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The effect of epoch length on estimated EEG functional connectivity and brain network

organisation

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2016 J. Neural Eng. 13 036015

(http://iopscience.iop.org/1741-2552/13/3/036015)

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The effect of epoch length on estimated EEGfunctional connectivity and brain networkorganisation

Matteo Fraschini1, Matteo Demuru2, Alessandra Crobe3,Francesco Marrosu4, Cornelis J Stam2 and Arjan Hillebrand2

1Department of Electrical and Electronic Engineering, University of Cagliari, Piazza D’armi, Cagliari,I-09123, Italy2Department of Clinical Neurophysiology and MEG Center, VU University Medical Center, Amsterdam,The Netherlands3Department of Mechanical, Chemical and Materials Engineering, PhD Course in Biomedical Engineering,University of Cagliari, Piazza d’Armi, Cagliari, Italy4Department of Medical Science ‘M. Aresu’, University of Cagliari, Cagliari, Italy

E-mail: fraschin@unica.it

Received 16 December 2015, revised 11 March 2016Accepted for publication 12 April 2016Published 3 May 2016

AbstractObjective. Graph theory and network science tools have revealed fundamental mechanisms offunctional brain organization in resting-state M/EEG analysis. Nevertheless, it is still not clearlyunderstood how several methodological aspects may bias the topology of the reconstructedfunctional networks. In this context, the literature shows inconsistency in the chosen length ofthe selected epochs, impeding a meaningful comparison between results from different studies.Approach. The aim of this study was to provide a network approach insensitive to the effects thatepoch length has on functional connectivity and network reconstruction. Two different measures,the phase lag index (PLI) and the amplitude envelope correlation (AEC) were applied to EEGresting-state recordings for a group of 18 healthy volunteers using non-overlapping epochs withvariable length (1, 2, 4, 6, 8, 10, 12, 14 and 16 s). Weighted clustering coefficient (CCw),weighted characteristic path length (Lw) and minimum spanning tree (MST) parameters werecomputed to evaluate the network topology. The analysis was performed on both scalp andsource-space data. Main results. Results from scalp analysis show a decrease in both mean PLIand AEC values with an increase in epoch length, with a tendency to stabilize at a length of 12 sfor PLI and 6 s for AEC. Moreover, CCw and Lw show very similar behaviour, with metricsbased on AEC more reliable in terms of stability. In general, MST parameters stabilize at shortepoch lengths, particularly for MSTs based on PLI (1–6 s versus 4–8 s for AEC). At the source-level the results were even more reliable, with stability already at 1 s duration for PLI-basedMSTs. Significance. The present work suggests that both PLI and AEC depend on epoch lengthand that this has an impact on the reconstructed network topology, particularly at the scalp-level.Source-level MST topology is less sensitive to differences in epoch length, therefore enabling thecomparison of brain network topology between different studies.

S Online supplementary data available from stacks.iop.org/JNE/13/036015/mmedia

Keywords: EEG, epoch length, time-window, functional connectivity, brain networks, restingstate, minimum spanning tree

(Some figures may appear in colour only in the online journal)

Journal of Neural Engineering

J. Neural Eng. 13 (2016) 036015 (10pp) doi:10.1088/1741-2560/13/3/036015

1741-2560/16/036015+10$33.00 © 2016 IOP Publishing Ltd Printed in the UK1

Introduction

In the last decade, the use of tools derived from graph theoryand network science in resting-state EEG and MEG analyseshave revealed fundamental mechanisms of normal andpathological functional brain organization (Bullmore andSporns 2009, Sporns 2013, Stam 2014). Nevertheless, it isstill not clearly understood how several methodologicalchoices may affect the topology of reconstructed functionalbrain networks, eventually hindering the meaningful com-parison of results from different studies. In a recent review,van Diessen and colleagues discussed the methodologicalchoices in EEG and MEG resting-state analysis that affect thereconstruction of functional network topology (van Diessenet al 2014), including the duration of the time-window overwhich functional connectivity (FC) is estimated.

