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.     

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。     

Local and global geometric influence on steady flow in distal anastomoses of peripheral bypass grafts

We consider the effect of geometrical configuration on the steady flow field of representative geometries from an in vivo anatomical data set of end-to-side distal anastomoses constructed as part of a peripheral bypass graft. Using a geometrical classification technique, we select the anastomoses of three representative patients according to the angle between the graft and proximal host vessels (GPA) and the planarity of the anastomotic configuration. The geometries considered include two surgically tunneled grafts with shallow GPAs which are relatively planar but have different lumen characteristics, one case exhibiting a local restriction at the perianastomotic graft and proximal host whilst the other case has a relatively uniform cross section. The third case is nonplanar and characterized by a wide GPA resulting from the graft being constructed superficially from an in situ vein. In all three models the same peripheral resistance was imposed at the computational outflows of the distal and proximal host vessels and this condition, combined with the effect of the anastomotic geometry, has been observed to reasonably reproduce the in vivo flow split. By analyzing the flow fields we demonstrate how the local and global geometric characteristics influences the distribution of wall shear stress and the steady transport of fluid particles. Specifically, in vessels that have a global geometric characteristic we observe that the wall shear stress depends on large scale geometrical factors, e.g., the curvature and planarity of blood vessels. In contrast, the wall shear stress distribution and local mixing is significantly influenced by morphology and location of restrictions, particular when there is a shallow GPA. A combination of local and global effects are also possible as demonstrated in our third study of an anastomosis with a larger GPA. These relatively simple observations highlight the need to distinguish between local and global geometric influences for a given reconstruction. We further present the geometrical evolution of the anastomoses over a series of follow-up studies and observe how the lumen progresses towards the faster bulk flow of the velocity in the original geometry. This mechanism is consistent with the luminal changes in recirculation regions that experience low wall shear stress. In the shallow GPA anastomoses the proximal part of the native host vessel occludes or stenoses earlier than in the case with wide GPA. A potential contribution to this behavior is suggested by the stronger mixing that characterizes anastomoses with large GPA.     

Flow patterns in the radiocephalic arteriovenous fistula: an in vitro study.

A significant number of late failures of arteriovenous fistulae for haemodialysis access are related to the progression of intimal hyperplasia. Although the aetiology of this process is still unknown, the geometry of the fistula and the local haemodynamics are thought to be contributory factors. An in-vitro study was carried out to investigate the local haemodynamics in a model of a Cimino-Brescia arteriovenous (AV) fistula with a 30 degrees anastomotic angle and vein-to-artery diameter ratio of 1.6. Flow patterns were obtained by planar illumination of micro-particles suspended in the fluid. Steady and pulsatile flow studies were performed over a range of flow conditions corresponding to those recorded in patients. Quantitative measurements of wall shear stress and turbulence were made using laser Doppler anemometry. The flow structures in pulsatile flow were similar to those seen in steady flow with no significant qualitative changes over the cardiac cycle. This was probably the result of the low pulsatility index of the flow waveform in AV fistulae. Turbulence was the dominant feature in the vein, with relative turbulence intensity > 0.5 within 10 mm of the suture line decreasing to a relatively constant value of about 0.10-0.15 between 40 and 70 mm from the suture line. Peak and mean Reynolds shear stress of 15 and 20 N/m2, respectively, were recorded at the suture line. On the floor of the artery, peak values of temporal mean and oscillating wall shear stress of 9.22 and 29.8 N/m2, respectively. In the vein, both mean and oscillating wall shear stress decreased with distance from the anastomosis.     

