Mathematical modeling and analysis of a tumor invasion problem with angiogenesis and taxis cascade

TL;DR

This paper develops a multiscale mathematical model for tumor invasion incorporating angiogenesis and taxis interactions, proving solution existence and performing simulations to analyze tumor behavior.

Contribution

It introduces a novel reaction-diffusion-taxis system with a taxis cascade, derived via informal parabolic upscaling from lower scales.

Findings

Global existence and uniqueness of solutions established

Numerical simulations illustrate tumor invasion dynamics

Model captures complex interactions between tumor cells and signals

Abstract

We propose a mathematical model for tumor invasion supported by angiogenesis and interactions with the surrounding tissue. For the model deduction we employ a multiscale approach starting from lower scales and obtaining by an informal parabolic upscaling a system of reaction-diffusion-taxis equations with a so-called 'taxis cascade', where one species is performing taxis towards a signal whose production/decay is controled by the other, for which it also serves as a tactic cue. We prove global existence and uniqueness of solutions to the obtained PDE-ODE system and perform numerical simulations to illustrate the behavior of solutions.