MRI measurement of time-resolved wall shear stress vectors in a carotid bifurcation model, and comparison with CFD predictions

Toward a Mesoscopic Modeling Approach of Magnetohydrodynamic Blood Flow in Pathological Vessels: A Comprehensive Review

The investigation of magnetohydrodynamic (MHD) blood flow within configurations that are pertinent to the human anatomy holds significant importance in the realm of scientific inquiry because of its practical implications within the medical field. This article presents an exhaustive appraisal of the diverse applications of magnetohydrodynamics and their computational modeling in biological contexts. These applications are classified into two categories: simple flow and pulsatile flow. An alternative approach of traditional CFD methods called Lattice Boltzmann Method (LBM), a mesoscopic method based on kinetic theory, is introduced to solve complex problems, such as hemodynamics. The results show that the flow velocity reduces considerably by increasing the magnetic field intensity, and the flow separation area is minimized by the increase of magnetic field strength. The LBM with BGK collision model has shown good results in terms of precision. Finally, this literature review has revealed a number of potential avenues for further research. Suggestions for future works are proposed accordingly.

Transient wall shear stress estimation in coronary bifurcations using convolutional neural networks

BACKGROUND AND OBJECTIVE

Haemodynamic metrics, such as blood flow induced shear stresses at the inner vessel lumen, are associated with the development and progression of coronary artery disease. Understanding these metrics may therefore improve the assessment of an individual's coronary disease risk. However, the calculation of such luminal Wall Shear Stress (WSS) using traditional Computational Fluid Dynamics (CFD) methods is relatively slow and computationally expensive. As a result, CFD based haemodynamic computation is not suitable for integrated and large-scale use in clinical settings.

METHODS

In this work, deep learning techniques are proposed as an alternative method to CFD, whereby luminal WSS magnitude can be predicted in coronary bifurcations throughout the cardiac cycle based on the steady state solution (which takes <120 seconds to calculate including preprocessing), vessel geometry and additional global features. The deep learning model is trained on a dataset of 101 patient-specific and 2626 synthetic left main bifurcation models with 26 separate patient-specific cases used as the test set.

RESULTS

The model showed high fidelity predictions with <5% (normalised against mean WSS magnitude) deviation to CFD derived values as the gold-standard method, while being orders of magnitude faster with on average <2 minutes versus 3 hours computation for transient CFD.

CONCLUSIONS

This method therefore offers a new approach to substantially reduce the computational cost involved in, for example, large-scale population studies of coronary haemodynamic metrics, and may therefore open the pathway for future clinical integration.

Hemolytic Performance in Two Generations of the Sputnik Left Ventricular Assist Device: A Combined Numerical and Experimental Study

Background: Currently, left ventricular assist devices (LVADs) are a successful surgical treatment for patients with end-stage heart failure on the waiting list or with contraindicated heart transplantation. In Russia, Sputnik 1 LVAD was also successfully introduced into clinical practice as a bridge-to-transplant and a destination therapy device. Development of Sputnik 2 LVAD was aimed at miniaturization to reduce invasiveness, optimize hemocompatibility, and improve versatility for patients of various sizes. Methods: We compared hemolysis level in flow path of the Sputnik LVADs and investigated design aspects influencing other types of blood damage, using predictions of computational fluid dynamics (CFD) and experimental assessment. The investigated operating point was a flow rate of 5 L/min and a pressure head of 100 mm Hg at an impeller rotational speed of 9100 min⁻¹. Results: Mean hemolysis indices predicted with CFD were 0.0090% in the Sputnik 1 and 0.0023% in the Sputnik 2. Averaged values of normalized index of hemolysis obtained experimentally for the Sputnik 1 and the Sputnik 2 were 0.011 ± 0.003 g/100 L and 0.004 ± 0.002 g/100 L, respectively. Conclusions: Obtained results indicate obvious improvements in hemocompatibility and sufficiently satisfy the determined miniaturization aim for the Sputnik 2 LVAD development.

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

PURPOSE

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.

METHODS

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 (8 mm in diameter) and stenosis (70% of stenosis) phantoms under a pulsatile flow condition. A human study was conducted from five healthy volunteers.

RESULTS

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 ± 0.16 Pa, respectively, for the anterior wall and 0.29 ± 0.11, 0.54 ± 0.24, and 0.23 ± 0.10 Pa, respectively, for the posterior wall.

CONCLUSIONS

All results indicated that WSS mapping has the potential to be a useful tool for vessel duplex scanning in the future.

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

PURPOSE

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.

METHODS

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.

RESULTS

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.

CONCLUSIONS

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%).

Geometrically induced wall shear stress variability in CFD-MRI coupled simulations of blood flow in the thoracic aortas

Aortic aneurysm is associated with aberrant blood flow and wall shear stress (WSS). This can be studied by coupling magnetic resonance imaging (MRI) with computational fluid dynamics (CFD). For patient-specific simulations, extra attention should be given to the variation in segmentation of the MRI data-set and its effect on WSS. We performed CFD simulations of blood flow in the aorta for ten different volunteers and provided corresponding WSS distributions. The aorta of each volunteer was segmented four times. The same inlet and outlet boundary conditions were applied for all segmentation variations of each volunteer. Steady-state CFD simulations were performed with inlet flow based on phase-contrast MRI during peak systole. We show that the commonly used comparison of mean and maximal values of WSS, based on CFD in the different segments of the thoracic aorta, yields good to excellent correlation (0.78-0.95) for rescan and moderate to excellent correlation (0.64-1.00) for intra- and interobserver reproducibility. However, the effect of geometrical variations is higher for the voxel-to-voxel comparison of WSS. With this analysis method, the correlation for different segments of the whole aorta is poor to moderate (0.43-0.66) for rescan and poor to good (0.48-0.73) for intra- and interobserver reproducibility. Therefore, we advise being critical about the CFD results based on the MRI segmentations to avoid possible misinterpretation. While the global values of WSS are similar for different modalities, the variation of results is high when considering the local distributions.

Computational fluid dynamics of the right atrium: Assessment of modelling criteria for the evaluation of dialysis catheters

Central venous catheters are widely used in haemodialysis therapy, having to respect design requirements for appropriate performance. These are placed within the right atrium (RA); however, there is no prior computational study assessing different catheter designs while mimicking their native environment. Here, a computational fluid dynamics model of the RA, based on realistic geometry and transient physiological boundary conditions, was developed and validated. Symmetric, split and step catheter designs were virtually placed in the RA and their performance was evaluated by: assessing their interaction with the RA haemodynamic environment through prediction of flow vorticity and wall shear stress (WSS) magnitudes (1); and quantifying recirculation and tip shear stress (2). Haemodynamic predictions from our RA model showed good agreement with the literature. Catheter placement in the RA increased average vorticity, which could indicate alterations of normal blood flow, and altered WSS magnitudes and distribution, which could indicate changes in tissue mechanical properties. All designs had recirculation and elevated shear stress values, which can induce platelet activation and subsequently thrombosis. The symmetric design, however, had the lowest associated values (best performance), while step design catheters working in reverse mode were associated with worsened performance. Different tip placements also impacted on catheter performance. Our findings suggest that using a realistically anatomical RA model to study catheter performance and interaction with the haemodynamic environment is crucial, and that care needs to be given to correct tip placement within the RA for improved recirculation percentages and diminished shear stress values.

Blood Flow Modeling in Coronary Arteries: A Review

Atherosclerosis is one of the main causes of cardiovascular events, namely, myocardium infarction and cerebral stroke, responsible for a great number of deaths every year worldwide. This pathology is caused by the progressive accumulation of low-density lipoproteins, cholesterol, and other substances on the arterial wall, narrowing its lumen. To date, many hemodynamic studies have been conducted experimentally and/or numerically; however, this disease is not yet fully understood. For this reason, the research of this pathology is still ongoing, mainly, resorting to computational methods. These have been increasingly used in biomedical research of atherosclerosis because of their high-performance hardware and software. Taking into account the attempts that have been made in computational techniques to simulate realistic conditions of blood flow in both diseased and healthy arteries, the present review aims to give an overview of the most recent numerical studies focused on coronary arteries, by addressing the blood viscosity models, and applied physiological flow conditions. In general, regardless of the boundary conditions, numerical studies have been contributed to a better understanding of the development of this disease, its diagnosis, and its treatment.

