{"title": "Understanding Brain Connectivity Patterns during Motor Imagery for Brain-Computer Interfacing", "book": "Advances in Neural Information Processing Systems", "page_first": 561, "page_last": 568, "abstract": "EEG connectivity measures could provide a new type of feature space for inferring a subject's intention in Brain-Computer Interfaces (BCIs). However, very little is known on EEG connectivity patterns for BCIs. In this study, EEG connectivity during motor imagery (MI) of the left and right is investigated in a broad frequency range across the whole scalp by combining Beamforming with Transfer Entropy and taking into account possible volume conduction effects. Observed connectivity patterns indicate that modulation intentionally induced by MI is strongest in the gamma-band, i.e., above 35 Hz. Furthermore, modulation between MI and rest is found to be more pronounced than between MI of different hands. This is in contrast to results on MI obtained with bandpower features, and might provide an explanation for the so far only moderate success of connectivity features in BCIs. It is concluded that future studies on connectivity based BCIs should focus on high frequency bands and consider experimental paradigms that maximally vary cognitive demands between conditions.", "full_text": "Understanding Brain Connectivity Patterns during\n\nMotor Imagery for Brain-Computer Interfacing\n\nMoritz Grosse-Wentrup\n\nMax Planck Institute for Biological Cybernetics\n\nSpemannstr. 38\n\n72076 T\u00a8ubingen, Germany\nmoritzgw@ieee.org\n\nAbstract\n\nEEG connectivity measures could provide a new type of feature space for inferring\na subject\u2019s intention in Brain-Computer Interfaces (BCIs). However, very little is\nknown on EEG connectivity patterns for BCIs. In this study, EEG connectivity\nduring motor imagery (MI) of the left and right is investigated in a broad frequency\nrange across the whole scalp by combining Beamforming with Transfer Entropy\nand taking into account possible volume conduction effects. Observed connec-\ntivity patterns indicate that modulation intentionally induced by MI is strongest\nin the \u03b3-band, i.e., above 35 Hz. Furthermore, modulation between MI and rest\nis found to be more pronounced than between MI of different hands. This is in\ncontrast to results on MI obtained with bandpower features, and might provide an\nexplanation for the so far only moderate success of connectivity features in BCIs.\nIt is concluded that future studies on connectivity based BCIs should focus on\nhigh frequency bands and consider experimental paradigms that maximally vary\ncognitive demands between conditions.\n\n1 Introduction\n\nBrain-Computer Interfaces (BCIs) are devices that enable a subject to communicate without uti-\nlizing the peripheral nervous system, i.e., without any overt movement requiring volitional motor\ncontrol. The primary goal of research on BCIs is to enable basic communication for subjects unable\nto communicate by normal means due to neuro-degenerative diseases such as amyotrophic lateral\nsclerosis (ALS). In non-invasive BCIs, this is usually approached by measuring the electric \ufb01eld of\nthe brain by EEG, and detecting changes intentionally induced by the subject (cf. [1] for a general\nintroduction to BCIs). The most commonly used experimental paradigm in this context is motor\nimagery (MI) [2]. In MI subjects are asked to haptically imagine movements of certain limbs, e.g.,\nthe left or the right hand. MI is known to be accompanied by a decrease in bandpower (usually most\nprominent in the \u00b5-band, i.e., roughly at 8-13 Hz) in that part of the motor cortex representing the\nspeci\ufb01c limb [3]. These bandpower changes, termed event related (de-)synchronization (ERD/ERS),\ncan be detected and subsequently used for inferring the subject\u2019s intention. This approach to BCIs\nhas been demonstrated to be very effective in healthy subjects, with only little subject training time\nrequired to achieve classi\ufb01cation accuracies close to 100% in two-class paradigms [4\u20136]. Further-\nmore, satisfactory classi\ufb01cation results have been reported with subjects in early to middle stages\nof ALS [7]. However, all subjects diagnosed with ALS and capable of operating a BCI still had\nresidual motor control that enabled them to communicate without the use of a BCI. Until now, no\ncommunication has been established with a completely locked-in subject, i.e., a subject without any\nresidual motor control. Establishing communication with a completely locked-in subject arguably\nconstitutes the most important challenge in research on BCIs.