible Disclosure Agreement Connect with us (opens in a new tab)(opens in a new tab)(opens in a new tab)(opens in a new tab)(opens in a new tab) Brainly.com
13241	https://pubmed.ncbi.nlm.nih.gov/35732476/	Clinical and laboratory aspects of condylomata lata lesions of syphilis - PubMed Clipboard, Search History, and several other advanced features are temporarily unavailable. Skip to main page content An official website of the United States government Here's how you know The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site. The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely. 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Clinical and laboratory aspects of condylomata lata lesions of syphilis Janet M Towns12,Ian Denham3,Eric P F Chow32,Stephen Graves4,Christopher K Fairley32,Deborah Williamson56,Francesca Azzato6,Marcus Y Chen32 Affiliations Expand Affiliations 1 Melbourne Sexual Health Centre, Alfred Health, Carlton, Victoria, Australia jtowns@mshc.org.au. 2 Central Clinical School, Monash University, Clayton, Victoria, Australia. 3 Melbourne Sexual Health Centre, Alfred Health, Carlton, Victoria, Australia. 4 Barwon Health, Australian Rickettsial Reference Laboratory, Geelong, Victoria, Australia. 5 Department of Infectious Diseases, The University of Melbourne, The Peter Doherty Institute for Infection and Immunity, Melbourne, Victoria, Australia. 6 Victorian Infectious Diseases Reference Laboratory, The Peter Doherty Institute for Infection and Immunity, Melbourne, Victoria, Australia. PMID: 35732476 DOI: 10.1136/sextrans-2021-055385 Item in Clipboard Clinical and laboratory aspects of condylomata lata lesions of syphilis Janet M Towns et al. Sex Transm Infect.2023 May. Show details Display options Display options Format Sex Transm Infect Actions Search in PubMed Search in NLM Catalog Add to Search . 2023 May;99(3):162-166. doi: 10.1136/sextrans-2021-055385. Epub 2022 Jun 22. Authors Janet M Towns12,Ian Denham3,Eric P F Chow32,Stephen Graves4,Christopher K Fairley32,Deborah Williamson56,Francesca Azzato6,Marcus Y Chen32 Affiliations 1 Melbourne Sexual Health Centre, Alfred Health, Carlton, Victoria, Australia jtowns@mshc.org.au. 2 Central Clinical School, Monash University, Clayton, Victoria, Australia. 3 Melbourne Sexual Health Centre, Alfred Health, Carlton, Victoria, Australia. 4 Barwon Health, Australian Rickettsial Reference Laboratory, Geelong, Victoria, Australia. 5 Department of Infectious Diseases, The University of Melbourne, The Peter Doherty Institute for Infection and Immunity, Melbourne, Victoria, Australia. 6 Victorian Infectious Diseases Reference Laboratory, The Peter Doherty Institute for Infection and Immunity, Melbourne, Victoria, Australia. PMID: 35732476 DOI: 10.1136/sextrans-2021-055385 Item in Clipboard Full text links Cite Display options Display options Format Abstract Objectives: Condylomata lata are a less common but distinctive syphilitic lesion. Variable theories as to their nature and origin exist. The aim of this study was to determine the clinical and laboratory characteristics of condylomata lata by determining (1): the most closely aligned stage of syphilis, based on the rapid plasma reagin (RPR) titre; (2) symptom duration and (3) Treponema pallidum PCR cycle threshold (C T) values, as an indicator of organism load. Methods: This was a retrospective study of patients with T. pallidum PCR-positive condylomata lata lesions, attending a clinic in Melbourne, Australia, between 2011 and 2021. Syphilis serology was undertaken and RPR titres compared between condylomata lata, primary and secondary syphilis cases. Results: 51 cases with T. pallidum PCR-positive condylomata lata were included. 41 cases were in men, 40 of whom were men who have sex with men (MSM), and 10 in women. Twelve of 51 (24%) cases were in HIV-positive MSM. Thirty-three of 51 (65%) had other mucocutaneous signs of secondary syphilis; 18 (35%) had no other signs of secondary syphilis. The median RPR titre among the 51 condylomata lata cases was 1:128, compared with the median RPR titre of primary syphilis (1:4) and of secondary syphilis (1:128). The median duration of lesions was 24 (IQR 10-60) days, with no significant difference between those with and without other signs of secondary syphilis (p=0.75). Median C T values for condylomata lata (C T=31) and primary syphilis (C T=31) were significantly lower than for other secondary syphilis lesion types (C T=33), indicating higher T. pallidum loads for condylomata lata and primary lesions compared with other secondary syphilis lesion types. Discussion: These findings support condylomata lata as lesions that occur during the secondary stage of syphilis and which are likely to be highly infectious. Keywords: DIAGNOSIS; Polymerase Chain Reaction; SYPHILIS. © Author(s) (or their employer(s)) 2023. No commercial re-use. See rights and permissions. Published by BMJ. PubMed Disclaimer Conflict of interest statement Competing interests: None declared. Similar articles Anal and oral detection of Treponema pallidum in men who have sex with men with early syphilis infection.Towns JM, Chow EPF, Wigan R, Fairley CK, Williamson D, Azzato F, Graves S, Zhang L, Chen MY.Towns JM, et al.Sex Transm Infect. 2022 Dec;98(8):570-574. doi: 10.1136/sextrans-2021-055370. Epub 2022 May 26.Sex Transm Infect. 2022.PMID: 35618414 Treponema pallidum detection in lesion and non-lesion sites in men who have sex with men with early syphilis: a prospective, cross-sectional study.Towns JM, Leslie DE, Denham I, Wigan R, Azzato F, Williamson DA, Lee D, Chow EPF, Fairley CK, Graves SR, Zhang L, Chen MY.Towns JM, et al.Lancet Infect Dis. 2021 Sep;21(9):1324-1331. doi: 10.1016/S1473-3099(20)30838-0. Epub 2021 Apr 22.Lancet Infect Dis. 2021.PMID: 33894904 Detection of Treponema pallidum DNA for diagnosis, resistance identification, and treatment outcome prediction in early syphilis among men who have sex with men.Wu TY, Lin KY, Sun HY, Huang YS, Liu WD, Su LH, Liu WC, Su YC, Chang SY, Hung CC.Wu TY, et al.Clin Microbiol Infect. 2025 Jun;31(6):1026-1032. doi: 10.1016/j.cmi.2025.02.017. Epub 2025 Feb 18.Clin Microbiol Infect. 2025.PMID: 39978634 Treponema pallidum PCR testing for diagnosis of mucocutaneous ulcers suspicious for syphilis.Junejo MH, Collery M, Whitlock G, McOwan A, Tittle V, Nugent D.Junejo MH, et al.Sex Transm Infect. 2022 Aug;98(5):380-382. doi: 10.1136/sextrans-2021-055192. Epub 2021 Nov 16.Sex Transm Infect. 2022.PMID: 34785619 Review. Secondary syphilis with extra-genital condyloma lata: A case report and review of the literature.Barei F, Murgia G, Ramoni S, Cusini M, Marzano AV.Barei F, et al.Int J STD AIDS. 2022 Oct;33(12):1022-1028. doi: 10.1177/09564624221124710. Epub 2022 Sep 14.Int J STD AIDS. 2022.PMID: 36113077 Review. See all similar articles Cited by Southern African HIV Clinicians Society Guideline for the clinical management of syphilis.Peters RPH, Nel JS, Sadiq E, Kufa T, Smit DP, Sorour G, Garrett N, Gill K, Makhakhe L, Chandiwana NC, Moran NF, Cohen K, Wattrus C, Moosa MY.Peters RPH, et al.South Afr J HIV Med. 2024 Apr 30;25(1):1577. doi: 10.4102/sajhivmed.v25i1.1577. eCollection 2024.South Afr J HIV Med. 2024.PMID: 38725703 Free PMC article. Visual clues - dermatological manifestations of sexually transmitted infections in men.Mass Lindenbaum M, Calderón D, Aslot V, Ljubetic B, Harlamova D, Bole R, Bajic P, Navarrete J.Mass Lindenbaum M, et al.Nat Rev Urol. 2025 Aug 13. doi: 10.1038/s41585-025-01071-1. Online ahead of print.Nat Rev Urol. 2025.PMID: 40804205 Review. Publication types Research Support, Non-U.S. Gov't Actions Search in PubMed Search in MeSH Add to Search MeSH terms Female Actions Search in PubMed Search in MeSH Add to Search Gastrointestinal Diseases Actions Search in PubMed Search in MeSH Add to Search Homosexuality, Male Actions Search in PubMed Search in MeSH Add to Search Humans Actions Search in PubMed Search in MeSH Add to Search Male Actions Search in PubMed Search in MeSH Add to Search Retrospective Studies Actions Search in PubMed Search in MeSH Add to Search Sexual and Gender Minorities Actions Search in PubMed Search in MeSH Add to Search Syphilis Serodiagnosis Actions Search in PubMed Search in MeSH Add to Search Syphilis / complications Actions Search in PubMed Search in MeSH Add to Search Syphilis, Cutaneous Actions Search in PubMed Search in MeSH Add to Search Treponema pallidum Actions Search in PubMed Search in MeSH Add to Search Supplementary concepts Syphilis, primary Actions Search in PubMed Search in MeSH Add to Search Syphilis, secondary Actions Search in PubMed Search in MeSH Add to Search Related information MedGen LinkOut - more resources Full Text Sources HighWire Full text links[x] HighWire [x] Cite Copy Download .nbib.nbib Format: Send To Clipboard Email Save My Bibliography Collections Citation Manager [x] NCBI Literature Resources MeSHPMCBookshelfDisclaimer The PubMed wordmark and PubMed logo are registered trademarks of the U.S. Department of Health and Human Services (HHS). 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13242	https://www.youtube.com/watch?v=xl0VT10B_Vk	Survey Problem: Intersection of 3 sets not given VC math 500 subscribers 35 likes Description 3656 views Posted: 13 Nov 2019 Survey Problem: Intersection of 3 sets not given. Uses Venn diagrams. 4 comments Transcript: [Instructor] Let's do a Venn diagram problem. We have this survey situation. In a survey of 300 people, 122 drive Fords, 150 drive Chevys, 62 drive Nissans, 38 drive Fords and Chevys, 20 drive Fords and Nissans, 28 drive Chevys and Nissans, and 36 drive none of these. So, we're gonna fill in the Venn diagram. You may be wondering why I've given you two. You'll see in just a minute. So, we always try to read through this and then typically, if you've noticed, if you've done a few of these, you start at the bottom and you work your way up. So, 36 drive none of these. So, which region in here, one, two, three, four, five, six, seven, eight, is none? Well, it's outside the circles, which is region eight. So, we're gonna put 36 out there. And then we start, you know, going up, like I said. Usually, kind of go up like this. We try to fill in the most restrictive region first . We really would like to fill in this region right here, region five first. Do we have any information here that talks about how many people drive Ford, Chevy, and Nissan? We don't. 'Cause if you look, we have information about pairs of these. Fords and Chevys, Fords and Nissans, Chevy and Nissan, but not all three. We have to start here. We need to know how many people drive all three. We don't know exactly, but we can represent that value by x. x represents some number, for now it's gonna be a place holder. We're just gonna call it x. Now, we're gonna go back here. 28 drive Chevys and Nissans. So, here's the Chevy circle. Here's the Nissan circle. We see that 28 drive Chevys and Nissans. So, Chevy and Nissan intersect in those two regions. You see that? I'm gonna erase this so you can sort of see what we're doing. These two regions right here must add up to 28. Well, it'd be really easy if I knew what this value was. For example, if this was eight, then this region would have to have 20 in it 'cause you would subtract. And, you know, if this was one, this would have to have 27 'cause the whole thing must sum up to 28. Well, the problem is, I don't know what x is. x is just a placeholder, it's a variable, it represents some value. We're gonna find it in a little bit. So, we're gonna do the same thing I just said. We're gonna subtract 28 minus whatever number's in there. Well, the number that's in there is x. So, we're gonna do 28 minus x is in that region right there. Okay, so we did that. So, 20 drive Fords and Nissans. So now, we're looking at the Ford circle and the Nissan circle. 20 drive Fords and Nissans. So, whatever these guys have in common. Which, as you can see, again, two regions. Both of these regions here, when you put them together, will add up to 20. So, how many people over here? If I knew what this middle region was, what number actually represented, you know, x took the place of, then I could just subtract, but I don't know. So, we would do 20 minus whatever number's here. So, we're gonna write that as 20 minus x. Okay. And then 38 drive Fords and Chevys. So, here's the Ford circle. Here's the Chevy circle. Fords and Chevys. Fords and Chevys, those two regions right there. Fords and Chevys. Both of these regions add up to 38, so hopefully you're starting to get the drill now. This is 38 minus x. 62 drive Nissans, so the whole Nissan circle has to add up to 62. Okay, so I'm just gonna leave it in this purple color. So, I'm just gonna circle like this, that's not purple. 62 drive Nissans, so the whole thing has to add up to 62. So, we do 62 minus the three values that are in the regions already. So, 20 minus x, minus x, minus 28 minus x. Okay, so let's do some scratch work. So, this is gonna be 62 minus, but we're going to distribute that negative sign in front. So, 62 minus 20 plus x, minus x, minus 28 plus x. And now we're gonna clean that up. So, we get what? 62 minus 20 minus 28. 62 minus 20 minus 28. So, this is 14. And look at the x's. We see that we have a plus x and a minus x, so those cancel. So, looks like we just end up with 14 plus x in here, okay? 14 plus x. Or x plus 14, same thing, right? Okay, so then we're gonna do the same thing with the other regions. The next piece says what? 150 drive Chevys. So, here's the Chevy circle. That whole circle has to add up to 150. I'm gonna go and write it up here so I have a little bit of room. So, that's 150 minus, whole thing's 150, so 150 minus this, minus this, minus this, will give us the number that's supposed to be in this region. So, 150 minus parentheses 38 minus x, minus x, minus 28 minus x. We're, again, gonna distribute these negative signs. So, we have 150 minus 38 plus x, 'cause we distributed negative times a negative. Minus x minus 28 plus x. So, we get 150 minus 38, minus 28, so it looks like we have an 84. Now, look at the x's again. We have a plus x and a minus x, so these are gonna cancel. We still have this guy, right? So, 84 plus x, and that is gonna go right in here. Okay, there's one more piece of information we haven't used yet. So, let's just, I guess I'll do it in green. 120 drive Fords. So, this whole circle adds up to a hundred, I'm sorry, 122 drive Fords. That whole circle adds up to 122. So again, I'm just gonna come over here just to scratch. So, I have 122 minus the three regions that are already labeled, right? So, 122 minus 38 minus x, minus x, minus 20 minus x. So, we're gonna distribute as we did before. So, 122 minus 38 plus x minus x, minus 20 plus x. So, we get 122, looks like minus 38, minus 20. You'll check me. So, it looks like this is a 64. Again, plus x minus x cancels out. We're left with just this x, so it looks like we have 64 plus x, and that goes in here, like that. How do we find x? We've labeled all the regions now. How do we find x? Well, how many people were surveyed? The only piece of information we haven't used yet is how many people were surveyed. In a survey of 300 people, so this is going to be the sum of all eight regions in the box inside our universal set U. Remember, U represents the whole box, not just the outside. So, if we're gonna sum up all the regions, we're gonna add that up, and we're gonna get 300. So, we're gonna do 64 plus x, plus 38, minus x, 64 plus x, plus 38, minus x, plus 84, plus x, you see where I'm doing this? 64 plus, 64 plus x, 38 minus x, 84 plus x, I'm just adding these up. Now, do these three regions, and this region, and this region. Okay, so, plus 84 plus x, so now I'm at plus 20 minus x. I'm gonna go and just continue the equation down here, sorry, plus x, plus 28 minus x, plus, looks it's 14 plus x, plus 36. So, this, this, this, this, and this, this right here, and the sum, they told us, is 300. Equals 300. So, let's start cleaning it up. We're gonna add all the numbers on the left, so it looks like we have 64 plus 38. Plus what's that? 84. Plus 20, plus 28, plus 14, plus 36. So, it looks like we have 284 on the left-hand side. Now, let's look at the x's. We have a plus x and a minus x, these guys are gonna cancel. We have a plus x and a minus x, these guys are gonna cancel. A plus x and a minus x, those are gonna cancel. We have one x that remains. So, 284 plus x equals 300. So, do 300 minus 284, we see that x equals 16. But, where was x? X was the value we put in the very, very middle most section, right? So, that means this is 16. Okay, and then we just go piece by piece. We have 28 minus x, so that's 28 minus 16. So, this is gonna be 12. Then, we have, over here, 20 minus x, so 20 minus 16 is four. Then, we have 14 plus x, so 14 plus 16, we end up with 30. Where are we now? So, 64 plus the middle of 16, you get what? 80 over here. I'm at 38 minus 16. Looks like that is 22 right here. 84 plus 16, give a hundred, And we knew we have 36 out here to begin with. Okay. So, now let's answer some questions now that we've filled in our Venn diagram. How many people do not drive Chevys? So, here's the Chevy circle. We're looking at the people who are not in the Chevy circle. Okay, so 80 plus four, plus 30, plus 36. So looks like that is what? 150? So, 150 people do not drive Chevys. Does that make sense? Okay, how many drive Fords or Chevys? So, Ford or Chevy or both. Remember, or both is implied, so we're gonna have 80 plus 22 plus 100, plus four, plus 16, plus 12. And what is that? 234. How many drive all three? Well, that's what we just found, that's the 16. How many drive only Fords? So, only Fords are gonna be the part of the circle that doesn't touch any other circles, so that's just 80. And then what? How many drive Fords but not Nissans? Fords but not Nissans. So, I'm looking at the Ford circle, and I'm saying, okay, I'm gonna use all of the Ford circle except the Nissan piece. So, 80 plus 22. Which is what, 102? Think there's one more question. Of those who drive Nissans, how many drive Fords? Okay, so of those that drive Nissans, now I'm looking at, here's the Nissans. Of those that drive Nissans, how many drive Fords? Okay, well, it's these right here, right? So, what, four plus 16? What is that? Four plus 16, we end up with 20. Do you have questions? Okay. Good times, fun stuff, right?
13243	https://research.cs.wisc.edu/areas/ai/airg/jones01taxonomy.pdf	Journal of Global Optimization 21: 345–383, 2001. © 2001 Kluwer Academic Publishers. Printed in the Netherlands. 345 A Taxonomy of Global Optimization Methods Based on Response Surfaces DONALD R. JONES General Motors Corporation, Mail Code 480-305-200, 6440 East 12 Mile Road, Warren, MI 48090, USA (e-mail: don.jones@gm.com) Abstract. This paper presents a taxonomy of existing approaches for using response surfaces for global optimization. Each method is illustrated with a simple numerical example that brings out its advantages and disadvantages. The central theme is that methods that seem quite reasonable often have non-obvious failure modes. Understanding these failure modes is essential for the development of practical algorithms that fulﬁll the intuitive promise of the response surface approach. Key words: global optimization, response surface, kriging, splines 1. Introduction Within the engineering community, response surfaces are gaining a popularity as a way of developing fast surrogates for time-consuming computer simulations. By running the simulations at a set of points (experimental design) and ﬁtting response surfaces to the resulting input-output data, we obtain fast surrogates for the object-ive and constraint functions that can be used for optimization. Further time is saved by exploiting the fact that all runs used to ﬁt the surfaces can be done in parallel, that runs can be started before one has even formulated the problem, and that runs can be reused when solving modiﬁed versions of the original problem (e.g., different constraint limits). One indication of the growing interest in this topic is that, at a recent Symposium on Multidisciplinary Analysis and Optimization (2000), no less than 13 papers dealt with the use of ‘response surfaces’ or ‘surrogates’ in optimization. In this paper, we will discuss the forces driving the interest in response surfaces and review the methods that have been proposed so far. The appeal of the response-surface approach goes beyond reducing compu-tation time. Because the approach starts with an experimental design, statistical analyses can be done to identify which input variables are the most important (highest contribution to the variance of the output) and ‘main effect plots’ can be created to visualize input-output relationships (see Booker, 1998; Jones et al., 1998). Using the surfaces as fast surrogates also makes it possible to quickly com-pute tradeoff curves between competing objectives. Multidisciplinary problems can be handled by linking response surfaces based on different engineering discip-lines (e.g., crashworthiness, structures, durability). Finally, in situations where no computer model is available, response surfaces provide a way to compute ‘trans-346 DONALD R. JONES Figure 1. (a) Contours of the Branin test function. (b) Contours of a kriging surface ﬁt to 21 points (shown as spheres). fer functions’ between inputs and outputs. These transfer functions can then be embedded in larger computer simulations or used directly for robust design and optimization. The intuitive promise of the response surface approach is illustrated in Figure 1. On the left of the ﬁgure we show the contours of the two-dimensional Branin test function Dixon and Szego, 1978. On the right, we show the contours of a ‘kriging’ response surface ﬁt to 21 points (shown as spheres). The kriging predictor is so accurate that some people do not even notice the difference between the contours in Figures 1(a) and 1(b). It is clear that we should be able to locate the global optimum quite accurately with only a few more function evaluations. Existing approaches that use response surfaces for global optimization can be classiﬁed based on the type of response surface and the method used to select search points. In the taxonomy shown in Figure 2, seven methods are identiﬁed that will be the subject of the remaining sections in the this paper. The meaning of the entries in the taxonomy will become clearer as we proceed, but a few words now will foreshadow some of the key messages and conclusions. At the highest level, response surfaces can be differentiated based on whether they are non-interpolating (minimize sum of squared errors from some pretermined functional form) or interpolating (pass through all points). We will show that non-interpolating surfaces, such as ﬁtted quadratic surfaces, are unreliable because the surface may not sufﬁciently capture the shape of the function. It is better to use surfaces that interpolate the data with a linear combination of ‘basis functions.’ Among basis-function methods, one can distinguish methods in which the basis functions are ﬁxed (thin-plate splines, Hardy multiquadrics) and those in which the basis functions have parameters that are tuned (kriging). In addition to having tuned basis functions, kriging has a statistical interpretation that allows one to construct an estimate of the potential error in the interpolator. This measure of potential error plays a key role in Methods 3, 4, and 5 (which is why those methods are not available for the non-kriging methods in Figure 2). GLOBAL OPTIMIZATION BASED ON RESPONSE SURFACES 347 Figure 2. Taxonomy of response-surface-based global optimization methods. The seven methods shown are discussed in the text. As for selecting search points, a key distinction will be between two-stage and one-stage methods. Most (but not all) current approaches are two-stage methods. In the ﬁrst stage, one ﬁts a response surface, estimating any required parameters. In the second stage, these parameters are treated as if they are ‘true’ and the surface is used to compute new search points. The potential pitfall with two-stage methods is that the initial sample may give a misleading picture of the function. As a result, one may grossly underestimate the error in the response surface and either stop prematurely or search too locally. One-stage methods skip the initial step of ﬁtting a surface to the observed data. Instead, the mathematical machinery of response surfaces is used to evaluate hy-potheses about the location of the optimum. For example, the ‘credibility’ of the hypothesis that the optimum occurs at a point x∗with function value f ∗may be determined by examining the properties of the best-ﬁtting response surface that passes through the observed data and the point (x∗, f ∗). At an intuitive level, the smoother is this surface, the more credible is the hypothesis (we will make this notion precise later). The key thing to note is that the credibility of the hypo-thesis is not based on parameters obtained by ﬁtting a surface to the observed data alone—parameters that may be greatly in error if the initial sample is sparse and misleading. In what follows, we will discuss all seven methods using graphical examples. As we will see, many of these methods have non-obvious failure modes. As we move from Method 1 to Method 7, we will progressively remove potential failure modes at the cost of increasing algorithmic complexity. Although the focus of this paper is on global optimization, along the way we will point out some highly successful ways in which response surfaces have been used for local optimization. 348 DONALD R. JONES Figure 3. In Method 1, one ﬁts a quadratic surface, ﬁnds the minimum of the surface, evaluates the function at this point, and iterates. The procedure may not even ﬁnd a local minimum. In a concluding section, we review the lessons learned and the opportunities for further work in this area. 2. Minimizing a quadratic surface In Method 1, we begin by sampling the function according to some experimental design. In each iteration, a quadratic surface is ﬁt to the sampled points, the min-imum of the quadratic is found, and the function is evaluated at this point. The potential failure mode of this approach is illustrated in Figure 3. The panel labeled ‘Start’ shows the hypothetical function that we are trying to minimize—let us call it True Function #1—as well as eight points at which this function has intially been sampled (the dots). In Iteration 1 we ﬁt a quadratic surface and ﬁnd the minimum of this surface. Notice that the minimum of the quadratic does not even lie close to either of the function’s two local minima. In Iteration 2 we have evaluated the function at the point that minimized the quadratic and updated the surface, but the new surface is largely unchanged from what it was in the previous iteration. The minimum of the new surface is nearly the same as before, and iterating the process further yields no improvement. This example shows that even for non-pathological functions, Method 1 can fail abysmally. The problem with the quadratic surface is that adding additional points will not necessarily lead to a more accurate surface. In constrast, interpolating methods, such as the natural cubic splines shown in Figure 4, become more and more accur-ate as new points are added, eventually converging to the true function. In the next section we will examine what will happen if we replace the quadratic surface with such an interpolating response surface. GLOBAL OPTIMIZATION BASED ON RESPONSE SURFACES 349 Figure 4. Data-adaptive surfaces like the natural cubic spline shown here adapt their shape to the data. As more points are added, the approximation approaches the function being ﬁtted. 3. Minimizing an interpolating surface Cubic splines, thin-plate spline, multiquadrics, and kriging are all methods that interpolate a set of scattered data using a linear combination of polynomial terms and special ‘basis function’ terms. Intuitively, the procedure is similar to expressing a complicated sound wave as a weighted sum of pure tones (sprectral decompos-ition). In both cases, a complicated function is expressed as a weighted sum of simple functions. Predictions can then be made by predicting the simple functions and combining these predictions using the weights. Now let us turn to the mathematics of the basis function approach. Let us as-sume that we have sampled a function at n points xi, i = 1, . . . , n, where each xi is a d-dimensional vector xi = (xi1 xi2 · · · xid)′. Denote the function values at these points by yi = y (xi). Also, let {πk (x) \| k = 1, . . . , m} be a basis of the set of all polynomials in x of degree G. Note that x is multidimensional, so that each πk (x) is a weighted sum of terms like xg1 1 xg2 2 · · · xgd d where g1 +g2 +· · ·+gd ⩽G. In the case G = 1, for example, a possible basis would be the set of d +1 functions consisting of the constant function π1 (x) = 1 and the linear terms π1+ℓ(x) = xℓ, ℓ= 1, . . . , d. Now, if we ﬁt a surface by least squares using only the m polynomial terms, we would be back to curve ﬁtting as in Method 1. The basis function approach differs from ﬁtting polynomials because the interpolator not only includes these polynomial terms, but also includes n ‘basis function’ terms, each centered around one of the sampled points. That is, our predictor at a new point x∗is of the form y x∗ = m k=1 ak πk x∗ + n j=1 bjϕ x∗−xj . (1) 350 DONALD R. JONES Possible choices for the basis function ϕ (z) are: ϕ (z) = ∥z∥ (linear) ϕ (z) = ∥z∥3 (cubic) ϕ (z) = ∥z∥2 log (∥z∥) (thin plate spline) ϕ (z) = ∥z∥2 + γ 2 (multiquadric) ϕ (z) = exp −d ℓ=1 θℓ\|zℓ\|pℓ (kriging) (2) Here ∥z∥is the Euclidean norm and, in the multiquadric case, γ is a prescribed positive constant. The basis function shown for kriging is only one possibility, but it is a popular choice that appeared in an inﬂuential article by Sacks et al. (1989). In this basis function, the parameters θℓand pℓare assumed to satisfy θℓ⩾0 and 00 of a sampled point,’ then the situation in Figure 6 might actually occur in practice. In any case, what Figure 6 certainly shows is that convergence cannot be guaranteed. The previous discussion suggests that, whenever Method 2 seems to have con-verged (i.e., the minimum of surface is near a sampled point), we should neverthe-less sample in a small neighborhood of the tentative solution to force the gradient of the surface to agree with the gradient of the true function (kriging can also be directly adapted to utilize derivative information; see Koehler and Owen, 1996). This idea is explored in Figure 7. We begin with the situation just described, where the minimum of the spline occurs at a sampled point. Since this means we have tentatively converged, we continue by sampling a little to the left and right of this point, since this will cause the gradient of the surface to match that of the function Having done this, further iterations quickly converge to the local minimum. Adding ‘gradient matching’ whenever the minimum of the surface is near a sampled point certainly makes Method 2 more robust. Whether or not one can prove that this method, if iterated inﬁnitely, must converge to a local optimum is an open research question. As we have suggested, the choice of stopping rule will be important in any practical implementation of Method 2. A tempting choice would be to stop when the improvement from one iteration to the next is small, but there is no reason to believe that the sequence of sampled function values will be decreasing. For ex-ample, Figure 8 shows what happens when we use the gradient-matching technique on another possible function (True Function #3). In this case, after the gradient-matching step, we overshoot the local minimum by so much that the new point yields no improvement. It is fairly clear, however, that if we add this point to the sample and continue iterating, we will converge to the local minimum. So lack of improvement from one iteration to the next is not a reliable stopping rule. GLOBAL OPTIMIZATION BASED ON RESPONSE SURFACES 353 Figure 7. To prevent premature convergence in Method 2, we can force the surface gradient to agree with the function gradient whenever we tentatively converge. Local convergence can be assured, however, if one combines gradient matching with a trust region approach. In particular, Alexandrov et al. (2000) develop an al-gorithm that uses a ‘correction factor’ approach to force gradient matching between the surface and function at the current iterate. To get the next iterate, the surface is optimized within a trust region around the incumbant solution. The optimum point is then sampled and, if the objective function fails to decrease, the trust region is contracted. They prove that this approach must converge to a critical point of the function. It is perhaps best to think of Alexandrov’s approach as a way of using re-sponse surfaces to accelerate an existing, provably convergent local optimization method—as opposed to thinking of it as a new, response-surface-based method. Alexandrov starts with the well-known trust-region algorithm; however, instead of ﬁnding the next iterate by minimizing a second-order Taylor-series approximation within the trust region, she minimizes the response surface within the trust region. Because the response surface will usually be more accurate than the Taylor ap-proximation, one will usually be able to take longer steps; hence, the algorithm will proceed faster. Gradient matching is necessary to preserve the convergence properties of the trust region approach. Response surfaces have also been used to accelerate derivative-free methods for local optimization. For example, Booker et al. (1999) use kriging response surfaces to accelerate the General Pattern Search algorithm of Dennis and Torczon (1991). In the original, un-accelerated version of the Pattern Search algorithm, one searches over a lattice of points around the current iterate until either one ﬁnds an 354 DONALD R. JONES Figure 8. Even if force gradient matching between the surface and function, the minimum of the surface may not be an improving point. To remedy this problem, optimization of the surface can be restricted to a trust region around the current iterate. improving point or until all the lattice points have been sampled. In the accelerated version, a kriging response surface is used to predict the function’s value at the points in the lattice, and the points are sampled starting with the ones that the kriging surface predicts will have the best values. In this way, an improving point is usually found much sooner than would be the case if the lattice points were sampled in a random order. Booker et al. found that the reduction in function evaluations can be substantial. While these local methods are exciting developments, we should bear in mind that the methods can only guarantee convergence to a critical point. It is entirely possible that this point will merely be a saddle point or ‘ﬂat spot’ of the function. This is illustrated in Figure 9 for yet another possible true function (True Func-tion #4). In this case, the response surface is minimized at a sampled point and the gradient of the function is zero at this point. Thus, all of the previous methods would have declared success. Yet we are not even at a local minimum, far less a global one. A well known theorem by Torn and Zilinskas (1987) tells us that, in order to converge to the global optimum for a general continuous function, the sequence of iterates must be dense. Of course, this is a rather trivial method of convergence; in essence, it says that, in order to guarantee convergence to the global optimum, we must converge to every point in the domain. The practical lesson of the theorem is that any globally convergent method must have a feature that forces it to pay attention to parts of the space that have been relatively unexplored and, from time to time, to go back and sample in these regions. Methods 1–2 failed to ﬁnd a global minimum in our examples because they have no such feature. GLOBAL OPTIMIZATION BASED ON RESPONSE SURFACES 355 Figure 9. In this example, surface minimum is at a sampled point and the gradient of the surface and function agree. We have converged, but only to a saddle point. Figure 10. The kriging predictor and its standard error for True Function #4. As mentioned in the introduction, kriging stands out from other basis function methods because it has a statistical interpretation. This interpretation not only al-lows us to compute an interpolator (or ‘predictor’), but also allows us to compute a measure of the possible error in the predictor. Figure 10 illustrates this idea by showing a kriging surface ﬁt to our deceptive True Function #4 of the previous example. In addition to the kriging predictor, we also show a curve labeled ‘stand-ard error.’ The standard error (right hand scale) goes to zero at the sampled points, indicating that we have no uncertainty about these values. In between the sampled points, the standard error rises. Intuitively, the further we are from the nearest sampled point, the more uncertain we are about the function, and the higher is the standard error. With kriging, we can develop search methods that put some emphasis on sam-pling where the standard error is high. In this way, we obtain the desired feature of ‘paying attention to parts of the space that have been relatively unexplored.’ Methods 3, 4, and 5 (discussed later) involve different ways of implementing this 356 DONALD R. JONES idea. Since kriging will play a large role in this discussion, we will ﬁrst digress to discuss it in more detail. 4. A gentle introduction to kriging Most articles and textbooks describe kriging as a way of ‘modeling the function as a realization of a stochastic process’. The kriging predictor is then shown to be the predictor that minimizes the expected squared prediction error subject to: (i), being unbiased and, (ii), being a linear function of the observed yi’s. (Although the predictor is linear in the yi’s, the coefﬁcients can be nonlinear functions of x, and hence the predictor can be nonlinear). While this is approach is rigorous and facilitates the derivation of key formulas, for most people the approach is not intuitive. In what follows, we will derive the kriging formulas using a somewhat different approach. Readers intesterested in the standard derivation may consult the article by Sacks et al. (1985). Suppose we want to make a prediction at some point x in the domain. Before we have sampled any points, we will be uncertain about the value of the func-tion at a this point. Let us model this uncertainty by saying that the value of the function at x is like the realization of a random variable Y(x) that is normally distributed with mean µ and variance σ 2. Intuitively, this means that we are saying that the function has a typical value of µ and can be expected to vary in some range like [µ −3σ, µ + 3σ]. Now consider two points xi and xj. Again, before we have sampled these points, we are uncertain about the associated function values. However, assuming the function being modeled is continuous, the function values y (xi) and y xj will tend to be close if the distance xi −xj is small. We can model this statistically by saying that the random variables Y(xi) and Y(xj) will be highly correlated if xi −xj is small. In particular, we will assume that the correlation between the random variables is given by Corr Y(xi), Y(xj) = exp − d ℓ=1 θℓ xiℓ−xjℓ pℓ . (5) This correlation function has the intuitive property that if xi = xj, then the cor-relation is 1. Similarly, as xi −xj →∞, the correlation tends to zero. The θℓparameter determines how fast the correlation ‘drops off’ as one moves in the ℓth coordinate direction. Large values of θℓserve to model functions that are highly active in the ℓth variable; for such variables, the function’s value can change rapidly even over small distances. The pℓdetermines the smoothness of the function in the ℓth coordinate direction. Values of pℓnear 2 help model smooth functions, while values of pℓnear 0 help model rough, nondifferentiable functions. GLOBAL OPTIMIZATION BASED ON RESPONSE SURFACES 357 Putting it all together, we can represent our uncertainty about the function’s values at the n points using the the random vector Y =    Y (x1) . . . Y (xn)   . (6) This random vector has mean equal to 1µ, where 1 is a n × 1 vector of ones, and covariance matrix equal to Cov(Y) = σ 2R, (7) where R is a n × n matrix with (i, j) element given by Eq. (5). The distribu-tion of Y—which depends upon the parameters µ, σ 2, θℓand pℓ(ℓ= 1, .., d)— characterizes how we expect the function to vary as one moves in different coordin-ate directions. To estimate the values of µ, σ 2, θℓand pℓ(ℓ= 1, .., d), we choose these para-meters to maximize the likelihood of the observed data. Let the vector of observed function values be denoted y =    y1 . . . yn   . (8) With this notation, the likelihood function may then be written as 1 (2π) n 2 σ 2 n 2 \|R\| 1 2 exp −(y −1µ)′ R−1 (y −1µ) 2σ 2 . (9) Choosing the parameters to maximize the likelihood function intuitively means that we want our model of the function’s typical behavior to be most consistent with the data we have seen. In practice it is more convenient to choose the parameters to maximize the log of the likelihood function, which—ignoring constant terms—is: −n 2 log σ 2 −1 2 log (\|R\|) −(y −1µ)′ R−1 (y −1µ) 2σ 2 . (10) Setting the derivatives this expression with respect to σ 2 and µ to zero and solving, we can express the optimal values of σ 2 and µ as functions of R: µ = 1′R−1y 1′R−11 (11) σ 2 = (y −1 µ)′ R−1 (y −1 µ) n . (12) 358 DONALD R. JONES Substituting Eqs. (11) and (12) into Eq. (10) we get the so-called ‘concentrated log-likelihood’ function. Ignoring constant terms, the concentrated log-likelihood function is: −n 2 log σ 2 −1 2 log (\|R\|) . (13) The concentrated log-likelihood function depends only on R and, hence, on the correlation parameters (θ’s and p’s). In practice, this is the function that we max-imize to get estimates θℓand pℓ(ℓ= 1, .., d). Given these estimates, we then use Eqs. (11) and (12) to compute the estimates µ and σ 2. To understand how we can make predictions at some new point x∗, suppose y∗were some guessed function value. To evaluate the quality of this guess, we may add the point (x∗, y∗) to the data as the (n + 1)th observation and compute the ‘augmented’ likelihood function using parameter values obtained in the max-imum likelihood estimation. As we have seen, these estimated parameters reﬂect the typical pattern of variation in the observed data. With these parameters ﬁxed, the augmented log-likelihood is simply a function of y∗and reﬂects how consistent the point (x∗, y∗) is with the observed pattern of variation. An intuitive predictor is therefore the value of y∗that maximizes this augmented likelihood function. It turns out that this value of y∗is the kriging predictor, and we will now proceed to derive it. Let y = (y′ y∗)′ denote the vector of function values when augmented by the new, (n + 1)th pseudo-observation (x∗, y∗). Also, let r denote the vector of correlations of Y(x∗) with Y(xi), for i = 1, . . . , n: r =    Corr [Y(x∗), Y(x1)] . . . Corr [Y(x∗), Y(xn)]    (14) The correlation matrix for the augmented data set, denoted R, is: R = R r r′ 1 . (15) Now if the reader looks again at the formula for the log-likelihood function in Eq. (10), it will be clear that the only part of the augmented log-likelihood function that depends upon y∗is −( y −1 µ)′ R−1 ( y −1 µ) 2 σ 2 . Substituting in the expressions for y and R, we may write this as − y −1 µ y∗− µ ′ R r r′ 1 −1 y −1 µ y∗− µ 2 σ 2 . (16) GLOBAL OPTIMIZATION BASED ON RESPONSE SURFACES 359 Now, from the partitioned inverse formula (Theil, 1971, p. 18), we have the follow-ing explicit expression for R−1: R−1 + R−1r 1 −r′R−1r −1 r′R−1 −R−1r 1 −r′R−1r −1 − 1 −r′R−1r −1 r′R−1 1 −r′R−1r −1 . Substituting this into Eq. (16), we may write the augmented log-likelihood as: −1 2 σ 2 1 −r′R−1r (y∗− µ)2 + r′R−1 (y −1 µ) σ 2 1 −r′R−1r (y∗− µ) + terms with-outy∗ . (17) Thus we see that the augmented likelihood is actually a quadratic function of y∗. The value of y∗that maximizes the augmented likelihood is found by taking the derivative of the above expression and setting it equal to zero: −1 σ 2 1 −r′R−1r (y∗− µ) + r′R−1 (y −1 µ) σ 2 1 −r′R−1r = 0. (18) Solving for y∗then gives us the standard formula for the kriging predictor: y x∗ = µ + r′R−1 (y −1 µ) . (19) Now if we let let ϕ (z) be the kriging basis function listed earlier in Eq. (2), then the ith element of r is just ϕ (x∗−xi). If we further let a = µ and let bi be the ith element of R−1 (y −1 µ), then the kriging predictor can be written as y x∗ = a + n i=1 biϕ x∗−xi . (20) Thus, the kriging predictor is indeed a linear combination of basis functions and polynomial terms (here just a constant). Now it makes intuitive sense that we should be more conﬁdent in our predictor if the augmented log-likelihood drops off dramatically as one moves away from the optimal value of y∗. Intuitively, this means that values of y∗that are different from the predictor are much less consistent with the pattern of variation in the observed data. This is illustrated in Figure 11 which shows two possible ways in which the augmented likelihood could depend upon y∗. In Figure 11(a), the augmented log-likelihood is fairly ﬂat. While there is a value of y∗that maximizes this function, we can hardly be conﬁdent in this estimate because other, quite different values of y∗perform almost as well. On the other hand, in Figure 11(b) the augmented log-likelihood is strongly peaked. In this case, values of y∗that differ substantially from the predictor are much less consistent with the data, and so we can be more conﬁdent in the kriging predictor. This line of thought suggests that our estimate of the potential error in the predictor should 360 DONALD R. JONES Figure 11. Two possible ways in which the augmented log-likelihood might depend upon the guessed value y∗for y x∗ . In both cases the best prediction is y∗= 5, but we would be more conﬁdent in case (b) than in case (a). be inversely related to the curvature of the augmented log-likelihood function. Low curvature (ﬂat function) suggests high potential error; likewise, high curvature (strongly peaked function) suggests low potential error. The curvature, in turn, can be measured by the absolute value of the second derivative of the augmented log-likelihood function with respect to y∗. From Eq. (17), we ﬁnd that the absolute value of the second derivative is: 1 σ 2 1 −r′R−1r . (21) Since we have argued that the error in the predictor is inversely related to this curvature, a natural measure of potential error is the reciprocal of the curvature: σ 2 1 −r′R−1r . (22) This is, in fact, very close to the formula for the mean-squared error of the predictor derived using the standard stochastic-process approach. This standard formula, which we will denote by s2 (x∗), is s2 x∗ = σ 2 1 −r′R−1r + 1 −r′R−1r 2 1′R−11 . (23) The extra term on the right hand side of Eq. (23) can be interpreted as representing the uncertainty that stems from our not knowing µ exactly, but rather having to estimate it from the data. The formula for s2 (x∗) has the intuitive property that it is zero at any sampled point. This is as it should be since we have no uncertainty about the points we have already sampled. To see this, note that if x∗= xi, then r is just the ith column of GLOBAL OPTIMIZATION BASED ON RESPONSE SURFACES 361 R. Hence, R−1r is the ith unit vector ei. It follows that r′R−1r = r′ei = ϕ x∗−xi = ϕ (xi −xi) = 1 (24) 1′R−1r = 1′ei = 1. (25) Substituting Eqs. (24) and (25) into Eq. (23), it follows that s2 (xi) = 0. It will often be convenient for us to work with the square root of the mean squared error, s = s2 (x∗). This provides a root mean squared error, or ‘standard error,’ for measuring uncertainty in our predictions. A key difference between kriging and other basis function methods is that the other methods usually have no parameters in their basis functions. A possible exception is the parameter γ used in multiquadrics, but this parameter is rarely ad-justed in any systematic manner. Moreover, the use of the Euclidean norm by many of the methods makes them sensitive to the units of measurement. For example, changing units from milimeters to meters could substantially change predictions. To avoid this problem, the standard procedure is to normalize all the data to the unit interval. While this certainly removes sensitivity to units of measurement, it also treats all variables as equally important—something that is almost never true. In constrast, kriging effectively uses a non-Euclidean distance metric given by distance xi, xj = d ℓ=1 θℓ xiℓ−xjℓ pℓ (26) Any change in the units can be absorbed by the θℓparameters. Moreover, the θℓand pℓparameters can be adjusted to reﬂect the relative importance of each variable. The maximum likelihood estimation of these parameters is essentially a way of optimally ‘tuning’ the basis functions. This tuning is the main reason kriging often outperforms other basis-function methods in terms of prediction accuracy. To see the importance of proper scaling, Figure 12 compares the performance of kriging and thin-plate splines on the Branin test function. Figure 12(a) shows the contours of Branin test function. Figure 12(b) shows the contours of a thin-plate spline ﬁt using normalized data to 21 points (shown as spheres). Figure 12(c) shows the kriging predictor ﬁt using normalized data with p1 = p2 = 2. The kriging predictor is clearly more accurate than the spline. In Figure 12(d) we do something special. In particular, we ﬁt the thin-plate spline with the data scaled in a way suggested by the estimated kriging parameters. In particular, we scale the ﬁrst variable to 0, θ1 and the second variable to 0, θ2 . This has the effect of causing the thin-plate spline to use the same distance metric as kriging. As one can see, the resulting contours are somewhat better (i.e., more like those of the true function), demonstrating the importance of proper scaling. 362 DONALD R. JONES Figure 12. Comparison of the contours of the Branin test function; a thin-plate spline ﬁt to the 21 points; a kriging surface; and a thin-plate spline ﬁt using the same variable scaling as kriging. 5. Minimizing a statistical lower bound The availability of a standard error in kriging immediately suggests the possibility of computing a ‘statistical lower bound’ on the function of the form y (x∗)−κs(x∗) for some value of κ. Why couldn’t we then use this bound to develop a sort of nonrigorous branch-and-bound algorithm? As long as κ>0, this would give us the desired property of putting some emphasis on searching in relatively un-sampled regions where the standard error is higher. In the literature, this idea has been pursued by Cox and John (1997). In Figure 13 we explore whether or not this approach will allow us to ﬁnd the global minimum of the deceptive Test Function #4. In each iteration, we ﬁt a kriging model, ﬁnd the minimum of y (x∗) −5s(x∗), evaluate the function at that point, and then iterate. One would think that using the mean minus ﬁve standard errors would be a very conservative bound. But one must remember that s(x∗) is only an estimate of the possible error in the predictor. In our case, the initial points are quite deceptive, making the function appear very smooth and almost quadratic. As a result, the standard errors are very small. After sampling the next two points, however, it becomes clear that the function is more variable than it had seemed, and the standard errors become larger (see Iteration 3). Nevertheless, in the region between the ﬁrst two points (which is where the global optimum lies) the lower bound is still above the current best function value. As a result, the search will not return to this region and the global optimum will not be found. Like a true branch-and-bound algorithm, the idea of minimizing a ‘statistical GLOBAL OPTIMIZATION BASED ON RESPONSE SURFACES 363 Figure 13. Selected iterations of Method 3 on a simple one-dimensional test function. In each iteration, we ﬁt a kriging surface to the data, ﬁnd the point that minimizes the predictor minus κ standard errors, and then evaluate the function at this point. lower bound’ will lead to the deletions of regions of the search space, and so the iterates will not be dense. But from the theorem of Torn and Zilinskas, the iterates must be dense if we are to guarantee convergence for general continuous functions. 364 DONALD R. JONES Figure 14. Using kriging, we can estimate the probability that sampling at a given point will ‘improve’ our solution, in the sense of yielding a value that is equal or better than some target T . 6. Maximizing the probability of improvement In the literature, one of the most popular approaches for selecting an iterate is to ﬁnd the point where the probability of improving the function beyond some target T is the highest. This concept is illustrated in Figure 14 (the standard error has been exaggerated for clarity). At any given point, we model our uncertainty about the function’s value by considering this value to ‘be like’ the realization of a random variable Y(x) with mean y (x) and standard error s(x). If we denote the current best function value as fmin, then our target value for the improvement will be some number T <fmin. The probability of improving this much (or more) is simply the probability that Y(x) ⩽T . Assuming the random variable is normally distributed, this probability is given by Prob Improvement = " T − y (x) s (x) (27) where " (·) is the Normal cumulative distribution function. This was the idea ﬁrst put forward by Harold Kushner in 1964. Kushner’s original algorithm was one dimensional, but Stuckman (1988), Perttunen (1991), Elder (1992), and Mockus (1994), have all heuristically extended the method to higher dimensions. Zilinskas (1992) introduced an axiomatic treatment of the method, which he calls the ‘P-algorithm.’ The key advantage of using the probability of improvement is that, under certain mild assumptions, the iterates will be dense. Gutmann (2001) proves this result for Kushner’s original one-dimensional algorithm (it is a special case of a more general convergence theorem). Intuitively, as the function is sampled more and more around the current best point, the standard error in this region becomes small. GLOBAL OPTIMIZATION BASED ON RESPONSE SURFACES 365 As a result, the term T − y(x) s(x) becomes extremely negative (since we usually have T < y (x)) and, hence, the prob-ability of improvement given by Eq. (27) will be small. Eventually, the probab-ility of improvement around the current best point becomes so small that we are driven to search elsewhere where the standard error is higher. This probability-of-improvement algorithm is ‘Method 4’ in the taxonomy of Figure 2. Figure 15 explores how this method works for Test Function #4 when we set our target T = fmin −0.25 \|fmin\|, that is, when we search for an improvement of at least 25%. The method works just as expected. It starts around the suboptimal local minimum, but after sampling there a few times, it moves on to search more globally. By Iteration 11, the algorithm has found the basin of convergence of the global minimum. The performance of Method 4 in Figure 15 is truly impressive. It would be quite natural if the reader, like so many others, became enthusiastic about this approach. But if there is a single lesson to be taken away from this paper, it is that nothing in this response-surface area is so simple. There always seems to be a counterexample. In this case, the difﬁculty is that Method 4 is extremely sensitive to the choice of the target T . If the desired improvement is too small, the search will be highly local and will only move on to search globally after searching nearly exhaustively around the current best point. On the other hand, if T is set too high, the search will be excessively global, and the algorithm will be slow to ﬁne-tune any promising solutions. This sensitivity to the setting of the target is illustrated in Figure 16 which contrasts the status of the search after 11 iterations when using a target of 25% versus 1% improvement. There are two ways to overcome this sensitivity. One way is to change the auxiliary function to something called ‘expected improvement.’ We will discuss this option in the next section. However, probably the best approach is to simply use several values of the target T corresponding to low, medium, and high desired improvement. This will lead to the selection of several search points in each itera-tion, causing us to search both locally and globally in each iteration. As a result, as soon as the global part of the search stumbles into the basin of convergence of the global minimum, the local part of the search will immediately begin to ﬁne-tune the solution in the next iteration. Moreover, generating several search points per iteration allows one to take advantage of any parallel computing capabilities that may be available. We will refer to this approach as ‘Enhanced Method 4’. To illustrate this, let us return to the ‘Start’ panel of Figure 14 and see what happens if we ﬁnd the point that maximizes the probability of improvement for several values of the target T . Now selecting any ﬁnite set of values for T must inevitably be somewhat arbitrary. In my experience, however, the following pro-cedure seems to work well. First, ﬁnd the minimum of the surface using multistart 366 DONALD R. JONES Figure 15. Illustration of Method 4 on a simple one-dimensional test function. In each it-eration, we ﬁt a kriging surface to the data, ﬁnd the point that maximizes probability of improvement (deﬁned as exceeding some target T ), and then evaluate the function at this point. In this example, the target T was set 25% below the minimum of the surface. GLOBAL OPTIMIZATION BASED ON RESPONSE SURFACES 367 Figure 16. Method 4 is sensitive to the desired improvement. On the left the target for im-provement was set 25% below the minimum of the surface, and the search is quite global. On the right, the target is set to 1% below the minimum of the surface, and the search is excessively local in nature. Table 1. The 27 values of α used to compute function-value targets in Enhanced Method 4. Target Number α Target Number α Target Number α 1 0.0 10 0.07 19 0.25 2 0.0001 11 0.08 20 0.30 3 0.001 12 0.09 21 0.40 4 0.01 13 0.10 22 0.50 5 0.02 14 0.11 23 0.75 6 0.03 15 0.12 24 1.00 7 0.04 16 0.13 25 1.50 8 0.05 17 0.15 26 2.00 9 0.06 18 0.20 27 3.00 and call this value smin. Also ﬁnd the minimum and maximum objective function value at the sampled points; call these fmin and fmax. Now construct targets using T = smin−α(fmax−fmin) using the 27 values of α shown in Table 1. (When α = 0, the point that maximizes the probability of improvement is the same as the point that minimizes the surface.) Figure 17 shows what happens when we use these 27 target values. In the ﬁgure, each diamond shows the result of maximizing the probability of improvement for a given target value T . The horizontal coordinate of the diamond is the x coordinate of the point that maximizes the probability of improvement. The vertical coordinate corresponds to the ‘target number’ from Table 1 and is shown on the right-hand scale. As one can see, targets near the current minimum (e.g., target number 1) result in search points close to the current best point. As the target level T decreases (target number increases), the point maximizing the probability of improvement moves away from the current best point towards a more unexplored part of the 368 DONALD R. JONES Figure 17. Location of the point that maximizes the probability of improvement (diamonds) as a function of the amount of improvement desired, given by the ‘target number’ (right hand scale). space. The diamonds corresponding to targets 1–20 cluster in one part of the space, whereas those for targets 21–27 cluster in a different areas. In practice, it makes sense to sample only one point from each region. What we do, therefore, is to cluster the points and, from each cluster, take the point associated with the lowest target. In Figure 17, these points are shown as open, unﬁlled diamonds. Choosing the point associated with the lowest target makes the search more global and insures that the sampled points will be dense. In Figure 18 we show what happens if we iterate this process on Test Function #4. In this ﬁgure, we use vertical, dotted lines to show the x values corresponding the new search points chosen via the clustering procedure. Thus, the two lines shown for Iteration 1 correspond to the two open diamonds in Figure 17. Because the method searches both globally and locally, we ﬁnd the basin of convergence of the global optimum much sooner (in Iteration 2). Moreover, because we sample between one and three points per iteration, some speed up from parallel computation is possible. Enhanced Method 4, like all of the methods described so far, is not limited to one-dimensional problems. For example, Figure 19 shows how the method per-forms on the two-dimensional Branin test function. By the sixth iteration the method has sampled near all three global minima (they are tied for the best value). The number of points sampled per iteration varies from 1 to 5. Some technical details of Enhanced Method 4 are given the Appendix. These details include the method for generating starting points for maximizing the prob-ability of improvement via multistart, and also the method for clustering the result-ing solutions. GLOBAL OPTIMIZATION BASED ON RESPONSE SURFACES 369 Figure 18. The ﬁrst ﬁve iterations of enhanced method #4 applied to test function #4. As an aside, note that we could also have constructed an ‘Enhanced Method 3’ by employing several values of the constant κ used to compute the ‘statistical lower bound’ y (x∗) −κs(x∗). This would be very similar in spirit to using several values of the target T in Method 4. There is no need to do this, however, because it produces exactly the same search! To see this, note that maximizing the probability of improvement is the same as maximizing " T − y (x) s (x) (28) which is the same as minimizing y (x) −T s (x) . (29) Now suppose that the minimum of the above ratio occurs at point x∗and that, at this point, the ratio is κ. If we then set T = y x∗ −κs(x∗), (30) 370 DONALD R. JONES Figure 19. First six iterations of enhanced method #4 on the Branin function. then the point x∗must also minimize y (x∗) −κs(x∗). To see this, suppose there were some point x′ such that y x′ −κs(x′) < T. (31) It would then follow that y x′ −T s (x′) < κ = y (x∗) −T s (x∗) , (32) which would contradict our assumption that point x∗minimized the ratio on the right hand side. Thus we see that there is an isomorphism between choices of T in Method 4 and choices of κ in Method 3. Matching pairs of T and κ give the same optimum of the auxiliary problem. Hence, using all possible values of T in Method 4 results in the same search as using all possible values of κ in Method 3. Note, however, that using one value of T is not the same as using one value of κ. The reason is that the value of κ that corresponds to a given T depends not only on T but also on the minimium value of this ratio in Eq. (29), which will change from iteration to iteration. Using several targets is probably the best way to resolve the sensitivity of Method 4 to the choice of the target improvement (or the sensitivity of Method 3 to the number of standard deviations κ). As mentioned earlier, however, there is another way that has also attracted a great deal of attention, based on the concept of ‘Expected Improvement.’ We consider this next. GLOBAL OPTIMIZATION BASED ON RESPONSE SURFACES 371 7. Maximizing Expected Improvement The ‘expected improvement approach,’ as the name suggests, involves comput-ing how much improvement we expect to achieve if we sample at a given point. As before, let Y(x) be a random variable describing our uncertainty about the function’s value at a point x, and assume that Y(x) is normally distributed with mean and variance given by the kriging predictor, that is, by y (x) and s2(x). If the current best function value is fmin, then we will achieve an improvement of I if Y(x) = fmin −I. The likelihood of achieving this improvement is given by the normal density function 1 √ 2πs (x) exp −(fmin −I − y (x))2 2s2 (x) (33) The expected improvement is simply the expected value of the improvement found by integrating over this density: E(I) = I=∞ I=0 I 1 √ 2πs (x) exp −(fmin −I − y (x))2 2s2 (x) ! dI (34) Using integration by parts, one can show that E(I) = s (x) [u" (u) + φ (u)] (35) where u = fmin − y(x) s(x) and where " and φ are the normal cumulative distribution function and density function, respectively. In Method 5, we will ﬁt a kriging model, ﬁnd the point that maximizes expected improvement, evaluate the function at this point, and iterate. The appeal of the expected improvement approach is three-fold. First, it avoids the need specify a desired improvement (i.e., the target T of the previous section). Second, Locateli (1997) has proved that under certain assumptions the iterates from this method are dense. Third, it provides a simple stopping rule: ‘stop when the ex-pected improvement from further search is less than some small positive number’. In the literature, this method has been pursued by Schonlau et al. (1997), and by Sasena (2000). The performance of this method on Test Function #4 is explored in Figure 20. As guaranteed by Locateli’s proof, the expected improvement method does ﬁnd the global minimum. But in this case it takes a long time to do so. The reason is that the initial sample is highly deceptive, leading to very small estimates of the standard error. As a result, only points that are close to the current best point have high expected improvement. It requires fairly exhaustive search around the initial best point before the algorithm begins to search more globally. 372 DONALD R. JONES Figure 20. Illustration of Method 5 on a simple one-dimensional test function. In each itera-tion, we ﬁt a kriging surface to the data, ﬁnd the point that maximizes expected improvement, and evaluate the function at this point. This potential for deception is a fundamental weakness of Methods 3–5. All of these methods rely on the standard error of the kriging predictor to force the algorithm to go back and explore regions where the sampled points are sparse. This is certainly better than completely ignoring the potential error in the surface. But all of these methods treat the estimated standard error as if it is correct, which will not always be the case. Test Function #4 is a good example where the standard GLOBAL OPTIMIZATION BASED ON RESPONSE SURFACES 373 Figure 21. The sample used to construct the initial surface can be extremely deceptive, leading to gross under-estimation of the error in the kriging predictor. This can lead to poor peform-ance in ‘two stage’ approaches (Methods 1–5 in the taxonomy) that ﬁrst ﬁt a response surface and then use the surface to select the next iterate. error may be greatly underestimated. An even more extreme case of deception is shown in Figure 21. In this case, the true function is the sine function, and we have unluckily sampled it at all the crests. The kriging predictor ﬁtted to this data would have µ = 1 and σ 2 = 0 and would predict that the probability of improvement and the expected improvement are equal to zero everywhere. In short, the fundamental ﬂaw of Methods 3–5 is that they are two-stage meth-ods. In stage 1, the kriging surface is ﬁt to the observed data, and all the relevant parameters are estimated. In the second stage, these parameter estimates are taken as correct and a calculation is done to determine where to search. Two-stage meth-ods can be deceived when the initial sample is sparse and gives a highly misleading view of the function. Because the misleading view is taken as ‘correct’ in stage 2, the algorithm may stop prematurely or become excessively local in its selection of search points. To avoid this pitfall, we must avoid estimating the parameters of the kriging model based only on the observed sample. While this may seem impossible, it is precisely what we do in the ‘one-stage’ methods we consider next. 8. One-stage approach for goal seeking In this section, we assume that we have a target value or ‘goal’ for the objective function. That is, instead of minimizing the function, we merely want to achieve a value f ∗which is considered to be desirable. For example, a goal might be set by benchmarking to competitive products. In this section we will explore a ‘one-stage approach’ for such goal-seeking problems. In the next section, we extend this method to the case of true optimization. In a one-stage approach, we posit a hypothesis about the location of the point that achieves the goal f ∗and use the machinery of response surfaces to measure the ‘credibility’ of this hypothesis. More speciﬁcally, suppose we hypothesize that the goal f ∗is achieved at a point x∗. To evaluate this hypothesis, we compute the likelihood of the observed data conditional upon the assumption that the surface 374 DONALD R. JONES goes through the point (x∗, f ∗). This conditional likelihood is: 1 (2π) n 2 σ 2 n 2 \|C\| 1 2 exp −(y −m)′ C−1 (y −m) 2σ 2 (36) where m and C are the conditional mean and correlation matrix: m = 1µ + r(f ∗−µ) (37) C = R −rr′ (38) Note that the value of x∗comes into play through the vector r of correlations between x∗and the n sampled points. When using the conditional log-likelihood to evaluate the hypothesis that the surface passes through (x∗, f ∗), we also optimize the kriging parameters µ, σ 2, θℓ and pℓ(ℓ= 1, .., d) to maximize the conditional likelihood. That is, the paramet-ers are adjusted to make the hypothesis seem as likely as possible. The resulting optimized likelihood can be considered to be a measure of the ‘credibility’ of our hypothesis. The next iterate is the value of x∗that maximizes the measure of credibility. Mechanically, it is found by globally maximizing the conditional log-likelihood over both x∗and the kriging parameters µ, σ 2, θℓand pℓ(ℓ= 1, .., d). As be-fore, one can concentrate out the parameters µ and σ 2 and thereby express the conditional log-likelihood as a function of only x∗and the correlation parameters θℓand pℓ(ℓ= 1, .., d). The key thing to note is that the next iterate is not based on parameters obtained by ﬁtting a surface to the observed data alone—parameters that can be greatly in error if the initial sample is sparse and misleading. To illustrate this concept, Figure 22 explores two hypothesized locations where Test Function #4 might reach a goal f ∗represented as a horizontal line. For both cases, we show the optimized conditional log-likelihood as well as the best-ﬁtting kriging surface through the hypothesized point and the data. I think most readers would agree that the graph on the right, which has the higher credibility value (conditional log-likelihood), is indeed the more believable hypothesis. The performance of Method 6 on our tricky Test Function #4 is shown in Fig-ure 23. In this example we have ‘cheated’ and set the goal f ∗equal to the global minimum—something that we could obviously not do in practice. The search ﬁnds the basis of the global minimum after only seven iterations. The perforance of Method 6 on Test Function #4 is comparable to that of Enhanced Method #4, but unlike that method, Method 6 can handle extremely deceptive problems like that shown in Figure 21. Of course, in Method 6 we have assumed we know the optimal function value f ∗or an appropriate goal to seek. But what should we do if we did not know the minimum or have a clear goal? We take up this topic in the next section. GLOBAL OPTIMIZATION BASED ON RESPONSE SURFACES 375 Figure 22. In Method 6, the credibility of the hypothesis that the surface passes through (x∗, f ∗) is based on the likelihood of the data conditional upon the surface passing through this point. The ﬁgure compares hypotheses for two possible values of x∗, both with the same value of f ∗. 9. One-stage approach for optimization When a search goal f ∗is not available, we can stil use the basic idea of Method 6 for optimization. We simply compute several search points using several values of f ∗0.1 and i−1>0.1, then set the criterion to 100 so that we start a new group. In this case, point i is quite distant from both point i −1 and point i +1 and should be in its own cluster. − Otherwise, if i>0.0005, then set the criterion to i−1/i. In this case, the criterion will be high if the distance from point i −1 to point i is high but the distance between point i and point i +1 is low—a condition that indicates 382 DONALD R. JONES that point i should be grouped with the points that follow it and not the ones that preceed it. − Otherwise, if i ⩾3 and i−1>0.0005, then set the criterion to i−1/ max(i−2, 0.0005). In this case, the criterion will be high if the distance from i −1 to i is much greater than the distance from i −2 to i −1. This, in turn would suggest that points i −2 and i −1 are in the same group but point i is so different from point i −1 that it should start a new group. − Otherwise, if i = 2 and 1>0.1 and 2<0.0005, then set the criterion to 100 to signal the need for a new group. In this case point 2 is very different from point 1. − If none of the above conditions are satisﬁed, set the criterion to zero so that we do not start a new group. At this point we will have assigned a group to the point generated using each of the 27 targets. For each group, we take the point associated with the highest target number as a ‘group representative’ to be sampled on the next iteration. This clustering procedure usually works very well. However, in implementing Method 7, I have found one strange failure mode for the clustering procedure, and it is necessary to correct this problem when it occurs. In particular, sometimes a later group (e.g., group 3) will be essentially the same as an earlier one (e.g., group 1). To handle this, after computing the list of group representatives as above, I scan them from group 2 to group ngroup, computing the root-mean-squared distance of each point to all the previous group representatives. As before, in computing this distance, all the variables are normalized to lie on the unit interval. If a point is within 0.03 of a previous group representative in terms of root-mean-squared distance, then I skip it. References Alexandrov, N.M., Lewis, R.M., Gumbert, C. R., Green, L.L., and Newman, P.A. Optimization with variable-ﬁdelity models applied to wing design. In Proceedings of the 38th Aerospace Sciences Meeting & Exhibit, January 2000. AIAA Paper 2000-0841. American Institute of Aeronautics and Astronautics. Proceedings of the 8thAIAA / USAF / NASA / ISMMO Symposium of Multidisciplinary Analysis & Optimization, September 2000. Available on CD-ROM from the AIAA at Booker, A. J. Examples of surrogate modeling of computer simulations. Presented at the ISSMO/NASA First Internet Conference on Approximations and Fast Reana-lysis in Engineering Optimization, June 14-27, 1998. Conference abstract available at Full text in pdf format available by sending email to andrew.j.booker@boeing.com. Booker, A. J., Dennis, J.E. Jr., Frank, P.D., Seraﬁni, D.B., Torczon, V. and Trosset M.W. (1999). A rigorous framework for optimization of expensive functions by surrogates. Structural Optimiza-tion, 17, 1–13. Cox, D. D and John S. (1997). SDO: A statistical method for global optimization. In N. Alexandrov, and M.Y. Hussaini, editors, Multidisciplinary Design Optimization: State of the Art, 315–329. SIAM, Philadelphia. GLOBAL OPTIMIZATION BASED ON RESPONSE SURFACES 383 Dennis, J.E. Jr. and Torczon, V. (1991). Direct search methods on parallel machines. SIAM Journal of Optimization, 1, 448–474. L.C.W. Dixon and G.P. Szego (1978). The global optimisation problem: an introduction. In L.C.W. Dixon and G.P. Szego, editors, Towards Global Optimisation 2, 1–15. North Holland, New York. J.F. Elder IV (1992). Global Rd optimization when probes are expensive: the GROPE algorithm. Proceedings of the 1992 IEEE International Conference on Systems, Man, and Cybernetics, Vol. 1, 577–582, Chicago. Gutmann, H.M. (2001). A radial basis function method for global optimization. Journal of Global Optimization, 19(3) pp. 201–227. Jones, D.R., Schonlau, M. and Welch W.J. (1998). Efﬁcient global optimization of expensive black-box functions. Journal of Global Optimization, 13, 455–492. J. Koehler and A. Owen. (1996). Computer experiments. In S. Ghosh and C.R. Rao, editors, Hand-book of Statistics, 13: Design and Analysis of Experiments, 261–308. North Holland, New York. H.J. Kushner (1964). A new method of locating the maximum point of an arbitrary multipeak curve in the presence of noise. Journal of Basic Engineering, 86, 97–106. M. Locatelli (1997). Bayesian algorithms for one-dimensional global optimization. Journal of Global Optimization 10, 57–76. J. Mockus. Application of Bayesian approach to numerical methods of global and stochastic optimization. Journal of Global Optimization, 4, 347–365, 1994. C. Perttunen (1991). A computational geometric approach to feasible region division in con-strained global optimization. Proceedings of the 1991 IEEE Conference on Systems, Man, and Cybernetics. J. Sacks, W. J. Welch, T.J. Mitchell, and H. P. Wynn (1989). Design and analysis of computer experiments (with discussion). Statistical Science 4, 409–435. Sasena, M.J., Papalambros, P.Y. and Goovaerts, P. Metamodeling sampling criteria in a global optimzation framework. In Proceedings of the 8thAIAA / USAF / NASA / ISMMO Symposium of Multidisciplinary Analysis & Optimization, September 2000. AIAA Paper 2000-4921. Schonlau, M., Welch, W.J. and Jones, D.R. Global versus local search in constrained optimization of computer models. In N. Flournoy, W.F. Rosenberger, and W.K. Wong, editors, New Developments and Applications in Experimental Design, Institute of Mathematical Statistics. Also available as Technical Report RR-97-11, Institute for Improvement in Quality and Productivity, University of Waterloo, Waterloo, Ontario, CANADA, December 1997. B.E. Stuckman (1988). A global search method for optimizing nonlinear systems. IEEE Transactions on Systems, Man, and Cybernetics 18, 965–977. Theil, H. (1971). Principles of Econometrics. John Wiley, New York. Torn, A. and Zilinskas, A. (1987). Global Optimization, Springer, Berlin. A. Zilinskas (1992). A review of statistical models for global optimization. Journal of Global Optimization 2, 145–153. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
