Estimation Of Wall Shear Stress Research Articles

Data-driven calculation of porous geometry-dependent permeability and fluid-induced wall shear stress within tissue engineering scaffolds

It is commonly known that mechanical stimulation, for example, wall shear stress (WSS), can affect cellular behaviours. In vitro experiments have been performed by applying fluid-induced WSS to investigate the cell physiology and pathology. Porous scaffolds are used in these experiments for housing and facilitating the micro-physical/chemical environment on cells during 3-dimensional (3D) cell culturing. It is known that scaffold porous geometries influence scaffold permeability and internal WSS. Computational simulations are commonly employed to determine the WSS; however, these simulations can be computationally expensive and may not be readily accessible to everyone due to a knowledge gap. To address this limitation, this study proposes an empirical equation for calculating the scaffold permeability based on the Kozeny-Carman equation. The new equation considers the porous geometric features, providing an accurate estimation of the scaffold permeability. Furthermore, the study introduces a new correlation between WSS and permeability, aiming to establish an efficient and precise estimation of internal WSS. This correlation enables efficient estimation of the WSS within porous scaffolds without relying on computationally demanding simulations. Therefore, the output from this study can negate the issues of using computational simulation for determining scaffold permeability and internal WSS under perfusion flow by providing empirical equations.

New momentum integral equation applicable to boundary layer flows under arbitrary pressure gradients

By incorporating the traditionally overlooked advective term in the wall-normal momentum equation, a new momentum integral equation is developed for two-dimensional incompressible turbulent boundary layers under arbitrary pressure gradients. The classical Kármán's integral arises as a special instance of the new momentum integral equation when the pressure gradient is weak. The new momentum integral equation's validity is substantiated by direct numerical simulation data. Unlike the classical Kármán's integral, which is limited to predicting wall shear stress within mild pressure gradients, the new momentum integral equation accurately computes wall shear stress across a broad range of pressure gradients, even in the presence of strong adverse pressure gradients that lead to flow separation. Moreover, a new pressure parameter $\beta _\kappa$ is introduced through examining terms in the new momentum integral equation. This parameter naturally quantifies the pressure gradient's influence on turbulent boundary layers and offers guidance for applying the classical Kármán's integral. Additionally, to facilitate experimental determination of wall shear stress under strong pressure gradients, an approximate integral equation is proposed that relies solely on easily measurable variables. Validation against direct numerical simulation data demonstrates that this simplified equation provides reasonably accurate estimates of wall shear stress in turbulent boundary layers experiencing strong pressure gradients.

Estimation of Mouse Carotid Arterial Wall Shear Stress Using High-Frequency Ultrasound Imaging.

Wall shear stress (WSS) is a crucial hemodynamic factor that promotes atherosclerosis (plaque) development in arteries; although the relationship between WSS and arterial atherosclerosis has been explored in many animal studies, it is not fully understood. No suitable tool, however, exists for rapidly estimating dynamic WSS in small-animal studies. This study proposes a 40-MHz high-frequency ultrasound (HFUS) imaging system for dynamic WSS estimation based on mouse carotid artery blood flow velocity gradient measurements by vector Doppler imaging (VDI). Aliasing reduces the accuracy of Doppler measurements, which can be prevented by increasing the imaging frame rate. Conventionally, imaging is performed at two tilted angles by alternating between the angles; in the proposed method, the frame rate was doubled by imaging at each tilted angle sequentially and by then temporally aligning the sequences based on pulsatile flow characteristics. Velocity estimation using this method had low errors for both a steady-flow straight-tube and pulsatile flow 60%-stenosis phantom. The method was tested for wild-type (WT) C57BL/6 mice at 16 weeks old and apolipoprotein E knockout (ApoE KO) mice at 16 and 24 weeks old; differences in time-averaged and oscillatory WSS were observed, and histology confirmed that the 24-week ApoE KO mice with the highest oscillatory WSS had the greatest plaque formation. The proposed HFUS WSS imaging method can predict the location and extent of plaque development; thus, this method is useful for small-animal studies investigating the WSS effect on atherosclerotic plaque development.