CFD validation using in-vitro MRI velocity data - Methods for data matching and CFD error quantification

Predicting blood flow velocities in patient-specific geometries with Computational Fluid Dynamics (CFD) can provide additional data for diagnosis and treatment planning but the solution can be inaccurate. Therefore, it is crucial to understand the simulation errors and calibrate the numerical model. In-vitro velocity-encoded MRI is a versatile tool to validate CFD. The comparison between CFD and in-vitro MRI velocity data, and the analysis of the simulation error are the objectives of this study. A three-step routine is presented to validate medical CFD data. First, a properly scaled model of the patient-specific geometry is fabricated to achieve high relative resolution in the MRI experiment. Second, the measured flow geometry is matched with the CFD data using one of two algorithms, Coherent Point Drift and Iterative Closest Point. The aligned data sets are then interpolated onto a common grid to enable a point-to-point comparison. Third, the global and local deviations between CFD and MRI velocity data are calculated using different algorithms to reliably estimate the simulation error. The routine is successfully tested with a patient-specific model of a cerebral aneurysm. In conclusion, the methods presented here provide a framework for CFD validation using in-vitro MRI velocity data.

In vitro Biomodels in Stenotic Arteries to Perform Blood Analogues Flow Visualizations and Measurements: A Review

Cardiovascular diseases are one of the leading causes of death globally and the most common pathological process is atherosclerosis. Over the years, these cardiovascular complications have been extensively studied by applying in vivo, in vitro and numerical methods (in silico). In vivo studies represent more accurately the physiological conditions and provide the most realistic data. Nevertheless, these approaches are expensive, and it is complex to control several physiological variables. Hence, the continuous effort to find reliable alternative methods has been growing. In the last decades, numerical simulations have been widely used to assess the blood flow behavior in stenotic arteries and, consequently, providing insights into the cardiovascular disease condition, its progression and therapeutic optimization. However, it is necessary to ensure its accuracy and reliability by comparing the numerical simulations with clinical and experimental data. For this reason, with the progress of the in vitro flow measurement techniques and rapid prototyping, experimental investigation of hemodynamics has gained widespread attention. The present work reviews state-of-the-art in vitro macro-scale arterial stenotic biomodels for flow measurements, summarizing the different fabrication methods, blood analogues and highlighting advantages and limitations of the most used techniques.

Measuring wall shear stress distribution in the carotid artery in an African population: Computational fluid dynamics versus ultrasound doppler velocimetry

INTRODUCTION

Computational fluid dynamics (CFD) and ultrasound Doppler velocimetry are diagnostic tools useful for determining carotid artery segments susceptible to atheromatous plaque development. This study computes and compares the difference in Wall Shear Stress (WSS) measurements between these two methods.

METHODS

The carotid artery of 204 volunteers selected using simple random sampling were scanned using standard carotid doppler protocols. Four segments of the carotid artery - the common, internal, external carotid, and the carotid bulb were sonographically assessed. The intima-media thickness, diameter, peak systolic velocity, and end-diastolic velocity were measured at a point 2 cm away from the carotid bifurcation for the three segments, while the carotid bulb was measured at the bifurcation. A 2D incompressible Navier-Stokes Equation for modelling Newtonian, pulsatile, and laminar flow in a viscoelastic pipe was applied to model velocity flow across the carotid artery using COMSOL software. WSS values were computed for experimental and CFD measurements and the results were compared.

RESULTS

The WSS values generated by the model had respectively peak and average values of 19.81 N/cm² and 15.76 ± 1.81 N/cm² for the common carotid, 10.77 N/cm² and 7.57 ± 1.66 N/cm² for the internal carotid, 11.51 N/cm² and 8.05 ± 1.65 N/cm² for the external carotid, 37.55 N/cm² and 26.55 ± 6.62 N/cm² for the carotid bifurcation, 1.39 N/cm² and 3.13 ± 1.34 N/cm² for the carotid bulb. The model measurements matched doppler velocimetry measurements with <15% variation.

CONCLUSION

Model based WSS values were higher but comparable with doppler velocimetry measurements. The carotid bulb had low WSS and is therefore the segment highly disposed to atheromatous plaque formation.

IMPLICATIONS FOR PRACTICE

Subject-specific mathematical models could be incorporated during cardiovascular scan work up for accurate WSS distribution and early prediction of possible atherosclerotic sites.

Possible Early Generation of Physiological Helical Flow Could Benefit the Triflo Trileaflet Heart Valve Prosthesis Compared to Bileaflet Valves

Background—Physiological helical flow in the ascending aorta has been well documented in the last two decades, accompanied by discussions on possible physiological benefits of such axial swirl. Recent 4D-MRI studies on healthy volunteers have found indications of early generation of helical flow, early in the systole and close to the valve plane. Objectives—Firstly, the aim of the study is to investigate the hypothesis of premature swirl existence in the ventricular outflow tract leading to helical flow in the valve plane, and second to investigate the possible impact of two different mechanical valve designs on the preservation of this early helical flow and its subsequent hemodynamic consequences. Methods—We use a pulse duplicator with an aortic arch and High-Speed Particle Image Velocimetry to document the flow evolution in the systolic cycle. The pulse-duplicator is modified with a swirl-generating insert to generate early helical flow in the valve plane. Special focus is paid to the interaction of such helical flow with different designs of mechanical prosthetic heart valves, comparing a classical bileaflet mechanical heart valve, the St. Jude Medical Regent valve (SJM Regent BMHV), with the Triflo trileaflet mechanical heart valve T2B version (Triflo TMHV). Results—When the swirl-generator is inserted, a vortex is generated in the core flow, demonstrating early helical flow in the valve plane, similar to the observations reported in the recent 4D-MRI study taken for comparison. For the Triflo trileaflet valve, the early helical flow is not obstructed in the central orifice, similar as in the case of the natural valve. Conservation of angular momentum leads to radial expansion of the core flow and flattening of the axial flow profile downstream in the arch. Furthermore, the early helical flow helps to overcome separation at the outer and inner curvature. In contrast, the two parallel leaflets for the bileaflet valve impose a flow straightener effect, annihilating the angular momentum, which has a negative impact on kinetic energy of the flow. Conclusion—The results imply better hemodynamics for the Triflo trileaflet valve based on hydrodynamic arguments under the discussed hypothesis. In addition, it makes the Triflo valve a better candidate for valve replacements in patients with a pathological generation of nonaxial velocity in the ventricle outflow tract.

From 2D to 4D Phase-Contrast MRI in the Neurovascular System: Will It Be a Quantum Jump or a Fancy Decoration?

Considering the crosstalk between the flow and vessel wall, hemodynamic assessment of the neurovascular system may offer a well-integrated solution for both diagnosis and management by adding prognostic significance to the standard CT/MR angiography. 4D flow MRI or time-resolved 3D velocity-encoded phase-contrast MRI has long been promising for the hemodynamic evaluation of the great vessels, but challenged in clinical studies for assessing intracranial vessels with small diameter due to long scan times and low spatiotemporal resolution. Current accelerated MRI techniques, including parallel imaging with compressed sensing and radial k-space undersampling acquisitions, have decreased scan times dramatically while preserving spatial resolution. 4D flow MRI visualized and measured 3D complex flow of neurovascular diseases such as aneurysm, arteriovenous shunts, and atherosclerotic stenosis using parameters including flow volume, velocity vector, pressure gradients, and wall shear stress. In addition to the noninvasiveness of the phase contrast technique and retrospective flow measurement through the wanted windows of the analysis plane, 4D flow MRI has shown several advantages over Doppler ultrasound or computational fluid dynamics. The evaluation of the flow status and vessel wall can be performed simultaneously in the same imaging modality. This article is an overview of the recent advances in neurovascular 4D flow MRI techniques and their potential clinical applications in neurovascular disease. LEVEL OF EVIDENCE: 5 TECHNICAL EFFICACY STAGE: 3.

