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Pharmacokinetics (from
Ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic pe ...
''pharmakon'' "drug" and ''kinetikos'' "moving, putting in motion"; see
chemical kinetics Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is to be contrasted with chemical thermodynamics, which deals with the direction in ...
), sometimes abbreviated as PK, is a branch of pharmacology dedicated to determining the fate of substances administered to a living organism. The substances of interest include any chemical xenobiotic such as:
pharmaceutical drug A medication (also called medicament, medicine, pharmaceutical drug, medicinal drug or simply drug) is a drug used to diagnose, cure, treat, or prevent disease. Drug therapy ( pharmacotherapy) is an important part of the medical field and ...
s, pesticides, food additives,
cosmetics Cosmetics are constituted mixtures of chemical compounds derived from either natural sources, or synthetically created ones. Cosmetics have various purposes. Those designed for personal care and skin care can be used to cleanse or protec ...
, etc. It attempts to analyze chemical
metabolism Metabolism (, from el, μεταβολή ''metabolē'', "change") is the set of life-sustaining chemical reactions in organisms. The three main functions of metabolism are: the conversion of the energy in food to energy available to run ...
and to discover the fate of a chemical from the moment that it is administered up to the point at which it is completely eliminated from the body. Pharmacokinetics is the study of how an organism affects a drug, whereas
pharmacodynamics 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 ...
(PD) is the study of how the drug affects the organism. Both together influence dosing, benefit, and
adverse effect An adverse effect is an undesired harmful effect resulting from a medication or other intervention, such as surgery. An adverse effect may be termed a " side effect", when judged to be secondary to a main or therapeutic effect. The term compl ...
s, as seen in PK/PD models.


Overview

Pharmacokinetics describes how the body affects a specific xenobiotic/chemical after administration through the mechanisms of absorption and distribution, as well as the metabolic changes of the substance in the body (e.g. by metabolic
enzyme Enzymes () are proteins that act as biological catalysts by accelerating chemical reactions. The molecules upon which enzymes may act are called substrates, and the enzyme converts the substrates into different molecules known as products ...
s such as
cytochrome P450 Cytochromes P450 (CYPs) are a superfamily of enzymes containing heme as a cofactor that functions as monooxygenases. In mammals, these proteins oxidize steroids, fatty acids, and xenobiotics, and are important for the clearance of various co ...
or glucuronosyltransferase enzymes), and the effects and routes of excretion of the metabolites of the drug. Pharmacokinetic properties of chemicals are affected by the route of administration and the dose of administered drug. These may affect the absorption rate. Models have been developed to simplify conceptualization of the many processes that take place in the interaction between an organism and a chemical substance. One of these, the multi-compartmental model, is the most commonly used approximations to reality; however, the complexity involved in adding parameters with that modelling approach means that ''monocompartmental models'' and above all ''two compartmental models'' are the most-frequently used. The various compartments that the model is divided into are commonly referred to as the ADME scheme (also referred to as LADME if liberation is included as a separate step from absorption): * Liberation – the process of release of a drug from the
pharmaceutical formulation Pharmaceutical formulation, in pharmaceutics, is the process in which different chemical substances, including the active drug, are combined to produce a final medicinal product. The word ''formulation'' is often used in a way that includes dosage ...
. See also IVIVC. * Absorption – the process of a substance entering the blood circulation. * Distribution – the dispersion or dissemination of substances throughout the fluids and tissues of the body. * Metabolism (or biotransformation, or inactivation) – the recognition by the organism that a foreign substance is present and the irreversible transformation of parent compounds into daughter metabolites. * Excretion – the removal of the substances from the body. In rare cases, some drugs irreversibly accumulate in body tissue. The two phases of metabolism and excretion can also be grouped together under the title elimination. The study of these distinct phases involves the use and manipulation of basic concepts in order to understand the process dynamics. For this reason, in order to fully comprehend the ''kinetics'' of a drug it is necessary to have detailed knowledge of a number of factors such as: the properties of the substances that act as excipients, the characteristics of the appropriate biological membranes and the way that substances can cross them, or the characteristics of the enzyme reactions that inactivate the drug. All these concepts can be represented through mathematical formulas that have a corresponding graphical representation. The use of these models allows an understanding of the characteristics of a
molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and b ...
, as well as how a particular drug will behave given information regarding some of its basic characteristics such as its acid dissociation constant (pKa), bioavailability and
solubility In chemistry, solubility is the ability of a substance, the solute, to form a solution with another substance, the solvent. Insolubility is the opposite property, the inability of the solute to form such a solution. The extent of the solubi ...
, absorption capacity and distribution in the organism. The model outputs for a drug can be used in industry (for example, in calculating
bioequivalence Bioequivalence is a term in pharmacokinetics used to assess the expected in vivo biological equivalence of two proprietary preparations of a drug. If two products are said to be bioequivalent it means that they would be expected to be, for all ...
when designing generic drugs) or in the clinical application of pharmacokinetic concepts. Clinical pharmacokinetics provides many performance guidelines for effective and efficient use of drugs for human-health professionals and in
veterinary medicine Veterinary medicine is the branch of medicine that deals with the prevention, management, diagnosis, and treatment of disease, disorder, and injury in animals. Along with this, it deals with animal rearing, husbandry, breeding, research on nutri ...
.