\n\n1\n\n\fUnfortunately, reasons for the failure of establishing communication with completely locked-in sub-\njects remain unknown. While cognitive de\ufb01cits in completely locked-in patients can at present not\nbe ruled out as the cause of this failure, another possible explanation is abnormal brain activity ob-\nserved in patients in late stages of ALS [8]. Our own observations indicate that intentionally induced\nbandpower changes in the electric \ufb01eld of the brain might be reduced in subjects in late stages of\nALS. To explore the plausibility of this explanation for the failure of current BCIs in completely\nlocked-in subjects, it is necessary to devise feature extraction algorithms that do not rely on mea-\nsures of bandpower. In this context, one promising approach is to employ connectivity measures\nbetween different brain regions. It is well known from fMRI-studies that brain activity during MI is\nnot con\ufb01ned to primary motor areas, but rather includes a distributed network including pre-motor,\nparietal and frontal regions of the brain [9]. Furthermore, synchronization between different brain\nregions is known to be an essential feature of cognitive processing in general [10]. Subsequently, it\ncan be expected that different cognitive tasks, such as MI of different limbs, are associated with dif-\nferent connectivity patterns between brain regions. These connectivity patterns should be detectable\nfrom EEG recordings, and thus offer a new type of feature space for inferring a subject\u2019s intention.\nSince measures of connectivity are, at least in principle, independent of bandpower changes, this\nmight offer a new approach to establishing communication with completely locked-in subjects.\n\nIn recent years, several measures of connectivity have been developed for analyzing EEG recordings\n(cf. [11] for a good introduction and a comparison of several algorithms). However, very few studies\nexist that analyze connectivity patterns as revealed by EEG during MI [12, 13]. Furthermore, these\nstudies focus on differences in connectivity patterns between MI and motor execution, which is not\nof primary interest for research on BCIs. In the context of non-invasive BCIs, connectivity measures\nhave been most notably explored in [14] and [15]. However, these studies only consider frequency\nbands and small subsets of electrodes known to be relevant for bandpower features, and do not take\ninto account possible volume conduction effects. This might lead to misinterpreting bandpower\nchanges as changes in connectivity. Consequently, a better understanding of connectivity patterns\nduring MI of different limbs as measured by EEG is required to guide the design of new feature\nextraction algorithms for BCIs. Speci\ufb01cally, it is important to properly address possible volume\nconduction effects, not con\ufb01ne the analysis to a small subset of electrodes, and consider a broad\nrange of frequency bands.\n\nIn this work, these issues are addressed by combining connectivity analysis during MI of the left\nand right hand in four healthy subjects with Beamforming methods [6]. Since it is well known that\nMI includes primary motor cortex [3], this area is chosen as the starting point of the connectivity\nanalysis. Spatial \ufb01lters are designed that selectively extract those components of the EEG originating\nin the left and right motor cortex. Then, the concept of Transfer Entropy [16] is used to estimate\nclass-conditional \u2019information \ufb02ow\u2019 from all 128 employed recording sites into the left and right\nmotor cortex in frequency bands ranging from 5 - 55 Hz.