Aortic wall shear stress in bicuspid aortic valve disease-10-year follow-up.

Bicuspid aortic valve (BAV) disease leads to deviant helical flow patterns especially in the mid-ascending aorta (AAo), potentially causing wall alterations such as aortic dilation and dissection. Among others, wall shear stress (WSS) could contribute to the prediction of long-term outcome of patients with BAV. 4D flow in cardiovascular magnetic resonance (CMR) has been established as a valid method for flow visualization and WSS estimation. The aim of this study is to reevaluate flow patterns and WSS in patients with BAV 10 years after the initial evaluation. Fifteen patients (median age 34.0 years) with BAV were re-evaluated 10 years after the initial study from 2008/2009 using 4D flow by CMR. Our particular patient cohort met the same inclusion criteria as in 2008/2009, all without enlargement of the aorta or valvular impairment at that time. Flow patterns, aortic diameters, WSS and distensibility were calculated in different aortic regions of interest (ROI) with dedicated software tools. Indexed aortic diameters in the descending aorta (DAo), but especially in the AAo did not change in the 10-year period. Median difference 0.05 cm/m2 (95% CI: 0.01 to 0.22; P=0.06) for AAo and median difference -0.08 cm/m2 (95% CI: -0.12 to 0.01; P=0.07) for DAo. WSS values were lower in 2018/2019 at all measured levels. Aortic distensibility decreased by median 25.6% in the AAo, while stiffness increased concordantly (median +23.6%). After a ten years' follow-up of patients with isolated BAV disease, indexed aortic diameters did not change in this patient cohort. WSS was lower compared to values generated 10 years earlier. Possibly a drop of WSS in BAV could serve as a marker for a benign long-term course and implementation of more conservative treatment strategies.

Wall Shear Stress Estimation for 4D Flow MRI Using Navier-Stokes Equation Correction.

This study introduces a novel wall shear stress (WSS) estimation method for 4D flow MRI. The method improves the WSS accuracy by using the reconstructed pressure gradient and the flow-physics constraints to correct velocity gradient estimation. The method was tested on synthetic 4D flow data of analytical Womersley flow and flow in cerebral aneurysms and applied to in vivo 4D flow data acquired in cerebral aneurysms and aortas. The proposed method's performance was compared to the state-of-the-art method based on smooth-spline fitting of velocity profile and the WSS calculated from uncorrected velocity gradient. The proposed method improved the WSS accuracy by as much as 100% for the Womersley flow and reduced the underestimation of mean WSS by 39 to 50% for the synthetic aneurysmal flow. The predicted mean WSS from the in vivo aneurysmal data using the proposed method was 31 to 50% higher than the other methods. The predicted aortic WSS using the proposed method was 3 to 6 times higher than the other methods and was consistent with previous CFD studies and the results from recently developed methods that take into account the limited spatial resolution of 4D flow MRI. The proposed method improves the accuracy of WSS estimation from 4D flow MRI, which can help predict blood vessel remodeling and progression of cardiovascular diseases.

Study on the radial sectional velocity distribution and wall shear stress associated with carotid artery stenosis

Atherosclerosis is an important cause of cardiovascular disease. The wall shear stress (WSS) is one of the key factors of plaque formation and dislodgement. Currently, WSS estimation is based on the measurement of the blood velocity gradient. However, due to the lack of flow field measurements in carotid stenosis vessels, the two distribution forms (parabolic and non-parabolic) commonly considered in numerical simulations could cause WSS estimates to differ by more than 40%, which could seriously affect the accuracy of mechanical analysis. This study applied three-dimensional (3D) printing technology to create an experimental model of real-structure carotid arteries. Microparticle image velocimetry was adopted to comprehensively measure blood velocity field data at the stenosis location, providing experimental validation of numerical simulation (Fluent; finite volume method) results. Then, the flow field was simulated at a normal human heart rate (45–120 beats per minute). The radial sectional velocity exhibited a plateau-like distribution with a similar velocity in the central region (more than 65% of the total channel width). This study provides an accurate understanding of the WSS at the carotid stenosis location and proposes a reliable method for the study of flow fields under various blood flow conditions.

