Blood flow in branched vessels with aneurysm

This paper is devoted to the blood flow symmetry loss study in the branching vessels with the aneurysm. Aneurysm appearance is possible in the damaged blood vessels that localized in different parts of the circulatory system with different types of flow (convergent and divergent). Aneurysms of aorta, peripheral vessels, heart, and brain can be distinguished. Regardless of the localization, the disease leads to serious consequences and requires surgical intervention. This paper presents mathematical modeling of blood flow in vessels with small diameter, which is characterized by small values of Reynolds number and rigidity. This representation corresponds to the cerebral vessels. The blood flow simulation is performed using rheological viscoelastic fluid model (FENE-P). This model predicts the blood flow properties corresponding to the real biological fluid, namely, the viscosity anomaly, variable longitudinal viscosity, and the finite time of stress relaxation. The governing parameters of the flows of such fluids is the Weissenberg number (We) characterizing the ratio of elastic properties of biological liquid to viscous ones, the Reynolds number (Re) describing the ratio of inertial to viscous properties, the ability of macromolecules of proteins included in blood change their orientation in the flow, the degree of disentanglement of macromolecules of protein L 2 and retardation coefficient characterizing the concentration of macromolecules in the blood. In this paper, the possibility of blood flow symmetry loss in bifurcation areas of the circulatory system at certain values of the parameters of the mathematical model for converging flow is discussed. The effect of the shape of aneurysm occurrence on the blood flow pattern is performed. Results comparison for blood flow in the channel of two types of cavities is performed.