\nIn this way, spatial topographies are\nobtained for each frequency band that depict by how much each area of the brain is in\ufb02uencing the\nleft/right motor cortex during MI of the left/right hand. Interestingly, the most pronounced changes\nin connectivity patterns are not observed in MI of the left vs. the right hand, but rather in rest vs. MI\nof either hand. Furthermore, these pattern changes are most pronounced in frequency bands not\nusually associated with MI. i.e., in the \u03b3-band above 35 Hz. These results suggest that in order\nto fully exploit the capabilities of connectivity measures for BCIs, and establish communication\nwith completely locked-in subjects, it might be advisable to consider \u03b3-band oscillations and adapt\nexperimental paradigms as to maximally vary cognitive demands between conditions.\n\n2 Methods\n\n2.1 Symmetric vs. Asymmetric Connectivity Analysis\n\nIn analyzing interrelations between time-series data it is important to distinguish symmetric from\nasymmetric measures. Consider Fig. 1, depicting two graphs of three random processes s1 to s3,\nrepresenting three EEG sources. The goal of symmetric connectivity analysis (Fig. 1.a) is to esti-\nmate some instantaneous measure of similarity between random processes, i.e., assigning weights\nto the undirected edges between the nodes of the graph in Fig. 1.a. Amplitude coupling and phase\nsynchronization fall into this category, which are the measures employed in [14] and [15] for feature\nextraction in BCIs. However, interrelations between EEG sources originating in different regions of\n\n2\n\n\fa)\n\nb)\n\ns1[t]\n\ns2[t]\n\ns3[t]\n\ns1[t]\n\ns2[t]\n\ns3[t]\n\ns1[t + 1]\n\ns2[t + 1]\n\ns3[t + 1]\n\ns1[t + 1]\n\ns2[t + 1]\n\ns3[t + 1]\n\nFigure 1: Illustration of symmetric- vs. asymmetric connectivity analysis for three EEG sources\nwithin the brain.\n\nthe brain can be expected to be asymmetric, with certain brain regions exerting stronger in\ufb02uence on\nother regions than vice versa. For this reason, asymmetric connectivity measures potentially provide\nmore information on cognitive processes than symmetric measures.\n\nConsidering asymmetric relations between random processes requires a de\ufb01nition of how the in\ufb02u-\nence of one process on another process is to be measured, i.e., a quantitative de\ufb01nition of causal\nin\ufb02uence. The commonly adopted de\ufb01nition of causality in time-series analysis is that si causes\nsj if observing si helps in predicting future observations of sj, i.e., reduces the prediction error of\nsj. This implies that cause precedes effect, i.e., that the graph in Fig. 1.b may only contain directed\narrows pointing forward in time. Note that there is some ambiguity in this de\ufb01nition of causality,\nsince it does not specify a metric for reduction of the prediction error of sj due to observing si. In\nGranger causality (cf. [11]), reduction of the variance of the prediction error is chosen as a metric,\nessentially limiting Granger causality to linear systems. It should be noted, however, that any other\nmetric is equally valid. Finally, note that for reasons of simplicity the graph in Fig. 1.b only contains\ndirected edges from nodes at time t to nodes at time t + 1. In general, directed arrows from nodes at\ntimes t, . . . , t \u2212 k to nodes at time t + 1 may be considered, with k the order of the random processes\ngenerating s[t + 1].\nTo assess Granger causality between bivariate time-series data a linear autoregressive model is \ufb01t to\nthe data, which is then used to compute a 2x2 transfer matrix in the frequency domain (cf. [11]). The\noff-diagonal elements of the transfer matrix then provide a measure of the asymmetric interaction\nbetween the observed time-series. Extensions of Granger causality to multivariate time-series data,\ntermed directed transfer function (DTF) and partial directed coherence (PDC), have been developed\n(cf. [11] and the references therein). However, in this work a related but different measure for asym-\nmetric interrelations between time-series is utilized. The concept of Transfer Entropy (TE) [16] de-\n\ufb01nes the causal in\ufb02uence of si on sj as the reduction in entropy of sj obtained by observing si. More\nprecisely, let si and sj denote two random processes, and let sk\nTE is then de\ufb01ned as\n\ni/j[t] := (cid:0)si/j[t], . . . , si/j[t \u2212 k](cid:1).