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In this paper, we present a mathematical and numerical model for bloodsolidification and its rupture in stenosed arteries. The interaction betweenthe blood flow and an existing stenosis in the arterial wall is modeled as athree dimensional fluid-structure interaction problem. The blood is assumed tobe a non-Newtonian incompressible fluid with a time-dependent viscosity thatobeys a modified Carreau's model and the flow dynamics is described by theNavier-Stokes equations. Whereas, the arterial wall is considered ahyperelastic material whose displacement satisfies the quasi-static equilibriumequations. Numerical simulations are performed using FreeFem++ on a twodimensional domain. We investigate the behavior of the viscosity of blood, itsspeed and the maximum shear stress. From the numerical results, bloodrecirculation zones have been identified. Moreover, a zone of the blood of highviscosity and low speed has been observed directly after the stenosis in theflow direction. This zone may correspond to a blood accumulation and thensolidification zone that is subjected to shear stress by the blood flow and toforces exerted by the artery wall deformation. Therefore, this zone is thoughtto break and then to release a blood clot that leads to the occlusion of smallarterioles.

Towards a Mathematical Model for the Solidification and Rupture of Blood in Stenosed Arteries