On the existence of synchrostates in multichannel EEG signals during face-perception tasks

Typical synchronisation can be studied from EEG signals in two domains, i.e. time and frequency. The work reported in (Lehmann et al 1987, Koenig et al 2014) considered brain electric states with consistent scalp electric field topography, and their sequence which led to what is commonly known as EEG microstates. Its most important characteristic is that the topography does not change randomly or continuously over time, but exhibits quasi-stable behaviour in the order of 80–120 ms; and abruptly switches from one topography to another—the number of unique topographies being small (typically 3–10) (Koenig et al 2002). Another way to study the synchronisation phenomenon is in the frequency domain. This is led by the assumption that if two points (i.e. two EEG electrode sites) are in coherence (i.e. maintaining constant phase relationship over time), they can be considered as functionally synchronised or connected (Fries et al 2001). Phase coupling has been studied in patients with mental disorders (Mulert et al 2011, Razavi et al 2013) and the merits of synchrony analysis have been found in the understanding of neurodevelopmental disorders (Uhlhaas et al 2008). Since the method for coherence analysis, like global field synchronisation (Kottlow et al 2012), uses Fourier transform, inherently it does not preserve the temporal information of synchronisation. This methodology was later modified by several researchers by using continuous wavelet transform (CWT) and Hilbert transform (HT) to compute the phase in transformed domains and for deriving the associated synchronisation indices from the coherence values thus obtained. The mean phase coherence measure (Mormann et al 2000) computes the synchronisation over the whole time series and therefore gives an average measure of synchronisation for the whole signal span. The phase locking value, although it varies with time, measures the inter-trial variability of phase difference (Rodriguez et al 1999) rather than temporal variability. Additionally, various other measures of phase synchronisation have been reported in (Quiroga et al 2002). Although useful, such approaches only give an insight into the phase synchronisation in a time-averaged way over all the frequency bands, rather than capturing the true picture of the temporal or transient evolution of phase synchrony in a band-specific way. On the other hand, in principle, CWT and HT both being time–frequency transform methods, have the potential to describe the temporal evolution of phase synchronisation at a sub-second resolution level, which could be more informative to understand the dynamics of the synchronisation phenomena from the onset of a given stimulus until the end of the corresponding cognitive action.

As evident from the foregoing discussion, the existing frequency domain methods compute the phase synchronisation over the entire post stimulus segment of the signal and therefore are unable to retain the transient information at finer temporal granularity, whereas the microstate method finds the unique electric potential patterns and their transients during the execution period of the task (Gianotti et al 2008). Ito et al studied the dynamics of spontaneous transitions between globally phase-synchronised states in the alpha band EEG activity (Ito et al 2007). Their method was applied to explore the phase dynamics of individuals with cerebral palsy (Daly et al 2014). The technique proposed in these articles investigates phase dynamics by segmenting the relative phase patterns into global phase pattern states by thresholding and using a criterion called the instantaneous instability index (III). The GPS pattern vectors are then clustered into six centroids. Here we propose a slightly different approach for studying the dynamical evolution of phase patterns by using intrinsic optimization criterion in the k-means clustering for segmentation of the images to form compact clusters or states without any prior thresholds. In this paper we merge two concepts, i.e. the concept of temporal switching (transient behaviour) of stable states along with the band specific phase locking by considering a joint time–frequency representation of the EEG signal.

The data analysis was conducted with four distinct samples of children: (1) with typical development, (2) diagnosed with ASD, (3) diagnosed with high-anxiety and (4) with low-anxiety. More specifically, we have used the data acquired during the experiments described in (Apicella et al 2013) and (Chronaki 2011). For more information regarding the data used in this study please refer to the supplementary material, available online. The main characteristics of these four populations are summarized in table 1.

