Network curvature as a hallmark of brain structural connectivity

Studies show that while brain networks are remarkably robust to a variety of adverse events, such as injuries and lesions due to accidents or disease, they may be fragile when the disturbance takes place in specific locations. This seems to be the case for diseases in which accumulated changes in network topology dramatically affect certain sensitive areas. To this end, previous attempts have been made to quantify robustness and fragility of brain functionality in two broadly defined ways: (i) utilizing model-based techniques to predict lesion effects, and (ii) studying empirical effects from brain lesions due to injury or disease. Both directions aim at assessing functional connectivity changes resulting from structural network variations. In the present work, we follow a more geometric viewpoint that is based on a notion of curvature of networks, the so-called Ollivier-Ricci curvature. A similar approach has been used in recent studies to quantify financial market robustness as well as to differentiate biological networks corresponding to cancer cells from normal cells. The same notion of curvature, defined at the node level for brain networks obtained from MRI data, may help identify and characterize the effects of diseases on specific brain regions. In the present paper, we apply the Ollivier-Ricci curvature to brain structural networks to: i) Demonstrate its unique ability to identify robust (or fragile) brain regions in healthy subjects. We compare our results to previously published work which identified a unique set of regions (called structural core) of the human cerebral cortex. This novel characterization of brain networks, complementary to measures such as degree, strength, clustering or efficiency, may be particularly useful to detect and monitor candidate areas for targeting by surgery (e.g. deep brain stimulation) or pharmaco-therapeutic agents; ii) Illustrate the power our curvature-derived measures to track changes in brain connectivity with healthy development/aging and; iii) Detect changes in brain structural connectivity in people with Autism Spectrum Disorders (ASD) which are in agreement with previous morphometric MRI studies.