Abstract:
In this thesis, we study a fluid structure interaction problem between the blood and the atherosclerosis plaque formed inside an artery. The formation of this plaque may lead to dangerous consequences such as its rupture, the formation of blood clot that might result in a heart attack or an ischemic stroke. The blood is modeled as an incompressible non-Newtonian viscous fluid using the Navier-Stokes equations, the lipid pool and the fibrous cap of the atheroma plaque are supposed to be hyperelastic materials. The interactions between the blood (the fluid) and the plaque of atherosclerosis (the structure) are done after the Arbitrary
Lagrangian Eulerian (ALE) method to handle employing the mesh displacement.
In a stenosed artery, we investigate the hyperviscosity effects of blood on the blood flow of a COVID 19 patients, and the non-Newtonian one on the recirculation downstream of the atheroma plaque. After a mathematical analysis of the model, a finite element method is used to provide numerical simulations. The main interests of the numerical results are the displacement of the plaque, the distribution of the stress over it and the recirculation of the blood.
Simulations show that the Newtonian model where the viscosity is constant overestimates the recirculation of the blood, underestimates the displacement of the plaque and the stress over it in comparison with the non-Newtonian one. In addition, it shows also that the increase in the viscosity of the blood in a COVID 19 patient overestimates the distribution of the stress over the plaque that will lead to its rupture.
