Coupled analysis of active biological processes for meniscus tissue regeneration

The starting point for this are clinical studies showing that partial and total meniscectomies lead to prevalence of premature osteoarthritis in knee joints. Accordingly, substantial efforts are being made towards finding adequate regenerative tissue for meniscus replacement. The presentation will first discuss the mathematical model that we have established so far and that forms a coupled system of  reaction-diffusion-taxis equations where cell densities play a dominant role. The main focus will then be placed on the numerical challenges, along with a report on the computational results that we have obtained so far and their validation with respect to experimental data. Also, recent results on non-intrusive model order reduction methods will be introduced. These turn out to be useful when tackling the parameter identification problem along with the computation of parameter sensitivities.