Page 1

Genuine and Spurious Phase Synchronization Strengths

during Consciousness and General Anesthesia

UnCheol Lee1*, HeonSoo Lee1,2, Markus Mu ¨ller3, Gyu-Jeong Noh4, George A. Mashour1,5

1Division of Neuroanesthesiology, Department of Anesthesiology, University of Michigan Medical School, Ann Arbor, Michigan, United States of America, 2Department

of Physics, POSTECH, Pohang, South Korea, 3Facultad de Ciencias, Universidad Auto ´noma del Estado de Morelos, Centro Internacional de Ciencias, Universidad Nacional

Auto ´noma de Me ´xico, Cuernavaca, Morelos, Me ´xico, 4Department of Clinical Pharmacology and Therapeutics, Department of Anesthesiology and Pain Medicine, Asan

Medical Center, University of Ulsan College of Medicine, Seoul, Korea, 5Neuroscience Graduate Program, University of Michigan, Ann Arbor, Michigan, United States of

America

Abstract

Spectral content in a physiological dataset of finite size has the potential to produce spurious measures of coherence. This is

especially true for electroencephalography (EEG) during general anesthesia because of the significant alteration of the

power spectrum. In this study we quantitatively evaluated the genuine and spurious phase synchronization strength (PSS)

of EEG during consciousness, general anesthesia, and recovery. A computational approach based on the randomized data

method was used for evaluating genuine and spurious PSS. The validity of the method was tested with a simulated dataset.

We applied this method to the EEG of normal subjects undergoing general anesthesia and investigated the finite size effects

of EEG references, data length and spectral content on phase synchronization. The most influential factor for genuine PSS

was the type of EEG reference; the most influential factor for spurious PSS was the spectral content. Genuine and spurious

PSS showed characteristic temporal patterns for each frequency band across consciousness and anesthesia. Simultaneous

measurement of both genuine and spurious PSS during general anesthesia is necessary in order to avoid incorrect

interpretations regarding states of consciousness.

Citation: Lee U, Lee H, Mu ¨ller M, Noh G-J, Mashour GA (2012) Genuine and Spurious Phase Synchronization Strengths during Consciousness and General

Anesthesia. PLoS ONE 7(10): e46313. doi:10.1371/journal.pone.0046313

Editor: Lawrence M. Ward, University of British Columbia, Canada

Received March 12, 2012; Accepted August 31, 2012; Published October 2, 2012

Copyright: ? 2012 Lee et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted

use, distribution, and reproduction in any medium, provided the original author and source are credited.

Funding: This study was supported by the Department of Anesthesiology, University of Michigan, Ann Arbor; National Institutes of Health KL2 grant (RR024987-

01) (GAM, UL); Consejo Nacional de Ciencia y Tecnologia, Mexico (MM). The funders had no role in study design, data collection and analysis, decision to publish,

or preparation of the manuscript.

Competing Interests: The authors have declared that no competing interests exist.

* E-mail: uclee@med.umich.edu

Introduction

The administration of general anesthetics results in dramatic

changes in behavioral state, which is accompanied by changes of

functional connectivity and information integration capacity in the

brain [1–6]. Phase synchronization is thought to be one potential

candidate for integrating neuronal sources distributed across

specialized brain areas [7–11]. As such, it has been widely used

to quantify the underlying mechanism of large scale integration in

the brain based on neurophysiologic recordings. Although a

valuable technique, several limitations in the evaluation of EEG

phase synchronization have also been noted [12–15]. Limitations

such as volume conduction, the active reference electrode and the

finite size effect due to spectral content are fundamental problems

causing spurious or distorted coherence measures of brain

activities. Several methods have been introduced to minimize

these problems, but the difficulty persists. Volume conduction,

which results when a neural source is observable at more than one

electrode, could be attenuated by baseline correction and the

method of localizing activities [12] [16]. A quiet reference

electrode and careful interpretation have been suggested for the

active reference electrode problem. Finally, the randomized data

test or bootstrap method have been suggested for the finite size

effect due to spectral content [12] [14–15]. However, the effects of

each of these limitations on the degree of spurious phase

synchronization have not been systematically quantified.

Random or spurious correlations within multivariate data sets

have been studied by random matrix theory (RMT), in which the

random part of a correlation can be predicted based on the

analytic results obtained from random matrix ensembles. Genuine

correlation can then be estimated based on significant deviation

from the analytic RMT predictions. Information about the

correlation structure of the multivariate data set is imprinted into

the structures of a correlation matrix [17–22]. By decomposing the

linear correlation matrix of multichannel EEG data into principle

structures and comparing them with randomized data, the

spurious and genuine correlation structures have been estimated

[23]. Genuine correlations were defined as the correlation values

that were above and beyond those found in the randomized

dataset. It is known that spectral content dominated by lower

frequencies is associated with larger spurious correlation [23]. As

such, the dramatic shift toward lower frequency spectral contents

during general anesthesia may seriously distort the coherence

estimation. Despite the known potential for distorted coherence

measures, there has been relatively little attention to quantitative

assessment of the phenomenon [24,25].

In the current study, indices of genuine, spurious and total

phase synchronization strength (PSS) were quantified in the EEG

of conscious and anesthetized human volunteers. First, simulated

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data based on the N-tori model were used to test the validity of

genuine PSS measures. This model simulated multichannel

oscillations and dynamic state transitions together with the

modulation of phase coherence and the dominant spectral content.

Second, in order to quantify spurious elements, we used

randomized data with the same spectral content as the original

EEG but with zero coherence. Third, the following were

investigated as different sources of spurious phase synchronization:

four types of EEG reference, six frequency bands and different

data lengths. Finally, we investigated the temporal evolution

pattern of the genuine, spurious and total PSS during general

anesthesia.

