Travelling waves in a coarse-grained model of volume-filling cell invasion: Simulations and comparisons

TL;DR

This paper derives and analyzes a reaction-diffusion model for cell invasion that incorporates volume-filling effects, comparing its behavior with simpler models to understand the impact of these effects on travelling wave solutions.

Contribution

It introduces a coarse-grained reaction-diffusion model with volume-filling effects derived from an agent-based approach, and systematically compares its solutions to existing simpler models.

Findings

Volume-filling effects influence wave speed and shape.

Simpler models can capture qualitative behavior in certain regimes.

New properties emerge from volume constraints that simpler models miss.

Abstract

Many reaction-diffusion models produce travelling wave solutions that can be interpreted as waves of invasion in biological scenarios such as wound healing or tumour growth. These partial differential equation models have since been adapted to describe the interactions between cells and extracellular matrix (ECM), using a variety of different underlying assumptions. In this work, we derive a system of reaction-diffusion equations, with cross-species density-dependent diffusion, by coarse-graining an agent-based, volume-filling model of cell invasion into ECM. We study the resulting travelling wave solutions both numerically and analytically across various parameter regimes. Subsequently, we perform a systematic comparison between the behaviours observed in this model and those predicted by simpler models in the literature that do not take into account volume-filling effects in the same way. Our study justifies the use of some of these simpler, more analytically tractable models in reproducing the qualitative properties of the solutions in some parameter regimes, but it also reveals some interesting properties arising from the introduction of cell and ECM volume-filling effects, where standard model simplifications might not be appropriate.