Spectral Entropy and Bispectral Index as Measures of the Electroencephalographic Effects of Sevoflurane

After approval by the Institutional Review Board (University of Bonn, Bonn, Germany), written informed consent was obtained from 16 patients aged 29 ± 8 yr (12 men and 4 women) scheduled to undergo minor surgery in general anesthesia. All participants had an American Society of Anesthesiologists physical status classification of I or II. Patients with a history of any disabling central nervous or cerebrovascular disease and patients who had received central nervous system–active drugs were excluded from the study.

After arrival in the induction room, an intravenous line was inserted into a large forearm vein, and standard monitors were applied. The electroencephalogram was recorded continuously using the Aspect A-2000 BIS® monitor (version XP) and the Entropy Module. After the skin of the forehead had been prepared with 70% isopropanol, the BIS® (BIS-XP sensor) and Entropy electrodes were positioned as recommended by the manufacturers.

Anesthesia was induced by sevoflurane inhalation only with a tight-fitting facemask and a 4-l airflow of 100% oxygen. As spontaneous breathing diminished, patients were manually assisted and, with cessation of spontaneous breathing, were mechanically ventilated via  the facemask to an end-tidal carbon dioxide of 35 mmHg. Sevoflurane concentration was initially increased until end-tidal concentrations of 5 vol% were achieved. Subsequently, sevoflurane concentrations were decreased and increased systematically two to four times to end-tidal sevoflurane concentrations between 1 and 4 vol%. Measurements were stopped thereafter, and patients were intubated for surgery.

Study data were automatically recorded in intervals of 5 s. BIS values were recorded and transferred to computer hard disk for off-line analysis using the software program HyperTerminal (Microsoft, Redmond, VA). Entropy values (SE and RE) as well as inspiratory and expiratory gas concentrations, measured by an infrared spectrophotometric analyzer (Julian; Dräger, Lübeck, Germany), were recorded with the Datex-Ohmeda software S/5 Collect (version 4.0) onto the computer hard disk. The smoothing time period for the BIS® monitor was set to 15 s.

The concept of spectral entropy as described by the manufacturer ††10is based on the Shannon entropy. If Shannon entropy is applied to the power spectrum of a signal, spectral entropy is obtained.11This concept is implemented in the Entropy Module. The power spectrum is first calculated for the different frequency ranges and then normalized so the sum of all spectral components equals to one with

where Q(f) is the sum of the normalized power spectral components over the considered frequency range and P(f) is the power spectrum. In a second step, the normalized power spectrum components are transformed by the Shannon function H(f): f(x) = log (1/x) to obtain transformed components:

In a final step, the transformed components are added, and the result is normalized to range between 1 (maximum irregularity) and 0 (complete regularity) by dividing the sum with the factor log (N), where N is equal to the total number of frequency components:

To optimize between time and frequency resolution, different sets of window durations are used within the Entropy Module so that each frequency component is obtained from a time window that is optimal for that particular frequency. The shortest time window is 1.92 s, used for frequencies between 32 and 47 Hz, and the longest time window is 60.12 s, used only for frequencies below 2 Hz.

Consistent with this concept, the Entropy Module calculates two different entropies derived from the time–frequency spectral entropy. One is the SE, computed over the frequency range from 0.8 to 32 Hz, with time windows ranging from 15 to 60 s and ranges on a scale from 0 to 91. The second is the RE, computed over a frequency range from 0.8 to 47 Hz, including both the electroencephalographic- and electromyographic-dominant parts of the spectrum, with time windows as short as 1.92 s for frequencies between 32 and 47 Hz and ranges on a scale from 0 to 100. A more detailed description of the Entropy Module algorithm has been published by Viertio-Oja.10 

State entropy and RE are calculated using equations 1–3across the entire range of anesthetic depth, except during burst suppression. Entropy values RE and SE are in principle computed in the same way as they are calculated at lighter levels of anesthesia. The part of the signal that contains a suppressed electroencephalogram is treated as a perfectly regular signal with zero entropy, whereas the entropy associated with the bursts is computed as described previously (equations 1–3).10 

