Principles and Practice of Pharmaceutical Medicine

concentrations that the elimination mechanism
becomes unsaturated, and first-order elimination
then supervenes; good examples include ethanol
and sodium dichloroacetate (Hawkins and Kalant,
1972; Curryet al., 1985; Foxet al., 1996).
The elimination rate for zero-order processes
may also be treated as a maximal rate of reaction
(Vmax), and thus this type of data may be subject to
ordinary Michaelis–Menten analysis (see further,
below). Note that first-order elimination curves are
so common that ‘drug disappearance’ curves are
routinely analyzed as semi-logarithmic plots
(which linearizes the curve). The literature is
sometimes ambiguous in its use of the term ‘linear
data’, authors may or may not assume that the
semi-logarithmic transformation is to be taken as
read.
When the elimination rate is known, then clear-
ance (Cl) is defined simply as:

Cl¼elimination rate=C

whereCis again the drug concentration. Note that
in first-order elimination processes, the elimination
rate of the drug (with units of mass/time) changes
with time (and drug concentration), and thus only
instantaneous clearances, specifying time or drug
concentration, can be stated.
Urinary clearance, obviously, may only partly
explain the rate of drug disappearance from
plasma. In any case, the urinary clearance of an
agent may be found from the familiar equation:

Cl¼ðUVÞ=P

whereUis the urinary concentration,Vis the
volume of urine excreted during a specified time
period, andPis the average plasma concentration
during that time period. For inulin and sodium
iothalamate, but not for creatinine or urea, the

urinary clearance is a good measure of glomerular

filtration rate.

These elementary aspects of clearance may be

revised in any textbook (e.g. Curry, 1980; Benet

et al., 1996). The purpose of the remainder of this

section is to show how much more informative the

concept of clearance may be and to provide an

illustration of its use.

Prediction of human drug clearance

For those compounds that are predominantly

cleared by metabolism, human blood clearance

can be predicted using simple enzyme kinetic

data (Houston, 1994; Ashforthet al., 1995; Iwat-

suboet al., 1996; Obach, 1996a). These predictions

may be strengthened by comparing preclinical

in vivodata with the predictions made fromin

vitrodata using tissues from the same preclinical

species (Raneet al., 1977). As an illustration, con-

sider compound X (anonymized but real). This

compound has a molecular weight less than 400

and a log D7.4value of approximately 0.5, suggest-

ing that it could undergo both renal and hepatic

clearances. Preclinicalin vivostudies indicate that

compound X is eliminated largely unchanged in

the urine in the rat (90%). Several oxidative

biotransformation pathways have nonetheless

been identified. In common with studies of com-

pound X clearance in humans, simplein vitro

enzyme kinetic studies were used in conjunction

with knowledge from ratin vivodata. The general

strategy for prediction of kinetic studies is shown in

Figure 8.2.

Using liver microsomes from different species,

the intrinsic clearance (Cl^0 int) for each species can

be determined and then scaled to hepatic clearance.

This is typically done by first determiningin vitro

Km(the Michaelis–Menten constant) andVmax(the

Km,Vmax for metabolic pathway

T1/2 for drug loss

or In vitroClint In vivoClint Hepatic clearance

Scaling Blood flow

Serum protein binding

Microsomal protein binding

Figure 8.2 Strategy for thein vitro–in vivoscaling of hepatic clearance (see for example Iwatsubo et al., 1996)

8.1 THE IN VITRO/IN VIVO PREDICTION 81