Numerical investigation of hemodynamic pattern in carotid artery dynamic aneurysm on bifurcation region for early clinical decision making

AbstractIn this paper, a numerical estimation of wall shear stress (WSS) and study on hemodynamic pattern in carotid artery (CA) near the bifurcation region with dynamic growth of aneurysm using computational fluid dynamics (CFD) for making early clinical decision is presented. Aneurysm in the carotid artery affects the blood supply to brain and if it is untreated at early stage may lead to sudden death. Computed tomography images of four different cases of stroke subjects scanned of 600 slices with 1 mm resolution with neighbouring layers from neck to head are considered for this study. Numerically a CA with bifurcation region is developed from these images and aneurysm is and allowed to grow dynamically from 10 to 20 mm. WSS and hemodynamic pattern is estimated numerically using Ansys platform at various region of interest in both rigid and compliant wall conditions. The arterial wall thinning was analytically estimated using thick cylinder theory to estimate the increase in aneurysm under various stress conditions (rest and exercise conditions). The findings show that WSS is found to reduce at the aneurysm region with a corresponding strong vortex pattern. Thus, the vortex pattern could be the cause of tissue damage and thinning rather than WSS. The corresponding increase in velocity gradient at the bifurcation region is also captured. This high gradient is the cause for higher WSS at the bifurcation region which is a possible cause for the formation of plaque and arteriosclerosis. It is interesting to note that the WSS did not change drastically for 10 and 15 mm aneurysm but a large change was seen from normal to 10 and 15–20 mm respectively. This study provides a better clinical insight on the effect of aneurysm in CA bifurcation region using a systematic approach to numerical modelling compared to traditional imaging modalities. It can be used as an adjunct tool for physicians and surgeons for planning necessary clinical interventions.

WSSNet: Aortic Wall Shear Stress Estimation Using Deep Learning on 4D Flow MRI.

Wall shear stress (WSS) is an important contributor to vessel wall remodeling and atherosclerosis. However, image-based WSS estimation from 4D Flow MRI underestimates true WSS values, and the accuracy is dependent on spatial resolution, which is limited in 4D Flow MRI. To address this, we present a deep learning algorithm (WSSNet) to estimate WSS trained on aortic computational fluid dynamics (CFD) simulations. The 3D CFD velocity and coordinate point clouds were resampled into a 2D template of 48 × 93 points at two inward distances (randomly varied from 0.3 to 2.0 mm) from the vessel surface (“velocity sheets”). The algorithm was trained on 37 patient-specific geometries and velocity sheets. Results from 6 validation and test cases showed high accuracy against CFD WSS (mean absolute error 0.55 ± 0.60 Pa, relative error 4.34 ± 4.14%, 0.92 ± 0.05 Pearson correlation) and noisy synthetic 4D Flow MRI at 2.4 mm resolution (mean absolute error 0.99 ± 0.91 Pa, relative error 7.13 ± 6.27%, and 0.79 ± 0.10 Pearson correlation). Furthermore, the method was applied on in vivo 4D Flow MRI cases, effectively estimating WSS from standard clinical images. Compared with the existing parabolic fitting method, WSSNet estimates showed 2–3 × higher values, closer to CFD, and a Pearson correlation of 0.68 ± 0.12. This approach, considering both geometric and velocity information from the image, is capable of estimating spatiotemporal WSS with varying image resolution, and is more accurate than existing methods while still preserving the correct WSS pattern distribution.

Feasibility of coronary blood flow simulations using mid-fidelity numeric and geometric models.

