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Pharmacokinetics, sometimes abbreviated as PK (from Ancient Greek pharmakon "drug" and kinetikos "moving, putting in motion"; see chemical kinetics), is a branch of pharmacology dedicated to determining the fate of substances administered externally to a living organism. The substances of interest include pharmaceutical agents, hormones, nutrients, and toxins. It attempts to discover the fate of a drug from the moment that it is administered up to the point at which it is completely eliminated from the body. Pharmacokinetics describes how the body affects a specific drug after administration through the mechanisms of absorption and distribution, as well as the chemical changes of the substance in the body (e.g. by metabolic enzymes such as cytochrome P450 or glucuronosyltransferase enzymes), and the effects and routes of excretion of the metabolites of the drug.^{[1]} Pharmacokinetic properties of drugs may be affected by elements such as the site of administration and the dose of administered drug. These may affect the absorption rate.^{[2]} Pharmacokinetics is often studied in conjunction with pharmacodynamics, the study of a drug's pharmacological effect on the body.
A number of different models have been developed in order to simplify conceptualization of the many processes that take place in the interaction between an organism and a drug. One of these models, the multicompartment model, gives the best approximation to reality; however, the complexity involved in using this type of model means that monocompartmental models and above all two compartmental models are the mostfrequently used. The various compartments that the model is divided into is commonly referred to as the ADME scheme (also referred to as LADME if liberation is included as a separate step from absorption):
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, 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, absorption capacity and distribution in the organism.
The model outputs for a drug can be used in industry (for example, in calculating bioequivalence 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 humanhealth professionals and in veterinary medicine.
The following are the most commonly measured pharmacokinetic metrics:^{[5]}
Characteristic  Description  Example value  Symbol  Formula 

Dose  Amount of drug administered.  500 mg  Design parameter  
Dosing interval  Time between drug dose administrations.  24 h  Design parameter  
C_{max}  The peak plasma concentration of a drug after administration.  60.9 mg/L  Direct measurement  
t_{max}  Time to reach C_{max}.  3.9 h  Direct measurement  
C_{min}  The lowest (trough) concentration that a drug reaches before the next dose is administered.  27.7 mg/L  Direct measurement  
Volume of distribution  The apparent volume in which a drug is distributed (i.e., the parameter relating drug concentration to drug amount in the body).  6.0 L  
Concentration  Amount of drug in a given volume of plasma.  83.3 mg/L  
Elimination halflife  The time required for the concentration of the drug to reach half of its original value.  12 h  
Elimination rate constant  The rate at which a drug is removed from the body.  0.0578 h^{−1}  
Infusion rate  Rate of infusion required to balance elimination.  50 mg/h  
Area under the curve  The integral of the concentrationtime curve (after a single dose or in steady state).  1,320 mg/L·h  
Clearance  The volume of plasma cleared of the drug per unit time.  0.38 L/h  
Bioavailability  The systemically available fraction of a drug.  0.8  
Fluctuation  Peak trough fluctuation within one dosing interval at steady state  41.8 %  where  
[  ]
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 steady state is reached when a time of 4 to 5 times the halflife for a drug after regular dosing is started.
The following graph depicts a typical time course of drug plasma concentration and illustrates main pharmacokinetic metrics:
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 concentrationtime graph. Compartmental methods estimate the concentrationtime 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 final 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 monocompartimental model presupposes that blood plasma 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).
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 tissue) that present a real barrier to the distribution of drugs, they 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 welldeveloped 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 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.^{[6]}
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 within the organism Vd_{F} and its volume of distribution in a tissue Vd_{T} the former will be described by an equation that takes into account all the tissues that act in different ways, that is:
This represents the multicompartment model with a number of curves that express complicated equations in order to obtain an overall curve. A number of computer programmes have been developed to plot these equations.^{[6]} 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 type of drug involved.
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) 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 concentrationtime curve.
Compartmental PK analysis uses kinetic models to describe and predict the concentrationtime curve. PK compartmental models are often similar to kinetic models used in other scientific disciplines such as chemical kinetics and thermodynamics. 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. Compartmentfree modelling based on curve stripping does not suffer this limitation. The simplest PK compartmental model is the onecompartmental PK model with IV bolus administration and firstorder elimination. The most complex PK models (called PBPK models) rely on the use of physiological information to ease development and validation.
Linear pharmacokinetics is socalled 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_{initial}*E^(kelt)
The graph for the nonlinear 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 MichaelisMenten kinetics. A reaction’s factors of non linearity include the following:
It can therefore be seen that nonlinearity can occur because of reasons that affect the whole of the pharmacokinetic sequence: absorption, distribution, metabolism and elimination.
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»).
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: ; 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:
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:^{[9]}
These concepts, which are discussed in detail in their respective titled articles, can be mathematically quantified and integrated to obtain an overall mathematical equation:
where Q is the drug’s purity.^{[9]}
where is the drug’s rate of administration and is the rate at which the absorbed drug reaches the circulatory system.
Finally, using the HendersonHasselbalch equation, and knowing the drug’s (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:
When two drugs have the same bioavailability, they are said to be biological equivalents or bioequivalents. This concept of bioequivalence is important because it is currently used as a yardstick in the authorization of generic drugs in many countries .
A number of phases occur once the drug enters into contact with the organism, these are described using the acronym LADME:
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, metabolization and excretion into a «disposition phase». Other authors include the drug’s toxicological aspect in what is known as ADMETox or ADMET.
Each of the phases is subject to physicochemical 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 behaviour and which place great emphasis on the relationships between drug plasma concentrations and the time elapsed since the drug’s administration.
Bioanalytical methods are necessary to construct a concentrationtime profile. Chemical techniques are employed to measure the concentration of drugs in biological matrix, 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.^{[10]}^{[11]}
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 LCMS 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 insuring data integrity with such complex sample matrices. Much attention is paid to the linearity of the standard curve; however it is not uncommon to use curve fitting with more complex functions such as quadratics since the response of most mass spectrometers is less than linear across large concentration ranges.^{[12]}^{[13]}^{[14]}
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.^{[15]}
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.^{[16]}^{[17]}^{[18]} Certain patient demographic, pathophysiological, and therapeutical features, such as body weight, excretory and metabolic functions, and the presence of other therapies, can regularly alter doseconcentration relationships. For example, steadystate concentrations of drugs eliminated mostly by the kidney are usually greater in patients suffering from renal failure than they are in patients with normal renal function receiving the same drug dosage. Population pharmacokinetics seeks to identify the measurable pathophysiologic factors that cause changes in the doseconcentration relationship and the extent of these changes so that, if such changes are associated with clinically significant shifts in 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).
Software packages used in population pharmacokinetics modelling include NONMEM, which was developed at the UCSF and newer packages which incorporate GUIs like Monolix as well as graphical model building tools; Phoenix NLME.
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 cyclosporine 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.^{[19]} However, it was then realized that it was possible to individualize a patient’s dose of cyclosporine 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:^{[20]}
Drugs where pharmacokinetic monitoring is recommended include:





 * Antiviral (HIV) medication 

Ecotoxicology is the study of toxic effects on a wide range of organisms and includes considerations of toxicokinetics and toxicodynamics.^{[21]}^{[22]}
Academic licenses are available for most commercial programs.
All model based software above.
Global centres with the highest profiles for providing indepth training include the Universities of Buffalo, Florida, Gothenburg, Leiden, Otago, San Francisco, Tokyo, Uppsala, Washington, Manchester, Monash University, and University of Sheffield.^{[23]}
