Comparison of EEG Approximate Entropy and Complexity Measures

Journal of Medical and Biological Engineering, 31(5): 359-366

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Comparison of EEG Approximate Entropy and Complexity Measures of Depth of Anaesthesia During Inhalational General Anaesthesia Shou-Zen Fan1

Jia-Rong Yeh2,3

Bo-Cun Chen2

Jiann-Shing Shieh2,3,*

1

Department of Anesthesiology, College of Medicine, National Taiwan University, Taipei 106, Taiwan, ROC 2 Department of Mechanical Engineering, Yuan Ze University, Taoyuan 320, Taiwan, ROC 3 Center for Dynamical Biomarkers and Translational Medicine, National Central University, Taoyuan 320, Taiwan, ROC Received 6 Aug 2010; Accepted 25 Oct 2010; doi: 10.5405/jmbe.820

Abstract Approximate entropy (ApEn) and Lempel-Ziv complexity (LZC), which are nonlinear quantification methods of the regularity of electroencephalogram (EEG) signals, have recently been proposed as measures of the depth of anaesthesia. The present study compares these two methods to two traditional linear methods, namely 95% spectral edge frequency (SEF95) and median edge frequency (MEF), and a commercial method, bispectral index (BIS), in pre-anaesthesia, maintenance, and recovery stages. Twenty-three patients (12 males and 11 females) with inhalational anaesthesia were enrolled. The BIS, SEF95, and MEF data of the anaesthetized subjects are collected using a BIS monitor. Raw EEG data are transmitted to a computer for off-line analysis to obtain ApEn and LZC values. The ApEn, LZC, SEF95, and MEF values are converted to a 0-100 range for comparison with BIS. There are significant differences (P < 0.05) in th results between the pre-anaesthesia and maintenance stages and between the recovery and maintenance stages obtained from BIS, ApEn, and LZC, which indicates that the three measures can differentiate the state of anaesthetia in a patient. There are no differences (P > 0.05) in the ApEn and LZC values between the pre-anaesthesia and recovery stages, indicating that ApEn and LZC show the increases in values from maintenance phase to recovery phase similar to the reductions in values from pre-anaesthesia phase to maintenance phase. The changes of ApEn and LZC in recovery stage are significantly larger than that exhibited by BIS. BIS shows a statistically reduced level from the pre-anaesthesia to the recovery stage, whereas ApEn and LZC show no difference. This indicates that ApEn and LZC respond more rapidly to recovery than does BIS. LZC and ApEn perform more sensitively than BIS in detecting the recovery of consciousness from non-responding to responding. Moreover, traditional assessments SEF95 and MEF perform poorly compared to BIS. Keywords: Approximate entropy (ApEn), Lempel-Ziv complexity (LZC), Electroencephalogram (EEG), Bispectral index (BIS)

1. Introduction Determining the depth of anaesthesia (DOA) is very challenging because direct measurements are unavailable. Awareness during anaesthesia is rare [1], but its incidence approaches 1% in high-risk patients [2]. Anaesthesia awareness can lead to anxiety and post-traumatic stress disorder [3]. Anaesthetists routinely monitor a range of clinical signs during general anaesthesia. Some signs, such as arterial pressure and heart rate, are expressed numerically, and others, such as sweating, lacrimation, and pupil response, have * Corresponding author: Jiann-Shing Shieh Tel: +886-3-4638800 ext. 2470; Fax: +886-3-4558013 E-mail: [email protected]

states [4-6]. Anaesthetists use this information to adjust the inflow of drugs. Measures based on the electroencephalogram (EEG) signal have been proposed for reliably monitoring DOA. The EEG, generated from within the central nervous system (CNS), is not affected by neuromuscular blockers. It is known that raw EEG signals show graded changes with increasing concentration of anaesthetic agents. The surface recording of EEG is potentially affected by electromyogram (EMG) activity and thus these measures may change with the concentration of neuromuscular blockers. Aspect Medical Systems Inc. developed the bispectral index (BIS) of EEG for monitoring DOA [7]. BIS is as an indicator of DOA based on a combination of spectral, bispectral, and temporal analysis. However, BIS uses linear algorithms, but EEG signals are totally nonlinear and

