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Abstract There are a growing number of neuroimaging studies motivating joint structural and functional brain connectivity. Brain connectivity of different modalities provides insight into brain functional organization by leveraging complementary information, especially for brain disorders such as schizophrenia. In this paper, we propose a multi-modal independent component analysis (ICA) model that utilizes information from both structural and functional brain connectivity guided by spatial maps to estimate intrinsic connectivity networks (ICNs). Structural connectivity is estimated through whole-brain tractography on diffusion-weighted MRI (dMRI), while functional connectivity is derived from resting-state functional MRI (rs-fMRI). The proposed structural-functional connectivity and spatially constrained ICA (sfCICA) model estimates ICNs at the subject level using a multi-objective optimization framework. We evaluated our model using synthetic and real datasets (including dMRI and rs-fMRI from 149 schizophrenia patients and 162 controls). Multi-modal ICNs revealed enhanced functional coupling between ICNs with higher structural connectivity, improved modularity, and network distinction, particularly in schizophrenia. Statistical analysis of group differences showed more significant differences in the proposed model compared to the unimodal model. In summary, the sfCICA model showed benefits from being jointly informed by structural and functional connectivity. These findings suggest advantages in simultaneously learning effectively and enhancing connectivity estimates using structural connectivity. 

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.