Sensitivity Analysis in Poro-Elastic and Poro-Visco-Elastic Models with Respect to Boundary Data

Abstract

In this article we consider poro-elastic and poro-visco-elastic models inspired by problems in medicine and biology, and we perform sensitivity analysis on the solutions of these fluid-solid mixture problems with respect to the imposed boundary data, which are the main drivers of the system. Moreover, we compare the results obtained in the elastic case vs. visco-elastic case, as it is known that structural viscosity of biological tissues decreases with age and disease. Sensitivity analysis is the first step towards optimization and control problems associated with these models, which is our ultimate goal.