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 (ke0) as well as first-order rate constant between arterial and venous concentrations (kv0). 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 ke0, kv0, and the drug's elimination half-life (T1/2); 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 ke0 (T1/2,e0), the half-life of kv0 (T1/2,v0), and T1/2. The simulations showed that a significant bias (up to 90%) in PD parameter estimates occurred for certain values of T1/2,e0, T1/2,v0, and T1/2 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 T1/2 of the drug in the time period in which the decline in pharmacological effect is most pronounced is greater than 5 times T1/2,e0 and T1/2,e0 is greater than T1/2,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 Emax, EC50 and N. If T1/2 is less than 5 times T1/2,e0 or if T1/2,v0 is greater than T1/2,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 T1/2.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.