Travelling waves in a volume-filling model of cell invasion into extracellular matrix #

Rebecca Crossley, Philip K Maini, Tommaso Lorenzi, Ruth E Baker

15:10 Tuesday in 4Q04.

Part of the Travelling waves session.

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 population-level reaction-diffusion equations with cross-dependent diffusion terms by coarse-graining an individual-based description of cell motility and proliferation alongside ECM degradation, taking into account the impact of both cell and ECM volume-filling effects on cell motility and proliferation. We analyse the resulting travelling wave solutions both numerically and analytically across various parameter regimes using phase plane analysis, asymptotics and perturbation techniques. Subsequently, we perform a systematic comparison between the population-level behaviours observed in this model and those predicted by simpler models in the literature, which 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 to reproduce the qualitative properties of the solutions in the limiting cases, as well as revealing some interesting properties caused by the introduction of cell and ECM volume-filling effects, where standard model simplifications might not be appropriate.