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The effect of isoflurane anesthesia on the electroencephalogram assessed by harmonic

wavelet bicoherence-based indices

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2011 J. Neural Eng. 8 056011

(http://iopscience.iop.org/1741-2552/8/5/056011)

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IOP PUBLISHING JOURNAL OF NEURAL ENGINEERING

J. Neural Eng. 8 (2011) 056011 (15pp) doi:10.1088/1741-2560/8/5/056011

The effect of isoflurane anesthesia on theelectroencephalogram assessed byharmonic wavelet bicoherence-basedindicesDuan Li1, Xiaoli Li2,5, Satoshi Hagihira3 and Jamie W Sleigh4

1 Institute of Information Science and Engineering, Yanshan University, Qinhuangdao 066004,People’s Republic of China2 National Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University,Beijing 100875, People’s Republic of China3 Department of Anesthesiology, Osaka University Graduate School of Medicine, Osaka, Japan4 Department of Anesthesia, Waikato Hospital, Hamilton, New Zealand

E-mail: xiaoli@bnu.edu.cn

Received 12 April 2011Accepted for publication 10 August 2011Published 1 September 2011Online at stacks.iop.org/JNE/8/056011

AbstractBicoherence quantifies the degree of quadratic phase coupling among different frequencycomponents within a signal. Previous studies, using Fourier-based methods of bicoherencecalculation (FBIC), have demonstrated that electroencephalographic bicoherence can berelated to the end-tidal concentration of inhaled anesthetic drugs. However, FBIC methodsrequire excessively long sections of the encephalogram. This problem might be overcome bythe use of wavelet-based methods. In this study, we compare FBIC and a recently developedwavelet bicoherence (WBIC) method as a tool to quantify the effect of isoflurane on theelectroencephalogram. We analyzed a set of previously published electroencephalographicdata, obtained from 29 patients who underwent elective abdominal surgery under isofluranegeneral anesthesia combined with epidural anesthesia. Nine potential indices of theelectroencephalographic anesthetic effect were obtained from the WBIC and FBIC techniques.The relationship between each index and end-tidal concentrations of isoflurane was evaluatedusing correlation coefficients (r), the inter-individual variations (CV) of index values, thecoefficient of determination (R2) of the PKPD models and the prediction probability (PK ). TheWBIC-based indices tracked anesthetic effects better than the traditional FBIC-based ones.The DiagBic_En index (derived from the Shannon entropy of the diagonal bicoherence values)performed best [r = 0.79 (0.66–0.92), CV = 0.08 (0.05–0.12), R2 = 0.80 (0.75–0.85), PK =0.79 (0.75–0.83)]. Short data segments of ∼10–30 s were sufficient to reliably calculate theindices of WBIC. The wavelet-based bicoherence has advantages over the traditionalFourier-based bicoherence in analyzing volatile anesthetic effects on theelectroencephalogram.

(Some figures in this article are in colour only in the electronic version)

5 Author to whom any correspondence should be addressed.

1741-2560/11/056011+15$33.00 1 © 2011 IOP Publishing Ltd Printed in the UK

J. Neural Eng. 8 (2011) 056011 D Li et al

1. Introduction

Bispectral analysis is a technology of the bispectral indexsystem (BIS) anesthesia monitor (Aspect Medical Systems,Newton, MA, USA) (Rampil 1998). It quantifies the degreeof quadratic phase coupling (QPC) among different frequencycomponents of a signal, from which the SynchFastSlowparameter is derived. The SynchFastSlow uses the bispectrum,which is related to both the amplitude of the signal at thatfrequency and the phase coupling. However, its normalizedform, the bicoherence, is independent of the amplitude ofthe signal and therefore can be used as an indicator of thedegree of phase coupling in signals. Bicoherence has beensuccessfully applied to evaluate nonlinear interactions in avariety of electroencephalographic studies (He and Thomson2009, Muthuswamy et al 1999, Ning and Bronzino 1989,Schack et al 2001, Shils et al 1996), including the effect ofanesthetic drugs on the electroencephalogram (e.g. Hagihiraet al 2002, 2004, Hayashi et al 2008, 2007, Johansen and Sebel2000, Morimoto et al 2006, Sigl and Chamoun 1994).

In early research, Sigl and Chamoun ( 1994) described thechanges of electroencephalographic bicoherence in the periodbetween induction and incision using isoflurane anesthesia.They used a Fourier-based method of calculation. Recently,the electroencephalographic bicoherence spectrum has beenfound to be related to the concentration of anesthetic drugs.Specifically, the bicoherence values in the α (at around10 Hz) and δ–θ (at around 4 Hz) bands along the diagonalline of the bicoherence matrix were found to correlate wellwith the concentrations of isoflurane or sevoflurane (Hagihiraet al 2002, Morimoto et al 2006). Hayashi et al (2008) foundthat sevoflurane caused bicoherence peaks in the α and δ–θ

bands along the diagonal line, as well as the third peak at thepair of α basal frequency and its doubled frequency, and thatdeeper anesthesia shifted all peaks to lower frequencies andcaused increased bicoherence in the δ–θ region. All thesefindings indicated that the bicoherence is a potential tool inthe estimation of the effects of anesthetic drugs on the brain(Hagihira et al 2002, Hayashi et al 2008).

However, an index that purely reflects anesthetic-drug related changes of the electroencephalogram may behard to apply in the real clinical world. First, theelectroencephalographic bicoherence pattern was only studiedunder a narrow range of drug concentrations (Hagihiraet al 2002, Hayashi et al 2008, Morimoto et al 2006).The analysis of the awake electroencephalogram was notconsidered, so a measure based on the bicoherence may notcomprehensively capture all the changes from wakefulnessto anesthesia. Second, in order to obtain a consistent andreliable estimate of the Fourier bicoherence, at least 3 minof electroencephalographic data are required (Hagihira et al2002). This makes for an unacceptably slow response time.Therefore, traditional Fourier-based methods of calculatingBIS-like bicoherence are not well suited for the real-timeapplication of monitoring of the electroencephalogram underanesthesia (Pilge et al 2006, Zanner et al 2009).

