EEG microstates as a continuous phenomenon

Journal Pre-proof EEG microstates as a continuous phenomenon Ashutosh Mishra, Bernhard Englitz, Michael X. Cohen PII:

S1053-8119(19)31045-6

DOI:

https://doi.org/10.1016/j.neuroimage.2019.116454

Reference:

YNIMG 116454

To appear in:

NeuroImage

Received Date: 3 June 2019 Revised Date:

5 October 2019

Accepted Date: 6 December 2019

Please cite this article as: Mishra, A., Englitz, B., Cohen, M.X., EEG microstates as a continuous phenomenon, NeuroImage (2020), doi: https://doi.org/10.1016/j.neuroimage.2019.116454. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Inc.

Title: EEG Microstates as a Continuous Phenomenon Authors: Ashutosh Mishra1,2, Bernhard Englitz*2, Michael X Cohen*1,3 1

SINS Lab, Department of Neuroinformatics, Donders Institute for Brain, Cognition and Behavior, Radboud

University Nijmegen, The Netherlands 2

Computational Neuroscience Lab, Department of Neurophysiology, Donders Institute for Brain, Cognition and

Behavior, Radboud University Nijmegen, The Netherlands 3

SINS Lab, Donders Institute for Brain, Cognition and Behavior, RadboudUMC, The Netherlands

* indicates equal contribution

Contact: {a.mishra,m.cohen,b.englitz}@donders.ru.nl

1

Abstract: In recent years, EEG microstate analysis has gained popularity as a tool to characterize spatio-temporal dynamics of large-scale electrophysiology data. It has been used in a wide range of EEG studies and the discovered microstates have been linked to cognitive function and brain diseases. EEG microstates are assumed to (1) be winner-take-all, meaning that the topography at any given time point is in one state; and (2) discretely transition from one state into another. In this study we investigated these assumptions by taking a geometric perspective of EEG data, treating microstate topographies as basis vectors for a subspace of the original channel space. We found that within- and across-microstate distance distributions were largely overlapping: for the low GFP (Global Field Power) range (lower 15%), individual time points labeled as one microstate are often equidistant to multiple microstate vectors, challenging the winner-take-all assumption. At high global field power, separability of microstates improved, but remained rather weak. Although many GFP peaks (which are the time points used for defining microstates) occur during high GFP ranges, low GFP ranges associated with poor separability also contain GFP peaks. Furthermore, the geometric analysis suggested that microstates and their transitions appear to be more continuous than discrete. The Analysis of rate of change of trajectory in sensor space suggests gradual microstate transitions as opposed to the classical binary view of EEG microstates. Taken together, our findings suggest that EEG microstates are better conceptualized as spatially and temporally continuous, rather than discrete activations or neural populations.

Keywords: Cortical dynamics, electroencephalography, EEG Microstates, k-means

2

Introduction EEG microstates Based on the observation that EEG map topographies have quasi-stable patterns, researchers in the early 1990’s began characterizing these stable topographical maps — “EEG microstates” (Lehmann et al. 1987a; Michel and Koenig 2018; Lehmann and Skrandies 1980; Michel et al. 1999), which were proposed to be “atoms of thought” (Lehmann 1990). EEG microstate analysis is considered a useful approach to study neural signatures of many cognitive processes, and is an insightful method for investigating EEG dynamics and linking those dynamics to cognition and disease. For example, microstate dynamics have been linked to perceptual awareness (Britz et al. 2014), visual processing (Britz and Michel 2011), neuropsychiatric disorders including schizophrenia (Lehmann et al. 2005; Kindler et al. 2011; Dierks et al. 1997), restingstate networks (Musso et al. 2010; Yuan et al. 2012; Khanna et al. 2015), and so on.

Winner-take-all assumption of microstate analysis The current microstate model is based on two key assumptions. First is the presence of a single state at any point in time, i.e., an underlying winner-take-all principle (Michel and Koenig 2018; Gschwind et al. 2016; Pascual-Marqui et al. 1995). This is based on the observation that for a period of ~60-120 ms the spatial pattern of scalp potential (“topomap”) retains a consistent topography. The winner-take-all assumption led Lehmann and colleagues to use clustering techniques to identify and track microstates (Koenig et al. 1999; Pascual-Marqui et al. 1995). Although this assumption appears sensible based on visual inspection of EEG scalp maps, to our knowledge this has not been rigorously investigated.

A geometric perspective on microstates Under the geometric perspective of EEG data, an M-channel EEG dataset can be conceptualized as an M-dimensional space, with the topography at each time point corresponding to a coordinate in that M-dimensional space. In the original space, each channel is a basis vector. However, because of the correlational structure of EEG data (due to volume conduction as well as spatial autocorrelation in large-scale brain dynamics), the channels are not necessarily optimal basis vectors. The goal of dimensionality-reduction and source 3

separation methods such as principal or independent components analysis is to find basis vectors that better characterize important “directions”, or sources of covariance, in the multichannel data. The weights across all channels that define each component can be conceptualized as a vector in the original channel space. The benefit of this conceptualization is that it allows detailed investigations into the temporal dynamics of the components, as well as the relations among the different components. Here we apply this perspective to microstates. Microstate analysis can also be viewed as a dimensionality reduction technique, which conceptualizes each microstate as a 1D subspace, i.e. characterized as a vector vi in sensor space. Distance from a microstate is measured by correlation along the sensor-dimensions, thus the polarity of the topomap is effectively ignored (Michel et al. 1999; Pascual-Marqui et al. 1995; Lehmann et al. 1987b). Hence, while in a particular microstate, the amplitude of the map can vary over time, but the topographical pattern remains the same. Presently, the assumption that the EEG data is distributed closely around a (small) number of microstate vectors, is referred to as the discreteness assumption. The general geometric perspective allows us to investigate the discreteness assumptions of microstates: If the discreteness assumption of microstate analysis holds, then the data points associated with each microstate should be distributed closely around its parent vector, and quickly transition to another microstate.

