Analysis and simulations of a Viscoelastic Model of Angiogenesis

TL;DR

This paper analyzes a viscoelastic model of angiogenesis, providing conditions for solution existence, capturing breakdown scenarios, and demonstrating the model's ability to replicate experimental blood vessel growth behaviors.

Contribution

It introduces a mathematical framework for angiogenesis modeling with proven solution conditions and numerical simulations that align with biological experiments.

Findings

Proven conditions for global existence of solutions.

Numerical capture of breakdown solutions.

Model reproduces various angiogenesis experimental scenarios.

Abstract

The work analyzes a one-dimensional viscoelastic model of blood vessel growth under nonlinear friction with surroundings, and provides numerical simulations for various growing cases. For the nonlinear differential equations, two sufficient conditions are proven to guarantee the global existence of biologically meaningful solutions. Examples with breakdown solutions are captured by numerical approximations. Numerical simulations demonstrate this model can reproduce angiogenesis experiments under various biological conditions including blood vessel extension without proliferation and blood vessel regression.