  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.
