Measuring phase synchrony in brain signals

Measuring Phase Synchrony in Brain Signals

Jean-Philippe Lachaux,Eugenio Rodriguez,Jacques Martinerie,

and Francisco J.Varela*

Laboratoire de Neurosciences Cognitives et Imagerie Ce′re′brale,CNRS UPR640

Ho?pital de La Salpe?trie`re,Paris,France

??Abstract:This article presents,for the?rst time,a practical method for the direct quanti?cation of frequency-speci?c synchronization(i.e.,transient phase-locking)between two neuroelectric signals.The motivation for its development is to be able to examine the role of neural synchronies as a putative mechanism for long-range neural integration during cognitive tasks.The method,called phase-locking statistics(PLS),measures the signi?cance of the phase covariance between two signals with a reasonable time-resolution(?100ms).Unlike the more traditional method of spectral coherence,PLS separates the phase and amplitude components and can be directly interpreted in the framework of neural integration. To validate synchrony values against background?uctuations,PLS uses surrogate data and thus makes no a priori assumptions on the nature of the experimental data.We also apply PLS to investigate intracortical recordings from an epileptic patient performing a visual discrimination task.We?nd large-scale synchronies in the gamma band(45Hz),e.g.,between hippocampus and frontal gyrus,and local synchronies, within a limbic region,a few cm apart.W e argue that whereas long-scale effects do re?ect cognitive processing, short-scale synchronies are likely to be due to volume conduction.W e discuss ways to separate such conduction effects from true signal synchrony.Hum Brain Mapping8:194–208,1999.?1999W iley-L iss,I nc.

Key words:neural synchrony;phase-locking;coherence;EEG;EcoG;epilepsy;gamma-band;deblurring ??

INTRODUCTION

Cognitive acts require the integration of numerous functional areas widely distributed over the brain and in constant interaction with each other[Friston et al., 1997;Tonini and Edelman,1998].It has become a topic of much interest to explore the possibility that such large-scale integration could be mediated by neuronal groups that oscillate in the gamma range(30–80Hz, also referred to as40Hz)that enter into precise phase-locking over a limited period of time.(Hereafter,we refer to these phenomena simply as‘‘synchrony’’or ‘‘phase synchrony’’.)Whence the importance for a reliable and robust method for directly measuring such phase synchrony in this frequency band for experimentally recorded biological signals,which are not spikes,but local?eld potentials(LFP)of various degrees of spatial resolution.The purpose of this report is to introduce,for the?rst time,an effective method to estimate the instantaneous phase relationship between two neuroelectric or biomagnetic signals and to apply it to intracortically recorded signals in humans.W e also intro-duce the required statistical means to test the validity of the measured synchrony against the background?uctua-tions in a given experimental situation.

The role of synchronization of neuronal discharges, although not a new idea,has been greatly highlighted by results from microelectrodes in animals[see,e.g.,

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Science Frontier.

*Correspondence to:Dr.Francisco J.Varela,LENA-CNRS UPR640,

Ho?pital de La Salpe?trie`re,47Bd de l’Ho?pital,75651Paris cedex13,

France.E-mail:fv@ccr.jussieu.fr

Received for publication13March1998;accepted17May1999

?H uman B rain M apping8:194–208(1999)?

Singer and Gray,1995].In fact,two scales of phase synchrony can be distinguished:most animal studies based on microelectrode recordings have dealt with short-range synchronies[e.g.,Gray et al.,1989;Neuen-schwander et al.,1996],or between adjacent areas corre-sponding to a single sensory modality[e.g.,Ko¨nig et al.,1995].These local synchronies have been inter-preted most commonly as subserving‘‘perceptual bind-ing.’’More recently,evidence has also been found for long-range synchronizations between widely separated brain regions[Roelfsema et al.,1997].This is in agreement with the more general notion that phase synchrony should subserve not just binding of sensory attributes, but the overall integration of all dimensions of a cognitive act,including associative memory,emotional tone,and motor planning[Damasio,1990;Varela,1995].

These multiunit studies in animals have been comple-mented by studies at coarser levels of resolution in humans and animals.In fact,gamma band responses can be recorded during visual discrimination protocols on the human scalp[Tallon-Baudry et al.,1997]and in subdural electrocorticograms[Le van Quyen et al., 1997;Lachaux et al.,1999a].One can distinguish an early(100ms)response phase-locked to the stimulus or evoked response,and a later(200ms)induced re-sponse nonphase-locked to the stimulus.Both these responses necessarily imply a degree of local phase-locking,since otherwise no signal would reach the surface of cortex or scalp with enough amplitude. They would annihilate due to the summation of phases distributed very broadly.Thus there is some evidence to suggest that synchronization mechanisms as those found in single-unit studies in animals also occur at large scales recorded with macroelectrodes; they are long-range synchronies.

