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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 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
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 .