Sevoflurane effect site concentrations were obtained by simultaneous pharmacokinetic and pharmacodynamic modeling.12To eliminate the hysteresis between end-tidal concentrations of sevoflurane and electroencephalographic parameter values (SE, RE, BIS), an effect site was introduced into the model:

where C^etis the end-tidal concentration, C^effis the effect site concentration, C^eff(t − 1) is the calculated effect site concentration of the previous data point (in our study, one data point was obtained every 5 s), and k^e0is the first-order rate constant determining the efflux from the effect site. The relation between estimated effect site concentrations and electroencephalographic parameter values was modeled with a fractional sigmoid E^maxmodel (Hill equation13):

where E⁰is the measured encephalographic parameter value (SE, RE, BIS) in the absence of the drug (= baseline or awake state), E^maxis the encephalographic parameter value corresponding to maximum drug effect, EC⁵⁰is the concentration that causes 50% of the maximum effect, and γ describes the slope of the concentration–response relation. The computations were performed on a spreadsheet using the Excel 2000 software program (Microsoft). Parameters were optimized with the Solver tool within Excel using nonlinear regression with ordinary least squares. Our aim was to maximize the correlation between the measured drug effect (SE, RE, or BIS) and the predicted drug effect. We chose the coefficient of determination14(R  ²) as an objective function:

The sum of squared errors (SSE) represents the sum of squares of the differences between observed measurements yⁱfor a given time and the corresponding model prediction,

The total sum of squares (SST) stands for the sum of squares of the differences between each actual measurement and the average of all the measurements,

Because SST is independent of the model parameters, maximizing R  ²is equivalent to minimizing SSE, i.e. , it is equivalent to nonlinear regression with ordinary least squares.

Because the classic fractional E^maxmodel did not adequately display the data where burst suppression occurred, we discharged epochs with burst suppression before fitting the hysteresis with the E^maxmodel. In a second step, the individually fitted k^e0for each patient derived from the E^maxmodel was then used to calculate the sevoflurane effect site concentration (equation 4). The correlation between effect site concentrations and SE, RE, and BIS was then investigated with the model-independent prediction probability (P^K),15including all epochs (i.e. , also the epochs where burst suppression occurred). Given two randomly selected data points with distinct anesthetic drug concentration, the P^Kvalue describes the probability that the encephalographic parameter correctly predicts which of the data points is the one with the higher (or lower) anesthetic drug concentration. As a nonparametric measure, the P^Kvalue is independent of scale units and does not require knowledge of underlying distributions or efforts to linearize or to otherwise transform scales. Furthermore, P^Kcan be computed for any degree of coarseness or fineness of the scales. Therefore, P^Kfully uses the available data without imposing additional arbitrary constraints. Prediction probability P^Khas been defined as

where P^c, P^d, and P^txare the respective probabilities that two data points drawn at random, independently and with replacement, from the population are a concordance, a discordance, or an x-only tie. A P^Kvalue of 1 means that the values of the predicting variable (SE/RE or BIS value) always correctly predict the value of the variable to be predicted (e.g. , estimated sevoflurane effect site concentration). A P^Kvalue of 0.5 means that the values of the indicator predict no better than by chance only. The P^Kvalues were calculated on a spreadsheet using the Excel 2000 software program. Because sevoflurane concentration increases as BIS, RE, and SE decrease, the actual P^Kvalue we measure is 1 − P^K.

Statistical analysis was performed using Sigma Stat 2.03 and Sigma Plot 2000 computer software (SPSS Inc., Erkrath, Germany). Statistical calculations were performed by Student t  test or Wilcoxon test where appropriate. All tests were two tailed, with a statistical significance defined as P < 0.05; data are presented as mean and SD.

The mean duration of measurements was 28.5 ± 8 min. During this time, 342 ± 96 artifact-free 5-s epochs per patient were included in the data analysis.

Figures 1A and Bshow the time course of the measurement of patient 1 where increasing sevoflurane concentrations were correlated with decreasing entropy and BIS values and vice versa . Plotting the end-tidal gas concentration of sevoflurane (C^et) against SE/RE and BIS values revealed a hysteresis (figs. 2A–C). Simultaneous pharmacokinetic and pharmacodynamic modeling (equations 4 and 5) of the hysteresis revealed nearly identical results for k^e0, E⁰, E^max, EC⁵⁰, and γ between SE/RE and BIS (table 1). The k^e0values were used to calculate the estimated effect site concentration (C^eff) of sevoflurane. Plotting C^effagainst SE/RE and BIS led to a collapse of the hysteresis (figs. 2D–F).