Previous studies have shown that estimates of FC arebiased by epoch length and that the severity of this bias variesfor different connectivity metrics (David et al 2004, Honeyet al 2007, Vinck et al 2011, Chu et al 2012, Bonitaet al 2014). Together with the observation of inhomogeneityin the length of EEG epochs across resting-state FC studies,these aspects may severely impede the meaningful compar-ison of results between studies. Similarly, recent papers haveshown that phase-based connectivity measures are biased bythe number of observations (sample size) (Vinck et al 2010,Aviyente et al 2011, Aydore et al 2013). However, the pre-sent work is more focused on the impact of the length of theselected epochs.

Furthermore, these biases in FC estimates may havedirect consequence for the estimation of network topology(van Wijk et al 2010). Approaches that allow for the char-acterization of brain networks, whilst avoiding arbitrarychoices, are therefore required. Recently, it has been shownthat the minimum spanning tree (MST), a backbone of theoriginal weighted network, enables an unbiased comparisonbetween networks (Stam et al 2014, Tewarie et al 2015),although it is unknown how epoch length affects the MST.

In this study we aimed to provide a network approachinsensitive to the effects that epoch length has on FC andnetwork reconstruction. We therefore first demonstrated theeffect of different durations (in the range of commonlyselected EEG segments for resting-state analysis) on twowell-known and widely used connectivity measures: thephase lag index (PLI) (Stam et al 2007) and the amplitudeenvelope correlation (AEC) (Brookes et al 2011, Hippet al 2012). These measures capture two distinct types ofintrinsic coupling (one arising from phase coupling, the otherfrom fluctuations of signal envelopes) that seem to play a rolein defining the interactions in on-going brain activity (Engelet al 2013, Guggisberg et al 2015). Furthermore, we inves-tigated the effect of epoch length on MST topology, as well ason some commonly used network measures: weighted clus-tering coefficient (CCw) and weighted characteristic pathlength (Lw). We hypothesized that traditional approaches tonetwork representation (CCw and Lw) would be stronglyaffected by the biases in FC estimates that are due to epochlength, since the strength of connections are taken into

account in weighted network analyses. In contrast, the MSTwas expected to be less affected as it is based on the rankorder of the connections rather than the (biased) absolutevalues.

Furthermore, many resting-state EEG studies still useactivity recorded at the scalp to estimate patterns of FC andbrain network organization. Nevertheless, in this case severalfactors (e.g. field spread and volume conduction effects) canaffect the reliability of the estimated parameters. Althoughthese problems cannot simply be overcome by using sourceanalysis, several methods that project scalp signals to theunderlying sources enable a more straightforward interpreta-tion of results (in terms of relation to anatomy) (Bailletet al 2001, Michel et al 2004). In order to assess differencesbetween these two approaches, the analyses were performedon both scalp EEG and sources-reconstructed time-series.

Material and methods

Participants

Eighteen healthy volunteers (13 male and 5 female;age=38.6±14.0 years) were enroled in the present study.Informed consent was obtained prior to the recordings. Thepresent study was approved by the local ethics committee.

Recordings

EEG signals were recorded using a 61 channels EEG system(Brain QuickSystem, Micromed, Italy) in eyes-closed resting-state condition. Recordings were acquired in sitting positionin a normal daylight room; a dimly lit and sound attenuatedroom and supine position were avoided to prevent drowsiness(van Diessen et al 2014). Signals were digitized with asampling frequency of 1024 Hz, low-pass filter at 70 Hz, thereference electrode was placed in close approximation of theelectrode POz and all signals were digitally offline re-refer-enced to the common average reference. For each subjectthree artifact-free segments of 32 s (32.768 samples) wereselected for the analysis. EEG segments were chosen as thefirst after the start of the recording (van Diessen et al 2014).Since it has been shown that EEG frequencies above 20 Hzmainly reflect myogenic artifacts (Whitham et al 2007, Popeet al 2009, Muthukumaraswamy 2013), EEG signals wereoff-line band-pass filtered between 1 and 20 Hz using two-way least-squares filtering method as implemented inEEGLAB with fir1 filter type. Data were converted to EDFformat and all analyses were performed using Matlab(MATLAB R2010a, The MathWorks Inc., Natick, MA),EEGLAB (version 13.1.1b) (Delorme and Makeig 2004) andthe Brain Connectivity Toolbox (version 2014_04_05)(Rubinov et al 2010).

