Wall Shear Stress Patterns Research Articles

In vivo wall shear stress patterns in carotid bifurcations assessed by 4D MRI

Summary We investigated the distribution of wall shears stress (WSS) within the carotid artery bifurcation of healthy volunteers and patients with internal carotid artery stenosis. WSS was determined by flow-sensitive 4D MRI and correlated with bifurcation angle, vessel tortuosity and the ratio of the diameter of the common (CCA) and internal carotid artery (ICA). Critical WSS occurred at the posterior wall of the physiologically dilated ICA bulb and the incidence of critical WSS values was dependent from individual bifurcation geometry. Moreover, we found that ICA stenosis changed physiological WSS distribution whereas carotid endarterectomy partially restored physiological WSS conditions.

Improved prediction of disturbed flow via hemodynamically-inspired geometric variables

Arterial geometry has long been considered as a pragmatic alternative for inferring arterial flow disturbances, and their impact on the natural history and treatment of vascular diseases. Traditionally, definition of geometric variables is based on convenient shape descriptors, with only superficial consideration of their influence on flow and wall shear stress patterns. In the present study we demonstrate that a more studied consideration of the actual (cf. nominal) local hemodynamics can lead to substantial improvements in the prediction of disturbed flow by geometry. Starting from a well-characterized computational fluid dynamics (CFD) dataset of 50 normal carotid bifurcations, we observed that disturbed flow tended to be confined proximal to the flow divider, whereas geometric variables previously shown to be significant predictors of disturbed flow included features distal to the flow divider in their definitions. Flaring of the bifurcation leading to flow separation was redefined as the maximum relative expansion of the common carotid artery (CCA), proximal to the flow divider. The beneficial effect of primary curvature on flow inertia, via suppression of flow separation, was characterized by the in-plane tortuosity of CCA as it enters the flare region. Multiple linear regressions of these redefined geometric variables against various metrics of disturbed flow revealed R2 values approaching 0.6, better than the roughly 0.3 achieved using the conventional shape-based variables, while maintaining their demonstrated real-world reproducibility. Such a hemodynamically-inspired approach to the definition of geometric variables may reap benefits for other applications where geometry is used as a surrogate marker of local hemodynamics.

Identification of Hemodynamically Optimal Coronary Stent Designs Based on Vessel Caliber

Coronary stent design influences local patterns of wall shear stress (WSS) that are associated with neointimal growth, restenosis, and the endothelialization of stent struts. The number of circumferentially repeating crowns N(C) for a given stent design is often modified depending on the target vessel caliber, but the hemodynamic implications of altering N(C) have not previously been studied. In this investigation, we analyzed the relationship between vessel diameter and the hemodynamically optimal N(C) using a derivative-free optimization algorithm coupled with computational fluid dynamics. The algorithm computed the optimal vessel diameter, defined as minimizing the area of stent-induced low WSS, for various configurations (i.e., N(C)) of a generic slotted-tube design and designs that resemble commercially available stents. Stents were modeled in idealized coronary arteries with a vessel diameter that was allowed to vary between 2 and 5 mm. The results indicate that the optimal vessel diameter increases for stent configurations with greater N(C), and the designs of current commercial stents incorporate a greater N(C) than hemodynamically optimal stent designs. This finding suggests that reducing the N(C) of current stents may improve the hemodynamic environment within stented arteries and reduce the likelihood of excessive neointimal growth and thrombus formation.

Magnetic resonance fluid dynamics for intracranial aneurysms—comparison with computed fluid dynamics

