Synchronization in monkey visual cortex analyzedwith an information-theoretic measure

Nikolay V. Manyakova� and Marc M. Van Hulleb�

K.U.Leuven, Laboratorium voor Neuro- en Psychofysiologie, Campus Gasthuisberg, O&N 2, Bus 1021,Herestraat 49, B-3000 Leuven, Belgium

�Received 15 February 2008; accepted 2 June 2008; published online 22 September 2008�

We apply an information-theoretic measure for phase synchrony to local field potentials recordedwith a multi-electrode array implanted in area V4 of the monkey visual cortex during a reinforce-ment pairing experiment. We show for the first time that �1� the phase synchrony is significantlyhigher for the rewarded stimulus than the unrewarded one, after training the monkey; �2� just afterthe stimuli reversal, the difference in phase synchronization is due to the stimuli, not the reward; �3�the difference between reward and no reward is most clear in two disconnected time intervalsbetween stimuli onset and the expected delivery of the reward; and �4� synchronous activity appearsin waves running over the array, and their timing correlates well with the time intervals where thedifference between reward and no reward is most prominent. © 2008 American Institute of Physics.�DOI: 10.1063/1.2949928�

An electrode array was implanted in a visual region ofthe monkey brain, and from which local field potentials(LFPs) were recorded. Local field potentials are extracel-lular current flows. We compute the phase of the LFPsusing the Hilbert transform. We determine the normal-ized mutual information between pairs of LFP phases,and consider them to be in synchrony when the mutualinformation is high. We analyze the evolution of thephase synchrony in a stimulus-reward pairing experi-ment, and show that synchronous activity appears aswaves propagating over the array.

I. INTRODUCTION

Visual cortical processing is said to improve for stimulithat are consistently paired with reinforcement, and couldtherefore be a mechanism underlying perceptual learning�Seitz and Watanabe, 2005�. Previously, it was shown thatthe responses of macaque visual cortical neurons change as aresult of paired stimulus-reinforcement learning �Frankó etal., 2006�. The activity of neurons in cortical area V4 wasrecorded using a chronically implanted micro-electrode arrayduring consecutive training sessions in a classical condition-ing paradigm in which one stimulus was consistently pairedwith a fluid reward and another stimulus not. In the currentanalysis, we look at a difference in phase synchrony betweenthe local field potential �LFP� responses to these stimuli as afunction of time after stimulus onset, but well before thereward is expected. Local field potentials are extracellularcurrent flows that correspond mainly to the summed postsyn-aptic potentials from local groups of neurons �Buzsáki,2004�.

Previously Montemurro and co-workers �2008� haveshown that the low-frequency LFP phase yields additional

information, compared to the spike counts, when recordingfrom the primary visual cortex of anesthetized macaques ob-serving natural movies. The additional amount of informa-tion decreases from 54% in the 1–4 Hz band of the LFPphase to become equal to the spike count information forLFP phases frequencies greater than 24 Hz �which corre-sponds to the range where the major power in the LFP signalspectrum is concentrated�. Hence, analyzing LFP phases is atopic of interest in decoding LFP signals.

The phases of two coupled nonlinear oscillators maysynchronize even if their amplitudes are uncorrelated �Pik-ovsky et al., 2001�. Unlike coherence, which computes thelinear correlation between two stationary signals as a func-tion of frequency �Clifford Carter, 1987�, and which does notseparate the effects of amplitude and phase in the correspon-dence between these signals �Lachaux et al., 1999�, phasesynchrony describes exactly the similarity of their rhythmici-ties. Two signals �x and y� are synchronized when the phaselocking condition, i.e., ��t�= ��x�t�−�y�t� � �const, with �x

and �y the phases of x and y, respectively, applies for anytime t. However, the �unwrapped� phase difference is rarelyanalyzed directly. Instead, indices of bivariate phase syn-chrony are used for estimating the level of synchronization�for a review, see Pereda et al., 2005�. For example, Palušused the mutual information in the phase domain, which heapplied to electroencephalogram �EEG� �Paluš et al., 2001�and electrocardiogram �ECG� signals �Paluš et al., 2004�.However, this index has not yet been applied to LFPs, nor tomulti-unit recordings where the spatial arrangement of theelectrodes could provide additional information.

Great interest was raised by the recent discovery ofpropagating waves of LFP activity, and that they would me-diate information transfer in the cortex �Rubino et al., 2006�.Heretofore, the phase of the LFP signal of each electrode ina micro-electrode array, implanted in the motor and premotorcortex of the macaque monkey, was determined with the Hil-

a�Electronic mail: NikolayV.Manyakov@med.kuleuven.be.b�Electronic mail: Marc.VanHulle@med.kuleuven.be.

