Principles and Practice of Pharmaceutical Medicine

expected to achieve a neuroprotective plasma con-
centration of 1500 ng ml
^1. To do this, we pre-
dicted the volume of distribution (V1cat) using data
collected from the volume of distribution in rat
(V1rat). For our calculations, we used a value of
0.938 for the power functionb(see Ings, 1990,
Table 2). In doing this, we made the standard
assumption that in the formula Y¼aWb the
value of the power functionbwas compound inde-
pendent and that the functionawas compound
dependent (Ings observed that the power function
bis reasonably constant for each pharmacokinetic
parameter). Substituting into the allometric for-
mula, logðV1catÞ¼blogWþloga, we found:

log 0:426l¼ 0 :938 log 0:3kgþloga

Thus,

loga¼ 0 : 120 :

By substituting back into the formula and using a
cat weight of 4 kg, we found:

V1cat¼ 4 :81 or 1:211 kg
^1 :

Our formula for calculating the dose to be admi-
nistered was:

Dosecat¼DoseratðV1cat=V1ratÞ

The formula for predicting the plasma half-life
was:

T 1 =2cat¼T 1 =2ratðWcat=WratÞy
x

in whichyis as defined earlier andxis a clearance
parameter (Boxenbaum and Ronfeld, 1983). The
measured plasma half-life in the rat was 4.53 h.
Filling in the formula (Boxenbaum and Ronfeld,
1983), we predicted a plasma half-life of 7.3 h in
the cat (¼ 4 : 53 ð 4 = 0 : 3 Þ^0 :^938
^0 :^75 ). The measured
plasma half-life in the cat was 6 h. We knew from
data collected in the rat that a dose of 3.06 mg kg
^1
administered over 15 min would give a plasma
Cmaxof 1500 ng ml
^1 of plasma. This equated to
a dose in the cat of 2.6 mg kg
^1 over 15 min or
175 mgkg
^1 min
^1 for 15 min.

When we performed studies to determine the

Cmaxin cats following a dose of 2.6 mg kg
^1 admi-

nistered over 15 min, our predicted values were

very close to the actual values, with a measured

Cmaxof 1240100 ng ml
^1.

Data from the rat can also be used to predict the

pharmacokinetics of compound X in humans. As

with the cat, we made our predictions prospec-

tively by assuming, that for the formula

Y¼aWb, the value of the power functionb(or

slope of the line from a log vs. log plot) was drug

independent and that the intercept functionawas

drug dependent. We assigned values of 0.75, 0.938

and 0.25 for clearance, volume of distribution and

plasma half-life, respectively, using the data taken

from the literature and discussed above. The inter-

cept functionawas then determined for each para-

meter by substituting the pharmacokinetic data

from rats, that is clearance¼0.54 l h
^1 kg
^1 ,

V 1 ¼1.421 kg
^1 ,Vdss¼3.33 l kg
^1. We estimated

the pharmacokinetic parameters for humans by

substituting the calculated intercept function

back into the formula and solving forYfor a 70-

kg human. The prediction of the plasma half-life in

humans was determined by three separate meth-

ods. For our predictions, we also assumed that the

protein binding was the same in rats and in humans

and that the metabolism of compound X was simi-

lar in both the species. Clearly, approaches such as

this could be a routine part of drug discovery.

The values estimated by allometric scaling were

compared with those observed in the single-dose

human volunteer study (Table 8.5). We predicted

that for compound X in humans, the plasma

Table 8.5 Predicted and actual pharmacokinetic

parameters for humans

Pharmacokinetic

parameter Predicted Actual

Clearance 0.138 l h
^1 kg
^1 0.123

Half-lifea 14.5 h 13.6 h

V 1 1.01 l kg
^1 1.02 l kg
^1

Vdss 2.4 l kg
^1 2.1 l kg
^1

aPlasma half-life is the average from three values by three

different methods: (a) T 1 =2 human¼ð 0 : 693 VdÞ=Clp; (b)

T 1 =2 human¼T 1 =2 ratðWhuman=WratÞy
x; and (c) logT 1 =2 human¼

logaþblogWhuman.

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