Results

Genuine PSS in a Simulated EEG Time Series

To test the validity of the genuine PSS, 20 EEG time series

simulated by the N-tori model were used (Figure 1). In the model,

the phase coherence and the mean frequency of 20 time series

were modulated in different ways across seven periods (see

Methods). Figure 1 (a) presents the EEG epochs of three different

levels of coherence: no coherence (0–20 s and 120–140 s),

coherence (40–100 s), and transition (20–40 s and 100–120 s).

Figure 1(b) presents the EEG epochs of two different mean

frequencies: 10 Hz (0–60 s), 1 Hz (80–140 s), and transition

between two mean frequencies (60–80 s). Figure 1 (c) and (d)

demonstrated the effect of mean frequencies (1, 6 and 10 Hz) and

the relationship of genuine, spurious and total PSS with the true

coherence given in the simulation.

In the first and the last 20 s epochs for each EEG time series

simulation, the partial phases di,j was chosen from a uniform

distribution ranging from 0 to 2p for no coherency. On the other

hand, during the 40–100 s epoch, the phases for the correspond-

ing frequencies were chosen from a normal distribution with mean

phase (i.e.,3p=4). Spurious PSS quantifies the PSS that is falsely

produced by finite size and certain spectral contents of the data.

Genuine PSS quantifies the phase synchronization strength that

deviates from that of the randomized data set. Total PSS reflects

all PSS (spurious and genuine) contained in a given set of data.

Figure 1(c) demonstrates the increasing or decreasing patterns of

genuine PSS at the two state transition periods and the large

genuine PSS during 40–100 s (p,0.0001, F (6, 63)=586, repeated

measures one-way analysis of variance (ANOVA) with Tukey’s

multiple comparison test). For the two zero-coherent periods (0–

20 s and 120–140 s), the genuine PSS had a value of zero. After

shifting the mean frequency from 10 Hz to 1 Hz during 60–120 s

(Figure 1(b)), the spurious PSS was significantly increased

(Figure 1(c)) (p,0.0001, F(6,63)=6,448). Furthermore, the spuri-

ous PSS exactly reflected the change of the mean frequency during

the period (60–80 s) (green line in Figure 1(c)). The total PSS was

affected by the genuine and spurious components. The mean

phase coherence, which is the average value over all pairs of 20

time series, showed a pattern that paralleled the total PSS.

However, as expected, the mean phase coherence did not have

zero-values in the two non-coherent periods (0–20 s and 120–

140 s). Furthermore, mean phase coherence showed a larger non-

zero value in the lower frequency dominant period (120–140 s).

These data directly demonstrate the contamination of mean phase

coherence measures by spurious coherence components.

In contrast, the spurious phase coherence components were

significantly reduced as the mean frequency was increased.

Figure 1 (d) shows the PSS indices and the mean phase coherence

for the time series with two mean frequencies (10 Hz for 0–60 s

and 6 Hz for 60–140 s). The spurious PSS had a certain non-zero

value over the whole period, showing a tendency of a slight

increase from 60 s after the mean frequency shifted toward 6 Hz.

Because of the flat spurious PSS, the total PSS and the mean phase

coherence showed a similar pattern with that of genuine PSS.

However, the problem of a non-zero value in the non-coherent

periods remained. It is also of note that the spurious phase

coherence component was significantly amplified as the mean

frequency was decreased below 6 Hz (Figure 1 (d), p,0.0001,

F(6,63)=736.5, repeated measures one-way ANOVA), which

corresponds to the theta and delta rhythms of the EEG.

Significant Change of Spectral Content during General

Anesthesia

Fig. 2 (a) demonstrates an example of the temporal evolution

of power spectra over the entire frequency range during general

anesthesia. The short-term Fourier transform method was

applied to each 10 second long window for 21 EEG channels

of a subject (Spectrogram, in Matlab toolbox). The averaged

short-term Fourier transform over 21 EEG channels is shown in

Figure 2(a). After induction of general anesthesia there was a

large increase of lower frequency power as well as an increased

variance of mean phase synchronizations over all pairs of EEG

channels (Figure 2(b)). The increased variance implies that the

structure of phase synchronizations

channels became more complex in the anesthetized states and

could produce various changes of PSS indices. The EEG

simulation with N-tori predicts that the increased lower-

frequency power in anesthetized state induces larger spurious

phase synchronization components, which could inaccurately

reflect the coherence of brain activities.

among the 21 EEG

Genuine, Spurious and Total PSS for Randomized Data

The spurious PSS was estimated from randomized human EEG

data in order to evaluate the influence of spectral shifts after

general anesthesia that were predicted by the N-Tori model. Since

the randomized data has the same power spectrum with that of the

broadband EEG but with zero-coherence by randomization, we

can selectively evaluate the effect of spectral shift on the spurious

PSS index. The temporal patterns of the spurious, genuine and

total PSS were examined by the moving window method to

investigate the effect of dynamic spectral change during state

transitions (around loss of consciousness [LOC] and return of

consciousness [ROC], at 5 and 10 minutes on the time axis,

respectively). The means and standard deviations over 20 EEG

data sets are presented in Figure 3, which demonstrates significant

increasesofthespuriousPSS

F(6,63)=57.58)andincreases

(p,0.0001, F(6,63)=59.93) after LOC. The spurious and total

PSS gradually decreased down to the level of the baseline waking

state, while the genuine PSS was nearly zero during the whole

experiment. The total PSS (green) has the same temporal pattern

as the spurious PSS (blue) because of the zero genuine PSS (red)

over the entire experiment. This indicates that the total PSS was

significantly influenced by the spurious phase synchronization,

primarily induced by the finite size effect of specific spectral

contents during general anesthesia.

