12 PHARMACOKINETICS
Clearance is the best measure of the efficiency with which a
drug is eliminated from the body, whether by renal excretion,
metabolism or a combination of both. The concept will be
familiar from physiology, where clearances of substances with
particular properties are used as measures of physiologically
important processes, including glomerular filtration rate and
renal or hepatic plasma flow. For therapeutic drugs, knowing
the clearance in an individual patient enables the physician
to adjust the maintenance dose to achieve a desired target
steady-state concentration, since
required administration rate desired CSSclearanceThis is useful in drug development. It is also useful in clinical
practice when therapy is guided by plasma drug concentrations.
However, such situations are limited (Chapter 8). Furthermore,
some chemical pathology laboratories report plasma concentra-
tions of drugs in molar terms, whereas drug doses are usually
expressed in units of mass. Consequently, one needs to know the
molecular weight of the drug to calculate the rate of administra-
tion required to achieve a desired plasma concentration.
When drug infusion is stopped, the plasma concentration
declines towards zero. The time taken for plasma concentration
to halve is the half-life (t1/2). A one-compartment model with
first-order elimination predicts an exponential decline in con-
centration when the infusion is discontinued, as shown in
Figure 3.1. After a second half-life has elapsed, the concentration
will have halved again (i.e. a 75% drop in concentration to 25%
of the original concentration), and so on. The increase in drug
concentration when the infusion is started is also exponential,
being the inverse of the decay curve. This has a very important
clinical implication, namely that t1/2not only determines the
time-course of disappearance when administration is stopped,
but also predicts the time-course of its accumulation to steady
state when administration is started.
Half-life is a very useful concept, as explained below.
However, it is not a direct measure of drug elimination, since
differences in t1/2can be caused either by differences in the effi-
ciency of elimination (i.e. the clearance) or differences in another
important parameter, the apparent volume of distribution (Vd).
Clearance and not t1/2must therefore be used when a measure
of the efficiency with which a drug is eliminated is required.SINGLE-BOLUS DOSE
The apparent volume of distribution (Vd) defines the relation-
ship between the mass of a bolus dose of a drug and the
plasma concentration that results. Vdis a multiplying factor
relating the amount of drug in the body to the plasma concen-
tration,Cp(i.e. the amount of drug in the bodyCpVd).
Consider a very simple physical analogy. By definition, con-
centration (c) is equal to mass (m) divided by volume (v):Thus if a known mass (say 300 mg) of a substance is dissolved
in a beaker containing an unknown volume (v) of water, vcan
be estimated by measuring the concentration of substance in a
sample of solution. For instance, if the concentration is
0.1 mg/mL, we would calculate that v3000 mL (vm/c).
This is valid unless a fraction of the substance has become
adsorbed onto the surface of the beaker, in which case the
solution will be less concentrated than if all of the substance
had been present dissolved in the water. If 90% of the sub-
stance is adsorbed in this way, then the concentration in
solution will be 0.01 mg/mL, and the volume will be corre-
spondingly overestimated, as 30 000 mL in this example. Based
on the mass of substance dissolved and the measured concen-
tration, we might say that it is ‘as if’ the substance were dis-
solved in 30 L of water, whereas the real volume of water in
the beaker is only 3 L.
Now consider the parallel situation in which a known
mass of a drug (say 300 mg) is injected intravenously into a
human. Suppose that distribution within the body occurs
instantaneously before any drug is eliminated, and that blood
is sampled and the concentration of drug measured in the
plasma is 0.1 mg/mL. We could infer that it is as if the drug
has distributed in 3 L, and we would say that this is the appar-
ent volume of distribution. If the measured plasma concen-
tration was 0.01 mg/mL, we would say that the apparent
volume of distribution was 30 L, and if the measured concen-
tration was 0.001 mg/mL, the apparent volume of distribution
would be 300 L.
What does Vdmean? From these examples it is obvious that
it is not necessarily the real volume of a body compartment,
since it may be greater than the volume of the whole body. At the
lower end, Vdis limited by the plasma volume (approximately
3 L in an adult). This is the smallest volume in which a drug
could distribute following intravenous injection, but there is no
theoretical upper limit on Vd, with very large values occurring
when very little of the injected dose remains in the plasma, most
being taken up into fat or bound to tissues.c
m
vKey points- Pharmacokinetics deals with how drugs are handled by
the body, and includes drug absorption, distribution,
metabolism and excretion. - Clearance (Cl) is the volume of fluid (usually plasma)
from which a drug is totally removed (by metabolism
excretion) per unit time. - During constant i.v. infusion, the plasma drug
concentration rises to a steady state (CSS) determined by
the administration rate (A) and clearance (CSSA/Cl). - The rate at which CSSis approached, as well as the rate
of decline in plasma concentration when infusion is
stopped are determined by the half-life (t1/2). - The volume of distribution (Vd) is an apparent volume
that relates dose (D) to plasma concentration (C): it is
‘as if’ dose Dmg was dissolved in VdL to give a
concentration of Cmg/L. - The loading dose is CpVdwhereCpis the desired
plasma concentration. - The maintenance doseCSSCl, where CSSis the
steady-state concentration.