Metrics

The following are the most commonly measured pharmacokinetic metrics: The units of the dose in the table are expressed in
moles Moles can refer to: * Moles de Xert, a mountain range in the Baix Maestrat comarca, Valencian Community, Spain *The Moles (Australian band) *The Moles, alter ego of Scottish band Simon Dupree and the Big Sound People * Abraham Moles, French engin ...
(mol) and molar (M). To express the metrics of the table in units of mass, instead of Amount of substance, simply replace 'mol' with 'g' and 'M' with 'g/dm3'. Similarly, other units in the table may be expressed in units of an equivalent
dimension In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coord ...
by scaling. In pharmacokinetics, ''steady state'' refers to the situation where the overall intake of a drug is fairly in dynamic equilibrium with its elimination. In practice, it is generally considered that once regular dosing of a drug is started, steady state is reached after 3 to 5 times its half-life.


Pharmacokinetic models

Pharmacokinetic modelling is performed by noncompartmental or compartmental methods. Noncompartmental methods estimate the exposure to a drug by estimating the area under the curve of a concentration-time graph. Compartmental methods estimate the concentration-time graph using kinetic models. Noncompartmental methods are often more versatile in that they do not assume any specific compartmental model and produce accurate results also acceptable for bioequivalence studies. The outcome of the transformations that a drug undergoes in an organism and the rules that determine this fate depend on a number of interrelated factors. A number of functional models have been developed in order to simplify the study of pharmacokinetics. These models are based on a consideration of an organism as a number of related compartments. The simplest idea is to think of an organism as only one homogenous compartment. This ''monocompartmental model'' presupposes that
blood plasma Blood plasma is a light amber-colored liquid component of blood in which blood cells are absent, but contains proteins and other constituents of whole blood in suspension. It makes up about 55% of the body's total blood volume. It is the int ...
concentrations of the drug are a true reflection of the drug's concentration in other fluids or tissues and that the elimination of the drug is directly proportional to the drug's concentration in the organism (
first order kinetics In chemistry, the rate law or rate equation for a reaction is an equation that links the initial or forward reaction rate with the concentrations or pressures of the reactants and constant parameters (normally rate coefficients and partial react ...
). However, these models do not always truly reflect the real situation within an organism. For example, not all body tissues have the same blood supply, so the distribution of the drug will be slower in these tissues than in others with a better blood supply. In addition, there are some tissues (such as the
brain A brain is an organ (biology), organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals. It is located in the head, usually close to the sensory organs for senses such as Visual perception, vision. I ...
tissue) that present a real barrier to the distribution of drugs, that can be breached with greater or lesser ease depending on the drug's characteristics. If these relative conditions for the different tissue types are considered along with the rate of elimination, the organism can be considered to be acting like two compartments: one that we can call the ''central compartment'' that has a more rapid distribution, comprising organs and systems with a well-developed blood supply; and a ''peripheral compartment'' made up of organs with a lower blood flow. Other tissues, such as the brain, can occupy a variable position depending on a drug's ability to cross the barrier that separates the organ from the blood supply. This ''two compartment model'' will vary depending on which compartment elimination occurs in. The most common situation is that elimination occurs in the central compartment as the
liver The liver is a major organ only found in vertebrates which performs many essential biological functions such as detoxification of the organism, and the synthesis of proteins and biochemicals necessary for digestion and growth. In humans, it i ...