13244	https://wiki.analog.com/university/courses/electronics/rl_transient_response	Resources and Tools Evaluation Boards & Kits FPGA Reference Designs Quick Start Guides Linux Software Drivers Microcontroller Software Drivers ACE Software Technical Guides Education Content University Program Overview ADALM1000 (M1k) Active Learning Module ADALM2000 (M2k) Active Learning Module ADALP2000 Parts kit for Circuits ADALM-PLUTO SDR Active Learning Module Teaching and Lab Materials Wiki Help Help About Wiki Playground Wiki Site Map Wiki Tools Admin Recent Changes Media Manager Sitemap Analog Devices Wiki Analog Devices Wiki Resources and Tools Evaluation Boards & Kits FPGA Reference Designs Quick Start Guides Linux Software Drivers Microcontroller Software Drivers ACE Software Technical Guides Education Content University Program Overview ADALM1000 (M1k) Active Learning Module ADALM2000 (M2k) Active Learning Module ADALP2000 Parts kit for Circuits ADALM-PLUTO SDR Active Learning Module Teaching and Lab Materials Wiki Help Help About Wiki Playground Wiki Site Map Wiki Tools Admin Recent Changes Media Manager Sitemap English 简体中文日本語 Руccкий This version (07 Feb 2022 14:14) was approved by Doug Mercer.The Previously approved version (23 Aug 2019 09:01) is available. Table of Contents Activity: Transient Response of an RL Circuit - ADALM2000 Objective: Background: Materials: Hardware setup: Procedure: Questions: Activity: Transient Response of an RL Circuit - ADALM2000 Objective: The objective of this Lab activity is to study the transient response of inductor circuits using a series RL configuration and understand the time constant concept. Background: This lab activity is similar to the “Transient response of an RC circuit” Lab activity, except that the capacitor is replaced by an inductor. In this experiment, you will apply a square waveform to the RL circuit to analyze the transient response of the circuit. The pulse width relative to the circuit's time constant determines how it is affected by the RL circuit. Time Constant (t): It is a measure of time required for certain changes in voltages and currents in RC and RL circuits. Generally, when the elapsed time exceeds five time constants (5t) after switching has occurred, the currents and voltages have reached their final value, which is also called steady-state response. The time constant of an RL circuit is the equivalent inductance divided by the Thévenin resistance as viewed from the terminals of the equivalent inductor. (1) A Pulse is a voltage or current that changes from one level to another and back again. If a waveform's high time equals its low time, it is called a square wave. The length of each cycle of a pulse train is its period (T). The pulse width (tp) of an ideal square wave is equal to half the time period. The relation between pulse width and frequency for the square wave is given by: (2) Figure 1: Series RL circuit In an R-L circuit, voltage across the inductor decreases with time while in the RC circuit the voltage across the capacitor increased with time. Thus, current in an RL circuit has the same form as voltage in an RC circuit: they both rise to their final value exponentially according to 1 - e (-tR/L). The expression for the current in the Inductor is given by: (3) where, V is the applied source voltage to the circuit for t = 0. The response curve is increasing and is shown in figure 2. Figure 2: Current in Inductor increasing in a Series RL circuit. (Time axis normalized by t) The expression for the current decay across the Inductor is given by: (4) where, I0 is the initial current stored in the inductor at t = 0 L/R = t is time constant. The response curve is a decaying exponential and is shown in figure 3. Figure 3: Current decay through the Inductor for Series RL circuit. Since it is possible to directly measure the current through the Inductor ( current supplied by driving source ) with the ALM1000, we will measure and compare both the current and the output voltage across the Resistor. The resistor waveform should be similar to the inductor current as VR=ILR. From the waveforms on the scope, we should be able to measure the time constant t which should be equal to t = L / Rtotal. Here, Rtotal is the total resistance and can be calculated from Rtotal = R inductance+ R. R inductance is the measured value of inductor resistance and can be measured by connecting inductance to an ohmmeter prior to running the experiment. Materials: ADALM2000 Active Learning ModuleSolder-less breadboard, and jumper wire kit1 100 Ω resistor1 1 mH inductor Hardware setup: Set up the circuit shown in Figure 4 on your solderless breadboard with the component values R1 = 100Ω and L1 = 1 mH. Figure 4. Series RL circuit schematic Figure 5. Breadboard connections of RL circuit Procedure: On Channel 1 of the oscilloscope you will visualize the input voltage, and on channel 2 the voltage on the resistor(it has the same shape as the current through the inductor). Generate a square wave on the channel 1 of the signal generator with 4V amplitude peak-to-peak. The frequency will be set according to t. Calculate the applied frequency using equation (2) for tp = 5t. Figure 6. Waveforms for pulsewidth equal to 5t The waveform on channel 2 (voltage on the resistor) has the same shape as IL(t) waveform. From it, measure time constant t and compare with the one that you calculated from L/Rtotal. (Hint: Find the time that corresponds to 0.63VR value). Observe the response of the circuit and record the results again for tp = 25t, and tp = 0.5t. Questions: • Include plots of IL and VR for different tp values given above in Procedure 4. • A Capacitor stores charge. What do you think an Inductor stores? Answer in brief. • How can you attenuate the spikes present on the input voltage? Lab Resources: Fritzing files:transient_response_RL_bb LTSpice files:transient_response_RL_ltspice Return to Lab Activity Table of Contents university/courses/electronics/rl_transient_response.txt · Last modified: 07 Feb 2022 14:14 by Doug Mercer Page Tools View Source History Backlinks Fold/unfold all [ Back to top ]
13245	https://ajronline.org/doi/10.2214/ajr.175.4.1750981	Appendicolith Revealed on CT in Children with Suspected Appendicitis How Specific Is It in the Diagnosis of Appendicitis? \| AJR Skip to main content American Journal of Roentgenology ================================= Search American Journal of Roentgenology Search Advanced search 0 Login \| Register Skip main navigation Close Drawer Menu Open Drawer MenuMenu Articles & Issues New Articles Issue in Progress Latest Issue All Issues Editor’s Choice (Free) Special Series Reviews Articles with Credit Best of AJR Top 10 Lists Collections Artificial Intelligence / Machine Learning Best Practices Diversity, Equity, & Inclusion Editor's Notebook Emergency Radiology Expert Panel Narrative Reviews Generative AI / Large Language Models Global Reading Room Articles with Study Guides Photon-Counting Detector CT Point/Counterpoint Sustainability Workforce Information About AJR Editorial Board Frequently Asked Questions Subscriptions Membership Permissions Institutional Admins AJR Alerts Sign Up Authors Author Guidelines Original Research Guide AJR Abbreviation List Submit Manuscript Reviewers Reviewer Guide Reviewer Spotlight Lifetime Awards Multimedia Visual Abstracts AJR Podcast Series AJR Conversations Trainee Podcasts AJR This Month X/Twitter Bluesky YouTube Facebook Instagram AJR Global Multimedia Archive Podcast Archive Sections Evidence Synthesis & Decision Analysis Breast Imaging Cardiothoracic Imaging Gastrointestinal Imaging Genitourinary Imaging Interventional Radiology Musculoskeletal Imaging Neuroradiology/Head & Neck Imaging Nuclear Medicine Pediatric Imaging Policy, Quality, & Practice Management Multispecialty SUBMIT SUBSCRIBE R3 Other Pediatric Imaging November 23, 2012 Appendicolith Revealed on CT in Children with Suspected Appendicitis: How Specific Is It in the Diagnosis of Appendicitis? Authors: Lisa H.Lowe, Michael W.Penney, Luis E.Scheker, Ramiro Perez, Jr., Sharon M.Stein, Richard M.Heller, Yu Shyr, and Marta Hernanz-SchulmanAuthor Info & Affiliations Volume 175, Issue 4 11,354 60 Metrics Total Downloads 11,361 Last 12 Months 901 Total Citations 60 Last 12 Months 5 View all metrics PDF Contents Abstract Introduction Materials and Methods Results Discussion Footnote References Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract OBJECTIVE. The purpose of this study was to determine the sensitivity, specificity, and positive and negative predictive values of a diagnosis of appendicitis when CT without enteric contrast material reveals an appendicolith in children with suspected appendicitis. MATERIALS AND METHODS. A retrospective review of children who underwent abdominal CT for suspected appendicitis over a 25-month period was performed to identify patients with an appendicolith. An age-matched group of patients examined for trauma served as controls. RESULTS. CT was performed in 104 children. Appendicitis was present in 60 (58%) of 104 children; 39 (65%) of 60 had an appendicolith. Appendicitis was not present in 44 (42%) of 104; six (14%) of 44 had an appendicolith. An appendicolith detected on CT had a sensitivity of 65% and a specificity of 86% for the radiologist diagnosing appendicitis. An appendicolith had a positive predictive value of 74% and a negative predictive value of 26%. Among the control population, two (3%) of 74 children had an appendicolith. This number was statistically significant compared with children in the study group with an appendicolith and abdominal pain, but without appendicitis (p = 0.02). CONCLUSION. Although an appendicolith is significantly associated with appendicitis, the detection of an isolated appendicolith on CT is not sufficiently specific to be the sole basis for the diagnosis of acute appendicitis. Introduction For the diagnosis of appendicitis in patients with abdominal pain, appendicoliths are widely accepted as the only radiographic criterion with a specificity of 100% and are seen on unenhanced radiographs in 10-15% of these patients [1, 2]. The recent application of CT to patients examined for suspected appendicitis identified appendicoliths with much greater frequency, ranging from 43% to 50% in series comprising patients of all ages [3,4,5,6,7,8]. Clearly, appendicoliths are revealed much more frequently on CT than on abdominal radiographs, yet little is written about the specificity of an appendicolith revealed on CT in the diagnosis of appendicitis. To our knowledge, no reports specifically address the sensitivity, specificity, and positive and negative predictive values of an appendicolith on CT of the abdomen without enteric contrast material or in pediatric patients. As CT supersedes abdominal radiography in the diagnosis of clinically equivocal appendicitis, an understanding of the significance of an appendicolith is important to optimize diagnostic accuracy and to direct therapy. The objective of this study was to determine the significance of an appendicolith detected on CT in children with abdominal pain by determining its sensitivity, specificity, and positive and negative predictive values for the diagnosis of appendicitis. Materials and Methods An institutional computerized database identified 104 consecutive children with abdominal pain and suspected appendicitis who underwent CT between April 1997 and May 1999. Pediatric surgeons, emergency physicians, faculty pediatricians, and community pediatricians referred patients. A retrospective review of the original CT reports identified 45 children with an appendicolith (25 boys and 20 girls) who were 3-17 years old (mean age, 10 years). In the study population, helical abdominal CT was performed at 5-mm collimation without sedation and oral or rectal contrast material on a Tomoscan AV (Philips Medical Systems, Shelton, CT) or Somatom Plus (Siemens Medical Systems, Iselin, NJ). IV contrast material was not part of the routine protocol, but was given in two patients. An attending pediatric radiologist reported initial CT findings regarding the presence or absence of appendicitis. Positive diagnostic criteria included an enlarged appendix (>6 mm) or inflammatory changes in the right lower quadrant (including periappendiceal inflammation, phlegmon, or abscess). After an initial false-positive finding of an isolated appendicolith found not to be associated with appendicitis surgically and pathologically, we did not consider an appendicolith alone as diagnostic. Negative diagnostic criteria included absence of an enlarged appendix and lack of periappendiceal inflammation, phlegmon, and abscess. Visualization of a normal appendix was not required for a negative diagnosis. A positive diagnosis of appendicitis was confirmed by surgical and pathologic findings. A negative diagnosis was confirmed by surgery or chart review until discharge and subsequent telephone follow-up, ranging from 6 to 16 months after the CT (mean time, 9.2 ± 3.9 months). Telephone follow-up included questions to determine if the patient had a subsequent appendectomy, was seen by another physician for similar symptoms, or had recurrence of symptoms. We could reach all patients in the study group with an appendicolith without appendicitis who did not have surgical confirmation of the negative diagnosis. Chart review to discharge in both patients in the control group with an appendicolith showed no evidence of abdominal pain or appendicitis. We could confirm a negative diagnosis by telephone follow-up in one of these two patients in the control group who did not have appendicitis at 6-months follow-up. However, the other patient moved and was lost to follow-up. Original CT reports identifying children with an appendicolith were correlated with the discharge diagnosis of appendicitis or no appendicitis by chart review. All CT scans of patients with an appendicolith, but without appendicitis, were pulled from files and reviewed by four attending pediatric radiologists; the presence of an appendicolith was confirmed by consensus. An appendicolith was defined as high-density material in the appendix with similar attenuation to that of adjacent bone. For an appendicolith to be defined for the purpose of the study, reviewers could not find radiodense material outside the appendix in adjacent bowel loops. In all children with an appendicolith, but without appendicitis, agreement was found between the initial report and the retrospective CT review. The sensitivity, specificity, positive predictive value, negative predictive value, and odds ratio for diagnosing appendicitis in the setting of an appendicolith revealed on CT were calculated and subjected to statistical analysis by a biostatistician. We analyzed these data using Fisher's exact test for categoric variables. We calculated the 95% confidence interval (CI), using binomial proportions for the difference between experimental and control groups. All tests of significance were two-tailed tests, and differences were considered statistically significant when a p of greater than 0.05 (SAS version 7.0; SAS Institute, Cary, NC) was used for all analyses. The institutional review board approved this study. Results In the study group, appendicitis was confirmed surgically and pathologically in 60 (58%) of 104 patients. Appendicitis was not present in 44 (42%) of 104 children. The prevalence of an appendicolith in children with appendicitis was 39 (65%) of 60, and the prevalence of it in those without appendicitis was six (14%) of 44. Conversely, of all children in the study group examined for suspected appendicitis, an appendicolith was identified on CT in 45 (43%) of 104. Among these patients, 39 (87%) of 45 had surgically and pathologically confirmed appendicitis; all 39 had associated appendiceal distention and periappendiceal inflammation (Fig. 1). However, six (13%) of 45 did not have appendicitis; in these six patients, the appendicolith was an isolated finding (i.e., no appendiceal distention or periappendiceal inflammation) (Fig. 2). These six cases were confirmed by surgery (n = 1) or by chart review with telephone follow-up (n = 5). Among these five patients, one received 10 days of oral trimethoprim sulfamethoxazole (Bactrim; Roche Labs, Grafton, WI) for presumed shigella infection; the others did not receive any antibiotic treatment. The difference between children with an appendicolith accompanied by appendicitis compared with those with an appendicolith, but without appendicitis, was statistically significant (p< 0.001). Open in Viewer Fig. 1. —8-year-old girl with abdominal pain, appendicolith, and appendicitis. Unenhanced CT scan shows enlarged appendix (arrow). Note associated appendicolith (arrowhead) and surrounding periappendiceal inflammation. Open in Viewer Fig. 2. —6-year-old boy with abdominal pain, appendicolith, and no appendicitis. Unenhanced CT scan reveals normal appendix containing small appendicolith (arrow). No periappendiceal inflammation or appendiceal dilatation is present. An appendicolith detected on CT had a sensitivity of 65% (95% CI, 53-77%) and a specificity of 86% (95% CI, 76-96%) for the diagnosis of appendicitis. The positive predictive value was 74% (95% CI, 66-82%), and the negative predictive value was 26% (95% CI, 18-34%). The prevalence of appendicitis in our series was 60 (58%) of 104 children; given the presence of an appendicolith, we found the odds ratio for having appendicitis was 6.4. In the control group, two patients (3%) of 74 had an appendicolith without appendiceal distention or inflammation (Fig. 3). The difference between six (14%) of 44 children who had an appendicolith without appendicitis in the study group compared with two (3%) of 74 in the control group was statistically significant (p = 0.02). Open in Viewer Fig. 3. —2-year-old girl who was examined for trauma had appendicolith and no appendicitis. CT scan with IV contrast material and no oral contrast material reveals normal appendix containing appendicolith (arrow). No periappendiceal inflammation or appendiceal dilatation is seen. Note superior aspect of bladder (B) medial to appendix. Discussion The presence of an appendicolith on abdominal radiographs radiography is broadly accepted as 100% specific for the diagnosis of appendicitis in patients with abdominal pain and is considered an indication for appendectomy [1, 2]. However, the recent application of CT to the examination of patients with appendicitis revealed that appendicoliths are more frequently identified on CT than on abdominal radiography, with a reported incidence of 43-50% in the general (mostly adult) population [4,5,6,7,8]. The increased rate of appendicolith detection on CT compared with abdominal radiography may be caused by greater contrast resolution and tomographic capabilities, permitting detection of smaller appendicoliths [4, 7]. Although we did not study the size of the individual appendicoliths because of inherent inaccuracies arising from volume averaging, all appendicoliths in patients without appendicitis occurred in normal-sized appendixes (by definition <6 mm). Despite their increased identification, the significance of an appendicolith on CT received scant attention in the literature [1, 2]. To our knowledge, the presence of an appendicolith without appendicitis, as documented in 14% of our CT patients and in 3% of the control group, has not been previously reported. The frequency of appendicoliths detected on CT and their specificity for the diagnosis of appendicitis differ in our study compared with previous reports [4,5,6,7,8,9]. In our series, 65% of children with proven appendicitis had an appendicolith on CT without oral contrast material; this percentage is greater than in previous reports of 43-50%. The specificity of an appendicolith on CT for the diagnosis of appendicitis in our series was 86%. This percentage differs from a specificity of 100% found by Rao et al. , the only other study addressing the specificity of an appendicolith identified on CT. However, unlike our series, Rao et al. performed their study on the general (mostly adult) population, and all patients received rectal contrast material. The explanation for the higher detection rate and decreased specificity of appendicoliths in our pediatric series compared with CT studies performed with enteric contrast material on the general population could be related to an increased frequency and diminished significance of appendicoliths in children. However, we believe that a more likely explanation is absence of enteric contrast material in our patients. Because enteric contrast material may accumulate in the appendix, an appendicolith may be obscured to the degree that visualization is not possible. In patients without appendicitis, an appendicolith in an otherwise normal appendix may not be easily differentiated from enteric contrast material and, therefore, may not be detected. Our data raise interesting questions regarding the pathophysiologic basis for an appendicolith in a child with abdominal pain but without appendicitis. Three possible explanations are suggested. First, an appendicolith may be the initiating event in developing appendicitis in some patients, resulting in abdominal pain, but this initial event may resolve before appendiceal distention and inflammatory changes ensue. Second, calcified material in the appendix may be a transient finding in healthy children. Third, a combination of the first and second explanation could be true. Calcified material could be a normal, and at times a transient finding, but with the potential to obstruct the appendiceal lumen and initiate appendicitis. We did not believe we were justified in performing follow-up CT in asymptomatic patients to determine whether the appendicoliths resolved spontaneously. This resolution could have been correlated with the cessation of abdominal pain. However, to further explore this intriguing question, we identified an age-matched control population without acute abdominal pain. The identification of an appendicolith in 3% of children in the control population suggests that a small amount of calcified material in the appendix of an asymptomatic child may be a normal finding. However, children with abdominal pain but without appendicitis were significantly more likely to have an appendicolith than those without abdominal pain in the control group (p = 0.02). Furthermore, children with abdominal pain and an appendicolith on CT were significantly more likely to have appendicitis (p< 0.001). Thus, although none of our patients with or without abdominal pain and an isolated appendicolith developed appendicitis, the significant association of an appendicolith with abdominal pain and appendicitis suggests that the third alternative may be correct. A small, isolated appendicolith may be a normal finding in pediatric patients, but, in some patients, appendicoliths may be associated with abdominal pain and perhaps represent one of several possible initiating events in the eventual development of appendicitis. In conclusion, in our series of 104 pediatric patients, an appendicolith detected on CT had a sensitivity of 65%, a specificity of 86%, a positive predictive value of 74%, and a negative predictive value of 26% for the diagnosis of appendicitis. An appendicolith was seen in 65% of CT scans of children with proven appendicitis and in 14% of children with abdominal pain but without appendicitis. Though the presence of an appendicolith is significantly associated with appendicitis, our data indicate that an appendicolith alone is insufficient to diagnose acute appendicitis on CT. Footnote Address Correspondence to M. Hernanz-Schulman. References 1. Siegel MJ. Acute appendicitis in childhood: the role of ultrasound. Radiology 1992; 185:341-342 Crossref PubMed Google Scholar a [...] radiographs in 10-15% of these patients b [...] considered an indication for appendectomy c [...] received scant attention in the literature 2. Kirks DR. The gastrointestinal tract. In: Practical pediatric imaging: diagnostic radiology of infants and children. Philadelphia: Lippincott-Raven, 1995: 945-952 Google Scholar a [...] radiographs in 10-15% of these patients b [...] considered an indication for appendectomy c [...] received scant attention in the literature 3. Lane MJ, Katz DS, Ross BA, Clautice-Engle TL, Mindelzun RE, Jeffrey RB Jr. Unenhanced helical CT for suspected acute appendicitis. AJR 1997; 168:405-409 Go to Citation Crossref PubMed Google Scholar 4. Birnbaum BA, Jeffrey RB Jr. CT and sonographic evaluation of acute right lower quadrant abdominal pain. AJR 1998; 170:361-371 Crossref PubMed Google Scholar a [...] in series comprising patients of all ages b [...] in the general (mostly adult) population c [...] detection of smaller appendicoliths d [...] in our study compared with previous reports 5. Friedland JA, Siegel MJ. CT appearance of acute appendicitis in childhood. AJR 1997; 168:439-442 Crossref PubMed Google Scholar a [...] in series comprising patients of all ages b [...] in the general (mostly adult) population c [...] in our study compared with previous reports 6. Balthazar EJ, Birnbaum BA, Yee J, Megibow AJ, Roshkow J, Gray C. Acute appendicitis: CT and US correlation in 100 patients. Radiology 1994; 190:31-35 Crossref PubMed Google Scholar a [...] in series comprising patients of all ages b [...] in the general (mostly adult) population c [...] in our study compared with previous reports 7. Malone AJ. Unenhanced CT in the evaluation of the acute abdomen: the community hospital experience. Semin Ultrasound CT MR 1999; 20:68-76 Crossref PubMed Google Scholar a [...] in series comprising patients of all ages b [...] in the general (mostly adult) population c [...] detection of smaller appendicoliths d [...] in our study compared with previous reports 8. Rao PM, Rhea JT, Novelline RA. Sensitivity and specificity of the individual CT signs of appendicitis: experience with 200 helical appendiceal CT examinations. J Comput Assist Tomogr 1997; 21:686-692 Crossref PubMed Google Scholar a [...] in series comprising patients of all ages b [...] in the general (mostly adult) population c [...] in our study compared with previous reports d [...] a specificity of 100% found by Rao et al. 9. Garcia Pena BM, Mandl KD, Kraus SJ, et al. Ultrasonography and limited computed tomography in the diagnosis and management of appendicitis in children. JAMA 1999; 282:1041-1046 Go to Citation Crossref PubMed Google Scholar Show all references Information & Authors Information Authors Information Published In American Journal of Roentgenology Volume 175 \| Issue 4 \| October 2000 Pages: 981 - 984 PubMed: 11000148 Copyright © American Roentgen Ray Society. History Submitted: December 3, 1999 Accepted: March 17, 2000 First published: November 23, 2012 Authors Affiliations Expand All Lisa H.Lowe Department of Radiology and Radiological Sciences, Vanderbilt University Children's Hospital and Medical Center, D-1120 Medical Center North, Nashville, TN 37232-2675. View all articles by this author Michael W.Penney Department of Radiology and Radiological Sciences, Vanderbilt University Children's Hospital and Medical Center, D-1120 Medical Center North, Nashville, TN 37232-2675. View all articles by this author Luis E.Scheker School of Medicine, Meharry Medical College, 1005 D.B. Todd Jr. Blvd., Nashville, TN 37208. View all articles by this author Ramiro Perez, Jr. School of Medicine, Meharry Medical College, 1005 D.B. Todd Jr. Blvd., Nashville, TN 37208. View all articles by this author Sharon M.Stein Department of Radiology and Radiological Sciences, Vanderbilt University Children's Hospital and Medical Center, D-1120 Medical Center North, Nashville, TN 37232-2675. View all articles by this author Richard M.Heller Department of Radiology and Radiological Sciences, Vanderbilt University Children's Hospital and Medical Center, D-1120 Medical Center North, Nashville, TN 37232-2675. View all articles by this author Yu Shyr Department of Biostatistics, Vanderbilt University Children's Hospital and Medical Center, Nashville, TN 37232. View all articles by this author Marta Hernanz-Schulman Department of Radiology and Radiological Sciences, Vanderbilt University Children's Hospital and Medical Center, D-1120 Medical Center North, Nashville, TN 37232-2675. View all articles by this author Metrics & Citations Metrics Citations Metrics Article Metrics Downloads Citations No data available. 11,354 60 Total 6 Months 12 Months Total number of downloads and citations See more details Posted by 1 X users 20 readers on Mendeley Citations Export Citations To download the citation to this article, select your reference manager software. Format Articles citing this article Appendicoliths in Children: Diagnostic Considerations and Postoperative Implications 17 Aug 2025 \| Cureus, Vol. 6 Appendicolith is Associated with Protracted Abdominal Pain and a High Risk of Appendicular Perforation in Pediatric Appendicitis June 16, 2025 \| Journal of Indian Association of Pediatric Surgeons Routine colonoscopy with a surprise in the cecum: It’s a giant appendicolith! 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January 12, 2022 Prevalence of Appendicoliths Detected at CT in Adults With Suspected Appendicitis January 21, 2021 \| American Journal of Roentgenology, Vol. 216, No. 3 Reference growth curves for normal appendiceal diameter in childhood July 22, 2020 \| Scientific Reports, Vol. 10, No. 1 Giant Appendicolith: A Case Report and Review of the Literature March 20, 2020 \| Military Medicine, Vol. 185, No. 9-10 Computed tomography for diagnosis of acute appendicitis in adults November 19, 2019 \| Cochrane Database of Systematic Reviews, Vol. 2019, No. 11 Size matters: Computed tomographic measurements of the appendix in emergency department scans 1 Aug 2019 \| The American Journal of Surgery, Vol. 218, No. 2 Beyond appendicitis: ultrasound findings of acute bowel pathology January 19, 2019 \| Emergency Radiology, Vol. 26, No. 3 Pediatric appendicitis with appendicolith often presents with prolonged abdominal pain and a high risk of perforation March 5, 2018 \| World Journal of Pediatrics, Vol. 14, No. 2 Appendicitis August 12, 2017 Acute Appendicitis October 29, 2017 Giant Appendicolith in Acute Exacerbation of Chronic Appendicitis: Case Report and Literature Review 1 Jan 2017 \| Surgical Science, Vol. 08, No. 11 Ultrasonography of Appendicitis May 27, 2016 \| Clinical Ultrasound, Vol. 1, No. 1 Acute appendicitis in children: ultrasound and CT findings in negative appendectomy cases May 20, 2014 \| Pediatric Radiology, Vol. 44, No. 10 Colique appendiculaire guérie par migration spontanée du stercolithe 1 Sep 2014 \| Journal de Chirurgie Viscérale, Vol. 151, No. 4 Resolution of appendiceal colic following migration of an appendicolith 1 Sep 2014 \| Journal of Visceral Surgery, Vol. 151, No. 4 JOURNAL CLUB: The Pediatric Appendix: Defining Normal April 23, 2014 \| American Journal of Roentgenology, Vol. 202, No. 5 Nonoperative Management of Appendiceal Phlegmon or Abscess with an Appendicolith in Children 1 Apr 2013 \| Journal of Gastrointestinal Surgery, Vol. 17, No. 4 Acute Appendicitis April 5, 2013 Role of the faecolith in modern-day appendicitis 1 Jan 2013 \| The Annals of The Royal College of Surgeons of England, Vol. 95, No. 1 Imaging of Acute Appendicitis in Children: Computed Tomography Including Radiation Issues September 9, 2011 Diagnostic power of various computed tomography signs in diagnosing acute appendicitis 1 Jan 2012 \| Clinical Imaging, Vol. 36, No. 1 Perforated Appendicitis and Appendicolith in a Child Presenting as Intussusception 1 Jul 2011 \| Pediatric Emergency Care, Vol. 27, No. 7 Acute Appendicitis 1 Jan 2011 Acute abdominal pain 1 Jan 2011 Prophylactic appendectomy: unnecessary in children with incidental appendicoliths detected by computed tomographic scan 1 Dec 2010 \| Journal of Pediatric Surgery, Vol. 45, No. 12 Appendicolith March 1, 2009 Normal Appendix in Adults: Reproducibility of Detection with Unenhanced and Contrast-Enhanced MDCT November 23, 2012 \| American Journal of Roentgenology, Vol. 191, No. 2 Appendiceal fecalith is associated with early perforation in pediatric patients 1 May 2008 \| Journal of Pediatric Surgery, Vol. 43, No. 5 Appendicoliths and appendectomy in the pediatric population 1 Feb 2008 \| European Surgery, Vol. 40, No. 1 Appendicitis 1 Jan 2008 Inflammatory and Infectious Diseases 1 Jan 2008 Appendicitis 1 Jan 2008 Are acute exacerbations of chronic inflammatory appendicitis triggered by coprostasis and/or coproliths? 1 Jan 2008 \| World Journal of Gastroenterology, Vol. 14, No. 20 Acute appendicitis: diagnostic value of nonenhanced CT with selective use of contrast in routine clinical settings December 16, 2006 \| European Radiology, Vol. 17, No. 8 Outcomes in 74 patients with an appendicolith who did not undergo surgery: is follow-up imaging necessary? April 25, 2007 \| Emergency Radiology, Vol. 14, No. 3 A retrospective study of CT findings in cases undergoing appendectomy at a single hospital 1 Jul 2007 \| Clinical Imaging, Vol. 31, No. 4 Pediatric Emergencies: Non-traumatic Abdominal Emergencies 1 Jan 2007 The usefulness of CT guided drainage of abscesses caused by retained appendicoliths 1 Oct 2006 \| European Journal of Radiology, Vol. 60, No. 1 Le stercolithe est-il un signe fiable d’appendicite ? 1 Apr 2006 \| Journal de Radiologie, Vol. 87, No. 4 CT for suspected appendicitis in children: an analysis of diagnostic errors February 7, 2006 \| Pediatric Radiology, Vol. 36, No. 4 Chronic appendicitis “syndrome” manifested by an appendicolith and thickened appendix presenting as chronic right lower abdominal pain in adults January 11, 2006 \| Emergency Radiology, Vol. 12, No. 3 Appendix 1 Jan 2006 CT appearance of the normal appendix in adults May 24, 2005 \| European Radiology, Vol. 15, No. 10 Evaluation of perforated and nonperforated appendicitis with CT 1 Nov 2004 \| Clinical Imaging, Vol. 28, No. 6 Mimics of Renal Colic: Alternative Diagnoses at Unenhanced Helical CT 1 Oct 2004 \| RadioGraphics, Vol. 24, No. suppl_1 CT Predictors of Failed Laparoscopic Appendectomy 1 Nov 2003 \| Radiology, Vol. 229, No. 2 Ultrasound of the acute pediatric abdomen March 1, 2003 \| Applied Radiology, Vol. 153 Value of Bone Window Settings on CT for Revealing Appendicoliths in Patients with Appendicitis November 23, 2012 \| American Journal of Roentgenology, Vol. 180, No. 1 CT of Appendicitis in Children 1 Aug 2002 \| Radiology, Vol. 224, No. 2 Literature Watch 1 Feb 2001 \| Journal of Laparoendoscopic & Advanced Surgical Techniques, Vol. 11, No. 1 View Options View options PDF View PDF PDF Download Download PDF Figures Open all in viewer Fig. 1. —8-year-old girl with abdominal pain, appendicolith, and appendicitis. Unenhanced CT scan shows enlarged appendix (arrow). Note associated appendicolith (arrowhead) and surrounding periappendiceal inflammation. Go to FigureOpen in Viewer Fig. 2. —6-year-old boy with abdominal pain, appendicolith, and no appendicitis. Unenhanced CT scan reveals normal appendix containing small appendicolith (arrow). No periappendiceal inflammation or appendiceal dilatation is present. Go to FigureOpen in Viewer Fig. 3. —2-year-old girl who was examined for trauma had appendicolith and no appendicitis. CT scan with IV contrast material and no oral contrast material reveals normal appendix containing appendicolith (arrow). No periappendiceal inflammation or appendiceal dilatation is seen. Note superior aspect of bladder (B) medial to appendix. Go to FigureOpen in Viewer Tables Media Share Share Copy the content Link Copy Link Copied! Copying failed. Share on social media FacebookX (formerly Twitter)LinkedInemail References References 1. Siegel MJ. Acute appendicitis in childhood: the role of ultrasound. Radiology 1992; 185:341-342 Crossref PubMed Google Scholar a [...] radiographs in 10-15% of these patients b [...] considered an indication for appendectomy c [...] received scant attention in the literature 2. Kirks DR. The gastrointestinal tract. In: Practical pediatric imaging: diagnostic radiology of infants and children. Philadelphia: Lippincott-Raven, 1995: 945-952 Google Scholar a [...] radiographs in 10-15% of these patients b [...] considered an indication for appendectomy c [...] received scant attention in the literature 3. Lane MJ, Katz DS, Ross BA, Clautice-Engle TL, Mindelzun RE, Jeffrey RB Jr. Unenhanced helical CT for suspected acute appendicitis. AJR 1997; 168:405-409 Go to Citation Crossref PubMed Google Scholar 4. Birnbaum BA, Jeffrey RB Jr. CT and sonographic evaluation of acute right lower quadrant abdominal pain. AJR 1998; 170:361-371 Crossref PubMed Google Scholar a [...] in series comprising patients of all ages b [...] in the general (mostly adult) population c [...] detection of smaller appendicoliths d [...] in our study compared with previous reports 5. Friedland JA, Siegel MJ. CT appearance of acute appendicitis in childhood. AJR 1997; 168:439-442 Crossref PubMed Google Scholar a [...] in series comprising patients of all ages b [...] in the general (mostly adult) population c [...] in our study compared with previous reports 6. Balthazar EJ, Birnbaum BA, Yee J, Megibow AJ, Roshkow J, Gray C. Acute appendicitis: CT and US correlation in 100 patients. Radiology 1994; 190:31-35 Crossref PubMed Google Scholar a [...] in series comprising patients of all ages b [...] in the general (mostly adult) population c [...] in our study compared with previous reports 7. Malone AJ. Unenhanced CT in the evaluation of the acute abdomen: the community hospital experience. Semin Ultrasound CT MR 1999; 20:68-76 Crossref PubMed Google Scholar a [...] in series comprising patients of all ages b [...] in the general (mostly adult) population c [...] detection of smaller appendicoliths d [...] in our study compared with previous reports 8. Rao PM, Rhea JT, Novelline RA. Sensitivity and specificity of the individual CT signs of appendicitis: experience with 200 helical appendiceal CT examinations. J Comput Assist Tomogr 1997; 21:686-692 Crossref PubMed Google Scholar a [...] in series comprising patients of all ages b [...] in the general (mostly adult) population c [...] in our study compared with previous reports d [...] a specificity of 100% found by Rao et al. 9. Garcia Pena BM, Mandl KD, Kraus SJ, et al. Ultrasonography and limited computed tomography in the diagnosis and management of appendicitis in children. 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Save this post for later Not now Thanks for your vote! You now have 5 free votes weekly. Free votes count toward the total vote score does not give reputation to the author Continue to help good content that is interesting, well-researched, and useful, rise to the top! To gain full voting privileges, earn reputation. Got it!Go to help center to learn more Calculate angle from slope in inverted Y axis Ask Question Asked 2 years, 7 months ago Modified2 years, 7 months ago Viewed 350 times This question shows research effort; it is useful and clear 0 Save this question. Show activity on this post. I currently have a series of lines drawn in a football pitch, each one formed by an X and Y point. These lines are the passes of a player and I want to see if it is a backward pass, forward pass, lateral pass depending on the angle of the slope with the X axis. Axis Y is inverted(Positive values going down) I have tried several ideas like arctan from numpy, from math, several calculations but I can't get the angle correctly. Results are not making any sense. At the moment, the only certainty is the correct calculation of the slope of each line. python df['Slope'] = np.where(df['X'] == df['X2'], 0, np.where((df['Y'] == df['Y2']), 0, -df['Y2'] + df['Y'])/ (df['X2'] - df['X'])) df['Radians'] = np.arctan(df['Slope'].astype(float)) df['Degrees'] = np.degrees(df['Radians']) %360 Some numbers and possibly angle expected: python A(40,48) and B(27,70): 210-230ª Actual result: 60º A(27,74) and B(9,52) : 130-140º Actual result: 310º A(9,64) and B(11,45) : 75-80º Actual result: 84º seems OK python pandas math angle Share Share a link to this question Copy linkCC BY-SA 4.0 Improve this question Follow Follow this question to receive notifications edited Feb 2, 2023 at 19:51 Carlos LozanoCarlos Lozano asked Feb 2, 2023 at 18:19 Carlos LozanoCarlos Lozano 53 7 7 bronze badges 2 Can you give some examples of numbers and what angles you want them to produce? Anyway, you probably want np.arctan2 (or math.atan2), possibly with a - thrown in somewhere.Ture Pålsson –Ture Pålsson 2023-02-02 18:44:33 +00:00 Commented Feb 2, 2023 at 18:44 @TurePålsson answered in edit Carlos Lozano –Carlos Lozano 2023-02-02 19:17:42 +00:00 Commented Feb 2, 2023 at 19:17 Add a comment\| 1 Answer 1 Sorted by: Reset to default This answer is useful 3 Save this answer. Show activity on this post. Here is a standard-library solution which seems to work. The same principle can be used with numpy. Key points: Use atan2 to get an answer in the right quadrant Since Y axis points "down", negate Y values Use % 360 to "fold" result to [0, 360] range. (I have to write something here to get the formatting right... why?) ```python from math import degrees, atan2 def angle(x1, y1, x2, y2): # (-a)-(-b) = -a+b return degrees(atan2(-y2+y1, x2-x1)) % 360 print(angle(40, 48, 27, 70)) # 239 print(angle(27, 74, 9, 52)) # 129 print(angle(9, 64, 11, 45)) # 84 ``` Share Share a link to this answer Copy linkCC BY-SA 4.0 Improve this answer Follow Follow this answer to receive notifications answered Feb 2, 2023 at 19:29 Ture PålssonTure Pålsson 7,041 2 2 gold badges 16 16 silver badges 21 21 bronze badges 2 Comments Add a comment Carlos Lozano Carlos LozanoOver a year ago I'm doing the same thing using numpy because I can't use the math library with the dataframe but I get different results. New code in edit 2023-02-02T19:50:55.047Z+00:00 0 Reply Copy link Carlos Lozano Carlos LozanoOver a year ago I solved trying another way to adapt your code to numpy. 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13247	https://math.stackexchange.com/questions/33874/relation-between-root-of-a-function-and-its-derivative	calculus - Relation between root of a function and its derivative - Mathematics Stack Exchange Join Mathematics By clicking “Sign up”, you agree to our terms of service and acknowledge you have read our privacy policy. Sign up with Google OR Email Password Sign up Already have an account? Log in Skip to main content Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Visit Stack Exchange Loading… Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company, and our products current community Mathematics helpchat Mathematics Meta your communities Sign up or log in to customize your list. more stack exchange communities company blog Log in Sign up Home Questions Unanswered AI Assist Labs Tags Chat Users Teams Ask questions, find answers and collaborate at work with Stack Overflow for Teams. Try Teams for freeExplore Teams 3. Teams 4. Ask questions, find answers and collaborate at work with Stack Overflow for Teams. Explore Teams Teams Q&A for work Connect and share knowledge within a single location that is structured and easy to search. Learn more about Teams Hang on, you can't upvote just yet. You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation and how do I get it? Instead, you can save this post to reference later. Save this post for later Not now Thanks for your vote! You now have 5 free votes weekly. Free votes count toward the total vote score does not give reputation to the author Continue to help good content that is interesting, well-researched, and useful, rise to the top! To gain full voting privileges, earn reputation. Got it!Go to help center to learn more Relation between root of a function and its derivative Ask Question Asked 14 years, 5 months ago Modified7 years, 10 months ago Viewed 18k times This question shows research effort; it is useful and clear 4 Save this question. Show activity on this post. I am given the following function f:R↦R,f(x)=x 4−4 x+p f:R↦R,f(x)=x 4−4 x+p and am asked to find p p such that f f has two identical real roots. The proposed solution is to get the root from the relation f(a)=f′(a)=0 f(a)=f′(a)=0. What I'm curious about is when this relation is valid. It obviously isn't always valid (linear functions for example). calculus functions Share Share a link to this question Copy linkCC BY-SA 3.0 Cite Follow Follow this question to receive notifications edited Apr 19, 2011 at 19:05 Ross Millikan 384k 28 28 gold badges 264 264 silver badges 472 472 bronze badges asked Apr 19, 2011 at 18:44 Paul MantaPaul Manta 3,595 7 7 gold badges 37 37 silver badges 50 50 bronze badges 2 The relation is f(a)=f′(a)=0 f(a)=f′(a)=0.André Nicolas –André Nicolas 2011-04-19 18:58:06 +00:00 Commented Apr 19, 2011 at 18:58 Ah yes, thank you for the correction.Paul Manta –Paul Manta 2011-04-19 18:59:06 +00:00 Commented Apr 19, 2011 at 18:59 Add a comment\| 3 Answers 3 Sorted by: Reset to default This answer is useful 7 Save this answer. Show activity on this post. If f f has a double root at x=a x=a, then f(x)=(x−a)2 g(x)f(x)=(x−a)2 g(x). Share Share a link to this answer Copy linkCC BY-SA 3.0 Cite Follow Follow this answer to receive notifications answered Apr 19, 2011 at 18:46 lhflhf 222k 20 20 gold badges 254 254 silver badges 585 585 bronze badges 4 Obviosuly, but I don't see how that relates to f′(x)f′(x). :\|Paul Manta –Paul Manta 2011-04-19 18:55:21 +00:00 Commented Apr 19, 2011 at 18:55 5 Then f′(x)=2(x−a)g(x)+(x−a)2 g′(x)f′(x)=2(x−a)g(x)+(x−a)2 g′(x) which has a root at x=a x=a Ross Millikan –Ross Millikan 2011-04-19 19:03:41 +00:00 Commented Apr 19, 2011 at 19:03 Thanks! So that relation is valid when the degree of the function is greater or equal to 2.Paul Manta –Paul Manta 2011-04-19 19:14:43 +00:00 Commented Apr 19, 2011 at 19:14 2 @Paul, you mean when the multiplicity of the root is greater than or equal to 2.Ross Millikan –Ross Millikan 2011-04-19 21:56:10 +00:00 Commented Apr 19, 2011 at 21:56 Add a comment\| This answer is useful 5 Save this answer. Show activity on this post. The question is already answered, but I wanted to add in my intuition for the why of the solution: The degree of a polynomial determines how many roots it can have. If we were to plot the function, the real-valued roots are places where the curve crosses zero on the y-axis. If the plot has a 'hump' that doesn't cross the y=0 y=0 axis, then the function has at least some imaginary roots. However, if the function just touches the y=0 y=0 axis, then both roots for that bump are in the same place: zero. When a bump on a curve only just brushes up against the axis, then it's tangent to that line at that point. Therefore, its first derivative is also equal to the slope of that line. Consequently, there would be two solutions to your problem if you were to solve it for this graph: You could translate the graph downward so that the middle bump was tangent with y=0 y=0, or you could translate the plot upward so that the left and right bumps were. Share Share a link to this answer Copy linkCC BY-SA 3.0 Cite Follow Follow this answer to receive notifications answered Apr 19, 2011 at 19:43 JCooperJCooper 464 3 3 silver badges 13 13 bronze badges Add a comment\| This answer is useful 5 Save this answer. Show activity on this post. The question is already answered (twice). It is however perhaps useful to make a comment about polynomials of degree less than 2 2, since the poster seems to believe they are an exception. Such polynomials are certainly uninteresting in this context, but they are not an exception. Below, we will tacitly assume that we are dealing with polynomial with real coefficients, though with the appropriate algebraic definition of the derivative, one can prove a more general result. Theorem: Let P(x)P(x) be a polynomial. Then the real number a a is an (at least) double root of P(x)P(x) if and only if P(a)=P′(a)=0 P(a)=P′(a)=0. (The "at least" is there because for example (x−1)3(x−1)3 has a triple root at x=1 x=1. There are two possible interpretations of the term "double root": multiplicity at least 2 2 or multiplicity exactly 2 2. I am just being careful.) The theorem holds for all polynomials, without exception. For example, let P(x)=x−17 P(x)=x−17. It is true that for any a a, ifa a is a double root of P(x)P(x), then P(a)=P′(a)=0 P(a)=P′(a)=0, for P(x)P(x) has no double roots. And it is true that ifP(a)=P′(a)=0 P(a)=P′(a)=0, then a a is a double root of P(x)P(x), since in fact there is no a a such that P(a)=P′(a)=0 P(a)=P′(a)=0. The same remark would hold for polynomials of degree 0 0 (non-zero constants). Finally, let us look at the 0 0 polynomial, which in algebra is usually said to have no degree, or degree −1−1, or degree −∞−∞. For this trivial polynomial, every a a is a root of multiplicity at least 2 2, indeed of infinite multiplicity. And it is true that for every a a, P(a)=P′(a)=0 P(a)=P′(a)=0. Share Share a link to this answer Copy linkCC BY-SA 3.0 Cite Follow Follow this answer to receive notifications answered Apr 19, 2011 at 20:48 André NicolasAndré Nicolas 515k 47 47 gold badges 584 584 silver badges 1k 1k bronze badges Add a comment\| You must log in to answer this question. Start asking to get answers Find the answer to your question by asking. Ask question Explore related questions calculus functions See similar questions with these tags. 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13248	https://www.quora.com/What-is-the-vector-method-to-prove-that-four-points-are-concyclic-cross-product-method	Something went wrong. Wait a moment and try again. Cross Product Concyclic Points Vectors (geometry) Proofs (mathematics) Concept of Geometry Points (Mathematics) Mathematical Evidences Geometric Mathematics 5 What is the vector method to prove that four points are concyclic (cross product method)? Priyesh Srivastava Mathematics \| Content-Writing \| Psychology and Sports · Author has 430 answers and 361.2K answer views · 5y This question can be easily proved by Ptlomey’s theorem: Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on a common circle). Ptolemy used the theorem as an aid to creating his table of chords, a trigonometric table that he applied to astronomy. If the vertices of the cyclic quadrilateral are A, B, C, and D in order, then the theorem states that: ACBD = ABCD + BCAB Finding the product of the lengths of the diagonals of the quadrilateral formed by the points. Finding the sum of the products of the measures This question can be easily proved by Ptlomey’s theorem: Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on a common circle). Ptolemy used the theorem as an aid to creating his table of chords, a trigonometric table that he applied to astronomy. If the vertices of the cyclic quadrilateral are A, B, C, and D in order, then the theorem states that: ACBD = ABCD + BCAB Steps: Finding the product of the lengths of the diagonals of the quadrilateral formed by the points. Finding the sum of the products of the measures of the pairs of opposite sides of the quadrilateral formed by the points. If these two values are equal, the points are concyclic. Hope you understand this explaination Related questions How do you deal with problems in life? How does a cross product of two vectors give a perpendicular vector? What is the angle when the cross product of two vectors is the maximum negative? How can we prove history? If a, b, c and d are four vectors, then how do you prove that their cross product is zero? Sindhiya Former Software Developer · Author has 2.5K answers and 11.9M answer views · 5y Finding the product of the lengths of the diagonals of the quadrilateral formed by the points. Finding the sum of the products of the measures of the pairs of opposite sides of the quadrilateral formed by the points. If these two values are equal, the points are concyclic. Ansh Keer Former Owner · Author has 6K answers and 1.7M answer views · Updated 1y Related How do you prove that points a [2,-4] b [3,-1] c [3, -3] and d [0,0]] are concyclic? We draw a figure and find that order of vertices isn't quite correct. The correct order is A (2,-4) B (3,-3) C (3,-1) D (0,0) Thus a = √2, b = 2, c = √10, d = √20 Diagonals AC = √10, BD = √18 According to Ptolemy’s Theorom, for a set of four points to be concyclic, ac + bd = AC BD ac + bd = √180 = 6√5, AC BD = √180 = 6√5 So points are concyclic. . Let's Shoelace B, C, D 3…...-1…….10……..3 3…….-3…….18…..…3 0………0………0……..0 3……….-1…….10……3 . x∆y = -6 + 0 + 0 = -6 Y∆SS = 12 + 0 + 0 = 12 SS∆x = -24 + 0 + 0 = -24. Cirumcentre (1, -2) R = √5 (x-1)^2 + (y+2)^2 = 5 (2,-4) also lies on this. Hence points are concyclic. Promoted by Coverage.com Johnny M Master's Degree from Harvard University (Graduated 2011) · Updated Sep 9 Does switching car insurance really save you money, or is that just marketing hype? This is one of those things that I didn’t expect to be worthwhile, but it was. You actually can save a solid chunk of money—if you use the right tool like this one. 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Haresh Sagar Studied Science & Mathematics (Graduated 1988) · Upvoted by Lalit Narayan Vyas , MSc. , Mathematics, BU Bhopal (2001) · Author has 6.2K answers and 7M answer views · 3y Related How do you prove the point P (3, 3), Q (7 , 1), R (4,0), and S (6 , 4) are concyclic? P(3,3),Q(7,1),R(4,0),S(6,4) Plot all the points on xy plane. When you do that you will realise that points are not as per alphabetical order. The quadrilateral is in PSQR order and looks like square. Let's find it out. P−S=(−3,−1)=13 S−Q=(−1,3)=−3 Q−R=(3,1)=13 R−P=(1,−3)=−3 Since opposite sides of this quadrilateral are parallel and adjacent sides are perpendicular, it must be either a square or a rectangle and both these quadrilaterals can be inscribed in a circle so given points are definitely concyclic. P(3,3),Q(7,1),R(4,0),S(6,4) Plot all the points on xy plane. When you do that you will realise that points are not as per alphabetical order. The quadrilateral is in PSQR order and looks like square. Let's find it out. P−S=(−3,−1)=13 S−Q=(−1,3)=−3 Q−R=(3,1)=13 R−P=(1,−3)=−3 Since opposite sides of this quadrilateral are parallel and adjacent sides are perpendicular, it must be either a square or a rectangle and both these quadrilaterals can be inscribed in a circle so given points are definitely concyclic. Assistant Bot · 1y To prove that four points A,B,C,D are concyclic using the vector method, specifically the cross product, we can use the property that the vectors formed by these points must satisfy a certain condition involving their cross products. Steps to Prove Concyclicity Define the Points: Let the points be represented as position vectors: A=⎛⎜⎝x1y1z1⎞⎟⎠ B=⎛⎜⎝x2y2z2⎞⎟⎠ C=⎛⎜⎝x3y3z3⎞⎟⎠ D=⎛⎜⎝x4y4z4⎞⎟⎠ Vect To prove that four points A,B,C,D are concyclic using the vector method, specifically the cross product, we can use the property that the vectors formed by these points must satisfy a certain condition involving their cross products. Steps to Prove Concyclicity Define the Points: Let the points be represented as position vectors: A=⎛⎜⎝x1y1z1⎞⎟⎠ B=⎛⎜⎝x2y2z2⎞⎟⎠ C=⎛⎜⎝x3y3z3⎞⎟⎠ D=⎛⎜⎝x4y4z4⎞⎟⎠ Vector Representation: Construct vectors based on these points: AB=B−A AC=C−A AD=D−A Cross Products: Compute the cross products of the vectors: AB×AC AB×AD AC×AD Condition for Concyclicity: The points A,B,C,D are concyclic if the scalar triple product formed by these vectors satisfies the following condition: (AB×AC)⋅AD=0 This condition implies that the vectors AB,AC, and AD are coplanar, which is equivalent to stating that the four points lie on the same circle. Detailed Explanation of the Condition The scalar triple product (AB×AC)⋅AD=0 indicates that the vector AD lies in the plane formed by the vectors AB and AC. If this condition holds true, it means that point D lies on the circumcircle of triangle ABC. Summary By using the cross product method, you can prove that four points are concyclic by checking the coplanarity of the vectors formed by these points. If the scalar triple product condition holds, the points are concyclic. Related questions How do I prove that the cross product of two vectors is perpendicular to the vector formed when subtracting them? I want to prove AxB is perpendicular to A-B. How does a cross product give a vector? How are a vector and its cross product related? How can you find two vectors when you are given the cross product and their sum? What is the proof of a vector cross product? Nikhil Panikkar Communications & Signal Processing Engineer · Author has 1.1K answers and 2.8M answer views · Updated 6y Related What do dot and cross vector products actually mean? Dot Product The dot product gives the relative orientation of two vectors in two - dimensional space. As you can see from the above figure, if both the vectors are normalized, then you get the relative orientation of the two vectors. Cross Product The cross product gives the orientation of the plane described by two vectors in three dimensional space. Consider the figure above. In two dimensional space, the vector A points towards East and the vector B points towards North East. Once you have your reference directions(North,South, East, West) laid down, there is no confusion regarding their orienta Dot Product The dot product gives the relative orientation of two vectors in two - dimensional space. As you can see from the above figure, if both the vectors are normalized, then you get the relative orientation of the two vectors. Cross Product The cross product gives the orientation of the plane described by two vectors in three dimensional space. Consider the figure above. In two dimensional space, the vector A points towards East and the vector B points towards North East. Once you have your reference directions(North,South, East, West) laid down, there is no confusion regarding their orientation. Now consider the same figure observed in three-dimensional space. For someone observing the vectors from above the plane, the vector B points North-East, but for someone observing the vectors from below the plane, the vector B points South-East. In other words, when you specify the location of a two - dimensional object in three-dimensional space, you have to specify the direction of the observer. This is the purpose the cross product serves. It does this by: 1.Associating the direction of the observer with the direction of the cross product vector. By defining the left/right/clockwise/anticlockwise directions for this observer. This is where the right hand and left hand rules come in. The fingers of the right hand, always curl in the anti-clockwise direction, when viewed in the direction of the thumb.The fingers of the left hand always curl in the clockwise direction when viewed in the direction of the thumb. So by specifying the direction of the thumb, you specify the direction of the observer and thus dismiss any confusions about left/right/clockwise/anticlockwise directions. The reason the cross product is able to do this is because sine is an odd function and the direction in which you measure the angle - clockwise or anticlockwise - affects the sign of the function. You know that the orientation of a plane can be be specified by its normal. The cross product is a specific type of normal that passes through the axis connecting the two vectors. Also see: Nikhil Panikkar's answer to How do you arrive at the formula with which you calculate the cross product? Promoted by Network Solutions® NetSol - Alicia Pringle B.A. in Bachelor of Arts Degrees in English & Communication, Misericordia University (Graduated 2008) · Aug 20 How do I prepare an e-commerce store for the holiday season? You’ve probably seen a holiday movie where a character sprints through a big retail store, frantically loading up on gifts at the last minute. As a small business owner, the holiday season can feel like a similar race to the finish, but with the right preparation, you can turn that chaos into a huge opportunity. Working for Network Solutions, a leading web presence company, I’ve helped a lot of small business owners establish their websites and eCommerce stores over the years, I've seen firsthand what separates the winners from those who get lost in the noise: preparedness and consistency. The You’ve probably seen a holiday movie where a character sprints through a big retail store, frantically loading up on gifts at the last minute. 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This centralized page is easy to link to from your social media and email campaigns. For local businesses, don't forget to update your store hours and promote any in-store pickup options. Harmonize Your Online Presence: Ensure your holiday messaging is consistent everywhere. Update your Google Business Profile with new photos of your holiday products and any special hours. On your social media channels, start teasing your holiday promos and products with photos or short videos. This consistency builds trust and helps AI systems understand your business better, which can lead to your business being featured in those valuable AI search results. Create a Marketing Calendar: Get organized with a 90-60-30-7 day plan. 90 Days Out (mid-September): Finalize your holiday product photos, spruce up your website copy with holiday keywords, and plan your promo calendar. 60 Days Out (mid-October): Start advertising early bird discounts. Update your Google Ads campaigns and business listings with holiday-themed content. Post your holiday product photos on social media. 30 Days Out (mid-November): Actively promote your deals across all channels, including social media, email, and text messaging. This is when the holiday rush really begins. 7 Days Out: Focus on last-minute shoppers. Promote shipping cutoffs, in-store pickup options, and digital gift cards. Remember, you don't need a massive campaign to see success. What you need is a solid, organized foundation. Use AI as a tool, control the content on your own website, and be consistent across your online channels. By being prepared, you’ll not only show up for your customers but also stand a chance to win big this holiday season. Want even more info on how to prepare your web presence for a successful holiday season? Check out our Holiday Visibility Playbook for SMBs. And best of luck to you and your business over the holidays and beyond! Anirukta Kundu Ex Student (2005–present) · Author has 802 answers and 299.7K answer views · 1y Related How do you prove that points a [2,-4] b [3,-1] c [3, -3] and d [0,0]] are concyclic? The equation of a circle centered at (p,q) with radius r is given by, (x-p)²+(y-q)²=r² for the first point, (2-p)²+(4+q)²=r² or 4-4p+p²+16+8q + q² = r² or 20 - 4p + 8q = r² - p² -q² =k ————(1) for the second point, 9 - 6p + p² + 1+2q +q² = r² or 10 - 6p + 2q = k—————(2) for the third point, 9 - 6p +p² + 9 + 6q +q² =r² or 18 - 6p +6q = k————-(3) Equating (2) and (3), we get, 10 + 2q = 18 + 6q or q = -2, Then from (1) and (2), we get, 20 - 4p + 8q = 10 - 6p + 2q = k or 20 - 16 -4p = 10 - 6p -4 or 4-4p = 6-6p or p =1 Hence r² = (2-p)² + (4+q)²=1+4=5 Now for the fourth point, p² +q² = 1² + (-2)² = 5 =r² is satisfied, The equation of a circle centered at (p,q) with radius r is given by, (x-p)²+(y-q)²=r² for the first point, (2-p)²+(4+q)²=r² or 4-4p+p²+16+8q + q² = r² or 20 - 4p + 8q = r² - p² -q² =k ————(1) for the second point, 9 - 6p + p² + 1+2q +q² = r² or 10 - 6p + 2q = k—————(2) for the third point, 9 - 6p +p² + 9 + 6q +q² =r² or 18 - 6p +6q = k————-(3) Equating (2) and (3), we get, 10 + 2q = 18 + 6q or q = -2, Then from (1) and (2), we get, 20 - 4p + 8q = 10 - 6p + 2q = k or 20 - 16 -4p = 10 - 6p -4 or 4-4p = 6-6p or p =1 Hence r² = (2-p)² + (4+q)²=1+4=5 Now for the fourth point, p² +q² = 1² + (-2)² = 5 =r² is satisfied, hence all the 4 given points a,b,c,d are concyclic. ( Proved) Subramanya R Former Retired Govt Employee, Interested in All Fields · Author has 2K answers and 1.5M answer views · Updated 1y Related How do you prove that points a [2,-4] b [3,-1] c [3, -3] and d [0,0]] are concyclic? How do you prove that points a [2,-4] b [3,-1] c [3, -3] and d [0,0]] are concyclic? General equation of the circle that passes through the origin is x2+y2−ax−by=0 where a and b are coords. of centre x and y intercepts of the circle and coordinates of centre of circle is (a2,b2) To find coefficients a and b we use points (3, -1) and (3, -3) 32+(−1)2−a(3)−b(−1)=0 b−3a=−10−−−−(1) And 32+(−3)2−a(3)−b(−3)=0 b−a=−6−−−(2) from (1) and (2)a−6−3a=−10 a=2 From (2) , we get b=−4 \text{Consequently, centre of t How do you prove that points a [2,-4] b [3,-1] c [3, -3] and d [0,0]] are concyclic? General equation of the circle that passes through the origin is x2+y2−ax−by=0 where a and b are coords. of centre x and y intercepts of the circle and coordinates of centre of circle is (a2,b2) To find coefficients a and b we use points (3, -1) and (3, -3) 32+(−1)2−a(3)−b(−1)=0 b−3a=−10−−−−(1) And 32+(−3)2−a(3)−b(−3)=0 b−a=−6−−−(2) from (1) and (2)a−6−3a=−10 a=2 From (2) , we get b=−4 Consequently, centre of the circle is C(22,−42) C(1,−2) Now equation of the circle is x2+y2−2x+4y=0 All given points satisfy this equation, therefore points are concyclic Dean Rubine I've watched hundreds of hours of Leonard Susskind's online physics lectures · Upvoted by David Joyce , Ph.D. Mathematics, University of Pennsylvania (1979) and Terry Moore , M.Sc. Mathematics, University of Southampton (1968) · Author has 10.6K answers and 23.7M answer views · 5y Related Can you cross product 2D vectors? Yes. The 2D dot product and cross product both produce scalars. We have Fibonacci's Identity, known to Diophantus in 250 AD: (a2+b2)(c2+d2)=(ac+bd)2+(ad−bc)2 Diophantus considered this a way to multiply two right triangles to get a third. We start with one with legs a and b (so squared hypotenuse a2+b2) and one with legs c and d (squared hypotenuse c2+d2). We get a new right triangle whose hypotenuse is the product of two hypotenuses and whose legs are given by the dot product and cross product respectively. These days we do this all the time without thinking. It’s complex multiplicatio Yes. The 2D dot product and cross product both produce scalars. We have Fibonacci's Identity, known to Diophantus in 250 AD: (a2+b2)(c2+d2)=(ac+bd)2+(ad−bc)2 Diophantus considered this a way to multiply two right triangles to get a third. We start with one with legs a and b (so squared hypotenuse a2+b2) and one with legs c and d (squared hypotenuse c2+d2). We get a new right triangle whose hypotenuse is the product of two hypotenuses and whose legs are given by the dot product and cross product respectively. These days we do this all the time without thinking. It’s complex multiplication by a conjugate, e.g. \|z\|2\|w\|2=\|z∗w\|2. That’s Fibonacci’s Identity because (a−bi)(c+di)=(ac+bd)+i(ad−bc) so taking squared magnitudes, (a2+b2)(c2+d2)=(ac+bd)2+(ad−bc)2✓ Complex multiplication adds angles. The conjugate means we really subtracting the angle of (a,b) from that of (c,d). If we think trigonometrically, we can see how this is really the two difference angle formulas, dot product for cosine, cross product for sine. I leave that to you to make explicit. It’s the dot product, here (a,b)⋅(c,d)=ac+bd, that defines our geometry. It gives us both our notion of perpendicularity (zero dot product) and squared distance (self dot product). Fibonacci's Identity tells us the 2D cross product must be (a,b)×(c,d)=ad−bc. The zero cross product is an indicator that two vectors are in the same direction. It’s easy to view things in terms of slopes or tangents b/a and d/c if we don’t worry too much about the zero denominator cases. So ad−bc=0 means ba=dc equal slopes. That indicates the vectors are in the same (or opposite) directions. The zero dot product gives the familiar negative reciprocal slopes to indicate perpendicularity: ac+bd=0 dc=−1ba We can actually generate relativistic two-D geometries using different dot products, but let’s say Euclidean. If we divide Fibonacci’s Identity by the sum of squares we get something that looks like cos2θ+sin2θ=1, and indeed cosθ=ac+bd√(a2+b2)(c2+d2) sinθ=ad−bc√(a2+b2)(c2+d2) So the cross product is related to the sine in a fundamental way. One easy way to see this to take the case where (a,b)=(1,0) so we’re doing the usual thing of comparing a ray to the positive x axis. In this case, cosθ=c√c2+d2,sinθ=d√c2+d2 which are the usual adjacent over hypotenuse and opposite over hypotenuse definitions. That relates the 2D cross product to the sine. The other relation is to the area. It’s often phrased as a statement about parallelograms; I prefer the looking at the area of the triangle with vertices (0,0),(a,b),(c,d). I won’t draw a picture, but if we arrange these in the first quadrant in a counterclockwise direction, 0<c<a,0<b<d, we get our triangle and three right triangles inside a rectangle of area ad. The three right triangles have area 12ab,12cd and 12(a−c)(d−b) so our triangle has area Δ=ad−12ab−12cd−12(ad−ab−cd+bc) Δ=12(ad−bc) If we had arranged the vertices in the opposite order we would have gotten the negation of the cross product, which makes sense, (c,d)×(a,b)=bc−ad. So the cross product really gives the signed area; the correct statement about the triangle area Δ is 4Δ2=(ad−bc)2 So we see even in the two D case, the cross product does what we want. It’s associated with parallelism, the sine, and area, just like in the 3D case. It’s a scalar in two D because there’s no direction for the cross product in two dimensions except for a sign. Steven Patamia Ph.D in Physics, general theorist · Upvoted by Terry Moore , M.Sc. Mathematics, University of Southampton (1968) · Author has 63 answers and 288K answer views · 8y Related What does a cross product actually MEAN in vectors? I remember seeing this question when it arrived and very nearly answered it but did not have time. I just saw it again and read the three answers received. They are good answers. The “Better Explained” article referenced in the third answer is very thorough and broadly useful. I am going to offer this additional response, however belatedly, because I have answered a number of questions in the past that I perceive to have originated as physics questions and can often give a physics-inspired explanation that I think is closer to why the question was asked in the first place. It is often dangerous I remember seeing this question when it arrived and very nearly answered it but did not have time. I just saw it again and read the three answers received. They are good answers. The “Better Explained” article referenced in the third answer is very thorough and broadly useful. I am going to offer this additional response, however belatedly, because I have answered a number of questions in the past that I perceive to have originated as physics questions and can often give a physics-inspired explanation that I think is closer to why the question was asked in the first place. It is often dangerous to form questions in the form “what does it mean.” Meaning itself is not usually well defined. Some better, perhaps even intended ways of stating the question include phrases like: “what does represent” or “what is the physical meaning of . I suspect that the questioner in this case did intend to probe physical significance. Physical significance is what counts in “physics” so I am going to address it as such. Preliminarily, however, the mathematical definition of the cross product is contrived to map a pair of vectors into a third vector. The definition, when applied to “physical vectors” (meaning those that describe a magnitude pointing in a specifiable direction) has the peculiar feature that it assumes an available space of 3 dimensions and always produces a new vector orthogonal (at right angles to) the plane containing the original two. The existing answers address this. (p.s. there are generalizations to higher dimensions, but that is beyond the scope of this answer.) Okay, so if I am a physicist and if I utilize or create a mathematical way to create a vector by doing math on two physical vectors, then I presume that the result is also a “physical vector” as opposed to an abstract property derived from the original two. The cross product is something with a magnitude and a direction. The questioner did not ask how to compute the cross product. The question was “what did it mean?” Being a physical vector means it must describe some measurable phenomenon and that means understanding it entails understanding the significance of both its magnitude and direction as physical realities. The excellent article from “Better Explained” neatly explains how two vectors describe (in an abstract way) an area. It leads then to the explanation that the area can be tied to the cross-product calculation in a way that distinguishes top and bottom of the “patch” of area. Indeed, the cross product of two physical vectors produces a magnitude corresponding to that “area” and the sign of its direction will be negative or positive depending on whether we are computing a x b or b x a. This is an intrinsic antisymmetry of the operation and physically it accommodates the very important reality usually referred to as chirality. The reality we live in really does distinguish clockwise from counter-clockwise. But this leads to something quite fascinating. Vectors formed from cross products of other vectors eerily capture an elusive piece of reality that other vectors cannot capture. The chirality — or rotational “sense” (clockwise v. counter-clockwise) — needs to be a phyical observable that does not depend on our choice of reference frame. Let’s explore this… I throw a football to a companion putting a spin on it. Lets say I am right handed and it leaves my grasp spinning in what I see as a clockwise rotation. Does the receiver perceive it rotating clockwise or counter clockwise? It turns out that the receiver sees the football coming at him spinning counter-clockwise. Where in all this is my vector attribute for the spin vector that shows the same chirality from the sender or receiver’s perspective? The answer is that by observation of the throw each participant can compute the spin vector direction that describes the the same actual direction for both! In other words, looking at the same vectors whose cross product produces the spin vector, both participants will compute the very same vector. The “meaning” of the cross product is that it constitutes a way of mathematically creating this result. A vector of the same magnitude pointing toward (or away from) the same direction as perceived by either participant. Indeed this does happen…. Here is how it works: As the one throwing the football I can imagine vector A as being, say straight up and B as pointing to my right. Compute S = A x B either using the right hand rule or by inventing some coordinate system. Now, A x B is NOT the same as B x A. The relationship is, as noted above, antisymmetric. The rule is A X B = -(B x A). We want both participants to use A x B or both participants to use B x A. Stay with me…. Now using the right hand rule turning A (up) into B (my right) leaves my right thumb pointing to the receiver. The receiver sees my imaginary up and right arrows as being up and (uh oh!) LEFT arrows. Mind you he sees the SAME A and B, but if he uses his own RIGHT hand turning from up to LEFT his thumb still points to himself as the receiver. If you do this by first creating a coordinate system shared by the participants and represent (project onto the basis of the coordinate system) the vectors in terms of their components this all still works. Its messy but try it. Remarkably, by defining S as an antisymmetric relationship between two vectors, all this works out. Antisymmetry appears to be a fundamental mathematical feature without which we cannot correctly model some aspects of our reality. Chirality matters. Without an antisymmetric operation of some kind we could not mathematically represent chirality such that its physical interpretation is invariant with changes in the coordinate system. It means also that you need at least three dimensions to model reality in full. This also infects the modeling of fundamental particles. Welcome to my world. Its your world too. Illustrator, cartoonist, sculptor knowing a bit of Physics · Author has 2.2K answers and 2.4M answer views · Updated 5y Related Why are vectors cross products? You mean ‘what are vector cross products, don’t you?’ Two vectors with an angle of θ between them enclose a parallelogram. Whereas the diagonal of the parallelogram is the sum of the two vectors, the area and orientation of the parallelogram too provide a useful measure of the interaction between the vectors. This parallelogram provides the basis for defining a Mathematical Operator known as the ‘Cross Product’ of the two vectors, the result of which is also a vector. The magnitude of the Cross Product of two vectors is the area of the parallelogram they enclose = \|A\|\|B\|sinθ The direc You mean ‘what are vector cross products, don’t you?’ Two vectors with an angle of θ between them enclose a parallelogram. Whereas the diagonal of the parallelogram is the sum of the two vectors, the area and orientation of the parallelogram too provide a useful measure of the interaction between the vectors. This parallelogram provides the basis for defining a Mathematical Operator known as the ‘Cross Product’ of the two vectors, the result of which is also a vector. The magnitude of the Cross Product of two vectors is the area of the parallelogram they enclose = \|A\|\|B\|sinθ The direction of the Cross Product Vector is given by the orientation of the parallelogram in space, which can be established from the direction of a straight line erected perpendicular to it. However, we can see that such a line can have two directions (up or down in the sketch above). This ambiguity is resolved by the rule that the cross product does not follow the commutative rule, that is, →A X →B is not the same as →B X →A . The correct direction is established by the right-hand screw rule. In the case of →A X →B, imagine that we rotate the first vector →A about the vertex towards the second vector →B, then the direction of the resulting cross product vector is given by the direction in which a right-hand screw would advance if made to rotate in a similar manner. In the diagram below, we find the cross product vector pointing downwards. →B X →A will have a direction that is opposite, or upwards. The Vector Cross Product Operation is not strictly a multiplication operation. The term ‘product’ has simply been borrowed from Arithmetic. It is a mathematical operation that seems to mimic many natural processes, and serves as a remarkably useful mathematical tool. Robert Edward Winkler Studied at San Rafael High School (Graduated 1958) · Author has 253 answers and 110.2K answer views · 5y Related What is the best way to approach a vector or cross products problem? Proper Prior Planning. One way to approach most technical problems is to apply the time honored traditional engineering problem solving methodology of GIVEN…FIND… SOLUTION. Identify and understand all of the givens, things that are known or provided. Specifically identify and understand what is to be found or what outcome you are looking for. Using all the mathematics, physics or other applicable knowledge you know to formulate a process to solve the problem. This may require the problem to be broken down into smaller individual problems and sequencing solving them to solve the major problem. Proper Prior Planning. One way to approach most technical problems is to apply the time honored traditional engineering problem solving methodology of GIVEN…FIND… SOLUTION. Identify and understand all of the givens, things that are known or provided. Specifically identify and understand what is to be found or what outcome you are looking for. Using all the mathematics, physics or other applicable knowledge you know to formulate a process to solve the problem. This may require the problem to be broken down into smaller individual problems and sequencing solving them to solve the major problem. If I can find A then I can use that to in turn find B, C, and D …, until I can finally solve the problem. Usually worked for me, hope this works for you also. Robert Smith Author of mathematical software · Author has 240 answers and 1.1M answer views · Updated 9y Related What do dot and cross vector products actually mean? I like to think about the dot and cross product geometrically. Cross Product If you have two vectors A and B (suppose your index and middle finger) which both "start" at the same point. Make another copy of A which starts at the end of B, and another copy of B which starts at the end of A. What do you have? A parallelogram (or, if the vectors were in a straight line, you just have a straight line). The area of this parallelogram is the length of the cross product. Of course, if they're in a straight line, the area is zero. What is the direction of the cross product? It's just the direction that mak I like to think about the dot and cross product geometrically. Cross Product If you have two vectors A and B (suppose your index and middle finger) which both "start" at the same point. Make another copy of A which starts at the end of B, and another copy of B which starts at the end of A. What do you have? A parallelogram (or, if the vectors were in a straight line, you just have a straight line). The area of this parallelogram is the length of the cross product. Of course, if they're in a straight line, the area is zero. What is the direction of the cross product? It's just the direction that makes a right angle with both of the vectors; it is the direction your thumb points. We can say that A and B lie on a plane, and A×B is normal to the plane. There's one little technicality. The cross product of A and B is not exactly the same as the cross of B and A. If your index finger is instead B, and your middle A, then the direction of the cross product, your thumb, is instead down. In other words, B×A=−(A×B). Its length is still the area of the parallelogram that A and B span, but its direction is just the opposite. Dot Product The dot product is another way to combine two vectors meaningfully. But instead of resulting in another vector, it instead results in just a number, a scalar. The dot product has to do with a concept called projection. Suppose we have a vector A and B with coinciding positions, and B is a unit vector—a vector of length one. If the sun is pointing down at B, then how long is the shadow cast by A? This shadow is the projection of A onto B. The length of this shadow is exactly the dot product: A⋅B. Using a bit of trigonometry, if the angle between the vectors is θ, then the length of the shadow cast is \|A\|cosθ. However, what if B isn't a unit vector? Simple: we still find the length of the shadow, but we multiply that length by the length of B. In other words, the dot product of A and B is the length of the shadow of A cast on B, multiplied by B's length. This is written mathematically as A⋅B=\|A\|\|B\|cosθ. Related questions How do you deal with problems in life? How does a cross product of two vectors give a perpendicular vector? What is the angle when the cross product of two vectors is the maximum negative? How can we prove history? If a, b, c and d are four vectors, then how do you prove that their cross product is zero? How do I prove that the cross product of two vectors is perpendicular to the vector formed when subtracting them? I want to prove AxB is perpendicular to A-B. How does a cross product give a vector? How are a vector and its cross product related? How can you find two vectors when you are given the cross product and their sum? What is the proof of a vector cross product? Is the cross product defined for all vectors? How do you know whether to use dot product or cross product in a vector problem? If two vectors are parallel, do they have a cross product? How can you prove the cross product of two vectors is there determinant? How do you prove that the cross product of vector b and vector a is equal to the cross product of vector a and vector b? About · Careers · Privacy · Terms · Contact · Languages · Your Ad Choices · Press · © Quora, Inc. 2025
