**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.

## Contents |

## 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 interchangeably.

### 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 -(d*x*/d*t*)/*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.

## 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.

## See also

## Further reading

- "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
- http://vam.anest.ufl.edu/demos/onecompbolus.html A free hydraulic analog simulation of a bolus in a one-compartment model
- http://www.thermo.com/pkpd Download trial version of an industry-standard pharmacokinetic solution - Kinetica