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.     

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.     

Design optimization of a helical endothelial cell culture device

The specific roles of mass transfer and fluid dynamic stresses on endothelial function, important in atherogenesis, are not known. Further, the effects of mass transfer and fluid dynamic stresses are difficult to separate because areas of “abnormal” mass transfer and “abnormal” wall shear stress tend to co-localize (where abnormal is defined as any deviation from the mass transfer rate or wall shear stress present in a long straight artery with the same flow rate and diameter). Our goal was to design a cell culture device which gives maximum separation between areas of abnormal shear stress and areas of abnormal mass transfer. We used design optimization principles to design a helical cell culture device. Using shear stress and mass transfer fields predicted by solving the governing equations, the area of the device which was exposed to low rates of mass transfer and normal levels of wall shear stress was determined. The design optimization method then maximized this area by varying the design variables, resulting in the optimum design. The optimum design had Reynolds number = 50, helical radius = 3.23 and helical pitch = 3.82. The area of the device which was exposed to low rates of mass transfer and regular levels of wall shear stress was about 4.5 times the inlet cross-sectional area of the device or about 5% of the device total internal surface area. An optimum design was successfully determined and the methodology used was shown to be robust. The area of the device which was exposed to low rates of mass transfer and regular levels of wall shear stress occurred in a defined region which should aid further experimental work.     

Investigation of hemodynamics in the development of dissecting aneurysm within patient-specific dissecting aneurismal aortas using computational fluid dynamics (CFD) simulations

Aortic dissecting aneurysm is one of the most catastrophic cardiovascular emergencies that carries high mortality. It was pointed out from clinical observations that the aneurysm development is likely to be related to the hemodynamics condition of the dissected aorta. In order to gain more insight on the formation and progression of dissecting aneurysm, hemodynamic parameters including flow pattern, velocity distribution, aortic wall pressure and shear stress, which are difficult to measure in vivo, are evaluated using numerical simulations. Pulsatile blood flow in patient-specific dissecting aneurismal aortas before and after the formation of lumenal aneurysm (pre-aneurysm and post-aneurysm) is investigated by computational fluid dynamics (CFD) simulations. Realistic time-dependent boundary conditions are prescribed at various arteries of the complete aorta models. This study suggests the helical development of false lumen around true lumen may be related to the helical nature of hemodynamic flow in aorta. Narrowing of the aorta is responsible for the massive recirculation in the poststenosis region in the lumenal aneurysm development. High pressure difference of 0.21 kPa between true and false lumens in the pre-aneurismal aorta infers the possible lumenal aneurysm site in the descending aorta. It is also found that relatively high time-averaged wall shear stress (in the range of 4-8 kPa) may be associated with tear initiation and propagation. CFD modeling assists in medical planning by providing blood flow patterns, wall pressure and wall shear stress. This helps to understand various phenomena in the development of dissecting aneurysm.     

Helical swimming can provide robust upwards transport for gravitactic single-cell algae; a mechanistic model

In still fluid, many phytoplankton swim in helical paths with an average upwards motion. A new mechanistic model for gravitactic algae subject to an intrinsic torque is developed here, based on Heterosigma akashiwo, which results in upwards helical trajectories in still fluid. The resultant upwards swimming speed is calculated as a function of the gravitactic and intrinsic torques. Helical swimmers have a reduced upwards speed in still fluid compared to cells which swim straight upwards. However a novel result is obtained when the effect of fluid shear is considered. For intermediate values of shear and intrinsic torque, a new stable equilibrium solution for swimming direction is obtained for helical swimmers. This results in positive upwards transport in vertical shear flow, in contrast to the stable equilibrium solution for straight swimmers which results in downwards transport in vertical shear flow. Furthermore, for strong intrinsic torque, when there is no longer a stable orientation equilibrium, we show that the average downwards transport of helical swimmers in vertical shear flow is greatly suppressed compared to straight swimmers. We hypothesise that helical swimming provides robustness for upwards transport in the presence of fluid shearing motions.     

