Wall Shear Stress Quantification Research Articles

Carotid plaque vulnerability assessed by combined shear wave elastography and ultrafast doppler compared to histology: the UF-plaque study

Abstract Purpose New biomarkers are needed to assess the vulnerability of carotid plaque to guide carotid surgery decision. Ultrafast Ultrasound Imaging (UUI) provides an estimation of plaque stiffness by Shear Wave Elastography (SWE) and the quantification of wall shear stress (WSS) by ultrafast Doppler. We aimed at evaluating the plaque stiffness and WSS applied on the plaque as potential biomarkers of plaque vulnerability. Methods Patients were referred for carotid endarterectomy because of symptomatic or asymptomatic carotid stenosis. Their plaques were evaluated by UUI within 48 hours before surgery. For each plaque, WSS and SWE were obtained on a longitudinal view at the stenosis. After endarterectomy, gross analysis and histology were performed on each removed plaque. Results 46 plaques with SWE data and 29 with WSS data were analysed. Histological analysis revealed 29 vulnerable and 17 stable plaques. Analysis of the Gray Scale Median by B mode, mean and standard deviation of stiffness by SWE were not helpful in identifying vulnerable plaques. Figure 1 presents the SWE acquisition on one plaque (A) and the distribution of plaque's stiffness average over all plaques showing the 4 ranges of stiffness (B). SWE analysis revealed that the percentage of stiffness range of [3–5] m/s was significantly increased in vulnerable plaques (p=0.048) (Figure 2A). WSS alone showed no significant difference between stable and vulnerable plaques regardless of which segment of the plaque was analysed. A multiparametric score using maximal WSS at the peak of the plaque associated with SWE texture analysis parameters was created by a stepwise analysis, leading to a score with a sensitivity of 80% and a specificity of 78%. The ROC curve of this score found an AUC of 0.85 (Figure 2B). Conclusions Multiparameter scoring including plaque stiffness and flow analysis using ultrafast ultrasound imaging allows an effective identification of histologically vulnerable carotid plaques. Funding Acknowledgement Type of funding sources: Foundation. Main funding source(s): Fédération Française de cardiologieSociété Française de Cardiologie Figure 1Figure 2

Uncovering near-wall blood flow from sparse data with physics-informed neural networks

Near-wall blood flow and wall shear stress (WSS) regulate major forms of cardiovascular disease, yet they are challenging to quantify with high fidelity. Patient-specific computational and experimental measurement of WSS suffers from uncertainty, low resolution, and noise issues. Physics-informed neural networks (PINNs) provide a flexible deep learning framework to integrate mathematical equations governing blood flow with measurement data. By leveraging knowledge about the governing equations (herein, Navier–Stokes), PINN overcomes the large data requirement in deep learning. In this study, it was shown how PINN could be used to improve WSS quantification in diseased arterial flows. Specifically, blood flow problems where the inlet and outlet boundary conditions were not known were solved by assimilating very few measurement points. Uncertainty in boundary conditions is a common feature in patient-specific computational fluid dynamics models. It was shown that PINN could use sparse velocity measurements away from the wall to quantify WSS with very high accuracy even without full knowledge of the boundary conditions. Examples in idealized stenosis and aneurysm models were considered demonstrating how partial knowledge about the flow physics could be combined with partial measurements to obtain accurate near-wall blood flow data. The proposed hybrid data-driven and physics-based deep learning framework has high potential in transforming high-fidelity near-wall hemodynamics modeling in cardiovascular disease.

