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TECHNOLOGY, COMPUTING, AND SIMULATION

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

Richard Klaus Ellerkmann, MD^*, Martin Soehle, MD^*, Thorsten Michael Alves^*, Vidal-Markus Liermann^*, Ingobert Wenningmann, MD^*, Heiko Roepcke, MD^*, Sascha Kreuer, MD, Andreas Hoeft, MD, PhD^*, and Jörgen Bruhn, MD^*

*Department of Anesthesiology and Intensive Care Medicine, University of Bonn; and Department of Anesthesiology and Intensive Care Medicine, University of Saarland, Homburg/Saar, Germany

Address correspondence and reprint requests to Richard Klaus Ellerkmann, MD, Sigmund Freud St. 25, 53105 Bonn, Germany. Address e-mail to richard.ellerkmann{at}ukb.uni-bonn.de.

	Abstract

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Recently, Datex-Ohmeda introduced the Entropy Module^TM for measuring depth of anesthesia. Based on the Shannon entropy of the electroencephalogram, state entropy (SE) and response entropy (RE) are computed. We investigated the dose-response relationship of SE and RE during propofol anesthesia in comparison with the Bispectral Index^TM (BIS). Twenty patients were studied without surgical stimulus. Anesthesia was induced by a constant propofol infusion of 2000 mg/h (451 ± 77 µg·min^–1·kg^–1) via a large forearm vein. Propofol was infused until substantial burst suppression occurred (more than 50%) or mean arterial blood pressure decreased to <60 mm Hg. Hereafter, infusions were stopped until recovery of BIS values up to 60 was reached. Subsequently, the constant propofol infusion of 2000 mg/h was restarted to increase depth of anesthesia and again decreased (infusion was stopped) within the BIS value range of 40–60. The coefficient of determination (R²) and the prediction probability (P_K) were calculated to evaluate the performance of SE, RE, and BIS to predict changing propofol effect-site concentrations. R² values for SE, RE, and BIS of 0.88 ± 0.08, 0.89 ± 0.07, and 0.92 ± 0.06, respectively, were similar. The calculated P_K values, however, revealed a significant difference between SE and RE compared with BIS, with P_K = 0.77 ± 0.09, 0.76 ± 0.10, and 0.84 ± 0.06, respectively. BIS seems to show slight advantages in predicting propofol effect-site concentrations compared with SE and RE, as measured by P_K but not as measured by R².

	Introduction

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Monitors intraoperatively analyzing the electroencephalogram (EEG) are used to measure anesthetic drug effect on the central nervous system. Because analyzing the raw EEG signal during anesthesia at real-time is difficult, several EEG monitors have been developed to extract and process EEG information and to present the content in a continuous index from 0 to 100.

Zero represents the deepest level of anesthesia (isoelectric EEG line) and 100 the awake state of a patient. The use of such EEG monitors can decrease drug consumption during anesthesia (1,2) and lead to a faster recovery from anesthesia (1,3). The use of the Bispectral Index^TM (BIS) monitor (Aspect Medical Systems, Newton, MA) may decrease the incidence of intraoperative awareness (4,5).

In this study, we investigated the dose-response relationship of the new Entropy Module^TM (Datex-Ohmeda, Helsinki, Finland) during propofol anesthesia in comparison with the BIS monitor. Whereas the BIS monitor uses different algorithms to calculate the BIS during the different stages of anesthesia, e.g., burst suppression (BS) (6) and frequency power calculation (7), as well as bispectral analysis (8), the Entropy Module^TM measures depth of anesthesia with a single algorithm, i.e., calculating the Shannon Entropy (9) of the power spectrum called the Spectral Entropy. The Entropy Module^TM calculates two different Spectral Entropy indicators: the state entropy (SE), computed over the frequency range from 0.8 to 32 Hz, reflecting the EEG-dominant part of the spectrum, in addition to the response entropy (RE), computed over the frequency range of 0.8 to 47 Hz, including both the EEG and electromyographic (EMG) dominant part of the recorded spectrum (10).