Protocol

To study the effect of epoch length on FC and brain networkorganization, the three segments were sub-divided in non-overlapping epochs with variable length of 1, 2, 4, 6, 8, 10,

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12, 14 and 16 s. All the results reported in the study refer tothe use of six epochs. Two epochs (as the first two in time)from each segment were selected. The three segments areextracted at different time during the recordings, so the sixepochs give a representation of different windows in time.Moreover, in order to investigate the effect of sample fre-quency, the analyses were also performed on the same datasetafter down-sampling to 128 and 256 Hz (see supplementarymaterial).

Source reconstruction

In order to explore differences between signal-space andsource-space, the analysis was also performed on source-reconstructed time-series. For this, a head model was gener-ated using a symmetric boundary element method in Open-MEEG (Kybic et al 2005, Gramfort et al 2010); the headmodel was based on a default anatomy derived from theMNI/Colin27 brain (Collins et al 1998). Sources, and theirtime-series, were reconstructed using weighted minimumnorm estimates (wMNE), which allows compensating for thetendency of MNE to favour superficial sources (Hämäläinenand Ilmoniemi 1994, Lin et al 2004, Eddy et al 2006). Toavoid differences between scalp- and source-analysis due todifferences in network size, source-reconstructed time-serieswere projected onto 64 regions of interest (ROIs) defined bythe Desikan-Killiany atlas (Desikan et al 2006), followingwhich time-series within the same region were averaged (afterflipping the sign of sources with opposite directions). Seesupplemental material for a list of the ROIs. All the analyseswere performed using the Brainstorm software (version 3.2)(Tadel et al 2011).

Functional connectivity

FC was estimated using two different measures: the PLI(Stam et al 2007) and the AEC (Brookes et al 2011, Hippet al 2012). The PLI quantifies FC on the basis of phase-relationships, whereas the AEC detects amplitude-basedcoupling among brain signals. Before estimating the corre-lation between amplitude envelopes (using the absolute valueof the analytical signal) the time-series were orthogonalizedby means of linear regression analysis (Brookes et al 2011,Hipp et al 2012), in order to remove trivial correlations thatare due to field spread or volume conduction (leakage-cor-rected AEC). For every epoch length, the mean value of PLIand AEC across all channels was estimated. Mean PLI andAEC values were successively averaged over epochs and oversubjects. In-house Matlab implementations were used forthese analyses.

Network measures

To evaluate the effects of epoch length on network measures,the clustering coefficient (CCw) and the characteristic pathlength (Lw), were computed for each weighted connectivitymatrix, where EEG electrodes/ROIs and PLI/AEC valueswere represented as nodes and edges of the network,respectively. CCw and Lw are two commonly used network

measures, which respectively reflect functional segregationand functional integration (Watts and Strogatz 1998, Rubinovand Sporns 2010). Even though graph measures are oftennormalized via random surrogate data, we decided not to usenormalized versions of CCw and Lw since it has been shownthat this procedure may increase the sensitivity to differencesin network size and average degree distribution (van Wijket al 2010). To avoid these biases altogether the MST wascomputed. The MST is an acyclic sub-graph that containsmost of the strongest connections5 of the original graph,which was computed from each weighted connectivity matrixusing Kruskal’s method (Kruskal 1956). MST topology wascharacterized using several parameters: leaf fraction (Lf,number of nodes with degree of 1 divided by the total numberof nodes), diameter (D, largest distance between any twonodes in the network6), tree hierarchy (Th, reflects the balancebetween diameter reduction and overload prevention),eccentricity (E, the longest distance between a node and anyother node) and kappa (K, the broadness of the degree dis-tribution). See (Boersma et al 2013, Demuru et al 2013, Stamet al 2014, Tewarie et al 2015) for a detailed description ofthese parameters. Network measures were evaluated for eachepoch and then averaged.

Statistical analysis

Non-parametric Friedman tests were used to detect the effectof different epoch lengths on FC measures and networkparameters. In case the Friedman test showed a significanteffect, the shortest epoch length that did not show a sig-nificant difference (using post-hoc Dunn’s multiple compar-ison tests) with any longer epoch was defined as the onset of astability zone. Linear regression analysis was used to estimatethe relationship between epoch lengths and the standard errorof the mean for the different measures. The level of sig-nificance was accepted at p<0.05. All statistical analyseswere performed using Prism (GraphPad, version 5.0f).

