The influence of out-of-plane geometry on pulsatile flow within a distal end-to-side anastomosis

We present an experimental and computational investigation of time-varying flow in an idealized fully occluded 45 degrees distal end-to-side anastomosis. Two geometric configurations are assessed, one where the centerlines of host and bypass vessels lie within a plane, and one where the bypass vessel is deformed out of the plane of symmetry, respectively, termed planar and non-planar. Flow experiments were conducted by magnetic resonance imaging in rigid wall models and computations were performed using a high order spectral/hp algorithm. Results indicate a significant change in the spatial distribution of wall shear stress and a reduction of the time-averaged peak wall shear stress magnitude by 10% in the non-planar model as compared to the planar configuration. In the planar geometry the stagnation point follows a straight-line path along the host artery bed with a path length of 0.8 diameters. By contrast in the non-planar case the stagnation point oscillates about a center that is located off the symmetry plane intersection with the host artery bed wall, and follows a parabolic path with a 0.7 diameter longitudinal and 0.5 diameter transverse excursion. A definition of the oscillatory shear index (OSI) is introduced that varies between 0 and 0.5 and that accounts for a continuous range of wall shear stress vector angles. In both models, regions of elevated oscillatory shear were spatially associated with regions of separated or oscillating stagnation point flow. The mean oscillatory shear magnitude (considering sites where OSI>0.1) in the non-planar geometry was reduced by 22% as compared to the planar configuration. These changes in the dynamic behavior of the stagnation point and the oscillatory shear distribution introduced by out-of-plane graft curvature may influence the localization of vessel wall sites exposed to physiologically unfavorable flow conditions.     

Computation in the rabbit aorta of a new metric – the transverse wall shear stress – to quantify the multidirectional character of disturbed blood flow

Spatial variation of the haemodynamic stresses acting on the arterial wall is commonly assumed to explain the focal development of atherosclerosis. Disturbed flow in particular is thought to play a key role. However, widely-used metrics developed to quantify its extent are unable to distinguish between uniaxial and multidirectional flows. We analysed pulsatile flow fields obtained in idealised and anatomically-realistic arterial geometries using computational fluid dynamics techniques, and in particular investigated the multidirectionality of the flow fields, capturing this aspect of near-wall blood flow with a new metric – the transverse wall shear stress (transWSS) – calculated as the time-average of wall shear stress components perpendicular to the mean flow direction. In the idealised branching geometry, multidirectional flow was observed downstream of the branch ostium, a region of flow stagnation, and to the sides of the ostium. The distribution of the transWSS was different from the pattern of traditional haemodynamic metrics and more dependent on the velocity waveform imposed at the branch outlet. In rabbit aortas, transWSS patterns were again different from patterns of traditional metrics. The near-branch pattern varied between intercostal ostia, as is the case for lesion distribution; for some branches there were striking resemblances to the age-dependent patterns of disease seen in rabbit and human aortas. The new metric may lead to improved understanding of atherogenesis.     

Post-stenotic core flow behavior in pulsatile flow and its effects on wall shear stress

Arteries of several species, including man, tend to adjust their diameters such that the mean wall shear stress is in the range of 10-20 dynes cm-2. Additionally, intimal thickening in the human carotid bifurcation correlates well with the reciprocal of wall shear stress as determined in model studies. The correlation indicates that wherever the local mean wall shear stress exceeds approximately 10 dynes cm-2, the artery tends to be spared from intimal thickening. However, it is not known whether mean shear stress, i.e. the time-averaged value, or the instantaneous shear stress is the appropriate correlative variable. Each of these variables suggests different mechanisms for the reaction of the artery wall to its hemodynamic environment. It is therefore important to devise means by which the effects of mean shear and pulsatile shear can be separated in the study of atherogenesis. The present investigation examines the post-stenotic flow field in Plexiglas models under pulsatile conditions approximating those in the aortas of the cynomolgus monkey, an animal often employed in atherogenesis research. Behavior of the core flow and its effects on wall shear stress are studied for stenoses of 75 and 90% area reductions using laser velocimetry. The results show that the post-stenotic field contains regions in which the mean wall shear stress is low, but the pulsatile excursions are large.(ABSTRACT TRUNCATED AT 250 WORDS)     

