Nonlinear brain connectivity from neurons to networks: quantification, sources and localization.

Connectivity is a widespread tool for the study of complex systems dynamics. Since the first studies in functional connectivity, Pearsons correlation has been the primary tool to determine interdependencies in the activity at different brain locations. Over the years, concern over the information neglected by correlation has pushed toward using different measures accounting for non-linearity. However, one may pragmatically argue that, at the most common clinical observation scales, a linear description of the brain captures a vast majority of the information. Therefore, we measured the fraction of information disregarded using a linear description and which regions would be most affected. To assess how the spatial and temporal observation scale impacts the amount of non-linearity across multiple orders of magnitude, we considered fMRI, EEG, iEEG, and single-unit spikes. We observe that by treating the system as linear, the information loss is relatively mild for modalities with large temporal or spatial averaging (fMRI and EEG) and gains relevance on more fine descriptions of the activity (iEEG and single unit spikes). We conclude that Pearsons correlation coefficient adequately describes pairwise interactions in time series from current recording techniques for most non-invasive human applications. At the same time, microscale (typically invasive) measurements might be a more suitable field for mining information on nonlinear interactions. Significance StatementIn complex systems research, including neuroscience, the ubiquitous interest in network characterization by statistical dependencies (functional connectivity) invites increasingly sophisticated approaches. Various nonlinear measures, ultimately Mutual Information, emerge as alternatives to the conventional linear Pearsons correlation coefficient. To fundamentally inform such decisions, we systematically assess the amount and reliability of non-linearity of brain functional connectivity across imaging modalities and spatial and temporal scales. We demonstrate more pronounced non-linearity in microscale recordings, while it is limited and unreliable in more accessible, non-invasive, large-scale modalities: functional magnetic resonance imaging and scalp electrophysiology. This result fundamentally supports the use of robust and easily interpretable linear tools in large-scale neuroimaging and brings essential insights concerning the non-linearity of microscale connectivity, including the link to brain state dynamics.