On the Wall Shear Stress Gradient in Fluid Dynamics

The gradient of the fluid stresses exerted on curved boundaries, conventionally computed in terms of directional derivatives of a tensor, is here analyzed by using the notion of intrinsic derivative which represents the geometrically appropriate tool for measuring tensor variations projected on curved surfaces. Relevant differences in the two approaches are found by using the classical Stokes analytical solution for the slow motion of a fluid over a fixed sphere and a numerically generated three dimensional dynamical scenario. Implications for theoretical fluid dynamics and for applied sciences are finally discussed.

THE INFLUENCE OF HEMODYNAMICS ON THE ULCERATION PLAQUES OF CAROTID ARTERY STENOSIS

The further rupture of atherosclerotic ulceration plaque is one of the main triggers of the carotid ischemic stroke. However, the abnormal hemodynamics is not well addressed yet. A lesion-based computational fluid dynamic (CFD) analysis is proposed to investigate the complex hemodynamic change of the ulceration plaque that prevails in patients. The 3D models including eight groups of ulcerations (six groups with single ulceration and two groups with two consecutive ulcerations), were reconstructed based on the computer tomography (CT) images, and the tetrahedral grid was taken to mesh the models with the appropriate numbers. After setting the boundary conditions, numerical simulation was carried out to analyze the pulsatile blood flow in the models. The complex flow in the vicinity of the ulcerations directly leads to a significant effect on the distribution of the wall shear stress (WSS). WSS is respectively from 3.29 to 35.41 Pa at the upstream, from 11.90 to 41.85 Pa at the downstream ulceration, and 18.60 and 30.60 Pa in the area between the two consecutive ulcerations. The rupture from these regions could cause the further rupture of ulceration plaques, particularly at the downstream ulceration and the area between the two consecutive ulcerations. The twisting and the curling of the flow at the ulcerations can lead to thrombosis which may break free later and go through the downstream stenosis by the effect of the flow. The different degrees of WSS in downstream and upstream ulcerations will damage the ulceration on the plaque because of pulling and stretching forces at the ulcerations. Furthermore, high wall shear stress gradient (WSSG) also increases the risk of the further rupture. Our study gives a better understanding in the further rupture mechanism of ulceration plaques and provides the information of the location of thrombosis after aggravated rupturing, which can be referred by surgeons to improve the surgical planning.

HEMODYNAMIC ANALYSIS OF CAROTID SIPHON WITH UNILATERAL STENOSIS: SIGNIFICANCE OF ARTERIAL GEOMETRY

Geometry of arteries has been considered as an important risk factor for atherosclerosis, because it influences the local hemodynamics. But the effect of the arterial shape on the internal carotid arterial (ICA) stenosis remains unknown. Four subjects with two geometrically different ICAs, diagnosed with unilateral stenosis, were investigated to clarify the association between the ICA shape and the stenosis. Magnetic resonance angiography (MRA) images of the two branches of ICA were acquired from the subject, and reconstructed into 3D models. The bifurcations and taper of the ICAs were removed. The pulsatile flow in the models was computationally simulated to evaluate the effect of the arterial geometry on hemodynamics. Because of the different geometry between the two branches of ICAs, the hemodynamic pattern is obviously different. The wall shear stress gradient (WSSG) and oscillating shear index (OSI) is lower in the left ICA branches, where helical flow is found, because of the large nonplanarity of bends. The difference of the arterial geometry is probably the only reason for the stenosis in this study. Furthermore, the planarity of the carotid siphon is the only geometric factor that is significantly different between the two branches. Consequently, the planarity is considered as the most important geometric factor for stenosis in ICAs.

High Wall Shear Stress and Positive Wall Shear Stress Gradient Trigger the Initiation of Intracranial Aneurysms

While the pathogenesis of an intracranial aneurysm (IA) is poorly understood, it has been generally postulated to be related to hemodynamic insult. IAs are predominantly located at apices of arterial bifurcations or outer curves on or near the Circle of Willis, suggesting a potential role of the specific hemodynamics at such locations characterized by high wall shear stress (WSS). Clinically, new IA formation has been observed following local flow increase.