Clinical Neurophysiology 123 (2012) 681–688

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Clinical Neurophysiology

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Multiscale rescaled range analysis of EEG recordings in sevoflurane anesthesia

Zhenhu Liang a, Duan Li a, Gaoxiang Ouyang a, Yinghua Wang a, Logan J. Voss b, Jamie W. Sleigh b,Xiaoli Li a,c,⇑a Institute of Electrical Engineering, Yanshan University, Qinhuangdao 066004, Chinab Department of Anesthesia, Waikato Hospital, Hamilton, New Zealandc National Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing 100875, China

a r t i c l e i n f o

Article history:Accepted 22 August 2011Available online 10 October 2011

Keywords:ElectroencephalographyAnesthesiaMaximal overlap discrete wavelet transformHurst exponent

1388-2457/$36.00 � 2011 International Federation odoi:10.1016/j.clinph.2011.08.027

⇑ Corresponding author at: National Key Laboratoand Learning, Beijing Normal University, Beijing 1005880 2032.

E-mail address: xiaoli@bnu.edu.cn (X. Li).

h i g h l i g h t s

� We have proposed a new index by combining of wavelet and rescaled range analysis.� The modeling and prediction probability have been used to evaluate the proposed index.� The proposed index can accurately track the anesthetic drug effect on brain activity.

a b s t r a c t

Objective: The Hurst exponent (HE) is a nonlinear method measuring the smoothness of a fractal timeseries. In this study we applied the HE index, extracted from electroencephalographic (EEG) recordings,as a measure of anesthetic drug effects on brain activity.Methods: In 19 adult patients undergoing sevoflurane general anesthesia, we calculated the HE of the rawEEG; comparing the maximal overlap discrete wavelet transform (MODWT) with the traditional rescaledrange (R/S) analysis techniques, and with a commercial index of depth of anesthesia – the responseentropy (RE). We analyzed each wavelet-decomposed sub-band as well as the combined low frequencybands (HEOLFBs). The methods were compared in regard to pharmacokinetic/pharmacodynamic (PK/PD)modeling, and prediction probability.Results: All the low frequency band HE indices decreased when anesthesia deepened. However theHEOLFB was the best index because: it was less sensitive to artifacts, most closely tracked the exact pointof loss of consciousness, showed a better prediction probability in separating the awake and unconsciousstates, and tracked sevoflurane concentration better – as estimated by the PK/PD models.Conclusions: The HE is a useful measure for estimating the depth of anesthesia. It was noted that HEOLFBshowed the best performance for tracking drug effect.Significance: The HEOLFB could be used as an index for accurately estimating the effect of anesthesia onbrain activity.� 2011 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights

reserved.

1. Introduction

It has been suggested that EEG-based anesthesia monitoringmay decrease surgical and anesthetic risk and reduce patientrecovery time (Bruhn, 2006; Jameson and Sloan, 2006; Johansenet al., 2000; Zikov et al., 2006). Commercial systems for anesthesiamonitoring have been developed, such as the BIS monitor (AspectMedical Systems, Newton, MA) and M-entropy module (GE Health-care, Helsinki, Finland). The BIS monitor provides an index derived

f Clinical Neurophysiology. Publish

ry of Cognitive Neuroscience875, China. Tel./fax: +86 10

from the power spectral analysis of the EEG, and the phasecoupling between different EEG frequencies (Rampil, 1998). TheM-entropy has two parameters: state entropy (SE) and responseentropy (RE). SE is calculated from the frequency band 0.8–32 Hzand reflects the cortical state of the patient. RE is calculated fromthe frequency range 0.8–47 Hz and includes the electromyogram(EMG)-dominated frequencies (Bruhn et al., 2000; Maksimowet al., 2007; Viertiö-Oja et al., 2004). These methods are based onlinear Fourier transformation to extract informative features fromthe anesthetic EEG recordings. However, the EEG is a non-station-ary signal derived from a nonlinear system (Cao et al., 2004; Jospinet al., 2007; Li et al., 2005; Nguyen-Ky et al., 2010; Vakorin et al.,2010). It would therefore seem reasonable to investigate the useof nonlinear algorithms as methods for analyzing anesthetic EEGdata.

ed by Elsevier Ireland Ltd. All rights reserved.

