Schizophrenia MEG Network Analysis Based on Kernel Granger Causality

Abstract

Network analysis is an important approach to explore complex brain structures under different pathological and physiological conditions. In this paper, we employ the multivariate inhomogeneous polynomial kernel Granger causality (MKGC) to construct directed weighted networks to characterize schizophrenia magnetoencephalography (MEG). We first generate data based on coupled autoregressive processes to test the effectiveness of MKGC in comparison with the bivariate linear Granger causality and bivariate inhomogeneous polynomial kernel Granger causality. The test results suggest that MKGC outperforms the other two methods. Based on these results, we apply MKGC to construct effective connectivity networks of MEG for patients with schizophrenia (SCZs). We measure three network features, i.e., strength, nonequilibrium, and complexity, to characterize schizophrenia MEG. Our results suggest that MEG of the healthy controls (HCs) has a denser effective connectivity network than that of SCZs. The most significant difference in the in-connectivity strength is observed in the right frontal network (p=0.001). The strongest out-connectivity strength for all subjects occurs in the temporal area, with the most significant between-group difference in the left occipital area (p=0.0018). The total connectivity strength of the frontal, temporal, and occipital areas of HCs exhibits higher values compared with SCZs. The nonequilibrium feature over the whole brain of SCZs is significantly higher than that of the HCs (p=0.012); however, the results of Shannon entropy suggest that healthy MEG networks have higher complexity than schizophrenia networks. Overall, MKGC provides a reliable approach to construct MEG brain networks and characterize the network characteristics.

Keywords: complexity; effective network; kernel Granger causality; nonequilibrium; schizophrenia MEG.

Figure 1

Layout of brain division of MEG recordings. Left frontal (LF), middle frontal (ZF), right frontal (RF), left central (LC), middle central (ZC), right central (RC), left temporal (LT), right temporal (RT), left parietal (LP), middle parietal (ZP), right parietal (RP), left occipital (LO), middle occipital (ZO), and right occipital (RO). The numbers represent the number of channels in each brain region.

Figure 2

(a) Original causal influence of 1→3, 1→4, 2→1 and 4→5 between the five coupled autoregressive processes. (b) BLGC, BKGC and MKGC of the five coupled autoregressive processes. The order of autoregression is $m=1$ chosen by the Bayesian information criterion; MKGC and BKGC analyses are performed with the IP kernel ($p=2$); and vertical bars indicate estimated standard errors.

Figure 3

Effective connectivity network at group level for HCs (a) and SCZs (b). The nodes are the 14 brain regions. The colors of the links between nodes represent the interregional causal interactions, and the arrows indicate the directions of connections. (c) The directed differential connectivity graph between HCs and SCZs ($p<0.05$). The colors of the links represent the p values obtained by the Mann–Whitney U test.

Figure 4

In-connectivity strength of brain regions. In-connectivity networks of HCs (a) and SCZs (b); the diameters of the nodes are positively related to the in-connectivity strength of the brain regions, and the colors of the links between nodes represent the causal interactions between the brain regions. (c) In-connectivity strength of brain regions (mean ± standard error); # and * indicate the statistical significance of $p<0.002$ and $p<0.05$ using the Mann–Whitney U test, respectively. (d) Brain regions with significant differences in in-connectivity strength. The fill color represents the p value obtained by the Mann–Whitney U test.

Figure 5

Out-connectivity strength of brain regions. Out-connectivity networks of HCs (a) and SCZs (b). The diameters of the nodes are positively related to the out-connectivity strengths of the brain regions and the colors of the links between nodes represent the interregional causal interactions. (c) The out-connectivity strength of brain regions (mean ± standard error); # and * indicate the statistical significance of $p<0.002$ and $p<0.05$ using the Mann–Whitney U test, respectively. (d) Brain regions with significant differences in out-connectivity strengths. The fill color represents the p value obtained by the Mann–Whitney U test.

Figure 6

Total connectivity strength of brain regions. Total connectivity networks of HCs (a) and SCZs (b). The diameters of the nodes are positively related to the total connectivity strength of the brain regions, and the colors of the links between nodes represent the causal interactions between the brain regions. (c) Total connectivity strength of brain regions (mean ± standard error). △ and * indicate the statistical significance of $p<0.005$ and $p<0.05$ using the Mann–Whitney U test, respectively. (d) Brain regions with significant differences in total connectivity strength. The fill color represents the p value obtained by the Mann–Whitney U test.

Figure 7

(a) Brain regional probabilistic difference $Y_{S_{-}}L$ of causal interactions (mean ± standard error). △ and * indicate the levels of significance ($p<0.005$ and $p<0.05$) of the probabilistic difference across groups using the Mann–Whitney U test. (b) Brain regions with significant differences in $Y_{S_{-}}L$. The fill color represents the p value obtained by the Mann–Whitney U test.

Figure 8

Nonequilibrium (mean ± standard error) of the MEG network constructed by MKGC over the whole brain for HCs and SCZs. The p value ($p=0.012$) is obtained by the Mann–Whitney U test.

Figure 9

Shannon entropy of HCs’ and SCZs’ networks. (a) Shannon entropy of in-connectivity strength (mean ± standard error). (b) Shannon entropy of out-connectivity strength (mean ± standard error). p values are obtained by the Mann–Whitney U test.