13249	https://www.youtube.com/watch?v=hSqeoAGt5WI	9. Differentiate the function. g(x)=x^2(1-2x) The SAT Tutor 8660 subscribers 10 likes Description 1243 views Posted: 18 Oct 2023 9. Differentiate the function. g(x)=x^2(1-2x) Calculus: Early Transcendentals Chapter 3: Differentiation Rules Section 3.1: Derivatives of Polynomials and Exponential Functions Problem 9 Video 1129 of Hourly Uploads - 10/16/2023 - 750 Subscribers - 143,699 Views Transcript: hello and welcome back to another video today we're looking at this function G of X is equal to x^2 in parentheses 1 - 2x we're asked to differentiate the function so we can find the derivative when it's in this form but it's going to be easier if we distribute the x^2 so we do that multiplying x^2 by each of these terms we G of X is equal to x^2 1 is x^ 2us x^2 X is X cubed the two out in front so this is our new form of G of X and this is going to be easier to differentiate so first just write out the derivative so G Prime of X is equal to and so what do we do here for the power function X2 well you drop down the exponent and turn it into a coefficient if we bring down the two and then we have X to 2 which is what we have minus one so you bring the exponent down down and then you subtract one from the exponent minus 2 and then X Cub same thing you bring the exponent down 3 x then subtract one from the exponent 3 - 1 now we can just simplify this so we have G Prime of x = 2 x^ 2 - 1 is just 1 x to the 1 is just X so we can just leave that as it is minus 2 3 is 6 x 3 - 1 is x 2 so the Dera of the function G Prime of X = 2x - 6x^2 and that's going to be your final answer as always thank you for liking and subscribing and I'll see you in the next video
13250	http://nationalcurvebank.org/deposits/pursuit2.html	National Curve Bank A Simulation of Pursuit Curves Custom Search \| \| \| --- \| \| \| Sort by: Relevance Relevance Date \| For best performance of the animation, please use Google Chrome or FireFox. First, to begin the animation look below. Change the speed settings for Achilles and the Tortoise by using the sliders. Secondly, click anywhere in the window to represent Achilles' starting position and then click elsewhere to represent the Tortoise's starting position. Once there are two circles on the screen press the Start button. Tortoise x Speed : 1 Tortoise y Speed : 1 Achilles Speed : 1 \| \| \| \| \| Achilles and the Tortoise Zeno's Paradox is more or less as follows: Given a head start by the tortoise, Achilles, the fastest runner in Greece, can never catch the tortoise. During the time it takes Achilles to cover the original distance, the tortoise has moved forward to a newer distance. If the images of Achilles and the Tortoise are placed at the bottom of the screen, and the velocities are adjusted to be 50%, as in Zeno's Paradox, then the viewer can enjoy seeing Achilles overtake the Tortoise! (Ha!) Calculus instructors often introduce the concept of convergence of infinite series - in this case, a convergent geometric series with r = 1/2 - by having students discuss Achilles and the Tortoise. Zeno of Elea was a Pythagorean. His four paradoxes on the divisibility of motion, time and space were preserved by Aristotle in his Physics. \| \| Historical Sketch: An excellent overview of the history of pursuit curves is found in a series of articles written by Arthur Bernhart (University of Oklahoma) and published in Scripta Mathematica in the 1950s. He organizes his review into four categories: pursuit curves where the pursued moves along a straight line; the chase takes place in a circular fashion; the race among several competitors is in a polygonal fashion; and finally, special cases involving dynamical pursuit with variable speeds, centers of gravity, and other aberrant properties. This series of articles cuts across centuries of time, countries and languages. A bit of historical background is fascinating. The publications by Bernhart and several others often begin in antiquity with Zeno's solution to the classic Achilles and the Tortoise, mention the work of Leonardo da Vinci, and then move to a Frenchman, Pierre Bouguer (1698-1758) who expanded pursuit to two dimensions. Interest crossed the border into Italy, where the problem became curva di caccia, and then into Germany where readers will find dachshunds in Hundekurven problems. Across the English Channel a spider was pursuing a fly in the well-known Ladies' Diary (1743,1750 and 1752). \| \| \| I. Category One: One dimensional pursuit in a plane with a linear track and uniform speeds. Let the point Q move along a given tract Q(t) while another point P moves always in the direction PQ on P(s). If the velocity vector dP/ds has the same sense as PQ, the locus P(t) is called a curve of pursuit, otherwise a curve of flight. \| \| II. Category Two: Pursuit curves for a circular track. "A dog at the center of a circular pond C makes straight for a duck which is swimming along the edge of the pond. If the rate of swimming of the dog is to the rate of swimming of the duck as m : 1, determine the equation of the curve of pursuit and the distance the dog swims to capture the duck." C is the center of the pond, Q is the "quacker," and the point of attack is K, which conveniently forms an inscribed right triangle. American Mathematical Monthly, 27 (1920), p. 31 A. S. Hathaway, Houston, Texas \| \| III. Category Three: Problems of triangular pursuit. "Three dogs are placed at the three vertices of an equilateral triangle; they run one after the other. What is the curve described by each of them? \| \| IV. Category Four: Differential equations valid for arbitrary track and variable speeds; Miscellaneous problems sometimes confused with pure pursuit curves. "Navigation: Does one swimmer P pursue another Q when his course is toward Q though his heading is somewhat upstream? If P swims through the water medium at speed e, and the current flows with speed f at an angle φ with the desired course PQ, then P must head off course by a correction angle ε in order to make good his course. \| \| \| --- \| \| Important References for this Specific Table \| \| \| Bernhart, Arthur, "Curves of Pursuit," Scripta Mathematica, 20, 1954, pp. 125-141. \| Bernhart, Arthur, "Curves of Pursuit II," Scripta Mathematica, 23, 1957, pp. 49-65. \| \| Bernhart, Arthur, "Polygons of Pursuit," Scripta Mathematica, 24, 1959, pp. 23-50. \| Bernhart, Arthur, "Curves of General Pursuit," Scripta Mathematica, 24, 1959, pp. 180-206. \| The opportunities for animation of pursuit curves are enormous. The NCB invites faculty and students to try their hand at some of these problems as class projects. Then hopefully you will add a "choice" effort to our NCB MATH Archive collection as a sampler of a fun activity from your campus. \| \| \| \| --- \| \| Useful Links and Books \| Click on the stamp to see Zeno in Raphael's "School of Athens" near the Sistine Chapel in the Vatican. \| \| For more information on Pursuit Curves: < > \| \| For a variety of Pursuit Problems: < > \| \| For the evolute in JAVA: < > Note: The French scientist Pierre Bouguer attempted to measure the density of the Earth by using a plumb line deflected by the attraction of gravity. He collected data on the top of a Peruvian mountain. While he was more or less unsuccessful, the thought that he would attempt this in South America in 1740 is slightly amazing. \| \| Gray, Alfred, Modern Differential Geometry of Curves and Surfaces with MATHEMATICA®, 2nd ed., CRC Press, 1998, pp. 66-69. \| \| Weisstein, Eric W., CRC Concise Encyclopedia of MATHEMATICS, CRC Press, 1999, p.1461. \| \| Yates, Robert C., Curves and Their Properties, NCTM, 1952, pp. 170-171. \| \| Yun Wang Java animation 2006 ywang80@gmail.com Jonathan Sahagun Webpage update 2018 jonathansahagun93@gmail.com \| \| \| \| \| --- \| \| \| \|
13251	https://ericrowland.github.io/investigations/tripleslist-long.html	\| \| \| Primitive Integral Solutions to x2 + y2 = z2 \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| 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\| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- 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--- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- \| This list begins with the first 957 primitive Pythagorean triples (those with hypotenuse less than 6000). Following these (in order of increasing hypotenuse) are: the 8 primitive triples with hypotenuse 32045, the 16 primitive triples with hypotenuse 1185665, the 32 primitive triples with hypotenuse 48612265, and the 64 primitive triples with hypotenuse 2576450045 the completion of the first 25 triples with \|x – y\| = 1 (designated by "C") Fermat's triple (4565486027761, 1061652293520, 4687298610289) ("F"), the smallest triple whose hypotenuse and sum of legs are both squares. Programs for generating triples can be found here. Triples with a common (composite) hypotenuse are bracketed. "P" designates a prime hypotenuse, and "P" designates a prime power hypotenuse (with exponent > 1). \| \| \| \| \| \| \| --- --- --- \| \| x \| y \| z \| \| r \| s \| \| 3 \| 4 \| 5 \| P \| 1 \| 1 \| C \| \| 5 \| 12 \| 13 \| P \| 2 \| 1 \| \| 15 \| 8 \| 17 \| P \| 1 \| 3 \| \| 7 \| 24 \| 25 \| P \| 3 \| 1 \| \| 21 \| 20 \| 29 \| P \| 2 \| 3 \| C \| \| 35 \| 12 \| 37 \| P \| 1 \| 5 \| \| 9 \| 40 \| 41 \| P \| 4 \| 1 \| \| 45 \| 28 \| 53 \| P \| 2 \| 5 \| \| 11 \| 60 \| 61 \| P \| 5 \| 1 \| \| 33 \| 56 \| 65 \| \| 4 \| 3 \| \| 63 \| 16 \| 65 \| 1 \| 7 \| \| 55 \| 48 \| 73 \| P \| 3 \| 5 \| \| 13 \| 84 \| 85 \| \| 6 \| 1 \| \| 77 \| 36 \| 85 \| 2 \| 7 \| \| 39 \| 80 \| 89 \| P \| 5 \| 3 \| \| 65 \| 72 \| 97 \| P \| 4 \| 5 \| \| 99 \| 20 \| 101 \| P \| 1 \| 9 \| \| 91 \| 60 \| 109 \| P \| 3 \| 7 \| \| 15 \| 112 \| 113 \| P \| 7 \| 1 \| \| 117 \| 44 \| 125 \| P \| 2 \| 9 \| \| 105 \| 88 \| 137 \| P \| 4 \| 7 \| \| 17 \| 144 \| 145 \| \| 8 \| 1 \| \| 143 \| 24 \| 145 \| 1 \| 11 \| \| 51 \| 140 \| 149 \| P \| 7 \| 3 \| \| 85 \| 132 \| 157 \| P \| 6 \| 5 \| \| 119 \| 120 \| 169 \| P \| 5 \| 7 \| C \| \| 165 \| 52 \| 173 \| P \| 2 \| 11 \| \| 19 \| 180 \| 181 \| P \| 9 \| 1 \| \| 57 \| 176 \| 185 \| \| 8 \| 3 \| \| 153 \| 104 \| 185 \| 4 \| 9 \| \| 95 \| 168 \| 193 \| P \| 7 \| 5 \| \| 195 \| 28 \| 197 \| P \| 1 \| 13 \| \| 133 \| 156 \| 205 \| \| 6 \| 7 \| \| 187 \| 84 \| 205 \| 3 \| 11 \| \| 21 \| 220 \| 221 \| \| 10 \| 1 \| \| 171 \| 140 \| 221 \| 5 \| 9 \| \| 221 \| 60 \| 229 \| P \| 2 \| 13 \| \| 105 \| 208 \| 233 \| P \| 8 \| 5 \| \| 209 \| 120 \| 241 \| P \| 4 \| 11 \| \| 255 \| 32 \| 257 \| P \| 1 \| 15 \| \| 23 \| 264 \| 265 \| \| 11 \| 1 \| \| 247 \| 96 \| 265 \| 3 \| 13 \| \| 69 \| 260 \| 269 \| P \| 10 \| 3 \| \| 115 \| 252 \| 277 \| P \| 9 \| 5 \| \| 231 \| 160 \| 281 \| P \| 5 \| 11 \| \| 161 \| 240 \| 289 \| P \| 8 \| 7 \| \| 285 \| 68 \| 293 \| P \| 2 \| 15 \| \| 207 \| 224 \| 305 \| \| 7 \| 9 \| \| 273 \| 136 \| 305 \| 4 \| 13 \| \| 25 \| 312 \| 313 \| P \| 12 \| 1 \| \| 75 \| 308 \| 317 \| P \| 11 \| 3 \| \| 253 \| 204 \| 325 \| \| 6 \| 11 \| \| 323 \| 36 \| 325 \| 1 \| 17 \| \| 175 \| 288 \| 337 \| P \| 9 \| 7 \| \| 299 \| 180 \| 349 \| P \| 5 \| 13 \| \| 225 \| 272 \| 353 \| P \| 8 \| 9 \| \| 27 \| 364 \| 365 \| \| 13 \| 1 \| \| 357 \| 76 \| 365 \| 2 \| 17 \| \| 275 \| 252 \| 373 \| P \| 7 \| 11 \| \| 135 \| 352 \| 377 \| \| 11 \| 5 \| \| 345 \| 152 \| 377 \| 4 \| 15 \| \| 189 \| 340 \| 389 \| P \| 10 \| 7 \| \| 325 \| 228 \| 397 \| P \| 6 \| 13 \| \| 399 \| 40 \| 401 \| P \| 1 \| 19 \| \| 391 \| 120 \| 409 \| P \| 3 \| 17 \| \| 29 \| 420 \| 421 \| P \| 14 \| 1 \| \| 87 \| 416 \| 425 \| \| 13 \| 3 \| \| 297 \| 304 \| 425 \| 8 \| 11 \| \| 145 \| 408 \| 433 \| P \| 12 \| 5 \| \| 203 \| 396 \| 445 \| \| 11 \| 7 \| \| 437 \| 84 \| 445 \| 2 \| 19 \| \| 351 \| 280 \| 449 \| P \| 7 \| 13 \| \| 425 \| 168 \| 457 \| P \| 4 \| 17 \| \| 261 \| 380 \| 461 \| P \| 10 \| 9 \| \| 31 \| 480 \| 481 \| \| 15 \| 1 \| \| 319 \| 360 \| 481 \| 9 \| 11 \| \| 93 \| 476 \| 485 \| \| 14 \| 3 \| \| 483 \| 44 \| 485 \| 1 \| 21 \| \| 155 \| 468 \| 493 \| \| 13 \| 5 \| \| 475 \| 132 \| 493 \| 3 \| 19 \| \| 217 \| 456 \| 505 \| \| 12 \| 7 \| \| 377 \| 336 \| 505 \| 8 \| 13 \| \| 459 \| 220 \| 509 \| P \| 5 \| 17 \| \| 279 \| 440 \| 521 \| P \| 11 \| 9 \| \| 435 \| 308 \| 533 \| \| 7 \| 15 \| \| 525 \| 92 \| 533 \| 2 \| 21 \| \| 341 \| 420 \| 541 \| P \| 10 \| 11 \| \| 33 \| 544 \| 545 \| \| 16 \| 1 \| \| 513 \| 184 \| 545 \| 4 \| 19 \| \| 165 \| 532 \| 557 \| P \| 14 \| 5 \| \| 403 \| 396 \| 565 \| \| 9 \| 13 \| \| 493 \| 276 \| 565 \| 6 \| 17 \| \| 231 \| 520 \| 569 \| P \| 13 \| 7 \| \| 575 \| 48 \| 577 \| P \| 1 \| 23 \| \| 465 \| 368 \| 593 \| P \| 8 \| 15 \| \| 551 \| 240 \| 601 \| P \| 5 \| 19 \| \| 35 \| 612 \| 613 \| P \| 17 \| 1 \| \| 105 \| 608 \| 617 \| P \| 16 \| 3 \| \| 527 \| 336 \| 625 \| P \| 7 \| 17 \| \| 429 \| 460 \| 629 \| \| 10 \| 13 \| \| 621 \| 100 \| 629 \| 2 \| 23 \| \| 609 \| 200 \| 641 \| P \| 4 \| 21 \| \| 315 \| 572 \| 653 \| P \| 13 \| 9 \| \| 589 \| 300 \| 661 \| P \| 6 \| 19 \| \| 385 \| 552 \| 673 \| P \| 12 \| 11 \| \| 675 \| 52 \| 677 \| P \| 1 \| 25 \| \| 37 \| 684 \| 685 \| \| 18 \| 1 \| \| 667 \| 156 \| 685 \| 3 \| 23 \| \| 111 \| 680 \| 689 \| \| 17 \| 3 \| \| 561 \| 400 \| 689 \| 8 \| 17 \| \| 185 \| 672 \| 697 \| \| 16 \| 5 \| \| 455 \| 528 \| 697 \| 11 \| 13 \| \| 651 \| 260 \| 701 \| P \| 5 \| 21 \| \| 259 \| 660 \| 709 \| P \| 15 \| 7 \| \| 333 \| 644 \| 725 \| \| 14 \| 9 \| \| 627 \| 364 \| 725 \| 7 \| 19 \| \| 725 \| 108 \| 733 \| P \| 2 \| 25 \| \| 407 \| 624 \| 745 \| \| 13 \| 11 \| \| 713 \| 216 \| 745 \| 4 \| 23 \| \| 595 \| 468 \| 757 \| P \| 9 \| 17 \| \| 39 \| 760 \| 761 \| P \| 19 \| 1 \| \| 481 \| 600 \| 769 \| P \| 12 \| 13 \| \| 195 \| 748 \| 773 \| P \| 17 \| 5 \| \| 273 \| 736 \| 785 \| \| 16 \| 7 \| \| 783 \| 56 \| 785 \| 1 \| 27 \| \| 665 \| 432 \| 793 \| \| 8 \| 19 \| \| 775 \| 168 \| 793 \| 3 \| 25 \| \| 555 \| 572 \| 797 \| P \| 11 \| 15 \| \| 759 \| 280 \| 809 \| P \| 5 \| 23 \| \| 429 \| 700 \| 821 \| P \| 14 \| 11 \| \| 629 \| 540 \| 829 \| P \| 10 \| 17 \| \| 41 \| 840 \| 841 \| P \| 20 \| 1 \| \| 123 \| 836 \| 845 \| \| 19 \| 3 \| \| 837 \| 116 \| 845 \| 2 \| 27 \| \| 205 \| 828 \| 853 \| P \| 18 \| 5 \| \| 825 \| 232 \| 857 \| P \| 4 \| 25 \| \| 287 \| 816 \| 865 \| \| 17 \| 7 \| \| 703 \| 504 \| 865 \| 9 \| 19 \| \| 805 \| 348 \| 877 \| P \| 6 \| 23 \| \| 369 \| 800 \| 881 \| P \| 16 \| 9 \| \| 451 \| 780 \| 901 \| \| 15 \| 11 \| \| 899 \| 60 \| 901 \| 1 \| 29 \| \| 663 \| 616 \| 905 \| \| 11 \| 17 \| \| 777 \| 464 \| 905 \| 8 \| 21 \| \| 43 \| 924 \| 925 \| \| 21 \| 1 \| \| 533 \| 756 \| 925 \| 14 \| 13 \| \| 129 \| 920 \| 929 \| P \| 20 \| 3 \| \| 215 \| 912 \| 937 \| P \| 19 \| 5 \| \| 741 \| 580 \| 941 \| P \| 10 \| 19 \| \| 301 \| 900 \| 949 \| \| 18 \| 7 \| \| 851 \| 420 \| 949 \| 7 \| 23 \| \| 615 \| 728 \| 953 \| P \| 13 \| 15 \| \| 387 \| 884 \| 965 \| \| 17 \| 9 \| \| 957 \| 124 \| 965 \| 2 \| 29 \| \| 945 \| 248 \| 977 \| P \| 4 \| 27 \| \| 473 \| 864 \| 985 \| \| 16 \| 11 \| \| 697 \| 696 \| 985 \| 12 \| 17 \| \| 925 \| 372 \| 997 \| P \| 6 \| 25 \| \| 559 \| 840 \| 1009 \| P \| 15 \| 13 \| \| 45 \| 1012 \| 1013 \| P \| 22 \| 1 \| \| 779 \| 660 \| 1021 \| P \| 11 \| 19 \| \| 897 \| 496 \| 1025 \| \| 8 \| 23 \| \| 1023 \| 64 \| 1025 \| 1 \| 31 \| \| 1015 \| 192 \| 1033 \| P \| 3 \| 29 \| \| 315 \| 988 \| 1037 \| \| 19 \| 7 \| \| 645 \| 812 \| 1037 \| 14 \| 15 \| \| 999 \| 320 \| 1049 \| P \| 5 \| 27 \| \| 861 \| 620 \| 1061 \| P \| 10 \| 21 \| \| 731 \| 780 \| 1069 \| P \| 13 \| 17 \| \| 495 \| 952 \| 1073 \| \| 17 \| 11 \| \| 975 \| 448 \| 1073 \| 7 \| 25 \| \| 1085 \| 132 \| 1093 \| P \| 2 \| 31 \| \| 585 \| 928 \| 1097 \| P \| 16 \| 13 \| \| 47 \| 1104 \| 1105 \| \| 23 \| 1 \| \| 817 \| 744 \| 1105 \| 12 \| 19 \| \| 943 \| 576 \| 1105 \| 9 \| 23 \| \| 1073 \| 264 \| 1105 \| 4 \| 29 \| \| 141 \| 1100 \| 1109 \| P \| 22 \| 3 \| \| 235 \| 1092 \| 1117 \| P \| 21 \| 5 \| \| 329 \| 1080 \| 1129 \| P \| 20 \| 7 \| \| 423 \| 1064 \| 1145 \| \| 19 \| 9 \| \| 903 \| 704 \| 1145 \| 11 \| 21 \| \| 1025 \| 528 \| 1153 \| P \| 8 \| 25 \| \| 765 \| 868 \| 1157 \| \| 14 \| 17 \| \| 1155 \| 68 \| 1157 \| 1 \| 33 \| \| 517 \| 1044 \| 1165 \| \| 18 \| 11 \| \| 1147 \| 204 \| 1165 \| 3 \| 31 \| \| 1131 \| 340 \| 1181 \| P \| 5 \| 29 \| \| 611 \| 1020 \| 1189 \| \| 17 \| 13 \| \| 989 \| 660 \| 1189 \| 10 \| 23 \| \| 855 \| 832 \| 1193 \| P \| 13 \| 19 \| \| 49 \| 1200 \| 1201 \| P \| 24 \| 1 \| \| 147 \| 1196 \| 1205 \| \| 23 \| 3 \| \| 1107 \| 476 \| 1205 \| 7 \| 27 \| \| 245 \| 1188 \| 1213 \| P \| 22 \| 5 \| \| 705 \| 992 \| 1217 \| P \| 16 \| 15 \| \| 1221 \| 140 \| 1229 \| P \| 2 \| 33 \| \| 1075 \| 612 \| 1237 \| P \| 9 \| 25 \| \| 441 \| 1160 \| 1241 \| \| 20 \| 9 \| \| 1209 \| 280 \| 1241 \| 4 \| 31 \| \| 799 \| 960 \| 1249 \| P \| 15 \| 17 \| \| 539 \| 1140 \| 1261 \| \| 19 \| 11 \| \| 1189 \| 420 \| 1261 \| 6 \| 29 \| \| 1035 \| 748 \| 1277 \| P \| 11 \| 23 \| \| 637 \| 1116 \| 1285 \| \| 18 \| 13 \| \| 893 \| 924 \| 1285 \| 14 \| 19 \| \| 1161 \| 560 \| 1289 \| P \| 8 \| 27 \| \| 1295 \| 72 \| 1297 \| P \| 1 \| 35 \| \| 51 \| 1300 \| 1301 \| P \| 25 \| 1 \| \| 255 \| 1288 \| 1313 \| \| 23 \| 5 \| \| 735 \| 1088 \| 1313 \| 17 \| 15 \| \| 1271 \| 360 \| 1321 \| P \| 5 \| 31 \| \| 357 \| 1276 \| 1325 \| \| 22 \| 7 \| \| 987 \| 884 \| 1325 \| 13 \| 21 \| \| 833 \| 1056 \| 1345 \| \| 16 \| 17 \| \| 1247 \| 504 \| 1345 \| 7 \| 29 \| \| 561 \| 1240 \| 1361 \| P \| 20 \| 11 \| \| 1081 \| 840 \| 1369 \| P \| 12 \| 23 \| \| 1365 \| 148 \| 1373 \| P \| 2 \| 35 \| \| 931 \| 1020 \| 1381 \| P \| 15 \| 19 \| \| 663 \| 1216 \| 1385 \| \| 19 \| 13 \| \| 1353 \| 296 \| 1385 \| 4 \| 33 \| \| 53 \| 1404 \| 1405 \| \| 26 \| 1 \| \| 1333 \| 444 \| 1405 \| 6 \| 31 \| \| 159 \| 1400 \| 1409 \| P \| 25 \| 3 \| \| 265 \| 1392 \| 1417 \| \| 24 \| 5 \| \| 1175 \| 792 \| 1417 \| 11 \| 25 \| \| 371 \| 1380 \| 1429 \| P \| 23 \| 7 \| \| 1305 \| 592 \| 1433 \| P \| 8 \| 29 \| \| 477 \| 1364 \| 1445 \| \| 22 \| 9 \| \| 1443 \| 76 \| 1445 \| 1 \| 37 \| \| 1435 \| 228 \| 1453 \| P \| 3 \| 35 \| \| 583 \| 1344 \| 1465 \| \| 21 \| 11 \| \| 1127 \| 936 \| 1465 \| 13 \| 23 \| \| 1269 \| 740 \| 1469 \| \| 10 \| 27 \| \| 1419 \| 380 \| 1469 \| 5 \| 33 \| \| 969 \| 1120 \| 1481 \| P \| 16 \| 19 \| \| 689 \| 1320 \| 1489 \| P \| 20 \| 13 \| \| 1395 \| 532 \| 1493 \| P \| 7 \| 31 \| \| 55 \| 1512 \| 1513 \| \| 27 \| 1 \| \| 1225 \| 888 \| 1513 \| 12 \| 25 \| \| 165 \| 1508 \| 1517 \| \| 26 \| 3 \| \| 795 \| 1292 \| 1517 \| 19 \| 15 \| \| 1363 \| 684 \| 1525 \| \| 9 \| 29 \| \| 1517 \| 156 \| 1525 \| 2 \| 37 \| \| 385 \| 1488 \| 1537 \| \| 24 \| 7 \| \| 1505 \| 312 \| 1537 \| 4 \| 35 \| \| 901 \| 1260 \| 1549 \| P \| 18 \| 17 \| \| 495 \| 1472 \| 1553 \| P \| 23 \| 9 \| \| 1173 \| 1036 \| 1565 \| \| 14 \| 23 \| \| 1323 \| 836 \| 1565 \| 11 \| 27 \| \| 1007 \| 1224 \| 1585 \| \| 17 \| 19 \| \| 1457 \| 624 \| 1585 \| 8 \| 31 \| \| 715 \| 1428 \| 1597 \| P \| 21 \| 13 \| \| 1599 \| 80 \| 1601 \| P \| 1 \| 39 \| \| 1591 \| 240 \| 1609 \| P \| 3 \| 37 \| \| 1275 \| 988 \| 1613 \| P \| 13 \| 25 \| \| 1421 \| 780 \| 1621 \| P \| 10 \| 29 \| \| 57 \| 1624 \| 1625 \| \| 28 \| 1 \| \| 1113 \| 1184 \| 1625 \| 16 \| 21 \| \| 285 \| 1612 \| 1637 \| P \| 26 \| 5 \| \| 399 \| 1600 \| 1649 \| \| 25 \| 7 \| \| 1551 \| 560 \| 1649 \| 7 \| 33 \| \| 935 \| 1368 \| 1657 \| P \| 19 \| 17 \| \| 1219 \| 1140 \| 1669 \| P \| 15 \| 23 \| \| 1519 \| 720 \| 1681 \| P \| 9 \| 31 \| \| 627 \| 1564 \| 1685 \| \| 23 \| 11 \| \| 1677 \| 164 \| 1685 \| 2 \| 39 \| \| 1045 \| 1332 \| 1693 \| P \| 18 \| 19 \| \| 1665 \| 328 \| 1697 \| P \| 4 \| 37 \| \| 741 \| 1540 \| 1709 \| P \| 22 \| 13 \| \| 1325 \| 1092 \| 1717 \| \| 14 \| 25 \| \| 1645 \| 492 \| 1717 \| 6 \| 35 \| \| 1479 \| 880 \| 1721 \| P \| 11 \| 29 \| \| 1155 \| 1292 \| 1733 \| P \| 17 \| 21 \| \| 59 \| 1740 \| 1741 \| P \| 29 \| 1 \| \| 177 \| 1736 \| 1745 \| \| 28 \| 3 \| \| 1617 \| 656 \| 1745 \| 8 \| 33 \| \| 295 \| 1728 \| 1753 \| P \| 27 \| 5 \| \| 413 \| 1716 \| 1765 \| \| 26 \| 7 \| \| 1763 \| 84 \| 1765 \| 1 \| 41 \| \| 969 \| 1480 \| 1769 \| \| 20 \| 17 \| \| 1431 \| 1040 \| 1769 \| 13 \| 27 \| \| 1265 \| 1248 \| 1777 \| P \| 16 \| 23 \| \| 531 \| 1700 \| 1781 \| \| 25 \| 9 \| \| 1581 \| 820 \| 1781 \| 10 \| 31 \| \| 1739 \| 420 \| 1789 \| P \| 5 \| 37 \| \| 649 \| 1680 \| 1801 \| P \| 24 \| 11 \| \| 767 \| 1656 \| 1825 \| \| 23 \| 13 \| \| 1537 \| 984 \| 1825 \| 12 \| 29 \| \| 885 \| 1628 \| 1853 \| \| 22 \| 15 \| \| 1845 \| 172 \| 1853 \| 2 \| 41 \| \| 61 \| 1860 \| 1861 \| P \| 30 \| 1 \| \| 183 \| 1856 \| 1865 \| \| 29 \| 3 \| \| 1833 \| 344 \| 1865 \| 4 \| 39 \| \| 305 \| 1848 \| 1873 \| P \| 28 \| 5 \| \| 1485 \| 1148 \| 1877 \| P \| 14 \| 27 \| \| 427 \| 1836 \| 1885 \| \| 27 \| 7 \| \| 1003 \| 1596 \| 1885 \| 21 \| 17 \| \| 1643 \| 924 \| 1885 \| 11 \| 31 \| \| 1813 \| 516 \| 1885 \| 6 \| 37 \| \| 1311 \| 1360 \| 1889 \| P \| 17 \| 23 \| \| 549 \| 1820 \| 1901 \| P \| 26 \| 9 \| \| 1785 \| 688 \| 1913 \| P \| 8 \| 35 \| \| 671 \| 1800 \| 1921 \| \| 25 \| 11 \| \| 1121 \| 1560 \| 1921 \| 20 \| 19 \| \| 1595 \| 1092 \| 1933 \| P \| 13 \| 29 \| \| 1425 \| 1312 \| 1937 \| \| 16 \| 25 \| \| 1935 \| 88 \| 1937 \| 1 \| 43 \| \| 793 \| 1776 \| 1945 \| \| 24 \| 13 \| \| 1927 \| 264 \| 1945 \| 3 \| 41 \| \| 1749 \| 860 \| 1949 \| P \| 10 \| 33 \| \| 1239 \| 1520 \| 1961 \| \| 19 \| 21 \| \| 1911 \| 440 \| 1961 \| 5 \| 39 \| \| 915 \| 1748 \| 1973 \| P \| 23 \| 15 \| \| 63 \| 1984 \| 1985 \| \| 31 \| 1 \| \| 1887 \| 616 \| 1985 \| 7 \| 37 \| \| 1705 \| 1032 \| 1993 \| P \| 12 \| 31 \| \| 315 \| 1972 \| 1997 \| P \| 29 \| 5 \| \| 1037 \| 1716 \| 2005 \| \| 22 \| 17 \| \| 1357 \| 1476 \| 2005 \| 18 \| 23 \| \| 1855 \| 792 \| 2017 \| P \| 9 \| 35 \| \| 2021 \| 180 \| 2029 \| P \| 2 \| 43 \| \| 1159 \| 1680 \| 2041 \| \| 21 \| 19 \| \| 2009 \| 360 \| 2041 \| 4 \| 41 \| \| 693 \| 1924 \| 2045 \| \| 26 \| 11 \| \| 1653 \| 1204 \| 2045 \| 14 \| 29 \| \| 1475 \| 1428 \| 2053 \| P \| 17 \| 25 \| \| 819 \| 1900 \| 2069 \| P \| 25 \| 13 \| \| 1281 \| 1640 \| 2081 \| P \| 20 \| 21 \| \| 1961 \| 720 \| 2089 \| P \| 8 \| 37 \| \| 1593 \| 1376 \| 2105 \| \| 16 \| 27 \| \| 1767 \| 1144 \| 2105 \| 13 \| 31 \| \| 65 \| 2112 \| 2113 \| P \| 32 \| 1 \| \| 195 \| 2108 \| 2117 \| \| 31 \| 3 \| \| 2115 \| 92 \| 2117 \| 1 \| 45 \| \| 1403 \| 1596 \| 2125 \| \| 19 \| 23 \| \| 2107 \| 276 \| 2125 \| 3 \| 43 \| \| 1071 \| 1840 \| 2129 \| P \| 23 \| 17 \| \| 455 \| 2088 \| 2137 \| P \| 29 \| 7 \| \| 2091 \| 460 \| 2141 \| P \| 5 \| 41 \| \| 585 \| 2072 \| 2153 \| P \| 28 \| 9 \| \| 1711 \| 1320 \| 2161 \| P \| 15 \| 29 \| \| 1197 \| 1804 \| 2165 \| \| 22 \| 19 \| \| 2067 \| 644 \| 2165 \| 7 \| 39 \| \| 715 \| 2052 \| 2173 \| \| 27 \| 11 \| \| 1525 \| 1548 \| 2173 \| 18 \| 25 \| \| 2035 \| 828 \| 2197 \| P \| 9 \| 37 \| \| 2205 \| 188 \| 2213 \| P \| 2 \| 45 \| \| 1829 \| 1260 \| 2221 \| P \| 14 \| 31 \| \| 1647 \| 1496 \| 2225 \| \| 17 \| 27 \| \| 2193 \| 376 \| 2225 \| 4 \| 43 \| \| 1995 \| 1012 \| 2237 \| P \| 11 \| 35 \| \| 67 \| 2244 \| 2245 \| \| 33 \| 1 \| \| 2173 \| 564 \| 2245 \| 6 \| 41 \| \| 201 \| 2240 \| 2249 \| \| 32 \| 3 \| \| 1449 \| 1720 \| 2249 \| 20 \| 23 \| \| 335 \| 2232 \| 2257 \| \| 31 \| 5 \| \| 1105 \| 1968 \| 2257 \| 24 \| 17 \| \| 469 \| 2220 \| 2269 \| P \| 30 \| 7 \| \| 2145 \| 752 \| 2273 \| P \| 8 \| 39 \| \| 1769 \| 1440 \| 2281 \| P \| 16 \| 29 \| \| 603 \| 2204 \| 2285 \| \| 29 \| 9 \| \| 1947 \| 1196 \| 2285 \| 13 \| 33 \| \| 1235 \| 1932 \| 2293 \| P \| 23 \| 19 \| \| 1575 \| 1672 \| 2297 \| P \| 19 \| 25 \| \| 737 \| 2184 \| 2305 \| \| 28 \| 11 \| \| 2303 \| 96 \| 2305 \| 1 \| 47 \| \| 2109 \| 940 \| 2309 \| P \| 10 \| 37 \| \| 871 \| 2160 \| 2329 \| \| 27 \| 13 \| \| 2279 \| 480 \| 2329 \| 5 \| 43 \| \| 1365 \| 1892 \| 2333 \| P \| 22 \| 21 \| \| 1891 \| 1380 \| 2341 \| P \| 15 \| 31 \| \| 2065 \| 1128 \| 2353 \| \| 12 \| 35 \| \| 2255 \| 672 \| 2353 \| 7 \| 41 \| \| 1005 \| 2132 \| 2357 \| P \| 26 \| 15 \| \| 1495 \| 1848 \| 2377 \| P \| 21 \| 23 \| \| 69 \| 2380 \| 2381 \| P \| 34 \| 1 \| \| 1139 \| 2100 \| 2389 \| P \| 25 \| 17 \| \| 345 \| 2368 \| 2393 \| P \| 32 \| 5 \| \| 483 \| 2356 \| 2405 \| \| 31 \| 7 \| \| 1827 \| 1564 \| 2405 \| 17 \| 29 \| \| 2013 \| 1316 \| 2405 \| 14 \| 33 \| \| 2397 \| 196 \| 2405 \| 2 \| 47 \| \| 2385 \| 392 \| 2417 \| P \| 4 \| 45 \| \| 1273 \| 2064 \| 2425 \| \| 24 \| 19 \| \| 2183 \| 1056 \| 2425 \| 11 \| 37 \| \| 2365 \| 588 \| 2437 \| P \| 6 \| 43 \| \| 759 \| 2320 \| 2441 \| P \| 29 \| 11 \| \| 897 \| 2296 \| 2465 \| \| 28 \| 13 \| \| 1407 \| 2024 \| 2465 \| 23 \| 21 \| \| 1953 \| 1504 \| 2465 \| 16 \| 31 \| \| 2337 \| 784 \| 2465 \| 8 \| 41 \| \| 2135 \| 1248 \| 2473 \| P \| 13 \| 35 \| \| 1755 \| 1748 \| 2477 \| P \| 19 \| 27 \| \| 2301 \| 980 \| 2501 \| \| 10 \| 39 \| \| 2499 \| 100 \| 2501 \| 1 \| 49 \| \| 1541 \| 1980 \| 2509 \| \| 22 \| 23 \| \| 2491 \| 300 \| 2509 \| 3 \| 47 \| \| 71 \| 2520 \| 2521 \| P \| 35 \| 1 \| \| 213 \| 2516 \| 2525 \| \| 34 \| 3 \| \| 1173 \| 2236 \| 2525 \| 26 \| 17 \| \| 355 \| 2508 \| 2533 \| \| 33 \| 5 \| \| 1885 \| 1692 \| 2533 \| 18 \| 29 \| \| 497 \| 2496 \| 2545 \| \| 32 \| 7 \| \| 2257 \| 1176 \| 2545 \| 12 \| 37 \| \| 2451 \| 700 \| 2549 \| P \| 7 \| 43 \| \| 1675 \| 1932 \| 2557 \| P \| 21 \| 25 \| \| 639 \| 2480 \| 2561 \| \| 31 \| 9 \| \| 1311 \| 2200 \| 2561 \| 25 \| 19 \| \| 781 \| 2460 \| 2581 \| \| 30 \| 11 \| \| 2419 \| 900 \| 2581 \| 9 \| 41 \| \| 2015 \| 1632 \| 2593 \| P \| 17 \| 31 \| \| 923 \| 2436 \| 2605 \| \| 29 \| 13 \| \| 2597 \| 204 \| 2605 \| 2 \| 49 \| \| 1809 \| 1880 \| 2609 \| P \| 20 \| 27 \| \| 2585 \| 408 \| 2617 \| P \| 4 \| 47 \| \| 2379 \| 1100 \| 2621 \| P \| 11 \| 39 \| \| 1065 \| 2408 \| 2633 \| P \| 28 \| 15 \| \| 2145 \| 1568 \| 2657 \| P \| 16 \| 33 \| \| 73 \| 2664 \| 2665 \| \| 36 \| 1 \| \| 1207 \| 2376 \| 2665 \| 27 \| 17 \| \| 1943 \| 1824 \| 2665 \| 19 \| 29 \| \| 2537 \| 816 \| 2665 \| 8 \| 43 \| \| 219 \| 2660 \| 2669 \| \| 35 \| 3 \| \| 2331 \| 1300 \| 2669 \| 13 \| 37 \| \| 365 \| 2652 \| 2677 \| P \| 34 \| 5 \| \| 511 \| 2640 \| 2689 \| P \| 33 \| 7 \| \| 1725 \| 2068 \| 2693 \| P \| 22 \| 25 \| \| 1349 \| 2340 \| 2701 \| \| 26 \| 19 \| \| 2501 \| 1020 \| 2701 \| 10 \| 41 \| \| 657 \| 2624 \| 2705 \| \| 32 \| 9 \| \| 2703 \| 104 \| 2705 \| 1 \| 51 \| \| 2695 \| 312 \| 2713 \| P \| 3 \| 49 \| \| 803 \| 2604 \| 2725 \| \| 31 \| 11 \| \| 2077 \| 1764 \| 2725 \| 18 \| 31 \| \| 2679 \| 520 \| 2729 \| P \| 5 \| 47 \| \| 1491 \| 2300 \| 2741 \| P \| 25 \| 21 \| \| 949 \| 2580 \| 2749 \| P \| 30 \| 13 \| \| 2655 \| 728 \| 2753 \| P \| 7 \| 45 \| \| 1095 \| 2552 \| 2777 \| P \| 29 \| 15 \| \| 1633 \| 2256 \| 2785 \| \| 24 \| 23 \| \| 2623 \| 936 \| 2785 \| 9 \| 43 \| \| 2211 \| 1700 \| 2789 \| P \| 17 \| 33 \| \| 2405 \| 1428 \| 2797 \| P \| 14 \| 37 \| \| 2001 \| 1960 \| 2801 \| P \| 20 \| 29 \| \| 1241 \| 2520 \| 2809 \| P \| 28 \| 17 \| \| 75 \| 2812 \| 2813 \| \| 37 \| 1 \| \| 2805 \| 212 \| 2813 \| 2 \| 51 \| \| 2583 \| 1144 \| 2825 \| \| 11 \| 41 \| \| 2793 \| 424 \| 2825 \| 4 \| 49 \| \| 1775 \| 2208 \| 2833 \| P \| 23 \| 25 \| \| 525 \| 2788 \| 2837 \| P \| 34 \| 7 \| \| 1387 \| 2484 \| 2845 \| \| 27 \| 19 \| \| 2773 \| 636 \| 2845 \| 6 \| 47 \| \| 2345 \| 1632 \| 2857 \| P \| 16 \| 35 \| \| 2139 \| 1900 \| 2861 \| P \| 19 \| 31 \| \| 825 \| 2752 \| 2873 \| \| 32 \| 11 \| \| 2745 \| 848 \| 2873 \| 8 \| 45 \| \| 1533 \| 2444 \| 2885 \| \| 26 \| 21 \| \| 1917 \| 2156 \| 2885 \| 22 \| 27 \| \| 975 \| 2728 \| 2897 \| P \| 31 \| 13 \| \| 2709 \| 1060 \| 2909 \| P \| 10 \| 43 \| \| 2915 \| 108 \| 2917 \| P \| 1 \| 53 \| \| 1679 \| 2400 \| 2929 \| \| 25 \| 23 \| \| 2479 \| 1560 \| 2929 \| 15 \| 37 \| \| 2059 \| 2100 \| 2941 \| \| 21 \| 29 \| \| 2891 \| 540 \| 2941 \| 5 \| 49 \| \| 2665 \| 1272 \| 2953 \| P \| 12 \| 41 \| \| 1275 \| 2668 \| 2957 \| P \| 29 \| 17 \| \| 77 \| 2964 \| 2965 \| \| 38 \| 1 \| \| 2867 \| 756 \| 2965 \| 7 \| 47 \| \| 231 \| 2960 \| 2969 \| P \| 37 \| 3 \| \| 385 \| 2952 \| 2977 \| \| 36 \| 5 \| \| 1825 \| 2352 \| 2977 \| 24 \| 25 \| \| 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\| 3145 \| \| 36 \| 7 \| \| 1463 \| 2784 \| 3145 \| 29 \| 19 \| \| 2263 \| 2184 \| 3145 \| 21 \| 31 \| \| 3127 \| 336 \| 3145 \| 3 \| 53 \| \| 711 \| 3080 \| 3161 \| \| 35 \| 9 \| \| 3111 \| 560 \| 3161 \| 5 \| 51 \| \| 2881 \| 1320 \| 3169 \| P \| 12 \| 43 \| \| 869 \| 3060 \| 3181 \| P \| 34 \| 11 \| \| 1027 \| 3036 \| 3205 \| \| 33 \| 13 \| \| 2627 \| 1836 \| 3205 \| 17 \| 37 \| \| 2409 \| 2120 \| 3209 \| P \| 20 \| 33 \| \| 3055 \| 1008 \| 3217 \| P \| 9 \| 47 \| \| 2829 \| 1540 \| 3221 \| P \| 14 \| 41 \| \| 1771 \| 2700 \| 3229 \| P \| 27 \| 23 \| \| 1185 \| 3008 \| 3233 \| \| 32 \| 15 \| \| 2175 \| 2392 \| 3233 \| 23 \| 29 \| \| 3245 \| 228 \| 3253 \| P \| 2 \| 55 \| \| 3015 \| 1232 \| 3257 \| P \| 11 \| 45 \| \| 1343 \| 2976 \| 3265 \| \| 31 \| 17 \| \| 3233 \| 456 \| 3265 \| 4 \| 53 \| \| 1925 \| 2652 \| 3277 \| \| 26 \| 25 \| \| 2555 \| 2052 \| 3277 \| 19 \| 35 \| \| 81 \| 3280 \| 3281 \| \| 40 \| 1 \| \| 2769 \| 1760 \| 3281 \| 16 \| 39 \| \| 405 \| 3268 \| 3293 \| \| 38 \| 5 \| \| 2325 \| 2332 \| 3293 \| 22 \| 31 \| \| 1501 \| 2940 \| 3301 \| P \| 30 \| 19 \| \| 567 \| 3256 \| 3305 \| \| 37 \| 7 \| \| 2967 \| 1456 \| 3305 \| 13 \| 43 \| \| 3185 \| 912 \| 3313 \| P \| 8 \| 49 \| \| 2079 \| 2600 \| 3329 \| P \| 25 \| 27 \| \| 891 \| 3220 \| 3341 \| \| 35 \| 11 \| \| 1659 \| 2900 \| 3341 \| 29 \| 21 \| \| 2701 \| 1980 \| 3349 \| \| 18 \| 37 \| \| 3149 \| 1140 \| 3349 \| 10 \| 47 \| \| 2911 \| 1680 \| 3361 \| P \| 15 \| 41 \| \| 1053 \| 3196 \| 3365 \| \| 34 \| 13 \| \| 3363 \| 116 \| 3365 \| 1 \| 57 \| \| 3355 \| 348 \| 3373 \| P \| 3 \| 55 \| \| 1817 \| 2856 \| 3385 \| \| 28 \| 23 \| \| 2233 \| 2544 \| 3385 \| 24 \| 29 \| \| 3339 \| 580 \| 3389 \| P \| 5 \| 53 \| \| 3315 \| 812 \| 3413 \| P \| 7 \| 51 \| \| 1377 \| 3136 \| 3425 \| \| 32 \| 17 \| \| 2847 \| 1904 \| 3425 \| 17 \| 39 \| \| 1975 \| 2808 \| 3433 \| P \| 27 \| 25 \| \| 83 \| 3444 \| 3445 \| \| 41 \| 1 \| \| 2387 \| 2484 \| 3445 \| 23 \| 31 \| \| 3053 \| 1596 \| 3445 \| 14 \| 43 \| \| 3283 \| 1044 \| 3445 \| 9 \| 49 \| \| 249 \| 3440 \| 3449 \| P \| 40 \| 3 \| \| 415 \| 3432 \| 3457 \| P \| 39 \| 5 \| \| 1539 \| 3100 \| 3461 \| P \| 31 \| 19 \| \| 581 \| 3420 \| 3469 \| P \| 38 \| 7 \| \| 747 \| 3404 \| 3485 \| \| 37 \| 9 \| \| 2133 \| 2756 \| 3485 \| 26 \| 27 \| \| 3243 \| 1276 \| 3485 \| 11 \| 47 \| \| 3477 \| 236 \| 3485 \| 2 \| 57 \| \| 2775 \| 2128 \| 3497 \| \| 19 \| 37 \| \| 3465 \| 472 \| 3497 \| 4 \| 55 \| \| 913 \| 3384 \| 3505 \| \| 36 \| 11 \| \| 2993 \| 1824 \| 3505 \| 16 \| 41 \| \| 3445 \| 708 \| 3517 \| P \| 6 \| 53 \| \| 1079 \| 3360 \| 3529 \| P \| 35 \| 13 \| \| 3195 \| 1508 \| 3533 \| P \| 13 \| 45 \| \| 2291 \| 2700 \| 3541 \| P \| 25 \| 29 \| \| 1863 \| 3016 \| 3545 \| \| 29 \| 23 \| \| 3417 \| 944 \| 3545 \| 8 \| 51 \| \| 1245 \| 3332 \| 3557 \| P \| 34 \| 15 \| \| 3381 \| 1180 \| 3581 \| P \| 10 \| 49 \| \| 1411 \| 3300 \| 3589 \| \| 33 \| 17 \| \| 3139 \| 1740 \| 3589 \| 15 \| 43 \| \| 2025 \| 2968 \| 3593 \| P \| 28 \| 25 \| \| 2449 \| 2640 \| 3601 \| \| 24 \| 31 \| \| 3599 \| 120 \| 3601 \| 1 \| 59 \| \| 85 \| 3612 \| 3613 \| P \| 42 \| 1 \| \| 255 \| 3608 \| 3617 \| P \| 41 \| 3 \| \| 1577 \| 3264 \| 3625 \| \| 32 \| 19 \| \| 3337 \| 1416 \| 3625 \| 12 \| 47 \| \| 595 \| 3588 \| 3637 \| P \| 39 \| 7 \| \| 2849 \| 2280 \| 3649 \| \| 20 \| 37 \| \| 3551 \| 840 \| 3649 \| 7 \| 53 \| \| 765 \| 3572 \| 3653 \| \| 38 \| 9 \| \| 3075 \| 1972 \| 3653 \| 17 \| 41 \| \| 1743 \| 3224 \| 3665 \| \| 31 \| 21 \| \| 2607 \| 2576 \| 3665 \| 23 \| 33 \| \| 935 \| 3552 \| 3673 \| P \| 37 \| 11 \| \| 3285 \| 1652 \| 3677 \| P \| 14 \| 45 \| \| 1105 \| 3528 \| 3697 \| P \| 36 \| 13 \| \| 2349 \| 2860 \| 3701 \| P \| 26 \| 29 \| \| 1909 \| 3180 \| 3709 \| P \| 30 \| 23 \| \| 3479 \| 1320 \| 3721 \| P \| 11 \| 49 \| \| 3003 \| 2204 \| 3725 \| \| 19 \| 39 \| \| 3717 \| 244 \| 3725 \| 2 \| 59 \| \| 2765 \| 2508 \| 3733 \| P \| 22 \| 35 \| \| 3225 \| 1888 \| 3737 \| \| 16 \| 43 \| \| 3705 \| 488 \| 3737 \| 4 \| 57 \| \| 2075 \| 3132 \| 3757 \| \| 29 \| 25 \| \| 3685 \| 732 \| 3757 \| 6 \| 55 \| \| 2511 \| 2800 \| 3761 \| P \| 25 \| 31 \| \| 3431 \| 1560 \| 3769 \| P \| 13 \| 47 \| \| 87 \| 3784 \| 3785 \| \| 43 \| 1 \| \| 3657 \| 976 \| 3785 \| 8 \| 53 \| \| 1615 \| 3432 \| 3793 \| P \| 33 \| 19 \| \| 435 \| 3772 \| 3797 \| P \| 41 \| 5 \| \| 2923 \| 2436 \| 3805 \| \| 21 \| 37 \| \| 3157 \| 2124 \| 3805 \| 18 \| 41 \| \| 609 \| 3760 \| 3809 \| \| 40 \| 7 \| \| 2241 \| 3080 \| 3809 \| 28 \| 27 \| \| 3621 \| 1220 \| 3821 \| P \| 10 \| 51 \| \| 1785 \| 3392 \| 3833 \| P \| 32 \| 21 \| \| 957 \| 3724 \| 3845 \| \| 38 \| 11 \| \| 3843 \| 124 \| 3845 \| 1 \| 61 \| \| 3835 \| 372 \| 3853 \| P \| 3 \| 59 \| \| 2407 \| 3024 \| 3865 \| \| 27 \| 29 \| \| 3577 \| 1464 \| 3865 \| 12 \| 49 \| \| 1131 \| 3700 \| 3869 \| \| 37 \| 13 \| \| 3819 \| 620 \| 3869 \| 5 \| 57 \| \| 1955 \| 3348 \| 3877 \| P \| 31 \| 23 \| \| 3081 \| 2360 \| 3881 \| P \| 20 \| 39 \| \| 3311 \| 2040 \| 3889 \| P \| 17 \| 43 \| \| 2835 \| 2668 \| 3893 \| \| 23 \| 35 \| \| 3795 \| 868 \| 3893 \| 7 \| 55 \| \| 3525 \| 1708 \| 3917 \| P \| 14 \| 47 \| \| 2573 \| 2964 \| 3925 \| \| 26 \| 31 \| \| 3763 \| 1116 \| 3925 \| 9 \| 53 \| \| 1479 \| 3640 \| 3929 \| P \| 35 \| 17 \| \| 89 \| 3960 \| 3961 \| \| 44 \| 1 \| \| 3239 \| 2280 \| 3961 \| 19 \| 41 \| \| 267 \| 3956 \| 3965 \| \| 43 \| 3 \| \| 1653 \| 3604 \| 3965 \| 34 \| 19 \| \| 2997 \| 2596 \| 3965 \| 22 \| 37 \| \| 3723 \| 1364 \| 3965 \| 11 \| 51 \| \| 445 \| 3948 \| 3973 \| \| 42 \| 5 \| \| 3965 \| 252 \| 3973 \| 2 \| 61 \| \| 2295 \| 3248 \| 3977 \| \| 29 \| 27 \| \| 3465 \| 1952 \| 3977 \| 16 \| 45 \| \| 623 \| 3936 \| 3985 \| \| 41 \| 7 \| \| 3953 \| 504 \| 3985 \| 4 \| 59 \| \| 2739 \| 2900 \| 3989 \| P \| 25 \| 33 \| \| 801 \| 3920 \| 4001 \| P \| 40 \| 9 \| \| 3675 \| 1612 \| 4013 \| P \| 13 \| 49 \| \| 979 \| 3900 \| 4021 \| P \| 39 \| 11 \| \| 2465 \| 3192 \| 4033 \| \| 28 \| 29 \| \| 3905 \| 1008 \| 4033 \| 8 \| 55 \| \| 1157 \| 3876 \| 4045 \| \| 38 \| 13 \| \| 3397 \| 2196 \| 4045 \| 18 \| 43 \| \| 2001 \| 3520 \| 4049 \| P \| 32 \| 23 \| \| 2905 \| 2832 \| 4057 \| P \| 24 \| 35 \| \| 3619 \| 1860 \| 4069 \| \| 15 \| 47 \| \| 3869 \| 1260 \| 4069 \| 10 \| 53 \| \| 1335 \| 3848 \| 4073 \| P \| 37 \| 15 \| \| 2635 \| 3132 \| 4093 \| P \| 27 \| 31 \| \| 2175 \| 3472 \| 4097 \| \| 31 \| 25 \| \| 4095 \| 128 \| 4097 \| 1 \| 63 \| \| 1513 \| 3816 \| 4105 \| \| 36 \| 17 \| \| 4087 \| 384 \| 4105 \| 3 \| 61 \| \| 3321 \| 2440 \| 4121 \| \| 20 \| 41 \| \| 4071 \| 640 \| 4121 \| 5 \| 59 \| \| 3071 \| 2760 \| 4129 \| P \| 23 \| 37 \| \| 3555 \| 2108 \| 4133 \| P \| 17 \| 45 \| \| 91 \| 4140 \| 4141 \| \| 45 \| 1 \| \| 1691 \| 3780 \| 4141 \| 35 \| 19 \| \| 273 \| 4136 \| 4145 \| \| 44 \| 3 \| \| 4047 \| 896 \| 4145 \| 7 \| 57 \| \| 455 \| 4128 \| 4153 \| P \| 43 \| 5 \| \| 2805 \| 3068 \| 4157 \| P \| 26 \| 33 \| \| 4015 \| 1152 \| 4177 \| P \| 9 \| 55 \| \| 819 \| 4100 \| 4181 \| \| 41 \| 9 \| \| 1869 \| 3740 \| 4181 \| 34 \| 21 \| \| 1001 \| 4080 \| 4201 \| P \| 40 \| 11 \| \| 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4517 \| P \| 46 \| 3 \| \| 4187 \| 1716 \| 4525 \| \| 13 \| 53 \| \| 4453 \| 804 \| 4525 \| 6 \| 61 \| \| 665 \| 4488 \| 4537 \| \| 44 \| 7 \| \| 3655 \| 2688 \| 4537 \| 21 \| 43 \| \| 3901 \| 2340 \| 4549 \| P \| 18 \| 47 \| \| 855 \| 4472 \| 4553 \| \| 43 \| 9 \| \| 4425 \| 1072 \| 4553 \| 8 \| 59 \| \| 2639 \| 3720 \| 4561 \| P \| 31 \| 29 \| \| 1045 \| 4452 \| 4573 \| \| 42 \| 11 \| \| 3115 \| 3348 \| 4573 \| 27 \| 35 \| \| 2139 \| 4060 \| 4589 \| \| 35 \| 23 \| \| 4389 \| 1340 \| 4589 \| 10 \| 57 \| \| 1235 \| 4428 \| 4597 \| P \| 41 \| 13 \| \| 2821 \| 3660 \| 4621 \| P \| 30 \| 31 \| \| 3567 \| 2944 \| 4625 \| \| 23 \| 41 \| \| 4623 \| 136 \| 4625 \| 1 \| 67 \| \| 4345 \| 1608 \| 4633 \| \| 12 \| 55 \| \| 4615 \| 408 \| 4633 \| 3 \| 65 \| \| 2325 \| 4012 \| 4637 \| P \| 34 \| 25 \| \| 3293 \| 3276 \| 4645 \| \| 26 \| 37 \| \| 4067 \| 2244 \| 4645 \| 17 \| 49 \| \| 4599 \| 680 \| 4649 \| P \| 5 \| 63 \| \| 1615 \| 4368 \| 4657 \| P \| 39 \| 17 \| \| 4575 \| 952 \| 4673 \| P \| 7 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\| 41 \| C \| \| 749 \| 5700 \| 5749 \| P \| 50 \| 7 \| \| 963 \| 5684 \| 5765 \| \| 49 \| 9 \| \| 5187 \| 2516 \| 5765 \| 17 \| 57 \| \| 2415 \| 5248 \| 5777 \| \| 41 \| 23 \| \| 5775 \| 152 \| 5777 \| 1 \| 75 \| \| 1177 \| 5664 \| 5785 \| \| 48 \| 11 \| \| 3193 \| 4824 \| 5785 \| 36 \| 31 \| \| 3737 \| 4416 \| 5785 \| 32 \| 37 \| \| 5767 \| 456 \| 5785 \| 3 \| 73 \| \| 5751 \| 760 \| 5801 \| P \| 5 \| 71 \| \| 1391 \| 5640 \| 5809 \| \| 47 \| 13 \| \| 4559 \| 3600 \| 5809 \| 25 \| 47 \| \| 4845 \| 3212 \| 5813 \| P \| 22 \| 51 \| \| 5429 \| 2100 \| 5821 \| P \| 14 \| 61 \| \| 4257 \| 3976 \| 5825 \| \| 28 \| 43 \| \| 5727 \| 1064 \| 5825 \| 7 \| 69 \| \| 1605 \| 5612 \| 5837 \| \| 46 \| 15 \| \| 5115 \| 2812 \| 5837 \| 19 \| 55 \| \| 3399 \| 4760 \| 5849 \| P \| 35 \| 33 \| \| 5695 \| 1368 \| 5857 \| P \| 9 \| 67 \| \| 3939 \| 4340 \| 5861 \| P \| 31 \| 39 \| \| 1819 \| 5580 \| 5869 \| P \| 45 \| 17 \| \| 5369 \| 2400 \| 5881 \| P \| 16 \| 59 \| \| 5655 \| 1672 \| 5897 \| P \| 11 \| 65 \| \| 2033 \| 5544 \| 5905 \| \| 44 \| 19 \| \| 4753 \| 3504 \| 5905 \| 24 \| 49 \| \| 3605 \| 4692 \| 5917 \| \| 34 \| 35 \| \| 5035 \| 3108 \| 5917 \| 21 \| 53 \| \| 3045 \| 5092 \| 5933 \| \| 38 \| 29 \| \| 5925 \| 308 \| 5933 \| 2 \| 75 \| \| 109 \| 5940 \| 5941 \| \| 54 \| 1 \| \| 4141 \| 4260 \| 5941 \| 30 \| 41 \| \| 327 \| 5936 \| 5945 \| \| 53 \| 3 \| \| 2247 \| 5504 \| 5945 \| 43 \| 21 \| \| 5607 \| 1976 \| 5945 \| 13 \| 63 \| \| 5913 \| 616 \| 5945 \| 4 \| 73 \| \| 545 \| 5928 \| 5953 \| P \| 52 \| 5 \| \| 763 \| 5916 \| 5965 \| \| 51 \| 7 \| \| 5893 \| 924 \| 5965 \| 6 \| 71 \| \| 981 \| 5900 \| 5981 \| P \| 50 \| 9 \| \| 2461 \| 5460 \| 5989 \| \| 42 \| 23 \| \| 3811 \| 4620 \| 5989 \| 33 \| 37 \| \| 3255 \| 5032 \| 5993 \| \| 37 \| 31 \| \| 5865 \| 1232 \| 5993 \| 8 \| 69 \| \| \| \| \| \| \| \| \| \| 2277 \| 31964 \| 32045 \| \| 122 \| 9 \| \| 8283 \| 30956 \| 32045 \| 109 \| 33 \| \| 17253 \| 27004 \| 32045 \| 86 \| 71 \| \| 21093 \| 24124 \| 32045 \| 74 \| 89 \| \| 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\| 909 \| \| 1164447 \| 223304 \| 1185665 \| 103 \| 981 \| \| 1177473 \| 139136 \| 1185665 \| 64 \| 1023 \| \| 4684659 \| 4684660 \| 6625109 \| \| 985 \| 1393 \| C \| \| 27304197 \| 27304196 \| 38613965 \| \| 2378 \| 3363 \| C \| \| 1547863 \| 48587616 \| 48612265 \| \| 4851 \| 157 \| \| 4206377 \| 48429936 \| 48612265 \| 4712 \| 427 \| \| 5031817 \| 48351144 \| 48612265 \| 4668 \| 511 \| \| 6365833 \| 48193656 \| 48612265 \| 4596 \| 647 \| \| 10400983 \| 47486544 \| 48612265 \| 4371 \| 1061 \| \| 14399273 \| 46430736 \| 48612265 \| 4136 \| 1477 \| \| 15368407 \| 46119024 \| 48612265 \| 4077 \| 1579 \| \| 16162697 \| 45846696 \| 48612265 \| 4028 \| 1663 \| \| 19412183 \| 44568144 \| 48612265 \| 3821 \| 2011 \| \| 21173033 \| 43759056 \| 48612265 \| 3704 \| 2203 \| \| 24544343 \| 41961024 \| 48612265 \| 3469 \| 2579 \| \| 26394487 \| 40822584 \| 48612265 \| 3333 \| 2791 \| \| 28590473 \| 39315864 \| 48612265 \| 3164 \| 3049 \| \| 29737897 \| 38455296 \| 48612265 \| 3072 \| 3187 \| \| 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\| 225058681 \| \| 5741 \| 8119 \| C \| \| 927538921 \| 927538920 \| 1311738121 \| \| 13860 \| 19601 \| C \| \| 44719563 \| 2576061916 \| 2576450045 \| \| 35579 \| 623 \| \| 70413237 \| 2575487684 \| 2576450045 \| 35398 \| 981 \| \| 185727093 \| 2569747124 \| 2576450045 \| 34574 \| 2589 \| \| 261457077 \| 2563149436 \| 2576450045 \| 34022 \| 3647 \| \| 272467083 \| 2562002444 \| 2576450045 \| 33941 \| 3801 \| \| 374359797 \| 2549107604 \| 2576450045 \| 33182 \| 5229 \| \| 478355403 \| 2531653796 \| 2576450045 \| 32389 \| 6693 \| \| 514731147 \| 2524509196 \| 2576450045 \| 32107 \| 7207 \| \| 531265077 \| 2521081564 \| 2576450045 \| 31978 \| 7441 \| \| 556386123 \| 2515656836 \| 2576450045 \| 31781 \| 7797 \| \| 599754357 \| 2505671476 \| 2576450045 \| 31438 \| 8413 \| \| 652093323 \| 2492562764 \| 2576450045 \| 31019 \| 9159 \| \| 809536587 \| 2445965116 \| 2576450045 \| 29723 \| 11423 \| \| 851138763 \| 2431801316 \| 2576450045 \| 29371 \| 12027 \| \| 861578997 \| 2428122004 \| 2576450045 \| 29282 \| 12179 \| \| 983035893 \| 2381540524 \| 2576450045 \| 28226 \| 13961 \| \| 1014492213 \| 2368311716 \| 2576450045 \| 27946 \| 14427 \| \| 1062959883 \| 2346957844 \| 2576450045 \| 27509 \| 15149 \| \| 1127400267 \| 2316692356 \| 2576450045 \| 26917 \| 16117 \| \| 1166751243 \| 2297125676 \| 2576450045 \| 26549 \| 16713 \| \| 1268493387 \| 2242547516 \| 2576450045 \| 25573 \| 18273 \| \| 1290799413 \| 2229782884 \| 2576450045 \| 25354 \| 18619 \| \| 1310700747 \| 2218143004 \| 2576450045 \| 25157 \| 18929 \| \| 1356862773 \| 2190209636 \| 2576450045 \| 24694 \| 19653 \| \| 1430107083 \| 2143102556 \| 2576450045 \| 23941 \| 20817 \| \| 1545325173 \| 2061568564 \| 2576450045 \| 22706 \| 22691 \| \| 1546414773 \| 2060751364 \| 2576450045 \| 22694 \| 22709 \| \| 1580263797 \| 2034910604 \| 2576450045 \| 22318 \| 23271 \| \| 1635884853 \| 1990471196 \| 2576450045 \| 21686 \| 24207 \| \| 1706671413 \| 1930121116 \| 2576450045 \| 20854 \| 25423 \| \| 1779167733 \| 1863506644 \| 2576450045 \| 19966 \| 26701 \| \| 1797667467 \| 1845666956 \| 2576450045 \| 19733 \| 27033 \| \| 1908352587 \| 1730978116 \| 2576450045 \| 18277 \| 29077 \| \| 1931111307 \| 1705550924 \| 2576450045 \| 17963 \| 29511 \| \| 1948027893 \| 1686203476 \| 2576450045 \| 17726 \| 29837 \| \| 1955450763 \| 1677589684 \| 2576450045 \| 17621 \| 29981 \| \| 1982910987 \| 1645040684 \| 2576450045 \| 17227 \| 30519 \| \| 2011028853 \| 1610545804 \| 2576450045 \| 16814 \| 31079 \| \| 2121456267 \| 1462025356 \| 2576450045 \| 15083 \| 33383 \| \| 2134454133 \| 1442983156 \| 2576450045 \| 14866 \| 33667 \| \| 2164203147 \| 1397969804 \| 2576450045 \| 14357 \| 34329 \| \| 2178040053 \| 1376312596 \| 2576450045 \| 14114 \| 34643 \| \| 2210274123 \| 1323927164 \| 2576450045 \| 13531 \| 35391 \| \| 2237513397 \| 1277352196 \| 2576450045 \| 13018 \| 36043 \| \| 2279404107 \| 1201004476 \| 2576450045 \| 12187 \| 37087 \| \| 2330784267 \| 1097970644 \| 2576450045 \| 11083 \| 38451 \| \| 2368900107 \| 1013117524 \| 2576450045 \| 10187 \| 39539 \| \| 2383231563 \| 978929084 \| 2576450045 \| 9829 \| 39969 \| \| 2387415477 \| 968680636 \| 2576450045 \| 9722 \| 40097 \| \| 2395988043 \| 947278276 \| 2576450045 \| 9499 \| 40363 \| \| 2414953653 \| 897827204 \| 2576450045 \| 8986 \| 40971 \| \| 2457808437 \| 772834084 \| 2576450045 \| 7702 \| 42469 \| \| 2482522827 \| 689329564 \| 2576450045 \| 6853 \| 43441 \| \| 2485540917 \| 678366556 \| 2576450045 \| 6742 \| 43567 \| \| 2492183883 \| 653539844 \| 2576450045 \| 6491 \| 43851 \| \| 2496413493 \| 637192676 \| 2576450045 \| 6326 \| 44037 \| \| 2531930997 \| 476886004 \| 2576450045 \| 4718 \| 45821 \| \| 2551964043 \| 354364724 \| 2576450045 \| 3499 \| 47139 \| \| 2557637067 \| 310785244 \| 2576450045 \| 3067 \| 47599 \| \| 2564327157 \| 249641876 \| 2576450045 \| 2462 \| 48237 \| \| 2568992523 \| 195888364 \| 2576450045 \| 1931 \| 48791 \| \| 2570818677 \| 170253236 \| 2576450045 \| 1678 \| 49053 \| \| 2572239243 \| 147241676 \| 2576450045 \| 1451 \| 49287 \| \| 2572848117 \| 136188844 \| 2576450045 \| 1342 \| 49399 \| \| 5406093003 \| 5406093004 \| 7645370045 \| \| 33461 \| 47321 \| C \| \| 31509019101 \| 31509019100 \| 44560482149 \| P \| 80782 \| 114243 \| C \| \| 183648021599 \| 183648021600 \| 259717522849 \| \| 195025 \| 275807 \| C \| \| 1070379110497 \| 1070379110496 \| 1513744654945 \| \| 470832 \| 665857 \| C \| \| 4565486027761 \| 1061652293520 \| 4687298610289 \| P \| 246792 \| 1904113 \| F \| \| 6238626641379 \| 6238626641380 \| 8822750406821 \| \| 1136689 \| 1607521 \| C \| \| 36361380737781 \| 36361380737780 \| 51422757785981 \| \| 2744210 \| 3880899 \| C \| \| 211929657785303 \| 211929657785304 \| 299713796309065 \| \| 6625109 \| 9369319 \| C \| \| 1235216565974041 \| 1235216565974040 \| 1746860020068409 \| P \| 15994428 \| 22619537 \| C \| \| 7199369738058939 \| 7199369738058940 \| 10181446324101389 \| \| 38613965 \| 54608393 \| C \| \| 41961001862379597 \| 41961001862379596 \| 59341817924539925 \| \| 93222358 \| 131836323 \| C \| \| 244566641436218639 \| 244566641436218640 \| 345869461223138161 \| \| 225058681 \| 318281039 \| C \| \| 1425438846754932241 \| 1425438846754932240 \| 2015874949414289041 \| \| 543339720 \| 768398401 \| C \| \| 8308066439093374803 \| 8308066439093374804 \| 11749380235262596085 \| \| 1311738121 \| 1855077841 \| C \| \| \| \| \| ProjectsExpositions Pascal's Simplices • Pythagorean Triples • Regular Polygons Regular Polyhedra • Regular Polytopes • Sums of Consecutive Powers Mathematical Induction • Modular Arithmetic • Polynomial Equations Investigations Home • Calculators • Popular Books Eric Rowland \|
13252	https://planetmath.org/indefinitesum	indefinite sum indefinite sum Recall that the finite difference operator Δ Δ defined on the set of functionsR→R ℝ→ℝ is given by Δ f(x):=f(x+1)−f(x).Δ⁢f⁢(x):=f⁢(x+1)-f⁢(x). The difference operator can be thought of as the discrete version of the derivative operator sending a function to its derivative (if it exists). With the derivative operation, there corresponds an inverse operation called the antiderivative, which, given a function f f, finds its antiderivative F F so that the derivative of F F gives f f. There is also a discrete analog of this inverse operation, and it is called the indefinite sum. The indefinite sum of a function f:R→R f:ℝ→ℝ is the set of functions {F:R→R∣Δ F=f}.{F:ℝ→ℝ∣Δ F=f}. This set is often denoted by Δ−1 f Δ-1⁢f or Σ f Σ⁢f, and any element in Δ−1 f Δ-1⁢f is called an indefinite sum of f f. Remark. Like the indefinite integral, the indefinite sum Δ−1 Δ-1 is shift invariant. This means that for any F∈Δ−1 f F∈Δ-1⁢f, then F+c∈Δ−1 f F+c∈Δ-1⁢f for any c∈R c∈ℝ. But, unlike the indefinite integral, the indefinite sum is also invariant by a shift of a periodicreal function of period 1 1. Conversely, the difference of two indefinite sums of a function f f is a periodic real function of period 1 1. In the following discussion, we consider the indefinite sum of a function as a function. Basic Properties 1.Δ Δ−1 f=f Δ⁢Δ-1⁢f=f, and Δ−1 Δ f=f Δ-1⁢Δ⁢f=f modulo a real function of period 1 1. 2. Modulo a real number, and treating Δ−1 Δ-1 as an operator taking a function into a function, we see that Δ−1 Δ-1 is linear, that is, –Δ−1(r f)=r Δ−1 f Δ-1⁢(r⁢f)=r⁢Δ-1⁢f for any r∈R r∈ℝ, and –Δ−1(f+g)=Δ−1 f+Δ−1 g Δ-1⁢(f+g)=Δ-1⁢f+Δ-1⁢g. 3.If F(x)=Δ−1 f(x)F⁢(x)=Δ-1⁢f⁢(x), then F(x+a)=Δ−1 f(x+a)F⁢(x+a)=Δ-1⁢f⁢(x+a). 4.If F=Δ−1 f F=Δ-1⁢f, then we see that F(a+1)−F(a)F⁢(a+1)-F⁢(a)==f(a),f⁢(a), F(a+2)−F(a+1)F⁢(a+2)-F⁢(a+1)==f(a+1),f⁢(a+1), ⋮⋮ F(x)−F(x−1)F⁢(x)-F⁢(x-1)==f(x−1).f⁢(x-1). where x−a x-a is a positive integer. Summing these expressions, we get F(x)−F(a)=x−a∑i=1 f(a+i−1).F⁢(x)-F⁢(a)=∑i=1 x-a f⁢(a+i-1). This is the discrete version of the fundamental theorem of calculus. Below is a table of some basic functions and their indefinite sums (C C is a real-valued periodic function with period 1 1): \| f(x)f⁢(x) \| Δ−1 f(x)Δ-1⁢f⁢(x) \| Comment \| --- \| r∈R r∈ℝ \| r x+C r⁢x+C \| \| \| x x \| x(x−1)2+C x⁢(x-1)2+C \| \| \| x 2 x 2 \| x(x−1)(2 x−1)6+C x⁢(x-1)⁢(2⁢x-1)6+C \| \| \| x 3 x 3 \| x 2(x−1)2 4+C x 2⁢(x-1)2 4+C \| \| \| x n x n \| T n(x)+C T n⁢(x)+C \| See this link ( for detail \| \| a x a x \| a x a−1+C a x a-1+C \| a≠1 a≠1 \| \| (x)n(x)n \| (x)n n+1+C(x)n n+1+C \| (x)n(x)n is the falling factorial of degree n n \| \| (x n)(x n) \| (x n+1)+C(x n+1)+C \| (x n):=(x)n n!(x n):=(x)n n! \| \| 1 x 1 x \| ψ(x)+C ψ⁢(x)+C \| ψ(x)ψ⁢(x) is the digamma function \| \| ln x ln⁡x \| ln Γ(x)+C ln⁡Γ⁢(x)+C \| Γ(x)Γ⁢(x) is the gamma function \| \| sin x sin⁡x \| −cos(x−1/2)2 sin(1/2)+C-cos⁡(x-1/2)2⁢sin⁡(1/2)+C \| \| \| cos x cos⁡x \| sin(x−1/2)2 sin(1/2)+C sin⁡(x-1/2)2⁢sin⁡(1/2)+C \| \| References 1 C.J o r d a n.Unknown node type: em,t h i r d e d i t i o n.C h e l s e a,N e w Y o r k(1965)Title indefinite sum Canonical name IndefiniteSum Date of creation 2013-03-22 17:35:14 Last modified on 2013-03-22 17:35:14 Owner CWoo (3771)Last modified by CWoo (3771)Numerical id 20 Author CWoo (3771)Entry type Definition Classification msc 39A99 Related topic FiniteDifference References 1⁢C.J⁢o⁢r⁢d⁢a⁢n.Unknown node type: em,t⁢h⁢i⁢r⁢d⁢e⁢d⁢i⁢t⁢i⁢o⁢n.C⁢h⁢e⁢l⁢s⁢e⁢a,N⁢e⁢w⁢Y⁢o⁢r⁢k⁢(1965)⁢Title indefinite sum Canonical name IndefiniteSum Date of creation 2013-03-22 17:35:14 Last modified on 2013-03-22 17:35:14 Owner CWoo (3771)Last modified by CWoo (3771)Numerical id 20 Author CWoo (3771)Entry type Definition Classification msc 39A99 Related topic FiniteDifference Generated on Fri Feb 9 20:48:11 2018 by LaTeXML
13253	https://www.geeksforgeeks.org/aptitude/puzzle-broken-clock/	Puzzle - Broken Clock - GeeksforGeeks Skip to content Tutorials Python Java DSA ML & Data Science Interview Corner Programming Languages Web Development CS Subjects DevOps Software and Tools School Learning Practice Coding Problems Courses DSA / Placements ML & Data Science Development Cloud / DevOps Programming Languages All Courses Tracks Languages Python C C++ Java Advanced Java SQL JavaScript Interview Preparation GfG 160 GfG 360 System Design Core Subjects Interview Questions Interview Puzzles Aptitude and Reasoning Data Science Python Data Analytics Complete Data Science Dev Skills Full-Stack Web Dev DevOps Software Testing CyberSecurity Tools Computer Fundamentals AI Tools MS Excel & Google Sheets MS Word & Google Docs Maths Maths For Computer Science Engineering Mathematics Switch to Dark Mode Sign In Quantitiative Aptitude Logical Reasoning Verbal Ability Aptitude Quiz Quantitiative Aptitude Quiz Verbal Ability Quiz Aptitude For Placements Interview Corner Practice Sets Sign In ▲ Open In App Puzzle - Broken Clock Last Updated : 25 Apr, 2023 Comments Improve Suggest changes 2 Likes Like Report You have a clock that is broken in such a way that it shows the correct time twice a day (at some unknown times). You have no way of knowing whether the clock shows AM or PM. You are allowed to set the clock correctly just once. How can you determine which is the correct time on the clock? Solution: Broken Clock One way to solve this puzzle is to use a bit of logic. Here are the steps: Set the clock to 12:00. Wait for a few minutes (let's say, 5 minutes). If the clock moves forward, then you set it at 12:05 AM. If it moves backward, then you set it at 11:55 AM. Wait until the clock shows the same time again (let's say, 6 hours later). If the clock shows 12:05, then it was set to 12:05 AM. If it shows 11:55, then it was set to 11:55 AM. The logic behind this solution is that if you set the clock at 12:00, then there are two possible times when the clock will show the correct time: 12:00 and some other time (let's call it x). If you wait for a few minutes and the clock moves forward, then x must be a time between 12:00 and 12:05. If the clock moves backward, then x must be a time between 11:55 and 12:00. By setting the clock to either 12:05 or 11:55, you eliminate one of the possibilities, and you can use the next reading of the clock to determine whether it was set to AM or PM. 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13254	https://pressbooks.pub/thermo/chapter/chapter-2/	5 We consider the First Law of Thermodynamics applied to stationary closed systems as a conservation of energy principle. Thus energy is transferred between the system and the surroundings in the form of heat and work, resulting in a change of internal energy of the system. Internal energy change can be considered as a measure of molecular activity associated with change of phase or temperature of the system and the energy equation is represented as follows: Energy Equation for Stationary Closed Systems Dividing each term by the system mass m [kg] we obtain the specific form of the Energy Equation: Heat [Q] Energy transferred across the boundary of a system in the form of heat always results from a difference in temperature between the system and its immediate surroundings. We will not consider the mode of heat transfer, whether by conduction, convection or radiation, thus the quantity of heat transferred during any process will either be specified or evaluated as the unknown of the energy equation. By convention, positive heat is that transferred from the surroundings to the system, resulting in an increase in internal energy of the system. Work [W] In this course we consider three modes of work transfer across the boundary of a system, as shown in the following diagram: Three forms of Work considered: a) Boundary Work Piston – Cylinder b) Shaft Work Paddle Wheel c) Electrical Work Volts (Amps) time In this course we are primarily concerned with Boundary Work due to compression or expansion of a system in a piston-cylinder device as shown above. In all cases we assume a perfect seal (no mass flow in or out of the system), no loss due to friction, and quasi-equilibrium processes in that for each incremental movement of the piston equilibrium conditions are maintained. By convention positive work is that done by the system on the surroundings, and negative work is that done by the surroundings on the system, Thus since negative work results in an increase in internal energy of the system, this explains the negative sign in the above energy equation. Boundary work is evaluated by integrating the force F multiplied by the incremental distance moved dx between an initial state (1) to a final state (2). We normally deal with a piston-cylinder device, thus the force can be replaced by the piston area A multiplied by the pressure P, allowing us to replace Adx by the change in volume dV, as follows: This is shown in the following schematic diagram, where we recall that integration can be represented by the area under the curve. (area under the curve) Note that work done is a Path Function and not a property, thus it is dependent on the process path between the initial and final states. Recall in Chapter 1 that we introduced some typical process paths of interest: Isothermal(constant temperature process) Isochoric or Isometric(constant volume process) Isobaric (constant pressure process) Adiabatic (no heat flow to or from the system during the process) It is sometimes convenient to evaluate the specific work done which can be represented by a _P-v_ diagram thus if the mass of the system is m [kg] we have finally: where: P is pressure [kPa], V is volume [m 3] m is mass[kg],v is specific volume W is work done [kJ], w is specific work done We note that work done by the system on the surroundings (expansion process) is positive, and that done on the system by the surroundings (compression process) is negative. Finally for a closed system Shaft Work (due to a paddle wheel) and Electrical Work (due to a voltage applied to an electrical resistor or motor driving a paddle wheel) will always be negative (work done on the system). Positive forms of shaft work, such as that due to a turbine, will be considered in Chapter 4 when we discuss open systems. Internal Energy [u] The third component of our Closed System Energy Equation is the change of internal energy resulting from the transfer of heat or work. Since specific internal energy is a property of the system, it is usually presented in the Property Tables such as in the Steam Tables. Enthalpy [h] In the case studies that follow we find that one of the major applications of the closed system energy equation is in heat engine processes in which the system is approximated by an ideal gas, thus we will develop relations to determine the internal energy for an ideal gas. We will find also that a new property called Enthalpy will be useful both for Closed Systems and in particular for Open Systems, such as the components of steam power plants or refrigeration systems. Enthalpy is not a fundamental property, however is a combination of properties and is defined as follows: Enthalpy [kJ]: Specific Enthalpy : As an example of its usage in closed systems, consider the following constant pressure process: Applying the energy equation we obtain: However, since the pressure is constant throughout the process: Substituting in the energy equation and simplifying: (constant pressure process) Values for specific internal energy (u) and specific enthalpy (h) are available from the Steam Tables, however for ideal gasses it is necessary to develop equations for Δu and Δh in terms of Specific Heat Capacities. We develop these equations in terms of the differential form of the energy equation in the next section of this chapter (Specific Heat Capacities of an Ideal Gas). Solved Example Two kilograms of water at 25°C are placed in a piston cylinder device under 3.2 MPa pressure as shown in the diagram (State (1)). Heat is added to the water at constant pressure until the temperature of the steam reaches 350°C (State (2)). Determine the work done by the fluid (W) and heat transferred to the fluid (Q) during this process using the energy equations, then compare this value of Q to that obtained from the change in enthalpy of the system. Solution Approach: We first draw the diagram of the process including all the relevant data as follows: What? Mass? Energy? Notice the four questions to the right of the diagram, which we should always ask before attempting to solve any thermodynamic problem. What are we dealing with – liquid? pure fluid, such as steam or refrigerant? ideal gas? In this case it is steam, thus we will use the steam tables to determine the various properties at the various states. Is the mass or volume given? If so we will specify and evaluate the energy equation in kiloJoules rather than specific quantities . Since work involves the integral of Pdv we find it convenient to sketch the _P-v_ diagram of the problem as follows: boundary work Notice on the _P-v_ diagram how we determine the specific work done as the area under the process curve. We also notice that in the Compressed Liquid region the constant temperature line is essentially vertical. Thus all the property values at State (1) (compressed liquid at 25°C) can be determined from the saturated liquid table values at 25°C. State (1) – Compressed liquid State (2) – Superheated vapor Process Energy Now to compare this value with that obtained using the change in enthalpy. From the steam tables we obtain the specific enthalpy values for the water (104.8 ) and for the steam (3110.45 ). We then multiply the difference of these two values by 2kg to get our solution: Specific Heat Capacities of an Ideal Gas (1) For a simple system, internal energy (u) is a function of two independent variables, thus we assume it to be a function of temperature T and specific volume v, hence: Substituting equation (2) in the energy equation (1) and simplifying, we obtain: Now for a constant volume process (dv = 0): where: C v is the specific constant volume heat capacity That is, the specific constant volume heat capacity of a system is a function only of its internal energy and temperature. Now in his classic experiment of 1843 Joule showed that the internal energy of an ideal gas is a function of temperature only, and not of pressure or specific volume. Thus for an ideal gas the partial derivatives can be replaced by ordinary derivatives, and the change in internal energy can be expressed as: Consider now the enthalpy. By definition h = u + Pv, thus differentiating we obtain: Again for a simple system, enthalpy (h) is a function of two independent variables, thus we assume it to be a function of temperature T and pressure P, hence: Substituting equation (6) in the energy equation (5), and simplifying: Hence for a constant pressure process, since dP = 0: where: C p is the specific constant pressure heat capacity That is, the specific constant pressure heat capacity of a system is a function only of its enthalpy and temperature. Now by definition: Now since for an ideal gas Joule showed that internal energy is a function of temperature only, it follows from the above equation that enthalpy is a function of temperature only. Thus for an ideal gas the partial derivatives can be replaced by ordinary derivatives, and the differential changes in enthalpy can be expressed as: Finally, from the definition of enthalpy for an ideal gas we have: Define: (ratio of specific heat capacities) Values of R, C P, C v and k for ideal gases are presented (at 300K) in the table on Properties of Various Ideal Gases. Note that the values of C P, C v and k are constant with temperature only for mon-atomic gases such as helium and argon. For all other gases their temperature dependence can be considerable and needs to be considered. We find it convenient to express this dependence in tabular form and have provided a table of Specific Heat Capacities of Air. The Stirling Cycle Engine Conceptually the Stirling engine is the simplest of all heat engines. It has no valves, and includes an externally heated space and an externally cooled space. It was invented by Robert Stirling, and an interesting website by Bob Sier includes a photograph of Robert Stirling, his original patent drawing of 1816, and an animated model of Stirling’s original engine. In its original single cylinder form the working gas (typically air or helium) is sealed within its cylinders by the piston and shuttled between the hot and cold spaces by a displacer. The linkage driving the piston and displacer will move them such that the gas will compress while it is mainly in the cool compression space and expand while in the hot expansion space. This is clearly illustrated in the adjacent animation which was produced by Richard Wheeler (Zephyris) of Wikipedia. Refer also to the animation produced by Matt Keveney in his Stirling engine animation website. Since the gas is at a higher temperature, and therefore pressure, during its expansion than during its compression, more power is produced during expansion than is reabsorbed during compression, and this net excess power is the useful output of the engine. Note that there are no valves or intermittent combustion, which is the major source of noise in an internal combustion engine. The same working gas is used over and over again, making the Stirling engine a sealed, closed cycle system. All that is added to the system is steady high temperature heat, and all that is removed from the system is low temperature (waste) heat and mechanical power. Athens, Ohio, is a hotbed of Stirling cycle machine activity, both engines and coolers, and includes R&D and manufacturing companies as well as internationally recognized consultants in the area of Stirling cycle computer analysis. The parent company of this activity is Sunpower, Inc. It was formed by William Beale in the early 1970’s, mainly based on his invention of the free-piston Stirling engine which we describe below. Update (Jan. 2013): Sunpower was recently acquired by AMETEK, Inc. in Pensylvania, however continues doing Stirling cycle machine development in Athens, Ohio. Update (Nov. 2013): Sunpower has recently introduced a 1 kW Stirling Developers Kit based on a free piston Stirling engine fired by Propane or natural gas. Some examples of single cylinder Stirling engines:Stirling Technology Inc. is a spinoff of Sunpower, and was formed in order to continue the development and manufacture of the 5 kW ST-5 Air engine. This large single cylinder engine burns biomass fuel (such as sawdust pellets or rice husks) and can function as a cogeneration unit in rural areas. It is not a free-piston engine, and uses a bell crank mechanism to obtain the correct displacer phasing. Another important early Stirling engine is Lehmann’s machine on which Gusav Schmidt did the first reasonable analysis of Stirling engines in 1871. Andy Ross of Columbus, Ohio built a small working replica of the Lehmann machine, as well as a model air engine. Solar Heat and Power Cogeneration: With the current energy and global warming crises, there is renewed interest in renewable energy systems, such as wind and solar energy, and distributed heat and power cogeneration systems. Cool Energy, Inc. of Boulder, Colorado, is currently in advanced stages of developing a complete solar heat and power cogeneration system for home usage incorporating Stirling engine technology for electricity generation. This unique application includes evacuated tube solar thermal collectors, thermal storage, hot water and space heaters, and a Stirling engine/generator. Ideal Analysis: Please note that the following analysis of Stirling cycle engines is ideal, and is intended only as an example of First Law Analysis of closed systems. In the real world we cannot expect actual machines to perform any better than 40 – 50% of the ideal machine. The analysis of actual Stirling cycle machines is extremely complex and requires sophisticated computer analysis (see for example the course notes on: Stirling Cycle Machine Analysis.) The free-piston Stirling engine developed by Sunpower, Inc is unique in that there is no mechanical connection between the piston and the displacer, thus the correct phasing between them occurs by use of gas pressure and spring forces. Electrical power is removed from the engine by permanent magnets attached to the piston driving a linear alternator. Basically the ideal Stirling engine undergoes 4 distinct processes, each one of which can be separately analyzed, as shown in the _P-V_ diagram below. We consider first the work done during all four processes. Process 1-2 is the compression process in which the gas is compressed by the piston while the displacer is at the top of the cylinder. Thus during this process the gas is cooled in order to maintain a constant temperature T C. Work W 1-2 required to compress the gas is shown as the area under the _P-V_ curve, and is evaluated as follows. Compression process Process 2-3 is a constant volume displacement process in which the gas is displaced from the cold space to the hot expansion space. No work is done, however as we shall see below, a significant amount of heat Q R is absorbed by the gas from the regenerator matrix. Process 3-4 is the isothermal expansion process. Work W 3-4 is done by the system and is shown as the area under the _P-V_ diagram, while heat Q 3-4 is added to the system from the heat source, maintaining the gas at a constant temperature T H. Expansion process Finally, process 4-1 is a constant volume displacement process which completes the cycle. Once again we will see below that heat Q R is rejected by the working gas to the regenerator matrix. The net work, W net, done over the cycle is given by: W net = (W 3-4 + W 1-2), where the compression work W 1-2 is negative (work done on the system). We now consider the heat transferred during all four processes, which will allow us to evaluate the thermal efficiency of the ideal Stirling engine. Recall from the previous section that in order to do a First Law analysis of an ideal gas to determine the heat transferred we needed to develop equations to determine the internal energy change Δu in terms of the Specific Heat Capacities of an Ideal Gas. The two constant volume processes are formed by holding the piston in a fixed position, and shuttling the gas between the hot and cold spaces by means of the displacer. During process 4-1 the hot gas gives up its heat Q R by passing through a regenerator matrix, which is subsequently completely recovered during the process 2-3. Constant processes 1 2 and 3 4 Now from the First Law for a cycle: Thus thermal efficiency: Note that: thus we find that: We will find in Chapter 5 that this is the maximum theoretical efficiency that is achievable from a heat engine, and usually referred to as the Carnot efficiency. Note that if no regenerator is present the heat QR must be supplied by the heater. Thus the efficiency will be significantly reduced to . Furthermore the cooler will then have to reject the heat that is normally absorbed by the regenerator, thus the cooling load will be increased to Q out + Q R. Recall that Q 2-3 = Q R = -Q 4-1. Note that the practical Stirling cycle has many losses associated with it and does not really involve isothermal processes, nor ideal regeneration. Furthermore since the Free-Piston Stirling cycle machines involve sinusoidal motion, the _P-V_ diagram has an oval shape, rather than the sharp edges defined in the above diagrams. Nevertheless we use the ideal Stirling cycle to get an initial understanding and appreciation of the cycle performance. The Stirling Cycle Cooler One important aspect of Stirling cycle machines that we need to consider is that the cycle can be reversed – if we put net work into the cycle then it can be used to pump heat from a low temperature source to a high temperature sink. Sunpower, Inc. has been actively involved in the development of Stirling cycle refrigeration systems and produces Stirling cycle cryogenic coolers for liquefying oxygen. In 1984 Sunpower developed a free piston Duplex Stirling Machine having only three moving parts including one piston and two displacers, in which a gas fired Stirling cycle engine powered a Stirling cycle cooler. Global Cooling, Inc. was established in 1995 as a spinoff of Sunpower, and was formed mainly in order to develop free-piston Stirling cycle coolers for home refrigerator applications. These systems, apart from being significantly more efficient than regular vapor-compression refrigerators, have the added advantage of being compact, portable units using helium as the working fluid (and not the HFC refrigerants such as R134a, having a Global Warming Potential of 1,300). More recently Global Cooling decided to concentrate their development efforts on systems in which there are virtually no competitive systems – cooling between -40°C and -80°C, and they established a new company name: Stirling Ultracold. We are fortunate to have obtained two original M100B coolers from Global Cooling. The one is used as a demonstrator unit, and is shown in operation in the following photograph. The second unit is set up as a ME Senior Lab project in which we evaluate the actual performance of the machine under various specified loads and temperatures. The Air-Standard Diesel Cycle (Compression-Ignition) Engine The Air Standard Diesel cycle is the ideal cycle for Compression-Ignition (CI) reciprocating engines, first proposed by Rudolph Diesel over 100 years ago. The following link by the Kruse Technology Partnership describes the four-stroke diesel cycle operation including a short history of Rudolf Diesel. The four-stroke diesel engine is usually used in motor vehicle systems, whereas larger marine systems usually use the two-stroke diesel cycle. Once again we have an excellent animation produced by Matt Keveney presenting the operation of the four-stroke diesel cycle. The actual CI cycle is extremely complex, thus in initial analysis we use an ideal “air-standard” assumption, in which the working fluid is a fixed mass of air undergoing the complete cycle which is treated throughout as an ideal gas. All processes are ideal, combustion is replaced by heat addition to the air, and exhaust is replaced by a heat rejection process which restores the air to the initial state. The ideal air-standard diesel engine undergoes 4 distinct processes, each one of which can be separately analyzed, as shown in the _P-V_ diagrams below. Two of the four processes of the cycle are adiabatic processes (adiabatic = no transfer of heat), thus before we can continue we need to develop equations for an ideal gas adiabatic process as follows: The Adiabatic Process of an Ideal Gas (Q=0) The analysis results in the following three general forms representing an adiabatic process: where k is the ratio of heat capacities and has a nominal value of 1.4 at 300K for air. Process 1-2 is the adiabatic compression process. Thus the temperature of the air increases during the compression process, and with a large compression ratio (usually > 16:1) it will reach the ignition temperature of the injected fuel. Thus given the conditions at state 1 and the compression ratio of the engine, in order to determine the pressure and temperature at state 2 (at the end of the adiabatic compression process) we have: Work W 1-2 required to compress the gas is shown as the area under the _P-V_ curve, and is evaluated as follows. Adiabatic compression process An alternative approach using the energy equation takes advantage of the adiabatic process (Q 1-2 = 0) results in a much simpler process: During process 2-3 the fuel is injected and combusted and this is represented by a constant pressure expansion process. At state 3 (“fuel cutoff”) the expansion process continues adiabatically with the temperature decreasing until the expansion is complete. Process 3-4 is thus the adiabatic expansion process. The total expansion work is W exp = (W 2-3 + W 3-4) and is shown as the area under the _P-V_ diagram and is analyzed as follows: : Constant pressure expansion : Adiabatic expansion Finally, process 4-1 represents the constant volume heat rejection process. In an actual Diesel engine the gas is simply exhausted from the cylinder and a fresh charge of air is introduced. The net work W net done over the cycle is given by: W net = (W exp + W 1-2), whereas before the compression work W 1-2 is negative (work done _on_ the system). In the Air-Standard Diesel cycle engine the heat input Q in occurs by combusting the fuel which is injected in a controlled manner, ideally resulting in a constant pressure expansion process 2-3 as shown below. At maximum volume (bottom dead center) the burnt gasses are simply exhausted and replaced by a fresh charge of air. This is represented by the equivalent constant volume heat rejection process Q out = -Q 4-1. Both processes are analyzed as follows: Constant pressure expansion At this stage we can conveniently determine the engine efficiency in terms of the heat flow as follows: Again from the First Law for a cycle: Thus thermal efficiency: The Air-Standard Otto Cycle (Spark-Ignition) Engine The Air Standard Otto cycle is the ideal cycle for Spark-Ignition (SI) internal combustion engines, first proposed by Nikolaus Otto over 130 years ago, and which is currently used most motor vehicles. The following link by the Kruse Technology Partnership presents a description of the four-stroke Otto cycle operation including a short history of Nikolaus Otto. Once again we have excellent animations produced by Matt Keveney presenting both the four-stroke and the two-stroke spark-ignition internal combustion engine operation. The analysis of the Otto cycle is very similar to that of the Diesel cycle which we analyzed in the previous section. We will use the ideal “air-standard” assumption in our analysis. Thus the working fluid is a fixed mass of air undergoing the complete cycle which is treated throughout as an ideal gas. All processes are ideal, combustion is replaced by heat addition to the air, and exhaust is replaced by a heat rejection process which restores the air to the initial state. The most significant difference between the ideal Otto cycle and the ideal Diesel cycle is the method of igniting the fuel-air mixture. Recall that in the ideal Diesel cycle the extremely high compression ratio (around 18:1) allows the air to reach the ignition temperature of the fuel. The fuel is then injected such that the ignition process occurs at a constant pressure. In the ideal Otto cycle the fuel-air mixture is introduced during the induction stroke and compressed to a much lower compression ratio (around 8:1) and is then ignited by a spark. The combustion results in a sudden jump in pressure while the volume remains essentially constant. The continuation of the cycle including the expansion and exhaust processes are essentially identical to that of the ideal Diesel cycle. A schematic diagram followed by an animated schematic of the cooler (both courtesy of Global Cooling) are shown below: Conceptually the cooler is an extremely simple device, consisting essentially of only two moving parts – a piston and a displacer. The displacer shuttles the working gas (helium) between the compression and expansion spaces. The phasing between the piston and displacer is such that when the most of the gas is in the ambient compression space then the piston compresses the gas while rejecting heat to the ambient. The displacer then displaces the gas through the regenerator to the cold expansion space, and then both displacer and piston allow the gas to expand in this space while absorbing heat at a low temperature.
