有锥度角的主动脉弓血液脉动流数值分析

目的 探求在正常生理脉动流条件下主动脉弓内血液流动速度和压力脉动分布，为动脉粥样硬化的成因和排除方法的研究提供理论依据。方法 运用计算流体力学方法和血流动力学的基本原理，对具有锥度角的主动脉弓内血液脉动流动进行数值模拟和可视化分析。结果 计算获得了具有锥度角的主动脉弓内血液流动在心动周期不同时刻的压力分布、速度分布、流线分布。结论 主脉弓内的血液脉动流流态表现复杂的原因是多方面的，而其中最为重要的原因就是主动脉弓的锥度角和曲率。     

Organ Dynamics and Fluid Dynamics of the HH25 Chick Embryonic Cardiac Ventricle as Revealed by a Novel 4D High-Frequency Ultrasound Imaging Technique and Computational Flow Simulations

Past literature has provided evidence that a normal mechanical force environment of blood flow may guide normal development while an abnormal environment can lead to congenital malformations, thus warranting further studies on embryonic cardiovascular flow dynamics. In the current study, we developed a non-invasive 4D high-frequency ultrasound technique, and use it to analyze cardiovascular organ dynamics and flow dynamics. Three chick embryos at stage HH25 were scanned with high frequency ultrasound in cine-B-mode at multiple planes spaced at 0.05 mm. 4D images of the heart and nearby arteries were generated via temporal and spatial correlation coupled with quadratic mean ensemble averaging. Dynamic mesh CFD was performed to understand the flow dynamics in the ventricle of the 2 hearts. Our imaging technique has sufficiently high resolution to enable organ dynamics quantification and CFD. Fine structures such as the aortic arches and details such as the cyclic distension of the carotid arteries were captured. The outflow tract completely collapsed during ventricular diastole, possible serving the function of a valve to prevent regurgitation. CFD showed that ventricular wall shear stress (WSS) were in the range of 0.1–0.5 Pa, and that the left side of the common ventricle experienced lower WSS than the right side. The pressure gradient from the inlet to the outlet of the ventricle was positive over most of the cardiac cycle, and minimal regurgitation flow was observed, despite the absence of heart valves. We developed a new image-based CFD method to elucidate cardiac organ dynamics and flow dynamics of embryonic hearts. The embryonic heart appeared to be optimized to generate net forward flow despite the absence of valves, and the WSS environment appeared to be side-specific.     

人体主动脉弓内三维血流动力学数值分析

目的阐明基于核磁共振数据进行数值建模的关键技术,利用计算流体动力学方法对人体主动脉弓内的血液流场进行了三维数值模拟。方法通过对临床核磁共振成像进行图像处理完成主动脉弓及分支血管的三维数字化重构,结合相关脉动血流量,模拟主动脉弓在心动周期不同时刻的血液流动细节。结果计算得到了人体主动脉弓内的血液流动在心动周期不同时刻的速度场、压力、壁面剪切应力的分布特征。结论基于核磁共振数据进行数值建模的关键技术有利于生物流体力学研究的深入开展,对主动脉弓进行血液流场的数值模拟有利于临床动脉粥样硬化、主动脉夹层的诊断和治疗。     

Correlation between local hemodynamics and lesion distribution in a novel aortic regurgitation murine model of atherosclerosis

Following surgical induction of aortic valve regurgitation (AR), extensive atherosclerotic plaque development along the descending thoracic and abdominal aorta of Ldlr ^−/− mice has been reported, with distinct spatial distributions suggestive of a strong local hemodynamic influence. The objective of this study was to test, using image-based computational fluid dynamics (CFD), whether this is indeed the case. The lumen geometry was reconstructed from micro-CT scanning of a control Ldlr ^−/− mouse, and CFD simulations were carried out for both AR and control flow conditions derived from Doppler ultrasound measurements and literature data. Maps of time-averaged wall shear stress magnitude (TAWSS), oscillatory shear index (OSI) and relative residence time (RRT) were compared against the spatial distributions of plaque stained with oil red O, previously acquired in a group of AR and control mice. Maps of OSI and RRT were found to be consistent with plaque distributions in the AR mice and the absence of plaque in the control mice. TAWSS was uniformly lower under control vs. AR flow conditions, suggesting that levels (>100 dyn/cm²) exceeded those required to alone induce a pro-atherogenic response. Simulations of a straightened CFD model confirmed the importance of anatomical curvature for explaining the spatial distribution of lesions in the AR mice. In summary, oscillatory and retrograde flow induced in the AR mice, without concomitant low shear, may exacerbate or accelerate lesion formation, but the distinct anatomical curvature of the mouse aorta is responsible for the spatial distribution of lesions.     