For groups I and II the data was acquired using a 128 channel EEG system and was segmented into a 1000 ms epoch with 150 ms baseline and 850 ms post-stimulus response. Epochs over a threshold of 200 μV were rejected as artefacts. Data was baseline corrected and band-pass filtered from 0.5 to 50 Hz for removing low-frequency drifts and high-frequency measurement noise using a 5th order Butterworth filter. On the other hand, for groups III and IV a 30 channel EEG system was used for data acquisition and data was epoched at 100 ms pre-stimulus to 1000 ms post-stimulus. Collected data was band-pass filtered in the range 0.1–70 Hz to eliminate the drift and noise as done in the former case. These pre-processed EEG signals were then transformed in the time–frequency domain using CWT, with particular focus on the two bands of interest viz. β (13–30 Hz) and γ (30–50 Hz). Only the response of the frequencies in these two bands of interest is then used for further processing. Being band-specific, this processing step allows us to compare the response of the signals across all the groups on a uniform platform, although they were acquired with different instruments. The studies in (Nunez et al 1997, Schiff 2005) point out that the use of average reference for calculating coherency is a good compromise against the effects and noise introduced by the reference electrode. In our study, all the signals were re-referenced to average reference data (average across all channels) and then were used for our calculation. The different data collection protocols adopted for groups I–II; and III–IV allows us to explore the effect of variability in the number of EEG electrodes.

It has been observed by researchers that the spectral power of different EEG bands significantly changes depending upon the stimulus given (Boiten et al 1992). As a consequence it may be assumed that the temporal stability of instantaneous phase difference topographies and hence the overall synchronisation pattern may manifest differently in different EEG bands. Therefore it appears to be more logical to study the synchronisation phenomenon in a band-specific way. Since CWT decomposes a signal to different scales (equivalent frequencies) at each time instant, it is possible to study the temporal evolution pattern of phase difference topographies for an isolated frequency band of interest. Therefore in our analysis we used CWT as the main analysis tool, more precisely, we have used a complex Morlet basis function as shown in (1) for computing the CWT of the EEG data

$$\begin{eqnarray}&&{\Psi }_{M}\left(t\right)=\displaystyle \frac{1}{\sqrt{\pi {F}_{b}}}{{\rm{e}}}^{2j\pi {F}_{{c}^{t}}}{{\rm{e}}}^{-\left({t}^{2}/{F}_{b}\right)},\end{eqnarray} \tag{ 1 }$$

where, $\left\{{F}_{b},{F}_{c}\right\}$ denote the bandwidth parameter and the centre frequency respectively. For our purpose we considered ${F}_{b}=1$ and ${F}_{c}=1.5$.

Considering N number of EEG channels placed over the scalp and ${x}_{1}\left(t\right),{x}_{2}\left(t\right),\cdots ,{x}_{N}\left(t\right)$ be the EEG signals acquired at the respective channels, application of complex Morlet CWT on ${x}_{i}\left(t\right),i\in \left\{1,2,\ldots ,N\right\}$ results in a complex time series ${W}_{i}\left(a,t\right)$ at the wavelet scale a at time t. ${W}_{i}\left(a,t\right)$ can be converted to a function of frequency and time ${W}_{i}\left(f,t\right)$ using the following relation (Addison 2010) in (2)

$$\begin{eqnarray}&&f={F}_{c}/(a\cdot \delta ),\end{eqnarray} \tag{ 2 }$$

where δ and f are the sampling period and the approximate pseudo-frequency, i.e. the frequencies corresponding to the scales, respectively. Subsequently, the instantaneous phase φ_i(f, t) of W_i(f, t) can be computed as (3)

$$\begin{eqnarray}&&{\varphi }_{i}\left(f,t\right)={\rm tan}^{-1}\left(\displaystyle \frac{{\rm Im}\left[{W}_{i}\left(f,\;\;t\right)\right]}{{\rm Re}\left[{W}_{i}\left(f,\;\;t\right)\right]}\right).\end{eqnarray} \tag{ 3 }$$

