To the Editor:— We congratulate Dr. Minto et al . 1for the introduction of the concept of and have several comments about its tpeakapplication.
The authors 1use a polyexponential equation (equation 1) to describe the time course of the plasma concentrations of a drug in lieu of a compartmental interpretation suggested by Sheiner et al . 2As a consequence, the effect compartment can now contain any amount of a drug and is not limited to being “negligibly small” as postulated by Sheiner et al .
Sheiner et al . 2introduced keoas the first-order transport rate constant from the effect compartment to “outside” but did not define the transport rate constant from plasma into the effect compartment. It follows from theorem 1 (appendix) that the authors use keoas the rate constant for drug transport from plasma into the effect compartment as well as for the transport from the effect compartment into plasma. Hence, the transport of a drug into and out of the effect compartment is defined differently from that of Sheiner et al. , but the authors retain the label keo.
The definition of tpeakis given once (page 324) as “the time of maximum effect site concentration following an intravenous bolus dose when there is no drug initially in the system” and again as “a model independent parameter, as it can be directly observed following a submaximal bolus dose.” Which definition takes precedence? Because any dose of a drug may be injected as a bolus intravenously, all clinically used doses are presumably “submaximal.” It is the pharmacologic effect that is submaximal or maximal, as the case might be, and not the dose. Also, the time to peak pharmacologic effect represents a single time point among the observed points relating the magnitude of the effect to the time after injection. It is not a pharmacodynamic parameter. In our view, the time to the peak submaximal effect is observed during the collection of the data and, along with other data points, provides information necessary to simulate the time course of drug concentrations in the effect compartment and, in conjunction with the pharmacodynamic parameters (γ and IC50), the time course of the effect.
As evident from equation 3 on page 325, tpeakand keoare interrelated, but only if the pharmacologic effect is submaximal. A maximal pharmacologic effect may be associated with a given concentration in the effect compartment or with one many times higher. In theory and with extremely high doses, circulation time represents the lower limit for the time to the maximal effect for most drugs.
Are the authors satisfied that measuring an effect to an endpoint defines the peak, but submaximal, effect? The endpoint measurements were used in some of the cited studies.
Overlapping of the curve “Shanks PK/PD” with that labeled “Shanks PK with Stanski tpeak” in figure 1 is only possible because the times to peak effect are nearly identical (Stanski and Maitre 3~ 1.75 min and Shanks et al . 4~ 1.73 min). The time course of the plasma concentrations described by Stanski and Maitre is markedly different from that described by Shanks et al. , and each description requires a separate keo(Stanski and Maitre = 0.58 min−1and Shanks et al. = 0.29 min−1). In spite of these differences, the peak concentration in the effect compartment is simulated at approximately identical times. It is not “naive” but mathematically and conceptually incorrect to substitute keofrom one study into another. Therefore, this maneuver may be a priori excluded. Even if the value of keo, calculated from tpeakof Stanski and Maitre (keo= 0.284 min−1), fits the concentration of Shanks et al. in the effect compartment well (fig. 1), so does the value of keo, calculated from tpeakof Shanks et al. (keo= 0.595 min−1), produce concentrations in the effect compartment that overlap those simulated by Stanski and Maitre. However, the peak concentration of thiopental in the effect compartment simulated by Stanski and Maitre is higher than that simulated by Shanks et al. (0.0655 vs. 0.0438 relative units). Although the tpeakapproach brings the two peak concentrations in the effect compartment to overlap in time, the approach does not reconcile the other aspects of the studies. The differences in the time course of the concentrations in plasma and the effect compartment, in the peak concentrations in the effect compartment, and, presumably, in the pharmacodynamic parameters (γ and IC50) remain. What can then be the purpose of the tpeakapproach?
The authors compare different scenarios for the time course of the concentrations of remifentanil in the effect compartment. However, no data for the time course of the pharmacologic effect are presented. In the absence of these data, no effect compartment can be postulated and, if one is postulated, it cannot be differentiated from any other peripheral compartment.
Concentrations of a drug in the effect compartment cannot be verified. Quality of simulations can be documented only by comparing the simulated with the observed time courses of (1) the plasma concentrations and (2) the effect. The goal of pharmacodynamic simulations is to reproduce the time course of the effect, but these simulations are missing in the article.
To conclude, we support the notion that the time to peak submaximal effect is important information to be obtained from the time course of the effect. It is important to stress that the peak effect must be submaximal. Simulation in a pharmacokinetic–pharmacodynamic model, if successful, produces a time course of the drug concentration in the effect compartment such that the peak concentration and the simulated peak effect occur at the time of the observed peak submaximal effect. Optimally, the whole simulated time course of the pharmacologic effect is close to the observed. The time to peak concentration in the effect compartment is a derived but unique function of keoand the parameters in the polyexponential description of the time course of plasma concentrations. The time to peak submaximal effect is an observed value.
Medical College of Ohio, Toledo, Ohio. firstname.lastname@example.org