The present study Here, we use standard microstate analysis in combination with orthogonal projection distance in empirical and simulated data to show that the time-points within one microstate are not necessarily confined around its parent microstate vector in the sensor space. Instead, single time-point topomaps can be close to multiple microstates, and their distances to the parent vs. other microstate vectors depend on global field power and change smoothly over time. Thus, we show that the assumptions of spatial and temporal discreteness may not accurately capture the nature of microstates. Further, we demonstrate that principal component analysis can be used to visualize the data distribution in 3D, as it preserves distances among and within different clusters. Materials and Methods 4

Data Description We analyzed two datasets in this study. Data from one dataset are reported in the main text, and data from a second dataset are reported in the Supplemental materials section. The dataset reported in the main text was taken from PRED+CT (http://predict.cs.unm.edu/; Access number d003) (Cavanagh et al. 2017). These fully anonymized data are available to all researchers for free use under the ODC Public Domain Dedication and License v1.0. We used this resting state (eye closed condition) dataset because (1) Results are reproducible for other researchers, (2) resting state (eye closed) EEG data has been the dominant condition used to conceptualize the EEG microstates as brain states (Lehmann and Michel 2011; Lehmann et al. 1998).

The overall dataset comprised 75 control subjects and 46 patients from depression/high BDI group, out of which we used 68 control subjects. Data from 7 other subjects were not included because of excessive noise. Data were resampled at 500 Hz. The dataset contains triggers for eye open and eye closed conditions. Here, we epoched the data based on eye closed triggers (occurring every 2000 ms) in the interest of consistency with previous EEG microstates literature.

Experimental Setup The data were recorded with a 64-channel Neuroscan system with an electrode layout according to the 10-10 international system. HEOG and VEOG channel information were available as electrooculogram (EOG) channel, which were removed from further analysis.

Data analysis Single-subject data were imported for analysis using the EEGLAB toolbox (biosig extension) in MATLAB (The Mathworks, Natick, USA). The data originally came with 66 channels, of which 60 were retained for analysis (excluding EOG and other external channels). Average referencing was performed before further analysis. Next, the data were bandpass filtered in the range of 130 Hz. The data were manually cleaned after performing ICA. The default ‘binica’ algorithm of EEGLAB was used for ICA. Components reflecting blinks or other clearly non-brain-related artifacts were removed (range 0-3, average 0.35). 5

Microstate Analysis Microstate analysis was performed as explained in (Lehmann 1971; Pascual-Marqui et al. 1995; Milz 2016). Briefly, the algorithm comprises the following steps: 1. Global Field Power (GFP), first defined in (Lehmann and Skrandies 1980), is computed for each time point. We used the L1 norm to compute GFP (L2 norm would provide similar microstate results; (Milz 2016). This produces a time series of GFP, which reflects

the

total

(

energy



in

)=

the

∑

topography

| ( ) −

over

time

( ) |

(Figure

1a-b).

(1)

2. Local Maxima of the GFP(t) are fed into a modified k-means clustering algorithm (step 37) (Figure 1c). We selected four clusters for the analysis because to be consistent with the default choice in the microstate literature (Michel and Koenig 2018). 3. The clustering process starts with selecting n template maps randomly, where n is the number of clusters or microstate maps. 4. Compute the spatial correlation of the n template maps with the data at GFP peaks. This results in a time series of absolute values of correlation coefficients for each of the template maps. Taking the absolute value of the spatial correlation ensures that the results are not dependent on topomap polarity. 5. The explained variance is calculated for the template maps (Milz 2016). 6. The next step is to redefine template maps. This is achieved by taking the first principal component of all the maps from each cluster (Koenig et al. 1999). 7. Steps 4 to 6 are repeated until the explained variance does not improve with more iterations. 8. A new set of n randomly selected template maps are chosen and Steps 3 to 7 are repeated. In the end, the set of template maps with highest explained variance is chosen as the final microstate vectors. 6

GFP peak points are labelled as one of the microstates according to the microstate template with which each time point has the strongest absolute-value correlation. We refer to the strongest-correlation template as the “parent” microstate for that time point. Finally, neighboring time points are assigned the parent microstate corresponding to the microstate of the nearest GFP peak. Temporal boundaries between the states were chosen as the midpoint of the peak GFPs in two subsequent states, consistent with the previous literature (Milz et al. 2016). Distance to microstate vectors In accordance with the microstate literature, we consider each microstate to be a 1D subspace embedded in an M-dimensional space, and the template map corresponds to a unit-length basis vector defining that subspace. This conceptualization allows us to compute orthogonal projection distances of each data point to all microstate subspaces, without concern for map polarity or the length of the microstate vector itself (Figure 2a). The idea is that if microstates are winner-take-all, then orthogonal projection distance from the topomap at each time point to the microstates should be small for the parent microstate, and large for all other microstates (Figure 2b). Furthermore, if microstates are discrete, then the time series trajectories should stay close to the parent microstate for the duration in which it is labeled as that microstate, and then make a large sudden jump to another microstate vector; conversely, if the EEG is continuous in the microstate space, then the trajectories will smoothly flow throughout the space without remaining close to any one microstate subspace (figure 2c). For average referenced data, the classical microstate model (Pascual-Marqui et al. 1995) can be written as the weighted sum of multiple microstates.

