Large-scale network-level processes during entrainment.

Visual rhythmic stimulation evokes a robust power increase exactly at the stimulation frequency, the so-called steady-state response (SSR). Localization of visual SSRs normally shows a very focal modulation of power in visual cortex and led to the treatment and interpretation of SSRs as a local phenomenon. Given the brain network dynamics, we hypothesized that SSRs have additional large-scale effects on the brain functional network that can be revealed by means of graph theory. We used rhythmic visual stimulation at a range of frequencies (4-30 Hz), recorded MEG and investigated source level connectivity across the whole brain. Using graph theoretical measures we observed a frequency-unspecific reduction of global density in the alpha band "disconnecting" visual cortex from the rest of the network. Also, a frequency-specific increase of connectivity between occipital cortex and precuneus was found at the stimulation frequency that exhibited the highest resonance (30 Hz). In conclusion, we showed that SSRs dynamically re-organized the brain functional network. These large-scale effects should be taken into account not only when attempting to explain the nature of SSRs, but also when used in various experimental designs.

Introduction

Neuronal oscillations are phylogenetically preserved processes observable at various spatial scales that are likely to be functionally relevant (Buzsaki and Draguhn, 2004). A potential fundamental role is that distributed neurons are temporally linked into assemblies affecting behavior at virtually all levels such as perception (Busch et al., 2009, Dijk et al., 2008, Hanslmayr et al., 2007, Mathewson et al., 2009, Thut et al., 2012) and the long-term consolidation of information (Destexhe and Sejnowski, 2003, Steriade, 2001; Wilson and McNaughton, 1994). However, establishing the causal role of brain oscillations in any behavior is a difficult undertaking, especially in human experiments.

Behavioral performance have been reported to be sensitive to 10 Hz entrainment (de Graaf et al., 2013, Spaak et al., 2014) or entrainment at its sub-harmonic of 5 Hz (de Graaf et al., 2013). When it comes to source imaging, the SSRs are very focal; thus it is commonly assumed that, whether we refer to SSRs, or sensory entrainment, rhythmic stimulation evokes local modulations of power, e.g., in the visual cortex. However, advanced connectivity analysis methods in neuroscience clearly point to the involvement of distributed neural networks to underlie cognitive states. Thus, the aim of this paper is to explore the network-level processes evoked by rhythmic stimulation.

External rhythmic stimuli are used in many studies to manipulate endogenous brain oscillation. They elicit a narrow-band ongoing response at the stimulation frequency, the so-called steady-state response (SSR). SSRs exhibit a high signal-to-noise ratio, which makes them an excellent tool including experimental designs with only a few trials. Due to their excellent temporal resolution electro- and magnetoencephalography (EEG/MEG) can perfectly trace SSRs.

There seems to be a frequency “preferred” by the visual system: visual SSR show particular resonance at ~15 Hz (Herrmann, 2001, Pastor et al., 2003) which is related to the photoparoxysmal response in patients with photosensitive epilepsy (Lopes da Silva and Harding, 2011, Takahashi and Tsukahara, 2000). SSRs further include a number of equally narrow-band higher order harmonics, implying non-linear responses to rhythmic stimuli (Roberts and Robinson, 2012). Interestingly, the differential topographies of frequency-following and frequency-doubling (harmonic) neural populations suggest that harmonics contribute to complementary functions, rather than having a redundant role (Kim and Robinson, 2007, Norcia et al., 2015). SSRs have been extensively used as an experimental choice to study cognitive load (Jacoby et al., 2012), attention (Andersen and Müller, 2010, Porcu et al., 2014), aging (Quigley and Müller, 2014), fear conditioning (Moratti et al., 2006), face and object processing (Koenig-Robert and VanRullen, 2013, Rossion et al., 2012), as well as two-percept segregation (Baldauf and Desimone, 2014).

In this study, we aimed to test the hypothesis that a change in local cortical power, especially because it influences behavior (de Graaf et al., 2013, Spaak et al., 2014), also affects network states in the brain. Brain functional connectivity provides the means to answer such a question: coupling and decoupling of distant brain regions, not explained completely by changes in power, have been reported to predict behavior (Leonardelli et al., 2015, Weisz et al., 2014). Going beyond classical approach to functional connectivity between two or more regions, we used graph theoretical tools to characterize global and local changes in the brain network involved in the processing of frequency-tagged stimulation. Graph theory gives access to aspects of brain network organization that are not evident in classical time–frequency analysis (Rubinov and Sporns, 2010). Here, we recorded MEG while stimulating with Gabor ellipsoids flickering at 9 different frequencies, covering a broad spectrum of visual SSRs from 4 to 30 Hz. Specifically our aim is to answer a) if functional connectivity is altered as a response to rhythmic visual stimuli globally and locally, b) how these connectivity modulations are related to enhanced power at stimulation frequency and harmonics as revealed by SSRs and c) if these effects depend on the stimulation frequency as already shown for the power of the SSRs.