Due to its more precise localization in both time andfrequency, the wavelet transform provides an appealing

alternative approach to calculate the bicoherence inelectroencephalographic signals. It has previously beenused to quantify the effects of anesthetic drugs on theelectroencephalogram or auditory evoked potentials (Hornet al 2009, Zikov et al 2006). Using shorter data segments, thewavelet transform can extract information more accuratelythan Fourier methods (Chung and Powers 1998, Larsenet al 2001, van Milligen et al 1995, Young and Eggermont2009, Olkkonen 2010). We have previously developed animproved wavelet bicoherence (WBIC) method (Li et al2009) based on the general harmonic wavelet transform(GHWT) (Newland 1993, Simonovski and Boltezar 2003),which can overcome the drawbacks of the frequently-usedMorlet wavelet that needs a relatively complex algorithmand some arbitrary parameter choices in its implementation.The improved WBIC method exploits a phase randomizationmethod to eliminate spurious information in the bicoherence,thus giving a reliable estimate for the cross-frequencyinteractions in neuronal populations. In the original study(Li et al 2009), this method was applied to the analysis ofslow-wave to rapid-eye-movement sleep transitions. In thisstudy, we have analyzed changes in the electroencephalogramduring isoflurane anesthesia, comparing the effectiveness ofvarious putative indices derived from the GHWT-based WBICand traditional Fourier bicoherence (FBIC).

2. Materials and methods

Protocol and data recordings

In this study, we re-analyzed electroencephalographic datafrom a previously reported study (Hagihira et al 2002). Thedata were obtained from 29 patients (nine men and 20 women,aged 34–77 years, American Society of Anesthesiologistphysical status I–II) who underwent elective abdominalsurgery under isoflurane general anesthesia combined withepidural anesthesia, after obtaining institutional approval(Osaka Prefectural Habikino Hospital, Osaka, Japan) andwritten informed consent from all participants. None ofthese participants had any neurologic or psychiatric disorders,nor were they receiving medication with any drugs known toinfluence anesthetic or analgesic effects.

Thirty minutes before the admission to the operatingroom, each patient received intramuscular premedicationwith 0.5 mg atropine. An epidural catheter was placedat the appropriate spinal location (T7/8, T8/9, T9/10 orT10/11). After confirming the effect of epidural analgesia,which was administered to minimize the influence of surgicalstress on electroencephalogram during surgery, anesthesiawas induced with 3 mg kg−1 thiopental. After trachealintubation, anesthesia was maintained with isoflurane, oxygenand nitrogen. Vecuronium was given as required. Lidocaine1% (80–110 mg h−1, initial dose 90–100 mg) was epidurallyadministered. Patients received controlled ventilation tomaintain adequate oxygenation and normocapnia. To keepthe mean blood pressure at 60 mmHg, as required, 2–5 μgkg−1 min−1 dopamine was administered.

Five electroencephalographic electrodes (A1, A2, FP1,FP2 and FPz; according to the International 10-20 System)

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were attached to the patients before induction of anesthesia.FPz was used as body ground. Electroencephalographic datawere collected from a single lead FP1–A1 using a 514X-2 electroencephalogram telemetry system (GE Marquette,Tokyo, Japan). Electroencephalographic signals in thewaking state were obtained before the induction of anesthesia.Isoflurane was initially increased to 1.5% and then steppeddown to 0.7%. To achieve a steady state, the end-tidalconcentration of isoflurane was purposely maintained at setlevels (1.5%, 1.3%, 1.1%, 0.9% and 0.7%) for 30 min,and then changed to another concentration. The expiredconcentration of isoflurane was continuously monitoredusing Capnomac (Datex, Helsinki, Finland) and recordedsimultaneously. This device was calibrated by means of thecalibration gas that was provided by the manufacturer everymonth. The electroencephalographic segments with the ‘burst-suppression’ pattern present were excluded from our analysis.

The electroencephalographic data were sampled at 512 Hzand down-sampled at 128 Hz by running resample.m in Matlab(Mathworks). Then, the raw electroencephalographic datawere preprocessed by the following steps: data points wererejected if the absolute amplitude values exceeded a threshold,which was selected as the mean plus c (normally five to seven)times the standard deviation of the data analyzed; a notch filterwas used to remove the power signal of 50 Hz; the stationarywavelet transform (mother wavelet: Daubechies-4, level ofdecomposition: 7) was applied to the electroencephalographicsignals and the wavelet coefficients below 0.5 Hz were reducedto 0, so as to remove the effect of baseline drift (Li et al 2010,2008).

Fourier bicoherence

The Fourier bicoherence (FBIC) used in this study wasimplemented by running bicoher.m in the higher order spectralanalysis (HOSA) toolbox (Swami et al 2000). In computingthe FBIC, the electroencephalographic signal was first dividedinto a series of epochs, and multiple epochs were examinedto analyze the phase coupling. The parameter setting usedin the BIS monitor was adopted in this study: epoch lengthof 2 s with an overlap of 75% (Hagihira et al 2001, Rampil1998). The bicoherence values were computed in all pairs offrequencies between 0.5 and 30 Hz at 0.5 Hz intervals from120 epochs of signals (61.5 s). The details of the computationof FBIC are shown in appendix A.

GHWT-based WBIC

The algorithm of the GHWT-based WBIC (Li et al 2009)can be found in appendix B. To obtain a reliable bicoherenceestimate, a segment-averaging approach (Hagihira et al 2001)was utilized for the WBIC as well. Signals were divided into aseries of 2 s epochs, with an overlap of 75%, identical to thoseused in the FBIC case. For each epoch, bicoherence valueswere computed in all pairs of frequencies from 1 to 30 Hz,with a step of 1 Hz and a bandwidth of 2 Hz. The selectionof the number of epochs is very important to derive reliablebicoherence estimation, and 120 epochs were used to computethe WBIC in order to be consistent with the FBIC.

