Graph Ricci curvatures reveal atypical functional connectivity in autism spectrum disorder

Abstract

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.

Discrete Ricci curvatures capture age-related changes in human brain functional connectivity networks

“…Using a sparsity-based filtering approach ensures that the resulting FCNs for different subjects have the same number of edges, which enables a direct mathematical comparison of discrete Ricci curvatures and other network properties across subjects [59–61]. We remark that such a two-step procedure with MST followed by sparsity-based thresholding was used previously by Achard et al [62] and Elumalai et al [40] to construct resting-state FCNs from FC matrices.…”

“…The mapping was performed using the MRIcron tool [81] by identifying the Brodmann area that contains the MNI centroid coordinates of a given Schaefer ROI. Note that a similar mapping approach was employed in our previous study by Elumalai et al [40]. Second, we determined the set of Brodmann ROIs corresponding to the target regions in non-invasive brain stimulation experiments that show evidence for improvements in motor performance in healthy elderly.…”

“…Forman-Ricci curvature (FRC) [24,26] and Ollivier-Ricci curvature (ORC) [25] are the two commonly-used notions of discrete Ricci curvature for analysis of complex real-world networks. Multiple studies have utilizied FRC and ORC to measure changes in structural and functional brain connectivity during neurodevelopmental disorders [36][37][38][39][40][41]. For example, Chatterjee et al [39] revealed differences in FRC in the FCNs of individuals with attention deficit hyperactivity disorder (ADHD) compared to the FCNs of healthy controls.…”

“…In the present work, we apply FRC and ORC to compare resting-state FCNs of healthy young and healthy elderly individuals. We constructed resting-state FCNs by applying a standard fMRI preprocessing pipeline [40] to raw rs-fMRI images of 225 healthy participants in the MPI-LEMON dataset [21]. We estimated whole-brain and region-level FRC and ORC differences between the young and elderly age groups.…”

Changes in the geometry and robustness of diffusion tensor imaging networks: Secondary analysis from a randomized controlled trial of young autistic children receiving an umbilical cord blood infusion

“…Multiple studies have shown the utility of ORC, a network-science based metric of robustness in a graph, for analyzing changes in biological networks including trials involving individuals diagnosed with autism and cancer ( 25 – 30 ). ORC is an extension of traditional node-to-node DTI streamline analyses since it provides a measure of network robustness between a given node and all the nodes within a connected neighborhood ( 31 ).…”