血流剪切力在动脉粥样硬化形成中的作用

血管内皮位于血管壁和血液的界面,直接与血流接触而持续受血流剪切力的作用。血管内皮细胞能感受血流机械力的变化,通过激活相应的信号通路调节血管内皮和平滑肌的结构和功能。研究发现,血液流动力的形式与动脉粥样硬化的发生发展有密切的关系。本综述将就血流剪切力与动脉粥样硬化的相互关系及作用机制的最新研究进展作简要介绍。     

Numerical 3D-simulation of pulsatile wall shear stress in an arterial T-bifurcation model

The structure of pulsatile blood flow and wall shear stress in a 90° T-bifurcation model is analysed numerically. The nonlinear Navier-Stokes equations for time-dependent incompressible Newtonian fluid flow are approximated using a newly developed pressure correction, finite element method. The wall shear stress is calculated from the finite element velocity field. The investigation shows viscous flow phenomena such as flow separation and stagnation and the distribution of high and low wall shear stress during the pulse cycle. Furthermore, the effect of a sharp corner the bifurcation edge on the wall shear stress is analysed. Detailed local flow investigation is required to examine fluid dynamic contribution to the development of arterial diseases such as atherosclerosis and thrombosis.     

犬不同血管搭桥方法及搭桥血管内流场的计算机数值模拟

目的血管搭桥术后的内膜增生往往导致手术失败,而内膜增生与搭桥血管内的流场密切相关,为改善搭桥血管中的流场结构,作者设计了偏心搭桥手术方法,利用计算机数值模拟技术,探索偏心搭桥和传统搭桥血管中流场的变化,为血管搭桥方法提供优化设计方案。方法16只犬随机分为偏心搭桥组和传统搭桥组进行血管搭桥,测定搭桥前后血管几何数据,搭桥后近心端及远心端吻合口血流量和血压。按测定的血管几何数据,FLUENT 6.2模拟搭桥血管内的流场。结果偏心搭桥近心端和远心端吻合口不在同一平面。传统搭桥中,主体动脉远心端吻合口对应面处存在一个较低壁面剪切应力（WSS）区域及流体停滞点,离脚跟较近的一部分流体会形成涡漩,血流进入主体动脉后,还会表现出迪恩涡二次流;偏心搭桥中,主体动脉吻合口对应面上的低WSS区域和流体停滞点消失,血流接触到吻合口底面后,以切向旋转的方式改变其流动方向,不会形成涡漩,且当血流进入主体动脉后,立即发生螺旋流态且能持续很长一段。结论偏心搭桥能够产生血液旋动流,显著增加远心端血流量、提高WSS。     

Wall shear rate measurements in an elastic curved artery model

Since atherosclerotic lesions tend to be localized at bends and branching points, knowledge of wall shear rate patterns in models of these geometries may help elucidate the mechanism of atherogenesis. This study uses the photochromic method of flow visualization to determine both the mean and amplitude of the wall shear rate waveform in straight and curved elastic arterial models to demonstrate the effects of curvature, elasticity, and the phase angle between the flow and pressure waveforms (impedance phase angle). Under sinusoidal flow conditions characteristic of large arteries, the mean shear rate at the inner wall of the curved tube is reduced 40–56% from its steady flow value, depending on the phase angle. Wall shear rate amplitudes in the curved tube are significantly reduced by wall motion (36–55% of the Womersley amplitude for a straight rigid tube). The shear rate amplitude at the outer wall decreases 30% as the phase angle is reduced from −20° to −66°, while the shear rate amplitude at the inner wall increases 45%. As a result, the oscillatory nature of flow at the outer wall decreases with decreasing negative phase angle, but flow at the inner wall becomes much more oscillatory. At large negative phase angles, characteristic of hypertension or vasoactive agents, the shear rate at the inner wall has a small mean and cycles through positive and negative values; the shear rate at the outer wall remains positive throughout the flow cycle. Thus, the impedance phase angle could affect atherogenesis along the inner wall if temporal and directional changes in wall shear rate play a role.     

