Simultaneous modeling of pharmacokinetics and pharmacodynamics: Application to d‐tubocurarine

Abstract

We propose a model of drug pharmacodynamic response that when integrated with a pharmacokinetic model allows characterization of the temporal aspects of pharmacodynamics as well as the time‐independent sensitivity component. The total model can accommodate extremes of effect. It allows fitting of simultaneous plasma concentration (Cp) and effect data from the initial distribution phase of drug administration, or from any non‐equilibrium phase. The model postulates a hypothetical effect compartment, the dynamics of which are adjusted to reflect the temporal dynamics of drug effect. The effect compartment is modeled as an additional compartment linked to the plasma compartment by a first‐order process, but whose exponential does not enter into the pharmacokinetic solution for the mass of drug in the body. The hypothetical amount of drug in the effect compartment is then related to the observed effect by the Hill equation, a nonlinear sigmoid form. Nonlinear least‐squares data fitting is used for parameter estimation. The model is demonstrated on two different sets of Cp and effect data for the drug d‐tubocurarine (dTC). In 7 normal subjects, the (mean ± SD) rate constant for equilibration of dTC effect (paralysis) and Cp is 0.13 ± 0.04 min−1 and the (mean ± SD) steady‐state Cp required to produce 50% paralysis is 0.37 ± 0.05 µg/ml.