=∑ Where



is the measured topography at time t,

microstate at time t.

are

+ microstates and

(2)

is amplitude of k-th

accounts for the noise at each time point. Given the discreteness

assumption of microstates (Pascual-Marqui et al. 1995), following constraints must be satisfied: at any time point, only one

should be non-zero. 7

Note that this is a conceptual model; we do not treat equation (2) as a generative model. The key point is that one should expect that in the M-dimensional space, all the data points should be closer to their parent microstate than to other microstates (in other words, at each time point, is large for one microstate and close to 0 for all other microstates). The orthogonal projection distance is computed by first projecting each data point onto the 1D subspace spanned by the microstate vector and computing the distance between the data point and its projection onto the microstate vector. =|

d

! − ( !. # ). # |

(3)

Where

!, the data at time point t, is an n-dimensional vector (n=60 [channels]) and

#

, k-th

microstate vector, is also an n-dimensional unit vector (n=60). Note that flipping the polarity of a data point does not alter the distance to the microstate subspace, which is how polarity is accounted for in our analysis. Since the data are referenced to the global average, the GFP and distance from the origin are related but not identical. A potentially important choice for the analysis is whether to normalize the data for each time-point, i.e. divide each instantaneous topography by its norm. Without this normalization, the absolute size of each topography will be taken into account when computing distances from microstates. Alternatively, with this normalization, the data is projected onto a unit sphere. As we show in the 'low GFP' analysis, since topographies that are close to a microstate vector and lie close to the origin, can be projected far away from it after normalization, and vice versa for large topographies. Hence, normalization could substantially influence the orthogonal projection distance. Since a focus of this work is the dependence of microstate analysis on the size of each topography (quantified by its GFP), we do not perform normalization in the main part of the analysis. However, we include normalization results in the supplementary material, which leads to quantitative changes, but in fact keeps the results qualitatively the same (see Supp. Fig. 6).

8

Grouping GFP into ranges In order to understand whether microstate distances depend on GFP, we defined three groups of GFP ranges (grouping done separately for each subject): (1) GFP peak points (Figure 1b). Importantly, GFP peaks are only local peaks, and therefore do not always correspond to high GFP values (Figure 2d and 3a) (2) High GFP. From the GFP value distribution per subject, we took 15% of the largest GFP values. (3) Low GFP. Same as in (2) but for the 15% of the lowest GFP values. All analyses were repeated for these three GFP ranges.

Visualizing data in 3-D space We applied principal component analysis (PCA) to visualize the data in lower dimensions. PCA detects the directions of highest variance in the original 60-dimensional space defined by the recorded electrodes, and we retained the first 3 principal components for visualization (see e.g. Figure 1). No additional temporal smoothing (aside from the filtering detailed above) was applied before dimensionality reduction. Ratio of intercluster and intracluster distance in sensor space and PC space To assess the extent to which microstates tended to group into clusters, and the effects of dimensionality-reduction on clustering, we computed the ratio of intercluster to intracluster distance. We use this measure to assess how well the distribution of data is preserved when transforming from sensor space to reduced space. This ratio is defined as



%$=

&'()

'( *')

(4)

Where +$% is the intercluster distance, defined as mean Euclidean distance of all pairs of points

between cluster i and j. +$ is intracluster distance, defined as mean Euclidean distance of all

pairs of points in cluster i.

9

In the case of EEG microstates, data belonging to one microstates (one cluster) are not necessarily confined in one orthant because of oscillatory nature of neural data. Thus, it is important to take polarity into account before computing such measures (Figure 4B-C). This index is useful for measuring two features for such high dimensional datasets. Higher values of this ratio suggest discreteness and higher separability of clusters. When the clusters are intermixed, r tends towards 1 (see Figure 4B-C for an illustration). A dimensionality reduction method is suitable if it preserves the features of data in lower dimension and thus has similar values of this ratio in two spaces.

Statistical Analysis of distances We applied the nonparametric Wilcoxon’s ranked sum test, and permutation testing to compare the differences in the distribution of distance values in different GFP ranges. This resulted in a matrix of dimension 68 (subjects) x 12 (comparison, 3 comparison for each panel in figure 2EG) for each GFP range. The distribution of z values for each range was compared.

To compare the intercluster and intracluster distance ratio in two spaces, Wilcoxon’s ranked sum test was used in each GFP range. This resulted in 6 comparisons (for 4 microstates) for each subject. Standard error of the mean (SEM) were computed on the average across runs on the ratio values. Error bars indicate 1 SEM. All statistical analyses were performed using the statistics toolbox in Matlab (The Mathworks, Natick). Trajectory speed and microstate dynamics If the EEG data remains stable in one microstate and then rapidly transitions to another microstate, the speed of the data trajectory in microstate space should be constant and close to zero within a microstate, and briefly high during transitions between microstates. In contrast, if the EEG are continuously traversing the microstate space, then the trajectory speed should be less extreme and with smoother transitions between microstates. We therefore used trajectory speed in order to distinguish between discrete and continuous temporal dynamics of EEG microstates. In particular, trajectory speed is defined as speed(t)= ,

- ! ,, -

(5) 10

Where ! is a 60-dim vector, referring to voltage at time t. | | indicates the vector norm. Thus speed is the vector norm of the gradient of voltage vector. The cases when the maps switch polarity, caused by the oscillatory nature of neural data, can be treated as transitions into the same microstate. We focused on the speed time series between microstates boundaries. A discrete process should have rectangular speed functions due to abrupt changes in the underlying topographical patterns. On the other hand, a continuous process should have Gaussian-shaped speed profiles. We quantified the speed profiles for each microstate transition as the fit to a cosine-tapered window function:

