A Novel Approach for Segment-Length Selection Based on Stationarity to Perform Effective Connectivity Analysis Applied to Resting-State EEG Signals

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Abstract
Connectivity among different areas within the brain is a topic that has been notably studied in the last decade. In particular, EEG-derived measures of effective connectivity examine the directionalities and the exerted influences raised from the interactions among neural sources that are masked out on EEG signals. This is usually performed by fitting multivariate autoregressive models that rely on the stationarity that is assumed to be maintained over shorter bits of the signals. However, despite being a central condition, the selection process of a segment length that guarantees stationary conditions has not been systematically addressed within the effective connectivity framework, and thus, plenty of works consider different window sizes and provide a diversity of connectivity results. In this study, a segment-size-selection procedure based on fourth-order statistics is proposed to make an informed decision on the appropriate window size that guarantees stationarity both in temporal and spatial terms. Specifically, kurtosis is estimated as a function of the window size and used to measure stationarity. A search algorithm is implemented to find the segments with similar stationary properties while maximizing the number of channels that exhibit the same properties and grouping them accordingly. This approach is tested on EEG signals recorded from six healthy subjects during resting-state conditions, and the results obtained from the proposed method are compared to those obtained using the classical approach for mapping effective connectivity. The results show that the proposed method highlights the influence that arises in the Default Mode Network circuit by selecting a window of 4 s, which provides, overall, the most uniform stationary properties across channels.

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