13255	https://math.libretexts.org/Courses/Kansas_State_University/Your_Guide_to_Intermediate_Algebra/02%3A_Introduction_to_Functions_and_Graphing/2.04%3A_Families_of_Functions	2.4.1 2.4.2 2.4.3 2.4.4 2.4.5 2.4.6 2.4.7 2.4.8 2.4.9 2.4.10 2.4.11 2.4.12 2.4.13 2.4.14 2.4.15 2.4.16 2.4.17 2.4.18 x−2−1012f(x)−5−2147(x,f(x))(−2,−5)(−1,−2)(0,1)(1,4)(2,7) x−4−2024f(x)76543(x,f(x))(−4,7)(−2,6)(0,5)(2,4)(4,3) x−3−2−10123f(x)\|−3\|+3=3+3=6\|−2\|+3=2+3=5\|−1\|+3=1+3=4\|0\|+3=0+3=3\|1\|+3=1+3=4\|2\|+3=2+3=5\|3\|+3=3+3=6(x,f(x))(−3,6)(−2,5)(−1,4)(0,3)(1,4)(2,5)(3,6) Skip to main content 2.4: Families of Functions Last updated : Aug 24, 2022 Save as PDF 2.3E: Exercises 2.4E: Exercises Page ID : 104847 ( \newcommand{\kernel}{\mathrm{null}\,}) Learning Objectives Identify families of functions based on their rule Identify families of functions based on their graphs Match functions and their graphs based on their family Families of Functions In the last few sections, we've studied functions and how we can represent them visually using a graph. So far, we've looked a wide variety of functions, and in some of the examples, you may have noticed that the resulting graphs looked really similar to each other. As it turns out, there are "families" of functions based on equations that result in specific shapes of graphs, where the only difference between them may be that they've been moved around or flipped over. In this section, we will identify the main families of functions and their graphs we are going to work with in this class. Of course, there are many more families of functions than we will talk about here, but these particular families will be the focus of our class! Linear Functions Our first family of functions is called linear functions. The "parent" function for this family is f(x)=xf(x)=x. As you may have guessed, these are the type of functions whose graphs are a straight line. The graph of f(x)=xf(x)=x looks like Graphs in this family may have different slants or be in a different location on the coordinate plane, but what they all have in common is their basic shape is a straight line. Their rules also all look similar, where the equation only has xx which may be multiplied by a constant or have a constant added to it, but that's it. Let's plot some other examples of linear functions: Example 2.4.12.4.1 Graph the following linear function using a table: f(x)=x+2f(x)=x+2 Solution First, let's make a table of ordered pairs we can plot; five points should be sufficient to create the graph xf(x)(x,f(x))−2−2+2=0(−2,0)−1−1+2=1(−1,1)00+2=2(0,2)11+2=3(1,3)22+2=4(2,4)x−2−1012f(x)−2+2=0−1+2=10+2=21+2=32+2=4(x,f(x))(−2,0)(−1,1)(0,2)(1,3)(2,4) Now let's plot the ordered pairs on a coordinate plane. Finally, we add the line. Example 2.4.22.4.2 Graph the following linear function using a table: f(x)=3x+1f(x)=3x+1 Answer : \| \| \| --- \| \| Table \| Graph \| \| xf(x)(x,f(x))−2−5(−2,−5)−1−2(−1,−2)01(0,1)14(1,4)27(2,7) \| \| Exercise 2.4.32.4.3 Graph the following linear function using a table: f(x)=−12x+5f(x)=−12x+5 Answer : \| \| \| --- \| \| Table \| Graph \| \| xf(x)(x,f(x))−47(−4,7)−26(−2,6)05(0,5)24(2,4)43(4,3) \| \| Other Linear Graphs We should also mention two other types of equations that result in graphs that are straight lines. The first is the function f(x)=af(x)=a, where aa is any number. This means that regardless of what xx is, the output is always the same. The result is a horizontal line at the height of aa since the yy components are all equal to aa. Example 2.4.42.4.4 Graph the function f(x)=2f(x)=2. Solution The graph of f(x)=2f(x)=2 is just a horizontal line at y=2y=2. Another equation that results in a straight line is the equation x=ax=a, where we only consider a single value of xx and then allow yy to be anything. This results in a vertical line at x=ax=a. However, it is important to notice that a vertical line does NOT represent a function, as it would not pass the vertical line test (the one xx value has infinitely many yy values corresponding to it!). Example 2.4.52.4.5 Graph the line x=−4x=−4 Solution The graph of x=−4x=−4 is just a vertical line at x=−4x=−4. Absolute value Our next family of functions is those that look like linear functions, but incorporate an absolute value. We might recall that the absolute values return the positive version of whatever is inside of it. Intuitively, if we have a positive number then we don't do anything; if we have a negative number then we make it into a positive. One way to think of this is as being a function that has two rules, one where we do nothing and one where we multiply negative values by a negative to make it a positive. Definition: Absolute value function f(x)=\|x\|={−xx≤0xx≥0 f(x)=\|x\|={−xxx≤0x≥0 The "parent" function for this family of functions is f(x)=\|x\|f(x)=\|x\|. It has a graph similar to the linear graph, except it has a "v" shape due to the absolute value changing the sign on half of the graph. All functions in this family will have graphs with this basic shape; however, they may be moved, flipped over (depending on how the rule has been changed, the graph may not always be positive!), or stretched. Let's look at some other examples of functions in this family. Our first example has been moved around horizontally. Example 2.4.62.4.6 Graph the following absolute value function using a table: f(x)=\|x−2\|f(x)=\|x−2\| Solution First, let's make a table to contain ordered pairs for plotting. We need to make sure include enough points to understand the shape of the graph. Since we expect the absolute value to have a "v" shape, we will use a couple more than we normally would. xf(x)(x,f(x))−2\|−2−2\|=\|−4\|=4(−2,4)−1\|−1−2\|=\|−3\|=3(−1,3)0\|0−2\|=\|−2\|=2(0,2)1\|1−2\|=\|−1\|=1(1,1)2\|2−2\|=\|0\|=0(2,0)3\|3−2\|=\|1\|=1(3,1)4\|4−2\|=\|2\|=2(4,2)x−2−101234f(x)\|−2−2\|=\|−4\|=4\|−1−2\|=\|−3\|=3\|0−2\|=\|−2\|=2\|1−2\|=\|−1\|=1\|2−2\|=\|0\|=0\|3−2\|=\|1\|=1\|4−2\|=\|2\|=2(x,f(x))(−2,4)(−1,3)(0,2)(1,1)(2,0)(3,1)(4,2) Let's plot the points. Finally, we sketch the graph. We use both the dots and the knowledge that we expect a "v" shape to do this. Our next example has been moved vertically. Example 2.4.72.4.7 Graph the following absolute value function using a table: f(x)=\|x\|+3f(x)=\|x\|+3 Answer : \| \| \| --- \| \| Table \| Graph \| \| xf(x)(x,f(x))−3\|−3\|+3=3+3=6(−3,6)−2\|−2\|+3=2+3=5(−2,5)−1\|−1\|+3=1+3=4(−1,4)0\|0\|+3=0+3=3(0,3)1\|1\|+3=1+3=4(1,4)2\|2\|+3=2+3=5(2,5)3\|3\|+3=3+3=6(3,6) \| \| One more example! This time, our graph has been moved horizontally, vertically, and flipped over! Example 2.4.82.4.8 Graph the following absolute value function using a table: f(x)=−\|x−2\|+3 Answer : \| \| \| --- \| \| Table \| Graph \| \| xf(x)(x,f(x))−3−\|−3−2\|+3=−\|−5\|+3=−(5)+3=−2(−3,−2)−2−\|−2−2\|+3=−\|−4\|+3=−(4)+3=−1(−2,−1)−1−\|−1−2\|+3=−\|−3\|+3=−(3)+3=0(−1,0)0−\|0−2\|+3=−\|−2\|+3=−(2)+3=1(0,1)1−\|1−2\|+3=−\|−1\|+3=−(1)+3=2(1,2)2−\|2−2\|+3=−\|0\|+3=−(0)+3=3(2,3)3−\|3−2\|+3=−\|1\|+3=−(1)+3=2(3,2) \| \| Quadratic Functions Our third family of functions we want to look at are the quadratic functions. These functions are the ones where the largest exponent appearing in the rule is a 2. That is, x is allowed to be squared or appear as just x, but we can't have anything that looks like x3, x4, etc in the rule. The "parent" function for this family is f(x)=x2. Similar to the absolute value function, this function has a graph that appears to have two branches reaching upward, since anything squared is positive, but it takes on more of a "U" shape since it curves smoothly around the base. All quadratic functions have this same basic shape. However, just like the absolute value based functions, the graphs of quadratic functions may appear flipped over, stretched, or moved up and down. Let's check out some other examples of quadratic functions! Our first example has been moved vertically. Example 2.4.9 Graph the following quadratic function using a table: f(x)=x2−4 Solution We start by making a table with several points to plot. Since we are expecting a "U" shape, we should use some extra points: xf(x)(x,f(x))−3(−3)2−4=5(−3,5)−2(−2)2−4=0(−2,0)−1(−1)2−4=−3(−1,−3)002−4=−4(0,−4)112−4=−3(1,−3)222−4=0(2,0)332−4=5(3,5) Plot the points on a graph. We connect the dots using a curved line, since quadratic functions all have a "U" shape, so the base of it should be rounded instead of being a corner. Let's look at another example where the exponent 2 isn't directly attached to the x. This still counts as a quadratic function because the exponent affects the x even though it is outside of parentheses! We will look at this in more detail in Section 4. In this example, the graph has been moved horizontally. Exercise 2.4.10 Graph the following quadratic function using a table: f(x)=(x+2)2 Answer : Notice that in this one, the points are a little "imbalanced", but since we know the general shape of the graph, we can be confident that the left side looks the same as the right side and we can complete the "U" shape in the sketch using that information. \| \| \| --- \| \| Table \| Graph \| \| xf(x)(x,f(x))−4(−4+2)2=(−2)2=4(−4,4)−3(−3+2)2=(−1)2=1(−3,1)−2(−2+2)2=02=0(−2,0)−1(−1+2)2=12=1(−1,1)0(0+2)2=22=4(0,4)1(1+2)2=32=9(1,9) \| \| Our next example is another format for a quadratic that includes the x2, an x term, and a constant term. This graph has been moved horizontally, vertically, and flipped over! Exercise 2.4.11 Graph the following quadratic function using a table: f(x)=−x2−2x+3 Answer : \| \| \| --- \| \| Table \| Graph \| \| xf(x)(x,f(x))−2−(−2)2−2(−2)+3=3(−2,3)−1−(−1)2−2(−1)+3=4(−1,4)0−(0)2−2(0)+3=3(0,3)1−(1)2−2(1)+3=0(1,0)2−(2)2−2(2)+3=−5(2,−5) \| \| Square root. Square root functions are closely related to quadratic functions, because as you may have already noticed, square roots "undo" squaring a number, and vice versa, squaring a number "undoes" a square root. As a result, the square root family of functions have graphs that somewhat resemble the quadratic graphs with two notable exceptions -- 1) they're sideways and 2) it's only half the graph. The "parent" functions for the square root family is f(x)=√x. Notice how the graph looks like half of the quadratic graph that's been turned on its side. The basic shape is a "swoosh", but just like with the previous families, other functions in this family may be modified so that their graph is flipped over vertically or horizontally, moved around, or stretched. There are three really important things about the square root functions to point out. Remember that when we take the square root of a number, we get both a positive and a negative answer. However, when we are thinking about square root as a function, we only want it to have ONE output, not two. In order for a square root to be considered a function, we only consider the positive results from square roots. Since every squared real number produces a positive number, going the opposite direction with a square root means we cannot take the square root of a negative number and get a real number back. That is, when we are looking at square roots as a function, we only take the square roots of positive numbers or 0. Always make the first point you graph the place where you are taking the square root of 0 to make sure the "swoosh" starts in the right place. When graphing these types of functions, it's pretty common to wind up with decimals for outputs because the inputs may not always result in taking "nice" square roots. If we want, we can choose "convenient" numbers to plug in that will always cause us to take square roots of these "nice" numbers (e.g., 0, 1, 4, 9, 16, etc), or we can just deal with the decimals. It's entirely up to you! Our first example has been moved horizontally. Example 2.4.12 Graph the following square root function using a table: f(x)=√x+1 Solution We first make the table with points to plot. Notice that since inside the square root is x+1, starting at x=−1 is fine because −1+1=0, which we are allowed to take the square root of! This will be the first point we want to include on the table. From here, we'd like to take square roots of the "nice" squared numbers 1, 4, and 9. So we want to plug in x=0,3, and 8. xf(x)(x,f(x))−1√−1+1=√0=0(−1,0)0√0+1=√1=1(0,1)3√3+1=√4=2(3,2)8√8+1=√9=3(8,3) Now we plot the points. We complete the graph by knowing that it starts at (-1, 0), and then must follow the "swoosh" shape to the right. Let's look at a version of the graph that has been moved around both horizontally and vertically. Example 2.4.13 Graph f(x)=√x+1−2 by plotting points. Answer : In regards to the table, notice that once again since inside the square root is x+1, starting at x=−1 is fine because −1+1=0, which we are allowed to take the square root of! This will be the first point we want to include on the table. From here, we'd like to take square roots of the "nice" squared numbers 1, 4, and 9. So we want to plug in x=0,3, and 8. \| \| \| --- \| \| Table \| Graph \| \| xf(x)(x,f(x))−1√−1+1−2=√0−2=−2(−1,−2)0√0+1−2=√1−2=−1(0,−1)3√3+1−2=√4−2=0(3,0)8√8+1−2=√9−2=1(8,1) \| \| Finally, let's look at an example where the square root "swoosh" has been moved horizontally, vertically, and flipped over. Exercise 2.4.14 Graph the following square root function using a table: f(x)=−√x+1−2 Answer : \| \| \| --- \| \| Table \| Graph \| \| xf(x)(x,f(x))−1−√−1+1−2=−√0−2=−2(−1,−2)0−√0+1−2=−√1−2=−3(0,−3)3−√3+1−2=−√4−2=−4(3,−4)8−√8+1−2=−√9−2=−5(8,−5) \| \| Quotient graph Our last family of functions is the quotient function. Quotient is just the math way of saying division, and these functions get their name from dividing by the input x. The parent function for this family is f(x)=1x. The graph of f(x)=1x is really distinct because unlike the previous functions, its graph has two pieces, and not just one. The two pieces show up because if you'll remember, we cannot divide by x=0. This means there is a gap in the horizontal direction whenever 0 may appear in the denominator of one of these functions. There is also a gap in the vertical direction due to the fact that nothing we divide by can ever cause the entire function to equal zero. These gaps have a special name: Definition: Asymptote A horizontal asymptote is the horizontal line that the graph approaches as x→±∞. A vertical asymptote is the vertical line that the graph approaches as the denominator approaches 0. Let's look at some other examples of functions that are in this family, starting with one that has been moved around vertically. Example 2.4.15 Graph the following quotient function using a table: f(x)=1x+4 Solution First, we make a table. With these kinds of functions, fractions will be a necessity to understand their general shape! Also, since there are two pieces to the graph, we want to make sure to use enough points to capture both pieces! xf(x)(x,f(x))−31−3+4=−13+4=113(−3,113)−21−2+4=−12+4=72(−2,72)−11−1+4=−1+4=3(−1,3)−121−1/2+4=−2+4=2(−12,2)−131−1/3+4=−3+4=1(−13,1)0???+4=??? draw vertical gap line at x=01311/3+4=3+4=7(13,7)1211/2+4=2+4=6(12,6)111+4=1+4=3(1,5)212+4=12+4=92(2,92)313+4=13+4=133(3,133) The vertical asymptote goes at the x value that make the denominator zero. In this example, the denomator is zero when x=0, so we can add a dashed line at x=0 to remind ourselves we don't want to graph there. The horizontal asymptote goes at the y value that each part of the graph are approaching. In this example, each half of the graph will approach y=4, so we can add a dashed line at y=4 to remind ourselves that we don't want to graph there. Now we plot the points and asymptotes. When we add the lines, we have the two curves, where the curves follow the points AND asymptotes. We can shift this graph too. Lets shift it in the same way as we did with √x. Example 2.4.16 Graph f(x)=1x+1−2 by plotting points. Answer : \| \| \| --- \| \| Table \| Graph \| \| xf(x)(x,f(x))−31−3+1−2=1−2−2=−52(−3,−52)−21−2+1−2=1−1−2=−3(−2,−3)−11−1+1−2=???−2=??? draw vertical gap line at x=−1 −121−1/2+1−2=11/2−2=0(−12,0)−131−1/3+1−2=32−2=−12(−13,−12)010+1−2=1−2=−1(0,−1)1311/3+1−2=34−2=−54(13,−54)1211/2+1−2=23−2=−43(12,−43)111+1−2=12−2=−32(1,−32)212+1−2=12+1−2=−53(2,−53)313+1−2=14−2=−74(3,−74) \| \| Here we see that x=-1 is a vertical asymptote and y=-2 is a horizontal asymptote. Identifying Graphs of Families of Functions The main point of this section is to highlight the fact that graphs of certain functions always appear a certain way, dependent on the key feature present in the rule. Being able to identify which type of graph goes with which type of function can really help your intuition for what is happening in the long run in this class! So we conclude with some examples of how you can match a function to its graph and vice versa simply based on what type of function it is. Example 2.4.17 Identify what family of functions each graph belongs to and then match it to the correct function. \| \| \| --- \| \| Graph \| Function \| \| a. \| 1. f(x)=2x−3 \| \| b. \| 2. f(x)=1x+3 \| \| c. \| 3. f(x)=−(x−4)2+3 \| \| \| f(x)=2\|x−2\|+4 \| Solution The first graph represents an absolute value function. Therefore, it must have come from the function f(x)=2\|x−2\|+4, option (4). The second graph represents a quotient function. Therefore, it must have come from the function f(x)=1x+3, option (2). The third graph represents a linear function. Therefore, it must have come from the function f(x)=2x−3, option (1). The final graph represents a quadratic function. Therefore, it must have come from the function f(x)=−(x−4)2+3, option (3). Try it out on your own! Exercise 2.4.18 Identify what family of functions each graph belongs to and then match it to the correct function. \| \| \| --- \| \| Graph \| Function \| \| a. \| 1. f(x)=−\|x−3\|−1 \| \| b. \| 2. f(x)=−2 \| \| c. \| 3. f(x)=1x−4+2 \| \| d. \| 4. f(x)=√−x+5−3 \| Answer : 1. The first graph represents a linear function. Therefore, it must have come from the function f(x)=−2, option (2). 2. The second graph represents an absolute value function. Therefore, it must have come from the function f(x)=−\|x−3\|−1, option (1). 3. The third graph represents a quotient function. Therefore, it must have come from the function f(x)=1x−4+2, option (3). 4. The final graph represents a square root function. Therefore, it must have come from the function f(x)=√−x+5−3, option (4). Key Concepts Functions can be grouped into families according to the main features in their rules. These main features control how functions appear when graphed, and therefore functions of the same family all have graphs with the same basic shape. \| \| \| \| --- \| Family \| Parent Function \| Basic Shape (graph of parent function) \| \| \| f(x)=x \| \| \| Absolute Value \| f(x)=\|x\| \| \| \| \| f(x)=x2 \| \| \| Square Root \| f(x)=√x \| \| \| \| f(x)=1x \| \| 2.3E: Exercises 2.4E: Exercises
13256	https://www.quora.com/How-do-I-find-a-tangent-line-with-a-derivative	Something went wrong. Wait a moment and try again. Meaning of Derivatives Mathematical Concepts Tangent Planes Geometric Lines Calculus (Mathematics) Derivatives and Integrati... Tangent Graph Tangent Lines 5 How do I find a tangent line with a derivative? Graham Dolby Author has 3.2K answers and 1.7M answer views · 4y If you have a point (a,f(a)) and determined the derivative at this point f′(a), then an equation of the tangent is y=f′(a)(x−a)+f(x). E.g. f(x)=x2−x,f′(x)=2x−1,f(2)=2,f′(2)=3→y=3(x−2)+2→y=3x−4 If you have a point (a,f(a)) and determined the derivative at this point f′(a), then an equation of the tangent is y=f′(a)(x−a)+f(x). E.g. f(x)=x2−x,f′(x)=2x−1,f(2)=2,f′(2)=3→y=3(x−2)+2→y=3x−4 Related questions How do I find the vertical tangent line? How do I find the tangent line in calculus? What is the derivative of tangent? How do we use differentiation to find the equation of a tangent line? Is the slope of a tangent line the derivative? Awnon Bhowmik Studied at University of Dhaka · Author has 3.7K answers and 11.2M answer views · 7y Related How can a derivative have a second derivative? In other words, how can a tangent line have a derivative? A2A Derivative changes at every point on a curve. This is why we define the derivative at any point x=c of an arbitrary function y=f(x) it as the slope of the tangent line at x=c, and this is written as f′(c). Now, consider a 3rd degree polynomial. Taking successive derivatives of a polynomial reduces its degree by one. Notice how the cubic turns into a quadratic and then to a straight line. Now I don’t have to tell you that if I take the third derivative This gives us a horizontal line. Now, lets work backwards. Notic A2A Derivative changes at every point on a curve. This is why we define the derivative at any point of an arbitrary function it as the slope of the tangent line at , and this is written as . Now, consider a 3rd degree polynomial. Taking successive derivatives of a polynomial reduces its degree by one. Notice how the cubic turns into a quadratic and then to a straight line. Now I don’t have to tell you that if I take the third derivative This gives us a horizontal line. Now, lets work backwards. Notice the and ? Do you see that the third derivative is the slope of the straight line that is defined by ? This is because we cannot draw a tangent to a straight line. Drawing a tangent line at any point of a straight line will be co-linear with the original. Do I need to explain any more? Subhasish Debroy Former SDE at Bharat Sanchar Nigam Limited (BSNL) · Author has 6.6K answers and 5.8M answer views · 4y Find the derivative of the curve at the point of tangency which indicates the slope of tangent of the curve at the said point (say x1,y1). As the tangent passes through the said point (x1,y1) with slope m1 already determined , eqn of tangent , y –y1 = m1(x–x1). Mark Eichenlaub physics curriculum developer at Art of Problem Solving · Upvoted by James Moosh , PhD in Pure Maths from the University of Leeds and Jay Wacker , theoretical physicist · Author has 393 answers and 10.3M answer views · 13y Related Derivatives and Differentiation (mathematics): How do I find the slope of a tangent line? A slope is rise/run. "Rise" means the change in the y-coordinate. "Run" means the change in the x-coordinate. These changes are found by subtraction, so for example the slope between the points (3,5) and (7,2) is The function you named looks like this The tangent line a the origin looks like this: The red dot is at the point (0, -4). Unfortunately, this does not let us compute the slope. We would need two points to do that, and we only have one. We could try to guess another point by picking one that looks like it's on the line, but we might be off by a lit A slope is rise/run. "Rise" means the change in the y-coordinate. "Run" means the change in the x-coordinate. These changes are found by subtraction, so for example the slope between the points (3,5) and (7,2) is The function you named looks like this The tangent line a the origin looks like this: The red dot is at the point (0, -4). Unfortunately, this does not let us compute the slope. We would need two points to do that, and we only have one. We could try to guess another point by picking one that looks like it's on the line, but we might be off by a little if we didn't draw the line just right. Instead, a more systematic way to estimate the slope is to choose another point on the original graph, like this: The red line here is not a perfect tangent line. It's a secant line. It goes through two nearby points. It is pretty close to the tangent line, but not exact. To get a better approximation, we should put the two points closer together, like this: That's still not perfect, though. We'd like to get the two points closer and closer and closer... To do that, we calculate the slope not for two concrete points, such as x = -3 and x = -3.01, but for one concrete point, and one point a tiny, but unknown distance away. That tiny distance is called "h". So the first point is x, the second is x + h. We now have two points and want to find the slope between them. The height of the graph at the first point (in your original example it's x = 0) is f(x). The value at the second is f(x+h). Subtracting them gives the difference in their heights - the rise. The difference horizontally, the run, is just h because that is the definition of h. Now we can find the slope between the two points via rise/run. That is the origin of the formula However, the slope we find depends on what h is. In the last two pictures, h is bigger in the first and smaller in the second. The true tangent line is when h becomes as small as possible. We can't just start out with h=0, though, because that would mean the two points are on top of each other and there is no slope between them. Instead, we look at the limit as h goes to zero. For example, with h=1 we get a slope of 0. With h = 0.1 we get -0.9. With h= 0.01 we get -0.99 etc. It appears that in the limit as h goes to zero, the slope goes to -1. In the particular calculation you showed, they find that the slope between a point at x and a point at x+h is 2x + h - 1. In the limit as h->0, this expression just becomes 2x - 1. When x = 0, it's -1. That's the slope of the tangent at x = 0. The precise meaning of "in the limit" from the phrase "in the limit where h goes to zero" is subtle enough that for a long time, mathematicians did calculus without a rigorous definition of what it meant. You may learn it later on in your course, but for now it is best just to try to get an intuitive feeling for "in the limit of", and worry about the details later. 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What is the process of finding tangent lines and normals using derivatives? Assistant Bot · Sep 6 To find the equation of a tangent line to the graph y = f(x) at a point x = a, use the derivative to obtain the slope and the point-slope form to write the line. Steps: Identify the point of tangency If given x = a, compute the point: (a, f(a)). If given a point (x0, y0) on the curve, set a = x0 and verify y0 = f(x0). Compute the slope (derivative) Calculate f '(x) using differentiation rules (power, product, quotient, chain, implicit differentiation, etc.). Evaluate the slope at a: m = f '(a). Write the tangent-line equation (point-slope form) Use point-slope: y − f(a) = m (x − a). O To find the equation of a tangent line to the graph y = f(x) at a point x = a, use the derivative to obtain the slope and the point-slope form to write the line. Steps: Identify the point of tangency If given x = a, compute the point: (a, f(a)). If given a point (x0, y0) on the curve, set a = x0 and verify y0 = f(x0). Compute the slope (derivative) Calculate f '(x) using differentiation rules (power, product, quotient, chain, implicit differentiation, etc.). Evaluate the slope at a: m = f '(a). Write the tangent-line equation (point-slope form) Use point-slope: y − f(a) = m (x − a). Or expand to slope-intercept: y = m x + b, where b = f(a) − m a. Examples: Example 1: f(x) = x^2, a = 2 f(a) = 4. f '(x) = 2x ⇒ f '(2) = 4. Tangent: y − 4 = 4(x − 2) ⇒ y = 4x − 4. Example 2: f(x) = sin x, a = π/4 f(a) = √2/2. f '(x) = cos x ⇒ f '(π/4) = √2/2. Tangent: y − √2/2 = (√2/2)(x − π/4). Example 3 (implicit curve): x^2 + y^2 = 25 at point (3,4) Differentiate implicitly: 2x + 2y y' = 0 ⇒ y' = −x/y. Slope at (3,4): m = −3/4. Tangent: y − 4 = −3/4 (x − 3). Notes and common pitfalls If derivative f '(a) is undefined (vertical tangent), the tangent may be vertical: x = a. For parametric curves x(t), y(t): slope = (dy/dt)/(dx/dt) evaluated at the parameter value, then use point-slope with (x(t0), y(t0)). For functions with corners or cusp points, no tangent line exists because the derivative doesn't exist there. Always confirm the point lies on the curve before forming the tangent. These steps cover explicit, implicit and parametric cases; apply the appropriate differentiation method and substitute the point to obtain the tangent line. B. S. Thomson Lived in Vancouver, BC · Author has 1.2K answers and 2.9M answer views · 3y Related How does the derivative of a function relate to the slope of the tangent line? When I was a child (and no doubt things have not changed much in mathematics instruction) I was told that the tangent line “touches” the curve at one point. If you were a child in the 18th century (I wasn’t) you might have been told about Leibnitz’s claim that the tangent line is that line through two “infinitely close” points on the curve. I thought I understood tangents, but in reality I couldn’t manage tangents to any other curves than circles. I could imagine them for ellipses and other conic sections but not at a technical level. This persisted in calculus. Pictures showing tangents and slo When I was a child (and no doubt things have not changed much in mathematics instruction) I was told that the tangent line “touches” the curve at one point. If you were a child in the 18th century (I wasn’t) you might have been told about Leibnitz’s claim that the tangent line is that line through two “infinitely close” points on the curve. I thought I understood tangents, but in reality I couldn’t manage tangents to any other curves than circles. I could imagine them for ellipses and other conic sections but not at a technical level. This persisted in calculus. Pictures showing tangents and slopes were related to derivatives and I was somehow convinced that the derivative was the slope of the tangent line. But in fact I didn’t have a clue as to what that really meant. If I couldn’t define “tangent” how could I accept the argument that the derivative was the slope of the tangent? Then all of that nonsense suddenly stopped. Definition. If a continuous function [math]f:\mathbb R\to\mathbb R [/math] is differentiable at a point [math]x_0 [/math] then the tangent line to the curve [math]y=f(x) [/math] is defined to be the straight line through math [/math] with slope [math]f’(x_0) [/math]. Your question makes no sense until you know what “tangent” really means and then, as soon as you know what it means, the question again loses any meaning since it is simply the definition. Some nonsense. There are many calculus “lessons” online that promote the phrase “tangent line touches the curve at one point.” Same nonsense my teachers drilled. Every calculus student should know this example: The horizontal axis [math]y=0 [/math] is the tangent to the curve [math]y=x^2\sin\frac1x [/math] at math [/math]. Curiously it is the only line that does not “touch” the curve, but intersects infinitely often near math[/math]. The ones that do “touch at one point” are not tangents. Gary Ward MaEd in Education & Mathematics, Austin Peay State University (Graduated 1997) · Author has 4.9K answers and 7.6M answer views · 3y Related How do I find the tangent line in calculus? How do I find the tangent line in calculus? The first derivative relative to x will give you a formula to find the slope at any x-value if the function exists for that x-value and is a smooth curve at that point. The first derivative relative to y will give you a formula to find the slope at any y-value if the function exists for that y-value and is a smooth curve at that point. Use the curves below for examples. The red curve looks like a function because it passes the vertical line test. y = 0.25x^3 - 4x is its equation; y’ = 0.75x² - 4 is the first derivative. Find the tangent at x = -2; y = 0.25 How do I find the tangent line in calculus? The first derivative relative to x will give you a formula to find the slope at any x-value if the function exists for that x-value and is a smooth curve at that point. The first derivative relative to y will give you a formula to find the slope at any y-value if the function exists for that y-value and is a smooth curve at that point. Use the curves below for examples. The red curve looks like a function because it passes the vertical line test. y = 0.25x^3 - 4x is its equation; y’ = 0.75x² - 4 is the first derivative. Find the tangent at x = -2; y = 0.25(-2)^3 - 4(-2) → y = -2 + 8 = 6 Tangent at (-2, 6) y’ = 0.75(-2)² - 4 = 3 - 4 = -1 The tangent’s equation is y - 6 = (-1)(x + 2) → y = 4 -x (y - 1)² = 4(x + 4) looks like a parabola and since the y-term is squared and positive it opens to the right. This would fail the vertical line test, but pass the horizontal line test, so solve it for x x = y²/4 - ½y -15/4; The first derivative is x’ = y/2 - ½ If we want the tangent at y = 7 then x = (7)²/4 - (7)/2 - 15/4 = (49 - 14 - 15)/4 = 20/4 = 5 so (5, 7) If we solve for x’ = (7)/2 - ½ = 3 we have the inverse slope relative to the x-axis, so slope is 1/3 y - 7 = (1/3)(x - 5) = x/3 -5/3 → y = x/3 + 16/3 is the equation of the tangent to the curve at (5, 7). Sponsored by Grammarly Is your writing working as hard as your ideas? Grammarly’s AI brings research, clarity, and structure—so your writing gets sharper with every step. Bob Collier Former EE Designed Specialized Computers for 33 Years. · Author has 3.1K answers and 1.6M answer views · 2y Related How can you use the definition of the derivative to find the tangent line to a curve at a point? If you are not willing to do the derivative thing, then draw the tangent line where you are interested and then draw large delta-x and delta-y lines above or below the line convenient to measure lengths and calculate slope of that line delta-y / delta-x. The definition would have you use very small deltas - terrible idea if you actually need to do it by hand. Or you could actually just do the arithmetic Maybe that’s not such a bad idea. Instead of guessing how tangent your freehand line is, calculate f(x1) & f(x2) where x1 = x0-d and x2 = x0+d and d is very small. Then f’(x0) = [f(x2) - f(x1)]/(2d) [de If you are not willing to do the derivative thing, then draw the tangent line where you are interested and then draw large delta-x and delta-y lines above or below the line convenient to measure lengths and calculate slope of that line delta-y / delta-x. The definition would have you use very small deltas - terrible idea if you actually need to do it by hand. Or you could actually just do the arithmetic Maybe that’s not such a bad idea. Instead of guessing how tangent your freehand line is, calculate f(x1) & f(x2) where x1 = x0-d and x2 = x0+d and d is very small. Then f’(x0) = [f(x2) - f(x1)]/(2d) [definition] B. S. Thomson Lived in Vancouver, BC · Author has 1.2K answers and 2.9M answer views · 1y Related Derivatives give the slope of tangent line. But is there the mathematical demonstration which assures us that the secant lines tend to the tangent when you approach the two points? Some comments about this one, relevant to many of the questions posed here from calculus students. Derivatives give the slope of tangent line. Well no. That is backwards. In your calculus textbook the tangent line is defined by the derivative. The derivative comes first. When you first walked in the door of a calculus class you didn't know beans about tangents, although you imagined you did since your grade seven teacher bluffed his way through that stuff. It was usually some mess about "lines" that "touch" a curve. Not mathematics. All that fluffy stuff in class about "tangent lines" and "slop Some comments about this one, relevant to many of the questions posed here from calculus students. Derivatives give the slope of tangent line. Well no. That is backwards. In your calculus textbook the tangent line is defined by the derivative. The derivative comes first. When you first walked in the door of a calculus class you didn't know beans about tangents, although you imagined you did since your grade seven teacher bluffed his way through that stuff. It was usually some mess about "lines" that "touch" a curve. Not mathematics. All that fluffy stuff in class about "tangent lines" and "slopes" was motivation for a precise definition of derivative. Nice pictures. Maybe intuitive. But in the end you learn the definitions. Then the slope of the tangent line is defined by derivatives. Derivatives "give" the slope of the tangent line only for a completely trivial reason: it is defined to be that way. The secant lines tend to the tangent when you approach the two points. Sorry, more fluff. More intuitive, hand waving. The definition of the derivative depends on a precise understanding of function limits. You are asking about lines converging to lines. Really? It is tough enough at this level to understand limits of functions at a point. You are miles away from any theory about curves or lines "tending" to anything. So there is no mathematical proof available for your question without a serious definition about the convergence of curves...and no calculus student is remotely prepared for that. Understand that, if someone has given you [like I see here] an animation of lines "tending" to other lines is was for intuitive purposes only. You definitely do not want to learn a rigorous definition for anything like this in a calculus class. ————————————- Parable. An enthusiastic middle school teacher is giving a lesson on circles. She arrives with plates, frisbees, graphs of circles, protractors, etc. and group activities with students in circles with one student in the center. Finally near the end of the class she presents the definition: A circle is the locus of points equidistant from a fixed point called the center of the circle. On the final exam she asks for the definition of a circle. All students answer "Circles are round." One student only draws a pizza. Sponsored by CDW Corporation What does your AI strategy look like? CDW can help you define a clear strategy with actionable steps for AI adoption success. Peter Shea B. Sc in Mathematics & Computer Science, Monash University (Graduated 1972) · Author has 5.2K answers and 1.2M answer views · 1y Related What is the process of finding tangent lines and normals using derivatives? Define a point for your tangent, e.g. “(x₀, y₀) is the intersection of f(x) with…”. Evaluate the slope at that point, e.g. m = df/dx at x₀. For the tangent, Solve y₀ = mx₀ + c for c. This will give you the tangent equation at (x₀, y₀). For the normal, Solve y₀ = -x₀/m + c for c. This will give you the normal equation at (x₀, y₀). Philip Lloyd Specialist Calculus Teacher, Motivator and Baroque Trumpet Soloist. · Author has 6.8K answers and 52.8M answer views · 1y Related How is the derivative used in finding maximums and minimums? How do you find a line tangent to a curve? This is a huge question to answer fully! Maxima and minima are also called TURNING points or STATIONARY points. ————————————————————————————————————— Consider the gradient of this curve at points along the curve: The above diagrams show that the gradient is zero when the curve has a maximum or minimum point. I should mention a special case when the gradient can be zero too! This is a huge question to answer fully! Maxima and minima are also called TURNING points or STATIONARY points. ————————————————————————————————————— Consider the gradient of this curve at points along the curve: The above diagrams show that the gradient is zero when the curve has a maximum or minimum point. I should mention a special case when the gradient can be zero too! Alfred Dominic Vella Life long educator in mathematics, computing and the sciences · Author has 4.7K answers and 4.4M answer views · 9y Related How does one find the equation of the tangent line to the function? Find the tangent line to the function h(x) = x^2 + 5x - 3 which is parallel to the secant line between (0,h(0) and (5,h(5)) I do not think that it is healthy to think of how these are solved as that means that you do not get used to thinking out of the box and cannot solve new problems. Now we ask ourselves three questions: a) What do we know? i) h(x) = x^2 + 5x - 3 ii) the secant goes between (0,h(0) and (5,h(5)) iii) the tangent is parallel to the secant b) What are we allowed to do? This is open ended and depends upon your skills so lets skip this but bear it in mind. c) What can we do that uses Find the tangent line to the function h(x) = x^2 + 5x - 3 which is parallel to the secant line between (0,h(0) and (5,h(5)) I do not think that it is healthy to think of how these are solved as that means that you do not get used to thinking out of the box and cannot solve new problems. Now we ask ourselves three questions: a) What do we know? i) h(x) = x^2 + 5x - 3 ii) the secant goes between (0,h(0) and (5,h(5)) iii) the tangent is parallel to the secant b) What are we allowed to do? This is open ended and depends upon your skills so lets skip this but bear it in mind. c) What can we do that uses what we know and takes us nearer to an answer? we can use i) and ii) to make ii) stronger - more specific iia) the secant goes between (0,h(0) and (5,h(5)) ie between (0, -3) and (5, 47) iiia) iii) tells us that the tangent is parallel to the secant so it has the same gradient which is math/(5 - 0) = 10[/math] Now we are looking for a line which touches h() and has gradient 10. The line [math]y = 10x + c[/math] could be such a line if we can find c. It crosses h() when [math]10x + c = x^2 + 5x - 3[/math] So when [math]x^2 - 5x - (c + 3) = 0[/math] We can use the quadratic formula to find the values of [math]x[/math] where the crossing takes place but we want just one crossing so that the formula must give us one. This happens when [math]5^2 + 4(c + 3) = 0[/math] That is when [math]25 + 12 = -4 c[/math] [math]c = -37/4[/math] So the tangent is y = 10x - 37/4 I might have slipped up or you might have slipped up so please check, its good for you ;) Thanks to Sin Keong Tong for pointing out the error in the original post. The diagram below is a general one - not to be taken literally. Dean Rubine Author of: It's not just π; all of trig is wrong! · Author has 10.6K answers and 23.6M answer views · 1y Related I am told to find the equation of the line of tangent, but how do I figure out the gradient of the tangent? That’s called calculus; you take the derivative and evaluate it at the tangent point. I use algebra. Let’s say we have a random algebraic curve with an integer point, say [math]f(x,y)=y^4 - 3xy^2 -x^2 + 9= 0[/math] tangent at math=(2,1)[/math] Let’s do the general case. We write [math]f(x,y) = f( r+ (x-r), s+(y-s)) = f(r+X, s+Y)[/math] where [math]X=x-r, Y=y-r[/math] [math]f(x,y)=(s+Y)^4 - 3(r+X)(s+Y)^2 -(r+X)^2 + 9[/math] [math]f(x,y)=(s^4+4s^3Y+ 6s^2Y^2+ 4sY^3+Y^4) - (3rs^2+6rsY+3rY^2 + \ \quad 3s^2X+6sXY+3Y^2) -(r^2+2rX + X^2) + 9[/math] [math]f(x,y)=(s^4 -3rs^2 - r^2 + 9) + (-3s^2-2r)X + (4s^3-6rs)Y \ \quad + X^2+ (6s^2-3r)Y^2-6sXY + 4sY^3-3XY^2 +Y^4[/math] [math]X[/math] and [math]Y[/math] are small w That’s called calculus; you take the derivative and evaluate it at the tangent point. I use algebra. Let’s say we have a random algebraic curve with an integer point, say [math]f(x,y)=y^4 - 3xy^2 -x^2 + 9= 0[/math] tangent at math=(2,1)[/math] Let’s do the general case. We write [math]f(x,y) = f( r+ (x-r), s+(y-s)) = f(r+X, s+Y)[/math] where [math]X=x-r, Y=y-r[/math] [math]f(x,y)=(s+Y)^4 - 3(r+X)(s+Y)^2 -(r+X)^2 + 9[/math] [math]f(x,y)=(s^4+4s^3Y+ 6s^2Y^2+ 4sY^3+Y^4) - (3rs^2+6rsY+3rY^2 + \ \quad 3s^2X+6sXY+3Y^2) -(r^2+2rX + X^2) + 9[/math] [math]f(x,y)=(s^4 -3rs^2 - r^2 + 9) + (-3s^2-2r)X + (4s^3-6rs)Y \ \quad + X^2+ (6s^2-3r)Y^2-6sXY + 4sY^3-3XY^2 +Y^4[/math] [math]X[/math] and [math]Y[/math] are small when math[/math] is near math[/math], exactly the case we’re interested in to find the tangent at math[/math]. Note the constant is [math]f(r,s)[/math], presumably zero as math[/math] is presumed on the curve. To approximate [math]f(x,y)=0[/math] linearly, we drop the higher order terms of the small differences and set the whole thing to zero: [math]0 = (-3s^2-2r)(x-r) + (4s^3 -6rs)(y-s)[/math] That’s the tangent line at math.[/math] It’s often the object we’re after, but this question asks for the slope, which is [math]m = \dfrac{3s^2+2r}{4s^3 - 6rs}[/math] At math=(2,1)[/math] we get a tangent line of [math]0 = (-3(1)^2-2(2))(x-2) + (4(1)^3 -6(2)(1))(y-1)[/math] [math] -7x - 8y = -7(2) -8(1) = -22[/math] The slope is [math]m= -\dfrac 7 8[/math] We can go farther with our middle school calculus that only uses algebra. How about the tangent conic at math[/math]. There are many; let’s do the one we get by keeping all terms up to second degree: [math]0= (-3s^2-2r)(x-r) + (4s^3-6rs)(y-s) + (x-r)^2 \ \qquad + (6s^2-3r)(y-s)^2-6s(x-r)(y-s)[/math] Setting [math]x=2, y=-1[/math] gives: [math]x^2 + 6 x y - 5 x - 4 y + 14 = 0[/math] That’s a hyperbola. Let’s plot our curve and our tangents to end this adventure in middle school calculus. plot xy=0, y^4 - 3xy^2 -x^2 + 9= 0, 7x+8y=22 , x^2 + 6 x y - 5 x - 4 y + 14 = 0 Related questions How do I find the vertical tangent line? How do I find the tangent line in calculus? What is the derivative of tangent? How do we use differentiation to find the equation of a tangent line? Is the slope of a tangent line the derivative? How can you use the definition of the derivative to find the tangent line to a curve at a point? Why can't we differentiate between two points on a curve, and what does this mean for finding derivatives (e.g., tangent lines)? How do I find the slope of a tangent line using derivatives? What is the use of the derivative beside using it to find the slope of a tangent line? What is the process of finding tangent lines and normals using derivatives? How do you find the tangent line approximation? How can a derivative have a second derivative? In other words, how can a tangent line have a derivative? Why do we use the tangent method to find the derivative? Why is the derivative the slope of the tangent? How do you find the tangent line of a function? About · Careers · Privacy · Terms · Contact · Languages · Your Ad Choices · Press · © Quora, Inc. 2025
13257	https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Introductory_Electrical_Engineering/A_First_Course_in_Electrical_and_Computer_Engineering_(Scharf)/05%3A_Vector_Graphics/5.06%3A_Three-Dimensional_Homogeneous_Coordinates	Skip to main content 5.6: Three-Dimensional Homogeneous Coordinates Last updated : May 22, 2022 Save as PDF 5.5: Homogeneous Coordinates 5.7: Projections Buy Print CopyView on Commons Donate Page ID : 9980 Louis Scharf Colorado State University via OpenStax CNX ( \newcommand{\kernel}{\mathrm{null}\,}) We now consider the storage and manipulation of three-dimensional objects. We will continue to use homogeneous coordinates so that translation can be included in composite operators. Homogeneous coordinates in three dimensions will also allow us to do perspective projections so that we can view a three-dimensional object from any point in space. Image Representation The three-dimensional form of the point matrix in homogeneous coordinates is The line matrix is exactly as before, pointing to pairs of columns in to connect with lines. Any other grouping matrices for objects, etc., are also unchanged. Image manipulations are done by a 4×4 matrix . To ensure that the fourth coordinate remains a 1, the operator must have the structure The new image has point matrix Exercise If the coordinates of the point in are , what are the coordinates of the point in when is as given in Equation 2? Exercise Write down the point matrix for the unit cube (the cube with sides of length 1, with one corner at the origin and extending in the positive direction along each axis). Draw a sketch of the cube, numbering the vertices according to their order in your point matrix. Now write down the line matrix to complete the representation of the cube. Left- and Right-Handed Coordinate Systems In this book we work exclusively with right-handed coordinate systems. However, it is worth pointing out that there are two ways to arrange the axes in three dimensions. Figure 1(a) shows the usual right-handed coordinates, and the left-handed variation is shown in Figure 1(b). All possible choices of labels , , and for the three coordinate axes can be rotated to fit one of these two figures, but no rotation will go from one to the other. Be careful to sketch a right-handed coordinate system when you are solving problems in this chapter. Some answers will not be the same for a left-handed system. Image Transformation Three-dimensional operations are a little more complicated than their two-dimensional counterparts. For scaling and translation we now have three independent directions, so we generalize the operators of Equation 10 from "Vector Graphics: Homogeneous Coordinates" as Exercise Show that T is the inverse of T undoes the work of . Rotation may be done about any arbitrary line in three dimensions. We will build up to the general case by first presenting the operators that rotate about the three coordinate axes. R rotates by angle about the x-axis, with positive going from the y-axis to the z-axis, as shown in Figure 2. In a similar fashion, positive rotation about the y-axis using R goes from to , and positive rotation about the z-axis goes from to , just as in two dimensions. We have the fundamental rotations A more general rotation about any line through the origin can be constructed by composition of the three fundamental rotations. Finally, by composing translation with the fundamental rotations, we can build an operator that rotates about any arbitrary line in space. Figure :Directions of Positive Rotation Example To rotate by angle about the line , which lies in the plane in Figure 3, we would rotate to the x-axis with R; rotate by about the x-axis with R; and rotate back to with R. The composite operation would be Figure : Composition of Rotations Direction Cosines As discussed in the chapter on Linear Algebra, a vector vv may be specified by its coordinates or by its length and direction. The length of is \|\|\|\|, and the direction can be specified in terms of the three direction cosines . The angle is measured between the vector and the x-axis or, equivalently, between the vector and the vector . We have Likewise, is measured between and , and is measured between and Missing superscript or subscript argumente_z=^. Thus The vector s a unit vector in the direction of , so we have Exercise Show that is a unit vector (i.e. 1 u\|\|=1u\|\|=1). The direction cosines are useful for specifying a line in space. Instead of giving two points and on the line, we can give one point plus the direction cosines of any vector that points along the line. One such vector is the vector from to . Arc tangents Consider a vector in two dimensions. We know that for the angle shown in Figure 4. If we know and , we can find using the arc tangent function Figure : Tangent and Arc Tangent In MATLAB, theta = atan(y/x) Unfortunately, the arc tangent always gives answers between and corresponding to points in quadrants I and IV. The problem is that the ratio is the same as the ratio −−−A so quadrant III cannot be distinguished from quadrant I by the ratio Likewise, quadrants II and IV are indistinguishable. The solution is the two-argument arc tangent function. In MATLAB, theta = atan2(y,x) will give the true angle and in any of the four quadrants. Example Consider the direction vector as shown in Figure 5. What is the angle between the projection of into the plane and the y-axis? This is important because it is Rthat will put in the plane, and we need to know the angle in order to carry out this rotation. First note that it is not the same as . From the geometry of the figure, we can write This gives us a formula for in terms of the direction cosines of . With the two-argument arc tangent, we can write Figure : Angles in Three Dimensions Exercise Suppose point is in the plane in three dimensions, . Find so that R will rotate to the positive z-axis. (Hint: Use the two-argument arc tangent. will be a function of and .) Let be any point in three-dimensional space, . Find so that R rotates into the plane. (Hint: Sketch the situation in three-dimensions, then sketch a two-dimensional view looking down at the plane from the positive z-axis. Compare with Example 2.) Your answers to parts (a) and (b) can be composed into an operator Z(p) that rotates a given point to the positive z-axis, Z(p)=RR. Let be a line in three-dimensional space specified by a point 1 = and the direction cosines . Use the following procedure to derive a composite operator R that rotates by angle about the line : translate 1 to the origin; let u= and use Z(u) to align with the z-axis; rotate by about the z-axis; undo step (ii); and undo step (i) 5.5: Homogeneous Coordinates 5.7: Projections
13258	https://aviation.stackexchange.com/questions/94939/how-can-i-calculate-the-total-drag-of-the-entire-airplane	Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Visit Stack Exchange Teams Q&A for work Connect and share knowledge within a single location that is structured and easy to search. Learn more about Teams How can I calculate the TOTAL drag of the ENTIRE airplane? Ask Question Asked Modified 3 years ago Viewed 4k times 2 $\begingroup$ I have an aircraft similar to a Cessna 172 and am using a virtual wind tunnel software (flowdesign) to get a drag estimate. I import the airplanes 3D model and I get around 2240 lbs of drag with a drag coefficient of 0.33 at a speed of 253fps, which I think is way too much to be trusted. I then tried to calculate it using an equation (although the equation is supposedly only for wing drag): D=qS(Cd0+CL^2/(ÏAR)) Where q is dynamic pressure, S is the wing surface area (208sqft in my case) and AR is the wing aspect ratio (6). I used a D/q value of 7 (to be conservative) and a Cd0 of 0.033. With that, I got a result of 560lbs of drag (remember, this is supposed to be just for the wing) at a speed of 253fps (which is the speed at which the best L/D ratio is supposed to be according to the equation - and is the same speed I used in the virtual wind tunnel) With that result, I then went to calculate how much thrust I would need for a climb rate of 1250fpm. The equation is: T=W(Vv/V+D/L) Where W is the weight of the airplane, Vv is the targeted vertical speed (1250fpm), V and D are the speed and drag for the best L/D ratio (so 560lbs and 253fps), L is probably the lift and I used the same value as the weight there. With that, I got the result of 923lbs of thrust needed. That is around 723 horsepower. Now if I go look up the horsepower of a Cessna 172, google says it is 180. The climb rate is 720fpm, which is half of what I targeted for, but the difference is still too big for my calculations to be right. The wing area is 175sqft, only about 30sqft less than I have. I then tried to calculate the drag with another equation, in which I additioned the induced and parasitic drag. The equation for the induced drag is: Di=CdiSq Where Cdi=Cl^2/(ÏAR) where Cl=W/(qS) and I got a result of about 118lbs of induced drag. For parasitic drag, I used Dp=D/qq and got around 284lbs of parasitic drag. The total drag is 403lbs, which I believe is still way too much to be true. I then tried using the wright equation, which is: D=CdqS, and I got a result of 3160 lbs of drag using a Cd of 0.033 (now I know I probably should have used something closer to what I got from the virtual wind tunnel, but the result would have been even greater) and a total area of 3160sqft (that is the total wetted area of the whole airplane). All of the above results could be countered with enough horsepower (and that is somewhat realistically doable), but when I compare the horsepower required, the climb rate and the wing area to other already existing planes, my calculations seem off. So what is a simple way of calculating the total drag of the entire airplane accurately? Sorry for the wall of text. P.S.: if anyone is interested, I am using these videos (or series of videos) to conceptualize an airplane design: , aircraft-design wing drag thrust wind-tunnel Share Improve this question asked Sep 18, 2022 at 15:50 Vincent CerowskiVincent Cerowski 14322 silver badges1111 bronze badges $\endgroup$ 3 4 $\begingroup$ So, you are basically calculating the drag with 3 equations which are the same and you get 3 different results. I suggest you to stick with a consistent system of units (best SI) and recheck the calculation. And get some standard book about general airplane design (Raymer for example) instead of online tutorials: they are really easy to read and full of (correct) numbers for any aerodynamic coefficient ð $\endgroup$ sophit – sophit 2022-09-18 17:17:56 +00:00 Commented Sep 18, 2022 at 17:17 1 $\begingroup$ Have also a look to this questions: aviation.stackexchange.com/questions/43410/… aviation.stackexchange.com/questions/56629/… $\endgroup$ sophit – sophit 2022-09-19 09:26:12 +00:00 Commented Sep 19, 2022 at 9:26 $\begingroup$ Does this answer your question? How is the zero-lift drag coefficient calculated? $\endgroup$ DeltaLima – DeltaLima ♦ 2022-09-19 19:18:24 +00:00 Commented Sep 19, 2022 at 19:18 Add a comment \| 2 Answers 2 Reset to default 3 $\begingroup$ EDIT Doing the math at a speed of 149kts (as suggested by @RobertDiGiovanni) and a weight halfway between EW and MTOW, gives a total drag of some 308lbs which should be a reasonable value. Try with: $C_{D_{total}}=0.02+0.05C^2_L$ this should give you a reasonable target for your simulations. How can I calculate the TOTAL drag of the ENTIRE airplane? Total drag polar for an aircraft can be calculated as the sum of 1. the polar of the wing plus 2. the drag of all the other components: $C_{D_{wing}}=C_{D_{min}}+ k(C_L-C_{L@C_{D_{min}}})^2$ $C_{D_{rest}}= C_{D_{fuselage}}+C_{D_{landing gear}}+C_{D_{nacelle}}+¦$ where: $C_{D_{min}}$, $k$ and $C_{L@C_{D_{min}}}$ depend on the particular airfoil(s) used for the wing and its geometry (sweep angle, aspect ratio, twist, ...). each term of $C_{D_{rest}}$ is normally estimated using known standard historical values, scaled via the basic dimension of each component. Each and every term depends also on the speed i.e. on Reynolds and Mach numbers. Drag terms of 2. may also depend on lift (landing gear for example). The sum of 1. and 2. gives the following general form for the drag coefficient: $C_{D_{total}}=a+bC_L+cC^2_L$ Normally the second term $b$ is neglected and the total drag coefficient assumes the well known form: $C_{D_{total}}=C_{D_0}+KC^2_L$ For a single-engine light-aircraft with symmetrical airfoil and flying at subsonic speed, plausible rough values for $C_{D_0}$ and $K$ based on historical values are: $C_{D_{total}}=0.02+0.05C^2_L$ Anyway a better approximation (within a ±10% error) can be achieved only evaluating each term of 1. and 2. I suppose that doing the math here for one particular case is beyond the scope of this Stackexchange, also because it would take some time and space. The values to be used and the general theory behind it can be found in any standard book of general airplane design, like the one by D. P. Raymer, Dr. J. Roskam, E. Torenbeek or L. Nicolai. All this books are really easy to read, fluent and with almost no equation. Share Improve this answer edited Sep 21, 2022 at 8:35 answered Sep 19, 2022 at 18:40 sophitsophit 17.9k11 gold badge3939 silver badges8383 bronze badges $\endgroup$ 4 $\begingroup$ Running the calcs at high cruise finds us squaring a Cl value of less than one. Why don't you show one calc at 149 knots. It'd be worth an upvote perhaps. $\endgroup$ Robert DiGiovanni – Robert DiGiovanni 2022-09-20 16:31:17 +00:00 Commented Sep 20, 2022 at 16:31 $\begingroup$ @RobertDiGiovanni: I don't believe in doing the homework of somebody else (not referring to you), I prefer to give the tools and show the path ;-) Anyway I'm going to do it, I just need some time $\endgroup$ sophit – sophit 2022-09-20 17:16:28 +00:00 Commented Sep 20, 2022 at 17:16 $\begingroup$ Thanks for the answer. Also, you were right in your comment under my question. My dumbass forgot to convert from knots to fps (should have been 150 fps, not knots). I have redone my calculations and now the result seem more reasonable. I also want to thank @RobertDiGiovanni for his answer, having something to compare my results to is very useful as a first rough "reality" check. $\endgroup$ Vincent Cerowski – Vincent Cerowski 2022-09-22 21:03:38 +00:00 Commented Sep 22, 2022 at 21:03 $\begingroup$ :-D glad I could help ð And seriously consider getting one of those books, older version can be found almost for free $\endgroup$ sophit – sophit 2022-09-23 06:46:47 +00:00 Commented Sep 23, 2022 at 6:46 Add a comment \| 3 $\begingroup$ Drag of the $entire$ airplane is readily available by gliding, or monitoring fuel consumption. Checking fuel consumption is a bit more complicated because what you really need is thrust. in steady state flight, thrust = drag But just to get "in the ball park", a 172 weighing 2400 lbs gliding 8:1 generates 300 lbs of drag at Vbg. That is about how much thrust you need for level flight, with around 300 lbs more available to climb. Of course these numbers will vary depending on airspeed and configuration but we can see even 923 lbs of thrust is a bit high. 253 feet per second comes out to 149 knots$^1$! Best L/D for a 172 is around 65 knots, or around 110 fps. Try that number and see what you get. $^1$ keep in mind "cruise" numbers in POH are true airspeed, where higher altitude will help. 403 pounds of total drag here seems to be closest to reality, especially considering decrease in fixed prop thrust at that airspeed. Share Improve this answer edited Sep 19, 2022 at 9:53 answered Sep 18, 2022 at 23:03 Robert DiGiovanniRobert DiGiovanni 22.6k22 gold badges3232 silver badges8282 bronze badges $\endgroup$ Add a comment \| You must log in to answer this question. Start asking to get answers Find the answer to your question by asking. Ask question Explore related questions aircraft-design wing drag thrust wind-tunnel See similar questions with these tags. Featured on Meta Introducing a new proactive anti-spam measure Spevacus has joined us as a Community Manager stackoverflow.ai - rebuilt for attribution Community Asks Sprint Announcement - September 2025 Linked How is the zero-lift drag coefficient calculated? 1 How to calculate the induced drag coefficient? 1 How is a carpet plot for aircraft sizing constructed? Related Is the induced drag independent of wing span? 5 How do you calculate total drag on a wing? 5 How can the zero-lift drag coefficient (parasitic drag) be calculated? 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13259	https://ember-energy.org/focus-areas/coal-mine-methane/	To provide the best experiences, we use technologies like cookies to store and/or access device information. Consenting to these technologies will allow us to process data such as browsing behavior or unique IDs on this site. Not consenting or withdrawing consent, may adversely affect certain features and functions. Please read our Privacy policy here. Functional Always active The technical storage or access is strictly necessary for the legitimate purpose of enabling the use of a specific service explicitly requested by the subscriber or user, or for the sole purpose of carrying out the transmission of a communication over an electronic communications network. Preferences The technical storage or access is necessary for the legitimate purpose of storing preferences that are not requested by the subscriber or user. Statistics The technical storage or access that is used exclusively for statistical purposes. The technical storage or access that is used exclusively for anonymous statistical purposes. Without a subpoena, voluntary compliance on the part of your Internet Service Provider, or additional records from a third party, information stored or retrieved for this purpose alone cannot usually be used to identify you. Marketing The technical storage or access is required to create user profiles to send advertising, or to track the user on a website or across several websites for similar marketing purposes. Manage options Manage services Manage {vendor_count} vendors Read more about these purposes View preferences Cookies Privacy Policy {title} Home / Focus Areas / Coal Mine Methane Coal Mine Methane Coal mines emit more methane than the gas industry, yet this pollution is often overlooked. Half of methane emissions from coal mines can be captured with proven technologies. OverviewOur workInsightsExperts Anchor point: Overview Highlights 40 Mt Methane leaked from coal mines in 2024 91% of coal mine methane emissions come from just 9 countries 54% Methane emissions that can be captured at coal mines using proven technologies Overlooked and underestimated Not only are coal mines being overlooked they are likely underreporting their methane emissions, with emissions potentially twice as large as reported. Setting up improved monitoring and implementing existing technologies to utilise or destroy methane should be the first priority for all coal producing countries. According to the IEA, 54% of methane emissions from coal mines could be captured for an average cost of $230 USD per tonne of methane. The biggest wins can be had by starting with super-emitting mines. As clean energy replaces coal in the electricity and steel sectors, the process of closing coal mines will need to ensure that methane is trapped, for example by flooding mines. Satellites are starting to show how big the issue is. However, these are most effective when used in conjunction with other forms of monitoring. Greater attention will mean that countries and companies won’t be able to ignore their emissions for much longer. Coal is dirtier than you think In this interactive explainer, find out more about coal mine methane: why it’s underestimated and how it can be monitored and reduced. Read more Anchor point: Our work Our work Cutting coal mine methane with data and policy Ember launched in 2020 with a focus on shifting the world from coal to clean electricity. While analysing the impact of coal power on the climate, it became clear that the massive methane emissions from coal mining were being overlooked and drastically underestimated. We set up a specialist unit working on coal mine methane to galvanise action in the world’s biggest emitters, by using data and analysis to highlight the scale of the issue and the solutions. Since launching this work in 2020, we’ve already had an impact in Australia, India, Indonesia and Germany, and with the global steel industry. “This issue is doubly overlooked. Methane is overlooked compared to carbon dioxide emissions. And methane emissions from coal mines in particular are being overlooked compared to the oil and gas sectors, and almost totally ignored in the steel industry.” Eleanor Whittle ‍Ember’s Programme Lead, Coal Mine Methane Anchor point: Insights Latest insights View all  Commentary It’s time for Europe to take stock of its abandoned coal mines – a major source of methane Coal Mine Methane European Union World 05 August 2025 Analysis Satellite analysis identifies 40% more methane from Australian coal mines Coal Mine Methane Australia G20 OECD 16 April 2025 Analysis Australia’s coal mining emissions paradox Australia Coal Mine Methane G20 OECD 27 March 2025 Analysis The geography factor: How environmental conditions shape methane monitoring from space Coal Mine Methane World 18 March 2025 Anchor point: Experts Our experts ### Sabina Assan Senior Analyst, CMM View full profile ### Dody Setiawan Senior Analyst Climate and Energy, Indonesia Ember View full profile ### Sarah Shannon Satellite Analyst, Coal Mine Methane Ember View full profile
13260	https://www.espressoenglish.net/100-gre-words-advanced-english-vocabulary-list/	Skip to content 100+ GRE Words: Advanced English Vocabulary List Let’s learn 100+ GRE words for more fluent English! This high-level vocabulary comes from lists that students use when preparing for the GRE – an exam to enter post-college programs for master’s and doctorate degrees. These advanced words will definitely level up your English fluency! Adamant (adj.) Definition: Refusing to be persuaded or to change one’s mind. Sentence: She was adamant about not attending the party, no matter what her friends said. Ambivalent (adj.) Definition: Having mixed feelings or contradictory ideas about something or someone. Sentence: He felt ambivalent about the job offer; the salary was good, but he didn’t like the location. Analogous (adj.) Definition: Comparable in certain respects, typically in a way that makes clearer the nature of the things compared. Sentence: The structure of an atom is analogous to the solar system, with electrons orbiting the nucleus like planets around the sun. Download lesson PDF Anomaly (n.) Definition: Something that deviates from what is standard, normal, or expected. Sentence: The sudden drop in temperature was an anomaly for that time of year. Appease (v.) Definition: To make someone less angry or hostile by giving in to their demands. Sentence: The manager tried to appease the disgruntled employees with a bonus and additional vacation days. Arduous (adj.) Definition: Involving a lot of effort and hard work. Sentence: Climbing the mountain was an arduous task, requiring both physical strength and mental determination. Benign (adj.) Definition: Harmless. Sentence: The tumor was benign, so there was no need for immediate surgery. Biased (adj.) Definition: Showing an unfair preference for or prejudice against something or someone. Sentence: The judge was removed from the case due to a conflict of interest and a perceived biased opinion. Bolster (v.) Definition: To support or strengthen. Sentence: The evidence presented in court helped bolster the defendant’s case. Candid (adj.) Definition: Truthful and straightforward; frank. Sentence: Her candid remarks about the project’s flaws were appreciated by the team. Capricious (adj.) Definition: Given to sudden and unaccountable changes of mood or behavior. Sentence: The weather in the mountains is often capricious, changing from sunny to stormy within minutes. Catalyst (n.) Definition: An agent that provokes or speeds significant change or action. Sentence: The new policy acted as a catalyst for much-needed reform in the organization. Clinch (v.) Definition: To confirm or settle something definitively. Sentence: The final goal of the game helped clinch the championship for the team. Coerce (v.) Definition: To persuade an unwilling person to do something by using force or threats. Sentence: The suspect was coerced into confessing after hours of intense interrogation. Cognizant (adj.) Definition: Being aware of or having knowledge of something. Sentence: She was cognizant of the risks involved in the investment but decided to proceed anyway. Condone (v.) Definition: To accept or allow behavior that is considered morally wrong or offensive. Sentence: The company does not condone any form of discrimination or harassment in the workplace. Confound (v.) Definition: To cause surprise or confusion in someone, especially by acting against their expectations. Sentence: The sudden success of the startup confounded many industry experts. Conspicuous (adj.) Definition: Easily noticeable or attracting attention. Sentence: The bright red jacket made her conspicuous in the crowd. Construe (v.) Definition: To interpret or understand the meaning of something in a particular way. Sentence: His comments were construed as an insult by some, though he meant them as a joke. Convoluted (adj.) Definition: Extremely complex and difficult to follow. Sentence: The plot of the novel was so convoluted that I had to read it twice to understand the ending. Copious (adj.) Definition: Abundant in supply or quantity. Sentence: She took copious notes during the lecture to ensure she didn’t miss any important details. Corroborate (v.) Definition: To confirm or give support to a statement, theory, or finding. Sentence: The witness’s testimony helped corroborate the defendant’s alibi. Counterintuitive (adj.) Definition: Contrary to what one would intuitively expect. Sentence: It was counterintuitive to think that eating more could actually help you lose weight. Debilitate (v.) Definition: To make someone weak and infirm. Sentence: The long illness had debilitated him, leaving him too weak to return to work. Debunk (v.) Definition: To expose the falseness or hollowness of a myth, idea, or belief. Sentence: The documentary aimed to debunk several popular myths about ancient civilizations. Deference (n.) Definition: Respect and esteem due to an elder or superior. Sentence: He showed deference to his mentor by listening carefully to his advice. Denigrate (v.) Definition: To criticize unfairly; to disparage. Sentence: The politician’s opponents attempted to denigrate his achievements. Discern (v.) Definition: To perceive or recognize something. Sentence: She could barely discern the details of the painting from across the room. Disregard (v.) Definition: To pay no attention to; ignore. Sentence: He chose to disregard the warnings and ski in the dangerous area. Dissonance (n.) Definition: Lack of harmony among musical notes or a clash of conflicting ideas. Sentence: The dissonance in the music created a feeling of tension and unease. Docile (adj.) Definition: Ready to accept control or instruction; submissive. Sentence: The docile puppy was easy to train and quickly learned new commands. Embellish (v.) Definition: To make something more attractive by adding decorative details; to enhance a story with exaggerated details. Sentence: She embellished the tale of her vacation with colorful anecdotes and exaggerations. Emulate (v.) Definition: To match or surpass (a person or achievement) by imitation. Sentence: He tried to emulate his father’s success in the business world. Enigma (n.) Definition: A person or thing that is mysterious or difficult to understand. Sentence: The disappearance of the ancient civilization remains an enigma to historians. Esoteric (adj.) Definition: Intended for or likely to be understood only by a small number of people with specialized knowledge. Sentence: The professor’s lecture on quantum mechanics was too esoteric for most students. Eulogy (n.) Definition: A speech or piece of writing that praises someone highly, typically someone who has just died. Sentence: The eulogy delivered at the funeral celebrated the remarkable life and contributions of the deceased. Exacerbate (v.) Definition: To make a problem or situation worse. Sentence: His refusal to acknowledge the issue only served to exacerbate the conflict. Exemplary (adj.) Definition: Serving as a desirable model; representing the best of its kind. Sentence: Her exemplary performance at work earned her the Employee of the Month award. Expedient (adj.) Definition: Convenient and practical, although possibly improper or immoral. Sentence: Using a shortcut was expedient, but it violated company policy. Finesse (n./v.) Definition: Skillful handling of a situation or delicate task; to handle with subtlety and skill. Sentence: She handled the negotiation with great finesse, securing a favorable deal for her company. Fledgling (adj.) Definition: A young or inexperienced person; just beginning. Sentence: The fledgling artist struggled to find his unique style in the competitive world of art. Fluctuate (v.) Definition: To change continually; to move up and down. Sentence: Stock prices tend to fluctuate greatly depending on market conditions. Fluke (n.) Definition: A surprising chance occurrence, especially a favorable one. Sentence: Winning the lottery was a fluke; he had never expected such luck. Frivolous (adj.) Definition: Not having any serious purpose or value; trivial. Sentence: The court dismissed the lawsuit, calling it frivolous and without merit. Garner (v.) Definition: To gather or collect something, especially information or approval. Sentence: Her research helped garner widespread support for the new policy. Idiosyncrasy (n.) Definition: A distinctive or peculiar feature or characteristic of a place or thing. Sentence: One of his idiosyncrasies was always tapping his pen when he was thinking. Immutable (adj.) Definition: Unchanging over time or unable to be changed. Sentence: The laws of physics are considered immutable and universal. Impediment (n.) Definition: A hindrance or obstruction in doing something. Sentence: His lack of formal education was seen as an impediment to his career advancement. Impervious (adj.) Definition: Not allowing fluid to pass through; unable to be affected by. Sentence: The new raincoat is made of a material that is impervious to water. Impetuous (adj.) Definition: Acting quickly and without thought or care; impulsive. Sentence: His impetuous decision to quit his job without a backup plan led to many difficulties. Inadvertent (adj.) Definition: Not resulting from or achieved through deliberate planning; accidental. Sentence: The mistake was inadvertent and not intended to cause harm. Incongruous (adj.) Definition: Not in harmony or keeping with the surroundings or other aspects. Sentence: The modern art piece seemed incongruous in the otherwise traditional museum. Ingenious (adj.) Definition: Clever, original, and inventive. Sentence: The ingenious design of the new gadget made it both functional and stylish. Innocuous (adj.) Definition: Not harmful or offensive. Sentence: The remark was intended as a joke and was completely innocuous. Insidious (adj.) Definition: Proceeding in a subtle way but with harmful effects. Sentence: The disease was insidious, showing symptoms only after it had already progressed significantly. Juncture (n.) Definition: A particular point in events or time; a critical moment. Sentence: At this juncture, we need to decide whether to proceed with the project or not. Juxtapose (v.) Definition: To place side by side for comparison. Sentence: The artist’s new exhibit juxtaposes modern art with classical sculptures. Laudable (adj.) Definition: Deserving praise and commendation. Sentence: Her efforts to improve the community were laudable and earned her widespread recognition. Lethargic (adj.) Definition: Sluggish and apathetic, low energy. Sentence: After the long flight, she felt lethargic and struggled to stay awake. Lull (n.) Definition: A temporary interval of quiet or lack of activity. Sentence: There was a lull in the conversation as everyone waited for the results. Makeshift (adj.) Definition: Temporary and of low quality, but used because of a sudden need. Sentence: They built a makeshift shelter using blankets and sticks to protect themselves from the rain. Mired (past participle of verb) Definition: Involved in a difficult situation that is hard to escape from. Sentence: The project was mired in delays and budget overruns. Mitigate (v.) Definition: To make something less severe, serious, or painful. Sentence: Measures were taken to mitigate the effects of the economic downturn. Myopic (adj.) Definition: Lacking imagination, foresight, or intellectual insight; short-sighted. Sentence: His myopic approach to problem-solving prevented him from seeing the bigger picture. Nascent (adj.) Definition: Just coming into existence and beginning to display signs of future potential. Sentence: The nascent tech startup showed great promise in the field of artificial intelligence. Download lesson PDF Nuance (n.) Definition: A subtle difference or variation in meaning, expression, tone, or feeling. Sentence: The actor’s performance captured the nuances of the character’s complex emotions. Obfuscate (v.) Definition: To deliberately make something unclear or difficult to understand. Sentence: The lawyer’s convoluted explanation seemed designed to obfuscate the truth. Obstinate (adj.) Definition: Stubbornly refusing to change one’s opinion or chosen course of action. Sentence: Despite all the evidence, he remained obstinate in his belief that he was right. Onerous (adj.) Definition: Involving a lot of effort and difficulty; burdensome. Sentence: The new regulations imposed onerous requirements on small businesses. Overshadow (v.) Definition: To appear more prominent or important than. Sentence: The young actor’s talent overshadowed that of his more experienced co-stars. Placate (v.) Definition: To make someone less angry or hostile by giving in to their demands. Sentence: The manager offered a discount to placate the upset customer. Plausible (adj.) Definition: Seeming reasonable or probable. Sentence: The scientist presented a plausible theory that explained the unexpected results. Polarizing (adj.) Definition: Causing strong division into opposing groups or opinions. Sentence: The controversial policy was polarizing and sparked heated debates across the community. Pragmatic (adj.) Definition: Dealing with things in a practical and sensible way rather than by theoretical considerations. Sentence: She took a pragmatic approach to solving the problem, focusing on what would work best in practice. Precarious (adj.) Definition: Not securely held or in position; dangerously likely to fall or collapse. Sentence: The ladder was in a precarious position, making it dangerous to climb. Precursor (n.) Definition: A person or thing that comes before another of the same kind; a forerunner. Sentence: The invention of the telephone was a precursor to many modern communication technologies. Predisposed (past participle of verb) Definition: Likely or inclined to be affected by something. Sentence: He was predisposed to heart disease because of his family history. Presumptuous (adj.) Definition: Failing to observe the limits of what is permitted or appropriate; overconfident. Sentence: It was presumptuous of him to assume that he would be promoted without discussing it first. Pristine (adj.) Definition: In its original condition; unspoiled. Sentence: The beach remained pristine and untouched by human activity. Prolific (adj.) Definition: Producing a lot of something; very productive. Sentence: The prolific writer published several novels each year. Prudent (adj.) Definition: Acting with or showing care and thought for the future. Sentence: It is prudent to save a portion of your salary for unexpected expenses. Quintessential (adj.) Definition: Representing the most perfect or typical example of a quality or class. Sentence: Her performance was the quintessential example of great acting. Redundant (adj.) Definition: Not or no longer needed or useful; superfluous. Sentence: The use of redundant phrases made the report unnecessarily lengthy. Respectively (adv.) Definition: Separately or individually and in the order already mentioned. Sentence: Bob and Jane will take their tests at 10 a.m. and 11 a.m., respectively. Reticent (adj.) Definition: Not revealing one’s thoughts or feelings readily; reserved. Sentence: She was reticent about discussing her personal life with colleagues. Revamp (v.) Definition: To change or improve something. Sentence: The company decided to revamp its marketing strategy to attract more customers. Rife (adj.) Definition: Abundant or widespread (especially something undesirable). Sentence: The neighborhood was rife with noise and pollution due to the construction work. Rudimentary (adj.) Definition: Basic or elementary; not advanced. Sentence: The rudimentary skills taught in the first year of training laid the foundation for more complex techniques. Savor (v.) Definition: To enjoy or appreciate something completely. Sentence: She took a moment to savor the beautiful sunset before heading home. Scrupulous (adj.) Definition: Very concerned to avoid doing wrong; diligent and attentive to details. Sentence: The accountant was scrupulous in checking every entry to ensure accuracy. Sparse (adj.) Definition: Thinly dispersed or scattered; not dense. Sentence: The vegetation in the desert is sparse, with only a few hardy plants surviving. Sporadic (adj.) Definition: Occurring at irregular intervals or only in a few places; scattered. Sentence: The sporadic rainfall made it difficult to plan outdoor events. Subside (v.) Definition: To become less intense, violent, or severe. Sentence: After the storm, the winds began to subside, and the rain eased. Succinct (adj.) Definition: Briefly and clearly expressed. Sentence: The summary was succinct, capturing all the key points in just a few paragraphs. Surmise (v.) Definition: To suppose that something is true without having evidence to confirm it. Sentence: I can only surmise that he was late due to traffic, based on his previous messages. Tangential (adj.) Definition: Diverging from the main point; not directly related. Sentence: The discussion became tangential, veering away from the main topic. Tantamount (adj.) Definition: Equivalent in seriousness to; virtually the same as. Sentence: His refusal to cooperate was tantamount to admitting guilt. Timely (adj.) Definition: Happening at the right time; opportune. Sentence: The paramedics’ timely intervention saved the woman’s life. Transient (adj.) Definition: Lasting only for a short time; temporary. Sentence: The city’s transient population meant that neighborhoods were constantly changing. Travesty (n.) Definition: A false, absurd, or distorted representation of something. Sentence: The trial was a travesty of justice, failing to properly address the evidence. Trivial (adj.) Definition: Of little value or importance. Sentence: The argument over who should wash the dishes seemed trivial compared to the bigger issues they were facing. Ubiquitous (adj.) Definition: Present, appearing, or found everywhere. Sentence: Smartphones have become ubiquitous in modern society, with nearly everyone owning one. Unconscionable (adj.) Definition: Not guided by conscience; shockingly unfair or unjust. Sentence: The conditions in the factory were unconscionable, with workers enduring unsafe and inhumane practices. Undermine (v.) Definition: To weaken or damage something gradually or covertly. Sentence: The constant criticism was meant to undermine her confidence and authority. Underscore (v.) Definition: To emphasize or highlight something. Sentence: The teacher used several examples to underscore the importance of following instructions. Unearth (v.) Definition: To dig up or discover something hidden. Sentence: Archaeologists unearthed ancient artifacts that provided new insights into the civilization. Unorthodox (adj.) Definition: Contrary to what is traditional or expected. Sentence: His unorthodox teaching methods were initially met with skepticism but eventually proved effective. Vestige (n.) Definition: A trace or remnant of something that is disappearing or no longer exists. Sentence: The ruins of the old castle were a vestige of a bygone era. Volatile (adj.) Definition: Subject to rapid or unpredictable change; easily evaporated. Sentence: The stock market can be volatile, with prices fluctuating wildly in short periods. Warranted (past participle of verb) Definition: Justified or required by the circumstances. Sentence: The use of extra security was warranted due to the high-profile nature of the event. Winsome (adj.) Definition: Attractive or charming in a sweet or innocent way. Sentence: Her winsome smile and friendly demeanor made her very popular at the party. Hope you enjoyed learning these GRE words! Join my Advanced Vocabulary and Collocations Course to learn 1,000+ advanced English words fast. Learn more: 30 Advanced Adverbs 100+ Advanced Phrases Advanced Vocabulary Quiz
13261	https://users.math.msu.edu/users/kadyrova/lectures/Lecture_11.pdf	Math 110 Reciprocal Function. CH. 3.6, 3.7 (part) (PART I). Lecture #11 Reciprocal Function (the most basic rational function). Definition. The Reciprocal Function is a function defined by ( ) 1 f x x = Problem #1. Find the domain of the reciprocal function. Problem #2. Sketch the graph of the reciprocal function by plotting points (using the table of function’s values). x 3 − 2 − 1 − 1 2 − 1 3 − 1 3 1 2 1 2 3 ( ) f x 1 Math 110 Reciprocal Function. CH. 3.6, 3.7 (part) (PART I). Lecture #11 Symbolic Description of the “end behavior” of ( ) 1 f x x = . As ( ) , 0 x f x →−∞ → and as ( ) , 0 x f x →∞ → The line 0 y = (x –axis) is said to be a horizontal asymptote of the graph of the reciprocal function. The curve approaches the x-axis. 2 Math 110 Reciprocal Function. CH. 3.6, 3.7 (part) (PART I). Lecture #11 Definition of a Horizontal Asymptote. The line y b = is a horizontal asymptote of the graph of a function f if ( ) f x approaches b as x increases or decreases without bound. Fill out the table for x values close to 0. x 0.5 − 0.1 − 0.01 − 0.001 − ( ) f x x 0.5 0.1 0.01 0.001 ( ) f x Problem #4. Make a sketch of the function ( ) 1 f x x = near 0. 3 Math 110 Reciprocal Function. CH. 3.6, 3.7 (part) (PART I). Lecture #11 Symbolic Description of the behavior of ( ) 1 f x x = near 0. As ( ) 0 , x f x + → →∞ and as ( ) 0 , x f x − → →−∞ The line (y –axis) is said to be a vertical asymptote of the graph of the reciprocal function. 0 x = The curve approaches, but does not touch, the y-axis. Definition of a Vertical Asymptote. The line is a vertical asymptote of the graph of a function f if x a = ( ) f x increases or decreases without bound as x approaches a. Range of the Reciprocal function. 4 Math 110 Reciprocal Function. CH. 3.6, 3.7 (part) (PART I). Lecture #11 Transformations of the reciprocal functions and graphs. Problem #5. a) Make a sketch of the graph of ( ) 1 3 g x x = −. b) Write the equations of the vertical asymptote. c) State the Domain of g. Graph of the basic reciprocal function is provided. 5 Math 110 Reciprocal Function. CH. 3.6, 3.7 (part) (PART I). Lecture #11 Problem #6. a) Make a sketch of the graph of ( ) 1 2 g x x = + . b) Write the equations of the vertical asymptote. c) State the Domain of g. Graph of the basic reciprocal function is provided. Problem #7. 6 Math 110 Reciprocal Function. CH. 3.6, 3.7 (part) (PART I). Lecture #11 a) Write a sequence of transformations that leads from ( ) ( ) 1 1 , to 4 2 f x h x x x = = − − + . b) Find the domain of h. c) Sketch the graph of h. Show all intermediate graphs. 7 Math 110 Reciprocal Function. CH. 3.6, 3.7 (part) (PART I). Lecture #11 Transformations of the basic reciprocal function belong to the class of Rational Functions. Definition of Rational Functions. Rational Functions are quotients of two polynomials: ( ) ( ) ( ) ( ) , 0 p x f x q x q x = ≠. Domain of Rational Functions. Vertical asymptotes. The domain of a rational function is the set of all real numbers except the x-values that make the denominator zero. If is a zero of the denominator of a rational function f , then 0 x x = 0 x x = is the equation for a vertical asymptote of the graph of f . 8 Math 110 Reciprocal Function. CH. 3.6, 3.7 (part) (PART I). Lecture #11 Problem #8. (That problem can be used as a supplementary material). Find the domain of the following rational functions. Write your answers using the interval notation. Write the equations of all vertical asymptotes for each function. 1. ( ) 2 1 2 1 x f x x x − = − + 2. ( ) 2 5 1 x g x x x + = + + 3. ( ) 2 2 2 3 x h x x x = − − 4. ( ) ( ) 2 8 3 10 k x x x x = + − 5. ( ) 2 10 6 17 m x x x = − + 5 6. ( ) ( ) 2 3 5 2 1 x s x x x − = − − 9 Math 110 Reciprocal Function. CH. 3.6, 3.7 (part) (PART I). Lecture #11 Modeling using variation. Quantities can vary directly, inversely, or jointly. We will consider only direct and inverse variation. Direct variation. If a situation is described by an equation in the form y kx = where k is a nonzero constant, we say that y varies directly as x or y is directly proportional to x. The number k is called the constant of variation or the constant of proportionality. Inverse variation. If a situation is described by an equation in the form k y x = where k is a nonzero constant, we say that y varies inversely as x or y is inversely proportional to x. The number k is called the constant of variation. 10 Math 110 Reciprocal Function. CH. 3.6, 3.7 (part) (PART I). Lecture #11 Problem #9. (Example #2, p. 355 , PART I). Height, H, varies directly as foot length, F. a) Write an equation that expressed this relationship. b) Photographs of large footprints were published in 1951. Some speculated that these footprints were made by the Abominable Snowman. Each footprint was 23 inches long. The Snowman’s height was determined to be 154.1 inches. Use the to find the constant 154.1 23 H and F = = of variation. Problem #10. a) y varies directly as x, 55 y = when 2.5 x = . Find y when . 12 x = b) y varies inversely as x, when . 55 y = 2.5 x = Find y when . 12 x = 11