Results

MEG was recorded while participants were exposed to visual rhythmic stimulation (i.e. an ellipsoid Gabor flickering at 4, 6, 8, 10, 13, 15, 18, 22 and 30 Hz). Each trial lasted 3 s and for each stimulation frequency, 80 trials were presented. During the experiment, participants were asked to fixate on the visual stimulus.

In the following paragraphs, first the source localization of SSR is presented as a sanity check, then the SSRs at the stimulation frequencies and their harmonics and finally the graph-theoretical analysis is described. When spatial clusters are shown, a cluster-based permutation test was performed controlling for multiple comparisons.

Sources of evoked responses and SSR

The visual flicker stimulus (averaged across all frequency conditions) evoked an M170, with main sources in the calcarine sulcus (Fig. 1A, maximum at MNI [10 −110 10], Calcarine R, t=12.56, p<0.001). The SSR showed main generators in visual areas (occipital and parietal cortex), and to a lesser extend in the cerebellum (SSR vs. baseline, p<0.01 for all conditions). SSR generators for 8 Hz are shown as an example in Fig. 1B.

Fig. 1

Verification of ERF and SSR on occipital cortex. (A) Transient evoked response (ERF) from those virtual sensors that covered the occipital cortex. When comparing post-stimulus (.160–.180 s) vs. baseline, the difference was localized at calcarine sulcus (p<.001). (B) SSR from virtual sensors that covered the occipital cortex when stimulating at 8 Hz. A contrast of post- (.5–3 s) vs. pre-stimulus activity showed generators in occipital cortex, precuneus and weaker responses in the cerebellum (p<.001).

SSRs at stimulation frequencies and harmonics

The SSR (relative change with respect to the baseline −0.5 until −0.1 s) of the virtual sensors covering the occipital lobe are presented in Fig. 2. A clear SSR pattern is evident in the stimulation frequencies and the second harmonics. For some frequencies (10, 13 and 15 Hz), there are even stronger SSR at harmonics with respect to the stimulation frequency itself. It is also worth noting that in the SSR harmonics beyond the second, i.e. when stimulating at 10 Hz, there are also sustained power increases at 30 and 40 Hz. In the lower panel, bars show the mean power at the stimulation frequencies and at their respective second harmonic. The power at the second harmonics follows a curve peaking at 26 Hz, the second harmonic at 13 Hz. The power at the stimulation frequency though, does not follow a similar pattern. Taking the power across stimulation frequencies and the second harmonics together, it seems that the SSRs that fall in the range between 26 and 30 Hz are particularly strong, while the highest power overall is observed at 30 Hz when stimulating at 30 Hz.

Fig. 2

SSRs and evoked power at different stimulation frequencies. (A) SSR represented in time–frequency space for all stimulation frequencies. (B) Power at the stimulation frequencies (averaged across .5–3 s) was plotted on the left and power at the second harmonics (2f) on the right. Red curves were fitted (stimulation frequencies: delta=.61, df=6, harmonics: delta=.37, df=6) to the mean power values to illustrate the trend along stimulation frequencies.

Global density changes as a response to rhythmic stimuli

Global density is the proportion of the actually existing functional connections of a network divided by the number of all possible connections. It ranges from 0 (no connections at all) to 1 (fully connected graph). Here, the global density of the brain network during visual rhythmic stimulation was calculated in a time–frequency manner, that is one global density value for each time–frequency bin. When global density values were averaged across all stimulation frequencies (Fig. 3A), a decrease (vs. baseline) was observed in the alpha band (8–12 Hz) starting immediately after the stimulation and lasting at least until its end (p<.05). This effect is present across different stimulation frequencies and is thus not frequency-specific. Rhythmic visual stimulation caused loss of functional connections and resulted in a sparser brain network. To exclude a possible confound of power modulations (alpha power decrease) on the global density decrease, the power and the global density were correlated and there was no prominent correlation in alpha band. However, global density is not informative as to which regions lost some of their connections. To localize this effect, the node degree was calculated. The node degree is the actual number of connections passing from each node and, in contrast to global density, a local metric. The node degree was statistically tested post- (.5–3 s) vs. pre- (−.5–0 s) stimulus. A significant cluster showed lower degree at visual cortex and cerebellum (p<.001). But, how is this loss of connections in visual cortex characterized across the brain? To answer to this question, a seed was placed where the node degree effect was maximal (MNI coordinates [25 −80 10], Calcarine R) and the values of connectivity in post- vs. pre-stimulus window were statistically tested. A significant cluster (p<.001) including middle cingulate gyrus and precuneus emerged showing lower connectivity with the visual cortex in the post-stimulus as compared to pre-stimulus period.

