Principles and Practice of Pharmaceutical Medicine

and is analogous to the ‘plasma disappearance’
curve (above):

XIV¼DIVe
Kt

The amount of drug in a single hypothetical com-
partment after an extravascular dose is then mod-
eled with first-order input/output kinetics:

Xpo¼

KaFDpo

Ka
K

½e
Kðt
tlagÞ
eKaðt
tlagފ

Concentration–time effect modeling is illustrated
by the following example, which was chosen to
illustrate a single dose of drug causing the reversal
of a symptom (pain). Many other types of examples
exist.
The plasma kinetics of the analgesic were
describable by the following expression after the
intravenous bolus dose, with C 0 ¼ 45 :0 and
K¼ 0 :50 h
^1 :

C¼ 45 :0e
^0 :^50 t

In the same study, effect measurements were
recorded during 80 min, as shown in Figure 8.5.
Often, drug effects do not parallel changes in
plasma concentration. This can result from distri-

bution phenomena, such as when the effect occurs

outside the plasma compartment (e.g. the sedative

effect of a dose of benzodiazepine which occurs in

the brain), or when the effect recorded reflects, for

example, a chain of biochemical events triggered

by the presence of drug (e.g. the aborting of a

migraine attack by a serotoninergic drug). In rela-

tion to the first of these possibilities, a model,

sometimes called a ‘link model’ (also called the

‘effect-compartment’ or the ‘effect-distribution’

model), allows estimation of thein vivopharma-

codynamic effect from nonsteady-state effect (E)

versus time and concentration (C) versus time data,

within which potential exists for observedEandC

to display temporal displacement with respect to

each other (Segre, 1968; Wagner, 1968; Dahlstrom

et al., 1978; Sheineret al., 1979). The rate of

change of drug amount (Ae) in a hypothetical effect

compartment can be expressed as:

dAe

dt

¼kleA 1 
ke0Ae

whereAis the amount of drug in the central com-

partment of a pharmacokinetic model, linked to the

effect compartment, with first-order rate constants

k1eandke0. The corresponding expression for the

amount of drug in the effect compartment, for a

0.0

0 10 20 30 40 50 60 70 80

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Time (h)

Response

Figure 8.5 Observed effect-time data for an analgesic

92 CH8 PHASE I: THE FIRST OPPORTUNITY FOR EXTRAPOLATION FROM ANIMAL DATA