MATHEMATICAL FORMALISM FOR THE PROPERTIES OF 4 BASIC MODELS OF INDIRECT PHARMACODYNAMIC RESPONSES

Four basic models for characterizing indirect pharmacodynamic response s were proposed previously and applied using differential equations. T hese models consider inhibition or stimulation by drug of the producti on ol loss of mediators or response variables. This report develops pa rtially integrated solutions for these models which allow more detaile d examination of the roles of model parameters and pharmacokinetic fun ctions in affecting the time course of drug effects. Because of the no nlinear Hill function, the solutions are represented by means of defin ite integrals containing kinetic and dynamic functions. These solution s allow a qualitative examination, using calculus, of how response is controlled by Dose, IC50 or SC50, I-max or S-max, and k(out) for drugs exhibiting monotonic or biphasic disposition. Characteristics of the response curves that were identified include shape, maximum or minimum , and changes with the above parameters and time. These relationships, together with simulation studies, provide a fundamental basis for und erstanding the temporal aspects of the basic indirect response models.