Investigation of Pulsatile Flowfield in Healthy Thoracic Aorta Models

Cardiovascular disease is the primary cause of morbidity and mortality in the western world. Complex hemodynamics plays a critical role in the development of aortic dissection and atherosclerosis, as well as many other diseases. Since fundamental fluid mechanics are important for the understanding of the blood flow in the cardiovascular circulatory system of the human body aspects, a joint experimental and numerical study was conducted in this study to determine the distributions of wall shear stress and pressure and oscillatory WSS index, and to examine their correlation with the aortic disorders, especially dissection. Experimentally, the Phase-Contrast Magnetic Resonance Imaging (PC-MRI) method was used to acquire the true geometry of a normal human thoracic aorta, which was readily converted into a transparent thoracic aorta model by the rapid prototyping (RP) technique. The thoracic aorta model was then used in the in vitro experiments and computations. Simulations were performed using the computational fluid dynamic (CFD) code ACE+^® to determine flow characteristics of the three-dimensional, pulsatile, incompressible, and Newtonian fluid in the thoracic aorta model. The unsteady boundary conditions at the inlet and the outlet of the aortic flow were specified from the measured flowrate and pressure results during in vitro experiments. For the code validation, the predicted axial velocity reasonably agrees with the PC-MRI experimental data in the oblique sagittal plane of the thoracic aorta model. The thorough analyses of the thoracic aorta flow, WSSs, WSS index (OSI), and wall pressures are presented. The predicted locations of the maxima of WSS and the wall pressure can be then correlated with that of the thoracic aorta dissection, and thereby may lead to a useful biological significance. The numerical results also suggest that the effects of low WSS and high OSI tend to cause wall thickening occurred along the inferior wall of the aortic arch and the anterior wall of the brachiocephalic artery, similar implication reported in a number of previous studies.     

Computational Fluid Dynamics of Developing Avian Outflow Tract Heart Valves

Hemodynamic forces play an important role in sculpting the embryonic heart and its valves. Alteration of blood flow patterns through the hearts of embryonic animal models lead to malformations that resemble some clinical congenital heart defects, but the precise mechanisms are poorly understood. Quantitative understanding of the local fluid forces acting in the heart has been elusive because of the extremely small and rapidly changing anatomy. In this study, we combine multiple imaging modalities with computational simulation to rigorously quantify the hemodynamic environment within the developing outflow tract (OFT) and its eventual aortic and pulmonary valves. In vivo Doppler ultrasound generated velocity profiles were applied to Micro-Computed Tomography generated 3D OFT lumen geometries from Hamburger-Hamilton (HH) stage 16-30 chick embryos. Computational fluid dynamics simulation initial conditions were iterated until local flow profiles converged with in vivo Doppler flow measurements. Results suggested that flow in the early tubular OFT (HH16 and HH23) was best approximated by Poiseuille flow, while later embryonic OFT septation (HH27, HH30) was mimicked by plug flow conditions. Peak wall shear stress (WSS) values increased from 18.16 dynes/cm(2) at HH16 to 671.24?dynes/cm(2) at HH30. Spatiotemporally averaged WSS values also showed a monotonic increase from 3.03 dynes/cm(2) at HH16 to 136.50?dynes/cm(2) at HH30. Simulated velocity streamlines in the early heart suggest a lack of mixing, which differed from classical ink injections. Changes in local flow patterns preceded and correlated with key morphogenetic events such as OFT septation and valve formation. This novel method to quantify local dynamic hemodynamics parameters affords insight into sculpting role of blood flow in the embryonic heart and provides a quantitative baseline dataset for future research.     

