Numerical simulations of the Gatenby-Gawlinski model with heterogeneous acid diffusion in one space dimension

TL;DR

This paper models acid-mediated tumor invasion in one dimension, incorporating heterogeneous acid diffusion, and demonstrates biologically relevant invasion patterns through numerical simulations.

Contribution

It introduces a variant of the Gatenby-Gawlinski model with heterogeneous diffusion and analyzes its long-term homogenization behavior.

Findings

Reproduction of invasion front formation

Emergence of interstitial gaps driven by pH changes

Homogenization phenomenon in long-term dynamics

Abstract

In this work, we introduce a variant of the Gatenby-Gawlinski model for acid-mediated tumor invasion in the one-dimensional experimental setting, accounting for heterogeneous diffusion of the lactic acid across the surrounding healthy tissues. Numerical simulations are performed by employing finite volume schemes on staggered cartesian grids, together with explicit time discretization. The effectiveness of such approach is proven by reproducing biologically relevant results like the formation of propagating invasion fronts and the emergence of an interstitial gap between normal and cancerous cells, which is driven by the pH lowering strategy and depends significantly on the non-homogenous diffusion rates. By means of a comparison analysis, we infer that a homogenization phenomenon arises in the long run for appropriate values of the physical parameters, thus paving the way for complex applications to interface diffusion problems of invasive processes.