Non-Newtonian effects of blood flow on hemodynamics in distal vascular graft anastomoses

Non-Newtonian fluid flow in a stenosed coronary bypass is investigated numerically using the Carreau-Yasuda model for the shear thinning behavior of the blood. End-to-side coronary bypass anastomosis is considered in a simplified model geometry where the host coronary artery has a 75% severity stenosis. Different locations of the bypass graft to the stenosis and different flow rates in the graft and in the host artery are studied. Particular attention is given to the non-Newtonian effect of the blood on the primary and secondary flow patterns in the host coronary artery and the wall shear stress (WSS) distribution there. Interaction between the jet flow from the stenosed artery and the flow from the graft is simulated by solving the three-dimensional Navier-Stokes equation coupled with the non-Newtonian constitutive model. Results for the non-Newtonian flow, the Newtonian flow and the rescaled Newtonian flow are presented. Significant differences in axial velocity profiles, secondary flow streamlines and WSS between the non-Newtonian and Newtonian fluid flows are revealed. However, reasonable agreement between the non-Newtonian and the rescaled Newtonian flows is found. Results from this study support the view that the residual flow in a partially occluded coronary artery interacts with flow in the bypass graft and may have significant hemodynamic effects in the host vessel downstream of the graft. Non-Newtonian property of the blood alters the flow pattern and WSS distribution and is an important factor to be considered in simulating hemodynamic effects of blood flow in arterial bypass grafts.     

Analysis of blood flow in an out-of-plane CABG model

Coronary artery bypass graft (CABG) is a routine surgical treatment for ischemic and infarcted myocardium. A large number of CABG fail postoperatively because of intimal hyperplasia within months or years. The cause of this failure is thought to be partly related to the flow patterns and shear stresses acting on the endothelial cells. An accurate representation of the flow field and associated wall shear stress (WSS) requires a detailed three-dimensional (3D) model of the CABG. The purpose of this study is to present a detailed analysis of blood flow in a 3D aorto/left CABG, bypassing the occluded left anterior descending coronary (LAD) artery. The analysis takes into account the influence of the out-of-plane geometry of the graft. The finite volume technique was employed to model the 3D blood flow pattern to determine the velocity and WSS distributions. This study presents the flow field distributions of the velocity and WSS at four instances of the cardiac cycle, two in systole and two in diastole. Our results reveal that the CABG geometry has a significant effect on the velocity distribution. The axial velocity profiles at different instances of the cardiac cycle exhibit strong skewing; significant secondary flow and vortex structures are seen in the in-plane velocity patterns. The maximum WSS on the bed of the occluded LAD artery opposite to the graft junction is 14 Pa in middiastole, whereas there is a significantly lower and more uniform distribution of WSS on the bed of the anastomosis. The present results indicate that nonplanarity of the blood vessel along with the inflow conditions has a substantial effect on the fluid mechanics of CABG that contribute to the patency of graft.     

Unsteady near wall residence times and shear exposure in model distal arterial bypass grafts

Building on previous studies of unsteady flow within model distal bypass grafts we analyse the near wall residence times and shear exposure in a 45 degrees anastomosis under symmetrical and symmetry breaking geometric configurations. We define residence time as the minimum time for a particle to exit a spherical region and shear exposure as a temporal integral of the Huber-Henky-von-Mises criterion along a particle path over a fixed time interval. Decomposing the pulsatile cycle into four equal intervals we find that the interval of peak residence time in the host vessel is from mid-deceleration to peak diastole and peak diastole to mid-acceleration. The asymmetric model is shown to have a significantly lower residence time during these intervals. Considering the shear exposure prior to the residence time evaluation we determine that a higher average shear exposure exists in the asymmetric model associated with the upstream geometry modification. Analysis of the regions of high residence time and shear exposure suggests that the "toe" region and the interface between the "heel" and bulk flow are more significant than the bed and heel region. Although the asymmetric model considered in this study reduces residence times in the host artery, the product of the measure of shear exposure and residence time is not found to be preferable. If shear exposure were to be considered as an important factor in particle activation, the findings imply that for junction optimisation, greater consideration needs to be given both to the local junction asymmetry and upstream influence on the shear history.     

