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Pharmacokinetics is a branch of pharmacology dedicated to the study of the time course of substances and their relationship with an organism or system. In practice, this discipline is applied mainly to drug substances, though in principle it concerns itself with all manner of compounds residing within an organism or system, such as nutrients, metabolites, endogenous hormones, toxins, etc. So, in basic terms, while pharmacodynamics explores what a drug does to the body, pharmacokinetics explores what the body does to the drug.
Pharmacokinetics has been broadly divided into two categories of study: absorption and disposition. Disposition is further subdivided into the study of the distribution, metabolism and elimination or excretion of a drug. Thus, pharmacokinetics is sometimes referred to as ADME. Once a drug is administered as a dose, these processes begin simultaneously.
- The process of absorption can be seen as increasing the amount of a compound or dose x introduced into a system. Absorption studies seek to define the rate of input, dx/dt, of the dose x. For example, a constant rate infusion, R, of a drug might be 1 mg/hr, while the integral over time of dx/dt is referred to as the extent of drug input, x(t), ie. the total amount of drug x administered up to that particular time t. Sometimes the drug is assumed to be absorbed from the gastrointestinal tract in the form of a 1st order process with a 1st-order rate of absorption designated as Ka. Complex absorption profiles can be created by the use of controlled, extended, delayed or timed release of drugs from a dosage form.
- The processes of disposition can be seen as clearing the system of a dose, or disposing of the dose. The disposition process distributes the compound or substance within the system, converts or metabolizes it, and eliminates the parent compound or products of the parent compound by passing them from the system into the urine, feces, sweat, exhalation or other routes of elimination. Sometimes compounds or their products may remain essentially indefinitely in the system by incorporation into the system.
The functional form of the apparent systemic clearance, Cl, of a drug x is -(dx/dt)/c(t), where x(t) is the amount of drug present and c(t) is the observed drug concentration (for example in blood plasma). For a one-compartmental drug given as an intravenous administration (bolus input) the governing first order differential equation is
The above equation (1) can be solved for c(t):
See the article on clearance for a more detailed and generalized explanation.
For a drug that is assumed to obey one-compartment pharmacokinetics (also known as the single pool model), the Cl is equal to K. V/K is an first-order elimination rate constant (analogous to the time constant in RC circuits) and V is the volume of distribution of the substance (drug), or proportionality constant between x(t) and c(t), ie. x(t)=c(t)*V. With equation (2), the half-life of the drug can be shown to be equal to ln(2)*V/K (set c(t)=c(0)/2 and solve for t). The total integral of c(t) over time (or the Area Under the Curve, AUC) is used to calculate the bioavailability, F, of a substance or compound, which gives the percent of a dose reaching the systemic circulation.
Linear systems theory has been applied to modeling many pharmacokinetic systems when linearity can be assumed. One test of a drug's linearity is obtained by observing the AUC for several different administered doses. If the AUC varies directly with administered dose then the apparent systemic clearance of the drug, Cl, remains constant. However, pharmacokinetics can be determined to be linear or nonlinear, and time-invariant or time-varying with respect to the mathematical modeling involved for any one of these processes. Linear pharmacokinetic processes are generally the least complex to study, while a nonlinear time-varying system can be very difficult to solve and may have no closed-form solutions (meaning they have to be solved numerically on a case-by-case basis). There is an extensive body of mathematical knowledge with many practitioners working in the area. This knowledge has roots in engineering, statistics, and medicine.
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