Pharmacokinetics (from Ancient Greek pharmakon 'drug' and kinetikos 'moving, putting in motion'; see chemical kinetics), sometimes abbreviated as PK, is a branch of pharmacology dedicated to describing how the body affects a specific substance after administration."Pharmacokinetics". In Mosby's Dictionary of Medicine, Nursing & Health Professions (2006). Philadelphia, PA: Elsevier Health Sciences The substances of interest include any chemical xenobiotics such as pharmaceutical drugs, pesticides, food additives, cosmetics, etc. PK attempts to analyze chemical metabolism and 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. PK is based on mathematical modeling that places great emphasis on the relationship between drug plasma concentration and the time elapsed since the drug's administration. Pharmacokinetics is the study of how an organism affects the drug, whereas pharmacodynamics (PD) is the study of how the drug affects the organism. Both together influence dosing, benefit, and adverse effects, as seen in PK/PD models.
ADME A number of phases occur once the drug enters into contact with the organism, these are described using the acronym ADME (or LADME if liberation is included as a separate step from absorption): Liberation – the process of active pharmaceutical ingredients (API) separating from its pharmaceutical formulation. See also IVIVC. Absorption – the process of a drug entering into systemic circulation from the site of administration. Distribution – the dispersion or dissemination of substances throughout the fluids and tissues of the body. Metabolism (or biotransformation, or inactivation) – the chemical reactions of the drug and irreversible breakdown into metabolites (e.g. by metabolic enzymes such as cytochrome P450 or glucuronosyltransferase enzymes). Excretion – the removal of the substance or metabolites from the body. In rare cases, some drugs irreversibly accumulate in body tissue.
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. The two phases of metabolism and excretion can 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 how various substances can cross them, or how several enzyme reactions may induce or inhibit the drug.
Metrics The following are the most commonly measured pharmacokinetic metrics: The units of the dose in the table are expressed in moles (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/L'. Similarly, other units in the table may be expressed in units of an equivalent dimension by scaling. + Pharmacokinetic metrics Characteristic Description Symbol Unit Formula Worked examplevalue Dose Amount of drug administered. 500 mmol Dosing interval Time interval between drug dose administrations. 24 h The peak plasma concentration of a drug after administration. 60.9 mmol/L Minimum time taken to reach . 3.9 h The lowest (trough) concentration that a drug reaches before the next dose is administered. 27.7 mmol/L The average plasma concentration of a drug over the dosing interval in steady state. 55.0 h×mmol/L Volume of distribution The apparent volume in which a drug is distributed (i.e., the parameter relating drug concentration in plasma to drug amount in the body). 6.0 L Concentration Amount of drug in a given volume of plasma. 83.3 mmol/L Absorption half-life The time required for 50% of a given dose of drug to be absorbed into the systemic circulation. 1.0 h Absorption rate constant The rate at which a drug enters into the body for oral and other extravascular routes. 0.693 h−1 Elimination half-life 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 mmol/h Area under the curve The integral of the concentration-time curve (after a single dose or in steady state). 1,320 h×mmol/L Clearance The volume of plasma cleared of the drug per unit time. 0.38 L/h Bioavailability The systemically available fraction of a drug. Unitless 0.8 Fluctuation Peak–trough fluctuation within one dosing interval at steady state. where 41.8%
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. In steady state and in linear pharmacokinetics, AUCτ=AUC∞.
Modeling
Models have been developed to simplify conceptualization of the many processes that take place in the interaction between an organism and a chemical substance. Pharmacokinetic modelling may be performed either by noncompartmental or compartmental methods. Multi-compartment models provide the best 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 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 human-health professionals and in veterinary medicine.
Models generally take the form of 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. A variety of analysis techniques may be used to develop models, such as nonlinear regression or curve stripping.
Noncompartmental analysis Noncompartmental methods estimate PK parameters directly from a table of concentration-time measurements. Noncompartmental methods are versatile in that they do not assume any specific model and generally produce accurate results acceptable for bioequivalence studies. 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 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 to maximum concentration), CL and Vd can also be reported using NCA methods.
Compartmental analysis Compartment models methods estimate the concentration-time graph by modeling it as a system of differential equations. These models are based on a consideration of an organism as a number of related compartments. Both single compartment and multi-compartment models are in use. 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 noncompartmental analysis is the ability to modify parameters and to extrapolate to novel situations. The disadvantage is the difficulty in developing and validating the proper model. Although compartment models have the potential to realistically model the situation within an organism, models inevitably make simplifying assumptions and will not be applicable in all situations. However complicated and precise a 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.
Single-compartment model
The simplest PK compartmental model is the one-compartmental PK model. This models an organism as one homogenous compartment. This monocompartmental model presupposes that blood plasma concentrations of the drug are the only information needed to determine the drug's concentration in other fluids and tissues. For example, the concentration in other areas may be approximately related by known, constant factors to the blood plasma concentration.
In this one-compartment model, the most common model of elimination is first order kinetics, where the elimination of the drug is directly proportional to the drug's concentration in the organism. This is often called linear pharmacokinetics, as the change in concentration over time can be expressed as a linear differential equation . Assuming a single IV bolus dose resulting in a concentration at time , the equation can be solved to give .
Two-compartment model Not all body tissues have the same blood supply, so the distribution of the drug will be slower in those tissues than in others with a better blood supply. Furthermore, there are some tissues (such as the brain tissue) that present a real barrier to the distribution of drugs, which may 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, which has a more rapid distribution and consists of organs and systems with a well-developed blood supply; and the peripheral compartment, which is 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 passively transport (high lipophilicity) and evade active efflux to cross the blood–brain barrier (BBB) that separates the organ from the blood supply.
Two-compartment models 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, elimination occurs in the peripheral compartment or even in both compartments. 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. FarmacocinéticaReverté 1982 pages 1–10. , 9788429155358
Multi-compartment models