Estimating effective connectivity in linear brain network models

Contemporary neuroscience has embraced network science to study the complex and self-organized structure of the human brain. One of the main outstanding issues is that of inferring, from functional magnetic resonance imaging (fMRI) data, the so-called effective connectivity in brain networks, which models the causal interactions among neuronal populations. This inverse problem is complicated by the fact that the BOLD (Blood Oxygenation Level Dependent) signal measured by fMRI is a dynamic and nonlinear function (the hemodynamic response) of neuronal activity. In this paper, we consider resting-state (rs) fMRI data: building upon a linear population model of the hemodynamic response and a stochastic linear DCM model, the model parameters are estimated through an EM-type iterative procedure, which alternately estimates the neuronal activity by means of the Rauch-Tung-Striebel (RTS) smoother, updates the connections among neuronal states and refines the parameters of the hemodynamic model. A state-of-the-art iteratively reweighted scheme is adapted to the problem to favour sparsity in the interconnection structure. Experimental results using rs-fMRI data are shown, demonstrating the effectiveness of our approach in comparison with state-of-the-art routines (SPM12 toolbox).