Both k-core percolation and directed graph analysis revealed succession and transition of voxels' spatiotemporal progress on dynamic correlation resting-state fMRI

Abstract

Introduction: Voxel hierarchy on dynamic brain graphs is produced by k-core percolation on functional dynamic amplitude correlation of resting-state fMRI.

Methods: Directed graphs and their afferent/efferent capacities are produced by Markov modeling of the universal cover of undirected graphs simultaneously with the calculation of volume entropy. Using these methods, state stationarity was tested for resting-state positive and unsigned negative brain graphs separately on sliding-window representation. The spatiotemporal progress of voxels was visualized and quantified.

Results and discussion: The voxel hierarchy of positive graphs revealed abrupt changes in coreness k (k-core) and maximum k-core (kmaxcore) voxels on animation maps representing state transitions interspersed among the succession. Afferent voxel capacities of the positive graphs revealed transient modules composed of dominant voxels and independent components as well as their exchanges compatible with transitions. Moreover, this voxel hierarchy and afferent capacity corroborated each other only on the positive directed functional connectivity graphs but not on the unsigned negative graphs. The Spatiotemporal progression of voxels on positive dynamic graphs constructed a hierarchy by k-core percolation and afferent information flow by volume entropy and directed graph methods. We disclosed the non-stationarity and its temporal progress pattern at rest, accompanied by diverse resting-state transitions on resting-state fMRI graphs in normal human subjects.

Keywords: afferent node capacity; graph node hierarchy; information flow; k-core percolation; resting-state fMRI; state transition; volume entropy.