Hybrid modeling of tumor-induced angiogenesis

TL;DR

This paper introduces a multiscale hybrid model for tumor-induced angiogenesis, combining stochastic vessel tip dynamics with deterministic field equations to better understand capillary network formation.

Contribution

It develops a novel multiscale modeling framework that couples stochastic vessel tip behavior with deterministic field equations for the first time.

Findings

The model captures key features of vessel branching and anastomosis.

Numerical simulations validate the model's ability to reproduce angiogenesis patterns.

Proper boundary conditions are essential for accurate simulations.

Abstract

When modeling of tumor-driven angiogenesis, a major source of analytical and computational complexity is the strong coupling between the kinetic parameters of the relevant stochastic branching-and-growth of the capillary network, and the family of interacting underlying fields. To reduce this complexity, we take advantage of the system intrinsic multiscale structure: we describe the stochastic dynamics of the cells at the vessel tip at their natural mesoscale, whereas we describe the deterministic dynamics of the underlying fields at a larger macroscale. Here, we set up a conceptual stochastic model including branching, elongation, and anastomosis of vessels and derive a mean field approximation for their densities. This leads to a deterministic integro-partial differential system that describes the formation of the stochastic vessel network. We discuss the proper capillary injecting boundary conditions and include the results of relevant numerical simulations.