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

Dong Soo Lee ^1* Hyun Joo Kim ² Youngmin Huh ¹ Yeon Koo Kang ¹ Wonseok Whi ¹ Hyekyoung Lee ¹ Hyejin Kang ¹

• ¹ Seoul National University, Seoul, Republic of Korea
• ² Korea University, Seoul, Republic of Korea

Voxel hierarchy on dynamic brain graphs is produced by k core percolation on functional dynamic amplitude correlation of resting-state fMRI. 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. Spatiotemporal progress of voxels was visualized and quantified. Voxel hierarchy of positive graphs revealed abrupt changes in coreness k and kmaxcore on animation maps representing state transitions interspersing among the succession. Afferent voxel capacities of the positive graphs revealed transient modules composed of dominating voxels/independent components and their exchanges compatible with transitions. Moreover, these voxel hierarchy and afferent capacity corroborated each other only on the positive directed functional connectivity graphs but not on the unsigned negative graphs. Spatiotemporal progress of voxels on positive dynamic graphs constructed the hierarchy by k core percolation and afferent information flow by volume entropy/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 individuals.