ON THE EFFECT OF APEX GEOMETRY ON WALL SHEAR STRESS AND PRESSURE IN TWO-DIMENSIONAL MODELS OF ARTERIAL BIFURCATIONS

Abstract

There is strong evidence to support the hypothesis that vascular geometry plays an important role in the initiation and development of cerebral aneurysms (see e.g. Refs. 24, 40 and 41) as well as other vascular diseases (see e.g. Refs. 25, 31 and 35) through its influence on hemodynamics. Cerebral aneurysms are nearly always found at arterial bifurcations in and near the circle of Willis.42 It is commonly believed that the cause of initiation and development of cerebral aneurysms is at least indirectly related to the effect of hemodynamic wall pressure and shear stress on the arterial tissue at arterial bifurcations (see e.g. Refs. 24, 39–41 and 44). In this work, we use analytical and numerical approaches to investigate the hypothesis that local geometric factors can have a significant impact on the magnitude and spatial gradients of wall pressure and shear stress at the apex of arterial bifurcations. We consider steady flow of incompressible, Newtonian fluids. We find that sharp corners such as those at arterial bifurcations and the juncture between grafted vessels can be a source of localized high wall pressure and shear stress. In fact, it can be shown analytically that perfectly sharp corners (zero radius of curvature) will lead to unbounded magnitudes of shear stress and pressure.26 Significantly, the unboundedness of the pressure and shear stress at perfectly sharp corners is unrelated to the fluid inertia. Whereas for zero radius of curvature, both the maximum pressure and shear stress occur at the apex; for nonzero radius of curvature, the pressure maximum is found at the apex, the shear stress is zero at the apex, and the shear stress maximum shifts to the lateral sides of the bifurcation. These results show that arterial bifurcations should not be idealized as perfectly sharp for studies of initiation and development of cerebral aneurysms.