Wall Shear Stress Measurements Based on Ultrasound Vector Flow Imaging: Theoretical Studies and Clinical Examples

Wall shear stress (WSS) is considered as a key factor for atherosclerosis development. Previous WSS research based on pulsed wave Doppler (PWD) showed limitations in complex flows. To improve accuracy for nonlaminar flow, a commercial ultrasound vector flow imaging (UVFI)-based WSS calculation is proposed. Errors for PWD are presented theoretically when flow is not laminar. Based on this, simulations of WSS calculations between PWD and UVFI were set up for different turbulent flows. Our simulations show that UVFI has obviously better performance than PWD in WSS calculations. Wall shear stress results in different flow conditions at carotid bifurcations are described.

A Systematic Review for the Design of In Vitro Flow Studies of the Carotid Artery Bifurcation

PURPOSE

In vitro blood flow studies in carotid artery bifurcation models may contribute to understanding the influence of hemodynamics on carotid artery disease. However, the design of in vitro blood flow studies involves many steps and selection of imaging techniques, model materials, model design, and flow visualization parameters. Therefore, an overview of the possibilities and guidance for the design process is beneficial for researchers with less experience in flow studies.

METHODS

A systematic search to in vitro flow studies in carotid artery bifurcation models aiming at quantification and detailed flow visualization of blood flow dynamics results in inclusion of 42 articles.

RESULTS

Four categories of imaging techniques are distinguished: MRI, optical particle image velocimetry (PIV), ultrasound and miscellaneous techniques. Parameters for flow visualization are categorized into velocity, flow, shear-related, turbulent/disordered flow and other parameters. Model materials and design characteristics vary between study type.

CONCLUSIONS

A simplified three-step design process is proposed for better fitting and adequate match with the pertinent research question at hand and as guidance for less experienced flow study researchers. The three consecutive selection steps are: flow parameters, image modality, and model materials and designs. Model materials depend on the chosen imaging technique, whereas choice of flow parameters is independent from imaging technique and is therefore only determined by the goal of the study.

NUMERICAL SIMULATION OF DILATION PATTERNS OF THE ASCENDING AORTA IN AORTOPATHIES

Aortic dilation is associated with congenital bicuspid aortic valve (BAV) disease, and its etiology is still not completely understood. The aim of this study is to provide further insight into aortic hemodynamics in a BAV population with different degrees of aortic dilation and regurgitation in comparison with a patient without pathology. A fluid–structure interaction (FSI) numerical approach is implemented regarding patient-specific geometries, where the aortic valves are defined by analytical orifices. Results show that, while the patient without pathology displays a typical hemodynamic behavior of flows in bends, BAV-related aortas present an accelerated flow along the outer aortic wall. Wall shear stress (WSS) overload in the outer curvature is observed, more marked in more dilated aortas. Moreover, helices in the ascending aorta are present in these patients, enhanced with greater dilation. These findings support the fact that hemodynamic factors play an important role in aortic dilation onset and development in BAV patients, caused by a prolonged exposure of the outer ascending aortic curvature to altered WSS. Besides, our results suggest that greater aortic regurgitation may be associated with abnormal WSS distributions in the ascending aorta during diastole, which can facilitate aortic root dilation.

Enhancing Magnetic Resonance Imaging With Computational Fluid Dynamics

The analysis of the blood flow in the great thoracic arteries does provide valuable information about the cardiac function and can diagnose the potential development of vascular diseases. Flow-sensitive four-dimensional flow cardiovascular magnetic resonance imaging (4D flow CMR) is often used to characterize patients' blood flow in the clinical environment. Nevertheless, limited spatial and temporal resolution hinders a detailed assessment of the hemodynamics. Computational fluid dynamics (CFD) could expand this information and, integrated with experimental velocity field, enable to derive the pressure maps. However, the limited resolution of the 4D flow CMR and the simplifications of CFD modeling compromise the accuracy of the computed flow parameters. In this article, a novel approach is proposed, where 4D flow CMR and CFD velocity fields are integrated synergistically to obtain an enhanced MR imaging (EMRI). The approach was first tested on a two-dimensional (2D) portion of a pipe, to understand the behavior of the parameters of the model in this novel framework, and afterwards in vivo, to apply it to the analysis of blood flow in a patient-specific human aorta. The outcomes of EMRI are assessed by comparing the computed velocities with the experimental one. The results demonstrate that EMRI preserves flow structures while correcting for experimental noise. Therefore, it can provide better insights into the hemodynamics of cardiovascular problems, overcoming the limitations of MRI and CFD, even when considering a small region of interest. EMRI confirmed its potential to provide more accurate noninvasive estimation of major cardiovascular risk predictors (e.g., flow patterns, endothelial shear stress) and become a novel diagnostic tool.

Noise estimation for the velocity in MRI phase-contrast

The purpose of this study is to estimate the precision or statistical variability of the velocity measurements computed from MRI phase-contrast. From the analytical probability density function (PDF) of the phase in the signal we obtain the PDF of the velocity by means of an auto-convolution. This PDF allows the estimation of the precision of the velocity, important for the correct interpretation of the many parameters that are based on it. We show that for high Signal-to-Noise Ratio (SNR) voxels, the distribution is well approximated by a Gaussian distribution. On the other hand, this is not true for lower SNR voxels, where the distribution adopts a form in between the Gaussian and the uniform distributions. This was confirmed empirically. Also, knowing the PDF on a coil by coil basis it is possible to combine the data from multiple coils in an optimal way. We showed that the optimal combination reduces the resulting global variability of the velocity, in comparison with the commonly used Weighted Mean or with a SENSE reconstruction with R = 1.

Suitability of lattice Boltzmann inlet and outlet boundary conditions for simulating flow in image-derived vasculature

The lattice Boltzmann method (LBM) is a popular alternative to solving the Navier-Stokes equations for modeling blood flow. When simulating flow using the LBM, several choices for inlet and outlet boundary conditions exist. While boundary conditions in the LBM have been evaluated in idealized geometries, there have been no extensive comparisons in image-derived vasculature, where the geometries are highly complex. In this study, the Zou-He (ZH) and finite difference (FD) boundary conditions were evaluated in image-derived vascular geometries by comparing their stability, accuracy, and run times. The boundary conditions were compared in four arteries: a coarctation of the aorta, dissected aorta, femoral artery, and left coronary artery. The FD boundary condition was more stable than ZH in all four geometries. In general, simulations using the ZH and FD method showed similar convergence rates within each geometry. However, the ZH method proved to be slightly more accurate compared with experimental flow using three-dimensional printed vasculature. The total run times necessary for simulations using the ZH boundary condition were significantly higher as the ZH method required a larger relaxation time, grid resolution, and number of time steps for a simulation representing the same physiological time. Finally, a new inlet velocity profile algorithm is presented for complex inlet geometries. Overall, results indicated that the FD method should generally be used for large-scale blood flow simulations in image-derived vasculature geometries. This study can serve as a guide to researchers interested in using the LBM to simulate blood flow.

COMPUTATIONAL STUDY OF THE INFLUENCE OF BIFURCATION ANGLE ON HAEMODYNAMICS AND OXYGEN TRANSPORT IN THE CAROTID BIFURCATION

In this study, blood flow associated with oxygen transport in the human carotid bifurcation was investigated numerically to assess the effects of bifurcation geometry on distribution and magnitude of the wall shear stress (WSS) and Sherwood number (Sh: dimensionless oxygen wall flux) at the favourable site of atherosclerotic lesion. Three-dimensional average models of the rigid-walled carotid bifurcation were constructed to perform simulations of steady blood flow under the wall boundary condition of a constant oxygen tension. The results demonstrated that changes in the bifurcation angle significantly altered the distribution of both the WSS and the Sh, even though the pattern of the axial flow was not very sensitive to the change in bifurcation angle. Flow with large inertia bifurcated at the flow divider and created a flow recirculation zone with low WSS and Sh on the outer wall of the internal carotid artery (ICA) sinus, where atherosclerotic lesions tend to develop. A wider bifurcation angle made the area of low Sh in the ICA sinus smaller, but the level of Sh along the outer wall of the ICA sinus extremely low. Another finding was that low Sh was associated with high WSS at the region distal to the ICA sinus. The Sh distribution did not readjust as fast as the WSS in this region, as reflected by the different rates of recovery of the WSS and Sh, thus uncoupling the transport process of oxygen transport from WSS.

