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Abstract In this work, we focus on explicitly nonlinear relationships in functional networks. We introduce a technique using normalized mutual information (NMI) that calculates the nonlinear relationship between different brain regions. We demonstrate our proposed approach using simulated data and then apply it to a dataset previously studied by Damaraju et al. This resting‐state fMRI data included 151 schizophrenia patients and 163 age‐ and gender‐matched healthy controls. We first decomposed these data using group independent component analysis (ICA) and yielded 47 functionally relevant intrinsic connectivity networks. Our analysis showed a modularized nonlinear relationship among brain functional networks that was particularly noticeable in the sensory and visual cortex. Interestingly, the modularity appears both meaningful and distinct from that revealed by the linear approach. Group analysis identified significant differences in explicitly nonlinear functional network connectivity (FNC) between schizophrenia patients and healthy controls, particularly in the visual cortex, with controls showing more nonlinearity (i.e., higher normalized mutual information between time courses with linear relationships removed) in most cases. Certain domains, including subcortical and auditory, showed relatively less nonlinear FNC (i.e., lower normalized mutual information), whereas links between the visual and other domains showed evidence of substantial nonlinear and modular properties. Overall, these results suggest that quantifying nonlinear dependencies of functional connectivity may provide a complementary and potentially important tool for studying brain function by exposing relevant variation that is typically ignored. Beyond this, we propose a method that captures both linear and nonlinear effects in a “boosted” approach. This method increases the sensitivity to group differences compared to the standard linear approach, at the cost of being unable to separate linear and nonlinear effects.
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This content will become publicly available on June 12, 2026
Providing context: Extracting non-linear and dynamic temporal motifs from brain activity
Approaches studying the dynamics of resting-state functional magnetic resonance imaging (rs-fMRI) activity often focus on time-resolved functional connectivity (tr-FC). While many tr-FC approaches have been proposed, most are linear approaches, e.g. computing the linear correlation at a timestep or within a window. In this work, we propose to use a generative non-linear deep learning model, a disentangled variational autoencoder (DSVAE), that factorizes out window-specific (context) information from timestep-specific (local) information. This has the advantage of allowing our model to capture differences at multiple temporal scales. We find that by separating out temporal scales our model’s window-specific embeddings, or as we refer to them, context embeddings, more accurately separate windows from schizophrenia patients and control subjects than baseline models and the standard tr-FC approach in a low-dimensional space. Moreover, we find that for individuals with schizophrenia, our model’s context embedding space is significantly correlated with both age and symptom severity. Interestingly, patients appear to spend more time in three clusters, one closer to controls which shows increased visual-sensorimotor, cerebellar-subcortical, and reduced cerebellar-visual functional network connectivity (FNC), an intermediate station showing increased subcortical-sensorimotor FNC, and one that shows decreased visual-sensorimotor, decreased subcortical-sensorimotor, and increased visual-subcortical domains. We verify that our model captures features that are complementary to - but not the same as - standard tr-FC features. Our model can thus help broaden the neuroimaging toolset in analyzing fMRI dynamics and shows potential as an approach for finding psychiatric links that are more sensitive to individual and group characteristics.
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- PAR ID:
- 10600765
- Editor(s):
- Giove, Federico
- Publisher / Repository:
- plos
- Date Published:
- Journal Name:
- PLOS One
- Volume:
- 20
- Issue:
- 6
- ISSN:
- 1932-6203
- Page Range / eLocation ID:
- e0324066
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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