Two measures, phase synchronization (nonlinear) and Pearson

correlation coefficient (linear), were compared to assess their

vulnerability to the finite size effect for this data set. For the

genuine, spurious and total linear correlation strengths, the mean

phase coherence in the definitions of genuine, spurious and total

PSS was replaced with Pearson correlation coefficient Cijbetween

two EEG datasets (i,j) [18]. In Figure 3, the spurious linear Pearson

(blue

total

dots)

PSS

(p,0.0001,

(green indots)

Phase Synchronization during Anesthesia

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correlation strength (black square) was slightly larger than the

spurious PSS (blue square), but not significantly different.

Finite Size Effects of Data Length, Frequency Band and

Reference for Empirical EEG Data

The finite size effects induced by data length, EEG reference

and frequency band were investigated using the EEG in the

baseline conscious state (Figure 4). The EEG (5minutes) was

segmented into different data lengths, from 5 second- to 60

second-long windows with a 2 second interval. The means of

genuine and spurious PSS were calculated over 5 minute-long

EEG for each data length. There was no significant dependence of

the genuine and spurious PSS on these data lengths.

In contrast to data length, the EEG reference had a significant

effect on the genuine and spurious PSS (Figure 4). The unipolar

reference (A2) had a relatively larger genuine PSS (blue solid line)

in all frequency bands, while the transverse bipolar reference had

the lowest genuine PSS (black solid line). The common reference

Figure 1. The test of the three PSS indices using the simulated EEG time series. (a) The phases of 50 sine waves for a simulated EEG time

series are presented. The non-coherent (0–20 s and 120–140 s) and coherent (40–100 s) phases are given to the simulation, with two linear state

transitions (20–40 s and 100–120 s). The color bar on the right side indicates a radian within 0 to 2p and the frequency index (j) reflects the indices of

first 50 sine waves among 5,000 (fj(j~1e50) of Eq.4) for visualization. (b) The time-frequency plot of a simulated EEG time series is presented. The two

spurious, genuine PSS and the mean phase coherence (MPC) for the two mean frequencies (10 Hz and 1 Hz) are presented. The genuine PSS (red)

correlates well with the modulated coherence, while the spurious PSS (green) correlates with the mean frequency. The MPC has non-zero values in

non-coherent periods, which appears amplified in the lower mean frequency period (1 Hz). (d) Same as (c), but with means frequencies of 10 and

6 Hz, respectively. The spurious PSS was significantly reduced with the mean frequency of 6 Hz, but was still larger than that of 10 Hz. The error bars

denote the standard deviation. The upper bars in (a)–(d) indicate the states of coherence and different mean frequencies across EEG epochs.

doi:10.1371/journal.pone.0046313.g001

time periods have two different dominant frequencies (10 Hz for the first half period and 1 Hz for the other half). The state transition between two

dominant frequencies takes place during 60–80 s. The color bar on the right side denotes the probability density for the frequencies. (c) The total,

Phase Synchronization during Anesthesia

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and the longitudinal bipolar reference (red and green solid lines,

respectively) had similar genuine PSS values over all frequency

bands.

The frequency band demonstrated the most significant effect on

spurious PSS. The lower frequency bands (delta, theta and alpha)

had a relatively larger spurious PSS, compared to the higher

frequency bands (beta, gamma). In general, the unipolar reference

produces relatively large coherence artificially.

In this study, there was a biased electrode distribution (primarily

frontal and parietal regions), which could produce biased PSS with

distant clustered electrodes. As such, it is difficult to distinguish the

effect of volume conduction and the effect of biased electrode

distribution on the PSS indices in this data. In the analysis of

anesthesia EEG, we assumed that the volume conduction was

Figure 2. Example of changes of power spectrum and phase synchronization after anesthesia. (a) The averaged spectrogram of 21 EEG

channels for a subject, and (b) the variance of phase synchronizations between 21 EEG channels for a subject during general anesthesia. This

demonstrates the significant changes of the power spectrum and the variance of phase synchronization during general anesthesia. The loss of

consciousness and the recovery of consciousness happen at 5 and 10 minutes.

doi:10.1371/journal.pone.0046313.g002

Figure 3. Spurious phase synchronization strength (PSS)

during general anesthesia. The mean of genuine, spurious and

total PSS over all randomized data sets generated from all subjects’

original EEG data are presented over time (the error bar denotes the

standard deviation). The spurious PSS (blue square) and the spurious

correlation strength by Pearson correlation coefficient (black square,

denoted as ‘‘CCS’’) were compared. (Vertical dotted lines: loss of

consciousness and return of consciousness points, sequentially). The

linear Pearson correlation and the phase synchronization produce a

large spurious component after anesthesia.

doi:10.1371/journal.pone.0046313.g003

Figure 4. The effects of EEG reference, data length and

frequency band on genuine and spurious phase synchroniza-

tion strength (PSS). Each symbol denotes the mean genuine PSS

(solid lines) or the mean spurious PSS (dotted lines) for the combination

of data length, type of EEG reference and frequency band. The EEG

reference mainly affects genuine PSS. Each color denotes a type of EEG

reference (blue: unipolar reference (A2); green: longitudinal bipolar; red:

common averaged reference; and black: transverse bipolar). The

unipolar reference has the largest genuine PSS over all frequency

bands. By contrast, the frequency band mainly influences spurious PSS.