Fig. 3

Graph theoretical measures and seeded connectivity effects during SSRs. (A) Non-frequency-specific reduction of global density at alpha band as a response to rhythmic visual stimulation (curve fitting parameters: delta=.086, df=6). The effect was localized in the occipital cortex, which exhibited less node degree during the post-stimulus with respect to the pre-stimulus time-window (p<.001). The connections lost were between occipital cortex and cingulate cortex showing lower connectivity in post-stimulus when compared to pre-stimulus (p<.001). (B) Increase of the global density at the second harmonic (30 Hz) as a response to 15 Hz steady-state stimulation (curve fitting parameters: delta=.02, df=6). The effect was localized in the occipital cortex and cerebellum, exhibiting more connections to the rest of the network during the stimulation with respect to the pre-stimulus time-window (p<.001). Placing a seed in the occipital cortex showed more connections with precuneus and cerebellum during the post-stimulus with respect to the pre-stimulus time-window (p<.01).

When looking at time–frequency resolved density for each stimulation frequency, not all of them exhibit a significant change of global density as a response to the rhythmic stimuli. This points to a frequency-specific phenomenon. The most dominant effect consists of significant differences at 30 Hz when stimulating at 15 Hz (Fig. 3B) and 30 Hz (supplementary figure at the end of the document). In Fig. 3B the baseline-corrected global density when stimulating at 15 Hz is illustrated. A significant cluster (p<.05) at 30 Hz shows a denser network during post-stimulus (.5–3 s) when compared to pre-stimulus (−.5–0 s). To exclude a possible confound of power modulations (strong SSR at 30 Hz) on the global density increase, the power and the global density were correlated and there was no prominent narrow-band correlation. The global density at the second harmonic for all stimulation frequencies is presented in the bar plot. The region with increased connections is the occipital cortex and cerebellum (p<.001). Placing a seed in occipital cortex (MNI coordinates [10 −81 16], Calcarine R, Cuneus R) revealed increased connectivity (p<.001) with the precuneus and cerebellum.

Discussion

In this study, we examined the hypothesis that a change in local cortical power evoked by rhythmic stimulation has a large-scale influence on the brain functional network. For this purpose we used visual steady-state stimulation at 9 frequencies and we investigated brain functional connectivity along with local power effects. Confirming our hypothesis, steady state stimulation evoked long-range interactions in addition to local power effects. Global density was decreased in the alpha band and this effect was independent of the stimulation frequency indicating a modulation of the endogenous alpha activity. A strong local power increase in the ‘preferred’ stimulation frequency was accompanied by increased coupling between the visual cortex and precuneus. We showed for the first time that steady-state responses, which until now has been treated and interpreted as a modulation of cortical power at a local level, significantly influences the brain function at network level.

Visual cortex is decoupled in the alpha band during visual stimulation

The brain functional network showed lower global density in the post-stimulus time window for all stimulation frequencies. It is well known that visual stimulation elicits a decrease in alpha power in the relevant brain regions (Jensen and Mazaheri, 2010, Klimesch, 1999, Pfurtscheller and Lopes, 1999), we report though, for the first time a global functional decoupling in the alpha band as a response to visual rhythmic stimulation. However, global density is a single number that characterizes the whole network while providing any information regarding the locus of the decreased amount of functional connections. The node degree analysis indeed revealed a meaningful region, the occipital cortex. Our findings suggest that as visual stimuli enter the brain, and demand resources in the visual system, the occipital cortex becomes disconnected from the rest of the brain. In particular, it loses its connections to the cingulate gyrus and precuneus, both regions being engaged in the default mode network (Bressler and Menon, 2010, Damoiseaux et al., 2006). The concept of integrating a region “more efficiently” in a distributed network when this region is engaged in stimulus perception has been already proposed (Weisz et al., 2014). Herein, a complementary function is suggested: the disconnection of the relevant region from regions that were connected with it during rest.