Mapping vascular response to in vivo Hemodynamics: application to increased flow at the basilar terminus

Hemodynamic forces play critical roles in vascular pathologies such as atherosclerosis, aneurysms, and stenosis. However, detailed relationships between the specific in vivo hemodynamic microenvironment and vascular responses leading to the triggering or exacerbation of pathological remodeling of the vessel remain elusive. We have developed a hemodynamics-biology co-mapping technique that enables in situ correlation between the in vivo blood flow field and vascular changes secondary to hemodynamic insult. The hemodynamics profile is obtained from computational fluid dynamics simulation within the vascular geometry reconstructed from three-dimensional in vivo images, whereas the vascular response is obtained from histology or immunohistochemistry on harvested vascular tissue. The hemodynamics field is virtually sectioned in the histological slicing planes and digitally co-mapped with the histological images, thereby enabling correlation of the specific local vascular responses with the inciting hemodynamic stresses. We demonstrate application of this technique to rabbit basilar terminus subjected to elevated flow. Morphological changes at the basilar terminus 5 days after the flow increase were co-mapped with the initial wall shear stress and wall shear stress gradient distributions, from which localization of destructive remodeling in a specific hemodynamic zone was noticed. This method paves the way for further investigations to determine the connection between in vivo mechanical stimuli and biological responses, such as initiation of aneurysmal remodeling.     

A numerical study of blood flow patterns in anatomically realistic and simplified end-to-side anastomoses.

PURPOSE: Recently, some numerical and experimental studies of blood flow in large arteries have attempted to accurately replicate in vivo arterial geometries, while others have utilized simplified models. The objective of this study was to determine how much an anatomically realistic geometry can be simplified without the loss of significant hemodynamic information. METHOD: A human femoral-popliteal bypass graft was used to reconstruct an anatomically faithful finite element model of an end-to-side anastomosis. Nonideal geometric features of the model were removed in sequential steps to produce a series of successively simplified models. Blood flow patterns were numerically computed for each geometry, and the flow and wall shear stress fields were analyzed to determine the significance of each level of geometric simplification. RESULTS: The removal of small local surface features and out-of-plane curvature did not significantly change the flow and wall shear stress distributions in the end-to-side anastomosis. Local changes in arterial caliber played a more significant role, depending upon the location and extent of the change. The graft-to-host artery diameter ratio was found to be a strong determinant of wall shear stress patterns in regions that are typically associated with disease processes. CONCLUSIONS: For the specific case of an end-to-side anastomosis, simplified models provide sufficient information for comparing hemodynamics with qualitative or averaged disease locations, provided the "primary" geometric features are well replicated. The ratio of the graft-to-host artery diameter was shown to be the most important geometric feature. "Secondary" geometric features such as local arterial caliber changes, out-of-plane curvature, and small-scale surface topology are less important determinants of the wall shear stress patterns. However, if patient-specific disease information is available for the same arterial geometry, accurate replication of both primary and secondary geometric features is likely required.     

Numerical simulations of pulsatile flow in an end-to-side anastomosis model

A potential interaction between the local hemodynamics and the artery wall response has been suggested for vascular graft failure by intimal hyperplasia (IH). Among the various hemodynamic factors, wall shear stress has been implicated as the primary factor responsible for the development of IH. In order to explore the role of hemodynamics in the formation of IH in end-to-side anastomosis, computational fluid dynamics is employed. To validate the numerical simulations, comparisons with existing experimental data are performed for both steady and pulsatile flows. Generally, good agreement is observed with the velocity profiles whereas some discrepancies are found in wall shear stress (WSS) distributions. Using the same end-to-side anastomosis geometry, numerical simulations are extended using a femoral artery waveform to identify the possible role of unsteady hemodynamics. In the current simulations, Carreau-Yasuda model is used to account for the non-Newtonian nature of blood. Computations indicated a disturbed flow field at the artery-graft junction leading to locally elevated shear stresses on the vascular wall. Furthermore, the shear stress distribution followed the same behavior with oscillating magnitude over the entire flow cycle. Thus, distal IH observed in end-to-side artery-graft models may be caused by the fluctuations in WSS's along the wall.     

