A comparison of different synchronization measures in electroencephalogram during propofol anesthesia

Electroencephalogram (EEG) synchronization is becoming an essential tool to describe neurophysiological mechanisms of communication between brain regions under general anesthesia. Different synchronization measures have their own properties to reflect the changes of EEG activities during different anesthetic states. However, the performance characteristics and the relations of different synchronization measures in evaluating synchronization changes during propofol-induced anesthesia are not fully elucidated. Two-channel EEG data from seven volunteers who had undergone a brief standardized propofol anesthesia were then adopted to calculate eight synchronization indexes. We computed the prediction probability (P K ) of synchronization indexes with Bispectral Index (BIS) and propofol effect-site concentration (C eff ) to quantify the ability of the indexes to predict BIS and C eff . Also, box plots and coefficient of variation were used to reflect the different synchronization changes and their robustness to noise in awake, unconscious and recovery states, and the Pearson correlation coefficient (R) was used for assessing the relationship among synchronization measures, BIS and C eff . Permutation cross mutual information (PCMI) and determinism (DET) could predict BIS and follow C eff better than nonlinear interdependence (NI), mutual information based on kernel estimation (KerMI) and cross correlation. Wavelet transform coherence (WTC) in α and β frequency bands followed BIS and C eff better than that in other frequency bands. There was a significant decrease in unconscious state and a significant increase in recovery state for PCMI and NI, while the trends were opposite for KerMI, DET and WTC. Phase synchronization based on phase locking value (PSPLV) in δ, θ, α and γ1 frequency bands dropped significantly in unconscious state, whereas it had no significant synchronization in recovery state. Moreover, PCMI, NI, DET correlated closely with each other and they had a better robustness to noise and higher correlation with BIS and C eff than other synchronization indexes. Propofol caused EEG synchronization changes during the anesthetic period. Different synchronization measures had individual properties in evaluating synchronization changes in different anesthetic states, which might be related to various forms of neural activities and neurophysiological mechanisms under general anesthesia.


