Zhongliang Zu^{1}, Yu Zhao^{1}, Yurui Gao^{1}, Muwei Li^{1}, Zhaohua Ding^{1}, and John C Gore^{1}

^{1}Vanderbilt University Medical Center, Nashville, TN, United States

We describe a novel graph analysis that includes a multigraph with multiple edges between a pair of nodes to model brain functional networks, and introduce a three-way correlation between BOLD signals from a pair of gray matter volumes (nodes) and one white matter bundle to define functional connectivity. Characteristics of inter-nodal communication may be derived from this analysis. By examining selected databases, we show inter-nodal communications vary with ages. By integrating fMRI signals from white matter as a third component in network analysis, more comprehensive descriptions of brain function may be obtained.

1. Ding ZH, Xu R, Bailey SK, et al. Visualizing functional pathways in the human brain using correlation tensors and magnetic resonance imaging. Magn Reson Imaging. 2016;34:8-17

2. Ding ZH, Huang YL, Bailey SK, et al. Detection of synchronous brain activity in white matter tracts at rest and under functional loading. P Natl Acad Sci USA. 2018;115:595-600

3. Lancaster JL, Woldorff MG, Parsons LM, et al. Automated talairach atlas labels for functional brain mapping. Human Brain Mapping. 2000;10:120-131

4. Oishi K, Faria A, Jiang H, et al. Atlas-based whole brain white matter analysis using large deformation diffeomorphic metric mapping: Application to normal elderly and alzheimer's disease participants. NeuroImage. 2009;46:486-499

5. Xia MR, Wang JH, He Y. Brainnet viewer: A network visualization tool for human brain connectomics. Plos One. 2013;8

Fig. 1 (a) Illustration of the structure of the multigraph
for analyzing brain functional connectivity considering both GM cortical areas
and WM bundles (blue lines indicate the edges). (b) The three-dimensional
GM-WM-GM correlation graph produced by the triple-wise correlation analysis.

Fig. 2 Simulated twCC for full triple-wise connections
(#1, the time courses for a pair of GM cortical areas and one WM bundle are the
same), no triple-wise and no pair-wise connections (#2, the three time courses
are different), no triple-wise but with pair-wise connections (#3), and partial
triple-wise connections (#4, there are common components in the GM cortical
areas and WM bundle), respectively. The average twCC of 1000 datasets for #1-#4
are 1, 0.04 0.03, 0.67, respectively. Note that the triple-wise correlation can
reflect the common component among the three parts.

Fig. 3 (a) Pattern CC between the 2D graph and the GM-GM
correlation map. (b-i) shows the normalized 2D graphs or maps (left) and its
corresponding brain network (right) for several representative WM bundles and
the conventional GM-GM correlation. Red nodes in the brain networks show the
hubs with degree higher than their mean plus standard deviation. The
corresponding WM bundles were also drawn in each brain network.

Fig. 4 (a) Pattern CC of the normalized 2D graphs for each
WM bundle (#1-48 of x-axis) and of the conventional GM-GM CC map, WM-WM CC map,
and the GM-WM CC map (#49, #50, #51 of x-axis) between the Age30, Age40, Age50,
Age60, Age70, and the control Age20. (b) shows the normalized 2D graphs and
their corresponding brain networks for WM bundle Fornix (column and body of
fornix) (FX). (c) shows the GM-GM correlation map and its corresponding brain
networks. (d) and (e) show the GM-WM correlation map and the WM-WM correlation
map, respectively.

DOI: https://doi.org/10.58530/2022/3322