The aim of our study was to investigate the ability of the EEG monitors to differentiate between different effect-site concentrations of propofol calculated by the prediction probability. In addition the correlation among the three EEG variables (SE, RE, and BIS) and estimated effect-site concentrations of propofol was investigated by simultaneous pharmacokinetic and pharmacodynamic modeling.

	Methods

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After IRB approval, written informed consent was obtained from 20 patients aged 43 ± 12 yr (range, 23–64 yr; 11 men and 9 women) scheduled for minor surgery with general anesthesia. All participants were ASA physical state I or II. Exclusion criteria were a history of any disabling central nervous or cerebrovascular disease or patients who had received central nervous system active drugs.

After arrival in the induction room, an IV catheter was inserted into a larger forearm vein, and standard monitors were applied. The EEG was recorded continuously using an Aspect A-2000 BIS^TM monitor (version XP) and the Entropy Module^TM (Datex-Ohmeda). The skin of the forehead was prepared with 70% isopropanol, and the BIS (BIS-XP sensor, Aspect Medical Systems) and the Entropy electrodes were positioned, as recommended by the manufacturers, onto the temporal-frontal area of the patient’s forehead. Measurements were started after the electrode impedance check of each monitor was completed. Impedance was automatically considered adequately low by the BIS monitor and the Entropy Module if kept to less than 10 k and 7.5 k, respectively.

Anesthesia was induced by a continuous 2% propofol infusion of 2000 mg/h (451 ± 77 µg·min^–1·kg^–1). No fluids were given before the induction of anesthesia. All patients were spontaneously breathing throughout the experiment through a face mask delivering 100% O₂. The propofol infusion was continued until substantial BS occurred (50% and more) or mean arterial blood pressure decreased to <60 mm Hg. The infusion was stopped hereafter until BIS recovered to values of 60. Subsequently, depth of anesthesia was again increased by a propofol infusion at 2000 mg/h and then decreased by stopping the propofol infusion in a way that targeted BIS values ranged from 40 to 60. Measurements were then stopped, and the patient’s trachea was intubated for surgery.

Study data were automatically recorded in intervals of 5 s and transferred to a computer hard disk in real time for further offline analysis. BIS values were recorded and transferred to computer hard disk using the software program HyperTerminal (Microsoft, Redmond, WA). The smoothing time period for the BIS^TM monitor was set to 15 s. Entropy values (SE and RE) were recorded with the Datex-Ohmeda software S/5^TM Collect (version 4.0) onto the computer hard disk. Propofol plasma concentrations were calculated within Excel as described by Bruhn et al. (11) using the parameter set published by Marsh et al. (12).

Propofol effect-site concentrations were obtained by simultaneous pharmacokinetic and pharmacodynamic modeling (13). To eliminate the hysteresis between plasma concentrations of propofol and the EEG variable values (SE, RE, and BIS), an effect site was introduced into the model:

C_pl is the plasma concentration, C_eff the effect-site concentration, and k_e0 is the first-order rate constant determining the efflux from the effect site. The relationship between estimated effect-site concentrations and EEG variable values was modeled by a variation of the classical E_max model (14) with two linked sigmoidal curves describing the EEG effect of propofol with (BS) and without BS (no BS), as published by Kreuer et al. (15):

For C_eff C_plateau:

For C_eff > C_plateau:

Both sigmoidal curves have their own variables. The first curve (Equation 2a) reaches from E₀, the EEG value in the absence of propofol, to E_plateau, where a transition occurs to the second curve (Equation 2b), which extends from E_plateau to E_max, the presumed maximum drug effect. C_plateau is the propofol concentration at E_plateau. C_eff is the apparent effect-site concentration. C_{50 no BS} is the propofol concentration associated with a 50% decrease from E₀ to E_plateau, and _{no BS} is the steepness of that relationship. C_{50 BS} is the propofol concentration associated with 50% decrease from E_plateau to E_max, and _BS is the steepness of that relationship.

