External data saved in *.xls or *.txt files can be added to a model creating a  model-data-couple . A mapping dialog allows to connect data column names to observed species names. Meta information in the data files comprise information about the experimental setting. Measurement errors are either stored in the data files, will be calculated using an error model, or are estimated automatically.


To fit a model to one or more data sets, the corresponding model-data-couples are combined into a  fitting-assembly . Parameters like initial values, rate constants, and scaling factors can be fitted in an experiment-wise or global fashion. The user may select from several numerical integrators, optimization algorithms, and calibration strategies like fitting in normal or logarithmic parameter space.


The quality of a fit is characterized by its  chi-squared  value.  As a rule of thumb, for
 N  fitted data points and  p  calibrated parameters, the chi-squared value should have a similar value
as  N  −  p  or at least  N . Statistically, this is expressed using a  chi-squared test  resulting in a  p-value  above a significance threshold of e.g. 0.05. For lower p-values, the model is


Apart from further chi-squared based characteristics like  AIC  and  BIC , data-model-residual analyses exist, e.g. to investigate whether the  residuals  follow a  Gaussian distribution . Finally, parameter  confidence intervals  may be estimated using either the  Fisher information matrix  approximation or based on the  profile-likelihood function , if parameters are not unambiguously identifiable.


If the fit is not acceptable, the model has to be refined and the procedure continues with step 2. Else, the dynamic model properties can be examined and predictions calculated.


If the model structure is not able to explain the experimental measurements, a set of physiologically reasonable alternative models should be created. In order to avoid redundant model paragraphs and copy-and-paste errors, this can be done using a common core-model which is the same for all variants.  Then,  daughter -models are created and fitted to the data, preferably using batch processing strategies based on MATLAB scripts. As a starting point to envision suitable model variants, the PottersWheel  equalizer  may be used to understand the dynamic behavior of the original system.


A mathematical model may serve to display the concentration time-profile of unobserved species, to determine sensitive parameters representing potential targets within a clinical setting, or to calculate model characteristics like the half-life of a species.


Each analysis step may be stored into a modeling report, which may be exported as a Latex-based PDF.


An experimental setting corresponds to specific characteristics of  driving input functions  and
initial concentrations. In a signal transduction pathway model the concentration of a ligand
like EGF may be controlled experimentally.  The driving input designer allows investigating the effect of a continuous, ramp, or pulse stimulation in combination with varying initial concentrations using the equalizer.  In order to discriminate competing model hypotheses, the designed experiment should have as different observable time-profiles as possible.


Many dynamical systems can only be observed partially, i.e. not all system species are accessible experimentally. For biological applications the amount and quality of experimental data is often limited. In this setting parameters can be structurally or practically non-identifiable. Then, parameters may compensate each other and fitted parameter values strongly depend on initial guesses. In PottersWheel non-identifiability can be detected using the  Profile Likelihood Approach . [ 2 ]  For characterizing functional relationships between the non-identifiable parameters PottersWheel applies random and systematic fit sequences. [ 3 ]


A  prodrug  is a pharmacologically inactive  medication  or compound that, after  intake , is  metabolized  (i.e., converted within the body) into a  pharmacologically active  drug. [ 1 ] [ 2 ]  Instead of administering a drug directly, a corresponding prodrug can be used to improve how the drug is absorbed, distributed, metabolized, and excreted ( ADME ). [ 3 ] [ 4 ]


Prodrugs are often designed to improve  bioavailability  when a drug itself is poorly absorbed from the  gastrointestinal tract . [ 2 ]  A prodrug may be used to improve how selectively the drug interacts with cells or processes that are not its intended target.  This reduces adverse or unintended effects of a drug, especially important in treatments like  chemotherapy , which can have severe unintended and undesirable side effects.


Compound that undergoes biotransformation before exhibiting  pharmacological  effects.


Note 1 : Modified from ref. [ 5 ]


Note 2 : Prodrugs can thus be viewed as  drugs  containing specialized nontoxic protective groups used in a transient manner to alter or to eliminate undesirable properties in the parent molecule. [ 6 ]


Many herbal extracts historically used in medicine contain  glycosides  (sugar derivatives) of the active agent, which are hydrolyzed in the intestines to release the active and more bioavailable  aglycone .  For example,  salicin  is a  β-D-glucopyranoside  that is cleaved by esterases to release  salicylic acid .   Aspirin , acetylsalicylic acid, first made by  Felix Hoffmann  at  Bayer  in 1897, is a synthetic prodrug of salicylic acid. [ 7 ] [ 8 ]   However, in other cases, such as  codeine  and  morphine , the administered drug is  enzymatically   activated  to form sugar derivatives (morphine- glucuronides ) that are more active than the parent compound. [ 2 ]


The first synthetic antimicrobial drug,  arsphenamine , discovered in 1909 by  Sahachiro Hata  in the laboratory of  Paul Ehrlich , is not toxic to bacteria until it has been converted to an active form by the body.  Likewise,  prontosil , the first  sulfa drug  (discovered by  Gerhard Domagk  in 1932), must be cleaved in the body to release the active molecule,  sulfanilamide .  Since that time, many other examples have been identified.


Terfenadine , the first non-sedating  antihistamine , had to be withdrawn from the market because of the small risk of a serious side effect.  However, terfenadine was discovered to be the prodrug of the active molecule,  fexofenadine , which does not carry the same risks as the parent compound.  Therefore, fexofenadine could be placed on the market as a safe replacement for the original drug.


Loratadine , another non-sedating antihistamine, is the prodrug of  desloratadine , which is largely responsible for the antihistaminergic effects of the parent compound.  However, in this case the parent compound does not have the side effects associated with terfenadine, and so both loratadine and its  active metabolite , desloratadine, are currently marketed. [ 9 ]


Approximately 10% of all marketed drugs worldwide can be considered prodrugs. Since 2008, at least 30 prodrugs have been approved by the  FDA . [ 1 ]  Seven prodrugs were  approved in 2015 and six in 2017. Examples of recently approved prodrugs are such as  dabigatran etexilate  (approved in 2010),  gabapentin enacarbil  (2011),  sofosbuvir  (2013),  tedizolid phosphate  (2014),  isavuconazonium  (2015),  aripiprazole lauroxil  (2015),  selexipag  (2015),  latanoprostene bunod  (2017),  benzhydrocodone  (2018),  tozinameran  (2020) and  serdexmethylphenidate  (2021).


Prodrugs can be classified into two major types, [ 10 ]  based on how the body converts the prodrug into the final active drug form:


Both major types can be further categorized into subtypes, based on factors such as (Type I) whether the intracellular bioactivation location is also the site of therapeutic action, or (Type 2) whether or not bioactivation occurs in the gastrointestinal fluids or in the circulation system.


Type IA prodrugs include many antimicrobial and chemotherapy agents (e.g., 5-flurouracil). Type IB agents rely on metabolic enzymes, especially in hepatic cells, to bioactivate the prodrugs intracellularly to active drugs. Type II prodrugs are bioactivated extracellularly, either in the milieu of GI fluids (Type IIA), within the systemic circulation and/or other extracellular fluid compartments (Type IIB), or near therapeutic target tissues/cells (Type IIC), relying on common enzymes such as esterases and phosphatases or target directed enzymes. Importantly, prodrugs can belong to multiple subtypes (i.e., Mixed-Type). A Mixed-Type prodrug is one that is bioactivated at multiple sites, either in parallel or sequential steps. For example, a prodrug, which is bioactivated concurrently in both target cells and metabolic tissues, could be designated as a "Type IA/IB" prodrug (e.g., HMG Co-A reductase inhibitors and some chemotherapy agents; note the symbol " / " applied here). When a prodrug is bioactivated sequentially, for example initially in GI fluids then systemically within the target cells, it is designated as a "Type IIA-IA" prodrug (e.g.,  tenofovir disoproxil ; note the symbol " - " applied here). Many antibody- virus- and gene-directed enzyme prodrug therapies ( ADEPTs ,  VDEPTs ,  GDEPTs ) and proposed  nanoparticle - or nanocarrier-linked drugs can understandably be Sequential Mixed-Type prodrugs. To differentiate these two Subtypes, the symbol dash " - " is used to designate and to indicate sequential steps of bioactivation, and is meant to distinguish from the symbol slash " / " used for the Parallel Mixed-Type prodrugs. [ 11 ] [ 12 ]


The  residence time  of a  fluid parcel  is the total time that the parcel has spent inside a  control volume  (e.g.: a  chemical reactor , a  lake , a  human body ). The residence time of a  set  of parcels is quantified in terms of the  frequency distribution  of the residence time in the set, which is known as  residence time distribution (RTD) , or in terms of its average, known as  mean residence time .


Residence time plays an important role in  chemistry  and especially in  environmental science  and  pharmacology . Under the name  lead time  or  waiting time  it plays a central role respectively in  supply chain management  and  queueing theory , where the material that flows is usually discrete instead of continuous.


The concept of residence time originated in models of chemical reactors. The first such model was an  axial dispersion model  by  Irving Langmuir  in 1908. This received little attention for 45 years; other models were developed such as the  plug flow reactor model  and the  continuous stirred-tank reactor , and the concept of a  washout function  (representing the response to a sudden change in the input) was introduced. Then, in 1953,  Peter Danckwerts  resurrected the axial dispersion model and formulated the modern concept of residence time. [ 1 ]


The time that a particle of fluid has been in a  control volume  (e.g. a reservoir) is known as its  age . In general, each particle has a different age. The frequency of occurrence of the age

 τ

 {\displaystyle \tau }

  in the set of all the particles that are located inside the control volume at time

 t

 {\displaystyle t}

  is quantified by means of the (internal)  age distribution

 I

 {\displaystyle I}

 . [ 2 ]


At the moment a particle leaves the control volume, its age is the total time that the particle has spent inside the control volume, which is known as its  residence time . The frequency of occurrence of the age

 τ

 {\displaystyle \tau }

  in the set of all the particles that are leaving the control volume at time

 t

 {\displaystyle t}

  is quantified by means of the  residence time distribution , also known as  exit age distribution

 E

 {\displaystyle E}

 . [ 2 ]


Both distributions are positive and have by definition unitary integrals along the age: [ 2 ]


In the case of  steady flow , the distributions are assumed to be independent of time, that is

 ∂

 t

 E
 =

 ∂

 t

 I
 =
 0

 ∀
 t

 {\displaystyle \partial _{t}E=\partial _{t}I=0\;\forall t}

 , which may allow to redefine the distributions as simple functions of the age only.


