An EEG Study of Brain Connectivity Dynamics at the Resting State

Transcription

1 Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 16, No. 1, pp Society for Chaos Theory in Psychology & Life Sciences An EEG Study of Brain Connectivity Dynamics at the Resting State Stavros I. Dimitriadis 1, University of Patras, Greece & Aristotle University, Thessaloniki, Greece Nikolaos A. Laskaris, Aristotle University, Thessaloniki, Greece Vasso Tsirka, University of Crete, Greece Michael Vourkas, Technical High School of Crete, Greece Sifis Micheloyannis, University of Crete, Greece Abstract: We investigated the dynamical behavior of resting state functional connectivity using EEG signals. Employing a recently introduced methodology that considers the time variations of phase coupling among signals from different channels, a sequence of functional connectivity graphs (FCGs) was constructed for different frequency bands and analyzed based on graph theoretic tools. In the first stage of analysis, hubs were detected in the FCGs based on local and global efficiency. The probability of each node to be identified as a hub was estimated. This defined a topographic function that showed widespread distribution with prominence over the frontal brain regions for both local and global efficiency. Hubs consistent across time were identified via a summarization technique and found to locate over forehead. In the second stage of analysis, the modular structure of each single FCG was delineated. The derived time-dependent signatures of functional structure were compared in a systematic way revealing fluctuations modulated by frequency. Interestingly, the evolution of functional connectivity can be described via abrupt transitions between states, best described as short-lasting bimodal functional segregations. Based on a distance function that compares clusterings, we discovered that these segregations are recurrent. Entropic measures further revealed that the apparent fluctuations are subject to intrinsic constraints and that order emerges from spatially extended interactions. Key Words: phase synchrony, evolving graphs, modularity, hubs, segregation motifs INTRODUCTION Many studies have been performed in order to evaluate the different types of brain functionality. Local and widespread neural activations are com- 1 Correspondence address: S. I. Dimitriadis, Electronics Laboratory, Department of Physics, University of Patras, Patras 26500, Greece. sdimitriadis@physics.upatras.gr 5

2 6 NDPLS, 16(1), Dimitriadis et al. pared during various mental tasks as a means of detecting and characterizing the different functional modes of brain activation, as well as contrasting them against the so-called rest situation. This situation refers to the state where the brain is doing nothing. What exactly is happening in the brain during this situation has been the matter of many studies. Berger expressed the idea that the brain during rest has activity (Gloor, 1969). The Swedish brain physiologist David Ingvar was the first to aggregate imaging findings from resting state and notice the importance of consistent, regionally specific activity patterns (Ingvar & Schwartz, 1974). Using the xenon- 133 inhalation technique to measure regional cerebral blood flow (rcbf), Ingvar and his colleagues observed that frontal activity reached high levels during resting condition. Brain imaging studies revealed a specific set of brain regions showing activity at rest and deactivations during cognitive tasks. Many studies, using positron emission tomography (PET) and functional magnetic resonance imaging (fmri) showed the most active regions at rest and, additionally, widespread activities in connection with the most active regions. The former form the Default Mode Network (DMN) (Debener et al., 2005; Laufs et al., 2003), while the latter the Resting State Network (RSN) (Jann et al., 2009; Mantini, Perrucci, Del Gratta, Romani, & Corbetta, 2007). The DMN is an ensemble of brain regions showing correlated, low-frequency activity during rest condition (Jann et al., 2009; Scheeringa et al., 2008). It includes the posterior cingulatedprecuneus, medial prefrontal cortex, and bilateral inferior parietal cortex. On the other hand, the RSN is a widespread extension of the DMN (Laufs et al., 2003; Mantini et al., 2007). Several fmri studies have shown coherent fluctuations in the resting brain (Chang & Glover, 2010) and established the belief that they constitute the dynamical substrate of the resting brain. These fluctuations are visible in fmri at low frequency (< 0.1 Hz). Nevertheless, these fluctuations are considered correlated with the electrical activity of brain (Cordes et al., 2001). By analyzing signals from combined EEG/fMRI recordings, the self-similarity of brain dynamics at resting state was revealed both in space and time (Mantini et al., 2007). Brain seems to operate through transitions, wavering between an excessive cortical integration and segregation (Rubinov, Sporns, van Leeuwen & Breakspear, 2009). The resting state is a condition of undirected wakefulness that may encompass varying levels of attention, mind wandering and arousal. Hence, one may hypothesize that the connectivity between and within sub-networks may undergo substantial changes (Mantini et al., 2007; Scheeringa et al., 2008). In a recent fmri study, the temporal variability in the relationship between nodes of the DMN and its anticorrelated network was examined (Chang & Glover, 2010). In this study, we attempted to characterize the resting state from the perspective of complex network analysis and with high temporal resolution. The main purpose was to add information related to the dynamics of associated brain connectivity based on EEG signals form different frequency bands (δ,, 1, 2, β, ). The realized experimentations aimed at the comparative examination of these bands and followed a recently developed methodology for time-varying

