spatial distribution of cell populations in the process of erythropoiesis

We study spatial cell distribution in the bone marrow taking into account cell self-renewal, differentiation and apoptosis as well as cell motion result- ing from cell proliferation. The model consists of reaction-diffusion equations in a porous medium. The existence of stationary solutions corresponding to normal erythropoiesis is proved. In the leukemic case, this stationary solution becomes un- stable. Malignant cells propagate as a travelling wave filling the marrow. We study this phenomenon numerically in the 2D case. An analytical approximation for the wave speed is compared with the numerical solution of the full problem.