The inflammatory process of atherosclerosis leads to the formation of an atheromatous plaque in the intima of the blood vessel. The plaque rupture may result from the interaction between the blood and the plaque. In each cardiac cycle, blood interacts with the vessel, considered as a compliant nonlinear hyperelastic. A three dimensional idealized fluid-structure interaction (FSI) model is constructed to perform the blood-plaque and blood-vessel wall interaction studies. An absorbing boundary condition (BC) is imposed directly on the outflow in order to cope with the spurious reflexions due to the truncation of the computational domain. The difference between the Newtonian and non-Newtonian effects is highlighted. It is shown that the von Mises and wall shear stresses are significantly affected according to the rigidity of the wall. The numerical results have shown that the risk of plaque rupture is higher in the case of a moving wall, while in the case of a fixed wall the risk of progression of the atheromatous plaque is higher.

The aim of this paper is to study the boundary feedback stabilization of a two dimensional Burgers type equation with a Dirichlet boundary control and boundary measurements. Thus we have to deal with highly unbounded control and observation operators. We study the well posedness of the infinite dimensional system obtained by coupling a linear estimator with a linear feedback control law for the corresponding linearized parabolic system in a neighborhood of an unstable stationary solution. We prove the local stabilization of the system obtained by applying to the nonlinear equation the linear feedback control coupled with the linear compensator. Numerical experiments confirm the theoretical results.

We present a fully automatic approach to recover boundary conditions and locations of the vessel wall, given a crude initial guess and some velocity cross-sections, which can be corrupted by noise. This paper contributes to the body of work regarding patient-specific numerical simulations of blood flow, where the computational domain and boundary conditions have an implicit uncertainty and error, that derives from acquiring and processing clinical data in the form of medical images. The tools described in this paper fit well in the current approach of performing patient-specific simulations, where a reasonable segmentation of the medical images is used to form the computational domain, and boundary conditions are obtained as velocity cross-sections from phase-contrast magnetic resonance imaging. The only additional requirement in the proposed methods is to obtain additional velocity cross-section measurements throughout the domain. The tools developed around optimal control theory, would then minimize a user defined cost function to fit the observations, while solving the incompressible Navier-Stokes equations. Examples include two-dimensional idealized geometries and an anatomically realistic saccular geometry description.

Bicuspid aortic valve (BAV) aortopathy remains of difficult clinical management due to its heterogeneity and further assessment of related aortic hemodynamics is necessary. The aim of this study was to assess systolic hemodynamic indexes and wall stresses in patients with diverse BAV phenotypes and dilated ascending aortas. The aortic geometry was reconstructed from patient-specific images while the aortic valve was generated based on patient-specific measurements. Physiologic material properties and boundary conditions were applied and fully coupled fluid-structure interaction (FSI) analysis were conducted. Our dilated aortic models were characterized by the presence of abnormal hemodynamics with elevated degrees of flow skewness and eccentricity, regardless of BAV morphotype. Retrograde flow was also present. Both features, predicted by flow angle and flow reversal ratios, were consistently higher than those reported for non-dilated aortas. Right-handed helical flow was present, as well as elevated wall shear stress (WSS) on the outer ascending aortic wall. Our results suggest that the abnormal flow associated with BAV may play a role in aortic enlargement and progress it further on already dilated aortas.