3 NDPLS, 16(1), Brain Connectivity Dynamics 7 network-analysis of functional connectivity (Dimitriadis, Laskaris, Tsirka, Vourkas, Micheloyannis & Fotopoulos, 2010), denoted hereafter as TVFCA. TVFCA facilitated the detection of systematics behind the emergence of hubs and the formation of functional modules via phase-coupling. Summarizing our enterprise: We detected a restricted repertoire of segregation motifs and revealed the deterministic character of changes in functional segregation by adopting entropic measures reflecting the time evolution of brain s modular structure. METHODS Introducing Time in the Analysis of Functional Connectivity. Brain connectivity may be modulated by rapid changes in time and, additionally, in a frequency-dependent manner. The necessity to track such a dynamic behaviour has been recently confirmed (Boccaletti, Latora, Moreno, Chavez, & Hwang, 2006). In this regard, selecting the appropriate window for estimating the time-frequency dependent network-properties is crucial for understanding the neural underpinnings of various cognitive functions. However, previous studies confined themselves to a firm selection for the time window (regardless of frequency) and connectivity analysis was performed in a piecewise manner (using consecutive signal segments without any overlap in time). This might be a severe drawback in the case of functional connectivity data derived from high temporal-resolution brain-imaging modalities like EEG/MEG. Based on our TVFCA methodology, we first adopted a frequency dependent criterion to define the width for the moving time-window. This is defined based on the lower frequency limit that corresponds to the - possibly - synchronized oscillations of each brain rhythm and equals the time interval of two cycles. Connectivity analysis was then realized in a sliding mode by using, each time, the signal segments enclosed inside the window in order to estimate a functional connectivity graph (FCG) and analyze it via graph-theoretic operators. Elements of Graph Theoretical Analysis Functional Connectivity Networks and Related Topological Properties To detect and precisely characterize neural synchrony between distinct recording sites, we employed a nonlinear estimator, the Phase Locking Index (PLI; see Appendix A.1) over the corresponding signals. These measures are applied, using signals filtered within a particular frequency band, to every possible pair. The derived quantities are tabulated in an [NxN] matrix, in which an entry conveys the strength of functional connection between a particular pair. Such a matrix has a natural graph representation, the functional connectivity graph (FCG), with nodes being the recording sites and edges the in-between links weighted by the tabulated value. In order to characterize a FCG, we used two well-known topological metrics established for weighted connectivity graphs: global/local efficiency (GE/LE) reflecting correspondingly integration and segregation tendencies (Latora & Machiori, 2001).

4 8 NDPLS, 16(1), Dimitriadis et al. The global efficiency for each node GE i is defined as: 1 ( dij ) (1) GE j N, j i i N 1 that is the inverse of the harmonic mean of the shortest path lengths (d ij ) between the i-th node and each other node in the graph. GE i reflects the contribution of the particular node to the global efficiency of parallel information transfer in the network (Achard and Bullmore,2007; Latora and Machiori, 2001). The local efficiency for each node LEi is defined as: 1 ( d jh ) (2) j, h G LEi i ki ( ki 1) where k i denotes to the total number of neighbours of the i-th node, N is the set of all nodes in the network and d jh denotes the shortest path length between every possible pair in the neighbourhood of the current node (G i denotes the spatial neighborhood and includes all the nodes that are directly connected to the i- th node according to the sensors physical locations). LE i can be understood as a measure of the fault tolerance of the network, indicating how well each subgraph exchanges information when the indexed node is eliminated (Achard & Bullmore, 2007). Identifying Significant Edges Based on Dijkstra s Algorithm To compute the adjacency matrix from a weighted connectivity graph, traditionally, a threshold is applied. A variety of thresholding schemes has been introduced in network analysis literature. In our TVFCA methodology, we have introduced an alternative technique to identify the most significant edges based on Dijkstra s algorithm (Dijkstra, 1959). According to this, an edge is considered significant (and hence used in the adjacency matrix) if it participates in the formation of, at least, one of the shortest paths spanning the FCG. Connections between electrodes located along the midline, are eliminated before executing Dijkstra s algorithm. Identifying Hubs An additional, useful, topological characteristic is the set of hubs (i.e. nodes of principal role in the overall communication) in the network. Hubs are readily identified from the adjacency graph with the following detection scheme. The average (μ) and standard deviation (σ) of the degree for all nodes are first derived and then used to detect those nodes with excess connectivity, i.e. with degree higher than μ+σ (Prabhakaran, Smith, Desmond, Glover, & Gabrieli, 1997). Here, we extended this thresholding scheme so as to apply to the GE (and LE) value of the nodes instead of the degree. After thresholding, the nodes that play a significant role to the functional integration (and segregation) in resting state condition are identified. Since the above procedure is repeated for each