Introduction
Understanding the neurophysiological mechanisms of anesthetic drug effect is an important issue for neuroscientists, anesthetists, as well as drug researchers [1].Cognitive binding is thought to be a fundamental mechanism in human consciousness, and a number of recent studies suggest that loss of consciousness (LoC) during general anesthesia is associated with breakdown of long-distance cortical connectivity across multiple brain regions [2][3][4][5], especially in the frontal-parietal cortices [5].
Numerous measures, derived from different signal processing methods and statistics, have been proposed for quantifying neuro-synchronization [6][7][8][9] and some of the synchronization measures were used to interpret the mechanism of neural synchronization for general anesthesia.However, the performances of these synchronization measures for evaluating brain information integration or connectivity are not fully understand.
Cross correlation is based on the relationship of the magnitude of the electroencephalogram (EEG) signal between two regions, which is defined in the time domain.Lagged cross correlation was used to evaluate the interregional relationships of the blood-oxygen-level dependent signals of depressed people and natural sleep [10,11].However, few studies adopted the lagged cross correlation in the monitoring of anesthetic states.Coherence is a time-frequency domain method and it can evaluate the relationship of time series from different brain regions at different frequency bands.Many studies used some methods based on coherence in the coupling analysis during anesthesia.Li et al. combined the magnitude square coherence with S-estimator to analyzed the synchronization during sevoflurane anesthesia in sheep and they found that the synchronization increased from the waking to the burst-suppression states and decreased during recovery in the α and β frequency bands [12].Hayashi et al. analyzed the bicoherence of frontal and occipital EEGs before and after induction of sevoflurane anesthesia and they found that there were delta and alpha power shift between frontal and occipital EEG with increasing sevoflurane concentration [13].
Phase synchronization analysis is a classical neuronal oscillation analysis method that is independent of the amplitude of the signal.It was sensitive to nonlinear coupling and it was a promising tool for quantifying coupling in multi-channel electroencephalogram or magnetoencephalogram (MEG) re-cordings [14][15][16].Koskinen et al. used the Hilbert transform based phase synchronization indices to investigate the phase coupling during propofol anesthetic induction and recovery periods and they found that the sub-delta band decreased during the induction and increased during the recovery, while the directions were reversed in the alpha band [17].Nicolaou et al. analyzed how anesthesia affected widespread patterns of phase synchrony and they found anesthesia caused different phase synchronization changes in different frequency bands [18].
Mutual information is an information theory method and it has been widely applied in EEG analysis as a way of estimating information integration between different EEG channels or brain regions for mechanism analysis and neurological disease diagnosis, such as epilepsy seizure, Alzheimer's disease and autism [19][20][21].We applied kernel density estimation and permutation entropy to quantify the mutual information.Kernel density estimation which was suggested by Moon et al. [22] was found to be superior to the histogram-based mutual information.However, there is no research using kernel density-based mutual information to evaluate the depth of anesthesia (DoA).On the contrary, permutation mutual information has been proved to be a promising method to tracking EEG dynamics during sevoflurane, isoflurane and remifentanil anesthesia [23,24].
Nonlinear interdependence is a measure of generalized synchronization in nonlinear systems, which evaluates the interdependency according to the distance of delay vectors of two time series.It was most applied for evaluating the EEG functional connectivity, seizure prediction of epilepsy patients in different brain regions [25,26].However, few studies used the NI to characterize the EEG interdependence during anesthesia.
DET in the recurrence quantification analysis is based on the reconstruction of the phase space of the signals.High value of DET means strong synchronization of two time series, and vice versa.Recurrence quantification analysis has been applied to the monitoring of the depth of anesthesia and this technique had been proved that it could separates consciousness from unconsciousness during sevoflurane and propofol anesthesia [27].Shalbaf et al. proposed the order patterns cross recurrence analysis to assess synchronization changes during propofol anesthesia [28].
Different measures for measuring synchronization rely on certain characteristic features of the dynamical system under investigation.However, the underlying dynamic properties of the synchronization measures applied to the EEG data in different anesthetic states are not completely known.We concentrated on the synchronization changes of two-channel EEG from prefrontal and primary motor cortices during propofol-induced anesthesia.We studied and compared a range of different synchronization measures: cross correlation (COR); magnitude squared coherence based on Fourier transform (FTC) and coherence based on wavelet transform (WTC); phase synchronization (PS) based on phase locking value, Shannon entropy and conditional probability; mutual information (MI) based on kernel density estimation and permutation; nonlinear interdependence (NI) and determinism (DET) in the recurrence quantification analysis (RQA).Using different synchronization measures, we aim to the describe their individual properties during the whole period of anesthesia, evaluate performance of distinguishing awake, unconscious and recovery states, find the effective measures for evaluating of clinical anesthetic depth, and help us to understand the underlying neurophysiological mechanisms of anesthesia.This paper is organized as follows.Section 2 describes each synchronization measure and Section 3 gives the statistical analysis methods.In Section 4, the details of EEG recording, preprocessing and the results of the application of the synchronization measures to the real EEG are presented.Finally, the discussion and conclusion are given in Section 5.The parameter selection of some synchronization measures were discussed in Appendix.

Synchronization measures 2.1 Cross correlation
The cross correlation is one of the most well-known measures for evaluating the linear coupling relationship between two time series.Given two time series )，the cross-correlation function [10,29] is defined as

Coherence
Coherence is a frequency domain based method which measures the linear correlations of two time series [30].In this study, we considered two coherence calculation methods: magnitude squared coherence based on Fourier transform and coherence based on wavelet transform.
where * denotes the complex conjugate and δ is a scalar that depends on frequency.w is the wavelet central angle frequency which is an optional value to adjust the time-frequency resolution, often 6 0 ≥ w .The details are described in [31].
The WTC index is used to evaluate synchronization in our study and the WTC index at the frequency band ] , [ where w N is the number of summands in the summation, WTC ranges from 0 to 1 [12].

