The Nonlinear Brain: Towards Uncovering Hidden Brain Networks Using Explicitly Nonlinear Functional Interaction

Estimating brain functional networks has been commonly accomplished by applying independent component analysis (ICA) on activity time series collected by resting state fMRI data. Our earlier provided a showcase for the benefit of applying ICA on voxel-wise functional connectivity (FC) commonly measured by second-order statistics such as Pearson correlation instead of activity time series. However, in both cases, i.e., applying ICA on activity time series or FC maps, previous methods are designed to identify brain networks that reflect linear FC. Here, we propose an approach to capture, for the first time, brain networks that are estimated from explicitly nonlinear FC. Results show that networks (e.g., the default mode network) calculated from the linear FC have a strong footprint in explicitly nonlinear FC, and the spatial distributions of the linear and nonlinear interactions differ. In addition, nonlinear information allows us to identify new networks hidden from linear FC, highlighting the possibility of discovering additional information by incorporating nonlinear patterns.