Kreuer et al. (15) have shown that this bi-sigmoidal model adequately fits the correlation between effect-site concentrations and BIS. To verify if this model is also adequate to describe the relationship between propofol effect-site concentrations and Spectral Entropy, we visually investigated the dose-response curve without any underlying model. A k_e0 value of 0.456 min^–1 (16) was chosen to calculate propofol effect-site concentrations obtained by Equation 1. Spectral Entropy also revealed a pronounced plateau leading to a biphasic dose-response curve, as shown exemplary for a patient in Figure 1. The bi-sigmoidal model was therefore used to fit the data of BIS and Spectral Entropy.

View larger version (14K): [in this window] [in a new window]   Figure 1. (A) Correlation between state entropy (SE) and propofol plasma concentration for a patient in whom an increasing propofol plasma concentration leads to burst suppression. (B) Correlation between SE and propofol effect-site concentration for the same patient. The effect-site concentration was obtained model-independently by incorporating a ke0 value of 0.456 min–1 into Equation 1.

The computations were performed on a spreadsheet using the Excel software program. Variables 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 determination (17) (R²) as an objective function:

SSE is the sum of squared errors and represents the sum of squares of the differences between observed measurements _i for a given time and the corresponding model prediction. SST is the total sum of squares and represents the sum of squares of the differences between each actual measurement and the average of all the measurements (_i). Because SST is independent of the model variables, maximizing R² is equivalent to minimizing SSE, i.e., it is equivalent to nonlinear regression with ordinary least squares.

In a second step, the correlation between effect-site concentrations and SE, RE, and BIS was investigated with the model-independent prediction probability (P_K) (18). Given two randomly selected data points with distinct anesthetic drug concentrations, the P_K value describes the probability that the EEG variable correctly predicts which of the data points is the one with the larger (or smaller) anesthetic drug concentration. As a nonparametric measure, the P_K value is independent of scale units and does not require knowledge of underlying distributions or efforts to linearize or to otherwise transform scales. Furthermore, P_K can be computed for any degree of coarseness or fineness of the scales. Thus, P_K fully uses the available data without imposing additional arbitrary constraints. P_K has been defined as:

where P_c, P_d, and P_tx are the respective probabilities that two data points drawn at random, independently, and with replacement from the population are a concordance, a discordance, or a x-only tie. A P_K value 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 propofol effect-site concentration). A P_K value of 0.5 means that the values of the indicator predict no better than by chance only. The P_K values were calculated on a spreadsheet using the Excel 2000 software program and the PKMACRO written by Warren Smith (18). Because propofol concentration increases as BIS, RE, and SE decrease, the actual P_K value we measure is 1-P_K.

A power analysis was performed using P_K as the target variable. The sample size calculation was aimed to show a clinically relevant difference in P_K of 0.05 (19). Based on a previous study (20), we estimated a standard deviation of 0.05 for P_K. To detect a difference in P_K between BIS and Entropy in a paired study design with a significance level of 5% ( = 0.05) and a power of 82% (ß = 0.18), at least 14 patients had to be included.

Statistical calculations were performed by Student’s t-test or Wilcoxon test where appropriate. All tests were two tailed, with statistical significance defined as P < 0.05; data are presented as mean ± sd.

	Results

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In 10 patients, increasing propofol concentrations led to substantial BS (>50%), as shown exemplary for one patient in Figure 2. Calculated effect-site concentrations were adequately fitted using a bi-sigmoidal E_max model (Equation 2a and 2b). The relationship between SE and changing propofol concentrations in patients with the best and worst fit (R² value) is displayed in Figure 3 together with the corresponding fit for the same patients for BIS. In the remaining 10 patients, propofol infusion was stopped before substantial BS occurred and after mean arterial blood pressure had decreased to less than 60 mm Hg. A single sigmoidal curve (Equation 2a) was sufficient to fit the data for these patients. The relationship between SE and changing propofol concentrations in patients with the best and worst fit (R² value) is displayed in Figure 4 together with the corresponding fit for the same patients for BIS. Calculated R² values describing the correlation of the EEG variables and the calculated propofol effect-site concentrations were comparable between BIS (0.92 ± 0.06), SE (0.88 ± 0.08), and RE (0.89 ± 0.07).

