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Encyclopedia of Physical Science and Technology EN011J-559 July 25, 2001 18:57

818 Pharmacokinetics

to be well mixed with a uniform concentration through-
out. The concentrations C i (t) and volumes V i (t) can all be
functions of time t. The mass balance around the central
compartment is
d(C 1 V 1 )
= R inf − (k 3,f + k elim + k 2,f )(C 1 V 1 )
dt
+ k 3,r (C 3 V 3 ) + k 2,r (C 2 V 2 ), (22)
where R inf is the rate of infusion or rate of delivery, which
can be constant or dependent on time. The k’s are rate
coefficients which must be determined from curve fits to
experimental data.
The mass balances for the other two compartments are
as follows:
d(C 2 V 2 )
= k 2,f (C 1 V 1 ) − k 2,r (C 2 V 2 ), (23)
dt
d(C 3 V 3 )
= k 3,f (C 1 V 1 ) − k 3,r (C 3 V 3 ). (24)
dt
Often, only the infusion rate, the elimination rate
(k elim C 1 V 1 ), and the volume and concentration of the cen-
tral compartment versus time are known. This leaves eight FIGURE 8 Physiologic model for transport between the blood
unknowns with only three equations. The number of vari- (body compartment) and a solution in the peritoneal cavity. The
model emphasizes the importance of the tissue surrounding
ables can be reduced to four by redefining mass (M i =
the cavity. Each tissue compartment can be characterized by
C i V i ) and equating k i,f to k i,r . Numerical fits to the data the mass of drug or the drug concentration and tissue-specific
can produce a range of possible parameters in order to fit volume of distribution. Input of the drug can be intravenous or in-
the central-compartment concentration data. traperitoneal. (i.p.). Drugs administered i.p. are typically done in
The compartmental model is primarily a mathematical the setting of peritoneal dialysis in which a portion of the drug
is typically not absorbed but drained out of the cavity. Drugs are
scheme to predict the plasma or central compartment con-
cleared from the plasma (body compartment) at a clearance rate
centration. It does not tell us about the mechanisms inside Clr BC . Here Q i is the blood flow to or from organ i , L i is the lymph
the body which control drug distribution and elimination. flow rate, and R i is the rate of mass transfer between peritoneal
cavity and the tissue in contact with the peritoneal solution.
B. Physiologic Pharmacokinetic Models
then is taken up by the blood circulation (Q i ) or lymph
In this modeling approach, anatomically or physiologi- circulation (L i ) and transports to the body compartment.
cally defined spaces within the body, along with blood That the hollow viscera drain directly into the liver via the
flows to and from each, rates of drug extraction, or portal vein is included in the model; if the drug is metabo-
metabolism by each compartment are modeled. These lized in the liver, this can be included in a submodel of the
models require significantly more detailed information liver. Each flow rate, compartment volume of distribution,
about a system than the typical compartmental approach. and rate of drug metabolism must be specified in such a
An example of such an approach is illustrated in Fig. 8, a model. Mass balances are written for each compartment
multicompartmental, physiologic model of exchange be- and are solved simultaneously to estimate concentrations
tween the body and fluid in the peritoneal cavity. The in each compartment. Since it has recently been shown
transport of substances between the body compartment that the extracellular volume of the tissues surrounding the
(the volume of drug distribution within the body with peritoneal cavity expand when large volumes of fluid are
which the plasma is in equilibrium) and the peritoneal infused into the cavity, volume balances must be written
cavity occurs via the tissue compartments which surround and solved to calculate the volume of each compartment.
the peritoneal cavity. Drugs may be introduced into the Physiologic models are very complex and require de-
peritoneal cavity (Input PC ) or into the body compartment tailed data to implement. The complexity of such models,
(Input BC ).Fromthebodycompartment,theycandistribute however, provides the capability of studying the effects of
to the tissue compartments around the cavity via the blood variationsinpartsofthetransportsystem.Forexample,the
flow to each tissue group (Q i ). From the peritoneal cav- role of lymphatic transport of solute from the peritoneal
ity, the drug transports into the tissue compartments and cavity to the body compartment could be investigated by