1/2{1 + 2 1/2{1 + 2

(3[

(3[ &5

6

&5

6

− 1])}, 0 ≤

=( ) = 1, &

6

&

6

< ≤

6

2

<

− + 1])}, (1 − ) ≤ 6

&

6

(1 − ) ≤

&

(6)

> is known as cosine fraction. For> ≤ 0, = is a rectangular window function, while for > ≥ 1, = is a Hann window function of length

. In order to find the best fitting window, we introduced a

width fraction parameter apart from the cosine fraction parameter. Function minimization was done using MATLAB’s fminsearch function. Squared pearson correlation coefficient between the speed and the fit has been used as a measure to assess the quality of fitting. Simulation We simulated neural generators of EEG (dipoles) using a rectangular window function (discrete case) or overlapping Hann window function (continuous case) activations. We achieve this by using a cosine-tapered function (MATLAB signal processing toolbox function tukeywin), with the cosine fraction parameter set to 0 and 1 for rectangular and Hann windows, respectively. We use a detailed dipole source model by the openmeeg software (Gramfort et al. 2010; Kybic et al. 2005). For predicting the scalp potentials, we use the corresponding leadfield matrix, also provided by openmeeg. In the simulation we compared discrete and continuous activations of scalp EEG generators. For this purpose, we selected 4 dipoles randomly out of the total set of 2004 dipoles, representing brain generators of the microstates. These 4 dipoles were selected such that they have distinct patterns when projected on the scalp. (Figure 5A1). Each simulation 11

case i.e. discrete activation and continuous activation case, has 50 trials of 10 second. Microstate analysis and trajectory speed analysis were performed independently on each trial.

12

Results We reanalyzed an EEG dataset (N=68) during a resting state, eye-closed condition aiming to provide a more refined understanding of the underpinnings of cortical microstates. We therefore performed microstate analysis as explained in (Milz 2016; Pascual-Marqui et al. 1995; Koenig et al. 1999). Since both L1 and L2 norms produce qualitatively the same result we focussed on the L1 norm while computing GFP. Distribution of GFP peak points in relation to the entire GFP GFP peak points are commonly used as the basis for estimating microstate vectors. The rationale is that the set of GFP peaks represents brain topography of high SNR. However, there are two potential caveats to this assumption. First, GFP peak points occur with a large range of amplitudes, and thus reflect locally high SNR (relative to their temporal neighbors). Consider the distribution of the entire GFP data and the GFP peaks for a single subject (Figure 2D2), which shows that GFP peak points comprise both high GFP and low GFP points. Standard microstate analysis includes these low GFP points when defining microstates, however, their influence has not been thoroughly investigated. Second, the peaks constitute just a small subset of the entire data set, and may thus be missing relevant information. For the bandpass filtered dataset (1-30 Hz, see Methods for details), we find that GFP peak points constitute 4.13 ±0.58 % of the timepoints. We have repeated the same analyses on a different data set with motor task (see supplementary information for more details) and results confirm the generalizability of this pattern (Supp. Figure 3-4).

Discreteness or continuity of microstates depends on GFP Microstates have often been conceptualized as discrete brain states with abrupt transitions. If this were the case, the data in sensor space should be closer to their parent microstate vectors. However, our analyses suggest that the data change more continuously, partly due to low-pass filtering and perhaps to the general continuity of large-scale brain processes that give rise to 13

EEG. Hence, assessing the degree to which the microstates are discrete or continuous is nontrivial, as clusters are necessarily connected by trajectories and broadened by noise. We quantified the distances from the data at each time point to all microstates. In general, for all GFP ranges and for all microstates, we observed a ex-Gaussian-like distribution of distances, with few time points exhibiting very small or very large distances to the microstate vectors (Figure 2E-G). The key questions are whether the mean of the distance distributions are smaller for the parent microstate compared to all other microstates, and to which degree they overlap. For data points at GFP peaks, distances to the parent microstate vectors had distributions closer to zero (Figure 2E) than for the other microstates. However, the parent and non-parent distance distributions also showed a high degree of overlap. Using the time points with the top 15% of the GFP value showed similar characteristics (Figure 2F). The distribution of distances from the parent microstate peaked closer to zero than distances to non-parent microstate vectors. Data taken from the bottom 15% of the GFP distribution (Figure 2G) did not follow this pattern, and instead, distances were roughly equivalent to the parent and non-parent microstate vectors. Statistical testing indicates varying extents of separability of states in different GFP range (see Figure 2H1-2H2). Overall, these findings do not provide strong support for the spatial discreteness assumption of EEG microstates, as distance distributions to all microstate subspaces are largely overlapping even in the case of GFP peaks, for which the k-means clustering was defined (and thus, when maximum separability is expected). We have included the result of distance analysis after normalization of data (Supp. Figure 6). Upon unit-normalization, we still find preference of data for their parent microstates (in terms of distance) in GPF peak and high GFP region, while no such preference in low GFP region was found. We obtained similar results when using correlation instead of orthogonal projection distance (Supp. Figure 7). This shows that our key observations are not biased by the specific analysis method.

