Estimation Of Wall Shear Stress Research Articles

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

Highly accelerated 4D flow cardiovascular magnetic resonance using a pseudo-spiral Cartesian acquisition and compressed sensing reconstruction for carotid flow and wall shear stress

Background4D flow cardiovascular magnetic resonance (CMR) enables visualization of complex blood flow and quantification of biomarkers for vessel wall disease, such as wall shear stress (WSS). Because of the inherently long acquisition times, many efforts have been made to accelerate 4D flow acquisitions, however, no detailed analysis has been made on the effect of Cartesian compressed sensing accelerated 4D flow CMR at different undersampling rates on quantitative flow parameters and WSS.MethodsWe implemented a retrospectively triggered 4D flow CMR acquisition with pseudo-spiral Cartesian k-space filling, which results in incoherent undersampling of k-t space. Additionally, this strategy leads to small jumps in k-space thereby minimizing eddy current related artifacts. The pseudo-spirals were rotated in a tiny golden-angle fashion, which provides optimal incoherence and a variable density sampling pattern with a fully sampled center. We evaluated this 4D flow protocol in a carotid flow phantom with accelerations of R = 2–20, as well as in carotids of 7 healthy subjects (27 ± 2 years, 4 male) for R = 10–30. Fully sampled 2D flow CMR served as a flow reference. Arteries were manually segmented and registered to enable voxel-wise comparisons of both velocity and WSS using a Bland-Altman analysis.ResultsMagnitude images, velocity images, and pathline reconstructions from phantom and in vivo scans were similar for all accelerations. For the phantom data, mean differences at peak systole for the entire vessel volume in comparison to R = 2 ranged from − 2.3 to − 5.3% (WSS) and − 2.4 to − 2.2% (velocity) for acceleration factors R = 4–20. For the in vivo data, mean differences for the entire vessel volume at peak systole in comparison to R = 10 were − 9.9, − 13.4, and − 16.9% (WSS) and − 8.4, − 10.8, and − 14.0% (velocity), for R = 20, 25, and 30, respectively. Compared to single slice 2D flow CMR acquisitions, peak systolic flow rates of the phantom showed no differences, whereas peak systolic flow rates in the carotid artery in vivo became increasingly underestimated with increasing acceleration.ConclusionAcquisition of 4D flow CMR of the carotid arteries can be highly accelerated by pseudo-spiral k-space sampling and compressed sensing reconstruction, with consistent data quality facilitating velocity pathline reconstructions, as well as quantitative flow rate and WSS estimations. At an acceleration factor of R = 20 the underestimation of peak velocity and peak WSS was acceptable (< 10%) in comparison to an R = 10 accelerated 4D flow CMR reference scan. Peak flow rates were underestimated in comparison with 2D flow CMR and decreased systematically with higher acceleration factors.

4D Flow MRI in Patients with Asymptomatic Abdominal Aortic Aneurysms: Reproducibility and Clinical Analysis