Characteristics of the bicoherence matrix

To quantify the electroencephalographic signal underanesthesia, we first obtained the FBIC and the GHWT-basedWBIC matrix, b. Each element, b(fp, fq), denotes thebicoherence value at frequency pair (fp, fq), with f L �fp, fq � f H . We chose f L = 1 Hz and f H = 30 Hz in thisstudy. The next step is an attempt to capture the most usefulinformation in the matrix. There are a number of differentpossible approaches to the problem of constructing a measurethat can optimally extract information from the bicoherencematrix.

Initially, we looked at the bicoherence matrix as a wholeto derive three indices.

(i) The total amount of bicoherence in the signal (denoted asTotalBic) between the frequency bands indicated belowby [f L, f H ] is defined as (van Milligen et al 1995)

T otalBic =∑f H

fp=f L

∑f H

fq=f Lb2(fp, fq), (1)

where the summation is extended over all frequencies offp and fq .

(ii) Because the bicoherence matrix is a symmetrical matrixabout the main diagonal line (fp = fq), we can considerthe eigenvalue decomposition of b:

bvi = λivi, (2)

where λi is the eigenvalue (λ1 � λ2 � · · · � λM ) andM the number of frequencies from f L to f H ; vi is theeigenvector corresponding to λi . The eigenvalues provideinformation about the cross-frequency synchronization ofthe signal. Two indices are considered:

(a) the maximal eigenvalue (denoted as maxEigen) (Liet al 2007, 2009) and

(b) the S-estimator (denoted as SI). This is the Shannonentropy of the eigenvalue distribution (Cui et al 2010,Dauwels et al 2010), which is defined as follows:

SI = −∑M

i=1 λi log(λi)

log(M), (3)

where λi = |λi |/∑M

j=1 |λj | is the normalizedabsolute eigenvalue. These two indices, maxEigenand SI, can be regarded as global phase couplingindices for the whole bicoherence matrix.

Second, we consider a subset of the bicoherence valuesalong the diagonal line of fp = fq (denoted as DiagBic) inthe bicoherence matrix. We did this because a significantchange in pattern with changing drug concentrations ofsevoflurane or isoflurane has previously been demonstrated—using Fourier-based bicoherence methods (Hagihira et al 2002,Hayashi et al 2008, Morimoto et al 2006). We define therelative power at 2–6 Hz and 7–13 Hz as DiagBic_Rlowand DiagBic_Rhigh, respectively, and the frequency at7–13 Hz with the maximum bicoherence value as the peakfrequency, denoted as DiagBic_PeakF. The Shannon entropycan be applied to quantify the flatness of the distributionof phase coupling along the diagonal line, similar to thespectral entropy applied in the Spectral Entropy (M-entropy

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module, GE Healthcare, Helsinki, Finland) monitor (Viertio-Oja et al 2004). The normalized form of DiagBic, denoted asnDiagBic, is first derived and the normalized entropy (denotedas DiagBic_En) can be calculated as

DiagBic En = − 1

log(M)

∑f H

f =f LnDiagBic(f )

× log(nDiagBic(f )), (4)

where M is the number of frequency components along thediagonal line of the bicoherence matrix. The values ofDiagBic_En are between 0 and 1.

Finally, a feature that can be derived from the bicoherencematrix is the summed bicoherence (denoted as SumBic) (vanMilligen et al 1995), which is defined as

SumBic(f ) =∑

b2(fp, fq), (5)

where the summation is over all frequencies fp and fq suchthat f = fp ±fq is satisfied. The summed bicoherence can beused to measure the distribution of phase coupling as a functionof frequency f . To further compress this information into aunitary quantity, Shannon entropy is applied to the normalizedform of the SumBic, and the index SumBic_En is defined(similar to equation (4)) to quantify the flatness of distributionof phase coupling in the SumBic. We also investigateda parameter denoted as SumBic_SFS which quantifies therelative phase coupling in the 40–47 Hz frequency band. Thisis analogous to SynchFastSlow, which is used in the BISmonitor (Miller et al 2004, Rampil 1998). The new measureis defined as

SumBic SFS = log

(∑47f =40 SumBic(f )∑47f =2 SumBic(f )

). (6)

Thus, a total of nine indices were derived from the WBICand FBIC of electroencephalographic signals, respectively:TotalBic, maxEigen, SI, DiagBic_Rlow, DiagBic_Rhigh,DiagBic_PeakF, DiagBic_En, SumBic_En and SumBic_SFS.

Pharmacokinetic–pharmacodynamic modeling

Pharmacokinetic–pharmacodynamic (PKPD) modeling wasperformed to derive the relationship between anesthetic drugconcentration and measured electroencephalographic index(McKay et al 2006). Briefly, an effect site was introducedby the first-order effect-site model

dCeff/dt = keo(Cet − Ceff), (7)

where Ceff is the effect-site concentration, Cet is the end-tidalconcentration and keo is the first-order rate constant for effluxfrom effect compartment. The relation between the estimatedCeff and the measured electroencephalographic index wasmodeled with a nonlinear inhibitory sigmoid Emax model

Eff ect = Emax − (Emax − Emin) × Cγ

eff

ECγ

50 + Cγ

eff

, (8)

where Effect is the processed electroencephalographicmeasure, Emax and Emin are the maximum and minimumEffect for each individual subject, EC50 is the isofluraneconcentration at which Effect is midway between this

maximum and minimum and γ is the slope of theconcentration–response relationship. Ceff was estimated byiteratively running the above model with a series of keo

steps. The optimal keo was determined yielding the greatestcoefficient of determination (R2) between the measured andmodeled electroencephalographic Effect for each subject. Thecoefficient of determination R2 is calculated by

R2 = 1 −∑n

i=1 (yi − yi )2∑n

i=1 (yi − y)2, (9)

where yi and yi are the measured and corresponding modeledEffect for a given time, and y is the average of themeasurements over time. Values of PD parameters γ andEC50 can be derived from the fitted inhibitory Emax curve.The performance of each electroencephalographic index wasassessed by the goodness-of-fit, as estimated by the coefficientof determination (R2) of the model.