and kidneys are organs with a good blood supply. However, in some situations it may be that elimination occurs in the peripheral compartment or even in both. This can mean that there are three possible variations in the two compartment model, which still do not cover all possibilities.Milo Gibaldi, Donald Perrier. ''Farmacocinética''Reverté 1982 pages 1–10. , 9788429155358 This model may not be applicable in situations where some of the enzymes responsible for metabolizing the drug become saturated, or where an active elimination mechanism is present that is independent of the drug's plasma concentration. In the real world each tissue will have its own distribution characteristics and none of them will be strictly linear. If we label the drug's
volume of distribution In pharmacology, the volume of distribution (VD, also known as apparent volume of distribution, literally, ''volume of dilution'') is the theoretical volume that would be necessary to contain the total amount of an administered drug at the same c ...
within the organism VdF and its volume of distribution in a tissue VdT the former will be described by an equation that takes into account all the tissues that act in different ways, that is: : Vd_F = Vd_ + Vd_ + Vd_ + \cdots + Vd_\, This represents the ''multi-compartment model'' with a number of curves that express complicated equations in order to obtain an overall curve. A number of
computer program A computer program is a sequence or set of instructions in a programming language for a computer to Execution (computing), execute. Computer programs are one component of software, which also includes software documentation, documentation and oth ...
s have been developed to plot these equations. However complicated and precise this model may be, it still does not truly represent reality despite the effort involved in obtaining various distribution values for a drug. This is because the concept of distribution volume is a relative concept that is not a true reflection of reality. The choice of model therefore comes down to deciding which one offers the lowest margin of error for the drug involved.


Noncompartmental analysis

Noncompartmental PK analysis is highly dependent on estimation of total drug exposure. Total drug exposure is most often estimated by area under the curve (AUC) methods, with the trapezoidal rule (
numerical integration In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equatio ...
) the most common method. Due to the dependence on the length of ''x'' in the trapezoidal rule, the area estimation is highly dependent on the blood/plasma sampling schedule. That is, the closer time points are, the closer the trapezoids reflect the actual shape of the concentration-time curve. The number of time points available in order to perform a successful NCA analysis should be enough to cover the absorption, distribution and elimination phase to accurately characterize the drug. Beyond AUC exposure measures, parameters such as Cmax (maximum concentration), Tmax(time at maximum concentration), CL and Vd can also be reported using NCA methods.


Compartmental analysis

Compartmental PK analysis uses kinetic models to describe and predict the concentration-time curve. PK compartmental models are often similar to kinetic models used in other scientific disciplines such as
chemical kinetics Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is to be contrasted with chemical thermodynamics, which deals with the direction in ...
and
thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws ...
. The advantage of compartmental over some noncompartmental analyses is the ability to predict the concentration at any time. The disadvantage is the difficulty in developing and validating the proper model. Compartment-free modelling based on curve stripping does not suffer this limitation. The simplest PK compartmental model is the one-compartmental PK model with IV bolus administration and first-order elimination. The most complex PK models (called
PBPK Physiologically based pharmacokinetic (PBPK) modeling is a mathematical modeling technique for predicting the absorption, distribution, metabolism and excretion (ADME) of synthetic or natural chemical substances in humans and other animal species ...
models) rely on the use of physiological information to ease development and validation.


