Explicitly Nonlinear Dynamic Functional Network Connectivity In Resting-State fMRI Data

Most dynamic functional connectivity in fMRI data is focused on linear correlations, and to our knowledge, no study has studied whole brain explicitly nonlinear dynamic relationships within the data. While some approaches have attempted to study overall connectivity more generally using flexible models, we are particularly interested in whether the non-linear relationships, above and beyond linear, are capturing unique information. This study thus proposes an approach to assess the explicitly nonlinear dynamic functional network connectivity derived from the relationship among independent component analysis time courses. Linear relationships were removed at each time point to evaluate, typically ignored, explicitly nonlinear dFNC using normalized mutual information. Simulations showed the proposed method accurately estimated NMI over time, even within relatively short windows of data. Results on fMRI data included 151 schizophrenia patients, and 163 healthy controls showed three unique, highly structured, mostly long-range, functional states that also showed significant group differences. This analysis identifies a higher level of explicitly nonlinear dependencies in transient connectivity within the visual network in healthy controls compared to schizophrenia patients. In particular, nonlinear relationships tend to be more widespread than linear ones. We also find highly significant differences in the relative co-occurrence of linear and explicitly nonlinear states in HC and SZ, suggesting these may be an important aspect of the disorder. Overall, this work suggests that quantifying nonlinear dependencies of dynamic functional connectivity may provide a complementary and potentially valuable tool for studying brain function by exposing relevant variation that is typically ignored. ### Competing Interest Statement The authors have declared no competing interest.