New mathematical implementation of generalized pharmacodynamic models: Method and clinical evaluation

A new method and experimental design are presented to unambiguously estimate the transduction function (φ) and the conduction function (ψ) of the generalized pharmacodynamic model: E = φ(ψ * r), when measured pharmacokinetic response r is (i) drug plasma concentration and (ii) drug input rate into the systemic circulation. φ relates the observed pharmacologic effect E to the concentration at the effect site: c(e) = (ψ * r), ψ defines transfer of drug from plasma site to effect site or from input site to effect site, and * represents the convolution integral. The model functions ψ and φ were expressed as cubic splines giving a very flexible description of those processes which is not biased by the structured assumptions of more conventional models, e.g., effect compartment models. The experimental design proposed addresses the problem of ambiguous identification of the model functions 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 simultaneous fitting of at least two administrations allows the unambiguous identification of the model functions without the need for unlikely or cumbersome constraints. The performance of the mathematical implementation and the robustness of the methods with respect to measurement noise and possible failure of some assumptions, such as intraindividual variability, were tested by computer simulations. The method was then applied 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 are suitable for application to clinical research. Two drug administrations were sufficient to unambiguously describe verapamil pharmacodynamics in the 6 human subjects studied.