\n\nTk (si[t] \u2192 sj[t + 1]) := H(cid:0)sj[t + 1]|s\n\n(1)\nwith k the order of the random processes and H(\u00b7) the Shannon entropy. TE can thus be understood\nas the reduction in uncertainty about the random process sj at time t + 1 due to observing the past\nk samples of the random process si. Both, Granger causality and TE, thus de\ufb01ne causal in\ufb02uence\nas a reduction in the uncertainty of a process due to observing another process, but employ different\nmetrics to measure reduction in uncertainty. While TE is a measure that applies to any type of\nrandom processes, it is dif\ufb01cult to compute in practice. Hence, in this study only Gaussian processes\n\nj [t](cid:1) \u2212 H(cid:0)sj[t + 1]|s\n\ni [t](cid:1) ,\n\nk\nj [t], s\n\nk\n\nk\n\nare considered, i.e., it is assumed that(cid:0)sj[t + 1], sk\n\nthen be computed as\n\nj [t], sk\n\ni [t](cid:1) is jointly Gaussian distributed. TE can\n\nT GP\nk (si[t] \u2192 sj[t + 1]) =\n\nlog\n\n1\n2\n\nj [t],sk\n\ndet R(sk\ndet R(sj [t+1],sk\n\ni [t]) det R(sj [t+1],sk\ni [t]) det R(sk\n\nj [t],sk\n\nj [t])\n\nj [t])\n\n,\n\n(2)\n\nwith R(\u00b7) the (cross-)covariance matrices of the respective random processes [17]. In comparison\nto Granger causality and related measures, TE for Gaussian processes possesses several advantages.\nIt is easy to compute from a numerical perspective, since it does not require \ufb01tting a multivariate\nautoregressive model including (implicit) inversion of large matrices. Furthermore, for continuous\nprocesses it is invariant under coordinate transformations [17]. Importantly, this entails invariance\nwith regard to scaling of the random processes.\n\nComputing TE for Gaussian processes requires estimation of the (cross-)covariance matrices\nin (2). Consider a matrix S \u2208 R2\u00d7T \u00d7N , corresponding to data recorded from two EEG\n\n3\n\n\fsources during an experimental paradigm with N trials of T samples each. In order to compute\n(s1[t] \u2192 s2[t + 1]) for t = k + 1, . . . , T \u2212 k \u2212 1, it is assumed that in each trial s1[t] and\nT GP\nk\ns2[t] are i.i.d. samples from the distribution p(s1[t], s2[t]), i.e., that the non-stationary Gaussian pro-\ncesses that give rise to the observation matrix S are identical for each of the N repetitions of the\nexperimental paradigm. For each instant in time, TE can then be evaluated by computing the sample\n(cross-)covariance matrices required in (2) across trials. Note that evaluating (2) requires speci\ufb01ca-\ntion of k. In general, k should be chosen as large as possible in order to maximize information on\nthe random processes contained in the (cross-)covariance matrices. However, choosing k too large\nleads to rank de\ufb01cient matrices with a determinant of zero. Here, for each observation matrix S the\nhighest possible k is chosen such that none of the matrices in (2) is rank de\ufb01cient.\n\n2.2 The Problem of Volume Conduction in EEG Connectivity Analysis\n\nThe goal of connectivity analysis in EEG recordings is to estimate connectivity patterns between\ndifferent regions of the brain. Unfortunately, EEG recordings do not offer direct access to EEG\nsources. Instead, each EEG electrode measures a linear and instantaneous superposition of EEG\nsources within the brain [18]. This poses a problem for symmetric connectivity measures, since\nthese assess instantaneous coupling between electrodes [18]. Asymmetric connectivity measures\nsuch as TE, on the other hand, are not based on instantaneous coupling, but rather consider prediction\nerrors. It is not obvious that instantaneous volume conduction also poses a problem for this type of\nmeasures. Unfortunately, the following example demonstrates that volume conduction also leads to\nincorrect connectivity estimates in asymmetric connectivity analysis based on TE.\n\nExample 1 (Volume Conduction Effects in Connectivity Analysis based on Transfer Entropy)\nConsider the EEG signals x1[t] and x2[t], recorded at two electrodes placed on the scalp, that\nconsist of a linear superposition of three EEG sources s1[t] to s3[t] situated somewhere within the\nbrain (Fig. 2.a). Let x[t] = (x1[t], x2[t])T and s[t] = (s1[t], s2[t], s3[t])T. Then x[t] = As[t],\nwith A \u2208 R2\u00d73 describing the projection strength of each source to each electrode. For sake of\nsimplicity, assume that A = (1 0 1 ; 0 1 1 ), i.e., that the \ufb01rst source only projects to the \ufb01rst\nelectrode with unit strength, the second source only projects to the second electrode with unit\nstrength, and the third source projects to both electrodes with unit