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*Department of Anaesthesia, Waikato Hospital, New Zealand; Department of Anaesthesiology, University of Auckland, New Zealand
Address correspondence and reprint requests to Logan J Voss, c/- Intensive Care Department, Waikato Hospital, P.O. Box 3200, Hamilton, New Zealand. Address e-mail to VossL{at}waikatodhb.govt.nz.
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Abstract |
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= 5.9 ± 2.3, EC50 = 1.7 ± 0.3. We found significant differences between values when the sevoflurane concentration was increasing (61.1 ± 55.2) compared with the decreasing part of the cycle (5.7 ± 2.8). Above an effect-site concentration of 3%, spectral entropy of the EEG is unresponsive to further increases in sevoflurane concentration. The effect-compartment inhibitory Emax model accurately describes the relation between sevoflurane concentration and spectral entropy of the EEG. Spectral entropy decreases with increasing sevoflurane concentrations up to 3%. The steepness of the dose-response curve varies between phases of increasing and decreasing anesthetic concentrations. |
Introduction |
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Processed electroencephalogram (EEG) parameters provide a reliable measure of the hypnotic effect of volatile anesthetics and gamma-aminobutyric acid-ergic IV anesthetic drugs, for example bispectral index, spectral edge frequency, and spectral entropy (1–4). Spectral entropy is calculated in the frequency domain and is a measure of the flatness of the power spectrum. When subjects are awake and alert, the power spectrum of the EEG is relatively flat but exhibits modest peaks in the 
and 
frequency ranges (1) and the spectral entropy is almost maximal (normalized to a value of one). With induction of anesthesia, a clear peak of power in the slow frequencies develops and the spectral entropy decreases towards zero. Datex-Ohmeda (Datex-Ohmeda Division, Instrumentarium Corp., Helsinki, Finland) has developed a commercially available depth-of-anesthesia monitor, the EntropyTM Module, that is based on the time-frequency balanced spectral entropy of the EEG (5). The output, two parameters called Response Entropy (RE) and State Entropy (SE), represent the spectral entropy scaled and further processed. The output values can range between 0 to 100 for RE and between 0 to 91 for SE; RE also includes electromyelogram frequencies whereas SE is predominantly calculated from EEG. Because of the higher frequency component contribution, the time windows for RE calculation are shorter than for SE (1.9-15.4 s compared to 15.0-60.0 s) (5). The actual time window used varies depending on the frequency being analyzed (time-frequency balanced).
PKPD modeling separates the relationship between drug dose and effect into two successive physiological processes. The pharmacokinetic side of the model describes how the blood concentration of the drug varies with time. When using sevoflurane for anesthesia, a rapid induction and recovery can be achieved and the end-tidal concentration at which consciousness is lost is clearly larger than the concentration at which the subject recovers. The same hysteresis is seen using processed EEG measures and probably reflects the time taken for the drug to move to and from its effect site. In this study we modeled this movement of drug as a single compartment exponential wash-in/washout process (equation 1). This assumes that the end-tidal sevoflurane concentration closely approximates the arterial partial pressure of this drug.
The pharmacodynamic side of the model describes the relationship between the concentration of drug at its effect site and its measured effect. In this study we used an inhibitory Emax model, or Hill equation (equation 2), to describe the relationship between effect-site (brain) sevoflurane concentration and spectral entropy. We assumed that changes in the spectral entropy caused by sevoflurane were primarily related to its effect-site partial pressure.
The purpose of the present study was to derive a PKPD model of the relationship between sevoflurane concentration and spectral entropy of the EEG using clean anesthetic cycles (sevoflurane only) and to compare this with sevoflurane cycles which included supplemental medications. We also examined path-dependent PKPD parameters, as it became apparent from our data that the relationship between effect-site sevoflurane and spectral entropy varied according to the anesthetic phase (i.e., deepening and lightening of anesthesia).