Carotid plaque vulnerability assessed by Shear Wave elastography and ultrafast Doppler compared to histology: The UF-plaque study

Ultrafast Ultrasound Imaging (UUI) provides an estimation of carotid plaque stiffness by shear wave elastography (SWE) and the quantification of wall shear stress (WSS) by ultrafast Doppler. We aimed to evaluate the combined criteria of plaque stiffness and WSS applied on the plaque as potential biomarkers of plaque vulnerability assessed by histology. We included patients for whom carotid endarterectomy had been decided by a multidisciplinary team. UUI was performed within 48 hours before surgery, and acquisitions were obtained on a carotid longitudinal view. After endarterectomy, gross examination and histological analysis were performed on each removed plaque. Forty-six plaques with SWE data and 29 with WSS data were analysed. Histological analysis revealed 29 vulnerable and 17 stable plaques. Gray Scale Median analysis by B mode, mean and standard deviation of stiffness by SWE did not differ between vulnerable and stable plaques. SWE analysis revealed that the percentage of stiffness range of [3–5] m/s was significantly increased in vulnerable plaques ( P = 0.048). WSS alone showed no difference between stable and vulnerable plaques regardless of the segment of the plaque which was analysed. A multiparametric score using maximal WSS at the peak of the plaque associated with SWE texture analysis parameters was calculated by stepwise regression, leading to a score with a sensitivity of 80% and a specificity of 78%. Area under the Receiver Operating Characteristics curve was 0.85. A multiparameter scoring system including plaque stiffness and flow analysis using UUI allows to effectively identify histologically vulnerable carotid plaques.

Parametric Sequential Method for MRI-Based Wall Shear Stress Quantification.

Wall shear stress (WSS) has been suggested as a potential biomarker in various cardiovascular diseases and it can be estimated from phase-contrast Magnetic Resonance Imaging (PC-MRI) velocity measurements. We present a parametric sequential method for MRI-based WSS quantification consisting of a geometry identification and a subsequent approximation of the velocity field. This work focuses on its validation, investigating well controlled high-resolution in vitro measurements of turbulent stationary flows and physiological pulsatile flows in phantoms. Initial tests for in vivo 2D PC-MRI data of the ascending aorta of three volunteers demonstrate basic applicability of the method to in vivo.

Towards quantitative evaluation of wall shear stress from 4D flow imaging

Wall shear stress (WSS) is a relevant hemodynamic indicator of the local stress applied on the endothelium surface. More specifically, its spatiotemporal distribution reveals crucial in the evolution of many pathologies such as aneurysm, stenosis, and atherosclerosis. This paper introduces a new solution, called PaLMA, to quantify the WSS from 4D Flow MRI data. It relies on a two-step local parametric model, to accurately describe the vessel wall and the velocity-vector field in the neighborhood of a given point of interest. Extensive validations have been performed on synthetic 4D Flow MRI data, including four datasets generated from patient specific computational fluid dynamics simulations on carotids. The validation tests are focused on the impact of the noise component, of the resolution level, and of the segmentation accuracy concerning the vessel position in the context of complex flow patterns. In simulated cases aimed to reproduce clinical acquisition conditions, the WSS quantification performance reached by PaLMA is significantly higher (with a gain in RMSE of 12 to 27%) than the reference one obtained using the smoothing B-spline method proposed by Potters et al. (2015) method, while the computation time is equivalent for both WSS quantification methods.

Two-Minute k-Space and Time-accelerated Aortic Four-dimensional Flow MRI: Dual-Center Study of Feasibility and Impact on Velocity and Wall Shear Stress Quantification.