Flow Residence Time and Regions of Intraluminal Thrombus Deposition in Intracranial Aneurysms

Thrombus formation in intracranial aneurysms, while sometimes stabilizing lesion growth, can present additional risk of thrombo-embolism. The role of hemodynamics in the progression of aneurysmal disease can be elucidated by patient-specific computational modeling. In our previous work, patient-specific computational fluid dynamics (CFD) models were constructed from MRI data for three patients who had fusiform basilar aneurysms that were thrombus-free and then proceeded to develop intraluminal thrombus. In this study, we investigated the effect of increased flow residence time (RT) by modeling passive scalar advection in the same aneurysmal geometries. Non-Newtonian pulsatile flow simulations were carried out in base-line geometries and a new postprocessing technique, referred to as “virtual ink” and based on the passive scalar distribution maps, was used to visualize the flow and estimate the flow RT. The virtual ink technique clearly depicted regions of flow separation. The flow RT at different locations adjacent to aneurysmal walls was calculated as the time the virtual ink scalar remained above a threshold value. The RT values obtained in different areas were then correlated with the location of intra-aneurysmal thrombus observed at a follow-up MR study. For each patient, the wall shear stress (WSS) distribution was also obtained from CFD simulations and correlated with thrombus location. The correlation analysis determined a significant relationship between regions where CFD predicted either an increased RT or low WSS and the regions where thrombus deposition was observed to occur in vivo. A model including both low WSS and increased RT predicted thrombus-prone regions significantly better than the models with RT or WSS alone.     

In vitro measurements of velocity and wall shear stress in a novel sequential anastomotic graft design model under pulsatile flow conditions

This study documents the superior hemodynamics of a novel coupled sequential anastomoses (SQA) graft design in comparison with the routine conventional end-to-side (ETS) anastomoses in coronary artery bypass grafts (CABG). The flow fields inside three polydimethylsiloxane (PDMS) models of coronary artery bypass grafts, including the coupled SQA graft design, a conventional ETS anastomosis, and a parallel side-to-side (STS) anastomosis, are investigated under pulsatile flow conditions using particle image velocimetry (PIV). The velocity field and distributions of wall shear stress (WSS) in the models are studied and compared with each other. The measurement results and WSS distributions, computed from the near wall velocity gradients reveal that the novel coupled SQA design provides: (i) a uniform and smooth flow at its ETS anastomosis, without any stagnation point on the artery bed and vortex formation in the heel region of the ETS anastomosis within the coronary artery; (ii) more favorable WSS distribution; and (iii) a spare route for the blood flow to the coronary artery, to avoid re-operation in case of re-stenosis in either of the anastomoses. This in vitro investigation complements the previous computational studies of blood flow in this coupled SQA design, and is another necessary step taken toward the clinical application of this novel design. At this point and prior to the clinical adoption of this novel design, in vivo animal trials are warranted, in order to investigate the biological effects and overall performance of this anastomotic configuration in vivo.     

A computational study on the biomechanical factors related to stent-graft models in the thoracic aorta

Endovascular aortic stent-graft is a new, minimally invasive procedure for treating thoracic aortic diseases, and has quickly evolved to be one of the standard treatments subject to anatomic constraints. This procedure involves the placement of a self-expanding stent-graft system in a high-flow thoracic aorta. Stent-graft deployment in the thoracic aorta, especially close to the aortic arch, normally experiences a significant drag force which might lead to the risk of stent-graft failure. A comprehensive investigation on the biomechanical factors affecting the drag force on a stent-graft in the thoracic aorta is thus in order, and the goal is to perform an in-depth study on the contributing biomechanical factors. Three factors affecting the deployed stent-graft are considered, namely, the internal diameter of the vessel, the starting position of the graft and the diameter of curvature of the aortic arch. Computational fluid dynamic techniques are applied to model the blood flow. The inlet velocity and outlet pressure are assumed to be pulsatile. The three-dimensional continuity equation and the time-dependent Navier–Stokes equations for an incompressible fluid were solved numerically. The drag force due to the change of momentum within the stent-graft and the shear stress were calculated and analyzed. The drag force on a stent-graft will depend critically on the internal diameter and the starting position of stent-graft deployment. Larger internal diameter leads to larger drag force and the stent-graft deployed at the more distal position may be associated with significantly diminished drag force. Smaller diameter of curvature of the aortic arch probably results in a decline of the drag force on the stent-graft, even though this factor merely causes only a modest difference. These findings may have important implications for the choice and design of stent-grafts in the future. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