Single-compartment model

''Linear pharmacokinetics'' is so-called because the graph of the relationship between the various factors involved ( dose, blood plasma concentrations, elimination, etc.) gives a straight line or an approximation to one. For drugs to be effective they need to be able to move rapidly from blood plasma to other body fluids and tissues. The change in concentration over time can be expressed as C=C_\text \times e^


Multi-compartmental models

The graph for the non-linear relationship between the various factors is represented by a curve; the relationships between the factors can then be found by calculating the dimensions of different areas under the curve. The models used in ''non-linear pharmacokinetics'' are largely based on Michaelis–Menten kinetics. A reaction's factors of non-linearity include the following: * Multiphasic absorption: Drugs injected intravenously are removed from the plasma through two primary mechanisms: (1) Distribution to body tissues and (2) metabolism + excretion of the drugs. The resulting decrease of the drug's plasma concentration follows a biphasic pattern (see figure). ** Alpha phase: An initial phase of rapid decrease in plasma concentration. The decrease is primarily attributed to drug distribution from the central compartment (circulation) into the peripheral compartments (body tissues). This phase ends when a pseudo-equilibrium of drug concentration is established between the central and peripheral compartments. ** Beta phase: A phase of gradual decrease in plasma concentration after the alpha phase. The decrease is primarily attributed to drug elimination, that is, metabolism and excretion. ** Additional phases (gamma, delta, etc.) are sometimes seen. * A drug's characteristics make a clear distinction between tissues with high and low blood flow. * Enzymatic saturation: When the dose of a drug whose elimination depends on biotransformation is increased above a certain threshold the enzymes responsible for its metabolism become saturated. The drug's plasma concentration will then increase disproportionately and its elimination will no longer be constant. * Induction or enzymatic inhibition: Some drugs have the capacity to inhibit or stimulate their own metabolism, in negative or positive feedback reactions. As occurs with fluvoxamine, fluoxetine and
phenytoin Phenytoin (PHT), sold under the brand name Dilantin among others, is an anti-seizure medication. It is useful for the prevention of tonic-clonic seizures (also known as grand mal seizures) and focal seizures, but not absence seizures. The in ...
. As larger doses of these pharmaceuticals are administered the plasma concentrations of the unmetabolized drug increases and the
elimination half-life Biological half-life (also known as elimination half-life, pharmacologic half-life) is the time taken for concentration of a biological substance (such as a medication) to decrease from its maximum concentration ( Cmax) to half of Cmax in the b ...
increases. It is therefore necessary to adjust the dose or other treatment parameters when a high dosage is required. * The kidneys can also establish active elimination mechanisms for some drugs, independent of plasma concentrations. It can therefore be seen that non-linearity can occur because of reasons that affect the entire pharmacokinetic sequence: absorption, distribution, metabolism and elimination.