The correlation of SE/RE and estimated sevoflurane effect site concentration proved to be slightly but not significantly better (R  ²= 0.87 ± 0.09 and 0.86 ± 0.10 for SE and RE, respectively) than for BIS (R  ²= 0.85 ± 0.12). Individual R  ²values are shown in figure 3Afor each patient. Because fitting using the E^maxmodel did not incorporate data with burst suppression, we used the model-independent prediction probability (P^K) to evaluate SE/RE and BIS including all data (i.e. , also data where burst suppression occurred). In figure 3B, the performance of SE, RE, and BIS to correctly differentiate between different effect site concentrations of sevoflurane expressed by P^Kis shown. SE and RE were slightly but not significantly better (0.84 ± 0.05 and 0.82 ± 0.06 for SE and RE, respectively) than BIS (0.80 ± 0.06) in differentiating between different effect site concentrations over the entire range of data points.

Burst suppression occurred in 9 of 16 patients and exceeded a burst suppression ratio (BSR) greater than 40% in seven measurements. Entropy (SE and RE) correlated linearly over the entire burst suppression range in all measurements (R  ²= 0.96 ± 0.02 fitted by the equation Entropy = a − BSR/b yielding the following values: a = 27.6 ± 9.2 and b = 3.97 ± 1.72). The fit of the pooled data is shown superimposed on the data in figure 4Aand yielded the following values: a = 29.0 and b = 3.25 (R  ²= 0.88). No correlation could be found between BIS and a BSR of less than 40% (fig. 4B). Increasing BSR greater than 40% leads to a linear correlation with BIS = a − BSR/b yielding the following values: a = 44.1 ± 2.0 and b = 2.25 ± 0.13, with little to no interindividual differences (R  ²= 0.99 ± 0.01). Fitting the pooled data for BSR greater than 40% yielded identical results, with a = 44.1 and b = 2.25, shown superimposed on the data in figure 4B.

Plotting SE and RE over BIS revealed a sigmoidal correlation between entropy parameters and the Bispectral Index (figs. 5A and B).

Plotting RE over SE shows a linear correlation with RE = 1.05 * SE + 0.31 (R  ²= 0.98) (fig. 6).

In figure 7, we show the sigmoidal correlation between SE (A) and BIS (B) and estimated sevoflurane effect site concentrations. RE also revealed a sigmoidal correlation similar to SE (data not shown).

In this study, we demonstrated a close correlation of SE and RE with sevoflurane effect site concentrations. SE and RE detected increasing and decreasing sevoflurane concentrations equally well as the BIS® monitor as judged by the correlation coefficient (R  ²) and the prediction probability (P^K). We could also show that different approaches of electroencephalographic analysis lead to nearly identical pharmacokinetic and pharmacodynamic parameters for k^e0, γ, and EC⁵⁰.

Our intention was to investigate the two monitors over the entire range of levels of anesthesia including burst suppression. Unfortunately, the E^maxmodel used for simultaneous pharmacokinetic and pharmacodynamic modeling was unable to fit the entire data range including burst suppression. A more sophisticated model incorporating two successive sigmoidal curves16was necessary. We therefore calculated the R  ²value for each measurement and excluded epochs if burst suppression occurred. Realizing the shortcomings of this approach, leading to a loss of important information regarding the ability of the two monitors to predict burst suppression, we used the model-independent calculation of the prediction probability to evaluate the performance of the monitors over the entire range of observed anesthetic depth, thereby including all epochs of each measurement. However, we used the individually fitted k^e0values derived from the E^maxmodel to calculate the effect site concentration necessary for the computation of the prediction probability. It has been shown previously that results obtained by prediction probability were confirmed by calculating R  ².17We could demonstrate that both approaches show satisfying correlations for both monitors.

