Model-Independent Steady-State Plasma Level Predictions in Autonomic Nonlinear Pharmacokinetics I: Derivation and Theoretical Analysis

Abstract

Current drug level predictions in nonlinear pharmacokinetics are based on specific pharmacokinetic models in contrast to the model-independent (structureless), dose-linearity, and superposition principles used in linear pharmacokinetics. Such model-dependent methods may not provide reliable predictions due to their inherent nonuniqueness, computational complexity, and often unrealistic kinetic assumptions. Some novel model-independent methods for predicting the steady-state drug levels of extravascular, intravenous bolus, and intravenous infusion administrations are presented that should overcome such disadvantages. The methods only assume an autonomic nonlinear kinetic behavior, which implies that following an intravenous bolus administration the derivatives of the drug concentration-time profile at arbitrary drug levels are independent of the dose given. Such a kinetic behavior is found for any nonlinear pharmacokinetic system when the rate of change of the drug level following an intravenous bolus administrations depends only on the drug level, i.e., dC/dt = −q(C), where q can be any function dependent only on C and time-invariant kinetic parameters. The basic approach presented represents a novel alternative which avoids the very difficult and often impractical task of identifying and incorporating the numerous kinetic parameters and processes responsible for the observed drug concentration data into a useful pharmacokinetic model. The focus in the kinetic analysis is instead on two much simpler processes: (a) fitting empirical functions to estimate the mean drug disposition behavior of the subject or population and (b) testing the validity of the assumptions involved.