On the effect of apex geometry on wall smear stress and pressure in two-dimensional models of arterial bifurcations

There is strong evidence to support the hypothesis that vascular geometry p lays an important role in the initiation and development of cerebral aneury sms (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 a neurysms are nearly always found at arterial bifurcations in and near the c ircle of Willis.(42) It is commonly believed that the cause of initiation a nd 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 th at local geometric factors can have a significant impact on the magnitude a nd spatial gradients of wall pressure and shear stress at the apex of arter ial bifurcations. We consider steady how of incompressible, Newtonian fluid s. We find that sharp corners such as those at arterial bifurcations and th e juncture between grafted vessels can be a source of localized high wall p ressure and shear stress. In fact, it can be shown analytically that perfec tly sharp corners (zero radius of curvature) will lead to unbounded magnitu des of shear stress and pressure.(26) Significantly, the unboundedness of t he pressure and shear stress at perfectly sharp corners is unrelated to the fluid inertia. Whereas for zero radius of curvature, both the maximum pres sure and shear stress occur at the apex; for nonzero radius of curvature, t he pressure maximum is found at the apex, the shear stress is zero at the a pex, and the shear stress maximum shifts to the lateral sides of the bifurc ation. These results show that arterial bifurcations should not be idealize d as perfectly sharp for studies of initiation and development of cerebral. aneurysms.