Although brain functionality is often remarkably robust to lesions and other insults, it may be fragile when these take place in specific locations. Previous attempts to quantify robustness and fragility sought to understand how the functional connectivity of brain networks is affected by structural changes, using either model-based predictions or empirical studies of the effects of lesions. We advance a geometric viewpoint relying on a notion of network curvature, the so-called Ollivier-Ricci curvature. This approach has been proposed to assess financial market robustness and to differentiate biological networks of cancer cells from healthy ones. Here, we apply curvature-based measures to brain structural networks to identify robust and fragile brain regions in healthy subjects. We show that curvature can also be used to track changes in brain connectivity related to age and autism spectrum disorder (ASD), and we obtain results that are in agreement with previous MRI studies.
Bibliographical noteFunding Information:
T.G.) and the Fulbright Program (H.F.). Data were provided in part by the Human Connectome Project, WU-Minn Consortium (Principal Investigators: David VanEssen and Kamil Ugurbil; 1U54MH091657) funded by the 16 NIH Institutes and Centers that support the NIH Blueprint for Neuroscience Research; and by the McDonnell Center for Systems Neuroscience at Washington University. Data were also provided in part by the Human Connectome Project, MGH-USC Consortium (Principal Investigators: Bruce R. Rosen, Arthur W. Toga, and Van Wedeen; U01MH093765) funded by the NIH Blueprint Initiative for Neuroscience Research grant; the National Institutes of Health grant P41EB015896; and the Instrumentation Grants S10RR023043, 1S10RR023401, 1S10RR019307. We thank Dr. Patric Hagmann for making the connectivity matrices, published in ref. 20, freely available via the USC MultimodalConnectivity Database. We also would like to thank Dr. Eric F. Lock from the Division of Biostatistics, School of Public Health, University of Minnesota, for his input with some of the statistical analyses.
This work was partly supported by AFOSR grant FA9550-17-1-0435 (T.T.G., A.T.), NIH grants P41 EB015894 (C.L.), P41 EB027061 (C.L.), P30 NS076408 (C.L.), P41 EB015902 (A.T.), U24 CA180924 (A.T.), R01 AG048769 (A.T.), NSF grant 1665031 (H.F., Y.C., T.
© 2019, The Author(s).