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non-stationary. Ferenets et al. [8] evaluated the performances of several complexity measures for DOA and found that approximate entropy (ApEn) and Lempel-Ziv complexity (LZC) perform well. These complexity measures are based on the regularity and randomness of signals, which reflect the nonlinear and non-stationary properties of signals. A previous study [9] demonstrated that BIS was greatly reduced when a muscle relaxant was given to wake volunteers who remained in a state of alertness, indicating a potential influence of EMG activity on EEG. Several algorithms based on spontaneous EEG or auditory evoked responses have been developed and commercialized for monitoring DOA, including the Entropy index (Datex Ohmeda, Finland) [10], the Narcotrend index (MonitorTechnik, Germany) [11], and the Alaris AEP (auditory evoked potential) (Alaris, Europe) [12]. A review of studies on EEG signals for monitoring brain function for anaesthesia and intensive was conducted by Lipping and Jantti [13]. The most widely used equipment is the BIS monitor, which has been approved by the Food and Drug Administration. BIS values range from 0 to 100, reflecting the absence of cortical activity and the completely awake state, respectively. However, according to recent research, anaesthesia awareness can occur at any time and at any BIS value, even when BIS values are within the target ranges [14]. These findings do not support routine BIS monitoring as part of standard practice. Hence, EEG-based anaesthesia monitoring methods have been extensively developed. Comparing or evaluating DOA monitoring methods has several challenges. First, the values (or indices) of various methods have different ranges, which makes them difficult to compare [15-17]. Second, most previous studies have focused on measurements during the induction stage but not the recovery stage [8,18-21]. Compared to the induction stage, the maintenance stage is a relatively steady stage and the recovery stage is an inverse stage to induction stage. Thus, these two stages are considered here. In the present study, five measures, namely BIS, 95% spectral edge frequency (SEF95), median edge frequency (MEF, frequency of half accumulative spectral power of EEG), ApEn, and LZC are used to quantify EEG signals during inhalational anaesthesia for pre-anaesthesia, maintenance, and recovery stages. The ApEn, LZC, SEF95, and MEF data were converted to a scale from 0 to 100 for comparison to the dimensionless BIS values. The main objective of this study is to determine which of the 5 measures is most suitable for monitoring DOA during the phases of general anaesthesia performed in a surgical procedure.

2. Materials and methods 2.1 Patients After obtaining approval from the Ethics Committee of National Taiwan University Hospital and written informed consent, twenty-three patients (12 males and 11 females) with American Society of Anesthesiologists physical status 1 or 2 were studied. The patients were scheduled for functional endoscopic sinus surgery of chronic paranasal sinusitis during

