A numerical model of pulsatile blood flow in compliant arteries of a truncated vascular system. (October 2015) - Kahveci, Kamil
Abstract: Three dimensional blood flow in compliant, tapering vessels of a truncated vascular system model containing two levels of bifurcation was investigated numerically using a commercially available finite element analysis and simulation software. Although the branching pattern and the geometry of the human vascular system are complex, they can be specified for small arteries using Murray's hypothesis that the structure of the vascular system obeys the principle of minimum work. Accordingly, in the current vascular system model, the parent/daughter diameter ratios and the angles of bifurcation were specified according to Murray's law. Another geometrical parameter, the ratio of blood vessel length to diameter, was determined according to data found in the literature. The vascular system model also includes a 5 mm thick layer of tissue surrounding the vessels. This tissue layer helps to resist artery deformation during the cardiac cycle. Experimentally measured time dependent blood velocity data, available in the literature, were used as the inlet boundary condition to represent the cardiac cycle. An outflow boundary model, consisting of an elastic tube followed by a contraction tube, was used at the four outlets to represent both the compliance and the pressure drop of the small arteries, arterioles, and capillaries that would follow the truncated vascular system. The results show that, at each bifurcation, the blood flow velocity decreases significantly in the transition from the parent vessel to the daughter vessels 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 along the arteries due to the tapering of the blood vessels. It can also be observed from the results that the pressure distributions and pressure drops along the vascular system are in good agreement with the physiological data found in the literature. The results also show that the velocity profiles immediately following a bifurcation are not initially symmetric, with their maxima shifted toward the inner part of the bifurcation in the daughter vessels. Finally, the results show that the maximum deformation is about 2% of the average vessel radius, which is relatively small and typical for small arteries.