Numerical solutions of a 2D fluid problem coupled to a nonlinear non-local reaction-advection-diffusion problem for cell crawling migration in a discoidal domain

TL;DR

This paper develops a finite volume numerical scheme to simulate 2D cell migration in a non-deformable discoidal domain, coupling fluid dynamics with nonlinear reaction-advection-diffusion processes.

Contribution

It introduces a novel finite volume method for a complex coupled nonlinear model of cell migration in a fixed discoidal domain.

Findings

The scheme captures various migration behaviors.

Simulations demonstrate the model's ability to reproduce biological phenomena.

The approach effectively handles nonlocal advection effects.

Abstract

In this work, we present a numerical scheme for the approximate solutions of a 2D crawling cell migration problem. The model, defined on a non-deformable discoidal domain, consists in a Darcy fluid problem coupled with a Poisson problem and a reaction-advection-diffusion problem. Moreover, the advection velocity depends on boundary values, making the problem nonlinear and non local. \parFor a discoidal domain, numerical solutions can be obtained using the finite volume method on the polar formulation of the model. Simulations show that different migration behaviours can be captured.