Results

Scalp analysis: effect on FC

Both PLI and AEC showed a decrease in mean values forincreasing epoch lengths (figure 1 left panel), with Friedmanstatistics χ2(8)=137.7.0, p<.0001 for PLI andχ2(8)=96.6, p<.0001 for AEC. The effect is slightly moreevident for the PLI, where the results stabilize for epochs withlengths of 12 s, compared to 6 s for the AEC. It is of interestto note that epoch length not only affects the mean FC values,but shorter epochs also show less clear (more blurred) FCpatterns than those obtained for longer epochs (figure 2, upperpanel).

5 For the construction of the MST, the edge weight is defined as 1–(functional connectivity estimate).6 The distance between nodes is expressed as the inverse of the sum of theweights on the shortest path between the nodes.

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Figure 1. Mean PLI and AEC values for scalp analysis (left panel) and source analysis (right panel). Error bars refer to standard error of themean. The white and black boxes indicate the stability zones for PLI and AEC, respectively.

Figure 2. Representation of FC patterns for different epoch lengths for PLI and AEC for scalp (upper panel) and source (lower panel) EEGanalysis. In order to allow comparison between conditions, images represent the rank order of the FC metric (see supplementary material for alist of channels/ROIs).

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Scalp analysis: effect on network measures

As for the FC, the weighted network measures also decreasedwith increasing epoch lengths. CCw and Lw stabilized earlierfor networks based on AEC than for those based on PLI (4versus 12 s for both metrics). In contrast, MST parametersalready stabilized for shorter epochs, namely for epochsbetween 1 and 6 s for PLI-based MSTs and for epochsbetween 4 and 6 s for AEC-based MSTs (depending on the

MST parameter). All the results are summarized in table 1,figures 3 and 4.

Scalp analysis: linear regression

A significant relation between epoch length and the standarderror of the mean was found for PLI, AEC, and the differentnetwork metrics (see table 3).

Source analysis: effect on FC

As for the scalp analysis, in the source space both PLI andAEC show a decrease of mean values for increasing epochlengths (figure 1 right panel), with Friedman statisticsχ2(8)=141.1, p<0.0001 for PLI and χ2(8)=99.2,p<0.0001 for AEC. The onset of the stability zone occurredfor epoch length of 6 s for AEC and 10 s for PLI. Again,shorter epochs show less clear (more blurred) FC patternsthan those obtained for longer epochs (figure 2, lower panel).

Source analysis: effect on network measures

As for the FC, the weighted network measures also decreasedwith increasing epoch lengths. CCw and Lw stabilized earlierfor networks based on AEC than for those based on PLI (6versus 12 s for both metrics, respectively). In contrast, as forscalp analysis, MST parameters already stabilized for shorterepochs, namely for epochs of 1 s for PLI-based MSTs (for all

Table 1. Statistics for PLI and AEC-based network measures at scalplevel, reporting the main effect from the Friedman test.

PLI-based networks AEC-based networks

Networkmeasure χ2(8) p χ2(8) p

CCw 137.0 0.0001 89.8 0.0001Lw 126.2 0.0001 73.7 0.0001MST leaffraction

36.6 0.0001 95.2 0.0001

MST diameter 15.2 ns (0.059) 61.5 0.0001MSTeccentricity

12.6 ns (0.126) 57.6 0.0001

MST hierarchy 22.4 0.004 65.6 0.0001MST kappa 11.0 ns (0.204) 59.5 0.0001

Figure 3. CCw (top panel) and Lw (bottom panel) values for scalp analysis (left panel) and source analysis (right panel). Error bars refer tostandard error of the mean. The white and black boxes indicate the stability zones for PLI and AEC-based networks, respectively.

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Figure 4.MST parameters for scalp analysis (left panel) and source analysis (right panel). Error bars refer to standard error of the mean. Thewhite and grey boxes indicate the stability zones for PLI and AEC-based networks respectively.

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MST parameters) and for epochs between 2 and 6 s for AEC-based MSTs (depending on MST parameter). All the resultsare summarized in table 2, figures 3 and 4.

Source analysis: linear regression

As for scalp analysis, for AEC a significant positive relationbetween epoch length and the standard error of the mean formost of the measures was observed, indicating an increase ofthe standard error with increasing epoch lengths (see table 3).For mean PLI and PLI-based networks (as for AEC basedMST- leaf fraction, eccentricity and hierarchy) no significantrelation with standard error was found.

