Pharmacokinetics

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.

Absorption and disposition

Pharmacokinetics has been broadly divided into two categories of study: absorption and disposition. Once a drug is administered as a dose, these processes begin simultaneously.

Absorption

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.

Pharmacokinetics has many applications in drug therapy. By studying absorption -- the amount of a drug which gets into the system (bloodstream) following administration -- pharmacokinetics may guide the formulation of drug products. The amount of drug released from different formulations may vary; for example, two different tablets containing the same amount of drug chemical may not release the same amount into the bloodstream; a pharmacokinetic absorption study can determine whether or not the two tablets are equivalent and can be used interchangably.

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.

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 one-compartmental case

The functional form of the systemic clearance, Cls, of a drug x is equal to -(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). The units of clearance are given in terms of volume/time so that a generalized, well stirred volume is cleared of an amount of a substance x per unit of time following introduction into such volume. This well stirred volume V is the volume of distribution of a substance x (drug), and is essentially a proportionality constant between x(t) and c(t), such that x(t)=c(t)×V.

The total apparent systemic clearance Cls/(F×F*) is related to Cls, where F signifies bioavailability and F* signifies the first pass effect of an administered substance. If F and F* are known, the true systemic clearance, Cls, can be obtained by multiplying the observed apparent systemic clearance Cls/(F×F*) by F and F*. Cls is composed of many clearance components, two of the most common are the renal and non-renal components of clearance, Clr and Clnr, respectively, such that Cls = Clr + Clnr.

For a one-compartmental drug x given as an intravenous administration (bolus input), the governing first order differential equation is:

\frac{dx(t)}{dt}=-k \cdot x{(t)} \qquad (1)

with a decay constant ''k' (equivalent to the time constant used in RC circuit analysis).

The above equation can be solved for x(t):

x(t)=x(0) \cdot e^{-k{ \cdot t}} \qquad (2)

For a drug that is assumed to obey one-compartment pharmacokinetics, Cl is equal to −k×V. From equation (2), the half-life of the drug can be shown to be equal to ${ln2}/k$ by setting $x(t) = \frac{1}{2}x(0)$ and solving for t. The total integral of c(t) over time (the Area under the curve, AUC) can be used in the calculation of the bioavailability, F, of a substance x.

Modeling pharmacokinetic systems

Pharmacokinetics systems 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 and 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.

Nonlinear time-varying systems 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.

Reference Books

"Pharmacokinetics" by Milo Gibaldi and Donald Perrier
"Clinical Pharmacokinetics: Concepts and Applications" by Malcolm Rowland, Thomas N. Tozer

External links

A source for further information site maintained by Dr. David W. A. Bourne, OU College of Pharmacy.
PKWIKI is a pharmacokinetics website with a Wikimedia engine at the University of Washington maintained by Dr. Arthur Roberts

Pharmacokinetics | Medicinal chemistry

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