Bioavailability

At a practical level, a drug's bioavailability can be defined as the proportion of the drug that reaches its site of action. From this perspective the intravenous administration of a drug provides the greatest possible bioavailability, and this method is considered to yield a bioavailability of 1 (or 100%). Bioavailability of other delivery methods is compared with that of intravenous injection (absolute bioavailability) or to a standard value related to other delivery methods in a particular study (relative bioavailability). : B_A = \frac : \mathit B_R = \frac Once a drug's bioavailability has been established it is possible to calculate the changes that need to be made to its dosage in order to reach the required blood plasma levels. Bioavailability is, therefore, a mathematical factor for each individual drug that influences the administered dose. It is possible to calculate the amount of a drug in the blood plasma that has a real potential to bring about its effect using the formula: :De = B \cdot Da\, where ''De'' is the effective dose, ''B'' bioavailability and ''Da'' the administered dose. Therefore, if a drug has a bioavailability of 0.8 (or 80%) and it is administered in a dose of 100 mg, the equation will demonstrate the following: :''De'' = 0.8 × 100 mg = 80 mg That is the 100 mg administered represents a blood plasma concentration of 80 mg that has the capacity to have a pharmaceutical effect. This concept depends on a series of factors inherent to each drug, such as:Michael E. Winter, Mary Anne Koda-Kimple, Lloyd Y. Young, Emilio Pol Yanguas ''Farmacocinética clínica básica'' Ediciones Díaz de Santos, 1994 pgs. 8–14 , 9788479781477 (in Spanish) *
Pharmaceutical form Dosage forms (also called unit doses) are pharmaceutical drug products in the form in which they are marketed for use, with a specific mixture of active ingredients and inactive components (excipients), in a particular configuration (such as a cap ...
* Chemical form * Route of administration * Stability *
Metabolism Metabolism (, from el, μεταβολή ''metabolē'', "change") is the set of life-sustaining chemical reactions in organisms. The three main functions of metabolism are: the conversion of the energy in food to energy available to run ...
These concepts, which are discussed in detail in their respective titled articles, can be mathematically quantified and integrated to obtain an overall mathematical equation: : De = Q\cdot Da\cdot B\, where Q is the drug's purity. : Va = \frac \tau where Va is the drug's rate of administration and \tau is the rate at which the absorbed drug reaches the circulatory system. Finally, using the Henderson-Hasselbalch equation, and knowing the drug's pKa\, ( pH at which there is an equilibrium between its ionized and non ionized molecules), it is possible to calculate the non ionized concentration of the drug and therefore the concentration that will be subject to absorption: : \mathrm = \mathrm + \log \frac B A When two drugs have the same bioavailability, they are said to be biological equivalents or bioequivalents. This concept of
bioequivalence Bioequivalence is a term in pharmacokinetics used to assess the expected in vivo biological equivalence of two proprietary preparations of a drug. If two products are said to be bioequivalent it means that they would be expected to be, for all ...
is important because it is currently used as a yardstick in the authorization of generic drugs in many countries.


LADME

A number of phases occur once the drug enters into contact with the organism, these are described using the acronym LADME: *
Liberation Liberation or liberate may refer to: Film and television * ''Liberation'' (film series), a 1970–1971 series about the Great Patriotic War * "Liberation" (''The Flash''), a TV episode * "Liberation" (''K-9''), an episode Gaming * '' Liberati ...
of the active substance from the delivery system, *
Absorption Absorption may refer to: Chemistry and biology *Absorption (biology), digestion **Absorption (small intestine) *Absorption (chemistry), diffusion of particles of gas or liquid into liquid or solid materials *Absorption (skin), a route by which s ...
of the active substance by the organism, *
Distribution Distribution may refer to: Mathematics * Distribution (mathematics), generalized functions used to formulate solutions of partial differential equations *Probability distribution, the probability of a particular value or value range of a vari ...
through the blood plasma and different body tissues, *
Metabolism Metabolism (, from el, μεταβολή ''metabolē'', "change") is the set of life-sustaining chemical reactions in organisms. The three main functions of metabolism are: the conversion of the energy in food to energy available to run ...
that is inactivation of the xenobiotic substance, and finally *
Excretion Excretion is a process in which metabolic waste is eliminated from an organism. In vertebrates this is primarily carried out by the lungs, kidneys, and skin. This is in contrast with secretion, where the substance may have specific tasks after ...
or elimination of the substance or the products of its metabolism. Some textbooks combine the first two phases as the drug is often administered in an active form, which means that there is no liberation phase. Others include a phase that combines distribution, metabolism and excretion into a disposition phase. Other authors include the drug's toxicological aspect in what is known as ''ADME-Tox'' or ''ADMET''. Each of the phases is subject to physico-chemical interactions between a drug and an organism, which can be expressed mathematically. Pharmacokinetics is therefore based on mathematical equations that allow the prediction of a drug's behavior and which place great emphasis on the relationships between drug plasma concentrations and the time elapsed since the drug's administration.