The effect of sample frequency

As reported in detail in the supplemental material no sig-nificant differences were observed in the mean PLI and in themean AEC when applying different sample frequencies (128,256 and 1024 Hz).

Discussion

The present study investigated the effect of epoch length onestimated FC and brain network organization in resting-state

EEG analysis. In summary, we found that (i) FC measures,namely PLI and AEC, are affected by the length of theselected EEG epoch; (ii) traditional network measures,namely CCw and Lw are affected by these biases; and (iii) thetopology of source-space PLI-based MST is almost unaf-fected by epoch length.

FC is biased by epoch length

Despite the different approach in the assessing FC and in theexperimental setup, our results are in line with previousfindings that have reported a similar behaviour for con-nectivity measures based on linear coupling (Chu et al 2012).Furthermore, the reported results confirm that FC measuresare relatively more efficient with longer time window (Davidet al 2004). It should be noted that, as previously reported(Tewarie et al 2014), AEC and PLI behave similarly at grouplevel analysis. Our results suggest to use epoch lengths of atleast of 6 s and to keep into consideration the types of cou-pling captured by the adopted metric. Moreover, even though,compared to PLI, results from AEC stabilize earlier as epochlength increases, this higher stability may be, at least in part,due to the reported increase of variance for AEC with longerepochs, which could be responsible for non-significant post-hoc tests.

It is of interest to note that epoch length not only affectsthe mean FC values but also it is evident (especially for AECmetric) that shorter epochs also show less clear (more blurred)FC patterns than those obtained for longer epochs (figure 2).The less clear FC patterns for shorter epochs may be due tointer-epoch variability in neuronal activity, which wouldsuggest to use shorter epochs to examine network dynamics.An alternative explanation is that the FC estimates are simplynoisier for shorter epochs due to the decrease in number ofsamples, although our results for downsampled data speakagainst this.

Traditional network measures are biased by epoch length

As expected, biases in estimates of FC affect the estimatedtopology of functional networks, at least for the common andwidely used metrics that allow estimating global network

Table 2. Statistics for PLI and AEC-based network measures atsource level, reporting the main effect from the Friedman test.

PLI-based networks AEC-based networks

Networkmeasure χ2(8) p χ2(8) p

CCw 139.3 0.0001 94.7 0.0001Lw 130.3 0.0001 80.1 0.0001MST leaffraction

15.5 ns (.051) 74.4 0.0001

MST diameter 21.0 0.007 52.4 0.0001MSTeccentricity

17.7 0.024 52.8 0.0001

MST hierarchy 4.0 ns (.85) 35.8 0.0001MST kappa 19.4 0.013 37.6 0.0001

Table 3. Linear regression analysis for standard errors and epoch lengths. The significant relations between epoch length and the standarderror of the mean was positive for all metrics, except for PLI, CCw and Lw based on PLI.

PLI AEC

Scalp Source Scalp Source

R2 p R2 p R2 p R2 p

FC 0.69 0.006 ns 0.92 0.0001 0.93 0.0001CCw 0.70 0.005 ns 0.92 0.0001 0.93 0.0001Lw 0.60 0.01 ns 0.76 0.002 0.67 0.007MST leaf fraction 0.79 0.001 ns 0.65 0.009 nsMST diameter 0.81 0.0009 ns ns 0.60 0.01MST eccentricity 0.71 0.005 ns ns nsMST hierarchy 0.71 0.004 ns 0.62 0.012 nsMST kappa ns ns 0.73 0.004 0.75 0.003

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integration (Lw) and segregation (CCw). These results suggestthat caution should be taken when comparing results fromstudies on network organization when the analysis is per-formed with different epoch length, especially for shortepochs. The use of epoch length shorter than 4 s should beavoided (figure 3). Furthermore, we noted that the clusteringcoefficients for the weighted networks as obtained with thePLI and AEC were similar, whereas the path length was muchlower for the PLI than for the AEC. This may be related to thefact that the two measures capture two distinct modes ofintrinsic coupling (one arising from phase coupling, the otherfrom fluctuations of signal envelopes) (Engel et al 2013,Guggisberg et al 2015). However, it could also be that this isan example of a bias introduced by the weighted networkapproach itself (van Wijk et al 2010). This interpretation issupported by figure 4, where the MST, a bias free approach,was used. This figure shows that the MST diameter, whichreflects comparable mechanism and correlates with pathlength (Tewarie et al 2015), is similar for the MSTs based onthe two connectivity metrics, particularly for medium to longepoch lengths.