View larger version (28K): [in this window] [in a new window]   Figure 2. (A) Typical example of the time courses of the measured electroencephalographic (EEG) variables state entropy (SE), response entropy (RE), bispectral index (BIS), burst suppression ratio (BS), and changing propofol effect-site concentrations (Ceff) of a patient in whom BS took place. Each symbol represents an EEG variable of a 5-s epoch.

View larger version (34K): [in this window] [in a new window]   Figure 3. (A and B) The relationship between state entropy (SE) and propofol plasma concentrations (Cpl) and propofol effect-site concentrations (Ceff) for two different patients in whom burst suppression was reached. (A) represents the best fit (same patient as in Fig. 2) and (B) the worst fit for SE. (C and D) The relationship between bispectral index (BIS) and propofol plasma concentrations (Cpl) and propofol effect-site concentrations (Ceff) for the same two different patients as in (A) and (B). Each symbol represents the electroencephalographic (EEG) variable of a 5-s epoch. The bi-sigmoidal fit (Equation 2a and 2b; bold line) is superimposed over the data points of each figure.

View larger version (31K): [in this window] [in a new window]   Figure 4. (A and B) The relationship between state entropy (SE) and propofol plasma concentrations (Cpl) and propofol effect-site concentrations (Ceff) for two different patients in whom burst suppression was not reached. (A) represents the best fit and (B) the worst fit for SE. (C and D) The relationship between bispectral index (BIS) and propofol plasma concentrations (Cpl) and propofol effect-site concentrations (Ceff) for the same two different patients as in (A and B). Each symbol represents the electroencephalographic (EEG) variable of a 5-s epoch. A single sigmoidal curve (Equation 2a) was sufficient to fit the data. The fitted curve is superimposed over the data points of each figure (bold line).

Pharmacokinetic variables revealed a significantly steeper slope factor _{no BS} for SE (4.65 ± 2.42) compared to BIS (2.68 ± 0.84) for the bi-sigmoidal model (P = 0.025; Table 1). A plateau was reached at smaller drug concentrations with C_plateau 3.72 ± 1.52 µg/mL for SE versus 5.18 ± 1.26 µg/mL for BIS (P = 0.03; Table 1).

All individual fits and their corresponding data points of all 20 patients are shown in Figure 5 for SE and BIS.

View larger version (42K): [in this window] [in a new window]   Figure 5. The relationship of (A) state entropy (SE) and (B) bispectral index (BIS) and the calculated propofol effect-site concentrations for all patients (n = 20). Corresponding individual fits for each patient for (C) SE and (D) BIS are presented.

Calculated P_K values proved to be significantly better for BIS (0.84 ± 0.06) compared with SE (0.77 ± 0.09) and RE (0.76 ± 0.10) (P = 0 0.01 for BIS versus SE).

The correlation of SE and RE could be best described by a linear function (RE = 1.08 x SE; R² = 0.985). No significant differences between SE and RE were detected for the fitting variables, R² values, and P_K values. We therefore showed the performance of SE compared with BIS in the figures and added all results of RE into Table 1.

	Discussion

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In this study, BIS showed a significant advantage in discriminating between changing propofol effect-site concentrations in comparison with SE and RE, as judged by the P_K values. This significant difference was not mirrored by a significant difference in R² values of BIS versus SE and RE.

One might criticize that R² values were calculated on the basis of the estimated propofol plasma concentration using the Marsh et al. (12) pharmacokinetic parameter set. This parameter set is slightly imprecise during the first few minutes in estimating the propofol plasma concentration. We therefore validated our R² values by refitting our data using the pharmacokinetic parameter set published by Schnider et al. (21). However, calculated R² values remained unchanged.

The discrepancy between R² and P_K values can, in part, be explained by the fitting algorithm for R². If increasing propofol concentrations lead to an initial steep decrease of the EEG index value (higher slope factor _{no BS}, as evident for SE and RE) followed by a pronounced plateau (expressed by lower C_plateau values for SE and RE), then calculated R² values can be high because the R² values only describe the degree of concordance of the measured data with the model-predicted data. However, the calculated P_K will be low because the monitor does not distinguish between increasing drug concentrations where a plateau is evident. This plateau is broader for the Entropy variables compared with BIS, as indicated by the early onset of the plateau described by lower C_plateau values (Table 1).