Evaluation of spatial distribution and characterization of wall shear stress in carotid sinus based on two-dimensional color Doppler imaging

Objective

This study aims to use a wall shear stress (WSS) quantitative analysis software to analyze and evaluate the carotid sinus WSS spatial distribution and characteristics in intima-media thickness (IMT) normal and thickening group by using two-dimensional color doppler flow imaging (CDFI) so as to assist clinicians to predict the location and risk of plaque formation.

Methods

According to IMT, 50 subjects was selected as IMT thickening group and 50 subjects as IMT normal group from subjects who had a carotid ultrasound examination in Shanghai East hospital during October 2016 to October 2017. This study presents the spatial distribution of the carotid sinus WSS based on the WSS quantitative analysis software and compared the spatial distribution and characteristics of the carotid sinus WSS between IMT thickening group and IMT normal group through two- and three-dimensional WSS maps and a fused WSS image.

Results

The distributional regularity of WSS in both two group was: carotid sinus < common carotid artery (CCA) < internal carotid artery (ICA) and posterior-interior wall of the carotid sinus < the anterior-lateral wall of the carotid sinus. Furthermore, the WSS of CCA, ICA, the anterior-lateral proximal wall of the carotid sinus, the anterior-lateral distal wall of the carotid sinus, the posterior-interior proximal wall of the carotid sinus, and the posterior-interior distal wall of the carotid sinus in IMT thickening group was lower than the corresponding part of IMT normal group (P < 0.05).

Conclusion

In summary, this WSS quantitative analysis framework by two-dimensional CDFI can measure and reflect the carotid sinus WSS spatial distribution and characteristics more accurately and visually. As a convenient tool, it may be used for clinical prediction of the plaque formation in carotid sinus in the future.

Spatial correlations between MRI-derived wall shear stress and vessel wall thickness in the carotid bifurcation

Background

To explore the possibility of creating three-dimensional (3D) estimation models for patient-specific wall thickness (WT) maps using patient-specific and cohort-averaged WT, wall shear stress (WSS), and vessel diameter maps in asymptomatic atherosclerotic carotid bifurcations.

Methods

Twenty subjects (aged 75 ± 6 years [mean ± standard deviation], eight women) underwent a 1.5-T MRI examination. Non-gated 3D phase-contrast gradient-echo images and proton density-weighted echo-planar images were retrospectively assessed for WSS, diameter estimation, and WT measurements. Spearman’s ρ and scatter plots were used to determine correlations between individual WT, WSS, and diameter maps. A bootstrapping technique was used to determine correlations between 3D cohort-averaged WT, WSS, and diameter maps. Linear regression between the cohort-averaged WT, WSS, and diameter maps was used to predict individual 3D WT.

Results

Spearman’s ρ averaged over the subjects was − 0.24 ± 0.18 (p < 0.001) and 0.07 ± 0.28 (p = 0.413) for WT versus WSS and for WT versus diameter relations, respectively. Cohort-averaged ρ, averaged over 1000 bootstraps, was − 0.56 (95% confidence interval [− 0.74,− 0.38]) for WT versus WSS and 0.23 (95% confidence interval [− 0.06, 0.52]) for WT versus diameter. Scatter plots did not reveal relationships between individual WT and WSS or between WT and diameter data. Linear relationships between these parameters became apparent after averaging over the cohort. Spearman’s ρ between the original and predicted WT maps was 0.21 ± 0.22 (p < 0.001).

Conclusions

With a combination of bootstrapping and cohort-averaging methods, 3D WT maps can be predicted from the individual 3D WSS and diameter maps. The methodology may help to elucidate pathological processes involving WSS in carotid atherosclerosis.

Electronic supplementary material

The online version of this article (10.1186/s41747-018-0058-1) contains supplementary material, which is available to authorized users.

Computational Fluid Dynamic Accuracy in Mimicking Changes in Blood Hemodynamics in Patients with Acute Type IIIb Aortic Dissection Treated with TEVAR

Background: We aimed to verify the accuracy of the Computational Fluid Dynamics (CFD) algorithm for blood flow reconstruction for type IIIb aortic dissection (TBAD) before and after thoracic endovascular aortic repair (TEVAR). Methods: We made 3D models of the aorta and its branches using pre- and post-operative CT data from five patients treated for TBAD. The CFD technique was used to quantify the displacement forces acting on the aortic wall in the areas of endograft, mass flow rate/velocity and wall shear stress (WSS). Calculated results were verified with ultrasonography (USG-Doppler) data. Results: CFD results indicated that the TEVAR procedure caused a 7-fold improvement in overall blood flow through the aorta (p = 0.0001), which is in line with USG-Doppler data. A comparison of CFD results and USG-Doppler data indicated no significant change in blood flow through the analysed arteries. CFD also showed a significant increase in flow rate for thoracic trunk and renal arteries, which was in accordance with USG-Doppler data (accuracy 90% and 99.9%). Moreover, we observed a significant decrease in WSS values within the whole aorta after TEVAR compared to pre-TEVAR (1.34 ± 0.20 Pa vs. 3.80 ± 0.59 Pa, respectively, p = 0.0001). This decrease was shown by a significant reduction in WSS and WSS contours in the thoracic aorta (from 3.10 ± 0.27 Pa to 1.34 ± 0.11Pa, p = 0.043) and renal arteries (from 4.40 ± 0.25 Pa to 1.50 ± 0.22 Pa p = 0.043). Conclusions: Post-operative remodelling of the aorta after TEVAR for TBAD improved hemodynamic patterns reflected by flow, velocity and WSS with an accuracy of 99%.

Assessment of boundary conditions for CFD simulation in human carotid artery

Computational fluid dynamics (CFD) is an increasingly used method for investigation of hemodynamic parameters and their alterations under pathological conditions, which are important indicators for diagnosis of cardiovascular disease. In hemodynamic simulation models, the employment of appropriate boundary conditions (BCs) determines the computational accuracy of the CFD simulation in comparison with pressure and velocity measurements. In this study, we have first assessed the influence of inlet boundary conditions on hemodynamic CFD simulations. We selected two typical patients suspected of carotid artery disease, with mild stenosis and severe stenosis. Both patients underwent digital subtraction angiography (DSA), magnetic resonance angiography, and the invasive pressure guide wire measured pressure profile. We have performed computational experiments to (1) study the hemodynamic simulation outcomes of distributions of wall shear stress, pressure, pressure gradient and (2) determine the differences in hemodynamic performances caused by inlet BCs derived from DSA and Womersley analytical solution. Our study has found that the difference is related to the severity of the stenosis; the greater the stenosis, the more the difference ensues. Further, in our study, the two typical subjects with invasively measured pressure profile and thirty subjects with ultrasound Doppler velocimeter (UDV) measurement served as the criteria to evaluate the hemodynamic outcomes of wall shear stress, pressure, pressure gradient and velocity due to different outlet BCs based on the Windkessel model, structured-tree model, and fully developed flow model. According to the pressure profiles, the fully developed model appeared to have more fluctuations compared with the other two models. The Windkessel model had more singularities before convergence. The three outlet BCs models also showed good correlation with the UDV measurement, while the Windkessel model appeared to be slightly better ([Formula: see text]). The structured-tree model was seen to have the best performance in terms of available computational cost and accuracy. The results of our numerical simulation and the good correlation with the computed pressure and velocity with their measurements have highlighted the effectiveness of CFD simulation in patient-specific human carotid artery with suspected stenosis.