Hemodynamics in intracranial aneurysms is thought to play an important role in their growth and rupture. Usual computed fluid dynamics (CFD) based on three-dimensional (3D) computed tomographic (CT) angiography requires a time-consuming process for analysis. Magnetic resonance fluid dynamics (MRFD) based on MR images is a new tool for analyzing flow dynamics and a promising method for obtaining such information more easily. We compared the data from MRFD and CFD and studied the clinical feasibility of MRFD. A total of 15 aneurysms, including two ruptured ones, in 15 patients were investigated with MR imaging and 3D-CT angiography. The flow data of MRFD and CFD, 3D stream lines, flow velocity profile and wall shear stress (WSS) were extracted from the image reconstruction and were compared each other. Both flow dynamics images showed quite similar 3D flow pattern and WSS map. However, the calculated value of maximum WSS was quite different and there was no significant correlation. Further, in one ruptured case, CFD showed less visualization to evaluate the intra-aneurysmal flow. Interestingly, one delayed rupture case showed a particular flow pattern with abnormal secondary flow in the bottom of the aneurysm before rupture, which might suggest the specific finding of rupture risk. MRFD is a valuable and less invasive tool to evaluate aneurysmal fluid dynamics. It can be obtained from the usual MRI examination without contrast medium and exposure to radiation. Although there is a problem of consistency of the absolute value of WSS between MRFD and conventional CFD, it may be useful to predict the risk of enlargement or rupture of aneurysms based on the information of the similar distribution of WSS and flow patterns. The quantifiable analysis and establishment of a meaningful threshold for high risk should be further studied.

Characterization of cerebral aneurysms using 4D FLOW MRI

Six patients with large or giant cerebral aneurysms were examined with 4D-Flow MRI and analyzed regarding 3D flow patterns and aneurysm wall shear stress (WSS). Two distinct groups of aneurysms were identified with fast swirling flow versus slow flow and significantly different WSS patterns, correlating with aneurysm morphology.

Numerical simulation of blood flow in a flexible stenosed abdominal real aorta

This study concerns an evaluation of pulsatile flow and arterial wall behavior in a real world model of a stenosed abdominal aorta and iliac arteries. Two different geometries of a healthy and severly stenosed abdominal aorta, extracted from CT scan images and simulations of fluid flow and tissue interaction (Fluid Solid Interaction), are carried out. The blood is taken as incompressible, non-Newtonian, and the arterial wall tissue is treated as isotropic, elastic material with uniform mechanical properties. The results of using two models with rigid and flexible walls are presented and compared. The computed pressure at the abdominal aorta for a flexible healthy wall is consistent with measured values in vivo conditions. Results show that the computed pressure is lower by 15% for the flexible model, as compared to the rigid and complaint models. Although results obtained from the FSI study of pulsatile healthy and stenosed models show a similar trend for Wall Shear Stress (WSS) patterns, considerable differences in magnitude exist. It is shown that for the cases presented here, the effects of wall flexibility and actual stenosed geometry on the flow performance of veins are noticeable.

Analysis of Fluid Flow and Wall Shear Stress Patterns Inside Partially Filled Agitated Culture Well Plates

The appearance of highly resistant bacterial biofilms in both community and hospitals environments is a major challenge in modern clinical medicine. The biofilm structural morphology, believed to be an important factor affecting the behavioral properties of these "super bugs", is strongly influenced by the local hydrodynamics over the microcolonies. Despite the common use of agitated well plates in the biology community, they have been used rather blindly without knowing the flow characteristics and influence of the rotational speed and fluid volume in these containers. The main purpose of this study is to characterize the flow in these high-throughput devices to link local hydrodynamics to observed behavior in cell cultures. In this work, the flow and wall shear stress distribution in six-well culture plates under planar orbital translation is simulated using Computational Fluid Dynamics (CFD). Free surface, flow pattern and wall shear stress for two shaker speeds (100 and 200 rpm) and two volumes of fluid (2 and 4 mL) were investigated. Measurements with a non-intrusive optical shear stress sensor and High Frame-rate Particle Imaging Velocimetry (HFPIV) are used to validate CFD predictions. An analytical model to predict the free surface shape is proposed. Results show a complex three-dimensional flow pattern, varying in both time and space. The distribution of wall shear stress in these culture plates has been related to the topology of flow. This understanding helps explain observed endothelial cell orientation and bacterial biofilm distributions observed in culture dishes. The results suggest that the mean surface stress field is insufficient to capture the underlying dynamics mitigating biological processes.