Im[W_i(f, t)] and Re[W_i(f, t)] are the imaginary and the real part of W_i(f, t) respectively. Consequently, the instantaneous phase difference $\Delta {\varphi }_{i,j}(f,\;t)$ between the channels i and j can be given by (4)

$$\begin{eqnarray}&&\Delta {\varphi }_{i,\;j}\left(f,\;t\right)=\;\left|{\varphi }_{i}\left(f,\;t\right)-{\varphi }_{j}\left(f,\;t\right)\right|.\end{eqnarray} \tag{ 4 }$$

Computation of $\Delta {\varphi }_{i,j}(f,\;t)$ at a time instant t₁ and frequency f₁ for $i,j\in \;\left\{1,2,\ldots ,N\right\}$ yields a symmetric square matrix $\left[\Delta \varphi ({f}_{1},\;{t}_{1})\right]$ that describes the pairwise relationship of phase difference at the frequency f₁ for all the EEG channels at t₁ time instant as shown in figure 1. For computing the average response within a subject group the individual $\Delta {\varphi }_{i,j}(f,\;t)$ were averaged over all the subjects to get the average wavelet response for the group under consideration. Therefore, if the frequency band of interest $B\in \left\{\beta ,\gamma \right\}$ is spanned over the frequencies $\left\{{f}_{1},{f}_{2},\cdots ,{f}_{M}\right\}$ then the instantaneous phase difference matrix for B at time t as shown in figure 2 can be formulated as (5)–(6)

$$\begin{eqnarray}&&\left[\Delta {\varphi }_{B}(t)\right]=\displaystyle \frac{1}{M}\displaystyle \sum _{i=1}^{M}\Delta \varphi \left({f}_{i},t\right),\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}&&{({b}_{i,j})}_{\Delta {\varphi }_{B}}\left(t\right)=\;\displaystyle \frac{1}{M}\displaystyle \sum _{k=1}^{M}{({a}_{i,j})}_{\Delta {\varphi }_{{f}_{k}}}(t),\end{eqnarray} \tag{ 6 }$$

where ${({b}_{i,j})}_{\Delta {\varphi }_{B}}\left(t\right)$ is the (i, j)th element of the matrix $\left[\Delta {\varphi }_{B}(t)\right]$ and ${({a}_{i,j})}_{\Delta {\varphi }_{{f}_{k}}}(t)$ is the (i, j)th element of $\left[\Delta {\varphi }_{{f}_{k}}(t)\right].$ Subsequently, $\left[\Delta {\varphi }_{B}(t)\right]$ can be computed at different time instants $\left\{{t}_{1},{t}_{2},\cdots ,{t}_{n}\right\}$ resulting in a set of such matrices $\left[\Delta {\varphi }_{B}\left({t}_{1}\right)\right],\;\left[\Delta {\varphi }_{B}\left({t}_{2}\right)\right],\cdots ,\;\left[\Delta {\varphi }_{B}\left({t}_{n}\right)\right]$ like that shown in figure 3, which describes the complete picture of temporal evolution of the phase difference from the onset of a stimulus until the end of the corresponding action in the particular frequency band B over all the EEG channels on the scalp. The whole process is pictorially depicted in figures 1–3. As evident, due the high dimensionality of the clustering problem, a simple cluster discrimination through a scatter plot is not possible in the present study. In our clustering framework, at each time instant the dimension of the feature space, denoting all possible cross-electrode phase information, becomes N² and the clustering algorithm considers the evolution of each element ${b}_{i,j}\left(t\right)$ along time.

