A Textbook of Clinical Pharmacology and Therapeutics

blood (from which samples are taken for analysis) plus the
extracellular spaces of some well-perfused tissues. The periph-
eral compartment consists of less well-perfused tissues into
which drug permeates more slowly.
The initial rapid fall is called the αphase, and mainly
reflects distribution from the central to the peripheral com-
partment. The second, slower phase reflects drug elimination.
It is called the βphase, and the corresponding t1/2is known as
t1/2. This is the appropriate value for clinical use.

NON-LINEAR (‘DOSE-DEPENDENT’)

PHARMACOKINETICS

Although many drugs are eliminated at a rate that is approxi-
mately proportional to their concentration (‘first-order’ kinet-
ics), there are several therapeutically important exceptions.
Consider a drug that is eliminated by conversion to an
inactive metabolite by an enzyme. At high concentrations, the
enzyme becomes saturated. The drug concentration and reac-
tion velocity are related by the Michaelis–Menten equation
(Figure 3.6). At low concentrations, the rate is linearly related

to concentration, whereas at saturating concentrations the rate

is independent of concentration (‘zero-order’ kinetics). The

same applies when a drug is eliminated by a saturable trans-

port process. In clinical practice, drugs that exhibit non-linear

kinetics are the exception rather than the rule. This is because

most drugs are used therapeutically at doses that give rise to

concentrations that are well below the Michaelis constant

(Km), and so operate on the lower, approximately linear, part

of the Michaelis–Menten curve relating elimination velocity to

plasma concentration.

Drugs that show non-linear kinetics in the therapeutic

range include heparin, phenytoinandethanol. Some drugs

(e.g. barbiturates) show non-linearity in the part of the toxic

range that is encountered clinically. Implications of non-linear

pharmacokinetics include:

1. The decline in concentration vs. time following a bolus
   dose of such a drug is not exponential. Instead, elimination

NON-LINEAR(‘DOSE-DEPENDENT’) PHARMACOKINETICS 15

Drug

Central

compartment

Peripheral (tissue)

compartment

Elimination

Blood

sample

Figure 3.5:Schematic representation of a two-compartment
model.

[S]→

Velocity (

V

)

Km

Vmax

Figure 3.6:Michaelis–Menten relationship between the velocity
(V) of an enzyme reaction and the substrate concentration ([S]).
[S] at 50% Vmaxis equal to Km, the Michaelis–Menten constant.

[Drug] in plasma

1

10

100

Time

Figure 3.7:Non-linear kinetics: plasma concentration–time curve

following administration of a bolus dose of a drug eliminated by

Michaelis–Menten kinetics.

Steady-state plasma [Drug]

Daily dose

Figure 3.8:Non-linear kinetics: steady-state plasma concentration

of a drug following repeated dosing as a function of dose.