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bert transform, and the timing of these phases visualized inthe array, which revealed the presence of waves.

In this article, we will apply an index based on mutualinformation in the phase domain for detecting and analyzingphase synchrony in a multi-electrode array but, since experi-mental LFP recordings are noisy, they exhibit random phaseslips of 2�, we will introduce phase locking modulo 2�.Furthermore, to permit an objective comparison of severalbivariate measurements, we will use the normalized mutualinformation. We will analyze phase synchrony in a multi-electrode array implanted in visual cortical area V4 of twomonkeys in a reinforcement pairing experiment, show thedifferences in synchrony as a function of learning, and showthat synchronous activity appears in waves running over thearray during certain time intervals, and show that the speedof wave propagation increases during learning.

II. STIMULI AND MULTI-ELECTRODE RECORDINGS

Two rhesus monkeys �macaques� were implanted with aUtah array �Cyberkinetics, Foxborough, USA� in the prelu-nate gyrus �area V4�. The array consists of 10�10 electrodes�four of them are wireless electrodes� covering a cortical area4�4 mm2 in size. Recordings were made using a BionicCerebrus system. Local field potential signals were extractedby filtering the recorded signals between 0.3 and 250 Hz. Ananalysis of the LFP spectrograms revealed that the power ofthe LFP spectrum was noticeably higher for frequencies upto 30 Hz. Hence, we can expect the same frequency range tobe important in the LFP phase. An exempler LFP time seriesand the extracted phase are shown in Fig. 1. A detailed analy-sis showed that the raw LFP signal and the low-pass filteredone �up to 30 Hz�, in essence, yielded the same results interms of the difference in phase synchrony between the re-warded and unrewarded stimuli.

The stimuli used are shown in Fig. 2, and consist ofobliquely oriented sinusoidal gratings �2 c /deg, diameter 4°visual angle for monkey 1 and 2° for monkey 2� and a noisebackground. Their phases are randomized across presenta-tions. The gratings were partially occluded by sinusoidalnoise �signal-to-noise ratio�20%�.

During conditioning, every 500 ms a different sinusoidalnoise background that filled the display was presented. Atrandom intervals, a sinusoidal grating was presented for 500ms. The grating orientation is, for the rewarded stimulus,157.5° for monkey 1 and 112.5° for monkey 2, and, for theunrewarded stimulus, 67.5° for monkey 1 and 22.5° for mon-key 2. The �fluid� reward was provided 400 ms after presen-tation of the grating pattern and, thus, partially overlappedwith the grating presentation. Each monkey was trained tofixate a small dot �1.25°–1.5° fixation window� and the re-ward was given only when the monkey maintained fixationduring stimulus presentation. Between one and six noisebackgrounds always preceded the gratings. The stimuli werepresented �7.2° eccentric in the right lower visual field formonkey 1 �foveally for monkey 2�, the position was based ona preliminary visual field mapping.

After 37 days of conditioning for monkey 1 and 55 daysfor monkey 2, the stimulus-reward pairing was reversed: theunrewarded stimulus became the rewarded one and the re-

warded stimulus became the unrewarded one, and afterwhich conditioning continued with this new setting for 20days more for the monkey 1 and 52 days for monkey 2.

III. LFPs ARE NONLINEAR

The first question that comes to mind is: Can we restrictourselves to a linear LFP index, or do we need a nonlinearone? In other words, are LFPs linear signals or not? To testthis conjecture, we took a randomly chosen subset of fivetime series from 96 recordings from the beginning of the firsttraining day, and tested the following null hypothesis: Thesignals can be modeled as a multivariate linear stochasticprocess with an arbitrary degree of cross-correlation�Andrzejak et al., 2003�. We used the method of surrogatedata �Theiler et al., 1992� to test this hypothesis. By usingthe iterative multivariate surrogate technique �Schreiber andSchmitz, 2000�, we constructed 99 surrogates that preservetheir auto- and cross-correlations in all constructed time se-ries and, thus, which comply with the null hypothesis. Non-linear redundancy was taken as a discriminant statistic�Paluš, 1996�. The null hypothesis was rejected for the sig-nificance level 0.01. This means that a multivariate autore-

FIG. 1. Exemplar LFP signal and its extracted phase.

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gressive model is not appropriate for our LFP data. We alsofound that every single electrode recording is nonlinear,which was tested using the surrogate data technique withVolterra series as a discriminant statistic �Kugiumtzis, 1999�.

