NEW MATHEMATICAL IMPLEMENTATION OF GENERALIZED PHARMACODYNAMIC MODELS- METHOD AND CLINICAL-EVALUATION

A new method and experimental design are presented to unambiguously es timate the transduction function (phi) and the conduction function (ps i) of the generalized pharmacodynamic model: E = phi(psi r), when me asured pharmacokinetic response r is (i) drug plasma concentration and (ii) drug input rate into the systemic circulation. phi relates the o bserved pharmacologic effect E to the concentration at the effect site : c(e) = (psi r), psi defines transfer of drug from plasma site to e ffect site or from input site to effect site, and represents the con volution integral. The model functions psi and phi were expressed as c ubic splines giving a very flexible description of those processes whi ch is not biased by the structured assumptions of more conventional mo dels, e.g., effect compartment models. The experimental design propose d addresses the problem of ambiguous identification of the model funct ions typical of these models; that is, there is more than one pair of very different functions describing the effect data collected after a single drug administration. We tested the hypothesis that the simultan eous fitting of at least two administrations allows the unambiguous id entification of the model functions without the need for unlikely or c umbersome constraints. The performance of the mathematical implementat ion and the robustness of the methods with respect to measurement nois e and possible failure of some assumptions, such as intraindividual va riability, were rested by computer simulations. The method was then ap plied to the results of a clinical study of verapamil pharmacodynamics in 6 healthy subjects. Results of these studies demonstrated that the mathematical implementation does not introduce bias or artifact into the estimated functions and that the models and the proposed methods a re suitable for application to clinical research. Two drug administrat ions were sufficient to unambiguously describe verapamil pharmacodynam ics in the 6 human subjects studied.