Statistical Shape Analysis of Brain Arterial Networks (BAN)

TL;DR

This paper introduces a novel mathematical framework for analyzing brain arterial network shapes as elastic shape graphs, enabling statistical comparisons and studying effects of age and gender on BAN morphology.

Contribution

It develops a Riemannian geometric approach to represent and analyze BAN shapes as elastic graphs, facilitating statistical shape analysis and covariate effect studies.

Findings

Age increases shape variance in BANs.

Gender effects on BAN shapes are inconclusive.

The framework successfully summarizes BAN shape variability.

Abstract

Structures of brain arterial networks (BANs) - that are complex arrangements of individual arteries, their branching patterns, and inter-connectivities - play an important role in characterizing and understanding brain physiology. One would like tools for statistically analyzing the shapes of BANs, i.e. quantify shape differences, compare population of subjects, and study the effects of covariates on these shapes. This paper mathematically represents and statistically analyzes BAN shapes as elastic shape graphs. Each elastic shape graph is made up of nodes that are connected by a number of 3D curves, and edges, with arbitrary shapes. We develop a mathematical representation, a Riemannian metric and other geometrical tools, such as computations of geodesics, means and covariances, and PCA for analyzing elastic graphs and BANs. This analysis is applied to BANs after separating them into four components -- top, bottom, left, and right. This framework is then used to generate shape summaries of BANs from 92 subjects, and to study the effects of age and gender on shapes of BAN components. We conclude that while gender effects require further investigation, the age has a clear, quantifiable effect on BAN shapes. Specifically, we find an increased variance in BAN shapes as age increases.