Principles and Practice of Pharmaceutical Medicine

half-life would be 14.5 h, the plasma clearance be
0.138 l h
^1 kg
^1 and theV 1 ,VdssandVdbbe 1.01,
2.37 and 2.56 l kg
^1 , respectively. The predictions
using rat data were within 15% of the actual mean
values in human volunteers. A complex Dedrick
plot of the rat and the human data showed
nearly superimposed concentration–time curves
(Figure 8.4).
This illustrates how allometric scaling is a useful
part of the drug discovery process: we avoided
studying irrelevant doses and saved time. Ideally,
allometric scaling should be done using pharma-
cokinetic data from at least four species, even
though accurate predictions can be made using
data from a single species. If possible, information
about differences in metabolism among species
should be considered when making predictions.

8.3 Pharmacokinetic/

pharmacodynamic models

Elementary aspects

The possibility that time since dose changes the
relationship between pharmacological effect size
and drug concentrations in plasma has been known
for a long time (Levy, 1964, 1966; Levy and

Nelson, 1965; Wagner, 1968; Curry, 1980). The

pioneering work was done by Levy and his collea-

gues in the 1960s on single dose–plasma level–

effect relationships and on the duration of action of

drugs as a function of dose. Brodie and colleagues

had shown even earlier how complicated the rela-

tionships are when drugs with multicompartment

distribution are studied in this context (e.g. Brodie,

1967). Lasagna and colleagues, using diuretics,

found that depending on whether a cumulative

effect (24-h urine production) or an ‘instant’ effect

(rate of urine flow at a particular time) were mea-

sured, different relationships of response were

possible (Murphyet al., 1961). Nagashimaet al.

(1969) demonstrated the relative time courses of

anticoagulant concentration and effect. Thus, the

relationship between effect size and concentration

of drug in plasma should not be expected to be

constant or simple, and it can vary with time.

The objectives of modern analysis of drug action

are to delineate the chemical or physical interac-

tions between drug and target cell and to character-

ize the full sequence and scope of actions of each

drug (Ross, 1996). Preclinical models describing

the relationship between the concentration of drug

in blood or plasma and drug receptor occupancy or

functional response provide clinically useful tools

regardingpotency,efficacyand the time course of

effect.

Potencyis an expression of the activity of a

compound, in terms of either the concentration or

amount needed to produce a defined effect.Emaxis

the maximal drug-induced effect. EC 50 is the con-

centration of an agonist that produces 50% of the

maximal possible response. An EC 50 can be

described for drug concentrations usingin vitro

assays, or as a plasma concentrationin vivo.IC 50

is the concentration of an antagonist that reduces a

specified response to 50% of its former value.

A measure of the tendency of a ligand and its

receptor to bind to each other is expressed asKdin

receptor occupancy studies.Kdis the equilibrium

constant for the two processes of drug–receptor

combination and dissociation.Kdmay be found

for both agonists and antagonists, although some-

times the former poses more technical challenge

due to alterations to the conformation of the bind-

ing site. In contrast,efficacyis a relative measure,

0

100

101

102

103

104

100

Normalized concentration

1234

6

Human time (h)

Rat time (h)

3 9 12 15

200

Apolysichrons (time/W0.19)

300 400 500

Rat

Human

Figure 8.4 Complex Dedrick plot of rat and human
data for compound X again showing very good scaling
between rat and human

8.3 PHARMACOKINETIC/PHARMACODYNAMIC MODELS 89