The Flow Field along the Entire Length of Mouse Aorta and Primary Branches

There is a spatial disposition to atherosclerosis along the aorta corresponding to regions of flow disturbances. The objective of the present study is to investigate the detailed distribution of hemodynamic parameters (wall shear stress (WSS), spatial gradient of wall shear stress (WSSG), and oscillatory shear index (OSI)) in the entire length of C57BL/6 mouse aorta with all primary branches (from ascending aorta to common iliac bifurcation). The detailed geometrical parameters (e.g., diameter and length of the vessels) were obtained from casts of entire aorta and primary branches of mice. The flow velocity was measured at the inlet of ascending aorta using Doppler flowprobe in mice. The outlet pressure boundary condition was estimated based on scaling law. The continuity and Navier–Stokes equations were solved using three-dimensional finite element method (FEM). The model prediction was tested by comparing the computed flow rate with the flow rate measured just before the common iliac bifurcation, and good agreement was found. It was also found that complex flow patterns occur at bifurcations between main trunk and branches. The major branches of terminal aorta, with the highest proportion of atherosclerosis, have the lowest WSS, and the relatively atherosclerotic-prone aortic arch has much more complex WSS distribution and higher OSI value than other sites. The low WSS coincides with the high OSI, which approximately obeys a power law relationship. Furthermore, the scaling law between flow and diameter holds in the entire aorta and primary branches of mice under pulsatile blood flow conditions. This model will eventually serve to elucidate the causal relation between hemodynamic patterns and atherogenesis in KO mice.     

主动脉夹层近心端不同破口形态下的血流动力学分析

目的探索病变后主动脉夹层的血流动力学性能,为胸主动脉夹层(thoracic aortic dissection,TAD)患者治疗提供更加科学的依据。方法基于1例复杂Stanford B型主动脉夹层患者的计算机断层扫描血管造影(computed tomography angiography,CTA)影像数据,建立个性化主动脉夹层近心端不同破口形态(H、O、V型)的夹层模型,结合计算流体动力学(computational fluid dynamics,CFD)与形态学分析方法,分析破口截面速度、血流状态、壁面压力以及壁面剪切力(wall shear stress,WSS)分布。结果 H型破口类型在破裂入口处的流速、最高压强差、WSS占比都表现出较其他两种类型较大的血流动力学参数,H型破口类型夹层破裂风险最大,V型次之,O型最小。结论研究结果为病例进一步数值分析和制定治疗方案提供有效的参考。     

Patient-specific flow analysis of brain aneurysms at a single location: comparison of hemodynamic characteristics in small aneurysms

The purpose of this study is to examine and compare the hemodynamic characteristics of small aneurysms at the same anatomical location. Six internal carotid artery-ophthalmic artery aneurysms smaller than 10 mm were selected. Image-based computational fluid dynamics (CFD) techniques were used to simulate aneurysm hemodynamics. Flow velocity and wall shear stress (WSS) were also quantitatively compared, both in absolute value and relative value using the parent artery as a baseline. We found that flow properties were similar in ruptured and unruptured small aneurysms. However, the WSS was lower at the aneurysm site in unruptured aneurysms and higher in ruptured aneurysms (P < 0.05). Hemodynamic analyses at a single location with similar size enabled us to directly compare the hemodynamics and clinical presentation of brain aneurysms. The results suggest that the WSS in an aneurysm sac can be an important hemodynamic parameter related to the mechanism of brain aneurysm growth and rupture.     

3D CFD Simulation of Pulsatile Blood Flow in the Human Aorta

INTRODUCTION　　The human aorta is the majorblood vessel of complex geometry including curva-tures in multiple planes,branches at the apex of the arch,significant tapering andwith distensible vessel wall ( as shown in Fig.1 ) . The blood flow structures in theaorta are very complex and attribute a lot to the development of atherosclerotic le-sions,which always occur in the vicinity of arterial branches,curvatures and bifur-cations〔1～ 5〕.In order to understand the complex nature of the …     