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Methods |
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IV access was obtained and standard monitoring applied to all patients (i.e., electrocardiogram, oxygen saturation, intermittent arterial blood pressure, and gas analysis). The spectral entropy was measured with a plug-in Datex-Ohmeda M-Entropy S/5TM Module (Datex-Ohmeda Division, Instrumentarium Corp., Helsinki, Finland). A composite electrode, the EntropyTM Sensor, composed of a self-adhering flexible band holding three electrodes was applied to the forehead and temple. Before sensor application, the skin was carefully cleaned with an alcohol swab and allowed to dry. Electrode skin impedance was checked to be <7.5 kOhm. Impedances were continuously monitored and corrective measures were taken if acceptable limits were exceeded. RE and SE were sampled at 0.2 Hz. Inspired and expired sevoflurane concentrations were measured at the mouth and sampled at 100 Hz. The data were recorded on a laptop computer and stored for later off-line analysis using MatLab (version 6; MathWorks, Natick, MA) computational and data analysis software.
A predefined anesthetic was administered according to the following protocol. Patients were connected via facemask to a semi-closed anesthesia breathing circuit, consisting of a partial rebreathing system with carbon dioxide reabsorber, directional valves, and a reservoir bag (6). Fresh gas flow was set at 4 L/min and the patients were administered oxygen to the satisfaction of the anesthesiologist in charge. After oxygen administration, the following anesthetic protocol was adhered to (cycle 1). Sevoflurane was delivered by vaporizer at 3% inspired for 2 min, followed immediately by 7% inspired concentration. Loss of consciousness (LOC) was assessed by loss of response to verbal command. SE and RE were recorded for comparison to awake values. The time at which RE decreased to 20 or less was noted and 7% sevoflurane was continued for a further 2 min. The sevoflurane was then turned off until RE returned to a value of 70 (lightening). No attempt was made to rouse the subjects. This was the end of the first anesthetic cycle. No supplemental medications were administered during the first cycle. If, at any stage during the first cycle, spontaneous ventilation did not result in satisfactory end-tidal capnograph plateaus, accurate end-tidal anesthetic sampling was ensured by gentle hand assistance of tidal volume at a rate of 1 assisted breath per 15 s. Subsequently (cycle 2), anesthesia was re-deepened, a laryngeal airway or endotracheal tube was inserted, and the elective surgery commenced. During the second anesthesia cycle, supplemental medications, including propofol, fentanyl, and muscle relaxants were administered at the discretion of the anesthesiologist. Data collection was discontinued before the end of surgery. The second anesthetic cycle therefore consisted of a deepening phase only.
Modeling of the effect-site (brain) sevoflurane partial pressure and pharmacodynamics of brain sevoflurane partial pressure and the measured effect (RE and SE) was performed on the first anesthetic cycle using MatLab (version 6). End-tidal sevoflurane concentration was interpolated from the inspired/expired sevoflurane waveform by taking the minimum expired value during adequate spontaneous ventilation and assisted ventilation via bag-mask. Plotting entropy versus end-tidal sevoflurane concentration produced the anticipated hysteresis loop (Fig. 1a), reflecting the lag between end-tidal (or arterial) and effect-site (brain) partial pressure. Effect-site partial pressure was estimated by minimizing the hysteresis between end-tidal sevoflurane concentration and entropy (Fig. 1b) using the classic first-order effect-site model:
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where Cet is the end-tidal concentration of the drug, Ceff is the effect compartment partial pressure of the drug, and Keo is the first order rate constant for efflux from the effect compartment.
In the present study, we estimated the brain partial pressure of sevoflurane by iteratively running this model with a series of Keo steps. For each iteration, a nonlinear inhibitory sigmoid Emax curve was fitted to the data using the MatLab "nlinfit" function (nonlinear least-squares data fitting), defined as follows:
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where effect is the spectral entropy of the EEG (either RE or SE), the Emax and Emin are the maximum and minimum entropy recorded for each individual patient, the EC50 is the sevoflurane concentration at which the entropy is midway between this maximum and minimum, the Ceff is the sevoflurane concentration at the effect site, and describes the slope of the concentration-response relationship. Keo was determined from the iteration yielding the greatest coefficient of determination (R2) for measured and modeled entropy for each subject. These procedures were repeated for both SE and RE. Values of the pharmacodynamic parameters, and EC50, were derived from the fitted inhibitory Emax curves.
