Incompressible limit of a continuum model of tissue growth for two cell populations

TL;DR

This paper studies the transition of a two-cell population growth model to an incompressible limit, resulting in a free boundary Hele Shaw type model, highlighting segregation properties and pressure-driven dynamics.

Contribution

It introduces the incompressible limit of a two-cell population model, linking it to a Hele Shaw type free boundary problem, which is a novel theoretical development.

Findings

Solutions maintain segregation during the limit process

The model converges to a Hele Shaw type free boundary problem

Pressure effects dominate cell population dynamics

Abstract

This paper investigates the incompressible limit of a system modelling the growth of two cells population. The model describes the dynamics of cell densities, driven by pressure exclusion and cell proliferation. It has been shown that solutions to this system of partial differential equations have the segregation property, meaning that two population initially segregated remain segregated. This work is devoted to the incompressible limit of such system towards a free boundary Hele Shaw type model for two cell populations.