682 Z. Liang et al. / Clinical Neurophysiology 123 (2012) 681–688

Some methods derived from nonlinear dynamics theories havebeen proposed to analyze the temporal evolution of EEG recordings(Cao et al., 2004; Jospin et al., 2007; Kapiris et al., 2005; Li et al.,2005, 2008a,b, 2010; Nguyen-Ky et al., 2010; Olofsen et al., 2008;Podobnik and Stanley, 2008). In particular, the Hurst exponent(HE) has been successfully applied to evaluate the self-similarityand correlation properties of EEG recordings (Acharya, 2005;Lalitha and Eswaran, 2007; Nguyen-Ky et al., 2010; Room Halland Area, 2007; Culic et al., 2010). This method measures thesmoothness of a fractal time-series derived from rescaled range(R/S) analysis or detrended fluctuation analysis (DFA) (Acharya,2005; Bassingthwaighte and Raymond, 1994; DePetrillo et al.,

Fig. 1. A flowchart of multiscale rescaled range analysis algorithm. Block 1: DecompositiSLD = 6, j = 1. Block 2: Construction of the high-pass filter and low-pass filter: ~hj;l ¼ ~hj;l=2j=

filter sequence. The length of filter for level j is: Lj ¼ ð2j � 1ÞðL� 1Þ þ 1. Block 3: Calculatiocoefficients, and Vj are the low frequency coefficients, where t ¼ 1; . . . ;N � 1. The signascaling coefficients ðjjSjj2 ¼

PJj¼1jjWjjj2 þ jjVJ jj2Þ. Block 4: Dividing the decomposed detail

an integer). Block 5: Calculation of the mean (Em) and the standard deviation (Sm) of the suof each sub-series, normalization of the data (Zi,m) through subtracting the sample mean Xthe normalized data by consecutively summing each point: Yi;m ¼

Pij¼1Xj;m , for i ¼ 1; . . .

length n: ðR=SÞn ¼ 1d

Pdm¼1Rm=Sm , where Rm is a new cumulative series which is the range

deviation. Block 9: The HE estimation. An ordinary least squares regression of log(n) (testimation of the HE.

1999; Jospin et al., 2007; Nguyen-Ky et al., 2010). In this study,we explored the use of HE to extract informative features fromEEG recordings and provide a new index to indicate the effect ofanesthetic drugs.

The R/S analysis and DFA are two classical fractal methods andhave all been applied to calculate the HE to reveal the fractal prop-erties in dynamical systems (Alvarez-Ramirez et al., 2008; Barunikand Kristoufek, 2010; Nguyen-Ky et al., 2010; Culic et al., 2010).The algorithms of the two methods are simple and have the advan-tage of high computational speed (Culic et al., 2010). However,these methods need to be optimized to reduce the effect of arti-facts (Alvarez-Ramirez et al., 2008). In this study, the maximal

on of the original series S. The number of scale level of decomposition (SLD) is set as2 and ~gj;l ¼ ~gj;l=2j=2. The MODWT filters satisfy

Pj�1l¼0

~hj;l ¼PLj�1

l¼0~gj;l , where l is the index

n of the jth level MODWT wavelet and scaling coefficients, Wj are the high frequencyls’ energy equals to the summation of square of wavelet coefficients and square ofcomponent Bj into d sub-series of length n (for each sub-series m ¼ 1; . . . ;n, and d isb-series, and setting of the initial regression value (IRV). Block 6: The pre-processingi;m ¼ Zi;m � Em , for i ¼ 1; . . . ;n. Block 7: Generation of a cumulative time series using;n. Block 8: Determination of the mean of the rescaled range for each sub-series ofby subtracting the minimum value from the maximum value and Sm is the standardhe independent variable) and logðR=SÞn (the dependent variable). The slope is the

Fig. 2. Illustration of a MODWT process. Original data was sampled at 100 Hz. Six order sub-band MODWT was used. Sub-band B1, B2, B3 corresponds to 6.25–12.5 Hz. Thisfrequency band mainly consists of a wave, which mostly appear in the awake stage. Sub-band B4 refers to h wave, which appears as anesthesia deepens. B5 and B6 are forfrequency band lower than 3.5 Hz, known as the d wave. It is also an important wave in deep anesthesia. As for EEG data, frequency band 0.78–12.5 Hz is interested, as thisband contains conscious features in anesthesia.

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overlap discrete wavelet transform (MODWT) was used to sup-press the effect of artifacts in the EEG data (Percival and Walden,2006); and the scaling properties of the data at designated fre-quency bands were calculated. The performance of the proposedmeasure was assessed by utilizing pharmacokinetic/pharmacody-namic (PK/PD) modeling and prediction probability analysis.

