Generalized Framework to Study Brain Weighted Networks

Abstract

In recent years, a great deal of attention has been given to the development of network theory and its application to the brain. Employing graph theory, high angular resolution diffusion imaging (HARDI) and tractography the brain can be studied as a network by defining anatomical regions as nodes and white matter fiber bundles as edges. Using a binary description of brain network connectivity, studies have shown that the brain is arranged following a small world topology. The topology of binary networks is determined by calculating the degree distribution, geodesic path length and clustering coefficient. These measures are influenced by spatial and angular resolution, seed density and thresholding. In this study, we use a dimensionless edge weight to minimize the effects of seed density and fiber scale in the network construction. This provides a generalized framework for analyzing weighted networks, which minimizes the effects of data acquisition and processing. We compare the analysis of brain connectivity using binary networks with the analysis using weighted networks, by employing generalizations of degree, geodesic path length and clustering coefficient. Human networks were created from HARDI data of ten repeated scans of one subject acquired using a 3T scanner, with an isotropic resolution of 2mm, 6 diffusion weightings of 100 s/mm2 and 64 with 1000 s/mm2. HARDI rat data was acquired from 4 excised rat brains on a 17.6T magnet, with an isotropic resolution of 190 μm, 7 diffusion weightings of 100 s/mm2 and 64 with 2225 s/mm2. Diffusion displacement probabilities were calculated with a model that estimates multiple fibers per voxel and allows the estimation of fiber crossings. Binary networks were analyzed using R and compared to their weighted counterparts. The proposed framework suggests that weighted networks are more robust and less effected by noise and thresholding.