Evaluation of aortic geometries created by magnetic resonance imaging data in healthy volunteers

The development of atherosclerotic plaques has been associated with the patterns of wall shear stress (WSS). However, much is still uncertain with the methods used to calculate WSS. Correct vessel geometries are mandatory to get reliable estimations, and the purpose of this study was to evaluate an in vivo method for creating aortic 3D geometry in human based on data from magnetic resonance imaging (MRI) with ultrasound as reference. The aortas of ten healthy men, 23·4 ± 1·6 years of age, were examined with a 1·5 T MRI system using a 3D gadolinium-enhanced gradient-echo sequence. Three-dimensional geometries were created using manual segmentation of images. Lumen diameters (LD) were measured in the abdominal aorta (AA) and the thoracic aorta (TA) with non-invasive B-mode ultrasound as a reference. The anteroposterior diameter of the AA was 13·6 ± 1·1 mm for the MRI and 13·8 ± 1·3 mm for the ultrasound (NS). Intraobserver variability (CV) for MRI and ultrasound was <0·92% and <0·40%, respectively. Interobserver variability for MRI and ultrasound was 0·96% and 0·56%, respectively. The diameter of the TA was 19·2 ± 1·4 mm for the MRI, and the intraobserver variability (CV) was <0·78% and interobserver variability (CV) was 0·92%. Specific arterial geometries can be constructed with a high degree of accuracy using MRI. This indicates that the MRI geometries may be used to create realistic and correct geometries in the calculation of WSS in the aorta of human.

Blood flow in the rabbit aortic arch and descending thoracic aorta

The distribution of atherosclerotic lesions within the rabbit vasculature, particularly within the descending thoracic aorta, has been mapped in numerous studies. The patchy nature of such lesions has been attributed to local variation in the pattern of blood flow. However, there have been few attempts to model and characterize the flow. In this study, a high-order continuous Galerkin finite-element method was used to simulate blood flow within a realistic representation of the rabbit aortic arch and descending thoracic aorta. The geometry, which was obtained from computed tomography of a resin corrosion cast, included all vessels originating from the aortic arch (followed to at least their second generation) and five pairs of intercostal arteries originating from the proximal descending thoracic aorta. The simulations showed that small geometrical undulations associated with the ductus arteriosus scar cause significant deviations in wall shear stress (WSS). This finding highlights the importance of geometrical accuracy when analysing WSS or related metrics. It was also observed that two Dean-type vortices form in the aortic arch and propagate down the descending thoracic aorta (along with an associated skewed axial velocity profile). This leads to the occurrence of axial streaks in WSS, similar in nature to the axial streaks of lipid deposition found in the descending aorta of cholesterol-fed rabbits. Finally, it was observed that WSS patterns within the vicinity of intercostal branch ostia depend not only on local flow features caused by the branches themselves, but also on larger-scale flow features within the descending aorta, which vary between branches at different locations. This result implies that disease and WSS patterns in the vicinity of intercostal ostia are best compared on a branch-by-branch basis.

Non‐Newtonian blood flow study in a model cavopulmonary vascular system

AbstractA transient haemodynamic study in a model cavopulmonary vascular system has been carried out for a typical range of parameters using a finite element‐based Navier–Stokes solver. The focus of this study is to investigate the influence of non‐Newtonian behaviour of the blood on the haemodynamic quantities, such as wall shear stress (WSS) and flow pattern. The computational fluid dynamics (CFD) model is based on an artificial compressibility characteristic‐based split (AC‐CBS) scheme, which has been adopted to solve the Navier–Stokes equations in space–time domain. A power law model has been implemented to characterize the shear thinning nature of the blood depending on the local strain rate. Using the computational model, numerical investigations have been performed for Newtonian and non‐Newtonian flows for different frequencies and input pulse forms. The haemodynamic quantities observed in total cavopulmonary connection (TCPC) for the above conditions suggest that there are considerable differences in average (about 25–40%) and peak (about 50%) WSS distributions, when the non‐Newtonian behaviour of the blood is taken into account. The lower WSS levels observed for non‐Newtonian cases point to the higher risk of lesion formation, especially at higher pulsation frequencies. A realistic pulse form is relatively safer than a sinusoidal pulse as it has more energy distributed in the higher harmonics, which results in higher average WSS values. The present study highlights the importance of including non‐Newtonian shear thinning behaviour for modelling blood flow in the vicinity of repaired arterial connections. Copyright © 2010 John Wiley &amp; Sons, Ltd.

