Drug Targeting Organ-Specific Strategies

13.2 Pharmacokinetics and Pharmacodynamics, Modelling, Simulation, and Data Analysis 341
creased number of parameters increases the problem of assigning reliable values to these parameters,
both in simulation (Section 13.2.7) and in data analysis (Section 13.2.8). As a general
rule, the number of compartments should be chosen carefully, according to the parsimony
principle: start the modelling with the simplest model that can discriminate the processes
of interest. If the chosen model does not provide satisfactory results (in terms of credible predictions
or satisfactory goodness-of-fit), the model can be explored further by adding compartments
or connections in a step-by-step procedure.
On the other hand, PB-PK models are frequently used in toxicokinetics for a different
purpose, that is, the model should be able to explain the drug distribution over a large number
of tissues as measured from in vivo animal studies, with the eventual goal of data extrapolation
to man. In this case, the starting point is a model including each organ and tissue from
which measurements are available. If necessary, the number of compartments can be reduced
by combining compartments with similar properties. A detailed description of the process of
explicit (or formal) combining has been given by Nestorov et al. [19] and Weiss [20].
The principles of PB-PK modelling will be explained using the model of Hunt [6], depicted
in Figure 13.4, a PB-PK model suited for evaluation of drug targeting strategies (Sections
13.3.2 and 13.4). For this model, the following set of differential equations describing the drug
transport (mass per unit of time) can be written according to mass balance:
V C · dC C = RC + Q R · C R + QT · C T + QE · C E – (QR + Q T + Q E) · C C
dt K R K T K E
V R · dC R = RR + Q R · C C – Q R · C R – CLR · C R
dt K R
V T · dC T = RT + Q T · C C – Q T · C T – CLT · C T
dt K T
V E · dC E = RE + Q E · C C – Q E · C E – CLE · C E
dt K E
(13.5)
(13.6)
(13.7)
(13.8)
where V is the volume of the compartment, C is the drug concentration, Q is the blood (or
plasma, whichever is the reference fluid) flow, K is the tissue/blood partition coefficient, CL
is the (elimination) clearance, and R is the rate of drug input; subscripts C, R, T and E refer
to the central compartment, response (or target) compartment, toxicity compartment, and
elimination compartment, respectively (Note: Hunt et al. [6] did not include the partition coefficient
K as such, in their equations. Rather, their tissue concentrations refer to a blood or
plasma concentration which is in equilibrium with the tissue concentration, equal to the ratio
C/K; consequently, their tissue volumes refer to apparent volumes, equal to the product K · V).
13.2.4.3 Compartmental Models Versus Physiologically-based Models
Although compartmental models and physiologically-based models may at first, seem quite
different, and are usually treated as two different classes of models, both approaches are actually
similar [17].When appropriately defined, probably any PB-PK model can be written as
a compartmental model and vice versa. This can be seen by comparing the models in Figures
13.1 and 13.3, and their mathematical descriptions in Eq. 13.1 and 13.5.