P1: PCX Printer: Yet To Come
9780521704632c06 CUFX213A/Peck 9780521618168 December 27, 2007 14:11
6 Mathematics and pharmacokineticson the ln(concentration) axis (ln(B) for the two compartment model) this gives a
concentration which, when divided into X (dose given), will give Vextrap:
Vextrap=X/B.
It greatly overestimates the total volume of distribution for many drugs, particularly
when the distribution phase contributes significantly to drug dispersion. The second
method, Varea,isofmore use because it is related both to clearance and the termi-
nal elimination constant. This uses the non-compartmental method of calculating
clearance from AUC and assumes that an ‘average’ rate constant for removal of drug
from plasma can be approximated by the inverse of the terminal elimination time
constant (βfor the two-compartment model):
Varea=Clearance/β=X/(AUC×β).
This gives a better estimate of volume of distribution than Vextrap, but is still an
overestimate; usingβas the ‘average’ rate constant is an underestimate, particularly
if there is significant distribution and re-distribution to and from compartments.
However, it has the advantage of being easily calculated from experimental data.
The final method Vssis entirely based on non-compartment models (see above) and
is calculated from the product of clearance and mean residence time:
Vss=(dose/AUC)×(AUMC/AUC)=dose×AUMC/AUC^2.
This gives an estimate of volume of distribution that is independent of elimination,
which can be useful. The estimate of volume of distribution using this method is
smaller than for either of the other methods, but is usually close to the area method:
Vextrap>Varea>Vss.Clearance
Clearance (Cl) is defined as that volume of plasma from which drug is completely
removed per unit time – the usual units are ml.min−^1 .For the one-compartment
model we saw that clearance is related to the rate constant for elimination; a high
rate constant reflects rapid removal of drug since a large fraction of the distribution
volume is cleared of drug. Clearance is simply the product of this rate constant and
the volume of distribution (Figure6.10). Clearance relates plasma concentration of
drug at a given time to the actual rate of drug elimination (Rateelin mg.min−^1 )at
that time:
Rateel=C×Cl.
As we saw above, for the one-compartment model the clearance (Cl) of drug from
the compartment is the product of the rate constant for elimination, k, and Vd,
the volume of distribution. We can find k from the slope of the linear ln(C)-time
graph and Vd from C 0 , the concentration at t=0, since we know the dose of drug
given.
Inthe multi-compartment model, we can talk about inter-compartmental clear-
ances as well as a clearance that describes loss of drug from the model. Quoted values