Unveiling the robustness and utility of nonlinear functional connectivity in resting-state fMRI

Increasing attention has been paid to the nonlinear functional activity of human brain regions. This paper extends Chatterjee's correlation coefficient (CCC) method to model nonlinear relationships in brain functional networks explicitly. Specifically, the reliability and effectiveness comparisons between CCC and the Pearson correlation coefficient (PCC) are demonstrated using simulated data and two real resting-state functional magnetic resonance imaging (rs-fMRI) datasets: The Midnight Scan Club dataset and the UCLA dataset. The results demonstrate that CCC accounts for both linear and nonlinear dependencies and that its reliability is better than that of PCC. Additionally, from a whole-brain perspective, the number of connections in different brain regions was observed in the following order: bipolar disorder (BP) and healthy controls (HC) > adult attention-deficit/hyperactivity disorder (ADHD) and HC > schizophrenia (SZ) and HC. The commonalities among the three psychiatric disorders compared to HC were differences in occipital, default, cerebellum, and the regions connected to the occipital. Besides, using CCC: occipital performed classification best (AUC: 0.657) between ADHD and HC, and (AUC: 0.622) between BP and HC, but fronto_parietal performed classification best (AUC: 0.700) between SZ and HC. This method enhances sensitivity to group differences and may provide new insights for exploring functional networks based on fMRI in the future.