Mathematical analysis of a pharmacodynamic model without plasma concentrations to extend its applicability

Using a mathematical approach, we analyzed the behavior of the PD model originally described by Bragg et al. The effect was dose-dependent modified until a maximum value (E(max)) was reached. Further increments in dose prolonged the E(max), but the recovery phase did not increase beyond a calculable asymptope. In the absence of plasma concentrations, it was impossible to distinguish the rate of plasma equilibration with the effect compartment (k(e0)) from the rate of drug elimination (k(e1)). Variations on the sigmoidicity affected both the onset and offset of drug effect. Sigmoidicity and the slowest rate constant had identical effects on the spontaneous reversion of the effect, as judged by the recovery index. The IR(50), the index of potency, merely shifted the dose-response relationship to the left or right. Changes in IR(50) were compensated for by making the same proportional changes in dose.