Reliable and efficient numerical simulation of a model of tissue differentiation in a bone chamber

For the study of peri-implant tissue differentiation, a repeated sampling bone chamber has been developed. Mathematical models that describe tissue differentiation help to gain insight into the processes taking place in the chamber. We consider here the numerical solution of a taxisdiffusion-reaction partial differential equation model. The general approach is the method of lines and we pay special attention to transfer qualitative features of the solution to the numerical approximation. These features are the conservation of mass principle and the nonnegativity of concentration values. This is achieved by following the finite volume idea and by employing positivity preserving spatial discretisations, respectively. An instructive example is given. The time integration is performed with ROWMAP, a suitable implicit time integration method with time step size control. Alltogether this yields a reliable and efficient numerical solution technique. A numerical simulation of the tissue differentiation process in the chamber is presented and discussed.