Introduction: Hemodynamics play an as of yet incompletely understood role in the progression (i.e. growth and rupture) of abdominal aortic aneurysms (AAAs), and are therefore relevant to study. Unfortunately, there are few methods to measure in vivo hemodynamics. One method is 4D flow magnetic resonance imaging (MRI), where in vivo blood flow is visualised for the estimation of wall shear stress (WSS). If robust, 4D flow MRI can be a valuable tool in the study of AAA hemodynamics. Therefore, this pilot study evaluated reproducibility of 4D flow MRI and performed a clinical analysis. Methods: Adult patients with an asymptomatic AAA of at least 30 millimetre in diameter were included in this study. 4D flow acquisitions were performed on a 3 Tesla MRI scanner (Philips, Best, Netherlands) in a sagittal oblique volume which ideally covered the abdominal aorta from the celiac artery to both common iliac arteries. Pulse sequence parameters were: spatial resolution = 2.5×2.5×2.5 mm; field of view = 315×275×77.5 mm; temporal resolution = 24 heart phases; velocity encoding = 0.52 metre per second (m/s) in all three velocity encoding directions. Participants were scanned twice with an interval of 1 week. Mimics (Materialise, Leuven, Belgium) was used to segment the aortic lumen between the celiac artery and the aortic bifurcation for the reproducibility analysis, while the aortic lumen inside the AAA (AAA lumen) was segmented for the clinical analysis. In-house MATLAB software was used to measure velocity and to estimate WSS in Pascal (Pa). Reproducibility was tested on a voxel-by-voxel basis by the calculating mean difference and limits of agreement in a Bland-Altman analysis, and with orthogonal regression analysis to calculate the slope, intercept and Pearson's r of the agreement between the two scans. The clinical analysis summarised mean and maximal velocity/WSS, and estimated Pearson's r between maximal AAA lumen diameter and mean velocity/WSS. A P value < .05 was considered significant. Results: Thirteen male participants with a mean maximal AAA diameter of 48 ± 10.4 millimetre (mm) and a mean maximal AAA lumen diameter of 35.92 ± 8 mm were included. Figure 1 shows velocity (A) and WSS (B) for six participants. As shown in table 1, Bland-Altman analysis revealed small differences in velocity and WSS (respectively 0.0004 m/s and 0.0124 Pa), while orthogonal regression showed moderate agreement (slope: 0.99077/0.9885, r = 0.8338/0.7131 for respectively velocity/WSS). Clinical analysis demonstrated a negative correlation between maximal AAA lumen diameter and WSS (r = -0.551, P = .051), but a positive correlation with velocity (r = 0.411, P = .163). Conclusion: 4D flow MRI is a robust method and can therefore be used to study AAA hemodynamics in larger longitudinal studies, with the aim of studying whether velocity and WSS may predict AAA rupture.Table 1Reproducibility and clinical analysisReproducibility in the entire segmentation volume (Celiac artery - aortic bifurcation)Clinical analysis in AAA lumenBland-Altmanorthogonal regression analysismean differencelimits of agreementslopeinterceptPearson´s raveraged mean over 13 participantsaveraged maximal over 13 participantsPearson´s rP valuevelocity (in metre per second)0.0004 ± 0.02890.1230 ± 0.03470.99077 ± 0.18060.0042 ± 0.02560.8338 ± 0.06430.1696 ± 0.03690.3191 ± 0.14010.411.163wall shear stress (in Pascal)0.0124 ± 0.05950.2621 ± 0.1210.9885 ± 0.21050.0487 ± 0.20070.7131 ± 0.16030.2386 ± 0.07900.4733 ± 0.1053-0.551.051 Open table in a new tab Disclosure: Nothing to disclose

A new approach for estimation of the skin friction in turbulent boundary layer under the adverse pressure gradient conditions

Clauser-chart is commonly regarded as the only indirect method capable for estimation of the local mean skin friction in a turbulent boundary layer based on velocity profile in the overlapping layer, where the logarithmic relation is observed. This approach suffers, however, from the following limitation: it is applicable only for zero and weak pressure gradient flows. However, as is known, in a number of practical configurations the flow has a non-canonical character and is affected, in particular, by the adverse pressure gradient – here airfoils, diffusers and turbines may serve as examples. Hence, with this paper we would like to present a new method which can yield an accurate estimation of wall shear-stress under the strong pressure gradient conditions. In this approach the skin friction can be directly estimated based on the location of intersection point between the inner-scaled streamwise velocity profile and the newly found logarithmic line in the location which covers with the point of the local maximum of large scale motion activity in the outer region of the turbulent boundary layer. It was verified that the proposed method allows for estimation of the skin friction velocity with uncertainty lower than 2.5% for the Clauser–Rota pressure parameter β up to 28 and for 1800 < Reτ < 3900 using data from available literature.