To investigate the two-center feasibility of highly k-space and time (k-t)-accelerated 2-minute aortic four-dimensional (4D) flow MRI and to evaluate its performance for the quantification of velocities and wall shear stress (WSS). This cross-sectional study prospectively included 68 participants (center 1, 11 healthy volunteers [mean age ± standard deviation, 61 years ± 15] and 16 patients with aortic disease [mean age, 60 years ± 10]; center 2, 14 healthy volunteers [mean age, 38 years ± 13] and 27 patients with aortic or cardiac disease [mean age, 78 years ± 18]). Each participant underwent highly accelerated 4D flow MRI (k-t acceleration, acceleration factor of 5) of the thoracic aorta. For comparison, conventional 4D flow MRI (acceleration factor of 2) was acquired in the participants at center 1 (n = 27). Regional aortic peak systolic velocities and three-dimensional WSS were quantified. k-t-accelerated scan times (center 1, 2:03 minutes ± 0:29; center 2, 2:06 minutes ± 0:20) were significantly reduced compared with conventional 4D flow MRI (center 1, 12:38 minutes ± 2:25; P < .0001). Overall good agreement was found between the two techniques (absolute differences ≤15%), but proximal aortic WSS was significantly underestimated in patients by using k-t-accelerated 4D flow when compared with conventional 4D flow (P ≤ .03). k-t-accelerated 4D flow MRI was reproducible (intra- and interobserver intraclass correlation coefficient ≥0.98) and identified significantly increased peak velocities and WSS in patients with stenotic (P ≤ .003) or bicuspid (P ≤ .04) aortic valves compared with healthy volunteers. In addition, k-t-accelerated 4D flow MRI-derived velocities and WSS were inversely related to age (r ≥-0.53; P ≤ .03) over all healthy volunteers. k-t-accelerated aortic 4D flow MRI providing 2-minute scan times was feasible and reproducible at two centers. Although consistent healthy aging- and disease-related changes in aortic hemodynamics were observed, care should be taken when considering WSS, which can be underestimated in patients.© RSNA, 2019See also the commentary by François in this issue.

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.

Volumetric segmentation-free method for rapid visualization of vascular wall shear stress using 4D flow MRI.

To develop a rapid segmentation-free method to visualize and compute wall shear stress (WSS) throughout the aorta using 4D Flow MRI data. WSS is the drag force-per-area the vessel endothelium exerts on luminal blood; abnormal levels of WSS are associated with cardiovascular pathologies. Previous methods for computing WSS are bottlenecked by labor-intensive manual segmentation of vessel boundaries. A rapid automated segmentation-free method for computing WSS is presented. Shear stress is the dot-product of the viscous stress tensor and the inward normal vector. The inward normal vectors are approximated as the gradient of fluid speed at every voxel. Subsequently, a 4D map of shear stress is computed as the partial derivatives of velocity with respect to the inward normal vectors. We highlight the shear stress near the wall by fusing visualization with edge-emphasized anatomical data. As a proof-of-concept, four cases with aortic pathologies are presented. Visualization allows for rapid localization of pathologic WSS. Subsequent analysis of these pathological regions enables quantification of WSS. Average WSS during peak systole measures approximately 50-60 cPa in nonpathological regions of the aorta and is elevated in regions of stenosis, coarctation, and dissection. WSS is reduced in regions of aneurysm. A volumetric technique for calculation and visualization of WSS from 4D Flow MRI data is presented. Traditional labor-intensive methods for WSS rely on explicit manual segmentation of vessel boundaries before visualization. This automated volumetric strategy for visualization and quantification of WSS may facilitate its clinical translation.

Uncertainty quantification of wall shear stress in intracranial aneurysms using a data-driven statistical model of systemic blood flow variability

Adverse wall shear stress (WSS) patterns are known to play a key role in the localisation, formation, and progression of intracranial aneurysms (IAs). Complex region-specific and time-varying aneurysmal WSS patterns depend both on vascular morphology as well as on variable systemic flow conditions. Computational fluid dynamics (CFD) has been proposed for characterising WSS patterns in IAs; however, CFD simulations often rely on deterministic boundary conditions that are not representative of the actual variations in blood flow. We develop a data-driven statistical model of internal carotid artery (ICA) flow, which is used to generate a virtual population of waveforms used as inlet boundary conditions in CFD simulations. This allows the statistics of the resulting aneurysmal WSS distributions to be computed. It is observed that ICA waveform variations have limited influence on the time-averaged WSS (TAWSS) on the IA surface. In contrast, in regions where the flow is locally highly multidirectional, WSS directionality and harmonic content are strongly affected by the ICA flow waveform. As a consequence, we argue that the effect of blood flow variability should be explicitly considered in CFD-based IA rupture assessment to prevent confounding the conclusions.

