**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 dx/dt=-KV*c(t) and can be solved for c(t) yielding c(t)=c(0)e^-(K*t). So, for a drug that is assumed to obey one-compartmental pharmacokinetics, the Cl is equal to *KV*, where *K* is an *apparent first-order elimination rate constant* and *V* is an *apparent volume of distribution*, or proportionality constant between x(t) and c(t), ie. x(t)=c(t)V. The *halflife* of the drug can be estimated as ln(2)/K. 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, or intractable. There is an extensive body of mathematical knowledge with many practitioners working in the area. This knowledge has roots in engineering, statistics, and medicine. A good source for further information and posting to experts is maintained by Dr. David W. A. Bourne, OU College of Pharmacy [1].

## See also

Last updated: 05-12-2005 12:14:33

Last updated: 05-13-2005 07:56:04