However,the quanti?cation of phase synchrony between macroelectrodes(EEG/MEG or intracortical recordings)requires methods that are entirely different that the cross-correlograms between spike discharges that suffice for microelectrode studies.This is the main purpose of the present study.But in this context,it is important to distinguish very sharply between syn-chrony(as de?ned above)and the classical measures of spectral covariance or coherence that have been extensively used elsewhere[Bullock and McClune, 1989;Bressler et al.,1993;Menon et al.,1996].Unfortu-nately,coherence is a measure that does not separate the effects of amplitude and phase in the interrelations between to signals.This point is discussed in detail later,but the novelty of our results is to a large extent simply to arrive at a measure where the phase compo-nent is obtained separately from the amplitude compo-nent for a given frequency.Only then can one proceed to test the synchrony hypothesis for brain integration. In a separate work,we have successfully applied the present method for the detection of gamma synchro-nies over the scalp during visual perception[Rod-riguez et al.,1999].Here,we present the methods in extenso on the basis of simulations and intracortical recordings as an ideal test case.

This report is divided into three main sections.The ?rst introduces a new technique for phase-locking detection:the phase-locking statistics(PLS).The sec-ond section applies PLS to LFP data from human intracortical recordings.In the third section,we exam-ine the problem of volume conduction and the choice of a reference electrode,the two main difficulties associated with the interpretation of synchrony results.

QUANTIFICATION OF PHASE-LOCKING

Phase-locking statistics

Here,we introduce our method of detecting syn-chrony in a precise frequency range between two recording sites.This method uses responses to a repeated stimulus and looks for latencies at which the phase difference between the signals varies little across trials(phase-locking).Given two series of signals x and y and a frequency of interest f,the procedure computes for each latency a measure of phase-locking between the components of x and y at frequency f(we call this measure phase-locking value,or PLV).This needs the extraction of the instantaneous phase of every signal at the target frequency.The procedure follows three steps (Fig.1).

Step1.We band-pass?lter(?nite impulse response of length?300ms)each signal between(f?2Hz). Step2.We compute its convolution with a complex Gabor wavelet centered at frequency f:

G(t,f)?exp1?t22?t22exp5j2?ft6.

Following Grossman[1989],we chose?t?7/f.For instance,?t?140ms for f?50Hz.The phase of this convolution?(t,n)is extracted for all time-bins t,trial n[1,...,N],and for each of the pair of electrodes. The phase locking value(PLV)is then de?ned at time t as the average value:

PLV t?

1

N0?n?1N exp(j?(t,n))

where?(t,n)is the phase difference?1(t,n)??2(t,n). PLV measures the intertrial variability of this phase

?P hase S ynchrony D etection?

difference at t:If the phase difference varies little across the trials,PLV is close to1;it is close to zero otherwise (Fig.2).This procedure can be repeated for several frequencies in order to study a broader frequency range.

Step 3.The third step,or‘‘test,’’is to build a statistical test based on surrogate data[Theiler et al., 1992,Mu¨ller-Gerking et al.,1996]to differentiate signi?-cant PLV against background?uctuations.Formerly, we test our samples of phase differences for random-ness against a unimodal distribution with an unspeci-?ed mean direction.The Raleigh test can be used [Fisher,1993]to test the H0hypothesis that our samples are drawn from a uniform distribution.However,in our case,the sampling distribution of a statistic is not known and we cannot assume uniformity.This can be seen in a simple example.Let us assume two indepen-dent neural populations that start to oscillate at40Hz in response to stimulation after a random delay of 50–55ms.The phase of these oscillations at55ms will vary from trial to trial from0–90°(5ms is about a quarter of a cycle at40Hz).Therefore,the phase difference between these two neural groups will reach values only between?90°and90°,which is not uniform.Yet,a Raleigh test would conclude that the phase differences are not uniformly distributed and

Figure1.

Evaluation of the instantaneous phase of a signal for a frequency f. As a?rst step,the raw signal s(t)is band-pass?ltered to generate f(t)(step1);the convolution of f(t)with a Morlet wavelet centered at frequency F provides the envelope a(t)and the instantaneous phase?(t)(step2).?(t)can also be inferred(bottom left)from a comparison between the latencies of f’s maxima(black points)and reference time markers(black ticks separated by a constant interval:1/f).Both methods give the same results.To test the methods,we generated a signal x(t)?sin(2?Ft??(t)),with abrupt phase variations,and computed?(t),an estimator of?(t). On the bottom right,inset shows cos(?(t))(rectangular function) together with cos(?(t))(smooth approximation).

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would detect a phase-locking between the groups. When the sampling distribution of a statistic is un-known,one must rely on recent techniques of random-ization,or bootstrap[Fisher,1993].Our statistical test is based on randomization and is adapted to our particular set of data.

The main advantage of this approach is that it does not require any a priori hypothesis on the signals.We test the H0hypothesis that the two series of phase values?1(n)and?2(n)are independent.For this purpose,we generate200new series of variables, which have the same characteristics as the original signal coming from electrode2,except that we built them to be independent of the signals coming from electrode1.These series are created by shuffling the trials within the measures of electrode2to make new series y?(n)?y(shuffle(n)),where(y(i)is the signal recorded at electrode2during trial i(Fig.2).

For each surrogate series y?,we measure the maxi-mum between x and y?in time.These200values are used to estimate the signi?cance of PLV between the original signals x and y.The proportion of surrogate values higher than the original PLV(between x and y) for a time t is called phase-locking statistics(PLS).It measures the probability of having false positives for a given level of signi?cance.In this study,we used a criterion of5%(PLS?5%)to characterize signi?cant synchrony,but this is,of course,a function of the required rigor of signi?cance in the context of the signals being studied.Our method is related to an approach proposed by Friston et al.[1997]to quantify MEG data.In fact,they propose to estimate the

Figure2.

