Pharmacokinetics

Pharmacokinetics, sometimes abbreviated as PK, is a branch of pharmacology dedicated to describing how the body affects a specific substance after administration. 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 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 :

Liberation – the process of active pharmaceutical ingredients 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 – the chemical reactions of the drug and irreversible breakdown into metabolites.
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 and molar. 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.

Characteristic	Description	Symbol	Unit	Formula	Worked example value
Dose	Amount of drug administered.				500 mmol
Dosing interval	Time interval between drug dose administrations.				24 h
Cmax \|	The peak plasma concentration of a drug after administration.				60.9 mmol/L
tmax \|	Minimum time taken to reach C_max.				3.9 h
	The lowest 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.				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.				1,320 h×mmol/L
Area under the curve	The integral of the concentration-time curve.				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, AUC_τ=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 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, 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 methods, with the trapezoidal rule 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, Tmax, 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.