Phase synchronization
Phase synchronization (PS) analysis has been independently proposed by Lachaux et al. [32], Mormann et al. [33] and is applied later by Allefeld and Kurths [34,35].This approach is based on the concept of synchronization of chaotic oscillators studied by Rosenblum et al [36].There are various estimation methods of phase synchronization.Instantaneous phase estimation and phase coupling quantification are the two fundamental steps in phase synchronization evaluation.
Li et al employed the windowed harmonic wavelet transform (WHWT) to extract the instantaneous phase of brain signals, and shows that WHWT performs better than traditional methods, such as the Hilbert transform (HT) [37].So we chose WHWT to calculate the instantaneous phase in this study.
The algorithm is described as follows: Given two time series The instantaneous phase ) (t There are three PS measures considered in this study.The first PS measure uses the phase locking value (PLV) [39], denoted as PSPLV.The calculation is based on a time window with a specified length L, where PSPLV is bound between 0 and 1.
The second PS measure is based on Shannon entropy (PSSE) of the distribution of is divided into M bins and k p is the probability that ψ is in the bin k.
Then this PS measure is defined as where and M S ln max = .It ranges from 0 for a uniform distribution of (t) Δ xy ϕ ,to 1 if the distribution is a delta function.The optimum number of M is found as where L is the number of data points in a time window.
The third PS measure is based on conditional probability (PSCP) [40] and it is described as follows: ) bins and binning the phase of time series where Each PS index is calculated across the frequency bands δ, θ, α, β and γ1.We divide the EEG data into a series of time epochs and the discussion of PS indexes at different epoch lengths Te is shown in Appendix A(1).

Mutual information based on kernel estimation (KerMI)
The mutual information evaluates the interdependence between variables and is widely used to analyze nonlinear systems.Given two discrete random variables X and Y , ) ) is the marginal probability of the event ) is the marginal probability of the event i y Y = and ) , ( is the joint probability of the event . Then the mutual information between X and Y is defined as As for the discrete random variables ), the most straightforward approach for estimating probabilities is partitioning ) bins of finite size, and counting the numbers of points falling into the each bins.The number of points within the bin are denoted as .Then, the marginal and joint probabilities can be denoted as Kernel techniques are an attractive alternative to binning a distribution which is discussed thoroughly in [42].Rather than simply counting the points, we can determine the distance-dependent weight of each point by using kernel function.Then, the marginal probability density and joint probability density which are estimated by the Gaussian kernel estimator [43] can be denoted as [44,45], ( ) where parameter h is called window width of the kernels.
Last, we obtain the mutual information based on kernel estimation, The approximately optimal window width h is given by

Permutation cross mutual information (PCMI)
Order pattern analysis is an important method for studying nonlinear dynamical time series [46].Calculation of the probability distribution of the order patterns is the core of PCMI calculation.Given the time series ), we can obtain the embedding vector ) with the embedding dimension m and time lag τ.Then, sorting the elements of vectors i x and i y in ascending order respectively and there are m! possible order patterns in each vectors, which is also called permutations.Next, counting the number of each order pattern of , and we can obtain the probability of each permutation Based on Shannon information theory, the permutation entropy (PE) of X and Y is The joint permutation entropy of X and Y is is the joint probability of permutation of vectors i x and i y .
Then, the PCMI of X and Y is defined as Previous study found that the parameter selection m=6 and τ=1 when the sampling rate of data is 100 Hz resulted in the best PCMI performance in distinguish different anesthetic state [47].Therefore, we used m=6 and τ=1 for the calculation of PCMI index in this study.

Nonlinear interdependence
Nonlinear interdependence is an important nonlinear synchronization measure in neural systems [48][49][50][51].The details of the algorithm are described as follows: Given the time series ), we can reconstruct delay vectors the ) with the embedding dimension m and time lag τ.We first denote j i r , and as the time indices of the k nearest neighbors of i x and i y , respectively.
For each i x , the mean squared Euclidean distance to its k neighbors is defined as The y-conditioned mean squared Euclidean distance is defined by replacing the nearest neighbors by the equal time partners of the closest neighbors of i y We can define the nonlinear interdependence [52] , where 1 , ) x .
The selection of three parameters of NI: embedding dimension m, time lag τ and the number of nearest neighbors k is discussed in Appendix A(2).