inhalational anaesthesia. The average age was 42 ± 13 years, and the average operation time was 110 ± 45 minutes. Thiopental (4 mg/kg) was used for the induction of anaesthesia. All patients were intubated after the administration of succinylcholine (1 mg/kg) and maintained with cisatracurium as the neuromuscular blocker. Isoflurane (1 minimum alveolar concentration, MAC) and fentanyl (2 µg/kg) were used for the maintenance of anaesthesia. Fentanyl was added when necessary to keep an adequate DOA. Patients were excluded if they had clinical evidence of severe respiratory, cardiovascular, hepatic, renal, or endocrine disease, uncontrolled hypertension, or previous adverse response to general anaesthesia. Patients were also excluded if they had a history of any neurologic or psychiatric disorders, or if they were taking any drugs likely to influence the course of anaesthesia. 2.2 Data collection and analysis The EEG signal, BIS, SEF95, and MEF of the anaesthetized subjects were collected using a BIS monitor (Aspect A-1050) via two RS232 ports (one port was used for raw EEG recording and the other was used to collect BIS, SEF95, and MEF data). The electrodes used to measure EEG signals were attached on the forehead of each subject as the center (CTR), ground (GND), and right (R) electrodes shown in the illustration of the two-channel referential (BIS) montage of the A-1050 electrode placement chart. The sampling time for BIS, SEF95, and MEF data was every 5 s. The sampling frequency for the raw EEG data was 128 Hz. All measured data were transmitted to a computer for further analysis. In order to compare the methods, the anaesthesia course was divided into four phases, namely pre-operative preparation, induction, maintenance, and recovery. The four phases are defined below. (1) Pre-operative preparation phase: from 5-10 minutes before intravenous injection of thiopental to the time of injection. (2) Induction phase: from the time of intravenous injection of thiopental to 1 minute after inhalation of the inhalant anaesthetics. (3) Maintenance phase: from 1 minute after inhalation of the inhalant anaesthetics to 1 minute after the inhalation of the inhalant anaesthetics is stopped. (4) Recovery phase: from 1 minute after the inhalation of the inhalant anaesthetics is stopped until the subject regains consciousness. In this study, the first two phases (pre-operative preparation and induction) are combined into the pre-anaesthesia stage for comparision with the maintenance (anaesthetic) and recovery stages. BIS is a statistics-based dimensionless index for DOA monitoring, which provides a weighted sum of derived parameters from EEG signals (such as time domain, frequency domain, and cross spectral parameters). The effectiveness, accuracy, and usefulness of BIS have been extensively examined. BIS values range from 0 (total sedation stage) to 100 (fully awake stage). A BIS value of between 40 and 60 indicates an appropriate management of general anaesthesia. Moreover, the SEF95 and MEF values obtained from the BIS monitor were in the range of 0.5-30 Hz. MEF defines the

EEG Approximate Entropy and Complexity Measure

frequency below which 50% of the total EEG energy lies. SEF95 defines the frequency below which 95% of the total EEG energy lies. In the scaling processes of MEF and SEF95, the accumulative percentage of spectral energy of the EEG in the frequency range of 0.5 to 30 Hz is derived using Fourier analysis. Then, MEF is determined as the frequency below which 50% of the spectral energy lies. Similarly, SEF95 is determined as the frequency below which 95% of the spectral energy lies. The frequencies of SEF95 and MEF vary with the consciousness of the subject from awake status of high frequency to unconscious status of low frequency. For comparison with other methods, the SEF95 and MEF values were converted to be in the range of 0 to 100, where 0 represents 0.5 Hz and 100 represents 30 Hz. 2.3 Calculation of approximate entropy The entropy module was proposed to quantify the complexity of EEG as an assessment of DOA [10]. The entropy module in commercial DOA monitoring equipment is based on spectral entropy, which has parameters of state entropy and response entropy at various frequency bands. A low ApEn value (meaning that the EEG recording is regular and predictable) indicates the anaesthetized state of the subject. A high ApEn value (meaning that the EEG recording is irregular and unpredictable) indicates that the subject is conscious. ApEn is defined as the unpredictability of subsequent samples in a time series based on the knowledge of previous samples. Predictability means subsequent samples can be predicted based on the knowledge of previous samples. The number of subsequent samples (m) defined as a vector for comparison and the tolerance coefficient (r) are used for determining whether two compared samples are similar or not. Methodologically, the predictability means the first subsequent samples of two compared vectors are similar as if the previous m samples in two vectors are similar. Moreover, the allowed tolerance of determination for a binary index of similarity between two compared samples is defined as a threshold, which is determined as the product of the tolerance coefficient and the standard deviation (SD) of the time series. The ApEn can be calculated as [22-24]: Approximate Entropy   m (r )   m1 (r )

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from a time series of data u(i), u(2)….u(N). The distance between vectors x(i) and x(j) is defined as: d[x(i)-x(j)] = max(|u(i + k - 1) - u(j + k - 1)|), where k = 1,....,m

(5)