Estimation of phase-locking value.Left:Our synchrony index is directly related to the intertrial variability of the phase differences between two electrodes(see description of the method for details).By averaging these phase differences across the trials,we obtain a complex value u(for each latency t),which amplitude(abs (u))is the phase-locking value.Right:Surrogate data are con-structed by shuffling the trials of one of the electrodes(see text for details).

?P hase S ynchrony D etection?

correlation coefficient between two signals at a precise frequency,which implies a degree of phase-locking. Also,their statistical analysis was markedly different from ours.

Some comments are in order.In step1,one may wonder if the?ltering step is not redundant with the wavelet convolution and if it does not introduce artifacts.It seems that?(t,n)could be obtained directly by a convolution of the wavelet with the un?ltered signal(call this method A),instead of using a?ltering step prior to the convolution(method B).In fact,both methods were tested and led to slightly different results.We could make the following veri?cations of method B:(1)when transient40Hz oscillations easily could be seen in raw(un?ltered)data,we checked that the latencies of their peaks were identical with those of the?ltered signals,and(2)when the?ltered signal had clear oscillations,its exact phase could be read straight-forwardly from the latencies of the maxima of these oscillations(this direct lag estimation is slow,but highly reliable).By comparing this phase with our evaluation,we could check the exactness of method B. Since method A occasionally gave different results,we relied on method B.

In step3,the statistical method we use should detect any signi?cant phase synchrony between two elec-trodes,except in one important case:when the phase values?1(n)and?2(n)remains constant across the trials.In that situation,shuffling the trials within the measures of electrode2does not change the phase-locking value,whereas signals are actually synchronous. These false negatives easily can be detected since they are associated with high PL V.Also,they easily can be detected using simpler techniques that estimate the intertrial vari-ability of the phase of each electrode as recently proposed [T allon-Baudry et al.,1996;Lachaux et al.,1999a].

Why not use coherence?

Most studies that have attempted directly to study the putative importance of synchrony so far have employed a measure traditionally called frequency coherence(or more speci?cally,magnitude squared coherence,MSC)[Clifford Carter,1987].Thus the improvements provided by PLS are best seen in con-trast to MSC.The most salient differences are twofold. Coherence can be applied only to stationary signals. Coherence is a measure of the linear co-variance between two spectra.In particular,for each frequency f,the MSC is de?ned for two zero-mean stochastic processes by the squared modulus of their cross-spectral density at frequency f,normalized by their respective auto-spectra.These spectra can be estimated from?nite sets of data by:(1)subdividing the whole data sets into segments,(2)computing approximations of the spectra of each segment using a DFT(Discrete Fourier Transform),and(3)averaging these subspectra across all the segments.The quality of the estimation depends on the number and size of the segments [Clifford-Carter,1987].Segments are usually succes-sive time intervals,de?ned by a window sliding in time over the whole recording.In that case,a single measure of coherence typically needs several seconds of data,which limits the temporal resolution of the method.However,for protocols with repeated stimula-tions,coherence can be computed with a much better resolution because the window that de?nes the seg-ments can be slided across trials instead of being slided in time(event-related coherence).Yet,both methods require that each segment of data correspond to the same process with the same spectral properties.Since this assumption of stationarity(in time or across trials) can rarely be validated,we prefer a measure of phase-locking that does not require stationarity. Coherence does not speci?cally quantify phase-relationships.Coherence also increases with ampli-tude covariance,and the relative importance of ampli-tude and phase covariance in the coherence value is not clear.Since phase-locking is sufficient to conclude that two brain regions interact,it is important to develop alternative measures for the sole detection of phase covariance.In fact,there is no clear interpretation for the changes in coherence between two neural signals, beyond an obvious indication of interdependency.

In addition,the classic statistical analysis of coher-ence is not based on a comparison with trial-shifted surrogate data,but rather on a comparison with independent white noise signals[Clifford-Carter,1987]. Therefore,coherence statistics test the H0hypothesis that pairs of neural signals behave like independent white-noise signals.Since neural signals are not white-noise signals,this H0hypothesis might be too strong and might be rejected too easily.

Simulations

We?rst tested PLS with two series of signals phase-locked during two well-de?ned intervals in order to validate its temporal resolution.These signals were derived from two independent series of50 signals obtained from intracortical recordings of an epileptic patient(see next section)(s1(t,n?1...50) and s2(t,n?1...50),totaling50responses to two different stimuli measured in two different brain loca-

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tions.We applied a ?nite impulse response band-pass ?lter (41–45Hz)to s 1and s 2to generate two new series

s 1?and s 2?and computed a third series c 1??Bell ·s 1?

?(1?Bell ·)·s 2?.(Bell was a function always equal to zero,except during two periods of 75ms and 200ms where it was equal to 1(Fig.3.)

Signal s 2was then modi?ed into c 2?s 2?s 2??c 1?

,a signal synchronous with s 1(41–45Hz)during two short intervals.We computed PLS between s 1and c 2(target frequency ?43Hz)to test whether this method could detect and separate these two episodes.As shown in Figure 3a,the temporal resolution of PLS was precise enough to do so.It can,therefore,be used to detect short episodes of synchrony (in this case,three oscillation cycles at 40Hz,75msec)with a relatively small number of trials (50).