Interestingly, different approaches of calculating drug effects on the electroencephalogram lead to similar results. The P^Kvalues show that both algorithms are equally sophisticated in predicting calculated effect site concentrations of sevoflurane. Comparing the almost identical pharmacokinetic and pharmacodynamic results seems even more astonishing because the BIS integrates several disparate descriptors of the electroencephalogram into a univariate variable,6–8whereas the Entropy Module uses the same algorithm over the entire range of anesthesia.10 

Pharmacokinetic and pharmacodynamic parameters have been published previously for BIS values after sevoflurane anesthesia.18–20Olofsen et al.  18,19reported t^1/2k^e0values of 3.5 ± 2.0 and 3.11 ± 0.32 min measured during sevoflurane anesthesia in combination with 70% nitrogen. When converting their t^1/2k^e0values to k^e0(t^1/2k^e0= ln²/k^e0), their calculated k^e0values were 0.20 and 0.22 min⁻¹,18,19which is 30% less than our measured k^e0value. Rehberg et al.  20reported a k^e0of 0.29 ± 0.04 for sevoflurane in the absence of nitrogen. Olofsen et al.  19discussed several factors influencing k^e0. They showed that remifentanil leads to a dose-dependent decrease in t^1/2k^e0(increase in k^e0). Besides physiologic factors, the time delay due to electroencephalographic parameter calculation by the monitor has a crucial influence on k^e0. During propofol anesthesia, calculated k^e0values differed up to 100% depending on very short calculation time windows of 2 s20or calculation time windows of 30 s using the BIS® monitor.21Kreuer et al.  21reported higher k^e0values for propofol when estimated using the Narcotrend monitor (MonitorTechnik, Bad Bramstedt, Germany) compared with the BIS® monitor (calculation time windows of 20 and 30 s, respectively). Accordingly, Olofsen and Dahan18reported different t^1/2k^e0values during sevoflurane anesthesia between BIS and spectral edge frequency. Because spectral edge frequency can be calculated immediately without a delay of 30 s, t^1/2k^e0values were faster compared with BIS t^1/2k^e0values.18The ideal encephalographic monitor would compute an index without a time delay, resulting in smaller t^1/2k^e0values. We found no significant differences between our calculated k^e0values for SE, RE, and BIS.

We further investigated the relation between entropy values and BIS by plotting all data points of SE and RE over BIS (fig. 5). We demonstrate that entropy values and BIS show a close correlation within the index range of 30–70. Because the original mathematical scale of the entropy values ranges between 0 and 1 and the most interesting range of adequate hypnosis and sedation lies between 0.5 and 1.0, a transformation from the original continuous entropy scale to an integer scale of 0–100 has been performed by a nonlinear transformation,10leading to the close correlation of entropy and BIS values within the index range of 30–70. This transformation is defined by a particular monotonous spline function transforming the original values between 0.5 and 1 to new values between 30 and 100. The slope of the spline function is steepest between 30 and 80, leading to an enhanced resolution. Below 30 and above 80, the slope becomes shallower. This could explain the sigmoidal correlation between both entropy parameters and BIS. The difference between entropy and BIS for index values less than 30, however, could also originate in different algorithms of incorporating burst suppression ratios into their corresponding index as shown in figures 4A and Band expressed by the different slope factors b (b = 3.25 for SE and 2.25 for BIS).

During burst suppression, SE equaled RE (data not shown), explained by the fact that the electromyogram equaled zero. In the awake state, an SE value of 91 equals an RE value of 100 because of the additional amount of electromyographic activity calculated by RE in the frequency range between 32 and 47 Hz. It is claimed that RE is able to detect upcoming arousal by detecting muscle activity and that RE is faster to respond to changing electroencephalographic and electromyographic signals because of shorter time windows for signal interpretation (as short as 1.92 s; see Materials and Methods). To prove that RE shows advantages in revealing electromyographic activation and in addition leading to a faster response to upcoming arousal of the patient, further investigations are needed with a different experimental setting including lighter levels of anesthesia and surgical stimuli. The high correlation between RE and SE (fig. 6) does not support the idea that RE actually reveals unique information.

We conclude that the Entropy Module is a useful monitor for measuring the electroencephalographic effects of increasing and decreasing sevoflurane concentrations over the entire range of observed anesthetic depth. Sevoflurane electroencephalographic effects were detected equally well by the Entropy Module and by the BIS® monitor.