P1: PCX Printer: Yet To Come
9780521704632c06 CUFX213A/Peck 9780521618168 December 27, 2007 14:11
6 Mathematics and pharmacokineticsThis is similar to the relationship for the two-compartment model, but with the
addition of a third exponential process resulting from the presence of an additional
compartment; the kinetic constants G andγdescribe that additional process. The
model consists of a central compartment into which a drug is infused and from
which excretion can occur, together with two peripheral compartments with which
drug can be exchanged (Figure6.9c). These may typically represent well-perfused
(the second compartment) and poorly perfused (the third compartment) tissues,
respectively, with the central compartment representing plasma. Distribution into
the second compartment is always faster than into the third compartment. This is
areasonable model for the majority of anaesthetic agents, where drug reaches the
plasma and is distributed to muscle and fat. The volume of distribution at steady-
state is the sum of the volumes of the three compartments. The mathematics is
similar to that for two compartments, but more complicated as transfer into and out
of the third compartment also must be taken into account.
As in the two-compartment model, there is final phase that can be described by
a single exponential and the half-life associated with this phase is known as the
terminal elimination half-life, which reflects both elimination from the body and
re-distribution from the peripheral compartments. The rate constant for elimination
is thereforenotthe inverse of the terminal elimination time constant; it can be
calculated once the model parameters have been found. Clearance of drug out of
the body is still defined as the product of V 1 and the rate constant for elimination;
as discussed below clearance is usually found using a non-compartmental method
and calculating the ratio of dose to the AUC.Non-compartmental models
Non-compartmental models make no assumptions about specific volumes but use
information from the AUC, as this reflects the removal of drug from plasma. The area
under the concentration–time curve can be used to find clearance because AUC is
the ratio of dose to clearance. Clearance (Cl) is therefore:Cl=dose/AUC.If weplot theproductof concentration and time on the y-axis against time we produce
what is known as the first moment curve. The area under this curve (AUMC) can be
used to find a parameter known as mean residence time (MRT). Mean residence time
is a measure of how long the drug stays in the body and is similar to a time constant
in the compartmental models.MRT=AUMC/AUC.The product of clearance and MRT is the steady-state volume of distribution (Vss)
according to this model. So volume of distribution is:Vss=Cl×MRT.