Modeling sparse connectivity between underlying brain sources for EEG/MEG

A. Functional brain connectivity The analysis of neural connectivity plays a crucial role for understanding the general functioning of the brain. In the past two decades such analysis has become possible thanks to tremendous progress that has been made in the fields of neuroimaging and mathematical modeling. Today, a multiplicity of imaging modalities exists, allowing to monitor brain dynamics at different spatial and temporal scales. Given multiple simultaneously-recorded time-series reflecting neural activity in different brain regions, a functional (taskrelated) connection (sometimes also called information flow or (causal) interaction in this paper) between two regions is commonly inferred, if a significant time-lagged influence between the corresponding time-series is found. Different measures have been proposed for quantifying this influence, most of them being formulated either in terms of the cross-spectrum (e.g., coherence, phase slope index [1]) or an autoregressive models (e.g., Granger causality [2], directed transfer function [3], partial directed coherence [4], [5]). B. Volume conduction problem in EEG and MEG In electroencephalography (EEG) and magnetoencephalography (MEG), sensors are placed outside the head and the problem of volume conduction arises. That is, rather than measuring activity of only one brain site, each sensor captures a linear superposition of signals from all over the brain. This mixing introduces instantaneous correlations in the data, which can cause traditional analyses to detect spurious connectivity [6].