Measuring the Non-linear Directed Information Flow in Schizophrenia by Multivariate Transfer Entropy

Abstract

People living with schizophrenia (SCZ) experience severe brain network deterioration. The brain is constantly fizzling with non-linear causal activities measured by electroencephalogram (EEG) and despite the variety of effective connectivity methods, only few approaches can quantify the direct non-linear causal interactions. To circumvent this problem, we are motivated to quantitatively measure the effective connectivity by multivariate transfer entropy (MTE) which has been demonstrated to be able to capture both linear and non-linear causal relationships effectively. In this work, we propose to construct the EEG effective network by MTE and further compare its performance with the Granger causal analysis (GCA) and Bivariate transfer entropy (BVTE). The simulation results quantitatively show that MTE outperformed GCA and BVTE under varied signal-to-noise conditions, edges recovered, sensitivity, and specificity. Moreover, its applications to the P300 task EEG of healthy controls (HC) and SCZ patients further clearly show the deteriorated network interactions of SCZ, compared to that of the HC. The MTE provides a novel tool to potentially deepen our knowledge of the brain network deterioration of the SCZ.

Keywords: bivariate transfer entropy; granger causality; multivariate transfer entropy; network deterioration; non-linear causal interaction; schizophrenia.

Figure 1

Estimation of MTE into a target node Y. Blue arrows show the estimation of MTE into a target node.

Figure 2

Original or predefined 8 nodes simulated network and estimated linear networks by GCA, MTE, and BVTE with Y = A × B.

Figure 3

Original or predefined 8 nodes simulated network and estimated non-linear networks by GCA, MTE, and BVTE with (r = f (x), $r=\frac{(2.40\times 9x)}{1+\text{exp}(-4x)}$).

Figure 4

Original or predefined 8 nodes simulated network and estimated non-linear networks by GCA, MTE, and BVTE with r = S (x), $r=\frac{1}{(1+\text{exp}(-x))}$.

Figure 5

Original or predefined 7 nodes simulated network and estimated linear networks by GCA, MTE, and BVTE with Y = A × B.

Figure 6

Original or predefined 7 nodes simulated network and estimated non-linear networks by GCA, MTE, and BVTE with (r = f (x), $r=\frac{(2.40\times 9x)}{1+\text{exp}(-4x)}$).

Figure 7

Original or predefined 7 nodes simulated network and estimated non-linear networks by GCA, MTE, and BVTE with r = S (x), $r=\frac{1}{(1+\text{exp}(-x))}$.

Figure 8

The timeline of a given P300 trial. In each P300 trail, a 750-ms cue, 150-ms stimulus, and 1,000-ms break were added. The squares and circles with a thin cross in the center represent the standard and target stimuli in that order.

Figure 9

Statistical analysis for the differential network topology between the HC and SCZ estimated by the GCA (A,B) and MTE (C,D). The first column depicts that the connectivity of HC is stronger than that of SCZ, whereas the second column depicts that the connectivity of SCZ is lesser or weaker than that of HC. In each subfigure, the red and green lines depict bidirectional and unidirectional connectivity, respectively.

Figure 10

Statistical comparison for the topographical difference between HCs and SCZ using out degree, estimated by the GCA (A,B) and MTE (C,D). The first column depicts the connectivity of HC is stronger than that of SCZ, whereas the second column depicts the connectivity of SCZ is weaker than that of HC.