Pharmacodynamic modeling of verapamil effects under steady-state and nonsteady-state conditions

Pharmacodynamic models relating the plasma concentration (Cp) of verapamil to the drug's effect (E) on the P-R interval were investigated after single dose infusions of (0.15-0.22 mg/kg) verapamil in 22 normal subjects. Model predictions of the steady-state Cp-E relationship were then compared to results from actual steady-state drug infusions in the same subjects. Two methods of estimating the steady-state concentration response relationship from the single dose data were examined: 1) the relationship of descending limb Cp vs. E and 2) the relationship of estimated effect site concentrations (Ce) vs. E. When compared to experimental steady-state measurements, the absolute errors of predictions from the Ce vs. E method were less than those from the Cp vs. E predictions (6.8 +/- 4.4 vs. 9.6 +/- 6.6, mean +/- S.D.). Similarly, the slope of the linear regression of E on Cp differed more from the observed steady-state slope than the slope of E on Ce. Sigmoid Emax models fit to Cp vs. E. data gave false Emax values even when data immediately following drug infusion were disregarded whereas Ce vs. E plots demonstrated that Emax was not reached (and Ce much less than Cp). Neither the postinfusion (descending limb) Cp vs. E nor Ce vs. E plots allowed analysis of higher concentration vs. effect relationships after usual (0.15-0.22 mg/kg) doses of verapamil. In summary, we have demonstrated that nonsteady-state postdrug infusion effect vs. plasma concentration data for verapamil does not reflect the true steady-state relationship and that use of a model to estimate effect site concentration provides a closer estimate of the true steady-state relationship.