Comparison of wall shear stress estimates obtained by laser Doppler velocimetry, magnetic resonance imaging and numerical simulations

The wall shear stress (WSS) acting on human vessel walls may play an important role in the emergence of cardiovascular diseases such as aneurysms or arteriosclerosis and is of great interest in the medical context. Magnetic resonance velocimetry (MRV) is a possible method to measure this quantity; however, the most appropriate procedure for the measurement and the achievable accuracy are open and controversial topics. In this study, we examine the accuracy of WSS estimates obtained from in vitro MRV measurements by comparing results with those obtained using laser Doppler velocimetry, with numerical simulations and for some cases with analytic solutions, all for flow conditions typical of the human aorta. The comparisons indicate that under certain conditions, WSS measurements from MRV are feasible and reliable. This work forms the basis for a systematic assessment of WSS estimators using newly developed post-processing algorithms and is considered a first step to improving the in vivo measurements of wall shear stress.

MR-based wall shear stress measurements in fully developed turbulent flow using the Clauser plot method

In arterial blood flow wall shear stress (WSS) quantifies the frictional force that flowing blood exerts on a vessel wall. WSS can be directly estimated from phase-contrast (PC) MR velocity measurements and has been suggested as a biomarker in cardio-vascular diseases. We present and investigate the application of the Clauser plot method for estimating WSS in fully developed turbulent stationary flow using PC velocity measurements. The Clauser plot method estimates WSS from the logarithmic region of boundary layer in fully developed turbulent stationary flow. The Clauser plot method was evaluated using 2D PC-MR phantom measurements at 3 T for different in-plane resolutions at various Reynolds numbers. WSS values derived from the Clauser plot were compared to results from Laser Doppler Velocimetry (LDV) measurements and theoretical results calculated using the friction factor formula for smooth pipe flow. For all Reynolds numbers, WSS values derived from the Clauser plot were in good agreement with results from LDV measurements and values using the friction factor formula (relative deviations ∼5%). Furthermore, Clauser plot derived results were almost independent of spatial resolution, in contrast to WSS results obtained with our in-house software tool for MR-based WSS quantification showing relative deviations of more than 100%. In fully developed turbulent flow, the Clauser plot method provides highly consistent WSS independent of the underlying spatial resolution. Therefore, it renders a valuable approach for MR-based WSS estimates in controllable flow settings. Although its direct in vivo applicability is severely limited because of the different flow character, it may serve as helpful approach for validation of MR-based WSS quantification algorithms prior to their clinical application.

Elevated diastolic wall shear stress in regurgitant semilunar valvular lesions.

Alterations in wall shear stress (WSS) assessed using 4D flow MRI have been shown to play a role in various vascular pathologies, such as bicuspid aortic valve aortopathy. Most studies have focused on systolic WSS, whereas altered diastolic hemodynamics in regurgitant semilunar valvular lesions have not so far been well characterized. To investigate diastolic WSS in aortic and pulmonary regurgitation. Retrospective data analysis. Thirty tetralogy of Fallot patients, 19 bicuspid aortic valve patients, 11 healthy volunteers. 5 T, 3D time-resolved phase-contrast MRI with 3D velocity encoding. Estimation of WSS and its axial and circumferential vector components along cardiac cycle timeframes in the proximal main pulmonary artery in pulmonary regurgitation (PR) and in the proximal ascending aorta in aortic regurgitation (AR) as well as in healthy volunteers. Wilcoxon matched pairs test was used for intra-group comparisons and Mann-Whitney test for intergroup comparisons. Correlations were assessed using Spearman correlation. WSS along the entire cardiac cycle was higher in PR and AR in comparison with controls (mean WSS 0.381 ± 0.070 vs. 0.220 ± 0.018, P < 0.0001; 0.361 ± 0.099 vs. 0.212 ± 0.030, P < 0.0001; respectively). Peak diastolic WSS was significantly higher than the mean WSS in AR and PR (P < 0.0001-0.005). The severity of PR correlated with the peak diastolic axial WSS (Spearman's r s = 0.454, P = 0.018), whereas the severity of AR correlated with both peak systolic and diastolic tangential WSS (Spearman's r s = 0.458, P = 0.049; r s = 0.539, P = 0.017, respectively). Elevated diastolic WSS is a component of the altered flow hemodynamics in AR and PR. This may give more insight into the pathophysiologic role of WSS in vascular remodeling in AR and PR. 4 Technical Efficacy Stage: 1 J. Magn. Reson. Imaging 2019;50:763-770.

