Three dimensional blood flow in a truncated vascular system is investigated numerically using a commercially available finite element analysis and simulation software. The vascular system considered in this study has three levels of symmetric bifurcation. Geometric parameters for daughter vessels, such as their diameters and their angles of bifurcation, are specified according to Murray’s law based on the principle of minimum work. The ratio of blood vessel length to diameter is based upon experimental data found in the literature. An experimentally obtained velocity profile, available in the literature, is used as the inlet boundary condition. An outflow boundary model, consisting of a contraction tube to represent the pressure drop of the small arteries, arterioles, and capillaries that would follow the truncated vascular system, is used to specify the boundary condition at the eight outlets. The results show that although the blood flow velocity experiences a sudden decrease after the bifurcation points due to the higher total cross-sectional area of the daughter vessels as compared to the parent vessel, this decrease in velocity is partially recovered due to the tapering of the blood vessels as they approach the next bifurcation point. The results also show that the secondary flow which is typical after the bifurcation of large arteries does not develop after the bifurcation of small arteries due to the presence of laminar blood flow with very low Reynolds number in the small arteries. The numerical model yields pressure distributions and pressure drops along the vascular system that agree quite well with the physiological data found in the literature. Finally, the results show that, immediately following a bifurcation, the blood flow velocity profile is not symmetrical about the longitudinal axes of blood vessel. However, symmetry is recovered as the blood flow proceeds down the vessel.
Three-Dimensional Visualization of Pulmonary Blood Flow Velocity Profiles in Lambs