Estimation of the Plasma Effect Site Equilibration Rate Constant (k^e0) of Propofol in Children Using the Time to Peak Effect: Comparison with Adults

After institutional ethics committee approval (School of Medicine, Pontificia Universidad Católica de Chile, Santiago, Chile) and obtaining informed consent, 25 adult patients aged 35–48 yr and 25 children aged 3–11 yr were studied. All patients were unpremedicated, had American Society of Anesthesiologists physical status I, and were scheduled to undergo elective surgery during general anesthesia. Exclusion criteria included a weight greater than 120% of ideal, long- or short-term (within the previous 48 h) intake of any sedative and analgesic drug, and any known adverse effect to the study drugs. In the operating room, after routine monitoring, three electrodes (A-Line electrodes; Medicotest A/S, Oelstykke, Denmark) were positioned at the mid forehead (+), the left forehead (reference), and the left mastoid (−) in all patients. A bilateral click stimulus of 70 db and 2 ms duration was applied by means of headphones, and the midlatency AEPs elicited were processed continuously using the Alaris A-Line AEP monitor, version 1.4 (Danmeter A/S, Odense, Denmark). The A-Line AEP monitor uses an Auto Regressive method with exogenous input (ARX) model to process the AEPs and displays the A-Line ARX-index (AAI), a dimensionless number from 100 (fully awake) to 0 (conceivably a flat electroencephalography). The index was obtained as “normal AAI,” which displays the on-line measured index at a rate of 1 Hz. Because the monitor initially needs a period of time to process the AEPs and give the first AAI value, the subsequent values are shown with a time delay of approximately 6 s. When the impedance of the electrodes was less than 5 kΩ and there were no warnings of poor quality signal on the screen of the monitor, a bolus dose of propofol (1%; Fresenius Kabi, Hamburg, Germany) producing a submaximal effect (i.e. , the minimum AAI value generated by the A-Line AEP monitor was > 0) was injected manually as fast as possible (always in less than 5 s) and followed by a flush of saline. Because initially the “useful” dose of propofol had to be determined, the first patients in both groups received different doses on a weight basis. Patients who did not lose the eyelash reflex were excluded from the study because their recording of AAI values did not always allow the detection of an evident minimum. Besides the confirmation of the presence or absence of the eyelash reflex, no other stimulation was applied (i.e. , noninvasive arterial pressure) to patients. When a minimum AAI value was obtained and partial recovery from propofol was evident as suggested by increasing AAI values, the study was finished and anesthesia continued according to the attending anesthesiologist.

The AAI values recorded by the AEP monitor at a frequency of 1 Hz were imported into an Excel (Microsoft Corporation, Redmond, WA) spreadsheet for off-line determination of the time of peak effect (t^peak, time from the beginning of injection of propofol until the minimum AAI value). In the few cases where a minimum AAI value remained constant for a few seconds (usually for 5–6 s), the time until the first lowest AAI value was considered the t^peak. Because the AAI value is displayed with a 6-s delay, for subsequent analysis, we subtracted 6 s from the t^peakdetermined off-line. Because at t^peakthe maximum effect site concentration (C^e) of propofol occurs and equals that of plasma (C^p), after a bolus, we can calculate these concentrations (μg/ml) with the dose (mg) and the Unit Disposition Function of the effect site at t^peak(C^e(t^peak)) with the formula

where A and λ are pharmacokinetic parameters. Then, using C^e(t^peak) the value of k^e0was calculated with the equation

This equation was solved for k^e0for each patient with the Solver function of Excel using the pharmacokinetic parameters for propofol determined by Schnider et al.  9for adults and those determined by Kataria et al.  10for children. In children, k^e0was also calculated with the pharmacokinetic model used in the Paedfusor. The constants of this model are k12 = 0.114, k13 = 0.0419, k21 = 0.055, k31 = 0.0033. Central compartment volume and k10 vary with age and weight, but for children aged 12 yr or younger they are V1 = 458.4 ml/kg and k10 = 0.1527 × weight^−0.3.11Finally, as a simple way to validate the model, in terms that the population k^e0determined for each group is capable to predict a t^peaksimilar to the measured t^peak, the median k^e0determined from all children and all adults was used to calculate, with the corresponding pharmacokinetic parameters, the “predicted” t^peakfor each patient.

Statistical analysis was with the Kolmogorov–Smirnov test as a test of normality. This was followed by paired and unpaired Student t  tests, and Wilcoxon and Mann–Whitney tests for variables with and without normal distribution, respectively. A P  value less than 0.05 was considered significant. Values are presented as mean ± SD or median (range).