strength. Furthermore, assume\nthat\n\n1\n0\n0\n0\n0\n0\n\n\uf8ee\n\n\uf8ef\uf8ef\uf8ef\uf8ef\uf8ef\uf8f0\n\n0\n0\n1\n0\n0\n1\n0\n0\n0\n0\n0 \u03b3\n\n0\n0\n0\n1\n0\n0\n\n0\n0\n0\n0\n0 \u03b3\n0\n0\n1\n0\n1\n0\n\n\uf8f9\n\n\uf8fa\uf8fa\uf8fa\uf8fa\uf8fa\uf8fb\n\np(s[t + 1], s[t]) = N (0, \u03a3) with \u03a3 =\n\n,\n\n(3)\n\ni.e., that all sources have zero mean, unit variance, are mutually independent, and s1 and s2 are\nuncorrelated in time. Only s3[t] and s3[t + 1] are assumed to be correlated with covariance \u03b3\n(Fig. 2.b). In this setting, it would be desirable to obtain zero TE between both electrodes, since\nthere is no interaction between the sources giving rise to the EEG. However, some rather tedious\nalgebraic manipulations reveal that in this case\n\nT GP\n1 (x2[t] \u2192 x1[t + 1]) =\n\n1\n2\n\nlog(cid:18) 3\n\n2(cid:19) +\n\n1\n2\n\nlog(cid:18) 4 \u2212 \u03b32\n\n6 \u2212 2\u03b32(cid:19) .\n\n(4)\n\nNote that (4) is zero if and only if \u03b3 = 0, i.e., if s3 represents white noise. Otherwise, TE between\nthe two electrodes is estimated to be greater than zero solely due to volume conduction effects from\nsource s3. Further note that qualitatively this result holds independently of the strength of the\nprojection of the third source to both electrodes.\n\n2.3 Attenuation of Volume Conduction Effects via Beamforming\n\nOne way to avoid volume conduction effects in EEG connectivity analysis is to perform source\nlocalization on the obtained EEG data, and apply connectivity measures on estimated current density\ntime-series at certain locations within the brain [11]. This is feasible to test certain hypothesis, e.g.,\nto evaluate whether there exists a causal link between two speci\ufb01c points within the brain. However,\ntesting pairwise causal links between more than just a few points within the brain is computationally\n\n4\n\n\fa)\n\nx1[t]\n\ns1[t]\n\nx2[t]\n\ns2[t]\n\ns3[t]\n\nb)\n\ns1[t]\n\ns2[t]\n\ns3[t]\n\ns1[t + 1]\n\ns2[t + 1]\n\ns3[t + 1]\n\nFigure 2: Illustration of volume conduction effects in EEG connectivity analysis.\n\nintractable. Accordingly, attenuation of volume conduction effects via source localization is not\nfeasible if a complete connectivity pattern considering the whole brain is desired. Here, a different\napproach is pursued. It is well known that primary motor cortex is central to MI as measured by\nEEG [3]. Accordingly, it is assumed that any brain region involved in MI displays some connectivity\nto the primary motor cortex. This (admittedly rather strong) assumption enables a complete analysis\nof the connectivity patterns during MI covering the whole brain in the following way. First, two\nspatial \ufb01lters, commonly known as Beamformers, are designed that selectively extract EEG sources\noriginating within the right and left motor cortex, respectively [6]. In brief, this can be accomplished\nby solving the optimization problem\n\nw\n\n\u2217 = argmax\n\nw\u2208RM ( wTR\u02dcxl/r\n\nwTRxw ) ,\n\nw\n\n(5)\n\nwith Rx \u2208 RM \u00d7M the covariance of the recorded EEG, and R\u02dcxl/r \u2208 RM \u00d7M model-based spatial\ncovariance matrices of EEG sources originating within the left/right motor cortex.\nIn this way,\nspatial \ufb01lters can be obtained that optimally attenuate the variance of all EEG sources not originating\nwithin the left/right motor cortex. The desired spatial \ufb01lters are obtained as the eigenvectors with\nw = \u03bbRxw (cf. [6] for a more\nthe largest eigenvalue of the generalized eigenvalue problem R\u02dcxl/r\ndetailed presentation).\n\nWith EEG sources originating within the left and right motor cortex extracted, TE from all EEG\nelectrodes into the left and right motor cortex can be computed. In this way, volume conduction\neffects from all sources within the brain into the left/right motor cortex can be optimally attenuated.\nHowever, volume conduction effects from the left/right motor cortex to any of the EEG electrodes\nstill poses a problem. Accordingly, it has to be veri\ufb01ed if any positive TE from an EEG electrode\ninto the left/right motor cortex could be caused by bandpower changes within the left/right motor\ncortex. Positive TE from any electrode into the left/right motor cortex can only be considered as a\ngenuine causal link if it is not accompanied by a bandpower change in the respective motor cortex.