Hyperbolic disc embedding of functional human brain connectomes using resting state fMRI

Abstract

The brain presents a real complex network of modular, small-world, and hierarchical nature, which are features of non-Euclidean geometry. Using resting-state functional magnetic resonance imaging (rs-fMRI), we constructed a scale-free binary graph for each subject, using internodal time-series correlation of regions-of-interest (ROIs) as a proximity measure. The resulted network could be embedded onto manifolds of various curvature and dimensions. While maintaining the fidelity of embedding (low distortion, high mean average precision), functional brain networks were found to be best represented in the hyperbolic disc. Using [Formula] model, we reduced the dimension of the network into 2-D hyperbolic space and were able to efficiently visualize the internodal connections of the brain, preserving proximity as distances and angles on the hyperbolic discs. Each individual disc revealed decentralized nature of information flow and anatomic relevance. Using the hyperbolic distance on the [Formula] model, we could detect the anomaly of network in autistic spectrum disorder (ASD) subjects. This procedure of embedding grants us a reliable new framework for studying functional brain networks and the possibility of detecting anomalies of the network in the hyperbolic disc on an individual scale.