Demographic data for both groups, the dose of propofol, and AAI values are shown in table 1. There was a wide variability in the baseline AAI values in both children and adults. Moreover, whereas there was no difference between children and adults in the AAI values measured awake, after propofol, adults reached a lower AAI value compared with children (fig. 1and table 1).

The t^peakwas 80 ± 20 s (43–108 s) in adults and 132 ± 49 s (53–209 s) in children (P < 0.001; fig. 2). In both groups, there was a non– statistically significant tendency to an increase of t^peakwith age. In all patients, it was possible to determine with equation 2the k^e0that exactly matched the measured t^peak(minus the 6-s delay) (fig. 3). The Kolmogorov–Smirnov test detected that the k^e0and t^1/2k^e0did not have normal distribution; consequently, they were analyzed with Mann–Whitney and Wilcoxon tests. The calculated median k^e0was 0.56 min⁻¹(0.30–2.00 min⁻¹) in adults. In children, the median k^e0was 0.41 min⁻¹(0.12–1.85 min⁻¹) using the model of Kataria and 0.91 min⁻¹(0.40–3.34 min⁻¹) with the Paedfusor parameters (P < 0.001, Wilcoxon test). These k^e0values led to a median t^1/2k^e0value of 1.24 min (0.35–2.33 min) in adults and 1.7 min (0.4–5.9 min) and 0.8 min (0.2–1.7 min) in children with the Kataria and Paedfusor models, respectively (P < 0.001, Wilcoxon test). When the k^e0and t^1/2k^e0from adults were compared with those from children, a statistically significant difference was found only with those parameters determined with the Paedfusor model (P < 0.01, Mann–Whitney test).

The “predicted” t^peakin adults using a k^e0of 0.56 min⁻¹was 82 ± 2 s (77–85 s) and was not significantly different from the measured t^peakwith the paired Student t  test. (fig. 4). In children, using a k^e0of 0.41 min⁻¹and the pharmacokinetic model of Kataria, the “predicted” t^peakwas 131 ± 25 s (94–184 s). In this same age group, using a k^e0of 0.91 min⁻¹and the Paedfusor pharmacokinetic model, the “predicted” t^peakwas 128 ± 3 s (125–140 s). These were not significantly different from the measured t^peakwith the paired Student t  test (fig. 4).

The main finding of this study is that the peak effect of propofol in children occurs significantly later as compared with adults. Expectedly, the calculated values of k^e0and t^1/2k^e0depend on the pharmacokinetic model used to derive these parameters.

Propofol is widely used for intravenous anesthesia; however, we are not aware of any study determining the k^e0of propofol in children. An accurate determination of a given drug’s k^e0is useful for targeting the effect site instead of the plasma concentration during computer-controlled drug administration, for designing and interpreting clinical pharmacologic research, and for simulations of the time course of a drug effect.

To calculate the k^e0, the t^peakmethod was used as proposed by Minto et al.  8The t^peakis a pharmacokinetic model–independent parameter that can be directly observed after a bolus dose of a drug, provided that the drug is given for the first time, that a submaximal response is elicited, and that its time course can be measured accurately.3,7,8In turn, this t^peakcan be mathematically related to any adequate pharmacokinetic model to calculate the corresponding k^e0that will result in a maximal effect site concentration at the moment of t^peak.3,6,8The mean t^peakof 80 s found in our study for adults is shorter than the t^peakof 96 s observed by Schnider et al.  6; however, we injected propofol in less than 5 s, whereas in the study of Schnider, the injection lasted 18 s (range, 13–24 s), and this might have lead to different t^peaks. Using the pharmacokinetic model for propofol of Schnider et al. ,9we found a median value for the k^e0of 0.56 min⁻¹and a t^1/2k^e0of 1.2 min in adults. This t^1/2k^e0calculated in our study is 20% smaller than the 1.5 min reported by Schnider et al.  6Although this difference (and that in k^e0) can be first accounted for by the differences found in t^peakvalues, it might also be secondary to the use of different monitors of drug effect. In addition, anthropometric differences in the populations under study leading to different pharmacokinetic variables and therefore to different k^e0values cannot be ruled out. The t^1/2k^e0of propofol reported in this study and that of Schnider are smaller than t^1/2k^e0s calculated in other studies and that go up to 4.0 min.4,5In this last case, however, these differences could be secondary to the use of different pharmacokinetic models for propofol because the value of k^e0is critically dependent on the pharmacokinetic model used.

