Key result
Analytical and numerical models demonstrate that perfectly sharp corners at arterial bifurcations lead to unbounded magnitudes of shear stress and pressure.
Computational modeling demonstrates that arterial bifurcations should not be idealized as perfectly sharp in studies of cerebral aneurysm initiation, as this leads to unbounded and non-physiological shear stress and pressure.
Bifurcation models must avoid sharp corners to prevent non-physiological stresses; leaves open optimal geometry assumptions in aneurysm initiation research.
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.
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Haljasmaa et al. (2001) studied Cerebral aneurysms. Apex geometry (sharp vs nonzero radius of curvature) was evaluated on Magnitude and spatial gradients of wall pressure and shear stress. Analytical and numerical models demonstrate that perfectly sharp corners at arterial bifurcations lead to unbounded magnitudes of shear stress and pressure.
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