A method for estimating and characterizing explicitly nonlinear dynamic functional network connectivity in resting-state fMRI data

The past 10 years have seen an explosion of approaches that focus on the study of time-resolved change in functional connectivity (FC). FC characterization among networks at a whole-brain level is frequently termed functional network connectivity (FNC). Time-resolved or dynamic functional network connectivity (dFNC) focuses on the estimation of transient, recurring, whole-brain patterns of FNC. While most approaches in this area have attempted to capture dynamic linear correlation, we are particularly interested in whether explicitly nonlinear relationships, above and beyond linear, are present and contain unique information. This study thus proposes an approach to assess explicitly nonlinear dynamic functional network connectivity (EN dFNC) 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 (NMI). Simulations showed the proposed method estimated explicitly nonlinearity over time, even within relatively short windows of data. We then, applied our approach on 151 schizophrenia patients, and 163 healthy controls fMRI data and found three unique, highly structured, mostly long-range, functional states that also showed significant group differences. In particular, explicitly nonlinear relationships tend to be more widespread than linear ones. Results also highlighted a state with long range connections to the visual domain, which were significantly reduced in schizophrenia. Overall, this work suggests that quantifying EN dFNC may provide a complementary and potentially valuable tool for studying brain function by exposing relevant variation that is typically ignored.