If the flow is steady (but a generalization to non-steady flow is possible [ 3 ] ) and is  conservative , then the exit age distribution and the internal age distribution can be related one to the other: [ 2 ]


Distributions other than

 E

 {\displaystyle E}

  and

 I

 {\displaystyle I}

  can be usually traced back to them. For example, the fraction of particles leaving the control volume at time

 t

 {\displaystyle t}

  with an age greater or equal than

 τ

 {\displaystyle \tau }

  is quantified by means of the  washout function

 W

 {\displaystyle W}

 , that is the complementary to one of the cumulative exit age distribution:


The  mean age  of all the particles inside the control volume at time  t  is the first  moment  of the age distribution: [ 2 ] [ 3 ]


The  mean residence time  or  mean transit time , that is the mean age of all the particles leaving the control volume at time  t , is the first moment of the residence time distribution: [ 2 ] [ 3 ]


The mean age and the mean transit time generally have different values, even in stationary conditions: [ 2 ]


If the flow is  steady  and  conservative , the mean residence time equals the ratio between the amount of fluid contained in the control volume and the flow rate through it: [ 2 ]


This ratio is commonly known as the  turnover time  or  flushing time . [ 4 ]  When applied to liquids, it is also known as the  hydraulic retention time  ( HRT ),  hydraulic residence time  or  hydraulic detention time . [ 5 ]  In the field of chemical engineering this is also known as  space time . [ 6 ]


The residence time of a specific compound in a mixture equals the turnover time (that of the compound, as well as that of the mixture) only if the compound does not take part in any chemical reaction (otherwise its flow is not conservative) and its concentration is  uniform . [ 3 ]


Although the equivalence between the residence time and the ratio

 m

 /

 f

 {\displaystyle m/f}

  does not hold if the flow is not stationary or it is not conservative, it does hold  on average  if the flow is steady and conservative  on average , and not necessarily at any instant. Under such conditions, which are common in  queueing theory  and  supply chain management , the relation is known as  Little's Law .


Design equations are equations relating the space time to the fractional conversion and other properties of the reactor. Different design equations have been derived for different types of the reactor and depending on the reactor the equation more or less resemble that describing the average residence time. Often design equations are used to minimize the reactor volume or volumetric flow rate required to operate a reactor. [ 7 ]


In an ideal  plug flow reactor  (PFR) the fluid particles leave in the same order they arrived, not mixing with those in front and behind. Therefore, the particles entering at time  t  will exit at time  t  +  T , all spending a time  T  inside the reactor. The residence time distribution will be then a  Dirac delta function  delayed by  T :


The mean is  T  and the variance is zero. [ 1 ]


The RTD of a real reactor deviates from that of an ideal reactor, depending on the hydrodynamics within the vessel. A non-zero variance indicates that there is some dispersion along the path of the fluid, which may be attributed to turbulence, a non-uniform velocity profile, or diffusion. If the mean of the distribution is earlier than the expected time  T  it indicates that there is  stagnant fluid  within the vessel. If the RTD curve shows more than one main peak it may indicate channeling, parallel paths to the exit, or strong internal circulation.


In PFRs, reactants enter the reactor at one end and react as they move down the reactor. Consequently, the reaction rate is dependent on the concentrations which vary along the reactor requiring the inverse of the reaction rate to be integrated over the fractional conversion.


Batch reactors are reactors in which the reactants are put in the reactor at time 0 and react until the reaction is stopped. Consequently, the space time is the same as the average residence time in a batch reactor.


In an ideal  continuous stirred-tank reactor  (CSTR), the flow at the inlet is completely and instantly mixed into the bulk of the reactor. The reactor and the outlet fluid have identical, homogeneous compositions at all times. The residence time distribution is exponential:


Where; the mean is  T  and the variance is 1. [ 1 ]  A notable difference from the plug flow reactor is that material introduced into the system will never completely leave it. [ 4 ]


In reality, it is impossible to obtain such rapid mixing, as there is necessarily a delay between any molecule passing through the inlet and making its way to the outlet, and hence the RTD of a real reactor will deviate from the ideal exponential decay, especially in the case of large reactors. For example, there will be some finite delay before  E  reaches its maximum value and the length of the delay will reflect the rate of mass transfer within the reactor. Just as was noted for a plug-flow reactor, an early mean will indicate some stagnant fluid within the vessel, while the presence of multiple peaks could indicate channeling, parallel paths to the exit, or strong internal circulation. Short-circuiting fluid within the reactor would appear in an RTD curve as a small pulse of concentrated tracer that reaches the outlet shortly after injection.
Reactants continuously enter and leave a tank where they are mixed. Consequently, the reaction proceeds at a rate dependent on the outlet concentration:


In a  laminar flow reactor , the fluid flows through a long tube or parallel plate reactor and the flow is in layers parallel to the walls of the tube. The velocity of the flow is a parabolic function of radius. In the absence of  molecular diffusion , the RTD is [ 8 ]


The variance is infinite. In a real reactor, diffusion will eventually mix the layers so that the tail of the RTD becomes exponential and the variance finite; but laminar flow reactors can have variance greater than 1, the maximum for CTSD reactors. [ 1 ]


Recycle reactors are PFRs with a recycle loop. Consequently, they behave like a hybrid between PFRs and CSTRs.


In all of these equations :

 −

 r

 A

 {\displaystyle -r_{A}}

  is the consumption rate of  A , a reactant. This is equal to the rate expression  A  is involved in. The rate expression is often related to the fractional conversion both through the consumption of  A  and through any  k  changes through temperature changes that are dependent on conversion. [ 7 ]


In some reactions the reactants and the products have significantly different densities. Consequently, as the reaction proceeds the volume of the reaction changes. This variable volume adds terms to the design equations. Taking this volume change into consideration the volume of the reaction becomes:


Plugging this into the design equations results in the following equations:


Generally, when reactions take place in the liquid and solid phases the change in volume due to reaction is not significant enough that it needs to be taken into account. Reactions in the gas phase often have significant changes in volume and in these cases one should use these modified equations. [ 7 ]


Residence time distributions are measured by introducing a non-reactive  tracer  into the system at the inlet. Its input concentration is changed according to a known function and the output concentration measured. The tracer should not modify the physical characteristics of the fluid (equal density, equal viscosity) or the  hydrodynamic  conditions and it should be easily detectable. [ 9 ]
In general, the change in tracer concentration will either be a  pulse  or a  step . Other functions are possible, but they require more calculations to  deconvolute  the RTD curve.


This method required the introduction of a very small volume of concentrated tracer at the inlet of the reactor, such that it approaches the  Dirac delta function . [ 10 ] [ 8 ]  Although an infinitely short injection cannot be produced, it can be made much smaller than the mean residence time of the vessel. If a mass of tracer,

 M

 {\displaystyle M}

 , is introduced into a vessel of volume

 V

 {\displaystyle V}

  and an expected residence
time of

 τ

 {\displaystyle \tau }

 , the resulting curve of

 C
 (
 t
 )

 {\displaystyle C(t)}

  can be transformed into a dimensionless residence time distribution curve by the following relation:


The concentration of tracer in a step experiment at the reactor inlet changes abruptly from 0 to

 C

 0

 {\displaystyle C_{0}}

 . The concentration of tracer at the outlet is measured and normalized to the concentration

 C

 0

 {\displaystyle C_{0}}

  to obtain the non-dimensional curve

 F
 (
 t
 )

 {\displaystyle F(t)}

  which goes from 0 to 1:


The step- and pulse-responses of a reactor are related by the following:


A step experiment is often easier to perform than a pulse experiment, but it tends to smooth over some of the details that a pulse response could show. It is easy to numerically integrate an experimental pulse response to obtain a very high-quality estimate of the step response, but the reverse is not the case because any noise in the concentration measurement will be amplified by numeric differentiation.


In  chemical reactors , the goal is to make components react with a high  yield . In a homogeneous,  first-order reaction , the probability that an atom or molecule will react depends only on its residence time:


for a  rate constant

 k

 {\displaystyle k}

 . Given a RTD, the average probability is equal to the ratio of the concentration

 a

 {\displaystyle a}

  of the component before and after: [ 1 ]


If the reaction is more complicated, then the output is not uniquely determined by the RTD. It also depends on the degree of  micromixing , the mixing between molecules that entered at different times. If there is no mixing, the system is said to be  completely segregated , and the output can be given in the form


For given RTD, there is an upper limit on the amount of mixing that can occur, called the  maximum mixedness , and this determines the achievable yield. A continuous stirred-tank reactor can be anywhere in the spectrum between completely segregated and  perfect mixing . [ 1 ]


The RTD of chemical reactors can be obtained by  CFD  simulations. The very same procedure that is performed in experiments can be followed. A pulse of inert tracer particles (during a very short time) is injected into the reactor. The linear motion of tracer particles is governed by Newton's second law of motion and a one-way coupling is stablished between fluid and tracers. In one-way coupling, fluid affects tracer motion by drag force while tracer does not affect fluid. The size and density of tracers are chosen so small that the  time constant  of tracers becomes very small. In this way, tracer particles exactly follow the same path as the fluid does. [ 11 ]


Hydraulic residence time (HRT) is an important factor in the transport of environmental toxins or other chemicals through  groundwater . The amount of time that a pollutant spends traveling through a delineated subsurface space is related to the saturation and the  hydraulic conductivity  of the soil or rock. [ 12 ]   Porosity  is another significant contributing factor to the mobility of water through the ground (e.g. toward the  water table ). The intersection between pore density and size determines the degree or magnitude of the flow rate through the media. This idea can be illustrated by a comparison of the ways water moves through  clay  versus  gravel . The retention time through a specified vertical distance in clay will be longer than through the same distance in gravel, even though they are both characterized as high porosity materials. This is because the pore sizes are much larger in gravel media than in clay, and so there is less  hydrostatic tension  working against the subsurface  pressure gradient  and gravity.