2. Material and methods

2.1. Subjects and EEG recordings

EEG data from 19 patients (aged 18–63 years), scheduled to un-dergo elective gynecologic, general, or orthopedic surgery, wereanalyzed in this study. All subjects were recruited from WaikatoHospital, Hamilton, New Zealand and were American Society of

Fig. 3. The EEG (left) and log(n) versus log(R/S) (right) in awake (A and

Anesthesiologists physical status I or II. Written informed consentwas obtained from all subjects following approval by the WaikatoHospital ethics committee.

EEG recordings were taken from the M-entropy module (GEHealthcare, Helsinki, Finland). Signals were recorded between fore-head and temporal electrodes (active = FpZ, earth = Fp1, and refer-ence = F8) using a self-adhering flexible band holding threeelectrodes. The electrode impedance was checked to be less than5 kX. The M-entropy module has a sampling rate of 1600/s, a fre-quency range of 0.5–118 Hz, and a noise level of <0.5 lV. The REand SE were downloaded every 5 s. The sevoflurane concentrationwas measured at the mouth and sampled at 100/s. The data wererecorded on a laptop computer and stored for later off-line analysisusing MATLAB (version 7, MathWorks Inc.) software. We thendown-sampled the recorded EEG signal to 100/s with MATLAB’sresample function.

B), moderate anesthesia (C and D), and deep anesthesia (E and F).

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All patients were connected to a closed anesthesia breathingcircuit via a face mask with the flow rate of fresh gas set at 4 L/min. Sevoflurane was delivered by vaporizer at an inspired concen-tration of 3% for 2 min, followed by 7%. The time at which RE de-creased to 20 or less was noted and 7% sevoflurane wascontinued for a further 2 min (deepening phase). The sevofluranewas then turned off until RE returned to a value of 70 (lighteningphase). All data in the present study are based on this single deep-ening and lightening anesthetic protocol. No attempt was made torouse the subjects and no supplemental medications were admin-istered. The point of loss of consciousness (LOC) was assessed byloss of response to verbal command. The data have been used pre-viously to assess sevoflurane PK/PD effects using the spectral en-tropy of the EEG (McKay et al., 2006).

2.2. EEG preprocessing

Artifacts in scalp EEG recordings mainly come from eye move-ment, muscle activity, and linear power frequency noise. To reducethese artifacts, we used methods in Li’s paper (Li et al., 2008a,b).First, statistical mean and standard deviation statistics were used

Fig. 4. An EEG recording from a patient and its analysis. Data was re-sampled at 100highlighted. Awake state shows low amplitude and high frequency, while anesthesia statshort-time Fourier transform, using a 10s Hamming window, 90% overlapping. Dark resevoflurane concentration (Cet) during the same time course (scaled by 10 for illustrativB4–B6, and approximation A6, HEOR. Time interval is 10 s, with a 7.5 s overlap. (For interweb version of this article.)

to remove the outlier points. A stationary wavelet transform wasused to reduce the electro-oculogram (EOG) artifact by setting anappropriate threshold (Krishnaveni et al., 2006). We utilized thetwo-way least-square FIR to remove 0–0.5 Hz fluctuations(Delorme and Makeig, 2004). This filter uses a zero-phase forwardand reverse operation, so that phase information of the signal isnot distorted (Mitra and Kuo, 1998). Finally, a Kalman filter wasused to estimate adaptive autoregressive parameters and aninverse filter was used to detect and remove EMG and otherhigh-amplitude transient artifacts in the scalp EEG data.

2.3. Multiscale rescaled range analysis

In this study we propose a novel multiscale rescaled range anal-ysis (MRRA) algorithm, which is based on the MODWT. Wavelettransform is a multi-resolution analysis tool which is able to de-scribe the characteristics of the signal in the joint time–frequencydomain (Liu et al., 2002). In contrast to the traditional wavelettransform, such as the discrete wavelet transform, the MODWT isbetter able to define the detail and approximation in the series.In particular it has the advantage that the time-shift of the details

Hz. (A) Preprocessed EEG recording. Awake state (I) and anesthesia state (II) aree shows high-amplitude and low frequency. (B) The data spectrogram computed viad means high power and blue for low power. The black solid line is the end-tidale purpose). (C) Time course of HE for each sub-band from B4 to B6, combination ofpretation of the references to color in this figure legend, the reader is referred to the

Fig. 5. HEOR, HEOLFB, and RE around LOC (from LOC �30 s to LOC +30 s) for all subjects (n = 19). (A) HEOR over time. (B) HEOLB over time. (C) RE over time. (D) Statisticalanalysis of the absolute slope of linear polynomial fitting for the two indices. Bar height indicates the mean value, and the lower and upper lines are the 95% confidenceinterval of the Hurst index values, respectively.