Importantly, this decoupling takes place in the alpha band indicating a relation to the endogenous alpha activity and its inhibitory function (Jensen and Mazaheri, 2010). The need to process continuous rhythmic visual stimulation, irrespective of its spectral characteristics, evoked a fast change in the functional architecture of the brain network (reduction in the global density) limited to the alpha band that lasted at least until the end of the stimulation. Going beyond power effects (Zumer et al., 2014), we observed a re-organization of the brain functional network in the alpha band in the presence of visual stimuli. In our view, this finding could be related to the known inhibitory function of alpha oscillations in a meaningful way.

Optimal coupling effects for the visual cortex at 15 and 30 Hz

In addition to the unspecific functional network reorganization in the alpha band, we also discovered changes in the brain functional network that were specific to the stimulation frequencies. In particular, the global density around 30 Hz increased as a response to stimulation at 15 and 30 Hz. This finding confirmed our initial hypothesis that a change in the local cortical power, that is the SSR in occipital cortex, also affects the brain functional network in a global manner. The ‘new’ connections are localized in the occipital lobe and integrate the latter with the cingulate cortex and the cerebellum. This finding shows for the first time that rhythmic stimulation evoked a broad and fast change at network level, being considered until now as a modulation of local cortical excitability (Di Russo et al., 2007, Fawcett et al., 2004, Pastor et al., 2007, Spaak et al., 2014).

This effect seems to be connected with the increase of the evoked power (SSR) in the occipital cortex: although the SSR was evident for all stimulation frequencies, the global density was significantly affected only when a strong SSR were observed, that is at 30 Hz. The fact that the brain shows a ‘preference’ to some frequencies in terms of power is not new and reflects the notion of the so-called natural frequency of a system. The auditory cortex shows strong SSR around 40 Hz (Azzena et al., 1995), the occipital cortex is particularly responsive to alpha band oscillations (Herrmann, 2001), while the frontal cortex is tuned to faster oscillations (21–50 Hz) (Rosanova et al., 2009). However, this is the first study to report a frequency-specific brain response at a network level and it seems to be related to the power effect at a local level. With the simple Gabor patch we used as stimuli, the brain seemed to ‘prefer’ the same specific frequency in both local power and network-level modulations: a pronounced evoked SSR and the strongest evoked increase of density were observed when stimulating at 30 Hz. The replication of the effect at the harmonic frequency when stimulating at 15 Hz, makes the point for a specific tuning frequency even stronger.

Regarding the presence of SSR at the harmonic frequencies, it is known that evoked responses can contain activity not only at the stimulus frequency F but also at its harmonics. This occurs because either the stimulus contains multiple temporal frequencies (as happened here where a square-wave temporal modulation profile is used) or the system is nonlinear, or both. If the visual stimulus is a perfect sine wave, it does not contain higher harmonics; if the visual response is linear, the response to this stimulus will be confined to the frequency bin corresponding to the stimulus frequency. However, even in that case, responses at harmonic frequencies are observed (Giani et al., 2012). In contrast, if the system is nonlinear, this will manifest itself in the presence of higher harmonic responses (for more details on nonlinearity in the SSVEP, see Norcia et al. (2015)).

The nature of the SSRs has been the topic of debates. One popular notion is that rhythmic stimulation entrains intrinsic brain rhythms and builds up the SSR (de Graaf et al., 2013, Mathewson et al., 2012, Spaak et al., 2014). Another concept is that SSRs are a means to “wiretap” cortical activity at any frequency defined by the experimenter and are not connected to spontaneous neuronal oscillations (Capilla et al., 2011, Keitel et al., 2014). Our results in fact point to the second notion: although there is no behavioral evidence, the most significant effects were found when stimulating at 30 Hz and not around alpha. Indeed, the effect on the alpha band on global density is not frequency-specific, a fact that speaks against entrainment of intrinsic brain rhythms, but more in favor of “reinforcing” cortical oscillations towards a narrow band around the stimulation frequency, a phenomenon that also drives network-level changes.

Finally, it is worthy to discuss the locus and the function of the nodes (visual cortex-seed, precuneus and cerebellum) involved in network-level changes evoked by rhythmic visual stimulation. The precuneus is indeed anatomically and, thus also functionally, connected with the visual cortex (Zhang and Li, 2013) and it is involved in visuo-spatial imagery and episodic memory retrieval (Cavanna, 2006). At least to our knowledge, there is no particular involvement of precuneus in SSR. One could speculate that it is the affinity of precuneus with the visual cortex the origin of the modulation of its functional connectivity in our paradigm. The cerebellum, on the other hand, has been reported to strongly respond to rhythmic stimulation both visual (Pastor et al., 2003) and auditory (Pastor and Artieda, 2002). In terms of power of SSRs, also frontal regions have been involved in attention (Ding, 2005) and memory tasks (Silberstein et al., 2001), however, our results do not suggest any modulation of their functional connectivity.