The fractional flow reserve index (FFR) is currently used as a gold standard to quantify coronary stenosis's functional relevance. Due to its highly invasive nature, the development of noninvasive surrogates based on simulations has drawn much attention in recent years, emphasizing efficient strategies that enable translational research. The focus of this work is twofold. First, to assess the feasibility of using a mid-fidelity numerical strategy (transversally enriched pipe element method, TEPEM), placed between low- and high-fidelity models, for the estimation of flow-related quantities, such as FFR and wall shear stress (WSS). Low-fidelity models, as zero- or one-dimensional models, are computationally inexpensive but in detriment of poorer spatially detailed predictions. On the other hand, high-fidelity models, such as classical three-dimensional numerical approximations, can provide detailed predictions but their transition to clinical application is prohibitive due to high computational costs. As a second goal, we quantify the impact of the length of lateral branches in the blood flow through the interrogated vessel of interest to further reduce the computational burden. Both studies are addressed considering a cohort of 17 coronary geometries. A total of 20 locations were selected to estimate the FFR index for a wide range of Coronary Flow Reserve (CFR) scenarios. Numerical results suggest that the mid-fidelity TEPEM model is a reliable approach for the efficient estimation of the FFR index and WSS, with an error in the order of [Formula: see text] and [Formula: see text], respectively, when compared to the high-fidelity prediction. Moreover, such mid-fidelity models require much less computational resources, in compliance with infrastructure frequently available in the clinic, by achieving a speedup between 30 and 60 times compared to a conventional finite element approach. Also, we show that shortening peripheral branches does not introduce considerable perturbations either in the flow patterns, in the wall shear stress, or the pressure drop. Comparing the different geometric models, the error in the estimation of FFR index and WSS is reduced to less than [Formula: see text] and [Formula: see text], respectively.

Moving shear stress towards the clinic: preclinical comparison of optical coherence tomography-based versus angiography-based time-averaged wall shear stress estimations

Abstract Introduction Identification of coronary atherosclerotic plaques at risk of causing future acute coronary syndromes remains a major unmet clinical challenge. The addition of vessel biomechanics to intracoronary imaging derived evaluation of plaque morphology, improves identification of plaques likely to develop high risk features. We and others have developed a framework for intracoronary imaging (optical coherence tomography [OCT]) based 3D reconstructions of coronary arteries for computational fluid dynamics (CFD) simulations of shear stress, which are considered the current gold standard approach for quantification of coronary arterial haemodynamics. However, these approaches are time consuming and computationally intensive, resulting in a barrier to clinical uptake. Purpose Determination of time averaged wall shear stress (TAWSS) based on 3D coronary geometries from non-invasive 3D Quantitative Coronary Angiography (3D-QCA) has recently been developed (Pie Medical Imaging, Netherlands), which enables results of shear stress simulations to be available within 30 minutes. We sought to compare TAWSS determined from 3D-QCA with gold standard OCT-based CFD simulations in both normal and stenotic arteries in minipigs. Methods 15 normal and 5 stenotic minipig coronary arteries were studied. Anatomically matched 3D arterial geometries were reconstructed from 3D-QCA and OCT using common centrelines. Boundary conditions for simulations included directly measured inlet blood velocities; parabolic inlet flow profiles, zero pressure outlet; no-slip arterial walls; blood density: 1.05 g/ml; blood dynamic viscosity: 0.035 g/cm.s. Blood was modelled as Newtonian. 3D-QCA TAWSS was obtained with a Kratos Multi-Physics CFD solver. OCT-based simulations were performed using Abaqus/CFD v6.14. TAWSS was calculated for 80 axially matched segments for both methods (1200 and 400 paired comparisons for normal and stenotic arteries, respectively). Data were analysed using Bland-Altman and Wilcoxon matched-pairs signed ranked tests. Results Computation times for 3D-QCA and OCT-based CFD were approximately 30 minutes and 2 hours respectively. Axial profiles of TAWSS were similar between the two methods and there was agreement in TAWSS magnitudes and narrow 95% limits of agreement (Figure 1 and Figure 2). Using co-registered TAWSS maps generated by each method, we find similar spatial regional distributions of TAWSS in both normal and stenotic arteries. Conclusions Our data suggest that 3D-QCA based TAWSS is feasible in both normal and stenotic arteries. Spatial TAWSS distributions between the two methods are similar with agreement in matched TAWSS comparisons, though there are some small systematic differences in the absolute values of TAWSS, due to different resultant arterial geometries. These encouraging data suggest that further clinical evaluation of rapid TAWSS from 3D-QCA is warranted, which may facilitate clinical adoption of TAWSS assessment. Funding Acknowledgement Type of funding sources: Public grant(s) – EU funding. Main funding source(s): Medical Research Council

Wall shear stress mapping for human femoral artery based on ultrafast ultrasound vector Doppler estimations.