Extent of discreteness for GFP peak and high GFP We next sought to quantify the level of discreteness for the different GFP groupings. To measure the amount of discreteness, we used the ratio between intercluster and intracluster distances, termed r (see Eq. 4 in Methods). For intermixed clusters, this ratio is expected to be 14

close to 1 (Figure 4). Moreover, such a measure serves as another indicator of difference between the trajectory structure in different GFP ranges. We expected that for the low GFP range, this value would be smaller than for a high GFP range and GFP peaks, as data points in the low GFP range are equidistant from all other microstates (Figure 2E-G). Before computing such a measure on EEG data, it is important to take polarity into account. In order to do this we have flipped topomaps at each time point such that correlation between topomaps at each time point with their parent microstates is always positive. We found that values of r were smaller for the low GFP range compared to the high GFP range and GFP peaks (Figure 4D1). However, we did not find relatively very high value (>>1) of r for any GFP range. This means that although there is some clustering of microstates, the amount of cluster-mixing increases in the low GFP range. This is in line with the previous result (Figure 2E-G). Thus, even in the case of GFP peaks and high GFP, the data do not lie in discrete clusters in sensor space. Moreover, for the low GFP range this intermixing of points is even stronger.

Using PCA to visualize the microstate data in sensor space We next asked whether dimensionality reduction via PCA might provide insights into the structure of the microstates, i.e. how the separability in the high-dimensional (sensor) space is affected by projecting into a lower dimensional space. We therefore quantified the relation between inter/intracluster distances (Eq. 4), before and after applying PCA, where the clusters were derived using the standard microstate analysis. Note that clustering (microstate analysis) has been performed in sensor space and the same clustering labels have been used in sensor space and PC space to compute the inter/intracluster distances. We projected the data along the three largest principal components. As in the previous analysis, we divided the data in three categories: GFP peaks, high GFP range, and low GFP range. We found that the ratio of intercluster and intracluster distances (Eq. 4) increased significantly after applying the PCA for all GFP groups (Figure 4D2), indicating increased separability in PC space (Figure 4B-C However, the values of r still stayed below 2 (which approximately corresponds to a cluster center distance of two standard deviations), suggesting a substantial degree of overlap between the clusters (note that the analysis here creates a separating plane without overlap between the clusters, which is thus not representative of the 15

ground truth). However, generally PCA appears to be a suitable technique for understanding microstates and their dynamics, as it improves the intercluster to intracluster ratios. We compared the clustering index (Eq 4) across cluster-combinations and across the different GFP ranges in both sensor space and PC space. We found that in both spaces, the value of the clustering index changed significantly across GFP ranges (p<<0.001, 2-way ANOVA, with factors cluster combinations (df=5) and GFP ranges (df=2), using post-hoc testing including Bonferroni correction for multiple testing). Low GFP was significantly smaller than GFP peak and high GFP for all cluster combinations (p<0.001). Because PCA is an orthogonal rotation of the original (sensor) space, it does not distort distances. Moreover, excluding smaller PCs helps suppress some noise and thus leading to the higher separability of clusters. Similar analyses on a different data set with motor task (see supplementary information for more details) again show the same relationship between GFP ranges and clustering indices (Supp. Figure 5).

Simulations for discrete and continuous activation of generators In order to understand the underlying mechanisms of EEG microstates, we simulated EEG data. The primary goal of the simulation was to investigate the features at the neural source level that might give rise to the different trajectory shapes of data at the scalp level. For this, we range the parameters between a temporally discrete or more continuous representation at the source level. The first part of the simulation focuses on discrete, binary activation of sources. For this, 4 dipoles were chosen such that they have different representation on scalp. In the 50 trials of each 10 second long simulation, each dipole was activated for 250 ms in a rectangular fashion (Figure 5B1). The next dipole was activated immediately thereafter. These activations were projected onto 64 channels on the scalp. Thereafter, microstate analysis was performed on the channel data, as described for the real EEG data. For visualization, the 64 dimensional data were projected onto the largest 3 principal components (Figure 5C1). It is evident that the discrete activation of dipoles results in well separable clusters. In the second part of the simulation, the microstate activations were continuous, modelled as overlapping Hann-window functions (Figure 5B2). Again the resultant scalp EEG 16

data was subjected to Microstate analysis. The continuous activation of dipoles led to correspondingly continuous trajectories in principal component space (Figure 5C2). In both cases, before projecting the data on the scalp, noise with a 1/f power spectral density to the data, appropriately scaled to achieve qualitative similar level of signal to noise ratio. In both cases, the 4 microstates produced were internally highly correlated, which is expected as they have the same sources. In each case, the resultant microstates could explain more than 80% of the variance. This simulation demonstrates in principle how continuous trajectories can be obtained at the sensor level by smoothly overlapping the activations of the underlying generators.

Trajectory speed and microstate dynamics Lastly, we assessed whether the temporal transitions between the detected microstates in the empirical data should be considered discrete or continuous. For this purpose, we quantified the dynamics of transitions between subsequent states via the overall gradient of the EEG signal, i.e. the 'speed curve' (see Methods for details). For comparison, we first computed the speed curves for the two simulation conditions (discrete/continuous) detailed above (see Figure 5D1,2 black, for an example). Speed curves are assessed between the peaks of the speed curve. This is also an indirect measure of how a state activates, is maintained and inactivates again. As expected for the simulated data, typical speed curves are more flat in the middle for discrete activations (Figure 5D1), and have a more ushaped progression in the case of continuous activations (Figure 5D2). A representative speed curve for the real data shows mostly a u-shaped appearance (Figure 5D3). In order to quantify the differences in the speed curves, we segmented the speed curve at the peaks and fitted a tapered cosine function to each segment(gray, Figure 5D1-3). This fit yielded parameter estimates for each transition, namely the width and cosine fractions. The cosine fraction is the main determinant of the sharpness of the transition: discrete transitions have a low cosine fraction (0.33±0.02 (SD)), while continuous transitions have a high cosine fraction (0.80±0.03 (SD)), see insets in Figure 5E1-3 for illustrations of the cosine tapered functions for different parameters (white).

