Numerical simulation of a contractivity based multiscale cancer invasion model

TL;DR

This paper develops a specialized second-order finite volume implicit-explicit numerical scheme for simulating a complex multiscale cancer invasion model involving coupled macroscopic and microscopic dynamics with challenging features.

Contribution

It introduces a novel numerical method tailored for a multiscale cancer invasion model with non-constant coefficients, time delay, and stiff reactions.

Findings

Successfully handles non-constant diffusion coefficients

Incorporates time delay through interpolation

Ensures stability with restricted time steps

Abstract

We present a problem-suited numerical method for a particularly challenging cancer invasion model. This model is a multiscale haptotaxis advection-reaction-diffusion system that describes the macroscopic dynamics of two types of cancer cells coupled with microscopic dynamics of the cells adhesion on the extracellular matrix. The difficulties to overcome arises from the non-constant advection and diffusion coefficients, a time delay term, as well as stiff reaction terms. Our numerical method is a second order finite volume implicit-explicit scheme adjusted to include a) non-constant diffusion coefficients in the implicit part, b) an interpolation technique for the time delay, and c) a restriction on the time increment for the stiff reaction terms.