Speaker
Description
In this presentation, we report about ongoing work on in silico research for the better understanding of an experimental study for meniscus regeneration. In essence, this experiment uses a nonwoven scaffold that is colonized by chondrocytes and human mesenchymal stem cells. The mathematical description involves active processes at the cell level, as well as macroscopic effects. The corresponding mathematical model consists of a set of coupled nonlinear parabolic partial differential equations where further effects, such as the mechanical deformation, can also be taken into account.
From the numerical point of view, also the vastly differing time scales ranging between seconds for the mechanical deformation and days for the processes related to the cells are hard problems which have to be addressed.
In view of efficient and fast computation, we transform the PDE system into a proper ODE system. The latter can be used to verify the numerical results of the PDE model and to get a better insight into the interactions between the quantities. However, both the PDE model and the ODE model depend on many parameters and several of them have to be regarded as unknowns. To deal with this issue, we perform a sensitivity analysis to identify the most important and influencing parameters. We see this also as a key step for a deeper understanding of the model and starting point of possible simplification strategies. It becomes apparent that our proposed ODE ansatz is especially suitable to perform such a sensitivity analysis. More precisely, we analyze one classical approach and two statistical methods. The first one is a so called local sensitivity analysis where sensitivities are computed directly by varying input parameters. The latter are so called global sensitivity analyses. We focus on the Sobol’ method which treats the input parameters as random variables and decomposes the variance of the model output into single contributions of the parameters, as well as on the extended Fourier amplitude sensitivity test which varies the input parameters with certain frequencies and performs a Fourier analysis on the model output. The numerical results of these different approaches will be compared and discussed.