5 NDPLS, 16(1), Brain Connectivity Dynamics 9 instance of FCG (and its adjacency matrix counterpart), we have established two different algorithmic procedures to describe the ensemble. The first procedure is based on computing the empirical probability of each node i to act as a hub (HubProb i ). This is assessed by dividing the number of times a node is identified as hub (employing either GE or LE), with the total number of FCGs. This gives rise to a spatially defined function, which can be represented topographically in the format of Fig. 1 (where values of HubProb function have been averaged across subjects). The second procedure goes beyond averaging and follows an aggregation scheme that detects, within two sequentially coupled steps, consistent hubs. Based on replicator dynamics technique (originated from evolutionary game theory (Weibull, 1995), commonalities were first detected along time (for a single subject data) and then across subjects. This technique constitutes an integral part of our TVFCA methodology and a detailed description can be found in (Dimitriadis et al., 2010). Quantifying Fluctuations in Modular Structure Modularity is an important concept in network analysis that reflects segregation and depends on the exact size and composition of network components. We applied a variant of a spectral community detection algorithm (Newman, 2006) to identify modules (communities) within each network. Newman s algorithm (Newman, 2006) is known to be quite accurate and sufficiently fast for small-sized networks. Here, we adopted its implementation from Brain Connectivity Toolbox (Rubinov & Sporns, 2009) and applied it, independently, to each one of the adjacency matrices (derived as described above). In this way, a time-evolving community structure was derived, and the dynamics of segregation could be studied based on the corresponding time-series of groupings. Ιt is important to stress here that the particular implementation can deal with the case of unknown number of communities and even of no-community at all. To quantify the contrast regarding community structure at two successive (in time) instances, we employed a novel metric called Variation of Information (VI) which is an information theoretic criterion that quantifies the dissimilarity between two distinct clusterings (see Appendix A.2). This gives rise to a signal that can be thought of as reflecting the instantaneous rate-ofchange in functional segregation (see Fig. 3). EXPERIMENTAL DATA EEG signals from 18 right-handed volunteers (students of the medical school of Iraklion/Greece; the study was approved by the local ethical committee and written informed consent was obtained from each participant) were recorded using 30 electrodes according to the international 10/20 system: FP2, F4, FC4, C4, CP4, P4, O2, F8, FT8, T4, TP8, PO8, Fz, FCz, Cz, CPz, Pz, Oz, FP1, F3, FC3, C3, CP3, P3, O1, F7, FT7, T3, TP7, PO7, and A1 + A2 as reference. Vertical and horizontal eye movements and blinks were monitored

