Absolute Wall Shear Stress Research Articles

The definition of low wall shear stress and its effect on plaque progression estimation in human coronary arteries

Wall shear stress (WSS), the frictional force of the blood on the vessel wall, plays a crucial role in atherosclerotic plaque development. Low WSS has been associated with plaque growth, however previous research used different approaches to define low WSS to investigate its effect on plaque progression. In this study, we used four methodologies to allocate low, mid and high WSS in one dataset of human coronary arteries and investigated the predictive power of low WSS for plaque progression. Coronary reconstructions were based on multimodality imaging, using intravascular ultrasound and CT-imaging. Vessel-specific flow was measured using Doppler wire and computational fluid dynamics was performed to calculate WSS. The absolute WSS range varied greatly between the coronary arteries. On the population level, the established pattern of most plaque progression at low WSS was apparent in all methodologies defining the WSS categories. However, for the individual patient, when using measured flow to determine WSS, the absolute WSS values range so widely, that the use of absolute thresholds to determine low WSS was not appropriate to identify regions at high risk for plaque progression.

Hemodynamic Differences Between Recurrent and Nonrecurrent Intracranial Aneurysms: Fluid Dynamics Simulations Based on MR Angiography.

Although the role of wall shear stress (WSS) in the initiation, growth, and rupture of intracranial aneurysms has been well studied, its influence on aneurysm recurrence after endovascular treatment requires further investigation. We aimed to compare WSS at necks of recurrent and nonrecurrent aneurysms. Nine recurrent coil-embolized aneurysms were identified and matched with nine nonrecurrent aneurysms. Patient-specific vessel geometries reconstructed from follow-up 3-D time-of-flight magnetic resonance angiography were analyzed using computational fluid dynamics (CFD) simulations. Absolute WSS and the percentage of abnormally low and high WSS at the aneurysm neck compared to the near artery were measured. The median percentage of abnormal WSS at the aneurysm neck was 49.3% for recurrent and 34.7% for nonrecurrent aneurysms (P = .011). The area under the receiver-operating-characteristic curve for distinguishing these aneurysms according to the percentage of abnormal WSS was .86 (95% CI .62 to .98). The optimal cut-off value of 45.1% resulted in a sensitivity and a specificity of 88.89% (95% CI 51.8% to 99.7%). Our findings indicate that necks of recurrent aneurysms are exposed to abnormal WSS to a larger extent. Abnormal WSS may serve as a metric to distinguish them from nonrecurrent aneurysms with CFD simulations a priori.

Functional and anatomical measures for outflow boundary conditions in atherosclerotic coronary bifurcations

The aim of this research was finding the influence of anatomy-based and functional-based outflow boundary conditions for computational fluid dynamics (CFD) on fractional flow reserve (FFR) and wall shear stress (WSS) in mildly diseased coronary bifurcations.For 10 patient-specific bifurcations three simulations were set up with different outflow conditions, while the inflow was kept constant. First, the outflow conditions were based on the diameter of the outlets. Second, they were based on the volume estimates of the myocardium that depended on the outlets. Third, they were based on a myocardial flow measure derived from computed tomography perfusion imaging (CTP).The difference in outflow ratio between the perfusion-based and the diameter-based approach was −7 p.p. [−14 p.p.:7 p.p.] (median percentage point and interquartiles), and between the perfusion-based and volume-based this was −2 p.p. [−2 p.p.:1 p.p.]. Despite of these differences the computed FFRs matched very well. A quantitative analysis of the WSS results showed very high correlations between the methods with an r2 ranging from 0.90 to 1.00. But despite the high correlations the diameter-based and volume-based approach generally underestimated the WSS compared to the perfusion-based approach. These differences disappeared after normalization.We demonstrated the potential of CTP for setting patient-specific boundary conditions for atherosclerotic coronary bifurcations. FFR and normalized WSS were unaffected by the variations in outflow ratios. In order to compute absolute WSS a functional measure to set the outflow ratio might be of added value in this type of vessels.

Aortic wall shear stress in Marfan syndrome

The aim of this study was to quantify changes in thoracic aortic wall shear stress (WSS) in asymptomatic patients with Marfan syndrome (MFS) compared with healthy controls. WSS in the thoracic aorta was quantified based on time-resolved 3D phase contrast MRI with three-directional velocity encoding (4D flow MRI, temporal resolution ∼44 ms, spatial resolution ∼2.5 mm) in 24 patients with confirmed MFS (age = 18 ± 12 years) and in 12 older healthy volunteers (age = 25 ± 3 years). Diameters of the thoracic aorta normalized to body surface area were similar for both groups. Peak systolic velocity, absolute WSS, time-averaged WSS, circumferential WSS, peak systolic WSS, and WSS eccentricity were calculated in eight analysis planes distributed along the thoracic aorta. Plane-wise comparison revealed significant differences between MFS patients and volunteers in the proximal ascending aorta for peak systolic velocities (1.11 ± 0.23 m/s vs. 1.34 ± 0.18 m/s, P = 0.004) and circumferential WSS (0.14 ± 0.03 N/m(2) vs. 0.11 ± 0.02 N/m(2), P = 0.007). WSS eccentricity was altered in most of the ascending aorta and proximal arch (P = 0.009-0.020). MFS patients demonstrated segmental differences in peak systolic WSS with a significantly higher WSS at the inner curvature in the proximal ascending aorta and at the anterior part in the more distal ascending aorta (P < 0.01). These findings indicate differences in WSS associated with MFS despite similar aortic dimensions compared to controls.

