Local and Sparse Linear Causal Models for fMRI Resting-State Signals

Modeling the human brain as a complex network (operating at many different scales) is a powerful tool to analyze both its structural and functional connections. Neuroimaging techniques, such as fMRI, capture the metabolic response to neural activity within voxels encompassing hundreds of thousands of neurons. Graph theory and graph signal processing provide a principled methodology to analyze the brain's functional interactions evidenced by the spatiotemporal patterns revealed by the neuroimaging. In this paper, we propose a methodology to identify a linear, first-order auto-regressive model describing the causal dependence among the fMRI activity on a subset of voxels. We assume the matrix of linear coefficients capturing the voxel-to-voxel interactions is a sum of two components: one low rank and one sparse. The low-rank component represents the dense local connections and the sparse component represents long-range connections that mediate or coordinate disparate brain regions. To enforce the dense connections to be local we use prior knowledge about the spatial proximity of voxels. We apply the proposed methodology on synthetic data and fMRI data captured during resting state. Our results show that the proposed methodology is able to capture causal structure explaining the variance of the resting-state activity. In particular, our methodology can predict intra-subject resting-state activity across different sessions (test-retest reliability).