6 10 NDPLS, 16(1), Dimitriadis et al. through a bipolar montage from the supraorbital ridge and the lateral canthus. The signals were filtered online with a Hz band pass and digitized at 500 Hz. During the acquisition, all subjects underwent a resting state recording period for which they were instructed only to keep their eyes closed and remain awake. EEG segments of 20s duration, without visible artefacts, were selected from each subject. EEG-signal was split into 6 different bands, which are traditionally defined and denoted as follows: δ (0.5 4 Ηz), θ (4-8 Hz), α 1 (8-10 Hz), α 2 (10-13Hz), β (13-30 Hz) and γ (30-45 Hz). Next, artifact reduction was performed using independent component analysis (ICA) (Onton, Westerfield, Townsend, & Makeig, 2006). Working on independently for each subject and using EEGLAB (the command runica ( that implements the extended Informax algorithm (Delorme & Makeig, 2004)), we zeroed the signal components that were associated with artifactual activity from eyes. Components related to eye movements were identified based on their scalp topography which included frontal sites and their temporal course which followed the EOG signals (for further details see Jung et al., 1998). RESULTS Hub Distribution as Reflected Over the Scalp After Averaging Across Time After quantifying the HubProb for every node based on the timeevolving graphs and representing it topographically as shown in Fig. 1, we detected brain regions active (i.e. participating in integration or segregation processes) during brain s self-organization at resting state. Figure 1 depicts, for each frequency band independently, the HubProb of each node averaged across subjects, with top/bottom row corresponding to the network characteristic of global/local efficiency. It can be seen from the included scalp topographies that various brain regions shows high probability (HubProb > 0.5) to host hubs. Over frontal regions, for all the bands and both characteristics, hubs appear permanently with high probability. The rest regions did not show any consistency regarding the emergence of hubs. Apparently, there are not significant differences in HubProb distribution among the frequency bands. We followed a statistical comparison at the level of individual electrodes, by applying onetailed paired t-test (based on single subjects measurements) and failed to detect a frequency-dependent difference in HubProb values (data not shown). After detecting consistent hubs With the aggregation step (based on replicator dynamics and described above) applied to the time-series reflecting the sequence of detected hubs, we identified the brain regions that consistently (over time and across subjects) play crucial role in integration/segregation during rest state. The procedure was repeated for every frequency-band independently and the results are provided in Fig. 2. The scalp topographies therein, showed a similar widespread distribution

7 NDPLS, 16(1), Brain Connectivity Dynamics 11 and frontal predominance with the topographies inn Figure 1. Moreover, there is a noticeable resemblance across frequency bands and network characteristics. Fig. 1. HubProb function, for each frequency band, after averaging across sub- efficiency, respectively (darker indicates higher HubProb). jects. Top and bottom rows relate to computations based on global and local Fig. 2. Topographic representationn of consistent t hubs (denoted with black cir- cles) after aggregating across time and subject, for each frequency band sepa- rately. Top and bottom rows refer to derivation based on global and local efficien- cy, respectively. Dynamical Behavior of Cortical Segregation as Reflected Over the Scalp Modularity reflects the degree to whichh a network is organized into a modular or community structure. By delineatingg the instantaneous modular structure and quantifying its change from one time instance to the next we derivedd a timeseries that is the time derivative of community structure. Figure 3 visualizes all these computations in the form of striped images (one for each frequency band) where each row corresponds to a single subject and each cell is the VI-distance between two successive segregations (instances of community structure; see an exemplar in Fig. 4). To facilitatee comparison, the individual VI-valuess have been normalized by dividing with the overall maximum across frequency-bands and subjects. Fluctuations in the functional segregation are evident for the vast majority of subjects and in every frequency band. Interestingly, the revealed changes appear to follow the oscillation of each frequency band.

8 12 NDPLS, 16(1), Dimitriadis et al. Fig. 3. Fluctuations in modular-structure quantifiedd via VI metric for every subject and frequency band. Individual VI values have been normalized according to the overall maximum VImax (the brighter the higher VII value).

9 NDPLS, 16(1), Brain Connectivity Dynamics 13 The fluctuations seen in Fig. 3. motivated us to investigate further the transient character of functional segregations. To distinguish between random perturbations in instantaneous community structure and thee existence of an underlying multimodal distribution (which would in turn indicate switching dynamics) we carried out the following summarization procedure, which exploits the fact that VI is a true -metric in the space of clusterings and, hence, of functional segregations. For the simplicity of presentation, wee will refer to the community structure (resulting from the execution of Newton ss algorithm) as a single clustering (Cl) and we conceptualize it as a list (e.g. [ , 1]) associating the nodes or electrodes to communities or clusters. It is importantt to notice that the adopted algorithm in every single case extracted two modules but with different spatial distribution. Workingg for each frequency-band independently, we first gathered all the instantaneous clusteringss across subjects. Among them, we identified all the distinct ones and then counted their relative frequency of appearance. We realized that it was only a restricted number of them ( 5 or 6 as shown in Fig. 5) that were repeatedly appearing during the observed fluctuations of functional segregation. We will referr to each one of them as segregation motif and in their ensemblee as repertoire. As noticed via visual inspection and further confirmed through VI measurements, the rest clusterings were slightly modified versions of onee of the basic motifs. Based on the nearest-neighbor rule, each isolated clustering was assigned to one of the basic motifs. VI-distance measurements showed that thee corresponding discrepancy was always smaller than the smaller inter-motiff VI-distance and hence the above motif-assignmen nt strategy complies with the concept of implementing Vector Quantization within the space of clusterings. Fig. 4. An exemplar (single subject data, delta band) of VI calculations: the dis- denote the first (more cohesive) cluster and white circles the second tances between successive clusterings have been estimated. Black circles one. The Repertoire of Functional Segregations