Analysis


Bioanalytical methods

Bioanalytical methods are necessary to construct a concentration-time profile. Chemical techniques are employed to measure the concentration of drugs in
biological matrix In chemical analysis, matrix refers to the components of a sample other than the analyte of interest. The matrix can have a considerable effect on the way the analysis is conducted and the quality of the results are obtained; such effects are calle ...
, most often plasma. Proper bioanalytical methods should be selective and sensitive. For example, microscale thermophoresis can be used to quantify how the biological matrix/liquid affects the affinity of a drug to its target. *


Mass spectrometry

Pharmacokinetics is often studied using mass spectrometry because of the complex nature of the matrix (often plasma or urine) and the need for high sensitivity to observe concentrations after a low dose and a long time period. The most common instrumentation used in this application is LC-MS with a triple quadrupole mass spectrometer. Tandem mass spectrometry is usually employed for added specificity. Standard curves and internal standards are used for quantitation of usually a single pharmaceutical in the samples. The samples represent different time points as a pharmaceutical is administered and then metabolized or cleared from the body. Blank samples taken before administration are important in determining background and ensuring data integrity with such complex sample matrices. Much attention is paid to the linearity of the standard curve; however it is common to use curve fitting with more complex functions such as quadratics since the response of most mass spectrometers is not linear across large concentration ranges. There is currently considerable interest in the use of very high sensitivity mass spectrometry for microdosing studies, which are seen as a promising alternative to animal experimentation. Recent studies show that Secondary electrospray ionization (SESI-MS) can be used in drug monitoring, presenting the advantage of avoiding animal sacrifice.


Population pharmacokinetics

''Population pharmacokinetics'' is the study of the sources and correlates of variability in drug concentrations among individuals who are the target patient population receiving clinically relevant doses of a drug of interest. Certain patient demographic, pathophysiological, and therapeutical features, such as body weight, excretory and metabolic functions, and the presence of other therapies, can regularly alter dose-concentration relationships and can explain variability in exposures. For example, steady-state concentrations of drugs eliminated mostly by the kidney are usually greater in patients with
kidney failure Kidney failure, also known as end-stage kidney disease, is a medical condition in which the kidneys can no longer adequately filter waste products from the blood, functioning at less than 15% of normal levels. Kidney failure is classified as eit ...
than they are in patients with normal kidney function receiving the same drug dosage. Population pharmacokinetics seeks to identify the measurable pathophysiologic factors and explain sources of variability that cause changes in the dose-concentration relationship and the extent of these changes so that, if such changes are associated with clinically relevant and significant shifts in exposures that impact the therapeutic index, dosage can be appropriately modified. An advantage of population pharmacokinetic modelling is its ability to analyse sparse data sets (sometimes only one concentration measurement per patient is available).


Clinical pharmacokinetics

Clinical pharmacokinetics (arising from the clinical use of population pharmacokinetics) is the direct application to a therapeutic situation of knowledge regarding a drug's pharmacokinetics and the characteristics of a population that a patient belongs to (or can be ascribed to). An example is the relaunch of the use of ciclosporin as an immunosuppressor to facilitate organ transplant. The drug's therapeutic properties were initially demonstrated, but it was almost never used after it was found to cause nephrotoxicity in a number of patients. However, it was then realized that it was possible to individualize a patient's dose of ciclosporin by analysing the patients plasmatic concentrations (pharmacokinetic monitoring). This practice has allowed this drug to be used again and has facilitated a great number of organ transplants. Clinical monitoring is usually carried out by determination of plasma concentrations as this data is usually the easiest to obtain and the most reliable. The main reasons for determining a drug's plasma concentration include: * Narrow therapeutic range (difference between toxic and therapeutic concentrations) * High toxicity * High risk to life.


