A tracer interaction method for nonlinear pharmacokinetics analysis: application to evaluation of nonlinear elimination

Abstract

A drug tracer is most commonly applied to get information about the pharmacokinetics (PK) of a drug that is not confounded by an endogenously produced drug or an unknown drug input. An equally important use of tracers that has not been fully recognized is their use in the study of nonlinear PK behavior. In the present study a system analysis is applied to examine the interaction between drug molecules characteristic and intrinsic to any nonlinear process which enables the nonlinearity to be identified and modeled using a drug tracer. The proposed Tracer Interaction Methodology (TIM) forms a general developmental framework for novel methods for examining nonlinear phenomena. Such methods are potentially much more sensitive and accurate than previous methods not exploiting the tracer principle. The methodology proposed is demonstrated in a simulation study and with real data in a specific implementation aimed at determining the Michaelis-Menten (MM) parameters of nonlinear drug elimination while accounting for drug distribution effects. The simulation study establishes that the TIM-based, MM parameter evaluation produces substantially more accurate parameter estimates than a nontracer (NT) conventional method. In test simulations the accuracy of the TIM was in many cases an order of magnitude better than the NT method without evidence of bias. The TIM-based, MM parameter estimation methodology proposed is ideally suitable for dynamic, non-steady-state conditions. Thus, it offers greater applicability and avoids the many problems specific to steady state evaluations previously proposed. TIM is demonstrated in an evaluation of the nonlinear elimination behavior of erythropoietin, a process that likely takes place via receptor-based endocytosis. Due to its high sensitivity, accuracy, and intrinsic nonlinearity the TIM may be suitable for in-vivo studies of receptor binding of the many biotechnology produced peptide drugs and endogenous compounds displaying receptor-mediated elimination.