10 14 NDPLS, 16(1), Dimitriadis et al. Fig. 5. The repertoiree of segregation motifs derivedd for each frequency band sep- the arately. In each row, motifs appear after ranking from the most frequent to most rare (*denotes the motif observed only in subject 5). Black circles denote the most compact cluster. This assignment of clusterings to thee basic motifss enabled us to establish entropic measures expressing the randomness in the time series of community structures. Figure 5 includes the repertoire corresponding to each frequency band, with motifs sorted from the most frequent to the least frequent one. We then estimated, for each subject separately, the entropy of time-varying segregations. Table 1 demonstrates the intermediate step of frequency estimation for each segregation motif, in the case of a single subject dataa in δ-band. The entropy of the observed segregation motifs iss defined, based on counting probabilities, as follows:

11 ( A) NDPLS, 16(1), Brain Connectivity Dynamics 15 M k 1 p log p k k M k 1 nk nk log N N where M denotes the number of segregation motifs, N the total number of sliding windows and n k the number of sliding windows where each segregation motifs was observed. We use base 2 logarithms. The overall results (after averaging across subjects) have been tabulated in Table 2. In summary, very low values for the entropy have been found and this provides evidence for the non-random character of time-evolution of communities during self-organization at resting-state. Table 1. Relative frequency of the segregation motifs observed in delta band for a single subject. The four motifs can be seen in first row of Fig.5. Probability of No of Motif Motifs 1 st nd rd th (3) Table 2. Entropy of the segregation time series. Entropy M (+- Std) (bits) δ θ α α β γ DISCUSSION We examined the dynamical behavior of the functional networks corresponding to EEG frequency bands using a nonlinear connectivity estimator and tools derived from the graph theory. The appearance and behavior of hubs in the cortex (as reflected at the EEG channels), and their evolution in time were studied during the resting, eyes closed, condition. Additionally, the evolution of modules for each individual was assessed. The results show that the probability for a node (i.e. the electrode position) to be a hub during the time evolution follows an irregular widespread distribution. Consistent hubs associated with

12 16 NDPLS, 16(1), Dimitriadis et al. both local, and global efficiency appear to be located frontally and for all frequency bands. Moreover, the evolution of functional connectivity can be described via short-lasting bimodal functional segregations. Based on a distance function that compares clusterings, we discovered that these segregations are recurrent. By adopting an entropic measure for the segregation motifs, we revealed that the apparent fluctuations are subject to intrinsic constraints and that order emerges from spatially extended interactions. This was a novel way to describe the complexity in brain-activity measurements. Deviating from previous approaches in which various entropic estimators, like approximate entropy, had been applied to EEG-signals (Rezek & Roberts, 1998), we aimed at describing the evolution of functional connectivity changes. The resting state of the brain has been studied for many years based on various neuroimaging techniques and bioelectrical signal recordings. Recently, resting condition brain activity is studied based, exclusively, on fmri measurements. With fmri active brain regions and low frequency diffused fluctuations are visible (Chang & Glover, 2010). Since there is bioelectrical signal related to these fluctuations, the study of DMN and RSN through related measurements is worth pursuing. EEG signals are easily recordable and the extracted information has a high temporal resolution. The present study explores the dynamical behavior of the neural networks as this is reflected over the surface of the head. Particular electrode positions appeared to act as hubs. Consistent hubs were located mainly in frontal brain regions. In previous studies, the EEG signal during the resting state was studied alone or in combination with the low frequency fmri fluctuations. It is difficult to compare the results of these previous studies with our results since we studied different parameters giving information about the dynamical network organization of the EEG bands and their changes in time. The previous studies showed EEG power band correlations with different fmri resting fluctuations (Debener et al., 2005; Laufs et al., 2003; Mantini et al., 2007). The EEG patterns can show differences during the rest situation (Laufs et al., 2003; Mantini et al., 2007). Additionally, the choice of the reference electrode can give different patterns of the EEG DMN (Qin, Xu, & Yao, 2010). The spectral power measurements, associated to regional activities of the DMN, that were described recently (about 80 years after the Berger s original description of EEG) gave a more detailed picture about the topographical distributions of the different bands (Chen, Feng, Zhao, Yin, & Wang, 2008). In the present study and in accordance with a recent one (Chen et al., 2008), the slow wave activity was identified, mainly, frontally. We found hubs for all the bands over frontal, parietal and occipital areas with high (HubProbi) and based on both the local and the global efficiency. Global and local efficiency are network metrics that quantify the functional integration/segregation of each node. The fact that we identified brain regions as hubs (mainly frontal, parietal and occipital) by both measures, implies that they play an important role in the communication of the whole network and also within their spatial neighborhood (Fig.1). Moreover, based on individual HubProbi values, we revealed the functional core of hubs consistent across time and subjects which includes mostly frontal sites (Fig.2)