17

Correspondingly, in the discrete, simulation case, we find a narrow distribution of cosine fractions closer to 0 (Figure 5E1). Conversely, in the continuous simulation case we find a narrow distribution closer to 1 (Figure 5E2). The empirical transitions exhibited a wider distribution of speed curve shapes that led to a range of cosine fractions >0.5, with a mean of 0.71 (± 9.1x10-4 (SD), see black dots in Figure 5E3). While we acknowledge the fact that the simulations are portraying the ends of the discrete/continuous spectrum, the empirical data appears to thus be better described by continuous than discrete activation in time. In all three cases the fitting explained a large part of the variance, quantified as the distribution of r2 values (Figure 5F1-3). Discussion The dynamics and complexities of EEG microstates Despite more than three decades of research into EEG microstates (Yuan et al. 2012; Britz et al. 2010; Lehmann et al. 1987b; Khanna et al. 2015), their neural basis and dynamics remain poorly understood. We sought to provide new insights into these dynamics by testing two key assumptions underlying microstate analysis. We found that microstates are temporally more continuous and spatially less discrete than previously assumed. Moreover, the nature of microstate trajectories in sensor space, and their relation to GFP, plays an important role in designing microstate analyses (Skrandies 1990) and interpreting the results. In this process we look into the overall structure of the data, using cluster analysis while relying on the test-retest reliability of EEG microstates (Khanna et al. 2014). Our analyses of empirical data and simulations refines the set of neural mechanisms that could underlie the observed microstates in the EEG.

Discrete vs. continuous EEG microstates The discrete model of EEG microstates appears to be most valid for data points at GFP peaks. This is not entirely surprising, considering that these are the points used to define the microstate vectors in the clustering analysis. It is also sensible, considering that GFP peaks feature the highest SNR compared to their neighbors in time (Lehmann 1990). However, the majority of the distance distributions remained overlapping for parent and non-parent vectors. Therefore, for 18

studies where discreteness of states is important but exact boundaries of the states are not, limiting analyses to GFP peaks appears to be a necessary approach.

On the other hand, GFP peak points include both low GFP and high GFP values, because GFP peaks can be found in time periods of high or low “tonic” GFP. Low GFP points provide the poorest separability of microstates (Figure 2G). Thus, GFP peak points in general are not necessarily points of maximal expression of states, and thresholding GFP peak points may provide better estimation of microstates. The geometric interpretation of this finding is that topomaps are close to their parent microstate basis vector primarily during GFP peaks with high GFP values (far away from the origin of the M-dimensional sensor space).

It is worth noting that the qualitative pattern remains unchanged upon normalization or using correlation instead of orthogonal projection distance. This adds to the generality of the results and shows that this is not mere consequence of choice of distance measure.

Our analysis of the transition dynamics between states, i.e. via the speed curves, further supports a rather continuous transition pattern, in contrast to the previous view of rather instantaneous activation and inactivation.

EEG microstates are not winner-take-all phenomena It seems that EEG microstates are less discrete than initially proposed, and the amount of discreteness depends on GFP. The presence of only one state per time point appears mostly valid mainly for GFP peaks (which can include low GFP time regions) and high GFP points. For low GFP points there appears to exist only little separation, which - based on our simulation results - we speculate may reflect a transition between states (Figure 6). While the resulting concept of the source activations is generally more in line with a continuity of brain dynamics, this was not included in the generally discrete nature of state analysis in previous studies (Lehmann et al. 1998; Britz and Michel 2011; Lehmann 1990). Moreover, our simulation suggest the resemblance of trajectory nature of empirical data with surrogate data generated by overlapping activation of sources. Our results therefore advocate a conceptualization of 19

microstates that incorporates non-discrete, overlapping source activations (e.g., non-zero and non-vanishing a coefficients in equation 2).

Implications for studying and understanding microstates Our simulations may provide additional insights into the nature of EEG microstates. For example, combined EEG-fMRI studies have suggested a close association of fMRI-defined resting state networks with EEG microstates (Yuan et al. 2012; Musso et al. 2010; Britz et al. 2010; Khanna et al. 2015). Similarly, microstates have been suggested to exist on the level of cortical columns in the population activity, e.g. in auditory cortex (Luczak et al. 2009). However, a one-to-one mapping of standard microstates with either resting-state networks or sensory cortices remains unclear. Based on our empirical and simulated results, it is possible that a clearer mapping between microstates and fMRI networks would emerge for GFP peaks and high GFP regions, whereas during low GFP, there may be no clear mapping between microstates and fMRI networks, or perhaps a weak all-to-all mapping would be present.

In conclusion, we stress that our findings are not in conflict with the existence of EEG microstates, nor do they invalidate many of the conclusions drawn from standard microstate analyses. Our findings clearly demonstrate a time-limited dominance of one microstate at a time during time windows with high GFP or during GFP peaks. However, we believe that any investigations into the biophysical origins or neurophysiological significances of microstates must incorporate the insight that microstates mostly comprise continuous trajectories that orbit the parent vector during high (local and global) GFP periods, as opposed to being discrete and isolated clusters. This is consistent with a recent report that uncertainties in the assignment of states for low GFP is high (Dinov and Leech 2017). The same work draws a similar conclusion about the utility of GFP peak points and proposes the idea of thresholding in local maxima of GFP.