13262	https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-pos-neg-exponents/a/negative-exponents-review	Published Time: Thu, 18 Sep 2025 20:18:13 GMT Negative exponents review (article) \| Khan Academy Skip to main content If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains .kastatic.org and .kasandbox.org are unblocked. Explore Browse By Standards Explore Khanmigo Math: Pre-K - 8th grade Math: High school & college Math: Multiple grades Math: Illustrative Math-aligned Math: Eureka Math-aligned Math: Get ready courses Test prep Science Economics Reading & language arts Computing Life skills Social studies Partner courses Khan for educators Select a category to view its courses Search AI for Teachers FreeDonateLog inSign up Search for courses, skills, and videos Help us do more We'll get right to the point: we're asking you to help support Khan Academy. We're a nonprofit that relies on support from people like you. If everyone reading this gives $10 monthly, Khan Academy can continue to thrive for years. Please help keep Khan Academy free, for anyone, anywhere forever. Select gift frequency One time Recurring Monthly Yearly Select amount $10 $20 $30 $40 Other Give now By donating, you agree to our terms of service and privacy policy. Skip to lesson content 8th grade math Course: 8th grade math>Unit 1 Lesson 7: Negative exponents Negative exponents Negative exponent intuition Negative exponents Negative exponents review Math> 8th grade math> Numbers and operations> Negative exponents © 2025 Khan Academy Terms of usePrivacy PolicyCookie NoticeAccessibility Statement Loading... Use of cookies Cookies are small files placed on your device that collect information when you use Khan Academy. Strictly necessary cookies are used to make our site work and are required. Other types of cookies are used to improve your experience, to analyze how Khan Academy is used, and to market our service. You can allow or disallow these other cookies by checking or unchecking the boxes below. You can learn more in our cookie policy Accept All Cookies Strictly Necessary Only Cookies Settings Privacy Preference Center When you visit any website, it may store or retrieve information on your browser, mostly in the form of cookies. This information might be about you, your preferences or your device and is mostly used to make the site work as you expect it to. The information does not usually directly identify you, but it can give you a more personalized web experience. Because we respect your right to privacy, you can choose not to allow some types of cookies. Click on the different category headings to find out more and change our default settings. However, blocking some types of cookies may impact your experience of the site and the services we are able to offer. More information Allow All Manage Consent Preferences Strictly Necessary Cookies Always Active Certain cookies and other technologies are essential in order to enable our Service to provide the features you have requested, such as making it possible for you to access our product and information related to your account. For example, each time you log into our Service, a Strictly Necessary Cookie authenticates that it is you logging in and allows you to use the Service without having to re-enter your password when you visit a new page or new unit during your browsing session. Functional Cookies [x] Functional Cookies These cookies provide you with a more tailored experience and allow you to make certain selections on our Service. For example, these cookies store information such as your preferred language and website preferences. Targeting Cookies [x] Targeting Cookies These cookies are used on a limited basis, only on pages directed to adults (teachers, donors, or parents). We use these cookies to inform our own digital marketing and help us connect with people who are interested in our Service and our mission. We do not use cookies to serve third party ads on our Service. Performance Cookies [x] Performance Cookies These cookies and other technologies allow us to understand how you interact with our Service (e.g., how often you use our Service, where you are accessing the Service from and the content that you’re interacting with). Analytic cookies enable us to support and improve how our Service operates. For example, we use Google Analytics cookies to help us measure traffic and usage trends for the Service, and to understand more about the demographics of our users. We also may use web beacons to gauge the effectiveness of certain communications and the effectiveness of our marketing campaigns via HTML emails. Cookie List Clear [x] checkbox label label Apply Cancel Consent Leg.Interest [x] checkbox label label [x] checkbox label label [x] checkbox label label Reject All Confirm My Choices
13263	https://www.sciencing.com/do-division-positive-negative-integers-7715163/	How To Do Long Division With Positive & Negative Integers Science- [x] Astronomy Biology Chemistry Geology Nature Physics Math- [x] Algebra Geometry Technology- [x] Electronics Features About Editorial Policies Privacy Policy Terms of Use © 2025 Static Media. All Rights Reserved How To Do Long Division With Positive & Negative Integers ScienceMathTechnologyFeatures Math How To Do Long Division With Positive & Negative Integers By C. Taylor Updated Mar 24, 2022 Long division refers to dividing numbers by hand. Whether the numbers are long or small, the method is the same, even if longer numbers seem a little more intimidating. Performing long division in integers simply means the numbers are whole numbers without fractions or decimals. A special case lies with negative numbers, but it doesn't change the procedure, only the final sign. If only one of the two numbers is negative, the resulting calculation will also be negative. If both numbers are negative, the resulting calculation will be positive, since the two negative signs cancel out each other. Step 1 Take note of the signs of the two numbers. If both signs are positive or both are negative, the resulting figure will be positive. If only one of the signs is negative, you will end up with a negative number. As an example, 78 divided by -5 would give you a negative quotient. Step 2 Set up the calculation by writing the dividend, or the number being divided into, with a division bracket over it. The divisor will go on the left. In the example, you would draw out: -5/78 You can safely ignore the negative sign, as long as you remember the final outcome will be negative. Step 3 Divide the first digit of the dividend by the divisor. If the first digit is smaller than the divisor, divide the divisor into the first two digits. Record the number of times the divisor evenly goes into the dividend digit(s) on the top, with the remainder written below. In the example, "1" would be written on top directly over the "7," and the remainder of "2" would be written under the "7." Step 4 Drop the next digit down next to the remainder. In the example, you would then have "28" with the two aligned under the "7." Step 5 Repeat the division into this new number. Record the whole number to the right of the preceding whole number at the top and write the remainder under the last digit you brought down. In the example, you would write "5" right after "1" and write "3" under the "8." Step 6 Repeat until you have a whole number written directly over the last digit of the dividend. In the example, you would pause at 15. Now you have a few choices. You can write the equation as "25 with a remainder of 3," or you could express it as a fraction by placing the remainder over the divisor, such that it looks like "25 3/5," or you can place a period after the "25" and continue until you have no remainder (or find a remainder that keeps repeating). In the example, the latter option would result in "25.6." Step 7 Add the negative sign, if required from your initial determination. In the example, the result requires a negative sign, so the result would be one of the following: -25 with a remainder of 3 -25 3/5 -25.6 Cite This Article MLA Taylor, C.. "How To Do Long Division With Positive & Negative Integers" sciencing.com, 24 April 2017. APA Taylor, C.. (2017, April 24). How To Do Long Division With Positive & Negative Integers. sciencing.com. Retrieved from Chicago Taylor, C.. How To Do Long Division With Positive & Negative Integers last modified March 24, 2022. Recommended These Extinct Creatures Would Destroy Earth Today Tragic Details About Allstate's Mayhem Guy The Disturbing Reality Behind TSA Body Scanners You Weren't Told The Most Unsettling Inbred Families In History
13264	https://stackoverflow.com/questions/59204259/recursively-generate-all-k-digit-numbers-whose-digit-sum-is-n	python - Recursively generate all k-digit numbers whose digit-sum is n - Stack Overflow Join Stack Overflow By clicking “Sign up”, you agree to our terms of service and acknowledge you have read our privacy policy. Sign up with Google Sign up with GitHub OR Email Password Sign up Already have an account? Log in Skip to main content Stack Overflow 1. About 2. Products 3. 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Save this post for later Not now Thanks for your vote! You now have 5 free votes weekly. Free votes count toward the total vote score does not give reputation to the author Continue to help good content that is interesting, well-researched, and useful, rise to the top! To gain full voting privileges, earn reputation. Got it!Go to help center to learn more Recursively generate all k-digit numbers whose digit-sum is n Ask Question Asked 5 years, 9 months ago Modified5 years, 9 months ago Viewed 886 times This question shows research effort; it is useful and clear 1 Save this question. Show activity on this post. I was working on a problem where I'm finding all k-digit numbers whose digits sum up the given n. I found how to do this and approach it as Integer Partitioning problem, however I would like to be able to only input n and k numbers (without the max_element) but when I try to delete it from the code it doesn't seem to work anymore. How can I change that plus reverse it? ```python def c(n, k, max_element): allowed = range(max_element, 0, -1) def helper(n, k, t): if k == 0: if n == 0: yield t elif k == 1: if n in allowed: yield t + (n,) elif 1 k <= n <= max_element k: for v in allowed: yield from helper(n - v, k - 1, t + (v,)) return helper(n, k, ()) for p in c(5, 3, 3): print(p) ``` I tried using the reversed method but apparently it doesn't work in the generator. Result: python (3, 1, 1) (2, 2, 1) (2, 1, 2) (1, 3, 1) (1, 2, 2) (1, 1, 3) Expected result: python 113 122 131 212 221 311 python python-3.x algorithm reverse Share Share a link to this question Copy linkCC BY-SA 4.0 Improve this question Follow Follow this question to receive notifications edited Dec 5, 2019 at 23:01 kaya3 51.6k 7 7 gold badges 86 86 silver badges 117 117 bronze badges asked Dec 5, 2019 at 22:35 HemalHemal 67 2 2 silver badges 7 7 bronze badges 1 @ggorlen oh you are right, I did not notice that. I want to have numbers in an increasing order Hemal –Hemal 2019-12-05 22:44:40 +00:00 Commented Dec 5, 2019 at 22:44 Add a comment\| 2 Answers 2 Sorted by: Reset to default This answer is useful 3 Save this answer. Show activity on this post. There are a couple of problems here; the first is that you want the numbers in order and this code generates them in reverse order, because of range(max_element, 0, -1). The other problem is that since you're generating digits, the minimum element should be 0 and the maximum element should always be 9. We can fix both by changing that range to range(10). We still need to be careful not to generate numbers starting with 0, so we'll make allowed a parameter and use range(1, 10) for just the first digit. I've also changed it to return the result as an integer instead of a tuple. For reference, the code for this generator function comes from my answer to another question. ```python def c(n, k): def helper(n, k, t, allowed): if k == 0: if n == 0: yield t elif k == 1: if n in allowed: yield 10t + n elif 0 <= n <= 9 k: for v in allowed: yield from helper(n - v, k - 1, 10t + v, range(10)) return helper(n, k, 0, range(1, 10)) ``` Example: ```python for p in c(5, 3): ... print(p) ... 104 113 122 131 140 203 212 221 230 302 311 320 401 410 500 ``` Share Share a link to this answer Copy linkCC BY-SA 4.0 Improve this answer Follow Follow this answer to receive notifications edited Dec 5, 2019 at 22:58 answered Dec 5, 2019 at 22:50 kaya3kaya3 51.6k 7 7 gold badges 86 86 silver badges 117 117 bronze badges 4 Comments Add a comment Hemal HemalOver a year ago They closed my post so I created a new one with the code you referred me to, but I was trying to delete the max as I only want to input n and k 2019-12-05T22:54:18.123Z+00:00 0 Reply Copy link Hemal HemalOver a year ago Could i then use " ".join to have 104 form instead of (1,0,4) ? 2019-12-05T22:56:12.223Z+00:00 0 Reply Copy link kaya3 kaya3Over a year ago The problem is to generate "all k-digit numbers whose digits sum up the given n" - there isn't anything to suggest 0 should be excluded, except that the OP's code doesn't include 0. I choose not to infer additional requirements from code which is known not to solve the problem. 2019-12-05T23:29:05.203Z+00:00 1 Reply Copy link ggorlen ggorlenOver a year ago I agree, plus it's a pretty trivial difference. Good answer--seems like the optimizations for the extra branch and checking the sum offer a major efficiency boost. 2019-12-05T23:30:45.983Z+00:00 0 Reply Copy link Add a comment This answer is useful 1 Save this answer. Show activity on this post. This function should do the trick ```python def c(n, k, max_element): allowed = range(max_element, 0, -1) def helper(n, k, t): if k == 0: if n == 0: yield t elif k == 1: if n in allowed: yield t + (n,) elif 1 k <= n <= max_element k: for v in allowed: yield from helper(n - v, k - 1, t + (v,)) return helper(n, k, ()) def reversed_iterator(iter): return reversed(list(iter)) for p in reversed_iterator(c(5, 3, 3)): print(p) ``` here is the output : python (1, 1, 3) (1, 2, 2) (1, 3, 1) (2, 1, 2) (2, 2, 1) (3, 1, 1) Share Share a link to this answer Copy linkCC BY-SA 4.0 Improve this answer Follow Follow this answer to receive notifications answered Dec 5, 2019 at 22:46 Skander HRSkander HR 620 4 4 silver badges 14 14 bronze badges 2 Comments Add a comment ggorlen ggorlenOver a year ago This totally defeats the purpose of using an iterator in the first place. reversed_iterator doesn't return an iterator as it advertises, it just exhausts the iterator and returns a list. 2019-12-05T22:47:08.57Z+00:00 0 Reply Copy link Hemal HemalOver a year ago What about deleting the max_element ? Any suggestions? 2019-12-05T22:47:52.66Z+00:00 0 Reply Copy link Your Answer Thanks for contributing an answer to Stack Overflow! Please be sure to answer the question. Provide details and share your research! But avoid … Asking for help, clarification, or responding to other answers. Making statements based on opinion; back them up with references or personal experience. To learn more, see our tips on writing great answers. Draft saved Draft discarded Sign up or log in Sign up using Google Sign up using Email and Password Submit Post as a guest Name Email Required, but never shown Post Your Answer Discard By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy. Start asking to get answers Find the answer to your question by asking. Ask question Explore related questions python python-3.x algorithm reverse See similar questions with these tags. 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13265	https://www.youtube.com/watch?v=KnVNFj53Eq4	Partial derivatives \| MIT 18.02SC Multivariable Calculus, Fall 2010 MIT OpenCourseWare 5940000 subscribers 301 likes Description 35940 views Posted: 4 Jan 2011 Partial derivatives Instructor: David Jordan View the complete course: License: Creative Commons BY-NC-SA More information at More courses at 10 comments Transcript: hello and welcome back to recitation the problem I'd like to work with you now is uh simply to compute some partial derivatives using the definitions we learned today in lecture uh so first we're going to compute the uh partial derivative in the X direction of this function x y^2 + x^2 y then we're going to compute its derivative in the y direction and then finally we're going to evaluate the partial derivative in the X Direction at a particular point one two it's the first problem and in the second problem we're going to compute uh second partial derivatives now these we just compute by taking the derivative of the derivative just as we do in one variable calculus so um why don't you work on these pause the tape and I'll check back in a moment and we'll see how I solve these okay welcome back let's get started so we have x^2 y excuse me X y^2 Plus x^2 y That's our F so when we take the partial derivative in the X Direction remember this just means that we uh treat y as if it were a constant and we just take an ordinary derivative in the X direction as we would do in one variable calculus so the derivative of this in the X dire direction is just y^2 because we only differentiate the X here similarly here the derivative of x^2 is 2X and Y just comes along for the right as if it were a constant for the partial derivative in the y direction we do the same thing except now um X is a constant and we're taking a ordinary derivative in the y direction so we have 2X y y + x^2 and then the final thing that we need to do is we want to evaluate partial F partial X in at the point one 2 and so all that means is that we have to plug in uh x = 1 and y = 2 into our previous computation and so we get 2^ 2 + 2 1 2 so all together we get eight so that's uh Computing uh partial derivatives now let's move on and compute the second partial derivatives so for instance if we want to compute partial the second partial derivative uh both times in the X Direction so all this means is that we when we took the first partial we we got a function of X and Y and now we just need to take its partial so uh we just need to take the derivative of this again in the X Direction so now the derivative of y^2 be careful the derivative of y^2 in the X direction is just zero because Y is a constant relative to X and so then alog together we just get 2 y when we take the derivative of this x we just get one so that's our partial derivative that's our second partial derivative in the X Direction and and now we can also take mixed partials so here we take uh a derivative in of f uh First We Take the derivative in the y direction and then we take a derivative of that in the X Direction so we can look at our derivative here partial F partial Y and we need to take its partial in the X Direction and so we get uh two y + 2 x now let's see what happens if we switch the order here and we take uh instead the partial derivative in the opposite order so now let's uh go back to our partial derivative of f in the X Direction and let's take its uh derivative now in the y direction so the first term there y^2 gives us a 2 Y and the second term gives us a 2X and I want to just note that these are equal in fact the uh mixed partial derivatives uh whether you take them in the XY order or the YX order uh for for the sorts of functions that we're going to be considering in this class uh for instance all polinomial functions and all um differentiable functions of several variables these mixed partials are going to be equal in in your textbook there are some examples of uh sort of pathological functions where these are not equal but uh for certainly for any polinomial functions these are always going to be equal and I think I'll leave it at that
13266	https://ntrs.nasa.gov/api/citations/20140002333/downloads/20140002333.pdf	NASA/TM-2013-217919 Simple Analytic Expressions for the Magnetic Field of a Circular Current Loop James C. Simpson NASA, Kennedy Space Center, Florida John E. Lane Dynacs, Inc., Kennedy Space Center, Florida Christopher D. Immer Dynacs, Inc., Kennedy Space Center, Florida Robert C. Youngquist NASA, Kennedy Space Center, Florida February 2001 NASA STI Program .. .in Profile Since its founding, NASA has been dedicated to the advancement of aeronautics and space science. The NASA Scientific and Technical Information (STI) program plays a key part in helping NASA maintain this important role. The NASA STI Program operates under the auspices of the Agency Chief Information Officer. It collects, organizes, provides for archiving, and disseminates NASA's STI. The NASA STI program provides access to the NASA Aeronautics and Space Database and its public interface, the NASA Technical Reports Server, thus providing one of the largest collections of aeronautical and space science STI in the world. Results are published in both non-NASA channels and by NASA in the NASA STI Report Series, which includes the following report types: • TECHNICAL PUBLICATION. Reports of completed research or a major significant phase of research that present the results of NASA programs and include extensive data or theoretical analysis. Includes compilations of significant scientific and technical data and information deemed to be of continuing reference value. NASA counterpart of peer-reviewed formal professional papers but has less stringent limitations on manuscript length and extent of graphic presentations. • TECHNICAL MEMORANDUM. Scientific and technical findings that are preliminary or of specialized interest, e.g., quick release reports, working papers, and bibliographies that contain minimal annotation. Does not contain extensive analysis. • CONTRACTOR REPORT. Scientific and technical fmdings by NASA-sponsored contractors and grantees. • CONFERENCE PUBLICATION. Collected papers from scientific and technical , conferences, symposia, seminars, or other meetings sponsored or cosponsored by NASA. • SPECIAL PUBLICATIONS. Scientific, technical, or historical information from NASA programs, projects, and missions, often concerned with subjects having substantial public interest. • TECHNICAL TRANSLATION. English-language translations of foreign scientific and technical material pertinent to NASA's mission. Specialized services also include creating custom thesauri, building customized databases, organizing and publishing research results. For more information about the NASA STI program, see the following: • Access the NASA STI program home page at .sti.nasa.gov • E-mail your question via the Internet to help@sti.nasa.gov • Fax your question to the NASA STI Help Desk at 443-757-5803 • Telephone the NASA STI Help Desk at 443-757-5802 • Write to: NASA Center for Aerospace Information (CASI) 7115 Standard Drive Hanover, MD 21076-1320 NASA/TM-2013-217919 Simple Analytic Expressions for the Magnetic Field of a Circular Current Loop James C. Simpson NASA, Kennedy Space Center, Florida John E. Lane Dynacs, Inc., Kennedy Space Center, Florida Christopher D. Immer Dynacs, Inc., Kennedy Space Center, Florida Robert C. Youngquist NASA, Kennedy Space Center, Florida · National Aeronautics and Space Administration Kennedy Space Center February 2001 NASA/TM-2013-217919 NASA Center for AeroSpace Information 7115 Standard Drive Hanover, MD 21076-1320 Available from: National Technical Information Service 5301 Shawnee Road Alexandria, VA 22312 Available in electronic form at 11 NASAffM-2013-217919 Preface In the late 1990s research was being performed at the Kennedy Space Center to develop in situ resource utilization technology for Mars. One study topic was the generation and storage of liquid oxygen (LOX) obtained from the atmosphere or regolith, but the transfer of this commodity was of concern. Mechanical LOX pumps were deemed potentially too heavy and unreliable for an autonomous mission to Mars, and alternatives were sought. One option was to use the paramagnetic property of LOX, which is significant enough that small quantities of LOX can be suspended against earth gravity with a rare earth magnet. With this application in mind, a small, internally funded project was initiated at the Kennedy Space Center in 2000 to study the use of pulsed magnetic fields to pump LOX. Proof-of-concept testing verified the LOX pumping predictions and resulted in a journal publication . Numerous small coils were fabricated on cryogenic flow lines and used to produce intense, short-duration magnetic fields resulting in dramatic motion of the LOX. In addition, effort was expended on modeling the paramagnetic forces in the LOX, which required modeling the magnetic field generated by the coils and the coil inductance, allowing the current versus time to be predicted and compared to experiment. While we were modeling the coil magnetic field, using Mathematica ™, we came upon a set of simple analytical expressions for the magnetic field and its spatial derivatives in Cartesian, cylindrical, and spherical coordinates generated by a simple, infinitesimally thin current loop. We wrote a short manuscript documenting these expressions, but did not proceed with publication. Instead, this manuscript entered the public domain through two different routes. It appeared first on the NASA Technical Reports Server (NTRS) at the following link: http:/lntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20010038494 2001057024.pdf and then later on the Open Channel Foundation, an organization that publishes software from academic and research institutions. The link for this second site is given below. .openchannelfoundation.org/proj ect/view docs.php? group id=288 Through this link, our manuscript was downloaded multiple times and cited seven times as of the writing of this NASA Technical Memorandum, but only by title and author list and sometimes by web site URL. We, the authors, have decided that there should be a clear, long-term citation for this work, yet we consider it too late to seek formal publication. So we have decided to issue a NASA Technical Memorandum, with the same title and authors as the original manuscript, allowing it to be located by the search engines, and providing a reliable, long-term source and citation for this work. The original manuscript, reformatted, but not in any other way altered, appears on the subsequent pages of this memorandum. We, the authors, would like to express our gratitude to J .M. Griffith, who found a typo in Equation (10) of the original manuscript. This memorandum contains the corrected equation. Youngquist, Robert C., lmmer, Christopher D., Lane, John E., and Simpson, James C., "Dynamics of a Finite Liquid Oxygen Column in a Pulsed Magnetic Field," IEEE Transactions on Magnetics, 39(4), July 4, 2003, pp. 2068-2073. lll NASA/TM-2013-217919 This page was intentionally left blank. iv NASA!TM-2013-217919 1 INTRODUCTION Analytic expressions for the magnetic induction (magnetic flux density, B) of a simple planar circular current loop have been published in Cartesian and cylindrical coordinates [1,2], and are also known implicitly in spherical coordinates . In this paper, we present explicit analytic expressions for B and its spatial derivatives in Cartesian, cylindrical, and spherical coordinates for a filamentary current loop. These results were obtained with extensive use of Mathematica ™ and are exact throughout all space outside of the conductor. The field expressions reduce to the well-known limiting cases and satisfy V · B = 0 and V x B = 0 outside the conductor. These results are general and applicable to any model using filamentary circular current loops. Solenoids of arbitrary size may be easily modeled by approximating the total magnetic induction as the sum of those for the individual loops. The inclusion of the spatial derivatives expands their utility to magnetohydrodynamics where the derivatives are required. The equations can be coded into any high-level programming language. It is necessary to numerically evaluate complete elliptic integrals of the first and second kind, but this capability is now available with most programming packages. 2 SPHERICAL COORDINATES We start with spherical coordinates because this is the system usually used in the standard texts. The Cartesian and cylindrical results in Sections 3 and 4 were derived from the spherical coordinate results. The current loop has radius a, is located in the x-y plane, is centered at the origin, and carries a current I which is positive as shown (Figure 1. ). It is assumed that the cross section of the conductor is negligible. z Po I Figure 1. Circular current loop geometry. 1 ,, NASA/TM-2013- 217919 The vector potential, A, of the loop is given by : 1 2 I d I A (r,B) = #o .Ia J rr COS(/J (/J '~' 4n ° ~a 2 +r 2 -2arsinBcoS(/J 1 =Po 4Ia [(2-e )K(k:)-2E(k 2 J], 4n .Ja2 + r2 + 2arsin e k (1) where r, 8, and qJ are the usual spherical coordinates, and the argument of the elliptic integrals is k 2 = 4arsin8 a2 + r2 + 2arsin8 Note that we use It- for the argument of the elliptic integrals. This choice is consistent with the convention of Abramowitz and Stegun where m =!C. For a static field with constant current, the B components in spherical coordinates are : B,. =_;_e 0° 8 (sin8 A"' ) rsm 1 a B = - --(r A ) H r Or rp Analytic expression for the field components and their derivatives in spherical coordinates are given below. For simplicity we use the following substitutions: a2 = a2 + r2 - 2ar sin 8, [I = a2 + / + 2ar sine, It- = 1- a2Jf, and c = # O 1/n. We note that if desired, further simplifications are possible using various substitutions and groupings. Field Components: B = Ca 2 cosO £lk2 ) ,. a2 fJ I' Spatial Derivatives of the Field Components: 2 (2) (3) (4) (5) (6) (7) (8) dB,= -Ca 2 {[a4 - ?a2r2+r4+ ae 4sin8a 4{3 3 cos 28 ( - 3a 4 + 2a 2r 2 - 3r4 )+ a 2r 2 cos4B]E(e)+ [2a 2 (a 2 +r 2 )cos 2 B]K(e)} oB11 = -C { [a6 _ 3a4r2 + a2r4 + or 4a 4,8 3rsin0 2r 6 + a 2(3r 2 - a 2 )(a 2 + r 2 )cos 20 + 3a 4r 2 cos40]E(k 2 )+ [ a 2 (-a4 + a 2r2 - 2r4 + a 2(a 2 - 3r 2 )cos 20)] K (k 2 )} dB 11 -C cos 8 { [s o 3 4 2 3 2 4 -- = a + a r -a r ae 4a 4{3 3 sin 2 B NASA/TM-20 13-21 7919 (9) (10) +2r. 6 + ( -3a 6 + 2a 4r 2 + 9a 2r 4 )cos 28 + a 4r 2 cos 48 J E(k 2 )-[ 3a 6 + 2a 4r 2 + a 2r 4 + 2r 6 + a 2(5r 2 -:-a 2 )(a2 +r2 )cos2B+ ( - 7a 5r+7a 3r 3 -4ar 5 )sinO+ a 3r(a 2 -5r2 )sin3B] K(k 2 J} 3 CARTESIAN COORDINATES (11) The field components and their derivatives in Cartesian coordinates are given below. These are easier to use when rotations or translations are needed and obviate the need to transform the basis vectors. The following substitutions are used for simplicity: p2 = x2 + l, r2 = x2 + l+ i, a 2 = a2 + r2 - 2ap, p2 = a2 + r2 + 2ap, k = 1- a2/p2, y = x2 -l, and C = p.o li1C. Note that p and r are non-negative. Field Components: (12) (13) 3 NASA/TM-2013-217919 Spatial Derivatives of the Field Components: dBx = C z { [a4 (-y( 3z2 + a2 )+ p2(8x2 _ / J)-dx 2a 4 f3 3p 4 a2 (p\5x2 + y 2 )-2p2z2(2x2 + y 2 )+3z4y)-r4 ( 2x4 + y(y2 + z2)) J E ( k 2) + [ a2 (y(a 2 + 2z 2 )- p2(3x2- 2y2 J)+ r 2 ( 2x4 + y(y 2 + z 2 ))] a 2 K (e)} dBx = C x y z { [3a4(3/ _ 222 )-r4(2r2 + p2 )-dy 2a4f33p4 2a 6 -2a2(2p4- /z2 +3z4) J E(e )+ [r2(2r2 + / )-a2(5p2 -4z2 )+ 2a4 J a2 K (e)} asx = Cx {~p2-a2y2(/+a2)+ az za4p3p2 2z2(a4- 6a2 p2 + p4 )+ z4(a2 + p2 ;] E(k2 )-~p2 -a2 i +z2(/ +a2 J]a2 K(k2}} dEY= dBx dx dy dEY= C z { [a4 (y(3z2 +a2 )+ /(Si -x2 J)-dy 2a4f33 p4 a2 (p4(5y2 +x2 )-2p2z2(2/ +x2 )-3z4y)-r4 (2y4 -y(x2 + z2 J)] E( k2 )+ [ a2 ( -y(a2 + 2z2)- / (3 y2 - 2x2)) + r 2 ( 2y4 - y(x2 + z 2))] a2 K (e)} ()B.v =L ()Bx dZ X dz dBz = dBx dx dz 4 (14) (15) (16) (17) (18) (19) (20) (21) NASA/TM-2013-217919 CJB CJBv _ z= -· dy dz dBz = C z {[6a2(p2 - z2 )-7a4 +r4]E(k2 )+ dz 2a4f3 3 a2 [ a2 - r2 J K(k2) 4 CYLINDRICAL COORDINATES The following substitutions are used for simplicity: a2 = a2 + / + i- 2ap, f = a2 + p2 + i + 2ap, /(- = 1 - a2if, and C = Jlo 117r:. Field Components: Spatial Derivatives of the Field Components: ()B -Cz { [ - " = 2 4 3 a6 +(p 2 + z2 /( 2p2 + z2 )+ dp 2p a fJ a\3 z 2- 8p2) + a 2(5p 4- 4p 2z2 + 3 z4)]E(e) -a 2[a 4- 3a 2p2+2p4+ (2a 2 +3p2 )z2 +z 4 ]K(k 2 )} ()B C { - " = 4 [(a2 + p2 )(z4 +(a2-// )+ ()z 2pa {33 2z2(a4 -6a2 / + p4) ]E(k2 )-a2 [(a2- P2 / +(a2 + P2 )z2 ]K(e J} dBz = Cz {[(6a 2(p 2-z2) - 7a4+ dz 2a 4f3 3 ( p 2 + z 2 / J E (k 2 ) + a 2 [a 2 - p 2 - z 2 J K ( k 2 ) } dBz = dBP dp dz 5 (22) (23) (24) (25) (26) (27) (28) (29) NASA/TM-2013- 217919 5 LIMITING CASES Several special limiting cases are given for completeness. We have confirmed that our results given above do indeed converge to these formulas. We also give additional expressions for Bx and By near the axis that may prove useful. Along the axis of the loop: Near the axis of the loop (x,y<>a): 6 CONCLUSIONS B _ Jlo /] 2 ) cos() - - ~,1ta --, 27C r3 B _ Jlo /] 2 ) sin() fl- - ~,1ta --47C r 3 (30) (31) (32) (33) (34) We have presented simple, closed-form algebraic formulas for the magnetic induction and its spatial derivatives of a filamentary current loop that are exact everywhere in space outside the conductor. Although these formulas are exact, they do require the numerical evaluation of elliptic integrals. Solenoids with circular cross sections of arbitrary size and configuration can be modeled by simply summing the contributions of each individual loop. There are, of course, other ways to obtain B for the basic circular current loop. For example, series expansions are available or numerical integration via a finite element approach can be performed. However, these suffer from limitations such as truncating the series expansions after some tolerance is reached or accepting some graininess when using a discrete grid. Our approach has neither of these limitations and yields results are that exact up to the limitations of the numerical arithmetic and the elliptic integral routines. The inclusion of the spatial derivatives allows convective derivatives to be found exactly and . . may prove useful for magnetohydrodynamics applications. 6 NASA!fM-2013-217919 References Chu, Y., ''Numerical Calculation for the Magnetic Field in Current-Carrying Circular Arc Filament," IEEE Trans. Magn., 34, 1998, pp. 502-504. Garrett, Milan Wayne, "Calculation of Fields, Forces, and Mutual Inductances of Current Systems by Elliptic Integrals," Journal of Applied Physics, 34(9), September 1963, pp. 2567-2573. Jackson, J.D., Classical Electrodynamics, 3rd Edition, John Wiley & Sons, 1998, pp. 181-183. [ 4] Abramowitz, M., and Stegun, I. A., Handbook of Mathematical Functions, Dover, 1972, p. 590. 7
13267	https://www.gauthmath.com/solution/1811112725083141/sin-37-cos-37-tan-37-	Solved: sin (37)= cos (37)= tan (37)= [Math] Drag Image or Click Here to upload Command+to paste Upgrade Sign in Homework Homework Assignment Solver Assignment Calculator Calculator Resources Resources Blog Blog App App Gauth Unlimited answers Gauth AI Pro Start Free Trial Homework Helper Study Resources Math Trigonometry Questions Question sin (37)= cos (37)= tan (37)= Gauth AI Solution 100%(3 rated) Answer $$\sin(37) = \frac{5.08}{8.44}$$sin(37)=8.44 5.08, $$\cos(37) = \frac{6.74}{8.44}$$cos(37)=8.44 6.74, $$\tan(37) = \frac{5.08}{6.74}$$tan(37)=6.74 5.08 Explanation Find $$\sin(37)$$sin(37) $$\sin(37) = \frac{AB}{AC} = \frac{5.08}{8.44}$$sin(37)=A C A B=8.44 5.08 Find $$\cos(37)$$cos(37) $$\cos(37) = \frac{BC}{AC} = \frac{6.74}{8.44}$$cos(37)=A C BC=8.44 6.74 Find $$\tan(37)$$tan(37) $$\tan(37) = \frac{AB}{BC} = \frac{5.08}{6.74}$$tan(37)=BC A B=6.74 5.08 Helpful Not Helpful Explain Simplify this solution Gauth AI Pro Back-to-School 3 Day Free Trial Limited offer! Enjoy unlimited answers for free. Join Gauth PLUS for $0 Previous questionNext question Related Select all true equations sin 37=cos 53 cos θ =sin 90- θ tan 37=tan 53 sin 37=sin 53 cos 37=sin 53 100% (4 rated) Select all true equations. sin 37=cos 53 tan 37=tan 53 cos θ =sin 90- θ cos 37=sin 53 sin 37=sin 53 100% (4 rated) elect all true equations. tan 37=tan 53 sin 37=cos 53 cos 37=sin 53 sin 37=sin 53 cos θ =sin 90- θ 100% (5 rated) Select all true equations. A cos 37=sin 53 B tan 37=tan 53 c sin 37=cos 53 D sin 37=sin 53 ε cos θ =sin 90- θ 100% (3 rated) Select all that apply: A. cos 37=sin 53 B. tan 37=tan 53 C. sin 37=cos 53 D. sin 37=sin 53 E. cos θ =sin 90- θ 100% (1 rated) Select the FALSE equation. Answer Attempt 1 out of 2 cos 37=sin 53 tan 37=tan 53 sin 37=sin 53 sin 37=cos 53 100% (2 rated) Question Select the FALSE equation. Answer Attempt 1 out of 2 cos 37=sin 53 tan 37=tan 53 sin 37=cos 53 sin 37=sin 53 100% (1 rated) Question : 73% Select the FALSE equation. Answer Attempt 1 out of 2 cos 37=sin 53 tan 37=tan 53 Sce on sin 37=cos 53 D sin 37=sin 53 100% (3 rated) This is the only question in this section. Question Select the FALSE equation. Answer Attempt 2 out of 2 cos 37=sin 53 tan 37=tan 53 sin 37=cos 53 sin 37=sin 53 100% (3 rated) Technology required. Ramps in a parking garage need to be steep. The maximum safe incline for a ramp is 8.5 degrees. Is this a safe ramp? Explain or show your reasoning. From Unit 4, Lesson 9. 6. Select all true equations. A. cos 37=sin 53 B. tan 37=tan 53 C. sin 37=cos 53 D. sin 37=sin 53 E. cos θ =sin 90- θ From Unit 4, Lesson 8. 100% (5 rated) Gauth it, Ace it! contact@gauthmath.com Company About UsExpertsWriting Examples Legal Honor CodePrivacy PolicyTerms of Service Download App
13268	https://math.stackexchange.com/q/2240535	Extend a fourier function to an odd function - Mathematics Stack Exchange Join Mathematics By clicking “Sign up”, you agree to our terms of service and acknowledge you have read our privacy policy. Sign up with Google OR Email Password Sign up Already have an account? Log in Skip to main content Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Visit Stack Exchange Loading… Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company, and our products current community Mathematics helpchat Mathematics Meta your communities Sign up or log in to customize your list. more stack exchange communities company blog Log in Sign up Home Questions Unanswered AI Assist Labs Tags Chat Users Teams Ask questions, find answers and collaborate at work with Stack Overflow for Teams. Try Teams for freeExplore Teams 3. Teams 4. Ask questions, find answers and collaborate at work with Stack Overflow for Teams. Explore Teams Teams Q&A for work Connect and share knowledge within a single location that is structured and easy to search. Learn more about Teams Hang on, you can't upvote just yet. You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation and how do I get it? Instead, you can save this post to reference later. Save this post for later Not now Thanks for your vote! You now have 5 free votes weekly. Free votes count toward the total vote score does not give reputation to the author Continue to help good content that is interesting, well-researched, and useful, rise to the top! To gain full voting privileges, earn reputation. Got it!Go to help center to learn more Extend a fourier function to an odd function Ask Question Asked 8 years, 5 months ago Modified8 years, 5 months ago Viewed 159 times This question shows research effort; it is useful and clear 1 Save this question. Show activity on this post. Given is a function f(x)= 1-x with 0 < x < 1 that should be extended on the interval [-1, 1] to get an odd function. Outside this interval it should be continued with a period of 2. If it would be an even function, I would extend it to f(x) = 1-\|x\| as even functions are symmetric around the y-axis. Would this be correct? Now I am not sure, how to extend it to an odd function. I remember that odd functions should be point symmetric around the origin, and I think that in this case it will stay the same: f(x)= 1-x. Can this be correct? functions fourier-analysis Share Share a link to this question Copy linkCC BY-SA 3.0 Cite Follow Follow this question to receive notifications asked Apr 18, 2017 at 17:41 mrs fouriermrs fourier 157 16 16 bronze badges Add a comment\| 1 Answer 1 Sorted by: Reset to default This answer is useful 1 Save this answer. Show activity on this post. You need 1−x 1−x on (0,1)(0,1) so on (−1,0)(−1,0) the result is −1−x−1−x. There is a discontinuity at 0 0, where any odd function must be 0 0. By periodicity, the function should vanish at all even integers. You can work out the function elsewhere; note that, except at discontinuities, the gradient is always −1−1. Share Share a link to this answer Copy linkCC BY-SA 3.0 Cite Follow Follow this answer to receive notifications answered Apr 18, 2017 at 17:47 J.G.J.G. 118k 8 8 gold badges 79 79 silver badges 146 146 bronze badges 1 Thanks a lot. This really makes sense. :)mrs fourier –mrs fourier 2017-04-22 16:28:19 +00:00 Commented Apr 22, 2017 at 16:28 Add a comment\| You must log in to answer this question. Start asking to get answers Find the answer to your question by asking. Ask question Explore related questions functions fourier-analysis See similar questions with these tags. Featured on Meta Introducing a new proactive anti-spam measure Spevacus has joined us as a Community Manager stackoverflow.ai - rebuilt for attribution Community Asks Sprint Announcement - September 2025 Report this ad Related 0Odd and even function properties... 0How to extend a given function to an odd function with period 2 (Fourier Series) 0What is f(18)f(18) if f f is odd with period 5 5 and f(−8)=1 f(−8)=1? 1Fourier series for a non-periodic function on an Interval 0Odd and even extension (fourier series) 0Fourier Analysis - Functions on a Circle 0What is the reason for the shape of these Fourier series graphs? Hot Network Questions Why do universities push for high impact journal publications? ICC in Hague not prosecuting an individual brought before them in a questionable manner? Numbers Interpreted in Smallest Valid Base Any knowledge on biodegradable lubes, greases and degreasers and how they perform long term? How to locate a leak in an irrigation system? 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13269	https://pmc.ncbi.nlm.nih.gov/articles/PMC7171457/	Rats - PMC Skip to main content An official website of the United States government Here's how you know Here's how you know Official websites use .gov A .gov website belongs to an official government organization in the United States. Secure .gov websites use HTTPS A lock ( ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites. Search Log in Dashboard Publications Account settings Log out Search… Search NCBI Primary site navigation Search Logged in as: Dashboard Publications Account settings Log in Search PMC Full-Text Archive Search in PMC Advanced Search Journal List User Guide New Try this search in PMC Beta Search PERMALINK Copy As a library, NLM provides access to scientific literature. Inclusion in an NLM database does not imply endorsement of, or agreement with, the contents by NLM or the National Institutes of Health. Learn more: PMC Disclaimer \| PMC Copyright Notice Clinical Veterinary Advisor . 2012 Dec 10:242–252. doi: 10.1016/B978-1-4160-3969-3.00138-4 Search in PMC Search in PubMed View in NLM Catalog Add to search Rats Editors: Jörg Mayer 1, Thomas M Donnelly 2,3 Author information Article notes Copyright and License information 1 Associate Professor of Zoological Medicine, Department of Small Animal Medicine & Surgery, College of Veterinary Medicine, The University of Georgia, Athens, Georgia 2 The Kenneth S. Warren Institute, Ossining, New York 3 Adjunct Associate Professor, Department of Clinical Sciences, Tufts Cummings School of Veterinary Medicine, North Grafton, Massachusetts Issue date 2013. Copyright © 2013 Elsevier Inc. All rights reserved. Since January 2020 Elsevier has created a COVID-19 resource centre with free information in English and Mandarin on the novel coronavirus COVID-19. The COVID-19 resource centre is hosted on Elsevier Connect, the company's public news and information website. Elsevier hereby grants permission to make all its COVID-19-related research that is available on the COVID-19 resource centre - including this research content - immediately available in PubMed Central and other publicly funded repositories, such as the WHO COVID database with rights for unrestricted research re-use and analyses in any form or by any means with acknowledgement of the original source. These permissions are granted for free by Elsevier for as long as the COVID-19 resource centre remains active. PMC Copyright notice PMCID: PMC7171457 Chromodacryorrhea Basic Information Definition Porphyrin-pigmented tears secreted by the harderian glands of rats. Chromodacryorrhea literally means “excessive production of colored tears” (chromo Gk = color; dacryo Gk = gland; rhea = to pour out). Synonym Red tears Epidemiology Species, Age, Sex Besides rats, red-pigmented harderian gland secretions are seen in certain strains of inbred mice (e.g., C3H, A, I, JK, C57 mice), Syrian hamsters, Chinese hamsters (Cricetulus griseus), and deer mice (Peromyscus leucopus). Old and sick rats are most commonly affected. Risk Factors • Stress • Overcrowding • Poor husbandry Contagion and Zoonosis Sialodacryoadenitis virus (SDAV) can directly affect the harderian glands. Associated Conditions and Disorders Pain, stress, systemic infection (Mycoplasma pneumoniae, SDAV). Any disease that leads to depression and reduced grooming. Chronic physiological stress in rats is likely to cause chromodacryorrhea. Clinical Presentation History, Chief Complaint • Sudden onset of red staining around the eyes and nostrils • Labored breathing • Reduced appetite • Lethargy • Recent purchase from a pet store Physical Exam Findings • Red staining around the eyes and nostrils, and occasionally the forepaws (from wiping the nares) • Usually clinical signs are associated with nutritional deficiencies, chronic physiologic stress (e.g., disease), chronic light exposure, or dacryoadenitis. Etiology and Pathophysiology • Any disease or condition that results in chronic stress will result in chromodacryorrhea. • Harderian glands of rodents with “red tears” exhibit a variety of histological autofluorescence patterns. In addition, their secretions are also affected by protoporphyrin binding to lipids, affecting fluorescence. ○Inflammation of the harderian gland (i.e., dacroadenitis) causes an increase in secretions. The most common cause is infection with SDAV, a coronavirus of rats. ○The tears are secreted via activation of the parasympathetic nervous system via muscarinic receptors. Anticholinergic drugs have been shown to block secretions. ○Harderian glands' secretions predominantly contain lipids that act as pheromones. The presence of porphyrins in Harderian gland secretions is more the exception than the rule when describing these secretions in rodents. Generally, porphyrins give color to secretions. Diagnosis Differential Diagnosis • Epistaxis • Conjunctivitis Initial Database • Wood's lamp examination reveals bright orange-red fluorescence; allows differentiation from dried blood • Further diagnostics will dependent on the clinical signs and suspected primary underlying disease, such as respiratory tract disease (see Respiratory Tract Disease, Acute, and Respiratory Tract Disease, Chronic). Treatment Therapeutic Goal Address specific underlying cause if known. Acute General Treatment • Depends on the underlying primary cause (e.g., nutritional deficiency, respiratory disease) • If due to SDAV, clinical signs will persist for 1 week, then will resolve spontaneously. Mortality is low. Chronic Treatment • Maintain proper husbandry. • Ensure proper diet. • Minimize stress. Recommended Monitoring If clinical signs persist longer than 1 week and no specific underlying cause can be identified, recommend recheck appointment for further diagnostics. Prognosis and Outcome Prognosis depends on underlying cause. If clinical signs are due to stress or husbandry, the prognosis is excellent if properly addressed. For other causes, the prognosis will vary from poor to good. Pearls & Considerations Comments Many clients will present in distress because their pet is “bleeding from the eyes.” They will be relieved to know that their pet is not actually bleeding but will need to understand that this clinical sign can be an indicator of a greater underlying disease that warrants investigation. Client Education Chromodacryorrhea is not an actual disease in most cases but an indicator for an underlying problem or stress. Suggested Reading Donnelly TM. What's your diagnosis? Blood-caked staining around the eyes in Sprague-Dawley rats. Lab Anim Sci. 1997;26(1):17–18. [Google Scholar] Harkness JE. Chromodacryorrhea in laboratory rats (Rattus norvegicus): etiologic considerations. Lab Anim Sci. 1980;30:841–844. [PubMed] [Google Scholar] Cross-References to Other Sections Respiratory Tract Disease, Acute Respiratory Tract Disease, Chronic AUTHOR: BRIAN A. EVANS and THOMAS M. DONNELLY EDITOR: CHRISTOPH MANS Mammary and Pituitary Tumors Client Education Sheet Available on Website Basic Information Definition Mammary gland tumors are the most frequently occurring tumors in female rats. Histologically, most are mammary fibroadenomas, although adenocarcinomas are also seen. Special Species Consideration Rats have 12 mammary glands along the mammary chain, which extends from the cervical region to the tail base. Mammary tumors can arise in any of these locations. Epidemiology Species, Age, Sex • Older animals are most frequently affected (>1 year of age). • Females are at higher risk than males; an incidence of 2% to 16% has been reported experimentally in male rats. Genetics and Breed Predisposition In inbred rat strains susceptible to mammary tumors expression levels of several prolactin-regulated genes are significantly elevated (e.g., messenger RNA's encoding prolactin and its cell surface receptor are amplified) indicating the presence of increased prolactin signaling in the mammary glands of mammary tumor susceptible rat strains. Risk Factors • Sex: females at higher risk than males • Age: higher risk at greater than 2 years of age • Nutrition: increased incidence with high-fat diets, reduced incidence with food restriction • Prolactin-secreting pituitary tumors: increased risk of mammary tumors • Neuter status: decreased risk if ovariectomized by 90 days of age; suspected to also have decreased risk even if ovariectomized after 90 days of age, but this has not been proven. • The frequency of mammary tumors and pituitary tumors is significantly lower in 18- to 24-month-old ovariectomized (4%) versus sexually intact (mammary tumors, 49%; pituitary tumors, 59%) rats. Therefore, the decreased frequency of mammary tumor development could be related to the decreased frequency of prolactin-secreting pituitary tumors. Associated Conditions and Disorders Prolactin-secreting pituitary tumors (see Risk Factors) Clinical Presentation History, Chief Complaint • Rapidly growing mass in region of mammary gland tissue • Bleeding and/or odor if secondarily infected or ulcerated Physical Exam Findings • Circumscribed, movable, firm, subcutaneous mass in the region of the mammary glands, which extends from the cervical region to the tail base. • The overlying skin may be ulcerated or infected if the mass is large, or if the surface has been traumatized. Etiology and Pathophysiology • As with other species, most mammary gland development occurs during puberty primarily under influence of estrogen and pregnancy under the influence of progesterone and prolactin. • Neutering sexually immature females removes estrogen influence during mammary growth and prevents mammary epithelial ductal elongation, bifurcation, and extension throughout the fat pad. Inhibition of ductal morphogenesis significantly reduces the risk of mammary tumors by limiting the amount of mammary tissue that develops. • Estrogen is an important stimulator of prolactin secretion that acts directly on pituitary lactotrophs and via the hypothalamus. Experimentally prolactinomas can be induced in rats by chronic estrogen administration. In the mammary gland, prolactin stimulates alveolar epithelial proliferation with its fibrous connective tissue support structure. • Aging female rats exhibit changes in estrous cycle and reproductive patterns. At 10-12 months of age, the once-regular ovulatory cycles gradually become lengthened and irregular and eventually develop into a prolonged period of constant estrus characterized by ovaries containing big follicles that secrete large quantities of estrogen. Neutering sexually mature females removes constant estrogen secretion and decreases prolactin secretion so benign mammary tumors either do not develop or do not increase in size. • Female rats with benign mammary tumors have 27 times higher plasma levels of prolactin than 6-month-old virgin rats, and prolactin levels similar to that of rats on the seventh day postpartum. Because of this, rats with prolactin-secreting pituitary tumors are at increased risk of mammary tumor development. • In aging rats, prolactin secretion is increased and is reflected in the high blood prolactin level in both sexes. This change is due to a reduction of hypothalamic dopamine activity. The escape from hypothalamic inhibitory control leads to lactotroph hyperplasia and a high incidence of prolactin cell adenomas in old rats. • Gene expression of spontaneous fibroadenomas and adenocarcinomas compared to a normal rat mammary gland in the same developmental state has shown that fibroadenomas do not progress to adenocarcinoma. • Adenocarcinomas arise de-novo (i.e., without prior adenoma stage) and represent fewer than 10% of mammary tumors in pet rats. • Fibroadenomas can reach 8-10 cm in diameter and do metastasize. Diagnosis Differential Diagnosis • Dermal/subcutaneous abscess (e.g., from bite wounds, foreign body penetration) • Neoplasia (e.g., lymphoma) • Mastitis Initial Database • Fine-needle aspirate: caution during interpretation because large mammary tumors may be necrotic and can be difficult to differentiate from an abscess on cytology • Blood work: complete blood count and serum biochemistry screening as a preoperative workup • Thoracic radiographs/CT: preoperative workup if underlying respiratory disease is suspected Advanced or Confirmatory Testing Histopathologic examination Treatment Therapeutic Goals • Stabilization of the patient if septic or has suffered blood loss • Complete surgical removal of the tumor (mastectomy) and prevention of recurrence Acute General Treatment • If necessary, stabilization of the patient if mammary tumor is infected/sepsis is present, or if blood loss has ensued from ulceration of the mass. • Complete surgical removal of the tumor and any ulcerated/infected skin or tissue is the treatment of choice. ○Because tumors may be quite large, closure of dead space is important to prevent seroma formation. ○Some masses are difficult to remove if they are in close association with the vulva. • Concurrent ovariectomy is recommended if patient is stable. Chronic Treatment Because recurrence of mammary tumors at different locations can frequently occur, repeated surgical removal might be necessary. Possible Complications Rats are notorious for mutilation of surgical sites, so appropriate pain medication with monitoring is compulsory. Use of an E-collar is necessary in some cases to prevent mutilation. Recommended Monitoring Tumors are likely to recur in other mammary glands in both male and female rats, especially if ovariectomy is not performed at the same time. Constant monitoring and palpation of the mammary glands are important. Prognosis and Outcome • In general, survival following mastectomy is good. • Quality of life is improved post mastectomy; however, controversy continues over whether tumor removal actually prolongs survival time. • Death can occur with sepsis or blood loss if the mammary mass is not surgically removed and becomes ulcerated or infected. Controversy • To date, the only proven treatment and prevention of mammary tumor development consists of surgical removal of the tumor and ovariectomy. Other treatments have been discussed but have not proven to be effective in preventing recurrence of spontaneous tumors or in decreasing their size once present. • Cabergoline is a prolactin inhibitor that suppresses pituitary prolactin secretion and can be given orally. It has been successfully used in the palliative treatment of a pituitary adenoma in a rat at a dose of 0.6 mg/kg PO q 72 h, and thus may be helpful in rats that have mammary tumor development secondary to prolactin-secreting pituitary tumors and in those unable to undergo ovariectomy. • Gonadotropin-releasing hormone (GnRH) agonists ○Deslorelin implants (4.7 mg) have been used experimentally to suppress estrus in rats for 1 year and may be useful in rats that cannot be ovariectomized. ○Leuprolide acetate has been experimentally shown to suppress the ability of the pituitary-gonadal system to secrete gonadotropin and testosterone for over 5 weeks; similar to deslorelin because it may be useful in rats that cannot undergo ovariectomy • Melatonin induces apoptosis of rat prolactin-secreting tumors. Experimentally, SC melatonin administration in experimentally induced tumor-bearing rats significantly increased survival time and reduced prolactin levels but did not change the mammary tumor growth rate. • Tamoxifen: antiestrogen used in the treatment of human breast cancer. This agent would be useful only in mammary adenocarcinomas that are estrogen receptor positive. This drug is NOT recommended, given the low incidence of adenocarcinoma in rats and the fact that it has been shown to induce hepatic cancer and proliferation of the rat uterus. Pearls & Considerations Comments Histopathologic examination of removed tumors should be performed because spontaneous mammary adenocarcinoma has a 5%-10% incidence. Individual genetic variability and environmental factors such as nutrition and maternal effects in utero and during lactation most likely affect quantitative trait loci (QTL) that control susceptibility to mammary adenocarcinoma. However, the individual genetic traits and QTL that influence gene function have not yet been elucidated. Prevention • Ovariectomy of female rats by 90 days of age • Treatment of prolactin-secreting pituitary tumors Client Education • All clients who own female rats should be educated about the importance of ovariectomy before 90 days of age. • Additionally, clients should be educated on the importance of early detection and removal of tumors before they become too large to be safely removed surgically. Suggested Readings Alkis I. Long term suppression of oestrus and prevention of pregnancy by deslorelin implant in rats. Bull Vet Inst Pulawy. 2011;55:237–240. [Google Scholar] Hotchkiss C. Effect of surgical removal of subcutaneous tumors on survival of rats. J Am Vet Med Assoc. 1995;206:1575–1579. [PubMed] [Google Scholar] Marxfeld H. Gene expression in fibroadenomas of the rat mammary gland in contrast to spontaneous adenocarcinomas and normal mammary gland. Exp Toxicol Pathol. 2006;58:145–150. doi: 10.1016/j.etp.2006.06.007. [DOI] [PubMed] [Google Scholar] Mayer J. Extralabel use of cabergoline in the treatment of a pituitary adenoma in a rat. J Am Vet Med Assoc. 2011;239:656–660. doi: 10.2460/javma.239.5.656. [DOI] [PubMed] [Google Scholar] Saez MC. Melatonin increases the survival time of animals with untreated mammary tumours: neuroendocrine stabilization. Mol Cell Biochem. 2005;278:15–20. doi: 10.1007/s11010-005-7755-9. [DOI] [PubMed] [Google Scholar] Open in a new tab Mammary and Pituitary Tumors Large mammary fibroadenoma on a female rat. Note the close proximity to the left hind leg which impeded normal ambulation. Open in a new tab Mammary and Pituitary Tumors A, An MRI scan of the head of a 3-year-old rat showing a large pituitary tumor within the brain. B, An MRI scan of the same rat shown in A eight weeks after treatment with cabergoline. Note the signifi cant shrinking of the tumor. (Photo courtesy Jörg Mayer, The University of Georgia, Athens.) AUTHOR: NICOLE R. WYRE and THOMAS M. DONNELLY EDITOR: CHRISTOPH MANS Renal Disease Basic Information Definition Kidney or renal disease is a general term that describes any damage that reduces the functioning of the kidney. Synonyms • Kidney disease: renal disease, kidney disease, kidney failure, chronic renal failure, nephropathy, suppurative pyelonephritis, suppurative nephritis • Chronic progressive nephrosis in rats: progressive renal disease in rats, progressive glomerulonephrosis, old rat nephropathy, glomerulosclerosis • Nephrocalcinosis: renal tubular mineralization Epidemiology Species, Age, Sex • Male rats develop a more severe form of chronic progressive nephrosis, usually earlier in life than females; lesions are more severe in rats over 12 months of age. • Nephrocalcinosis is more common in females and can be found in animals as young as 7 weeks of age. Blood estrogen levels may play a role in that the disease can be prevented by ovariectomy and is induced in castrated male and female rats by estrogen administration. Genetics and Breed Predisposition A significantly higher prevalence of chronic progressive nephrosis is seen in the Sprague-Dawley strain of rat. Osborne-Mendel and Buffalo strains are relatively insusceptible. Elevated prolactin levels are suspected of contributing to more severe disease. Risk Factors • Chronic progressive nephrosis: high-protein diets designed for superior body growth result in earlier onset of more severe disease • Nephrocalcinosis: may be the result of a number of dietary factors, including magnesium deficiency, elevated dietary phosphorus or calcium, and diet preparations with a low calcium-to-phosphorus ratio • Suppurative pyelonephritis/nephritis: isosthenuria, urolithiasis, and lower urinary tract infections Clinical Presentation Disease Forms/Subtypes • Chronic progressive nephrosis • Nephrocalcinosis • Suppurative pyelonephritis/nephritis History, Chief Complaint • Clinical signs vary with severity of kidney pathology: ○Polydipsia and polyuria ○Anorexia ○Weight loss ○Lethargy Physical Exam Findings • In any rat with renal disease, morbidity may vary from slight to none to significant, depending on the progression and severity of disease. ○Lethargy ○Weight loss ○Cachexia ○Dehydration ○Poor fur quality ○Abdominal pain ○Diarrhea ○Hypertension Etiology and Pathophysiology • Chronic progressive nephrosis ○A high protein diet may acutely increase the glomerular filtration rate, possibly causing intraglomerular hypertension, which would lead to progressive loss of renal function. ○Albuminuria not only serves as a marker of glomerular injury but is also associated with tubulointerstitial injury. • Nephrocalcinosis ○In rats, no single mechanism has been identified that explains the association between all dietary factors that have been related to the prevalence of nephrocalcinosis. ○Nutritional studies have shown that diets high in phosphorus or low in calcium, with a net Ca : P molar ratio of less than 1.0, contribute to the development of nephrocalcinosis lesions. Increasing the calcium and phosphorus content and the Ca : P ratio to greater than 1.0 and closer to 1.3 markedly decreased the incidence and severity or prevented the occurrence of nephrocalcinosis lesions. • Suppurative pyelonephritis/nephritis ○Caused by various predominantly gram-negative bacterial organisms (e.g., Pseudomonas, Escherichia coli, Proteus mirabilis), which usually ascend to renal pelvis from lower urinary tract. ○Chronic pyelonephritis is more common and frequently is clinically inapparent. Diagnosis Differential Diagnosis • Hydronephrosis • Neoplasia • Polycystic kidney disease • Calculi-associated obstructive disease • Toxic nephrosis • Ischemic injury Initial Database • Urinalysis ○Isosthenuria (normal specific gravity, 1.022-1.050) ○Proteinuria (mild proteinuria is normal in rats) ○Hematuria ○Sediment analysis: casts, crystals, inflammatory or neoplastic cells, bacteria • Urine culture • Complete blood count: may be normal ○Nonregenerative anemia ○Leukocytosis • Serum biochemistry profile ○BUN elevation ○Creatinine elevation ○Hyperphosphatemia ○Hypocalcemia or hypercalcemia ○Hypokalemia or hyerpkalemia ○Hypercholesterolemia ○Hypoproteinemia • Diagnostic imaging ○Radiography: assess for increases or decreases in kidney size, radiopaque calculi within the urinary tract, abdominal masses associated with the urinary tract, and bladder distention. ○Ultrasonography: discern size, contour, and texture of the kidneys, allowing for differentiation of focal versus diffuse disease Advanced or Confirmatory Testing • Perform ultrasound-guided fine-needle aspiration for cytology • Contrast urography • Histopathologic examination Treatment Therapeutic Goals • Delay progression of renal disease. • Preserve overall patient well-being and quality of life. • Promote diuresis and diminish the consequences of azotemia. • Treat underlying or concurrent urinary tract infection, Acute General Treatment • Discontinue any potentially nephrotoxic drugs. • Identify and treat any prerenal or postrenal abnormalities. • Identify any treatable conditions such as urolithiasis or pyelonephritis. • Fluid therapy ○To induce diuresis and correct azotemia, electrolyte, and acid-base imbalances ○Use of isotonic crystalloids ○Subcutaneous administration: 60-100 mL/kg/d ○ Intravenous fluid therapy ▪Use lateral coccygeal or cephalic vein. ▪Maintenance fluids are 3-4 mL/kg/h. ○Potassium supplementation of fluids based on blood potassium measurement • Antibiotic therapy ○Indicated for cases of suppurative pyelonephritis/nephritis and cystitis ○Antibiotic selection should be based on culture and susceptibility whenever possible. ○For empirical treatment, or for cases with negative urine culture, despite clinical suspicion, use antibiotics, which are effective against Gram-negative organisms and are renally excreted, to reach high tissue concentrations. ○Amoxicillin/clavulanic acid 15-20 mg/kg PO q 8-12 h ○Trimethoprim-sulfa 15-30 mg/kg PO q 12 h ○Enrofloxacin 10-20 mg/kg PO q 12-24 h • If hyperphosphatemic, alter diet and initiate enteric phosphate binders: ○Aluminum hydroxide 30-90 mg/kg/d, divided and administered with food • Treat increased gastric acidity with H2 blockers: ○Famotidine 0.5 mg/kg PO, SC q 24 h ○Ranitidine 1-2 mg/kg PO, SC q 12 h • Multivitamin supplementation is recommended because the excessive amount of urine produced by failing kidneys commonly results in loss of water-soluble vitamins. Chronic Treatment • Maintain long-term dialysis with maintenance subcutaneous fluid therapy (owners can be taught to do this at home): 60-100 mL/kg/d SC. • Antibiotic therapy for chronic pyelonephritis should be at least 4-6 weeks. • Dietary management: high protein appears to be the major cause of severe nephropathy, and the term protein-overload nephropathy is often used. Changing the source of protein to one such as soy protein, restricting caloric intake, or modifying the diet to decrease protein consumption could decrease the severity of nephropathy. Changing the diet so that the Ca:P ratio is greater than 1.0 and is closer to 1.3 may decrease the incidence and severity of nephrocalcinosis in rats. • The hyperphosphatemia that occurs in chronic renal failure is closely related to dietary protein intake because protein-rich diets are also high in phosphorus. • Consider use of omega-3 fatty acid supplements based on studies showing their beneficial effects in other species. Possible Complications • Anorexia • Gastrointestinal ulceration • Hyperphosphatemia • Acidosis • Anemia Recommended Monitoring • Overall condition and clinical response to therapy should be assessed in all patients with renal disease. Frequency of follow-up assessments varies with initial diagnosis and severity of disease. Periodic assessments for azotemia, anemia and phosphorus, and potassium and protein imbalances are recommended. • Monitor body weight and condition, and adjust nutrition accordingly. • Urinalysis and urine culture in patients being treated for pyelonephritis Prognosis and Outcome • With any diagnosis of renal insufficiency or failure, prognosis varies with severity of clinical pathologic findings, duration of disease, and severity of primary renal failure. If secondary to infection or obstructive disease, prognosis is determined by duration of the disease process and success in treatment—medical or surgical—of the underlying condition of secondary renal insufficiency. • Depending on initial diagnosis, disease severity, and response to therapy, quality of life issues and euthanasia should be discussed with the owner in terms of any patient with renal disease. Controversy Hematology, clinical chemistry, and urinalysis values may vary significantly with strain or breed of animal, nutritional status, sex, sampling site or frequency, time of day, stressors, age, health status, drug exposure, and environment. Therefore, normal values are broad; these variables should be kept in mind when interpreting individual animal values. Pearls & Considerations • Many different terms are used to describe renal function and its deterioration. ○Azotemia refers to increased concentrations of urea nitrogen and creatinine and other nonproteinaceous nitrogenous waste products in the blood. Renal azotemia denotes azotemia caused by renal parenchymal changes. ○Uremia is the presence of all urine constituents in the blood. Usually a toxic condition, it may occur secondary to renal failure or postrenal disorders, including urethral blockage. ○Renal reserve may be thought of as the percentage of “extra” nephrons—those not necessary to maintain normal renal function. Although it probably varies from animal to animal, this value is greater than 50% in most mammals. ○Renal insufficiency begins when the renal reserve is lost. Animals with renal insufficiency outwardly appear normal, but have a reduced capacity to compensate for stresses such as infection or dehydration and have lost urine concentrating ability. ○Renal failure is a state of decreased renal function that allows persistent abnormalities (azotemia and inability to concentrate urine) to exist; it refers to a level of organ function rather than a specific disease entity. Acute renal failure generally refers to cases of sudden decline of glomerular filtration rate resulting in an accumulation of nitrogenous waste products and inability to maintain normal fluid balance. Chronic renal failure generally refers to an insidious onset with slow progression (usually months to years) of azotemia and inadequately concentrated urine. • It is important to realize that most of the renal diseases discussed can manifest as varying stages of compromise in renal reserve, renal insufficiency, or renal failure. If or when the disease process progresses depends on variables such as the specific disease in question, environmental factors, and the individual animal itself. Comments • NTP-2000 open formula is one diet available in laboratory medicine that is low in protein (14.0%) and has a Ca:P ratio approximating 1.3 : 1; it has been found to decrease the incidence of nephrocalcinosis in rats. • Another laboratory rat diet, AIN-93G, has a lower phosphorus content (0.3%) and a higher Ca:P ratio and has been shown to lower the incidence of nephrocalcinosis. • Dietary salt content has been found to have an effect on hypertension associated with hydronephrosis in rats. Hydronephrosis as a result of partial ureteral blockage led to increased blood pressure, which worsened significantly on a high-salt diet versus a low-salt diet. • High levels of dietary soy isoflavones induced nephrocalcinosis formation, depending on the strain of laboratory rat. Client Education Chronic renal failure requires continuous treatment and monitoring. Unless a specific underlying cause is diagnosed and treated successfully, treatment in many cases will be lifelong. Suggested Readings Fisher PG. Exotic mammal renal disease: causes and clinical presentation. Vet Clin North Am Exotic Anim Pract. 2006;9:33–67. doi: 10.1016/j.cvex.2005.10.004. [DOI] [PubMed] [Google Scholar] Fisher PG. Exotic mammal renal disease: diagnosis and treatment. Vet Clin North Am Exotic Anim Pract. 2006;9:69–96. doi: 10.1016/j.cvex.2005.10.002. [DOI] [PubMed] [Google Scholar] Rao GN. Diet and kidney diseases in rats. Toxicol Pathol. 2002;30:651–656. doi: 10.1080/01926230290166733. [DOI] [PubMed] [Google Scholar] AUTHOR: PETER G. FISHER EDITOR: CHRISTOPH MANS Respiratory Tract Disease, Acute Basic Information Definition Acute bacterial pneumonia in rats is caused by subclinical infection with Streptococcus pneumoniae and/or Corynebacterium kutscheri, which develops into clinical pneumonia and/or septicemia secondary concurrent infection or immunosuppression. Synonyms • Pseudotuberculosis (Corynebacterium kutscheri) • Pneumococcal infection (Streptococcus pneumoniae) • Diplococcal infection (Streptococcus pneumoniae) Epidemiology Species, Age, Sex Older animals are at increased risk for C. kutscheri. Younger animals are at increased risk for S. pneumoniae. Risk Factors • Concurrent infection with Mycobacterium pulmonis or CAR bacillus • Immune suppression Contagion and Zoonosis • Corynebacterium kutscheri ○Gram-positive bacillus bacteria ○Transmission probably occurs through direct contact or oronasal exposure • Streptococcus pneumoniae ○Alpha-hemolytic Gram-positive diplococcal bacteria ○Transmission probably occurs through direct contact or oronasal exposure ○Zoonotic potential Associated Conditions and Disorders Chronic respiratory disease (murine respiratory mycoplasmosis) Clinical Presentation Disease Forms/Subtypes With both of these bacterial infections, animals can have no apparent clinical signs or can have severe respiratory disease and/or acute death. History, Chief Complaint • Acute death • Labored breathing • Sneezing • Oculonasal discharge • Lethargy • Lameness • Head tilt Physical Exam Findings • Dyspnea • Tachypnea • Cyanosis • Rales • Porphyrin epiphora (chromodacryorrhea) • Nasal discharge—with or without porphyrin staining • Muffled heart sounds • Collapse, tachycardia, poor peripheral pulses if septic shock • Torticollis and/or nystagmus if otitis media present • Arthralgia if arthritis present Etiology and Pathophysiology • Both S. pneumoniae and C. kutscheri colonize the upper respiratory tract (nasopharynx and tympanic bulla with S. pneumoniae and oropharynx, cervical, and submandibular lymph nodes with C. kutcheri) and can remain subclinical in the absence of concurrent disease. • Concurrent infection with other pathogens (see Respiratory Tract Disease, Chronic) and confounding stressors lead to immune suppression, triggering a latent infection to become clinical. • Suppurative inflammation of the upper respiratory tract is followed by infection of the lower respiratory tract, leading to bronchopneumonia and pleuritis. • Bacteremia can lead to infection in other organs such as arthritis, meningitis, pericarditis, hepatitis, splenitis, and peritonitis or acute death. Diagnosis Differential Diagnosis • Respiratory signs ○Congestive heart failure ○Chronic respiratory disease (if owners have not been aware of respiratory disease) • Acute death ○Sepsis from other bacterial infections (e.g., salmonellosis) • Otitis media ○Extension of otitis externa Initial Database • Thoracic radiographs/CT: findings consistent with pulmonary consolidation and/or pleural effusion • Skull radiographs/CT/MRI: tympanic bullae sclerosis or effusion if otitis media is present • Serologic testing: C. kutscheri (ELISA) • Complete blood count: neutrophilia, neutropenia if septic • Serum biochemistry: hypoglycemia if septic • Brochoalveolar lavage: ○ Cytology, Gram stain ▪S. pneumoniae: encapsulated Gram-positive diplococci ▪C. kutscheri: slightly curved Gram-positive rods ○Aerobic culture and sensitivity • Submandibular lymph node aerobic culture for C. kutscheri: caution as nonclinical animals can harbor bacteria in these lymph nodes Advanced or Confirmatory Testing • Histopathologic examination • C. kutscheri: necrotizing and suppurative pulmonary lesions, fibrinopurulent fibrosis with intralesional bacterial colonies that are pathognomonic (diphtheroid appearance of the bacilli with “Chinese letter” configurations) Treatment Therapeutic Goals • Stabilization of the septic patient • Eradication of the bacterial infection • Management of concurrent disease (see Respiratory Tract Disease, Chronic) Acute General Treatment • Oxygen therapy if patient is dyspneic and/or cyanotic • Fluid therapy: may require intraosseous administration if patient is severely compromised • Antibiotic therapy should be based on aerobic culture and sensitivity results: ○ S. pneumoniae: highly resistant strains are found in humans, so appropriate antibiotic use is extremely important ▪Amoxicillin/clavulanic acid 15-20 mg/kg PO, SC q 12 h ▪Azithromycin 15-30 mg/kg PO q 12 h ○ C. kutscheri ▪Amoxicillin/clavulanic acid 15-20 mg/kg PO, SC q 12 h ▪Ampicillin 20-50 mg/kg PO, SC, IM q 12 h ▪Chloramphenicol 30-50 mg/kg PO, SC, IM q 8-12 h ▪Doxycycline 5-10 mg/kg PO q 12 h Chronic Treatment See Respiratory Tract Disease, Chronic. Possible Complications Oral doxycycline should not be given with any dairy products or other products containing calcium because this will decrease its bioavailability. Recommended Monitoring • Patients with severe disease should be hospitalized until they are able to go home on oral medications. • Patients should be closely monitored for signs of chronic respiratory disease. Prognosis and Outcome Little is known about the prognosis of pure acute bacterial pneumonia because co-infection with other respiratory pathogens is common, as are subclinical infections. Pearls & Considerations Prevention Because both of these bacteria can be present without causing clinical disease, preventive measures are focused on decreasing stress, avoiding immune suppressive drugs, and maintaining appropriate diet/husbandry to avoid conversion to clinical disease. Client Education All clients owning rats should understand the frequency of respiratory disease in rats and the importance of proper housing (good ventilation, avoidance of crowding, avoidance of dusty bedding such as wood shavings) and close observation for any signs of respiratory disease, so that treatment can be administered as soon as possible. Suggested Readings Amao H. Natural and subclinical Corynebacterium kutscheri infection in rats. Lab Anim Sci. 1995;45:11–14. [PubMed] [Google Scholar] Barthold SW. The effect of selected viruses on Corynebacterium kutscheri infection in rats. Lab Anim Sci. 1988;38:580–583. [PubMed] [Google Scholar] Borkowski GL. Diagnostic exercise: pneumonia and pleuritis in a rat [Streptococcus pneumoniae] Lab Anim Sci. 1990;40:323–325. [PubMed] [Google Scholar] Corning BF. Group G streptococcal lymphadenitis in rats. J Clin Microbiol. 1991;29:2720–2723. doi: 10.1128/jcm.29.12.2720-2723.1991. [DOI] [PMC free article] [PubMed] [Google Scholar] Cross-References to Other Sections Respiratory Tract Disease, Chronic AUTHOR: NICOLE R. WYRE EDITOR: CHRISTOPH MANS Respiratory Tract Disease, Chronic Client Education Sheet Available on Website Basic Information Definition Chronic respiratory disease (CRD) in rats is a multifactorial respiratory tract infection caused primarily by Mycoplasma pulmonis, commonly in association with other concurrent infections, resulting in chronic bronchitis and bronchiectasis. Synonyms CRD, murine respiratory mycoplasmosis (MRM) Epidemiology Species, Age, Sex Older animals are at increased risk. Risk Factors • Immune status (e.g., age, genotype of certain rats) • Concurrent diseases (e.g., diabetes mellitus, neoplasia) • General ventilation of housing • Ammonia levels in bedding • Nutritional status (e.g., deficiency of vitamin A or E) • Obesity Contagion and Zoonosis • This disease complex is due to the synergism of several pathogens transmitted directly, through aerosol or in utero. The major pathogen is Mycoplasma pulmonis, but other pathogens involved in establishing infection include the following: ○Cilia-associated respiratory bacillus (CAR bacillus, Gram-negative filamentous bacterium) ○Sendai virus (paramyxovirus) ○Sialodacryoadenitis virus (coronavirus) Associated Conditions and Disorders • Otitis media and torticollis (secondary to M. pulmonis middle ear infection) • Reduced fertility (secondary to M. pulmonis oophoritis and salpingitis infection) Clinical Presentation History, Chief Complaint • Nasal discharge • Sneezing • Labored breathing • Lethargy • Head tilt Physical Exam Findings • Porphyrin epiphora (chromodacryorrhea) • Nasal discharge—with or without porphyrin staining • Dyspnea • Tachypnea • Rales • Cyanosis • Muffled heart sounds • Torticollis and/or nystagmus with otitis media Etiology and Pathophysiology • M. pulmonis colonizes the epithelial cells of the respiratory tract, middle ear, and epithelia of female genital tract. • Although M. pulmonis causes upper and lower respiratory system lesions, the primary lesion is subacute chronic bronchitis that resembles chronic obstructive respiratory disease in humans. • CRD in rats is a chronic inflammatory condition resulting in the hypersecretion and impaired clearance of mucus in which elevated levels and activation of macrophages and neutrophils play an important role. • Once established in the lower respiratory tract, chronic bronchitis and bronchiolitis develop and progress to bronchiectasis and bronchiolectasis. Collections of mucus, leukocytes, and cellular debris accumulate in the lumen due to ciliostasis. There may be rupture of the bronchiolar walls, releasing inflammatory cells, mucus, and debris into the adjacent parenchyma, and developing pulmonary abscessation. • As the airways become filled with mucus, bronchiolar lumen diameter decreases and a biofilm develops over bronchiolar epithelium, protecting secondary bacterial invaders from immune defenses and most antibiotics. • M. pulmonis also causes an atrophic rhinitis in which the nasal turbinates become inflamed with a mixed pyogranulomatous infiltrate. The rhinitis accounts for the upper respiratory signs seen in CRD of rats. Because rats are obligate nose breathers, rhinitis results in open mouth breathing, hypoxia, and its associated metabolic disorders such as respiratory acidosis and myocyte irritability. Diagnosis Differential Diagnosis • Respiratory signs ○Neoplasia (primary pulmonary or metastatic) ○Acute bacterial pneumonia (see Respiratory Tract Disease, Acute) ○Congestive heart failure • Otitis media ○Extension of otitis externa Initial Database • Thoracic radiographs/CT: findings are consistent with bronchopneumonia, bronchitis, and/or atelectasis • Skull radiographs/CT/MRI: tympanic bullae sclerosis or effusion if otitis media is present • Complete blood count: may be normal or consistent with chronic inflammation (neutrophilia, monocytosis) • Serologic testing: M. pulmonis, CAR bacillus, Sendai virus • Bronchoalveolar lavage for PCR testing (M. pulmonis) and aerobic culture (for secondary bacterial pathogens). Culture for M. pulmonis requires special mycoplasma media. Advanced or Confirmatory Testing • Histopathologic examination ○Silver-impregnation staining needed to diagnose CAR bacillus co-infection Treatment Therapeutic Goal Elimination of the disease is impossible. The goal of therapy is to improve the rat's quality of life by controlling secondary bacterial infections and preventing acute dyspneic episodes. Acute General Treatment • Oxygen therapy • Fluid support if presence of secondary dehydration Chronic Treatment • Antibiotic therapy will not eliminate the pathogen. Antibiotic selection ideally is based on culture and sensitivity results. • Doxycycline 5-10 mg/kg PO q 12 h: preferred antibiotic because it has additional antiinflammatory properties and is secreted by respiratory epithelial cells • Enrofloxacin 10-20 mg/kg PO, IM, SC q 24 h: CAUTION with SC or IM injection as can cause severe pain and tissue necrosis. Dilute with sterile saline before injection. • Tylosin 10 mg/kg PO, SC IM q 12-24 h: not recommended as use in drinking water because it may reduce water consumption • Azithromycin 15-30 mg/kg PO q 24 h • Nutritional support as animals may lose weight with chronic disease Drug Interactions Oral doxycycline should not be given with any dairy or other products containing calcium because this will decrease its bioavailability. Recommended Monitoring • Respiratory rate and effort • Body weight/condition • Appetite Prognosis and Outcome Because many factors contribute to rat respiratory issues, the disease cannot be eliminated, but clinical signs may be ameliorated with antibiotics and supportive care. Controversy • Use of corticosteroids as antiinflammatory agents has been recommended to decrease the inflammation. Most (experimental) studies in rats have found steroids do not affect signs, function, and indices of inflammation. There is also significant concern that corticosteroid efficacy will be accompanied by consequential impairment of the rat's immune defenses leading to fatal pulmonary abscessation and/or pneumonia. • Use of bronchodilators (both oral and inhaled) has been recommended because these agents are helpful in humans with chronic bronchitis. Specific studies with bronchodilators have not been performed in rats with chronic respiratory disease, but they may be helpful. • Nebulized hypertonic saline solution (7%) has been used successfully in humans with cystic fibrosis as a mucolytic agent. It breaks down the mucous biofilm and gives relief for ~8 hours. • Concurrent nebulization with bronchodialators and/or antibiotics has been recommended to directly deliver medications. Specific studies using these nebulizations have not been performed in rats with chronic respiratory disease but may be helpful. Pearls & Considerations Prevention This disease complex (M. pulmonis) is thought to be ubiquitous in pet rats; thus prevention of infection is nearly impossible. Preventing contributing factors such as proper ventilation, bedding, and diet and decreasing stress can be helpful. Client Education All clients who own rats should be educated about the ubiquitous nature of M. pulmonis and the importance of ventilation, low cage ammonia levels, avoidance of dusty bedding such as wood shavings, and appropriate nutrition in decreasing the potential severity of chronic respiratory disease in rats. Suggested Reading Deeb B. Respiratory disease in pet rats. Exotic DVM. 2005;7:31–33. [Google Scholar] Donnelly TM. Application of laboratory animal immunoassays to exotic pet practice. Exotic DVM. 2006;8:19–26. [Google Scholar] Rempe S. Tetracyclines and pulmonary inflammation. Endocr Metab Immune Disord Drug Targets. 2007;7:232–236. doi: 10.2174/187153007782794344. [DOI] [PubMed] [Google Scholar] Schoeb TR. Effects of viral and mycoplasmal infections, ammonia exposure, vitamin A deficiency, host age, and organism strain on adherence of Mycoplasma pulmonis in cultured rat tracheas. Lab Anim Sci. 1993;43:417–424. [PubMed] [Google Scholar] Wark P. Nebulised hypertonic saline for cystic fibrosis. Cochrane Database Syst Rev. 2009 doi: 10.1002/14651858.CD001506.pub3. CD001506. [DOI] [PubMed] [Google Scholar] Cross-References to Other Sections Respiratory Tract Disease, Acute Open in a new tab Respiratory Tract Disease, Chronic Rat lungs, abscesses secondary to chronic infection. AUTHOR: NICOLE R. WYRE EDITOR: CHRISTOPH MANS Skin Diseases Basic Information Definition Infectious and noninfectious diseases of the integument Synonyms Dermatitis, pyoderma, ulcerative dermatitis, ringworm, dermatophytosis, acariasis, ring tail, abscesses, bite wounds Epidemiology Risk Factors Inappropriate bedding (e.g., cedar, pine) can cause contact dermatitis. Contagion and Zoonosis • Dermatophytes are potentially zoonotic. • Ornithonyssus bacoti (tropical rat mite) is a zoonotic parasite. Associated Conditions and Disorders • Conspecific trauma • Nutritional deficiencies • Chronic renal insufficiency Clinical Presentation Disease Forms/Subtypes • Ectoparasitosis • Bacterial dermatitis/ulcerative dermatitis • Abscesses • Dermatophytosis • Ringtail • Neoplasia History, Chief Complaint • Skin wounds • Rough hair coat • Pruritus • Hair loss • Weight loss • Lethargy • Swellings on body • Tail tip lesion Physical Exam Findings Will vary depending on cause: • Alopecia • Pruritus • Localized erythema • Abrasions, excoriations, ulcerations • Scaling, crusting • Lichenification • Cutaneous or subcutaneous masses Etiology and Pathophysiology • Bacterial dermatitis/ulcerative dermatitis ○Staphylococcus spp. ○Usually secondary to self-trauma due to pruritus from mites or pruritus/pain over skin of salivary glands during sialodacryoadenitis (SDA) virus infection; dermatophytosis, fight wounds • Abscesses ○Staphylococcus aureus, Streptococcus spp., Pasteurella pneumotropica, Actinomyces bovis ○Often secondary to conspecific trauma • Parasites ○All ectoparasitic infections can be complicated by secondary infections and self-mutilation. These secondary complications need to be identified and treated. ○Rat fur mite (Radfordia ensifera): common; mild infestation produces few ill effects, but heavy infestation causes pruritus, leading to self-traumatization, and ulcerative dermatitis. Transmission is by direct contact. ○Sarcoptic mites (e.g., Sarcoptes scabiei, Sarcoptes anacanthos, Trixacarus diversus): less common. Transmission is by direct contact. Leads to pruritus, crusting, and hyperkeratosis. Animals with clinical signs are often immune compromised. ○Notoedres muris: causes typical papulous lesions on ear pinnae ○Tropical rat mite (Ornithonyssus bacoti): Blood sucking mite; opportunistic ectoparasite. It spends a relatively short time on a host (usually at night) and penetrates the skin for feeding only. Cause severe pruritus. Animals appear nervous, particular in evening hours and at night. Severe infestations can cause anemia, debilitation, and death. ○Demodectic mites (Demodex ratti, Demodex norvegicus, Demodex ratticola): rare ○Lice (Polyplax serrata, Polyplax spinulosa): Common; blood sucking lice. Located mainly at neck, at shoulders, and over back; poor fur condition and pruritus, which leads to self-mutilation ○Pinworms (Syphacia obvelata): perianal pruritus and tail base mutilation • Dermatophytosis ○Microsporum spp., Trichophyton mentagrophytes ○Clinical signs vary: alopecia, erythema, dandruff formation. Animals usually are not pruritic, unless secondary bacterial infection present. ○Immune deficiency or stress may be underlying cause in chronic cases. • Neoplasia: fibroadenoma of the mammary glands (most common), mammary adenocarcinoma, lymphoma, etc. (see Mammary and Pituitary Tumors) • Ringtail ○Occurs in young rats (7-19 days) and is characterized by dry skin and formation of annular constrictions, which might progress to swelling, and tissue necrosis. Autoamputation might occur. ○Low environmental relative humidity (less than 20%-40%) appears to be the cause; it is more often seen in rats housed in hanging cages and is rarely seen in pet rats. Diagnosis Differential Diagnosis • Alopecia: trauma, dermatophytosis, chronic kidney disease, nutritional deficiency (low protein), neoplasia, barbering (behavorial) • Ulcerative and crusting lesions: self-trauma, due to mites, secondary bacterial infections, fight wounds, neoplasia • Pruritus: mites, secondary bacterial infections • Crusting or flaking of skin: dermatophytosis, mites, nutritional deficiencies • Cutaneous masses: neoplasia, inflammation, abscesses • Localized erythema or pododermatitis: contact allergy, contact irritation (cleaners), trauma from bedding/cage material Initial Database • Full dietary history • Dermatologic examination ○Skin scraping (sedation or general anesthesia may be required) ○Acetate tape preparation ○Impression smears • Fine-needle aspirate and cytology of cutaneous and subcutaneous masses • Dermatophyte culture • Bacterial culture and sensitivity Advanced or Confirmatory Testing • Serum biochemistry: if underlying organ disease is suspected • Radiographs: to rule out underlying skeletal abnormalities (e.g., osteoarthritis; osteomyelitis) in cases of pododermatitis • Biopsy and histopathologic examination of skin lesion Treatment Therapeutic Goals • Eliminate pruritus and discomfort. • Treat primary and secondary infections. • Promote healing of skin lesions. Acute General Treatment • If animal is self-mutilating: shorten and blunt nail tips. In severe case, temporarily apply bandages to hindfeet. Apply E-collar to prevent removal of bandages. • Ectoparasites ○Ivermectin 0.2-0.4 mg/kg SC, PO q 7-14 d ○Selamectin 10-25 mg/kg topically q 21-28 d ○Treat until clinical signs are resolved and no more parasites are found on the animals. ○Treat in-contact animals. ○Treat the environment to prevent reinfection: regular bedding changes and cage cleaning. Discard cage furnishing that cannot be disinfected (e.g., wood-based furnishing). • Bacterial dermatitis/ulcerative dermatitis ○If indicated, provide systemic antibiotic therapy based on culture and sensitivity whenever possible ○ Start empirical treatment pending culture and sensitivity: ▪Cephalexin 30 mg/kg PO q 12 h ▪Amoxicillin/clavulanic acid 15-20 mg/kg PO q 12 h ▪Trimethoprim-sulfa 15-30 mg/kg PO q 12 h ▪Chloramphenicol 30-50 mg/kg PO q 8-12 h ▪Enrofloxacin 10-20 mg/kg PO, q 12-24 h • Skin abscesses ○Lance, débride, and flush or remove in toto if possible. ○If indicated, provide systemic antibiotic therapy based on culture and sensitivity whenever possible. • Dermatophytosis ○ Systemic antifungal therapy ▪Terbinafine 20-30 mg/kg PO q 24 h ▪Itraconazole 5-10 mg/kg PO q 24 h ○ Topical antifungal therapy ▪Enilconazole (1 : 50, emulsion as spray or moist wipe) ▪Miconazole/chlorhexidine shampoos ▪Lime sulfur dips (1 : 40, q 7 d) ▪Used alone or in combination with systemic therapy ▪Used preferably in cases of suspected dermatophytosis, while dermatophyte culture results are awaited ○Environmental decontamination: frequent damp mopping of hard surfaces rather than sweeping can reduce environmental spread of spores; 1 : 10 bleach solution can be used to clean environment. Contact time: 10 minutes • Monitoring: once-weekly dermatophyte test medium (DTM) cultures. Discontinue treatment when two consecutive negative cultures are obtained. • Antihistamines ○Diphenhydramine 1-2 mg/kg PO q 12 h ○Hydroxyzine 2 mg/kg PO q 8-12 h • Antiinflammatory drugs: meloxicam 0.3-0.5 mg/kg PO, SC q 12-24 h • Neoplasia: surgical mass removal (see Mammary and Pituitary Tumors) • Nutritional deficiency: improve diet; provide access to commercial pelleted diet Chronic Treatment Dermatophytosis will often require long-term therapy. Recommended Monitoring • Resolution of clinical signs • Repeated evaluation for presence of ectoparasites • Weekly DTM cultures for dermatophytosis cases Prognosis and Outcome Good to fair Pearls & Considerations Prevention • Provision of a commercial diet • Quarantine all new incoming animals for a minimum of 30 days before allowing contact with other animals. Client Education Dermatophytes are contagious; clients should seek medical advice if lesions are found on humans in the household. Suggested Readings Agren MS. Effect of topical zinc oxide on bacterial growth and inflammation in full-thickness skin wounds in normal and diabetic rats. Eur J Surg. 1991;157:97–101. [PubMed] [Google Scholar] Galler JR. Ulcerative dermatitis in rats with over fifteen generations of protein malnutrition. Br J Nutr. 1979;41:611–618. doi: 10.1079/bjn19790076. [DOI] [PubMed] [Google Scholar] Honma M. Plantar decubitus ulcers in rats and rabbits. Jikken Dobutsu. 1989;38:253–258. doi: 10.1538/expanim1978.38.3_253. [DOI] [PubMed] [Google Scholar] Taylor DK. Lanolin as a treatment option for ringtail in transgenic rats. J Am Assoc Lab Anim Sci. 2006;45:83–87. [PubMed] [Google Scholar] Cross-References to Other Sections Mammary and Pituitary Tumors Open in a new tab Skin Disease This skin lesion in a rat was caused by a subcutaneous injection of enrofloxacin; always dilute the drug if it needs to be injected SC or IM. (Photo courtesy Jörg Mayer, The University of Georgia, Athens.) Open in a new tab Skin Disease Skin lesions located over the shoulder and neck area, which were induced by fighting with cage mates. Isolation of the rat led to complete resolution of the skin lesions. Self-trauma, secondary to ectoparasite induced pruritus, can present in similar fashion. AUTHOR: CHRISTOPH MANS EDITOR: THOMAS M. DONNELLY Articles from Clinical Veterinary Advisor are provided here courtesy of Elsevier ACTIONS View on publisher site PDF (1.9 MB) Cite Collections Permalink PERMALINK Copy RESOURCES Similar articles Cited by other articles Links to NCBI Databases Cite Copy Download .nbib.nbib Format: Add to Collections Create a new collection Add to an existing collection Name your collection Choose a collection Unable to load your collection due to an error Please try again Add Cancel Follow NCBI NCBI on X (formerly known as Twitter)NCBI on FacebookNCBI on LinkedInNCBI on GitHubNCBI RSS feed Connect with NLM NLM on X (formerly known as Twitter)NLM on FacebookNLM on YouTube National Library of Medicine 8600 Rockville Pike Bethesda, MD 20894 Web Policies FOIA HHS Vulnerability Disclosure Help Accessibility Careers NLM NIH HHS USA.gov Back to Top