Limitations

One could speculate that the reported decrease in global density at alpha band as well as the increase at 30 Hz could be an epiphenomenon of related power modulations. Alpha power is certainly decreased due to the processing of visual stimuli and the particularly strong SSR at 30 Hz reflects a high signal-to-noise ratio for both 15 Hz and 30 Hz stimulation frequencies. However, the performed seeded connectivity analysis speaks against this confound. If the effect of connectivity was only explained by the power modulations, one would have expected that it would be the region around the seed to show reduced connectivity. Instead, the regions exhibited significant connectivity effects were in a certain distance, a fact that points against an epiphenomenon of signal-to-noise ratio. To the same direction, there was not a prominent increase of correlation between power and global density neither in alpha band, not around 30 Hz. Also, recent literature reported that the relationship between power and connectivity is not straightforward. For example, an increase of power was accompanied by decreases (Popov et al., 2013) and increases of connectivity at the same region (Leske et al., 2015). Although we cannot rule out this concern, our finding clearly suggests a functional decoupling at alpha band on both global and local levels.

The connectivity metric used in this study was the imaginary part of coherency. The advantage of using the imaginary part of coherency to study brain interactions is that, if present, it cannot be generated as an artifact of volume conduction (Nolte et al., 2004). This is because the imaginary part of coherency is only sensitive to coupling between two signals or processes when the latter are time-lagged to each other. This means that in case of very small time-lag between two processes, the imaginary part of coherence will not capture this synchronization which in that case would be reflected in the eliminated real part. Thus, it is likely that this connectivity metric misses parts or even all of the brain interaction, particularly possible for very local effects. Yet, if coupling is observed, it is certainly not an artifact.

Conclusions

To sum up, intrigued by the view of the brain as a dynamically changing functional network, we challenged the widely accepted notion that SSRs are a local phenomenon. Indeed, we discovered large-scale effects both specific and unspecific to the frequency of the rhythmic stimulation. Our findings suggest that SSRs, apart from local modulations of cortical power, also evoke large-scale effects in the brain functional network. This should be taken into consideration not only when attempting to explain the nature of SSRs, but also when using them in experimental designs. Thus, the behavioral effects observed during entrainment could be, at least partially, due to network level changes rather than local excitability modulations.

Experimental procedure

Participants

Twenty-one right-handed participants (11 females; age: M=28.05, SD=3.3 years) with normal or corrected-to-normal vision, no neurological or psychiatric disorders and no family history of photic epilepsy took part in the experiment. The Ethical Committee of the University of Trento approved the experimental protocol and the experiments were undertaken with the understanding and written consent of each participant.

Visual stimuli and procedure

Participants viewed a Gabor ellipsoid (tilted 45°) back-projected on a translucent screen by a Propixx DLP projector (VPixx technologies, Canada) at a refresh rate of 180 frames per second. The stimuli were presented at the center of the screen in a distance of 110 cm from the eyes of the participant. During each trial the Gabor patch flickered for 3 s in one of 9 different frequencies: 4, 6, 8.18, 10, 12.8, 15, 18, 22.5 and 30 Hz translated in number of frames on/off as 22, 15, 11, 9, 7, 6, 5, 4, and 3. For each stimulation frequency, 80 trials were presented. During the experiment, participants were asked to fixate on the visual stimulation while they were listening to music. The same music collection was chosen for all them, but the starting point was randomly chosen.

MEG recordings

MEG was recorded at a sampling rate of 1 kHz using a 306-channel (204 first order planar gradiometers, 102 magnetometers) VectorView MEG system (Elekta-Neuromag Ltd., Helsinki, Finland) in a magnetically shielded room (AK3B, Vakuumschmelze, Hanau, Germany). Before the experiment individual head shapes were acquired for each participant including fiducials (nasion, pre-auricular points) and around 200 digitized points on the scalp with a Polhemus Fastrak digitizer (Polhemus, Vermont, USA). Head positions of the individuals relative to the MEG sensors were continuously controlled within a block using five coils. Head movements did not exceed 1.5 cm within and between blocks.

