A computer simulation of the flow field at the aortic bifurcation.

Abstract

Curvatures, junctions and bifurcations of the large and medium arteries are severely affected by atherosclerosis. It has been suggested that fluid dynamics may play a role in the genesis and progression of the disease. The arterial walls in these regions are exposed to high and/or low shear stresses, which can either cause the cell degradation or disturb local mass transfer. To further the understanding of a possible role of fluid dynamics in the atherogenesis, three finite difference models have been developed for the study of the blood flow field at the aortic bifurcation. In the first model, the simplest one, blood was assumed to be Newtonian and the arteries were assumed to be rigid. The elliptic type of coordinate transformation was adopted to deal with the complicated geometric shape. With vorticity and stream function as primary variables, the alternate direction implicit (ADI) and successive over-relaxation (SOR) methods were utilized to solve the vorticity transport and Poisson equations, respectively. Parametric studies were performed to understand the roles of the area ratio, the Reynolds number, the corner curvatures, the Womersely numbers, the bifurcation angles and the pulsatile nature of the flow at the aortic bifurcation. No permanent eddies were found due to the pulsatile nature of a physiological flow and the vertex wedge effect. Only a temporary eddy existed downstream of the hip under certain conditions, for instance, a large area ratio. These results agreed qualitatively with the existing experimental observations. There were two peak shear stress points, one on the outer wall near the outer corner and the other on the inner wall downstream from the vertex. The latter generally had the highest shear stress. The maximum shear stress was as high as 280 dyn/$cm\sp2$. The second model took into account the non-Newtonian property of blood while the rigid wall assumption was kept. The blood rheology was represented by the Casson equation, a weak form of which was formulated in the numerical simulations. The SOR method was used to solve both the vorticity and Poisson equations. The non-Newtonian property of blood did not drastically change the flow patterns. It did, however, increase the shear stresses about 5%. The third model incorporated the flexibility of the arteries into the boundary conditions while the Newtonian blood assumption was kept. The wall behavior was described by a linear viscoelastic constitutive equation. The arbitrary Lagrangian-Eulerian method was used to deal with the moving boundary problem. The SOR method was used to solve both the vorticity and Poisson equations. A flexible bifurcation experienced the shear stresses about 10% lower than those of a rigid one.