Groundwater flow is important parameter for consideration in the design of waste rock basins for  mining  operations. Waste rock is heterogeneous material with particles varying from boulders to clay-sized particles, and it contains  sulfidic pollutants  which must be controlled such that they do not compromise the quality of the water table and also so the runoff does not create environmental problems in the surrounding areas. [ 12 ]   Aquitards  are clay zones that can have such a degree of impermeability that they partially or completely retard water flow. [ 5 ] [ 13 ]  These clay lenses can slow or stop seepage into the water table, although if an aquitard is fractured and contaminated then it can become a long-term source of groundwater contamination due to its low permeability and high HRT. [ 13 ]


Primary treatment  for wastewater or drinking water includes settling in a  sedimentation  chamber to remove as much of the solid matter as possible before applying additional treatments. [ 5 ]  The amount removed is controlled by the hydraulic residence time (HRT). [ 5 ]  When water flows through a volume at a slower rate, less energy is available to keep solid particles entrained in the stream and there is more time for them to settle to the bottom. Typical HRTs for sedimentation basins are around two hours, [ 5 ]  although some groups recommend longer times to remove  micropollutants  such as pharmaceuticals and hormones. [ 14 ]


Disinfection  is the last step in the  tertiary treatment  of wastewater or drinking water. The types of pathogens that occur in untreated water include those that are easily killed like  bacteria  and  viruses , and those that are more robust such as  protozoa  and  cysts . [ 5 ]  The disinfection chamber must have a long enough HRT to kill or deactivate all of them.


Atoms and molecules of gas or liquid can be trapped on a solid surface in a process called  adsorption . This is an  exothermic process  involving a release of  heat , and heating the surface increases the probability that an atom will escape within a given time. At a given temperature

 T

 {\displaystyle T}

 , the residence time of an adsorbed atom is given by


where

 R

 {\displaystyle R}

  is the  gas constant ,

 E

 a

 {\displaystyle E_{\mathrm {a} }}

  is an  activation energy , and

 τ

 0

 {\displaystyle \tau _{0}}

  is a prefactor that is correlated with the vibration times of the surface atoms (generally of the order of

 10

 −
 12

 {\displaystyle 10^{-12}}

  seconds). [ 15 ] : 27  [ 16 ] : 196


In  vacuum technology , the residence time of gases on the surfaces of a vacuum chamber can determine the pressure due to  outgassing . If the chamber can be heated, the above equation shows that the gases can be "baked out"; but if not, then surfaces with a low residence time are needed to achieve  ultra-high vacuums . [ 16 ] : 195


In environmental terms, the residence time definition is adapted to fit with ground water, the atmosphere,  glaciers , lakes, streams, and oceans. More specifically it is the time during which water remains within an aquifer, lake, river, or other water body before continuing around the  hydrological cycle . The time involved may vary from days for shallow gravel  aquifers  to millions of years for deep aquifers with very low values for  hydraulic conductivity . Residence times of water in rivers are a few days, while in large lakes residence time ranges up to several decades. Residence times of continental ice sheets is hundreds of thousands of years, of small glaciers a few decades.


Ground water residence time applications are useful for determining the amount of time it will take for a pollutant to reach and  contaminate  a ground water drinking water source and at what concentration it will arrive. This can also work to the opposite effect to determine how long until a ground water source becomes uncontaminated via inflow, outflow, and volume. The residence time of lakes and streams is important as well to determine the concentration of pollutants in a lake and how this may affect the local population and marine life.


Hydrology, the study of water, discusses the water budget in terms of residence time. The amount of time that water spends in each different stage of life (glacier, atmosphere, ocean, lake, stream, river), is used to show the relation of all of the water on the earth and how it relates in its different forms.


A large class of  drugs  are  enzyme inhibitors  that bind to  enzymes  in the body and inhibit their activity. In this case it is the drug-target residence time (the length of time the drug stays bound to the target) that is of interest. The residence time is defined as the reciprocal value of the koff rate constant (residence time = 1/koff). Drugs with long residence times are desirable because they remain effective for longer and therefore can be used in lower doses. [ 17 ] : 88   This residence time is determined by the  kinetics  of the interaction, [ 18 ]  such as how complementary the shape and charges of the target and drug are and whether outside solvent molecules are kept out of the  binding site  (thereby preventing them from breaking any bonds formed), [ 19 ]  and is proportional to the  half-life  of the  chemical dissociation . [ 18 ]  One way to measure the residence time is in a  preincubation-dilution  experiment where a target enzyme is incubated with the inhibitor, allowed to approach equilibrium, then rapidly diluted. The amount of product is measured and compared to a control in which no inhibitor is added. [ 17 ] : 87–88


Residence time can also refer to the amount of time that a drug spends in the part of the body where it needs to be absorbed. The longer the residence time, the more of it can be absorbed. If the drug is delivered in an oral form and destined for the  upper intestines , it usually moves with food and its residence time is roughly that of the food. This generally allows 3 to 8 hours for absorption. [ 20 ] : 196   If the drug is delivered through a  mucous membrane  in the mouth, the residence time is short because  saliva  washes it away. Strategies to increase this residence time include  bioadhesive   polymers , gums,  lozenges  and dry powders. [ 20 ] : 274


In  size-exclusion chromatography , the residence time of a molecule is related to its volume, which is roughly proportional to its molecular weight. Residence times also affect the performance of  continuous fermentors . [ 1 ]


Biofuel cells  utilize the metabolic processes of anodophiles ( electronegative  bacteria) to convert chemical energy from organic matter into electricity. [ 21 ] [ 22 ] [ 23 ]  A biofuel cell mechanism consists of an  anode  and a  cathode  that are separated by an internal  proton exchange membrane  (PEM) and connected in an external circuit with an external load. Anodophiles grow on the anode and consume biodegradable organic molecules to produce electrons, protons, and  carbon dioxide  gas, and as the electrons travel through the circuit they feed the external load. [ 22 ] [ 23 ]  The HRT for this application is the rate at which the feed molecules are passed through the anodic chamber. [ 23 ]  This can be quantified by dividing the volume of the anodic chamber by the rate at which the feed solution is passed into the chamber. [ 22 ]  The hydraulic residence time (HRT) affects the substrate loading rate of the microorganisms that the anodophiles consume, which affects the electrical output. [ 23 ] [ 24 ]  Longer HRTs reduce substrate loading in the anodic chamber which can lead to reduced anodophile population and performance when there is a deficiency of nutrients. [ 23 ]  Shorter HRTs support the development of non- exoelectrogenous  bacteria which can reduce the  Coulombic efficiency  electrochemical performance of the fuel cell if the anodophiles must compete for resources or if they do not have ample time to effectively degrade nutrients. [ 23 ]


This is a table of  volume of distribution  (V d ) for various  medication . For comparison, those with a V d  L/kg body weight of less than 0.2 are mainly distributed in  blood plasma , 0.2-0.7 mostly in the  extracellular fluid  and those with more than 0.7 are distributed throughout total body water.


Targeted drug delivery , sometimes called  smart drug delivery , [ 1 ]  is a method of delivering  medication  to a patient in a manner that increases the  concentration  of the medication in some parts of the body relative to others. This means of delivery is largely founded on nanomedicine, which plans to employ  nanoparticle -mediated drug delivery in order to combat the downfalls of conventional drug delivery. These nanoparticles would be loaded with drugs and targeted to specific parts of the body where there is solely diseased tissue, thereby avoiding interaction with healthy tissue. The goal of a targeted  drug delivery  system is to prolong, localize, target and have a protected drug interaction with the diseased tissue.  The conventional  drug delivery system  is the absorption of the drug across a  biological membrane , whereas the  targeted release system  releases the drug in a dosage form.  The advantages to the targeted release system is the reduction in the frequency of the dosages taken by the patient, having a more uniform effect of the drug, reduction of drug  side-effects , and reduced fluctuation in circulating drug levels. The disadvantage of the system is high cost, which makes productivity more difficult, and the reduced ability to adjust the dosages.


Targeted drug delivery systems have been developed to optimize regenerative techniques. The system is based on a method that delivers a certain amount of a therapeutic agent for a prolonged period of time to a targeted diseased area within the body. This helps maintain the required plasma and tissue drug levels in the body, thereby preventing any damage to the healthy tissue via the drug.  The drug delivery system is highly integrated and requires various disciplines, such as chemists, biologists, and engineers, to join forces to optimize this system. [ 2 ]


In traditional  drug delivery  systems such as oral ingestion or intravascular injection, the medication is distributed throughout the body through the systemic  blood circulation . For most therapeutic agents, only a small portion of the medication reaches the organ to be affected, such as in chemotherapy where roughly 99% of the drugs administered do not reach the tumor site. [ 3 ]  Targeted drug delivery seeks to concentrate the medication in the tissues of interest while reducing the relative concentration of the medication in the remaining tissues. For example, by avoiding the host's defense mechanisms and inhibiting non-specific distribution in the liver and spleen, [ 4 ]  a system can reach the intended site of action in higher concentrations. Targeted delivery is believed to improve  efficacy  while reducing  side-effects .


When implementing a targeted release system, the following design criteria for the system must be taken into account: the drug properties, side-effects of the drugs, the route taken for the delivery of the drug, the targeted site, and the disease.


Increasing developments to novel treatments requires a controlled microenvironment that is accomplished only through the implementation of therapeutic agents whose side-effects can be avoided with targeted drug delivery.  Advances in the field of targeted drug delivery to cardiac tissue will be an integral component to regenerate cardiac tissue. [ 5 ]


There are two kinds of targeted drug delivery: active targeted drug delivery, such as some  antibody  medications, and passive targeted drug delivery, such as the  enhanced permeability and retention effect  (EPR-effect).


This ability for nanoparticles to concentrate in areas of solely diseased tissue is accomplished through either one or both means of targeting: passive or active.


Passive targeting is achieved by incorporating the therapeutic agent into a macromolecule or nanoparticle that passively reaches the target organ. In passive targeting, the drug's success is directly related to circulation time. [ 6 ]  This is achieved by cloaking the nanoparticle with some sort of coating. Several substances can achieve this, with one of them being polyethylene glycol (PEG). By adding PEG to the surface of the nanoparticle, it is rendered hydrophilic, thus allowing water molecules to bind to the oxygen molecules on PEG via hydrogen bonding. The result of this bond is a film of hydration around the nanoparticle which makes the substance antiphagocytic. The particles obtain this property due to the hydrophobic interactions that are natural to the  reticuloendothelial system (RES) , thus the drug-loaded nanoparticle is able to stay in circulation for a longer period of time. [ 7 ]  To work in conjunction with this mechanism of passive targeting, nanoparticles that are between 10 and 100 nanometers in size have been found to circulate systemically for longer periods of time. [ 8 ]


Active targeting of drug-loaded nanoparticles enhances the effects of passive targeting to make the nanoparticle more specific to a target site. There are several ways that active targeting can be accomplished. One way to actively target solely diseased tissue in the body is to know the nature of a receptor on the cell for which the drug will be targeted to. [ 9 ]  Researchers can then utilize cell-specific ligands that will allow the nanoparticle to bind specifically to the cell that has the complementary receptor. This form of active targeting was found to be successful when utilizing transferrin as the cell-specific ligand. [ 9 ]  The transferrin was conjugated to the nanoparticle to target tumor cells that possess transferrin-receptor mediated endocytosis mechanisms on their membrane. This means of targeting was found to increase uptake, as opposed to non-conjugated nanoparticles. Another cell-specific ligand is the  RGD motif  which binds to the integrin  αvβ3 . [ 10 ]  This integrin is upregulated in tumor and activated endothelial cells. [ 11 ]  Conjugation of RGD to chemotherapeutic-loaded nanoparticles has been shown to increase cancer cell uptake  in vitro  and therapeutic efficacy  in vivo . [ 10 ]


Active targeting can also be achieved by utilizing magnetoliposomes, which usually serves as a contrast agent in magnetic resonance imaging. [ 9 ]  Thus, by grafting these liposomes with a desired drug to deliver to a region of the body, magnetic positioning could aid with this process.


