A stenosis is the narrowing of the artery, this narrowing is usually the result of the
formation of an atheromatous plaque infiltrating gradually the artery wall, forming a bump
in the ductus arteriosus. This arterial lesion falls within the general context of
atherosclerotic arterial disease that can affect the carotid arteries, but also the
arteries of the heart (coronary), arteries of the legs (PAD), the renal arteries... It can
cause a stroke (hemiplegia, transient paralysis of a limb, speech disorder, sailing before
the eye). In this paper we study the blood-plaque and blood-wall interactions using a
fluid-structure interaction model. We first propose a 2D analytical study of the
generalized Navier-Stokes equations to prove the existence of a weak solution for
incompressible non-Newtonian fluids with non standard boundary conditions. Then, coupled,
based on the results of the theoretical study approach is given. And to form a realistic
model, with high accuracy, additional conditions due to fluid-structure coupling are
proposed on the border undergoing inetraction. This coupled model includes (a) a fluid
model, where blood is modeled as an incompressible non-Newtonian viscous fluid, (b) a
solid model, where the arterial wall and atherosclerotic plaque will be treated as non
linear hyperelastic solids, and (c) a fluid-structure interaction (FSI) model where
interactions between the fluid (blood) and structures (the arterial wall and atheromatous
plaque) are conducted by an Arbitrary Lagrangian Eulerian (ALE) method that allows
accurate fluid-structure coupling.