Using the Time of Maximum Effect Site Concentration to Combine Pharmacokinetics and Pharmacodynamics

Abstract

Background To simulate the time course of drug effect, it is sometimes necessary to combine the pharmacodynamic parameters from an integrated pharmacodynamic-pharmacodynamic study (e.g., volumes, clearances, k(e0) [the effect site equilibration rate constant], C(50) [the steady state plasma concentration associated with 50% maximum effect], and the Hill coefficient) with pharmacokinetic parameters from a different study (e.g., a study examining a different age group or sampling over longer periods of time). Pharmacokinetic-pharmacodynamic parameters form an interlocked vector that describes the relationship between input (dose) and output (effect). Unintended consequences may result if individual elements of this vector (e.g., k(e0)) are combined with pharmacokinetic parameters from a different study. The authors propose an alternative methodology to rationally combine the results of separate pharmacokinetic and pharmacodynamic studies, based on t(peak), the time of peak effect after bolus injection. Methods The naive approach to combining separate pharmacokinetic and pharmacodynamic studies is to simply take the k(e0) from the pharmacodynamic study and apply it naively to the pharmacokinetic study of interest. In the t(peak) approach, k(e0) is recalculated using the pharmacokinetics of interest to yield the correct time of peak effect. The authors proposed that the t(peak) method would yield better predictions of the time course of drug effect than the naive approach. They tested this hypothesis in three simulations: thiopental, remifentanil, and propofol. Results In each set of simulations, the t(peak) method better approximated the postulated "true" time course of drug effect than the naive method. Conclusions T(peak) is a useful pharmacodynamic parameter and can be used to link separate pharmacokinetic and pharmacodynamic studies. This addresses a common difficulty in clinical pharmacology simulation and control problems, where there is usually a wide choice of pharmacokinetic models but only one or two published pharmacokinetic-pharmacodynamic models. The results will be immediately applicable to target-controlled anesthetic infusion systems, where linkage of separate pharmacokinetic and pharmacodynamic parameters into a single model is inherent in several target-controlled infusion designs.