Scalable Algorithms for Generating and Analyzing Structural Brain Networks with a Varying Number of Nodes

Abstract: Diffusion Magnetic Resonance Imaging (MRI) exploits the anisotropic diffusion of water molecules in the brain to enable the estimation of the brain's anatomical fiber tracts at a relatively high resolution. In particular, tractographic methods can be used to generate whole-brain anatomical connectivity matrix where each element provides an estimate of the connectivity strength between the corresponding voxels. Structural brain networks are built using the connectivity information and a predefined brain parcellation, where the nodes of the network represent the brain regions and the edge weights capture the connectivity strengths between the corresponding brain regions. This paper introduces a number of novel scalable methods to generate and analyze structural brain networks with a varying number of nodes. In particular, we introduce a new parallel algorithm to quickly generate large scale connectivity-based parcellations for which voxels in a region possess highly similar connectivity patterns to the rest of the regions. We show that the corresponding regional structural consistency is always superior to randomly generated parcellations over a wide range of parcellation sizes. Corresponding brain networks with a varying number of nodes are analyzed using standard graph-theorectic measures, as well as, new measures derived from spectral graph theory. Our results indicate increasingly more statistical power of brain networks with larger numbers of nodes and the relatively unique shape of the spectral profile of large brain networks relative to other well-known networks.