We devised a second simulation intended to illus-trate the inability MSC to separate phase and ampli-tude covariance.We used two series of signals phase-locked during two well-de?ned intervals,but with independent amplitudes.We expected that a lack of amplitude covariance would induce MSC ignore syn-chrony,but not PLS.

This simulation was very similar to the previous one:using two independent series (50trials)of data s ?1and s ?2,we repeated the above procedure to generate

two series s ?1?and s ?2?and a third series c ?1??Bell ?·s ?1??(1?Bell ?·)·s ?2?.(In this case,Bell ?had two

nonzero periods lasting 200ms each.)s 2was this time

modi?ed into c 2?s 2?s 2??random ·c 1?

,where random was a value randomly chosen between 0and 1and different for each trial.This number was introduced to make the amplitudes of the signals independent,so that synchronous periods speci?ed by Bell ?corre-sponded solely to phase-coupling and not to ampli-tude covariance.The results of this simulation are shown in Figure 3b;as expected,MSC was reduced to the level of noise during the ?rst episode of synchrony .In contrast,PLS detects both episodes of synchrony correctly .Interestingly,in our simulations MSC did not give false positives when there was amplitude covariance,but not phase locking.Thus our tentative conclusion so far is that MSC is fooled specially by synchronies that are not accompanied by high amplitude covariances.

MEASURING SYNCHRONIES IN HUMAN

INTRACORTICAL RECORDINGS

Subjects and recordings

Here,we examine the results of applying PLS to subdural recordings of an epileptic patient performing a visual discrimination task.Details of the experimen-tal conditions can be found elsewhere [Lachaux et al.,1999a].This right medial temporal epilepsy patient (subject PI)required intracranial EEG monitoring to con?rm the exact site of the epileptogenic zone before surgical treatment.Four electrodes plots,each with eight recording sites,were inserted along occipito-Figure 3.

(a ).Estimation of PLV’s temporal resolution.Two periods of high synchrony are simulated.Synchrony periods are characterized by nonzero values of the bell function (see text for details).Values are plotted as a function of time;values above the horizontal line are signi?cant (PLS ?0.05).Synchrony can be detected in segments as short as 75ms.(b ).Estimation of PLV’s detection resolution.As in Figure 3,two periods of high synchrony are simulated (nonzero values of the bell function (see text for details).PLV and MSC values are plotted as a function of time;PLV above the horizontal line are signi?cant (PLS ?0.05).During periods of low amplitude co-variance,MSC gives a false negative.

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limbic and fronto-cingulate trajectories.The positions of the electrodes obtained from IRM are given in Table

I.The task was a classic visual oddball discrimination:

a panel of80red-light diodes(targets)was lighted randomly interleaved with320green diodes(nontar-gets).The stimuli were turned on for40ms,with an interstimulus interval varying randomly between800 ms and1,200ms.The patient had to press a button in response to target stimuli only.Electrical data were recorded relative to an average reference.

In a previous study of gamma emission from compa-rable human data using the same protocol,we had found that a speci?c response around45Hz is trig-gered speci?cally by the stimuli[Lachaux et al.,1999a]. Accordingly,we focused our study of PLS only around this frequency.

Results

The matrices of PLS values for all pairs of electrodes and both target and nontarget stimuli are shown in Figure4(see legend for conventions).As for the stimulation effect,signi?cant synchronies are slightly more common between left hippocampus and frontal-cingulate regions.On the whole,however,the syn-chrony patterns are roughly comparable for both conditions,although slightly increased for the nontar-get condition.It is important to make it clear that our purpose here was not to study in detail the neuro-signi?cance of phase-locking related to the visual task performed by the subject.This would entail a careful analysis of the time courses of synchrony and of the differences between target vs.nontarget,following Rodriguez and colleagues[1999].For subject PI,such a study is made difficult by the clinical constraints for electrode placement,preventing a choice of positions that would be more consonant given the chosen cognitive task.Thus we?nd only a very limited change in synchrony over time and between condi-tions.Accordingly,our aim here is more modest:to apply our method to real signals(subdural LFP poten-tials)in order to verify the existence of stimulus-triggered gamma synchronies between electrodes from signals of this intermediate level of resolution(as compared to scalp recordings)and to distinguish between short-range and long-range synchrony. Local synchronies.If we?rst focus on the short range for synchronies found within the same region of electrodes(limbic or frontal,left or right),it is easily seen that the intensity of phase-locking(quanti?ed by PLV)decreases steadily with interelectrode separation. For instance,in the right limbic recordings of this patient (which correspond to a necrotic hippocampus where the epileptic focus was diagnosed),synchrony extends up to interelectrode distances of up8cm(Fig.5).

However,these observations are an artifact due to the fact that neighboring electrodes simply will record the same?eld potential due to volume conduction and are thus trivially synchronous.To distinguish between volume conduction and true synchrony is actually the main difficulty that limits the understanding of syn-chrony at short range.The right hippocampus contains damaged tissues with a higher conductivity than normal,thus enhancing volume conduction locally.In contrast,in the left limbic region,synchrony decreased much faster with electrode separation,and it did not extend beyond2cm.This result coincides very well with the?ndings by Menon et al.[1996]on normal human subdural recordings,showing that short range synchrony decreased sharply after2cm of in-terelectrode distance.They explained these results by strong local lateral connections that would induce synchronization of neighboring neurons within the2 cm radius.In our view,simple passive volume conduc-tion also may create such spurious synchrony(see next section).

