Background: Several recent studies have analyzed the relationship between pharmacokinetic parameters and the rate of decrease in concentration after discontinuation of a continuous drug infusion. Although these studies have clarified our understanding of those aspects of pharmacokinetics most relevant to anesthesia practice, they do not directly address the issue of the duration of drug effect, which will be a function of both pharmacokinetic and pharmacodynamic variables. This paper extends these concepts by presenting a method to unify pharmacokinetics and pharmacodynamics in a measure of duration of drug effect that is applicable when the drug effect is assessed in a binary, response/no response fashion.
Methods: The parameter proposed to quantify duration of drug effect is the area under the curve expressing probability of drug effect as a function of time after the agent is discontinued. This parameter is denoted the mean effect time. It is calculated using the logistic (or Hill) equation to relate the probability of drug effect to drug concentration, which in turn can be calculated as a function of time by pharmacokinetic simulation. Mean effect times were calculated for sufentanil, alfentanil, propofol, and midazolam using the logistic equation describing recovery and by assuming that drug blood concentrations during maintenance of anesthesia were sufficient to reduce the probability of responsiveness to surgical stimulation to 10% (C90). Published pharmacokinetic and pharmacodynamic parameters were used for these calculations. These results were compared to the relevant decrement times (as defined in this paper, the time required for the concentration to decrease from C90 to the concentration at which 50% of patients are responsive and/or able to maintain adequate ventilation, denoted C50). It was assumed that C90 and C50 were independent variables.
Results: Mean effect times for midazolam and propofol, for which the steepness parameter delta for recovery (responsiveness and adequate ventilation) is less than 4, are significantly greater than the decrement time. Mean effect times for sufentanil and alfentanil (delta = 6 and 10, respectively) are close to decrement times. The discrepancy between mean effect time and decrement time becomes greater as the duration of drug administration increases. The incorporation of pharmacokinetic variability into the calculations had little effect on the results.
Conclusions: Context-sensitive half-times or other decrement times have been shown to be the most useful measures of the kinetics of drug concentrations. Mean effect time may be a useful concept for understanding the recovery from drug effects.