Wall shear stress (WSS), a type of friction exerted on the artery wall by flowing blood, is considered a crucial factor in atherosclerotic plaque development. Currently, achieving a reliable WSS mapping of an artery noninvasively by using existing imaging modalities is still challenging. In this study, a WSS mapping based on vector Doppler flow velocity estimation was proposed to measure the dynamic WSS on the human femoral artery. Because ultrafast ultrasound imaging was used here, flow-enhanced imaging was also performed to observe the moving blood flow condition. The performance of WSS mapping was verified using both straight (8mm in diameter) and stenosis (70% of stenosis) phantoms under a pulsatile flow condition. A human study was conducted from five healthy volunteers. Experimental results demonstrated that the WSS estimation was close to the standard value that was obtained from maximum velocity estimation in straight phantom experiments. In a stenosis phantom experiment, a low WSS region was observed at a site downstream of an obstruction, which is a high-risk area for plaque formation. Dynamic WSS mapping was accomplished in measurement in the femoral artery bifurcation. In measurements, the time-averaged WSS of the common femoral artery, superficial femoral artery, and deep femoral artery was 0.52± 0.19, 0.44 ± 0.21, and 0.29 ± 0.16Pa, respectively, for the anterior wall and 0.29 ± 0.11, 0.54 ± 0.24, and 0.23 ± 0.10Pa, respectively, for the posterior wall. All results indicated that WSS mapping has the potential to be a useful tool for vessel duplex scanning in the future.

Optimization of 4D flow MRI velocity field in the aorta with divergence-free smoothing.

Divergence-free smoothing with wall treatment (DFSwt) method is proposed for processing with four-dimensional (4D) flow magnetic resonance imaging (MRI) data of blood flows to enhance the quality of flow field with physical constraints. The new method satisfies the no-slip wall boundary condition and applies wall function of velocity profile for better estimating the velocity gradient in the near-wall region, and consequently improved wall shear stress (WSS) calculation against the issue of coarse resolution of 4D flow MRI. In the first testing case, blood flow field obtained from 4D flow MRI is well smoothed by DFSwt method. A great consistency is observed between the post-processed 4D flow MRI data and the computational fluid dynamics (CFD) data in the interested velocity field. WSS has an apparent improvement due to the proposed near-wall treatment with special wall function comparing to the result from original 4D flow MRI data or the DFS-processed data with no wall function. The other five cases also show the same performance that smoothed velocity field and improved WSS estimation are achieved on 4D flow MRI data optimized by DFSwt. The improvements will benefit the study of hemodynamics regarding the determination of location or the potential possibility of lesions.

The Role of Elevated Wall Shear Stress in Progression of Pulmonary Vein Stenosis: Evidence from Two Case Studies

Pulmonary vein stenosis is a serious condition characterized by restriction or blockage due to fibrotic tissue ingrowth that develops in the pulmonary veins of infants or children. It is often progressive and can lead to severe pulmonary hypertension and death. Efforts to halt or reverse disease progression include surgery and catheter-based balloon dilation and stent implantation. Its cause and mechanism of progression are unknown. In this pilot study, we propose and explore the hypothesis that elevated wall shear stress at discrete pulmonary venous sites triggers stenosis. To assess this theory, we retrospectively analyzed cardiac catheterization, lung scan, and X-ray computed tomography data to estimate wall shear stress in the pulmonary veins at multiple time points during disease progression in two patients. Results are consistent with the existence of a level of elevated wall shear stress above which the disease is progressive and below which progression is halted. The analysis also suggests the possibility of predicting the target lumen size necessary in a given vein to reduce wall shear stress to normal levels and remove the trigger for stenosis progression.