Novel and facile criterion to assess the accuracy of WSS estimation by 4D flow MRI.

Four-dimensional flow magnetic resonance imaging (4D flow MRI) is a versatile tool to obtain hemodynamic information and anatomic information simultaneously. The wall shear stress (WSS), a force exerted on a vessel wall in parallel, is one of the hemodynamic parameters available with 4D flow MRI and is thought to play an important role in clinical applications such as assessing the development of atherosclerosis. Nevertheless, the accuracy of WSS obtained with 4D flow MRI is rarely evaluated or reported in literature, especially in the in vivo studies. We propose a novel and facile criterion called Reynolds resolution to assess the accuracy of WSS estimation in 4D flow MRI studies. Reynolds resolution consists of a spatial resolution, encoding velocity, kinematic viscosity of a working fluid, and signal-to-noise ratio, which are readily accessible information in 4D flow MRI measurements. We explored the relationship between Reynolds resolution and the WSS error. To include diverse and extensive cases, we measured three circular tubing flows with a diameter of 40, 8, and 2 mm. The 40 mm tubing flow was measured by 3Tesla (T) human MR scanner with a knee coil and spatial resolution of 0.5 mm. The 8 and 2 mm tubing flows were both measured by 4.7 T MR scanner, but the scans were performed with a conventional birdcage coil (8 mm tubing) and a custom-made solenoid coil (2 mm tubing), respectively. The spatial resolution was varied from 0.2, 0.4 or 0.8 mm for the 8 mm tubing flow, but was fixed at 0.090 mm for 2 mm tubing flow. In addition, the near-wall velocity gradient, required to be determined prior to the WSS, was calculated using two methods; these included assuming a linear velocity profile or quadratic velocity profile near wall. The accuracy of WSS obtained using each method and tubing flow was evaluated against the theoretical WSS value. As a result, we found that Reynolds resolution is in logarithmic relation to the WSS error.

Characterization and estimation of turbulence-related wall shear stress in patient-specific pulsatile blood flow

Disturbed, turbulent-like blood flow promotes chaotic wall shear stress (WSS) environments, impairing essential endothelial functions and increasing the susceptibility and progression of vascular diseases. These flow characteristics are today frequently detected at various anatomical, lesion and intervention-related sites, while their role as a pathological determinant is less understood. To present-day, numerous WSS-based descriptors have been proposed to characterize the spatiotemporal nature of the WSS disturbances, however, without differentiation between physiological laminar oscillations and turbulence-related WSS (tWSS) fluctuations. Also, much attention has been focused on magnetic resonance (MR) WSS estimations, so far with limited success; promoting the need of a near-wall surrogate marker. In this study, a new approach is explored to characterize the tWSS, by taking advantage of the tensor characteristics of the fluctuating WSS correlations, providing both a magnitude and an anisotropy measure of the disturbances. These parameters were studied in two patient-specific coarctation models (sever and mild), using large eddy simulations, and correlated against near-wall reciprocal Reynolds stress parameters. Collectively, results showed distinct regions of differing tWSS characteristics, features which were sensitive to changes in flow conditions. Generally, the post-stenotic tWSS was governed by near axisymmetric fluctuations, findings that where not consistent with conventional WSS disturbance predictors. At the 2–3 mm wall-offset range, a strong linear correlation was found between tWSS magnitude and near-wall turbulence kinetic energy (TKE), in contrast to the anisotropy indices, suggesting that MR-measured TKE can be used to assess elevated tWSS regions while tWSS anisotropy estimates request well-resolved simulation methods.

Evidence for non-Newtonian behavior of intracranial blood flow from Doppler ultrasonography measurements.

