Persistent Homology Analysis of Brain Artery Trees

Area of Science:

• Neuroscience
• Data Science
• Topology

Background:

• Statistical analysis of brain artery trees is crucial for understanding neurovascular health.
• Previous methods had limitations in capturing complex vascular structures and their correlations with biological factors.

Purpose of the Study:

• To introduce novel representations of tree-structured data objects for brain artery trees.
• To improve statistical analyses by enhancing correlations with covariates such as age and sex.

Main Methods:

• Utilized concepts from topological data analysis to create new data tree representations.
• Employed persistence diagrams to quantify vessel branching and looping at multiple scales.
• Developed novel statistical analysis approaches using summaries of persistence diagrams.

Main Results:

• The new representations significantly improved correlations with covariates like age and sex compared to earlier analyses.
• The correlation with age remained statistically significant even after accounting for previous findings.
• Persistence diagrams effectively quantified multi-scale branching and looping features.

Conclusions:

• Topological data analysis offers powerful new tools for analyzing complex biological structures like brain artery trees.
• These enhanced statistical methods provide deeper insights into how factors like age influence cerebrovasculature.