Fig. 6. Box plot of HEOLB and HEOR at awake (I), induced (II), light anesthesia (III),deep anesthesia (IV) states. Lower and upper lines of the ‘‘box’’ are the 25th and75th percentiles of the sample, distance between the top and bottom of the box isthe sample median. Outliers (plus sign) are cases with values that are more than 1.5times the interquartile range. The notches in the box are a graphic confidenceinterval (95%) about the median of a sample.

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and approximation series are consistent with that of the input sig-nals (Percival and Walden, 2006). In this algorithm, MODWT wasused to decompose the EEG signal into multiple time series atthe different frequency bands.

The rescaled range analysis is a classic method to estimate theHE in nonlinear time series (Mandelbrot and Wallis, 1969). Be-cause it needs no prior assumptions, it can be conveniently em-ployed to calculate the HE from any nonlinear stochastic anddeterministic system (Bassingthwaighte and Raymond, 1994; Liet al., 2009; Matos et al., 2008; Naslund and Russell, 2002). MRRAoffers a scale-based multi-resolution analysis, which can be de-fined for all sample sizes (no ‘power of 2’ restrictions) and caneliminate ‘alignment’ artifacts. The details of the MRRA methodare shown in Fig. 1.

HE describes the characteristics of persistent or non-persistentproperties of the signal (Watters and Martin, 2004). The range0 < H < 0.5 indicates non-persistency; meaning that if the fluctua-tions increase in a period, they are likely to decrease in the intervalimmediately followed and vice versa (Balasis et al., 2009; Lalithaand Eswaran, 2007; Room Hall and Area, 2007; Culic et al.,2010). An ordinary least squares regression was used to calculatethe HE (Weron, 2002).

2.4. PK/PD modeling and statistical analysis

We used a standard inhibitory sigmoid/first-order effect-site,PK/PD model to analyze the relationship between anesthetic drugconcentration and estimated EEG index (McKay et al., 2006). Themodel has been successfully used to evaluate the proposed EEGindices by several researchers (Li et al., 2008a,b; Olofsen et al.,2008). To evaluate the correlation between the measured EEG in-dex and underlying anesthetic drug effect, prediction probability(Pk) statistics were applied, as described in Smith et al. (1996). Con-sidering the negative monotonic relation between the sevofluraneconcentration and the measured EEG index, the resultant Pk valueis replaced by 1 � Pk.

In order to analyze the change and distribution of the index dur-ing anesthesia, the distribution of the HE of the raw (HEOR) EEG and

HE of low frequency bands (HEOLFB) values during: the awake state,induction, deep anesthesia, and light anesthesia for all 19 subjectswere analyzed. The coefficient of determination (R2) between theHE index and the sevoflurane effect site concentration after PK/PDmodeling was calculated for each individual, and the average R2 cal-culated across the group. The objective of this analysis was to com-pare each algorithm’s ability to track sevoflurane effect siteconcentration. The Kolmogorov Smirnov test was used to determinewhether the data sets were normally distributed. In addition, therelative coefficient of variation (CV) (the ratio of the SD to the mean)

Table 1Parameters of PK/PD models.

Parameters t1=2keo (MIN) r Emax Emin EC50 R2

B4 0.96 ± 0.35 16.08 ± 10.04 0.06 ± 0.02 0.47 ± 0.09 0.90 ± 0.52 0.78 ± 0.08B5 0.76 ± 0.28 12.66 ± 10.78 0.07 ± 0.01 0.02 ± 0.01 0.90 ± 0.35 0.84 ± 0.08B6 0.51 ± 0.31 22.36 ± 10.62 0.08 ± 0.01 0.02 ± 0.01 1.28 ± 0.44 0.79 ± 0.05A6 0.60 ± 0.41 22.23 ± 11.84 0.06 ± 0.01 0.02 ± 0.01 1.71 ± 0.53 0.73 ± 0.18HEOLFB 0.31 ± 0.15 15.19 ± 10.03 0.14 ± 0.01 0.04 ± 0.01 1.71 ± 0.26 0.83 ± 0.06HEOR 0.39 ± 0.16 10.68 ± 9.27 0.18 ± 0.05 0.04 ± 0.02 1.34 ± 0.40 0.82 ± 0.07RE 0.46 ± 0.27 4.44 ± 2.58 0.47 ± 0.09 0.04 ± 0.02 1.46 ± 0.73 0.82 ± 0.07