Computational fluid dynamics (CFD) studies of intracranial hemodynamics often use Newtonian viscosity model to close the shear rate term in the Navier-Stokes equation. This is based on a commonly accepted hypothesis which state that non-Newtonian effects can be neglected in intracranial blood flow. This study aims to examine the validity of such hypothesis to guide future CFD studies of intracranial hemodynamics. Doppler ultrasonography (DUS) measurements of systolic and diastolic vessel diameter and blood velocity were conducted on 16 subjects (mean age 50.6). The measurements were conducted on the internal carotid (ICA), middle cerebral (MCA), and anterior communicating (AComA) arteries. Systolic and diastolic wall shear stress (WSS) values were calculated via the Hagen-Poiseuille exact solution using Newtonian and three different non-Newtonian models: namely Carreau, power-law and Herschel-Bulkley models. The Weissenberg-Rabinowitsch correction for blood shear-thinning viscosity was applied to the non-Newtonian models. The error percentage between the two sets of models was calculated and discussed. The Newtonian hypothesis was tested statistically and discussed using paired t tests. Significant differences (P < 0.0001) were found between the Newtonian and non-Newtonian WSS in ICA. In MCA and AComA, similar differences were found except in the systole and diastole for the Herschel-Bulkley and power-law models (P = 0.0669, P = 0.7298), respectively. The error between the Newtonian and non-Newtonian models ranged from -27 to 30% (0.2 to 2.2Pa). These values could affect the physical interpretation of IA CFD studies. Evidence suggests that the Newtonian assumption may be inappropriate to investigate intracranial hemodynamics. Graphical abstract The WSS estimation error resulting from using the Newtonian assumption compared to three non-Newtonian models for ICA, MCA, and AComA in systole and diastole conditions, based on TCCD measurements of 16 subjects. The error due to the Newtonian assumption ranged from 0.2 to 2.2Pa (- 27 to 30%). These values could affect the physical interpretation of IA CFD studies.

Estimating hemodynamic shear stress in murine peripheral collateral arteries by two-photon line scanning.

Changes in wall shear stress of blood vessels are assumed to be an important component of many physiological and pathophysiological processes. However, due to technical limitations experimental in vivo data are rarely available. Here, we investigated two-photon excitation fluorescence microscopy as an option to measure vessel diameter as well as blood flow velocities in a murine hindlimb model of arteriogenesis (collateral artery growth). Using line scanning at high frequencies, we measured the movement of blood cells along the vessel axis. We found that peak systolic blood flow velocity averaged 9mm/s and vessel diameter 42µm in resting collaterals. Induction of arteriogenesis by femoral artery ligation resulted in a significant increase in centerline peak systolic velocity after 1day with an average of 51mm/s, whereas the averaged luminal diameter of collaterals (52µm) changed much less. Thereof calculations revealed a significant fourfold increase in hemodynamic wall shear rate. Our results indicate that two-photon line scanning is a suitable tool to estimate wall shear stress e.g., in experimental animal models, such as of arteriogenesis, which may not only help to understand the relevance of mechanical forces in vivo, but also to adjust wall shear stress in ex vivo investigations on isolated vessels as well as cell culture experiments.

Measurement of Wall Shear Stress Exerted by Flowing Blood in the Human Carotid Artery: Ultrasound Doppler Velocimetry and Echo Particle Image Velocimetry