Ecotoxicology

Ecotoxicology Ecotoxicology is the study of the effects of toxic chemicals on biological organisms, especially at the population, community, ecosystem, and biosphere levels. Ecotoxicology is a multidisciplinary field, which integrates toxicology and ecolog ...
is the branch of science that deals with the nature, effects, and interactions of substances that are harmful to the environment such as microplastics and other biosphere harmful substances. Ecotoxicology is studied in pharmacokinetics due to the substances responsible for harming the environment such as pesticides can get into the bodies of living organisms. The health effects of these chemicals is thus subject to research and safety trials by government or international agencies such as the
EPA The Environmental Protection Agency (EPA) is an independent executive agency of the United States federal government tasked with environmental protection matters. President Richard Nixon proposed the establishment of EPA on July 9, 1970; it be ...
or WHO. How long these chemicals stay in the body, the lethal dose and other factors are the main focus of Ecotoxicology.


See also

*
Bateman equation In nuclear physics, the Bateman equation is a mathematical model describing abundances and activities in a decay chain as a function of time, based on the decay rates and initial abundances. The model was formulated by Ernest Rutherford in 1905 a ...
*
Blood alcohol concentration Blood alcohol content (BAC), also called blood alcohol concentration or blood alcohol level, is a measurement of alcohol intoxication used for legal or medical purposes; it is expressed as mass of alcohol per volume or mass of blood. For example ...
* Biological half-life * Bioavailability *
Cooperstown cocktail The Cooperstown cocktail refers to a panel of four drug probes used in human pharmacokinetic studies to determine the activity of drug metabolising enzymes. The terminology 'cocktail' refers to the fact that the drug probes are given together. ...
* Enzyme kinetics *
Pharmacodynamics 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 ...
* Idiosyncratic drug reaction * Drug interaction *
Patlak plot A Patlak plot (sometimes called Gjedde–Patlak plot, Patlak–Rutland plot, or Patlak analysis) is a graphical analysis technique based on the compartment model that uses linear regression to identify and analyze pharmacokinetics of tracers involv ...
*
Pharmacometrics Pharmacometrics is a field of study of the methodology and application of models for disease and pharmacological measurement. It uses mathematical models of biology, pharmacology, disease, and physiology to describe and quantify interactions between ...
* Pharmacy *
Bioequivalence Bioequivalence is a term in pharmacokinetics used to assess the expected in vivo biological equivalence of two proprietary preparations of a drug. If two products are said to be bioequivalent it means that they would be expected to be, for all ...
* Generic drugs *
Physiologically based pharmacokinetic modelling Physiologically based pharmacokinetic (PBPK) modeling is a mathematical modeling technique for predicting the absorption, distribution, metabolism and excretion (ADME) of synthetic or natural chemical substances in humans and other animal species. ...
*
Plateau principle The plateau principle is a mathematical model or scientific law originally developed to explain the time course of drug action ( pharmacokinetics).Goldstein A, Aronow L, and Kalman SM. Principles of Drug Action. The Basis of Pharmacology. Harper a ...
*
Toxicokinetics 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. Relation to Pharmacokinetics It is an application of pha ...


References


External links


Software

; Noncompartmental * Freeware
bear
an

for R
MetidaNCA
for Julia * Commercial: MLAB
EquivTestKineticaMATLAB/SimBiologyPKMPPhoenix/WinNonlinRapidNCA
; Compartment based * Freeware
ADAPTBoomerGUI

SBPKPD.org (Systems Biology Driven Pharmacokinetics and Pharmacodynamics)WinSAAM
for R
PharmaCalc and PharmaCalcCL
Java applications. * Commercial
PrecisePKImalytics
Kinetica
MATLAB/SimBiologyPhoenix/WinNonlin
PK Solutions,
PottersWheel PottersWheel is a MATLAB toolbox for mathematical modeling of time-dependent dynamical systems that can be expressed as chemical reaction networks or ordinary differential equations (ODEs). It allows the automatic calibration of model parameter ...

