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

TL;DR

This paper develops a continuum model for two segregated cell populations, driven by pressure, cohesion, and proliferation, and demonstrates its approximation to a Hele Shaw type free boundary model through analytical and numerical methods.

Contribution

It introduces a novel two-population tissue growth model that captures segregation and links it to a Hele Shaw type free boundary problem.

Findings

Model approximates a Hele Shaw type free boundary problem

Analytical characterization of the model

Numerical validation of the approximation

Abstract

This paper proposes a model for the growth two interacting populations of cells that do not mix. The dynamics is driven by pressure and cohesion forces on the one hand and proliferation on the other hand. Following earlier works on the single population case, we show that the model approximates a free boundary Hele Shaw type model that we characterise using both analytical and numerical arguments.