Prediction probability

The association between the derived electroencephalographicmeasures and the underlying anesthetic drug effect-siteconcentration Ceff was assessed by the prediction probability(PK ) (Ellerkmann et al 2004, Ihmsen et al 2008, Smithet al 1996, Vanluchene et al 2004). PK was calculatedfor each subject, with the isoflurane effect-site concentrationas an independent variable, and the electroencephalographicmeasure as a dependent variable. For positive correlation, aPK value of 1 means that the electroencephalographic indexis perfectly concordant with the underlying anesthetic depthCeff . A PK value of 0.5 means that the electroencephalographicindex is not superior to that obtained by chance. The resultantPK value is replaced by 1−PK , when a negative correlationappears between the isoflurane concentration and the measuredelectroencephalographic index.

Statistical analysis

For each patient, we obtained a measure of the performanceof the WBIC- and FBIC-based indices with respect to thefollowing.

(1) The correlation (r) with isoflurane end-tidal concentra-tions (before induction of anesthesia and 0.7%, 0.9%,1.1%, 1.3% and 1.5%). For each subject, the Spear-man rank correlation coefficient was used to quantifythe strength of the relationship between various WBIC-and FBIC-derived electroencephalographic indices withisoflurane end-tidal concentrations.

(2) The inter-individual variations of these indices. For allthe study periods, the inter-individual variations wereassessed using the relative coefficient of variation (CV)(ratio of the standard deviation to the mean) of theseindices for all the subjects.

(3) The coefficient of determination (R2) from the PKPDmodeling. For each subject, R2 indicated the extent thatthe changes in the WBIC- and FBIC-based indices couldbe explained by changes in the effect-site concentrationsof isoflurane—as estimated from PKPD modeling.

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(4) The prediction probability (PK ). For each subject, PK

quantified the ability of the WBIC- and FBIC-basedindices to predict the underlying anesthetic depth, asestimated by the effect-site concentrations of isofluranederived from PKPD modeling.

Data were exported to SPSS (Version 13.0, SPSS Inc.,Chicago, IL) for statistical analysis. After applying theKolmogorov–Smirnov test to determine whether the measurer was normally distributed, the WBIC-based indices andcorresponding FBIC-based ones were compared using apairwise t-test. One-way repeated-measures ANOVA withBonferroni post hoc was used to compare the performanceof the nine WBIC-derived indices in r, R2 and PK . Ifthe assumption of homogeneity of covariance was violatedby Mauchly’s test of sphericity, the Greenhouse–Geissercorrection method was used. One-way normal ANOVA withBonferroni post hoc was used to compare the performanceof the nine WBIC-derived indices in CV. The Levene testwas used in advance to check whether the variances werehomogeneous across multiple groups. Additionally, we lookedat the number of epochs required to give a stable computationof the WBIC. The mean and variance values of indices usingdata from 20 to 120 epochs were compared using a pairwise t-test and an F-test, respectively. For all tests, p < 0.05 wasconsidered significant. Data are presented as mean (95%confidence interval), unless specially stated.

3. Results

Figure 1(A) shows typical electroencephalographic signalsbefore induction of anesthesia, and at different isofluraneconcentrations. The contour plots of corresponding FBIC andWBIC are shown in figures 1(B) and (C). Figures 1(D) and (E)show the summed bicoherence (SumBic) and the bicoherencealong the diagonal line (DiagBic) for both the FBIC andWBIC cases. As can be seen from the figures, the bicoherencepatterns change with changing isoflurane concentrations, andthe changes are more distinct in the WBIC than in the FBIC.From figure 1(C), it is obvious that the WBIC topographiesbefore and after the induction of anesthesia are different. Inthe awake state, higher frequency band (20–30 Hz) phasecoupling is relatively strong. As the isoflurane concentrationincreases, the bicoherence values become concentrated inlower frequencies. These changes can be clearly seen inthe WBIC-based SumBic in figure 1(D) and the WBIC-basedDiagBic in figure 1(E).

The mean (SD) values of the indices at each studyperiod (before induction of anesthesia and at isofluraneconcentrations of 0.7%, 0.9%, 1.1%, 1.3% and 1.5%) arepresented in figure 2. A useful property of any index isthat it should change monotonically with increasing end-tidalconcentration of isoflurane. In this respect, the WBIC-derivedindices performed better than the corresponding FBIC-derivedindices in differentiating different drug concentrations. Theexceptions were maxEigen and DiagBic_Rhigh. These twoindices consistently decreased when isoflurane concentrationincreases from 0.7% to 1.5%, while failing to correctlyquantify the awake states.

Figure 3 shows that the correlations between the isofluraneconcentrations and the WBIC-derived indices were larger thanthose of the corresponding FBIC indices, except TotalBicand maxEigen. However, the two indices failed to correctlyclassify the electroencephalographic signals at awake or atisoflurane concentration of 1.5%, as can be seen in figures 2(A)and (B). One subject was excluded, because artifact-free EEGsignals were available for only one of the six study periods,and thus the correlation analysis made no sense. These resultsindicate the superiority of the WBIC over traditional FBICin distinguishing different isoflurane end-tidal concentrations.Therefore, we concentrate on the WBIC-based indices, andevaluate the performance of these indices in the followingsections.