For comparison with other methods, the calculated ApEn values were scaled to be within a range of 0 to 100. Thus, the linearized ApEn values were used to represent the degree of conscious and the DOA for a subject. 2.4 Calculation of Lempel-Ziv complexity EEG signals have strong nonlinear and dynamic properties [25,26]. Lempel and Ziv proposed a measure of the complexity of EEG recordings [27]. LZC counts the number of different patterns in a sequence, starting from short patterns to longer ones. LZC is commonly used in the field of cryptography. In this study, LZC is used for EEG analysis, since it can effectively characterize the development of spatio-temporal activity patterns in nonlinear systems of high-dimensionality [28], such as the brain or heart. Moreover, the concept of C(n) is simple to understand and its computation is easy. In LZC analysis, a signal is transformed into a binary sequence. A value which is below or equal to the mean of the data is represented by “0” and a value which is above the mean of the data is represented by “1”. The complexity reflects the number of distinct patterns contained in the binary sequence S=s1, s2, …, sn [29] using the accumulated number of words, c(n). The complexity of a random sequence with length n, b(n), for a sequence which consists of different binary codes with equal probability can be calculated as: b(n) = n/log2(n)

(6)

The normalized LZC, C(n), is obtained using: C(n) = c(n)/b(n)

(7)

For comparison with other EEG methods, the LZC values were linearly transformed to be within a range of 0 to 100. The linearized LZC values were used to represent the degree of conscious and the DOA for a subject.

(1) 2.5 Scale conversion

where Φm(r) is the function of predictability, defined as:

 m (r )  ( N  m  1) 

N  m 1

 ln Cim (r )

(2)

i 1

m

where Ci (r ) is the matching rate of vector comparisons, defined as:

Cim (r ) = (number of x(j) such that d[x(i)-x(j)] ≤ r × SD)/(N-m+1)

(3)

where x(i) and x(j) are vectors, respectively defined as: x(i) = [u(i),…..,u(i+m-1)] x(j) = [u(j),…..,u(j+m-1)]

(4)

For comparison with BIS, whose values range from 0 to 100, the ApEn, LZC, SEF95, and MEF values were converted to a scale from 0 to 100. The scale conversions of SEF95 and MEF are different from those of ApEn and LZC. For SEF95 and MEF, the scales present the frequencies normalized by the frequency range of 0.5 to 30 Hz. For SEF95 and MEF, a value of 0 presents the frequency of 0.5 Hz and a value of 100 presents the frequency of 30 Hz. For the complexity measures ApEn and LZC, the maxima and minima were set up according to the relative maximum and minimum values of BIS measurement. The scales of these two complexity measures were then linearly translated to the new scale range.

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2.6 Statistical analysis Since EEG values are not normally distributed, the non-parametric test should be used in statistical analysis. In this study, the Kruskal-Wallis test was used to find statistically significant differences in the median differences of average values of BIS, SEF95, MEF, ApEn, and LZC from pre-anaesthesia to maintenance stages and from recovery to maintenance stages. The Mann-Whitney rank sum test was conducted for multiple comparisons when the null hypothesis was not applicable. P < 0.05 was considered statistically significant [30].

median values of the EEG measures in the pre-anaesthesia and recovery phases are expectedly used to reflect the ensemble index of the translating status between responding and non-responding. According to our analysis results, both ApEn and LZC values have insignificant differences between the pre-anaesthesia and recovery phases, whereas the BIS values are significantly different between pre-anaesthesia and recovery phases. The BIS value in the pre-anaesthesia phase is higher than that in the recovery phase. According to this analysis result, BIS performs insensitively in the process of consciousness regaining and sentively in that of consciousness losing. Thus, ApEn and LZC reflect a more significant change of consciousness regaining than BIS does in recovery phase.

