Reconstructing multivariate causal structure between functional brain networks through a Laguerre-Volterra based Granger causality approach.

Classical multivariate approaches based on Granger causality (GC) which estimate functional connectivity in the brain are almost exclusively based on autoregressive models. Nevertheless, information available from past samples is limited due to both signal autocorrelation and necessarily low model orders. Consequently, multiple time-scales interactions are usually unaccounted for. To overcome these limitations, in this study we propose the use of discrete-time orthogonal Laguerre basis functions within a Wiener-Volterra decomposition of the BOLD signals to perform effective GC assessments of brain functional connectivity. We validate our method in synthetic noisy oscillator networks, and analyze experimental fMRI data from 30 healthy subjects publicly available within the Human Connectome Project (HCP). Synthetic results demonstrate that our Laguerre-Volterra based GC estimates outperform classical approaches in terms of accuracy in detecting true causal links while rejecting false causal links in complex nonlinear networks. Human data analysis shows for the first time that the default mode network modulates both the salience network as well as fronto-temporal circuits in a causal fashion.