Lower frequency bands have larger spurious PSS over all types of EEG

references. The error bars denote the standard deviations over the EEG

data sets for 27 data lengths (from 5 to 60 seconds, with 2 second

intervals). Six frequency bands were studied: delta band (0.5–4 Hz),

theta band (4–8 Hz), alpha band (8–13 Hz), beta band (13–25 Hz),

gamma band (25–55 Hz) and whole band (0.5–55 Hz).

doi:10.1371/journal.pone.0046313.g004

Phase Synchronization during Anesthesia

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preserved across states and therefore focused on the increase or

decrease of PSS indices relative to those of the baseline state.

The Temporal Patterns of Genuine, Spurious and Total

PSS during General Anesthesia

The three PSS indices were applied to EEG data recorded

during baseline conscious, unconscious (loss of consciousness,

LOC) and recovery states (return of consciousness, ROC). Each

state consists of a 5 minute-long EEG epoch. Figure 5(a)–(f)

demonstrates the temporal patterns of genuine, spurious and total

PSS for the six frequency bands across different states of

consciousness. For clarity of statistical analysis, each state was

separated into two equal sub-periods (baseline waking state: B1

and B2, anesthetized state: A1 and A2, and recovery state: R1 and

R2). The results of the statistical tests for the changes of the three

PSS indices are presented in Table 1. In Figure 5, the means and

standard deviations of the three PSS indices over all EEG datasets

are presented. The EEG of different frequency bands had distinct

temporal patterns for each PSS. Here, the temporal patterns for

the unipolar EEG reference were presented; the other EEG

references showed a qualitatively similar behavior.

Repeated measures one-way ANOVA with Tukey’s multiple

comparison test was applied to the six sub-states for each

frequency band in the 20 EEG datasets (Table 1). The genuine

PSS of the delta band was preserved across states (P.0.05), while

the spurious PSS was significantly increased in A1 (p,0.0001). By

contrast, no significant change of spurious PSS was found at A1 in

the theta and gamma bands, but their genuine PSS were decreased

(p,0.0001 and p,0.05). For the alpha band, the largest decreases

took place in the three PSS indices after anesthesia. For the

gamma band, the genuine PSS was decreased (p,0.0001) without

significant change of spurious PSS. For the whole EEG band, the

genuine PSS was reduced (p,0.0001), while the spurious PSS was

significantly increased after LOC (p,0.0001).

Regarding the temporal evolution pattern, the genuine PSS was

decreased after LOC in most frequency bands except the delta

band. The decreased genuine PSS level of the alpha band was

maintained until the end of recording, while the genuine PSS for

the theta, gamma and whole frequency bands recovered in a short

time. The alpha and gamma bands showed relatively large

decreases of genuine PSS.

Regarding the spurious PSS, the delta, beta and whole

frequency bands showed an increase after the induction of

anesthesia. Conversely, the alpha band showed a large decrease

after LOC. The total PSS of the delta and the whole frequency

bands increased after LOC, while it significantly decreased for the

other bands. The total PSS of the whole frequency band changed

in the opposite direction of the genuine PSS after LOC.

Discussion

The major findings of this study are (1) our measure of genuine

PSS reflects true phase synchronization, as demonstrated by the

N-Tori model, (2) spurious PSS significantly increases during

general anesthesia, (3) the most influential factor for genuine PSS

is the EEG reference while the most influential factor for spurious

PSS is the low frequency spectra, and (4) there were individual

temporal patterns for genuine and spurious PSS in each frequency

band during general anesthesia.

Spurious PSS Increases as Frequency Decreases in

Simulated Data

The simulated model data clearly demonstrates the potential

problem with conventional mean phase coherence by revealing

spurious phase coherence for a time series with periods of zero true

coherence. The problem is exacerbated when simulated frequen-

Table 1. The statistical test for genuine (g), spurious(s) and total (t) PSS indices.

DeltaThetaAlphaBetaGammaWhole

gstgstgstgstgstgst

B1/B2

B1/A1*** ************************** *********

B1/A2** *************

B1/R1********* ******

B1/R2*************

B2/A1 *** ******************************* ***

B2/A2**************

B2/R1************

B2/R2*************

A1/A2 *****************

A1/R1******* ***** ******

A1/R2******* ******** ******

A2/R1

A2/R2

Tukey’s multiple comparison test with repeated one-way ANOVA.

***p,0.0001,

**p,0.01,

*p,0.05.

Each period was separated into two sub-periods. Baseline conscious states: B1 and B2, Anesthetized states: A1 and A2, Recovery states: R1 and R2. The number of states

is 6, and the number of each PSS index at each state is 20. The comparison to A1 is highlighted with bold font.

doi:10.1371/journal.pone.0046313.t001

Phase Synchronization during Anesthesia

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cies are decreased and resolves as frequency increases. Significant

spurious PSS began to appear from the mean frequency below

about 6 Hz, which corresponds to the theta and delta rhythms of

EEG. Consequently, our data suggest that, for an EEG that has a

dominant frequency below the theta rhythm, spurious component

measures should be taken into account.

Change of Spectral Content during General Anesthesia is

Associated with Increased Spurious PSS

The analysis of randomized EEG data acquired during

anesthesia demonstrated the effect of spectral content on the

three PSS indices (Figure 3). The spurious PSS was significantly

increased after LOC, in which the lower frequency spectral

Figure 5. The temporal evolution of genuine, spurious and total PSS during general anesthesia for the six frequency bands. The

mean genuine, spurious and total PSS are denoted by different colors (red: genuine PSS; green: spurious PSS; and blue: total PSS). The error bar

denotes the standard deviations of genuine, spurious and total PSS values over all EEG datasets. The vertical dotted lines indicate the loss of

consciousness and recovery of consciousness, sequentially. Six frequency bands were studied: delta band (0.5–4 Hz), theta band (4–8 Hz), alpha band

(8–13 Hz), beta band (13–25 Hz), gamma band (25–55 Hz) and whole band (0.5–55 Hz).

doi:10.1371/journal.pone.0046313.g005

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content dominates (Figure 2a). The spurious PSS gradually

returned to the level of the baseline state in association with the

returned spectral contents after ROC. As expected, the genuine

PSS for randomized data had nearly zero values and the total PSS

had the same pattern of temporal change as that of the spurious

PSS. This result clearly demonstrates the potential unreliability of

conventional coherence measures (nonlinear phase synchroniza-

tion and linear Pearson correlation coefficient) without monitoring

the finite size effect of the EEG during anesthesia. This would also

hold true for analyses of non-stationary physiological data such as

epilepsy, sleep and pharmacologically-induced states. Considering

the numerous uses of both coherence measures in brain network

analysis, careful interpretation is necessary.