3. Results Figure 1 shows example waveforms of BIS, SEF95, MEF, ApEn, and LZC values in the pre-anaesthesia, maintenance, and recovery phases of anaesthesia. The change of DOA in the 23 subjects was statistically investigated to determine whether the 5 measures perform as good assessment for quantifying these phases. As shown in Table 1, there is no statistical difference (P > 0.05) between values obtained in the pre-anaesthesia stage and the maintenance stage in the SEF95 and MEF analyses, which means that these two measures were consistent with the changes in the anaesthetized state of the patient. There were significant differences (P < 0.05) between analytical results for the pre-anaesthesia stage and the maintenance stage and between the recovery stage and the maintenance stage obtained from BIS, ApEn, and LZC, indicating that these three measures can effectively differentiate the conscious state and the anaesthetized state of a subject. There was no statistical difference (P > 0.05) between analysis results of ApEn and LZC in the pre-anaesthesia stage and the recovery stage. Clinically, pre-anaesthesia phase performs a translational process in physiology from responding to non-responding, and recovery performs an inverse phase of pre-anaesthesia. The

Figure 1. Sample BIS, SEF95, MEF, ApEn, and LZC waveforms for the induction, maintenance, and recovery phases of anaesthesia.

Table 1. Differences between pre-anaesthesia, maintenance, and recovery phases obtained using BIS, SEF95, MEF, ApEn, and LZC. The pre-operative preparation and induction phases are combined into the „Pre_anaesth‟ phase.

BIS (Pre_anaesth) BIS (Maintenance) BIS (Recovery) SEF95 (Pre_anaesth) SEF95 (Maintenance) SEF95 (Recovery) MEF (Pre_anaesth) MEF (Maintenance) MEF (Recovery) ApEn (Pre_anaesth) ApEn (Maintenance) ApEn (Recovery) LZC (Pre_anaesth) LZC (Maintenance) LZC (Recovery)

Number 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23

Kruskal Wallis test Median (Range) P < 0.05 80.6 (67.7,89.2) 46.5 (29.5,64.6) yes 61.4 (47.8,72.8) 60.4 (45.2,82.9) 53.3 (40.5,70.1) yes 69.7 (61.1,87.9) 27.1 (17.1,56.2) 30.3 (15.9,46.6) yes 47.3 (31.4,67.2) 77.2 (61.8,88.8) 52.6 (18.8,69.7) yes 72.6 (56.2,84.6) 75.6 (62.2,89.0) 48.1 (13.5,68.8) yes 69.8 (49.1,88.3)

Mann-Whitney rank sum test BIS(Pre_anaesth) vs BIS(Maintenance) BIS(Pre_anaesth) vs BIS(Recovery) BIS(Recovery) vs BIS(Maintenance) SEF95(Pre_anaesth) vs SEF85(Maintenance) SEF95(Pre_anaesth) vs SEF95(Recovery) SEF95(Recovery) vs SEF95(Maintenance) MEF(Pre_anaesth) vs MEF(Maintenance) MEF(Pre_anaesth) vs MEF(Recovery) MEF(Recovery) vs MEF(Maintenance) ApEn(Pre_anaesth) vs ApEn(Maintenance) ApEn(Pre_anaesth) vs ApEn(Recovery) ApEn(Recovery) vs ApEn(Maintenance) LZC(Pre_anaesth) vs LZC(Maintenance) LZC(Pre_anaesth) vs LZC(Recovery) LZC(Recovery) vs LZC(Maintenance)