Furthermore, a nanoparticle could possess the capability to be activated by a trigger that is specific to the target site, such as utilizing materials that are pH responsive. [ 9 ]  Most of the body has a consistent, neutral pH. However, some areas of the body are naturally more acidic than others, and, thus, nanoparticles can take advantage of this ability by releasing the drug when it encounters a specific pH. [ 9 ]  Another specific triggering mechanism is based on the redox potential. One of the side effects of tumors is  hypoxia , which alters the redox potential in the vicinity of the tumor. By modifying the redox potential that triggers the payload release the vesicles can be selective to different types of tumors. [ 12 ]


By utilizing both passive and active targeting, a drug-loaded nanoparticle has a heightened advantage over a conventional drug. It is able to circulate throughout the body for an extended period of time until it is successfully attracted to its target through the use of cell-specific ligands, magnetic positioning, or pH responsive materials. Because of these advantages, side effects from conventional drugs will be largely reduced as a result of the drug-loaded nanoparticles affecting only diseased tissue. [ 13 ]  However, an emerging field known as nanotoxicology has concerns that the nanoparticles themselves could pose a threat to both the environment and human health with side effects of their own. [ 14 ]  Active targeting can also be achieved through peptide based drug targeting system. [ 15 ]


There are different types of drug delivery vehicles, such as polymeric micelles, liposomes, lipoprotein-based drug carriers, nano-particle drug carriers, dendrimers, etc. An ideal drug delivery vehicle must be non-toxic, biocompatible, non-immunogenic, biodegradable, [ 5 ]  and must avoid recognition by the host's defense mechanisms [3] .


Cell Surface Peptides provide one way to introduce drug delivery into a target cell. [ 16 ]  This method is accomplished by the peptide binding to a target cells surface receptors, in a way that bypasses immune defenses that would otherwise compromise a slower delivery, without causing harm to the host. In particular, peptides, such as intercellular adhesion molecule-1, have shown a great deal of binding ability in a target cell. This method has shown a degree of efficacy in treating both autoimmune diseases as well as forms of cancer as a result of this binding affinity. [ 17 ]  Peptide mediated delivery is also of promise due to the low cost of creating the peptides as well as the simplicity of their structure.


The most common vehicle currently used for targeted drug delivery is the  liposome . [ 19 ]  Liposomes are non-toxic, non- hemolytic , and non- immunogenic  even upon repeated injections; they are  biocompatible  and biodegradable and can be designed to avoid  clearance  mechanisms (reticuloendothelial system (RES), renal clearance, chemical or enzymatic inactivation, etc.) [ 20 ] [ 21 ]  Lipid-based, ligand-coated  nanocarriers  can store their payload in the hydrophobic shell or the hydrophilic interior depending on the nature of the drug/ contrast agent  being carried. [ 5 ]


The only problem to using liposomes  in vivo  is their immediate uptake and clearance by the RES system and their relatively low  stability  in vitro. To combat this,  polyethylene glycol  (PEG) can be added to the surface of the liposomes. Increasing the mole percent of PEG on the surface of the liposomes by 4-10% significantly increased circulation time  in vivo  from 200 to 1000 minutes. [ 5 ]


PEGylation of the liposomal nanocarrier elongates the half-life of the construct while maintaining the passive targeting mechanism that is commonly conferred to lipid-based nanocarriers. [ 22 ]  When used as a delivery system, the ability to induce instability in the construct is commonly exploited allowing the selective release of the encapsulated therapeutic agent in close proximity to the target tissue/cell  in vivo . This nanocarrier system is commonly used in anti-cancer treatments as the acidity of the tumour mass caused by an over-reliance on glycolysis triggers drug release. [ 22 ] [ 23 ] [ 24 ]


Additional endogenous trigger pathways have been explored through the exploitation of inner and outer tumor environments, such as reactive oxygen species, glutathione, enzymes, hypoxia, and adenosine-5’- triphosphate (ATP), all of which are generally highly present in and around tumors. [ 25 ]  External triggers are also used, such as light, low frequency ultrasound (LFUS), electrical fields, and magnetic fields. [ 26 ]  In specific, LFUS has demonstrated high efficacy in the controlled trigger of various drugs in mice, such as cisplatin and calcein. [ 27 ] [ 28 ]


Another type of drug delivery vehicle used is polymeric  micelles . They are prepared from certain  amphiphilic   co-polymers  consisting of both hydrophilic and hydrophobic monomer units. [ 2 ]  They can be used to carry drugs that have poor solubility.  This method offers little in the terms of size control or function malleability. Techniques that utilize reactive polymers along with a hydrophobic additive to produce a larger  micelle  that create a range of sizes have been developed. [ 29 ]


Dendrimers  are also polymer-based delivery vehicles.  They have a core that branches out in regular intervals to form a small, spherical, and very dense nanocarrier. [ 30 ]


Biodegradable particles have the ability to target diseased tissue as well as deliver their payload as a  controlled-release therapy . [ 31 ]  Biodegradable particles bearing ligands to  P-selectin , endothelial selectin ( E-selectin ) and  ICAM-1  have been found to adhere to inflamed  endothelium . [ 32 ]  Therefore, the use of biodegradable particles can also be used for cardiac tissue.


There are biocompatible  microalgae   hybrid microrobots  for active drug-delivery in the lungs and the gastrointestinal tract. The  microrobots  proved effective in tests with mice. In the two studies, "Fluorescent dye or cell membrane–coated nanoparticle functionalized algae motors were further embedded inside a pH-sensitive capsule" and "antibiotic-loaded neutrophil membrane-coated polymeric nanoparticles [were attached] to natural microalgae". [ 33 ] [ 34 ] [ 35 ]


The success of  DNA nanotechnology  in constructing  artificially designed  nanostructures out of  nucleic acids  such as  DNA , combined with the demonstration of systems for  DNA computing , has led to speculation that artificial nucleic acid nanodevices can be used to target drug delivery based upon directly sensing its environment.  These methods make use of DNA solely as a structural material and a chemical, and do not make use of its biological role as the carrier of genetic information.  Nucleic acid logic circuits that could potentially be used as the core of a system that releases a drug only in response to a stimulus such as a specific  mRNA  have been demonstrated. [ 36 ]  In addition, a DNA "box" with a controllable lid has been synthesized using the  DNA origami  method.  This structure could encapsulate a drug in its closed state, and open to release it only in response to a desired stimulus. [ 37 ]


Targeted drug delivery can be used to treat many diseases, such as the  cardiovascular diseases  and  diabetes . However, the most important application of targeted  drug delivery  is to treat  cancerous tumors . In doing so, the passive method of targeting tumors takes advantage of the  enhanced permeability and retention (EPR) effect . This is a situation specific to tumors that results from rapidly forming blood vessels and poor lymphatic drainage. When the blood vessels form so rapidly, large fenestrae result that are 100 to 600 nanometers in size, which allows enhanced nanoparticle entry. Further, the poor lymphatic drainage means that the large influx of nanoparticles are rarely leaving, thus, the tumor retains more nanoparticles for successful treatment to take place. [ 8 ]


The American Heart Association rates cardiovascular disease as the number one cause of death in the United States. Each year 1.5 million myocardial infarctions (MI), also known as heart attacks, occur in the United States, with 500,000 leading to deaths. The costs related to heart attacks exceed $60 billion per year. Therefore, there is a need to come up with an optimum recovery system.  The key to solving this problem lies in the effective use of pharmaceutical drugs that can be targeted directly to the diseased tissue. This technique can help develop many more  regenerative techniques  to cure various diseases. The development of a number of regenerative strategies in recent years for  curing  heart disease represents a paradigm shift away from conventional approaches that aim to  manage  heart disease. [ 5 ]


Stem cell therapy  can be used to help regenerate myocardium tissue and return the contractile function of the heart by creating/supporting a microenvironment before the MI. Developments in targeted drug delivery to tumors have provided the groundwork for the burgeoning field of targeted drug delivery to cardiac tissue. [ 5 ]  Recent developments have shown that there are different endothelial surfaces in tumors, which has led to the concept of endothelial  cell adhesion  molecule-mediated targeted drug delivery to tumors.


Liposomes  can be used as drug delivery for the treatment of  tuberculosis . The traditional treatment for TB is skin to chemotherapy which is not overly effective, which may be due to the failure of chemotherapy to make a high enough concentration at the infection site. The liposome delivery system allows for better microphage penetration and better builds a concentration at the infection site. [ 38 ]  The delivery of the drugs works intravenously and by inhalation. Oral intake is not advised because the liposomes break down in the Gastrointestinal System.