Factors Affecting Genuine and Spurious PSS

We investigated which factor among the data length, type of

EEG reference and frequency bands amplifies the finite size effect.

Genuine PSS depends on the type of EEG reference and the

frequency band of EEG. The unipolar EEG reference (A2) had the

largest genuine PSS compared to those of the other EEG

references. This may be due to the common contribution of a

reference’s fluctuation to all of the EEG channels. For genuine

PSS, there was no tendency of linear increases or decreases over

different frequency bands. For spurious PSS, the frequency band

was the most influential factor in comparison with the changes

induced by the EEG reference and window size. Lower frequency

bands produced more spurious phase synchronization in EEG (in

Figure 4: delta, theta and alpha .. beta, gamma and whole). The

two types of bipolar EEGs and common average reference had a

similar level of spurious PSS. Consequently, the most influential

factors on the finite size effect were different for genuine and

spurious PSS. Among the examined factors, the EEG reference

was the most influential factor for the genuine PSS, whereas the

power spectrum was the most influential for the spurious PSS. The

window size, tested from 5 seconds to 60 seconds, had no

significant influence on either genuine or spurious PSS estima-

tions. Although a small window size produces less robust PSS

estimation, the large size of an ensemble (for instance, 147

windows for 5 seconds) seems to reduce the variance of the PSS

estimations. The significant influence of the EEG reference on the

calculation of phase synchronization has been discussed in several

studies [12–14], but its effect on the genuine and spurious phase

synchronization components under various conditions was a novel

aspect of our study. However, our measure of genuine PSS could

not be the direct solution for the fundamental measurement

problems of EEG such as volume conduction, which gives rise to a

larger coherence for EEG recording. One way to reduce the

volume conduction effect in the PSS indices would be to use a

coherence measure that is relatively robust for volume conduction,

instead of using mean phase synchronization and Pearson

correlation coefficient. For instance, phase lag index [26] or

weighted phase lag index [27] could be potential candidates., The

PSS indices presented in this study will be useful for optimizing

coherence measurements and the simultaneous measurement of

genuine and spurious PSS can help prevent incorrect interpreta-

tions of phase synchronization structure for a given EEG dataset.

Patterns of the three PSS Indices during General

Anesthesia

The genuine, spurious and total PSS evolved with typical

temporal patterns corresponding to the states of consciousness and

different frequency bands during general anesthesia (Fig.5a–f).

After LOC, the genuine PSS decreased in most frequency bands.

The decreased level of genuine PSS for the alpha band persisted

until the end of the experiment, while for the other frequency

bands it returned to the baseline during the anesthetized state (, 1

minute). It is also of interest to note that the mean values of

genuine PSS for the gamma band corresponded to the subject’s

behavioral responses by remaining decreased during the uncon-

scious state and increasing in association with behavioral

responsiveness. A notable difference between the alpha and

gamma bands is that the decreased level of genuine PSS persisted

after ROC in the alpha band, while it returned to the baseline

level in the gamma band. Therefore, these typical temporal

patterns of genuine PSS for different frequency bands seem to

reveal diverse functional mechanisms for modulating phase

synchronization–andpossibly

general anesthesia. The reduced genuine PSS is consistent with

the loss of functional connectivity in the brain during unconscious

state [4][28–30]. Otherwise, the largely increased spurious PSS in

the whole frequency band demonstrated the potential risk for

inaccuratedeterminationof functional

unconscious states.

The spurious PSS also showed diverse temporal evolution

patterns depending on the state of consciousness and the frequency

band. After LOC, the spurious PSS was significantly increased in

the delta, beta and whole frequency bands. Conversely, the

spurious PSS of the alpha band EEG significantly decreased in

unconscious state. The spurious PSS had a distinct temporal

evolution pattern corresponding to each frequency band: in-

creased and returned (delta and whole), unchanged (theta and

gamma), decreased and then unchanged (alpha), gradually

increased (beta).

informationintegration–during

connectivityduring

Limitations

This study has a number of limitations. The genuine PSS may

not control for all possible factors that can generate spurious

elements. In particular, the spurious PSS mainly focuses on the

random phase synchronization components generated by spectral

content. It does not, however, consider the volume conduction

effect at all. We therefore use the term ‘‘genuine’’ with respect to

PSS based on previously published terminology and acknowledge

that it may not reflect true PSS with perfect accuracy.

Furthermore, in order to normalize the total, spurious and

genuine coherence components, the three PSS indices were

divided with different denominators. Thus, the PSS indices

represent relative rather than absolute genuine or spurious

coherence for a given EEG dataset. The total PSS is therefore

not exactly the sum of genuine and spurious PSS. Another

limitation is that the N-tori model cannot represent the

hierarchical functional structure of the brain; thus, a more

sophisticated model is needed for realistic anesthesia EEG

simulation [31]. We demonstrated the validity of PSS indices

with the model data, but for EEG recorded during anesthesia we

assumed the consistency of volume conduction across states.

