Mathematical formalism and characteristics of four basic models of indirect pharmacodynamic responses for drug infusions

Indirect response models require differential equations to describe the nonlinear inhibition or stimulation of the production or loss (k(out)) of the response variable. Partially integrated solutions for these models developed previously for iv bolus or biphasic pharmacokinetics were extended to consider drug infusions for limited or extended durations. Qualitative examination was made of the role of infusion rate and duration, type and rate of drug disposition, I(max) or S(max) capacity factors, IC₅₀ or SC₅₀ sensitivity factors, and k(out) values. Properties of the response curves characterized include curve shapes, maximum or minimum response, onset rate, steady-state, and return to baseline. Some comparisons were made with behavior of iv bolus doses. These relationships provide both a formal and practical basis for better understanding of the time-course of basic indirect response models.