Acknowledgement: MXC is funded by an ERC-Stg (638589) awarded to MXC. 20

AM is funded by a joint doctoral grant awarded to MXC and BE by the Donders Center of Neuroscience. BE was supported by a European Commission's Marie Curie Grant (660328), a NWO VIDI Grant (016.189.052) and a NWO ALW Open Grant (ALWOP.346).

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Figure 1. EEG Microstate computation method and possible underlying mechanisms (simulated data). A Simulated EEG data with channels on y axis and time on x axis. B Corresponding global field power (GFP) time series, which can be thought of as the total energy in the topography at each time point. The dots indicate local maxima (“GFP peaks”). EEG data at GFP local maxima are then fed into a clustering algorithm. C Microstate vectors are produced by the clustering algorithm, and are visualized as topographical maps. D-E EEG microstate temporal dynamics can be visualized by reducing the data into in PCA space, which leads to two potential possibilities for microstate dynamics: The discreteness assumption of EEG microstate model predicts spread of data as shown in D1; on the other hand, data might follow continuous trajectories in space as in E1. D2-E2 shows the possible underlying mechanisms behind state activation for the two cases. For discrete states (D2), only one of the generators dominates during the whole period of one state. As the EEG data switches to a new microstate, a different underlying brain state dominates. In the case of continuous trajectories (E2), one brain state dominates only for a short period of time, while other brain states might be simultaneously but slightly less active.

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Figure 2: Geometric interpretation of discreteness and continuity of EEG microstates, and its exploration in real data. A-C show simulated data to illustrate distance computation and data possibilities. A Computation of distance of data points from different subspaces defined by microstate vectors. The distance measure is independent of polarity as these microstate vectors are treated as 1-D subspaces and thus projection on negative orthant is same as positive after setting the polarity to be positive. B Discrete model of EEG microstates. All data points remain closer to their parent microstate vector than

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to the non-parent microstate vectors. C Continuous model of EEG microstates. Some data points are close to their parent microstate vector, but trajectories move throughout this space and can be roughly equidistant across multiple microstate vectors. D-G show empirical data (see also supplemental figure SF 3). D1 Distribution of empirical GFP values and GFP peak points for all 68 subjects. D2 Distribution of empirical GFP values and GFP peak points for one example subject (distributions from all subjects were qualitatively similar). Notice that GFP peak points contain low GFP and high GFP values. Dashed lines show the boundaries of low GFP (bottom 15%) and high GFP (top 15%) for this subject (thresholds were subject- and session-specific). E Distributions of distances from each data point to all microstate vectors. Note that distances to parent microstate vectors are overlapping though shifted towards smaller distances compared to non-parent microstate vectors for GFP peaks (E) and high GFP (F), but not for low GFP (G). H1 Distribution of z values obtained using permutation testing on comparisons of distances from different microstate vectors and parent microstate (Figure 2 E,F,G) in different GFP range. z values for GFP peak and high GFP points are far from zero while for low GFP it is closer to zero. H2 Same analysis as in (H1) using Wilcoxon’s ranked sum test. z values closer to zero for low GFP suggest poor separability of states, while z values far from zero suggest preference to one state over others.

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Figure 3: Example of how GFP peaks in high GFP range can approach discreteness while GFP peaks in low GFP range can be continuous. A GFP time series and dots show which state was assigned to each peak. On the same plot, the GFP distribution and boundaries for low GFP (bottom 15%) and high GFP (top 15%) are shown. B Time series of the distances of the maps at each time point to all four microstate vectors. Notice that the GFP peak that lies in high GFP range is nearer to its parent microstate (green dashed line) while another GFP peak which is in low GFP range (blue dashed line) does not show preference to any microstate vector in terms of distance.

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Figure 4: EEG data are more intermixed in low GFP range, and PC projection increases intercluster and intracluster distance ratios. A Simulated data to illustrate the clustering index. A visual explanation of the formula for comparing intra- to inter-cluster distances. B1 intermixed clusters

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after polarity inversion (B2) lead to r≈1. C1 Higher separability in clusters after polarity inversion (C2) leads to r>1. D1 Empirical data in sensor space. Ratio index r for sensor space for three GFP ranges exhibit higher separability for GFP peak and high GFP in comparison to low GFP range. D2 Empirical data in principal component space (3 largest PCs). Ratio index r for PC space displays similar characteristics as in sensor space. E Mean of difference between the PC space and sensor space. Values between the two spaces differ significantly. Positive difference suggests improved separability of clusters in PC space.

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Figure 5: Simulated EEG data to provide insight into possible mechanisms of continuous trajectories in microstate space. A1 For the simulation, 4 dipoles were simulated (each dipole generates distinct scalp topography). A2 For real EEG data, the active dipole configurations are unknown. B1 Each dipole becomes active in successive manner (rectangular function) for 250 ms; these time courses (in total 10 seconds) plus noise are projected to the 64 scalp channels. B2 Each dipole is activated as overlapping (50% overlap) Hann functions; similar to discrete case, these time courses (in total 10 seconds) plus noise are projected to the 64 scalp channels. B3 In real EEG data, the time course of dipole activation is unknown. C1 EEG data (first 1 second) along largest three principal components when generated by discrete activation of dipoles as shown in B1. The discrete activation of dipoles leads to more separable clusters in PC space which is not found in real data. C2 EEG data (first 1 second) along largest three principal components when generated by overlapping activation of dipoles as shown in B2. This continuous activation of dipoles leads to trajectory like structure in PC space which is more similar to real data. C3 Real EEG signal from one subject, projected along the largest three principal components. Each dot is a time point and the colors correspond to microstate labels. D1 A typical segment of trajectory speed computed from discrete activation simulation data (black) and a fitted cosine tapered function (gray) suggest sharp changes in the speed. D2 Same as D1 for continuous data suggests gradual changes in speed. D3 A representative trajectory speed segment (with fitting parameters in the range of mean fitting parameters from all the subjects ±0.01) suggests more resemblance with the continuous dipole activation case. E1 Probability density of fitting parameters, cosine fraction and width fraction, for all the speed segments (discrete activation simulation data). White curves show shapes of fitting functions at different locations in parameter space. The black dots represent mean parameters from each trial (mean cosine fraction=0.33, mean width fraction=0.89). E2 same as E1 for continuous activation simulation data. The black dots represent mean parameters from each trial (mean cosine fraction=0.80, mean width fraction=0.87). E3 same as E1 for real data for all subjects. The black dots represent mean parameters from each subject (mean cosine fraction=0.71, mean width fraction=0.77). F1 Distribution of square of pearson correlation coefficient for discrete activation simulation. F2 same as F1 for continuous activation simulation. F3 same as F1 for real data.

