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

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.

Keywords: EEG; effective connectivity; kurtosis; resting-state connectivity; stationarity.

Figure 1

Outline of the segmentation approach performed on EEG signals. (Each color is associated to a specific window length duration: red $-$ w_l1, purple $-$ w_l2, green $-$ w_l3, and so on).

Figure 2

(a) Individual kurtosis distributions for the channels F1, F4, PO5, and PO4. (b) Superimposition of the kurtosis distributions. Estimated for subject 10 during closed-eyes resting-state condition.

Figure 3

Searching space boundaries relative to the kurtosis limits, estimated for subject 2 (S2) in open-eyes condition. (a) At the channel level. (b) From the distribution point of view.

Figure 4

3D matrix of the segments obtained from a generic selected window ($t_W,\dots , N·t_W$) containing the DTF connectivity values among channels (Chn) at each frequency.

Figure 5

The number of channels as a function of the segment length and the searching interval in terms of the kurtosis variance. (a) S2 Open-eyes resting state. (b) S2 Closed-eyes resting state.

Figure 6

Effective connectivity diagrams considering a window of 4 s (a) for the eyes-open state and (b) for the eyes-closed state estimated for the 8–13 Hz frequency band (Alpha rhythm).

Figure 7

Effective connectivity diagrams considering a window of 20 s. (a) for the eyes-open state. (b) for the eyes-closed state estimated for the 8–13 Hz frequency band (Alpha rhythm).