P < 0.05 yes yes yes no yes yes no yes yes yes no yes yes no yes

EEG Approximate Entropy and Complexity Measure

Table 2. Differences of the averages of BIS, SEF95, MEF, ApEn, and LZC from the pre-anaesthesia stage to the maintenance stage. BIS SEF95 MEF ApEn LZC Patient1 44.4 33.9 40.3 21.7 34.7 Patient2 30.2 3.4 6.8 22.3 25.6 Patient3 22.1 -9.0 -5.1 24.6 13.4 Patient4 23.5 6.4 -5.1 10.7 19.2 Patient5 32.5 10.3 -0.1 30.4 60.1 Patient6 43.2 19.2 4.5 30.0 45.2 Patient7 34.9 -1.1 -15.4 27.6 38.7 Patient8 53.1 12.2 -4.8 47.6 49.9 Patient9 8.2 -12.3 -16.6 17.8 25.6 Patient10 58.3 15.9 28.5 58.4 59.6 Patient11 39.5 23.1 23.7 22.3 18.9 Patient12 34.3 25.4 -10.6 27.1 31.7 Patient13 44.5 0.7 -2.6 48.6 75.5 Patient14 46.5 14.2 12.9 30.2 40.2 Patient15 13.4 -20.7 -18.0 15.2 5.8 Patient16 40.2 -6.3 1.6 22.0 23.9 Patient17 31.6 -4.7 -18.2 29.5 34 Patient18 29.0 -8.3 -7.7 39.6 41.3 Patient19 51.7 4.5 13.7 24.2 13.4 Patient20 40.8 29.1 13.7 9.6 13.1 Patient21 16.5 4.5 -4.9 22.3 18.1 Patient22 25.6 -8.9 5.5 6.2 0.1 Patient23 35.4 28.1 -11.6 35.6 40 Median 34.3 4.5 -2.6 24.6 31.7 Range (8.2,52.3) (-20.7,33.9) (-18.2,40.3) (6.2,58.4) (0.1,75.5) BIS vs SEF95 vs MEF vs ApEn vs LZC, P < 0.05 by Kruskal Wallis Test. BIS vs SEF95, P < 0.05 by Mann-Whitney Rank Sum Test BIS vs MEF, P < 0.05 by Mann-Whitney Rank Sum Test BIS vs ApEn, P < 0.05 by Mann-Whitney Rank Sum Test BIS vs LZC, P > 0.05 by Mann-Whitney Rank Sum Test

Two nonlinear methods (ApEn and LZC) were compared to the two linear methods (SEF95 and MEF) and the commercial method (BIS) during the pre-anaesthesia, maintenance, and recovery stages. As shown in Table 2, the median values of differences between the pre-anaesthesia stage and the maintenance stage of anaesthesia for BIS, SEF95, MEF, ApEn, and LZC are 34.9, 4.5, -2.6, 24.6, and 31.7, respectively. A positive value in Table 2 indicates that the value of the EEG measure for pre-anaesthesia phase is larger than that for the anaesthesia phase and a positive value in Table 3 indicates that the value of the EEG measure for the recovery phase is larger than that for the anaesthesia phase. The P values for the differences between SEF95, MEF, and ApEn in comparison to BIS are below 0.05. This indicates that SEF95, MEF, and ApEn have significant differences compared to BIS. However, the value of difference from this ApEn is a little less than that of BIS Index but values of differences from these SEF95 and MEF two methods were less than that of BIS Index. Both SEF95 and MEF failed to recognize the change from the conscious state to the anaesthetized state. As shown in Table 2, BIS, ApEn, and LZC show significant changes in the anaesthesia stages from responding to non-responding. Moreover, these measures of DOA performed the similar fluctuation patterns of consciousness for the whole group data and data of individuals. This proves that these three measures have similar reliability in monitoring the state of anaesthesia. During the recovery phase of anaesthesia, the subject gradually regains consciousness. A quantitative method was used to compare changes of BIS, SEF95, MEF, ApEn, and

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LZC during the recovery and the maintenance phases of anaesthesia. The results in Table 3 indicate that the median values of the differences between the recovery and the maintenance phases of anaesthesia obtained by the 5 analytical methods are 14.4, 12.7, 16.8, 20.5, and 21.6, respectively. The P values for the differences between SEF95 and BIS and between MEF and BIS are over 0.05, indicating that both SEF95 and MEF are capable of predicting the course from an anaesthetized state to consciousness. In contrast, the P values for the differences between ApEn and BIS and between LZC and BIS are below 0.05, and the median values of ApEn and LZC were higher than that of BIS. This indicates that ApEn and LZC are more effective than BIS in predicting the subjects‟ course from the maintenance to recovery phases. Table 3. Differences of averages of BIS, SEF95, MEF, ApEn, and LZC from the recovery stage to the maintenance stage. Patient1 Patient2 Patient3 Patient4 Patient5 Patient6 Patient7 Patient8 Patient9 Patient10 Patient11 Patient12 Patient13 Patient14 Patient15 Patient16 Patient17 Patient18 Patient19 Patient20 Patient21 Patient22 Patient23 Median Range

