Persistent homology analysis of brain artery trees

TL;DR

This paper introduces topological data analysis techniques, specifically persistent homology, to represent and analyze brain artery trees, revealing stronger correlations with age and sex than previous methods.

Contribution

It develops new topological representations and statistical summaries of brain artery trees, enhancing the detection of associations with demographic covariates.

Findings

Persistence diagram summaries correlate with age and sex.

New representations improve statistical analysis of brain artery trees.

Correlation with age remains significant after controlling for other summaries.

Abstract

New representations of tree-structured data objects, using ideas from topological data analysis, enable improved statistical analyses of a population of brain artery trees. A number of representations of each data tree arise from persistence diagrams that quantify branching and looping of vessels at multiple scales. Novel approaches to the statistical analysis, through various summaries of the persistence diagrams, lead to heightened correlations with covariates such as age and sex, relative to earlier analyses of this data set. The correlation with age continues to be significant even after controlling for correlations from earlier significant summaries