\n\n3 Experimental Results\n\nTo investigate connectivity patterns during MI the following experimental paradigm was employed.\nSubjects sat in a dimly lit and shielded room, approximately two meters in front of a silver screen.\nEach trial started with a centrally displayed \ufb01xation cross. After three seconds, the \ufb01xation cross was\noverlaid with a centrally placed arrow pointing to the left or right. This instructed subjects to begin\nMI of the left or right hand, respectively. Subjects were explicitly instructed to perform haptic MI,\nbut the exact choice of the type of imaginary hand movement was left unspeci\ufb01ed. After a further\nseven seconds the arrow was removed, indicating the end of the trial and start of the next trial. 150\ntrials per class were carried out by each subjects in randomized order. During the experiment, EEG\nwas recorded at 128 electrodes placed according to the extended 10-20 system with electrode Cz as\nreference. EEG data was re-referenced to common average reference of\ufb02ine. Four healthy subjects\nparticipated in the experiment, all of which were male and right handed with an age of 27 \u00b1 2.5\nyears. For each subject, electrode locations were recorded with an ultrasound tracking system. No\nartifact correction was employed and no trials were rejected.\nFor each subject, model-based covariance matrices R\u02dcxl/r for EEG sources within the left/right motor\ncortex were computed as described in [6]. The EEG covariance matrix Rx was computed for each\nsubject using all available data, and the two desired Beamformers, extracting EEG sources from the\nleft and right motor cortex, were computed by solving (5). The EEG sources extracted from the\nleft/right motor cortex as well as the un\ufb01ltered data recorded at each electrode were then bandpass-\n\n5\n\n\f\ufb01ltered with sixth-order Butterworth \ufb01lters in \ufb01ve frequency bands ranging from 5 to 55 Hz in steps\nof 10 Hz. Then, TE was computed from all EEG electrodes into the left/right motor cortex at each\nsample point as described in Section 2.1. Furthermore, for each subject class-conditional bandpower\nchanges (ERD/ERS) of sources extracted from the left/right motor cortex were computed in order\nto identify frequency bands with common modulations in bandpower and TE. Two subjects showed\nsigni\ufb01cant modulations of bandpower in all \ufb01ve frequency bands. These were excluded from further\nanalysis, since any observed positive TEs could have been confounded by volume conduction. The\nresulting topographies of mean TE between conditions of the two remaining subjects are shown\nin Fig. 3. Here, the \ufb01rst two columns show mean TE from all electrodes into the left/right motor\ncortex during MI of either hand (3.5-10s) minus mean TE during baseline (0.5-3s) in each of the\n\ufb01ve frequency bands. The last two columns show mean differences in TE into the left/right motor\ncortex between MI of the left and right hand (both conditions also baseline corrected). Note that\nthe topographies in Fig. 3 have been normalized to the maximum difference across conditions to\nemphasize differences between conditions. Interestingly, no distinct differences in TE are observed\nbetween MI of the left and right hand. Instead, strongest differences in TE are observed in rest\nvs. MI of either hand (left two columns). The amount of decrease in TE during MI relative to\nrest increases with higher frequencies, and is most pronounced in the \u03b3-band from 45-55 Hz (last\nrow, left two columns). Topographically, strongest differences are observed in frontal, pre-central,\nand post-central areas. Observed changes in TE are statistically signi\ufb01cant with signi\ufb01cance level\n\u03b1 = 0.01 at all electrodes in Fig. 3 marked with red crosses (statistical signi\ufb01cance was tested non-\nparametrically and individually for each subject, Beamformer, and condition by one thousand times\nrandomly permuting the EEG data of each recorded trial in time and testing the null-hypothesis that\nchanges in TE at least as large as those in Fig.3 are observed without any temporal structure being\npresent in the data). Due to computational resources only a small subset of electrodes was tested\nfor signi\ufb01cance. The observed changes in TE display opposite modulations in comparison to mean\nbandpower changes observed in left/right motor cortex relative to baseline (Fig. 4, only signi\ufb01cant\n(\u03b1 = 0.01) bandpower changes relative to baseline (0-3s) plotted). Here, strongest modulation of\nbandpower is found in the \u00b5- (\u223c 10 Hz) and \u03b2-band (\u223c 25 Hz). Frequencies above 35 Hz show very\nlittle modulation, indicating that the observed differences in TE at high frequencies in Fig. 3 are not\ndue to volume conduction but genuine causal links.