3D Quantification of Wall Shear Stress and Oscillatory Shear Index Using a Finite-Element Method in 3D CINE PC-MRI Data of the Thoracic Aorta.

Several 2D methods have been proposed to estimate WSS and OSI from PC-MRI, neglecting the longitudinal velocity gradients that typically arise in cardiovascular flow, particularly on vessel geometries whose cross section and centerline orientation strongly vary in the axial direction. Thus, the contribution of longitudinal velocity gradients remains understudied. In this work, we propose a 3D finite-element method for the quantification of WSS and OSI from 3D-CINE PC-MRI that accounts for both in-plane and longitudinal velocity gradients. We demonstrate the convergence and robustness of the method on cylindrical geometries using a synthetic phantom based on the Poiseuille flow equation. We also show that, in the presence of noise, the method is both stable and accurate. Using computational fluid dynamics simulations, we show that the proposed 3D method results in more accurate WSS estimates than those obtained from a 2D analysis not considering out-of-plane velocity gradients. Further, we conclude that for irregular geometries the accurate prediction of WSS requires the consideration of longitudinal gradients in the velocity field. Additionally, we compute 3D maps of WSS and OSI for 3D-CINE PC-MRI data sets from an aortic phantom and sixteen healthy volunteers and two patients. The OSI values show a greater dispersion than WSS, which is strongly dependent on the PC-MRI resolution. We envision that the proposed 3D method will improve the estimation of WSS and OSI from 3D-CINE PC-MRI images, allowing for more accurate estimates in vessels with pathologies that induce high longitudinal velocity gradients, such as coarctations and aneurisms.

Characterizations and Correlations of Wall Shear Stress in Aneurysmal Flow.

Wall shear stress (WSS) is one of the most studied hemodynamic parameters, used in correlating blood flow to various diseases. The pulsatile nature of blood flow, along with the complex geometries of diseased arteries, produces complicated temporal and spatial WSS patterns. Moreover, WSS is a vector, which further complicates its quantification and interpretation. The goal of this study is to investigate WSS magnitude, angle, and vector changes in space and time in complex blood flow. Abdominal aortic aneurysm (AAA) was chosen as a setting to explore WSS quantification. Patient-specific computational fluid dynamics (CFD) simulations were performed in six AAAs. New WSS parameters are introduced, and the pointwise correlation among these, and more traditional WSS parameters, was explored. WSS magnitude had positive correlation with spatial/temporal gradients of WSS magnitude. This motivated the definition of relative WSS gradients. WSS vectorial gradients were highly correlated with magnitude gradients. A mix WSS spatial gradient and a mix WSS temporal gradient are proposed to equally account for variations in the WSS angle and magnitude in single measures. The important role that WSS plays in regulating near wall transport, and the high correlation among some of the WSS parameters motivates further attention in revisiting the traditional approaches used in WSS characterizations.

Measuring Wall Shear Stress Using Velocity-Encoded MRI

This study reviews the application of velocity-encoded magnetic resonance imaging (MRI) for the calculation of wall shear stress (WSS). The basics of velocity-encoded MRI and WSS are reviewed and calculation methods for estimation of the WSS from 2D or 3D (cine) velocity-encoded MRI data are presented. In recent years, there has been a trend towards 3D WSS quantification methods. Current clinical applications of WSS are discussed, including an overview of estimated WSS magnitudes in different patient groups at multiple anatomical locations (aorta, carotid arteries, and intracranial aneurysms). A large variation was found between different WSS calculation methods. The future of MRI-based WSS calculations depends on its prognostic and diagnostic value, both of which need to be further explored in clinical studies. In this context, both further improvement of the quality of velocity-encoded MRI data and scan time reduction are pivotal.