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Once all the cross-electrode phase difference matrices for a particular band are formulated over the entire duration of a specified time interval—in our case, we are interested to see the temporal evolution of these topographies at subsecond order time interval—the next pertinent question is whether there exists any unique 'spatio-temporal patterns' of phase difference topographies during the execution of the cognitive task. The first step for that is to identify all 'possibly unique' topographies over the entire time duration of interest. A certain class of pattern recognition techniques could be employed for this purpose. The k-means clustering is one such unsupervised pattern recognition technique. For a given dataset X, $X=\left\{{x}_{p}\right\},p\in \left[1,\cdots ,P\right],$ assuming the number of underlying clusters is known, the k-means algorithm iteratively minimizes a cost function given below (7)

$$\begin{eqnarray}&&J\left(\theta ,U\right)=\displaystyle \sum _{p=1}^{P}\displaystyle \sum _{q=1}^{m}{u}_{pq}{\| {x}_{p}-{\theta }_{p}\| }^{2},\end{eqnarray} \tag{ 7 }$$

where $\theta ={\left[{\theta }_{T1}\ldots \;{\theta }_{Tm}\right]}^{T},$ $\| \cdot \|$ is the Euclidean distance, ${\theta }_{q}$ is the centre of a cluster and ${u}_{pq}=1$ if x_p lies closest to θ_q; 0 otherwise. Initially k centroids are defined and depending on how near the data vector is to the centroids, it is assigned to a class. The k centroids are iteratively recalculated and the data is reassigned to these new centroids until the data vectors from X form compact clusters and the cost function J is minimized. Initially a range [m_min, m_max] is defined for possible clusters m for the dataset X. The k-means clustering runs n (n random initializations) times for each m within that range and for every n runs the minimum value of the cost function J_m (as shown in (7)) is calculated and stored. The cost function J_m essentially indicates the sum of distances of the data-points from the nearest cluster mean when m clusters are considered. The value of J_m is dependent on the number of clusters and also the dataset under consideration, whereas a high value of J_m represents a less compact cluster. Thus we search for a 'knee' in the plot of J_m against m as an indication of the number of optimal clusters underlying the data. If the plot of J_m against m shows a significant 'knee' at m = m₁ (say) then it signifies that the number of optimum clusters underlying the dataset X is likely to be m₁. To be noted that in the plot of J_m versus m it is typical to have multiple such knees as m varies within its selected range. In cases, where there is an increase in the J_m value, it indicates that the distance between all the data points with respect to the nearest mean of clusters has increased. This increase could be due to the splitting of large compact clusters into several smaller ones, caused by increasing the value of m. In such a case, one needs to consider the earliest and the most prominent knee as the characteristic knee and the corresponding m as the underlying number of clusters as it explains the dataset with minimum complexity. Another important point to note that the absolute value of J_m in the plot of J_m against m is not important but the value of m at which J_m attains minimum value (the significant knee) is the important parameter indicating the number of underlying clusters. This method is also known as the incremental k-means or elbow method and is widely used to find the optimum number of clusters in a given data-set.

In a higher dimensional feature space, the landscape of the cost function J(θ) may have multiple local minima and there is small probability of finding a higher value of the cost function if a local minima has been found by the optimization process. Since the k-means clustering has the problem of getting trapped to local minima, it should be run multiple times with different initialization of the cluster means and the best result with the minimum value of the cost function should be considered. Therefore in our method, the best-results of the k-means algorithm for each choice of k is considered out of n = 10 different random initializations of the cluster means. This way the incremental k-means plots the best cost function to obtain the J_m as also suggested in (Theodoridis et al 2010).

The unsupervised learning technique adopted here is based on the concept of hard clustering, i.e. a single data-point corresponding to each time instant should belong to one of the clusters, because in a temporal resolution of a millisecond, we assume that the brain stays only in one state. Other paradigms of soft clustering like fuzzy c-means or similar methods (Dimitriadis et al 2013) where a single data-point can be associated with more than one cluster according to its degree of associativity with different classes, could also be applied to the present problem.

