Generalized pharmacokinetic modeling for drugs with nonlinear binding: I. Theoretical framework

The following integrodifferential equation is proposed as the basis for a generalized treatment of pharmacokinetic systems 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)=∫ ₀ ^t g(t−u)c_udu.Possible physical interpretations of the functions q, g and f are: q (c_u)≡ rate at which drug leaves the sampling compartment, g * c_u ≡ rate at which drug returns to the sampling compartment from the peripheral system (tissues that are kinetically distinct from the sampling compartment), and φ(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 binding occurs within the sampling compartment, i.e., in the systemic circulation or in tissues to which drug is rapidly distributed. The proposed relationship is a generalization of most existing models for drugs with nonlinear binding. It can serve as a general theoretical framework for such models or as the basis for “model-independent” methods for analyzing the pharmacokinetics of drugs with nonlinear binding. Computer programs for the numerical solution of the integrodifferential equation are presented. Methods for pharmacokinetic system characterization, prediction and bioavailability are presented and demonstrated.