Saturable Fractal Pharmacokinetics and Its Applications - Mathematical Methods and Models in Biomedicine - page 336

Fig. 3 Schematic illustration of a multi-compartment physiologically-based model

rate coefficients are all constant, such that the fraction of drug transferred between
any two compartments is constant in time. The system is described by coupled first-
order differential equations whose solutions take the form of a sum of terms that are
exponential in time.
Within the pharmacokinetic model, the body is represented with a number of
compartments depending on the availability of parameter values and a specific
application of the model. Each compartment has a given volume. Of particular
interest is the “Tissue Compartment” which represents all body tissues not otherwise
accounted for in the model. The compound concentrations in this compartment
determine the intensity of physiologic effects. This is shown in Fig. 3 by the dashed
connection to the adjacent “Response” box. The movement of blood that carries
with it drug molecules between compartments is shown with arrows. Initial doses
enter the stomach if the drug is orally available, while the colon, liver, and kidneys
are sites of potential elimination of the drug from the system.
Classical kinetics is based on the law of mass action, which states that the rate v
of a chemical reaction is directly proportional to the product of the concentrations
of the N reactants each raised to the power n i :

N
i = 1 C n i

v = k , (18)

i