Haemodynamics of angioaccess venous anastomoses

A large percentage of arteriovenous haemodialysis angioaccess loop grafts (AVLG) fail within the first year after surgery, the occlusive lesions being found predominantly at the venous anastomosis site. This paper presents a detailed flow dynamic study of the AVLG system using three elastic, transparent bench-top flow models, which were based on the geometry of silicone rubber casts obtained at different times from a chronic animal model. Each model thus represented a different stage of the lesion development. Flow visualization and laser Doppler anemometer surveys of the flow field confirmed that the hydrodynamic factors favour lesion development near the stagnation point opposite the anastomotic toe, where the momentum of the impinging jet stream, combined with the oscillating wall shear stress generated in the vicinity of the stagnation point, acts in both directions. The accumulation of tracer particles in the region of flow separation is believed to be a combined contribution from the hydraulic forces and the inward motion of the vessel wall. As these hydrodynamic factors are enhanced upon further development of the occlusive lesion, a vicious cycle may be formed.     

Analysis of temporal shear stress gradients during the onset phase of flow over a backward-facing step

Endothelial cells in blood vessels are exposed to bloodflow and thus fluid shear stress. In arterial bifurcations and stenoses, disturbed flow causes zones of recirculation and stagnation, which are associated with both spatial and temporal gradients of shear stress. Such gradients have been linked to the generation of atherosclerotic plaques. For in-vitro studies of endothelial cell responses, the sudden-expansion flow chamber has been widely used and described. A two-dimensional numerical simulation of the onset phase of flow through the chamber was performed. The wall shear stress action on the bottom plate was computed as a function of time and distance from the sudden expansion. The results showed that depending on the time for the flow to be established, significant temporal gradients occurred close to the second stagnation point of flow. Slowly ramping the flow over 15 s instead of 200 ms reduces the temporal gradients by a factor of 300, while spatial gradients are reduced by 23 percent. Thus, the effects of spatial and temporal gradients can be observed separately. In experiments on endothelial cells, disturbed flow stimulated cell proliferation only when flow onset was sudden. The spatial patterns of proliferation rate match the exposure to temporal gradients. This study provides information on the dynamics of spatial and temporal gradients to which the cells are exposed in a sudden-expansion flow chamber and relates them to changes in the onset phase of flow.     

Helical flow as fluid dynamic signature for atherogenesis risk in aortocoronary bypass. A numeric study

The main purpose of the study was to verify if helical flow, widely observed in several vessels, might be a signature of the blood dynamics of vein graft anastomosis. We investigated the existence of a relationship between helical flow structures and vascular wall indexes of atherogenesis in aortocoronary bypass models with different geometric features. In particular, we checked for the existence of a relationship between the degree of helical motion and the magnitude of oscillating shear stress in conventional hand-sewn proximal anastomosis. The study is based on the numerical evaluation of four bypass geometries that are attached to a simplified computer representation of the ascending aorta with different angulations relative to aortic outflow. The finite volume technique was used to simulate realistic graft fluid dynamics, including aortic compliance and proper aortic and graft flow rates. A quantitative method was applied to evaluate the level of helicity in the flow field associated with the four bypass models under investigation. A linear inverse relationship (R = -0.97) was found between the oscillating shear index and the helical flow index for the models under investigation. The results obtained support the hypothesis that an arrangement of the flow field in helical patterns may elicit damping in wall shear stress temporal gradients at the proximal graft. Accordingly, helical flow might play a significant role in preventing plaque deposition or in tuning the mechanotransduction pathways of cells. Therefore, results confirm that helical flow constitutes an important flow signature in vessels, and its strength as a fluid dynamic index (for instance in combination with magnetic resonance imaging flow visualization techniques) for risk stratification, in the activation of both mechanical and biological pathways leading to fibrointimal hyperplasia.     

Numerical simulation of aortic bifurcation flows: The effect of flow divider curvature

Two dimensional steady flow calculations in computational regions obtained from radiographs of human aortic bifurcations correlate well with unsteady measurements of wall shear in flow-through casts of the same vessels. The results suggest that wall slope may be an important factor affecting the variability of shear along the medial walls of this arterial segment. If extremes of shear stress promote atherogenesis, then variations in the curvature of the proximal iliac arteries may affect the susceptibility of these vessels to vascular disease on their medial aspect.     

