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In this work, we focus on explicitly nonlinear relationships in functional networks. We introduce a technique using normalized mutual information (MI), that calculates the nonlinear correlation between different brain regions. We demonstrate our proposed approach using simulated data, then apply it to a dataset previously studied in (Damaraju et al., 2014). 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 nonlinear dependencies between schizophrenia patients and healthy controls particularly in visual cortex, with controls showing more nonlinearity in most cases. Certain domains, including cognitive control, and default mode, appeared much less nonlinear, 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.Further, we propose a method that captures both linear and nonlinear effects in a ‘boosted’ approach. This method increases the sensitivity to group differences in comparison to the standard linear approach, at the cost of being unable to separate linear and nonlinear effects. |
