Towards a Mathematical Model for the Solidification and Rupture of Blood in Stenosed Arteries
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In this paper, we present a mathematical and numerical model for blood solidification and its rupture in stenosed arteries. The interaction between the blood flow and an existing stenosis in the arterial wall is modeled as a three dimensional fluid-structure interaction problem. The blood is assumed to be a non-Newtonian incompressible fluid with a time-dependent viscosity that obeys a modified Carreau's model and the flow dynamics is described by the Navier-Stokes equations. Whereas, the arterial wall is considered a hyperelastic material whose displacement satisfies the quasi-static equilibrium equations. Numerical simulations are performed using FreeFem++ on a two dimensional domain. We investigate the behavior of the viscosity of blood, its speed and the maximum shear stress. From the numerical results, blood recirculation zones have been identified. Moreover, a zone of the blood of high viscosity and low speed has been observed directly after the stenosis in the flow direction. This zone may correspond to a blood accumulation and then solidification zone that is subjected to shear stress by the blood flow and to forces exerted by the artery wall deformation. Therefore, this zone is thought to break and then to release a blood clot that leads to the occlusion of small arterioles.
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