Frequently, the hysteresis loop generated by the first cycle of anesthesia did not collapse down to a simple sigmoid curve. Rather the collapsed curve had a skewed figure-eight appearance, implying that the relationship between sevoflurane effect-site concentration and spectral entropy was not constant over the cycle. Path-dependent pharmacodynamic parameters were therefore estimated by fitting an inhibitory Emax curve separately to the deepening phase and the lightening phase of this complex effect-site concentration versus entropy curve. This analysis assumes Keo to be constant and equal to the value previously derived from the entire hysteresis loop. Differences between the pharmacodynamic parameters of the deepening and lightening phases were compared. Both the detection of end-tidal sevoflurane and the EEG entropy involve imprecisely determined lag times. To test whether the values obtained for were sensitive to a differential in the time delay between the entropy and the end-tidal signal, we applied a time shift to the EEG entropy of ±5 s relative to sevoflurane end-tidal concentration and compared these results with those without the time-lag adjustment.
To examine the effect of supplemental medications on the PKPD model, we used the PD parameter values obtained for the clean first anesthetic cycle to predict the entropy time course for the second cycle anesthetic deepening. If the supplemental medications had no effect on the entropy algorithm, then the first-cycle parameters should accurately predict the second cycle entropy time course. In 9 cases, sevoflurane was not continued into the second anesthetic cycle for clinical reasons. Thus, 11 subjects provided a second sevoflurane cycle for analysis. Effect-site sevoflurane partial pressure for the second anesthetic cycle was derived from Equation 1, using the individual Keo values obtained for the first anesthetic cycle. The and EC50 values derived from the first cycle deepening phase were substituted into Equation 2, giving predicted entropy time courses for second cycle deepening.
The goodness of fit of the modeled data was determined by calculating the median weighted residual (WR) (bias) and median absolute weighted residual (AWR) (overall error). For group comparisons of predicted versus measured entropy, PKPD, and LOC data, normally distributed data were analyzed using repeated-measures analysis of variance with Bonferroni’s multiple comparison test. Non-Gaussian paired data were compared using the Wilcoxon test. Normality of all data was assessed using the Kolmogorov-Smirnov test. Predicted entropy for the second cycle was compared with measured entropy from the Datex-Ohmeda Entropy Module by calculating the limits of agreement, as described by Bland and Altman (7). Data are presented as mean ± sd.
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Results |
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(5.9 ± 2.3 compared with 7.4 ± 3.5, respectively, P < 0.05, Wilcoxon test).
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The relationship between entropy and effect-site sevoflurane was not consistent across all phases of the anesthetic cycles (Fig. 3). When each anesthetic path was assessed independently, for cycle 1 deepening was significantly higher than the subsequent lightening phase (P < 0.01, repeated-measures analysis of variance) (Table 2). Path-dependent EC50 values were not significantly different. PD parameter values derived from the cycle 1 deepening phase were relatively poor predictors of second cycle entropy (limits of agreement 33.8 ± 13.8 compared with 17.4 ± 8.3 for second cycle prediction of itself, P < 0.05, repeated-measures analysis of variance).
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Time shifting the entropy data by 5 s relative to end-tidal sevoflurane did not have a significant effect on Keo for the first cycle (2.4 ± 1.5 min and 2.3 ± 1.5 min for the positive and negative shifts, respectively), although a small but significant difference in was noted for the positive time shift (6.4 ± 2.3, P < 0.01 paired t-test). The large differential in path-dependent values remained; with 48.2 ± 39.7 (deepening) versus 5.8 ± 2.7 (lightening) for the negative shift (P < 0.001 paired t-test), and 50.9 ± 42.7 versus 6.4 ± 3.4 for the positive shift (P < 0.001 paired t-test).
Overall, LOC occurred at slightly lower entropy compared with awake baseline values: SE awake of 88.0 ± 2.9 compared with 73.0 ± 25.0 at LOC (P < 0.01, Wilcoxon test); RE awake of 97.1 ± 1.7 compared with 81.5 ± 24.1 at LOC (P < 0.01, Wilcoxon test). Individually, the point at which consciousness was lost occurred at a wide spread of values of RE and SE and was typically before the rapid decrease in entropy. The relationship between the point of LOC and RE is shown in Figure 4.