The multiple comparison of r values for the nineWBIC-derived indices revealed significant differences (one-way repeated-measures ANOVA with Greenhouse–Geissercorrection, F(2.705, 216) = 6.38, p < 0.001). Post hoc analysisshowed that r values in maxEigen were significantly lower thanthose in all the other indices, except in DiagBic_Rhigh (p =0.358 > 0.05). Multiple comparisons of r values for the nineFBIC-derived indices showed no significant differences (one-way repeated-measures ANOVA with Greenhouse–Geissercorrection, F(2.753, 216) = 1.071, p = 0.363 > 0.05).

Figure 4 shows the relative coefficients of variation (CV)of the measured WBIC-derived indices among subjects, at allthe six study periods, for each index. Multiple comparisonof CV values for the nine WBIC-based indices revealedsignificant differences (one-way ANOVA, F(8, 45) = 17.247,p < 0.001). Post hoc analysis showed that the CV values in SI,DiagBic_PeakF, DiagBic_En, SumBic_En and SumBic_SFSwere significantly lower than those in TotalBic, DiagBic_Rlowand DiagBic_Rhigh, and also the CV values in SumBic_Enwere significantly lower than those in maxEigen.

Then, we applied the nine WBIC-derived electroence-phalographic measures to the entire electroencephalographicrecordings under isoflurane general anesthesia combined withepidural anesthesia. In figure 5, we have plotted an exampleof the time course of isoflurane end-tidal concentration, andcorresponding WBIC-based electroencephalographic indicesfor the same subject as in figure 1. All the nine indices trackedthe gross changes in electroencephalogram with changingisoflurane concentrations to some degree. Of note, the plotof DiagBic_PeakF showed large fluctuations at isofluraneend-tidal concentrations of 0.9% and 0.7%; the maxEigenindex increased when the isoflurane end-tidal concentrationdecreased from 1.5% to 0.9%, but decreased paradoxicallyat isoflurane end-tidal concentration 0.7%; the plots ofDiagBic_En, SumBic_En, and SumBic_SFS seemed smootherthan others.

To minimize the influence of thiopental, we collected thedata 10 min after the isoflurane for the PKPD modeling.We were able to obtain a PKPD model for all the nineindices in 17 of 29 subjects. No fit was possible in otherpatients because the range of isoflurane concentrations wastoo restricted. The modeled parameters yielding the greatestcoefficients of determination are listed in table 1. Plotting theisoflurane effect-site concentration (Ceff) against the measured

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(A) (B) (C) (D) (E)

Figure 1. Typical bicoherence patterns from a sample electroencephalogram in a 49-year-old man undergoing pancreatoduodenectomy withisoflurane anesthesia combined with epidural anesthesia. (A) Raw signal epochs, representative of electroencephalogram recorded during1 min with no isoflurane (awake) and with increasing isoflurane concentrations of 0.7%, 0.9%, 1.1%, 1.3% and 1.5%. (B) CorrespondingFBIC matrix values. (C) Corresponding GHWT-based WBIC matrix values. (D) The summed bicoherence (SumBic) for WBIC and FBIC.(E) The bicoherence along the diagonal line (DiagBic) for WBIC and FBIC.

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(A) (B) (C)

(D) (E) (F)

(G) (H) (I)

Figure 2. The indices derived from the WBIC and FBIC for all the 29 subjects, at different study periods: steady state with no drug (0) andisoflurane end-tidal concentrations of 0.7%, 0.9%, 1.1%, 1.3% and 1.5%: (A) TotalBic, (B) maxEigen, (C) SI, (D) DiagBic_Rlow, (E)DiagBic_Rhigh, (F) DiagBic_PeakF, (G) DiagBic_En, (H) SumBic_En and (I) SumBic_SFS. The values are given in the form of mean ± SD.

electroencephalographic indices showed the necessity of usingthe sigmoid Emax model, and figure 6 shows an example ofthe fit for the same subject in figure 5. The R2 values foreach index are shown in figure 7(A). Multiple comparisonof R2 values for the nine WBIC-derived indices revealedsignificant differences (one-way repeated-measures ANOVAwith Greenhouse–Geisser correction, F(2.355, 128) = 82.02,p < 0.001). Post hoc analysis showed that the R2 valuesof 0.80(0.75–0.85) in DiagBic_En and 0.80(0.75–0.85) inTotalBic were significantly higher than those in all the otherindices, and the DiagBic_PeakF presented the lowest R2 valuesamong all the indices (p < 0.001), and then followed theDiagBic_Rhigh index, which was significantly lower thanother indices except maxEigen and DiagBic_Rlow.

The PK values for each index are shown in figure 7(B).Multiple comparison of PK values for the nine WBIC-derivedindices revealed significant differences (one-way repeated-measures ANOVA, F(8, 128) = 12.66, p < 0.001). Posthoc analysis showed that the PK values of 0.81(0.78–0.84) inTotalBic were significantly higher than those in maxEigen, SI,DiagBic_Rhigh, DiagBic_PeakF and DiagBic_PeakF; the PK

values of 0.79(0.75–0.83) in DiagBic_En were significantlyhigher than those in maxEigen and DiagBic_PeakF; andDiagBic_PF presented the lowest PK values among all theother indices, except SumBic_SFS.

