  We present a computational framework for analysis and visualization of
non-linear functional connectivity in the human brain from resting state
functional MRI (fMRI) data for purposes of recovering the underlying network
community structure and exploring causality between network components. Our
proposed methodology of non-linear mutual connectivity analysis (MCA) involves
two computational steps. First, the pair-wise cross-prediction performance
between resting state fMRI pixel time series within the brain is evaluated. The
underlying network structure is subsequently recovered from the affinity matrix
constructed through MCA using non-metric network partitioning/clustering with
the so-called Louvain method. We demonstrate our methodology in the task of
identifying regions of the motor cortex associated with hand movement on
resting state fMRI data acquired from eight slice locations in four subjects.
For comparison, we also localized regions of the motor cortex through a
task-based fMRI sequence involving a finger-tapping stimulus paradigm. Finally,
we integrate convergent cross mapping (CCM) into the first step of MCA for
investigating causality between regions of the motor cortex. Results regarding
causation between regions of the motor cortex revealed a significant
directional variability and were not readily interpretable in a consistent
manner across all subjects. However, our results on whole-slice fMRI analysis
demonstrate that MCA-based model-free recovery of regions associated with the
primary motor cortex and supplementary motor area are in close agreement with
localization of similar regions achieved with a task-based fMRI acquisition.
Thus, we conclude that our computational framework MCA can extract and
visualize valuable information concerning the underlying network structure and
causation between different regions of the brain in resting state fMRI.