13 NDPLS, 16(1), Brain Connectivity Dynamics 17 (Laufs et al., 2003; Mantini et al., 2007). It is worthwhile noticing that previous studies (Chen et al., 2008; Dimitriadis, Laskaris, Tsirka, Vourkas, & Micheloyannis 2010) found an increase of power frontally, only, in the delta band, during an eyes open recording condition. On the contrary, here we detected hubs with high (HubProbi ) frontally in all bands under investigation. Patterns of functional connectivity in the brain (Friston, Frith, Liddle, & Frackowiak, 1993) are believed to reflect the patterns of interaction between transiently formed neuronal assemblies (Fingelkurts, Fingelkurts, & Kahkonen, 2005) and to be associated with attention, perception, cognition (Varela, Lachaux, Rodriguez, & Martinerie, 2001) and eventually with consciousness (Fingelkurts & Fingelkurts, 2001,2006; Fingelkurts, Fingelkurts, & Neves, 2009, 2010; Fingelkurts & Fingelkurts,2011). Changes in functional brain modules due to ageing and performing a cognitive task have been recently identified (Meunier, Achard, Morcom, & Bullmore, 2009). In the present study, the interesting finding is the fluctuations of interconnections in the modules and between them as well as their differences in different bands and different individuals. Delta band shows relative high stability in the connections of modules and their interconnections and for all the individuals compared to gamma band which show low stabilities in most individuals. The behavior of the other bands lies between the behavior observed in delta and gamma band. Higher fluctuations are evident as we move from lower to higher bands. The observed changes do not show periodicity or alternations between constancy and transitions. They reflect continuous change. This finding shows a connectivity microfluctuation behavior on the surface of the cortex. It has been already shown that resting state functional connectivity assessed using fmri is not static in time (Honey et al., 2009) and functional connectivity can reconfigure within a few hundred milliseconds (Basset, Meyer-Lindenberg, Achard, Duke, & Bullmore, 2006). Comparing functional time-dependent signatures in a systematic way revealed fluctuations modulated by frequency. Evolution of functional connectivity can be described via bimodal functional segregations. Employing a distance measure that compares clusterings, we discovered that these segregations are recurrent. Moreover, observed fluctuations are subject to spatially extended interactions leading to order along the axis of time-evolution. The trace of connectivity microfluctuation at rest should be compared with the dynamics associated with cognition and this might open a new window to the neural correlates of behavior. Finally, we need to stress here that the presented observations were based on a particular estimator of functional dependence, namely the Phase Locking Index. It is, in general, considered a suitable measure for studying neural synchrony through oscillatory activity. However, functional connectivity could be derived via alternative estimators as well. Some of them can provide, in addition, directionality information regarding the coupling among distinct recording sites (Astolfi et al., 2004; Babiloni et al., 2005). By extending this work, with the incorporation of such estimators, further insights regarding the transient character of brain s functional organization at rest can be provided.