Normal and shear stresses influence the spatial distribution of intracellular adhesion molecule-1 expression in human umbilical vein endothelial cells exposed to sudden expansion flow

Patterns in cell adhesion molecule expression by endothelial cells may play a role in atherogenesis. Previous studies have shown dependence of intracellular adhesion molecule-1 (ICAM-1) expression in human umbilical vein endothelial cells (HUVEC) on shear stress and have indirectly linked ICAM-1 expression to spatial gradients in shear stress. The spatial distribution of ICAM-1 in HUVEC pre-exposed to flow for 8h was determined using fluorescence microscopy and a sudden expansion flow chamber with a 2.66 expansion ratio to simulate gradients in wall shear stress found near arterial branches in vivo. When ICAM-1 expression in the disturbed flow region was compared to theoretical stress distributions obtained from a computational model of sudden expansion flow, a modest trend (R2 = 0.327, p < 0.01)was observed between ICAM-1 and shear stress but the correlation between ICAM-1 and shear stress gradient was insignificant. In contrast, a moderately strong trend (R2 = 0.873, p < 0.01) was evident between ICAM-1 expression and the component of normal stress induced by the expansion. Thus, in this in vitro model, normal stress arising from sudden expansion flow modulates the effect of shear stress on ICAM-1 expression.     

Pulsed ultrasonic Doppler velocity measurements inside a left ventricular assist device

In this study we have employed a single channel, pulsed ultrasonic Doppler velocimeter to measure instantaneous velocity distributions within the pumping chamber of a ventricular assist device. Instantaneous velocities have been decomposed into periodic mean and turbulent fluctuating components from which estimates of Reynolds stresses within the chamber and mean shear stresses along the wall of the chamber have been obtained. A review of the complete data set indicates a maximum value of the mean wall shear stress of 25 dynes/cm2 and a maximum Reynolds stress of 212 dynes/cm2. These values are lower than those measured distal to aortic valve prostheses in vitro and are well below levels known to damage blood components. Core flow patterns, wall washing patterns and flow stagnation points are also revealed.     

The effect of angle and flow rate upon hemodynamics in distal vascular graft anastomoses: an in vitro model study.

A steady flow, in vitro model of distal arterial bypass graft junctions was used to examine the effects of junction angle and flow rate on the local velocity field. Three test sections were fabricated from Plexiglas tubing having anastomotic junction angles of either 30, 45, or 60 deg. Flow visualization revealed velocity profiles skewed toward the outer wall with a flow split around a clear stagnation point along the outer wall. Laser Doppler anemometry [LDA] measurements confirmed a distinct stagnation point at the outer wall and both reverse and forward shear were detected immediately upstream and downstream, respectively, of this site. Axial velocities and shear rates along the outer wall were higher than along the inner wall and occurred in the junction angle order: 45, 60, and 30 deg. This study clearly identified changes in wall shear which varied with the anastomotic angle and flow rate.     

Towards a concept of thrombosis in accelerated flow: rheology, fluid dynamics, and biochemistry

The predilection sites of arterial thrombosis are characterized by local increase in wall shear stress, flow separation with eddy formation and stagnation point flow. The defenders of high shear, as well as those of low shear theory of thrombogenesis, point to correlations of predilection sites and the respective flow abnormalities. Experimental evidence is provided, that high shear rates can damage both red cells and platelets, that lysed red cells constitute a potent platelet stimulant, due to their content of adenine nucleotides, and that platelets do not adhere to surfaces unless transported onto them by convective motion, the effectiveness of the platelet-wall interaction being enhanced by platelet activation. Based on these facts, a resolution of the contrast between high and low shear theory of thrombosis is attempted in a way, that the different flow regimens, with blood cells sequentially passing them, are each considered important and interdependent steps on the way to thrombosis.     

Effects of wall shear stress and fluid recirculation on the localization of circulating monocytes in a three-dimensional flow model

There is a correlation between the location of early atherosclerotic lesions and the hemodynamic characteristics at those sites. Circulating monocytes are key cells in the pathogenesis of atherosclerotic plaques and localize at sites of atherogenesis. The hypothesis that the distribution of monocyte adhesion to the vascular wall is determined in part by hemodynamic factors was addressed by studying monocyte adhesion in an in vitro flow model in the absence of any biological activity in the model wall.

Suspensions of U937 cells were perfused (Re = 200) through an axisymmetric silicone flow model with a stenosis followed by a reverse step. The model provided spatially varying wall shear stress, flow separation and reattachment, and a three-dimensional flow pattern. The cell rolling velocity and adhesion rates were determined by analysis of videomicrographs. Wall shear stress was obtained by numerical solution of the equations of fluid motion. Cell adhesion patterns were also studied in the presence of chemotactic peptide gradients.

