GENERALIZED PHARMACOKINETIC MODELING FOR DRUGS WITH NONLINEAR BINDING.1. THEORETICAL FRAMEWORK

The following integrodifferential equation is proposed as the basis fo r a generalized treatment of pharmacokinetic system in which nonlinear binding occurs phi'(c(u))c(u)' = -q(c(u)) + g c(u) + f where c(u) = unbound plasma drug concentration, f = drug input rate, indicates the derivative of a function, and indicates the convolution operation: (g c(u))(t) = integral-t/0 g(t-u)c(u)(u) du. Possible physical inter pretations of the functions q, g and f are: q (c(u)) = rate at which d rug leaves the sampling compartment, g c(u) = rate at which drug ret urns to the sampling compartment from the peripheral system (tissues t hat are kinetically distinct from the sampling compartment), and phi(c (u) = amount of drug in the sampling compartment. The approach assumes that drug binding is sufficiently rapid that it may be treated as an equilibrium process. It may be applied to systems in which nonlinear b inding occurs within the sampling compartment, i.e., in the systemic c irculation or in tissues to which drug is rapidly distributed. The pro posed relationship is a generalization of most existing models for dru gs with nonlinear binding. It can serve as a general theoretical frame work for such models or as the basis for ''model-independent'' methods for analyzing the pharmacokinetics of drugs with nonlinear binding. C omputer programs for the numerical solution of the integrodifferential equation are presented Methods for pharmacokinetic system characteriz ation, prediction and bioavailability are presented and demonstrated.