14 18 NDPLS, 16(1), Dimitriadis et al. APPENDIX A: PHASE LOCKING INDEX PLI computation is based on estimates of instantaneous phase obtained from the convolution of Morlet wavelet with the EEG signals x i (n) filtered within one of the frequency bands under study. The resulting Dyadic Wavelet Transform of a discrete sequence x(n) sampled with time spacing δ t and consisting of N data points (n=0,1,..n-1) is denoted as: X W ( n, s) (A.1) where * denotes complex conjugation with the consecutive scaled and translated versions of the principal wavelet function, the complex Morlet wavelet ψ o (n): ( n) 0 / s t e N 1 n' 0 e 1/ 4 iω0n x( n') (( n' n) / s) 2 n / 2 0* (A.2) where ω 0 is the nondimensional frequency, here taken to be 6 (Torrence & Compo 1998). A set of different scales s is implied in Eq. A.1. Writing the scales as fractional powers of two: s j s o J 2 1 j j j, j 0,1,..., J log ( N / s ) 2 t o (A.3) where s o is the smallest resolvable scale and J the largest scale. Our analysis starts by estimating the optimal δ j for each band/condition (see pg. 9 and Fig. 3b). The instantaneous phase φ Xi (n,f) is then calculated as follows: Xi imag( W ( n, s) arctan real( W Xi Xi ( n, s)) ( n, s)) (A.4) The successive phases values (originally ranging in [-π π]) underwent an unwarping transform to get rid of discontinuities (in accordance with the phase correction algorithm described in (Freeman & Rogers, 2002)). Finally, the PLI index for a pair of signals x k (n) and x l (n) recorded at different sites was computed by averaging the instantaneous phase differences PLI( x (f,n),x (f,n)) k l 1 N. s n N s2 ( f ) 1 s( f ) s1 ( f ) (A.5) where N is the number of time points (samples), s 1 /s 2 refer to the scale limits, Δ denotes the corresponding range and f the studying frequency band (Lachaux, Rodriguez, Martinerie, Varela, 1999). A zero PLI-value means that the phases of two encountered signals were not coupled at all, while the PLI-value of one corresponds to phase values that are completely synchronized. t x exp(i ( k x (s(f),n)- l (s(f),n))

15 NDPLS, 16(1), Brain Connectivity Dynamics 19 APPENDIX B: VARIATION OF INFORMATION Having all the communities available, (output of the modularity algorithm was a 30-tuple c=[c1,,c30], (e.g. c=[ ])) reflecting the nonoverlapping modules), we quantified the contrast of two successive clusterings in time, using the VI-metric as the dissimilarity measure (Meila 2007). Variation of Information (VI; Meila 2007) is a novel informationtheoretic criterion, that has been introduced for comparing two different clusterings of the same data set and which measures the amount of information that is lost or gained in changing from clustering c to clustering c'. VI is a nonnegative, symmetric metric which is more intuitive compared to other relevant measures and moreover overcomes previous limitations (for instance, it satisfies the triangular inequality). VI is defined by the function: VI(c, c' ) [H(c) - I(c,c' )] [H(c') - I(c,c' )] (A.6) H(c) denotes the entropy associated with clustering c and I(c,c ) denotes the mutual information between the two clusterings c and c. The probability that a randomly selected node from partition A will be a member of community k is P(k)=n k /N, where n k is the number of nodes in community k and N is the total number of nodes in the system. The entropy of a given community structure is defined as q A nk nk ( ) log (A.7) k 1 N N where q A is the number of communities in partition A. The mutual information I(A,B) evaluates the level of interdependence in two sets of data. We define a confusion matrix for partitions A and B by identifying how many nodes n ij of community i of partition A are in community j of partition B. The mutual information is q A qb nij nijn I( A, B) log (A.8) i 1 j 1 N nin j where n i is the number of nodes in community i of partition A and n j is the number of nodes in community j of partition B. The range of values for VI is 0 V ( A, B) log N. We use base 2 logarithms. REFERENCES Achard, S. & Bullmore E. (2007). Efficiency and cost of economical brain functional networks. PLoS Computational Biology, 3, e17. Astolfi, L., Cincotti, F., Mattia, D., Salinari, S., Babiloni, C., et al. (2004). Estimation of the effective and functional human cortical connectivity with structural equation modeling and directed transfer function applied to high-resolution EEG. Magnetic Resonance Imaging, 22,

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