Generalized Navier–Stokes equations with non-standard conditions for blood flow in atherosclerotic artery

Abstract

In this paper, we consider the blood flow in a stenosed artery. We give an analytical study of the equations for a non-Newtonian fluid modeling the blood for which the behavior is obeying to Carreau's law. The case we treat is different than classic cases where the total pressure is in the natural boundary conditions. For this, we use the Faedo-Galerkin method to prove the existence of a weak solution for the fluid problem. Then we use a coupled approach between the fluid equations and the solid model of the arterial wall and the atheromatous plaque. A special attention is paid to the effects of the wall motion on the local fluid displacement, on the stresses, and on strains in the diseased arterial wall. These relevant quantities are analyzed extensively through numerical results.

Numerical simulations of a 3D fluid-structure interaction model for blood flow in an atherosclerotic artery

“…In the case of a moving wall, the highest von Mises stress (13.48 KPa) is observed in the region upstream the stenosis, whereas for the fixed wall configuration the highest value (10.45 KPa) is observed downstream the stenosis. This result is in contradiction with the study presented in [3] where the maximum value of the von Mises stress is located upstream the stenosis in the case of the rigid wall. However, two major considerations distinguish our study: (1) the inlet pressure wave and the absorbing BC chosen for the inlet and outlet, respectively and (2) the differentiation between Young modulus values for the vessel wall (E = 3 · 10 5 Pa in the upstream and downstream extended sections and E = 6 · 10 5 Pa in the vessel wall surrounding the plaque).…”

“…They showed that considering the classical models of interaction between the blood flow (modeled as a Newtonian fluid), the vessel wall and the atherosclerotic plaque, the risk of rupture is less predictive because it underestimates the stress over the plaque comparing with the case where blood is modeled as a non-Newtonian fluid. These previous results were extended by considering a 3D geometry of an idealized blood vessel in order to be more realistic, the aim being to analyze the evolutionary non-linear 3D flow characteristics of blood in a stenosed artery [3]. However, for the numerical simulations based on the theoretical study, the fluid and the structures were described using a 2D axi-symmetric model in order to reduce the overall computational complexity.…”

“…In this study a 3D FSI model incorporating fluid-structure interaction (bloodplaque and blood-wall) as well as non-Newtonian effects in a 3D geometry to analyze the flow and structures stresses is considered. It consists of a generalization of the study done in [3] with more realistic pressure input profile [1] at the inlet and a linear absorbing condition (LAC) at the outlet [24,36].…”

Virtual FFR Quantified with a Generalized Flow Model Using Windkessel Boundary Conditions

“…On the one hand, a realistic blood flow simulation requires the use of an adequate flow model. For instance, Boujena et al [5] presented a non-Newtonian flow model adapted to describe blood flow in the presence of atherosclerosis. Simulation in their paper was performed in 2D and 3D simplified geometries.…”

“…On the other hand, the choice of suitable boundary conditions is crucial. In our previous paper [1], we presented a first virtual FFR estimation using the generalized fluid model in [5] and conducted different simulations to study the impact of the lesions parameters on the FFR value. However, we considered a simplified 2D geometry and reduced boundary conditions.…”