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Supplementary Information We have repeated the analyses on a different dataset. This helps us extend our conclusion to task dataset and strengthens the claims made in this study.

Data Description

We have used data available for public use from PhysioNet1. This data has been contributed by the developers of the BCI2000 instrumentation system (Schalk et al. 2004; Goldberger et al. 2000). This fully anonymized data is available to all researchers for free use under the ODC Public Domain Dedication and License v1.0.

The overall dataset comprised 109 subjects, out of which we used the first 20 subjects. Data were sampled at 160 Hz. Here, we used only one of these tasks for the analysis.

Experimental procedure

In this experiment, subjects perform either real or imaginary motor tasks. Four different tasks had to be performed in the actual experiment. In this task subjects were asked to squeeze either their feet or fists when a target appeared at the bottom or the top of the screen, respectively. Subjects relaxed again after the target disappeared. The task was performed three times, and each repetition lasts in the range of 126-128 s. Experimental Setup

The data were recorded with a 64-channel BCI2000 system with an electrode layout according to the 10-10 international system. Electrooculogram (EOG) channel information was not available.

Data analysis 1

https://www.physionet.org/pn4/eegmmidb/

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We performed exactly same analyses as done for resting eye-closed data. The datasets were preprocessed before this analyses. Data for each subject were available in the EDF format. Individual subjects were imported for analysis using the EEGLAB toolbox (biosig extension) in MATLAB (The Mathworks, Natick, USA). Since there was no EOG information available, the data were manually cleaned after performing ICA. The default ‘binica’ algorithm of EEGLAB was used for ICA. In most of the cases, 2-3 independent components were identified as ocular muscle artefacts and removed from further analysis.

SF 1. Mean microstate maps extracted from 68 subjects resting state eyes-closed EEG. These four maps have high resemblance with the four standard microstate maps.

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SF 2. Subject averaged power spectrum (resting state eye-closed data) at Pz channel shows high power at alpha frequency.

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SF 3. distribution of distance of data from their parent microstate and other microstates (motor task data). A Distribution of gfp values and gfp peak points for one session of one subject. This is the nature of these distributions for all the subjects. It can be noticed that gfp peak points contain low gfp and high gfp peak points as well. Dashed lines show the boundaries of low gfp (bottom 15 %) and high gfp (top 15%) for this subject. This has been computed for each subject and each session for further analysis. B For gfp peak points, distribution of distance from it’s parent microstate and other microstates. Distance from parent microstate peaks earlier. C same analysis for high GFP points. They show similar characteristics as gfp peak points. D low gfp points fail to show the separability of states. E1 Distribution of z values obtained using permutation testing on comparisons of distances from different microstate vectors and parent microstate (SF 3 B,C,D) in different GFP range. z values for GFP peak and high GFP points are far from zero while for low GFP it is closer to zero. E2 Same analysis as in (E1) using Wilcoxon’s ranked sum test. Z values closer to zero for low GFP suggest poor separability of states, while z values far from zero suggest preference to one state over others.

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SF 4. GFP peaks in High GFP range approach discreteness while GFP peaks in low GFP range are more continuous (Motor task EEG data ) A GFP time series and dots show which state was assigned to each peak. On the same plot, the GFP distribution and boundaries for Low GFP (bottom 15%) and High GFP (top 15%) are shown. B Time series of the distances of the maps at each time point to all four microstate vectors. Notice that the GFP peak that lies in high GFP range is nearer to its parent.

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SF 5. EEG data (Motor task data) are more intermixed in low GFP range, and PC projection increases intercluster and intracluster distance ratios A Empirical data in sensor space. Ratio index r for sensor space for three GFP ranges exhibit higher separability for GFP peak and high GFP in comparison to low GFP range. B Empirical data in principal component space (3 largest PCs). Ratio index r for PC space displays similar characteristics as in sensor space. C Mean difference between the PC space and sensor space. Values between the two spaces differ significantly. Positive difference suggests improved separability of clusters in PC space.

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SF 6. distribution of distance of normalized data from their parent microstate and other microstates (eyeclosed resting state EEG data) shows preference for one state in GFP peak (Panel A) and high GFP (Panel B) range while no preference for one single state in low GFP range (Panel C)

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SF 7. Distribution of correlation of data with microstate maps in different GPF ranges. A correlation of data with all microstate maps in GFP peak points show a higher correlation with parent microstate. However overlap among correlation distribution curves can be seen. B In High GFP range shows similar pattern as GFP peak points. C Low GFP does not indicate preference to any microstate in terms of correlation unlike GFP peak and high GFP case,

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