Conclusion

In conclusion, our proposed measures of genuine and spurious

PSS can clarify the interpretations of phase synchronization

structure for a given EEG dataset. Genuine and spurious PSS are

associated with complex temporal evolution patterns depending on

the state of consciousness. Because of significant spurious phase

synchronization, simultaneous monitoring of genuine and spurious

PSS is necessary. This approach may also be beneficial in

elucidating true functional connectivity based on coherence

measures for non-stationary physiological data in which very low

frequency spectra dominate.

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Materials and Methods

The Institutional Review Board (IRB) of Asan Medical Center

approved this study in human volunteers. After IRB approval and

written informed consent, ten normal human subjects were studied

on two separate occasions with 21-channel EEG. Three states

were investigated: 1) baseline consciousness, 2) general anesthesia,

defined as loss of response to a command after 2 mg/kg propofol,

and 3) recovery, defined as return of responsiveness. The EEG

data were originally gathered and analyzed using different

methods for a study of the frontoparietal system; full details of

anesthetic protocol can be found in [3].

The EEGs of 21 channels (Fp1, Fp2, F3, F4, F5, F6, F7, F8, Fz,

C3, C4, Cz, T7, T8, P3, P4, P5, P6, P7, P8, Pz referenced by A2,

10–20 system) were recorded on the bed with closed eyes, with a

sampling frequency of 256 Hz and 16-bits analog-to-digital

precision by WEEG-32H (LXE3232-RF, Laxtha Inc., Daejeon,

Korea). Baseline EEG was recorded for 5 min before an

intravenous bolus of propofol. EEG was recorded continuously

during and after the intravenous bolus of propofol, and up to

10 min after ROC. For the band pass filtering we used the fourth

order Butterworth filter to avoid a possible shifting of the signal

phases (in Matlab Signal Processing Toolbox).

Estimation of Genuine, Spurious and Total Phase

Synchronization Strengths

The genuine, spurious and total PSS were defined based on the

decomposition of spatial synchronization structures of multi-

channel EEG data and the comparison with its randomized data

set. The decomposition of a phase synchronization matrix S into

principle components reduces the number of entries from

M(M21)/2 R M, where M is the number of EEG channels. This

simplifies the problem compared to using all entries of phase

synchronization matrix S. By using principle components, we were

also able to detect a typical coherence structure of multivariate

data such as an ‘‘eigenvalue repulsion’’ in which the smallest

principle component could produce statistically more significant

information than that of the largest eigenvalue [18]. In other

words, the local components contain important information about

the correlation structure of a multivariate dataset; therefore,

considering each local component is important.

The phases pi(t) of an EEG channel Xi(t) were defined by the

Hilbert transform method, and the mean phase coherence

sijbetween two phase sequences (pi(t),pj(t)) was calculated with

the average of phase differences [32]. The entries of phase

synchronization matrix S were constructed by the mean phase

coherences of all possible pairs of EEG channels. The singular

value decomposition of matrix S produces eigenvalues li and

eigenvectors v!i:

Svi

!~livi

!, liƒliz1, i~1,???,M

(1) If all channel data are ‘‘completely independent,’’ all non-

diagonal elements of S will tend to zero if the length of data

TR‘. Then, all eigenvalues liare 1.

(2) For any finite T, the non-diagonal elements sij(i=j)have non-

zero values. The non-zero values are randomly distributed

around unity, even in the case of completely independent

data. The width of the distribution is determined by the length

of data T and the frequency contents of the signals, therefore,

the width associates with spurious PSS [13] [20].

(3) If all Xi(t)are ‘‘identical’’, only one nonzero eigenvalue exists,

w h i l et h eo t h e re i g e n v a l u e s

lM~M, li~0, i~0,???,M{1:

These properties were used to evaluate how much a given EEG

data set deviates from completely independent or identical data

(the property (1) and (3)). With the property (2), we can estimate

the spurious PSS.

Randomized data sets that have the same spectral contents and

amplitude distribution, but without the phase coherence between

signals, were used for estimating the spurious PSS [33]. All

eigenvalues for random data are supposed to be li~1 by the

property (1). The non-zero eigenvalues (li=1) indicate the

random coherence generated for a given EEG data. The spurious

phase synchronization depends on the combination of a specific

spectral content and a specific length data.

a r ez e r o .

(a)Genuine PSS quantifies the phase synchronization that

deviates from that of the randomized data set [34]. Genuine

PSS is defined as the fraction of the difference between the

original and randomized EEG to the difference between

completely correlated data and randomized EEG,

genuinePSS ~

P

M

i~1

Dli{l

s

iDUi

P

M{1

i~1

l

s

iz(M{l

s

M)

,

ð1Þ

where liand l

the original data set and the randomized data set,

respectively. The significant deviation was determined with

the Mann-Whitney Wilcoxon U-test. If the null hypothesis

for equal means liand l

Ui~1, otherwise, Ui~0. If the average eigenvalues of the

original data are not significantly deviated from those of the

randomized data, the numerator has a zero value. On the

other hand, if all phases are identical, then the largest

eigenvalue lM~Mand the others equal zero. Since the

numerator and denominator (normalization factor) are

identical, the genuine PSS is 1. Therefore, the genuine

PSS has a value between 0 and 1.