The cell rolling velocity varied linearly with wall shear stress. The adhesion rate tended to decrease with increasing local wall shear stress, but was also affected by the radial component of velocity and the dynamics of the recirculation region and flow reattachment. Adhesion was increased in the vicinity of chemotactic peptide sources downstream of the expansion site. Results with human monocytes were qualitatively similar to the U937 experiments.

Differences in the adhesion rates of U937 cells occurring solely as a function of the fluid dynamic properties of the flow field were clearly demonstrated in the absence of any biological activity in the model wall.     

Numerical flow studies in human carotid artery bifurcations: basic discussion of the geometric factor in atherogenesis

In this study fluid dynamic variables are analysed numerically in different human carotid artery bifurcation models in order to clarify the geometric factor in carotid bifurcation atherogenesis. The geometric variations describe healthy human carotid bifurcation anatomy and concern the shape of the carotid sinus and the angle between the branches. The flow conditions remain unchanged. The governing Navier-Stokes equations describing incompressible, pulsatile, three-dimensional viscous flow are approximated using a pressure correction finite element procedure which has been developed for time-consuming, three-dimensional, time-dependent viscous flow problems. The study concentrates on flow velocity, on detailed analysis of flow separation and flow recirculation, and on wall shear stress distribution. The results show that the extension and the location of the recirculation zone in the sinus as well as the duration of separated flow during the pulse cycle are affected by the geometrical variations. In view of the significance of the reversed flow zones and of the accompanied low shear regions in atherogenesis the geometry-dependent flow separation characteristics in the sinus is of substantial interest.     

Pulsatile poststenotic flow studies with laser Doppler anemometry

The pulsatile flow field distal to axisymmetric constrictions in a straight tube was studied using laser Doppler anemometry. The upstream centerline velocity waveform was sinusoidal at a frequency parameter of 7.5 and mean Reynolds number of 600. Stenosis models of 25, 50 and 75% area reduction were employed and velocity data were derived by ensemble averaging methods. Extensive measurements of the pulsatile velocity profiles are reported, and wall shear rates were computed from the near wall velocity profile gradients. The experiments indicate that a permanent region of poststenotic flow separation does not exist even for the severest constriction, in contrast to results for steady flow. Values of wall shear stress were greatest near the throat of the constriction and were relatively low in the poststenotic region, including the region of most intense flow disturbance. Turbulence was found only for the 75% stenosis model and was created only during a segment of the cycle. Although much emphasis has been placed upon turbulence in the detection of arterial stenoses, particularly as identified by Doppler ultrasound spectral broadening, the present study implies that identification of flow disturbances of an organized nature may be more fundamental in recognizing mild to moderate disease. Additionally, the relationship of these flow field results to the animal aortic coarctation model often employed in atherogenesis studies is discussed.     

Frequency dependence of dynamic curvature effects on flow through coronary arteries

The flow through a curved tube model of a coronary artery was investigated computationally to determine the importance of time-varying curvature on flow patterns that have been associated with the development of atherosclerosis. The entry to the tube was fixed while the radius of curvature varied sinusoidally in time at a frequency of 1 or 5 Hz. Angiographic data from other studies suggest that the radius of curvature waveform contains significant spectral content up to 6 Hz. The overall flow patterns were similar to those observed in stationary curved tubes; velocity profile skewed toward the outer wall, secondary flow patterns, etc. The effects of time-varying curvature on the changes in wall shear rate were expressed by normalizing the wall shear rate amplitude with the shear rate calculated at the static mean radius of curvature. It was found that the wall shear rate varied as much as 94 percent of the mean wall shear rate at the mid wall of curvature for a mean curvature ratio of 0.08 and a 50 percent change in radius of curvature. The effects of 5 Hz deformation were not well predicted by a quasi-static approach. The maximum values of the normalized inner wall shear rate amplitude were found to scale well with a dimensionless parameter equivalent to the product of the mean curvature ratio (delta), normalized change in radius of curvature (epsilon), and a Womersley parameter (alpha). This parameter was less successful at predicting the amplitudes elsewhere in the tube, thus additional studies are necessary. The mean wall shear rate was well predicted with a static geometry. These results indicate that dynamic curvature plays an important role in determining the inner wall shear rates in coronary arteries that are subjected to deformation levels of epsilon delta alpha > 0.05. The effects were not always predictable with a quasi-static approach. These results provide guidelines for constructing more realistic models of coronary artery flow for atherogenesis research.