Numerical simulation of the blood flow behavior in the circle of Willis

• Published in: Bioimpacts 2014-01, Vol.4 (2), p.89-94
• Main Authors: Razavi, Seyyed Esmail, Sahebjam, Rana
• Format: Article
• Language: English
• Subjects: Blood; Circle of Willis; FEM; Navier-Stokes equations; Newtonian fluid; NMR; non-Newtonian fluid; Nuclear magnetic resonance; Studies; Veins & arteries
• ISSN: 2228-5652; 2228-5660
• DOI: 10.5681/bi.2014.008

This paper represents numerical simulation of blood flow in the circle of Willis (CoW). CoW is responsible for oxygenated blood distribution into cerebral mass. To investigate blood behavior, two Newtonian and non-Newtonian viscosity models were considered and results were compared under steady state conditions. Methodologically, arterial geometry was obtained using 3D magnetic resonance angiography data. The blood flow through the cerebral vasculature was considered to be steady and laminar, and Galerkin's finite element method was applied to solve the systems of non-linear Navier-Stokes equations. Flow patterns including flow rates and shear rates were obtained through simulation. The minimal magnitude of shear rates was greater than 100 s^sup -1^ through larger arteries; thus, non-Newtonian blood viscosity tended to approach the constant limit of infinite shear viscosity through CoW. So, in larger arteries, non-Newtonian nature of blood was less dominant and it would be treated as Newtonian fluid. The only exception was the anterior communicating artery in which blood flow showed different behavior for Newtonian and non-Newtonian cases.