Quantification of near-wall hemodynamic risk factors in large-scale cerebral arterial trees

Detailed hemodynamic analysis of blood flow in pathological segments close to aneurysm and stenosis has provided physicians with invaluable information about the local flow patterns leading to vascular disease. However, these diseases have both local and global effects on the circulation of the blood within the cerebral tree. The aim of this paper is to demonstrate the importance of extending subject-specific hemodynamic simulations to the entire cerebral arterial tree with hundreds of bifurcations and vessels, as well as evaluate hemodynamic risk factors and waveform shape characteristics throughout the cerebral arterial trees. Angioarchitecture and in vivo blood flow measurement were acquired from healthy subjects and in cases with symptomatic intracranial aneurysm and stenosis. A global map of cerebral arterial blood flow distribution revealed regions of low to high hemodynamic risk that may significantly contribute to the development of intracranial aneurysms or atherosclerosis. Comparison of pre-intervention and post-intervention of pathological cases further shows large angular phase shift (~33.8°), and an augmentation of the peak-diastolic velocity. Hemodynamic indexes of waveform analysis revealed on average a 16.35% reduction in the pulsatility index after treatment from lesion site to downstream distal vessels. The lesion regions not only affect blood flow streamlines of the proximal sites but also generate pulse wave shift and disturbed flow in downstream vessels. This network effect necessitates the use of large-scale simulation to visualize both local and global effects of pathological lesions.

A comparison of 4D flow MRI-derived wall shear stress with computational fluid dynamics methods for intracranial aneurysms and carotid bifurcations - A review

BACKGROUND

4D flow MRI is a relatively quick method for obtaining wall shear stress (WSS) in vivo, a hemodynamic parameter which has shown promise in risk stratification for rupture of cerebrovascular diseases such as intracranial aneurysms and atherosclerotic plaques. The accuracy of such measurements is still largely unknown.

OBJECTIVE

To quantify the accuracy of 4D flow MRI-derived wall shear stress values for intracranial aneurysms and carotid bifurcations.

METHOD

We performed a review of all original research articles which compared the magnitudes of WSS derived from 4D flow MRI with corresponding values derived from computational fluid dynamics (CFD) within both intracranial aneurysms and carotid bifurcations.

RESULT

For intracranial aneurysms and carotid bifurcations, 4D flow MRI-derived WSS estimations are generally lower in magnitude compared to WSS derived by CFD methods. These differences are more pronounced in regions of higher WSS. However, the relative distributions of WSS derived from both methods are reasonably similar.

CONCLUSION

Pooled analysis suggests that WSS magnitudes obtained by 4D flow MRI are underestimated, while the relative distribution is reasonably accurate, the latter being an important factor for determining the natural history of intracranial aneurysms and other cerebrovascular diseases. 4D flow MRI shows enormous potential in providing new risk stratification parameters which could have significant impact on individualized treatment decisions and improved patient outcomes.

Vessel wall characterization using quantitative MRI: what's in a number?

The past decade has witnessed the rapid development of new MRI technology for vessel wall imaging. Today, with advances in MRI hardware and pulse sequences, quantitative MRI of the vessel wall represents a real alternative to conventional qualitative imaging, which is hindered by significant intra- and inter-observer variability. Quantitative MRI can measure several important morphological and functional characteristics of the vessel wall. This review provides a detailed introduction to novel quantitative MRI methods for measuring vessel wall dimensions, plaque composition and permeability, endothelial shear stress and wall stiffness. Together, these methods show the versatility of non-invasive quantitative MRI for probing vascular disease at several stages. These quantitative MRI biomarkers can play an important role in the context of both treatment response monitoring and risk prediction. Given the rapid developments in scan acceleration techniques and novel image reconstruction, we foresee the possibility of integrating the acquisition of multiple quantitative vessel wall parameters within a single scan session.

Computational and experimental assessment of influences of hemodynamic shear stress on carotid plaque

Background

Studies have identified hemodynamic shear stress as an important determinant of endothelial function and atherosclerosis. In this study, we assess the influences of hemodynamic shear stress on carotid plaques.

Methods

Carotid stenosis phantoms with three severity (30, 50, 70%) were made from 10% polyvinyl alcohol (PVA) cryogel. The phantoms were placed in a pulsatile flow loop with the same systolic/diastolic phase (35/65) and inlet flow rate (16 L/h). Ultrasonic particle imaging velocimetry (Echo PIV) and computational fluid dynamics (CFD) were used to calculate the velocity profile and shear stress distribution in the carotid stenosis phantoms. Inlet/outlet boundary conditions used in CFD were extracted from Echo PIV experiments to make sure that the results were comparable.

Results

Echo PIV and CFD results showed that velocity was largest in 70% than those in 30 and 50% at peak systole. Echo PIV results indicated that shear stress was larger in the upper wall and the surface of plaque than in the center of vessel. CFD results demonstrated that wall shear stress in the upstream was larger than in downstream of plaque. There was no significant difference in average velocity obtained by CFD and Echo PIV in 30% (p = 0.25). Velocities measured by CFD in 50% (93.01 cm/s) and in 70% (115.07 cm/s) were larger than those by Echo PIV in 50% (60.26 ± 5.36 cm/s) and in 70% (89.11 ± 7.21 cm/s).

Conclusions

The results suggested that Echo PIV and CFD could obtain hemodynamic shear stress on carotid plaques. Higher WSS occurred in narrower arteries, and the shoulder of plaque bore higher WSS than in bottom part.

Minimizing the blood velocity differences between phase-contrast magnetic resonance imaging and computational fluid dynamics simulation in cerebral arteries and aneurysms

The integration of phase-contrast magnetic resonance images (PC-MRI) and computational fluid dynamics (CFD) is a way to obtain detailed information of patient-specific hemodynamics. This study proposes a novel strategy for imposing a pressure condition on the outlet boundary (called the outlet pressure) in CFD to minimize velocity differences between the PC-MRI measurement and the CFD simulation, and to investigate the effects of outlet pressure on the numerical solution. The investigation involved ten patient-specific aneurysms reconstructed from a digital subtraction angiography image, specifically on aneurysms located at the bifurcation region. To evaluate the effects of imposing the outlet pressure, three different approaches were used, namely: a pressure-fixed (P-fixed) approach; a flow rate control (Q-control) approach; and a velocity-field-optimized (V-optimized) approach. Numerical investigations show that the highest reduction in velocity difference always occurs in the V-optimized approach, where the mean of velocity difference (normalized by inlet velocity) is 19.3%. Additionally, the highest velocity differences appear near to the wall and vessel bifurcation for 60% of the patients, resulting in differences in wall shear stress. These findings provide a new methodology for PC-MRI integrated CFD simulation and are useful for understanding the evaluation of velocity difference between the PC-MRI and CFD.

Natural History of Carotid Atherosclerosis in Relation to the Hemodynamic Environment

Carotid atherosclerosis may lead to devastating clinical outcomes such as stroke. Data on the value of local factors in predicting progression in carotid atherosclerosis are limited. Our aim was to investigate the association of local endothelial shear stress (ESS) and low-density lipoprotein (LDL) accumulation with the natural history of atherosclerotic disease using a series of 3 time points of human magnetic resonance data. Three-dimensional lumen/wall reconstruction was performed in 12 carotids, and blood flow and LDL mass transport modeling were performed. Our results showed that an increase in plaque thickness and a decrease in lumen size were associated with low ESS and high LDL accumulation in the arterial wall. Low ESS (odds ratio [OR]: 2.99; 95% confidence interval [CI]: 2.31-3.88; P < .001 vs higher ESS) and high LDL concentration (OR: 3.26; 95% CI: 2.44-4.36; P < .001 vs higher LDL concentration) were significantly associated with substantial local plaque growth. Low ESS and high LDL accumulation both presented a diagnostic accuracy of 67% for predicting plaque growth regions. Modeling of blood flow and LDL mass transport show promise in predicting progression of carotid atherosclerosis.