\n\n4 Discussion\n\nIn this study, Beamforming and TE were employed to investigate the topographies of \u2019informa-\ntion \ufb02ow\u2019 into the left and right motor cortex during MI as measured by EEG. To the best of the\nauthor\u2019s knowledge, this is the \ufb01rst study investigating asymmetric connectivity patterns between\nbrain regions during MI of different limbs considering a broad frequency range, a large number of\nrecordings sites, and properly taking into account volume conduction effects. However, it should\nbe pointed out that there are several issues that warrant further investigation. First, the presented\nresults are obtained from only two subjects, since two subjects had to be excluded due to possible\nvolume conduction effects. Future studies with more subjects are required to validate the obtained\nresults. Also, no out\ufb02ow from primary motor cortex and no TE between brain regions not including\nprimary motor cortex have been considered. Finally, the methodology presented in this study can\nnot be applied in a straight-forward manner to single-trial data, and is thus only of limited use for\nactual feature extraction in BCIs.\n\nNever the less, the obtained results indicate that bandpower changes in motor cortex and connectiv-\nity between motor cortex and other regions of the brain are processes that occupy distinct spectral\nbands and are modulated by different cognitive tasks. In conjunction with the observation of no\ndistinct changes in connectivity patterns between MI of different limbs, this indicates that in [14]\nand [15] bandpower changes might have been misinterpreted as connectivity changes. This is further\nsupported by the fact that these studies focused on frequency bands displaying signi\ufb01cant modula-\ntion of bandpower (8-30 Hz) and did not control for volume conduction effects. In conclusion, the\npronounced modulation of connectivity between MI of either hand vs. rest in the \u03b3-band observed in\nthis study underlines the importance of also considering high frequency bands in EEG connectivity\nanalysis. Furthermore, since the \u03b3-band is thought to be crucial for dynamic functional connectivity\nbetween brain regions [10], future studies on connectivity patterns in BCIs should consider exper-\nimental paradigms that maximally vary cognitive demands in order to activate different networks\nwithin the brain across conditions.\n\n6\n\n\fMotor Imagery - Rest\n\nLeft - Right Motor Imagery\n\nLeft MC\n\nRight MC\n\nLeft MC\n\nRight MC\n\nC3\n\nC4\n\nC3\n\nC4\n\nC3\n\nC4\n\nC3\n\nC4\n\nC3\n\nC4\n\n5-15 Hz\n\n15-25 Hz\n\n25-35 Hz\n\n35-45 Hz\n\n45-55 Hz\n\n1\n\n0\n\n-1\n\nFigure 3: Topographies of mean Transfer Entropy changes into left/right motor cortex (MC). C3/C4\nmark electrodes over left/right motor cortex. Red crosses indicate statistically signi\ufb01cant electrodes.\nPlotted with [19].\n\nLeft Motor Cortex\n\nRight Motor Cortex\n\n50 Hz\n40 Hz\n30 Hz\n20 Hz\n10 Hz\n\n50 Hz\n40 Hz\n30 Hz\n20 Hz\n10 Hz\n\ny\nr\ne\ng\na\nm\n\nI\n\nd\nn\na\nH\n\nt\nf\ne\nL\n\ny\nr\ne\ng\na\nm\n\nI\n\nd\nn\na\nH\n\nt\nh\ng\ni\nR\n\n0s\n\n3s\n\n10s\n\n0s\n\n3s\n\n8 dB\n\n0 dB\n\n-8 dB\n\n10s\n\nFigure 4: Class-conditional mean ERD/ERS in left/right motor cortex relative to baseline (0-3s).\nHorizontal line marks start of motor imagery. Plotted with [19].\n\n7\n\n\fReferences\n\n[1] J.R. Wolpaw, N. Birbaumer, D.J. McFarland, G. Pfurtscheller, and T.M. Vaughan. Brain-\ncomputer interfaces for communication and control. Clinical Neurophysiology, 113(6):767\u2013\n791, 2002.\n\n[2] S.G. Mason, A. Bashashati, M. Fatourechi, K.F. Navarro, and G.E. Birch. A comprehensive\nsurvey of brain interface technology designs. Annals of Biomedical Engineering, 35(2):137\u2013\n169, 2007.\n\n[3] G. Pfurtscheller and F.H. 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