Comparison of flow characteristics in a bench‐scale system with commercial‐scale pipelines: Use of computational fluid dynamics (CFD)

The challenges for scale-up are often encountered in cleaning operations during the interpretation of data from clean-in-place (CIP) research. The objective of this investigation was to design and characterize flow characteristics in a bench-scale system in a manner that evaluates scale-up to a commercial-scale CIP operation. A bench-scale temperature-controlled vessel was designed for evaluation of in-place cleaning, and for development of scale-up parameters. The wall shear stress was selected as the parameter for the comparison, as it is the significant parameter associated with deposit removal. Using the traditional prediction models, the wall shear stress of bench-scale ranged 0.015 to 4.99Pa with impeller speeds from 50 to 900rpm. For the commercial-scale with 0.022m of inside diameter, prediction ranged from 1.43 to 7.90Pa with the mean fluid velocity from 0.72 to 1.67m/s. Computational fluid dynamics (CFD) was used to predict wall shear stress on the surfaces within the bench-scale and commercial-scale systems. The predicted wall shear stress values ranged from 0.016 to 2.42Pa for surfaces within the bench-scale system, and from 1.33 to 7.20Pa for the commercial-scale system. The differences between two calculation methods are attributed to the averaging the magnitude over the whole area and the overestimation of friction coefficients employed in the traditional prediction. The results confirm that CFD provided more reliable wall shear stress estimates for surfaces of interest. The wall shear stress estimates for a bench-scale compare favorably to estimates for a commercial-scale pie section in a CIP system. PRACTICAL APPLICATION: The current investigation demonstrates that the computational fluid dynamics (CFD) simulation provides accurate estimates for the scale-up parameters. Both academic and industrial researchers will benefit from the proposed methodologies to compare the flow properties of the bench-scale and commercial-scale CIP operation that facilitate the practical implementation of the systems.

Comparison of LBM and FVM in the estimation of LAD stenosis.

The finite volume method (FVM)-based computational fluid dynamics (CFD) technology has been applied in the non-invasive diagnosis of coronary artery stenosis. Nonetheless, FVM is a time-consuming process. In addition to FVM, the lattice Boltzmann method (LBM) is used in fluid flow simulation. Unlike FVM solving the Navier-Stokes equations, LBM directly solves the simplified Boltzmann equation, thus saving computational time. In this study, 12 patients with left anterior descending (LAD) stenosis, diagnosed by CTA, are analysed using FVM and LBM. The velocities, pressures, and wall shear stress (WSS) predicted using FVM and LBM for each patient is compared. In particular, the ratio of the average and maximum speed at the stenotic part characterising the degree of stenosis is compared. Finally, the golden standard of LAD stenosis, invasive fractional flow reserve (FFR), is applied to justify the simulation results. Our results show that LBM and FVM are consistent in blood flow simulation. In the region with a high degree of stenosis, the local flow patterns in those two solvers are slightly different, resulting in minor differences in local WSS estimation and blood speed ratio estimation. Notably, these differences do not result in an inconsistent estimation. Comparison with invasive FFR shows that, in most cases, the non-invasive diagnosis is consistent with FFR measurements. However, in some cases, the non-invasive diagnosis either underestimates or overestimates the degree of stenosis. This deviation is caused by the difference between physiological and simulation conditions that remains the biggest challenge faced by all CFD-based non-invasive diagnostic methods.

Toward an accurate estimation of wall shear stress from 4D flow magnetic resonance downstream of a severe stenosis.

