Key result
A 2D fluid-structure interaction model mathematically proves weak solutions exist for non-Newtonian stenosed artery flow.
Why the study?
The interactions between blood flow and atherosclerotic plaques in arteries require detailed modeling to understand fluid-structure dynamics in stenosed vessels.
The study develops a 2D mathematical fluid-structure interaction model to simulate blood flow and its interactions with atherosclerotic plaques and arterial walls.
Model existence proof advances theoretical FSI analysis; leaves open experimental validation before any clinical use.
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.
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Boujena et al. (2014) studied Atherosclerosis. 2D Fluid-Structure Interaction Model was evaluated on Existence of a weak solution for the generalized Navier-Stokes problem. The study proposes a 2D fluid-structure interaction model and mathematically proves the existence of a weak solution for incompressible non-Newtonian blood flow in a stenosed artery.
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