BIS SEF95 MEF ApEn LZC 20.8 26.2 31.4 16.1 26.0 8.1 10.6 9.4 16.7 13.1 17.6 -1.8 3.4 10.0 13.3 8.2 6.4 14.0 12.0 11.0 7.1 14.7 13.1 30.9 33.7 30.1 18.6 12.5 23.9 27.1 8.6 10.4 22.5 26.5 22.0 16.6 11.6 26.2 35.8 49.5 6.8 8.5 25.3 10.2 11.0 27.4 31.0 40.7 39.9 37.7 20.7 21.8 31.8 15.6 16.2 29.5 12.8 11.1 23.2 18.2 22.5 18.2 16.8 40.3 35.6 21.0 15.4 10.9 14.5 28.0 4.9 17.8 27.3 18.4 21.6 11.7 10.6 10.9 18.4 25.5 4.4 6.1 10.9 12.2 16.1 11.7 12.7 17.1 23.8 27.6 15.1 21.0 24.6 22.2 18.1 24.3 21.5 23.3 22.6 34.0 13.8 10.4 22.7 22.4 13.5 14.4 10.6 10.1 13.8 16.7 7.2 6.3 1.2 20.5 18.3 14.4 12.7 16.8 20.5 21.6 (4.4,30.1) (-1.8,31.0) (1.2,40.7) (10,40.3) (11,49.5)

BIS vs SEF95 vs MEF vs ApEn vs LZC, P < 0.05 by Kruskal Wallis Test. BIS vs SEF95, P > 0.05 by Mann-Whitney Rank Sum Test BIS vs MEF, P > 0.05 by Mann-Whitney Rank Sum Test BIS vs ApEn, P < 0.05 by Mann-Whitney Rank Sum Test BIS vs LZC, P < 0.05 by Mann-Whitney Rank Sum Test

4. Discussion There are two limitations in this study. First, no actual measure of consciousness was made. Since consciousness cannot be measured directly, there are many indices and measurements of EEG for monitoring the consciousness of patients as an index of the DOA. These indices can be used as the representative assessments of consciousness and as references for comparing EEG measures. Second, averaging over the pre-anaesthesia and recovery periods blurred any changes in the EEG measures occurring during the time window and made the measures appear less sensitive than they actually are. In fact, the averages of DOA of pre-anaesthasia and recovery perform well enough as a indicators for quantifying the consciousness status when the same criterion was used.