First, to investigate the agreement between velocity, velocity gradient, and Reynolds stress obtained from four-dimensional flow magnetic resonance (4D flow MRI) measurements and direct numerical simulation (DNS). Second, to propose and optimize based on DNS, 2 alternative methods for the accurate estimation of wall shear stress (WSS) when the resolution of the flow measurements is limited. Thirdly, to validate the 2 methods based on 4D flow MRI data. In vitro 4D MRI has been conducted in a realistic rigid stenosed aorta model under a constant flow rate of 12 L/min. A DNS of transitional stenotic flow has been performed using the same geometry and boundary conditions. Time-averaged velocity and Reynolds stresses are in good agreement between in vitro 4D MRI data and DNS (errors between 2% and 8% of the reference downsampled data). WSS estimation based on the 2 proposed methods applied to MRI data provide good agreement with DNS for slice-averaged values (maximum error is less than 15% of the mean reference WSS for the first method and 25% for the second method). The performance of both models is not strongly sensitive to spatial resolution up to 1.5 mm voxel size. While the performance of model 1 deteriorates appreciably at low signal-to-noise ratios, model 2 remains robust. The 2 methods for WSS magnitude give an overall better agreement than the standard approach used in the literature based on direct calculation of the velocity gradient close to the wall (relative error of 84%).

The impact of 4D flow displacement artifacts on wall shear stress estimation.

To investigate the amplitude and spatial distribution of errors in wall shear stress (WSS) values derived from 4D flow measurements caused by displacement artifacts intrinsic to the 4D flow acquisition. Phase-contrast MRI velocimetry was performed in a model of a stenotic aorta using two different timing schemes, both of which are commonly applied in vivo but differ in their resulting displacement artifacts. Whereas one scheme is optimized to minimize the duration of the encoding gradients (herein called FAST), the other aims to specifically minimize displacement artifacts by synchronizing all three spatial-encoding time points (called ECHO). WSS estimates were calculated and compared to unbiased WSS values obtained by a 5-hour single-point imaging acquisition. In addition, MRI simulations based on computational fluid dynamics data were carried out to investigate the impact of gradient timings corresponding to different spatial resolutions. 4D flow displacement artifacts were found to have an impact on the quantified WSS peak values, spatial location, and overall WSS pattern. FAST leads to the underestimation of local WSS values in the phantom arch by up to 90%. Moreover, the corresponding WSS estimates depend on the image orientation. This effect was avoided using ECHO, which, however, results in biased WSS values within the stenosis, yielding an underestimation of peak WSS by up to 17%. Computational fluid dynamics-based simulation results show that the bias in WSS due to displacement artifacts increases with increasing spatial resolution, thus counteracting the resolution benefit for WSS due to reduced partial volume effects and segmentation errors. 4D flow displacement artifacts can significantly impact the WSS estimates and depend on the timing scheme as well as potentially the image orientation. Whereas FAST might allow correct WSS estimation for lower resolutions, ECHO is recommended especially when spatial resolutions of 1mm and smaller are used. Users need to be aware of this nonnegligible effect, particularly when conducting inter-site studies or studies between vendors. The timing scheme should thus be explicitly mentioned in publications.

Effect of Reynolds number on turbulent channel flow over a superhydrophobic surface

The slip boundary and the near-wall statistics of a fully developed turbulent channel flow over a superhydrophobic surface (SHS) was investigated in a low Reynolds number (Re) range. The Re was varied from 6200 to 9400, based on the bulk velocity and the full-channel height. The root-mean-square of the surface roughness, normalized by the inner flow scaling, varied from 0.26 to 0.35 with increasing Re. Time-resolved, two-dimensional particle tracking velocimetry (PTV) was used to obtain the mean velocity profile in the linear viscous sublayer. Furthermore, time-resolved three-dimensional PTV was applied to obtain the Reynolds stresses. The estimated wall shear stress showed that the drag reduction of the SHS increased slightly from 37% to 42% when Re increased. With increasing Re, the slip velocity increased linearly from 0.25 m/s to 0.34 m/s, and the slip length reduced from 97.5 μm to 69.6 µm. When normalized using inner scaling, slip velocity and length remained constant with increasing Re. The mean velocity of the SHS demonstrated a log-law with the universal von Kármán constant but shifted upward by an amount equal to the normalized slip velocity. The SHS increased the dimensional Reynolds stresses in the near-wall region and attenuated them farther away from the wall. With increasing Re, the differences between the dimensional Reynolds stresses of the smooth surface and the SHS increased. However, when Reynolds stresses were normalized using friction velocity, the Reynolds stresses of the SHS overlapped for all the investigated Re and were larger than the normalized Reynolds stresses of the smooth surface.

