Nonlinear brain connectivity from neurons to networks: quantification, sources and localization
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Abstract
Connectivity is a widespread tool for the study of complex systems’ dynamics. Since the first studies in functional connectivity, Pearson’s 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 Pearson’s 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.
In 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 Pearson’s 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.
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This Zenodo record is a permanently preserved version of a PREreview. You can view the complete PREreview at https://prereview.org/reviews/14286180.
Raffaeli and colleagues present a systematic comparison of linear versus nonlinear bivariate dependency structures in the brain across spatial and temporal scales in both human and mouse.
Major issues
An old and heuristic method for computing mutual information is used (equiprobable binning) despite fast, sophisticated modern methods exist for continuous data, but these are not quantitatively compared to their binning approach. cf. https://github.com/jlizier/jidt for an open implementation.
It's unclear whether the heuristic to decompose MI through ratios is theoretically valid.
Previous work has indeed compared linear vs. nonlinear coupling metrics in fMRI and other modalities, contrary to …
This Zenodo record is a permanently preserved version of a PREreview. You can view the complete PREreview at https://prereview.org/reviews/14286180.
Raffaeli and colleagues present a systematic comparison of linear versus nonlinear bivariate dependency structures in the brain across spatial and temporal scales in both human and mouse.
Major issues
An old and heuristic method for computing mutual information is used (equiprobable binning) despite fast, sophisticated modern methods exist for continuous data, but these are not quantitatively compared to their binning approach. cf. https://github.com/jlizier/jidt for an open implementation.
It's unclear whether the heuristic to decompose MI through ratios is theoretically valid.
Previous work has indeed compared linear vs. nonlinear coupling metrics in fMRI and other modalities, contrary to the statement "A principled approach for its quantification in terms of extra-Gaussian information has so far only been applied to a single modality ([10])" cf.:
Nozari et al. (2023) https://www.nature.com/articles/s41551-023-01117-y
Blinowski & Malinowski (1991): https://link.springer.com/article/10.1007/BF00243291
Zhao et al. (2013): https://ieeexplore.ieee.org/document/6542649/
Important work explaining why measured brain dynamics may become more linear (e.g., when averaging across space/time) is missing: e.g.:
Nozari et al. (2023) https://www.nature.com/articles/s41551-023-01117-y
Messe et al. (2015) http://dx.doi.org/10.1016/j.neuroimage.2015.02.001
Important context on methods for computing pairwise dependence (beyond MI and Pearson correlation) is missing, e.g.,:
Smith et al. (2011): http://linkinghub.elsevier.com/retrieve/pii/S1053811910011602
Liu et al. (2024): https://www.biorxiv.org/content/10.1101/2024.05.07.593018v1
Mohanty et al. (2020): https://www.nature.com/articles/s41598-020-57915-w
Prado et al. (2023): https://www.sciencedirect.com/science/article/pii/S096999612300061X
Cliff et al. (2023): https://www.nature.com/articles/s43588-023-00519-x
Minor issues
Concepts of "Gaussianity" and "linearity" are distinct but are not clearly distinguished (~L178), when it is important to do so.
Competing interests
The authors declare that they have no competing interests.
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