Characterization of the dose-dependent time of peak effect in indirect response models

The general conceptual model for non-steady state pharmacokinetic/pharmacodynamic data includes a distribution phase between the plasma and the biophase compartments, which can be expressed by a link model, and inhibition or stimulation of the production or removal of a mediator, which can be expressed by an indirect response model. The inhibition or the stimulation step modeled by an indirect response model generates dose-dependent time of peak effect. This report provides a mathematical expression for this time of peak effect which is then used to determine how this time depends on dose, the endogenous elimination rate of the mediator, and the pharmacokinetic parameters of the drug. The report then uses this time of peak effect to find the response versus time curve. The mathematical relationship for the time of peak effect and the response vs. time curve are then developed for a cascade of two indirect steps. The approach presented here is easily implemented on a spreadsheet and does not require numerically solving nonlinear differential equations. The approach should help to analyze various issues related to fitting indirect response models to non-steady state pharmacokinetic/pharmacodynamic data, especially, when one is trying to fit data to a cascade of indirect steps.