The Effect of Spatial and Temporal Resolution of Cine Phase Contrast MRI on Wall Shear Stress and Oscillatory Shear Index Assessment

Introduction

Wall shear stress (WSS) and oscillatory shear index (OSI) are associated with atherosclerotic disease. Both parameters are derived from blood velocities, which can be measured with phase-contrast MRI (PC-MRI). Limitations in spatiotemporal resolution of PC-MRI are known to affect these measurements. Our aim was to investigate the effect of spatiotemporal resolution using a carotid artery phantom.

Methods

A carotid artery phantom was connected to a flow set-up supplying pulsatile flow. MRI measurement planes were placed at the common carotid artery (CCA) and internal carotid artery (ICA). Two-dimensional PC-MRI measurements were performed with thirty different spatiotemporal resolution settings. The MRI flow measurement was validated with ultrasound probe measurements. Mean flow, peak flow, flow waveform, WSS and OSI were compared for these spatiotemporal resolutions using regression analysis. The slopes of the regression lines were reported in %/mm and %/100ms. The distribution of low and high WSS and OSI was compared between different spatiotemporal resolutions.

Results

The mean PC-MRI CCA flow (2.5±0.2mL/s) agreed with the ultrasound probe measurements (2.7±0.02mL/s). Mean flow (mL/s) depended only on spatial resolution (CCA:-13%/mm, ICA:-49%/mm). Peak flow (mL/s) depended on both spatial (CCA:-13%/mm, ICA:-17%/mm) and temporal resolution (CCA:-19%/100ms, ICA:-24%/100ms). Mean WSS (Pa) was in inverse relationship only with spatial resolution (CCA:-19%/mm, ICA:-33%/mm). OSI was dependent on spatial resolution for CCA (-26%/mm) and temporal resolution for ICA (-16%/100ms). The regions of low and high WSS and OSI matched for most of the spatiotemporal resolutions (CCA:30/30, ICA:28/30 cases for WSS; CCA:23/30, ICA:29/30 cases for OSI).

Conclusion

We show that both mean flow and mean WSS are independent of temporal resolution. Peak flow and OSI are dependent on both spatial and temporal resolution. However, the magnitude of mean and peak flow, WSS and OSI, and the spatial distribution of OSI and WSS did not exhibit a strong dependency on spatiotemporal resolution.

Four-dimensional MRI flow examinations in cerebral and extracerebral vessels - ready for clinical routine?

PURPOSE OF REVIEW

To evaluate the feasibility of 4-dimensional (4D) flow MRI for the clinical assessment of cerebral and extracerebral vascular hemodynamics in patients with neurovascular disease.

RECENT FINDINGS

4D flow MRI has been applied in multiple studies to qualitatively and quantitatively study intracranial aneurysm blood flow for potential risk stratification and to assess treatment efficacy of various neurovascular lesions, including intraaneurysmal and parent artery blood flow after flow diverter stent placement and staged embolizations of arteriovenous malformations and vein of Galen aneurysmal malformations. Recently, the technique has been utilized to characterize age-related changes of normal cerebral hemodynamics in healthy individuals over a broad age range.

SUMMARY

4D flow MRI is a useful tool for the noninvasive, volumetric and quantitative hemodynamic assessment of neurovascular disease without the need for gadolinium contrast agents. Further improvements are warranted to overcome technical limitations before broader clinical implementation. Current developments, such as advanced acceleration techniques (parallel imaging and compressed sensing) for faster data acquisition, dual or multiple velocity encoding strategies for more accurate arterial and venous flow quantification, ultrahigh-field strengths to achieve higher spatial resolution and streamlined postprocessing workflow for more efficient and standardized flow analysis, are promising advancements in 4D flow MRI.

Evaluation of the impact of carotid artery bifurcation angle on hemodynamics by use of computational fluid dynamics: a simulation and volunteer study

In this study, we evaluated the hemodynamics of carotid artery bifurcation with various geometries using simulated and volunteer models based on magnetic resonance imaging (MRI). Computational fluid dynamics (CFD) was analyzed by use of OpenFOAM. The velocity distribution, streamline, and wall shear stress (WSS) were evaluated in a simulated model with known bifurcation angles (30°, 40°, 50°, 60°, derived from patients' data) and in three-dimensional (3D) healthy volunteer models. Separated flow was observed at the outer side of the bifurcation, and large bifurcation models represented upstream transfer of the point. Local WSS values at the outer bifurcation [both simulated (<30 Pa) and volunteer (<50 Pa) models] were lower than those in the inner region (>100 Pa). The bifurcation angle had a significant negative correlation with the WSS value (p<0.05). The results of this study show that the carotid artery bifurcation angle is related to the WSS value. This suggests that hemodynamic stress can be estimated based on the carotid artery geometry. The construction of a clinical database for estimation of developing atherosclerosis is warranted.

[Quantitative Analysis of Wall Shear Stress for Human Carotid Bifurcation at Cardiac Phases by the Use of Phase Contrast Cine Magnetic Resonance Imaging: Computational Fluid Dynamics Study]

PURPOSE

Detailed strategy for regional hemodynamics is significant for knowledge of plaque development on vascular diseases such as atherosclerosis. The aim of this study was to derive relation between atherosclerosis and hemodynamics at human carotid bifurcation by the use of computational fluid dynamics (CFD), and to provide more accurate hemodynamic information.

METHODS

Blood velocity datasets at common carotid artery were obtained by phase-contrast cine magnetic resonance imaging (PC cine MRI). Carotid bifurcation model was computed for systolic, mid-diastolic, and end-diastolic phase. Comparison of wall shear stress (WSS) was performed for each cardiac phase.

RESULTS

PC cine MRI provided velocity measurement for common carotid artery with various cardiac phases. The blood velocity had acute variation from 0.21 m/s to 1.07 m/s at systolic phase. The variation of WSS during cardiac phase was presented at carotid bifurcation model. High shear stress area was observed at dividing wall for all cardiac phases. The systole-diastole WSS ratio was 10.15 at internal carotid side of bifurcation. And low shear stress (<0.5 Pa) was observed at internal carotid side of bifurcation.

CONCLUSION

Bifurcation area represented low shear stress and changed significantly WSS. The specific area with significant change in shear stress and low shear stress had good agreement with predilection sites of atherosclerosis. The result suggested that hemodynamics was related to atherosclerosis, and CFD analysis with various cardiac phases that were provided by PC cine MRI was allowed to determine an accurate analysis condition. This led to the representation of hemodynamics in vivo.

Computational fluid dynamic simulation of human carotid artery bifurcation based on anatomy and volumetric blood flow rate measured with magnetic resonance imaging

Blood flow patterns and local hemodynamic parameters have been widely associated with the onset and progression of atherosclerosis in the carotid artery. Assessment of these parameters can be performed noninvasively using cine phase-contrast (PC) magnetic resonance imaging (MRI). In addition, in the last two decades, computational fluid dynamics (CFD) simulation in three dimensional models derived from anatomic medical images has been employed to investigate the blood flow in the carotid artery. This study developed a workflow of a subject-specific CFD analysis using MRI to enhance estimating hemodynamics of the carotid artery. Time-of-flight (TOF) MRI scans were used to construct three-dimensional computational models. PC-MRI measurements were utilized to impose the boundary condition at the inlet and a 0-dimensional lumped parameter model was employed for the outflow boundary condition. The choice of different viscosity models of blood flow as a source of uncertainty was studied, by means of the axial velocity, wall shear stress, and oscillatory shear index. The sequence of workflow in CFD analysis was optimized for a healthy subject using PC-MRI. Then, a patient with carotid artery stenosis and its hemodynamic parameters were examined. The simulations indicated that the lumped parameter model used at the outlet gives physiologically reasonable values of hemodynamic parameters. Moreover, the dependence of hemodynamics parameters on the viscosity models was observed to vary for different geometries. Other factors, however, may be required for a more accurate CFD analysis, such as the segmentation and smoothness of the geometrical model, mechanical properties of the artery's wall, and the prescribed velocity profile at the inlet.