Cross recurrence analysis
The recurrence of states, meaning that states are arbitrarily close after some time, is a fundamental property of dynamical systems [53].The cross recurrence plot (CRP) which is a bivariate extension of the recurrence plot (RP) is introduced to analyze the dependencies between two different systems [54,55].
Considering two time series ), we reconstruct the embedding vector ) with the embedding dimension m and time lag τ.The cross recurrence matrix which is also called cross recurrence plot is defined by, ) ( where ε is the threshold distance, ) (⋅ Θ is the Heaviside function, ⋅ is the Euclidean norm and Q is the number of embedding vector. The recurrence quantification analysis [56,57] defined several measures based on diagonal oriented lines in RP, such as recurrence rate, determinism (DET), maximal length of diagonal structures, entropy and trend.The determinism is ratio of recurrence points forming diagonal structures (of at least length lmin) to all recurrence points in CRP.Long diagonal structures show similar phase space behavior of two time series, while stochastic time series cause short diagonals.In our study, we use DET to evaluate the synchronization of the two time series, where l is the length of the diagonal which parallels the main diagonal, ) (l P is the corresponding distribution probability.lmin is the threshold of diagonal length. The selection of three parameters of DET: embedding dimension m, time lag τ and threshold of diagonal length lmin is discussed in Appendix A(3).

Statistical analysis
The aim of this study is to evaluate the performance of different synchronization measures for tracking synchronization changes during anesthetic period and the ability of distinguish different anesthetic states.We used the prediction probability (PK) [58,59] to evaluate the ability of predicting BIS and propofol effect-site concentration (Ceff) (derived from pharmacokinetic/pharmacodynamic (PK/PD) modeling [60]) of all synchronization measures.
Given mine the significant difference of the index values between awake and unconscious states and between unconscious and recovery states.The coefficient of variation (CV) (the ratio of standard deviation (SD) to mean) was used to evaluate the index stability during propofol-induced anesthesia process [61].Moreover, in order to gain the relation among different synchronization measures, Bispectral Index (BIS) and Ceff, we calculated the Pearson correlation coefficient R of all subjects.

Subjects and EEG recordings
We studied the EEG data of seven human volunteers from previously published work [60].With the permission of the Waikato Hospital Ethical Committee, the volunteers (American Society of Anesthesiologists physical status I or II) were recruited to undergo a brief propofol anesthetic and recovered in accordance with normal procedures of the Australian and New Zealand College of Anaesthesia (A.N.Z.C.A) guidelines.All subjects gave written informed consent after obtaining the permission of the hospital ethical committee.The silver-silver chloride scalp electrodes were placed at the position of Fp1-F7 and C3-T3 according to the 10-20 international system to produce bipolar signals (Fig. 1A).The ground electrode was placed at FpZ.The Aspect A-1000 EEG monitor (Aspect Medical Systems, Natick, MA, USA) was used to collected both the raw EEG signal (The sampling frequency is 256 Hz) and the BIS (The sampling frequency is 0.2 Hz).
The experimental sequence diagram is shown in Fig. 1B.The propofol intravenous infusion was 150ml/h (1500mg/h) in an antecubital vein via a syringe driver pump initially, and the BIS and raw EEG data were recorded when the infusion started.Then, a verbal list of dissimilar objects was read to the subject at 30-second intervals who held a syringe filled with water between forefinger and thumb.When the syringe dropped (LoC time), the infusion and the read of the list of dissimilar stopped, and the time was recorded as "syringe-drop time".The subject was then allowed to awake and given the play of a pre-recorded tape of random numbers and some verbal commands such as "move your right foot".The verbal commands lasted 5 seconds and they were at 10-second intervals.
We recorded the time as "command time" as soon as the subject responded the verbal command correctly (recovery of consciousness (RoC) time).The subject were questioned as to the first number that they could recall and the last object that they could remember during propofol induction, and these two time points were recorded as "number time" and "object time" respectively.The study was terminated about 60 seconds after LoC time.The study four recorded times of all subjects are shown in Table 1.