ProcessDBSAAM II
; Physiologically based * Freeware
MCSim
* Commercial
acslXCloe PKGastroPlusMATLAB/SimBiologySimcypEntelos PhysioLabPhoenix/WinNonlinADME Workbench
; Population PK * Freeware:
WinBUGS WinBUGS is statistical software for Bayesian analysis using Markov chain Monte Carlo (MCMC) methods. It is based on the BUGS ( Bayesian inference Using Gibbs Sampling) project started in 1989. It runs under Microsoft Windows, though it can als ...
, ADAPT, S-ADAPT / SADAPT-TRAN, Boomer
PKBugsPmetrics
for R. * Commercial
PrecisePK
Kinetica
MATLAB/SimBiologyMonolix
NONMEM NONMEM is a non-linear mixed-effects modeling software package developed by Stuart L. Beal and Lewis B. Sheiner in the late 1970s at University of California, San Francisco, and expanded by Robert Bauer at Icon PLC. Its name is an acronym for NON- ...

Phoenix/NLME
for SAAM II
USC*PACKDoseMe-RxNavigator Workbench
; Therapeutic drug monitoring (TDM) * Commercial
PrecisePK
; Simulation All model based software above. * Freeware: COPASI, Berkeley Madonna
MEGen


Educational centres

Global centres with the highest profiles for providing in-depth training include the Universities of Buffalo,
Florida Florida is a state located in the Southeastern region of the United States. Florida is bordered to the west by the Gulf of Mexico, to the northwest by Alabama, to the north by Georgia, to the east by the Bahamas and Atlantic Ocean, and ...
,
Gothenburg Gothenburg (; abbreviated Gbg; sv, Göteborg ) is the second-largest city in Sweden, fifth-largest in the Nordic countries, and capital of the Västra Götaland County. It is situated by the Kattegat, on the west coast of Sweden, and has ...
,
Leiden Leiden (; in English and archaic Dutch also Leyden) is a city and municipality in the province of South Holland, Netherlands. The municipality of Leiden has a population of 119,713, but the city forms one densely connected agglomeration w ...
, Otago,
San Francisco San Francisco (; Spanish for " Saint Francis"), officially the City and County of San Francisco, is the commercial, financial, and cultural center of Northern California. The city proper is the fourth most populous in California and 17t ...
,
Beijing } Beijing ( ; ; ), Chinese postal romanization, alternatively romanized as Peking ( ), is the Capital city, capital of the China, People's Republic of China. It is the center of power and development of the country. Beijing is the world's Li ...
, Tokyo,
Uppsala Uppsala (, or all ending in , ; archaically spelled ''Upsala'') is the county seat of Uppsala County and the fourth-largest city in Sweden, after Stockholm, Gothenburg, and Malmö. It had 177,074 inhabitants in 2019. Located north of the ca ...
,
Washington Washington commonly refers to: * Washington (state), United States * Washington, D.C., the capital of the United States ** A metonym for the federal government of the United States ** Washington metropolitan area, the metropolitan area centered o ...
,
Manchester Manchester () is a city in Greater Manchester, England. It had a population of 552,000 in 2021. It is bordered by the Cheshire Plain to the south, the Pennines to the north and east, and the neighbouring city of Salford to the west. The ...
, Monash University, and University of
Sheffield Sheffield is a city in South Yorkshire, England, whose name derives from the River Sheaf which runs through it. The city serves as the administrative centre of the City of Sheffield. It is historically part of the West Riding of Yorkshire ...
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