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Graph Ricci Curvatures Reveal Disease-related Changes in Autism Spectrum Disorder
Pavithra Elumalai, Yasharth Yadav, Nitin Williams, Emil Saucan, Jürgen Jost and Areejit Samal
Autism Spectrum Disorder (ASD) is a set of neurodevelopmental disorders that pose a significant global health burden. Measures from graph theory have been used to characterise ASD-related changes in resting-state fMRI functional connectivity networks (FCNs), but recently developed geometry-inspired measures have not been applied so far. In this study, we applied geometry-inspired graph Ricci curvatures to investigate ASD-related changes in resting-state fMRI FCNs. To do this, we applied Forman-Ricci and Ollivier-Ricci curvatures to compare networks of ASD and healthy controls (N = 1112) from the Autism Brain Imaging Data Exchange I (ABIDE-I) dataset. We performed these comparisons at the brain-wide level as well as at the level of individual brain regions, and further, determined the behavioral relevance of region-specific differences with Neurosynth meta-analysis decoding. We found brain-wide ASD-related differences for both Forman-Ricci and Ollivier-Ricci curvatures. For Forman-Ricci curvature, these differences were distributed across 83 of the 200 brain regions studied, and concentrated within the Default Mode, Somatomotor and Ventral Attention Network. Meta-analysis decoding identified the brain regions showing curvature differences as involved in social cognition, memory, language and movement. Notably, comparison with results from previous non-invasive stimulation (TMS/tDCS) experiments revealed that the set of brain regions showing curvature differences overlapped with the set of brain regions whose stimulation resulted in positive cognitive or behavioural outcomes in ASD patients. These results underscore the utility of geometry-inspired graph Ricci curvatures in characterising disease-related changes in ASD, and possibly, other neurodevelopmental disorders.