3D printing  is also used by doctors to investigate how to target  cancerous tumors  in a more efficient way. By printing a plastic 3D shape of the tumor and filling it with the drugs used in the treatment the flow of the liquid can be observed allowing the modification of the doses and targeting location of the drugs. [ 39 ]


Therapeutic drug monitoring (TDM)  is a branch of  clinical chemistry  and  clinical pharmacology  that specializes in the measurement of  medication  levels in  blood . Its main focus is on drugs with a narrow  therapeutic range , i.e. drugs that can easily be under- or overdosed. [ 1 ]  TDM aimed at improving patient care by individually adjusting the dose of drugs for which clinical experience or clinical trials have shown it improved outcome in the general or special populations.  It can be based on a  a priori  pharmacogenetic, demographic and clinical information, and/or on the  a posteriori  measurement of blood concentrations of drugs (pharmacokinetic monitoring) or biological surrogate or end-point markers of effect (pharmacodynamic monitoring). [ 2 ]


There are numerous variables that influence the interpretation of drug concentration data: time, route and dose of drug given, time of blood sampling, handling and storage conditions, precision and accuracy of the analytical method, validity of pharmacokinetic models and assumptions, co-medications and, last but not least, clinical status of the patient (i.e. disease, renal/hepatic status, biologic tolerance to drug therapy, etc.). [ 3 ]


Many different professionals ( physicians ,  clinical pharmacists ,  nurses ,  medical laboratory scientists , etc.) are involved with the various elements of drug concentration monitoring, which is a truly multidisciplinary process. Because failure to properly carry out any one of the components can severely affect the usefulness of using drug concentrations to optimize therapy, an organized approach to the overall process is critical. [ 3 ]


A priori  TDM consists of determining the initial dose regimen to be given to a patient, based on clinical endpoint and on established population  pharmacokinetic - pharmacodynamic  ( PK/PD ) relationships.  These relationships help to identify sub-populations of patients with different dosage requirements, by utilizing demographic data, clinical findings, clinical chemistry results, and/or, when appropriate, pharmacogenetic characteristics. [ 2 ]


The concept of  a posteriori  TDM corresponds to the usual meaning of TDM in medical practice, which refers to the readjustment of the dosage of a given treatment in response to the measurement of an appropriate marker of drug exposure or effect. TDM encompasses all aspects of this  feedback control , namely: [ 2 ]


In  pharmacotherapy , many medications are used without monitoring of blood levels, as their dosage can generally be varied according to the clinical response that a patient gets to that substance. For certain drugs, this is impracticable, while insufficient levels will lead to undertreatment or resistance, and excessive levels can lead to toxicity and tissue damage.


Indications in favor of therapeutic drug monitoring include: [ 4 ] [ 5 ]


TDM determinations are also used to detect and diagnose poisoning with drugs, should the suspicion arise.


Examples of drugs widely analysed for therapeutic drug monitoring: [ 1 ]


TDM increasingly proposed for a number of therapeutic drugs, e.g. many  antibiotics , small molecule  tyrosine kinase inhibitors  and other  targeted anticancer agents ,  TNF inhibitors  and other biological agents,   antifungal agents ,  antiretroviral agents  used in HIV infection,  psychiatric drugs [ 7 ]  etc.


Automated analytical methods such as  enzyme multiplied immunoassay technique  or  fluorescence polarization immunoassay  are widely available in  medical laboratories  for drugs frequently measured in practice. Nowadays, most other drugs can be readily measured in blood or plasma using versatile methods such as  liquid chromatography–mass spectrometry  or  gas chromatography–mass spectrometry , which progressively replaced  high-performance liquid chromatography . Yet, TDM is not limited to the provision of precise and accurate concentration measurement results, it also involves appropriate medical interpretation, based on robust scientific knowledge.


In order to guarantee the quality of this clinical interpretation, it is essential that the sample be taken under good conditions: i.e., preferably under a stable dosage, at a standardized sampling time (often at the end of a dosing interval), excluding any source of bias (sample contamination or dilution, analytical interferences) and having carefully recorded the sampling time, the last dose intake time, the current dosage and the influential patient's characteristics.


The interpretation of a drug concentration result goes through the following stages: [ 8 ]


Ideally, the usefulness of a TDM strategy should be confirmed through an  evidence-based  approach involving the performance of well-designed  controlled clinical trials . In practice however, TDM has undergone formal clinical evaluation only for a limited number of drugs to date, and much of its development rests on empirical foundations.


Point-of-care tests  for an easy performance of TDM at the medical practice are under elaboration. [ 10 ]


The evolution of  information technology  holds great promise for using the methods and knowledge of  pharmacometrics  to bring patient treatment closer to the ideal of  precision medicine  (which is not just about adjusting treatments to genetic factors, but encompasses all aspects of therapeutic individualization).  Model-informed precision dosing  (MIPD) should enable significant progress to be made in taking into account the many factors influencing drug response, in order to optimize therapies ( a priori  TDM ). It should also make it possible to take optimal account of TDM results to individualize drug dosage  ( a posteriori   TDM ). Ideally, these computational approaches will be integrated into the electronic patient record in the form of  clinical decision support systems  (CDSS), automatically and seamlessly linking laboratory resources and pharmacological expertise with clinicians and caregivers at the patient's bedside. Software tools already exist and continue to be developed for this purpose. They are set to play an increasingly important role in patient treatment, in the same way that instrument piloting has become the norm in aviation.


The  therapeutic index  ( TI ; also referred to as  therapeutic ratio ) is a quantitative measurement of the relative safety of a drug with regard to risk of overdose. It is a comparison of the amount of a therapeutic agent that causes toxicity to the amount that causes the  therapeutic effect . [ 1 ]  The related terms  therapeutic window  or  safety window  refer to a range of doses optimized between efficacy and toxicity, achieving the greatest therapeutic benefit without resulting in unacceptable side-effects or toxicity.


Classically, for clinical  indications  of an approved drug, TI refers to the ratio of the  dose  of the drug that causes adverse effects at an incidence/severity not compatible with the targeted indication (e.g. toxic dose in 50% of subjects,  TD 50 ) to the dose that leads to the desired pharmacological effect (e.g. efficacious dose in 50% of subjects, ED 50 ). In contrast, in a  drug development  setting TI is calculated based on plasma  exposure  levels. [ 2 ]


In the early days of pharmaceutical toxicology, TI was frequently determined in animals as lethal dose of a drug for 50% of the population ( LD 50 ) divided by the minimum  effective dose  for 50% of the population (ED 50 ). In modern settings, more sophisticated toxicity endpoints are used.


For many drugs, severe toxicities in humans occur at sublethal doses, which limit their maximum dose. A higher safety-based therapeutic index is preferable instead of a lower one; an individual would have to take a much higher dose of a drug to reach the lethal threshold than the dose taken to induce the therapeutic effect of the drug. However, a lower efficacy-based therapeutic index is preferable instead of a higher one; an individual would have to take a higher dose of a drug to reach the toxic threshold than the dose taken to induce the therapeutic effect of the drug.


Generally, a drug or other therapeutic agent with a narrow therapeutic range (i.e. having little difference between toxic and therapeutic doses) may have its dosage adjusted according to measurements of its blood levels in the person taking it. This may be achieved through  therapeutic drug monitoring  (TDM) protocols. TDM is recommended for use in the treatment of psychiatric disorders with  lithium  due to its narrow therapeutic range. [ 3 ]


Based on  efficacy  and  safety  of drugs, there are two types of therapeutic index:


T

 I

 safety

 =

 L

 D

 50

 E

 D

 50

 {\displaystyle TI_{\text{safety}}={\frac {LD_{50}}{ED_{50}}}}

It is desirous for the value of LD 50  to be as large as possible, to decrease risk of lethal effects and increase the therapeutic window. In the above formula, TI safety  increases as the difference between LD 50  and ED 50  increases—hence, a higher safety-based therapeutic index indicates a larger therapeutic window, and vice versa.


T

 I

 efficacy

 =

 E

 D

 50

 T

 D

 50

 {\displaystyle TI_{\text{efficacy}}={\frac {ED_{50}}{TD_{50}}}}

Ideally the ED 50  is as low as possible for faster drug response and larger therapeutic window, whereas a drugs TD 50  is ideally as large as possible to decrease risk of toxic effects. In the above equation, the greater the difference between ED 50  and TD 50 , the greater the value of TI efficacy . Hence, a lower efficacy-based therapeutic index indicates a larger therapeutic window.


Similar to safety-based therapeutic index, the  protective index  uses TD 50  (median  toxic  dose) in place of LD 50 .


Protective index

 =

 T

 D

 50

 E

 D

 50

 =

 1

 T

 I

 efficacy

 {\displaystyle {\text{Protective index}}={\frac {TD_{50}}{ED_{50}}}={\frac {1}{TI_{\text{efficacy}}}}}


For many substances, toxicity can occur at levels far below lethal effects (that cause death), and thus, if toxicity is properly specified, the protective index is often more informative about a substance's relative safety. Nevertheless, the safety-based therapeutic index (

 T

 I

 safety

 {\displaystyle {TI_{\text{safety}}}}

 ) is still useful as it can be considered an  upper bound  of the protective index, and the former also has the advantages of objectivity and easier comprehension.


Since the protective index (PI) is calculated as TD 50  divided by ED 50 , it can be mathematically expressed that:


which means that

 T

 I

 efficacy

 {\displaystyle TI_{\text{efficacy}}}

  is a  reciprocal  of protective index.


All the above types of therapeutic index can be used in both  pre-clinical trials  and  clinical trials .


A low efficacy-based therapeutic index (

 T

 I

 efficacy

 {\displaystyle TI_{\text{efficacy}}}

 ) and a high safety-based therapeutic index (

 T

 I

 safety

 {\displaystyle TI_{\text{safety}}}

 ) are preferable for a drug to have a favorable efficacy vs safety profile. At the early discovery/development stage, the clinical TI of a drug candidate is unknown. However, understanding the preliminary TI of a drug candidate is of utmost importance as early as possible since TI is an important indicator of the probability of successful development. Recognizing drug candidates with potentially suboptimal TI at the earliest possible stage helps to initiate mitigation or potentially re-deploy resources.


TI is the quantitative relationship between pharmacological efficacy and toxicological safety of a drug, without considering the nature of pharmacological or toxicological endpoints themselves. However, to convert a calculated TI into something useful, the nature and limitations of pharmacological and/or toxicological endpoints must be considered. Depending on the intended clinical indication, the associated unmet medical need and/or the competitive situation, more or less weight can be given to either the safety or efficacy of a drug candidate in order to create a well balanced indication-specific efficacy vs safety profile.


In general, it is the exposure of a given tissue to drug (i.e. drug concentration over time), rather than dose, that drives the pharmacological and toxicological effects. For example, at the same dose there may be marked inter-individual variability in exposure due to polymorphisms in metabolism, DDIs or differences in body weight or environmental factors. These considerations emphasize the importance of using exposure instead of dose to calculate TI. To account for delays between exposure and toxicity, the TI for toxicities that occur after multiple dose administrations should be calculated using the exposure to drug at steady state rather than after administration of a single dose.


A review published by Muller and Milton in  Nature Reviews Drug Discovery  critically discusses TI determination and interpretation in a translational drug development setting for both small molecules and biotherapeutics. [ 2 ]


The therapeutic index varies widely among substances, even within a related group.


For instance, the  opioid   painkiller   remifentanil  is very forgiving, offering a therapeutic index of 33,000:1, while  Diazepam , a  benzodiazepine   sedative-hypnotic  and skeletal  muscle relaxant , has a less forgiving therapeutic index of 100:1. [ 9 ]  Morphine is even less so with a therapeutic index of 70.