t1=2keo: blood effect-site equilibration constant.r: slope parameter of the concentration–response relation.Emax: EEG parameter value corresponding to the maximum drug effect.Emin: EEG parameter value corresponding to the minimum drug effect.EC50: concentration that causes 50% of the maximum effect.R2: maximum coefficients of determination.

686 Z. Liang et al. / Clinical Neurophysiology 123 (2012) 681–688

was used to determine the predictive performance of the derived HEfor sevoflurane effect compartment concentrations.

3. Results

Application of the MODWT method on EEG data analysis isillustrated in Fig. 2. The raw EEG data was decomposed into sevensub-bands using the Daubechies-4 wavelet function. The low fre-quency range of 0.5–12.5 Hz was of principal interest, because thisband is most affected by increasing doses of most inhalation anes-thetics (Jameson and Sloan, 2006).

The details of HE analysis based on the MRRA are shown inFig. 3. The EEG (left) and log(n) versus log(R/S) (right) in awake

Fig. 7. Dose–response curves between the HEOLFB (A) and HEOR (B) and the sevofluranecoefficient of determination (R2) shown in the upper-right part of the figures. The dots are

(A and B), moderate anesthesia (C and D), and deep anesthesia (Eand F) states are illustrated. There are obvious changes in the slopeof HE in sub-bands B4, B5, B6 and in the combination of sub-bandsfrom B4 to B6, as well as of HEOR in different states. The awaketime was chosen at 50 s before LOC, moderate anesthesia at 10 safter LOC, and deep anesthesia at 50 s after LOC. The length foreach EEG epoch was 10 s.

Fig. 4 shows a recording during a complete anesthesia course ina single patient; and HE analysis results based on the MODWT.Fig. 4(A) shows the raw EEG signal during a complete anesthesiacycle. In the awake state (I), the EEG spectral power covers a widefrequency range (0–50 Hz). While in the anesthetized state (II) thelow frequency band dominates and the amplitudes increased. The

effect-site concentration (Ceff) for best fit, median fit and worst fit, with the greatestthe measured Hurst index values. The lines are the PK/PD-modeled entropy values.

Fig. 8. The prediction probability (Pk) value of all patient (n = 19) for B4 to A6 andHEOLFB, HEOR, RE.

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detailed spectrogram is shown in Fig. 4(B), computed by short-time Fourier transform. We used a Hamming window with a lengthof 10 s and 75% overlap. Dark red indicates a high spectral powerand blue a low power. This pattern is typical of that seen duringgeneral anesthesia (Vakkuri, 2000). The index of each multiscalewavelet based sub-band is shown in Fig. 4(C). The various HE indi-ces (B4, B5, B6, HEOR, and HEOLFB) all decreased with increasingsevoflurane concentration, but the HEOLFB showed smaller fluctu-ations in the awake state as compared to the other indices.

Fig. 5 shows the change of the HE calculated from the raw EEG(Fig. 5(A)), integrated sub-bands (Fig. 5(B)), and RE calculated fromraw EEG (Fig. 5(C)) before and after LOC for each of the 19 patients.The actual point of LOC typically occurred just before a rapid de-crease in the HE values. The absolute value of the linear-fittedpolynomials versus time for HEOR, HEOLFB, and RE were 0.16(0.03–0.22), 0.18 (0.03–0.25), and 0.15 (0.04–0.23), respectively,as shown in Fig. 5(D). The HEOLFB index is the most sensitive fordetecting the change in EEG pattern at the time of LOC.

To meet the criteria of a good index of anesthesia depth, the va-lue of the index during induction must exhibit a large change. Abox plot of HEOLFB and HEOR under four states (awake, induction,light and deep anesthesia) is displayed in Fig. 6. The CVs of HEORfor all patients were 0.05 (0.401 ± 0.022, mean ± SD), 0.13(0.323 ± 0.045), 0.09 (0.313 ± 0.029), and 0.07 (0.277 ± 0.021) forawake, induction, light, and deep anesthesia, respectively. TheCVs of HEOLFB were 0.03 (0.385 ± 0.012), 0.13 (0.323 ± 0.042),0.04 (0.321 ± 0.012), and 0.06 (0.285 ± 0.018) for the correspondingstates. The CVs of HEOLFB were smaller than the HEOR in all states.