MST is almost unaffected by epoch length

Importantly, the use of the MST, which has been shown to beas sensitive to alterations in network topology as conventionalnetwork measures (Tewarie et al 2015), provides stableresults also for very short epochs. This can be explainedobserving that even though mean FC values are affected byepoch length, the rank order is less influenced (figure 2),especially for PLI based FC. This result implies that resultsfrom different studies can be meaningfully compared usingthe MST. In particular, by the combination of PLI (as FCindex) and MST (for network characterization) in sourcespace it is possible to obtain results that are already stable fortime-windows of 1 s. This latter result is also of importance inthe context of time-varying (dynamic) network analysis,which is currently a hot topic in (EEG) resting-state analysis(Betzel et al 2012, Hutchison et al 2013, Mehrkanoonet al 2014, Khanna et al 2015). Indeed, our study, whichshows how results depend on the specific approach, canstrengthen the idea that time-varying approaches can generatespurious signs of non-stationary dynamics (induced by theprocedure itself) even when applied to a stationary process(Hlinka and Hadrava 2015). In this context, the stability ofparameters extracted from the MST would give the opportu-nity to study topology changes (at least at time-scale of 1 s)and to investigate how this topology may correspond tointrinsic resting-state networks (Greicius et al 2003, Mantiniet al 2007).

Effect of epoch length is reduced in source-space

Better behaviour (in terms of stability) was observed formeasures extracted from source analysis as compared withresults from scalp analysis. This finding suggests that the useof techniques to reconstruct the time-series at the level of thesources reduces the dependency on epoch length, possibly

due to demixing of signals, consequent reduction of volumeconduction effects and increased signal to noise ratio. Thisphenomenon is particularly evident for PLI and PLI-basednetwork parameters, where, differently from other metrics, norelationship between epoch length and the standard error wasobserved. It should be noted though that many approachesexist to reconstruct source time-series (Baillet et al 2001,Hillebrand and Barnes 2005, Hillebrand et al 2005). How-ever, the main focus of this work was not to investigatedetails, advantages, and/or limitations of these differenttechniques, but to understand the effect of epoch length insource-space. We therefore decided to use a method (wMNE)that is widely used in EEG analysis and easy to implementwith available tools. Furthermore, it has been recently sug-gested that the combination of wMNE and phase synchroni-zation measures represent a reliable solution to characterizeEEG networks (Hassan et al 2014). Nevertheless, we expectthat the general conclusions would hold for other techniques(Hillebrand et al 2012), where the spatial filtering character-istics of e.g. beamforming may aid to reduce the effects ofepoch length even further.

Limitations

Even though the reported results show some clear patternswith respect to epoch length, it should be noted that in realEEG analysis, the real FC patterns are unknown. Thus it maystill be difficult to know whether the PLI and AEC (andnetwork measures) converge, for long epochs, to somethingthat is closer to realistic neurophysiological processes orrepresent simply some stable statistical estimates unrelated tounderlying biological mechanism. It would be of relevancefor future works trying to elucidate these mechanisms usingsimulated data from neural mass modelling approaches,where the ground truth is known (Deco et al 2008). Fur-thermore, it should be noted that the present study showsresults with a lower limit of 1 s epoch length. However, tostudy dynamics at millisecond resolution different approachedshould be investigated, as recently proposed by (Valenciaet al 2008, Dimitriadis et al 2010, Mutlu et al 2012, Shineet al 2015).

Sampling frequency seems to play a less important rolein the estimation of both FC and network topology, con-firming that our results strongly depend on the definition ofthe epoch length itself (see supplemental material) and notjust on the number of samples.

Conclusion

Our results show that epoch length has an important impacton both FC and estimated network topology. Furthermore, thetopology of the MST, which has been shown to represent avalid alternative to traditional network analyses, can be reli-ably estimated for a range of epoch lengths, and may thusfacilitate the comparison between results from differentstudies.

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Conflict of interest statement

None of the authors has any conflict of interest to disclose inrelation to this work.

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