We showed that increasing propofol concentrations leading to BS exert a biphasic response in the BIS and Entropy Index. Fitting the data with a bi-sigmoidal curve adequately described this biphasic response. This phenomenon has been described for isoflurane (15), sevoflurane (22), and desflurane (23) between BIS and Narcotrend Index versus drug effect.

Previously, we could show a close correlation of SE and RE with changing sevoflurane effect-site concentrations and equally high P_K values among SE, RE, and BIS (20). Vanluchene et al. (24) investigated the correlation of propofol with SE and BIS and observed higher P_K values for BIS and a significantly higher Spearman rank correlation for BIS compared with SE. In the same study, the authors report a steeper slope factor for SE and RE, leading to a less graded response of the EEG variable and thereby loosing discrimination compared with BIS. In a more recent study (25), the same authors describe a less smooth decrease of SE and RE after increasing propofol concentrations compared with BIS. These studies, however, investigated only increasing propofol concentrations, and it was our intention to evaluate the monitors for increasing and decreasing propofol effect-site concentrations. Our results confirmed their findings, revealing a significantly steeper slope factor _{no BS} for SE (4.65 ± 2.42) compared to BIS (2.68 ± 0.84) for the bi-sigmoidal model and a steeper _{no BS} for SE (4.61 ± 2.80) compared to BIS (3.54 ± 1.80) for the mono-sigmoidal model.

Schmidt et al. (19) and Vakkuri et al. (26) have provided information concerning the clinical benefit of the Entropy Module^TM. Schmidt et al. (19) showed that the SE index correlated better with sedation levels compared with BIS. Vakkuri et al. (26) reported that RE indicated emergence from anesthesia 11 seconds earlier than SE and 12.4 seconds earlier than BIS. The manufacturer claims that RE is able to detect upcoming arousal by detecting increasing EMG activity, and RE responds faster to changing EEG and EMG signals because of shorter time windows for signal interpretation. We could not detect any significant differences between SE and RE. However, our clinical investigations did not include emergence from anesthesia or surgical stimuli. Further clinical trials are required to show that the improved discrimination of the BIS is clinically relevant.

Our data investigating increasing and decreasing propofol plasma concentrations enabled us to estimate the time constant k_e0, revealing information about the efflux of propofol from the effect site. As a time constant, k_e0 is assumed to remain constant over the entire observed propofol-concentration range. This is perhaps only an adequate approximation to reality. We report higher k_e0 values for SE compared with BIS independent of the underlying model used to fit the data (Table 1). k_e0 values for propofol range between 0.2 and 1.21 min^–1, depending on the EEG variable or monitor used to measure the EEG effect, as well as the pharmacokinetic parameter set used to calculate the propofol plasma concentration and the model used to estimate the effect-site concentration of propofol (27–32). The k_e0 value not only contains information about the time delay the anesthetic drug requires to reach the effect site, but also about how long the monitor requires to detect the drug effect. Shorter time windows for calculating the respective EEG index, 2 seconds for the canonical univariate variable (29), 15 seconds for the BIS (Methods), 20 seconds for the Narcotrend Index (28), and optimized time-frequency windows ranging from 1.92 to 60 seconds for SE and RE (10), lead to higher k_e0 values. Improved artifact algorithms may influence k_e0 values by increasing the amount of interpretable EEG data within a certain time window and therefore possibly permit a better resolution of the time course of drug effect. The different k_e0 values estimated for SE and BIS can, in part, be explained by different time windows required for calculating the index.

In summary, BIS seems to show slight advantages in predicting propofol effect-site concentrations compared with SE and RE, as measured by the P_K. However, this difference was not mirrored by significantly different R² values between BIS versus SE and RE.

	Footnotes

 
Accepted for publication December 21, 2005.

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