Less safe are  cocaine  (a  stimulant  and  local anaesthetic ) and  ethanol  (colloquially, the "alcohol" in  alcoholic beverages , a widely available  sedative  consumed worldwide): the therapeutic indices for these substances are 15:1 and 10:1, respectively. [ 10 ]   Paracetamol , alternatively known by its trade names  Tylenol  or Panadol, also has a therapeutic index of 10. [ 11 ]


Even less safe are drugs such as  digoxin , a  cardiac glycoside ; its therapeutic index is approximately 2:1. [ 12 ]


Other examples of drugs with a narrow therapeutic range, which may require drug monitoring both to achieve therapeutic levels and to minimize toxicity, include  dimercaprol ,  theophylline ,  warfarin  and  lithium carbonate .


Some antibiotics and antifungals require monitoring to balance efficacy with minimizing  adverse effects , including:  gentamicin ,  vancomycin ,  amphotericin B  (nicknamed 'amphoterrible' for this very reason), and  polymyxin B .


Radiotherapy aims to shrink tumors and kill cancer cells using high energy. The energy arises from  x-rays ,  gamma rays , or  charged  or heavy particles. The therapeutic ratio in radiotherapy for cancer treatment is determined by the maximum radiation dose for killing cancer cells and the minimum radiation dose causing acute or late morbidity in cells of normal tissues. [ 13 ]  Both of these parameters have  sigmoidal   dose–response curves . Thus, a favorable outcome in dose–response for tumor tissue is greater than that of normal tissue for the same dose, meaning that the treatment is effective on tumors and does not cause serious morbidity to normal tissue. Conversely, overlapping response for two tissues is highly likely to cause serious morbidity to normal tissue and ineffective treatment of tumors. The mechanism of radiation therapy is categorized as direct or indirect radiation. Both direct and indirect radiation induce  DNA mutation  or  chromosomal rearrangement  during its repair process. Direct radiation creates a DNA  free radical  from radiation energy deposition that damages DNA. Indirect radiation occurs from  radiolysis  of water, creating a free  hydroxyl radical ,  hydronium  and electron. The hydroxyl radical transfers its radical to DNA. Or together with hydronium and electron, a free hydroxyl radical can damage the base region of DNA. [ 14 ]


Cancer cells cause an imbalance of signals in the  cell cycle . G1 and G2/M arrest were found to be major checkpoints by irradiating human cells. G1 arrest delays the repair mechanism before synthesis of DNA in  S phase  and  mitosis  in M phase, suggesting it is a key checkpoint for survival of cells. G2/M arrest occurs when cells need to repair after S phase but before mitotic entry. It is known that S phase is the most resistant to radiation and M phase is the most sensitive to radiation.  p53 , a tumor suppressor protein that plays a role in G1 and G2/M arrest, enabled the understanding of the cell cycle through radiation. For example, irradiation of  myeloid leukemia  cells leads to an increase in p53 and a decrease in the level of DNA synthesis. Patients with  Ataxia telangiectasia  delays have hypersensitivity to radiation due to the delay of accumulation of p53. [ 15 ]  In this case, cells are able to replicate without repair of their DNA, becoming prone to incidence of cancer. Most cells are in G1 and S phase. Irradiation at G2 phase showed increased radiosensitivity and thus G1 arrest has been a focus for therapeutic treatment.
Irradiation of a tissue induces a response in both irradiated and non-irridiated cells. It was found that even cells up to 50–75 cell diameters distant from irradiated cells exhibit a  phenotype  of enhanced genetic instability such as micronucleation. [ 16 ]  This suggests an effect on cell-to-cell communication such as  paracrine  and  juxtacrine signaling . Normal cells do not lose their  DNA repair  mechanism whereas cancer cells often lose it during radiotherapy. However, the high energy radiation can override the ability of damaged normal cells to repair, leading to additional risk of  carcinogenesis . This suggests a significant risk associated with radiation therapy. Thus, it is desirable to improve the therapeutic ratio during radiotherapy. Employing IG-IMRT, protons and heavy ions are likely to minimize the dose to normal tissues by altered fractionation. Molecular targeting of the DNA repair pathway can lead to radiosensitization or radioprotection. Examples are direct and indirect inhibitors on DNA  double-strand breaks . Direct inhibitors target proteins ( PARP family ) and  kinases  (ATM, DNA-PKCs) that are involved in DNA repair. Indirect inhibitors target protein tumor cell signaling proteins such as  EGFR  and  insulin growth factor . [ 13 ]


The effective therapeutic index can be affected by  targeting , in which the therapeutic agent is concentrated in its desirable area of effect. For example, in  radiation therapy  for cancerous tumors, shaping the radiation beam precisely to the profile of a tumor in the "beam's eye view" can increase the delivered dose without increasing toxic effects, though such shaping might not change the therapeutic index. Similarly, chemotherapy or radiotherapy with infused or injected agents can be made more efficacious by attaching the agent to an oncophilic substance, as in  peptide receptor radionuclide therapy  for  neuroendocrine tumors  and in  chemoembolization  or radioactive microspheres therapy for liver tumors and metastases. This concentrates the agent in the targeted tissues and lowers its concentration in others, increasing efficacy and lowering toxicity.


Sometimes the term  safety ratio  is used, particularly when referring to  psychoactive drugs  used for non-therapeutic purposes, e.g. recreational use. [ 10 ]  In such cases, the  effective  dose is the amount and frequency that produces the  desired  effect, which can vary, and can be greater or less than the therapeutically effective dose.


The  Certain Safety Factor , also referred to as the  Margin of Safety (MOS) , is the ratio of the  lethal dose  to 1% of population to the  effective dose  to 99% of the population (LD 1 /ED 99 ). [ 17 ]  This is a better safety index than the  LD 50  for materials that have both desirable and undesirable effects, because it factors in the ends of the spectrum where doses may be necessary to produce a response in one person but can, at the same dose, be lethal in another.


A therapeutic index does not consider drug interactions or  synergistic  effects. For example, the risk associated with  benzodiazepines  increases significantly when taken with alcohol, opiates, or stimulants when compared with being taken alone. [ medical citation needed ]  Therapeutic index also does not take into account the ease or difficulty of reaching a toxic or lethal dose. This is more of a consideration for recreational drug users, as the purity can be highly variable.


The  therapeutic window  (or pharmaceutical window) of a drug is the range of drug dosages which can treat disease effectively without having toxic effects. [ 18 ]  Medication with a small therapeutic window must be administered with care and control, frequently measuring blood concentration of the drug, to avoid harm. Medications with narrow therapeutic windows include  theophylline ,  digoxin ,  lithium , and  warfarin .


Optimal biological dose (OBD) is the quantity of a drug that will most effectively produce the desired effect while remaining in the range of acceptable toxicity.


The  maximum tolerated dose  (MTD) refers to the highest dose of a radiological or  pharmacological  treatment that will produce the desired effect without unacceptable  toxicity . [ 19 ] [ 20 ]  The purpose of administering MTD is to determine whether long-term exposure to a chemical might lead to unacceptable  adverse health effects  in a population, when the level of exposure is not sufficient to cause premature  mortality  due to short-term  toxic effects . The maximum dose is used, rather than a lower dose, to reduce the number of  test subjects  (and, among other things, the cost of testing), to detect an effect that might occur only rarely. This type of analysis is also used in establishing  chemical residue  tolerances in foods. Maximum tolerated dose studies are also done in  clinical trials .


MTD is an essential aspect of a drug's profile. All modern healthcare systems dictate a maximum safe dose for each drug, and generally have numerous safeguards (e.g. insurance quantity limits and government-enforced maximum quantity/time-frame limits) to prevent the prescription and dispensing of quantities exceeding the highest dosage which has been demonstrated to be safe for members of the general patient population.


Patients are often unable to tolerate the theoretical MTD of a drug due to the occurrence of side-effects which are not innately a manifestation of toxicity (not considered to severely threaten a patient's health) but cause the patient sufficient distress and/or discomfort to result in non-compliance with treatment. Such examples include emotional "blunting" with antidepressants,  pruritus  with  opiates , and blurred vision with  anticholinergics .


Toxication ,  toxification  or  toxicity exaltation  is the conversion of a  chemical compound  into a more toxic form in living organisms or in substrates such as  soil  or  water . The conversion can be caused by  enzymatic   metabolism  in the organisms, as well as by  abiotic   chemical reactions . While the parent drug is usually less active, both the parent drug and its metabolite can be chemically active and cause  toxicity , leading to mutagenesis, teratogenesis, and carcinogenesis. [ 1 ] [ 2 ]  Different classes of enzymes, such as  P450 monooxygenases ,  epoxide hydrolase , or  acetyltransferases  can catalyze the process in the cell, mostly in the liver. [ 2 ]


Parent non-toxic chemicals are generally referred to as  protoxins . While toxication is generally undesirable, in certain cases it is required for the  in vivo  conversion of a  prodrug  to a metabolite with desired pharmacological or toxicological activity.   Codeine  is an example of a prodrug, metabolized in the body to the active compounds  morphine  and  codeine-6-glucuronide .


Phase I of  drug metabolism  are bioactivation pathways, which are catalyzed by  CYP450  enzymes, produce toxic metabolites and thus have the potential to damage cells. The unusual level of activity CYP450 enzymes might lead to the changes in drug metabolism and convert drugs into their more toxic forms. Among Phase I CYP450 enzymes, the subfamilies  CYP2D6  and  CYP3A  are responsible for  hepatotoxicity  during drug metabolism with a number of different drugs, including  flucloxacillin ,  troleandomycin , and  troglitazone . [ 3 ]   Hepatotoxicity indicates the drug's toxicity to liver.


