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. 2018 Mar 21:2018:2406909.
doi: 10.1155/2018/2406909. eCollection 2018.

Assessment of Multivariate Neural Time Series by Phase Synchrony Clustering in a Time-Frequency-Topography Representation

M A Porta-Garcia  1 , R Valdes-Cristerna  1 , O Yanez-Suarez  1
Affiliations

Assessment of Multivariate Neural Time Series by Phase Synchrony Clustering in a Time-Frequency-Topography Representation

M A Porta-Garcia et al. Comput Intell Neurosci. .

Abstract

Most EEG phase synchrony measures are of bivariate nature. Those that are multivariate focus on producing global indices of the synchronization state of the system. Thus, better descriptions of spatial and temporal local interactions are still in demand. A framework for characterization of phase synchrony relationships between multivariate neural time series is presented, applied either in a single epoch or over an intertrial assessment, relying on a proposed clustering algorithm, termed Multivariate Time Series Clustering by Phase Synchrony, which generates fuzzy clusters for each multivalued time sample and thereupon obtains hard clusters according to a circular variance threshold; such cluster modes are then depicted in Time-Frequency-Topography representations of synchrony state beyond mere global indices. EEG signals from P300 Speller sessions of four subjects were analyzed, obtaining useful insights of synchrony patterns related to the ERP and even revealing steady-state artifacts at 7.6 Hz. Further, contrast maps of Levenshtein Distance highlight synchrony differences between ERP and no-ERP epochs, mainly at delta and theta bands. The framework, which is not limited to one synchrony measure, allows observing dynamics of phase changes and interactions among channels and can be applied to analyze other cognitive states rather than ERP versus no ERP.

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Figures

Figure 1
Figure 1
Example of hexadecimal cluster labeling for an 8-channel EEG array, where AC represents the cluster containing Fz, Pz, P3, and P4.
Figure 2
Figure 2
Depiction of how a TFT map is generated. Using the settings for the assessment of cEEG (sampling rate of 256 Hz), the size of each window is υ = 16. Hence, each scalp map in the TFT map represents the cluster modes within the cEEG window of size υ for each electrode.
Figure 3
Figure 3
Depiction of how an iTFT map (blue background) is constructed. Following the same principle of a grand average for ERP (computing modes instead), the scalp maps in the green TFT map contain the ITCM of epochs 1,2,…, M. For illustration purposes only, let us consider the final step, that is, computing the modes of every window over the discrete time axis, setting υ = 2 samples (indicated with the red rectangles and arrows) with a sampling rate of 1 kHz. Thereby, each topographic map in the iTFT map represents the cluster modes of all samples of the array containing the ITCM within the window of size υ for each electrode.
Figure 4
Figure 4
Block diagram of the framework pipeline. Blocks a, b, and c are described in Sections 2.2.1, 2.2.2, and 2.2.3, respectively. This is a general pipeline, and as such another phase extraction technique might be used in block a (we opted for CWT). In block b, other PS criteria can be introduced (we opted for circular variance) to perform mCPS. The blocks contained in d are described in Section 2.2.5, where condition 1 and condition 2 refer to ERP and no-ERP epochs, obtained after segmentation of the time series of cluster labels cEEG. Additionally, TF maps of each channel for both conditions (not depicted in this block diagram) can be used together with the TFL maps of block e for visual analysis.
Figure 5
Figure 5
(a) Grand average of each channel; (b) corresponding spectra and scalp distribution of power at 1.6 Hz. Both images were generated with EEGLAB [31]. (c) TFT map at 1500 ms, 1.6 Hz, and SNR = 0.328 dB. (d) TFT map at same time and frequency of grand average, with SNR = 3.16 dB.
Figure 6
Figure 6
Grand averages of ERP (blue) versus no-ERP (red) condition for each subject (run 4 for S2 and S5, run 7 for S6, and run 6 for S7).
Figure 7
Figure 7
(a) A portion of iTFT maps for S2, showing only the row of bins centered at 2 Hz and 2.5 Hz, from 250 ms to 875 ms of ERP epochs; (b) same fk depicted for no-ERP epochs. (c) An example of the cluster related with the steady-state artifact. (d) TFL map for P4. (e) TF map for P4 for ERP and (f) TF map for P4 for no ERP.
Figure 8
Figure 8
(a) A portion of iTFT maps for S5, showing only the row of bins centered at 1.6, 2, 2.5, and 3.1 Hz, from 250 ms to 875 ms of ERP epochs; (b) same fk depicted for no-ERP epochs. (c) TFL map for P3. (d) TF map for P3 for ERP, and (e) TF map for P3 for no ERP.
Figure 9
Figure 9
(a) A portion of iTFT maps for S6, showing only the row of bin centered at 3.1 Hz, from 62.5 ms to 687.5 ms of ERP epochs; (b) same fk depicted for no-ERP epochs. (c) TFL map for Pz. (d) TF map for Pz for ERP and (e) TF map for Pz for no ERP.
Figure 10
Figure 10
(a) A portion of iTFT maps for S7, showing only the row of bin centered at 2, 2.5, and 3.1 Hz, from 62.5 ms to 687.5 ms of ERP epochs; (b) same fk depicted for no-ERP epochs. (c) TFL map for P3. (d) TF map for P3 for ERP and (e) TF map for P3 for no ERP.
Algorithm 1
Algorithm 1
Multivariate Time Series Clustering by Phase Synchrony (mCPS).
See this image and copyright information in PMC

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