Relation between wall shear stress and carotid artery wall thickening MRI versus CFD

Wall shear stress (WSS), a parameter associated with endothelial function, is calculated by computational fluid dynamics (CFD) or phase-contrast (PC) MRI measurements. Although CFD is common in WSS (WSSCFD) calculations, PC-MRI-based WSS (WSSMRI) is more favorable in population studies; since it is straightforward and less time consuming. However, it is not clear if WSSMRI and WSSCFD show similar associations with vascular pathology. Our aim was to test the associations between wall thickness (WT) of the carotid arteries and WSSMRI and WSSCFD. The subjects (n=14) with an asymptomatic carotid plaque who underwent MRI scans two times within 4 years of time were selected from the Rotterdam Study. We compared WSSCFD and WSSMRI at baseline and follow-up. Baseline WSSMRI and WSSCFD values were divided into 3 categories representing low, medium and high WSS tertiles. WT of each tertile was compared by a one-way ANOVA test. The WSSMRI and WSSCFD were 0.50±0.13Pa and 0.73±0.25Pa at baseline. Although WSSMRI was underestimated, a significant regression was found between WSSMRI and WSSCFD (r(2)=0.71). No significant difference was found between baseline and follow-up WSS by CFD and MRI-based calculations. The WT at baseline was 1.36±0.16mm and did not change over time. The WT was 1.55±0.21mm in low, 1.33±0.20mm in medium and 1.21±0.21mm in the high WSSMRI tertiles. Similarly, the WT was 1.49±0.21mm in low, 1.33±0.20mm in medium and 1.26±0.21mm in high WSSCFD tertiles. We found that WSSMRI and WSSCFD were inversely related with WT. WSSMRI and WSSCFD patterns were similar although MRI-based calculations underestimated WSS.

MRI-based biomechanical parameters for carotid artery plaque vulnerability assessment

Carotid atherosclerotic plaques are a major cause of ischaemic stroke. The biomechanical environment to which the arterial wall and plaque is subjected to plays an important role in the initiation, progression and rupture of carotid plaques. MRI is frequently used to characterize the morphology of a carotid plaque, but new developments in MRI enable more functional assessment of carotid plaques. In this review, MRI based biomechanical parameters are evaluated on their current status, clinical applicability, and future developments. Blood flow related biomechanical parameters, including endothelial wall shear stress and oscillatory shear index, have been shown to be related to plaque formation. Deriving these parameters directly from MRI flow measurements is feasible and has great potential for future carotid plaque development prediction. Blood pressure induced stresses in a plaque may exceed the tissue strength, potentially leading to plaque rupture. Multi-contrast MRI based stress calculations in combination with tissue strength assessment based on MRI inflammation imaging may provide a plaque stress-strength balance that can be used to assess the plaque rupture risk potential. Direct plaque strain analysis based on dynamic MRI is already able to identify local plaque displacement during the cardiac cycle. However, clinical evidence linking MRI strain to plaque vulnerability is still lacking. MRI based biomechanical parameters may lead to improved assessment of carotid plaque development and rupture risk. However, better MRI systems and faster sequences are required to improve the spatial and temporal resolution, as well as increase the image contrast and signal-to-noise ratio.

Computational fluid dynamics simulations of blood flow regularized by 3D phase contrast MRI

Background

Phase contrast magnetic resonance imaging (PC-MRI) is used clinically for quantitative assessment of cardiovascular flow and function, as it is capable of providing directly-measured 3D velocity maps. Alternatively, vascular flow can be estimated from model-based computation fluid dynamics (CFD) calculations. CFD provides arbitrarily high resolution, but its accuracy hinges on model assumptions, while velocity fields measured with PC-MRI generally do not satisfy the equations of fluid dynamics, provide limited resolution, and suffer from partial volume effects. The purpose of this study is to develop a proof-of-concept numerical procedure for constructing a simulated flow field that is influenced by both direct PC-MRI measurements and a fluid physics model, thereby taking advantage of both the accuracy of PC-MRI and the high spatial resolution of CFD. The use of the proposed approach in regularizing 3D flow fields is evaluated.

Methods

The proposed algorithm incorporates both a Newtonian fluid physics model and a linear PC-MRI signal model. The model equations are solved numerically using a modified CFD algorithm. The numerical solution corresponds to the optimal solution of a generalized Tikhonov regularization, which provides a flow field that satisfies the flow physics equations, while being close enough to the measured PC-MRI velocity profile. The feasibility of the proposed approach is demonstrated on data from the carotid bifurcation of one healthy volunteer, and also from a pulsatile carotid flow phantom.

Results

The proposed solver produces flow fields that are in better agreement with direct PC-MRI measurements than CFD alone, and converges faster, while closely satisfying the fluid dynamics equations. For the implementation that provided the best results, the signal-to-error ratio (with respect to the PC-MRI measurements) in the phantom experiment was 6.56 dB higher than that of conventional CFD; in the in vivo experiment, it was 2.15 dB higher.

Conclusions

The proposed approach allows partial or complete measurements to be incorporated into a modified CFD solver, for improving the accuracy of the resulting flow fields estimates. This can be used for reducing scan time, increasing the spatial resolution, and/or denoising the PC-MRI measurements.

Velocity Measurement in Carotid Artery: Quantitative Comparison of Time-Resolved 3D Phase-Contrast MRI and Image-based Computational Fluid Dynamics

Background:

Understanding hemodynamic environment in vessels is important for realizing the mechanisms leading to vascular pathologies.

Objectives:

Three-dimensional velocity vector field in carotid bifurcation is visualized using TR 3D phase-contrast magnetic resonance imaging (TR 3D PC MRI) and computational fluid dynamics (CFD). This study aimed to present a qualitative and quantitative comparison of the velocity vector field obtained by each technique.

Subjects and Methods:

MR imaging was performed on a 30-year old male normal subject. TR 3D PC MRI was performed on a 3 T scanner to measure velocity in carotid bifurcation. 3D anatomical model for CFD was created using images obtained from time-of-flight MR angiography. Velocity vector field in carotid bifurcation was predicted using CFD and PC MRI techniques. A statistical analysis was performed to assess the agreement between the two methods.

Results:

Although the main flow patterns were the same for the both techniques, CFD showed a greater resolution in mapping the secondary and circulating flows. Overall root mean square (RMS) errors for all the corresponding data points in PC MRI and CFD were 14.27% in peak systole and 12.91% in end diastole relative to maximum velocity measured at each cardiac phase. Bland-Altman plots showed a very good agreement between the two techniques. However, this study was not aimed to validate any of methods, instead, the consistency was assessed to accentuate the similarities and differences between Time-resolved PC MRI and CFD.

Conclusion:

Both techniques provided quantitatively consistent results of in vivo velocity vector fields in right internal carotid artery (RCA). PC MRI represented a good estimation of main flow patterns inside the vasculature, which seems to be acceptable for clinical use. However, limitations of each technique should be considered while interpreting results.

A new methodology for accurate 3-dimensional coronary artery reconstruction using routine intravascular ultrasound and angiographic data: implications for widespread assessment of endothelial shear stress in humans

AIMS

To develop and validate a new methodology that allows accurate 3-dimensional (3-D) coronary artery reconstruction using standard, simple angiographic and intravascular ultrasound (IVUS) data acquired during routine catheterisation enabling reliable assessment of the endothelial shear stress (ESS) distribution.

METHODS AND RESULTS

Twenty-two patients (22 arteries: 7 LAD; 7 LCx; 8 RCA) who underwent angiography and IVUS examination were included. The acquired data were used for 3-D reconstruction using a conventional method and a new methodology that utilised the luminal 3-D centreline to place the detected IVUS borders and anatomical landmarks to estimate their orientation. The local ESS distribution was assessed by computational fluid dynamics. In corresponding consecutive 3 mm segments, lumen, plaque and ESS measurements in the 3-D models derived by the centreline approach were highly correlated to those derived from the conventional method (r>0.98 for all). The centreline methodology had a 99.5% diagnostic accuracy for identifying segments exposed to low ESS and provided similar estimations to the conventional method for the association between the change in plaque burden and ESS (centreline method: slope= -1.65%/Pa, p=0.078; conventional method: slope= -1.64%/Pa, p=0.084; p =0.69 for difference between the two methodologies).