Aortic Hemodynamics in Patients With and Without Repair of Aortic Coarctation

The purpose of this study was to characterize hemodynamic alterations and flow-derived vessel wall parameters in aortic coarctation (CoA) patients with and without operative repair by time-resolved, 3-dimensional, and 3-directional velocity sensitive, phase-contrast magnetic resonance imaging (4D PC MRI) in comparison with healthy subjects. Twenty-four patients, 12.5 ± 6.4 years after CoA repair, 4 patients without treatment for CoA, and 19 healthy subjects were examined. The study was approved by the institutional review board and signature of written informed consent was obtained from the participants. Echocardiography was performed in patients before participation. MRI studies were conducted by applying flow-sensitive 4D phase-contrast MRI at either 1.5 T (n = 5 patients) or 3 T (all 19 healthy subjects, n = 23 patients). Blood flow visualization was used to evaluate overall aortic helicity, presence of pronounced or additional localized helix flow, and vortex development. Quantitative evaluation comprised the calculation of regional time-averaged absolute wall shear stress (WSS(mag)), peak velocities, and oscillatory shear index at 8 locations distributed along the thoracic aorta and additionally at the site of CoA. Inter- and intraobserver variabilities of calculations were determined. Volunteers and patients demonstrated the same amount of overall aortic helicity. In contrast, the number of additional localized helix flow or vortex formation was significantly increased in patients (25/28 patients vs. 5/19 normal controls, Fisher exact test: P < 0.001). Vortices in the orifices of the supra-aortic branches were detected in 64.3% (18/28) of patients but in only 11.8% (2/19) of controls (P < 0.001). Quantitative analyses revealed a significant increase in overall aortic WSS(mag) (0.44 ± 0.17 N/m(2) in patients vs. 0.27 ± 0.08 N/m(2) in volunteers, P < 0.005) and a decrease in overall oscillatory shear index. Repeated quantitative analysis showed moderate interobserver and low intraobserver variability. Correlation with echocardiography showed good agreement with MRI which tended to underestimate peak velocities (r = 0.76; Bland-Altman analysis, limits of agreement = -0.57-2.16 m/s, mean = 0.79 m/s). Alterations in aortic hemodynamics after CoA repair are not limited to the specific region of repair, but can be found in the entire aorta. The presented findings highlight the systemic nature of the disease and the need for a systemic diagnostic approach which can be provided by flow-sensitive 4D PC MRI. Furthermore, valuable additional insights on the hemodynamic consequences of coarctation have been shown that may help understanding secondary complications such as restenosis, aneurysm formation, and arterial hypertension.

In Vivo Wall Shear Stress Distribution in the Carotid Artery

Background— The purpose of this study was to analyze the in vivo distribution of absolute wall shear stress (WSS abs ) and oscillatory shear index (OSI) in the carotid bifurcation and to evaluate its dependence on bifurcation geometry, the presence of internal carotid artery (ICA) stenosis, and recanalization therapy. Methods and Results— Time-resolved 3D blood flow was acquired with flow-sensitive 4D MRI in 64 normal carotid bifurcations and 17 carotid arteries with moderate ICA stenosis (48±6%) or after surgical recanalization. Among 64 normal arteries, atherogenic wall parameters were consistently concentrated in proximal bulb regions of the common (CCA) and internal (ICA) carotid arteries. The fraction of the carotid bulb exposed to atherosclerosis-prone wall parameters (low WSS abs below and high OSI above group-defined 20% and 10% thresholds) was correlated with the individual bifurcation geometry. Multiple regressions revealed significant ( P &lt;0.01) relationships (β, 0.44 to 0.48) between the areas with atherosclerosis-prone wall parameters and the d ICA /d CCA diameter ratio. The size of regions exposed to high OSI demonstrated highly significant ( P ≤0.01) relationships with all analyzed geometry parameters (d ICA /d CCA β, 0.48; tortuosity β, ≤−0.56; bifurcation angle β, ≥0.47). Moderate ICA stenosis altered the distribution of wall parameters (45%/61% reduction of individually low WSS abs /high OSI in the proximal ICA), which were relocated to segments distal to the arterial stenosis. WSS abs /OSI topology after recanalization was similar compared with the normal wall parameter distribution. Conclusions— Flow-sensitive 4D MRI identified alterations in the segmental in vivo WSS distribution associated with atherosclerotic disease, surgical therapy, and individual bifurcation geometry and could be a valuable technique to assess the individual risk of flow-mediated atherosclerosis and carotid plaque progression.