13270	https://www.southlandorganics.com/blogs/case-studies/transforming-waste-management-port?srsltid=AfmBOoqW7iH83jOYxkGCCf6AK995iLCfmnA3tbKz849dw96rSIpZJJAp	Transforming Waste Management: The Incredible Story of How a Paper Mil - Southland Organics American Express Apple Pay Diners Club Discover Google Pay PayPal Shop Pay Visa Find anything you need HomePoultry ProductsPoultry BroilersPoultry Layers and BreedersTurkeyGame BirdsBackyard BirdsPoultry Biosecurity Lawn & Garden ProductsLawn CareLawn Care ProgramsGardenHydroseedersLandscapersGolf CoursesHumate Hub Septic & Waste ProductsSeptic CareOdor ControlSanitizers SwineAbout ContactBlogCase StudiesWhy Southland?Loyalty ProgramFAQs [x] Log inRegisterView cart [x] 0 [x] HomePoultry- [x] ProductsPoultry BroilersPoultry Layers and BreedersTurkeyGame BirdsBackyard BirdsPoultry Biosecurity Lawn & Garden- [x] ProductsLawn CareLawn Care ProgramsGardenHydroseedersLandscapersGolf CoursesHumate Hub Septic & Waste- [x] ProductsSeptic CareOdor ControlSanitizers SwineAbout- [x] ContactBlogCase StudiesWhy Southland?Loyalty ProgramFAQs Log inRegister [x] 0 Item added to cart! %title%%variant% You have %itemCount% in your cart. Total being %total% Continue shoppingView cartCheckout Transforming Waste Management: The Incredible Story of How a Paper Mill Slashed Total Suspended Solids by Nearly 60% Using PORT By: Mike Usry on 03/05/2018 A major paper mill used PORT in its waste treatment facility and saw a 58.9% decrease in TSS and a 63.5% decrease in BOD. PORT, an innovative outdoor restroom and holding tank treatment, has revolutionized waste management for a major paper mill in the southeastern United States. By leveraging PORT's capability to rapidly degrade waste and control odors, the paper mill has not only enhanced its operational efficiency but also significantly improved its environmental sustainability. PORT's unique formulation, which is harmless to humans, animals, and marine life and capable of breaking down tough compounds, underscores its exceptional benefits. This case study illustrates the crucial role of PORT in resolving the mill's waste management challenges, reinforcing the importance of advanced, eco-friendly solutions in industrial settings. PORT's Remarkable Results The use of PORT at a paper mill demonstrated remarkable results in managing waste in the facility’s aeration pond. Following a 10-day treatment period, the Total Suspended Solids (TSS) levels in the pond saw a dramatic reduction to 5,810 pounds, marking a 58.9% decrease. Furthermore, the Biochemical Oxygen Demand (BOD) levels significantly dropped to an average of 16,000, translating to a 63.5% reduction. These results not only signify PORT's effectiveness in breaking down and managing waste but also highlight its ability to substantially improve the overall efficiency of waste treatment processes at the mill. Moving forward, the management team at the paper mill has decided to integrate PORT into their regular waste management routine. They plan to use this solution continuously to maintain low levels of TSS and BOD in their aeration pond. By doing so, they aim to extend the operational lifespan of their waste treatment facilities and further reduce their environmental impact. They stated: "We are incredibly pleased with the results provided by PORT and Southland Organics' solution. It has surpassed our expectations in effectively managing our waste issues, significantly reducing odor, and enhancing the efficiency of our wastewater treatment processes. The cost-effectiveness and environmental benefits have solidified our decision to continue using this treatment as part of our long-term sustainability strategy." Why It Worked At the heart of this case study lies the transformative impact of PORT on operational efficiency and environmental compliance. Recognized for their substantial waste management needs and commitment to sustainable practices, the implementation of PORT offered a seamless and effective solution to their challenges. Effective Waste Degradation and Odor Control One of the primary benefits realized by the paper mill was PORT's exceptional ability to rapidly degrade waste and control odors. Unlike conventional methods that mask odors, PORT eliminates them at the source by breaking down solid waste and clearing bio-solids. This ensured a healthier and more pleasant environment for both employees and the surrounding community, aligning with the paper mill's goals of maintaining high environmental standards. Environmental Protection and Safety Central to the paper mill's mission was the commitment to minimizing its ecological footprint. PORT's eco-friendly formulation was perfectly aligned with this goal. Being harmless to human, animal and marine life, the product bolstered the mill's environmental stewardship. Moreover, its ability to digest toxic compounds without harming beneficial bacteria or causing corrosion to equipment marked a significant advantage, ensuring the mill's operations did not detrimentally impact local ecosystems. Operational Efficiency and Cost Savings Implementing PORT led to a noticeable improvement in the mill's operational efficiency. With its ability to digest even difficult detergents, fats, oils, tissues and hydrocarbons, PORT kept the mill's waste management systems running smoothly, significantly reducing the likelihood of clogs and the need for frequent maintenance. This not only extended the life of the mill's infrastructure, but also translated to substantial cost savings in terms of maintenance and operational downtime. Enhanced Compliance and Reputation In an industry where regulatory compliance and reputation are crucial, the adoption of PORT helped the paper mill meet stringent waste management regulations while bolstering its reputation as a leader in environmental stewardship. The non-corrosive, non-pathogenic nature of PORT meant that the mill was not only in compliance with environmental standards but was also setting a benchmark for sustainable practices in the industry. Conclusion Through the implementation of PORT, the paper mill successfully addressed its waste management challenges, showcasing a commitment to environmental excellence and operational efficiency. The tangible benefits realized—ranging from effective waste degradation and odor control to operational cost savings and enhanced environmental compliance—underscore the significance of adopting innovative, sustainable solutions in today's industrial landscape. PORT not only provided a solution to immediate challenges but also positioned the paper mill as a forward-thinking, environmentally responsible entity within the industry. The use of PORT demonstrated remarkable results in managing waste in the facility’s aeration pond. Following a 10-day treatment period, the Total Suspended Solids (TSS) levels in the pond saw a dramatic reduction to 5,810 pounds, marking a 58.9% decrease. Furthermore, the Biochemical Oxygen Demand (BOD) levels significantly dropped to an average of 16,000, translating to a 63.5% reduction. These results not only signify PORT's effectiveness in breaking down and managing waste but also highlight its ability to substantially improve the overall efficiency of waste treatment processes at the mill. Tags: Waste About The Author Mike Usry This was written by Mike Usry, the President of Southland Organics. Mike is an entrepreneur and soil enthusiast with a passion for educating on agriscience-based topics to help business owners and homeowners alike grow plants, turf, poultry and more. Mike received his Bachelor of Science in Education from the University of Georgiaand his MBA from the University of South Florida. The combination of his education and experience has given him a deep understanding of both business and the science behind our products. Mike founded Southland Organics in 2009. Learn more about Mike Usry Isabella (Izy) Dobbins Marketing Manager This was edited by Isabella (Izy) Dobbins, Southland Organics' Marketing Manager. Izy has devoted her education and career to communicating science-related topics. With an enthusiasm for sharing accurate and honest content relating to science and agriculture, she ensures Southland Organics' publications are as informative as they are interesting. Izy graduated from theUniversity of Georgiawith a bachelor's degree in advertising, minors in both Spanish and environmental health science and a Certificate in Sustainability. She has been working at Southland Organics since 2021. Learn more about Izy Dobbins Other Interesting Posts Understanding Anaerobic Bacteria in Septic Tanks: A Complete Guide Optimal Solutions for Reduction in TSS (Total Suspended Solids) Preventing Heat Stroke in Chickens Southland Organics 189 Luke Road Bogart, GA 30622 800-608-3755 NavigateWhy Choose SouthlandStore LocatorBecome a DistributorShopify CollectivePoultry Biosecurity ResourcesBlog PostsCase StudiesSearchContactRewards ProgramSubscriber Portal Product SpecialtiesHomePoultryLawn & GardenSeptic & WasteSwineAbout Let's Be Social Sam.Gov Southland Organics is fully registered with Sam.gov! Entity ID: L9GTYJCHK2Q5 © 2025 Southland Organics \| Terms Of Use \| Privacy Policy \| Shipping & Returns 00 DAYS 00 HRS 00 MIN 00 SEC
13271	https://www.italki.com/en/post/question-499865	italki - What is the difference between 'aleviate', 'mitigate', 'soften', 'dampen'? Home1-on-1 teacherGroup ClassCommunityBecome a teacher Signup/Login Find English Teachers Signup/Login [Deleted] What is the difference between 'aleviate', 'mitigate', 'soften', 'dampen'? May 6, 2020 9:56 PM 2 0 Answers · 2 B Bill Holt 0 a. Alleviate = make easier to endure; mitigate b. mitigate = lessen in force or intensity; make less severe c. soften = to make soft or softer, to become soft or softer d. dampen = (a) to (cause to) become damp or moist, (b) to (cause to) become dull or depressed, (c) to damp (= to check or retard the action of (something that vibrates or oscillates)) ...Read more May 7, 2020 0 0 Rusty Newton 0 These words can all be used as synonyms. However, I think an easy way to remember the differences in these is to think of the context. As a native English speaker, here are the contexts I would use these words in. Alleviate = Medical or physical context, often referring to reducing pain. Mitigate = Business or scientific context. Often referring to risk. This is sort of an intellectual word. Soften = Any context, more of a physical description. Soft is the opposite of hard. However, soften can simply be used as the word "reduce". Dampen = This one is the most different from the others. Sometimes used very similar to soften, but mostly used to mean adding water to an object. EXAMPLES: This new medicine will help alleviate your pain. My financial product will help mitigate any risk from overspending your budget. Being kind when speaking will help soften the blow of bad news. Adding a blanket to a hard sofa will help soften it. Dampen the rag so that you can wipe your face off. Being mean when speaking will dampen the spirits of those around you. ...Read more May 6, 2020 0 0 Still haven’t found your answers? Write down your questions and let the native speakers help you! Ask Now Articles You May Also Like Speak More Fluently with This Simple Technique by Chris 10 likes · 2 Comments How to Read and Understand a Business Contract in English by Charnelle (Business) 16 likes · 3 Comments 6 Ways italki Can Help You Succeed in Your School Language Classes by Rose - Kids & Adults 12 likes · 7 Comments More articles English teachers for you Bobbi 4.9 · 201 lessons Lesson from $5 Walid 4.9 · 5001 lessons Lesson from $15 Alicia I 5.0 · 1267 lessons Lesson from $8 Ambar Suber ツ 5.0 · 1879 lessons Lesson from $11 Mason Pronunciation 5.0 · 5341 lessons Lesson from $20 Evgeniya 5.0 · 1197 lessons Lesson from $6 More teachers Download the italki App Interact with native speakers around the world. 00:00 00:00 Language teachers English teachersSpanish teachersFrench teachersJapanese teachersGerman teachersChinese teachersKorean teachersItalian teachersRussian teachersPortuguese teachersArabic teachersHindi teachersAll teachers Learn a language Learn EnglishLearn SpanishLearn JapaneseLearn FrenchLearn GermanLearn ChineseLearn KoreanLearn ItalianLearn RussianLearn PortugueseLearn ArabicLearn Hindi Lessons 1-on-1 LessonsGroup Class Teaching Become a teacherTeaching Code of Conduct Learning resources italki Language Testitalki Language Challengeitalki Podcastsitalki Quizitalki Community Promotions Refer a FriendBuy a Gift Carditalki BusinessAffiliate ProgramPartnership Program More FAQitalki BlogDownload App © 2025 italki HK Limited. About usCareersPressSupportLegalPrivacyContact We use cookies to ensure that we provide you the best experience on our website. By clicking on "Accept", you agree to our privacy policy. Cookie settings Accept
13272	https://www.youtube.com/watch?v=jcVW8TjDuKQ	GeoGebra Demonstration\| Corresponding angles are equal \| Parallel lines and transversal Mathematics Learning 15900 subscribers 14 likes Description 873 views Posted: 14 Jun 2021 parallelLines #CorrespondingAngles #LinesAndAngles #Class8Mathematics #Class9Mathematics #CBSEClass9Mathematics #InteractiveMathematics #GeoGebraandMathematics When two parallel lines are cut by a transversal then corresponding angles are equal. Corresponding angles are equal \| Parallel lines and transversal GeoGebra Applet Playlists of Videos Class 8 Mathematics Squares and Square Roots Cubes and Cube Roots Exponents and Radicals Direct and Inverse Variation Proft, Loss and Discount Simple Interest and Compound Interest Algebraic Identities Polynomials Linear Equations in One Variables Understanding Quadrilaterals Construction of Quadrilaterals Parallel lines Mensuration Introduction to Graphs Statistics and Probability Rational Numbers Ch 1 NCERT Class VIII Symmetry Playlists of Videos Class 9 Mathematics Number System Lines and Angles Circles Playlists of Videos for Teachers Creative tools for teaching online Using Kahoot Using GeoGebra (in Hindi) Using GeoGebra on mobile Using Google Docs Using Google Slides Playlists of Videos for Creating Interest in Mathematics Short cut techniques of fast calculations Paper Folding [Origami and Mathematics ] Using GeoBoard in Mathematics Using Isometric Paper in Mathematics Recreational Puzzles and Activities in Mathematics Mathematics Activities Using GeoGebra Playlist Case Study based Questions 2 comments Transcript: हेलो हेलो एवरीवन सैम बेस्ट वेब सम इंटरेस्टिंग जरा प्ले लिस्ट ऑन अंडरस्टैंडिंग एंड सर्विंग रिलेशनशिप बिटवीन थे लाइंस आफ इंटरएक्टिव लिंक डिस्क्रिप्शन आफ ए सेल ओर लाइन लाइन लाइन लाइन लाइन चीफ सीईओ पॉइंट्स पे ठेर रिस्पेक्ट्स टो नो व्हाट इज द मीनिंग ऑफ ई पॉन्टिंग टेंशन टू द जंगल दी डेढ़ सी व्हाट इज द प्रेसिडेंट 63.82 डिग्री कोर्स फॉर 2GB रैम 2जीबी डायग्राम एंड सी व्हाट इज द करंट अफेयर्स वॉटर विल चेंज इट्स कि दंगल एवरीडे यू नो व्हाट इज द मीनिंग ऑफ द सेंटेंस 7.3 डिग्री से कल सुबह ट्रू लाइंस पैरेलल लाइंस वेयर इंस्ट्रक्टेड बाय ट्रांसफर द क्वेश्चन इंडियन गर्ल्स ऑलवेज इन थिस क्वेस्ट फॉर द सब्सक्राइब zee5 सब्सक्राइब एंड शेयर ऑल चीफ एंड सी द 202 ए बी डिफ़ाल्ट पर विनोद इज द फर्स्ट ईयर ऑफ फॉरेस्ट एनिमल्स इक्वल कैन यू टेल मी द ईयर गैस्ट्राइटिस ईपीए एंड डिफेंडेड इट्स मीनिंग आफ मीडिया एंड यूज दिस पॉइंट टू डिफरेंट सिचुएशंस पॉइंट है टॉर्च लाइट संशोधन इंटरएक्टिव यह प्लेट टू विजुलाइज थे कॉरस्पॉडिंग ऐंगल्स अ इक्वल व्हेन टू लाइंस ट्रांसपोर्ट व्ह
13273	https://ictv.global/report/chapter/filoviridae/filoviridae	Skip to main content Book: Filoviridae Family: Filoviridae Genus: Cuevavirus Genus: Dianlovirus Genus: Oblavirus Genus: Orthoebolavirus Genus: Orthomarburgvirus Genus: Striavirus Genus: Tapjovirus Genus: Thamnovirus Authors: Filoviridae Citation: Filoviridae References: Filoviridae Resources: Filoviridae Species List: Filoviridae Family: Filoviridae Nadine Biedenkopf, Alexander Bukreyev, Kartik Chandran, Nicholas Di Paola, Pierre B. H. Formenty, Anthony Griffiths, Adam J. Hume, Elke Mühlberger, Sergey V. Netesov (Нетёсов Сергей Викторович), Gustavo Palacios, Janusz T. Pawęska, Sophie Smither, Ayato Takada (高田礼人), Victoria Wahl and Jens H. Kuhn The citation for this ICTV Report chapter is the summary published as: Biedenkopf, N., Bukreyev, A., Chandran, K., Di Paola, N., Formenty, P. B. H., Griffiths, A., Hume, A. J., Mühlberger, E., Netesov, S. V., Palacios, G., Pawęska, J. T., Smither, S., Takada, A., Wahl, V., & Kuhn, J. H. (2024). ICTV Virus Taxonomy Profile: Filoviridae 2024, Journal of General Virology 105, 001955 Corresponding author: Jens H. Kuhn (kuhnjens@mail.nih.gov) Edited by: Jens H. Kuhn, Stuart G. Siddell, and Peter J. Walker Posted: March 2019, updated October 2020, January 2024, June 2024 Summary Filoviridae is a family for negative-sense RNA viruses with genomes of about 13.1–20.9 kb that infect fish, mammals, and reptiles (Table 1.Filoviridae). The filovirid genome is a linear, non-segmented RNA with 5 canonical open reading frames (ORFs) that encode a nucleoprotein (NP), a polymerase cofactor (VP35), a glycoprotein (GP1,2), a transcriptional activator (VP30), and a large protein (L) containing an RNA-directed RNA polymerase (RdRP) domain. All filovirids genomes encode additional proteins that vary among genera. Several filovirids (e.g., Ebola virus, Marburg virus) are pathogenic for humans and are highly virulent. Table 1.Filoviridae. Characteristics of members of the family Filoviridae. \| \| \| --- \| \| Characteristic \| Description \| \| Example \| Marburg virus (DQ217792), species Orthomarburgvirus marburgense \| \| Virion \| Enveloped, variously shaped but predominantly filamentous, typically with a single nucleocapsid \| \| Genome \| 13.1–20.9 kb of linear, negative-sense, non-segmented RNA \| \| Replication \| The genome forms ribonucleoprotein complexes, which serve as templates for transcription and replication. Encapsidated antigenomic RNA is a replication intermediate \| \| Translation \| From multiple monocistronic 5′-capped and 3′-polyadenylated mRNAs \| \| Host range \| Fish (oblaviruses, striaviruses, thamnoviruses), mammals (cuevaviruses, dianloviruses, orthoebolaviruses, orthomarburgviruses), reptiles (tapjoviruses) \| \| Taxonomy \| Realm Riboviria, phylum Negarnaviricota, subphylum Haploviricotina, class Monjiviricetes, order Mononegavirales; the family includes 9 genera and 17 species \| Filovirids form a monophyletic clade based on phylogenetic analysis of RNA-directed RNA polymerase (RdRP) sequences (Wolf et al., 2018). Genomes of viruses from all eight genera have a similar genomic architecture but differ in the number of open reading frames (ORFs) and the number and location of gene overlaps (Kuhn et al., 2020). Piscine Hosts Genus Oblavirus. This genus includes one species for one virus (Oberland virus [OBLV]), discovered in diseased farmed European perch (family Percidae) exported from Germany to Switzerland. Oblaviruses are notable for genomes that contain at least two proteins without obvious homologs in viruses of other filovirid genera, and do not encode matrix protein (VP40) or RNP complex associated protein (VP24) encoded by all mammalian filovirids (Hierweger et al., 2021). Oblaviruses have not been cultured to date. Genus Striavirus. This genus includes one species for one virus (Xīlǎng virus [XILV]), discovered in captured frogfish (family Antennariidae) from the East China Sea. Striaviruses are notable for encoding at least four proteins without obvious homologs in other filovirid genera, and do not encode VP24 (Shi et al., 2018, Hume and Mühlberger 2019). Striaviruses have not been cultured to date. Genus Thamnovirus. This genus includes three species for three viruses (Fiwi virus [FIWIV], Kander virus [KNDV], Huángjiāo virus [HUJV]), discovered in captured filefish (family Monacanthidae) from the East China Sea and in diseased farmed European perch (family Percidae) exported from Germany to Switzerland. Thamnoviruses are notable for genomes that encode at least two proteins without obvious homologs in viruses of other filovirid genera and do not encode matrix protein (VP40) or VP24 (Shi et al., 2018, Hume and Mühlberger 2019, Hierweger et al., 2021). Thamnoviruses have not been cultured to date. Mammalian Hosts Genus Cuevavirus. This genus includes one species for one virus (Lloviu virus [LLOV]), discovered in miniopterid bats in Europe. The organization of cuevavirus genomes is reminiscent of orthoebolavirus genomes. Similar to orthoebolaviruses, cuevaviruses encode VP24 and VP40, and GP1,2 production relies on RNA editing (Negredo et al., 2011, Kemenesi et al., 2018, Kemenesi et al., 2022, Tóth et al., 2023). Genus Dianlovirus. This genus includes one species for one virus (Měnglà virus [MLAV]), discovered in pteropodid bats. Dianloviruses have only been reported from Asia (Yang et al., 2017, Yang et al., 2019, Paskey et al., 2020, Makenov et al., 2023). The organization of dianlovirus genomes is highly reminiscent of orthomarburgvirus genomes (Yang et al., 2019). Similar to orthomarburgviruses, dianloviruses encode VP24 and VP40, and RNA editing is not required for GP1,2 production. Dianloviruses have not been cultured to date. Genus Orthoebolavirus. This genus includes six species for six viruses. One of these viruses, Bombali virus (BOMV), has been detected in molossid bats (Goldstein et al., 2018b). Infectious BOMV has been generated using recombinant DNA technology. No naturally occurring BOMV isolates have been cultured to date. Two additional viruses, Ebola virus (EBOV) and Reston virus (RESTV), are suspected to be harbored by bats as natural hosts. Five orthoebolaviruses (Bundibugyo virus [BDBV], EBOV, RESTV, Sudan virus [SUDV], and Taï Forest virus [TAFV]) are pathogenic for nonhuman primates. BDBV, EBOV, and SUDV are highly lethal human pathogens. TAFV has caused only a single case of severe but non-lethal human disease, and RESTV has only caused one inapparent human infection. RESTV has also been found in domestic pigs. RESTV appears to be endemic in South-eastern Asia; all other orthoebolaviruses circulate in Africa (Kuhn et al., 2020). Orthoebolaviruses encode VP40 and VP24. They are notable for expressing three distinct proteins from their glycoprotein (GP) genes, a strategy they share with cuevaviruses (Volchkov et al., 1995, Sanchez et al., 1996, Negredo et al., 2011). Genus Orthomarburgvirus. This genus includes one species for two viruses found in pteropodid bats in Africa. Both viruses (Marburg virus [MARV] and Ravn virus [RAVV]) are highly lethal human pathogens (Kuhn et al., 2020). Orthomarburgviruses encode VP40 and VP24. Reptilian Hosts Genus Tapjovirus. This genus includes one species for one virus (Tapajós virus [TAPV]), discovered during a metagenomic analysis in a viperid snake from Brazil. Tapjoviruses are notable for genomes that are closely related to piscine filovirids (striaviruses) but having the genomic organization of mammalian filovirids (Horie 2021). Tapjoviruses have not been cultured to date. Virion Morphology Virion morphology (Figure 1.Filoviridae) has only been studied for cuevaviruses, orthoebolaviruses, and orthomarburgviruses and is described in the respective genus subchapter pages. \| \| \| \| \| Figure 1.Filoviridae. A) Scanning electron micrograph of Marburg virus particles (red) budding from an infected grivet (Chlorocebus aethiops (Linnaeus, 1758)) Vero E6 cell. B) Transmission electron micrograph of Marburg virus particles (red) found both as extracellular particles and budding particles from Vero E6 cells. Images are colorized for clarity. Courtesy of John G. Bernbaum and Jiro Wada, NIH/NIAID/DCR/IRF Frederick, Fort Detrick, MD, USA. \| Physicochemical and physical properties Physicochemical and physical properties have only been described for individual orthoebolaviruses and orthomarburgviruses and are described in the respective genus pages. Nucleic acid Filovirid genomes are linear non-segmented RNA molecules of negative polarity. The genomes vary from about 13.1 kb (thamnoviruses) to about 19 kb (cuevaviruses, orthoebolaviruses, and orthomarburgviruses) (Feldmann et al., 1992, Sanchez et al., 1993, Negredo et al., 2011, Shi et al., 2018). The genome of an unclassified virus from pteropodid bats, Déhóng virus (DEHV), reaches 20.9 kb (He et al., 2023). Proteins Filovirids express 6–10 proteins depending on genus. RNP complexes are composed of a genomic RNA molecule and several structural proteins, including nucleoprotein, VP35, VP30, and L (Hume and Mühlberger 2019). Lipids The filovirion envelope is derived from host cell membranes and is considered to have a lipid composition similar to that of the host-cell plasma membrane (Bavari et al., 2002). Some filovirid proteins may be acylated (Funke et al., 1995, Ito et al., 2001). Carbohydrates Carbohydrate composition has only been described for individual orthoebolaviruses and orthomarburgviruses and is described in the respective genus pages. Genome organization and replication Filovirid genomes are organized like most mononegaviral genomes, with the general mononegaviral gene order 3′ N P M (G) L 5′ (terminology for filovirids: 3′-NP-VP35-(VP40)-(GP)-L-5′), but differ in that they may contain additional genes (Figure 2.Filoviridae) (Feldmann et al., 1992, Sanchez et al., 1993, Negredo et al., 2011, Shi et al., 2018, Yang et al., 2019, Hierweger et al., 2021, Horie 2021, Seuberlich et al., 2023). The extragenic sequences at the extreme 3′-end (leader) and 5′-end (trailer) of filovirid genomes are conserved, and short sections of these end sequences are complementary. Genes of non-fish filovirids are flanked by conserved transcriptional initiation and termination (polyadenylation) sites typically containing the highly conserved pentamer 3′-UAAUU-5′. While containing divergent transcriptional initiation sites, striaviruses and thamnoviruses retain relatively conserved transcriptional termination sites(Hume and Mühlberger 2019). Genes may be separated by non-conserved intergenic sequences or overlaps. Most genes possess relatively long 3′- and 5′-noncoding regions. Co-transcriptional editing is used by cuevaviruses and orthoebolaviruses to express nonstructural proteins from the GP gene (Brauburger et al., 2015, Hume and Mühlberger 2019, Kuhn et al., 2020). \| \| \| \| \| Figure 2.Filoviridae. Schematic representation of filovirid genome organization. Genomes are drawn to scale. Wavy lines indicate incomplete genome ends. \| The replication strategies of filovirids (Figure 3.Filoviridae) have only been studied in depth using EBOV and MARV and are discussed in the respective Orthoebolavirus and Orthomarburgvirus genus subchapters. \| \| \| \| \| Figure 3.Filoviridae. Replication cycle of filovirids (possibly excluding oblaviruses, striaviruses, and thamnoviruses). Virions attach to cell-surface attachment factors (orange Ys) and are taken into the cell via endocytosis (Davey et al., 2017). The filovirion glycoproteins (yellow clubs) bind to endosomal NPC intracellular cholesterol transporter 1 (NPC1, white zigzag) and catalyze the fusion of viral and cellular membranes to release the filovirid RNP complex (green helix) (Carette et al., 2011, Côté et al., 2011, Ng et al., 2014). The polymerase complex (consisting of VP35 [purple dots] and L [blue ovals]) transcribes filovirid mRNAs, which are translated into filovirid proteins, and replicates filovirid genomic RNA via antigenomic intermediates (Brauburger et al., 2015). Genomic RNA and antigenomic RNA occur only as ribonucleoprotein complexes, which serve as templates for replication and/or transcription. Assembly of filovirid proteins and progeny genomes occurs in the cytoplasm and results in budding and release of virions at the plasma membrane (Kolesnikova et al., 2017). Courtesy of Jiro Wada, NIH/NIAID/DCR/IRF-Frederick, Fort Detrick, MD, USA. \| Biology Filovirids are endemic in Eastern Africa (BDBV, MARV, RAVV, SUDV), Middle Africa (BDBV, EBOV, MARV), Southern Africa (MARV), Western Africa (BOMV, EBOV, MARV, TAFV), South America (TAPV), Eastern Asia (HUJV, MLAV, RESTV, XILV), South-eastern Asia (RESTV), Eastern and Southern Europe (LLOV), and Western Europe (FIWIV, KNDV, OBLV). Naturally infected hosts of filovirids are bats (BOMV and likely also other orthoebolaviruses, LLOV, MARV, MLAV, RAVV), actinopterygian fish (FIWIV, HUJV, KNDV, OBLV, XILV), domestic pigs (RESTV), nonhuman primates (MARV, TAFV), humans (BDBV, EBOV, MARV, RAVV, SUDV, TAFV), and viperid snakes (TAPV) (Negredo et al., 2011, Amman et al., 2017, Goldstein et al., 2018b, Kemenesi et al., 2018, Shi et al., 2018, Yang et al., 2019, Kuhn et al., 2020, Hierweger et al., 2021, Horie 2021, Koundouno et al., 2022, Makenov et al., 2023). Antigenicity Due to the absence of replicating dianlovirus, oblavirus, striavirus, tapjovirus, and thamnovirus isolates, pan-filovirid antigenicity studies have not been performed. Derivation of names antennarii: from genus Antennarius to which the presumed hosts of Xīlǎng virus, striated frogfish, have been assigned (Shi et al., 2018). bombaliense: from Bombali District, Sierra Leone, where Bombali virus was discovered (Goldstein et al., 2018a). bothropis: from genus Bothrops to which the presumed hosts of Tapajós virus, fer-de-lances, have been assigned (Horie 2021). bundibugyoense: from Bundibugyo District, Uganda, where Bundibugyo virus was discovered (Towner et al., 2008). Cuevavirus: from Cueva del Lloviu, a cave in Asturias Principality, Spain, where Lloviu virus was first discovered (Negredo et al., 2011). Dianlovirus: from 滇 [diān], an abbreviation denoting China’s Yúnnán Province, and filovirid (Yang et al., 2017). Filoviridae: from the Latin filum, “thread,” referring to the morphology of filovirid particles. kanderense: from Kander River in Bernese Oberland, Switzerland, where Kander virus was discovered (Kiley et al., 1982). lloviuense: from Cueva del Lloviu, a cave in Asturias Principality, Spain, where Lloviu virus was first discovered (Negredo et al., 2011). marburgense: from Marburg an der Lahn, the city in West Germany where the first registered outbreak of Marburg virus disease occurred (Siegert et al., 1967). menglaense: from 勐腊县 (Měnglà County), Yúnnán Province, China, where Měnglà virus was discovered (Yang et al., 2019). Oblavirus: from Bernese Oberland, Switzerland, where Oberland virus was first discovered (Hierweger et al., 2021). Orthoebolavirus: from the Greek ὀρθός (orthós), meaning “straight, right, proper” and the Ebola (Legbala) River in Zaire/Democratic Republic of the Congo, where the first registered outbreak of Ebola virus disease occurred (Henry 2015). Orthomarburgvirus: from the Greek ὀρθός (orthós), meaning “straight, right, proper” and Marburg an der Lahn, the city in West Germany where the first registered outbreak of Marburg virus disease occurred (Siegert et al., 1967). percae: from genus Perca to which the presumed hosts of Fiwi and Oberland viruses, European perch, have been assigned (Hierweger et al., 2021). restonense: from Reston, Virgina, USA, where Reston virus was discovered (Jahrling et al., 1990). Striavirus: from Antennarius striatus, the fish species to which the presumed hosts of Xīlǎng virus, striated frogfish, have been assigned (Shi et al., 2018). sudanense: from Sudan, where Sudan virus was discovered (Bowen et al., 1977). taiense: from Taï Forest, Côte d’Ivoire, where Taï Forest virus was discovered (Le Guenno et al., 1995). Tapjovirus: from Tapajós National Forest, Brazil, where Tapajós virus was discovered (Horie 2021). thamnaconi: from genus Thamnaconus to which the presumed host of Huángjiāo virus, horse-face filefish, has been assigned (Shi et al., 2018). Thamnovirus: from Thamnaconus septentrionalis, the fish species to which the presumed host of Huángjiāo virus, greenfin horse-faced filefish, has been assigned (Shi et al., 2018). zairense: from Zaire (today Democratic Republic of the Congo), where Ebola virus was discovered (Johnson et al., 1977). Genus demarcation criteria PAirwise Sequence Comparison (PASC) using coding-complete filovirid genomes is the primary tool for filovirid genus demarcation. Genomic sequences of filovirids of different genera differ from each other by ≥55% (Bào et al., 2017). Genomic features, such as the number and location of gene overlaps, the number of open reading frames (ORFs) and/or genes, filovirid host and geographic distribution, and filovirid pathogenicity for different organisms are also taken into account for genus assignment. Relationships within the family Phylogenetic relationships across the family have been established from maximum likelihood trees generated using coding-complete or complete genome sequences (Figure 4.Filoviridae) or by phylogenetic analysis of RdRP sequences (Wolf et al., 2018). \| \| \| \| \| \| \| Figure 4.Filoviridae. Phylogenetic relationships of filovirids. Maximum-likelihood tree (midpoint-rooted) inferred by using A) coding-complete or complete filovirus genome sequences and (B) filovirus RNA-directed RNA polymerase gene (L) sequences. Sequences were translationally aligned using Clustal-Omega version 1.2.3 ( and were manually curated in Geneious version R9 ( or Unipro UGENE version 35 ( Trees were inferred in FastTree version 2.1 ( using a General Time Reversible (GTR) model with 20 Gamma-rate categories, 5,000 bootstrap replicates, and exhaustive search parameters (-slow) and pseudocounts (-pseudo). Numbers near nodes on the trees indicate bootstrap values in percentages. Tree branches are scaled to nucleotide substitutions per site (scale bars). \| Relationships with other taxa Filovirids are closely related to other viruses in the order Mononegavirales, in particular paramyxovirids, pneumovirids, and sunvirids (Wolf et al., 2018). Related, unclassified viruses \| \| \| \| \| --- --- \| \| Virus name \| Accession number \| Virus abbreviation \| Reference \| \| blue spotted goatfish filovirus \| MT579873 \| \| (Geoghegan et al., 2021) \| \| BtFiloYN2162 \| KX371873 \| \| (Yang et al., 2017) \| \| BtFiloYN2176 \| KX371874 \| \| (Yang et al., 2017) \| \| BtFiloYN2180 \| KX371875 \| \| (Yang et al., 2017) \| \| BtFiloYN2181 \| KX371876 \| \| (Yang et al., 2017) \| \| BtFiloYN2190 \| KX371879 \| \| (Yang et al., 2017) \| \| BtFiloYN9434 = Vietnam-R.amplexicaudatus-91-2020 \| KX371883; OP653723 \| \| (Yang et al., 2017, Makenov et al., 2023) \| \| BtFiloYN9435 \| KX371885 \| \| (Yang et al., 2017) \| \| BtFiloYN9442 \| KX371884 \| \| (Yang et al., 2017) \| \| BtFiloYN9445 \| KX371886 \| \| (Yang et al., 2017) \| \| BtFiloYN9447-2 = Vietnam-R.amplexicaudatus-91-2020 \| KX371888; OP653723 \| \| (Yang et al., 2017, Makenov et al., 2023) \| \| BtFiloYN9447-3 \| KX371889 \| \| (Yang et al., 2017) \| \| BtFiloYN9447-4 \| KX371890 \| \| (Yang et al., 2017) \| \| BtFV/DH04 \| KP233864 \| \| (He et al., 2015) \| \| Déhóng virus \| OP924273 \| DEHV \| (He et al., 2023) \| \| John dory filovirus \| MT579881 \| \| (Geoghegan et al., 2021) \| \| Lötschberg virus \| OQ186623 \| LTBV \| (Seuberlich et al., 2023) \| \| Vietnam-R.leschenaultii-39-2020 \| OP653722 \| \| (Makenov et al., 2023) \| \| Vietnam-R.leschenaultii-123-2020 \| OP653721 \| \| (Makenov et al., 2023) \| Virus names and abbreviations are not official ICTV designations. Coding region sequence incomplete. Additional unclassified filovirids that are probable members of existing genera are listed under individual genus descriptions. International Committee on Taxonomy of Viruses Unless otherwise noted, this work is licensed under the CC BY 4.0, Creative Commons Attribution 4.0 International License Support is provided by the National Institute of Allergy and Infectious Diseases, U.S. National Institutes of Health, Award U24AI162625 Copyright © 2025 (ICTV) \| Privacy \| Disclaimer \|
13274	https://math.answers.com/other-math/What_is_the_next_number_in_the_pattern_of_7_11_19_35	What is the next number in the pattern of 7 11 19 35? - Answers Create 0 Log in Subjects>Math>Other Math What is the next number in the pattern of 7 11 19 35? Anonymous ∙ 15 y ago Updated: 4/28/2022 67 7 + 4 = 11 11 + 8 = 19 19 + 16 = 35 35 + 32 = 67 67 + 64 = 131 ... Wiki User ∙ 15 y ago Copy Add Your Answer What else can I help you with? Search Continue Learning about Other Math ### What would be the next number in this series 15 12 13 10 11 8? What would be the next number in this series 15 12 13 10 11 8? ### Next number in the series 7 11 19 35? 59 is the next number in this series. ### The next number in the series 6 12 7 14 11 22 19 is? The next number in the series is 38. Take a look at the pairs of numbers:6 and 127 and 1411 and 2219 and ____The pattern rule is that each second number is twice the size as the first number. 62=12, 72=14, 112=22.Knowing this, double 19. 192=38. ### Which number comes next in these series 5 7 11 19 35? 67 ### What number comes after 7 11 19 35? The answer is 67 because the pattern is 2x(x-1)-3 11-7 is 4 19-11 is 8 which is twice 4 35-19 is 16 which is twice 8 so the next difference is twice 16, =32 so the next number is 35+32 =67 Related Questions Trending Questions Which type of lines pass through the points 5 5 7 1 and 5 5 8 4 on a grid?How do you say this number 0.0125?What is 38 divisible by?How do you multiply to the power two thirds?If x equals 3 and y equals 2 then 7x plus 5y equals?How do you write the standard form for 1.8 x 10 to the 3rd power?All paragraphs should have one main idea. True False?How many zeros in 6.01 million?What is a number called to the third power?What is the arithmetic mean?Data in order from smallest to largest or vice-versa is called?There must be at least students in a room to ensure there are at least nine boy or nine girls.?What is 50000 divided by 700?Is 1.006 and 1.06 equivalent?A straight path of points that goes on forever in two directions?What is 288 divided 8?What is a spar on a kite?Does 8 divided by 208 have a remainder?What is 129 rounded to the nearest tens?What are the dimentions of a 355mL can? Resources LeaderboardAll TagsUnanswered Top Categories AlgebraChemistryBiologyWorld HistoryEnglish Language ArtsPsychologyComputer ScienceEconomics Product Community GuidelinesHonor CodeFlashcard MakerStudy GuidesMath SolverFAQ Company About UsContact UsTerms of ServicePrivacy PolicyDisclaimerCookie PolicyIP Issues Copyright ©2025 Answers.com. All Rights Reserved. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Answers.
13275	https://www.youtube.com/watch?v=mmlO3nZxg_c	More Minimising Without Calculus Dr Barker 27200 subscribers 303 likes Description 8111 views Posted: 7 Jun 2024 We minimise a^2 + b^2 + c^2 + d^2, subject to the constraint abcd = 9. 00:00 Intro 00:20 2 variable problem 03:56 Building on this case 05:00 Considering negatives 06:00 3 variable problem 10:03 4 variable problem 30 comments Transcript: Intro okay so we're going to solve a problem where we want to find the smallest possible value of a s + b s + C 2 + d^2 where we've got this constraint that the product of a b c and d has got to be equal to 9 so now our approach to this problem is going to be to actually consider some similar but simpler cases and then build up gradually so the first 2 variable problem simpler problem that we'll consider is what if we just had two variables so let's imagine we were trying to minimize just a 2 + B2 where again the product of A and B had to be constants let's say perhaps a b got to be equal to 9 and you'll find by exploring this just in the two variable case that we seem to get the smallest possible value actually when a is equal to B so let's see if we can prove this in the two variable case so we could start off with some values of A and B that aren't equal to each other and a nice way of writing this is instead of having a and b we'll write it as a and some constant Lambda a for our value of B where Lambda isn't equal to one so that then we've got a and b aren't equal to each other so then if we find the sum a^2 + b² our value of a 2 + b s is just going to be a 2 + Lambda 2 a 2 and this factorizes to 1 + Lambda 2 a 2 so this is what we get when a and b aren't equal to each other so what do we do if we want to make a and b equal to each other well remember that the product has got to be constant so at the moment we've got the a Lambda a is equal to 9 so how do we split this Lambda and distribute this evenly between the two numbers so that the product stays the same well we just need to take the square root of Lambda you'll notice here that actually because the product has got to be a positive number the S of a and Lambda a is the same so actually Lambda is positive so there's no issues with taking the square root here so we have Lambda a < TK of Lambda a again is still equal to 9 so if we try now instead of A and B we've got our root Lambda a and again we've got rooot Lambda a so we've kept the product the same let's see what happens to our a 2 + b 2 now so a 2 + b s is just going to be two lots of when we Square the root Lambda we just get Lambda so we get 2 Lambda a 2 and now we're going to compare our values of a 2 + b^2 in the two different cases so in the first case we'll call this one where they're not equal to each other we had 1 + Lambda 2 and here we've got 2 Lambda a 2 when we've now tweaked the numbers to make them equal to each other so if we do 1 - 2 find what is the difference between the two values we'll get 1 + Lambda Square both of them have a factor of a 2 so 1 + Lambda 2 - 2 Lambda in Brackets a 2 and this quadratic in Lambda actually factorizes to become Lambda minus1 all SAR time a^ 2 you can see now we're on to something that the difference between these two values is something which is a square number so this is always going to be positive so this is telling us then that our original value is always going to be bigger than what we get by tweaking the numbers to make a and b equal to each other but we can actually say not just that it's greater than or equal to zero but this is actually strictly greater than zero because remember we imposed earlier that Lambda can't be equal to one so if Lambda was equal to one then we'd be starting with values where are actually equal to each other so the only case where it wouldn't be bigger would actually be when a is equal to B to begin with so you can see then in this two variable case if you have a and b aren't equal to each other you can always further reduce it by setting a and b equal so this tells us then in the two variable case the smallest value possible of a 2 + b^ 2 is indeed achieved when A and B are equal to each other and now if we consider a similar Building on this case problem but with three variables where we want to minimize the sum of squares subject to the product being constant we can actually use some of what we already know from the two variable case so let's imagine our three values of a B and C are all different to each other we could have for example root3 3 < tk3 and one could be our values of a b and c so now we already know from the two variable case that if you've got different values of A and B then we can further reduce a 2 + b^ 2 by tweaking these numbers num to make them equal to each other so we could change this to 3 3 and 1 and this would actually reduce the value of a^2 + b^2 and hence it would also reduce the value of a 2 + b 2 + c^ 2 so you can see here using this fact that we already know from the two variable case that actually we don't need to consider cases where a B and C are all different from each other we only need to consider the case where two of them are equal versus the case where all three of a B and C are equal to each other Considering negatives and now you could consider examples where there's negatives involved as well so you could make things a little bit awkward by introducing some negative signs on these numbers but remember that whether a B and C are positive or negative that isn't going to affect the value of a 2 + b 2 + C S and similarly because the product remains constant if you've got two negatives here you could just replace those by the positive versions of those numbers and you would still get a solution where ABC would be equal to 9 and the sum of squares would stay the same and actually the same logic applies to our original problem as well that if you have a solution involving negatives you could just change those negatives into positives without any loss of generality and you would get another solution so if you assume you have a minimum with some negatives then you could just replace them by positives and You' get some other values of a b c and d which would also minimize your solution so we can proceed from here then just saying that a b c and d are all going to be positive so now now we want to compare the case 3 variable problem with a three variable case where first of all A and B are equal to each other that c is different so we'll write these as a a and then our value of C will write as actually Lambda cubed a where in order for these not to be equal to each other we just again impose that Lambda isn't equal to one so now our value of a 2 + b s + c^ 2 we got a 2 + a 2 + Lambda 6 a 2 so we get Lambda 6 + 2 all a 2 for our value of a 2 b 2 c² in this case so then if we want to redistribute this Lambda to make all of our a b and c equal to each other we're going to be working now with Lambda a Lambda a and Lambda a so in this case our value of a 2 + b^ 2 plus c^ 2 is just going to be 3 lots of Lambda 2 a 2 so now just like before we want to find the difference between the two so if we do the sum a 2 + B2 + c^ 2 in the case where they're different minus the sum where they're all the same so we do this 1 minus 2 once again we're going to get Lambda the 6 + 2 then we take away this 3 Lambda 2 all time a 2 so we've got Lambda to 6 + 2 - 3 Lambda 2 all time a 2 which we can then so that's Lambda to 6 we can then write all of this as Lambda 6 - 3 Lambda 2 + 2 all multiplied by a s so the idea now is we want to show that this quadratic in Lambda is always going to be positive but actually to reduce this and make it a little bit nicer to work with we'll introduce a new variable U which we'll just Define as equal to Lambda squ so now this becomes a cubic U Cub - 3 U + 2 all multip by a s and we want to show then that this is strictly greater than zero so that the sum a s + b^ S + c^ S is always bigger when you have different values of a b and c versus making them all the same so now we can see that this a s term is always going to be positive so we only really need to focus on this cubic in U so we focus on U Cub - 3 U + 2 and if we want to factorize this you can see just quite easily by inspection that if U is equal to one this is going to be zero so if we've got a root at one we can take out a factor uus one so then we could do this by polinomial division or again just by inspection you'll see that we need to have u^2 we need to have a plus u and finally we need minus 2 in order for this to be equal and then we can factorize this quadratic in U as well so we keep our uus one and this becomes U -1 U + 2 so the whole cubic in U is actually just U -1 all 2ar U + 2 but then remember that U is actually equal to Lambda squar so we can write all of this then as Lambda s - 1 all sared multiplied Lambda 2 + 2 so this is looking really good because now we've got something Lambda 2 + 2 is definitely always positive and then we've also got something squared here which is again always going to be positive and we can actually say this is going to be strictly positive because first of all we've imposed that Lambda can't be equal to one and we also couldn't have Lambda equal to negative one just cuz we're working without any loss of generality now in the case where a B and C are all positive so this is indeed always positive which tells us then that the difference between our a s b^ 2 plus c^ 2 in either case is bigger when we have different values so we're saying then that the minimum is achieved in the three variable case where a B and C are all equal to each other and now we're ready to tackle the 4 variable problem original problem with four variables so again we can build on what we know from the three variable Case by considering first of all if all four of our a b c and d were different or perhaps if only two of them were equal to each other then we know that we could tweak the values of three of them make them all equal to each other and this would reduce the value of our a 2 + b 2 + C 2 and because we've left D alone there it would hence also reduce the value of the total sum of all of the squares there so in this case where a b c are different or if two of them are equal to each other we know from the three variable case that we can reduce the sum just by setting them all equal to each other and remember as well we're working without any loss of generality in the case where a b c and d are all positive so if any of them were negative you could just replace them by their positive counterparts without affecting the value of the product or the sum of squares there so we only really need to consider now either we've got the case where three of them are equal and the other one takes a different value or all four of our values are equal to each other because we know that having two equal or none of them equal doesn't give us a minimum solution for the sum of squares so if we look at the case where three of them are equal to each other and the other one is different we'll write our a b c and d as a and the other one we'll write as Lambda s a so this is fine so long as Lambda squ isn't equal to 1 and you'll note that we have something positive there but that's fine because we're working in this case where a b c and d are all positive so then the sum of squares is just going to be a^ 2 3 plus we'll have Lambda 2^ 2 a so the sum of squares is going to be 3 + Lambda to^ 4 a 2 in this case so let's imagine now we want to redistribute this Lambda squar evenly between a c and D so then a b c and d are all just equal to root Lambda a so we've got root Lambda a for our values of a b c and d so then when we find a s + b 2 + C 2 + d^2 in this case we do root Lambda s just gives us Lambda a 2 then we got four copies of this so we've got four Lambda a 2 is our value of the sum of squares in this case where we've tweaked the values to make them all equal to each other so again we're going to now do the first value minus the second value to see what the difference is so if we calculate 1 - 2 we're going to end up with we've got Lambda 2 + 3 and then we take away the four Lambda so we'll write this as Lambda to 4 - 4 Lambda + 3 all multiplied by a 2 so again we want to show that this is positive so that the sum of squares in the case where they're different is bigger than the sum of squares in this case where we've redistributed to make a b c and d all equal to each other so we want to show then that Lambda 4 - 4 Lambda 2 + 3 is greater than zero because we know that this a s is going to be positive and again if we want to try and factorize this quartex we want to factorize this expression Lambda 4 - 4 Lambda + 3 you can again see just by inspection this is going to have a root when Lambda is equal to one so we can take out a factor of Lambda -1 then we're left with a cubic which is just Lambda cubed + Lambda 2 + Lambda - 3 so you could verify this using just expanding or by polinomial division to get this then we've got a nice cubic term which we can actually again see by inspection is going to be zero when Lambda equals 1 so we can pull out another factor of Lambda minus one here so we'll write this whole thing as lambda-1 all SAR we've got a second factor of Lambda minus one and then the quadratic term we're left with you can check is Lambda 2 + 2 Lambda + 3 so unfortunately this quadratic doesn't have as nice a factorization as before but we can still apply completing the square now so we leave the Lambda minus one squared term alone and then in the bracket here we've got Lambda + 1 all squar gives us Lambda s + 2 Lambda + one we need this to be plus three though so we just add two on the outside so then you can see we've got an expression which is something squar + 2 so this is definitely always positive and similarly Lambda minus 1 all squar is going to be positive so we know it can't be equal to zero because Lambda can't be equal to one there so this can't be zero so then we can say that this whole thing is indeed greater than zero so we're saying then that because this was the difference between the sum of squares where we had different values of a b c and d versus having them all the same we get a bigger value for the sum of squares when a a b c and d are different versus them all being the same so this tells us then that the minimum does indeed occur where a b c and d are all equal to each other so to actually solve this problem then we just need to find values of a b c and d that are all equal so that a c d equals 9 so we need a b c and d are actually all just going to be equal to < tk3 so then our sum of squares is just going to be four lots of < tk3 2 or 4 3 so the minimum possible value for a s + b^2 + c^2 + d^2 subject to this constraint the product has to be 9 is going to be 12 then and you can also achieve this by using some negative so you could have pairs of negative root3 you could have two or you could have all four of a b c and d could be negative < tk3 and you would still maintain the same product being N9 and the sum of squares would still be 12 the minimum there
13276	https://www.quora.com/When-I-m-solving-a-system-of-equations-why-is-it-that-when-I-isolate-a-variable-on-one-side-and-then-replace-it-with-what-s-on-the-other-side-I-end-up-with-0-0-or-1-1	When I’m solving a system of equations why is it that when I isolate a variable on one side and then replace it with what’s on the other side I end up with 0=0 or 1=1? - Quora Something went wrong. Wait a moment and try again. Try again Skip to content Skip to search Sign In Mathematics Variable Substitution Symbolic Manipulation Systems of Linear Equatio... Mathematical Problems Solving Equations Substitution (mathematics... Algebraic Equations Algebra 5 When I’m solving a system of equations why is it that when I isolate a variable on one side and then replace it with what’s on the other side I end up with 0=0 or 1=1? Ad by Grammarly Stuck on the blinking cursor? Move your great ideas to polished drafts without the guesswork. Try Grammarly today! Download All related (32) Sort Recommended Alberto Beron Bachelor of Sciece (BS) in Electronic Engineering (Course)&Mathematics, California State University, Los Angeles · Author has 1.9K answers and 896.5K answer views ·6y There are three cases when solving a system of two equations and two variables. The system has one unique solution . If you graph it, the two lines cross each other. The system has no solution . if you graph it, the lines are parallel The system has infinite solutions. If you graph it, the two lines are the same In case 2 and 3 the variables canceled out How to identify if it is case 2 or 3 ? After the variables canceled out. a) If you are left with a false statement. For exp 2 = 1 , it is case 2 If you are left with true statement , exp 1 =1 , It is case 3 in your case it is 3. There are infinite sol Continue Reading There are three cases when solving a system of two equations and two variables. The system has one unique solution . If you graph it, the two lines cross each other. The system has no solution . if you graph it, the lines are parallel The system has infinite solutions. If you graph it, the two lines are the same In case 2 and 3 the variables canceled out How to identify if it is case 2 or 3 ? After the variables canceled out. a) If you are left with a false statement. For exp 2 = 1 , it is case 2 If you are left with true statement , exp 1 =1 , It is case 3 in your case it is 3. There are infinite solutions Note: You get the same results if by mistake after you solve for y in equation 1, you replace y in equation 1 again , instead of equation 2 Upvote · 9 1 Related questions More answers below What is the value of 1/0, 1/1,0/0 and 0/1? What answer was 1\0-0\1? How do you solve for X when given an equation with one variable and one unknown number (e.g., y=mx+b)? Can a variable be considered "zero" if its value is not actually going to be determined at any point during solving an equation? Can I substitute any ingredients in beer duck if I can't find certain items like garlic sprouts or rock sugar? Dinarte Santos Engineer at Oil Refinery (1987–present) · Author has 403 answers and 509.4K answer views ·6y It happens when one of the equations is a linear function of the other. Suppose you have two linear equations like these x + 1 = 0 x + 1 = 0 They are obviously the same, so one is a linear function (identity) of the other. Subtract one from the other. You’ll get 0 + 0 = 0 Add the first two terms. Then 0 = 0 Now multiply the second equation by 2. This results in a system in which the second equation is a linear function of the first (The first equation multiplied by a constant). Then x + 1 = 0 2 x + 2 = 0 Solve the first equation for x. Then x = -1 Replace x in the second equation. 2 (-1) + 2 = 0 -2 + 2 = 0 0 = Continue Reading It happens when one of the equations is a linear function of the other. Suppose you have two linear equations like these x + 1 = 0 x + 1 = 0 They are obviously the same, so one is a linear function (identity) of the other. Subtract one from the other. You’ll get 0 + 0 = 0 Add the first two terms. Then 0 = 0 Now multiply the second equation by 2. This results in a system in which the second equation is a linear function of the first (The first equation multiplied by a constant). Then x + 1 = 0 2 x + 2 = 0 Solve the first equation for x. Then x = -1 Replace x in the second equation. 2 (-1) + 2 = 0 -2 + 2 = 0 0 = 0 It is possible to replace the second equation with any linear combination of the first (the first multiplied by a constant, and another constant added to it), and the end result will be the same. Upvote · 9 1 Sponsored by Singapore Global Network Thinking of moving abroad? Jennifer’s journey shows the ups and downs of starting fresh - and why she chose Singapore. Learn More 999 131 Alon Amit Math Circle educator, Proof School trustee · Upvoted by Paul King , Data Scientist, Computational Neuroscientist and Justin Rising , PhD in statistics · Author has 8.8K answers and 173.8M answer views ·7y Related If 3 0=1 3 0=1, then, by taking the square root of 0 of both sides, we have 3=0√1 3=1 0. Why? “Taking the square root of 0 of both sides” is not a meaningful phrase, even if you rewrite it as what you had actually meant, which is “taking the 0 th 0 th root of both sides”. There’s no function or operation which takes a number and returns its “0 th 0 th root”, and you can see why: since 3 0=7 0=23 0=1 000 000 0=1 3 0=7 0=23 0=1 000 000 0=1, we cannot in any meaningful way provide a useful value for the expression 0√1 1 0, nor to 0√23 23 0 or any other number. So, we don’t assign any meaning to those expressions, and there’s no operator called 0√0, much like there isn’t an operator /0/0 or log 1 log 1 Continue Reading “Taking the square root of 0 of both sides” is not a meaningful phrase, even if you rewrite it as what you had actually meant, which is “taking the 0 th 0 th root of both sides”. There’s no function or operation which takes a number and returns its “0 th 0 th root”, and you can see why: since 3 0=7 0=23 0=1 000 000 0=1 3 0=7 0=23 0=1 000 000 0=1, we cannot in any meaningful way provide a useful value for the expression 0√1 1 0, nor to 0√23 23 0 or any other number. So, we don’t assign any meaning to those expressions, and there’s no operator called 0√0, much like there isn’t an operator /0/0 or log 1 log 1 or log 0 log 0. Upvote · 999 502 99 33 Paul Holloway Author has 2.1K answers and 3.3M answer views ·1y Related How do you solve a system of linear equations with two unknowns if you cannot isolate one of the variables? Through algebraic manipulation, you should always be able to isolate one of the variables - especially if they are linear equations. However, if you simply don’t know how to isolate one of the variables, you could try graphing the system of equations - plot both lines on the same graph with the same scale and simply read off the co-ordinates where they intersect. Let’s take for example the system of Continue Reading Through algebraic manipulation, you should always be able to isolate one of the variables - especially if they are linear equations. However, if you simply don’t know how to isolate one of the variables, you could try graphing the system of equations - plot both lines on the same graph with the same scale and simply read off the co-ordinates where they intersect. Let’s take for example the system of linear equations: 2x + 3y = 28 and 7y - 3x = 27 Now we could do some algebraic manipulation and isolate one of the variables - for example: 2x = 28–3y x = (28–3y)/2 now we can shove that into the second equation. It will get a little messy but we can do it. However, let’s pretend we don’t know how to do this and solve this without using algebra. Let’s begin with the first equation, we can begin with an easy one set x = 0. The first equation becomes: 3y = 28 so dividing through by 3 we get y = 9.333 Now let’s do another easy one and set y = 0 2x = 28 so dividing through by 2 we get x = 14 Now we know that linear equations are called linear equations because they graph as straight lines. Just plot the points for x = 0 and y = 0 and we have our graph. For neatness sake, it’s good to label that line so you know which equation is which since both lines are going to be plotted on the same graph. Now we just repeat the process for the second equation, we can pick any value for x and y but putting x = 0 and y = 0 and getting the corresponding values makes it easy to plot the straight line. This time, however we plot the graph on the same graph and we’re looking for the point where the lines intersect. Now we can just read off the values. If it’s not easy to read off becaus... Upvote · 9 1 Related questions What is the value of 1/0, 1/1,0/0 and 0/1? What answer was 1\0-0\1? How do you solve for X when given an equation with one variable and one unknown number (e.g., y=mx+b)? Can a variable be considered "zero" if its value is not actually going to be determined at any point during solving an equation? Can I substitute any ingredients in beer duck if I can't find certain items like garlic sprouts or rock sugar? When an equation has more than one solution, how many solutions will there be if we solve for each variable independently (using substitution)? What is 1-5-0-0-1? Is there a more basic math equation than 1+1=2? If 0 0=1 1 0 0=1 1, then would 0 equal 1? How can I write a math equation where 1 is equal to continuous amount of growing values between 0 and 1 proving that 0 should always be considered to have a positive value? To what does this truth table apply? 1+1=1, 1+0=-1, 0+0=1? In matrix representation, what is [(1, 0), (0, 0)], [(0, 0), (1, 0)], and [(0, 0), (0, 1)]? How is “HSYVS JSGS S” written as “SHHSBS D”? What is the range of this set: {(-1,0), (1, 0), (0,1), (0,-1)}? How do you solve 0÷1×0? Related questions What is the value of 1/0, 1/1,0/0 and 0/1? What answer was 1\0-0\1? How do you solve for X when given an equation with one variable and one unknown number (e.g., y=mx+b)? Can a variable be considered "zero" if its value is not actually going to be determined at any point during solving an equation? Can I substitute any ingredients in beer duck if I can't find certain items like garlic sprouts or rock sugar? 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13277	https://www.youtube.com/watch?v=H5D6EAezsXQ	SUBSETS AND POWER SETS - DISCRETE MATHEMATICS TrevTutor 308000 subscribers 9128 likes Description 692347 views Posted: 21 Jan 2018 Today we look at subsets and power sets. This includes the empty set, and the power set of the empty set. Support me on Patreon: Visit my website: Subscribe on YouTube: --Playlists-- Discrete Mathematics 1: Discrete Mathematics 2: --Recommended Textbooks-- Discrete and Combinatorial Mathematics (Grimaldi): Discrete Mathematics (Johnsonbaugh): Discrete Mathematics and Its Applications (Rosen): Book of Proof (Hammack): Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding. 358 comments Transcript: Intro in this video we're going to talk about subsets and power sets and I'm going to represent subsets visually first if a is a subset of B then every element in a must also be in B visually this means that a must be contained within B and we would write this a is a subset of B now it can also be the case that a is exactly the same as B so if we have a and B the same size this is also a subset and you can see this by the little line underneath if we have the subset symbol with a line underneath that means subset which means they can be smaller or equivalent or contained or equivalent but if we have something like a proper subset B without the little bar at the bottom this means that a must be strictly smaller than B let's do some Examples examples so these are just true or false questions I'm asking is the set containing a B a a a subset of the set containing a b c the first thing we have to remember is that repeated elements do not matter so we can remove the remaining A's so now we're asking is a be a subset of ABC well we have to check is everything in the smaller is everything in a here also in B so we take a look at a we say okay is a and B the answer is yes okay that's good what about B is B in the second set yes it is that's good therefore the set a B is a subset of ABC so this would be true and we could even draw this we could do one I shouldn't use numbers we should use a B and C and we can circle them right we can say okay a B is a and then we can circle a B and C which is B and we'll notice that a is contained in B therefore a is a subset of B you can do it visually or you can just do it by definition so what about CD is CD a subset of CD the answer is yes that is true and that's because every element in our set a here is a member of the set B so C is an a therefore C isn't B D is an a therefore D is in B now what about the next one well the next one I'm asking is the set containing a a subset of the set containing the set containing a that was a very difficult sentence to say essentially what I'm asking is this element a in our second set and the answer here is no so if I were to list out all the elements really I have a on the left and on the right I have the set containing a now a little a is in our set a well this set containing a is in B so we can see a is not in B a is not a subset of B we don't see a anywhere and B we just see the set containing a okay so no this is false this is not the case so what we could say is we just stick a line through it and that means that is not a subset okay finally the empty set is the empty set of subsets of XYZ the answer is yes it is true the empty set is a subset of every set because the definition says everything in here must be in here well there is nothing in the empty set therefore this is trivially true the subset is a I've said the empty set is a subset of every single set okay Power Sets so now that we have a kind of a rough idea of what subsets are we can now talk about power sets so the power set of a with this little P a is the set containing all possible subsets of a and this could be a little bit of a confusing concept to wrap your head around first let's figure out how to generate all possible subsets first this is how I like to think of it with every element in the original set a we start with an empty set and we ask ourselves do we add the first element so here I'm starting with the empty set and I'm asking myself should I add a if I add a then I get the set containing a if I don't add a I'm left with the empty set now we move to the next element and we ask ourselves should we add B if the answer is yes then we end up with a set a and B if we don't then we end up with the site containing a over on the empty set side we can ask ourselves the same question should we add B if yes then we have the set containing B if no then we have the empty set and now each of these is a possible subsets of the set containing a and B so if we have ten elements in our original set then we have to ask ourselves yes or no ten times which means is going to be two to the ten possible subsets so this tree doesn't really work when you get more and more elements because it's just more and more writing and it's really impossible at that point and even super tedious to write it out now these are all the possible subsets the power set is the set containing all of that so this would be the set containing the empty set the set containing a the set containing B and the set containing a and B and those are all in the same set another way of doing this would be to say okay the power set I can have no elements so I can have the NP said I could have a set with just one of the elements so a and B I can have a bunch of subsets with all the pairs of elements a and B so on and so forth now really talking about Power Set Size counting the reason why I showed you that tree was so we can talk about the size of the set so if your original set a has n elements then the power set the size of the power set will have two to the size of a or two to the N and this might sound a little bit confusing at first but really for each we're either adding it to a subset or were not so there's two choices per element so we can see before imagine if our subset our original set a just had no elements in it then we can have two to the zero which is one possible subset that would be the empty set if there was just a we'd be asking ourselves do we add a or not a then we'd have two to the one equals two possible subsets with two elements here we see that there are two to the two equals four possible subsets so let's say I have that a has six elements in it then the cardinality of the power set of a would have two to the size of a which is just two to the six which should be I think 32 2 4 8 16 32 should be 64 possible subsets and that's quite a bit of subsets that's quite a lot of possible subsets you would never be asked to write the power set of something this large on an exam back to 2 the 3 is probably the highest you would go writing it up by hand or maybe 2 to the 4 if your professor is a little bit sadistic but I hope this intuitively describes why the power set grows like this in powers of 2 it's because for each element you have a choice of putting it in or not so now that we've Tricky Questions covered power sets with simple examples of course if you're a little bit confused post comments rewatch the video write it out by hand try to follow along we're gonna cover some of these tricky questions the first one of course is the power set of the empty set okay the power sort of the empty set what okay well remember that the empty set is essentially size zero so the size of the empty set is equal to zero this means the size of the power set of the empty set should be two to the zero equals one so we should have one element in there and here's a cool thing to remember the empty set is an element of every single power set so the power set of the empty set is just the set containing the empty set so there's a set containing no elements inside the power set again another way to write this would be just the set containing the set with nothing so if you don't like the zero with a line through it you can just remember this as the set containing nothing in it okay what if I have the power set of the set containing the empty set okay now this is a little bit more confusing but if we remember that okay the set containing the empty set the size of this is 1 so the power set of the set containing the empty set should have 2 to the 1 equals 2 elements in it so the first one would just be the empty set because the empty set is an element of every power set and then you'll also have the set containing the empty set as an element ok now this might be a little bit hard to wrap your head around but remember if we just draw our tree for this we can just draw the tree the same way we did it before we can start with the empty set if we don't add the empty set in we're just left with the empty set if we add the empty set in then we have the set containing the empty set so therefore the power set is just going to be these two possible subsets in a set so again this is how we can figure out these tricky situations without being confused by the notation here now two more theoretical questions is a a subset of the power set of a for any a well let's look this here in this example is a and here we have a so we see that a is an element but does this hold for every single set and is a a subset of the power sort of a for NEA the answer is no it's not a subset but it is an element now let's think about this well let's go back to this example here is a a is a second taining a and B if we add all of our elements we get the possible subset which is itself so we get a back as a possible subset but remember that these subsets are elements of the power set so whatever your original set is it will be an element of the power set there are some cases where the original set is a subset of the power set but not all cases for instance the set a B is not a subset of the power set it's just an element in this case but if we compare it to this example we would see that a is a subset of the power set but this is just one situation in which it does occur so all the time a is an element of the power set but not all the time is a subset of the power set ok so let's just do some exercises I'm not looking forward to the second one but we can do the first second and third the first one says let's see the size of C equal K and the size of D equal chain what is the size of the power set of C cross T ok well let's remember the size of C cross B is just the same thing as the size of C times the size of D so this is just K times J okay which means that the size of the power set of C cross D will just be 2 to the size of C cross D which we know is just equal to 2 to the K times J so when you take Cartesian products with power sets things get really crazy really fast the second one asks this the elements of the power set of the power set of the empty set well we do the step by step so the power set of the empty set is just the set containing the empty set so now we want the power set of the set containing the empty set and again we've done this before this is just the set containing the empty set as well as the set containing the empty set okay so we can take power sets of power sets and once again it becomes a pain really quickly to write out the final one is more theoretical so if the size of a is equal to n what is the size of the power set of the power set of the power set of a well we can take this step by step so the size of the power set in fact I'm not going to write this out again this is just going to be equal to two to the size of the power set of the power set of a okay and this is just equal to 2 to the 2 to the power set of a which is just equal to 2 to the 2 to the 2 of the size of a which of course is equal to 2 to the 2 to the 2 to the M so once again your professor if he is really sadistic could just ask you about the cardinality of the power so that the power sort of the power set of the power set of some set and ask you for the size so that is subsets and power sets if you have any questions please leave them in the comments below and I will do my best to answer them
13278	https://artofproblemsolving.com/wiki/index.php/Law_of_Sines?srsltid=AfmBOooUM6hjFZxAaLNUAl15i3p2yAlONoAefHb9ai2ZQZ4R7DxjMh9m	Art of Problem Solving Law of Sines - AoPS Wiki Art of Problem Solving AoPS Online Math texts, online classes, and more for students in grades 5-12. Visit AoPS Online ‚ Books for Grades 5-12Online Courses Beast Academy Engaging math books and online learning for students ages 6-13. Visit Beast Academy ‚ Books for Ages 6-13Beast Academy Online AoPS Academy Small live classes for advanced math and language arts learners in grades 2-12. Visit AoPS Academy ‚ Find a Physical CampusVisit the Virtual Campus Sign In Register online school Class ScheduleRecommendationsOlympiad CoursesFree Sessions books tore AoPS CurriculumBeast AcademyOnline BooksRecommendationsOther Books & GearAll ProductsGift Certificates community ForumsContestsSearchHelp resources math training & toolsAlcumusVideosFor the Win!MATHCOUNTS TrainerAoPS Practice ContestsAoPS WikiLaTeX TeXeRMIT PRIMES/CrowdMathKeep LearningAll Ten contests on aopsPractice Math ContestsUSABO newsAoPS BlogWebinars view all 0 Sign In Register AoPS Wiki ResourcesAops Wiki Law of Sines Page ArticleDiscussionView sourceHistory Toolbox Recent changesRandom pageHelpWhat links hereSpecial pages Search Law of Sines The Law of Sines is a useful identity in a triangle, which, along with the law of cosines and the law of tangents can be used to determine sides and angles. The law of sines can also be used to determine the circumradius, another useful function. Contents [hide] 1 Statement 2 Proof 2.1 Method 1 2.2 Method 2 3 Method 3 4 Problems 4.1 Introductory 4.2 Intermediate 4.3 Olympiad 5 See Also Statement In triangle , where is the side opposite to , opposite to , opposite to , and where is the circumradius: Proof Method 1 In the diagram above, point is the circumcenter of . Point is on such that is perpendicular to . Since , and . But making . We can use simple trigonometry in right triangle to find that The same holds for and , thus establishing the identity. Method 2 This method only works to prove the regular (and not extended) Law of Sines. The formula for the area of a triangle is . Since it doesn't matter which sides are chosen as , , and , the following equality holds: Assuming the triangle in question is nondegenerate, . Multiplying the equation by yields: Method 3 We can circumvent some of the work in Method 1 by setting up the circle in a different way. Let be a diameter and be the center of the circle, and let be on . Furthermore, let , and let , , and . We have that is a right angle, as is a diameter. Therefore, , so, rearranging, we have , or . Likewise, . Finally, we observe that , so evidently . Combining all three equalities, Problems Introductory If the sides of a triangle have lengths 2, 3, and 4, what is the radius of the circle circumscribing the triangle? (Source) Intermediate Triangle has sides , , and of length 43, 13, and 48, respectively. Let be the circlecircumscribed around and let be the intersection of and the perpendicular bisector of that is not on the same side of as . The length of can be expressed as , where and are positive integers and is not divisible by the square of any prime. Find the greatest integer less than or equal to . (Source) Olympiad Let be a convex quadrilateral with , , and let be the intersection point of its diagonals. Prove that if and only if . (Source) See Also Trigonometry Trigonometric identities Geometry Law of Cosines Retrieved from " Categories: Theorems Trigonometry Art of Problem Solving is an ACS WASC Accredited School aops programs AoPS Online Beast Academy AoPS Academy About About AoPS Our Team Our History Jobs AoPS Blog Site Info Terms Privacy Contact Us follow us Subscribe for news and updates © 2025 AoPS Incorporated © 2025 Art of Problem Solving About Us•Contact Us•Terms•Privacy Copyright © 2025 Art of Problem Solving Something appears to not have loaded correctly. Click to refresh.
