Mean Residence Time Concepts for Pharmacokinetic Systems with Nonlinear Drug Elimination Described by the Michaelis–Menten Equation

Equations for the mean residence time (MRT) of drug in the body and related functions are derived for drugs which are intravenously administered into a one- or two-compartment system with Michaelis–Menten elimination. This MRT is a function of the steady-state volume of distribution and time-average clearance obtained from the dose and area under the curve (dose/AUC). The differences between the MRT calculated by the proposed method and by using the moment theory method (AUMC/AUC) are demonstrated both mathematically and by computer simulations. The validity of the proposed method for calculation of MRT and its relationship to the moment theory result have also been assessed by examining the percentage of the administered dose eliminated and the percentage of the total area attained at MRT and at AUMC/AUC in relation to the dose. The equations evolved should be helpful in clarifying residence time derivations and in defining the disposition characteristics and differences between linear and nonlinear systems. Direct methods are provided for calculation of Michaelis–Menten parameters based on the relationship between MRT and dose.