Brain connectivity alteration detection via matrix-variate differential network model

Abstract

Brain functional connectivity reveals the synchronization of brain systems through correlations in neurophysiological measures of brain activities. Growing evidence now suggests that the brain connectivity network experiences alterations with the presence of numerous neurological disorders, thus differential brain network analysis may provide new insights into disease pathologies. The data from neurophysiological measurement are often multidimensional and in a matrix form, posing a challenge in brain connectivity analysis. Existing graphical model estimation methods either assume a vector normal distribution that in essence requires the columns of the matrix data to be independent or fail to address the estimation of differential networks across different populations. To tackle these issues, we propose an innovative matrix-variate differential network (MVDN) model. We exploit the D-trace loss function and a Lasso-type penalty to directly estimate the spatial differential partial correlation matrix and use an alternating direction method of multipliers algorithm for the optimization problem. Theoretical and simulation studies demonstrate that MVDN significantly outperforms other state-of-the-art methods in dynamic differential network analysis. We illustrate with a functional connectivity analysis of an attention deficit hyperactivity disorder dataset. The hub nodes and differential interaction patterns identified are consistent with existing experimental studies.

Keywords: brain network; differential network analysis; fMRI; graphical model; matrix data; variable selection.

Figure 1.

Illustration of brain connectivity analysis: (A) Brain imaging data; (B) Matrix data; (C) Correlation structure; (D) Brain connectivity network; ➀ indicates directly estimating the differential network, i.e., the different of two precision matrices; ➁ and ➂ indicates separately estimating the connectivity network. This figure appears in color in the electronic version of this article, and any mention of color refers to that version.

Figure 2.

Three types of graph used in our simulation studies: (A) Hub graph; (B) Scale-free graph; (C) Small-world graph. This figure appears in color in the electronic version of this article, and any mention of color refers to that version.

Figure 3.

ROC curve (upper panels) and Precision-Recall curve (lower panels) for Scenario 1 with p = 50, 100, 300 and autoregressive temporal covariance structure. Solid, dotted, dashed, dot-and-dash, and long dashed lines represent MVDN, the convex method, the non-convex method, GLASSO and CLIME respectively. The sample size n₁ = n₂ = 20 and q = 50. This figure appears in color in the electronic version of this article, and any mention of color refers to that version.

Figure 4.

ROC curve (upper panels) and Precision-Recall curve (lower panels) for Scenario 2 with p = 50, 100, 300 and autoregressive temporal covariance structure. Solid, dotted, dashed, dot-and-dash, and long dashed lines represent MVDN, the convex method, the non-convex method, GLASSO and CLIME respectively. The sample size n₁ = n₂ = 20 and q = 50. This figure appears in color in the electronic version of this article, and any mention of color refers to that version.

Figure 5.

ROC curve (upper panels) and Precision-Recall curve (lower panels) for for Scenario 3 with p = 50, 100, 300 and autoregressive temporal covariance structure. Solid lines represent MVDN, dotted lines represent convex method, dashed lines represent non-convex method, dot-and-dash lines represent GLASSO, and long dashed lines represent CLIME. The sample size n₁ = n₂ = 20 and q = 50. This figure appears in color in the electronic version of this article, and any mention of color refers to that version.

Figure 6.

Differential edges and the associated brain regions identified by various procedures for the ADHD resting-state fMRI data. (A)-(C) corresponds to the MVDN method, (D)-(F) corresponds to the non-convex method and (G)-(I) corresponds to the convex method. Orange edges show an increase in partial correlation dependency from TDC group to ADHD group; grey edges show a decrease. This figure appears in color in the electronic version of this article, and any mention of color refers to that version.