Volumetric arterial wall shear stress calculation based on cine phase contrast MRI

To assess the accuracy and precision of a volumetric wall shear stress (WSS) calculation method applied to cine phase contrast magnetic resonance imaging (PC-MRI) data. Volumetric WSS vectors were calculated in software phantoms. WSS algorithm parameters were optimized and the influence of spatial resolution and segmentation was evaluated. Subsequently, 2D cine PC-MRI data in the carotid and the aorta at varying spatial resolutions were obtained (n = 2) and compared with the simulations. Finally, volumetric WSS was calculated in 3D cine PC-MRI data of the carotid bifurcation and the aorta (n = 6). We found that at least 8 voxels across the diameter are required to obtain a WSS accuracy of 5% and a precision of 20% in software phantoms. Systematic WSS quantification errors up to 40% were found in the case of segmentation errors. The in vivo measurements using 2D cine PC-MRI exhibited WSS increase at increasing spatial resolutions, similar to the results in software phantoms. Volumetric WSS vectors were successfully calculated in three healthy carotid bifurcations and aortas. The effects of resolution and segmentation on the accuracy and precision of the WSS algorithm were quantified. We were able to calculate volumetric WSS in the carotid bifurcation and the aorta.

3D quantification of wall shear stress using finite-element interpolations from 4D flow MR data in the Thoracic Aorta

Background Actual methods to quantify wall shear stress (WSS) are performed on reformatted 2D planes from 4D flow data sets. This approach has the inherit limitation that only a few planes are analyzed on specific locations of the aorta, even though the full 3D velocity field is usually available. Another problem with this approach is that the process of locating 2D planes manually is dependent on the user and may lead to results that have low reproducibility. These problems can be circumvented by calculating the WSS in 3D directly. A few methods based on computational fluid dynamics (CFD) have been proposed to obtain 3D WSS. These methods use realistic vascular geometries extracted from MR data, however, assumptions are made on the properties of the walls and on flow velocity profiles that may not be fully realistic. In this work, we propose a novel methodology based on finite-element (FE) interpolations to compute the 3D WSS of the whole thoracic aorta from 4D flow MRI data.

4D MRI-based wall shear stress quantification in the carotid bifurcation: a validation study in volunteers using computational fluid dynamics

Background Remodeling of the vessel wall is associated with wall shear stress (WSS) magnitude (Malek, 1999). It has been suggested that local low or high WSS may respectively promote or prevent atherosclerotic lesions in the carotid vessel wall. The current procedure for WSS quantification is computational fluid dynamics (CFD), which is time-consuming and not always patient-specific. In the past years, methods that derive WSS directly from MRI 4D flow measurements have been developed. These allow patient-specific WSS quantifications while using less computational power and time. We tested to what extent MRI-based WSS maps match the patient-specific CFD-base maps. To accomplish this, a pipeline for simultaneous MRIand CFD-based WSS calculations was developed and applied to the carotid arteries of 6 healthy volunteers.

Compound ex vivo and in silico method for hemodynamic analysis of stented arteries.

Hemodynamic factors such as low wall shear stress have been shown to influence endothelial healing and atherogenesis in stent-free vessels. However, in stented vessels, a reliable quantitative analysis of such relations has not been possible due to the lack of a suitable method for the accurate acquisition of blood flow. The objective of this work was to develop a method for the precise reconstruction of hemodynamics and quantification of wall shear stress in stented vessels. We have developed such a method that can be applied to vessels stented in or ex vivo and processed ex vivo. Here we stented the coronary arteries of ex vivo porcine hearts, performed vascular corrosion casting, acquired the vessel geometry using micro-computed tomography and reconstructed blood flow and shear stress using computational fluid dynamics. The method yields accurate local flow information through anatomic fidelity, capturing in detail the stent geometry, arterial tissue prolapse, radial and axial arterial deformation as well as strut malapposition. This novel compound method may serve as a unique tool for spatially resolved analysis of the relationship between hemodynamic factors and vascular biology. It can further be employed to optimize stent design and stenting strategies.