CONCLUSIONS

The centreline methodology provides geometrically correct models and permits reliable ESS computation. The ability to utilise data acquired during routine coronary angiography and IVUS examination will facilitate clinical investigation of the role of local ESS patterns in the natural history of coronary atherosclerosis.

Endothelial shear stress and blood viscosity in peripheral arterial disease

This review examines the emerging role of endothelial shear stress (ESS) and blood viscosity on the initiation and progression of atherosclerosis in peripheral arterial disease. Among the variables determining ESS, blood viscosity has to date been the most overlooked by clinical researchers. Blood viscosity is a laboratory assessment that is minimally invasive and modifiable using pharmacologic therapy as well as by hemodilution. Monitoring and controlling blood viscosity not only modulates ESS, but also reduces peripheral vascular resistance and increases blood flow to the lower extremities.

Methodology for implementing patient-specific spatial boundary condition during a cardiac cycle from phase-contrast MRI for hemodynamic assessment

Pulmonary insufficiency (PI) can render the right ventricle dysfunctional due to volume overloading and hypertrophy. The treatment requires a pulmonary valve replacement surgery. However, determining the right time for the valve replacement surgery has been difficult with currently employed clinical techniques such as, echocardiography and cardiac MRI. Therefore, there is a clinical need to improve the diagnosis of PI by using patient-specific (PS) hemodynamic endpoints. While there are many reported studies on the use of PS geometry with time varying boundary conditions (BC) for hemodynamic computation, few use spatially varying PS velocity measurement at each time point of the cardiac cycle. In other words, the gap is that, there are limited number of studies which implement both spatially- and time-varying physiologic BC directly with patient specific geometry. The uniqueness of this research is in the incorporation of spatially varying PS velocity data obtained from phase-contrast MRI (PC-MRI) at each time point of the cardiac cycle with PS geometry obtained from angiographic MRI. This methodology was applied to model the complex developing flow in human pulmonary artery (PA) distal to pulmonary valve, in a normal and a subject with PI. To validate the methodology, the flow rates from the proposed method were compared with those obtained using QFlow software, which is a standard of care clinical technique. For the normal subject, the computed time average flow rates from this study differed from those obtained using the standard of care technique (QFlow) by 0.8 ml/s (0.9%) at the main PA, by 2 ml/s (3.4%) at the left PA and by 1.4 ml/s (3.8%) at the right PA. For the subject with PI, the difference was 7 ml/s (12.4%) at the main PA, 5.5 ml/s (22.6%) at the left PA and 4.9 ml/s (18.0%) at the right PA. The higher percentage differences for the subject with PI, was the result of overall lower values of the forward mean flow rate caused by excessive flow regurgitation. This methodology is expected to provide improved computational results when PS geometry from angiographic MRI is used in conjunction with PS PC-MRI data for solving the flow field.

Wall shear stress calculations based on 3D cine phase contrast MRI and computational fluid dynamics: a comparison study in healthy carotid arteries

Wall shear stress (WSS) is involved in many pathophysiological processes related to cardiovascular diseases, and knowledge of WSS may provide vital information on disease progression. WSS is generally quantified with computational fluid dynamics (CFD), but can also be calculated using phase contrast MRI (PC-MRI) measurements. In this study, our objectives were to calculate WSS on the entire luminal surface of human carotid arteries using PC-MRI velocities (WSSMRI ) and to compare it with WSS based on CFD (WSSCFD ). Six healthy volunteers were scanned with a 3 T MRI scanner. WSSCFD was calculated using a generalized flow waveform with a mean flow equal to the mean measured flow. WSSMRI was calculated by estimating the velocity gradient along the inward normal of each mesh node on the luminal surface. Furthermore, WSS was calculated for a down-sampled CFD velocity field mimicking the MRI resolution (WSSCFDlowres ). To ensure minimum temporal variation, WSS was analyzed only at diastole. The patterns of WSSCFD and WSSMRI were compared by quantifying the overlap between low, medium and high WSS tertiles. Finally, WSS directions were compared by calculating the angles between the WSSCFD and WSSMRI vectors. WSSMRI magnitude was found to be lower than WSSCFD (0.62 ± 0.18 Pa versus 0.88 ± 0.30 Pa, p < 0.01) but closer to WSSCFDlowres (0.56 ± 0.18 Pa, p < 0.01). WSSMRI patterns matched well with those of WSSCFD. The overlap area was 68.7 ± 4.4% in low and 69.0 ± 8.9% in high WSS tertiles. The angles between WSSMRI and WSSCFD vectors were small in the high WSS tertiles (20.3 ± 8.2°), but larger in the low WSS tertiles (65.6 ± 17.4°). In conclusion, although WSSMRI magnitude was lower than WSSCFD , the spatial WSS patterns at diastole, which are more relevant to the vascular biology, were similar. PC-MRI-based WSS has potential to be used in the clinic to indicate regions of low and high WSS and the direction of WSS, especially in regions of high WSS.

Regional variation of wall shear stress in ascending thoracic aortic aneurysms

The development of an ascending thoracic aortic aneurysm is likely caused by excessive hemodynamic loads exerted on the aneurysmal wall. Computational fluid-dynamic analyses were performed on patient-specific ascending thoracic aortic aneurysms obtained from patients with either bicuspid aortic valve or tricuspid aortic valve to evaluate hemodynamic and wall shear parameters, imparting aneurysm enlargement. Results showed an accelerated flow along the outer aortic wall with helical flow in the aneurysm center for bicuspid aortic valve ascending thoracic aortic aneurysms. In a different way, tricuspid aortic valve ascending thoracic aortic aneurysms exhibited normal systolic flow without substantial secondary pattern. Analysis of wall shear parameters evinced a high and locally varying wall shear stress on the outer aortic wall and high temporal oscillations in wall shear stress (oscillatory shear index) on either left or right side of aneurysmal aorta. These findings may explain the asymmetric dilatation typically observed in ascending thoracic aortic aneurysms. Simulations of a hypertensive scenario revealed an increase in wall shear stress upon 44% compared to normal systemic pressure models. Computational fluid-dynamics–based analysis may allow identification of wall shear parameters portending aneurysm dilatation and hence guide preventative intervention.

In Vitro Validation of Patient-Specific Hemodynamic Simulations in Coronary Aneurysms Caused by Kawasaki Disease

To perform experimental validation of computational fluid dynamics (CFD) applied to patient specific coronary aneurysm anatomy of Kawasaki disease. We quantified hemodynamics in a patient-specific coronary artery aneurysm physical phantom under physiologic rest and exercise flow conditions. Using phase contrast MRI (PCMRI), we acquired 3-component flow velocity at two slice locations in the aneurysms. We then performed numerical simulations with the same geometry and inflow conditions, and performed qualitative and quantitative comparisons of velocities between experimental measurements and simulation results. We observed excellent qualitative agreement in flow pattern features. The quantitative spatially and temporally varying differences in velocity between PCMRI and CFD were proportional to the flow velocity. As a result, the percent discrepancy between simulation and experiment was relatively constant regardless of flow velocity variations. Through 1D and 2D quantitative comparisons, we found a 5-17% difference between measured and simulated velocities. Additional analysis assessed wall shear stress differences between deformable and rigid wall simulations. This study demonstrated that CFD produced good qualitative and quantitative predictions of velocities in a realistic coronary aneurysm anatomy under physiological flow conditions. The results provide insights on factors that may influence the level of agreement, and a set of in vitro experimental data that can be used by others to compare against CFD simulation results. The findings of this study increase confidence in the use of CFD for investigating hemodynamics in the specialized anatomy of coronary aneurysms. This provides a basis for future hemodynamics studies in patient-specific models of Kawasaki disease.

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

PURPOSE

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.

MATERIALS AND METHODS

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).

RESULTS

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.

CONCLUSION

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.