Helical flows and asymmetry of blood jet in dilated ascending aorta with normally functioning bicuspid valve

Bicuspid aortic valve (BAV) is associated with aortic dilatation and aneurysm. Several studies evidenced an eccentric systolic flow in ascending aorta associated with increased wall shear stresses (WSS) and the occurrence of an helical systolic flow. This study seeks to elucidate the connections between jet asymmetry and helical flow in patients with normally functioning BAV and dilated ascending aorta. We performed a computational parametric study by varying, for a patient-specific geometry, the valve area and the flow rate entering the aorta and drawing also a tricuspid valve (TAV). We considered also phase-contrast magnetic resonance imaging of four BAV and TAV patients. Measurement of normalized flow asymmetry index, systolic WSS and of a new index (positive helix fraction, PHF) quantifying the presence of a single a single helical flow were performed. In our computation, BAV cases featured higher values of all indices with respect to TAV in both numerical and imaged-based results. Moreover, all indices increased with decreasing valve area and/or with increasing flow rate. This allowed to separate the BAV and TAV cases with respect to the jet asymmetry, WSS localization and helical flow. Interestingly, these results were obtained without modeling the leaflets.     

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。     

Laser Doppler anemometer measurements of pulsatile flow in a model carotid bifurcation

Hemodynamics at the human carotid bifurcation is important to the understanding of atherosclerotic plaque initiation and progression as well as to the diagnosis of clinically important disease. Laser Doppler anemometry was performed in a large scale model of an average human carotid. Pulsatile waveforms and physiologic flow divisions were incorporated. Disturbance levels and shear stresses were computed from ensemble averages of the velocity waveform measurements. Flow in the common carotid was laminar and symmetric. Flow patterns in the sinus, however, were complex and varied considerably during the cycle. Strong helical patterns and outer wall flow separation waxed and waned during each systole. The changing flow patterns resulted in an oscillatory shear stress at the outer wall ranging from -13 to 9 dyn cm-2 during systole with a time-averaged mean of only -0.5 dyn cm-2. This contrasts markedly with an inner wall shear stress range of 17-50, (mean 26) dyn cm-2. The region of transient separation was confined to the carotid sinus outer wall with no reverse velocities detected in the distal internal carotid. Notable disturbance velocities were also time-dependent, occurring only during the deceleration phase of systole and the beginning of diastole. The present pulsatile flow studies have aided in identifying hemodynamic conditions which correlate with early intimal thickening and predict the physiologic level of flow disturbances in the bulb of undiseased internal carotid arteries.     

Hemodynamics simulation and identification of susceptible sites of atherosclerotic lesion formation in a model abdominal aorta

Employing the rabbit's abdominal aorta as a suitable atherosclerotic model, transient three-dimensional blood flow simulations and monocyte deposition patterns were used to evaluate the following hypotheses: (i) simulation of monocyte transport through a model of the rabbit abdominal aorta yields cell deposition patterns similar to those seen in vivo, and (ii) those deposition patterns are correlated with hemodynamic wall parameters related to atherosclerosis. The deposition pattern traces a helical shape down the aorta with local elevation in monocyte adhesion around vessel branches. The cell deposition pattern was altered by an exercise waveform with fewer cells attaching in the upper abdominal aorta but more attaching around the renal orifices. Monocyte deposition was correlated with the wall shear stress gradient and the wall shear stress angle gradient. The wall stress gradient, the wall shear stress angle gradient and the normalized monocyte deposition fraction were correlated with the distribution of monocytes along the abdominal aorta and monocyte deposition is correlated with the measured distribution of monocytes around the major abdominal branches in the cholesterol-fed rabbit. These results suggest that the transport and deposition pattern of monocytes to arterial endothelium plays a significant role in the localization of lesions.     