Wall shear stress quantification in the human conjunctival pre-capillary arterioles in vivo

Blood volume flow (Q), wall shear rate (WSR) and wall shear stress (WSS) were quantified, for the first time, in the conjunctival pre-capillary arterioles of normal human volunteers with diameters (D) between 6 and 12μm. The variation of the blood velocity throughout the cardiac cycle was taken into account using high speed video microcinematography. The dual effect of arteriolar diameter, firstly on the WSR and secondly on the dynamic viscosity of blood, was taken into account in the estimation of WSS. The average Q, WSR and WSS, throughout the cardiac cycle ranged from 13 to 202 pl/s, 587 to 3515s−1 and 1.7 to 21.1N/m2 respectively. The best fit power law equations, giving the increase of Q and the decrease of WSR and WSS with diameter, are presented for the systolic and diastolic phase as well as for the averages throughout the cardiac cycle. According to the WSS best fit equation, the average WSS decreases from 10.5N/m2 at D=6μm down to 2.1N/m2 at D=12μm.

Optimization of Cardiovascular Stent Design Using Computational Fluid Dynamics

Coronary stent design affects the spatial distribution of wall shear stress (WSS), which can influence the progression of endothelialization, neointimal hyperplasia, and restenosis. Previous computational fluid dynamics (CFD) studies have only examined a small number of possible geometries to identify stent designs that reduce alterations in near-wall hemodynamics. Based on a previously described framework for optimizing cardiovascular geometries, we developed a methodology that couples CFD and three-dimensional shape-optimization for use in stent design. The optimization procedure was fully-automated, such that solid model construction, anisotropic mesh generation, CFD simulation, and WSS quantification did not require user intervention. We applied the method to determine the optimal number of circumferentially repeating stent cells (N(C)) for slotted-tube stents with various diameters and intrastrut areas. Optimal stent designs were defined as those minimizing the area of low intrastrut time-averaged WSS. Interestingly, we determined that the optimal value of N(C) was dependent on the intrastrut angle with respect to the primary flow direction. Further investigation indicated that stent designs with an intrastrut angle of approximately 40 deg minimized the area of low time-averaged WSS regardless of vessel size or intrastrut area. Future application of this optimization method to commercially available stent designs may lead to stents with superior hemodynamic performance and the potential for improved clinical outcomes.

Reproducibility of flow and wall shear stress analysis using flow‐sensitive four‐dimensional MRI

To systematically investigate the scan-rescan reproducibility and observer variability of flow-sensitive four-dimensional (4D) MRI in the aorta for the assessment of blood flow and global and segmental wall shear stress. ECG and respiration-synchronized flow-sensitive 4D MRI data (spatio-temporal resolution = 1.7 × 2.0 × 2.2 mm(3) /40.8 ms) were acquired in 12 healthy volunteers. To analyze scan-rescan variability, flow-sensitive 4D MRI was repeated in 10 volunteers during a second visit. Data analysis included calculation of time-resolved and total flow, peak systolic velocity, and regional and global wall shear stress (WSS) in up to 24 analysis planes distributed along the aorta. Scan-rescan, inter-observer, and intra-observer agreement was excellent for the calculation of total flow and peak systolic velocity (mean differences <5% of the average flow parameter). Global WSS demonstrated moderate agreement and increased variability regarding wall shear stress (scan-rescan, inter-observer, and intra-observer agreement; mean differences <10% of the average WSS parameters). The segmental distribution of wall shear stress in the thoracic aorta could reliably be reproduced (r > 0.87; P < 0.001) for different observers and examinations. Flow-sensitive 4D MRI-based analysis of aortic blood flow can be performed with good reproducibility. Robustness of global and regional WSS quantification was limited, but spatio-temporal WSS distributions could reliably be replicated.

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

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