EEG preprocessing
Generally, there are three main artifacts in EEG recordings: baseline drift, head movement noise and physiological noise (such as electrooculogram (EOG) and electromyogram (EMG)).For each source of noise we adopted a different artifact-rejection approach.Firstly, baseline drift and head movement noise are usually in the low frequency band (<0.5 Hz) and the function eegfilt.m in EEGLAB was used to reduce this noise [62].Low-pass filter and the mains notch were set at 70 Hz and 50 Hz respectively.Secondly, raw EEG data exceeding an amplitude of 200 μV were removed as outlier points.Using statistical mean and standard deviation (SD) methods [63], amplitude values beyond the range mean±2SD were also considered as outliers.Then, EOG artifacts were reduced through a stationary wavelet transform based on an appropriate threshold [61].Inverse filtering was used to identify transient events in the EEG, and was the method employed to detect and remove EMG and other high-amplitude transient artifacts [64,65].Finally, the EEG data were downsampled to 100 Hz by the function resample.m in Matlab.
In our study, in order to evaluate the synchronization during the whole experimental period, the EEG data were divided into a series of 10-second epochs, with an overlap of 75% (In particular, the data were divided into different length of time epoch for the calculation of PS indexes.).We used the EEG data in each epochs to calculate the synchronization indexes.Also, we chose three states from the whole period: awake state (the period before "Object time"), unconscious state (the period between LoC time and "Number time") and recovery state (the period after "command time") in order to evaluate the ability of different synchronization measures to distinguish different anesthetic states.

Results
We first analyzed the FTC and WTC of the two-channel EEG signals of all subjects to find a better coherence method to quantify the synchronization in frequency domain.The EEG recordings of two channels from one subject and their corresponding time-frequency spectrogram were shown in Fig. 2 A and Fig. 2B.The power in δ, α and β frequency bands increased with the increasing propofol ef-fect-site concentration.Fig. 2C and Fig. 2D showed the FTC and WTC spectrums during the whole period.In terms of FTC spectrum, two-channel EEG signals were divided into a series of 10-second epochs with an overlap of 75%.The epochs were windowed using a Hamming window and FFT length was set to be 128.As can be seen from the figure, FTC spectrum could not reflect the changes of coherence during the whole period (Fig. 2C), while the WTC spectrum in the δ, α and β frequency bands increased obviously during unconscious state (Fig. 2D), which had the similar results as the spectrogram analysis.Therefore, we extracted the WTC index from WTC spectrum to quantify the synchronization during propofol-induced anesthesia period.
We then computed the synchronization indexes of all subjects during the whole anesthetic period.Fig. 3A was the preprocessed EEG signals of one subject from the left prefrontal and left primary motor cortex respectively.Fig. 3B and Fig. 3C were the corresponding BIS and Ceff.Fig. 3D showed the values of all synchronization indexes for the same subject.We computed three PS indexes at frequency bands δ, θ, α, β and γ1 and we found that the PSPLV and PSCP had similar results, which was consistent with previously reported results in [51], and the PSCP will be not further reported.As can be seen from the Fig. 3D, the PCMI, NI, PSPLV (δ, θ, α and γ1), PSSE (δ, β) saw a decreasing trend with the increasing Ceff value, whereas KerMI, DET and WTC (δ, θ and α) showed an increasing trend which were consistent with the Ceff.Ceff.By contrast, WTC (α) predicted significantly better than WTC (γ1) with BIS, and WTC (α, β) predicted significantly better than WTC (γ1) with Ceff (p<0.01)."Fig.4" "Table 2" Furthermore, the ability to distinguish different anesthetic states of synchronization measures is essential for DoA monitoring.The synchronization indexes were computed at three anesthetic states (awake, unconscious and recovery) and the boxplots of the index values were shown in Fig. 5.The Kolmogorov-Smirnov test showed that the index value of each measure in each state were not normally distributed, so we adopted the Kruskal-Wallis test and Multiple comparison test to estimate the significant difference among between three states, using the notation *, ** and *** to indicate significant difference at p<0.05, p<0.01 and p<0.001 respectively.It can be seen from Fig. 5 that KerMI, PCMI, NI and DET could significantly distinguish awake and unconscious states as well as unconscious and recovery states (p<0.001),whereas COR could only distinguish awake and unconscious states (p<0.001).There was an increase in unconscious state and a decrease in recovery state for KerMI and DET, while the trends were opposite for PCMI and NI.In terms of PSPLV, the phase synchronization dropped significantly in unconscious state for PSPLV (δ, θ, α and γ1) and had no significant changes in recovery state, while PSPLV (β) could not distinguish the three anesthetic states (Fig. 5F-J).PSSE could only distinguish three states at θ and β frequency bands (Fig. 5K-O).As for WTC, there was a significant rise in unconscious state and a significant drop in recovery state for all frequency bands (Fig. 5P-T).
In addition, the stability of the index value during the anesthetic sates is important for the reliable DoA monitoring.We calculated the CV of all synchronization indexes of all subjects at awake, un-conscious and recovery states and the CV values were shown in Table 3.As can be seen from Table .3, PCMI had the low CV in awake state (CV=0.085),unconscious state (CV=0.146)and recovery state (CV=0.105).The CV of NI, PSPLV, PSSE and DET were lower than COR and KerMI, which were all smaller than WTC in awake and unconscious states.By contrast, the CV of COR, NI, PSPLV, PSSE, DET gained smaller values than KerMI and WTC in recovery state.These results illustrated that PCMI, NI, PS and DET had a better robustness to noise during the propofol-induced anesthesia."Fig.5" "Table 3" To further evaluate the relationship among synchronization measures, BIS and Ceff, we calculated the correlation coefficients R among different synchronization measures, BIS and Ceff of all subjects and the averaged R over all subjects were shown in Fig. 6.KerMI, DET, WTC index curves and Ceff during the whole period were reversed when calculating the correlation coefficients.As can be seen from Fig. 6, PCMI had the highest correlation coefficient with BIS (R=0.846) and Ceff (R=0.739).

