Nonlinear brain connectivity from neurons to networks: quantification, sources and localization
This article has been Reviewed by the following groups
Listed in
- Evaluated articles (PREreview)
Abstract
Since the first studies in functional connectivity, Pearson’s correlation has been the primary tool to determine relatedness between the activity of different brain locations. Over the years, concern over the information neglected by correlation pushed toward using different measures accounting for non-linearity. However, some studies suggest that, at the typical observation scale, a linear description of the brain captures a vast majority of the information. Therefore, we measured the fraction of information that would be lost using a linear description and which regions would be affected the most. We considered fMRI, EEG, iEEG, and single unit spikes to assess how the observation scale impacts the amount of non-linearity. We observe that the information loss is reduced 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 for most human applications, Pearson’s correlation coefficient adequately describes pairwise interactions in time series from current recording techniques.
In neuroimaging, as in other complex systems fields, the increasing interest in network inference by statistical dependencies (i.e. functional connectivity) invites advanced ways to quantify it. Various nonlinear measures, ultimately the Mutual Information, are used as alternatives to conventional linear Pearson’s correlation coefficient. We systematically assess the amount and reliability of detectable non-linearity of brain functional connectivity across imaging modalities and spatial scales. We demonstrate more pronounced nonlinearity in micro-scale recordings, while rather limited and unreliable in more accessible, noninvasive, large-scale modalities: functional magnetic resonance imaging and scalp electro-physiology. This fundamentally supports the use of robust and easily interpretable linear tools in large-scale neuroimaging, and important insights concerning the microscale connectivity nonlinearity, including the link to brain state dynamics.
Article activity feed
-
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.
-