Spurious PSS quantifies the spurious phase synchronization

produced by finite size and certain spectral contents of the

data. Spurious PSS is defined as the fraction of the difference

between independent data and randomized EEG to the

difference between independent data and completely

correlated data,

s

idenote the averages of the ith eigenvalue for

s

iwas rejected with p,0.05, then

(b)

spurious PSS ~

P

2M{2

M

i~1

D1{l

s

iD

ð2Þ

Since the randomized data are uncorrelated across channels,

l

a spurious component produced by the specific combination

of a data length T and spectral content.

s

i~1for all i according to the property (1). If D1{l

s

iD=0, it is

(c)Total PSS measures the amount of total phase synchroni-

zation strength (spurious and genuine PSS) contained in a

given set of data. Total PSS is defined as the fraction of the

Phase Synchronization during Anesthesia

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Page 9

difference between independent data and original EEG to

the difference between independent data and completely

correlated data,

total PSS~

P

2M{2

M

i~1

D1{liD

ð3Þ

The total PSS quantifies the deviation of the eigenvalues of a given

dataset from those of the ideal case (completely uncorrelated and

TR‘). Since the given dataset may contain genuine and spurious

phase synchronization components, the difference from the ideally

uncorrelated case estimates the amount of spurious and genuine

phase synchronization strengths for a given dataset. For (b) and (c),

the denominator 2 M22 is the normalization factor. For the

completely uncorrelated case the numerator is 0, while for

completely correlated case the numerator D1{0DzD1{0Dz

???zD1{MD~M{1zD1{MD~2M{2: Therefore, the genuine

PSS, spurious PSS and total PSS have a value within 0 and 1,

respectively. See Table 2 for a glossary of terms.

In the equations (1), (2) and (3), the PSS indices were estimated

based on the ensemble average from segmented small windows. In

the equations (1), (2) and (3), a 10 second-long EEG epoch was

segmented into smaller windows (2 seconds). The average

eigenvalue li for an EEG epoch (i) was estimated from the

ensemble of small windows. For l

were generated for the original EEG epoch and segmented into

smaller windows in the same way. The randomized data set has

the same power spectrum and amplitude distribution of the

original data [33]. This ensemble average reduces the variability in

the estimation of phase synchronization for a given EEG epoch.

s

i, 20 randomized EEG datasets

Testing the Performance of this Method with Simulated

EEG Data

The validity of the genuine and spurious PSS was tested with

multivariate model data, in which the mean frequency and the

phase coherence were modulated. We hypothesized that lower

mean frequency produces higher spurious PSS and that genuine

PSS correlates well with the given phase coherence. With the

simulated EEG time series, we investigated the effects of mean

frequency, phase coherence and their combination on the

spurious, genuine and total PSS. Twenty time series were

generated from N-tori [35]:

Xi(t)~

X

Nf

j~1

Ai(fj)sin(2pfjtzdi,j),

i~1,2,???,20:

ð4Þ

The amplitudes Ai(fi) was adjusted with the Wigner distribution

[36]:

Ai(x)2~p

2xe{px2=4,where x~

f

vfw:

ð5Þ

A time series, Xiis the superposition of Nf~5,000 sine waves

with randomly chosen frequencies f[½0,100Hz?. The mean

frequency, SfjT, was set to be 10 Hz in the first half of the period,

and it was linearly shifted to 1 Hz in the second half to see the

effect of mean frequency on the PSS indices. However, the total

power was kept constant over all time series and throughout a time

series. The phase coherence between time series was determined

by the partial phase of sine wave di,j. For no phase coherency

between time series, the partial phases di,j for each time series

Xiwas chosen from a uniform distribution ranging from 0 to 2p.

On the other hand, for a phase coherency between time series, the

partial phase di,j for each time series was chosen from a normal

distribution with mean phase (i.e.,3p=4). The strength of phase

coherence was modulated with the standard deviation of phase

distribution: a smaller standard deviation produces stronger phase

coherence. The sampling frequency was 200 Hz in this simulated

dataset. The mean frequency and the phase coherence of the time

series were modulated in different ways in seven time periods (See

Table 3).

(1) The first period (0–20 s): the phases di,j were set to be

uniformly distributed (0–2p) and SfTis 10 Hz. Thus the time

series are independent. Zero genuine PSS but non-zero

spurious PSS were expected.

(2) The second period (20–40 s): the distribution of phases was

transformed from the uniform distribution to the normal

distribution with mean of3p=4and standard deviation of1p=6.

Table 2. Glossary.

Term Definition

Spurious PSSEstimation of spurious elements produced by a specific spectral content in a finite data length in the phase synchronization for

a given two EEG signals.

Genuine PSSEvaluation of how much the phase synchronization of a given EEG signal deviates from the estimated spurious PSS.

Total PSSEstimation of the amount of total phase synchronization (spurious and genuine PSS) between two EEG signals.

Eigenvalue/eigenvectorThese concepts are used in linear algebra, representing the properties of a matrix. In a diagonalized matrix, the eigenvalues are

the numbers on the diagonal and the eigenvectors are the basis vector to which these numbers refer. This enables the analysis

of a given matrix in a way similar to a diagonal matrix, which simplifies the process. In a diagonalized coherence matrix, we can

more easily determine the principle coherence elements with large eigenvalues.

Randomized (surrogate) dataA replica of a given EEG signal that retains the original spectral contents but with randomized phases.

Ensemble averageA given time series is replicated many times over in order to generate an enormous number of copies. The replica is allowed to

differ microscopically in the time series, while retaining the same general properties (such as spectral content). Such a collection

of replicated time series is called an ensemble, and the average is called an ensemble average.

Definitions of terminology used. PSS=phase synchronization strength, EEG=electroencephalogram.

doi:10.1371/journal.pone.0046313.t002

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Thus, the phase coherence was gradually increasing. A

gradually increasing genuine PSS was expected.

(3) The third period (40–60 s): the same normal distribution of

phases was given. Therefore, the phase coherence is

maintained at the same level. No changes were expected in

genuine and spurious PSS.