3D network model of NO transport in tissue

We developed a mathematical model to simulate shear stress-dependent nitric oxide (NO) production and transport in a 3D microcirculatory network based on published data. The model consists of a 100 μm × 500 μm × 75 μm rectangular volume of tissue containing two arteriole-branching trees, and nine capillaries surrounding the vessels. Computed distributions for NO in blood, vascular walls, and surrounding tissue were affected by hematocrit (Hct) and wall shear stress (WSS) in the network. The model demonstrates that variations in the red blood cell (RBC) distribution and WSS in a branching network can have differential effects on computed NO concentrations due to NO consumption by RBCs and WSS-dependent changes in NO production. The model predicts heterogeneous distributions of WSS in the network. Vessel branches with unequal blood flow rates gave rise to a range of WSS values and therefore NO production rates. Despite increased NO production in a branch with higher blood flow and WSS, vascular wall NO was predicted to be lower due to greater NO consumption in blood, since the microvascular Hct increased with redistribution of RBCs at the vessel bifurcation. Within other regions, low WSS was combined with decreased NO consumption to enhance the NO concentration.     

Differential Response of Endothelial Cells to Simvastatin When Conditioned with Steady,Non-Reversing Pulsatile or Oscillating Shear Stress

Few studies have investigated whether fluid mechanics can impair or enhance endothelial cell response to pharmacological agents such as statin drugs. We evaluated and compared Kruppel-like factor 2 (KLF2), endothelial nitric oxide synthase (eNOS), and thrombomodulin (TM) expression in human abdominal aortic endothelial cells (HAAEC) treated with increasing simvastatin concentrations (0.1, 1 or 10 μM) under static culture and shear stress (steady, non-reversing pulsatile, and oscillating). Simvastatin, steady flow, and non-reversing pulsatile flow each separately upregulated KLF2, eNOS, and TM mRNA. At lower simvastatin concentrations (0.1 and 1 μM), the combination of statin and unidirectional steady or pulsatile flow produced an overall additive increase in mRNA levels. At higher simvastatin concentration (10 μM), a synergistic increase in eNOS and TM mRNA expression was observed. In contrast, oscillating flow impaired KLF2 and TM, but not eNOS expression by simvastatin at 1 μM. A higher simvastatin concentration of 10 μM overcame the inhibitory effect of oscillating flow. Our findings suggest that oscillating shear stress renders the endothelial cells less responsive to simvastatin than cells exposed to unidirectional steady or pulsatile flow. Consequently, the pleiotropic effects of statins in vivo may be less effective in endothelial cells exposed to atheroprone hemodynamics.     

Numerical Study of the Influence of Anastomotic Configuration on Hemodynamics in Miller Cuff Models

Enhanced hemodynamics via geometric alteration is believed to play a role in the favorable redistribution of intimal hyperplasia (IH) in infragenicular supplementary vein cuffs. We aimed to elucidate the consequence of altering geometric configuration in anastomotic hemodynamics in cuff models. A well-validated numerical scheme was used to simulate pulsatile flows in three cuffed anastomotic models with length-to-height ratio (LHR) of 1.4, 2.2 and 3.2, and a St. Mary’s boot with LHR of 2.2 at a mean flow rate of 130 mL/min. Characteristic flow patterns and wall shear stress (WSS) distributions were compared. A cohesive vortex is only present in the cuff of LHR = 1.4 and in the boot. The vortex in the cuffs becomes increasingly disorganized with increasing cuff LHR. The area of flow separation at the graft toe, prominent in the cuff of LHR = 3.2, is significantly reduced in the cuff of LHR = 1.4 and eliminated in the boot. All cuffs are characterized by flow separation, flow reversal and a sharp drop in WSS immediately distal to the cuff toe, phenomena not observed in the boot. The cuff configuration, specifically the LHR, is critical in controlling local hemodynamics. A large LHR could lead to reduced cuff performance. The study suggests the benefits of geometric optimization for reconstruction of cuffed anatomoses.     

Hemodynamic patterning of the avian atrioventricular valve

In this study, we develop an innovative approach to rigorously quantify the evolving hemodynamic environment of the atrioventricular (AV) canal of avian embryos. Ultrasound generated velocity profiles were imported into Micro‐Computed Tomography generated anatomically precise cardiac geometries between Hamburger‐Hamilton (HH) stages 17 and 30. Computational fluid dynamic simulations were then conducted and iterated until results mimicked in vivo observations. Blood flow in tubular hearts (HH17) was laminar with parallel streamlines, but strong vortices developed simultaneous with expansion of the cushions and septal walls. For all investigated stages, highest wall shear stresses (WSS) are localized to AV canal valve–forming regions. Peak WSS increased from 19.34 dynes/cm² at HH17 to 287.18 dynes/cm² at HH30, but spatiotemporally averaged WSS became 3.62 dynes/cm² for HH17 to 9.11 dynes/cm² for HH30. Hemodynamic changes often preceded and correlated with morphological changes. These results establish a quantitative baseline supporting future hemodynamic analyses and interpretations. Developmental Dynamics, 2011. © 2010 Wiley‐Liss, Inc.     