In the case of children aged 3–11 yr, we found a t^peakof 132 s, which is significantly larger than that of adults. Therefore, our initial hypothesis of a shorter or faster t^peakin children than adults, which would agree with the tendency to an increase of t^peakwith age in adults,6is not supported by our findings. The t^peakor time of maximal effect site concentration of a drug after a bolus depends on two simultaneously occurring processes: One is the decreasing plasma concentration, and the other is the increasing effect site concentration. The faster the decrease of plasma concentration is, the sooner t^peakoccurs. As shown in figures 4 and 5, the pharmacokinetic models of propofol of both Kataria and the Paedfusor in children predict a slower decrease of plasma concentration compared with the model of Schnider in adults. This could be an explanation for a slower t^peakin this age group. The larger variability of t^peakin children could be also secondary to the much larger variability in pharmacokinetic parameters within children aged 3–11 yr compared with adults aged 35–48 yr, as shown in figure 5.

When the t^peakfound was used to calculate the k^e0, the results were significantly different depending on the pharmacokinetic model used. With the model of Kataria et al. ,10the k^e0was 0.41 min⁻¹, resulting in a t^1/2k^e0of 1.7 min that supports a slower t^peakin children than in adults, whereas with the Paedfusor parameters, the k^e0was 0.91 min⁻¹, and the t^1/2k^e0was 0.8 min. These results emphasize two facts: One is that the k^e0value is critically determined by the particular set of pharmacokinetic parameters used to calculate it; therefore, k^e0cannot be used interchangeably with different models. The other is that despite a shorter t^1/2k^e0, as occurs with the value determined by the Paedfusor, compared with that from adults, t^peakcan be longer secondary to a much slower decrease of plasma concentration. We are not aware of any other reported value for these variables in children, and these findings must be prospectively confirmed.

To validate the estimates of k^e0, we compared the mean measured t^peakwith the mean predicted t^peakin each population using the median k^e0. The observed time of peak effect in adults (80 s) agrees almost exactly with the predicted t^peakof 82 s using the pharmacokinetics of Schnider et al.  9and a k^e0of 0.56 min⁻¹. In children, the predicted t^peakof 131 s using the pharmacokinetics reported by Kataria et al.  10and a k^e0of 0.41 min⁻¹and the predicted t^peakof 128 s with the Paedfusor parameters and a k^e0of 0.91 min⁻¹also match almost exactly the observed value of 132 s. This good agreement between mean measured and predicted t^peaks suggests that the incorporation of the appropriate k^e0calculated in this study to the pharmacokinetics of Kataria and the Paedfusor may result in adequate models for targeting the effect site concentration of propofol in children.3 

A criticism of our methodology might be related to the specific electroencephalographic monitor used. The Alaris AEP monitor (version 1.4) used in our study delivers a dimensionless number (AAI value) derived from the processing of the midlatency AEPs and might be regarded as very different from the electroencephalographic-derived measures in several aspects. While Alaris AEP monitor must be validated in children, the similarity of the t^peakin our study with that obtained by Schnider et al.  6suggests that both monitors are measuring, at least in adults, a similar underlying process that is modified by propofol. The baseline AAI values were similar in children and adults, whereas the minimum value was significantly higher in children. Although figure 5shows that both pediatric models for propofol predict a lower peak effect site concentration than in adults, thus suggesting that a pharmacokinetic difference may explain different minimum AAI values, pharmacodynamic differences cannot be ruled out.

As previously mentioned, at least theoretically, the effect site is a more logical target than plasma. This reduces the delay to obtain a given drug effect and possibly also its variability, which occurs when the target is plasma concentration.2,3Because targeting the effect site is initially accompanied by a high plasma concentration or “overshoot,” the possibility that this might lead to more incidence of adverse effects (e.g. , hypotension in the case of propofol)1is a potential disadvantage of this technique. However, controlled studies with propofol have not shown more adverse effects when targeting an effect site concentration instead of plasma.2,3 

In conclusion, we have measured the time to peak effect of propofol in children and adults. Although this time is significantly longer in children, the finally calculated k^e0is particular to the model used to derive this parameter. The k^e0s obtained from the models of Kataria and the Paedfusor for propofol in children can be used with caution with the corresponding models to target effect site concentration of propofol in children. However, these parameters must be further validated before their widespread use in clinical anesthesia.