The Impact of Arteriovenous Concentration Differences on Pharmacodynamic Parameter Estimates

Abstract

In many pharmacodynamic investigations venous drug concentrations are measured and linked to effect-site concentrations by means of a traditional first-order effect-compartment model to estimate pharmacodynamic (PD) parameters. This analysis ignores the underlying physiology that arterial blood supplies both the venous sampling site and effect site. Recently, an extended effect-compartment model has been proposed that reflects physiology by postulating a first-order rate constant of equilibrium between arterial and effect-site concentrations (k_e0 ) as well as a first-order rate constant between arterial and venous concentrations (k_v0 ). In the current paper, we evaluate the bias in PD parameter estimates if venous drug concentrations are measured and linked to effect-site concentrations by a traditional effect compartment as a function k_e0 , k_v0 , and the drug's elimination half-life (T_1/2 ); we present an analytical solution to the differential equations characterizing the extended effect-compartment model; and we evaluate the performance of the extended effect-compartment model to estimate pharmacodynamic parameters on the basis of venous drug concentrations. Time profiles of venous drug concentrations and drug effect were simulated for a wide range of different values of the half-life of k_e0 (T_1/2,e0 ), the half-life of k_v0 (T_1/2,v0 ), and T_1/2 . The simulations showed that a significant bias (up to 90%) in PD parameter estimates occurred for certain values of T_1/2,e0 , T_1/2,v0 , and T_1/2 if venous drug concentrations are linked to effect-site concentrations by a traditional effect-compartment model. This model misspecification is not apparent from the results of the fitting procedure. The extended effect-compartment model provided unbiased but imprecise PD parameter estimates. The extended effect-compartment model was also able to analyze instances in which the venous concentrations equilibrate slower with the arterial concentrations than the effect-site concentrations, and proteresis is observed in the concentration–effect relationship. It is concluded that if the apparent T_1/2 of the drug in the time period in which the decline in pharmacological effect is most pronounced is greater than 5 times T_1/2,e0 and T_1/2,e0 is greater than T_1/2,v0 there is no need to model the underlying arteriovenous equilibrium delay. Under these conditions a traditional first-order link between venous and effect-site concentrations will yield accurate and reliable (less than 10% bias) estimates of the PD parameters such as E_max , EC₅₀ , and N. If T_1/2 is less than 5 times T_1/2,e0 or if T_1/2,v0 is greater than T_1/2,e0 , the underlying arteriovenous equilibration delay needs to be taken into account in the model to obtain unbiased estimates of the PD parameters. This applies for almost all values of T_1/2,v0 . Arteriovenous equilibration delay can be best taken into account by measuring arterial blood concentrations. If this is not possible, the extended effect-compartment link model can be used. However, a large number of effect measurements needs to be obtained to estimate the model parameters accurately.