Paracetamol  (acetaminophen, APAP) is converted into the hepatotoxic metabolite  NAPQI  via the  cytochrome P450 oxidase  system, mainly by the subfamily CYP2E1. Hepatic reduced glutathione (GSH) will detoxify this formed NAPQI quickly if APAP is taken at a proper level. In the case of overdoses, the storage of GSH will not be enough for NAPQI detoxication, thereby resulting in acute liver injury. [ 4 ]


Oxidoreductases  are enzymes that catalyze the reactions that involve the transfer of electrons.  Methanol  in itself is toxic due to its  central nervous system depression  properties, but it can be converted to formaldehyde by alcohol dehydrogenase and then converted to formic acid by aldehyde dehydrogenase, which are significantly more toxic.  Formic acid  and  formaldehyde  can cause severe  acidosis , damage to the  optic nerve , and other life-threatening complications. [ 5 ]


Ethylene glycol  (common antifreeze) can be converted into toxic  glycolic acid ,  glyoxylic acid  and  oxalic acid  by aldehyde dehydrogenase, lactate dehydrogenase (LDH) and glycolate oxidase in mammalian organisms. [ 5 ] [ 6 ]  The accumulation of the end product of the ethylene glycol mechanism,  calcium oxalate , may cause malfunction in the kidney and lead to more severe consequences. [ 5 ]


Other examples of toxication by enzymatic metabolism include:


Increases in toxicity can also be caused by  abiotic   chemical reactions.  Non-living elements affect the abiotic chemical reactions. Anthropogenic trace compounds (ATCs) have potential toxicity to the organisms in aquatic system. [ 9 ]


Arsenic  contamination in drinking water can be chemically toxic. The uptake and metabolism of arsenic may result in damage to the body. When organic arsenic is converted into more toxic inorganic arsenic, it causes carcinogenesis, cytotoxicity (toxic to cells) and genotoxicity (causing mutations in genes). [ 10 ]


Toxicokinetics  (often abbreviated as 'TK') is the description of both what rate a chemical will enter the body and what occurs to excrete and metabolize the compound once it is in the body.


It is an application of  pharmacokinetics  to determine the relationship between the systemic exposure of a compound and its  toxicity .  It is used primarily for establishing relationships between exposures in  toxicology  experiments in animals and the corresponding exposures in humans. However, it can also be used in environmental risk assessments in order to determine the potential effects of releasing chemicals into the environment. In order to quantify toxic effects, toxicokinetics can be combined with toxicodynamics. Such toxicokinetic-toxicodynamic (TKTD) models are used in  ecotoxicology  (see  ecotoxmodels  a website on mathematical models in ecotoxicology).


Similarly, physiological toxicokinetic models are  physiological pharmacokinetic models  developed to describe and predict the behavior of a toxicant in an animal body; for example, what parts (compartments) of the body a chemical may tend to enter (e.g. fat, liver, spleen, etc.), and whether or not the chemical is expected to be metabolized or excreted and at what rate.


Four potential processes exist for a chemical interacting with an animal:  absorption , distribution, metabolism and excretion (ADME). Absorption describes the entrance of the chemical into the body, and can occur through the air, water, food, or soil. Once a chemical is inside a body, it can be distributed to other areas of the body through diffusion or other biological processes. At this point, the chemical may undergo metabolism and be biotransformed into other chemicals ( metabolites ). These metabolites can be less or more toxic than the parent compound. After this potential  biotransformation  occurs, the metabolites may leave the body, be transformed into other compounds, or continue to be stored in the body compartments.


A well designed toxicokinetic study may involve several different strategies and depends on the scientific question to be answered.  Controlled  acute  and repeated toxicokinetic animal studies are useful to identify a chemical's biological persistence, tissue and whole body  half-life , and its potential to bioaccumulate. Toxicokinetic profiles can change with increasing exposure duration or dose. Real world environmental exposures generally occur as low level mixtures, such as from air, water, food, or tobacco products. Mixture effects may differ from individual chemical toxicokinetic profiles because of chemical interactions, synergistic, or competitive processes. For other reasons, it is equally important to characterize the toxicokinetics of individual chemicals constituents found in mixtures as information on behavior or fate of the individual chemical can help explain environmental, human, and wildlife biomonitoring studies. [ 1 ]


In  pharmacology , the  volume of distribution  (V D , also known as  apparent volume of distribution , literally,  volume of dilution [ 1 ] ) is the theoretical  volume  that would be necessary to contain the total amount of an administered  drug  at the same concentration that it is observed in the  blood plasma . [ 2 ]  In other words, it is the ratio of  amount of drug in a body (dose)  to  concentration of the drug that is measured in blood, plasma, and un-bound in interstitial fluid . [ 3 ] [ 4 ]


The V D  of a drug represents the degree to which a drug is distributed in body tissue rather than the plasma. V D  is directly proportional with the amount of drug distributed into tissue; a higher V D  indicates a greater amount of tissue distribution. A V D  greater than the total volume of body water (approximately 42 liters in humans [ 5 ] ) is possible, and would indicate that the drug is highly distributed into tissue. In other words, the volume of distribution is smaller in the drug staying in the plasma than that of a drug that is widely distributed in tissues. [ 6 ]


In rough terms, drugs with a high lipid solubility (non-polar drugs), low rates of ionization, or low plasma protein binding capabilities have higher volumes of distribution than drugs which are more polar, more highly ionized or exhibit high plasma protein binding in the body's environment. Volume of distribution may be increased by  kidney failure  (due to fluid retention) and  liver failure  (due to altered body fluid and  plasma protein binding ). Conversely it may be decreased in dehydration.


The  initial volume of distribution  describes blood concentrations prior to attaining the apparent volume of distribution and uses the same formula.


The volume of distribution is given by the following equation:


Therefore, the dose required to give a certain plasma concentration can be determined if the V D  for that drug is known. The V D  is  not  a physiological value; it is more a reflection of how a drug will distribute throughout the body depending on several physicochemical properties, e.g. solubility, charge, size, etc.


The unit for Volume of Distribution is typically reported in  litres.  As body composition changes with age, V D  decreases.


The V D  may also be used to determine how readily a drug will displace into the body tissue compartments relative to the blood:


If you administer a dose D of a drug intravenously in one go (IV-bolus), you would naturally expect it to have an immediate blood concentration

 C

 0

 {\displaystyle C_{0}}

  which directly corresponds to the amount of blood contained in the body

 V

 b
 l
 o
 o
 d

 {\displaystyle V_{blood}}

 . Mathematically this would be:


C

 0

 =
 D

 /

 V

 b
 l
 o
 o
 d

 {\displaystyle C_{0}=D/V_{blood}}


But this is generally not what happens. Instead you observe that the drug has distributed out into some other volume (read organs/tissue). So probably the first question you want to ask is: how much of the drug is no longer in the blood stream?
The volume of distribution

 V

 D

 {\displaystyle V_{D}}

  quantifies just that by specifying how big a volume you would need in order to observe the blood concentration actually measured.


An example for a simple case (mono-compartmental) would be to administer D=8 mg/kg to a human. A human has a blood volume of around

 V

 b
 l
 o
 o
 d

 =

 {\displaystyle V_{blood}=}

 0.08 L/kg
. [ 7 ]
This gives a

 C

 0

 =

 {\displaystyle C_{0}=}

 100 μg/mL if the drug stays in the blood stream only, and thus its volume of distribution is the same as

 V

 b
 l
 o
 o
 d

 {\displaystyle V_{blood}}

  that is

 V

 D

 =

 {\displaystyle V_{D}=}

  0.08 L/kg. If the drug distributes into all body water the volume of distribution would increase to approximately

 V

 D

 =

 {\displaystyle V_{D}=}

 0.57 L/kg
 [ 8 ]


If the drug readily diffuses into the body fat the volume of distribution may increase dramatically, an example is  chloroquine  which has a

 V

 D

 =

 {\displaystyle V_{D}=}

 250-302 L/kg
 [ 9 ]


In the simple mono-compartmental case the volume of distribution is defined as:

 V

 D

 =
 D

 /

 C

 0

 {\displaystyle V_{D}=D/C_{0}}

 , where the

 C

 0

 {\displaystyle C_{0}}

  in practice is an extrapolated concentration at time = 0 from the first early plasma concentrations after an IV-bolus administration (generally taken around 5 min - 30 min after giving the drug).


Pharmacodynamics  ( PD ) is the study of the  biochemical  and  physiologic  effects of  drugs  (especially  pharmaceutical drugs ). The effects can include those manifested within  animals  (including humans),  microorganisms , or combinations of  organisms  (for example,  infection ).


Pharmacodynamics and  pharmacokinetics  are the main branches of  pharmacology ,  being itself a topic of  biology  interested in the study of the interactions of both endogenous and exogenous chemical substances with living organisms.


In particular, pharmacodynamics is the study of how a drug affects an organism, whereas pharmacokinetics is the study of how the organism affects the drug. Both together influence  dosing , benefit, and  adverse effects . Pharmacodynamics is sometimes abbreviated as PD and  pharmacokinetics  as PK, especially in combined reference (for example, when speaking of  PK/PD models ).


Pharmacodynamics places particular emphasis on  dose–response relationships , that is, the relationships between drug  concentration  and effect. [ 1 ]   One dominant example is drug-receptor interactions as modeled by


where  L ,  R , and  LR  represent ligand (drug), receptor, and ligand-receptor complex concentrations, respectively. This equation represents a simplified model of  reaction dynamics  that can be studied mathematically through tools such as  free energy  maps.


Pharmacodynamics : Study of pharmacological actions on living systems, including the reactions with and binding to cell constituents, and the biochemical and physiological consequences of these actions. [ 2 ]


There are four principal protein targets with which drugs can interact:


NMBD = neuromuscular blocking drugs; NMDA = N-methyl-d-aspartate; EGF = epidermal growth factor. [ 3 ]


The majority of drugs either


There are 7 main drug actions: [ 4 ]


The desired activity of a drug is mainly due to successful targeting of one of the following:


General anesthetics  were once thought to work by disordering the neural membranes, thereby altering the Na +  influx.  Antacids  and  chelating agents  combine chemically in the body. Enzyme-substrate binding is a way to alter the production or metabolism of key  endogenous  chemicals, for example  aspirin  irreversibly inhibits the enzyme  prostaglandin synthetase (cyclooxygenase)  thereby preventing  inflammatory  response.  Colchicine , a drug for gout, interferes with the function of the structural protein  tubulin , while  digitalis , a drug still used in heart failure, inhibits the activity of the carrier molecule,  Na-K-ATPase pump . The widest class of drugs act as ligands that bind to receptors that determine cellular effects. Upon drug binding, receptors can elicit their normal action (agonist), blocked action (antagonist), or even action opposite to normal (inverse agonist).


In principle, a pharmacologist would aim for a target  plasma  concentration of the drug for a desired level of response. In reality, there are many factors affecting this goal. Pharmacokinetic factors determine peak concentrations, and concentrations cannot be maintained with absolute consistency because of metabolic breakdown and excretory clearance.  Genetic  factors may exist which would alter metabolism or drug action itself, and a patient's immediate status may also affect indicated dosage.


Undesirable effects of a drug include:


The therapeutic window is the amount of a  medication  between the amount that gives an effect ( effective dose ) and the amount that gives more  adverse effects  than desired effects. For instance, medication with a small pharmaceutical window must be administered with care and control, e.g. by frequently measuring blood concentration of the drug, since it easily loses effects or gives adverse effects.