In our case, X is the dataset of all pairwise EEG instantaneous phase differences $\left[\Delta {\varphi }_{B}\left({t}_{1}\right)\right],\;\left[\Delta {\varphi }_{B}\left({t}_{2}\right)\right],\;\mathrm{..}.,\;\left[\Delta {\varphi }_{B}\left({t}_{n}\right)\right],$ as a function of time. We clustered the dataset X along time t, for a chosen frequency band B, to find out unique phase difference patterns. The algorithm yields k centroids, ${\theta }_{j}$ for each cluster or state and a vector of length n with the corresponding state or cluster labels for each $\left[\Delta {\varphi }_{B}(t)\right]$ for every time instance over which we clustered. The centroids hold average information for each of the clustered states whereas the cluster labels signify when in time each state has occurred. Once the phase-difference matrices are uniquely clustered over different time instances, the centroids are translated into corresponding colour-coded head-map topographies following arbitrary colour coding convention. This is done by first calculating the average phase difference seen at a particular electrode with respect to the rest of the electrodes i.e. taking the row-wise average of $[\Delta {\varphi }_{B}\left(t\right)]$ and considering it as the average phase difference at that electrode index corresponding to the considered row and assigning a particular colour corresponding to the numerical value of that phase difference and finally transforming it to a contour plot. Such head-map topographies give a visual representation of the distribution of average phase differences between different regions of the brain over the scalp. Note that these plots should not be viewed or compared to the typical EEG potential plots or the power spectrum plot typically generated in quantitative EEG (qEEG) analysis. Here the plots show the gross phase difference between different electrodes over the scalp over a particular time window. Higher numerical values represent a greater gross phase difference of the electrode with all the other electrodes and low values indicate that the electrode has a relatively lower phase difference than all the other electrodes in that configuration. We term the set of topography clusters identified using k-means algorithm as synchrostates. The state labels are used to construct a transition plot to illustrate the switching sequence of the synchrostates over the time of the EEG recording. This is simply done by plotting the time labels yielded by the clustering algorithm.

Figure 4 shows the results of the k-means clustering algorithm in both bands for all the given stimuli from the population average of 12 children with typical development (group I). It is clear that the dominant knee of cost function for all three stimuli appears at k = 3, although in some cases after the knee the cost function increases and then again decreases. These are the typical situations already discussed in section 2.4 and, accordingly, where the earliest knee appeared needs to be considered only. This means that in the dataset considered, there exist three unique phase difference matrix configurations—synchrostates—from the onset of stimulus until the end of an action.

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In figure 5, from the corresponding head-plots it is evident that the topographies of all three synchrostates are very similar for all the different stimuli in the β band. A similar result is observed for the γ band in figure 6 where the synchrostate topographic plots are similar and more importantly closely resemble those obtained in the β band, although differing slightly in the numerical values, in particular in the reddish hue regions. Here, each of the colours in the head topographies signify a particular range of phase differences as shown in the legend (in a normalized scale with respect to the maximum and minimum phase difference amongst all the states). However, an interesting difference is observed in the state transition plots shown in figure 7. Although in both bands the transitions start from state 2, the overall transition patterns are markedly different not only between the β and γ band but also between different stimuli within a band. This demonstrates the stimulus specific nature of the synchrostates.

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The k-means clustering results for the ASD population (group II in table 1) is shown in figure 8 for the β and γ bands for all three applied stimuli, i.e. fearful, happy and neutral faces. Once again the significant knee appears at k = 3 implying the existence of three synchrostates similar to the typical case. The corresponding phase difference topographies over the scalp are shown in figures 9–10 as head plots. It appears that although the stimuli are different, the topographies are nearly similar in the β bands (in figure 9) in particular for state 1 and state 3. However, topographies corresponding to state 2 are markedly different. On the other hand, in the γ band the state 1 for happy and neutral stimuli are similar, while it differs significantly for fear stimulus (figure 10). State 3 shows close similarity under all three stimuli. The time-course plots of the synchrostate transition are shown in figure 11. In both bands the time course plots are markedly different depending upon the stimulus and thereby indicating a different temporal stability period of the synchrostates at different points in time.

