F1-24presents the plasma concentration of fentanyl as a function of time after the infusion is discontinued, as well as the probability of drug effect predicted for these plasma concentrations using the logistic equation with C 50= 5 and delta = 2 or 10. MethodsĪn intuitive understanding of this parameter is illustrated in Figure 1for the hypothetical recovery from a continuous infusion of fentanyl that has maintained a plasma concentration of 10 ng/ml for 60 min. In this paper, I extend the context-sensitive half-time/decrement time concept and propose a parameter, mean effect time (MET), which can be used to quantify the duration of drug effect when dealing with binary (response or no response) data and consider the implications of this approach for several commonly used intravenous anesthetic agents. However, for smaller values of delta, this may not be true, because there will still be a finite probability of drug effect even when the concentration is less than C 50.
In this case, the duration of drug effect will be the decrement time between the drug concentration maintained during anesthesia and C 50, because the transition between effect and no effect is very sharp. If delta is very large, the probability of drug effect is nearly 1 when C is larger than C 50(even if only slightly larger) and nearly 0 when C is less than C 50. At any specific drug concentration, there is a probability of drug effect, and it usually is assumed that this probability can be described within the framework of the logistic distribution as P = C delta/(C delta+ C 50 delta), where P is the probability of drug effect, C is the drug concentration, C 50is the concentration at which the probability of drug effect is 50%, and delta is a parameter determining the steepness of the relationship. However, in anesthesiology, we often deal with binary data, i.e., the patient is responsive or not, ventilation is adequate or not, and so on. An example is recovery from muscle relaxants, as was demonstrated by Kern. The duration of drug effect can be identified with the appropriate decrement time if the drug effect can be measured by a continuous variable for which there is a well defined value of recovery. This concept can be generalized to "decrement times," whereby, for example, the 80% decrement time is the time needed for the plasma or effect site concentration to decrease by 80%. This parameter is a function of the "context", i.e., the duration of drug administration before its discontinuation. introduced the term context-sensitive half-time to indicate the time necessary for a 50% decrease in plasma drug concentration. These authors have demonstrated, using computer simulation, that the rate of decrease of either the effect site (Shafer and Varvel) or plasma (Hughes et al.) concentration after continuous intravenous infusion cannot be simply related to any one pharmacokinetic parameter and is highly dependent on the duration of infusion. The influence of pharmacokinetic variables has been significantly clarified by papers by Shafer and Varvel and Hughes et al. THE duration of drug effect is a function of both pharmacokinetic and pharmacodynamic properties. It was assumed that C 90and C 50were independent variables. These results were compared to the relevant decrement times (as defined in this paper, the time required for the concentration to decrease from C 90to the concentration at which 50% of patients are responsive and/or able to maintain adequate ventilation, denoted C 50). Published pharmacokinetic and pharmacodynamic parameters were used for these calculations.
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%(C 90). 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. This parameter is denoted the mean effect time. 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.
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