Effect of reverse flow on the pattern of wall shear stress near arterial branches

Atherosclerotic lesions have a patchy distribution within arteries that suggests a controlling influence of haemodynamic stresses on their development. The distribution near aortic branches varies with age and species, perhaps reflecting differences in these stresses. Our previous work, which assumed steady flow, revealed a dependence of wall shear stress (WSS) patterns on Reynolds number and side-branch flow rate. Here, we examine effects of pulsatile flow. Flow and WSS patterns were computed by applying high-order unstructured spectral/hp element methods to the Newtonian incompressible Navier-Stokes equations in a geometrically simplified model of an aorto-intercostal junction. The effect of pulsatile but non-reversing side-branch flow was small; the aortic WSS pattern resembled that obtained under steady flow conditions, with high WSS upstream and downstream of the branch. When flow in the side branch or in the aortic near-wall region reversed during part of the cycle, significantly different instantaneous patterns were generated, with low WSS appearing upstream and downstream. Time-averaged WSS was similar to the steady flow case, reflecting the short duration of these events, but patterns of the oscillatory shear index for reversing aortic near-wall flow were profoundly altered. Effects of reverse flow may help explain the different distributions of lesions.

Three-band decomposition analysis of wall shear stress in pulsatile flows

Space-time patterns of wall shear stress (WSS) resulting from the numerical simulation of pulsating hemodynamic flows in semicoronal domains are analyzed, in the case of both regular semicoronal domains and semicoronal domains with bumpy insertions, mimicking aneurysm-like geometries. A new family of cardiovascular risk indicators, which we name three-band diagrams (TBDs), are introduced, as a sensible generalization of the two standard indicators, i.e., the time-averaged WSS and the oscillatory shear index. TBDs provide a handy access to additional information contained in the dynamic structure of the WSS signal as a function of the physiological risk threshold, thereby allowing a quick visual assessment of the risk sensitivity to individual fluctuations of the physiological risk thresholds. Due to its generality, TBD analysis is expected to prove useful for a wide host of applications in science, engineering, and medicine, where risk assessment plays a central role.

Aortic dissection: visualisation of aortic blood flow and quantification of wall shear stress using time-resolved, 3D phase-contrast MRI

Background Aortic blood flow in healthy people is characterised by helical flow in the ascending and descending aorta, with corresponding patterns of wall shear stress (WSS) imposed upon the wall of the aorta by moving blood. Flow and WSS patterns in the aortic root and sinuses of Valsalva, and the flow patterns in diseased aortas are incompletely defined. We describe the use of a validated, time-resolved, 3D flow MRI sequence to characterize flow and WSS in the aorta, focusing on the aortic root, and demonstrate the flow and WSS in the aorta of healthy volunteers and patients with prior aortic dissection.

Cardiac magnetic resonance imaging can detect early vascular changes in children with type 1 diabetes (T1DM)

