Nonlinear functional network connectivity in resting functional magnetic resonance imaging data

Sara M. Motlaghian, Aysenil Belger, Juan R. Bustillo, Judith M. Ford, Armin Iraji, Kelvin Lim, Daniel H. Mathalon, Bryon A. Mueller, Daniel O'Leary, Godfrey Pearlson, Steven G. Potkin, Adrian Preda, Theo G.M. van Erp, Vince D. Calhoun

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)4556-4566
Number of pages11
JournalHuman Brain Mapping
Issue number15
StatePublished - Oct 15 2022

Bibliographical note

Funding Information:
This study was funded by NIH grants R01MH118695, R01MH123610, R01EB006841 and NSF grant #2112455.

Publisher Copyright:
© 2022 The Authors. Human Brain Mapping published by Wiley Periodicals LLC.


  • functional network connectivity
  • mutual information
  • nonlinear functional network connectivity
  • time courses


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