Flow pattern analysis in a highly stenotic patient-specific carotid bifurcation model using a turbulence model

The aim of this study is to investigate the blood flow pattern in carotid bifurcation with a high degree of luminal stenosis, combining in vivo magnetic resonance imaging (MRI) and computational fluid dynamics (CFD). A newly developed two-equation transitional model was employed to evaluate wall shear stress (WSS) distribution and pressure drop across the stenosis, which are closely related to plaque vulnerability. A patient with an 80% left carotid stenosis was imaged using high resolution MRI, from which a patient-specific geometry was reconstructed and flow boundary conditions were acquired for CFD simulation. A transitional model was implemented to investigate the flow velocity and WSS distribution in the patient-specific model. The peak time-averaged WSS value of approximately 73 Pa was predicted by the transitional flow model, and the regions of high WSS occurred at the throat of the stenosis. High oscillatory shear index values up to 0.50 were present in a helical flow pattern from the outer wall of the internal carotid artery immediately after the throat. This study shows the potential suitability of a transitional turbulent flow model in capturing the flow phenomena in severely stenosed carotid arteries using patient-specific MRI data and provides the basis for further investigation of the links between haemodynamic variables and plaque vulnerability. It may be useful in the future for risk assessment of patients with carotid disease.     

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.     

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.     

A numerical study of flow in curved tubes simulating coronary arteries

Numerical simulations of pulsatile flow in coronary arteries which take into account the curvature associated with the bending of arteries over the surface of the heart are presented for resting, excited and drug induced states. The study was motivated by reported observations of atherosclerotic plaque localization on the inner curvature of coronary arteries. The simulated flow field appears quasi-steady under resting conditions with wall shear stress always highest on the outside wall and only a single secondary flow vortex in the half tube. However, reversal of wall shear stress direction at the inside wall does occur under resting flow conditions and this is not a quasi-steady characteristic. The flow field is markedly unsteady under excited conditions with wall shear stress sometimes peaking on the inside wall and an increase in the magnitude of wall shear stress reversal on the inside wall. However, only a single secondary flow vortex in the half tube is observed. Implications of the simulations for the role of fluid mechanics in coronary artery atherosclerosis are also discussed.     

The effect of simple shear flow on the helix–coil transition of poly‐L‐lysine

Studies of the helix‐to‐coil transition in dilute solutions of poly‐L ‐lysine, dissolved in mixtures of water and methanol (MeOH), have been carried under shear flow using flow birefringence and modulated polarimetry. The fraction of helical conformations in a given solution remains independent of shear rate for MeOH concentrations above and below the critical value for the helix‐coil transition (i.e., 87.5% MeOH). For the 87.5% MeOH solutions, a shear‐induced helix‐to‐“stretched” coil transition occurs above a critical shear rate. Induction times for the transition show a temperature and shear rate dependence that can be described in terms of an activated jump process. Measurements of circular birefringence on cessation of flow also show that the transition is reversible, with the stretched coil reverting to the helical state on a time scale of several seconds. The activation energy for the jump process is found to be 16.2 kJ/mole. © 1999 John Wiley & Sons, Inc. Biopoly 50: 589–594, 1999     

Flow-induced wall shear stress in abdominal aortic aneurysms: Part II--pulsatile flow hemodynamics

In continuing the investigation of AAA hemodynamics, unsteady flow-induced stresses are presented for pulsatile blood flow through the double-aneurysm model described in Part I. Physiologically realistic aortic blood flow is simulated under pulsatile conditions for the range of time-average Reynolds numbers 50< or =Re(m) < or =300. Hemodynamic disturbance is evaluated for a modified set of indicator functions which include wall pressure (p(w)), wall shear stress (tau(w)), Wall Shear Stress Gradient (WSSG), time-average wall shear stress (tau(w)*), and time-average Wall Shear Stress Gradient WSSG*. At peak flow, the highest shear stress and WSSG levels are obtained at the distal end of both aneurysms, in a pattern similar to that of steady flow. The maximum values of wall shear stresses and wall shear stress gradients are evaluated as a function of the time-average Reynolds number resulting in a fourth order polynomial correlation. A comparison between numerical predictions for steady and pulsatile flow is presented, illustrating the importance of considering time-dependent flow for the evaluation of hemodynamic indicators.     

