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Section IBasic principlesbetween plasma concentration and drug activity pharmacodynamic effects can also
be predicted. There is a variety of models that can be used; most commonly we use
compartmental models. In compartmental models we assume a single, central com-
partment is connected to one or two peripheral compartments. Drug is assumed to
enter and leave only through the central compartment, although it can distribute
to and re-distribute from the peripheral compartments. For each peripheral com-
partment we use an exponential term to model its volume and inter-compartmental
clearance; the central compartment is also represented by an exponential term, but
drug can be removed from the model entirely, so clearance from this compartment
reflects removal from the body. There are also complex physiological models that
can more closely predict drug concentrations in different organs as well as non-
compartmental models based on the statistical concept of mean residence time. In
this text we will concentrate on compartmental models.Single bolus dose
The one-compartment model
The simplest model is that of a single, well-stirred, homogenous compartment. If a
single dose of drug is given, then the model predicts that it instantaneously disperses
evenly throughout this compartment and is eliminated in an exponential fashion
with a single rate constant for elimination (Figure6.9a). This is the one-compartment
model that we have discussed in the mathematics section. Although such a model
is not directly relevant to clinical practice, it is important to understand because it
introduces the concepts that are further developed in more complex compartmental
models. The pharmacokinetic parameters introduced are volume of distribution,
clearance, rate constant for elimination, time constant and half-life. If we take C as
drug concentration and t as time since administration of drug then this model is
described by an equation with a single exponential term:
C=C 0 e−kt,
where C 0 is the concentration at time t=0 and k is the rate constant for elimination.
The volume of the single compartment is the volume of distribution, Vd, and the
proportion of plasma from which drug is removed per minute is the rate constant for
elimination, k. For example, if k is 0.1, then every minute a tenth of the compartment
will have drug completely removed from it. The total volume cleared of drug every
minute must therefore be the product of k and the compartment volume (k×Vd)
(Figure6.10). This is known as the clearance (Cl) of drug from the compartment;
clearance has units of ml.min−^1 :
Cl=k×Vd.
Because the time constantτis the inverse of the rate constant, clearance also can be
expressed as the ratio of the volume of distribution and the time constant:
Cl=Vd/τ.