The  duration of action  of a drug is the length of time that particular drug is effective. [ 5 ]   Duration of action is a function of several parameters including  plasma half-life , the time to equilibrate between plasma and target compartments, and the off rate of the drug from its  biological target . [ 6 ]


In recreational psychoactive drug spaces, duration refers to the length of time over which the  subjective effects  of a  psychoactive substance  manifest themselves.
Duration can be broken down into 6 parts: (1) total duration (2) onset (3) come up (4) peak (5) offset and (6) after effects. Depending upon the substance consumed, each of these occurs in a separate and continuous fashion.


The total duration of a substance can be defined as the amount of time it takes for the effects of a substance to completely wear off into  sobriety , starting from the moment the substance is first  administered .


The onset phase can be defined as the period until the very first changes in perception (i.e. "first alerts") are able to be detected.


The "come up" phase can be defined as the period between the first noticeable changes in perception and the point of highest subjective intensity. This is colloquially known as "coming up."


The peak phase can be defined as period of time in which the intensity of the substance's effects are at its height.


The offset phase can be defined as the amount of time in between the conclusion of the peak and shifting into a sober state. This is colloquially referred to as "coming down."


The after effects can be defined as any residual effects which may remain after the experience has reached its conclusion. After effects depend on the substance and usage. This is colloquially known as a "hangover" for negative after effects of substances, such as  alcohol ,  cocaine , and  MDMA  or an "afterglow" for describing a typically positive, pleasant effect, typically found in substances such as  cannabis ,  LSD  in low to high doses, and  ketamine .


The binding of ligands (drug) to receptors is governed by the  law of mass action  which relates the large-scale status to the rate of numerous molecular processes. The rates of formation and un-formation can be used to determine the equilibrium concentration of bound receptors. The  equilibrium dissociation constant  is defined by:


where  L =ligand,  R =receptor, square brackets [] denote concentration. The fraction of bound receptors is


Where

 p

 L
 R

 {\displaystyle {p}_{LR}}

  is the fraction of receptor bound by the ligand.


This expression is one way to consider the effect of a drug, in which the response is related to the fraction of bound receptors (see:  Hill equation ). The fraction of bound receptors is known as occupancy. The relationship between occupancy and pharmacological response is usually non-linear. This explains the so-called  receptor reserve  phenomenon i.e. the concentration producing 50% occupancy is typically higher than the concentration producing 50% of maximum response. More precisely, receptor reserve refers to a phenomenon whereby stimulation of only a fraction of the whole receptor population apparently elicits the maximal effect achievable in a particular tissue.


The simplest interpretation of receptor reserve is that it is a model that states there are excess receptors on the cell surface than what is necessary for full effect. Taking a more sophisticated approach, receptor reserve is an integrative measure of the response-inducing capacity of an  agonist  (in some receptor models it is termed intrinsic efficacy or  intrinsic activity ) and of the signal amplification capacity of the corresponding receptor (and its downstream signaling pathways). Thus, the existence (and magnitude) of receptor reserve depends on the agonist ( efficacy ), tissue (signal amplification ability) and measured effect (pathways activated to cause signal amplification). As receptor reserve is very sensitive to agonist's intrinsic efficacy, it is usually defined only for full (high-efficacy) agonists. [ 7 ] [ 8 ] [ 9 ]


Often the response is determined as a function of log[ L ] to consider many orders of magnitude of concentration. However, there is no biological or physical theory that relates effects to the log of concentration. It is just convenient for graphing purposes. It is useful to note that 50% of the receptors are bound when [ L ]= K d  .


The graph shown represents the conc-response for two hypothetical receptor agonists, plotted in a semi-log fashion. The curve toward the left represents a higher potency (potency arrow does not indicate direction of increase) since lower concentrations are needed for a given response. The effect increases as a function of concentration.


The concept of pharmacodynamics has been expanded to include  Multicellular Pharmacodynamics  (MCPD). MCPD is the study of the static and dynamic properties and relationships between a set of drugs and a dynamic and diverse multicellular four-dimensional organization. It is the study of the workings of a drug on a minimal multicellular system (mMCS), both  in vivo  and  in silico .  Networked Multicellular Pharmacodynamics  (Net-MCPD) further extends the concept of MCPD to model regulatory genomic networks together with signal transduction pathways, as part of a complex of interacting components in the cell. [ 10 ]


Toxicodynamics (TD) and pharmacodynamics (PD) link a therapeutic agent or toxicant, or toxin (xenobiotic)'s dosage to the features, amount, and time course of its biological action. [ 11 ]  The mechanism of action is a crucial factor in determining effect and toxicity of the drug, taking in consideration the pharmacokinetic (PK) factors. [ 12 ]  The sort and extent of altered cellular physiology will depend on the combination of the drug's presence (as established by pharmacokinetic (PK) studies) and/or its mechanism and duration of action (PD). Types of xenobiotic-target interaction can be described either by reversible, irreversible, noncompetitive, and allosteric interaction or agonist, partial agonist, antagonist, and inverse interactions.  In vitro, ex vivo,  or  in vivo  studies can be used to assess PD and TD from the molecule to the level of the entire organism.


The mechanism of drug action and adverse drug reaction is either physiochemical property based and biochemical based. Adverse drugs reactions can be classified as either idiosyncratic (type B) or intrinsic (type A). Idiosyncratic toxicity is not dosage dependent and defy the mass-action relationship. Immune-mediated processes are frequently cited as the source of type B reactions. [ 13 ]  These cannot be accurately described in preclinical research or clinical trials due to their low incidence frequency. Type A reactions are dosage (concentration) dependent. Usually, this kind of side effect is an extension of an ongoing treatment.


Pharmacokinetics and pharmacodynamics are termed  toxicokinetics  and  toxicodynamics  in the field of  ecotoxicology . Here, the focus is on toxic effects on a wide range of organisms. The corresponding models are called toxicokinetic-toxicodynamic models. [ 14 ]


An  agonist  is a chemical that activates a  receptor  to produce a biological response. Receptors are  cellular   proteins  whose activation causes the cell to modify what it is currently doing. In contrast, an  antagonist  blocks the action of the agonist, while an  inverse agonist  causes an action opposite to that of the agonist.


The word originates from the  Greek  word  αγωνιστής  (agōnistēs), contestant; champion; rival <  αγων  (agōn), contest, combat; exertion, struggle <  αγω  (agō), I lead, lead towards, conduct; drive.


Receptors  can be activated by either  endogenous  agonists (such as  hormones  and  neurotransmitters ) or  exogenous  agonists (such as  drugs ), resulting in a biological response. A  physiological agonist  is a substance that creates the same bodily responses but does not bind to the same receptor.


New findings that broaden the conventional definition of pharmacology demonstrate that  ligands  can concurrently behave as agonist  and  antagonists at the same receptor, depending on effector pathways or tissue type. Terms that describe this phenomenon are " functional selectivity ", "protean agonism", [ 5 ] [ 6 ] [ 7 ]  or  selective receptor modulators . [ 8 ]


As mentioned above, agonists have the potential to bind in different locations and in different ways depending on the type of agonist and the type of receptor. [ 9 ]  The process of binding is unique to the receptor-agonist relationship, but binding induces a conformational change and activates the receptor. [ 9 ] [ 10 ]  This conformational change is often the result of small changes in  charge  or changes in  protein folding  when the agonist is bound. [ 10 ] [ 11 ]  Two examples that demonstrate this process are the  muscarinic acetylcholine receptor  and  NMDA receptor  and their respective agonists.


For the  muscarinic acetylcholine receptor , which is a  G protein-coupled receptor [ 10 ] (GPCR), the  endogenous agonist  is  acetylcholine . The binding of this  neurotransmitter  causes the conformational changes that propagate a signal into the cell. [ 10 ]  The conformational changes are the primary effect of the agonist, and are related to the agonist's binding affinity and agonist  efficacy . [ 9 ] [ 12 ]  Other agonists that bind to this receptor will fall under one of the different categories of agonist mentioned above based on their specific binding affinity and efficacy.


The  NMDA receptor  is an example of an alternate mechanism of action, as the NMDA receptor requires co-agonists for activation. Rather than simply requiring a single specific agonist, the NMDA receptor requires both the  endogenous agonists ,  N-methyl-D-aspartate  (NMDA) and  glycine . [ 11 ]  These co-agonists are both required to induce the conformational change needed for the NMDA receptor to allow flow through the  ion channel , in this case calcium. [ 11 ]  An aspect demonstrated by the NMDA receptor is that the mechanism or response of agonists can be blocked by a variety of chemical and biological factors. [ 11 ]  NMDA receptors specifically are blocked by a  magnesium  ion unless the cell is also experiencing  depolarization . [ 11 ]


These differences show that agonists have unique mechanisms of action depending on the receptor activated and the response needed. [ 9 ] [ 10 ]  The goal and process remains generally consistent however, with the primary mechanism of action requiring the binding of the agonist and the subsequent changes in conformation to cause the desired response at the receptor. [ 9 ] [ 12 ]  This response as discussed above can vary from allowing flow of  ions  to activating a  GPCR  and transmitting a signal into the  cell . [ 9 ] [ 10 ]


Potency is the amount of agonist needed to elicit a desired response. The  potency  of an agonist is inversely related to its  half maximal effective concentration  (EC 50 ) value. The EC 50  can be measured for a given agonist by determining the concentration of agonist needed to elicit half of the maximum biological response of the agonist. The EC 50  value is useful for comparing the potency of drugs with similar  efficacies  producing physiologically similar effects.  The smaller the EC 50  value, the greater the potency of the agonist, the lower the concentration of drug that is required to elicit the maximum biological response.


When a drug is used therapeutically, it is important to understand the margin of safety that exists between the dose needed for the desired effect and the dose that produces unwanted and possibly dangerous side-effects (measured by the TD 50 , the dose that produces toxicity in 50% of individuals). This relationship, termed the  therapeutic index , is defined as the ratio  TD 50 : ED 50 . In general, the narrower this margin, the more likely it is that the drug will produce unwanted effects. The therapeutic index emphasizes the importance of the margin of safety, as distinct from the potency, in determining the usefulness of a drug.


In pharmacology the term  agonist-antagonist  or  mixed agonist/antagonist  is used to refer to a drug which under some conditions behaves as an  agonist  (a substance that fully activates the receptor that it binds to) while under other conditions, behaves as an  antagonist  (a substance that binds to a receptor but does not activate and can block the activity of other agonists).


Types of mixed agonist/antagonist include  receptor ligands  that act as agonist for some receptor types and antagonist for others [ 1 ]  or agonist in some tissues while antagonist in others (also known as  selective receptor modulators ).