Integrated functions for four basic models of indirect pharmacodynamic response

The integrated solutions (ABEC, area between baseline and effect curve) of four basic models of indirect pharmacodynamic responses are developed. These models assume that drug can inhibit or stimulate the production or loss of the response variable. For two models (I and III) with monoexponential drug disposition, explicit formulas for the ABEC were obtained, where ABEC is a function of ln (1 + (D/V)/IC50) or ln (1 + (D/V)/SC50) where D = dose, V = volume, and IC50 or SC50 = 50% effective concentration. Two other models (II and IV) were treated asymptotically with respect to small and large doses. Approximate formulas [e.g., ABEC = constant(1) . ln (1 + (D/V)/IC50) + constant (2)] were derived and the asymptotic behavior of the ABEC was established. In addition, simulations were performed to assess the effects of drug absorption rates and polyexponential disposition on ABEC values. These models show how pharmacokinetic and pharmacodynamic factors jointly determine the net response to a single dose of drug.