MEG data processing

Data were analyzed offline using the Fieldtrip toolbox (Oostenveld et al., 2011). First, a high-pass filter at 1 Hz (6th order Butterworth IIR) was applied to continuous data. Then, trials of 1 s pre- and 4 s post-stimulus were extracted and trials containing physiological or acquisition artifacts were rejected. The number of trials was equalized across the 9 conditions for each subject to ensure that our results were not confounded by systematic differences in signal-to-noise ratio. Bad channels were excluded from the whole data set. Sensor space trials were projected into source space using linearly constrained minimum variance beamformer filters (Van Veen et al., 1997) and further analysis was performed on the obtained time-series of each brain voxel. The procedure is described in detail here: www.fieldtriptoolbox.org/tutorial/shared/virtual_sensors. In short, the structural magnetic resonance images were aligned to the MEG space with the information from the head shapes and an equally spaced 1.5 cm grid in Montreal Neurological Institute (MNI) was warped in the individual brain volume. Using a grid (889 voxels) in MNI space allowed us to average and compute statistics since each grid point in the warped grid, despite different space coordinates, belongs to the same brain region across participants. The aligned brain volumes were further used to create single-sphere head models and lead field matrices (Nolte, 2003). The average covariance matrix, the head model and the lead field matrix were used to calculate beamformer filters. The filters were subsequently multiplied with the sensor space trials resulting in source space trials. A Fast Fourier Transform (Hanning tapers; 2–70 Hz in 1 Hz steps; time windows of 5 cycles per frequency; −1 to 4s sliding in 50 ms steps) was applied on the virtual sensors. To estimate power values at the beginning and at the end of each trial data were zero-padded from −1.5 to −0.5 s and from 4 to 4.5 s.

Graph theoretical analysis

A Fast Fourier Transform (Hanning tapers; 2–70 Hz in 2 Hz steps; time windows of 5 cycles per frequency; −1 to 4 s sliding in 50 ms steps) was applied to the virtual sensors as described above. An imaginary part of coherency (Nolte et al., 2004) was calculated for all possible pairs of voxels resulting in time–frequency resolved (−1 to 4 s, 2–70 Hz) all-to-all connectivity values. To obtain a binary adjacency matrix (zeros indicating absence, ones indicating presence of a functional connection) for graph theoretical analysis, the all-to-all connectivity matrix needs to be thresholded. There is no objective way to decide the threshold value in graph theoretical approaches (van Wijk et al., 2010). A range of reasonable thresholds (.04,.05,.06,.07) was applied to coherence values to transform weighted to binary graphs. Thresholding yielded an adjacency matrix (889×889) for each point in time–frequency space. Global and local graph theoretical measures were calculated on the adjacency matrices. We obtained global density for each time–frequency bin and node degrees for each voxel and for each time–frequency bin.

Node degree was used to localize global density changes. The degree of a node is the number of edges connected to the node assessing the importance of nodes within a network, possibly identifying hubs, that is, brain regions that facilitate functional integration and interact with many other regions (Rubinov and Sporns, 2010). As a last step, we studied seeded connectivity, using as a seed region the voxel in the occipital lobe where the node degree effect was maximal. We compared pre- (−.8 to .1 s) vs. post- (.5–3 s) stimulus connectivity of the seed to the whole network averaging over time windows.

Statistical analysis

A dependent samples t-test was carried out on time–frequency represented values (power or global density) to test for differences between the pre- and the post-stimulus time-windows. To control for multiple comparisons, a non-parametric Monte-Carlo randomization test was undertaken (Maris and Oostenveld, 2007). The t-test was repeated 1000 times on data shuffled across conditions and the largest t-value of a cluster coherent in time and frequency was kept in memory. The observed clusters were compared against the distribution obtained from the randomization procedure and were considered significant when their probability was below 5%.

At a source level, effects on evoked responses, power, node degree and connectivity were tested with a dependent samples t-test (Monte-Carlo correction) comparing the pre-stimulus with the post-stimulus periods. For the node degree and the seeded connectivity, this comparison was performed in the time–frequency windows derived from the effects on the global density. Significant clusters were identified in space.

Regarding the graph theoretical measures (global density and node degree), statistics were performed for the whole range of thresholds and only effects that survived across all thresholds are presented in the paper. For illustration we used a threshold of.04.

The curves fitted on the barplots are produced with the matlab functions polyfit and polyval. A 2nd degree polynomial was fitted; we reported the degrees of freedom and the estimate of the standard deviation of the error when predicting any future observation (delta).