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Discussion |
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of approximately 4 reported by Ellerkmann et al. compared with a of approximately 6 in this study. The present findings are also similar to those reported previously for Bispectral index and 95% spectral edge frequency (4,9). The median AWR values derived are comparable to previously published PKPD analyses (10) and confirm the adequacy of this Hill model for describing the effect-site sevoflurane and EEG data. The errors in fitting the model could largely be attributed to differences in the maximum rate of change in entropy during induction compared with lightening. It is noteworthy that at more than an effect-site concentration of 3%, the spectral entropy of the EEG is almost unresponsive to further increases in sevoflurane concentration.
The steepness of the dose-response curve during induction of anesthesia was much greater than that seen during the subsequent lightening phase. This is a novel observation and is reflected by the average value of 61 for induction (versus 5.7 for lightening). This is more than 10 times the reported for sevoflurane anesthesia using Bispectral index (9) and more than 20 times that for propofol (11). To test whether this large disparity could have resulted from a difference in the time delay between end-tidal sevoflurane sampling and EEG processing, we applied a time shift to the EEG entropy (RE). A positive and negative time shift was used because the time window for EEG entropy calculation varies depending on the dominant frequency in the EEG. The path-dependent values were insensitive to both positive and negative shifts of the entropy signal relative to sevoflurane end-tidal concentration. Could changes in the pharmacokinetic side of the PKPD analysis better explain the extreme path dependence of the model’s parameter values? We modeled a shift in Keo of ± 30% and found this altered , on average, by 11%–12% (results not shown). This is much less than the 10-fold difference in observed between the lightening and deepening phases of the first anesthetic cycle. Clearly, a change in pharmacokinetics cannot fully explain the very large differential observed in the present study.
We would suggest that the most likely explanation is pharmacodynamic. The process of losing consciousness is sudden. There is growing evidence from cortical modeling data that the transition between conscious states (and concomitant change in spectral entropy) is characterized by a very rapid shift in cortical function once a threshold brain anesthetic concentration is reached (12–14). The subjects in this study remained unconscious at the end of the first cycle, which may account for the more gradual dose response during the lightening phase. This in itself is an interesting finding, as it highlights two quite different processes causing the EEG changes during the anesthetic cycle: 1) the process that is associated with losing (and regaining) consciousness, an effect that does not appear to be driven by sevoflurane, but rather by the cortical processes governing the transition in state, and 2) the effect of changing concentrations of sevoflurane. That the subjects were unconscious at the beginning of the second cycle may also partly explain the poor prediction of second cycle entropy based on the first cycle PD parameter values. There was no convincing statistical relationship between supplemental medications and inhibitory Emax curve shape for the second cycle. However, a direct effect of muscle relaxants and/or antinoceptive drugs on the spectral entropy algorithm seems likely, given the well documented effects of such drugs on the EEG (15).
The values observed in this study were highly variable, in particular for the deepening phase of the anesthetic cycle. One of the reasons for this is that is calculated as a tangent to the steepest part of the inhibitory Emax curve slope. This value tends towards infinity as one approaches 90 degrees. For this reason, with steep curves, very small changes in the slope of the Emax curve will result in very large changes in the value. This may also explain the apparent difference in values between the present study and that reported by Ellerkmann et al. (8). The higher reported for SE compared with RE, but similar EC50s, shows that, while SE is slower to respond to changes in EEG frequency, when it changes it does so more precipitously. The delayed SE response is consistent with the much longer averaging windows for SE compared with RE (up to 60 seconds compared with 15 seconds) (5).
Most patients lost consciousness either before or near the beginning of the rapid decrease in entropy (Fig. 4), as has been previously reported with BIS and spectral edge frequency (16,17). However, the actual value at which a particular patient became unresponsive during induction of anesthesia had a wide spread. This inter-individual variation is a significant constraint on the clinical usefulness of the EEG in anesthesia. At present, it is unclear whether the variation is primarily the result of the inherent nonlinearity of the process of changing conscious state or inconsistencies and artifacts in the signal processing (extraction of the entropy value from the raw EEG signal).
In conclusion, spectral entropy decreases with increasing sevoflurane concentrations up to 3%. From our data it is apparent that the steepness of the dose response curve for sevoflurane is not constant and hence not adequately modeled by a single value of . We suggest this is most readily explained by a pharmacodynamic mechanism.
The equipment used to collect the data was provided by Datex-Ohmeda.
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