Numerical Flow Simulations of Blood in Arteries

Abstract

LOOD is a suspension of red blood cells, white blood cells and platelets in plasma. The viscoelastic fluid behavior of blood is associated with the elastic properties of the red cell membrane and the viscosity of internal and external fluids. Red blood cells constitute more than 99% of the particulate matter in blood and 40-45% of the blood by volume (hematocrit). The material properties of the red blood cell membrane, and the fluidity of its internal contents make it easy for the cell to deform into a variety of shapes. However, the deformation of the red blood cells in vitro or in vivo in the circulation occurs at an essentially constant area, which can be attributed to the relatively high dilatational modulus of the cell membrane. B After red blood cell, white blood cells are the largest in number. However, they constitute only less than 1% of the total volume of blood cells in normal human blood and exert little influence on the bulk rheological properties of blood. The white blood cells are much less deformable than the red blood cells. The white blood cells have a viscoelastic interior that makes them several orders of magnitude stiffer than the red blood cells under rapid deformations. The stress required to cause the deformation of white blood cells is much greater than for the red blood cells. This indicates that white blood cells are more viscous as compared to red blood cells. The platelets occupy even less of the blood volume than the white blood cells. They play important role in blood clotting, but they are rheologically unimportant to consider for the normal blood simulation. Adhesion of both red blood cells and white blood cells to blood-vessel walls increases the apparent viscosity. Since one must consider different viscosities for both the red blood cells and the white blood cells, the blood must be considered as a non-Newtonian fluid for simulations. There are various aspects of the circulation of blood in the literature. There is particularly a large amount of research work and related publications because of the continued widespread incidence of cardiovascular diseases, especially coronary infarctions and arteriosclerosis. Most of the literature on blood flow is concerned about the bifurcation of the arteries, the velocity profile, pressure distribution and the shear stress induced in the bifurcation and along the walls of the artery. In most of the investigations, arterial walls are assumed to behave as rigid instead of elastic walls, whereas the concept of using elasticity is needed to obtain practical and more realistic results. With the expansion of Computational Fluid Dynamics (CFD), it has become possible to investigate blood flow in the arteries by including most of physical aspects of blood flow. Investigators have used various numerical methods,