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The k-means clustering when run on the population average of the children with low anxiety for the β band resulted in four states for all three stimuli, i.e. angry, happy and neutral face. This is shown in figure 12 as all three plots have the earliest significant 'knee' in the cost function plot at k = 4. However, in the γ band the number of states is different for the neutral face perception case. The number of states in the γ band for the angry and happy face remain unchanged at k = 4 whereas for the neutral face it is 6. In the head topographies for the β band, (figure 13) although the number of synchrostates is consistently four, their characteristics for each different task are quite different. From the γ band head plots in figure 14 it can be seen that states 1, 4, 5 and 6 head plots are almost similar and common for all three stimuli. However the neutral stimulus has two extra states which do not exist in the other two stimuli of angry and happy, as can be seen from figure 14. The transition of the states in the β band is shown for each specific stimulus in figure 15. It can be observed that during the execution of the angry face stimulus the inter-state transition is not as frequent as compared to the other two stimuli viz. happy and neutral. The β band state transition shows that except for the angry stimulus for both the other stimuli the sequence starts with state 4, whereas for the angry visual stimulus it starts from state 2. In the γ band, the state transitions are more frequent in the neutral face perception compared to the other two stimuli, as shown in figure 15.

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For the group of high anxiety subjects, as shown in figure 16, for both bands the number of synchrostates is consistently four for different stimuli. The head plots for the average β responses of the children as can be seen from figure 17 are to some extent similar across all the stimuli. This close similarity is even more prominent in the γ band head plots depicted in figure 18. Looking at the transitions of the states in β, shown in figure 19, we see that they end in state 1 for all three stimuli. Also state 3 is the most occurring state over the duration shown for the happy and neutral face. This is also the case for γ band state transitions for all stimuli, as shown in the figure 19.

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So far the reported figures for the group-wise analysis highlight subtle changes in the average phase difference topographies over the scalp and state transition plots for different stimuli. Now the statistical measures like the median, inter-quartile ranges of the inter-person variability for the optimal number of synchrostates in both β and γ band are shown in the box-plots given in figure 20. The red line in the plot indicates the median and the crosses show the outliers. The blue boxes denote the inter quartile range for the data. This is obtained by applying k-means clustering on the phase-difference matrices obtained from individual subjects at different time instants under different stimuli. The variability in the number of synchrostates observed when results from the individual subjects are compared to the respective population average is not significant. For the pool of typical children we consistently got three states for every child in the γ band but in the β band the number of states for the children varies from 3 to 7. This observation leads us to believe that the number of synchrostates is person-specific, although this number is bounded within a small range only. Also in figure 20, for the ASD group in the β and γ band, only a few subjects show 5 synchrostates whereas the population average result as well as for the other subjects, the number of synchrostates is consistently 3. For the low anxiety and high anxiety groups (low-density EEG) it is interesting to note that the median of the number of synchrostates varies between 5 and 6 whereas the median is consistently 3 for the ASD and typical children (high-density EEG). The important factor to note here is that only 30 electrodes were used for EEG acquisition for the anxiety groups (III and IV). This reduced number of electrodes inherently introduced less resolution in computing the phase difference matrix and as a consequence may introduce a larger variability in the synchrostate formulation. Therefore it is evident that the optimal number of synchrostates largely depends on the number of electrodes and high-density EEGs (as in the first two groups, typical and ASD) are more likely to give a consistent result. Apart from that, the small variability observed in all four cases is also expected because of inter-person and inter-trial variability, and the possible existence of parallel background processes not related to the cognitive task given.