Long-range synchronies.In contrast with synchrony within regions(short-range synchrony),synchrony be-tween locations(long-range synchrony)varied in time

TABLE I.Electrodes positions for subject PI*

1.R anterior amygdalia

2.R hippocampus—head

3.R hippocampus—anterior

4.R hippocampus—body

5.R white matter

6.R white matter

7.R temporo-occipital sulcus

8.R temporo-occipital gyrus

9.L anterior amygdalia

10.L hippocampus—head

11.L hippocampus—anterior

12.L hippocampus—body

13.L white matter/hippo-

campus(posterior)

14.L white matter

15.L white matter

16.L temporo-occipital sulcus

17.R medial gyrus

18.R anterior cingulate

gyrus 19.R anterior cingulate

gyrus

20.R frontal superior gyrus

21.R frontal superior gyrus

22.R frontal superior gyrus

23.R front superior gyrus/

arachnoide space

24.R perimeningeal space

25.L medio orbital gyrus/

olfactory sulcus

26.L anterior cingulate

gyrus/cingular sulcus 27.L anterior cingulate

gyrus

28.L frontal superior gyrus

29.L frontal superior gyrus

30.L frontal superior gyrus

31.L front superior gyrus/

arachnoide space

32.L perimeningeal space

*R?right hemisphere;L?left hemisphere.

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and occurred only between speci?c pairs of electrodes with no relation to interelectrode separation.For in-stance,the right-limbic vs.left-frontal quadrant of the matrix in Figure 4shows the localized emergence and disappearance of synchronies over time.The timing of this pair is quite different from its converse,with the left-limbic region.

We conclude that these observations are convincing evidence that signi?cant long-range synchronies are established during this cognitive task involving deep limbic and frontal regions.These synchronies cannot be explained by volume conduction;it seems more likely that they represent a partial correlate of the functional integration mechanism during visual dis-crimination.A detailed account and cognitive analysis of long-range synchronies in intracortical recordings of

several epileptic patients will be presented elsewhere.The present results,along with previous reports [Bressler et al.,1993;Desmedt and Tomberg,1994;Friston et al.,1997;Roelfsema et al.,1997],strongly support the view that gamma synchrony acts as distributed unify-ing mechanism [Rodriguez et al.,1999].

SEPARATING SYNCHRONY FROM VOLUME

CONDUCTION As noted above,synchrony between two macro recordings is not always due to neural interactions.Whereas animal studies of synchrony are based on the coincidence of spikes recorded from microelectrodes (single or multiunit recordings),human studies use surface or implanted electrodes that integrate neural

Figure 4.

PLV values for subject PI.Values are presented for six consecutive time windows (stimulation occurs at zero ms).Boxes above diagonal (up-left)correspond to the target stimulation;those under diagonal (down-right)to nontargets.Each box represents the synchrony value for an electrode pair.If synchrony does not reach signi?cance,the box is ?lled by a circle with a dot in the center.When it reaches signi?cance threshold (PLS ?0.05),the square is ?lled to an extent proportional to the PLV value.

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activity over large volumes.When the volumes re-corded by two electrodes overlap,the shared neuronal population creates spurious synchrony between the signals (see Appendix).Here,we discuss ways to reduce such synchrony due to volume conduction (or ‘‘conduction synchrony’’)better to identify synchrony due to actual neural couplings (‘‘true synchrony’’).Two factors are important to examine:(1)volume conduction,and (2)an inappropriate choice of the reference electrode.In?uence of volume conduction on synchrony Separation between conduction synchrony and true synchrony.The separation between these two types of synchrony is difficult because they can occur at the same latencies and in the same frequency range (Fig.4).This contradicts a common assumption that conduc-tion synchrony should be broad-band and roughly constant in time,whereas true synchrony should be more speci?c.Another common assumption is that the phase difference between electrodes should be zero in case of conduction synchrony.This is usually false:even if two electrodes record the same group of sources,the signals of these electrodes are different linear combinations of the sources amplitudes,be-cause each source is recorded by the two electrodes in two different ways that depend on the relative position of the source and the electrodes.Therefore,the phase

of the signals recorded by the two electrodes should be different,except if all the sources have the same phase.One can still suggest a rule of thumb based on intersite comparison.If volume conduction creates high synchrony between two electrodes,then high synchrony also should be observed between their neighbors.In other words,in general,when there is synchrony due to diffusion,there should be diffusion of synchrony.This diffusion of synchrony is precisely the effect shown in Figure 4within regions,but not between them.Y et,this rule of thumb falls short of providing a reliable test to identify conduction synchronies.

Reducing volume conduction.Since there is no univer-sal rule to distinguish true synchrony from conduction synchrony,one must rely on recordings with high spatial resolution in which the overlap between the brain volumes recorded by different probes is mini-mum.In this sense,subdural recordings constitute an ideal study case.To study normal subjects,the use of EEG or MEG is the most common option.MEG should be preferred:volume effects are less severe because the head tissues induce no diffusion of the magnetic ?eld,in contrast with electrical potential [Ha ¨ma ¨la ¨inen et al.,1993].Also,the amplitude of the magnetic ?eld de-creases faster with distance than the electrical poten-tial,so that the volume recorded by an EEG electrode is larger than that recorded by a MEG sensor.In addition,the spatial resolution of MEG can be increased before estimating synchronies [Friston et al.,1997].