(4) The fourth period (60–80 s): Using the normal distribution of

phases, the mean frequency SfT was shifted from 10 Hz to

1 Hz. A gradually increasing spurious PSS was expected.

(5) The fifth period (80–100 s): the same normal distribution of

phases and the mean frequency SfT=1 Hz are used. No

changes were expected in genuine and spurious PSS.

(6) The sixth period (100–120 s): the distribution of phases is

transformed from the normal distribution to the uniform

distribution, while SfT=1 Hz. The phase coherence is

gradually decreasing. Thus, a gradually decreasing genuine

PSS was expected.

(7) The seventh period (120–140 s): the uniform distribution of

phases is maintained, while SfT=1 Hz. No changes were

expected in genuine and spurious PSS.

Application to EEG during General Anesthesia

The PSS indices were applied to anesthesia EEG data, which

consisted of three different states: baseline conscious state,

unconscious state (loss of consciousness, LOC) and recovery state

(return of consciousness, ROC). Each state consisted of a 5

minute-long EEG epoch. The moving window method was used

to investigate the temporal evolution patterns of the genuine,

spurious and total PSS during general anesthesia. The window size

of 10 seconds without overlap was used to achieve the appropriate

time resolution for the fast state transitions during general

anesthesia, which take place in a short term after LOC and

before ROC. To obtain an ensemble of phase synchronization

matrices in the equation (1), (2) and (3), the 10 second-long

windows were segmented into five sub-windows (2 second long

windows without overlapping). Thus, for a 10 second-long EEG

window, 5 sub-windows of original EEG data and 100 (=5620)

sub-windows of 20 randomized data sets were generated. The

mean and standard deviation of eigenvalues were calculated with

these ensembles of sub-windows for the original EEG and

randomized EEG data sets. The 2 second-long sub-window was

determined as the smallest among various sizes that gave similar

PSS indices as larger sub-windows tested. The 10 second long

window was determined by a trade-off of the best time resolution

to assess the temporal pattern of state transitions and the

robustness of the PSS results, which was accomplished by

searching various sizes of the window (10 to 30 seconds). In

addition, since anesthesia EEG is highly non-stationary, this

ensemble average with sub-windows would reduce the variability

in the estimation of PSS indices.

Assessing the Role of EEG References

The effect of EEG reference on the genuine, spurious and total

PSS indices was studied with four different types of EEG

references (unipolar, common average, longitudinal bipolar and

transverse bipolar). For the unipolar EEG reference, the A2

channel was used as the referential electrode; for the common

average EEG reference, the averaged EEG over 21 EEG channels

at each time t was used as the reference. For the longitudinal

bipolar EEG reference, (Fp1-F7, F7-T7, T7-P7, Fp1-F5, F5-C3,

Fp2-F6, F4-C4, F8-T8, CZ-P4, Fz-Cz, Fp1-F3, F3-C3, C3-P3,

Fp2-F4, F6-C4, T8-P8, C4-P6, Cz-Pz:18 longitudinal bipolar

montage) were used. For the transverse bipolar EEG reference,

(FP1-Fp2, Fp2-F8, F7-F5, F5-F3, F3-Fz, Fz-F4, F4-F6, F6-F8, T7-

C3, C3-Cz, Cz-C4, C4-T8, P7-P5, P5-P3, P3-P4, Pz-P4, P4-P6,

P6-P8:18 transverse bipolar montage) were used. The referential

montages were chosen according to the standard electrode

montage of the American Clinical Neurophysiology Society [37].

Since O1 and O2 channels were not recorded in this study, we

used a modified referential montage without O1 and O2.

Statistical Analysis

The moving window analysis was not well-suited to a repeated

measures one-way ANOVA because of the many repeated

measurements (, 30 windows). Thus, to apply the conventional

ANOVA and post-hoc analysis, each state (consciousness,

anesthesia, recovery) was separated into two sub-states. The

Baseline conscious state was separated into B1 (from 0 to 2.5

minutes) and B2 (from 2.5 minutes to 5 minutes), the Anesthetized

state was separated into A1 (0 to 2.5 minutes after LOC) and A2

(22.5 to 0 minutes before ROC) and the Recovery state was

separated into R1 (0 to 2.5 minutes after ROC) and R2 (2.5 to 5

minutes after ROC). Since the duration of the anesthetized state is

different for each subject, we separated the sub-states based on the

LOC and ROC times in order to facilitate statistical comparison.

The three PSS indices were compared across the six sub-states; the

significance was assessed by a repeated measures one-way

ANOVA and a post hoc analysis using Tukey’s multi-comparison

test. A p value ,0.05 was considered significant. The GraphPad

Prism Version 5.0c (GraphPad Software Inc. San Diego CA) was

used.

Author Contributions

Conceived and designed the experiments: UCL GAM. Performed the

experiments: GJN. Analyzed the data: UCL HSL MM. Contributed

reagents/materials/analysis tools: GJN. Wrote the paper: UCL HSL MM

GAM.

Table 3. The dominant frequency and phase coherence of the seven periods in the simulation data.

Time period (second)0–20 20–4040–6060–8080–100100–120120–140

Phase distributionUURNNNNNRUU

Dominant frequency (Hz)10 101010R1111

Expected genuine/spurious Phase

coherence

0/«

X/«

q/«

q/X

q/q

Y/q

0/q

‘U’ indicates the uniform distribution of phases (0–2p), and ‘N’ indicates the normal distribution of mean of3p=4and standard deviation ofp=6. URN denotes the linear

transition from the uniform distribution to the normal distribution, and vice versa for NRU. ‘«’ denotes a maintained value. ‘q’ denotes an increased value. ‘X’ denotes

a linearly increasing value. ‘Y’ is vice versa.

doi:10.1371/journal.pone.0046313.t003

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