Three‐dimensional analysis of segmental wall shear stress in the aorta by flow‐sensitive four‐dimensional‐MRI

To assess the distribution and regional differences of flow and vessel wall parameters such as wall shear stress (WSS) and oscillatory shear index (OSI) in the entire thoracic aorta. Thirty-one healthy volunteers (mean age = 23.7 +/- 3.3 years) were examined by flow-sensitive four-dimensional (4D)-MRI at 3T. For eight retrospectively positioned 2D analysis planes distributed along the thoracic aorta, flow parameters and vectorial WSS and OSI were assessed in 12 segments along the vascular circumference. Mean absolute time-averaged WSS ranged between 0.25 +/- 0.04 N/m(2) and 0.33 +/- 0.07 N/m(2) and incorporated a substantial circumferential component (-0.05 +/- 0.04 to 0.07 +/- 0.02 N/m(2)). For each analysis plane, a segment with lowest absolute WSS and highest OSI was identified which differed significantly from mean values within the plane (P < 0.05). The distribution of atherogenic low WSS and high OSI closely resembled typical locations of atherosclerotic lesions at the inner aortic curvature and supraaortic branches. The normal distribution of vectorial WSS and OSI in the entire thoracic aorta derived from flow-sensitive 4D-MRI data provides a reference constituting an important perquisite for the examination of patients with aortic disease. Marked regional differences in absolute WSS and OSI may help explaining why atherosclerotic lesions predominantly develop and progress at specific locations in the aorta.

Asymptotic Profiles for the Blasius and Sakiadis flows in a Darcy–Brinkman Isotropic Porous Medium Either with Uniform Suction or with Zero Transverse Velocity

The Blasius and Sakiadis flows with uniform suction or with zero transverse velocity, at the asymptotic state, in a Darcy–Brinkman porous medium are investigated in this note. Exact analytical solutions are derived for velocity as well as for the integral quantities. It is found that both the dimensional and non-dimensional displacement thickness, momentum thickness, energy thickness and the absolute wall shear stress are identical in both Blasius and Sakiadis flows at the asymptotic state.

Asymptotic suction profiles for the Blasius and Sakiadis flow with constant and variable fluid properties

A theoretical study of the effect of variable fluid properties on the Blasius and Sakiadis flow with uniform suction at the asymptotic state is presented in this paper. The investigation concerns air and water taking into account the variation of their physical properties with temperature. Velocity and temperature profiles are presented as well as values of the displacement thickness, momentum thickness, shape factor, wall shear stress and Nusselt number for different temperatures of the plate and the ambient fluid. It is found that the nondimensional displacement thickness, momentum thickness, shape factor, absolute wall shear stress and Nusselt number are identical in both Blasius and Sakiadib flow at the asymptotic state for a fluid with constant properties. The same is valid for any fluid with variable properties if the temperature boundary conditions are the same in Blasius and Sakiadis flow.

Deformation and Alignment of the Subconfluent Cultured Endothelial Cell Model under Fluid Shear Stress. Computational Fluid Mechanical Simulation.

The spontaneous alignment of arterial endothelial cells under flow conditions was simulated using a three dimensional computational fluid mechanical model of cultured endothelial cells. Endothelial cells were simulated using a 2D Gaussian distribution function. The nearly round model cells were randomly placed on a flat plate with random orientation. Navier-Stokes equations of a Newtonian fluid were solved using a finite volume method, and the absolute wall shear stress (WSS) at the summit of cells was calculated. Model cells were assumed to change their shape and orientation randomly and only the deformation of cells, which reduces the WSS, was assumed to be conserved under steady flow conditions. The model cells eventually demonstrated alignment during the simulation, which closely resembled that of real cells. This deformation and alignment was thought to simulate the flow induced self reorganization of the endothelial cells observed in vivo.

Deformation and Alignment of Arterial Endothelial Cells along Blood Flow.(A Computational Fluid Mechanical Study)

The mechanism of arterial endothelial cell deformation and alignment was studied using a three-dimensional computational fluid mechanical model of the arteriolar wall with regularly arranged intraluminal undulation simulating endothelial cells. Endothelial cells were simulated using a 2D Gaussian distribution function, which had three parameters used to define the shape of the cells. They were the elongation factor, which is the correlation coefficient of the Gaussian distribution function, the height of the cells, and the cellular angle against the blood flow. The Navier-Stokes equations of the Newtonian fluid under steady flow conditions were solved using a finite volume method, and the absolute wall shear stress (WSS) at the summit of the cells was calculated. The WSS at the nuclear bulge varied in a complex manner, and the hypothesis that the endothelial cells change their shape and alignment to minimize the WSS at the nuclear bulge was presented to explain the computed results.