Still,most studies turn to EEG data since MEG remains a rare and expensive technique and because EEG can record sources con?guration not recorded by MEG.Two main techniques have been used to im-prove the spatial precision of EEG:(1)inverse deblur-ring [Le and Gevins,1993],and (2)the derivation of the scalp current density pro?les (SCD)[Pernier et al.,1988].W e tested on a simulation the efficiency of both methods for the study of synchrony from surface EEG recordings.This simulation mimics the experimental setting of a classic EEG sensory task in which 50repetitions of the same stimulus generate independent responses in two cortical locations.We selected two independent series of 50recordings from subject PI and used them as amplitudes of two sources placed in a spherical model of the head [for details see Lachaux et al.,1997].This three-layered model comprised:(1)brain (conductiv-ity ?1,arbitrary units;radius ?8.5cm),(2)skull (conductivity ?0.0128;radius ?9.2cm),(3)skin (con-ductivity ?1;radius,10cm)(in?nite reference:poten-tial is zero far from the sphere).Electrical sources were expressed as two dipoles with radial orientations with respect to the scalp,located in two super?cial symmet-Figure 5.

PLV as a function of distance for the right temporal electrodes of subject PI.A regular 1cm spacing separates eight electrodes.The synchrony decreases almost linearly from 1to 0when the interelectrodes distance increases.

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ric positions in each hemisphere (see Fig.6).The surface activity induced by these dipoles was com-puted (forward calculation)using the software BESA [Scherg,1990]in 55scalp positions for all 50trials.

The EEG thus obtained was treated by a variation of the deblurring technique originally proposed by Le and Gevins [1993]to calculate the corresponding ECoG (backward calculation).Using BESA,we also computed the potential generated by the two dipoles on the cortex (i.e.,the true EcoG,forward problem)to check the accuracy of the ECoG reconstructed by deblurring.The dipole model and the corresponding EEG and ECoG are shown in Figure 6.

We then computed the phase-locking values for the scalp and cortical positions lying on a left-right axis (T7-Cz-T8).For comparison,we computed the scalp

current density on this spherical model [Pernier et al.,1988]and the PLV between the SCDs at these same scalp positions (Fig.7,EEG and ECoG;Fig.8,SCD).Since the sources of this model were indepen-dent,all signi?cant PLS were due to conduction synchrony.

As shown in Figure 7,deblurring sharpened the borders of synchronous regions and reduced spurious synchronies (Fig.7).SCD produced comparable ef-fects,but slightly less detailed.Therefore,these meth-ods seem useful ?rst steps before the estimation of synchrony from EEG recordings.In practical cases,SCD may be preferred because its computation is much simpler than deblurring.Precise deblurring requires a description of the geometry and the conduc-tivity of each individual’s skull and skin.

Figure 6.

Simulation of an EEG and its corresponding ECoG.Two radial dipoles were placed in symmetric positions in the (T7-Cz-T8)plane,containing both ears and the head’s vertex (c ).EEG generated by these dipoles was computed,and ECoG reconstructed using a deblurring technique.(a )EEG cartography for two dipoles with same amplitude (b )corresponding ECoG.(d )EEG and ECoG contributions of each dipole as a function of laterality along a T7-Cz-T8axis.

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P hase S ynchrony D etection ?

In a recent study,Nunez and colleagues[1997]tested the effect of volume conduction on the correlation between electrodes and found converging conclusions. Independent distributed sources were simulated in a volume conductor model of the head,the correspond-ing EEG was calculated in64scalp positions,and the squared correlation coefficient was computed as a function of interelectrode separation.Granted,correla-tion coefficient is not a close estimate of synchrony; Nunez et al.[1997]also suggested using SCD or EcoG estimations to reduce conduction interactions.

In?uence of the reference-electrode on synchrony Apart from volume conduction,the other major problem in synchrony estimation is the choice of the reference electrode.This problem uniquely concerns EEG;another reason to prefer the MEG technique.For electric recordings,a review of the literature on fre-quency coherence provides no general agreement on the optimal reference.In the present study,we took an average reference to study epileptic data and an in?nite reference in the electrocorticogram simulation. Figure9shows results obtained with other references. When subtracting a reference term,it is not clear whether synchrony should decrease(because a common part of the signals is removed),or increase(because a common term is arti?cially added to all the signals).When studying EEG, the computation of scalp current density is often a way to solve the reference problem,because spatial derivation makes this term disappear.But our simulations(Fig.9) show that this processing can create arti?cial synchronies. However,we used here spline interpolations to estimate SCDs[Pernier et al.,1988];other approaches are possible and they may yield a better estimation[Lagerlund et al., 1995].Nunez and colleagues[1997]proposed a detailed

Figure7.