Adult studies have shown that cardiac magnetic resonance (CMR) can image vascular changes including altered aortic compliance and early plaque which correlates well with Framingham risk score and endothelial function. Impaired endothelial function, measured with brachial artery reactivity testing, is recognized as an early and modulating process in the pathophysiology of atherosclerotic plaque development. No CMR imaging studies of early atherosclerosis and vascular health exist in diabetic pediatric populations. This prospective pilot CMR proof of concept study hypothesized that children with T1DM will have thoracic aortic wall characteristics, as well as CMR-derived aortic computational fluid dynamic (CFD) models, different from age-matched control subjects. Furthermore, a positive correlation was sought between key CMR data and brachial artery reactivity measures, as well as cardiac venous biomarkers in T1DM. 7 control and 8 T1DM pediatric subjects had same-day fasting CMR scan, brachial artery testing, and venous blood draw (for lipid panel, HgbA1c, glucose, high sensitivity c-reactive protein (hs-cRP), fibrinogen, and homocysteine). Enrolled T1DM and control subjects were similar: age (14.5 ±1.7 versus (vs.) 15.2 ± 2.7 years), sex (4 male and 4 female T1DM vs. 5 male and 2 female controls), weight (55.7 ± 14.8 vs. 67.6 ± 23.5 kg), body mass index (20.8 ± 4.3 vs. 23.1 ± 5.7 kg/m2) and systolic blood pressure (113 ± 11.4 vs. 116 ± 8.8). They had no significant differences in lipid values, fibrinogen, or hs-cRP, but did differ with regard to glucose (182.1 ± 100.8 vs. 85.4 ± 5.7, p < 0.02), HgbA1c (9.0 ± 2.2 vs. 5.2 ± 0.3, p < 0.001), and homocysteine (4.3 ± 0.6 vs. 5.7 ± 1.0, p < 0.04). While brachial artery reactivity did not change with age, CMR determined ascending aortic (AAo) compliance decreased with increasing age in T1DM (R2 = 0.54, p < 0.09), but not for controls. In T1DM, CMR determined ascending aortic (AAo) compliance declined, as hs-cRP increased (R2 = 0.66, p < 0.05).No other significant correlations existed between AAo compliance and venous biomarkers. Preliminary qualitative analyses of aortic CFD models show different patterns of aortic wall shear stress and oscillatory shear index (OSI) for T1DM versus age-matched control pediatric subjects (Figure ​(Figure1).1). In conclusion, this pilot CMR study of T1DM and control pediatric subjects illustrates that early differences in vascular characteristics can be detected by MRI and correlate with age and with select venous biomarkers. Figure 1

Non-dimensional modeling in flow simulation studies of coronary arteries including side-branches: A novel diagnostic tool in coronary artery disease

AimsBlood flow, vascular shape and size and local remodeling of the vascular wall are linked through wall shear stress (WSS) signaling. Inter-individual comparison of shape and WSS is hampered by large differences in size of flow and shape. We performed non-dimensional modeling to discriminate different types of coronary artery remodeling based on WSS patterns and vessel morphology. Methods and resultsBlood flow was simulated in three-dimensional reconstructed right coronary artery trees from seven controls, five patients with coronary artery disease (CAD) and five patients with aneurysmatic CAD (AnCAD) classified by expert visual diagnosis. A discriminant model using low WSS area, a remodeling index, and cross-correlation of WSS in main trunks and complete trees (K) as non-dimensional parameters classified CAD and AnCAD correctly and identified three patients with high risk profile and functional disease in controls. The new model was compared with discriminant analysis of identical cases simulated without side-branches. The inclusion of K (information from side-branches) and replacement of the mean diameter by a non-dimensional remodeling index improved the model. We found significant (p<0.005) gender differences in the remodeling index. ConclusionThe combination of non-dimensional modeling and WSS profiling should be further investigated as a novel diagnostic tool in CAD beyond local stenosis.

Morphological Evidence for a Change in the Pattern of Aortic Wall Shear Stress With Age

The distribution of atherosclerosis around branch sites changes with age in human and rabbit aortas. We tested whether that reflects a change in the pattern of wall shear stress by examining shear-dependent morphological features of endothelial cells. Endothelial cells and their nuclei align and elongate with applied shear. These parameters were examined in the descending thoracic aorta of immature and mature rabbits. The use of Häutchen preparations, fluorescent stains, and automated image analysis allowed nuclear morphology to be mapped reliably at high resolution over large areas. Cells and their nuclei were most elongated downstream of branch ostia in immature aortas but upstream of them in mature aortas. Elongation was generally greater in mature animals, and nuclei aligned toward the ostia more in these animals, consistent with a greater flow into the branch. Morphology away from branches was indicative of helical flow in the aorta, with greatest shear on the dorsal wall, at both ages. The data are consistent with age-related changes in the pattern of shear around aortic branches. Maps of nuclear elongation closely resembled maps of lesion frequency. The association was positive, implying that lesions occur at sites of high shear stress at both ages.