Vascular endothelial cells lining the arteries are sensitive to wall shear stress (WSS) exerted by flowing blood. An important component of the pathophysiology of vascular diseases, WSS is commonly estimated by centerline ultrasound Doppler velocimetry (UDV). However, the accuracy of this method is uncertain. We have previously validated the use of a novel, ultrasound-based, particle image velocimetry technique (echo PIV) to compute 2-D velocity vector fields, which can easily be converted into WSS data. We compared WSS data derived from UDV and echo PIV in the common carotid artery of 27 healthy participants. Compared with echo PIV, time-averaged WSS was lower using UDV (28 ± 35%). Echo PIV revealed that this was due to considerable spatiotemporal variation in the flow velocity profile, contrary to the assumption that flow is steady and the velocity profile is parabolic throughout the cardiac cycle. The largest WSS underestimation by UDV was found during peak systole (118 ± 16%) and the smallest during mid-diastole (4.3± 46%). The UDV method underestimated WSS for the accelerating and decelerating systolic measurements (68 ± 30% and 24 ± 51%), whereas WSS was overestimated for end-diastolic measurements (−44 ± 55%). Our data indicate that UDV estimates of WSS provided limited and largely inaccurate information about WSS and that the complex spatiotemporal flow patterns do not fit well with traditional assumptions about blood flow in arteries. Echo PIV-derived WSS provides detailed information about this important but poorly understood stimulus that influences vascular endothelial pathophysiology.

Retrospective Study of Hemodynamic Changes Before and After Carotid Stenosis Formation by Vessel Surface Repairing

Prospective observation of hemodynamic changes before and after the formation of atherosclerotic stenosis in the carotid artery is difficult. Thus, a vessel surface repairing method was used for retrospective hemodynamic study before and after atherosclerotic stenosis formation in carotid artery. The three-dimensional geometry of sixteen sinus atherosclerotic stenosis carotid arteries were repaired and restored as normal arteries. Computational fluid dynamics analysis was performed to estimate wall shear stress (WSS), velocity and vortex in atherosclerosis-free areas and sinus in stenosis-repaired carotid artery. The analysis was also performed in the stenotic segment and upstream and downstream of stenosis in stenotic carotid artery. Compared to the atherosclerosis-free areas in stenosis-repaired carotid artery, sinus presented significantly lower WSS (P < 0.05), lower velocity (P < 0.05) and apparent vortex. Compared to the sinus, the WSS in the upstream of stenosis was lower (P < 0.05), while in the downstream area was similar (P = 0.87), both upstream and downstream of stenosis demonstrated similar velocity to sinus (P = 0.76 and P = 0.36, respectively) and apparent vortex. Atherosclerosis-prone areas including normal carotid sinus and upstream and downstream of stenosis in stenotic carotid artery were subjected to lower WSS and velocity as well as apparent vortex, thereby might be associated with the formation and progress of atherosclerosis.

Wall shear stress estimation in the aorta: Impact of wall motion, spatiotemporal resolution, and phase noise.

Wall shear stress (WSS) presents an important parameter for assessing blood flow characteristics and evaluating flow-mediated lesions in the aorta. To investigate the robustness of WSS and oscillatory shear index (OSI) estimation based on 4D flow MRI against vessel wall motion, spatiotemporal resolution, and velocity encoding (VENC). Simulated and prospective. Synthetic 4D flow MRI data of the aorta, simulated using the Lattice-Boltzmann method; in vivo 4D flow MRI data of the aorta from healthy volunteers (n = 11) and patients with congenital heart defects (n = 17). 1.5T; 4D flow MRI with PEAK-GRAPPA acceleration and prospective electrocardiogram triggering. Predicated upon 3D cubic B-splines interpolation of the image velocity field, WSS was estimated in mid-systole, early-diastole, and late-diastole and OSI was derived. We assessed the impact of spatiotemporal resolution and phase noise, and compared results based on tracked-using deformable registration-and static vessel wall location. Bland-Altman analysis to assess WSS/OSI differences; Hausdorff distance (HD) to assess wall motion; and Pearson's correlation coefficient (PCC) to assess correlation of HD with WSS. Synthetic data results show systematic over-/underestimation of WSS when different spatial resolution (mean ± 1.96 SD up to -0.24 ± 0.40 N/m2 and 0.5 ± 1.38 N/m2 for 8-fold and 27-fold voxel size, respectively) and VENC-depending phase noise (mean ± 1.96 SD up to 0.31 ± 0.12 N/m2 and 0.94 ± 0.28 N/m2 for 2-fold and 4-fold VENC increase, respectively) are given. Neglecting wall motion when defining the vessel wall perturbs WSS estimates to a considerable extent (1.96 SD up to 1.21 N/m2 ) without systematic over-/underestimation (Bland-Altman mean range -0.06 to 0.05). In addition to sufficient spatial resolution and velocity to noise ratio, accurate tracking of the vessel wall is essential for reliable image-based WSS estimation and should not be neglected if wall motion is present. 2 Technical Efficacy: Stage 2 J. Magn. Reson. Imaging 2018.