Figure 8 demonstrates how varying the number ofepochs used for analysis affects the WBIC-based indicesSI, DiagBic_En and SumBic_En. For this example, weused pooled electroencephalographic data from all subjectsat isoflurane end-tidal concentration of 1.1%. The mean andvariance of index values (when using 10-, 20-, 30-, 40-, 60-,and 90-epoch data) are compared to those using 120-epochdata. For the SumBic_En index, only the variance valueswith 10-epoch data were significantly higher than those with120-epoch data (F-test, N = 364, p < 0.05), and the meanvalues showed no difference (pairwise t-test, N = 364, p =0.618 > 0.05). We can conclude that 20-epoch (=∼10 s)data can be used to achieve comparative performance with120-epoch data. For the DiagBic_En index, at least 60-epoch(=∼30 s) data were required to obtain comparative mean andvariance with 120-epoch data. As regarding the SI index, themean value significantly decreased with increasing numbers

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Figure 3. Correlation coefficients (Spearman rank r) between the WBIC- (bold bar) and FBIC-derived indices (hollow bar) and theend-tidal isoflurane concentrations. The values are given in the form of absolute mean ± SEM. The notations ∗∗ and ∗ indicate a significantdifference in the WBIC-derived index compared with the corresponding FBIC one through a pairwise t-test (N = 28) at p < 0.01 and p <0.05, respectively.

Figure 4. CV of the measured WBIC-based indices among all subjects, at the six study periods: steady-state with no drug (0) and isofluraneend-tidal concentrations of 0.7%, 0.9%, 1.1%, 1.3% and 1.5%, for each of the WBIC-derived indices.

of epochs (p < 0.001). It is likely that the use of largenumbers of epochs results in less noise in the bicoherenceestimation, thus obtaining a more robust distribution of theabsolute eigenvalues, which in turn leads to a lower SIvalue. Analysis with the other six WBIC-based indicesgenerated similar results with the indices DiagBic_En orSumBic_En.

4. Discussion

We investigated several indices that might be used to quantifythe electroencephalogram under isoflurane anesthesia. The

correlation analysis of the electroencephalographic indiceswith the isoflurane end-tidal concentrations suggested thatthe WBIC-based indices performed significantly better thanthe traditional FBIC-based ones. The new proposed WBIC-based indices were then compared by estimating the inter-individual variation of each index, and their ability to track thedynamical changes in real electroencephalographic recordingsunder isoflurane general anesthesia (using PKPD modelingand PK ). The highest correlation coefficient and lowest CVwere found in the DiagBic_En index; although the highest R2

and PK were found with the TotalBic index, the values for theDiagBic_En index were not much less, making it the overallwinner.

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Figure 5. An example of the WBIC-derived indices over the entire electroencephalographic recording for the same patient as in figure 1.(A) The isoflurane end-tidal concentration and (B) corresponding WBIC-derived indices during the same time course. 120 epochs (60.15 s)were selected to compute the electroencephalographic indices because the synchronous information of isoflurane end-tidal concentration isgiven only at every minute. It should be noted that anesthesia was induced with thiopental at the second minute, and isoflurane entered attenth minute.

Consideration of methodology

Qualitatively, the contour plots in figures 1(B) and (C) showthat both the FBIC and WBIC demonstrated distinct patternsat different anesthetic levels. Although the WBIC showedless detail—due to its coarser frequency resolution (2 Hz

bandwidth in steps of 1 Hz in the WBIC, compared to aresolution of 0.5 Hz in the FBIC)—the overall features weresimilar to the FBIC. Further, the noise level in the WBICwas much lower than in the FBIC. We note that the FBICwas implemented traditionally (Hagihira et al 2002) withno additional processing, while in the GHWT-based WBIC

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(A) (B)

(C) (D)

Figure 6. An example of PKPD modeling (for the same patient as in figure 1): (A) Total, (B) SI, (C) DiagBic_En and (D) SumBic_En.

Table 1. Parameters of the PKPD models.

Parameters keo (min) γ Emax Emin EC50

TotalBic 0.21 ± 0.15 8.42 ± 6.30 6.63 ± 0.91 2.91 ± 0.81 0.91 ± 0.20MaxEigen 0.25 ± 0.21 23.23 ± 14.81 0.37 ± 0.03 0.27 ± 0.04 0.99 ± 0.20SI 0.24 ± 0.29 15.04 ± 18.05 0.61 ± 0.08 0.41 ± 0.04 0.72 ± 0.19DiagBic_Rlow 0.14 ± 0.10 11.19 ± 8.45 −1.27 ± 0.50 −0.51 ± 0.20 0.74 ± 0.19DiagBic_Rhigh 0.22 ± 0.20 25.29 ± 21.16 −1.00 ± 0.20 −1.96 ± 0.51 1.02 ± 0.16DiagBic_PeakF 0.17 ± 0.17 16.22 ± 20.86 12.95 ± 13.50 6.79 ± 0.81 0.87 ± 0.28DiagBic_En 0.21 ± 0.18 9.26 ± 14.05 0.85 ± 0.08 0.59 ± 0.09 0.82 ± 0.22SumBic_En 0.25 ± 0.27 13.18 ± 13.44 0.88 ± 0.10 0.69 ± 0.09 0.72 ± 0.20SumBic_SFS 0.13 ± 0.08 18.97 ± 19.65 −3.56 ± 1.31 −7.22 ± 1.10 0.75 ± 0.25

keo = first-order rate constant for efflux from effect compartment;γ = slope parameter of the concentration–response relation;Emax = electroencephalographic parameter value corresponding to the maximum drug effect;Emin = electroencephalographic parameter value corresponding to the minimum drug effect;EC50 = concentration that causes 50% of the maximum effect;TotalBic = total bicoherence of the WBIC matrix at 1–30 Hz;MaxEigen = maximum eigenvalues of the WBIC matrix based on eigenvalue decomposition;SI = S-estimator that quantifies the distributions of the eigenvalues of the WBIC matrix;DiagBic_Rlow = relative power at 2–6 Hz of WBIC along the diagonal line;DiagBic_Rhigh = relative power at 7–13 Hz of WBIC along the diagonal line;DiagBic_PeakF = peak frequency at 7–13 Hz with maximum value of WBIC along the diagonal line;DiagBic_En = Shannon entropy of WBIC along the diagonal line;SumBic_En = Shannon entropy of the summed WBIC;SumBic_SFS = relative phase coupling in the 40–47 Hz of the summed WBIC.

