Statistical shape analysis of brain arterial networks (BAN)

Abstract

The arterial networks in the human brain, termed brain arterial networks or BANs, are complex arrangements of individual arteries, branching patterns, and interconnectivity. BANs play an essential role in characterizing and understanding brain physiology, and one would like tools for statistically analyzing the shapes of BANs. These tools include quantifying shape differences, comparing populations of subjects, and studying the effects of covariates on these shapes. This paper mathematically represents and statistically analyzes BAN shapes as elastic shape graphs. Each elastic shape graph consists of nodes, or points in 3D, connected by 3D curves, or edges, with arbitrary shapes. We develop a mathematical representation, a Riemannian metric and other geometrical tools, such as computations of geodesics, means, covariances, and PCA, for helping analyze BANs as elastic graphs. We apply this analysis to BANs after dividing them into four components—top, bottom, left, and right. The framework is then used to generate shape summaries of BANs from 92 subjects and study the effects of age and gender on shapes of BAN components. While gender effects require further investigation, we conclude that age has a clear, quantifiable effect on BAN shapes. Specifically, we find an increased variance in BAN shapes as age increases.