Topological data analysis distinguishes parameter regimes in the Anderson-Chaplain model of angiogenesis

TL;DR

This paper uses topological data analysis to distinguish different parameter regimes in a computational model of angiogenesis, revealing how vessel network structures vary with parameters.

Contribution

It introduces a TDA pipeline to systematically analyze and differentiate vessel architectures in the Anderson-Chaplain angiogenesis model based on simulation data.

Findings

TDA effectively stratifies parameter space by vessel morphology.

Topological descriptors correlate with biological vessel network features.

Methodology applicable to various biological and synthetic data sets.

Abstract

Angiogenesis is the process by which blood vessels form from pre-existing vessels. It plays a key role in many biological processes, including embryonic development and wound healing, and contributes to many diseases including cancer and rheumatoid arthritis. The structure of the resulting vessel networks determines their ability to deliver nutrients and remove waste products from biological tissues. Here we simulate the Anderson-Chaplain model of angiogenesis at different parameter values and quantify the vessel architectures of the resulting synthetic data. Specifically, we propose a topological data analysis (TDA) pipeline for systematic analysis of the model. TDA is a vibrant and relatively new field of computational mathematics for studying the shape of data. We compute topological and standard descriptors of model simulations generated by different parameter values. We show that TDA of model simulation data stratifies parameter space into regions with similar vessel morphology. The methodologies proposed here are widely applicable to other synthetic and experimental data including wound healing, development, and plant biology.