13279	https://dictionary.cambridge.org/ja/dictionary/english/insurgent	英語での insurgent の意味 Your browser doesn't support HTML5 audio Your browser doesn't support HTML5 audio トピックで関連した単語、句、類義語も探せます: insurgent \| アメリカ英語辞典 Your browser doesn't support HTML5 audio insurgentの例 insurgent の翻訳早くて無料の翻訳！閲覧する今日の言葉 Victoria sponge Your browser doesn't support HTML5 audio Your browser doesn't support HTML5 audio a soft cake made with eggs, sugar, flour, and a type of fat such as butter. It is made in two layers with jam or cream, or both, between them ブログ Calm and collected (The language of staying calm in a crisis) 新しい言葉 lawnmower poetry © Cambridge University Press & Assessment 2025 © Cambridge University Press & Assessment 2025 もっと学ぶ +Plus もっと学ぶ +Plus To add insurgent to a word list please sign up or log in. insurgent を下のリストに加える。または新しいリストを作成する。 {{message}} {{message}} エラーが発生しました。 {{message}} {{message}} エラーが発生しました。 {{message}} {{message}} レポートが送れません。 {{message}} {{message}} レポートが送れません。
13280	https://artofproblemsolving.com/wiki/index.php/2022_AIME_I_Problems/Problem_6?srsltid=AfmBOoqN2UQcxVfdakkRwiU25XQSG9IIzX3LzV7JpesjPpHoGoSQyOh9	Art of Problem Solving 2022 AIME I Problems/Problem 6 - AoPS Wiki Art of Problem Solving AoPS Online Math texts, online classes, and more for students in grades 5-12. Visit AoPS Online ‚ Books for Grades 5-12Online Courses Beast Academy Engaging math books and online learning for students ages 6-13. Visit Beast Academy ‚ Books for Ages 6-13Beast Academy Online AoPS Academy Small live classes for advanced math and language arts learners in grades 2-12. Visit AoPS Academy ‚ Find a Physical CampusVisit the Virtual Campus Sign In Register online school Class ScheduleRecommendationsOlympiad CoursesFree Sessions books tore AoPS CurriculumBeast AcademyOnline BooksRecommendationsOther Books & GearAll ProductsGift Certificates community ForumsContestsSearchHelp resources math training & toolsAlcumusVideosFor the Win!MATHCOUNTS TrainerAoPS Practice ContestsAoPS WikiLaTeX TeXeRMIT PRIMES/CrowdMathKeep LearningAll Ten contests on aopsPractice Math ContestsUSABO newsAoPS BlogWebinars view all 0 Sign In Register AoPS Wiki ResourcesAops Wiki 2022 AIME I Problems/Problem 6 Page ArticleDiscussionView sourceHistory Toolbox Recent changesRandom pageHelpWhat links hereSpecial pages Search 2022 AIME I Problems/Problem 6 Contents [hide] 1 Problem 2 Solution 1 3 Solution 2 (Rigorous) 4 Solution 3 5 Solution 4 6 See Also Problem Find the number of ordered pairs of integers such that the sequenceis strictly increasing and no set of four (not necessarily consecutive) terms forms an arithmetic progression. Solution 1 Since and cannot be an arithmetic progression, or can never be . Since and cannot be an arithmetic progression, and can never be . Since , there are ways to choose and with these two restrictions in mind. However, there are still specific invalid cases counted in these pairs . Since cannot form an arithmetic progression, . cannot be an arithmetic progression, so ; however, since this pair was not counted in our , we do not need to subtract it off. cannot form an arithmetic progression, so . cannot form an arithmetic progression, so . cannot form an arithmetic progression, ; however, since this pair was not counted in our (since we disallowed or to be ), we do not to subtract it off. Also, the sequences , , , , and will never be arithmetic, since that would require and to be non-integers. So, we need to subtract off progressions from the we counted, to get our final answer of . ~ ihatemath123 Solution 2 (Rigorous) We will follow the solution from earlier in a rigorous manner to show that there are no other cases missing. We recognize that an illegal sequence (defined as one that we subtract from our 231) can never have the numbers {3, 4} and {4,5} because we have not included a 6 in our count. Similarly, sequences with {30,40} and {40,50} will not give us any subtractions because those sequences must all include a 20. Let's stick with the lower ones for a minute: if we take them two at a time, then {3,5} will give us the subtraction of 1 sequence {3,5,7,9}. We have exhausted all pairs of numbers we can take, and if we take the triplet of single digit numbers, the only possible sequence must have a 6, which we already don't count. Therefore, we subtract from the count of illegal sequences with any of the single-digit numbers and none of the numbers 30,40,50. (Note if we take only 1 at a time, there will have to be 3 of , which is impossible.) If we have the sequence including {30,50}, we end up having negative values, so these do not give us any subtractions, and the triplet {30,40,50} gives us a 20. Hence by the same reasoning as earlier, we have 0 subtractions from the sequences with these numbers and none of the single digit numbers {3,4,5}. Finally, we count the sequences that are something like (one of 3,4,5,), , (one of 30, 40, 50). If this is to be the case, then let be the starting value in the sequence. The sequence will be ; We see that if we subtract the largest term by the smallest term we have , so the subtraction of one of (30,40,50) and one of (3,4,5) must be divisible by 3. Therefore the only sequences possible are . Of these, only the last is invalid because it gives , larger than our bounds . Therefore, we subtract from this case. Our final answer is ~KingRavi Solution 3 Denote . Denote by a subset of , such that there exists an arithmetic sequence that has 4 terms and includes but not . Denote by a subset of , such that there exists an arithmetic sequence that has 4 terms and includes but not . Hence, is a subset of , such that there exists an arithmetic sequence that has 4 terms and includes both and . Hence, this problem asks us to compute First, we compute . We have . Second, we compute . : . We have . Thus, the number of solutions is 22. : . We have . Thus, the number of solutions is 9. Thus, . Third, we compute . In , we have . However, because , we have . Thus, . This implies . Note that belongs in . Thus, . Fourth, we compute . : In the arithmetic sequence, the two numbers beyond and are on the same side of and . Hence, . Therefore, the number solutions in this case is 3. : In the arithmetic sequence, the two numbers beyond and are on the opposite sides of and . : The arithmetic sequence is . Hence, . : The arithmetic sequence is . Hence, . : The arithmetic sequence is . Hence, . However, the sequence is not strictly increasing. Putting two cases together, Therefore, ~Steven Chen (www.professorchenedu.com) Solution 4 divide cases into .(Notice that can't be equal to , that's why I divide them into two parts. There are three cases that arithmetic sequence forms: .(NOTICE that IS NOT A VALID SEQUENCE!) So when , there are possible ways( 3 means the arithmetic sequence and 13 means there are 13 "a" s and b cannot be 20) When , there are ways. In all, there are possible sequences. ~bluesoul See Also 2022 AIME I (Problems • Answer Key • Resources) Preceded by Problem 5Followed by Problem 7 1•2•3•4•5•6•7•8•9•10•11•12•13•14•15 All AIME Problems and Solutions These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 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13281	https://www.physicsforums.com/threads/solving-a-physics-problem-ladder-facing-a-wall.919599/	Classical Physics Quantum Physics Special and General Relativity Atomic and Condensed Matter Nuclear and Particle Physics Beyond the Standard Model Astronomy and Astrophysics Other Physics Topics The discussion revolves around a physics problem involving a ladder leaning against a wall, where the goal is to determine the frictional force needed to prevent the ladder from falling. The analysis includes concepts of static equilibrium, where the normal force and gravitational force must balance, and the role of friction in maintaining equilibrium. There is confusion about how the normal force can be equal to the weight of the ladder when the forces are applied at different points, but it is clarified that the system is in static equilibrium without rotational acceleration. The conversation emphasizes the importance of understanding both the kinematics of the ladder and the effects of added friction, suggesting that solving both frictionless and friction-included scenarios will provide clarity. Ultimately, the participants agree to work through the problem together to solidify their understanding. : 19 : 0 Hey everybody. I just took a test where a problem described, "a ladder is leaning against a wall with an angle of A. It has a length L and it weighs mg. Assume no friction against the vertical wall and a frictional coefficient of B, find Ffriction" My dad, a quantum physicist, explained how the problem was done, saying that the normal force was mg because the forces in the Y direction added up to 0, the coefficient wasn't needed, and he used Torque (clockwise) = Torque (counterclockwise) to solve for Ffriction in a systems of equations. However, first of all, it wouldn't make sense that there was extra info in the problem, and second of all, I don't understand how the Fn could be mg if it was applied to the end (it just makes logical sense that if it is applied further from the weight center, it affects the translation force less.) I think he may be out of shape in terms of classical physics and forgot the exact way to do this problem and thus I'd like somebody to explain how to ACTUALLY do the problem. Physics news on Phys.org Simulations reveal pion's interaction with Higgs field with unprecedented precision Hidden turbulence discovered in polymer fluids Two quantum computers with 20 qubits manage to simulate information scrambling Nidum Science Advisor : 2,992 : 852 What is the friction force that is needed to act on the foot of the ladder to ensure that the ladder doesn't fall down ? 3 Chestermiller Staff Emeritus Science Advisor Homework Helper Insights Author 2024 Award : 23,696 : 5,914 It sounds to me like your dad's analysis is right-on. Have you drawn a free body diagram of the ladder? 4 jasonpeng : 19 : 0 Chestermiller said: It sounds to me like your dad's analysis is right-on. Have you drawn a free body diagram of the ladder? yeah. the normal force is at the bottom of the ladder while the MG is at the middle (center of gravity) so how do those 2 cancel out? if you put a pencil on a table, pushing it in the center to make it translate if way easier than pushin on the edge because it rotates at the same time, so part of the force becomes rotational acceleration, right? 5 Chestermiller Staff Emeritus Science Advisor Homework Helper Insights Author 2024 Award : 23,696 : 5,914 jasonpeng said: yeah. the normal force is at the bottom of the ladder while the MG is at the middle (center of gravity) so how do those 2 cancel out? if you put a pencil on a table, pushing it in the center to make it translate if way easier than pushin on the edge because it rotates at the same time, so part of the force becomes rotational acceleration, right? In your problem, there is no rotational acceleration. It is in static equilibrium. Do you believe that, for a rigid body in static equilibrium, you must have a balance of forces and a balance of moment? Yes or no? 6 jasonpeng : 19 : 0 Chestermiller said: In your problem, there is no rotational acceleration. It is in static equilibrium. Do you believe that, for a rigid body in static equilibrium, you must have a balance of forces and a balance of moment? Yes or no? I do. However, here what I've considered. If there were no side wall and the floor had no friction, what would happen is that the object would rotate & accelerate CCW but the center of mass would go downwards at the same time. That means the Fnormal is not as much as mg. Once you add the leaning wall, the F(leaning-wall-normal) will push the ladder sideways, but it still rotates and translates downwards. Only when the friction is added, another sideways force, then does the object reach equilibrium. So if the normal force wasn't enough to counteract the mg when there was no ground friction, why would it suddenly increase if you add a ground friction? essentially what happens is that if there is no friction on the ground, the normal force causes the ladder to rotate and it also keeps falling. If there is a leaning wall, it does the same thing, except the wall will apply a sideways force on the ladder and make it translate sideways while rotating and falling at the same time (the sideways translation keeps the end of the ladder touching the wall in the same X-coordinate). But once the ground friction is added, the leader stops both rotating and translating. 7 jasonpeng : 19 : 0 Nidum said: What is the friction force that is needed to act on the foot of the ladder to ensure that the ladder doesn't fall down ? that's what I'm trying to find out. the Ffriction on the ground. If you mean the leaning wall, it has no friction. 8 Chestermiller Staff Emeritus Science Advisor Homework Helper Insights Author 2024 Award : 23,696 : 5,914 jasonpeng said: I do. However, here what I've considered. If there were no side wall and the floor had no friction, what would happen is that the object would rotate & accelerate CCW but the center of mass would go downwards at the same time. That means the Fnormal is not as much as mg. Once you add the leaning wall, the F(leaning-wall-normal) will push the ladder sideways, but it still rotates and translates downwards. Only when the friction is added, another sideways force, then does the object reach equilibrium. So if the normal force wasn't enough to counteract the mg when there was no ground friction, why would it suddenly increase if you add a ground friction? It doesn't suddenly increase. You are talking about two different problems. essentially what happens is that if there is no friction on the ground, the normal force causes the ladder to rotate and it also keeps falling. If there is a leaning wall, it does the same thing, except the wall will apply a sideways force on the ladder and make it translate sideways while rotating and falling at the same time (the sideways translation keeps the end of the ladder touching the wall in the same X-coordinate). But once the ground friction is added, the leader stops both rotating and translating. This is all correct. So? My recommendation is that you solve both problems so you can compare the results and get a better understanding of their relationship. It should be pretty interesting. 9 jasonpeng : 19 : 0 so the normal force is bigger if I add a frictional force sideways? 10 russ_watters Mentor Insights Author : 23,686 : 11,111 jasonpeng said: However, first of all, it wouldn't make sense that there was extra info in the problem... It is, and it is critical that you get used to this. FrI'm now on, in school and in real life, you may be given extra (or not enough!) information and have to figure out what you need and what you dont. 11 Chestermiller Staff Emeritus Science Advisor Homework Helper Insights Author 2024 Award : 23,696 : 5,914 jasonpeng said: so the normal force is bigger if I add a frictional force sideways? We can continue speculating about this forever, of we can get down to business and actually solve both versions of the problem to see how this all plays out. I can help you solve the frictionless sliding version of the problem if you are game to try. Are you? 12 jasonpeng : 19 : 0 Chestermiller said: We can continue speculating about this forever, of we can get down to business and actually solve both versions of the problem to see how this all plays out. I can help you solve the frictionless sliding version of the problem if you are game to try. Are you? Yep. Would love to. Let me get my pencil and paper 13 jasonpeng : 19 : 0 russ_watters said: It is, and it is critical that you get used to this. FrI'm now on, in school and in real life, you may be given extra (or not enough!) information and have to figure out what you need and what you dont. not in the questions from the book's tests though. I mean it would make sense in real life if there was extra info, but not from that book's problems 14 jbriggs444 Science Advisor Homework Helper 2024 Award : 13,297 : 7,957 jasonpeng said: not in the questions from the book's tests though. I mean it would make sense in real life if there was extra info, but not from that book's problems It is good design to provide extra information in a problem. It helps train the student for real life. And it works to prevent the pattern matching "what formulas do I have that take a distance, a time and a force as inputs" approach to problem solving. 15 Chestermiller Staff Emeritus Science Advisor Homework Helper Insights Author 2024 Award : 23,696 : 5,914 jasonpeng said: not in the questions from the book's tests though. I mean it would make sense in real life if there was extra info, but not from that book's problems The first step in the analysis is to quantify the kinematics of the ladder motion. We will use the figure below to address that: From the geometry of this figure, what are the x and y coordinates of the center of mass of the ladder (in terms of L and )? Attachments Ladder.png 2.6 KB · Views: 495 16 jasonpeng : 19 : 0 Chestermiller said: The first step in the analysis is to quantify the kinematics of the ladder motion. We will use the figure below to address that: View attachment 206788 From the geometry of this figure, what are the x and y coordinates of the center of mass of the ladder (in terms of L and ##\theta##)? Well I've found some example problems of the exact same question online, and I know HOW to do it, but I don't know why. How come the normal force is larger when it is in equilibrium but less when there is no friction on the ground if it's the same ladder, same gravity, etc.? 17 jasonpeng : 19 : 0 Chestermiller said: The first step in the analysis is to quantify the kinematics of the ladder motion. We will use the figure below to address that: View attachment 206788 From the geometry of this figure, what are the x and y coordinates of the center of mass of the ladder (in terms of L and ##\theta##)? but for the sliding object: the center of mass is at .5lsin(theta) and .5lcos(theta). 18 Chestermiller Staff Emeritus Science Advisor Homework Helper Insights Author 2024 Award : 23,696 : 5,914 jasonpeng said: Well I've found some example problems of the exact same question online, and I know HOW to do it, but I don't know why. How come the normal force is larger when it is in equilibrium but less when there is no friction on the ground if it's the same ladder, same gravity, etc.? Like I said (several times), this will all reveal itself when we actually analyze the problem. Until then, we are just waving our hands. 19 jasonpeng : 19 : 0 Chestermiller said: Like I said (several times), this will all reveal itself when we actually analyze the problem. Until then, we are just waving our hands. alright, let's go on then. Sorry for the delay by the way, I'm in a summer camp so I'm busy a lot of the time 20 Chestermiller Staff Emeritus Science Advisor Homework Helper Insights Author 2024 Award : 23,696 : 5,914 jasonpeng said: but for the sliding object: the center of mass is at .5lsin(theta) and .5lcos(theta). Excellent. Now, using these results, in terms of L, , and , what are the x and y components of the velocity of the center of mass? Please do me a favor. Please use LaTex to do the equations. There is a LaTex tutorial in the Physics Forums help. 21 jasonpeng : 19 : 0 Chestermiller said: Like I said (several times), this will all reveal itself when we actually analyze the problem. Until then, we are just waving our hands. sorry, what's d? 22 Chestermiller Staff Emeritus Science Advisor Homework Helper Insights Author 2024 Award : 23,696 : 5,914 jasonpeng said: sorry, what's d? You have had calculus, correct? 23 jasonpeng : 19 : 0 jasonpeng said: sorry, what's d? scratch that, could you lead me through how I would find the acceleration of the center of mass? I'm just confuse over how the center of mass moves translationaly if forces are being applied to the object away from the cetner of mass. 24 jasonpeng : 19 : 0 Chestermiller said: You have had calculus, correct? No, I have not. I'm in 10th grade at the moment. this problem showed up in a book I bought for high school physics so I could learn it on my own time 25 jasonpeng : 19 : 0 Is there a way that the problem can be solved without calculus? 26 Chestermiller Staff Emeritus Science Advisor Homework Helper Insights Author 2024 Award : 23,696 : 5,914 jasonpeng said: Is there a way that the problem can be solved without calculus? Unfortunately I don't think that the sliding problem can be adequately analyzed without using calculus. Are you familiar with the concepts of angular acceleration, angular velocity, and moment of inertia? In this sliding problem, the acceleration of the center of mass of the ladder, and the angular acceleration of the ladder are not constant, but are functions of time. 27 jasonpeng : 19 : 0 Chestermiller said: Unfortunately I don't think that the sliding problem can be adequately analyzed without using calculus. Are you familiar with the concepts of angular acceleration, angular velocity, and moment of inertia? In this sliding problem, the acceleration of the center of mass of the ladder, and the angular acceleration of the ladder are not constant, but are functions of time. Yes, I've learned precalculus so I do know my angular things. 28 Chestermiller Staff Emeritus Science Advisor Homework Helper Insights Author 2024 Award : 23,696 : 5,914 jasonpeng said: Yes, I've learned precalculus so I do know my angular things. OK. Fasten your seatbelt. The sliding motion of the latter is completely described once we know how the angle varies as a function of time t: . The angular velocity of the ladder at time t, , is equal to the rate of change of the angle with respect to time, and is represented symbolically (using calculus) by The angular acceleration of the ladder at time t, , is equal to the rate of change of the angular velocity with respect to time, and is represented symbolically (using calculus) by Using calculus, we can also obtain equations for the acceleration of the center of mass of the ladder in terms of the angular velocity and angular acceleration. We thereby obtain, for the horizontal and vertical components of the CofM acceleration, the following: Notice that none of what we have done so far in any way relates to the original static equilibrium friction problem that you were solving. All of this is completely new and different. This is an indication of how very different the two problems are. This completes what we wanted to do in terms of analyzing the kinematics of the ladder slippage. Now let's get to the dynamics. Please write down the Newton's 2nd law force balance equations for the sliding ladder in the horizontal and vertical directions, in terms of , , mg, , and . (Note that this will not yet complete the dynamic equations, because we will also need a moment balance about the center of mass, involving the angular acceleration and moment of inertia of the ladder). 29 Chestermiller Staff Emeritus Science Advisor Homework Helper Insights Author 2024 Award : 23,696 : 5,914 @jasonpeng : With respect, I feel that this analysis has gotten a little too complicated, even for a smart 10th grader like yourself. So I am going to fill in some of the intermediate steps, and then let you complete the solution for the reaction forces. To simplify things, we will confine attention only to the initial state in which we first release the ladder to start sliding. At this initial point in time, the angular velocity of the ladder is zero, and the accelerations of the center of mass in the horizontal and vertical directions become: where now is the initial angle of the ladder and is its initial angular acceleration. The Newton's 2nd law force balances on the ladder in the horizontal and vertical directions, and the moment balance on the ladder are given by: where is the moment of inertia of the ladder about its center of mass. Do these relationships in any way make sense to you? The next step is your turn. Your assignment is to solve these three linear algebraic equations for the three unknowns , , and in terms of m, g, and . We will then be able to directly compare the results for these reaction forces with those obtained for the ladder problem with friction. Last edited: 30 jasonpeng : 19 : 0 coudl you explain how you got the m(l^2/12)alpha part? 31 jasonpeng : 19 : 0 jasonpeng said: coudl you explain how you got the m(l^2/12)alpha part? and how about the translational acceleration? how do the normal forces act on that? and also, isn't alpha also an unknown variable? 32 Chestermiller Staff Emeritus Science Advisor Homework Helper Insights Author 2024 Award : 23,696 : 5,914 jasonpeng said: coudl you explain how you got the m(l^2/12)alpha part? For a finite rigid body experiencing both translation and rotation, in addition to satisfying the force balances (net force = ma) in the horizontal and vertical directions, one must also satisfy a balance of moments. The balance of moments is the rotational analog of a force balance. It says that the sum of the moments of the forces about the center of mass of the body is equal to the moment of inertia I (analogous to mass) times the angular acceleration (analogous to translational acceleration). That is (net moment = I ). For a rigid rod or a rigid ladder, the moment of inertia I is equal to . You can look this up online in a Googled table of moments of inertia for various objects. The derivation of the relationship for the moment of inertia is obtained using calculus. Last edited: 33 Chestermiller Staff Emeritus Science Advisor Homework Helper Insights Author 2024 Award : 23,696 : 5,914 jasonpeng said: and how about the translational acceleration? how do the normal forces act on that? and also, isn't alpha also an unknown variable? Eqns. 1 and 2 in post #29 describe the translational acceleration. The sum of the external forces are equal to the mass times the acceleration of the center of mass (for the horizontal and vertical directions). Eqn. 3 is the moment balance describing the angular acceleration. In my post #29, I said "the three unknowns , , and " ; so, yes, is also an unknown variable 34 jasonpeng : 19 : 0 could you also explain the equations 1 and 2 relating Ax with alpha? 35 Chestermiller Staff Emeritus Science Advisor Homework Helper Insights Author 2024 Award : 23,696 : 5,914 jasonpeng said: could you also explain the equations 1 and 2 relating Ax with alpha? That follows from the geometry/kinematics of the motion. To derive this, you need to take the coordinates of the center of mass at each time, use these equations and calculus to get the velocity of the center of mass, and then do the same thing again to get the acceleration of the center of mass. 36 scottdave Science Advisor Homework Helper Insights Author : 2,009 : 974 Going back to the original problem (not sliding), since it is not moving or accelerating, the sum of the vertical forces = zero, and sum of horizontal forces = 0. How much vertical force does the wall provide on the ladder? How much vertical force does the ground provide on the ladder? Your father is correct, in this: the coefficient of static friction does not play a role in determining the amount of force, only if there is enough friction available to provide that force. 37 PaulK2 : 4 : 0 Agreeing with Scott, it seems good to solve the original static problem. Chester's diagram on the first page sums it up (although for the way I think about it, I'd add a horizontal force at the foot of the ladder, exerted by the ground, which is what's asked for in the original question). Last edited: 38 scottdave Science Advisor Homework Helper Insights Author : 2,009 : 974 In order to find the horizontal components of force: summing the moments about a point is the way to go. 39 Chestermiller Staff Emeritus Science Advisor Homework Helper Insights Author 2024 Award : 23,696 : 5,914 PaulK2 said: Agreeing with Scott, it seems good to solve the original static problem. Chester's diagram on the first page sums it up (although for the way I think about it, I'd add a horizontal force at the foot of the ladder, exerted by the ground, which is what's asked for in the original question). We are going to solve both problems (with and without friction) and then compare the results. The OP is particularly interested in how things change when the frictional force (or externally imposed horizontal force at the base of the ladder) is removed. 40 alvino Isn't this just a statics problem? Sum of forces and sum of moments must be zero if the ladder is resting on a wall and not moving. Sum of forces (=zero)can allow the relation between the normal force exerted by the wall to the frictional force exerted by the ground(equal to the product of coefficient of static friction and weight). Sum of moments (about the point on the ladder touching the ground;equals zero)can then allow you to relate the "wall" normal force to the weight of the ladder. These two combined can give you an expression that relates the coefficient of friction to a geometric expression. ...I think. This is my first post here so I come before you as humble learner. I just read the problem and didn't think it was asking about a dynamic system (especially if OP is in the 10th grade and without calculus). Attachments image.jpg 35.5 KB · Views: 399 41 Chestermiller Staff Emeritus Science Advisor Homework Helper Insights Author 2024 Award : 23,696 : 5,914 alvino said: Isn't this just a statics problem? Sum of forces and sum of moments must be zero if the ladder is resting on a wall and not moving. Sum of forces (=zero)can allow the relation between the normal force exerted by the wall to the frictional force exerted by the ground(equal to the product of coefficient of static friction and weight). Sum of moments (about the point on the ladder touching the ground;equals zero)can then allow you to relate the "wall" normal force to the weight of the ladder. These two combined can give you an expression that relates the coefficient of friction to a geometric expression. ...I think. This is my first post here so I come before you as humble learner. I just read the problem and didn't think it was asking about a dynamic system (especially if OP is in the 10th grade and without calculus). If you check back through the posts, you will see that the OP became intrigued by the dynamic frictionless problem and it's comparison with the static problem. I have tried to accommodate him as much as I can, given his limited mathematical background. This has not been easy. Similar threads Force of the Ladder on a Wall Torque Replies : 5 Views : 3K The Force Of The Ladder Against The Wall Replies : 2 Views : 2K Normal force at the base of a ladder Replies : 20 Views : 2K Force of the wall against the ladder is from static friction? 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Save this post for later Not now Thanks for your vote! You now have 5 free votes weekly. Free votes count toward the total vote score does not give reputation to the author Continue to help good content that is interesting, well-researched, and useful, rise to the top! To gain full voting privileges, earn reputation. Got it!Go to help center to learn more Division by zero depending on parameter Ask Question Asked 4 years ago Modified4 years ago Viewed 263 times This question shows research effort; it is useful and clear 3 Save this question. Show activity on this post. I am using the FixedRotation component and get a division by zero error. This happens in a translated expression of the form var = nominator/fixedRotation.R_rel_inv.T[1,3] because T[1,3] is 0 for the chosen parameters: n={0,1,0} angle=180 deg. It seems that Openmodelica keeps the symbolic variable and tries to be generic but in this case this leads to division by zero because it chooses to put T[1,3] in the denominator. What are the modifications in order to tell the compiler that the evaluated values T[1,3] for the compilation shall be considered as if the values were hard coded? R_rel is internally in fixedRotation not defined with Evaluate=true... Should I use custom version of this block? (when I copy paste the source code to a new model and set the parameters R_rel and R_rel_inv to Evalute=true then the simulation works without division by zero)... BUT is there a modifier to tell from outside that a parameter shall be Evaluate=true without the need to make a new model? Any other way to prevent division by zero? modelica openmodelica Share Share a link to this question Copy linkCC BY-SA 4.0 Improve this question Follow Follow this question to receive notifications edited Sep 8, 2021 at 6:45 marco 6,753 13 13 silver badges 25 25 bronze badges asked Sep 7, 2021 at 19:18 CimiCimi 43 3 3 bronze badges Add a comment\| 2 Answers 2 Sorted by: Reset to default This answer is useful 2 Save this answer. Show activity on this post. Try propagating the parameter at a higher level and setting annotation(Evaluate=true) on this. For example: ``` model A parameter Real a=1; end A; model B parameter Real aPropagated = 2 annotation(Evaluate=true); A Ainstance(a=aPropagated); end B; ``` Share Share a link to this answer Copy linkCC BY-SA 4.0 Improve this answer Follow Follow this answer to receive notifications answered Sep 10, 2021 at 6:50 user2024223user2024223 485 2 2 silver badges 10 10 bronze badges Comments Add a comment This answer is useful 0 Save this answer. Show activity on this post. I don't understand how the Evaluate annotation should help here. The denominator is obviously zero and this is what shall be in fact treated. To solve division by zero, there are various possibilities (e.g. to set a particular value for that case or to define a small offset to denominator, you can find examples in the Modelica Standard Library). You can also consider the physical meaning of the equation and handle this accordingly. Since the denominator depends on a parameter, you can also set an assert() to warn the user there is wrong parameter value. Btw. R_rel_inv is protected and shall, thus, not be used. Use R_rel instead. Also, to deal with rotation matrices, usage of functions from Modelica.Mechanics.MultiBody.Frames is a preferrable way. And: to use custom version or own implementation depends on your preferences. Custom version is maintained by the comunity, own version is in your hands. Share Share a link to this answer Copy linkCC BY-SA 4.0 Improve this answer Follow Follow this answer to receive notifications edited Sep 27, 2021 at 8:17 answered Sep 24, 2021 at 9:52 modelicaFanmodelicaFan 148 9 9 bronze badges Comments Add a comment Your Answer Thanks for contributing an answer to Stack Overflow! Please be sure to answer the question. Provide details and share your research! 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13283	https://www.mathworksheets4kids.com/area-annulus.php	Area of an Annulus Worksheets [x] Login Child Login Main MenuMathLanguage ArtsScienceSocial StudiesInteractive WorksheetsBrowse By GradeBecome a Member Become a Member Math Interactive Worksheets Kindergarten 1st Grade 2nd Grade 3rd Grade 4th Grade 5th Grade 6th Grade 7th Grade 8th Grade Worksheets by Grade Kindergarten 1st Grade 2nd Grade 3rd Grade 4th Grade 5th Grade 6th Grade 7th Grade 8th Grade Number Sense and Operations Number Recognition Counting Skip Counting Place Value Number Lines Addition Subtraction Multiplication Division Word Problems Comparing Numbers Ordering Numbers Odd and Even Prime and Composite Roman Numerals Ordinal Numbers Properties Patterns Rounding Estimation In and Out Boxes Number System Conversions More Number Sense Worksheets Measurement Size Comparison Time Calendar Money Measuring Length Weight Capacity Metric Unit Conversion Customary Unit Conversion Temperature More Measurement Worksheets Financial Literacy Writing Checks Profit and Loss Discount Sales Tax Simple Interest Compound Interest Statistics and Data Analysis Tally Marks Pictograph Line Plot Bar Graph Line Graph Pie Graph Scatter Plot Mean, Median, Mode, Range Mean Absolute Deviation Stem-and-leaf Plot Box-and-whisker Plot Factorial Permutation and Combination Probability Venn Diagram More Statistics Worksheets Geometry Positions Shapes - 2D Shapes - 3D Lines, Rays and Line Segments Points, Lines and Planes Angles Symmetry Transformation Area Perimeter Rectangle Triangle Circle Quadrilateral Polygon Ordered Pairs Midpoint Formula Distance Formula Slope Parallel, Perpendicular and Intersecting Lines Scale Factor Surface Area Volume Pythagorean Theorem More Geometry Worksheets Pre-Algebra Factoring GCF LCM Fractions Decimals Converting between Fractions and Decimals Integers Significant Figures Percents Convert between Fractions, Decimals, and Percents Ratio Proportions Direct and Inverse Variation Order of Operations Exponents Radicals Squaring Numbers Square Roots Scientific Notations Logarithms Speed, Distance, and Time Absolute Value More Pre-Algebra Worksheets Algebra Translating Algebraic Phrases Evaluating Algebraic Expressions Simplifying Algebraic Expressions Algebraic Identities Equations Quadratic Equations Systems of Equations Functions Polynomials Inequalities Sequence and Series Matrices Complex Numbers Vectors More Algebra Worksheets Trigonometry Calculus Math Workbooks English Language Arts Summer Review Packets Science Social Studies Holidays and Events Support Worksheets> Math> Geometry> Circles> Circumference and Area> Area of an Annulus Area of an Annulus Worksheets Burst into practice with our printable area of an annulus worksheets and get a jump on your grade 8 and high school peers! Concentric circles are circles with the same center but different radii. With pdf exercises that flit between three levels of difficulty, children learn by rote the formula and work out the area between two concentric circles or the annular region. They use the whole-number and decimal radii and adeptly determine the area of circular rings. Get a wiggle on, for you must try our free worksheet on the area of an annulus! Select the Measurement Units U.S. Customary Units Metric Units Area of an Annulus - Easy Point out to 8th grade children the ring-shaped region bounded by a pair of concentric circles as the annular region and uplift them with guided practice on finding the area of circular rings in terms of π. Download the set Area of an Annulus - Moderate Scoop up these pdf worksheets on the area between two concentric circles and help high school students press on! Subtract the area of the inner circle from the area of the outer circle to obtain the area of an annulus. Download the set Area of an Annulus - Difficult Chock-a-block with rings having decimal radii, these printables are by far the hardest of all. Plug the radii(R & r) of the concentric circles in the formula A = π(R 2 - r 2) to find the area of the shaded region in between. Download the set Related Worksheets »Area of the Segment »Arc Length and Area of Sector »Area of Compound Shapes »Area Home Become a Member Membership Information Login Printing Help FAQ How to Use Interactive Worksheets How to Use Printable Worksheets About Us Privacy Policy Terms of Use Contact Us Follow us Copyright © 2025 - Math Worksheets 4 Kids × This is a members-only feature! Not a member yet? Sign Up for complete access at only $24.95/year - about 7 cents a day! Printable Worksheets ✎40,000+ PDF worksheets ✎Access all subjects and all grades ✎Unlock answer keys ✎Add worksheets to "My Collection" ✎Create customized workbooks Interactive Worksheets ✎2000+ Math and ELA practice ✎Generate randomized questions ✎Exclusive child login ✎100% Child safe ✎Auto-correct and track progress
13284	https://onlinemathcenter.com/blog/math/math-symbols-and-their-meanings-part-v-basic-logic/	Math Symbols and Their Meanings \| Basic Logic \|OMC Math Blog Skip to content Online Math Center Math Classes Enrollment Still Open! Click Here For More. Programs Middle school High school Individual tutoring Competitions SAT Tutoring About us Why choose OMC? How is OMC different? Timetable Our curriculum F.A.Q. Pricing Blog Contact us Menu Programs Middle school High school Individual tutoring Competitions SAT Tutoring About us Why choose OMC? How is OMC different? Timetable Our curriculum F.A.Q. Pricing Blog Contact us Try a Free Lesson Math Classes Enrollment Still Open! Click Here For More. Programs Middle school High school Individual tutoring Competitions SAT Tutoring About us Why choose OMC? How is OMC different? Timetable Our curriculum F.A.Q. Pricing Blog Contact us Menu Programs Middle school High school Individual tutoring Competitions SAT Tutoring About us Why choose OMC? How is OMC different? Timetable Our curriculum F.A.Q. Pricing Blog Contact us Try a Free Lesson Click here HomeMath Symbols and Their Meanings Part V: Basic Logic Math Symbols and Their Meanings Part V: Basic Logic by Online Math Center 11/18/2021 Published: 11-18-2021 Math Symbols and Their Meanings Part V: Basic Logic HomeMath Symbols and Their Meanings Part V: Basic Logic Published: 11.18.2021 Figuring out the best way to study mathematics can be overwhelming and difficult. Luckily, we have composed a very helpful series about Math Symbols and Their Meanings so you can understand the language behind mathematics easier and faster. Logic is the unlocking key to understanding and operating in mathematical language. Moreover, in exercises and problems that require proof or a demonstration, students are required to solve problems with a logical method. In our previous article, we have discussed set theory which is a subarea of basic mathematical logic. Components Of Mathematical Logic Mathematical statements, also referred to as propositions are well-defined affirmations that can be either true or false, such as: 146 – 31 = 115 … True statement 1 x 0 = 1 …. False statement Propositional Logic A mathematical system that explains the propositions/statements and how they relate to each other, also known as Boolean Logic. Statements are composed of variables and logical connectives. In general, variables are indicated by lower-case letters, such as a, b, p, x. Logical connectives are indicated by: “¬” This symbol defines a logical negation. Given the variable p, “¬p” (non-p) is false only if “p” is true. Example: Given the statement p: 6 + 7 = 12 (false). The logical negation: “It is not the case that p is true”, then “¬p” is true because p is false. “∧” This symbol defines logical conjunction(and). Given the variables p and q, the proposition“p ∧ q” is true only if both variables are true. Example: Given the statements p and q, where p is 5 + 5 = 10, q is 4 + 4 = 8, the following statement is a logical conjunction: “p ∧ q” is True. However, if q is false, as in 4 + 4 = 6, the following statement: ““p ∧ q” is False. “∨” A logical disjunction, named “or”, in which the statement “p∨q” is true if variable p or q is true. When it comes to disjunctions, one of the statements must be true, they cannot be both false. Example: Given the statements p and q, where p is 5 + 5 = 10 (true), q is 4 + 4 = 7 (false), the following statement is a logical disjunction: “p ∨ q” is True. However, if p is 5 + 5 = 11 or q is 4 + 4 = 7, this is False, as both statements are false. Therefore, when it comes to logical disjunctions, at least one statement must be true. “→” This symbol indicates a relation of implication between two variables. Given the statement “p→q”, it means that if p is true, then q is true, as well. Things get a bit confusing when p is false, as there is no relevance of the value of statement q. Example: Given the following statements, p is 3 = 3, and q is 3 2 = 6, then “p→q” is True; p is true which implies that q is also true. When p is false, it implies that q is also false (regardless of the fact that q can actually be true). “↔” This symbol indicates that there is a biconditionality between two variables. Therefore, the statement “p↔q” is true when the two are equal in value, thus, both are true or both are false, whereas in the implication statement p can be true and q can be false. Example: Given the statement p: y – 4 = 2, and q: y = 6, then the biconditional relation “p↔q” indicates that: “y – 4 = 2 only when y = 6”. What Are The Symbols For A True Or False Statement? “True” and “false” are not logical connectives per se, they are more like values of variables, but in mathematics, they are still used in the area of the connective. “⊤” – this indicates that a value is always true; “⊥” – this indicates that a value is always false. Predicate Logic Every concept in mathematics has limitations in proving a variable in a statement or the value of a variable. Where propositional logic ends, predicate logic begins. Predicate logic deals with quantifiers. In propositional logic, the only possible statement relations are non, and, or (negation, conjunction, and disjunction). Predicate logic adds to these relations the symbols that have been presented in our previous article about the comparison. You might have noticed a similarity of linguistic terms – predicates also exist in mathematical language. A statement has two parts. For example, the statement: “X > 7”. X is the subject of the statement. “>7” is the predicate of the statement. In order to indicate how a predicate behaves in regards to the subject, in mathematics we use quantifiers. Universal Quantification When a statement indicates that a condition is met by all the values of a variable, we use universal quantifiers. The symbol for a universal quantifier is “∀”. A statement is indicated as∀xP(x). ∀xP(x) is true only if P(x) is true, regardless of the value of x. Example: For any x, x 2≥ 0 This statement is true and it would be noted as ∀x ∈ p (x 2≥ 0) A false statement would be: For any X, x 2< 0. This can be proven by a simple calculus, however universal quantifiers refer to those aspects of a statement that are true, hence all the values of a variable that exist by the given condition. Existential quantification The symbol of existential qualification is “∃”. If in the case of universal quantification, all values had to meet the given condition that makes the statement true, in existential qualification, a statement is true if at least one valuemeets the condition that makes the statement true. Example: Determine if the following statement is true, ∃x ∈ p (x > 2). Solution: The statement is true because x = 3. In order to determine if a statement is true in the case of existential qualification, we need to find only one value or at least one value that respects the condition ( x > 2). In our case, if x = 3, then x > 2 which proves that the statement is true. Practice Basic Logic The easiest way to practice basic mathematical logic and also have a better understanding on how propositional operations work is to create truth tables. This is a great exercise to improve critical thinking and develop a logical sense. A fun fact about basic mathematical logic is that basic logic is the foundation of puzzles and riddles. 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13285	https://chem.libretexts.org/Courses/Athabasca_University/Chemistry_360%3A_Organic_Chemistry_II/Chapter_20%3A_Carboxylic_Acids_and_Nitriles/20.04_Substituent_Effects_on_Acidity	Skip to main content 20.4 Substituent Effects on Acidity Last updated : Aug 8, 2024 Save as PDF 20.3 Biological Acids and the Henderson-Hasselbalch Equation 20.5 Preparing Carboxylic Acids Page ID : 90984 ( \newcommand{\kernel}{\mathrm{null}\,}) Objectives After completing this section, you should be able to list a given series of carboxylic acids in order of increasing or decreasing acidity. explain the difference in acidity between two or more given carboxylic acids. arrange a series of substituted benzoic acids in order of increasing or decreasing acidity. determine whether a given substituted benzoic acid will be more or less acidic than benzoic acid. decide which of two or more substituted benzoic acids is the most acidic, and explain your decision on the basis of the electron‑withdrawing or electron‑releasing ability of the substituent. use the Ka (or pKa ) of a substituted benzoic acid to predict the effect that the substituent has on the susceptibility of the benzene ring to electrophilic attack. Study Notes You have already seen how the presence of an electron‑withdrawing or electron‑releasing group affects the stability of a positively charged carbocation. Now you see how these groups affect the stability of carboxylate anions, and in turn, determine the dissociation constant of a carboxylic acid. The resonance effect described here is undoubtedly the major contributor to the exceptional acidity of carboxylic acids. However, inductive effects also play a role. For example, alcohols have pKa's of 16 or greater but their acidity is increased by electron withdrawing substituents on the alkyl group. The following diagram illustrates this factor for several simple inorganic and organic compounds (row #1), and shows how inductive electron withdrawal may also increase the acidity of carboxylic acids (rows #2 & 3). The acidic hydrogen is colored red in all examples. Water is less acidic than hydrogen peroxide because hydrogen is less electronegative than oxygen, and the covalent bond joining these atoms is polarized in the manner shown. Alcohols are slightly less acidic than water, due to the poor electronegativity of carbon, but chloral hydrate, Cl3CCH(OH)2, and 2,2,2,-trifluoroethanol are significantly more acidic than water, due to inductive electron withdrawal by the electronegative halogens (and the second oxygen in chloral hydrate). In the case of carboxylic acids, if the electrophilic character of the carbonyl carbon is decreased the acidity of the carboxylic acid will also decrease. Similarly, an increase in its electrophilicity will increase the acidity of the acid. Acetic acid is ten times weaker an acid than formic acid (first two entries in the second row), confirming the electron donating character of an alkyl group relative to hydrogen, as noted earlier in a discussion of carbocation stability. Electronegative substituents increase acidity by inductive electron withdrawal. As expected, the higher the electronegativity of the substituent the greater the increase in acidity (F > Cl > Br > I), and the closer the substituent is to the carboxyl group the greater is its effect (isomers in the 3rd row). Substituents also influence the acidity of benzoic acid derivatives, but resonance effects compete with inductive effects. The methoxy group is electron donating and the nitro group is electron withdrawing (last three entries in the table of pKa values). Withdrawing Inductive Effects A fluorine atom is more electronegative than a hydrogen atom, and thus it is able to ‘induce’, or ‘pull’ the electron density of covalent bonds towards itself. In the fluoroacetate anion, the electrons in the C-F covalent bond are pulled toward the fluorine giving the carbon a partial positive charge. The positively charged carbon, in turn, draws electron density away from the carboxylate anion, dispersing the charge, and creating a stabilizing effect. Stabilizing the carboxylate anion increases the acidity of the corresponding carboxylic acid. In this context, the fluorine substituent is acting as an electron-withdrawing group. Fluoroacetate anion stabilized by electron withdrawing inductive effect of fluorine A similar effect is seen when other electron-withdrawing groups are attached to -CH2CO2H. As the power of the electron-withdrawing group becomes stronger there is a corresponding drop in the pKa of the carboxylic acid. The presence of multiple electron-withdrawing groups compounds the inductive effect and continues to increase the acidity of the carboxylic acid. Dichloroacetic is a stronger acid than chloroacetic acid, and trichloroacetic acid is even stronger. The inductive effects of chlorine be clearly seen when looking at the electrostatic potential maps of acetic acid (Left) and trichloroacetic acid (Right). The O-H bond in trichloroacetic acid is highly polarized, as shown by the dark blue color making it a much stronger acid than acetic acid. Because inductive effects are not transmitted effectively through covalent bonds, the acid-strengthening effect falls off rapidly as the number of sigma bonds between the carboxylic acid and the electron-withdrawing group increases. A distance of three sigma bonds almost completely eliminates chlorine's inductive effect in 4-chlorobutanoic acid, giving it a similar pKa value to unsubstituted butanoic acid. Donating Inductive Effects Alkyl groups (hydrocarbons) are inductively electron-donating. In this case, the inductive effects pushes electron density onto the carboxylate anion, producing a destabilizing effect, decreasing the acidity of the carboxylic acid. Lengthening the alkyl chain of a carboxylic acid can increase this inductive effect but it no longer decreases the acidity further after the chain is about three carbons long. Acidity of Substituted Benzoic Acids Electron-withdrawing groups The conjugate base of benzoic acid is stabilized by electron-withdrawing groups (EWG). This makes the acid more acidic by delocalizing the charge of the carboxylate ion. Electron-withdrawing groups deactivate the benzene ring to electrophilic attack and make benzoic acids more acidic. Electron-donating groups The conjugate base of benzoic acid is destabilized by electron-donating groups (EDG). This makes the acid less acidic by pushing more electron density toward the negative charge in the carboxylate. Electron-donating groups activate the benzene ring to electrophilic attack and make benzoic acids less acidic. Several examples of electron donating groups. Contributors Layne Morsch (University of Illinois Springfield) Notice the trend in the following table where electron donating substituents (X) at the para position lead to weaker acids while those having more electron withdrawing groups, further down the table, generate stronger acids. Dissociation Constants of p-Substituted Benzoic Acid \| X \| pKa \| \| \| —N(CH3)2 \| 6.03 \| \| \| —NHCH3 \| 5.04 \| \| —OH \| 4.57 \| \| —OCH3 \| 4.50 \| \| —C(CH3)3 \| 4.38 \| \| —H \| 4.20 \| \| —Cl \| 4.00 \| \| —Br \| 3.96 \| \| —CHO \| 3.77 \| \| —CN \| 3.55 \| \| —NO2 \| 3.43 \| Example 20.4.1 The following molecule, p-cyanobenzoic acid, has a pKa of 3.55. Does the cyano substituent activate or deactivate the aromatic ring towards electrophilic aromatic substitution? Solution The pKa of benzoic acid is 4.2 which means it is a weaker acid than p-cyanobenzoic acid. This this means that the cyano substituent is deactivating the ring. Exercises Exercise 20.4.1 Draw the bond-line structures and arrange the following compounds in order of increasing acidity: 4-nitrobenzoic acid; 4-aminobenzoic acid; 4-chlorobenzoic acid; and benzoic acid. Try to use the expected inductive effects of the substituents to determine the acidity rather than looking at the pKa table. Answer Exercise 20.4.2 For the following pairs, which is expected to be the stronger acid? Explain your answer. Answer : a) Consider the inductive effects of the substituents attached to the carboxylic acid. The tert-butyl group is electron-donating which should decrease the acidity of the carboxylic acid. The trimethylammonium substituent is positively charged and can be a powerful electron-withdrawing substituent. This should increase the acidity of the carboxylic acid. The compound (CH3)3NCH2CO2H is expected to be a stronger acid than (CH3)3CCH2CO2H. The acidity constants for these two compounds match the predictions. b) Having an electron-withdrawing hydroxyl group at the C-2 stabilizes the carboxylate ion of lactic acid through inductive effects. This should make lactic acid more acidic than propanoic acid. c) Due to the presence of a highly electronegative oxygen, the carbonyl group is expected to be more strongly electron-withdrawing than a carbon–carbon double bond. Thus, pyruvic acid should be a stronger acid than acrylic acid. Exercise 20.4.3 Oxalic acid is a dicarboxylic acid with two acidic protons. The first proton is much more acidic (pKa = 1.20) than a typical carboxylic acid. However, Heptanedioic acid's first acidic proton has a pKa much closer to that of a typical carboxylic acid. Explain these differences. Answer : With oxalic acid one carboxyl group acts as an inductive electron-withdrawing group which increases the acidity of the other carboxylic acid. This inductive effect is only relevant with the two carboxyl groups are separated by only a few bonds. In heptanedioic acid, the carboxyl groups are separated by five carbon which effectively negates the inductive effect. Exercise 20.4.4 The carboxylic acid of 4-formylbenzoic acid has a pKa of 3.75. Is this molecule likely to be more reactive or less reactive than benzene toward electrophilic aromatic substitution? Answer : Benzoic acid (pKa = 4.2) has a higher pKa and is less acidic than 4-formylbenzoic acid (pKa = 3.75). This means that the formyl group is removing electrons from the aromatic ring making it deactivated toward electrophilic aromatic substitution. Contributors and Attributions Dr. Dietmar Kennepohl FCIC (Professor of Chemistry, Athabasca University) Prof. Steven Farmer (Sonoma State University) William Reusch, Professor Emeritus (Michigan State U.), Virtual Textbook of Organic Chemistry 20.3 Biological Acids and the Henderson-Hasselbalch Equation 20.5 Preparing Carboxylic Acids
13286	https://drive.uqu.edu.sa/_/ahnasr/files/FM-Chap3.pdf	Fluid Mechanics: Fundamentals and Applications, 4th edition Yunus A. Cengel, John M. Cimbala Lecture slides by Mehmet Kanoglu ©McGraw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw-Hill Education. ©McGraw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw-Hill Education. Chapter 3 FLUID KINEMATICS ©McGraw-Hill Education. © StockTrek/Getty Images RF Satellite image of a hurricane near the Florida coast; water droplets move with the air, enabling us to visualize the counterclockwise swirling motion. However, the major portion of the hurricane is actually irrotational, while only the core (the eye of the storm) is rotational. ©McGraw-Hill Education. Objectives • Understand the role of the material derivative in transforming between Lagrangian and Eulerian descriptions • Distinguish between various types of flow visualizations and methods of plotting the characteristics of a fluid flow • Appreciate the many ways that fluids move and deform • Distinguish between rotational and irrotational regions of flow based on the flow property vorticity • Understand the usefulness of the Reynolds transport theorem ©McGraw-Hill Education. 3–1 ■ LAGRANGIAN AND EULERIAN DESCRIPTIONS Kinematics: The study of motion. Fluid kinematics: The study of how fluids flow and how to describe fluid motion. There are two distinct ways to describe motion: Lagrangian and Eulerian Lagrangian description: To follow the path of individual objects. This method requires us to track the position and velocity of each individual fluid parcel (fluid particle) and take to be a parcel of fixed identity. With a small number of objects, such as billiard balls on a pool table, individual objects can be tracked. In the Lagrangian description, one must keep track of the position and velocity of individual particles. ©McGraw-Hill Education. A more common method is Eulerian description of fluid motion. In the Eulerian description of fluid flow, a finite volume called a flow domain or control volume is defined, through which fluid flows in and out. Instead of tracking individual fluid particles, we define field variables, functions of space and time, within the control volume. The field variable at a particular location at a particular time is the value of the variable for whichever fluid particle happens to occupy that location at that time. For example, the pressure field is a scalar field variable. We define the velocity field as a vector field variable.   : , , , Pressure field P P x y z t    : , , , Velocity field V V x y z t      : , , , Acceleration field a a x y z t    Collectively, these (and other) field variables define the flow field. The velocity field can be expanded in Cartesian coordinates as         , , , , , , , , , , , V u v w u x y z t i v x y z t j w x y z t k         ©McGraw-Hill Education. (Bottom) Photo by John M. Cimbala. (a) In the Eulerian description, we define field variables, such as the pressure field and the velocity field, at any location and instant in time. (b) For example, the air speed probe mounted under the wing of an airplane measures the air speed at that location. In the Eulerian description we don’t really care what happens to individual fluid particles; rather we are concerned with the pressure, velocity, acceleration, etc., of whichever fluid particle happens to be at the location of interest at the time of interest. While there are many occasions in which the Lagrangian description is useful, the Eulerian description is often more convenient for fluid mechanics applications. Experimental measurements are generally more suited to the Eulerian description. ©McGraw-Hill Education. A Steady Two-Dimensional Velocity Field       , 0.5 0.8 1.5 0.8 V u v x i y j         Velocity vectors for the velocity field of Example 4–1. The scale is shown by the top arrow, and the solid black curves represent the approximate shapes of some streamlines, based on the calculated velocity vectors. The stagnation point is indicated by the blue circle. The shaded region represents a portion of the flow field that can approximate flow into an inlet. Flow field near the bell mouth inlet of a hydroelectric dam; a portion of the velocity field of Example 4-1 may be used as a first-order approximation of this physical flow field. ©McGraw-Hill Education. Acceleration Field The equations of motion for fluid flow (such as Newton’s second law) are written for a fluid particle, which we also call a material particle. If we were to follow a particular fluid particle as it moves around in the flow, we would be employing the Lagrangian description, and the equations of motion would be directly applicable. For example, we would define the particle’s location in space in terms of a material position vector xparticle(t), yparticle(t), zparticle(t) Newton’s second law applied to a fluid particle; the acceleration vector (purple arrow) is in the same direction as the force vector (green arrow), but the velocity vector (blue arrow) may act in a different direction. particle particle particle : Newton's second law F m a    particle particle : dV Accelerationof a fluid particle a dt    ©McGraw-Hill Education.       particle particle particle particle , , , V t V x t y t z t t      particle particle particle particle particle particle particle particle particle particle particle , , , dV x y z t dV dV a dt dt dt dx dy dz V dt V V V t dt x dt y dt z dt                          particle , , , dV V V V V a x y z t u v w dt t x y z                      : , , , Acceleration of a fluid particle expressed as a field variable dV V a x y z t V V dt t                  V t    Local acceleration V V           Advective (convective) acceleration : , , , Gradient or del operation i j k x y z x y z                         ©McGraw-Hill Education. When following a fluid particle, the x-component of velocity, u, is defined as dxparticle/dt. Similarly, v=dyparticle/dt and w=dzparticle/dt. Movement is shown here only in two dimensions for simplicity. The components of the acceleration vector in cartesian coordinates: x y z u u u u a u v w t x y z v v v v a u v w t x y z w w w w a u v w t x y z                                     ©McGraw-Hill Education. Flow of water through the nozzle of a garden hose illustrates that fluid particles may accelerate, even in a steady flow. In this example, the exit speed of the water is much higher than the water speed in the hose, implying that fluid particles have accelerated even though the flow is steady. ©McGraw-Hill Education. Residence time Δt is defined as the time it takes for a fluid particle to travel through the nozzle from inlet to outlet (distance Δx). A first-order finite difference approximation for derivative dq/dx is simply the change in dependent variable (q) divided by the change in independent variable (x). ©McGraw-Hill Education. Material Derivative   , , , dV V a x y z t V V dt t                   The total derivative operator d/dt in this equation is given a special name, the material derivative; it is assigned a special notation, D/Dt, in order to emphasize that it is formed by following a fluid particle as it moves through the flow field. Other names for the material derivative include total, particle, Lagrangian, Eulerian, and substantial derivative. The material derivative D/Dt is defined by following a fluid particle as it moves throughout the flow field. In this illustration, the fluid particle is accelerating to the right as it moves up and to the right. ©McGraw-Hill Education. : D d V Dt d Material derivative t t                : , , , DV dV V a x Mat y z erial accele t V V Dt dt t ration                    : DP dP P Material derivativeof pressure V P Dt dt t               The material derivative D/Dt is composed of a local or unsteady part and a convective or advective part. ©McGraw-Hill Education. Material Acceleration of a Steady Velocity Field       , 0.5 0.8 1.5 0.8 V u v x i y j         Acceleration vectors for the velocity field of Examples 4–1 and 4–3. The scale is shown by the top arrow, and the solid black curves represent the approximate shapes of some streamlines, based on the calculated velocity vectors. The stagnation point is indicated by the red circle. ©McGraw-Hill Education. 3–2 ■ FLOW PATTERNS AND FLOW VISUALIZATION Flow visualization: The visual examination of flow field features. While quantitative study of fluid dynamics requires advanced mathematics, much can be learned from flow visualization. Flow visualization is useful not only in physical experiments but in numerical solutions as well [computational fluid dynamics (CFD)]. In fact, the very first thing an engineer using CFD does after obtaining a numerical solution is simulate some form of flow visualization. Courtesy of Professor Thomas J. Mueller from the Collection of Professor F.N.M. Brown. Spinning baseball. The late F. N. M. Brown devoted many years to developing and using smoke visualization in wind tunnels at the University of Notre Dame. Here the flow speed is about 23 m/s and the ball is rotated at 630 rpm. ©McGraw-Hill Education. Streamlines and Streamtubes Streamline: A curve that is everywhere tangent to the instantaneous local velocity vector. Streamlines are useful as indicators of the instantaneous direction of fluid motion throughout the flow field. For example, regions of recirculating flow and separation of a fluid off of a solid wall are easily identified by the streamline pattern. Streamlines cannot be directly observed experimentally except in steady flow fields. For two-dimensional flow in the xy-plane, arc length 𝑑𝑟 = 𝑑𝑥, 𝑑𝑦 along a streamline is everywhere tangent to the local instantaneous velocity vector 𝑉= 𝑢, 𝑣. ©McGraw-Hill Education. Consider an infinitesimal arc length 𝑑𝑟 = 𝑑𝑥𝑖 + 𝑑𝑦𝑗 + 𝑑𝑧𝑘 along a streamline; 𝑑𝑟 must be parallel to the local velocity vector 𝑉= 𝑢𝑖 + 𝑣𝑗 + 𝑤𝑘 by definition of the streamline. By simple geometric arguments using similar triangles, we know that the components of 𝑑𝑟 must be proportional to those of 𝑉 (Fig. 4–16). Hence, : dr dx dy dz Equation for a streamline V u v w    (4-15) where dr is the magnitude of 𝑑𝑟 and V is the speed, the magnitude of velocity vector 𝑉. Equation 4–15 is illustrated in two dimensions for simplicity in Fig. 4–16. For a known velocity field, we integrate Eq. 4–15 to obtain equations for the streamlines. In two dimensions, (x, y), (u, 𝜐), the following differential equation is obtained: alongastreamline -: dy v Streamlineinthe xy plane dx u        (4-16) In some simple cases, Eq. 4–16 may be solvable analytically; in the general case, it must be solved numerically. In either case, an arbitrary constant of integration appears. Each chosen value of the constant represents a different streamline. The family of curves that satisfy Eq. 4–16 therefore represents streamlines of the flow field. ©McGraw-Hill Education. Streamlines for a steady, incompressible, two-dimensional velocity field       , 0.5 0.8 1.5 0.8 V u v x i y j         Streamlines (solid black curves) for the velocity field of Example 4–4; velocity vectors (blue arrows) are superimposed for comparison. The agreement is excellent in the sense that the velocity vectors point everywhere tangent to the streamlines. Note that speed cannot be determined directly from the streamlines alone. ©McGraw-Hill Education. A streamtube consists of a bundle of streamlines much like a communications cable consists of a bundle of fiber-optic cables. Since streamlines are everywhere parallel to the local velocity, fluid cannot cross a streamline by definition. Fluid within a streamtube must remain there and cannot cross the boundary of the streamtube. Both streamlines and streamtubes are instantaneous quantities, defined at a particular instant in time according to the velocity field at that instant. A streamtube consists of a bundle of individual streamlines. In an incompressible flow field, a streamtube (a) decreases in diameter as the flow accelerates or converges and (b) increases in diameter as the flow decelerates or diverges. ©McGraw-Hill Education. Pathlines Pathline: The actual path traveled by an individual fluid particle over some time period. A pathline is a Lagrangian concept in that we simply follow the path of an individual fluid particle as it moves around in the flow field. Thus, a pathline is the same as the fluid particle’s material position vector (xparticle(t), yparticle(t), zparticle(t)) traced out over some finite time interval. A pathline is formed by following the actual path of a fluid particle. ©McGraw-Hill Education. Wallet, A & Ruellan, F. 1950, La Houille Blanche 5: 483–489. Used by permission. Pathlines produced by white tracer particles suspended in water and captured by time-exposure photography; as waves pass horizontally, each particle moves in an elliptical path during one wave period. ©McGraw-Hill Education. Particle image velocimetry (PIV): A modern experimental technique that utilizes short segments of particle pathlines to measure the velocity field over an entire plane in a flow. Recent advances also extend the technique to three dimensions. In PIV, tiny tracer particles are suspended in the fluid. However, the flow is illuminated by two flashes of light (usually a light sheet from a laser) to produce two bright spots (recorded by a camera) for each moving particle. Then, both the magnitude and direction of the velocity vector at each particle location can be inferred, assuming that the tracer particles are small enough that they move with the fluid. ©McGraw-Hill Education. Photo by Michael H. Krane, ARL-Penn State. Stereo PIV measurements of the wing tip vortex in the wake of a NACA-66 airfoil at angle of attack. Color contours denote the local vorticity, normalized by the minimum value, as indicated in the color map. Vectors denote fluid motion in the plane of measurement. The black line denotes the location of the upstream wing trailling edge. Coordinates are normalized by the airfoil chord, and the origin is the wing root. ©McGraw-Hill Education. 3–2 ■ FLOW PATTERNS AND FLOW VISUALIZATION(9) Pathlines can also be calculated numerically for a known velocity field. Specifically, the location of the tracer particle is integrated over time from some starting location 𝑥 start and starting time 𝑡start to some later time t. start start : t t Tracer particle location at time t x x Vdt      (4-17) When Eq. 4–17 is calculated for t between tstart and tend, a plot of 𝑥 𝑡 is the pathline of the fluid particle during that time interval, as illustrated in Fig. 4–20. For some simple flow fields, Eq. 4–17 can be integrated analytically. For more complex flows, we must perform a numerical integration. If the velocity field is steady, individual fluid particles follow streamlines. Thus, for steady flow, pathlines are identical to streamlines. ©McGraw-Hill Education. Streaklines Streakline: The locus of fluid particles that have passed sequentially through a prescribed point in the flow. Streaklines are the most common flow pattern generated in a physical experiment. If you insert a small tube into a flow and introduce a continuous stream of tracer fluid (dye in a water flow or smoke in an air flow), the observed pattern is a streakline. A streakline is formed by continuous introduction of dye or smoke from a point in the flow. Labeled tracer particles (1 through 8) were introduced sequentially. ©McGraw-Hill Education. Courtesy of ONERA. Photo by Werlé. Streaklines produced by colored fluid introduced upstream; since the flow is steady, these streaklines are the same as streamlines and pathlines. Streaklines, streamlines, and pathlines are identical in steady flow but they can be quite different in unsteady flow. The main difference is that a streamline represents an instantaneous flow pattern at a given instant in time, while a streakline and a pathline are flow patterns that have some age and thus a time history associated with them. A streakline is an instantaneous snapshot of a time-integrated flow pattern. A pathline, on the other hand, is the time-exposed flow path of an individual particle over some time period. ©McGraw-Hill Education. In the figure, streaklines are introduced from a smoke wire located just downstream of a circular cylinder of diameter D aligned normal to the plane of view. When multiple streaklines are introduced along a line, as in the figure, we refer to this as a rake of streaklines. The Reynolds number of the flow is Re = 93. Photos by John M. Cimbala. Smoke streaklines introduced by a smoke wire at two different locations in the wake of a circular cylinder: (a) smoke wire just downstream of the cylinder and (b) smoke wire located at x/D = 150. The time-integrative nature of streaklines is clearly seen by comparing the two photographs. ©McGraw-Hill Education. Because of unsteady vortices shed in an alternating pattern from the cylinder, the smoke collects into a clearly defined periodic pattern called a Kármán vortex street. A similar pattern can be seen at much larger scale in the air flow in the wake of an island. Photo from Landsat 7 WRS Path 6 Row 83, center: -33.18, -79.99, 9/15/1999, earthobservatory.nasa.gov. Courtesy of USGS EROS Data Center Satellite System Branch/NASA. Kármán vortices visible in the clouds in the wake of Alexander Selkirk Island in the southern Pacific Ocean. ©McGraw-Hill Education. For a known velocity field, a streakline can be generated numerically. We need to follow the paths of a continuous stream of tracer particles from the time of their injection into the flow until the present time, using Eq. 4–17. Mathematically, the location of a tracer particle is integrated over time from the time of its injection tinject to the present time tpresent. Equation 4–17 becomes present inject injection : t t Integrated tracer particlelocation x x V dt      (4-18) In a complex unsteady flow, the time integration must be performed numerically as the velocity field changes with time. When the locus of tracer particle locations at t = tpresent is connected by a smooth curve, the result is the desired streakline. start start : t t Tracer particlelocationat timet x x V dt      (4-17) ©McGraw-Hill Education. Comparison of Flow Patterns in an Unsteady Flow         , 0.5 0.8 1.5 2.5sin 0.8 V u v x i t y j           An unsteady, incompressible, two-dimensional velocity field Streamlines, pathlines, and streaklines for the oscillating velocity field of Example 4–5. The streaklines and pathlines are wavy because of their integrated time history, but the streamlines are not wavy since they represent an instantaneous snapshot of the velocity field. ©McGraw-Hill Education. 3–3 ■ PLOTS OF FLUID FLOW DATA Regardless of how the results are obtained (analytically, experimentally, or computationally), it is usually necessary to plot flow data in ways that enable the reader to get a feel for how the flow properties vary in time and/or space. You are already familiar with time plots, which are especially useful in turbulent flows (e.g., a velocity component plotted as a function of time), and xy-plots (e.g., pressure as a function of radius). In this section, we discuss three additional types of plots that are useful in fluid mechanics: profile plots vector plots contour plots ©McGraw-Hill Education. Profile Plots A profile plot indicates how the value of a scalar property varies along some desired direction in the flow field. In fluid mechanics, profile plots of any scalar variable (pressure, temperature, density, etc.) can be created, but the most common one used in this book is the velocity profile plot. Since velocity is a vector quantity, we usually plot either the magnitude of velocity or one of the components of the velocity vector as a function of distance in some desired direction. Profile plots of the horizontal component of velocity as a function of vertical distance; flow in the boundary layer growing along a horizontal flat plate: (a) standard profile plot and (b) profile plot with arrows. ©McGraw-Hill Education. Vector Plots A vector plot is an array of arrows indicating the magnitude and direction of a vector property at an instant in time. Streamlines indicate the direction of the instantaneous velocity field, they do not directly indicate the magnitude of the velocity (i.e., the speed). A useful flow pattern for both experimental and computational fluid flows is thus the vector plot, which consists of an array of arrows that indicate both magnitude and direction of an instantaneous vector property. Vector plots can also be generated from experimentally obtained data (e.g., from PIV measurements) or numerically from CFD calculations. Fig. 4-4: Velocity vector plot Fig. 4-14: Acceleration vector plot. Both generated analytically. ©McGraw-Hill Education. Results of CFD calculations of flow impinging on a block: (a) streamlines (b) velocity vector plot of the upper half of the flow (c) velocity vector plot, close-up view revealing more details in the separated flow region ©McGraw-Hill Education. Contour Plots A contour plot shows curves of constant values of a scalar property (or magnitude of a vector property) at an instant in time. Contour plots (also called isocontour plots) are generated of pressure, temperature, velocity magnitude, species concentration, properties of turbulence, etc. A contour plot can quickly reveal regions of high (or low) values of the flow property being studied. A contour plot may consist simply of curves indicating various levels of the property; this is called a contour line plot. Alternatively, the contours can be filled in with either colors or shades of gray; this is called a filled contour plot. Contour plots of the pressure field due to flow impinging on a block, as produced by CFD calculations; only the upper half is shown due to symmetry; (a) filled color scale contour plot and (b) contour line plot where pressure values are displayed in units of Pa gage pressure. ©McGraw-Hill Education. 3–4 ■ OTHER KINEMATIC DESCRIPTIONS Types of Motion or Deformation of Fluid Elements In fluid mechanics, an element may undergo four fundamental types of motion or deformation: (a) translation, (b) rotation, (c) linear strain (also called extensional strain), and (d) shear strain. All four types of motion or deformation usually occur simultaneously. It is preferable in fluid dynamics to describe the motion and deformation of fluid elements in terms of rates such as velocity (rate of translation), angular velocity (rate of rotation), linear strain rate (rate of linear strain), and shear strain rate (rate of shear strain). In order for these deformation rates to be useful in the calculation of fluid flows, we must express them in terms of velocity and derivatives of velocity. Fundamental types of fluid element motion or deformation: (a) translation, (b) rotation, (c) linear strain, and (d) shear strain. ©McGraw-Hill Education. A vector is required in order to fully describe the rate of translation in three dimensions. The rate of translation vector is described mathematically as the velocity vector. : Rate of translation vector in Cartesian coordinates V u i v j wk        Rate of rotation (angular velocity) at a point: The average rotation rate of two initially perpendicular lines that intersect at that point. Rate of rotation of fluid element about point P 1 2 2 a b d v u dt x y                        For a fluid element that translates and deforms as sketched, the rate of rotation at point P is defined as the average rotation rate of two initially perpendicular lines (lines a and b). ©McGraw-Hill Education. The rate of rotation vector is equal to the angular velocity vector. : 1 1 1 2 2 2 Rateof rotation vector in Cartesian coordin w v u w v u i j k y z z x x ate y s                                      Linear strain rate: The rate of increase in length per unit length. Mathematically, the linear strain rate of a fluid element depends on the initial orientation or direction of the line segment upon which we measure the linear strain. : xx yy zz Linear strain rate in Cartesian coo u v w x rdinates y z             ©McGraw-Hill Education. Volumetric strain rate or bulk strain rate: The rate of increase of volume of a fluid element per unit volume. This kinematic property is defined as positive when the volume increases. Another synonym of volumetric strain rate is also called rate of volumetric dilatation, (the iris of your eye dilates (enlarges) when exposed to dim light). The volumetric strain rate is the sum of the linear strain rates in three mutually orthogonal directions. 1 : 1 xx yy zz Volumetric strain rate in Cartesian coordinates D d u v w Dt dt x y z                 V V V V The volumetric strain rate is zero in an incompressible flow. ©McGraw-Hill Education. Shear strain rate at a point: Half of the rate of decrease of the angle between two initially perpendicular lines that intersect at the point. For a fluid element that translates and deforms as sketched, the shear strain rate at point P is defined as half of the rate of decrease of the angle between two initially perpendicular lines (lines a and b). ©McGraw-Hill Education. , - -: 1 1 2 2 xy a b Shear strain rate initially perpendicular lines in the x and y directions d u v dt y x               1 1 1 2 2 : 2 xy zx yz Shear strain rate in Cartesian coordinate u v w u v w y s x x z z y                                    : 1 1 2 2 1 1 2 2 1 1 2 2 xx xy xz ij yx yy yz zx zy zz u u v u w x y x z x v u v v w x y y Strain rate tensor in Cartesia z y w u w v w x z y n coordinates z z                                                                                                           ©McGraw-Hill Education. Figure shows a general (although two-dimensional) situation in a compressible fluid flow in which all possible motions and deformations are present simultaneously. In particular, there is translation, rotation, linear strain, and shear strain. Because of the compressible nature of the fluid flow, there is also volumetric strain (dilatation). You should now have a better appreciation of the inherent complexity of fluid dynamics, and the mathematical sophistication required to fully describe fluid motion. A fluid element illustrating translation, rotation, linear strain, shear strain, and volumetric strain. ©McGraw-Hill Education.       , 0.5 0.8 1.5 0.8 V u v x i y j         Streamlines for the velocity field of Example 4–6. The stagnation point is indicated by the red circle at x = −0.625 m and y = 1.875 m. ©McGraw-Hill Education. Deformation of an initially square parcel of marked fluid subjected to the velocity field of Example 4–6 for a time period of 1.5 s. The stagnation point is indicated by the red circle at x = −0.625 m and y = 1.875 m, and several streamlines are plotted. ©McGraw-Hill Education. 3–5 ■ VORTICITY AND ROTATIONALITY Another kinematic property of great importance to the analysis of fluid flows is the vorticity vector, defined mathematically as the curl of the velocity vector : curl( ) Vorticity ve V tor V c        1 1 : curl 2 2 2 Rate of rotation vector V V                  Vorticity is equal to twice the angular velocity of a fluid particle The direction of a vector cross product is determined by the right-hand rule. The vorticity vector is equal to twice the angular velocity vector of a rotating fluid particle. ©McGraw-Hill Education. If the vorticity at a point in a flow field is nonzero, the fluid particle that happens to occupy that point in space is rotating; the flow in that region is called rotational. Likewise, if the vorticity in a region of the flow is zero (or negligibly small), fluid particles there are not rotating; the flow in that region is called irrotational. Physically, fluid particles in a rotational region of flow rotate end over end as they move along in the flow. The difference between rotational and irrotational flow: fluid elements in a rotational region of the flow rotate, but those in an irrotational region of the flow do not. ©McGraw-Hill Education. : Vorticity vector in Cartesian coordina w v u w v u i j k y z z x x y tes                                      : Two - dimensional flow in Cartesian coordinates v u k x y              For a two-dimensional flow in the xy-plane, the vorticity vector always points in the z- or z-direction. In this illustration, the flag-shaped fluid particle rotates in the counterclockwise direction as it moves in the xy-plane; its vorticity points in the positive z-direction as shown. ©McGraw-Hill Education. Contour plot of the vorticity field 𝜁z due to flow impinging on a block, as produced by CFD calculations; only the upper half is shown due to symmetry. Blue regions represent large negative vorticity, and red regions represent large positive vorticity. ©McGraw-Hill Education. Determination of Rotationality in a Two-Dimensional Flow steady, incompressible, two-dimensional velocity field:     2 , 2 1 V u v x i xy j          2 0 2 v u k y k y k x y                     Vorticity Deformation of an initially square fluid parcel subjected to the velocity field of Example 4–8 for a time period of 0.25 s and 0.50 s. Several streamlines are also plotted in the first quadrant. It is clear that this flow is rotational. ©McGraw-Hill Education.   : 1 1 z r z r r z Vorticity vector in cylindrical coordinates ru u u u u u e e e r z z r r r                                                 - : 1 r Two dimensional flow in cylindrical coordinates ru u k r r                  For a two-dimensional flow in the r-plane, the vorticity vector always points in the z (or z) direction. In this illustration, the flag-shaped fluid particle rotates in the clockwise direction as it moves in the ru-plane; its vorticity points in the z-direction as shown. ©McGraw-Hill Education. Comparison of Two Circular Flows - : 0 and : 0 and r r Flow A solid body rotation u u r K FlowB line vortex u u r              2 1 - : 0 2 1 : 0 0 r Flow A solid body rotation k k r r K FlowB line vortex k r r                                 Streamlines and velocity profiles for (a) flow A, solid-body rotation and (b) flow B, a line vortex. Flow A is rotational, but flow B is irrotational everywhere except at the origin. The (oversized) fluid elements in flow B would also distort as they move, but in order to illustrate only particle rotation, such distortion is not shown here. ©McGraw-Hill Education. (a) © McGraw-Hill Education/Mark Dierker, photographer (b) © DAJ/Getty Images RF A simple analogy: (a) rotational circular flow is analogous to a roundabout, while (b) irrotational circular flow is analogous to a Ferris wheel. As children revolve around a roundabout, they also rotate at the same angular velocity as that of the ride itself. This is analogous to a rotational flow. In contrast, children on a Ferris wheel always remain oriented in an upright position as they trace out their circular path. This is analogous to an irrotational flow. ©McGraw-Hill Education. 1 : and 0 2 r Line sink u u L r     V Streamlines in the r𝜃-plane for the case of a line sink.
13287	https://ocw.uc3m.es/pluginfile.php/3910/mod_page/content/20/Module2_notes.pdf	Module 2: Analysis of DC circuits Bel´ en Garc´ ıa Electrical Engineering Department In this module we will study diﬀerent methods that can be applied to the systematic analysis of electrical circuits and we will apply them to the analysis of circuits supplied in Direct Current (DC). The same methods will be applied to the analysis of Alternating Current (AC) circuits in Module 3. 1 Deﬁnitions Prior to introducing the methods we need to deﬁne some terms related with the topology of electrical circuits: • Branch: Part of the circuit with two terminals • Node: Junction of two or more branches • Loop: Closed path in a circuit • Mesh: Closed path in a circuit that does not have any other closed path inside it -+ -+ mesh branch node loop 2 Mesh current method Mesh current method (also referred to as mesh analysis) is a systematic method based in the application of Kirchhoﬀ’s voltage law (KVL) to every mesh of a circuit. The method can be applied to the analysis of any planar circuit 1. 1Planar circuits are the ones that can be drawn in a plane with no crossing branches 1 2.1 Application of mesh current method Imagine that we want to solve the circuit of the ﬁgure. The circuit has two mesh: mesh 1 at the left and mesh 2 at the right. Note that R1 is part of mesh 1 and R2 is part of mesh 2, while R3 is shared by both mesh. -+ -+ R1 R2 ug2 ug1 R3 mesh 1 mesh 2 ib ia ic To calculate the branch currents of the circuit (ia, ib and ic) using mesh current method the steps below must be followed: 1. Deﬁne a ”mesh current” for each mesh of the circuit. We consider that all the mesh currents ﬂow in the same direction 2 -+ -+ R1 R2 ug2 ug1 R3 i1 i2 2. Apply KVL to every mesh of the circuit considering that the current that ﬂows through each mesh is the correspondent mesh current. X k uk = 0 Note that: • A sign criteria must be adopted to apply KVL. Any criteria is valid if we are consistent with it. In this notes we consider: Voltage drops + Voltage rises -• As resistors are passive elements we consider that there is always a voltage drop across them. The value of the voltage drop can be calculated according to Ohm’s law: R uR=R·i + -i 2It is valid to deﬁne the mesh currents with diﬀerent directions. However, for the sake of simplicity clockwise direction will be assigned to all the mesh currents in these notes. 2 3. We obtain a system of equations with as many equations as mesh in the circuit: Equation for mesh 1: −ug1 + R1 · i1 + R3 · (i1 −i2) = 0 Equation for mesh 2: R2 · i2 + R3 · (i2 −i1) + ug2 = 0 4. We solve the system of equations and ﬁnd the values for mesh currents i1 and i2. It is useful to write mesh equations in matrix form to solve the system more easily. This is specially interesting for circuits with three or more mesh. The mesh equations in matrix form are: R1 + R3 −R3 −R3 R2 + R3 · i1 i2 = ug1 −ug2 These equations can be generalized as: R · Imesh = Ug where R is the ”resistance matrix” whose terms are: Rjj = Total resistance in mesh j Rjk = −Total resistance shared by mesh j and mesh k The vector Imesh contains the mesh currents and the terms of the vector Ug are the voltage rises produced by sources across every mesh: Ugi = P voltage rises across voltage sources in mesh i 5. Finally we calculate the branch currents or other requested variables (power, volt-ages..), using the values of the mesh currents. -+ -+ R1 R2 ug2 ug1 R3 ib ia ic i1 i2 ia = i1 ib = i2 ic = i1 −i2 3 2.2 Application of mesh current method in circuits with current sources The application of mesh current method to the analysis of circuits that contain resistors and voltage sources is quite straightforward; the voltage drop across resistors is deﬁned by Ohm’s law and the voltage drop across voltage sources is given by the output voltage of the source. The case of circuits that incorporate current sources is more challenging because current sources provide a certain value of current, but the voltage drop across them depends on the circuit conﬁguration and then it is not so immediate to include these elements in mesh equations. Depending on the conﬁguration of the current sources diﬀerent approaches can be considered, as is explained in this section. 2.2.1 Real current sources As was studied in module 1, real current sources can always be redrawn as equivalent real voltage sources according to the following transformation rule: R ig -+ R ug ug = ig · R In circuits with real current sources, the next steps might be followed to facilitate the application of mesh current method: 1. Redraw the real current sources as real voltage sources. 2. Solve the circuit applying mesh current method. 3. Go back to the original circuit and use the obtained mesh currents to ﬁnd the requested variables (i.e. voltages, currents, powers..). 2.2.2 Ideal current sources that belong to one mesh If we want to solve a circuit that contains an ideal current source in a circuit that belongs exclusively to one mesh, we can just assume that the mesh current equals the current of the current source. In the following circuit: R1 R2 ig1 R3 i1 i2 ig2 4 The mesh equations can be written as: Mesh 1: i1 = ig1 Mesh 2: i2 = −ig2 Note that the resistors R1 and R2 that are in series with the ideal current sources have no eﬀect on the current ﬂowing through the branches. 2.2.3 Ideal current sources that belong to more than one mesh There are other cases in which the circuit contains an ideal current source that belongs to more than one mesh: -+ -+ R1 R2 ug2 ug1 ig3 In this case we can not redraw the current source as a voltage source and neither can identify the current of the source with any of the mesh current. However, two diﬀerent strategies might be applied to ﬁnd the mesh equations: 1. Deﬁne a new unknown ”ux”,which is the voltage drop across the ideal current source. -+ -+ R1 R2 ug2 ug1 i1 i2 ig3 + -ux This new unknown is included in the equations. The system must be completed with an additional equation that relates the current of the ideal current source with the mesh currents: Mesh 1: −ug1 + R1 · i1 + ux = 0 Mesh 2: R2 · i2 −ux + ug2 = 0 Additional equation: ig3 = i2 −i1 These equations might be expressed in matrix form as well as:   R1 0 1 0 R2 −1 −1 1 0  ·   i1 i2 ux  =   ug1 −ug2 ig3   5 2. As an alternative to the previous approach, the supermesh method can be applied. A supermesh is a closed path that contains the branch where the ideal current source is connected. In the previous example, we might take the external part of the circuit as supermesh. -+ -+ R1 R2 ug2 ug1 i1 i2 ig3 supermesh Applying KVL to the supermesh: Supermesh equation: −ug1 + R1 · i1 + R2 · i2 + ug2 = 0 The system of equations must be completed with an additional equation that relates the mesh currents with the current of the ideal current source. Additional equation: ig3 = i2 −i1 2.3 Example Solve the circuit using mesh analysis and do a power balance. 2 A -+ 2 4 2 3 3 A 8 V Solution The problem is solved using mesh analysis method, although there are other methods and simpliﬁcations that could lead to the same solution in a faster way. Firstly a mesh current is assigned to each mesh of the circuit and the voltage ux is deﬁned: 6 2 A -+ 2 4 2 3 3 A 8 V i1 i2 i3 + -ux The mesh equations are: Mesh 1: i1 = 2 Mesh 2: 3 · i2 + ux + 2 · (i2 −i3) = 0 Mesh 3: 2 · (i3 −i2) + 2 · (i3 −i1) + 8 = 0 Additional equation: i1 −i2 = 3 We could write these equations in matrix form or solve the system using any other chosen method:     1 0 0 0 0 5 −2 1 −2 −2 4 0 1 −1 0 0    ·     i1 i2 i3 ux    =     2 0 −8 3     Solving the equations we ﬁnd that i1 = 2A i2 = −1A i3 = −3/2A ux = 2V The currents ﬂowing through all the branches of the circuit are obtained: 2 A -+ 2 4 2 3 3 A 8 V + -2 A 1 A 3/2 A 7/2 A 1/2 A 2 V 7 And calculate the power balance. Power absorbed by resistors: pR = P k Rk · ik = 4 · 22 + 3 · 12 + 2 · (7/2)2 + 2 · (1/2)2 = 44W Power delivered by sources: pg = P k uk · ik p3A = 2 · 3 = 6W p8V = 8 · 3/2 = 12W The voltage drop across the current source of 2A is calculated applying KVL to a closed path that contains the source: 2 A 2 4 3 A 7 V + -2 V + -+ -+ -8 V u2A −u2A + 8 + 7 −2 = 0 u2A = 13V p2A = 2 · 13 = 26W psources = 26 + 6 + 12 = 44W Then, the power balance is veriﬁed: Power generated by sources = Power absorbed by resistors 3 Node voltage method Node voltage method (also referred to as nodal analysis) is a systematic method based in the application of Kirchoﬀ’s current law (KCL) to all the nodes of a circuit. 3.1 Application of node voltage method Imagine that we want to solve the circuit below and ﬁnd the branch currents i1, i2 and i3: 8 R1 R2 ig1 ig2 R3 i1 i2 i3 The application of node voltage method consists of the following steps: 1. Firstly we identify the independent nodes of the circuit, i.e. the nodes that have a diﬀerent voltage level. The circuit of the ﬁgure has three independent nodes. All the branches at the bottom of the circuit have the same voltage level, so that part of the circuit is taken as one node. We label the nodes with numbers 1, 2 and 3. R1 R2 node 1 ig1 ig2 R3 node 2 node 3 The node voltage method consists of ﬁnding the voltage of each node with respect to a ”reference node”, whose voltage level is zero. In the previous example we assign nodal voltages u1, u2 and u3 to the three nodes and take node 3 as reference node (u3 = 0). The objective is to ﬁnd the voltage of each non reference node with respect the reference node. 3 R1 R2 u1 ig1 ig2 R3 u3= 0 u2 2. We apply KCL to each node of the circuit considering that the voltage of each node is the correspondent node voltage: X k ik = 0 Note that: 3In some problems the reference node is speciﬁed while in other cases we will need to assign it. Any node can be taken as reference node. The ﬁnal solution of the problem is the same for any choice. 9 • We should adopt a sign criteria to apply 1KL. Any criteria is valid if we are consistent with it. In this notes we will consider that the currents that ﬂow out of a node are positive and the currents that ﬂow into a node are negative. Current ﬂowing out of a node + Current ﬂowing into a node -• The currents ﬂowing through a resistor can be calculated using Ohms’s law if we know the voltage drop across it. Then, we calculate the current ﬂowing through each resistor of the circuit as a function of the nodal voltages at their two terminals. The current can be considered to be ﬂowing towards the right or towards the left by changing its sign. R iright ua ub R ileft ua ub iright = ua −ub R ileft = ub −ua R 3. We obtain a system of equations with as many equations as nodes in the circuit Equation for node 1: −ig1 + u1 R1 + u1 −u2 R3 = 0 Equation for node 2: ig1 + u2 R2 + u2 −u1 R3 = 0 4. We solve the system and ﬁnd the values for the node voltages. Sometimes it is useful to express nodal equations in matrix form to solve them more easily. This is specially interesting for circuits with three or more non-reference nodes. The equations in matrix notation for the example are: 1 R1 + 1 R3 −1 R3 −1 R3 1 R2 + 1 R3 · u1 u2 = ig1 −ig2 Solving these equations we ﬁnd the values of u1 and u2 The nodal equations in matrix form can be generalized as: G · Unode = Ig where G is the so called ”conductance matrix” G = G11 G12 G21 G22 10 The terms of the main diagonal of the conductance matrix are the self conductances (i.e. total conductance connected to the analysed node) and the non diagonal terms are the shared conductances (i.e. conductance shared by two nodes) with negative sign. G11 = Total conductance connected to node 1 G22 = Total conductance connected to node 2 G12 = G21 = −Total conductance connected between node 1 and node 2 The vectors Unode and Ig are: Unode = u1 u2 Ig = P Current injected by current sources into node 1 P Current injected by current sources into node 2 5. Finally, the branch currents i1, i2 and i3 are calculated using the node voltages: R1 R2 u1 ig1 ig2 R3 u3= 0 u2 i1 i2 i3 i1 = u1 R1 i2 = u2 R2 i3 = u1 −u2 R3 3.2 Application of nodal analysis in circuits with voltage sources The presence of voltage sources introduces a diﬃculty for the application of node voltage method to the analysis of a circuit. Voltage sources have a well deﬁned voltage drop but the current ﬂowing through them depends on the conﬁguration of the circuit. In this section several procedures are explained to apply nodal analysis to circuits that incorporate voltage sources. 3.2.1 Real voltage sources As was studied in module 1, a real voltage source can always be redrawn as an equivalent real current source according to the following transformation rule: 11 -+ R R ug ig ig = ug R Then, to solve circuits that include real voltage sources using nodal analysis, the next steps may be followed: 1. Redraw the real voltage sources as real current sources 2. Solve the circuit applying node voltage method as explained before 3. Go back to the original circuit and use the information obtained from the nodal analysis to ﬁnd the wanted variables (i.e. voltages, currents, powers..) 3.2.2 Ideal voltage sources connected to the reference node If we have an ideal voltage source in a circuit which is connected between a non-reference node and the reference node, as the case shown in the drawing below, we can assume that the node voltage equals the voltage of the voltage source. R1 R2 u1 ug1 ug2 R3 u3= 0 u2 -+ -+ In that case the nodal equations in this case may be written as: Node 1: u1 = ug1 Node 2: u2 = −ug2 Note that the resistors R1 and R2, which are in parallel with the ideal voltage sources, have no eﬀect on the voltage drop across the nodes. 3.2.3 Ideal voltage sources connected between two non-reference nodes There are other cases in which the ideal voltage source is connected between two non-reference nodes, as in the following circuit: 12 R1 R2 u1 ig1 ig2 u3= 0 u2 ug3 -+ In this case we can not redraw the voltage source as a current source and can not identify the voltage of the source with any of the nodal voltages either. Two diﬀerent strategies can be applied to solve the circuit with node voltage method: 1. Deﬁne a new unknown current ix, which is the current ﬂowing through the ideal voltage source. R1 R2 u1 ig1 ig2 u3= 0 u2 ug3 -+ ix This new unknown will be included in the equations. As we have three unknowns now we need an additional equation to ﬁnd the node voltages. The additional equation relates the voltage of the ideal voltage source with the node voltages. The nodal equations for this case are: Node 1: −ig1 + u1 R1 −ix = 0 Node 2: ig2 + u2 R2 + ix = 0 Additional equation: u1 −u2 = ug3 These equations can be expressed in matrix form as well:   1 R1 0 −1 0 1 R2 1 1 −1 0  ·   u1 u2 ix  =   ig1 −ig2 ug3   2. As alternative to the previous method we can write a ”supernode” equation. The supernode is a ﬁctional node that contains the ideal voltage source. The supernode is signaled with a discontinuous line in the diagram below: 13 R1 R2 u1 ig1 ig2 u3= 0 u2 ug3 -+ supernode The system must be completed with an additional equation that relates the node voltages with the voltage of the ideal voltage source. Supernode equation: −ug1 + u1 R1 + u2 R2 + ug2 = 0 Additional equation: ug3 = u1 −u2 3.3 Example Solve the following circuit using node voltage method 5 -+ -+ 2 2 4 6 V 10 V 6 A 10 A Solution Firstly we have to identify the independent nodes and assign them a node voltage. We set the reference node in node 4. 14 5 -+ -+ 2 2 4 6 V 10 V 6 A 10 A u1 u2 u3 u4=0 ix We apply KCL to nodes 1, 2 and 3 and write the nodal equations: Node 1: u1 = 10 Node 2: u2 −u1 2 + u2 2 −6 + ix = 0 Node 3: −10 + u3 −u1 5 + u3 4 −ix = 0 Additional equation: u3 −u2 = 6 We can solve the system using matrix algebra or any other chosen method. The system in matrix form would be:     1 0 0 0 −1 2 1 0 1 −1 5 0 1 5 + 1 4 −1 0 −1 1 0    ·     u1 u2 u3 ix    =     10 6 10 6     Solving the equations we ﬁnd: u1 = 10V u2 = 14V u3 = 20V ix = −3A We could have also written the nodal equations using the supernode method. Consid-ering a supernode that contains nodes 2 and 3 we ﬁnd the following system of equations: Node 1: u1 = 10 Supernode: u2 −u1 2 + u2 2 −6 −10 + u3 −u1 5 + u3 4 = 0 15 Additional equation: u3 −u2 = 6 The solution of that system leads to the same solution: u1 = 10V u2 = 14V u3 = 20V We can now obtain the current in every branch of the circuit considering that the current ﬂows from the node with highest voltage to the node of lower voltage and that the value of the current is calculated as: i = uhigh −ulow R Additionally the currents ﬂowing through voltage sources can be calculated applying KCL to the nodes where they are connected: 5 -+ -+ 2 2 4 6 V 10 V 6 A 10 A u1=10V u2=14 V u3=20V u4= 0V 2 A 2 A 7 A 5 A 6 A 3 A Finally we calculate the power balance: • Power absorbed by resistors: pR = P k Rk ·ik = 5·22 +2·22 +2·72 +4·52 = 226W • Power delivered by sources: pg = P k uk · ik 4 p10A = 10 · 10 = 100W p6V = −6 · 3 = −18W p6A = 14 · 6 = 84W 4Sources absorb power if the relative polarity of the voltage and current is such that current ﬂows from + to -. In that case the power of the source will be taken as negative. Note that that is the case for the 6V voltage source in this example. 16 p10V = −10 · 6 = −60W psources = 100 −18 + 84 + 60 = 226W 4 Superposition principle The superposition principle states that ”the response of a linear circuit subjected to several excitation sources acting simultaneously equals the sum of the responses of the circuits when the sources act separately”. A circuit is linear if the relation between the voltages and currents in all their elements verify a linear relation, which is the case of all the circuits that will be studied in this course. Superposition principle can be applied to calculate the current i1 and the voltage u1 in the circuit below: R1 ig1 ug2 u1 i1 -+ + -R2 The current i1 is the sum of the current that ﬂows through the resistor if only the current source is working and the current that ﬂows though it if only the voltage source is working. The same statement is valid for the calculation of voltage u1. To apply the superposition principle we ”turn oﬀ” the sources one by one and calculate the response of the circuit to each source. Then we obtain the whole response of the circuit as a sum of both responses. Note that: • Cancelling a voltage source consists of considering that its voltage drop is zero. This is equivalent to redrawing it as a short-circuit. ug ug=0 turn off the sorce -+ • Cancelling a current source consists of considering that the current ﬂowing through it is zero. This is equivalent to transform the source into open-circuit. 17 ig ig=0 turn off the sorce Then, to solve the circuit in the ﬁgure using the superposition principle: 1. We ”turn oﬀ” the voltage source and analyse the response of the circuit when only the current source acts as excitation: R1 ig1 u'1 i'1 + -R2 We can calculate the current i′ 1 using the current divider (note that the two resistors are now in parallel) or any other method that we choose: i′ 1 = R2 R1 + R2 · ig1 The voltage u′ 1 is: u′ 1 = R1 · R2 R1 + R2 · ig1 2. We ”turn oﬀ” the current source and analyse the response of the circuit when only the voltage source acts as excitation: R1 ug2 u''1 i''1 -+ + -R2 In this case, the two resistors are in series and the current i′′ 1 is: i′′ 1 = ug2 R1 + R2 and the voltage u′′ 1 is: u′′ 1 = R1 R1 + R2 · ug2 18 3. Finally, we ﬁnd the current i1 and the voltage u1 as the sum of the separate responses: i1 = i′ 1 + i′′ 1 u1 = u′ 1 + u′′ 1 Two last remarks about the superposition principle: • The superposition principle can not be used to calculate the power absorbed by an element of the circuit. If we want to calculate the power absorbed by a resistor (i.e. pR1) we should remember that: pR1 ̸= pR1 + p′′ R1. However, we could use the superposition principle to calculate the current i1 and then use it to obtain the power: pR1 = i1 · R2 1 • As will be seen later in the course, the superposition principle is very important when we want to solve an AC circuit that incorporates sources of diﬀerent frequencies. 5 Application of Thevenin’s theorem for circuit analysis 5.1 Thevenin’s theorem Any linear circuit seen from two terminals can be replaced by a simpliﬁed circuit consisting of an ideal voltage source in series with a resistor. This simpliﬁed circuit is the ”Thevenin equivalent of the circuit”. uth -+ Rth Linear circuit A B A B Thevenin equivalent This means that any element (a resistor, a voltage source, a current source...anything!) connected between A and B would have identical behaviour (i.e. same current ﬂow and same voltage drop across it) if the initial circuit is considered or if the equivalent circuit is considered. It would not be possible to distinguish between the conﬁguration at the left side of the ﬁgure below and the conﬁguration at the right side of it: 19 uth -+ Rth Linear circuit A B A B element element u + -i u + -i Thevenin’s theorem has many practical application such as electronic circuits design or power system analysis. To apply Thevenin’s theorem we need to learn how to calculate the two parameters of the equivalent circuit: uth and Rth. 5.2 Determination of the Thevenin equivalent of a circuit We want to ﬁnd the Thevenin equivalent of the following circuit: ig2 R2 R1 R3 -+ ug1 A B Remember that calculating the Thevenin equivalent of the circuit means determining what couple of values uth and Rth make the behaviour of the simpliﬁed circuit represented below identical to the one of the initial circuit, from the point of view of the couple of terminals A B. uth -+ Rth A B The original circuit and the Thevenin equivalent are equivalent if any element connected between A and B behaves in the same way if we consider the original circuit or the equivalent circuit. To calculate uth and Rth we evaluate how both circuits behave under two particular situations: 1. The behaviour of the two circuits when we leave A B in open circuit (this is the same than connecting a resistance of value inﬁnite between A and B) 2. The behaviour of the two circuits when we place a short circuit between A and B (this is the same than connecting a resistor of value zero) 20 5.2.1 Calculation of the Thevenin voltage (uth): open circuit analysis Firstly, we analyse the behaviour of the equivalent circuit when the circuit is open. In that case the current ﬂowing through between A and B is null and the voltage drop across Rth is also zero. As can be seen, under this condition uAB = uth uth -+ Rth A B i=0 uAB = uth + -+ -uRth=0 Then, the analysis of the original circuit without connecting anything between A and B provides the value of uth i ig2 uAB=uth + -R2 R1 R3 -+ ug1 A B The current i is: i = ug1 R1 + R2 + R3 and the voltage between A and B: uAB = R1 · i = R1 · ug1 R1 + R2 + R3 = uth 5.2.2 Calculation of Thevenin resistance (Rth): short circuit analysis To obtain the value of Rth we analyse the behaviour of the equivalent circuit and the original circuit when a short circuit (i.e. an element of resistance 0) is placed between A and B. In that case, a short circuit current (isc) ﬂows through the circuit: uth -+ Rth A B isc = uth/Rth + -uRth=uth isc 21 It can be seen that the voltage drop across the resistor Rth equals uth (we just have to apply KVL to the circuit). Then, applying Ohm’s law: uth = Rth · isc and Rth can be calculated as a function of uth and isc: Rth = uth isc To calculate the value of isc we need to go back to the original circuit. As both circuits are equivalent we may ﬁnd isc as the current ﬂowing through a short-circuit placed between A and B: ig2 R2 R1 R3 -+ ug1 A B isc Our goal is to calculate the current isc ﬂowing from A to B. We could use any method of analysis to this end. It is easy to ﬁnd the value of isc if we consider that, as R1 is now in parallel with a short circuit it can be cancelled 5 i=0 ig2 R2 R1 R3 -+ ug1 A B isc ig2 R2 R3 -+ ug1 A B isc The current isc is: isc = ug1 R2 + R3 and then Rth = uth isc = R1 · ug1 R1 + R2 + R3 : ug1 R2 + R3 = R1 · (R2 + R3) R1 + R2 + R3 5Note that no current ﬂows through a resistor that is connected in parallel with a short circuit because all the current entering to node A would ”choose” to ﬂow through the zero-resistance path. Another way to think of it is to consider that now we have a null resistor in parallel with resistor the R1 and then the obtained equivalent resistance is zero. 22 5.2.3 Alternative method to calculate Rth: passive circuit An alternative method to calculate Rth consists of passivizing the circuit and calculate the equivalent resistance between terminals A and B. To passivize the circuit we should turn oﬀthe sources. As was explained before voltage sources are turned into short circuits and current sources into open circuits. Then the equivalent circuit and the original circuit would turn into: Rth A B Req AB = Rth -R2 R1 R3 A B Req AB=R1\|\|(R2+R3) The equivalent resistance between terminals A and B is Rth Rth = R1 · (R2 + R3) R1 + R2 + R3 5.3 Example 1 Find the Thevenin equivalent of the circuit below between terminals A and B 5 -+ -+ 2 2 4 6 V 10 V 6 A 10 A A B In this example we are requested to calculate the Thevenin equivalent of the whole circuit (ti.e including all the elements of the circuit in it). We need to calculate the parameters of the Thevenin equivalent: uth and Rth 1. Calculation of Thevenin voltage To obtain the value of Thevenin voltage we calculate the voltage drop between terminals A and B in the original circuit (uAB). We might apply mesh or nodal analysis to ﬁnd that voltage. 23 In section 3.3 the same circuit was solved using nodal analysis ﬁnding that uAB = 20V . Then: uth = uAB = 20V 2. Calculation of Thevenin resistance To calculate Rth we have two alternative methods: The calculation of the short-circuit current and the calculation of the equivalent resistance between A B in the passive circuit. (a) Method 1: Calculation of isc We place a short-circuit between A and B and calculate the current ﬂowing from A to B (isc). 5 -+ -+ 2 2 isc 6 V 10 V 6 A 10 A A B We apply nodal analysis to solve the circuit. Since the 4Ωresistor is in parallel with a short-circuit and no current will ﬂow through it and it can be eliminated from the circuit. Taking B as reference node, and considering that now uA = uB, it is easy to obtain the remaining node voltage and branch currents. 5 -+ -+ 2 2 =isc=29A 6 V 10 V 6 A 10 A A B 10=u1 -6V=u2 u3=uA=0V 3 A 8A 2A 17A 20 A As can be seen isc = 29A 24 Finally we calculate Rth as Rth = uth isc = 20 29 = 0.69Ω (b) Method 2: Calculation of ReqAB The circuit is passivized turning oﬀthe voltage and current sources and ﬁnding the following net: 5 2 2 A B 4 Seen from terminals A B, the four resistors are in parallel. In consequence we calculate Thevenin resistance as: Rth = ReqAB = 2Ω\|\|2Ω\|\|5Ω\|\|4Ω= 0.69Ω The original circuit is equivalent to the simpliﬁed Thevenin circuit whose pa-rameters have been obtained in this example: 5 -+ -+ 2 2 6 V 10 V 6 A 10 A A B uth=20V -+ Rth=0.69 A B 5.4 Example 2 Use Thevenin’s Theorem to calculate the current iR ﬂowing through the 2 Ωresistor connected between A and B. 25 2 A -+ 2 4 2 3 3 A 8 V A B iR Solution This second example shows how to apply Thevenin equivalent to the analysis of a particular element of a circuit. In this case we must not include the resistor that we want to study (the 2Ωone) in the equivalent. Then, we calculate the equivalent of the circuit that results when the resistor is removed. Once obtained the Thevenin’s equivalent of the remaining circuit we connect the 2 Ω resistor to the equivalent and calculate the requested current (iR): 2 A -+ 2 4 3 3 A 8 V A B uth -+ Rth A B iR 2 1. Calculation of uth Thevenin voltage is the voltage drop between terminals A B of the original circuit after removing the 2 Ωresistor: uth = uAB = −6 + 8 = 2V 26 2 A -+ 2 4 3 3 A 8 V A B uth=uAB + -+ - 6 V 3 A 2. Calculation of Rth (a) Method 1: Short circuit current We place a short-circuit between A and B and obtain the current that ﬂows through it. 2 A -+ 2 4 3 3 A 8 V A B isc=1A -+ - 8 V 4 A As can be seen isc = 1A. Then: Rth = uth isc = 2 1 = 2Ω (b) Method 2: Equivalent resistance As an alternative, we can ”turn oﬀ” the all the sources and calculate the equiv-alent resistance between terminals A B. 27 2 4 3 A B As the resistors of 3 and 4 Ωare in series with open circuits, the only resistor that contributes to the equivalent resistance is the 2 Ωone. Thus: Rth = ReqAB = 2Ω Finally we use the obtained Thevenin equivalent to calculate iR: uth=2V -+ Rth=2 A B iR 2 iR = uth Rth + 2 = 2 2 + 2 = 0.5A It can be noted that the obtained value of iR agrees with the calculation carried out in a previous example using mesh analysis (section 2.3). 5.5 Norton’s theorem Norton’s theorem states that ”any linear circuit can be replaced by an ideal current source in parallel with a resistor”. Linear circuit A B Norton equivalent iN RN A B For the calculation of the Norton equivalent of a circuit the sources transformation rules can be applied. 28 iN RN A B uth -+ Rth A B RN = Rth iN = uth Rth Note that iN coincides with the short circuit current of the circuit that was deﬁned in section 5.2.2 5.6 Maximum power transference theorem In some applications we want to determine the value of the resistor that extract the maximum amount of power from a circuit. This is the case of the dessign of antennas or audio systems. To ﬁnd the value of that resistor, we could redraw the circuit as its Thevenin equivalent and then calculate the R that absorbs the maximum power from the circuit. uth -+ Rth Linear circuit A B A B u + -i u + -i R R The power supplied to the resistor R is: p = R · i2 = R · u2 th (Rth + R)2 Maximizing the power we obtain that the resistor that absorbs the maximum amount of power from the circuit coincides with the circuit’s Thevenin resistance. dp dR = 0 R = Rth 29
13288	https://link.springer.com/book/10.1007/978-3-642-76894-1	Physiology and Pharmacology of the Blood-Brain Barrier \| SpringerLink Your privacy, your choice We use essential cookies to make sure the site can function. We also use optional cookies for advertising, personalisation of content, usage analysis, and social media. By accepting optional cookies, you consent to the processing of your personal data - including transfers to third parties. Some third parties are outside of the European Economic Area, with varying standards of data protection. See our privacy policy for more information on the use of your personal data. Manage preferences for further information and to change your choices. Accept all cookies Skip to main content Advertisement Log in Menu Find a journalPublish with usTrack your research Search Cart Search Search by keyword or author Search Navigation Find a journal Publish with us Track your research Home Book × Physiology and Pharmacology of the Blood-Brain Barrier Book © 1992 1st edition View latest edition Accessibility Information Overview Editors: Michael W. B. Bradbury0 Michael W. B. Bradbury Physiology Group Biomedical Sciences Division King’s College London, University of London, London, Great Britain View editor publications Search author on:PubMedGoogle Scholar Part of the book series:Handbook of Experimental Pharmacology (HEP, volume 103) 7628 Accesses 71 Citations This is a preview of subscription content, log in via an institution to check access. Access this book Log in via an institution Softcover Book USD 109.99 Price excludes VAT (USA) Compact, lightweight edition Dispatched in 3 to 5 business days Free shipping worldwide - see info Buy Softcover Book Tax calculation will be finalised at checkout Licence this eBook for your library Learn about institutional subscriptions Other ways to access Licence this eBook for your library Institutional subscriptions About this book The blood-brain barrier is still not completely understood and therefore the subject of fascinating study. How are endogenous substances transported through the blood-brain barrier? What are the known therapeutic and toxic agents? How are they transported across cerebral microvessels? The discussion of these and other questions with far-reaching consequences for all neuroscientists can be found in this volume. This authoritative and up-to-date review of the blood-brain barrier gives a proper understanding of the topic. The experimental principles, the results of very recent research, as well as the implications that experimental research has for clinical treatment are thoroughly covered. Information is given on: - new findings based on classical physiological and pharmacological techniques, - results obtained from brain capillaries in vitro and in culture, - results obtained from the new scanning techniques (PET and MRI), - the immunology of the blood-brain barrier, - trace metal transport, - the pathological breakdown of the barrier and - the modification of drugs to increase their entry into the brain. Here is a source of information that is invaluable to specialists concerned with basic research in the neurosciences, with the design of neuropharmacological agents, with the radiological diagnosis of cerebral pathology or with the treatment of cerebral lesions! Similar content being viewed by others Restoring brain barriers: an innovative approach for treating neurological disorders Article Open access 10 July 2025 Anatomy and Physiology of the Blood-Brain Barriers Chapter© 2022 The Blood–Brain Barrier: Much More Than a Selective Access to the Brain Article 22 October 2021 Explore related subjects Discover the latest articles, books and news in related subjects. Biochemistry Neurology Neurosurgery Nuclear Medicine Pharmacology Search within this book Search Table of contents (21 chapters) Front Matter Pages I-XXIII Download chapter PDF 2. Ultrastructure of Brain Endothelium M. W. Brightman Pages 1-22 Methods of Study Q. R. Smith Pages 23-52 Diffusional and Osmotic Permeability to Water P. A. Fraser Pages 53-64 Blood-Brain Glucose Transfer A. Gjedde Pages 65-115 Transport of Amino Acids J.-M. Lefauconnier Pages 117-150 Peptides and the Blood-Brain Barrier D. J. Begley Pages 151-203 The Movement of Vitamins Into the Brain O. E. Pratt Pages 205-220 Electrolyte Transport G. P. Schielke, A. L. Betz Pages 221-243 Secretion and Bulk Flow of Interstitial Fluid H. F. Cserr, C. S. Patlak Pages 245-261 Trace Metal Transport at the Blood-Brain Barrier M. W. B. Bradbury Pages 263-278 Transport of Drugs P. J. Robinson, S. I. Rapoport Pages 279-300 Clinical Assessment of Blood-Brain Barrier Permeability: Magnetic Resonance Imaging D. Barnes Pages 301-312 Clinical Assessment of the Blood-Brain Barrier: Positron Emission Tomography D. J. Brooks Pages 313-325 Ontogenetic Development of Brain Barrier Mechanisms N. R. Saunders Pages 327-369 Comparative Physiology of the Blood-Brain Barrier N. J. Abbott Pages 371-396 Immunology of Brain Endothelium and the Blood-Brain Barrier D. K. Male Pages 397-415 The Blood-Brain Barrier In Vitro and in Culture J. J. Laterra, G. W. Goldstein Pages 417-437 Opening of the Barrier in Cerebral Pathology P. J. Luthert Pages 439-457 Experimental Manipulation of the Blood-Brain ”and Blood-Retinal Barriers J. Greenwood Pages 459-486 1 2 Next page Back to top Editors and Affiliations Physiology Group Biomedical Sciences Division King’s College London, University of London, London, Great Britain Michael W. B. Bradbury Accessibility Information PDF accessibility summary This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format. Bibliographic Information Book Title: Physiology and Pharmacology of the Blood-Brain Barrier Editors: Michael W. B. Bradbury Series Title: Handbook of Experimental Pharmacology DOI: Publisher: Springer Berlin, Heidelberg eBook Packages: Springer Book Archive Copyright Information: Springer-Verlag Berlin Heidelberg 1992 Softcover ISBN: 978-3-642-76896-5 Published: 06 December 2011 eBook ISBN: 978-3-642-76894-1 Published: 06 December 2012 Series ISSN: 0171-2004 Series E-ISSN: 1865-0325 Edition Number: 1 Number of Pages: XXIV, 549 Topics: Pharmacology/Toxicology, Biochemistry, general, Neurology, Neurosurgery, Nuclear Medicine Keywords Amino acid Blood-Brain Barrier Blut-Hirn-Schranke Cerebral Capillaries Cerebral Endothelium Hirnkreislauf Permeability of Blood-Brain Barrier diagnosis neuroscience physiology positron emission tomography Publish with us Policies and ethics Back to top Access this book Log in via an institution Softcover Book USD 109.99 Price excludes VAT (USA) Compact, lightweight edition Dispatched in 3 to 5 business days Free shipping worldwide - see info Buy Softcover Book Tax calculation will be finalised at checkout Licence this eBook for your library Learn about institutional subscriptions Other ways to access Licence this eBook for your library Institutional subscriptions Sections Overview About this book Table of contents (21 chapters) Editors and Affiliations Accessibility Information Bibliographic Information Publish with us Discover content Journals A-Z Books A-Z Publish with us Journal finder Publish your research Language editing Open access publishing Products and services Our products Librarians Societies Partners and advertisers Our brands Springer Nature Portfolio BMC Palgrave Macmillan Apress Discover Your privacy choices/Manage cookies Your US state privacy rights Accessibility statement Terms and conditions Privacy policy Help and support Legal notice Cancel contracts here 34.34.225.89 Not affiliated © 2025 Springer Nature
13289	https://artofproblemsolving.com/wiki/index.php/Ceiling_function?srsltid=AfmBOorDchCmFkVqGNQHluSqQHwFDl2FxYl5ei2ucp23qC3KVzw0VemQ	Art of Problem Solving Ceiling function - AoPS Wiki Art of Problem Solving AoPS Online Math texts, online classes, and more for students in grades 5-12. Visit AoPS Online ‚ Books for Grades 5-12Online Courses Beast Academy Engaging math books and online learning for students ages 6-13. Visit Beast Academy ‚ Books for Ages 6-13Beast Academy Online AoPS Academy Small live classes for advanced math and language arts learners in grades 2-12. Visit AoPS Academy ‚ Find a Physical CampusVisit the Virtual Campus Sign In Register online school Class ScheduleRecommendationsOlympiad CoursesFree Sessions books tore AoPS CurriculumBeast AcademyOnline BooksRecommendationsOther Books & GearAll ProductsGift Certificates community ForumsContestsSearchHelp resources math training & toolsAlcumusVideosFor the Win!MATHCOUNTS TrainerAoPS Practice ContestsAoPS WikiLaTeX TeXeRMIT PRIMES/CrowdMathKeep LearningAll Ten contests on aopsPractice Math ContestsUSABO newsAoPS BlogWebinars view all 0 Sign In Register AoPS Wiki ResourcesAops Wiki Ceiling function Page ArticleDiscussionView sourceHistory Toolbox Recent changesRandom pageHelpWhat links hereSpecial pages Search Ceiling function The ceiling function, also known as the "least integer function," gives the least integer greater than or equal to its argument. The ceiling of is usually denoted by . The action of the function is also described by the phrase "rounding up." On the negative real numbers, this corresponds to the action "dropping everything after the decimal point". Examples Relation to the Floor Function For an integer, the ceiling function is equal to the floor function. For any other number, the ceiling function is the floor function plus one. See Also Floor function Fractional part Retrieved from " Category: Functions Art of Problem Solving is an ACS WASC Accredited School aops programs AoPS Online Beast Academy AoPS Academy About About AoPS Our Team Our History Jobs AoPS Blog Site Info Terms Privacy Contact Us follow us Subscribe for news and updates © 2025 AoPS Incorporated © 2025 Art of Problem Solving About Us•Contact Us•Terms•Privacy Copyright © 2025 Art of Problem Solving Something appears to not have loaded correctly. Click to refresh.
