Persistence diagrams for exploring the shape variability of abdominal aortic aneurysms

Area of Science:

• Cardiovascular Research
• Medical Imaging Analysis
• Computational Topology

Background:

• Abdominal aortic aneurysm (AAA) is a dangerous circulatory system pathology characterized by aortic dilation.
• Aortic shape and hemodynamics are critical factors in AAA development and progression.
• Associated pathologies include calcifications and intraluminal thrombi, complicating diagnosis and treatment.

Purpose of the Study:

• To apply Topological Data Analysis (TDA) for characterizing aortic lumen shape irregularities.
• To correlate TDA-derived features with hemodynamic factors in abdominal aortic aneurysms.
• To validate the effectiveness of TDA descriptors in supervised and unsupervised learning models for AAA.

Main Methods:

• Utilizing computed tomography angiography (CTA) data from patients.
• Employing TDA tools to generate persistence diagrams representing aortic lumen topology.
• Developing shape-related descriptors from persistence diagrams.
• Conducting supervised and unsupervised machine learning case studies to evaluate descriptor efficacy.

Main Results:

• Persistence diagrams effectively capture complex geometric features of the aortic lumen.
• TDA-derived descriptors provide quantifiable measures of aortic shape irregularities.
• Demonstrated utility of these descriptors in differentiating patient cohorts and identifying patterns in AAA.

Conclusions:

• Topological Data Analysis offers a novel approach to quantifying aortic shape in the context of abdominal aortic aneurysms.
• Shape descriptors derived from TDA hold potential for improving AAA risk stratification and understanding disease mechanisms.
• This methodology provides a robust framework for analyzing complex vascular geometries from medical imaging.