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We now model the temporal switching sequence of the synchrostates in a probabilistic framework for a representative case of the typical and ASD group. This is chosen due to the fact that the high-density EEG system used in data acquisition for these two groups resulted in consistent results in synchrostates as mentioned earlier. However without loss of generality the same method could be applied for analysing the anxiety groups as well. We construct the transition probability (${P}_{ij}={n}_{ij}/\sum _{j}{n}_{ij})$ of the synchrostate sequence which show the probabilistic nature of each of the state transitions. Here, n_ij is the number of transitions from state i to j. The three probability values—P₁₁, P₂₂, and P₃₃—show how long each state remain stable, i.e. how stable each of the states (${S}_{1},{S}_{2},{S}_{3})$ are in terms of the probability of staying in the same state, for different population groups, as shown in figure 21. The elements of the state transition matrix (${P}_{ij},\left\{i,j\right\}\in \left[1,\;2,\;3\right])$ for different population are more informative, although the phase difference topographies for two different populations could be similar. Therefore, the average value of the self-transitions ($\left(1/N\right)\sum _{i=1}^{N}{P}_{ii},$ N being the optimal number of synchrostates) for a particular band, can be considered as one of the discriminating measures between two groups as shown in table 2. It is evident from table 2 that in the β band with fear and happy stimuli the ASD group has got a higher probability of self-transition than the typical case. On the contrary the γ band shows an increase in self-transition for fear and neutral stimuli.

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Before continuing discussion about the implications of this result one needs to eliminate possible artefact effects that may bias the observation. Once again we need to emphasize that the head plots shown here are fundamentally different from those obtained from qEEG analysis where the average power spectrum is plotted over the scalp. Any possible artefact in such cases is manifested as a strong correlation at the scalp edges. On the contrary, the head plots shown here are more like the visualization of the phase difference patterns distributed over the scalp. The bluish hues imply nearly zero phase difference whereas the reddish hue implies large phase difference.

Here, each of the head plots show phase difference topographies existing of the order of ms. While processing the data, as mentioned in section 2, we eliminated the epochs above 200 μV as possible artefacts. Therefore the data used in our analysis is likely to be artefact free in the first place. Secondly, since the synchrostate topographies are constructed in the ms order and as the transition diagrams show that the topographies switch from one configuration to another and back, in the ms order time interval, in the presence of possible artefacts, all of the states should exhibit a similar phase relation at the scalp edge for all the states, which is not the case. Therefore, while interpreting the results one may eliminate the effect of possible artefacts. This argument is also valid for eliminating the effect of volume conduction, which one may also view as possible artefacts. The synchrostate phenomenon we report here cannot be explained by volume conduction since electrical impulses within the human brain spread almost instantaneously through any volume. Hence, zero phase lag is a characteristic of volume conduction (Thatcher et al 2008) and phase delays are attributes of network formation. Synchrostates do not report zero phase delays and thus this suggests that the synchronies are not artefactual. In addition, the spurious synchronisation phenomena typically observed due to the presence of volume conduction does not account for the different synchronisation and desynchronisation patterns in the ms order in the switching characteristics of the synchrostates, as such an effect is expected to be present for all the synchrostate topographies in that case, while in reality the synchrostate topographies for a stimulus are different from each other. Synchrony caused due to volume conduction would render a constant synchronisation pattern (phase difference) throughout the scalp over the observed time-course of the signal. This is not the case in synchrostates as the phase patterns change suddenly both in strength and between electrodes over time and again remains stable for a finite duration. From these points one may conclude that the results shown in this work are not due to possible artefacts but manifestation of the phenomena of transient phase difference dynamics triggered by different face perception stimuli.

The most important finding of this study is that over the four different subject groups and a total of 44 subjects a small set of unique phase difference patterns—synchrostates—each being stable of the order of ms, have been found to exist in the β and γ band. These synchrostates switch from one to another abruptly, thereby constructing a characteristic time-course to the applied stimulus. This is qualitatively similar to the results obtained with microstates (Koenig et al 2005), albeit the microstate topographies are constructed in the EEG amplitude domain where the number of states is up to 10. From our experiments, we observe that the number of synchrostates is bounded between 3 and 7 depending on individual subjects, stimuli and also the number of EEG electrodes for recording. From the time-course plots it is evident that different synchrostates show a different duration of stability at different time points depending on the applied stimulus and thereby possibly capturing the dynamics of phase synchronisation at a finer temporal granularity level.

