Drug Targeting Organ-Specific Strategies

342 13 Pharmacokinetic/Pharmacodynamic Modelling in Drug Targeting
The major difference between both approaches is not in the mathematical or pictorial description,
but in the interpretation of the parameters. In compartmental modelling, the starting
point is the parameters that do not necessarily have a particular anatomical or physiological
meaning. This meaning, however, may become clear after a careful analysis of the
data, including measurements in different organs and tissues. On the other hand, PB-PK
starts with a model with physiologically meaningful parameters. It should be stated that,
when applying a PB-PK model to real data, the identification of the parameters may become
a major problem in the interpretation (see Section 13.2.8.4).
13.2.4.4 Principles of Modelling
In both types of models, the quantity or concentration of the drug in various sites of the body
is described by mathematical equations quantifying drug administration, drug transport and
drug elimination. These mathematical representations are usually in the form of differential
equations, which can be solved numerically. In some simple cases an explicit analytical solution
of the differential equations can be obtained, thus facilitating the calculations. The numerical
procedure of solving the differential equations is more generally applicable, but is
complicated by the necessity to find a compromise between accuracy and speed of execution.
However, using modern, user-friendly software and fast-performing hardware, this is much
less of an issue today (see Section 13.7).
13.2.5 Pharmacodynamic Models
Pharmacodynamic (PD) models are used to describe the relationship between drug concentration
and drug effect.An overview of various PD models can be found in the literature [21].
The essential elements will be treated in the following sections.
13.2.5.1 Sigmoid E max Model
For simplicity, a linear relationship between concentration and effect is often assumed, reducing
the problem of PK/PD to the pharmacokinetics. However, the concentration–effect
relationship of any drug tends towards a plateau, and a sigmoidal model (sigmoid E max model
or Hill equation) is more appropriate [21–24]:
E = E 0 + E max ·
C e γ
C e γ + EC50 γ
(13.9)
where E is the drug effect (arbitrary unit; same unit as E 0 and E max), E 0 is the drug effect
in the absence of drug (typically zero, or baseline effect), E max is the maximum achievable
drug effect, C e is the drug concentration at the effector site, γ is a dimensionless value, indicating
the gradient of the concentration–effect relationship, and EC 50 is the drug concentration
at which the drug effect is 50% of the maximum effect E max.