Alladi Ramakrishnan Hall

Analyzing human brain functional connectivity networks using discrete Ricci curvatures

Yasharth Yadav

Division of Mathematical Sciences, Nanyang Technological University, Singapore

Functional connectivity refers to the temporal correlations between activation patterns of distinct brain regions, which can be measured using functional magnetic resonance imaging (fMRI). Recently, there has been growing interest in the geometric and topological characterization of brain connectivity. In this talk, I will present the results of two recent data-driven studies where we applied discrete Ricci curvatures, namely Forman-Ricci and Ollivier-Ricci curvature, to investigate human brain functional connectivity networks. In the first study, we used discrete Ricci curvatures to compare functional connectivity networks of individuals with autism spectrum disorder (ASD) and typically developing controls from the Autism Brain Imaging Data Exchange I (ABIDE-I) dataset. We found brain-wide ASD-related changes in functional connectivity for both Forman-Ricci and Ollivier-Ricci curvatures. Further, we found that Forman-Ricci curvature can identify potential ASD related regions in the brain and explored the functional role of these regions in ASD. Finally, we provided an external validation of our results by collecting experimental evidence from non-invasive brain stimulation studies. We showed that brain regions with curvature differences overlap with those brain regions whose non-invasive stimulation improves ASD-related symptoms. In the second study, we used discrete Ricci curvatures to compare functional connectivity networks of healthy young and old subjects from the Max Planck Institute Leipzig Study for Mind-Body-Emotion Interactions (MPI-LEMON) dataset. We found that discrete Ricci curvatures show brain-wide and region-level differences in functional connectivity related to healthy aging. Further investigation into the behavioral relevance of age-related differences revealed that curvatures can identify brain regions that are associated with the domains of movement, affective processing, and somatosensory processing. Finally, we found that curvatures can capture brain regions whose non-invasive stimulation shows evidence for improvement in motor performance of healthy older adults. Our results demonstrate the utility of discrete Ricci curvatures in identifying clinically relevant brain regions and informing future interventions for preserving cognitive function during neurodevelopmental disorders and healthy aging.

References:
[1] Elumalai, P.*, Yadav, Y.*, Williams, N., Saucan, E., Jost, J., & Samal, A. Graph Ricci curvatures reveal atypical functional connectivity in autism spectrum disorder. Sci Rep 12, 8295 (2022).
doi.org/10.1038/s41598-022-12171-y (*equal contribution)
[2] Yadav, Y., Elumalai, P., Williams, N., Jost, J., & Samal, A. Discrete Ricci curvatures capture age-related changes in human brain functional connectivity networks. Front Aging Neurosci (2023). doi.org/10.3389/fnagi.2023.1120846