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
This work provides a numerical method for a specific biophysical model of cell migration, but the approach is tailored to a discoidal domain and the results are qualitative without quantitative benchmarks.
The authors developed a numerical scheme for a 2D cell crawling migration model coupling Darcy flow, Poisson, and reaction-advection-diffusion equations on a discoidal domain. Simulations demonstrated the ability to capture different migration behaviors.
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.