The effect of proximal artery flow on the hemodynamics at the distal anastomosis of a vascular bypass graft: computational study

The formation of distal anastomotic intimal hyperplasia (IH), one common mode of bypass graft failure, has been shown to occur in the areas of disturbed flow particular to this site. The nature of theflow in the segment of artery proximal to the distal anastomosis varies from case to case depending on the clinical situation presented. A partial stenosis of a bypassed arterial segment may allow residual prograde flow through the proximal artery entering the distal anastomosis of the graft. A complete stenosis may allow for zero flow in the proximal artery segment or retrograde flow due to the presence of small collateral vessels upstream. Although a number of investigations on the hemodynamics at the distal anastomosis of an end-to-side bypass graft have been conducted, there has not been a uniform treatment of the proximal artery flow condition. As a result, direct comparison of results from study to study may not be appropriate. The purpose of this work was to perform a three-dimensional computational investigation to study the effect of the proximal artery flow condition (i.e., prograde, zero, and retrograde flow) on the hemodynamics at the distal end-to-side anastomosis. We used the finite volume method to solve the full Navier-Stokes equations for steady flow through an idealized geometry of the distal anastomosis. We calculated the flow field and local wall shear stress (WSS) and WSS gradient (WSSG) everywhere in the domain. We also calculated the severity parameter (SP), a quantification of hemodynamic variation, at the anastomosis. Our model showed a marked difference in both the magnitude and spatial distribution of WSS and WSSG. For example, the maximum WSS magnitude on the floor of the artery proximal to the anastomosis for the prograde and zero flow cases is 1.8 and 3.9 dynes/cm2, respectively, while it is increased to 10.3 dynes/cm2 in the retrograde flow case. Similarly, the maximum value of WSSG magnitude on thefloor of the artery proximal to the anastomosis for the prograde flow case is 4.9 dynes/cm3, while it is increased to 13.6 and 24.2 dynes/cm3, respectively, in the zero and retrograde flow cases. The value of SP is highest for the retrograde flow case (13.7 dynes/cm3) and 8.1 and 12.1 percent lower than this for the prograde (12.6 dynes/cm3) and zero (12.0 dynes/cm3) flow cases, respectively. Our model results suggest that the flow condition in the proximal artery is an important determinant of the hemodynamics at the distal anastomosis of end-to-side vascular bypass grafts. Because hemodynamic forces affect the response of vascular endothelial cells, the flow situation in the proximal artery may affect IH formation and, therefore, long-term graft patency. Since surgeons have some control over the flow condition in the proximal artery, results from this study could help determine which flow condition is clinically optimal.     

Flow and wall shear stress in end-to-side and side-to-side anastomosis of venous coronary artery bypass grafts

Purpose  

Coronary artery bypass graft (CABG) surgery represents the standard treatment of advanced coronary artery disease. Two major types of anastomosis exist to connect the graft to the coronary artery, i.e., by using an end-to-side or a side-to-side anastomosis. There is still controversy because of the differences in the patency rates of the two types of anastomosis. The purpose of this paper is to non-invasively quantify hemodynamic parameters, such as mass flow and wall shear stress (WSS), in end-to-side and side-to-side anastomoses of patients with CABG using computational fluid dynamics (CFD).     

Simulation of Flow through a Miller Cuff Bypass Graft

Unnatural temporal and spatial distributions of wall shear stress in the anastomosis of distal bypass grafts have been identified as possible factors in the development of anastomotic intimal hyperplasia in these grafts. Distal bypass graft anastomoses with an autologus vein cuff (a Miller cuff) interposed between the graft and artery have been shown to alleviate the effects of intimal hyperplasia. In this study, pulsatile flow through models of a standard end-to-side anastomosis and a Miller cuff anastomosis are computed and the resulting wall shear stress and pressure distributions analysed. The results are inconclusive, and could be taken to suggest that the unnatural distributions of shear stress that do occur along the anastomosis floor may not be particularly important in the development of intimal hyperplasia. However, it seems more likely that the positive effects of the biological and material properties of the vein cuff, which are not considered in this study, somehow outweigh the negative effects of the shear stress distributions predicted to occur on the floor of the Miller-cuff graft.     

Simulation of flow through a Miller cuff bypass graft

Unnatural temporal and spatial distributions of wall shear stress in the anastomosis of distal bypass grafts have been identified as possible factors in the development of anastomotic intimal hyperplasia in these grafts. Distal bypass graft anastomoses with an autologus vein cuff (a Miller cuff) interposed between the graft and artery have been shown to alleviate the effects of intimal hyperplasia. In this study, pulsatile flow through models of a standard end-to-side anastomosis and a Miller cuff anastomosis are computed and the resulting wall shear stress and pressure distributions analysed. The results are inconclusive, and could be taken to suggest that the unnatural distributions of shear stress that do occur along the anastomosis floor may not be particularly important in the development of intimal hyperplasia. However, it seems more likely that the positive effects of the biological and material properties of the vein cuff, which are not considered in this study, somehow outweigh the negative effects of the shear stress distributions predicted to occur on the floor of the Miller-cuff graft.     