IV. PHASE SYNCHRONY

We use the Hilbert transform to extract the phase, andwrap the phase module 2�. As an index of bivariate phasesynchrony, the mutual information �MI� in the phase domain�Paluš, 1997� was taken, but normalized �nMI� by the sum ofthe marginal entropies H �in this case nMI� �0,1��, becausedifferent electrode pairs need to be objectively compared in alater stage:

nMI��x�t�,�y�t�� =2 · MI��x�t�,�y�t��H��x�t�� + H��y�t��

. �1�

Mutual information was estimated with the binless estimator�Kraskov et al., 2004�, whereas a distance between phasevalues min����t1�−��t2� � ;2�− ���t1�−��t2� � � was taken be-cause of the occurrence of wrapped phases.

V. RESULTS

We calculated the index of phase synchrony between allpossible pairs of electrodes in the Utah array in the timeperiod of 300 ms after stimulus onset �thus, 100 ms beforefluid reward�. For the analysis, only those recordings of therewarded and unrewarded stimuli were considered whenthree background images before and after the stimulus have

been observed by the monkey without failing to fixate asmall dot on the screen. In this way, on average 262 re-warded and 282 unrewarded recordings per day were re-tained for analysis, for the first monkey, and 147 rewardedand 168 unrewarded recordings for the second monkey. Wecompute the average phase synchrony, averaged over the ar-ray and over all trials in each daily session, and plot as func-tion of time the difference between the average phase syn-chrony of the rewarded stimulus and the unrewarded one�Fig. 3�. Note that these plots show the difference as a func-tion of time �in days�, but not every day corresponds to atraining day �indicated by gray strips�. We observe that, priorto the reversal, the difference in average phase synchronyincreases over the training sessions for both monkeys. Thedifference goes from nonsignificantly different in the firstsessions towards significantly different in later sessions. Sta-

FIG. 2. Rewarded �A� and unrewarded �B� stimuli.

FIG. 3. �Color online� Time course of the difference in average synchronybetween rewarded and unrewarded stimuli �vertical axis� in the Utah arrayof monkey 1 �A� and monkey 2 �B� as a function of time �in days� �hori-zontal axis�. Gray strips �yellow in color� indicate training days; white stripsindicate no recordings; vertical thick line �red line in color� indicates thereward reversal moment.

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tistical significance was tested by using a permutation testand p�0.05 �Good, 1994�.

Just after the reversal of the rewarded and unrewardedstimuli, the difference is due to the stimulus, not the reward.But after some days of further training, the difference is re-established but now with respect to the stimulus that receivesreward. We also observe that for monkey 2 the absence oftraining over a longer time span results in a drop in thedifference of average synchrony �see Fig. 3�B��.

We also determined the evolution �in ms� of the differ-ence in average phase synchrony after the stimulus onset�Figs. 4�A� and 4�C��. For this, we computed the averagelevel of phase synchrony in a sliding window of length 40ms. The coordinates on the vertical axis in Figs. 4�A� and4�C� are the starting points of these windows. Based on theseresults, we conclude that the difference in synchrony is moreprominent in two intervals: one between 50–120 ms and170–260 ms for the first monkey, and 80–150 ms and200–260 ms for the second monkey. For these time inter-

vals, we have traced �and smoothened�, over the trainingdays, the local maximum in the absolute value of the differ-ence in average phase synchrony �pink and blue curves inFigs. 4�A� and 4�C��. For these traces, we have also plottedthe difference in average phase synchrony �in correspondingcolors, see Fig. 4�B� and 4�D��. From this we conclude that,after the stimulus reversal, and for the first time interval de-fined above, the restoration in the difference in average syn-chrony is slower than for the second interval. From thesefigures, we also see that the longer absence in training�broadest white strips� results in a drop in the difference inaverage synchrony.

Similar to Rubino and co-workers �2006�, we have alsocomputed the phase of the LFP signals of all electrodes, andrepresented them in the Utah array, so as to able to detect thepresence of propagating waves in the array. When the phasesignals are similar, and the difference in phase at a giventime instant of a given electrode is larger than for a secondelectrode; then the wave propagates from the first towards

FIG. 4. �Color� �A, C� Temporal evolution in the difference in average synchrony between rewarded and unrewarded stimuli after stimulus onset �vertical axesin milliseconds� for each day of training �horizontal axes� for the first �A� and second �C� monkey. The two curves in the panels trace the peaks in the absolutedifference in average synchrony for two different time intervals �see text�. The blue curve is for the early interval; the pink line for the late interval. The blackline indicates the reversal moment; the dashed lines the breaks in training �no recording�. �B, D� Time courses of the difference in average synchronycorresponding to the two curves of panels �A� and �C�, respectively �in corresponding colors�. Same convention as in Fig. 3.

