Problèmes Directs et Inverses en Interaction Fluide-Structure. Application à l'hémodynamique

摘要

In this thesis we deal with the simulation of fluid-structure interac- tion (FSI) problems in hemodynamics, with the emphasis in data assimilation and simulation in physiological regimes. The first part presents and analyzes a semi-implicit coupling scheme between the three-dimensional Navier-Stokes equations (NSE) and lumped parameter models, when the NSE are solved in a projection framework. This allows to simulate fluid and FSI problems more robustly, i.e., avoiding instabilities that may occur when dealing with realistic test-cases. The second part of the work is devoted to the study of sequential data assimila- tion techniques in FSI. We first present a study about the application of a reduced- order Unscented Kalman Filter for the effective estimation of relevant physical pa- rameters, like the stiffness distribution of the vessel wall and the proximal resistance in the fluid, from displacement measurements at the fluid-structure interface. Next, we analyze some Luenberger observers from solid mechanics in FSI, with the aim to construct tractable state estimators for large-scale FSI problems. In the third and final part, we apply some of the aforementioned methodologies to real physical problems. First, we perform the estimation of the wall stiffness (for linear and non-linear solid models) from data coming from MR-images of a silicone rubber aortic phantom. To finish, we deal with the forward analysis of a real aorta with repaired coarctation and we test the estimation techniques with synthetic data and show some results with the patient's data.