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(A)

(B)

Figure 7. Coefficient of determination (R2) values (A) and prediction probability (PK ) values (B) of the nine WBIC-derived indices (n =17). The values are given in the form of mean ± SEM.

Figure 8. WBIC values of SI, DiagBic_En and SumBic_En during isoflurane anesthesia (1.1%) with varying number of epochs. The valuesare given in the form of mean ± SD. The notations ∗∗∗ and ∗ indicate a significant difference in mean values compared with those with120-epoch data through a pairwise t-test at p < 0.001 and p < 0.05, respectively, and +++ and + indicate a significant difference in variancevalues compared to those with 120-epoch data through the F-test at p < 0.001 and p < 0.05, respectively.

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method, three improved strategies for post-processing wereimposed to ensure reliable and robust bicoherence values (Liet al 2009); for details see appendix B.

One of the practical issues in the WBIC analysis isthe selection of the number of data epochs that will allowreliable bicoherence estimation. The commercial BIS monitorcalculates the FBIC from 120 epochs (61.5 s) with an epochlength of 2 s and an overlap of 75% (Rampil 1998). However,this is still too short for reliable estimation of the bicoherencestatistic. Hagihira et al (2002) suggested that at least 360epochs (∼3 min) of data are required to calculate reliablebicoherence values. However, such a time delay is too long ina practical clinical setting—which requires a faster responseto closely track the changes in electroencephalogram underanesthesia (Pilge et al 2006, Zanner et al 2009). For theGHWT-based WBIC method, a reliable estimation of theDiagBic_En and SumBic_En indices can be achieved fromrelatively short (10–30 s) segments of data (figure 8), which isa valuable property in the possible future clinical monitoringof the depth of anesthesia.

Feature extraction based on the bicoherence

We looked at nine features of the bicoherence matrix:TotalBic, maxEigen, SI, DiagBic_Rlow, DiagBic_Rhigh,DiagBic_PeakF, DiagBic_En, SumBic_En and SumBic_SFS.The TotalBic index quantifies the total bicoherence at thefrequency band of 1–30 Hz. It correlated well withisoflurane end-tidal concentrations (figure 3) and effect-siteconcentrations (figure 7), but problematically had significantlylarger inter-individual variations (figure 4). This may bedue to the lack of appropriate normalization. The indicesmaxEigen and SI were based on the eigenvalue decompositionof the bicoherence matrix. The former calculates the maximaleigenvalue, and the latter quantifies the overall distribution ofall eigenvalues. For both indices, the inter-individual variationwas low (figure 4). However, the maxEigen index correlatedworst with the isoflurane end-tidal concentrations (figure 3).

The four indices DiagBic_Rlow, DiagBic_Rhigh,DiagBic_PeakF and DiagBic_En were derived from thebicoherence values along the diagonal line. Previous researchin changes of FBIC-based bicoherence during anesthesia hasfocused on the diagonal line (Hagihira et al 2002, Hayashiet al 2008, Morimoto et al 2006). Monotonic decreases withincreasing isoflurane end-tidal concentrations were found inthe peak frequency at α frequency band along the diagonalline (Hagihira et al 2002, Morimoto et al 2006). Similarpattern changes were found in the DiagBic_PeakF indicesbased on the FBIC, as well as on the WBIC, as can be seen infigure 2. However, the WBIC-based DiagBic_PeakF index isnot a reliable measure, because it showed large fluctuationswhen applied to the entire electroencephalographic recording(figure 5), and it performed worst in coefficient ofdetermination (R2) and prediction probability (PK ) (figure 7).

To be reliable, DiagBic_Rlow and DiagBic_Rhigh weredefined as the relative power at 2–6 Hz (θ band) and7–13 Hz (α band), respectively, instead of the single peakheight of bicoherence (Hagihira et al 2002, Hayashi et al 2008,

Morimoto et al 2006). As in previous research (Hagihiraet al 2002, Morimoto et al 2006), no obvious monotonicchanges with increasing isoflurane end-tidal concentrationswere present with the FBIC-based indices. However, thiswas not the case with the WBIC-based DiagBic_Rlow andDiagBic_Rhigh indices. The DiagBic_Rlow index correlatedwell with isoflurane end-tidal (figure 3) and effect-siteconcentrations (figure 7). The DiagBic_Rhigh index is nota good measure, because it could not correctly quantify theawake electroencephalogram (figure 2(E)), and gave lower rvalues (figure 3), as well as significantly larger inter-individualvariations (figure 4).

The DiagBic_En index was the best measure. It not onlycorrelated well with the isoflurane end-tidal concentrations(figure 3) and the effect-site concentrations (figure 7), but alsohad significantly lower inter-individual variations (figure 4).With increasing isoflurane concentration, the distribution ofdiagonal bicoherence values (DiagBic) moved toward lowerfrequencies, and a more narrow distribution (figure 1(E)). TheDiagBic_En index quantifying this distribution could reliablydescribe the change of bicoherence patterns.

Based on SumBic, two indices SumBic_En andSumBic_SFS were proposed. SumBic measures thedistribution of phase coupling along the frequency axis, and italso moved toward lower frequencies, and became narrower,as the isoflurane concentration increases (figure 1(D)). Aswith the DiagBic_En index, the SumBic_En index quantifiesthis distribution based on Shannon entropy. It performedcomparatively well compared to the DiagBic_En index. TheSumBic_SFS index concentrates on the relative phase couplingin 40–47 Hz, which correlated well with the isoflurane end-tidal concentrations (figure 3), but not with the effect-siteconcentrations (figure 7(B)).