Pulsatile Flow Effects on the Hemodynamics of Intracranial Aneurysms

High-resolution numerical simulations are carried out to systematically investigate the effect of the incoming flow waveform on the hemodynamics and wall shear stress patterns of an anatomic sidewall intracranial aneurysm model. Various wave forms are constructed by appropriately scaling a typical human waveform such that the waveform maximum and time-averaged Reynolds numbers, the Womersley number (α), and the pulsatility index (PI) are systematically varied within the human physiologic range. We show that the waveform PI is the key parameter that governs the vortex dynamics across the aneurysm neck and the flow patterns within the dome. At low PI, the flow in the dome is similar to a driven cavity flow and is characterized by a quasi-stationary shear layer that delineates the parent artery flow from the recirculating flow within the dome. At high PI, on the other hand, the flow is dominated by vortex ring formation, transport across the neck, and impingement and breakdown at the distal wall of the aneurysm dome. We further show that the spatial and temporal characteristics of the wall shear stress field on the aneurysm dome are strongly correlated with the vortex dynamics across the neck. We finally argue that the ratio between the characteristic time scale of transport by the mean flow across the neck and the time scale of vortex ring formation can be used to predict for a given sidewall aneurysm model the critical value of the waveform PI for which the hemodynamics will transition from the cavity mode to the vortex ring mode.

Flow simulation studies in coronary arteries—Impact of side-branches

Aims Wall shear stress (WSS) may induce local remodeling of the vascular wall and the WSS pattern in turn depends on vascular geometry. We aimed to elucidate the impact of side-branches on local WSS. Methods and results Steady numerical flow simulation studies were performed in three-dimensional reconstructed right coronary artery (RCA) trees. RCA from seven controls, five patients with coronary artery disease (CAD) and five patients with aneurysmatic CAD (AnCAD) classified by expert visual diagnosis were studied. Then three transient flow simulations were performed with cases representative for each group in order to evaluate the impact of pulsatile flow simulation. As vascular size and flow rates vary considerably between patients, non-dimensional approaches were applied for group comparison. A point-to-point comparison of the WSS in the same tree with and without side-branches revealed local differences in WSS of up to 12.0 Pa. This was caused by a reduction of volume flow of up to 78.7% in the trunk. Differences are not only limited to bifurcation sites but also affect local narrowings and strongly curved segments. The point-to-point comparison of steady and transient simulations found an average increase of WSS of below 7% in transient simulations. No significant differences were found between histograms of pulsatile and steady simulations, showing a high cross-correlation of >0.97. Conclusion Side-branches must not be neglected in numerical flow simulation (steady and transient) studies. Steady simulations are valid for an assessment of time-averaged WSS distributions.

Quantifying Turbulent Wall Shear Stress in a Stenosed Pipe Using Large Eddy Simulation

Large eddy simulation was applied for flow of Re=2000 in a stenosed pipe in order to undertake a thorough investigation of the wall shear stress (WSS) in turbulent flow. A decomposition of the WSS into time averaged and fluctuating components is proposed. It was concluded that a scale resolving technique is required to completely describe the WSS pattern in a subject specific vessel model, since the poststenotic region was dominated by large axial and circumferential fluctuations. Three poststenotic regions of different WSS characteristics were identified. The recirculation zone was subject to a time averaged WSS in the retrograde direction and large fluctuations. After reattachment there was an antegrade shear and smaller fluctuations than in the recirculation zone. At the reattachment the fluctuations were the largest, but no direction dominated over time. Due to symmetry the circumferential time average was always zero. Thus, in a blood vessel, the axial fluctuations would affect endothelial cells in a stretched state, whereas the circumferential fluctuations would act in a relaxed direction.

A computational and experimental study inside microfluidic systems: the role of shear stress and flow recirculation in cell docking

In this paper, microfluidic devices containing microwells that enabled cell docking were investigated. We theoretically assessed the effect of geometry on recirculation areas and wall shear stress patterns within microwells and studied the relationship between the computational predictions and experimental cell docking. We used microchannels with 150 microm diameter microwells that had either 20 or 80 microm thickness. Flow within 80 microm deep microwells was subject to extensive recirculation areas and low shear stresses (<0.5 mPa) near the well base; whilst these were only presented within a 10 microm peripheral ring in 20 microm thick microwells. We also experimentally demonstrated that cell docking was significantly higher (p < 0.01) in 80 microm thick microwells as compared to 20 microm thick microwells. Finally, a computational tool which correlated physical and geometrical parameters of microwells with their fluid dynamic environment was developed and was also experimentally confirmed.