Development and transformation of the aortic arches in the equine embryos with special attention to the formation of the definitive arch of the aorta and the common brachiocephalic trunk

Summary The development and transformation of the aortic arches were studied in 84 equine embryos (5 to 35 mm CRL; approximately 21–49 days of gestation). The arch of the aorta and the vessels which originate from it were also examined in several fetuses (41–335 mm CRL) and in a full-term fetus.There are six pairs of aortic arches that originate from the ventral aortic root. The first and second aortic arches regress very early, while the fifth pair appears in a vestigial form relatively late in the development, when the truncus arteriosus divides into the aortic and pulmonary channels. The development of the cervical intersegmental arteries is described and the formation of the subclavian arteries is discussed. The primitive arch of the aorta appears at the earliest in the 14–15.5 mm CRL equine embryos (approximately 35 days of gestation). The segments of the aortic arches system which are incorporated in the formation of the definitive arch of the aorta are discussed.Three vessels, the innominate (brachiocephalic) artery, the left common carotid artery, and the left subclavian artery, originate from the primitive arch of the aorta. This arrangement of the vessels is regarded as the primitive mammalian pattern.Two more stages precede the development of the definitive arch of the aorta and the common brachiocephalic trunk in the equine embryos, at approximately 42 days of gestation. The secondary changes, which occur in the process of formation of the arch of the aorta and the common brachiocephalic trunk, are described and discussed. Certain anomalies of the arrangement of the vessels from the arch of the aorta are also discussed. In memoriam of Professor Dr. L. Kundzin (1855–1940).The investigation reported herein was supported by a Research Grant-in-Aid from the Washington State University.     

Wall shear stress calculations based on 3D cine phase contrast MRI and computational fluid dynamics: a comparison study in healthy carotid arteries

Wall shear stress (WSS) is involved in many pathophysiological processes related to cardiovascular diseases, and knowledge of WSS may provide vital information on disease progression. WSS is generally quantified with computational fluid dynamics (CFD), but can also be calculated using phase contrast MRI (PC‐MRI) measurements. In this study, our objectives were to calculate WSS on the entire luminal surface of human carotid arteries using PC‐MRI velocities (WSS_MRI) and to compare it with WSS based on CFD (WSS_CFD). Six healthy volunteers were scanned with a 3 T MRI scanner. WSS_CFD was calculated using a generalized flow waveform with a mean flow equal to the mean measured flow. WSS_MRI was calculated by estimating the velocity gradient along the inward normal of each mesh node on the luminal surface. Furthermore, WSS was calculated for a down‐sampled CFD velocity field mimicking the MRI resolution (WSS_CFDlowres). To ensure minimum temporal variation, WSS was analyzed only at diastole. The patterns of WSS_CFD and WSS_MRI were compared by quantifying the overlap between low, medium and high WSS tertiles. Finally, WSS directions were compared by calculating the angles between the WSS_CFD and WSS_MRI vectors. WSS_MRI magnitude was found to be lower than WSS_CFD (0.62 ± 0.18 Pa versus 0.88 ± 0.30 Pa, p < 0.01) but closer to WSS_CFDlowres (0.56 ± 0.18 Pa, p < 0.01). WSS_MRI patterns matched well with those of WSS_CFD. The overlap area was 68.7 ± 4.4% in low and 69.0 ± 8.9% in high WSS tertiles. The angles between WSS_MRI and WSS_CFD vectors were small in the high WSS tertiles (20.3 ± 8.2°), but larger in the low WSS tertiles (65.6 ± 17.4°). In conclusion, although WSS_MRI magnitude was lower than WSS_CFD, the spatial WSS patterns at diastole, which are more relevant to the vascular biology, were similar. PC‐MRI‐based WSS has potential to be used in the clinic to indicate regions of low and high WSS and the direction of WSS, especially in regions of high WSS. Copyright © 2014 John Wiley & Sons, Ltd.