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the second electrode. Hence, from this, we can infer the di-rection of wave propagation in the array. We discovered thatthe wave propagates during certain time intervals afterstimulus onset and only in two directions �forward andback�. The directions were described along two referencepoints on opposite borders of the array. Figures 5�A� and5�C� show, for monkey 1, the timing of the two wave direc-tions �vertical axis� as a function of training days �horizontalaxis�, for the rewarded and unrewarded stimuli �panels A andC�. We have also determined whether these directions aresignificant �t-test, p�0.05�, which means that we have thesame wave direction in each trial within the same day. Theresult is shown in Figs. 5�B� and 5�D�. We also plotted, againfor monkey 1, the relative delays in the phases of each elec-trode in the array, relative to the leading phase, centered at70 and 160 ms after stimulus onset, for the rewarded stimu-lus only, and for the first and 37th day of training �Fig. 6�.We observe that, as a result of training, the speed of propa-gation increases �smaller range in delays�.

Comparing Figs. 5�B� and 5�D� with the synchrony re-sults in Fig. 4�A� reveals that the time interval of significantwave propagation in the same direction �region A1 in Figs.5�B� and 5�D�� correspond to the early time interval of aprominent difference in average synchrony between the re-warded and unrewarded stimuli. Concerning the second timeinterval, we conclude that when for the unrewarded stimulusa significant wave propagation occurs �region A2 in Fig.5�D��, but that, for the rewarded stimulus, there is no wave�all LFPs are in synchrony� �Fig. 5�B��. The same conclusionalso holds for the second monkey �result not shown�.

VI. DISCUSSION

Propagating waves have been discovered by Rubino andco-workers in the motor and premotor cortex of the macaquemonkey �Rubino et al., 2006�. They used the Hilbert trans-form of beta-range filtered recordings made with a two-dimensional array of electrodes �Utah array�. They discov-

FIG. 5. �Color online� �A, C� Changes in the direction of wave propagation in the Utah array for the first monkey during presentation of the rewarded �A� andthe unrewarded �C� stimuli as a function of time after stimulus onset �in milliseconds� �vertical axis� and as a function of training days �horizontal axis�. Whiteand black indicate the two propagation directions �forward and back�. �B, D� Indicates when the propagation directions are significant �white and black as inpanels A and C� and nonsignificant �gray� for the rewarded �B� and unrewarded �D� stimuli. The vertical thick line �red line in color� indicates the rewardreversal moment.

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ered that waves of activity propagate over the array, also in aforward and back direction, and they hypothesized that thesewaves mediate the information transfer in the motor cortex.They did, however, not quantify the synchrony between theelectrodes �they only talk about oscillations that are visuallypresent in the LFP amplitudes�, they did not consider theeffect of training, and did not determine whether the wavesare statistical significant. In this article, we have quantifiedphase synchrony in the visual cortex, and have shown thatthe phase synchrony is significantly higher for the rewardedstimulus than for the unrewarded one, which is attributed tothe lower frequencies. We have also determined when syn-chrony occurs, and shown that synchrony appears in wavesof which the timing correlates well with the time intervalswhere the difference between reward and no reward is mostprominent. Finally, we have also shown that the wavespropagate faster as a result of training. We conjecture that theobserved enhanced synchrony contributes to an enhancedrepresentation of the rewarded stimulus, and that the wavesmediate the information transfer in area V4.

ACKNOWLEDGMENTS

The authors are deeply indebted to Professor R. Vogels,of the same lab, for sharing his experimental data. N.V.M. issupported by the European Commission �IST-2004-027017�.M.M.V.H. is supported by research grants received from theExcellence Financing �EF 2005� and CREA Financing�CREA/07/027� programs of the K.U.Leuven, the BelgianFund for Scientific Research – Flanders �G.0248.03 andG.0234.04�, the Interuniversity Attraction Poles Programme– Belgian Science Policy �IUAP P5/04�, the Flemish Re-gional Ministry of Education �Belgium� �GOA 2000/11�, andthe European Commission �NEST-2003-012963, STREP-2002-016276, IST-2004-027017, and IST-2007-217077�.

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FIG. 6. �A, B� Wave propagation in the Utah array for the first monkey, during the first day of training, using LFP phases centered at 70 ms after the onsetof the rewarded stimulus �A�, and during the last day of training �day 37�, also centered at 70 ms after the onset of the rewarded stimulus �B�. �C, D� Samebut for the first day of training, and using LFP phases centered at 160 ms after the onset of the rewarded stimulus �C�, and for the last day of training �day37�, also centered at 160 ms �D�. Grayscales indicate delays in milliseconds of wave propagation; the scale is shown right to each panel �note the differencesin range�. Crosses indicate wireless electrodes.

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