While standard graph-theoretic measures have been widely used to characterize atypical resting-state functional connectivity in autism spectrum disorder (ASD), geometry-inspired network measures have not been applied. In this study, we apply Forman–Ricci and Ollivier–Ricci curvatures to compare networks of ASD and typically developing individuals (N = 1112) from the Autism Brain Imaging Data Exchange I (ABIDE-I) dataset. We find brain-wide and region-specific ASD-related differences for both Forman–Ricci and Ollivier–Ricci curvatures, with region-specific differences concentrated in Default Mode, Somatomotor and Ventral Attention networks for Forman–Ricci curvature. We use meta-analysis decoding to demonstrate that brain regions with curvature differences are associated to those cognitive domains known to be impaired in ASD. Further, we show that brain regions with curvature differences overlap with those brain regions whose non-invasive stimulation improves ASD-related symptoms. These results suggest the utility of graph Ricci curvatures in characterizing atypical connectivity of clinically relevant regions in ASD and other neurodevelopmental disorders.

Geometry-inspired notions of discrete Ricci curvature have been successfully used as markers of disrupted brain connectivity in neuropsychiatric disorders, but their ability to characterize age-related changes in functional connectivity is unexplored. Here, we apply Forman-Ricci curvature and Ollivier-Ricci curvature to compare functional connectivity networks of healthy young and older subjects from the Max Planck Institute Leipzig Study for Mind-Body-Emotion Interactions (MPI-LEMON) dataset (N= 225). We found that both Forman-Ricci curvature and Ollivier-Ricci curvature can capture whole-brain and region-level age-related differences in functional connectivity. Meta-analysis decoding demonstrated that those brain regions with age-related curvature differences were associated with cognitive domains known to manifest age-related changes – movement, affective processing and somatosensory processing. Moreover, the curvature values of some brain regions showing age-related differences exhibited correlations with behavioral scores of affective processing. Finally, we found an overlap between brain regions showing age-related curvature differences and those brain regions whose non-invasive stimulation resulted in improved movement performance in older adults. These results suggest that both Forman-Ricci curvature and Ollivier-Ricci curvature correctly identify brain regions that are known to be functionally or clinically relevant. Our results add to a growing body of evidence demonstrating the sensitivity of discrete Ricci curvature measures to changes in the organisation of functional connectivity networks, both in health and disease.

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.

IntroductionGeometry-inspired notions of discrete Ricci curvature have been successfully used as markers of disrupted brain connectivity in neuropsychiatric disorders, but their ability to characterize age-related changes in functional connectivity is unexplored.MethodsWe apply Forman-Ricci curvature and Ollivier-Ricci curvature to compare functional connectivity networks of healthy young and older subjects from the Max Planck Institute Leipzig Study for Mind-Body-Emotion Interactions (MPI-LEMON) dataset (N = 225).ResultsWe found that both Forman-Ricci curvature and Ollivier-Ricci curvature can capture whole-brain and region-level age-related differences in functional connectivity. Meta-analysis decoding demonstrated that those brain regions with age-related curvature differences were associated with cognitive domains known to manifest age-related changes—movement, affective processing, and somatosensory processing. Moreover, the curvature values of some brain regions showing age-related differences exhibited correlations with behavioral scores of affective processing. Finally, we found an overlap between brain regions showing age-related curvature differences and those brain regions whose non-invasive stimulation resulted in improved movement performance in older adults.DiscussionOur results suggest that both Forman-Ricci curvature and Ollivier-Ricci curvature correctly identify brain regions that are known to be functionally or clinically relevant. Our results add to a growing body of evidence demonstrating the sensitivity of discrete Ricci curvature measures to changes in the organization of functional connectivity networks, both in health and disease.