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The results were often difficult to compare due to differences in the recording setup and in the range of indices. Applying several monitoring devices in parallel makes the recording setup complex. In clinical practice, a maximum of three systems can be compared. Most related studies only studied the induction stage of anaesthesia [8,18-20,31,32]. There have been no reported comparisons of these indices over the induction, maintenance, and recovery stages. The present study collected EEG data from only one machine, the BIS monitor. A total of 5 measures (BIS, SEF95, MEF, ApEn, and LZC) were used to quantify the DOA of patients under inhalational anaesthesia. For comparison, the ApEn, LZC, SEF95, and MEF values were converted to a 0~100 range for comparison with dimensionless BIS values. Although many indices have been proposed for measureing the DOA, no index can reliably detect consciousness during general anaesthesia. According to recent research, anaesthesia awareness can occur even when BIS values are within the target ranges [14]. Those findings do not support routine BIS monitoring as part of standard practice. An investigation that used the isolated forearm technique showed that the Narcotrend DOA monitor cannot reliably detect consciousness during general anaesthesia [33]. This is because EEG signals originate from the brain cortex but deep anaesthesia is related to brain stem functions. Brain stem activity should thus be evaluated to improve DOA monitoring reliability. However, the activity of the brain stem cannot be measured directly. The most common way of determining the activity of the brain stem is to quantify the spectrum of heart rate variability, which reflects the activity of the sympathetic and parasympathetic nervous systems, which are controlled by the brain stem [34]. Moreover, ECG signals are easily disturbed by drugs (atropine) [35,36] and electrical noise (surgical diathermy) [37,38]. Cerebral blood flow velocity measured with transcranial Doppler may thus be a better signal for monitoring brain stem function and auto-regulation. Its resistance to interference makes the cerebral blood flow velocity more appropriate than ECG signals for measuring deep DOA [39,40]. Approximate entropy or sample entropy are currently used in many fields of study [18,41]. The absolute value of the approximate or sample entropy depends on three parameters: the filtering level (r), the number of data points per epoch (N), and the number of previous values used for the prediction of the subsequent value (m). These three parameters should be optimized. The optimal choice of parameters has been theoretically determined [20,42,43]. According to Pincus [22], the filtering level (r) should range from 0.1 to 0.2 times the standard deviation of the original signals. However, biopotential signals (e.g., EEG, ECG) are easily affected by disturbances (e.g., electrosurgical noise) in the operating room. Furthermore, EEG and ECG signals can easily develop the baseline drift caused by muscle contraction and respiration. Therefore, the standard deviation of the EEG original signal under these circumstances will become large. In order to avoid this problem, advanced signal processing techniques must be used.

EEG signals are potentially affected by EMG. EEG-based consciousness measures cannot completely eliminate the influences from EMG signals. Thus, it is possible that the 5 measures used in this study respond to the pure brain cortex activities when the EMG activity is restrained by neuromuscular blockers or the combination of EMD and brain cortex activities. Moreover, the BIS values depend on the BIS algorithm, which is regularly upgraded by manufacturers.

5. Conclusions EEG measures ApEn and LZC were used to quantify the complexity of EEG recordings for assessing consciousness under general anaesthesia. The changes of ApEn and LZC in the recovery phase were significantly larger than that of BIS. BIS showed a statistically reduced level from the pre-anaesthesia phase to the recovery phase, but ApEn and LZC showed no difference between these phases. This indicates that ApEn and LZC respond more rapidly to recovery than does BIS. The pre-operative and induction phases were combined into the pre-anaesthesia phase. According to our definitions, the pre-operative is a steadily active phase of consciousness; the induction is a translational phase in consciousness from responding to non-responding. As the inverse of pre-anaesthesia, the recovery phase is also a translatiional phase in consciousness from non-responding to responding. In clinical practice, detecting the recovery from deep anaesthesia to awareness is very important for avoiding anaesthesia awareness. However, the pre-anaesthesia and recovery phases are not similar states. This is a critical weakness of our assumption. BIS is a DOA indicator based on spectral, bispectral, and temporal analyses. These analyses are based on the assumption of linearity. Theoretically, the BIS algorithm is insufficient for monitoring a nonlinear system. However, the effectiveness, accuracy, and usefulness of BIS have been examined by numerous studies. So far, BIS has been found to be a reliable comparison standard for DOA monitoring. BIS was thus used as a referred measure in this study. Results show that the performances of LZC and ApEn are different from that of BIS in detecting the recovering process of consciousness from non-responding to responding. Moreover, the traditional assessments (SEF95 and MEF) perform poorly compared to BIS. LZC and ApEn can be used to quantify the complexity of EEG to assess consciousness.

Acknowledgements The authors acknowledge the National Science Council (NSC) of Taiwan for supporting this research under grant NSC 97-2221-E-002-212. This research was also supported by the Center for Dynamical Biomarkers and Translational Medicine which is sponsored by NSC (Grant Number: NSC 99-2911-I-008-100).

EEG Approximate Entropy and Complexity Measure

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