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.

Keywords:

• non-Newtonian fluids
• Faedo–Galerkin method
• blood flow
• atheromatous plaque

AMS Subject Classifications:

• 35Q30
• 92C50
• 74F10

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work has been supported by the PHC Volubilis grant from the French foreign office and the Moroccan ministry of education and research MA/11/246.