Flow-induced Wall Shear Stress in Abdominal Aortic Aneurysms: Part II - Pulsatile Flow Hemodynamics

In continuing the investigation of AAA hemodynamics, unsteady flow-induced stresses are presented for pulsatile blood flow through the double-aneurysm model described in Part I. Physiologically realistic aortic blood flow is simulated under pulsatile conditions for the range of time-average Reynolds numbers 50 h Re m h 300. Hemodynamic disturbance is evaluated for a modified set of indicator functions which include wall pressure ( p w ), wall shear stress ( w ), Wall Shear Stress Gradient (WSSG), time-average wall shear stress ( w *), and time-average Wall Shear Stress Gradient WSSG *. At peak flow, the highest shear stress and WSSG levels are obtained at the distal end of both aneurysms, in a pattern similar to that of steady flow. The maximum values of wall shear stresses and wall shear stress gradients are evaluated as a function of the time-average Reynolds number resulting in a fourth order polynomial correlation. A comparison between numerical predictions for steady and pulsatile flow is presented, illustrating the importance of considering time-dependent flow for the evaluation of hemodynamic indicators.     

Numerical investigation of oxygen mass transfer in a helical-type artery bypass graft

Local oxygen lack in arterial walls (hypoxia) plays a very important role in the initiation, progression and development of intimal hyperplasia (IH) and thrombosis. Aiming to find out whether a helical-type artery bypass graft (ABG) is hypoxia beneficial, a numerical study was carried out to compare oxygen transport between a helical-type ABG and a conventional-type ABG. The dimensionless mass transfer coefficient (Sherwood number) was introduced to evaluate the oxygen mass transfer distribution and detailed oxygen wall flux was computed. The results show that the intrinsic geometry of a helical-type ABG resulted in improved hypoxia and the oxygen-depleted fluid located proximally to the occluded section as compared with that of a conventional-type ABG. However, benefits aside, distinct double low regions (low wall shear stress (WSS) and hypoxia) which might be most prone to IH and more localised and thicker boundary layer of oxygen-depleted fluid were observed at the helical-type ABG. This may explain why the helical flow plays a detrimental role at some locations in the human body. In addition, it was observed that although low WSS region was always accompanied with low oxygen supply, the oxygen transport rate did not adjust simultaneously with flow. The change in oxygen distribution usually lagged behind the flow change. A physiological WSS region may be associated with hypoxia condition. This study captured the qualitative trend of oxygen distribution in ABGs and the effect of helical geometry on reducing hypoxia, which is useful in the structural design of swirling flow vascular devices.     

Numerical simulation of sinusoidal flow in a straight elastic tube: effects of phase angles

Numerical simulations of flow in straight elastic (moving wall) tubes subjected to a sinusoidal pressure gradient were performed for conditions prevailing in large and medium sized arteries. The effects of varying the phase angle between the pressure gradient and the tube radius, the amplitude of wall motion, and the unsteadiness parameter (alpha) on flow rate and wall shear stress were investigated. Mean and peak flow rates and shear stresses were found to be strongly affected by the phase angle between the pressure gradient and the tube radius with greater sensitivity at higher diameter variation and higher alpha. In large artery simulations (alpha = 12), means flow rate was found to be 60% higher and peak flow rate to be 73% higher than corresponding rigid tube values for certain phase angles, while a threefold increase in mean wall shear stress and sevenfold increase in peak wall shear stress were observed in a sensitive phase angle range. Significant reversal in the wall shear stress direction occurred in the sensitive phase angle range even when there was negligible flow rate reversal. All effects were greatly diminished in simulations of medium sized vessels (alpha = 4). Some experimental evidence to support the predictions of a strong effect of phase angle on wall shear stress in large vessels is presented. Finally, physiological implications of the present work are discussed from a basis of aortic input impedance data, and a physical explanation for the extreme sensitivity of the flow field to small amplitude wall motion at high alpha is given.