13290	https://artofproblemsolving.com/wiki/index.php/Principle_of_Inclusion-Exclusion?srsltid=AfmBOooacUfFcryQqrr26M-Bk1x89ZJ5v7Dm0Y4xFGyHUVjIRtgnVm6Y	Art of Problem Solving Principle of Inclusion-Exclusion - AoPS Wiki Art of Problem Solving AoPS Online Math texts, online classes, and more for students in grades 5-12. Visit AoPS Online ‚ Books for Grades 5-12Online Courses Beast Academy Engaging math books and online learning for students ages 6-13. Visit Beast Academy ‚ Books for Ages 6-13Beast Academy Online AoPS Academy Small live classes for advanced math and language arts learners in grades 2-12. Visit AoPS Academy ‚ Find a Physical CampusVisit the Virtual Campus Sign In Register online school Class ScheduleRecommendationsOlympiad CoursesFree Sessions books tore AoPS CurriculumBeast AcademyOnline BooksRecommendationsOther Books & GearAll ProductsGift Certificates community ForumsContestsSearchHelp resources math training & toolsAlcumusVideosFor the Win!MATHCOUNTS TrainerAoPS Practice ContestsAoPS WikiLaTeX TeXeRMIT PRIMES/CrowdMathKeep LearningAll Ten contests on aopsPractice Math ContestsUSABO newsAoPS BlogWebinars view all 0 Sign In Register AoPS Wiki ResourcesAops Wiki Principle of Inclusion-Exclusion Page ArticleDiscussionView sourceHistory Toolbox Recent changesRandom pageHelpWhat links hereSpecial pages Search Principle of Inclusion-Exclusion The Principle of Inclusion-Exclusion (abbreviated PIE) provides an organized method/formula to find the number of elements in the union of a given group of sets, the size of each set, and the size of all possible intersections among the sets. Contents [hide] 1 Important Note(!) 2 Application 2.1 Two Set Example 2.2 Three Set Example 2.3 Four Set Example 2.3.1 Problem 2.3.2 Solution 2.4 Five Set Example 2.4.1 Problem 2.4.2 Solution 3 Statement 4 Proof 5 Remarks 6 Examples 7 See also Important Note(!) When using PIE, one should understand how to strategically overcount and undercount, in the end making sure every element is counted once and only once. In particular, memorizing a formula for PIE is a bad idea for problem solving. Application Here, we will illustrate how PIE is applied with various numbers of sets. Two Set Example Assume we are given the sizes of two sets, and , and the size of their intersection, . We wish to find the size of their union, . To find the union, we can add and . In doing so, we know we have counted everything in at least once. However, some things were counted twice. The elements that were counted twice are precisely those in . Thus, we have that: . Three Set Example Assume we are given the sizes of three sets, and , the size of their pairwise intersections, , and , and the size their overall intersection, . We wish to find the size of their union, . Just like in the Two Set Example, we start with the sum of the sizes of the individual sets . We have counted the elements which are in exactly one of the original three sets once, but we've obviously counted other things twice, and even other things thrice! To account for the elements that are in two of the three sets, we first subtract out . Now we have correctly accounted for them since we counted them twice originally, and just subtracted them out once. However, the elements that are in all three sets were originally counted three times and then subtracted out three times. We have to add back in . Putting this all together gives: . Four Set Example Problem Six people of different heights are getting in line to buy donuts. Compute the number of ways they can arrange themselves in line such that no three consecutive people are in increasing order of height, from front to back. (2015 ARML I10) Solution Let be the event that the first, second, and third people are in ordered height, be the event that the second, third, and fourth people are in ordered height, be the event that the third, fourth, and fifth people are in ordered height, and be the event that the fourth, fifth and sixth people are in ordered height. By a combination of complementary counting and PIE, we have that our answer will be . Now for the daunting task of evaluating all of this. For , we just choose people and there is only one way to put them in order, then ways to order the other three guys for . Same goes for , , and . Now, for , that's just putting four guys in order. By the same logic as above, this is . Again, would be putting five guys in order, so . is just choosing guys out of , then guys out of for . Now, is just the same as , so , is so , and is so . Moving on to the next set: is the same as which is , is ordering everybody so , is again ordering everybody which is , and is the same as so . Finally, is ordering everybody so . Now, lets substitute everything back in. We get a massive expression of . Five Set Example Problem There are five courses at my school. Students take the classes as follows: 243 take algebra. 323 take language arts. 143 take social studies. 241 take biology. 300 take history. 213 take algebra and language arts. 264 take algebra and social studies. 144 take algebra and biology. 121 take algebra and history. 111 take language arts and social studies. 90 take language arts and biology. 80 take language arts and history. 60 take social studies and biology. 70 take social studies and history. 60 take biology and history. 50 take algebra, language arts, and social studies. 50 take algebra, language arts, and biology. 50 take algebra, language arts, and history. 50 take algebra, social studies, and biology. 50 take algebra, social studies, and history. 50 take algebra, biology, and history. 50 take language arts, social studies, and biology. 50 take language arts, social studies, and history. 50 take language arts, biology, and history. 50 take social studies, biology, and history. 20 take algebra, language arts, social studies, and biology. 15 take algebra, language arts, social studies, and history. 15 take algebra, language arts, biology, and history. 10 take algebra, social studies, biology, and history. 10 take language arts, social studies, biology, and history. 5 take all five. None take none. How many people are in my school? Solution Let A be the subset of students who take Algebra, L-languages, S-Social Studies, B-biology, H-history, M-the set of all students. We have: Thus, there are people in my school. Statement If are finite sets, then: . Proof We prove that each element is counted once. Say that some element is in sets. Without loss of generality, these sets are We proceed by induction. This is obvious for If this is true for we prove this is true for For every set of sets not containing with size there is a set of sets containing with size In PIE, the sum of how many times these sets are counted is There is also one additional set of sets so is counted exactly once. Remarks Sometimes it is also useful to know that, if you take into account only the first sums on the right, then you will get an overestimate if is odd and an underestimate if is even. So, , , , and so on. Examples 2011 AMC 8 Problems/Problem 6 2017 AMC 10B Problems/Problem 13 2005 AMC 12A Problems/Problem 18 2001 AIME II Problems/Problem 9 2002 AIME I Problems/Problem 1 2020 AIME II Problems/Problem 9 2001 AIME II Problems/Problem 2 2017 AIME II Problems/Problem 1 See also Combinatorics Overcounting Retrieved from " Category: Combinatorics Art of Problem Solving is an ACS WASC Accredited School aops programs AoPS Online Beast Academy AoPS Academy About About AoPS Our Team Our History Jobs AoPS Blog Site Info Terms Privacy Contact Us follow us Subscribe for news and updates © 2025 AoPS Incorporated © 2025 Art of Problem Solving About Us•Contact Us•Terms•Privacy Copyright © 2025 Art of Problem Solving Something appears to not have loaded correctly. Click to refresh.
13291	https://math.stackexchange.com/questions/482742/how-to-calculate-the-gradient-of-xt-a-x	Skip to main content Asked Modified 5 years, 11 months ago Viewed 100k times This question shows research effort; it is useful and clear 30 Save this question. Show activity on this post. I am watching the following video lecture: In there, he talks about calculating gradient of xTAx and he does that using the concept of exterior derivative. The proof goes as follows: y=xTAx dy=dxTAx+xTAdx=xT(A+AT)dx (using trace property of matrices) dy=(∇y)Tdx and because the rule is true for all dx ∇y=xT(A+AT) It seems that in step 2, some form of product rule for differentials is applied. I am familiar with product rule for single variable calculus, but I am not understanding how product rule was applied to a multi-variate function expressed in matrix form. It would be great if somebody could point me to a mathematical theorem that allows Step 2 in the above proof. Thanks! Ajay matrices multivariable-calculus derivatives differential-forms quadratic-forms Share CC BY-SA 4.0 Follow this question to receive notifications edited Sep 15, 2019 at 16:43 Rodrigo de Azevedo 23.3k77 gold badges4949 silver badges115115 bronze badges asked Sep 3, 2013 at 5:13 user855user855 46911 gold badge66 silver badges1010 bronze badges 7 Step 2 is using product rule rather than chain rule. – Shuhao Cao Commented Sep 3, 2013 at 5:16 Thanks. It's product rule indeed. But, where can I find a proof for the product rule for multivariable functions using differentials? I am not finding en.wikipedia.org/wiki/Product_rule convincing because uses the term differential very loosely. Is there a product rule proof using differential form properties? – user855 Commented Sep 3, 2013 at 5:40 2 d(fg)=∑ni=1∂(fg)∂xidxi=∑ni=1(∂f∂xig+f∂g∂xi)dxi=(∑ni=1∂f∂xidxi)g+f(∑ni=1∂g∂xidxi=gdf+fdg) – user71352 Commented Sep 3, 2013 at 5:56 thousandfold.net/cz/2013/11/12/… – venrey Commented Mar 31, 2019 at 8:20 Related: math.stackexchange.com/q/222894/339790 – Rodrigo de Azevedo Commented Sep 15, 2019 at 16:43 \| Show 2 more comments 7 Answers 7 Reset to default This answer is useful 23 Save this answer. Show activity on this post. dy=d(xTAx)=d(Ax⋅x)=d(∑i=1n(Ax)ixi)=d(∑i=1n∑j=1nai,jxjxi)=∑i=1n∑j=1nai,jxidxj+∑i=1n∑j=1nai,jxjdxi=∑i=1n(Ax)dxi+∑i=1n(Adx)xi=(dx)TAx+xTAdx=(dx)TAx+(dx)TATx=(dx)T(A+AT)x. Share CC BY-SA 4.0 Follow this answer to receive notifications edited Feb 5, 2019 at 12:48 ViktorStein 5,03466 gold badges2121 silver badges5959 bronze badges answered Sep 3, 2013 at 5:39 user71352user71352 13.2k22 gold badges2121 silver badges2929 bronze badges 5 The lecture says that using the properties of external definition of derivative, we can avoid representing it as "sums" and this simplifies the whole calculation – user855 Commented Sep 3, 2013 at 5:46 The above comments by others indicate that he applied the product rule for differentials. Unfortunately, I am unable to find a proof for the result of product rule for differentials. Any help there would be great. – user855 Commented Sep 3, 2013 at 5:47 I wonder why d(xTAx)=d(Ax⋅x) – Allan Ruin Commented Nov 21, 2015 at 1:38 13 @AllanRuin I know this is rather late but: by definition xTAx is exactly the same as taking the dot product of x with Ax. This can be written as xTAx=x⋅Ax=Ax⋅x. – NoseKnowsAll Commented Oct 13, 2016 at 6:20 What is d(x^T)? – JobHunter69 Commented Dec 10, 2024 at 0:13 Add a comment \| This answer is useful 17 Save this answer. Show activity on this post. Step 2 might be the result of a simple computation. Consider u(x)=xTAx, then u(x+h)=(x+h)TA(x+h)=xTAx+hTAx+xTAh+hTAh, that is, u(x+h)=u(x)+xT(A+AT)h+rx(h) where rx(h)=hTAh (this uses the fact that hTAx=xTATh, which holds because m=hTAx is a 1×1 matrix hence mT=m). One sees that rx(h)=o(∥h∥) when h→0. This proves that the differential of u at x is the linear function ∇u(x):Rn→R, h↦xT(A+AT)h, which can be identified with the unique vector z such that ∇u(x)(h)=zTh for every h in Rn, that is, z=(A+AT)x. Share CC BY-SA 3.0 Follow this answer to receive notifications edited Sep 3, 2013 at 6:09 answered Sep 3, 2013 at 5:51 DidDid 285k2727 gold badges332332 silver badges613613 bronze badges 0 Add a comment \| This answer is useful 12 Save this answer. Show activity on this post. Here's a method which calculates the gradient of xTAx without using the exterior derivative. I know that this is not what you are after, but it is worth noting how to prove it without the exterior derivative. This also allows for comparison with the exterior derivative method to see how much easier it is. Let A be n×n, A=[aij]. If x∈Rn, x=(x1,…,xn)T, then y=∑i=1n∑j=1naijxixj. Then we have ∂y∂xk=∑i≠k∂∂xk(∑j=1naijxixj)+∂∂xk(∑j=1nakjxkxj)=∑i≠k(∂∂xk(∑j≠kaijxixj)+∂∂xk(aikxixk))+∑j≠k∂∂xk(akjxkxj)+∂∂xk(akkx2k)=∑i≠kaikxi+∑j≠kakjxj+2akkxk=∑i=1naikxi+∑j=1nakjxj=(xTA)k+(Ax)k where (xTA)k is the kth component of the row vector xTA and (Ax)k is the kth component of the column vector Ax. By taking the transpose of Ax we obtain the row vector xTAT which has the same kth component as Ax does. Therefore ∂y∂xk=(xTA)k+(xTAT)k. Therefore ∇y=xTA+xTAT=xT(A+AT). Share CC BY-SA 3.0 Follow this answer to receive notifications answered Sep 3, 2013 at 5:58 Michael AlbaneseMichael Albanese 104k2222 gold badges225225 silver badges493493 bronze badges Add a comment \| This answer is useful 4 Save this answer. Show activity on this post. Another approach is to use a multivariable product rule. Suppose g and h are differentiable functions from Rn to Rm, and f(x)=⟨g(x),h(x)⟩ for all x∈Rn. Then if Δx∈Rn is small we have f(x+Δx)=⟨g(x+Δx),h(x+Δx)⟩≈⟨g(x)+g′(x)Δx,h(x)+h′(x)Δx⟩=⟨g(x),h(x)⟩+⟨h(x),g′(x)Δx⟩+⟨g(x),h′(x)Δx⟩+small term≈f(x)+⟨g′(x)Th(x),Δx⟩+⟨h′(x)Tg(x),Δx⟩=f(x)+⟨g′(x)Th(x)+h′(x)Tg(x),Δx⟩. This suggests that ∇f(x)=g′(x)Th(x)+h′(x)Tg(x). This is our multivariable product rule. (This derivation could be made into a rigorous proof by keeping track of error terms.) In the case where g(x)=x and h(x)=Ax, we see that ∇f(x)=Ax+ATx=(A+AT)x. (Edit) Explanation of notation: Let f:Rn→Rm be differentiable at x∈Rn. Then f′(x) is the m×n matrix defined informally by f(xn×1+Δxn×1)≈f(x)m×1+f′(x)m×nΔxn×1. (The approximation is good when Δx is small.) When f:Rn→R, f′(x) is a 1×n row vector. The gradient of f at x, defined by ∇f(x)=f′(x)T, is an n×1 column vector. Notice that, in this case, f(x+Δx)≈f(x)+f′(x)1×nΔxn×1=f(x)+⟨∇f(x),Δx⟩. Share CC BY-SA 3.0 Follow this answer to receive notifications edited Nov 21, 2015 at 9:36 answered Sep 3, 2013 at 6:24 littleOlittleO 54.2k88 gold badges106106 silver badges187187 bronze badges 5 I have some difficulties in understanding the derivations below the row ends with "+ small term" in the equation array, could you give me some hints? Thank you! – craftsman.don Commented Oct 27, 2013 at 13:34 1 I am confused by the ' in ∇f(x)=g′(x)Th(x)+h′(x)Tg(x) , is it ′=∇ ? – Allan Ruin Commented Nov 21, 2015 at 1:58 @AllanRuin I added an explanation of notation at the end, hopefully it helps. – littleO Commented Nov 21, 2015 at 9:37 can you clarify what f is? Also is x a row or a column vector? Same with x⊤ is that a row or a column vector? What are the dimensions of A? – Charlie Parker Commented May 9, 2019 at 16:26 @CharlieParker x is an n×1 column vector, xT is a 1×n row vector, A is an n×n matrix, and f(x)=xTAx=⟨x,Ax⟩. – littleO Commented Apr 19, 2021 at 20:12 Add a comment \| This answer is useful 3 Save this answer. Show activity on this post. I think it's pretty straightforward. First consider xTAx=(xT)(Ax), so that you now have xTAx as product of two functions. And it's easy to see that (xT)˙=x˙T, and (Ax)˙=Ax˙ So now you have d(xTAx)=(dx)TAx+xTA(dx), which is essentially what you want. Share CC BY-SA 4.0 Follow this answer to receive notifications answered Oct 9, 2018 at 0:40 hzhhzh 33033 silver badges1010 bronze badges Add a comment \| This answer is useful 3 Save this answer. Show activity on this post. The exterior derivative has nothing to do here. How could a student understand such a proof ! "Did" gave a good answer. The gradient ∇(f) of a function f:E→R is defined, modulo a dot product ⟨⋅,⋅⟩ on the vector-space E, by the formula ⟨∇(f)(x),h⟩=Dfx(h), where Dfx is the derivative of f in x. Example 1: Let f:x∈Rn→xTAx∈R. Then, Dfx(h)=hTAx+xTAh=xT(A+AT)h (it's the derivative of a non-commutative product!); we consider the dot product u.v=uTv. Thus, Dfx(h)=⟨((A+AT)x),h⟩ and ∇(f)(x)=(A+AT)x, that is ∇(f)=A+AT. Example 2: Let f:X∈Mn(R)→Trace(XTAX)∈R, where Mn(R) is the set of all n×n Matrices on R. Since Trace is a linear function, we have DfX(H)=Trace(HTAX+XTAH)=Trace(XT(A+AT)H); we consider the dot product ⟨U,V⟩=Trace(UTV). Thus, DfX(H)=⟨((A+AT)X),H⟩ and ∇(f)(X)=(A+AT)X, that is ∇(f)=(A+AT)⊗I. (Kronecker product). Example 3 (more difficult): Let f:X∈Mn(R)→det(X)∈R. The we have DfX(H)=Trace(adjoint(X)H)=⟨adjoint(X)T,H⟩and∇(f)(X)=adjoint(X)T. Example 4: Let f:X∈Mn(R)→XTAX∈Mn(R). Then we have DfX(H)=HTAX+XTAH. Here the gradient of f does not exist. In a pinch, we can define n2 gradients, the ∇(fi,j) (componentwise) but these functions have no geometric meanings. Share CC BY-SA 4.0 Follow this answer to receive notifications edited Feb 5, 2019 at 12:51 ViktorStein 5,03466 gold badges2121 silver badges5959 bronze badges answered Sep 4, 2013 at 17:43 user91684user91684 0 Add a comment \| This answer is useful 0 Save this answer. Show activity on this post. First consider the two ways a unknown vector can be dotted with a scalar vector to get a scalar k. k=x⃗ Ta⃗ =a⃗ Tx⃗ =[x1a1+x2a2+...+xnan]1×1 Define the derivative of scalar w.r.t to a vector in most natural manner possible. dkdx⃗ =[dkdx1,dkdx2,⋯,dkdxn]=a⃗ T1×n Now using the above, apply it to find the gradient/derivative of x⃗ TAx⃗ . Apply product rule, note that the terms in the bracket are considered as constants when differentiating. d(x⃗ TAx⃗ )dx⃗ =d((x⃗ TA)1×nx⃗ n×1)dx⃗ +d(x⃗ T(Ax⃗ ))dx⃗ Note how x⃗ TA and Ax⃗ can now be treated as a scalar vector and apply the above formula for derivative of scalar w.r.t to vector. d(x⃗ TAx⃗ )dx⃗ =(x⃗ TA)+(Ax⃗ )T=x⃗ T(A+AT) Here we can better understand the product rule at work, if we elaborate what is happening there, let A be thought of as having r⃗ 1,⋯,r⃗ n as the row vectors, each of size 1×n or being made of c⃗ 1,⋯,c⃗ n as column vectors, each of size n×1. x⃗ TAx⃗ =[x1x2⋯xn]⎡⎣⎢⎢⎢r⃗ 1r⃗ 2⋯r⃗ n⎤⎦⎥⎥⎥n×n⎡⎣⎢⎢⎢x1x2⋯xn⎤⎦⎥⎥⎥ From this we can multiple either x⃗ T to A first or A to x first, giving us 2 ways of seeing this scalar quantity, =[∑i=1nxir⃗ i]1×nx⃗ n×1=x⃗ T1×n[∑i=1nxic⃗ i]n×1 Thus we see how the two terms of A and AT appear, since in one term we have the rows and in the other we have the columns Share CC BY-SA 4.0 Follow this answer to receive notifications edited Aug 23, 2018 at 11:57 answered Aug 23, 2018 at 11:33 Aditya PAditya P 59877 silver badges2525 bronze badges Add a comment \| Start asking to get answers Find the answer to your question by asking. Ask question Explore related questions matrices multivariable-calculus derivatives differential-forms quadratic-forms See similar questions with these tags. Featured on Meta Upcoming initiatives on Stack Overflow and across the Stack Exchange network... Community help needed to clean up goo.gl links (by August 25) Linked 83 How to take the gradient of the quadratic form? 4 Differentiating second order term of Taylor polynomial (multivariable) 5 Clean/simple way of computing ∇f(UUT) with respect to U 3 Why is ∇xxTAx=2Ax? 1 Is there a clean way to derive the gradient of xTAx? i.e. ∇xxTAx? 2 The derivative of xTAx w.r.t t 2 Questions on "painless conjugate gradient": take gradient of a quadratic form 0 How to find the minimum value of f(x)=xTAx+bTx+c? 1 Partial derivatives of \|Ax−b\|2? 2 gradient of xtAy with respect of y and gradient of the Euclidean norm. 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13292	https://farelaboratorio.accademiadellescienze.it/experiences/549/additions/712	ESPERIMENTO SULLA DILATAZIONE TERMICA L’esperienza mostra che un corpo solido o fluido a contatto o vicino ad una fonte di calore si riscalda. Ma cosa comporta tale riscaldamento? Attività: I fili metallici si allungano Tempo : 30 minuti Per questo esperimento serve: • Un ferro per lavorare a maglia di metallo • due bottiglie di vetro vuote (per esempio, bottiglie di vino) • un tappo di sughero per chiudere una delle bottiglie • un set di chiavi o altri oggetti ( per appesantire un’estremità del ferro da calza) • una pila di libri (o altri oggetti per sostenere l'apparato) • un ago da cucire • una cannuccia • una candela, • alcuni fiammiferi. Obiettivo: osservare la dilatazione lineare Esecuzione Tappa una delle bottiglie lasciando fuori metà del tappo. Inserisci la punta del ferro da maglia in un lato del tappo, in modo che il ferro tocchi l’apertura della bottiglia. Appoggia l'altra estremità del ferro da calza sulla bocca della seconda bottiglia. Fai passare l'ago per cucire attraverso la cannuccia, per un terzo della sua lunghezza: il foro deve essere abbastanza piccolo in modo tale che la cannuccia non può muoversi intorno all'ago. Appoggia l'ago per cucire (con cannuccia) sulla bocca della seconda bottiglia, sotto il ferro da calza e perpendicolarmente ad esso. Appendi un peso (ad esempio chiavi) sull'estremità libera del ferro da calza. Punta la cannuccia verso il basso. Posiziona una pila di libri tra le due bottiglie. Posiziona la candela in cima alla pila di libri. Regola l'altezza della pila in modo che la parte superiore della candela sia posizionata a circa 3 cm dal ferro da calza. Accendi la candela. domande Cosa succede alla cannuccia? Perché si muove? EXPLAINE Il calore fornito dalla candela al ferro da calza, lo fa dilatare. Quando questo si allunga, fa spostare l'ago per cucire. La cannuccia amplifica i piccoli movimenti dell'ago per cucire. Il fenomeno della dilatazione termica lineare, caratteristico di tutti i corpi solidi, consiste nell'allungamento di una sbarretta del materiale in esame. L’allungamento risulta essere direttamente proporzionale all'aumento della temperatura. Per tutti i solidi la dilatazione termica lineare è espressa da una legge sperimentale, secondo la quale se L o è la lunghezza della sbarretta alla temperatura T = 0 °C, la lunghezza L alla generica temperatura T sarà data dalla relazione: )1(0 t λ+= ℓℓ , dove λ è detto coefficiente di dilatazione lineare , il cui valore varia a seconda della sostanza ( ). Su questa legge si basano i termometri a dilatazione. Per avere un'idea della dilatazione lineare nei materiali, si pensi che una sbarra lunga 1 m di un qualsiasi materiale si allunga di circa 1 mm se la sua temperatura aumenta di 100 °C .Attività: Le superfici si allargano Tempi : 20 minuti Per questo esperimento serve: • una moneta da 5 centesimi (monetine da 5 e 10 lire in lega di alluminio) • un filo di ferro a cui dai la forma di anello con un diametro leggermente maggiore di quello della moneta: la moneta deve passare attraverso l’anello • una pinza • un fornellino Obiettivo: osservare la dilatazione superficiale Esecuzione Dopo aver verificato che la moneta passa attraverso l’anello, si riscalda la moneta sul fornellino per quindici minuti tenendola con la pinza. Poi si verifica, rapidamente, che la moneta riscaldata non passa più attraverso l’anello. Domanda Che cosa è successo? Perché la moneta non attraversa più l’anello? EXPLAINE Il riscaldamento della moneta ha prodotto un aumento delle sue dimensioni. Per questo motivo essa non riesce più ad attraversare il foro metallico. Il fenomeno della dilatazione termica superficiale, caratteristico di tutti i corpi, consiste nell'aumento della superficie di un corpo in esame dovuto all'aumento della temperatura. Per tutti i corpi la dilatazione superficiale èespressa da una legge sperimentale, secondo la quale se A o è la superficie iniziale del corpo alla temperatura T = 0 °C, allora la superficie A, alla generica temperatura T sarà data dalla relazione: )21(0 tAA λ+= dove λ è il coefficiente di dilatazione lineare. È grazie a queste proprietà che, in una pavimentazione, bisogna lasciare margini ben definiti. In particolare le pavimentazioni stradali devono essere costruite con piccole sezioni, onde evitare deformazioni. Domande Ora se nella moneta viene fatto un foro, in caso di aumento della temperatura della moneta, come si comporta il foro? Si allarga o si restringe? Perché? Attività: I solidi si ingrossano Tempi : 20 minuti Per questo esperimento servono: • due ditalini di metallo uno di dimensione leggermente maggiore dell’altro • una pinza • un fornellino Obiettivo: osservare la dilatazione volumica nei solidi Esecuzione Dopo aver verificato che i due ditalini si inseriscono uno dentro l’altro, quasi perfettamente, mettiamo il ditalino più piccolo sul fornellino per circa 15 minuti. Il ditalino riscaldato lo inseriamo rapidamente in quello più grande: ora i due ditalini non si incastrano più perfettamente (Video I ditali) Domanda Che cosa è successo? Perché i due ditalini non si incastrano più perfettamente? EXPLAINE Il riscaldamento del ditalino ha prodotto un piccolo aumento delle sue dimensioni, per cui esso non riesce più ad incastrarsi in quello più grande. Il fenomeno della dilatazione termica volumica, caratteristico di tutti i corpi, consiste nell'aumento di volume di un corpo in esame dovuto all'aumento della temperatura. Per tutti i corpi la dilatazione volumica è espressa da una legge, secondo la quale se V o è il volume iniziale del corpo alla temperatura T = 0 °C, allora il volume V alla generica temperatura T sarà data dalla relazione: V = V 0(1+ α t) dove α è detto coefficiente di dilatazione volumica. Lo stesso esperimento può essere ripetuto con una pallina metallica e un anello. Il riscaldamento della pallina produce un aumento delle sue dimensioni. Per questo motivo essa non riesce più ad attraversare il foro metallico. Attività: Il palloncino si gonfia Tempi : 15 minuti Per questo esperimento serve: • una bottiglia di vetro; • palloncini; • un fornellino; • un contenitore metallico; • acqua. Obiettivo: osservare la dilatazione volumica dei gas Esecuzione Prendiamo la bottiglia di vetro e infiliamo sulla sua apertura un palloncino sgonfio (a). Poi poniamo la bottiglia nell’acqua molto calda, dopo un po’ di tempo il palloncino inizia a gonfiarsi (b). Domande Il palloncino si gonfia, perché? Cosa c’è nella bottiglia che fa gonfiare il palloncino? EXPLAINE Nella bottiglia c’è aria. L’aria, riscaldata, aumenta di volume facendo gonfiare il palloncino. La legge che regola sempre quella della dilatazione volumica V = V0(1+ α t) dove α è fisso per tutti i gas , e vale 1/273,15 K -1 e l’espansione dei gas è molto maggiore rispetto a quella dei solidi e dei liquidi. Domande Ora se mettiamo una pallina da ping-pong ammaccata nell’acqua in ebollizione, cosa si può notare? L’ammaccatura scompare? Perché? Questo lo si può verificare tranquillamente a casa. Quindi se riscaldiamo un volume d’aria, esso si espande. Ma se espandiamo un volume d’aria essa si riscalda o si raffredda? Perché? Ma ci si può chiedere se oltre al calore, c’è ancora qualcosa che può far aumentare le dimensioni di un palloncino. APPROFONDIMENTO Video sul comportamento dei gas: ; dal video emerge che anche la pressione gioca un ruolo nella dilatazione dei gas. Caratterizziamo meglio il concetto di pressione di un gas, dicendo che, a livello microscopico, è legato agli urti che le particelle hanno contro le pareti del recipiente che le contiene. domande Ora sarebbe corretto dire che la causa per cui un gas si riscalda è il fatto che le sue molecole si urtano più frequentemente? Cosa è più corretto dire che le molecole si urtano più frequentemente, perché il gas si riscalda, oppure che il gas si riscalda perché le sue molecole si urtano più velocemente? La risposta è celata nella definizione data di temperatura. Ricordiamo che essa è un indice delle loro energie cinetiche, non delle loro frequenze d’urto. Attività: I liquidi aumentano di livello Tempi : 30 minuti Per questo esperimento serve: • due bottigliette di vetro con tappo di plastica in cui è facile praticare dei fori o sughero; • due cannucce trasparenti; • acqua colorata; • olio; • una vaschetta che può contenere ambedue le bottiglie; • plastilina e acqua calda. Obiettivo: osservare la dilatazione volumica dei liquidi Esecuzione Riempi completamente le due bottigliette rispettivamente con l’acqua colorata e l’olio, chiudi le bottiglie con i tappi in cui hai inserito le cannucce trasparenti, metti la plastilina tra la cannuccia e il tappo in modo da impedire ai liquidi di fuoriuscire. Metti le due bottigliette nella vaschetta, riempi questa con acqua molto calda e aspetta qualche minuto. Domande Cosa osservi? (Video Esperimento sui liquidi) In liquido è salito nelle cannucce ma il livello raggiunto è differente. Come spieghi quanto hai osservato? Foto da internet EXPLAINE Anche per i liquidi, se riscaldati, si osserva un aumento di volume. I livelli raggiunti dall’acqua colorata e dall’olio sono differenti. I due liquidi pur avendo lo stesso volume iniziale, pur sottoposti alla stessa variazione di temperatura subiscono dilatazioni diverse. Per un approfondimento vedere il sito .
13293	https://pdg.lbl.gov/2024/reviews/rpp2024-rev-sum-neutrino-masses.pdf	Sum of neutrino masses 1 Sum of Neutrino Masses Revised August 2023 by K.A. Olive (University of Minnesota). Neutrinos decouple from thermal equilibrium in the early universe at temperatures O(1) MeV. The limits on low mass (mν < ∼1 MeV) neutrinos apply to mtot given by mtot = X ν mν . Stable neutrinos in this mass range decouple from the thermal bath while still relativistic and make a contribution to the total energy density of the Universe which is given by ρν = mtotnν ≃mtot(3/11)(3.045/3)3/4nγ , where the factor 3/11 is the ratio of (light) neutrinos to photons and the factor (3.045/3)3/4 corrects for the fact that the eﬀective number of neutrinos in the standard model is 3.045 when taking into account e+e−annihilation during neutrino decoupling. Writing Ων = ρν/ρc, where ρc is the critical energy density of the Universe, and using nγ = 410.7 cm−3, we have Ωνh2 ≃mtot/(93 eV) . While an upper limit to the matter density of Ωmh2 < 0.12 would constrain mtot < 11 eV, much stronger constraints are obtained from the observations of the CMB, combined with lensing and baryon acoustic oscillations data. These combine to give an upper limit of around 0.12 eV, and may, in the near future, be able to provide a lower bound on the sum of the neutrino masses. The current lower bound of mtot > 0.06 eV implies a lower limit of Ωνh2 > 6 × 10−4. See our review on ”Neutrinos in Cosmology” for more details. S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024) May 31, 2024 10:21
13294	https://www.youtube.com/watch?v=uj6k22WubCk	Area of Parallelograms \| How to Find the Area of a Parallelogram Math with Mr. J 1710000 subscribers 5414 likes Description 841185 views Posted: 22 Mar 2020 Welcome to Area of Parallelograms with Mr. J! Need help with how to find the area of a parallelogram? You're in the right place! Whether you're just starting out, or need a quick refresher, this is the video for you if you need help with parallelogram area. Mr. J will go through area of parallelograms examples and explain how to calculate the area of a parallelogram step by step. About Math with Mr. J: This channel offers instructional videos and mastery checks (practice videos to gauge understanding) that are directly aligned with math standards (5th grade, 6th grade, 7th grade, etc.). Videos can be used to introduce content, reteach content, or as a study tool. Teachers, parents/guardians, and students from around the world have used this channel to help with math content in many different ways. All material is absolutely free. Click Here to Subscribe to the Greatest Math Channel On Earth: Follow Mr. J on Twitter: @MrJMath5 Email: math5.mrj@gmail.com Music: Hopefully this video is what you're looking for when it comes to area of parallelograms. Have a great rest of your day and thanks again for watching! 468 comments Transcript: Intro welcome to math with mr. J in this video I'm going to be going through how to find the area of a parallelogram and up top we have the formula that we're going to use area equals base times height and we're going to talk a little bit about why that formula works so let's jump in the number one here the first of four examples that we'll go through together in order to get this down so for number one the first thing I always like to do I always like to write out my formula for each problem then we will plug in the base and height and lastly write our answer so again the formula is area equals base times height so our base is this five feet here so plug in the five for the base times this height of two feet now that line in the parallelogram there is not part of that shape it's just there to represent that height of two feet so formula plug in and now we write our answer for the area five times two gives us an area of ten and this is square feet so when we take a look at a Area of a Rectangle parallelogram it kind of looks like a rectangle it just doesn't have those four 90-degree angles and when we find the area of a rectangle we either use area equals base times height or length times width so essentially we're doing the same thing here and this is how it works if we were to take this portion of the parallelogram and move it over to the right side kind of like a puzzle piece we would actually now have a rectangle so we didn't change any of the measurements and we're still able to use the area equals base times height to give us the area an answer for a parallelogram so we're doing the same thing we do with rectangles and that's why so number two let's write out our formula area equals base times height we will plug in the base of 10 times the height of seven again this line here is not part of the shape it's just there to represent that seven inches so we get an area of seventy square inches next number three let's write out our formula area equals base times height plug in the base here is Area of a Base this 14 it's okay that it's up top the measurement this bottom side is the same it's congruent to the top so it doesn't matter where the measurement is listed so 14 times a height of two and we get an area of 28 square meters and then lastly we have a base of six centimeters so let's write out our formula base times height plug in our base of six times our height of nine and we get an answer of 54 square centimeters so there Outro you have it there's how you find the area of a parallelogram area equals base times height and just a reminder if you take a look at number three it works because if we take a portion of our parallelogram and move it to the other side it'll actually give us a rectangle that line doesn't perfectly line up but hopefully you kind of see the point there where I'm going with things so this would be our rectangle here okay so hopefully that helped thanks so much for watching until next time peace
13295	https://forum.image.sc/t/find-area-of-contact-using-imagej/112812	Find area of contact using ImageJ - Image Analysis - Image.sc Forum This website uses cookies to ensure you get the best experience on our website. Learn more Got it! Skip to main content zulipchat-light relatedforums-light zulipchat-dark relatedforums-dark Sign Up Log In Topics Upcoming Events More Categories Announcements Development Image Analysis Job Opportunities Usage & Issues All categories Tags imagej fiji cellprofiler qupath macro All tags Community Partners All Topics AGAVE AICSImageIO Aydin BAND BIAFLOWS BiaPy BiofilmQ Bio-Formats BioImageIO BoneJ BrainGlobe CAREamics Cell-ACDC Cellpose CellProfiler CLIJ CytoMAP Cytomine DAIM DeepLabCut Fiji FLIMLib GerBI GloBIAS Icy IDR ilastik ImageC ImageJ ImageJ2 ImgLib2 ImJoy iRODS JIPipe Mars MCMICRO mesoSPIM MIA MIB μManager μSAM Microscopy Nodes MoBIE ModularImageAnalysis MorphoGraphX MorphoNet napari NFDI4BIOIMAGE OME OMERO OpenSPIM Orbit Piximi PolusAI PYME Python-Microscope QUAREP-LiMi QuPath SBEMimage scenery SCIFIO scikit-image sciview SmartMicroscopy SpotMAX StarDist TeamTomo TissUUmaps vedo webKnossos ZeroCostDL4Mic Your Icon Here Dormant Partners Sponsored by Related Communities Find area of contact using ImageJ Image Analysis fiji,segmentation You have selected 0 posts. select all cancel selecting 70 views 3 3 May 25 1 / 7 May 25 May 28 Monami Bhuyan May 25 Background Cockraoch_1_Before_10mN_0.3 752×480 186 KB Here I have attached a picture of a brightfield microscopy image to analyse and measure the area of the dark region which is the area of contact when a glass slide moves across a small insect sample. I am trying to use Fiji ImageJ2 to try to do the same. Your analysis goals I am fairly new to ImageJ and I have tried a bunch of trials and errors but I am never able to finf the right threshold limits. I tried cropping the image, inverting and gaussian filters as well as different threshold methods. Any suggestions would be highly appreciated. 70 views 3 3 Guenter Pudmichgupu May 25 Welcome @Monami_Bhuyan If the “area of contact” is only the sharp area it can be roughly isolated from the out-of-focus area by variance auto selectImage("Cockraoch_1_Before_10mN_0.3.png"); run("Duplicate...", "title=var8"); run("32-bit"); // expand numerical range run("Variance...", "radius=8"); // variance filter with radius 8 pixel setAutoThreshold("Default dark no-reset"); setOption("BlackBackground", true); run("Convert to Mask"); run("Create Selection"); selectImage("Cockraoch_1_Before_10mN_0.3.png"); run("Restore Selection"); to get this Result 402×300 61.3 KB Monami Bhuyan May 25 Hi @gupu thank you so much for your help. This is almost what I want. However, in your suggested solution, there are areas (the little dots outside the bigger blob) which are just specks on the glass surface. Is there a way to isolate those? Additionally, inside the larger sharp area, the points of contact are the darker black regions. Should I be able to measure those specific regions? Thanks in advance. 2 Replies Reply Related topics Topic list, column headers with buttons are sortable.\| Topic \| Replies \| Views \| Activity \| --- --- \| \| Getting accurate results Image Analysis imagej,fiji \| 5 \| 504 \| Jun 2018 \| \| Threshold and area of particles Image Analysis imagej \| 1 \| 1.2k \| Jul 2017 \| \| Best way to objectively select area of interest using images with different levels of brightness Image Analysis imagej \| 8 \| 3.1k \| Jul 2018 \| \| Selecting and measuring area and pigment value of dark areas in image Image Analysis imagej \| 3 \| 2.7k \| Nov 2016 \| \| Inconsistent area measurements Image Analysis imagej \| 5 \| 4.2k \| Jun 2017 \| Invalid date Invalid date
13296	https://ucilnica2223.fmf.uni-lj.si/mod/resource/view.php?id=60721	Spletna učilnica FMF 2022/23: Log in to the site Skip to main content To je arhiv spletne učilnice za leto 2022/23. Aktualna spletna učilnica je na naslovu Spletna učilnica FMF 2022/23 Skip to create new account Username Password [x] Remember username Log in Forgotten your username or password? Cookies must be enabled in your browser Some courses may allow guest access Log in as a guest Is this your first time here? Predavatelji in asistenti:prijavite se z univerzitetno identiteto, ki ima uporabniško ime praviloma oblikeime.priimek@fmf.uni-lj.si. Študenti:prijavite se z univerzitetno identiteto, ki ima uporabniško ime praviloma oblikeab1234@student.uni-lj.si. Vsi brez univerzitetne identitete:uporabniški račun si ustvarite sami.Uporabniško ime naj bo oblike imepriimek, da bomo lahko uporabniška imena povezali s pravimi ljudmi na predavanjih in vajah. Ostala uporabniška imena znamo brez opozorila pobrisati. Študenti, ki imajo univerzitetno uporabniško ime, morajo uporabljati le tega in se ne smejo samoregistrirati z novim uporabniškim imenom. Kazen bo vzgojna. Create new account You are not logged in. Home Data retention summary Get the mobile app
13297	https://www.barnesandnoble.com/w/nomenclature-of-inorganic-chemistry-neil-g-connelly/1143852697	true 500 × Uh-oh, it looks like your Internet Explorer is out of date. For a better shopping experience, please upgrade now. Nomenclature of Inorganic Chemistry: IUPAC Recommendations 2005 The Rules of Inorganic Nomenclature (the 'Red Book'), first published in 1958 by the International Union of Pure and Applied Chemistry (IUPAC), was most recently updated as Nomenclature of Inorganic Chemistry 1990. This new edition of the Red Book clarifies and updates recommendations concerning the names and formulae of inorganic compounds and reflects major recent developments in inorganic chemistry. Moreover, it presents recommendations fully consistent with the principles of the nomenclature of organic chemistry. In order to choose the most appropriate of the various nomenclature systems described, a flowchart is provided to guide the reader to a section or chapter where rules can be found for a particular type of compound or species. Copious examples are supplemented by an extensive subject index. Nomenclature of Inorganic Chemistry: Recommendations 2005 is the definitive guide for scientists working in academia or industry, for scientific publishers of books, journals and databases, and for organisations requiring internationally approved nomenclature in a legal or regulatory environment. 1143852697 Nomenclature of Inorganic Chemistry: IUPAC Recommendations 2005 The Rules of Inorganic Nomenclature (the 'Red Book'), first published in 1958 by the International Union of Pure and Applied Chemistry (IUPAC), was most recently updated as Nomenclature of Inorganic Chemistry 1990. This new edition of the Red Book clarifies and updates recommendations concerning the names and formulae of inorganic compounds and reflects major recent developments in inorganic chemistry. Moreover, it presents recommendations fully consistent with the principles of the nomenclature of organic chemistry. In order to choose the most appropriate of the various nomenclature systems described, a flowchart is provided to guide the reader to a section or chapter where rules can be found for a particular type of compound or species. Copious examples are supplemented by an extensive subject index. Nomenclature of Inorganic Chemistry: Recommendations 2005 is the definitive guide for scientists working in academia or industry, for scientific publishers of books, journals and databases, and for organisations requiring internationally approved nomenclature in a legal or regulatory environment. 70.0 In Stock 5 1 Nomenclature of Inorganic Chemistry: IUPAC Recommendations 2005 378 by Neil G Connelly (Editor), Ture Damhus (Editor), Richard M Hartshorn (Editor), Alan T Hutton (Editor) Neil G Connelly View More \| Editorial Reviews Add to Wishlist Nomenclature of Inorganic Chemistry: IUPAC Recommendations 2005 378 by Neil G Connelly (Editor), Ture Damhus (Editor), Richard M Hartshorn (Editor), Alan T Hutton (Editor) Neil G Connelly View More \| Editorial Reviews Hardcover $70.00 Learn more SHIP THIS ITEM In stock. Ships in 3-7 days. Typically arrives in 3 weeks. PICK UP IN STORE Your local store may have stock of this item. Available within 2 business hours Want it Today? Check Store Availability Related collections and offers English 0854044388 70.0 In Stock Overview The Rules of Inorganic Nomenclature (the 'Red Book'), first published in 1958 by the International Union of Pure and Applied Chemistry (IUPAC), was most recently updated as Nomenclature of Inorganic Chemistry 1990. This new edition of the Red Book clarifies and updates recommendations concerning the names and formulae of inorganic compounds and reflects major recent developments in inorganic chemistry. Moreover, it presents recommendations fully consistent with the principles of the nomenclature of organic chemistry. In order to choose the most appropriate of the various nomenclature systems described, a flowchart is provided to guide the reader to a section or chapter where rules can be found for a particular type of compound or species. Copious examples are supplemented by an extensive subject index. Nomenclature of Inorganic Chemistry: Recommendations 2005 is the definitive guide for scientists working in academia or industry, for scientific publishers of books, journals and databases, and for organisations requiring internationally approved nomenclature in a legal or regulatory environment. You May Also Like Add to Wishlist QUICK ADD Uniform Output Regulation of Nonlinear Systems: A Convergent Dynamics Approach by Alexey Victorovich Pavlov Add to Wishlist QUICK ADD Microbial Enzymes and Biotransformations by Jose Luis Barredo Add to Wishlist QUICK ADD Modern Heuristic Search Methods by V. J. Rayward-Smith Add to Wishlist QUICK ADD Electronic Composites: Modeling, Characterization, Processing, and MEMS Applications by Minoru Taya Add to Wishlist QUICK ADD Quantitative Feedback Design of Linear and Nonlinear Control Systems by Oded Yaniv Add to Wishlist QUICK ADD Mathematics of Large Eddy Simulation of Turbulent Flows by Luigi Carlo Berselli Add to Wishlist QUICK ADD Food Flavor and Chemistry: Explorations Into The 21st Century by Cynthia Mussinan Add to Wishlist QUICK ADD Radiation Effects on Embedded Systems by Raoul Velazco Product Details Table of Contents What People Are Saying Product Details \| \| \| --- \| \| ISBN-13: \| 9780854044382 \| \| Publisher: \| RSC \| \| Publication date: \| 11/22/2005 \| \| Pages: \| 378 \| \| Product dimensions: \| 10.85(w) x 8.60(h) x (d) \| Table of Contents 1: General Aims, Functions and Methods of Chemical Nomenclature; 1.1: Introduction; 1.2: History of chemical nomenclature; 1.3: Aims of chemical nomenclature; 1.4: Functions of chemical nomenclature; 1.5: Methods of inorganic nomenclature; 1.6: Changes to previous IUPAC recommendations; 1.7: Nomenclature recommendations in other areas of chemistry; 1.8: References; 2: Grammar; 2.1: Introduction; 2.2: Enclosing marks; 2.3:Hyphens, plus and minus signs, 'em' dashes and bond indicators; 2.4: Solidus; 2.5: Dots, colons, commas and semicolons; 2.6: Spaces; 2.7: Elisions; 2.8: Numerals; 2.9: Italic letters; 2.10: Greek alphabet; 2.11: Asterisks; 2.12: Primes; 2.13: Multiplicative prefixes; 2.14: Locants; 2.15: Ordering principles; 2.16: Final remarks; 2.17: References; 3: Elements;3.1: Names and symbols of atoms; 3.2: Indication of mass, charge and atomic number using indexes (subscripts and superscripts); 3.3: Isotopes; 3.4: Elements (or elementary substances); 3.5: Elements in the periodic table; 3.6: References; 4: Formulae; 4.1: Introduction; 4.2: Definitions of types of formula; 4.3: Indication of ionic charge; 4.4: Sequence of citation of symbols in formulae; 4.5: Isotopically modified compounds; 4.6: Optional modifiers of formulae; 4.7: References; 5: Compositional Nomenclature, and Overview of Names of Ions and Radicals; 5.1: Introduction; 5.2: Stoichiometric names of elements and binary compounds; 5.3: Names of ions and radicals; 5.4: Generalized stoichiometric names; 5.5: Names of (formal) addition compounds; 5.6: Summary; 5.7: References; 6: Parenthydride Names and Substitutive Nomenclature; 6.1: Introduction; 6.2: Parent hydride names; 6.3: Substitutive names of derivatives of parent hydrides; 6.4: Names of ions and radicals derived from parent hydrides; 6.5: References; 7: Additive Nomenclature; 7.1: Introduction; 7.2: Mononuclear entities; 7.3: Polynuclear entities; 7.4: Inorganic chains and rings; 7.5: References; 8: Inorganic Acids and Derivatives; 8.1: Introduction and overview; 8.2: General principles for systematic naming of acids; 8.3: Additive names; 8.4: Hydrogen names; 8.5: Abbreviated hydrogen names for certain anions; 8.6: Functional replacement names for derivatives of oxoacids; 8.7: References; 9: Coordination Compounds; 9.1: Introduction; 9.2: Describing the constitution of coordination compounds; 9.3: Describing the configuration of coordination entities; 9.4: Final remarks; 9.5: References; 10: Organometallic Compounds; 10.1: Introduction; 10.2: Nomenclature of organometallic compounds of the transition elements; 10.3: Nomenclature of organometallic compounds of the main group elements; 10.4: Ordering of central atoms in polynuclear organometallic Compounds; 10.5: References; 11: Solids; 11.1: Introduction; 11.2: Names of solid phases; 11.3: Chemical composition; 11.4: Point defect (Kroeger-Vink) notation; 11.5: Phase nomenclature; 11.6: Non-stoichiometric phases; 11.7: Polymorphism; 11.8: Final remarks; 11.9: References; Tables; Table I: Names, symbols and atomic numbers of the elements; Table II: Temporary names and symbols for elements of atomic number greater Than 111; Table III: Suffixes and endings; Table IV: Multiplicative prefixes; Table V: Geometrical and structural affixes; Table VI: Element sequence; Table VII: Ligand abbreviations; Table VIII: Structural formulae of selected ligands; Table IX: Names of homoatomic, binary and certain other simple molecules, ions, compounds, radicals and substituent groups; Table X: Anion names, 'a' terms used in substitutive nomenclature and 'y' terms used in chains and rings nomenclature Show More What People are Saying About This From the Publisher Perhaps the most significant addition to the recommendations is the chapter on the nomenclature of organometallic compounds. The Red Book can help chemists create names from structures, or decipher names to give structures. 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13298	https://pressbooks.pub/linearalgebraandapplications/chapter/rank-one-matrices-2/	Skip to content Want to create or adapt books like this? Learn more about how Pressbooks supports open publishing practices. Rank-one matrices Recall that the rank of a matrix is the dimension of its range. A rank-one matrix is a matrix with rank equal to one. Such matrices are also called dyads. We can express any rank-one matrix as an outer product. Theorem: outer product representation of a rank-one matrix \| \| \| Every rank-one matrix can be written as an ‘‘outer product’’, or dyad: where . \| \| \| The interpretation of the corresponding linear map for a rank-one matrix is that the output is always in the direction , with coefficient of proportionality a linear function of . We can always scale the vectors and in order to express as where , , with and . The interpretation for the expression above is that the result of the map for a rank-one matrix can be decomposed into three steps: we project on the -axis, getting a number ; we scale that number by the positive number ; we lift the result (which is the scalar to get a vector proportional to . See also: Single factor model of financial price data.
13299	https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_(Tradler_and_Carley)/18%3A_Addition_of_Angles_and_Multiple_Angles/18.01%3A_Addition_and_subtraction_of_angles	18.1: Addition and subtraction of angles - Mathematics LibreTexts Skip to main content Table of Contents menu search Search build_circle Toolbar fact_check Homework cancel Exit Reader Mode school Campus Bookshelves menu_book Bookshelves perm_media Learning Objects login Login how_to_reg Request Instructor Account hub Instructor Commons Search Search this book Submit Search x Text Color Reset Bright Blues Gray Inverted Text Size Reset +- Margin Size Reset +- Font Type Enable Dyslexic Font - [x] Downloads expand_more Download Page (PDF) Download Full Book (PDF) Resources expand_more Periodic Table Physics Constants Scientific Calculator Reference expand_more Reference & Cite Tools expand_more Help expand_more Get Help Feedback Readability x selected template will load here Error This action is not available. 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Precalculus (Tradler and Carley) 5. 18: Addition of Angles and Multiple Angles 6. 18.1: Addition and subtraction of angles Expand/collapse global location Precalculus (Tradler and Carley) Front Matter 1: The Absolute Value 2: Lines and Functions 3: Functions by Formulas and Graphs 4: Introduction to the TI-84 5: Basic Functions and Transformations 6: Operations on Functions 7: The Inverse of a Function 8: Dividing Polynomials 9: Graphing Polynomials 10: Roots of Polynomials 11: Rational Functions 12: Polynomial and Rational Inequalities 13: Exponential and Logarithmic Functions 14: Properties of Exponentials and Logarithms 15: Applications Exponentials and Logarithms 16: Half-life and Compound Interest 17: Trigonometric Functions 18: Addition of Angles and Multiple Angles 19: Inverse Trigonometric Functions 20: Trigonometric Equations 21: Complex Numbers 22: Vectors in the Plane 23: Sequences and Series 24: The Geometric Series 25: The Binomial Theorem 26: Appendix A - Introduction to the TI-84 27: Reviews Back Matter 18.1: Addition and subtraction of angles Last updated May 2, 2022 Save as PDF 18: Addition of Angles and Multiple Angles 18.2: Double and half angles picture_as_pdf Full Book Page Downloads Full PDF Import into LMS Individual ZIP Buy Print Copy Print Book Files Buy Print CopyReview / Adopt Submit Adoption Report View on CommonsDonate Page ID 49066 Thomas Tradler and Holly Carley CUNY New York City College of Technology via New York City College of Technology at CUNY Academic Works ( \newcommand{\kernel}{\mathrm{null}\,}) Table of contents 1. Proposition: Addition and Subtraction of Angles Formulas 2. Example 18.1.1 3. Note 4. Example 18.1.2 In the previous section we found exact values of the trigonometric functions for specific angles of 0,π 3,π 4,π 6 plus possibly any multiple of π 2. Using these values, we can find many other values of trigonometric functions via the following addition and subtraction of angles formulas, which we state now. Proposition: Addition and Subtraction of Angles Formulas For any angles α and β, we have: sin⁡(α+β)=sin⁡α⁢cos⁡β+cos⁡α⁢sin⁡β sin⁡(α−β)=sin⁡α⁢cos⁡β−cos⁡α⁢sin⁡β cos⁡(α+β)=cos⁡α⁢cos⁡β−sin⁡α⁢sin⁡β cos⁡(α−β)=cos⁡α⁢cos⁡β+sin⁡α⁢sin⁡β tan⁡(α+β)=tan⁡α+tan⁡β 1−tan⁡α⁢tan⁡β tan⁡(α−β)=tan⁡α−tan⁡β 1+tan⁡α⁢tan⁡β Proof We start with the proof of the formulas for sin⁡(α+β) and cos⁡(α+β) when α and β are angles between 0 and π 2=90∘. We prove the addition formulas (for α,β∈(0,π 2)) in a quite elementary way, and then show that the addition formulas also hold for arbitrary angles α and β. To find sin⁡(α+β), consider the following setup. Note, that there are vertically opposite angles, labelled by γ, which are therefore equal. These angles are angles in two right triangles, with the third angle being α. We therefore see that the angle α appears again as the angle among the sides b and f. With this, we can now calculate sin⁡(α+β). sin⁡(α+β)=opposite hypotenuse=e+f d=e d+f d=a d+f d=a c⋅c d+f b⋅b d=sin⁡(α)⁢cos⁡(β)+cos⁡(α)⁢sin⁡(β) The above figure displays the situation when α+β≤π 2. There is a similar figure for π 2<α+β<π. (We recommend as an exercise to draw the corresponding figure for the case of π 2<α+β<π.) Next, we prove the addition formula for cos⁡(α+β). The following figure depicts the relevant objects. We calculate cos⁡(α+β) as follows. cos⁡(α+β)=adjacent hypotenuse=g d=g+h d−h d=g+h d−k d=g+h c⋅c d−k b⋅b d=cos⁡(α)⁢cos⁡(β)−sin⁡(α)⁢sin⁡(β) Again, there is a corresponding figure when the angle α+β is greater than π 2. (We encourage the student to check the addition formula for this situation as well.) We therefore have proved the addition formulas for sin⁡(α+β) and cos⁡(α+β) when α and β are angles between 0 and π 2, which we will now extend to all angles α and β. First, note that the addition formulas are trivially true when α or β are 0. (Check this!) Now, by observing that sin⁡(x) and cos⁡(x) can be converted to each other via shifts of π 2, (or, alternatively, by using the identities [EQU:basic-trig-eqns-wrt-pi] and [EQ:cos=sin+pi2]), we obtain, that sin⁡(x+π 2)=cos⁡x,cos⁡(x+π 2)=−sin⁡(x),sin⁡(x−π 2)=−cos⁡x,cos⁡(x−π 2)=sin⁡(x). With this, we extend the addition identities for α by ±π 2 as follows: sin⁡((α+π 2)+β)=sin⁡(α+β+π 2)=cos⁡(α+β)=cos⁡(α)⁢cos⁡(β)−sin⁡(α)⁢sin⁡(β)=sin⁡(α+π 2)⁢cos⁡(β)+cos⁡(α+π 2)⁢sin⁡(β)sin⁡((α−π 2)+β)=sin⁡(α+β−π 2)=−cos⁡(α+β)=−cos⁡(α)⁢cos⁡(β)+sin⁡(α)⁢sin⁡(β)=sin⁡(α−π 2)⁢cos⁡(β)+cos⁡(α−π 2)⁢sin⁡(β)cos⁡((α+π 2)+β)=cos⁡(α+β+π 2)=−sin⁡(α+β)=−sin⁡(α)⁢cos⁡(β)−cos⁡(α)⁢sin⁡(β)=cos⁡(α+π 2)⁢cos⁡(β)−sin⁡(α+π 2)⁢sin⁡(β)cos⁡((α−π 2)+β)=cos⁡(α+β−π 2)=sin⁡(α+β)=sin⁡(α)⁢cos⁡(β)+cos⁡(α)⁢sin⁡(β)=cos⁡(α−π 2)⁢cos⁡(β)−sin⁡(α−π 2)⁢sin⁡(β) There are similar proofs to extend the identities for β. An induction argument shows the validity of the addition formulas for arbitrary angles α and β. The remaining formulas now follow via the use of trigonometric identities. tan⁡(α+β)=sin⁡(α+β)cos⁡(α+β)=sin⁡α⁢cos⁡β+cos⁡α⁢sin⁡β cos⁡α⁢cos⁡β−sin⁡α⁢sin⁡β=sin⁡α⁢cos⁡β+cos⁡α⁢sin⁡β cos⁡α⁢cos⁡β cos⁡α⁢cos⁡β−sin⁡α⁢sin⁡β cos⁡α⁢cos⁡β=sin⁡α cos⁡α+sin⁡β cos⁡β 1−sin⁡α cos⁡α⁢sin⁡β cos⁡β This shows that tan⁡(α+β)=tan⁡α+tan⁡β 1−tan⁡α⁢tan⁡β. For the relations with α−β, we use the fact that sin and tan are odd functions, whereas cos is an even function, see identities [EQ:sin-odd-cos-even] and [EQ:tan-odd]. sin⁡(α−β)=sin⁡(α+(−β))=sin⁡(α)⁢cos⁡(−β)+cos⁡(α)⁢sin⁡(−β)=sin⁡α⁢cos⁡β−cos⁡α⁢sin⁡β cos⁡(α−β)=cos⁡(α+(−β))=cos⁡(α)⁢cos⁡(−β)−sin⁡(α)⁢sin⁡(−β)=cos⁡α⁢cos⁡β+sin⁡α⁢sin⁡β tan⁡(α−β)=tan⁡(α+(−β))=tan⁡(α)+tan⁡(−β)1−tan⁡(α)⁢tan⁡(−β)=tan⁡α−tan⁡β 1+tan⁡α⁢tan⁡β This completes the proof of the proposition. Before giving examples of the above proposition, we recall the elementary function values of the sin, cos, and tan from the previous section: x 0=0∘π 6=30∘π 4=45∘π 3=60∘π 2=90∘π=180∘sin⁡(x)0 1 2 2 2 3 2 1 0 cos⁡(x)1 3 2 2 2 1 2 0−1 tan⁡(x)0 3 3 1 3 undef.0 Example 18.1.1 Find the exact values of the trigonometric functions. cos⁡(π 12) tan⁡(5⁢π 12) cos⁡(11⁢π 12) Solution The key is to realize the angle π 12 as a sum or difference of angles with known trigonometric function values. Note, that π 3−π 4=4⁢π−3⁢π 12=π 12, so that cos⁡(π 12)=cos⁡(π 3−π 4)=cos⁡π 3⁢cos⁡π 4+sin⁡π 3⁢sin⁡π 4=1 2⋅2 2+3 2⋅2 2=2 4+6 4=2+6 4 We remark that the last expression is in the simplest form and cannot be simplified any further. Again we can write the angle 5⁢π 12 as a sum involving only special angles given in the table above: 5⁢π 12=2⁢π 12+3⁢π 12=π 6+π 4. Therefore, tan⁡(5⁢π 12)=tan⁡(π 6+π 4)=tan⁡π 6+tan⁡π 4 1−tan⁡π 6⁢tan⁡π 4=3 3+1 1−3 3⋅1=3+3 3 3−3 3=3+3 3⋅3 3−3=3+3 3−3≈3.732 Here, we may simplify the last expression further by rationalizing the denominator. This is done by multiplying (3+3) to numerator and denominator. tan⁡(5⁢π 12)=(3+3)⋅(3+3)(3−3)⋅(3+3)=3⁢3+3 2+9+3⁢3 3 2−3 2=3+9+6⁢3 9−3=12+6⁢3 6=2+3≈3.732 Again we need to write the angle 11⁢π 12 as a sum or difference of the above angles. In fact, we can do so in at least two different ways: 11⁢π 12=6⁢π 12+5⁢π 12 and also 11⁢π 12=12⁢π 12−π 12=π−π 12. In either case, we first need to calculate some other trigonometric functions, namely those for either 5⁢π 12 or π 12. We choose the second solution, and using part (a), we have cos⁡(π 12)=2+6 4 and sin⁡(π 12)=sin⁡(π 3−π 4)=sin⁡π 3⁢cos⁡π 4−cos⁡π 3⁢sin⁡π 4=3 2⋅2 2−1 2⋅2 2=6 4−2 4=6−2 4 With this, we have cos⁡(11⁢π 12)=cos⁡(π−π 12)=cos⁡π⁢cos⁡π 12+sin⁡π⁢sin⁡π 12=(−1)⋅2+6 4+0⋅6−2 4=−(2+6)4≈0.9569 Generalizing the previous example, we can obtain any multiple of π 12 as a sum or difference of known angles coming from the 30∘−60∘−90∘ and 45∘−45∘−90∘ triangles. Note Starting from the angles π 6=2⁢π 12, π 4=3⁢π 12, π 3=4⁢π 12, and π 2=6⁢π 12, we obtain multiples of the angle π 12 by addition and subtraction, such as: π 12=4⁢π 12−3⁢π 12,5⁢π 12=2⁢π 12+3⁢π 12,7⁢π 12=4⁢π 12+3⁢π 12,8⁢π 12=4⁢π 12+4⁢π 12,9⁢π 12=6⁢π 12+3⁢π 12,10⁢π 12=6⁢π 12+4⁢π 12,11⁢π 12=6⁢π 12+5⁢π 12=12⁢π 12−π 12 Here, the trigonometric function values of the last fraction is obtained from the previously obtained trigonometric values, as in part (c) of example 18.1.1 above. Higher multiples of π 12 can be obtained from the above list by adding multiples of π to it. Note also that in many instances there are several ways of writing an angle as a sum or difference. For example: 8⁢π 12=4⁢π 12+4⁢π 12=6⁢π 12+2⁢π 12=12⁢π 12−4⁢π 12 Example 18.1.2 Using proposition [PROP:trig-add-subt-formulas] we can prove other related trigonometric identities with the addition and subtraction formulas. We rewrite cos⁡(x+π 2) by using the subtraction formula. Solution cos⁡(x+π 2)=cos⁡x⋅cos⁡π 2−sin⁡x⋅sin⁡π 2=cos⁡x⋅0+sin⁡x⋅1=sin⁡(x) This page titled 18.1: Addition and subtraction of angles is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Thomas Tradler and Holly Carley (New York City College of Technology at CUNY Academic Works) via source content that was edited to the style and standards of the LibreTexts platform. Back to top 18: Addition of Angles and Multiple Angles 18.2: Double and half angles Was this article helpful? Yes No Recommended articles 18.2: Double and half angles 18.3: Exercises Front Matter 1: The Absolute Value 2: Lines and Functions Article typeSection or PageAuthorThomas Tradler and Holly CarleyLicenseCC BY-NC-SALicense Version4.0Show Page TOCno Tags source@ © Copyright 2025 Mathematics LibreTexts Powered by CXone Expert ® ? The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Privacy Policy. Terms & Conditions. Accessibility Statement.For more information contact us atinfo@libretexts.org. Support Center How can we help? Contact Support Search the Insight Knowledge Base Check System Status× contents readability resources tools ☰ 18: Addition of Angles and Multiple Angles 18.2: Double and half angles Complete your gift to make an impact

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