We used the PK/PD model to compare the performance of thevarious indices in tracking the changes in sevoflurane concentra-tion in the brain. The modeled parameters are listed in Table 1.In this Table, data are expressed as mean ± SD, the value t1=2keo ¼ln2=keo is the estimated effect-site equilibration half-life. The R2

values for HEOLFB, HEOR, and RE were >0.8, with B5 having thehighest value. All HEOLFB parameters were similar to that of HEOR(see Table 1). The sigmoid Emax model was used to analyze the rela-tionship between HEOLFB/HEOR and effect-site sevoflurane con-centration (Ceff). Fig. 7 shows the curve fits for HEOLFB (A), andHEOR (B) in patients with the best, median and worst models.

The prediction probability Pk values for all the patients and allthe indices are shown in Fig. 8. Overall the Pk value for HEOLFB(0.82 (0.72–0.91)) was significantly higher than for the HEOR(0.78 (0.65–0.88), p = 0.0018, paired t-test).

4. Discussion

In this study, a new MODWT-based HE analysis was applied toanesthetic EEG recordings to describe the effect of sevoflurane onthe brain. The new measure is comparable to an existing commer-cial index (the RE) as regards prediction probability around loss ofconsciousness and in PK/PD modeling of drug effect.

A number of advantages of our HE based approach should benoted. The RE is a frequency domain method, based on the Fouriertransformation; while the MODWT-based HE is a time–frequencyanalysis method, which has a better time resolution. As a multi-scale analysis method, the MODWT describes the complexity of atime series over multiple scales. In particular it has the advantagethat the time-shift of the details and approximation series are con-sistent with that of the input signals (Percival and Walden, 2006).The HE based on MODWT is also resistant to EMG artifact. As thecharacteristics of the EEG vary with frequency, the frequency bandselection is important in this study. RE is calculated from the EEGfrequency band 0.8–47 Hz. High frequency EMG activity maytherefore contribute to the RE index, especially in the awake state.In our research, the Hurst calculation focuses on a much lower fre-quency band, 0–12.5 Hz. The impact of EMG should thus beavoided.

The R/S analysis is a nonlinear fractal analysis method. There-fore, the derived HE can reveal the fractal properties of the timeseries. We found Hurst values <0.5 (see Figs. 4 and 6), indicatingan anti-persistent property of the EEG in anesthesia. The resultsare in accordance with the findings obtained in sleep state analysis(Acharya, 2005) and during music stimuli (Natarajan et al., 2004).However, the nonlinear analysis in epilepsy (Culic et al., 2010)showed an opposite trend (0.5 < HE < 1).

Additionally, we found that the HEOLFB had several otheradvantages over HEOR:

(1) As a nonlinear multiscale index, HEOLFB is less sensitive toartifacts during the awake state. This was reflected in thelower value of CV for HEOLFB, as well as the higher correla-tion coefficient for the modeled sevoflurane concentrationand HEOLFB.

(2) The HEOLFB provides a more robust estimation of the exactpoint of LOC. Both HEOLFB and HEOR could distinguishbetween awake and anesthetized states (see Fig. 5). Thereaction time for the transition between the awake state tomoderate anesthesia for HEOLFB is shorter than for HEOR.

(3) The better prediction ability of HEOLFB for all anesthesiastates was also reflected in the significantly higher Pk valuethan HEOR.

(4) The HEOLFB is slightly better correlated to the sevofluraneeffect site concentration (R2) than the other HE indices, ascould be seen in Table 1.

The PK/PD model used in this study employed only onecompartment. In further studies, we may consider two or three-compartment pharmacokinetic models (Jacobs, 2002; Lister andSanders, 1999).

In conclusion, MODWT-based HE analysis can be used to mea-sure the complexity of the anesthetic EEG series and generate animproved index (HEOLFB) for tracking the anesthetic effect ofsevoflurane.

Disclosure

The authors declare no conflict of interest.

Acknowledgments

This research was supported by National Natural Science Foun-dation of China (61025019, 90820016) and Natural Science Foun-dation of Hebei, China. Authors would like to thank editor andreviewers for helpful comments to improve this manuscript.

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