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Section IBasic principlesτhas units of time, usually minutes, then k has units of time−^1 , usually min−^1 .Inthe
section above we saw that the time constantτis longer than the half-life; there is a
simple inverse relationship between k andτ, whereas k=ln(2)/t1/2,soitiseasier to
use time constants rather than half-lives when discussing models.Multi-compartment models
Multi-compartment models make allowance for the uptake of drug by different tis-
sues within the body, and for the different blood flow rates to these tissues. Differ-
ent tissues that share pharmacokinetic properties form compartments. Convenient
labels include ‘vessel rich’ and ‘vessel poor’ compartments. The number of theoret-
ical compartments that may be included in any model is limitless, but more than
three compartments become experimentally indistinguishable. In these models it is
important to realize that elimination can occur only from the central compartment
and that the ‘effect compartment’ is in equilibrium with the central compartment.
The volume of this effect compartment is very small so it does not contribute to
the total volume, but is useful for predicting the onset and offset of the response
when the observed effect is proportional to effect site concentration. Models for
individual drugs differ in the volume of compartments and in transfer rates between
compartments; the values for these pharmacokinetic parameters can vary enor-
mously and depend on the physicochemical properties of a drug as well as the site
and rate of drug metabolism.Twocompartments
Inthe two-compartment model the central compartment connects with a second
compartment; the volume of the central compartment is V 1 and that of the peripheral
compartment V 2 (Figure6.9b). The total volume of distribution is the sum of these
two volumes. Unlike the single compartment model, there are now two pathways for
drug elimination from plasma: an initial rapid transfer from the central to peripheral
compartment and removal from the central compartment. The latter removes drug
from the system, whereas after distribution to the second compartment, the drug
can re-distribute to the central compartment when conditions allow. Inspection of
the concentration–time curve shows that the initial rate of decline in plasma con-
centration is much faster than would be expected from a single compartment model;
this represents rapid distribution to the second compartment. A semi-logarithmic
plot of ln (C) against time is now a curve, rather than a straight line, which is the sum
of two straight lines representing the exponential processes with rate constantsα
andβ(Figure6.12).
Transfer between compartments is assumed to occur in an exponential fashion at
arate depending on the concentration difference between compartments and the
equilibrium constants for transfer. Rate constants for transfer in each direction are
described: k 12 is the rate constant for the transfer from the central to peripheral com-
partment and k 21 is the rate constant for the transfer from the peripheral to central