Discussion and conclusions
Despite the emergence of many DoA monitoring over the last few years, the neurophysiological mechanisms by which anesthetic drugs caused loss of consciousness are still unknown [1].Many studies suggest that long-range synchronization of neuronal populations is a fundamental principle of cortical processing and communication.Multi-channel EEG is more suited for understanding the mechanisms of anesthetic effect and it could provide a more robust measure of anesthetic depth for clinical application.In this study, we considered ten synchronization measures, including cross correlation, two coherence measures, three phase synchronization measures, two mutual information measures, nonlinear interdependence and cross recurrence analysis.We sought to identify synchronization changes of EEG between two brain regions during different anesthetic states and evaluate the performance in tracking anesthetic drug concentration and the ability of distinguishing different anesthetic states of the synchronization measures.
In our results, COR performed worse in correlating with BIS and Ceff and distinguishing the anesthetic states in this study.We compared the Fourier transform coherence and wavelet transform coherence.The results showed that the coherence based on wavelet transform could reflect the synchronization changes during anesthetic states (Fig. 2C and D) and we used the WTC index which was extracted from WTC spectrum to quantify the synchronization in our study.With increasing WTC in unconscious state and decreasing WTC in recovery state, propofol makes the neural oscillations more synchronous after loss of consciousness, which is consistent with previously reported results in the reference [12].Furthermore, recent studies using bicoherence [13], global coherence [66] reflected different forms of EEG synchronization in various frequency bands at different brain region under general anesthesia.Therefore, the coherence based synchronization measures are essential and promising for evaluating the communication among brain regions and describe the mechanism of general anesthesia.
The instantaneous phase extraction was based on the WHWT which had been proved that it was better than Hilbert transform [37] and Phase locking and Shannon entropy were used to quantify the phase synchronization.The results showed that propofol caused a decrease phase synchronization in δ, θ, α, β and γ1 frequency bands and PSPLV performed better than PSSE in distinguishing unconscious state from awake state.However, this founding is not consistent with other studies about phase synchronization changes during anesthesia, which may be due to the different EEG functional connectivity of subjects or patients under different anesthesia procedures.
PCMI is related to the probability distribution of permutation pattern.Our results of decreasing PCMI in unconscious state and increasing PCMI in recovery state revealed that propofol lead to the decrease of permutation pattern of EEG signals, which means that the EEG signal is more regular when anesthetized [67,68].Also, PCMI presented a better performance than other indexes in evaluating EEG synchronization changes during anesthesia.It has the highest PK and R values with BIS and Ceff (Fig. 4), strong robustness to noise and it can significantly distinguish awake, unconscious and recovery states (Fig. 5).These results illustrated that PCMI is a meaningful measure for characterizing EEG dynamics during anesthesia.As for KerMI, Gaussian kernel was used to quantify the probability density of mutual information.Our results showed that KerMI increased with increasing depth of anesthesia, which had an opposite trend with PCMI.Maybe it is the regular EEG signals in unconscious state which have small difference between adjacent signals that makes the increasing KerMI in unconscious state.
As for NI, the significant drop of NI in unconscious state in our study demonstrates that propofol weaken the interdependence and lead to the disconnection of two brain regions, which has been previously reported that brain functional integration decreased during propofol-induced loss of consciousness [5,69].Also, NI had close relation with BIS and Ceff and the ability to distinguish different anesthetic states.Therefore, as a nonlinear synchronization index, NI is suit for detecting the changes of interdependence of EEG signal during anesthesia.DET performed good in following the Ceff and had good robustness to noise.Increasing in unconscious states and decreasing in recovery state means that propofol causes the increase of synchronization, which is consistent with the result in the recent study [28].Accordingly, DET can be effectively evaluate the EEG synchronization changes during anesthesia.
In conclusion, most synchronization measures can detect the EEG dynamics during anesthesia.Each measure has their properties and performance on evaluating synchronization changes because of their own calculating principles, which may reflect different mechanism of anesthesia.Although our experiment data are limited which means that more investigation of these synchronization measures should be conducted for describing the underlying dynamics of these measures, we still characterize the EEG dynamics during propofol-induced anesthesia using different synchronization measures.
through the WHWT and the phase difference