Near-Wall Stress Balance in Front of a Wall-Mounted Cylinder

The stress balance in the near-wall flow in front of a cylinder mounted on a flat plate at moderate Reynolds number is investigated by applying highly resolved Large-Eddy Simulation (LES). The flow around wall-mounted bluff bodies is subject of research due to its wide relevance for engineering applications. However, the structure of the vortex system in front of such a bluff body is complex, bears strong velocity and pressure gradients in each spatial direction and has rich dynamics. Furthermore, the vortex system is located close to the investigated flat bottom wall (Dargahi, Exp. Fluids 8(1-2):1–12, 1989; Devenport and Simpson, J. Fluid Mech. 210:23–55, 1990). Thus, classical models for the treatment of the near-wall flow based on the logarithmic law of the wall or a power law cannot be expected to suffice in such kind of flow (Pope 2011). This paper assesses which contributors to the stress balance have significant influence on the balances residual and thus have to be considered by an approach to model the investigated near-wall flow. To do so, the momentum equation in streamwise direction is integrated in wall-normal direction and applied to the results gained from the LES. The evaluation of the stress balance along four selected wall-normal profiles indicates that the significance of each single term depends on where the profile is located. Outside the viscous layer, no term except the viscous stresses can be neglected in general. The amplitude of the pressure gradient as well as horizontal gradients of mean and fluctuating velocity are multiples of the estimated wall shear stress. Wall models not including a spatial approach are therefore most likely to fail in such kind of flow.

P 1 Computational fluid dynamic simulations of maternal circulation – Wall shear stress in the human placenta and its biological implications

Introduction In the human placenta the maternal blood circulates in the intervillous space (IVS). The syncytiotrophoblast (STB) is in direct contact with maternal blood. The wall shear stress (WSS) exerted by the maternal blood flow on the STB has not been evaluated. Our objective was to determine the physiological WSS exerted on the surface of the STB during the third trimester of pregnancy. Material and methods To gain insight into the shear stress levels that the STB is expected to experience in vivo, we have formulated three different computational models of varying levels of complexity that reflect different physical representations of the IVS. Computations of the flow fields in all models were performed using the CFD module of the finite element code COMSOL Multiphysics 4.4. The mean velocity of maternal blood in the IVS during the third trimester was measured in vivo with dynamic MRI (0.94±0.14 mm.s−1). To investigate if the in silico results are consistent with physiological observations, we studied the cytoadhesion of human parasitized (Plasmodium falciparum) erythrocytes to primary human STB cultures, in flow conditions with different WSS values. Results The WSS applied to the STB is highly heterogeneous in the IVS. The estimated average values are relatively low (0.5±0.2 to 2.3±1.1 dyn.cm−2). The increase of WSS from 0.15 to 5 dyn.cm−2 was associated with a significant decrease of infected erythrocyte cytoadhesion. No cytoadhesion of infected erythrocytes was observed above 5 dyn.cm−2 applied for one hour. Conclusion Our study provides for the first time a WSS estimation in the maternal placental circulation. In spite of high maternal blood flow rates, the average WSS applied at the surface of the chorionic villi is low ( Download : Download high-res image (581KB) Download : Download full-size image Download : Download high-res image (658KB) Download : Download full-size image