ESTIMATION OF WALL SHEAR STRESS OF COMPLIANT THORACIC AORTA WITH ANEURYSM

In this paper, a numerical estimation of wall shear stress (WSS) in a compliant Thoracic Aorta (TA) with aneurysm is modeled and the hemodynamic pattern is studied using Computational Fluid Dynamics (CFD). Thoracic Aortic Aneurysm (TAA) is an excessively localized enlargement of TA caused by weakness in the arterial wall and it can rupture the inner wall intima and continue on to the outer wall adventitia. WSS is a tangential force exerted by blood flow on the vessel wall, and its estimation is clinically very important because any change in WSS is considered as a vital cue in the onset of aneurysm. In this work, a three-dimensional (3D) model of a TAA reconstructed from computed tomography (CT) images comprising of 600 slices with 1-mm resolution from neck to hip is considered and patient-specific simulations have been carried out in compliant TA under rest and exercise conditions. The findings show that the change in wall geometry was marginal due to variation in pressure forces inside and is not the primary source for expansion of an aneurysm. It was inferred that expansion was rather due to thinning of the wall, owing to damage caused to the inner lining of the tissues, at regions of high WSS. It was found that the geometry extraction is important as any change in length causes a corresponding variation in mass flow through it. Although mass conservation is maintained irrespective of the length, it does affect the rate of flow due to shifting in the pressure boundary conditions with the length as it varies the pressure inside the system. Modeling of the geometry is very important as the change in mass flow will affect the outlet velocity and strength of vortices. Surprisingly, the split-up of flow is consistent but the geometric change in the model has no effect on WSS values and flow pattern. The results of this study provide important information such as blood flow pattern and pressure drops in the compliant TA on WSS estimations with TAA diseases.

Analysis of the wall shear stress in a generic aneurysm under pulsating and transitional flow conditions

In this study, the flow through a generic abdominal aneurysm under realistic pulsating flow conditions is examined with magnetic resonance velocimetry (MRV), laser Doppler velocimetry (LDV) and computational fluid dynamics (CFD). The influence of flow phenomena on the wall shear stress (WSS) is examined. It is seen that a strong vortex ring develops during systole at the proximal end of the aneurysm and subsequently travels downstream and decays. The vortex formation plays a major role in the temporal and spatial distribution of the WSS, which is analyzed in detail. A peak of the WSS is observed for a very limited time and in a very localized region where the vortex ring initially develops. The intrinsic temporal averaging during the acquisition of the MRV data is found to significantly decrease this peak. CFD and LDV results, which are averaged in the same manner, show a similar behavior. This indicates that besides the spatial resolution, the temporal resolution is a crucial factor, which needs to be considered especially in flows where vortex rings are observed. Results from LDV and CFD show excellent agreement for the velocity field obtained by MRV. While the flow is found to be laminar in the undilated diameter, results show laminar–turbulent transitional behavior for specific phases of the cycle within the aneurysm bulk. Although MRV is not capable of measuring instantaneous velocity fluctuations, we show that the periodic increase in turbulence intensity can be observed from image artifacts in the MRV data. These artifacts increase the velocity uncertainty, which correlates well with the velocity fluctuations measured with LDV. Although the flow encounters laminar and transitional conditions as well as multiple vortices and stagnation and reattachment points, the improved instability-sensitive Reynolds stress model, which is used for the numerical simulations of this work, shows very good agreement with the measurements. Significant effort has been expended by numerous research groups in recent years in improving the estimation of WSS from MRV data. However, an assessment of these various post-processing methods is only possible if the true values of the WSS are known. The present study is therefore aimed at providing such ground truth WSS values as well as the corresponding MRV data, allowing also other research groups to validate their WSS estimation methods using the experimental data set presented in this work.Graphic