PLV values for simulated EEG and https://www.wendangku.net/doc/db3668891.html,ing the same presenta-tion as for Figure5,PLV is presented for n electrodes lying on the T7-Cz-T8lines.Electrodes are referred by their position along this axis from left(left ear)to right(right ear).For some electrode pairs,synchrony is signi?cant between a and b(up-left part of the matrix),but not between b and a(bottom-right part of the matrix). In other words,maps are not rigorously symmetric.This is because the surrogate PLV distributions are not strictly the same in the two cases,and thus the5%signi?cance thresholds may be slightly different.

?L achaux et al.?

study of the in?uence of reference on interelectrode corre-lation coefficients.They argue that it is impossible to predict the effect of a reference on scalp coherence without both an accurate volume conductor model and a priori knowledge of all sources locations.

In brief,the question of the distinction between synchrony due to volume conduction and synchrony as functional neural integration is still inconclusive.Here,we note some steps in that direction,but none that provide a complete solution.

DISCUSSION

Narrow vs.broad frequency bands

One of the main limitations of the method presented here is that it depends crucially on the choice of a

speci?c frequency for analysis in order to separate the amplitude and phase components of the signals.This separation is meaningless if one needs to work with a broad band.Further,choosing a given frequency needs ?lters with excellent resolutions in both time and frequency,which do not change the phase.(Our choice,a classic ?nite impulse response ?lter,may not be optimum.)

Yet,a careful time frequency analysis of intracortical and scalp data shows that their spectral content is very broad (between 0–80Hz0,and the relative amplitudes varies considerably over time during an experimental situation [Tallon-Baudry et al.,1997;Lachaux et al.,1999a;Rodriguez et al.,1999].It is of the greatest interest to investigate if there are interactions between frequencies located in different bands and what,if any,is their functional signi?cance.PLS permits only a

Figure 8.

PLV values for simulated scalp current density.SCD is computed from EEG presented on Figure 6.Up-left:Contributions of each dipole to SCD are presented as a function of laterality along a T7-Cz-T8axis.Right:PLV values are presented for electrodes lying on this axis.

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P hase S ynchrony D etection ?

limited answer to these questions,since the same analysis can be repeated over several bands.However,a complete answer would require a method based on a broad-band calculation of synchrony.Such an ap-proach takes us far away from classical methods,but is an active area of study in mathematical physics.

Average vs.single trial

A second important limitation of the method intro-duced here is that it focuses on the detection of phase-locking between pairs recordings across trials:i.e.,the likelihood that phase-difference between the oscillations of two neural populations remains the same from trial to trial for a given delay in time.This excludes those synchronies that are not established with a ?xed delay from trial to trial.In order to extract

such information,one needs to introduce averaging or smoothing procedures over time and to work on the basis of single trials,not averages.An analogy for the study of gamma band emission can be helpful here.PLS can be compared to the procedures that detect the evoked gamma emission,but fail to detect the induced responses.In fact,induced responses are not stimulus locked and thus require a trial by trials analysis to construct a probability distribution [Tallon-Baudry et al.,1997;Lachaux et al.,1999a].PLS cannot detect this second type of single-trial phase locking if the phase-difference varies in latency between trials.

The detection of this second type of phase-locking in single trials is possible using a recent technique,smoothed phase locking statistics (SPLS)that we have introduced recently [Lachaux et al.,1999b].The appli-cation of this improved approach will tell,in time,if

Figure 9.

Effect of reference electrode on PLV values.We computed PLV for the simulated EEG data presented in Figure 7,using an average electrode (left),instead of the in?nite reference used for Figure 7.We also computed synchrony for subject PI for both stimulation conditions using no reference instead of average reference;spurious synchronies appear for almost all pairs.

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functional neural synchronies are more common than we have shown in this report.

NOTE ADDED IN PROOF

After this paper was sent for publication,a recent publication introduced an alternative method to com-pute phase synchorny between bivariate data based on the Hilbert transform(Tass et al.,Physical Rev Letters 81:3291–94,1998).The two approaches are comparable in several respects.A study of their comparative advantages is being carried out.

ACKNOWLEDGMENTS

This work began a few years ago thanks to the essential contribution of Johannes Mu¨ller-Gerkin on MSC calculations.Our thanks also to Laurent Hugue-ville for his help on EcoG methods.

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?P hase S ynchrony D etection?

APPENDIX

Source of spurious synchronies

Here,we consider how volume conduction can induce spurious correlations between electrode poten-tials.For this purpose,we consider a set of micro-electrodes located within a brain area to record local-?eld potentials produced by an assembly of neurons with uncorrelated activities.

In response to a stimulation s,each neuron has an activation p(x,t,s),which is a function of its position x, time t,and s.Suppose to?x ideas that p(x,t,s)is a white-noise such that the mean value of p(x,t,s)2over time is unity.Since the neurons have uncorrelated activities,the mean value of p(x,t,s)·p(x?,t,s)across time and trials(we note it7p(x)·p(x?)8)is then?(x,x1), (i.e.,1if x?x?,0if not).

The local-?eld potential recorded by an electrode located in y,can be expressed as a linear combination of the sources amplitudes:

e(y,t,s)??h(y,x)·p(x,t,s)dx.

