# Estimating effective connectivity in linear brain network models

## TL;DR

This paper introduces a novel EM-based method for estimating effective brain connectivity from resting state fMRI data, accounting for the nonlinear hemodynamic response and promoting sparse network structures.

## Contribution

It presents a new linear population model combined with an iterative EM procedure to accurately infer neuronal interactions from fMRI data, improving upon existing methods.

## Key findings

- Effective estimation of brain connectivity demonstrated on rs-fMRI data.
- Method outperforms state-of-the-art routines like SPM12.
- Sparsity in network connections is effectively enforced.

## Abstract

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 measure data, chiefly functional Magnetic Resonance Imaging (fMRI), the so-called effective connectivity in brain networks, that is the existing interactions among neuronal populations. This inverse problem is complicated by the fact that the BOLD (Blood Oxygenation Level Dependent) signal measured by fMRI represent a dynamic and nonlinear transformation (the hemodynamic response) of neuronal activity. In this paper, we consider resting state (rs) fMRI data; building upon a linear population model of the BOLD signal 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; sparsity in the interconnection structure is favoured using an iteratively reweighting scheme. Experimental results using rs-fMRI data are shown demonstrating the effectiveness of our approach and comparison with state of the art routines (SPM12 toolbox) is provided.