The limitations of methods and future work

There are a number of provisos to our results. First, the WBICanalysis of the electroencephalographic ‘burst-suppression’pattern was not investigated in this study, although this patternwas found in the electroencephalographic recordings at 1.3%isoflurane for five patients and at 1.5% for one other. Theepisodic nature of burst-suppression patterns is likely to bewell suited to WBIC analysis, but is the subject of a futurestudy. In the current study, we prefer a similar strategy tothat found in the BIS monitor (Rampil 1998) to correctlyquantify this electroencephalographic pattern, which is tocombine the WBIC index with another measure, such as burst-suppression ratio. Second, the GHWT-based WBIC measurescould not be directly used in real-time monitoring system,due to the implementation involving the employment of thetime-consuming surrogate technique to improve performance.A solution may be to run the WBIC analysis on the graphicsprocessing unit. Spectral entropy based on ensemble empiricalmode decomposition of the electroencephalographic data hasbeen proposed to estimate the depth of anesthesia in a real-timemanner (Chen et al 2010).

In conclusion, the GHWT-based WBIC can be utilizedto indicate the dynamical changes of electroencephalographicsignals under isoflurane anesthesia.

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Figure A1. The algorithm of the WBIC based on the GHWT.

Acknowledgments

This research was partly supported by the National NaturalScience Foundation of China (61025019, 90820016) andNatural Science Foundation of Hebei China (F2009001638).

Appendix

A.1. Fourier bicoherence

To estimate the bicoherence based on the Fourier transform,the data x(t) are segmented into overlapping epochs. For the

kth epoch xk(t), the mean is removed, a Blackman window isapplied, the Fourier transform is computed and its bispectrumis estimated as

BFk (fp, fq) = Xk(fp)Xk(fq)X

∗k (fp + fq), (A.1)

where Xk(·) are the FFT of xk(t) and ∗ denotes the conjugateoperation. The spectrum is computed as Pk(·) = |Xk(·)|2. Thebispectral and spectral estimates are smoothed across multipleepochs, and the bicoherence is then estimated as

bF (fp, fq) = |BF (fp, fq)|2P(fp)P (fq)P (fp + fq)

, (A.2)

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where BF (fp, fq) is the average estimate of the bispectrumover multiple epochs and P(·) is the average estimate of thepower spectrum. The smoothing procedure was implementedby the trimmed mean, to be consistent with that used in thefollowing case of GHWT-based WBIC.

A.2. GHWT-based WBIC

Figure A1 demonstrates the flow chart of the GHWT-basedWBIC algorithm (Li et al 2009), and the details are as follows.

(1) The signal x(t) are segmented into N overlapping epochs,xk(t), k = 1, 2, . . . , N .

(2) For each epoch xk(t)with its mean removed, GHWT isconducted, obtaining the wavelet coefficients ak(fp, t),at frequency bands with center frequency fp (p = 1, 2,. . . , L) and bandwidth fb. The general harmonic waveletfunction is obtained by multiplying the Hanning windowby ejηt , and defined as (Simonovski and Boltezar 2003)

ψ(t, η) =⎧⎨⎩

[1√3

+1√3

cos(πt)

]ejηt , |t | < 1

0, otherwise.(A.3)

(3) The wavelet bispectrum is calculated (van Milligen et al1995):

BWk (fp, fq) =

∫T

ak(fp, τ )ak(fq, τ )a∗k (fp + fq, τ ) dτ ,

(A.4)

where T is the finite time interval. Then, the waveletbispectrum is expressed by its magnitude Ak and biphaseϕk:

BWk (fp, fq) = Ak(fp, fq) ejϕk(fp,fq ), (A.5)

where the biphase is

ϕk(fp, fq) = ϕ(fp) + ϕ(fq) − ϕ(fp, fq).

(4) To eliminate spurious values, the phase randomizedwavelet bispectrum can be calculated by (Kim et al 2007,Li et al 2009)

BWk (fp, fq) =

∫T

ak(fp, τ )ak(fq, τ )a∗k

× (fp + fq, τ ) ejRϕk(fp,fq ,τ ) dτ, (A.6)

where R ∈ (−π, π ] is a random variable. If a QPC occursat time τ , the biphase ϕk = 0, and R has no effects onthe bispectrum; in contrast, if the QPC does not occur,i.e. the biphase ϕk �= 0, the variable R considerablyreduces the bispectrum.

(5) The normalized squared WBIC is calculated by (vanMilligen et al 1995)

bWk (fp, fq)

=∣∣BW

k (fp, fq)∣∣2∫

T|ak(fp, τ )ak(fq, τ )|2 dτ · ∫

T|ak(fp + fq, τ )|2 dτ

.

(A.7)

It ranges from 0 to 1, and characterizes the quadratic phasecoupling between different frequency components of thesignal.

(6) A surrogate method is employed to obtain a reliablebicoherence measure of statistical significance. First,replacing ϕk(fp, fq) in equation (A.6) with a new biphaseϕ′

k(fp, fq) = ϕk(fp, fq) + θ , where θ ∈ (−π, π ] isa random variable, a surrogated bicoherence value canbe derived. The above procedure runs 100 times and100 bicoherence values are obtained at frequency pair(fp, fq

). Then, at each frequency pair, the 95% statistical

threshold is determined by mean plus 1.96 times standarddeviations (Zar 2007). Finally, the bicoherence valueestimated from the original data greater than the thresholdwill be preserved; otherwise, it is set to zero.

(7) The bicoherence values from multiple epochs areaveraged to derive a robust estimate of WBIC. To removethe effect of the transients and random noises in EEGepochs, a Q-test method is used to obtain the trimmedmean in order to exclude the outlier values in the segment-averaging approach (Barnett and Lewis 1994). First, thebicoherence values from multiple epochs are arrangedin ascending order; then, the statistic Q-value (Q) iscalculated and compared with a critical Q-value (Qc) at aconfidence level (e.g. CL = 95%); if QQc, then the suspectvalue can be characterized as an outlier and removed, andthen the remaining values are averaged to obtain a robustestimate of WBIC, bW(fp, fq), for signal x(t).

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