We consider further that all the electrodes are roughly located at the same distance around the sources,so that7e(y)8is roughly the same for all the electrodes. Thus we get a fair approximation of the correlation between the potentials in two positions y and y?by computing7e(y)·e(y?)8.This is done as follows.For any time t and sample s,

e(y,t,s)·e(y?,t,s)

?1?h(y,x)·p(x,t,s)·dx2·1?h(y?,x?)·p(x?,t,s)·dx?2 or

e(y,t,s)·e(y?,t,s)

???h(y,x)h(y?,x?)·p(x,t,s)·p(x?,t,s)dxdx?so that when averaging,

7e(y)·e(y?)8???h(y,x)h(y?,x?)·7p(x)·p(x?)8dxdx?or,

7e(y)·e(y?)8???h(y,x)h(y?,x?)·?(x,x?)dxdx??nally,

7e(y)·e(y?)8??h(y,x)h(y?,x)dx.

Thus due to volume-conduction,7e(y)·e(y?)8is non-zero even if there is no correlation at all between the two sources of activities.

?L achaux et al.?

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徐涛背诵大作战1—14天汇总

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恩格斯早就提出了自然界“对人进行报复”以及“人类同自然的和解”问题。实践的规律与人类不断自觉遵循物质世界的规律是一致的。正确的实践观点是理解人与自然关系、人与自然统一的关键。 四、小结 关于人与自然的辩证关系，相信有这些文字，考到这类题目我们肯定是能拿分的，但是在考场上还需要大家灵活处理，把它扩充为更多更详实的答案就可以了。 DAY2 【马原】意识的能动作用 一、使用场景 在做答马哲论述题的时候，如果题干材料中的主人公出现了以下两种情况，我们都用这个原理去进行做答： 1.人们遇到了一些困难时，开动脑子去思考解决困难的办法。一律用这个原理。 他为什么会思考呢、寻找解决问题的办法呢？就是因为他有意识，且意识有能动性，意识的能动性可以帮助我们去解决困难。 2.当人们利用自己的创意、设计去改变生活的时候。也要用这个原理。 因为我们有意识，而意识有能动性。 总结：只要是开动脑子去琢磨、思考、寻找、设计、想象等等的情况，一律都用这个原理进行作答。 下面这些文字必须要背熟，并且写上去。

徐之明马原详解

徐之明马原 马原24 单选：1-4 多选：17-21 分析：34 哲学-原理 政经-运用 科社-结果 第一章 本章为前言，三大内容：马克思主义产生、发展、属性 易考记忆形选择题 逻辑图很重要，把书读薄 第二章、第三章、第五章重点 内容：内容理论性强，考核目标一能力为主，难度最大 方法：弄懂概念，多做练习 二、 （一）、资本主义生产方式是发展为马克思主义的产生提供了经济、社会历史条件和客观基础。 （二）、马克思主义不是凭空产生的，对文明成果的继承与创新，是马克思主义产生的重要条件。其中，德国古典哲学、英国古典政治经济学和法国、英国的空想社会主义是马克思主义的直接的思想渊源。 命题模式：整体与局部 辩证法思想是黑格尔哲学体系的“合理内核” （三）无产阶级反对资产阶级的斗争、马克思恩格斯的革命实践，是马克思主义产生的实践基础。 19世纪30-40年代所发生的法国里昂工人起义、英国宪章运动以及德国西里西亚纺织工人的起义，标志着现代物产阶级作为独立的政治力量已经登上了历史舞台。 无产阶级是马克思主义的阶级基础（阶级性），无产阶级反对资产阶级的斗争，构成为马克思主义产生的现实需要。 （四）19世纪40-60年代，马克思恩格斯批判地继承了前人的成果，创立了唯物史观和剩余价值学说（两大发现），使社会主义从空想发展到科学，实现了人类思想史上的伟大革命。 1848年2月《共产党宣言》的发展，是主义产生的标志。马克思主义哲学、马克思主义政治经济学和科学社会主义，是马克思主义理论体系不可分割的三个主要组成部分。 第二节 马克思主义从产生到发展所表现出的强大生命力的（根源），在于它以实践为基础的（科学性）和（革命性）的统一。 马克思主义发展始终保持蓬勃生命力的（关键），是与时俱进的理论品质。一、马克思主义最根本的世界观和方法论 辩证唯物主义与历史唯物主义（马克思主义哲学）是马克思主义最根本的世界观和方法论。

小游戏----密室逃脱

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今天，老师带你们玩密室逃脱，你知道这个游戏怎么玩吗？师讲解游戏规则： 密室逃脱就是我们进入房间，通过数房间里各种物品的数量来推算出房门的密码，从而打开房门，逃出密室。 2、报数游戏： 让幼儿数数接龙。 师： 清点人数完毕，请你们摆一个最漂亮、最帅气的姿势跟老师们打个招呼，不然，待会出不来可能没有人来救你。 3、谈话： 你能数到几？ 师： 刚才集体报数完全正确，现在，我问问小朋友，你最多能数到几？我说一个数字，你接着往下数，往下数（）个数。（教师一方面关注幼儿数数是否正确，另一方面关注幼儿从十位数数到百位数数的能力，同时，观察其他幼儿，聆听每个幼儿的数数情况。）师： 小朋友们都能数到很大的数，真了不起！但你们数数的正确性怎么样呢？老师会在游戏中检查你们的本领。 2、进入密室： 探索正确数数的方法。 第一环节： 来到密室一： 出示PPT2

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