.
within the bin are denoted as k M .Then, for all the time points when k-th bin, we compute the corresponding phase value The PS index is denoted as being the dimension of Gaussian kernel estimation and σ the average marginal SD[42].

"Fig. 2 ""Fig. 3 "
To quantify the ability of predicting BIS ( BIS K P _ ) and the relation with Ceff ( eff C K P _ ) of the synchronization measures, we calculated the PK.The PK values of each synchronization indexes with BIS and Ceff of all subjects and their corresponding box plots were shown in Fig. 4. The median (1st quartile (Q1), 3rd quartile (Q3)) of PK values of all measures were displayed in Table 2.It can be seen from Fig. 4 and Table 2 that PCMI had the highest PK value with BIS ( BIS K P _ =0.855(0.775, 0.875)) and Ceff ( eff C K P _ =0.794(0.703,0.842)).DET ranked second with the value BIS K P _ =0.823(0.806,0.869) and eff C K P _ =0.781(0.695,0.816).These figures demonstrated that PCMI and DET could best predict the BIS and follow the Ceff.The PK values of NI, KerMI and COR were smaller than PCMI and DET.Kolmogorov-Smirnov test showed that the PK values of each index were not normally distributed.The statistical significant difference among the synchronization indexes were marked at the top of Fig. 4A and B, using the notation *, ** and *** to indicate significant difference at p<0.05, p<0.01 and p<0.001 respectively (Friedman test and Multiple comparison test).As for PSPLV and PSSE, there was no significant difference among different frequency bands in tracking the BIS and 843) and Ceff (R=0.703) and NI also had a high value with BIS (R=0.729) and Ceff (R=0.638).As for PS and WTC, PSPLV (δ) and WTC (α) correlated with BIS and Ceff higher than that of other frequency bands.In terms of the relation among different synchronization measures, PCMI correlated closely with DET (R=0.949) and NI (R=0.838).Strong relation was obtained between KerMI and WTC (δ) (R=0.833) and between NI and DET(R=0.798)."Fig.6"

Fig. 5
Fig. 5 Box plots of synchronization indexes in different studied periods (I: awake state, II: unconscious state, III: recovery state).The notation *, ** and *** indicate significant difference at p<0.05, p<0.01 and p<0.001 respectively, through Kruskal-Wallis test and Multiple comparison test.