Characteristic functional cores revealed by hyperbolic disc embedding and k-core percolation on resting-state fMRI

Abstract

Hyperbolic disc embedding and k-core percolation reveal the hierarchical structure of functional connectivity on resting-state fMRI (rsfMRI). Using 180 normal adults’ rsfMRI data from the human connectome project database, we visualized inter-voxel relations by embedding voxels on the hyperbolic space using the $${\mathbb{S}}^{1} /{\mathbb{H}}^{2}$$ S 1 / H 2 model. We also conducted k-core percolation on 30 participants to investigate core voxels for each individual. It recursively peels the layer off, and this procedure leaves voxels embedded in the center of the hyperbolic disc. We used independent components to classify core voxels, and it revealed stereotypes of individuals such as visual network dominant, default mode network dominant, and distributed patterns. Characteristic core structures of resting-state brain connectivity of normal subjects disclosed the distributed or asymmetric contribution of voxels to the kmax-core, which suggests the hierarchical dominance of certain IC subnetworks characteristic of subgroups of individuals at rest.

Time-varying hierarchical core voxels disclosed by k-core percolation on dynamic inter-voxel connectivity resting-state fMRI

“…k -core percolation and the visualization of voxels were reported to disclose hierarchical structures of voxels (nodes) in functional intervoxel connectivity on rsfMRI ( 23 ). k max -core voxels represent the uppermost voxels on these hierarchical structures, which change upon time progression spontaneously at rest during acquisition period.…”

“…In HCP data, threshold was found to be 0.65 and in Kirby weekly, 0.8 to meet the criteria of as many voxels included but with confirmed scale-free degree distribution. The uppermost voxels were designated as k max -core voxels (23), and plotted in three ways, 1) bar plots showing numbers of k max -core voxels on animation, 2) stacked histograms DMN/SN/DAN/CEN/SMN/AN/VN/UNC k max -core voxels colored with cyan-rainbow colorsgray on animation, and 3) axial and sagittal brain-rendered images containing k max -core voxels colored the same way to their belonging to ICs and on animation (Fig. 2A cerebellar k max -core voxels mostly belonging to UNC and rarely CEN/DMN within the cerebellum (Fig.…”

“…In our previous investigation (23) and in static analysis of HCP data of this investigation, we counted the number of individuals showing VN-dominant (50% of the voxels belonging to VN), DMN/CEN co-dominant or distributed among 30 or 180 individuals, respectively. Prevalence of distributed/dominance types was presented.…”

“…The copyright holder for this preprint this version posted June 26, 2022. ; https://doi.org/10.1101/2022.06. 23.497413 doi: bioRxiv preprint intervoxel connectivity. This also enabled us to pay attention to the intervoxel anti-correlation to yield the negative-influence networks.…”

“…We recently introduced a method to observe hierarchical structure of brain functional network, revealing the characteristic core voxels disclosed by k -core percolation on the adjacency matrix of static functional intervoxel connectivity acquired by the established method using <0.1 Hz rsfMRI signals ( 23 ). k -core percolation enables disclosure of functional hierarchical position of every voxel on recursive decomposition while k values are increased and the voxels with lower degrees are removed.…”