Blood flow and vessel mechanics in a physiologically realistic model of a human carotid arterial bifurcation

The pulsatile flow in an anatomically realistic compliant human carotid bifurcation was simulated numerically. Pressure and mass flow waveforms in the carotid arteries were obtained from an individual subject using non-invasive techniques. The geometry of the computational model was reconstructed from magnetic resonance angiograms. Maps of time-average wall shear stress, contours of velocity in the flow field as well as wall movement and tensile stress on the arterial wall are all presented. Inconsistent with previous findings from idealised geometry models, flow in the carotid sinus is dominated by a strong helical flow accompanied by a single secondary vortex motion. This type of flow is induced primarily by the asymmetry and curvature of the in vivo geometry. Flow simulations have been carried out under the rigid wall assumption and for the compliant wall, respectively. Comparison of the results demonstrates the quantitative influence of the vessel wall motion. Generally there is a reduction in the magnitude of wall shear stress, with its degree depending on location and phase of the cardiac cycle. The region of slow or reversed flow was greater, in both spatial and temporal terms in the compliant model, but the global characteristics of the flow and stress patterns remain unchanged. The analysis of mechanical stresses on the vessel surface shows a complicated stress field. Stress concentration occurs at both the anterior and posterior aspects of the proximal internal bulb. These are also regions of low wall shear stress. The comparison of computed and measured wall movement generally shows good agreement.     

Flow profiles and wall shear stress distribution at a hemodialysis venous anastomosis: preliminary study

The phasic velocity field in the vicinity of the venous anastomosis in a hemodialysis angioaccess arteriovenous fistula loop graft (AVLG) is investigated employing a laser Doppler anemometer (LDA) system. Detailed LDA velocity profiles are obtained by sectional survey performed in a transparent, elastic flow model which was fabricated to represent the geometry of the AVLG system under physiological pressure and flow waveforms. The geometry of the flow model was based on a silicone rubber cast obtained from an experimental dog model. In the present study, detailed distribution of velocity profiles is obtained. The distribution of wall shear stress in the model is computed from the slope of the local velocity profiles near the wall. The relationship between the results obtained by flow visualization and the LDA measurement is discussed.     

Three-dimensional numerical simulations of flow through a stenosed coronary bypass

This work analyzes the flow patterns at the anastomosis of a stenosed coronary bypass. Three-dimensional numerical simulations are performed using a finite elements method. We consider a geometrical model of the host coronary artery with and without a 75% severity stenosis for three different locations from the anastomosis. The flow features - velocity profiles, secondary motions and wall shear stresses - are compared for different configurations of the flow rate and of the distance of the anastomosis from the site of occlusion (called distance of grafting). The combination of the junction flow effects - counter rotating vortices - with the stenosis effects - confined jet flow - is particularly important when the distance of grafting is short. Given that the residual flow issued from the pathologic stenosis being non-negligible after two weeks grafting, models without stenosis cannot predict the evolution of the wall shear stress in the vicinity of the anastomosis.     

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.     

Alteration of mean wall shear stress near an oscillating stagnation point.

The site opposite an end-to-side anastomosis, resulting from femoral bypass surgery, and the carotid sinus are two regions well known to be prone to fibrous intimal hyperplasia or atherogenesis, respectively. The blood flow at these two sites features a stagnation point, which oscillates in strength and position. Mathematical models are used to determine some of the features of such a flow; in particular, the mean wall shear stress is calculated. The positional oscillations cause a significant change in the distribution and magnitude of the mean wall shear stress from that of the well-studied case of a stagnation point that oscillates only in strength. It is therefore proposed that the recorded effect of time dependence in the flow upon atherogenesis could still be a result of the distribution of the mean and not the time-varying components of the wall shear stress.