Validation of numerical simulation methods in aortic arch using 4D Flow MRI

Computational fluid dynamics (CFD) are the gold standard in studying blood flow dynamics. However, CFD results are dependent on the boundary conditions and the computation model. The purpose of this study was to validate CFD methods using comparison with actual measurements of the blood flow vector obtained with four-dimensional (4D) flow magnetic resonance imaging (MRI). 4D Flow MRI was performed on a healthy adult and a child with double-aortic arch. The aortic lumen was segmented to visualize the blood flow. The CFD analyses were performed for the same geometries based on three turbulent models: laminar, large eddy simulation (LES), and the renormalization group k–ε model (RNG k–ε). The flow-velocity vector components, namely the wall shear stress (WSS) and flow energy loss (EL), of the MRI and CFD results were compared. The flow rate of the MRI results was underestimated in small vessels, including the neck vessels. Spiral flow in the ascending aorta caused by the left ventricular twist was observed by MRI. Secondary flow distal to the aortic arch was well realized in both CFD and MRI. The average correlation coefficients of the velocity vector components of MRI and CFD for the child were the highest for the RNG k–ε model (0.530 in ascending aorta, 0.768 in the aortic arch, 0.584 in the descending aorta). The WSS and EL values of MRI were less than half of those of CFD, but the WSS distribution patterns were quite similar. The WSS and EL estimates were higher in RNG k–ε and LES than in the laminar model because of eddy viscosity. The CFD computation realized accurate flow distal to the aortic arch, and the WSS distribution was well simulated compared to actual measurement using 4D Flow MRI. However, the helical flow was not simulated in the ascending aorta. The accuracy was enhanced by using the turbulence model, and the RNG k–ε model showed the highest correlation with 4D Flow MRI.

Influence of hydrodynamic stress on the frictional drag of biofouling communities

The role of hydrodynamic wall shear stresses on the development of the fouling community structure and resulting frictional drag were examined using a commercially available fouling release coating. Immersed test panels were exposed to three different hydrodynamic treatments, one static and two dynamic (corresponding to an estimated wall shear stress of 7.0 and 25.5 Pa). The drag of the panels was measured in a hydrodynamic test chamber at discrete time intervals over 35 days. The fouling community composition on the static panels was significantly different from the organisms observed on the dynamic panels. Despite different fouling community composition, the drag forces measured on the panels were very similar. This suggests that the frictional drag of low form and soft fouling communities are similar and that there may be a stepwise increase in frictional drag associated with the presence of mature calcareous organisms.

Computational Fluid Dynamic Simulations of Maternal Circulation: Wall Shear Stress in the Human Placenta and Its Biological Implications.

IntroductionIn the human placenta the maternal blood circulates in the intervillous space (IVS). The syncytiotrophoblast (STB) is in direct contact with maternal blood. The wall shear stress (WSS) exerted by the maternal blood flow on the STB has not been evaluated. Our objective was to determine the physiological WSS exerted on the surface of the STB during the third trimester of pregnancy.Material and MethodsTo gain insight into the shear stress levels that the STB is expected to experience in vivo, we have formulated three different computational models of varying levels of complexity that reflect different physical representations of the IVS. Computations of the flow fields in all models were performed using the CFD module of the finite element code COMSOL Multiphysics 4.4. The mean velocity of maternal blood in the IVS during the third trimester was measured in vivo with dynamic MRI (0.94±0.14 mm.s-1). To investigate if the in silico results are consistent with physiological observations, we studied the cytoadhesion of human parasitized (Plasmodium falciparum) erythrocytes to primary human STB cultures, in flow conditions with different WSS values.ResultsThe WSS applied to the STB is highly heterogeneous in the IVS. The estimated average values are relatively low (0.5±0.2 to 2.3±1.1 dyn.cm-2). The increase of WSS from 0.15 to 5 dyn.cm-2 was associated with a significant decrease of infected erythrocyte cytoadhesion. No cytoadhesion of infected erythrocytes was observed above 5 dyn.cm-2 applied for one hour.ConclusionOur study provides for the first time a WSS estimation in the maternal placental circulation. In spite of high maternal blood flow rates, the average WSS applied at the surface of the chorionic villi is low (<5 dyn.cm-2). These results provide the basis for future physiologically-relevant in vitro studies of the biological effects of WSS on the STB.