An interesting observation for the case of typical development population is that the topographies of population average synchrostates are almost similar for all the applied stimuli in both bands. This is similar to our earlier observation (Jamal et al 2013a, 2013b) where initial exploration was carried out with a single normal adult subject. Intuitively this implies that although different stimuli have been applied, since all of them belong to the general class of face perception task, the fundamental phase relationship over the scalp remains nearly the same, indicating a specific type of information integration phenomenon pertaining to the general face perception scenario. However the effect of different stimuli within the general class of face perception is reflected in the respective time-course plot which showed a marked difference as the characteristic of the applied stimulus. On the other hand, although the topographies in the case of ASD population showed certain similarities, they are more variable compared to the typical case along with their time-course. This may be due to the difference in information processing in the brain between the two subject groups. In addition, it is apparent that generally for the ASD group the gross phase difference of each electrode across the scalp is higher than that compared to the typical group as there are more red and yellow hues in the ASD states in the γ band (figure 10) compared to more blue hues in the states for the typical (figure 6) group. This implies predominantly loose synchronisation in the former case, which also falls in the line of already established theory that ASD brains show less synchronisation in information processing compared to typically growing children. Individuals with autism present atypical neural activity in face processing and eye gaze tasks, and this has been associated with later diagnosed autism (Elsabbagh et al 2012). Similar considerations apply to the children with anxiety. However, as discussed in section 3.5 it seems that determination of the optimal number of synchrostates depends on the electrode systems used for EEG recording and more consistent results could be obtained using a high-density system. Given this fact a direct comparison between groups I–II and III–IV could be misleading as they do not share the same number of electrode configurations. But despite this fact it is evident that the number of synchrostates in all four cases does not vary widely and is bounded within a small number of 3–7 depending on the pathophysiological conditions of the subject.

Synchrostates are the states within which the inter-electrode relative phase difference varies little over time, and the corresponding transition plot indicates how long each of these phase-difference topographies remain stable. Hence the interpretation of these states cannot be done in an isolated way from its transition plots. Interpretation of the synchrostate topographies and the state transitions should be done together, combining the stability duration and their respective numerical values of phase difference. When considered together one can formulate a synchronisation index corresponding to each of the synchrostates from which a scalp-level functional connectivity network could be derived. These dynamic networks are governed by the nature of switching patterns of the synchrostates and therefore in essence capture the temporal evolution of functional connectivity in a stimulus-specific way at fine temporal granularity level. Fundamental graph-theoretic measures could be used for characterizing such networks for gaining quantitatively deeper insight into the temporal dynamics of the connectivity pattern prevailing after the onset of stimuli, and therefore may provide a quantitative means for assessing cognitive functionalities. This approach has been adopted in (Jamal et al 2014) to classify a population of typical and ASD children. Therefore, synchrostates and their associated temporal switching sequences may be considered as a new tool for analysing the scalp-level functional connectivity dynamics at a fine temporal scale, given a type of stimulus indicating towards the dynamics of information exchange in a person-centric, and frequency band-specific manner. A major implication is that comparing the graph-theoretic measures, extracted from the functional connectivity networks formulated through synchrostates, may provide a new way of classifying different neurodevelopment disorders.

Why such synchrostates exist and, given the fact that EEG has poor spatial resolution, how the phase difference configurations described by the synchrostates corroborate with the actual anatomical level (or source level) connectivity and information exchange, is still an open question and requires further experiments and modelling activities. Thus the neurological perspective of synchrostate topographies, their numbers and transitions needs to be explored in future research. Another important fact is that the results reported here are only for face perception tasks. Whether the same phenomenon exists with other types of stimuli, e.g. auditory stimuli or different real-life cognitive activities is still a question to answer. Also whether the existence of synchrostates is associated only with the active cognitive states or not, is an area to explore.