Computer modelling of haematopoietic stem cells migration
A mathematical model for migration of haematopoietic stem cells towards their niche in the bone marrow has been proposed in the literature. It consists of a chemotaxis system of partial differential equations with nonhomogeneous boundary conditions and an additional ordinary differential equation on a part of the computational boundary. The aim of the current work is to extend appropriately a second order positivity preserving central upwind scheme, originally proposed for a chemotaxis system with zero-flux boundary conditions and to apply it for the numerical solution of the considered problem. This paper introduces a first glance of such modification and outlines open questions in the handling of the nonlinear boundary conditions in a way that preserves the positivity of the solution. The presented numerical tests illustrate the need of the development of new specialized schemes for more complex chemotaxis systems.
haematopoietic stem cells chemotaxis nonhomogeneous boundary conditions finite volume method