Comparison of Different Methods for Sensitivity Analysis Applied to a Model for Meniscus Tissue Engineering

ABSTRACT

Mathematical models describing physical or biological processes are often involved and need a lot of parameters whose values may be unknown and hence must be estimated. Some parameters may have a strong impact on the solution and are hence important to know in order to obtain accurate results, whereas other parameters may have little impact on the solution and thus can be set to an arbitrary value. The sensitivity analysis tackles this problem of measuring the importance of parameters and identifying the most relevant ones. In this paper, we investigate a system describing the dynamics of a seeding experiment where a fibrous scaffold material is colonized by two types of cell populations. The specific application that we have in mind is related to the idea of meniscus tissue regeneration. Two methods of global sensitivity analysis, namely the method of Sobol' and the Fourier amplitude sensitivity test, will be utilized to analyze this system. It turns out that both approaches work here satisfactory and provide similar results of the parameters' importance. In particular, the parameters that control the rates in the reaction terms of the model are shown to have a strong influence on the outcome of the in silico experiment and are key for optimizing the tissue production.