Assessment of turbulent flow effects on the vessel wall using four-dimensional flow MRI

A clinician's guide to understanding aortic 4D flow MRI

Four-dimensional flow magnetic resonance imaging is an emerging technique which may play a role in diagnosis and risk-stratification of aortic disease. Some knowledge of flow dynamics and related parameters is necessary to understand and apply this technique in clinical workflows. The purpose of the current review is to provide a guide for clinicians to the basics of flow imaging, frequently used flow-related parameters, and their relevance in the context of aortic disease.Clinical relevance statement Understanding normal and abnormal aortic flow could improve clinical care in patients with aortic disease.

In-vitro and In-Vivo Assessment of 4D Flow MRI Reynolds Stress Mapping for Pulsatile Blood Flow

Imaging hemodynamics play an important role in the diagnosis of abnormal blood flow due to vascular and valvular diseases as well as in monitoring the recovery of normal blood flow after surgical or interventional treatment. Recently, characterization of turbulent blood flow using 4D flow magnetic resonance imaging (MRI) has been demonstrated by utilizing the changes in signal magnitude depending on intravoxel spin distribution. The imaging sequence was extended with a six-directional icosahedral (ICOSA6) flow-encoding to characterize all elements of the Reynolds stress tensor (RST) in turbulent blood flow. In the present study, we aimed to demonstrate the feasibility of full RST analysis using ICOSA6 4D flow MRI under physiological conditions. First, the turbulence analysis was performed through in vitro experiments with a physiological pulsatile flow condition. Second, a total of 12 normal subjects and one patient with severe aortic stenosis were analyzed using the same sequence. The in-vitro study showed that total turbulent kinetic energy (TKE) was less affected by the signal-to-noise ratio (SNR), however, maximum principal turbulence shear stress (MPTSS) and total turbulence production (TP) had a noise-induced bias. Smaller degree of the bias was observed for TP compared to MPTSS. In-vivo study showed that the subject-variability on turbulence quantification was relatively low for the consistent scan protocol. The in vivo demonstration of the stenosis patient showed that the turbulence analysis could clearly distinguish the difference in all turbulence parameters as they were at least an order of magnitude larger than those from the normal subjects.

Data Assimilation by Stochastic Ensemble Kalman Filtering to Enhance Turbulent Cardiovascular Flow Data From Under-Resolved Observations

We propose a data assimilation methodology that can be used to enhance the spatial and temporal resolution of voxel-based data as it may be obtained from biomedical imaging modalities. It can be used to improve the assessment of turbulent blood flow in large vessels by combining observed data with a computational fluid dynamics solver. The methodology is based on a Stochastic Ensemble Kalman Filter (SEnKF) approach and geared toward pulsatile and turbulent flow configurations. We describe the observed flow fields by a mean value and its covariance. These flow fields are combined with forecasts obtained from a direct numerical simulation of the flow field. The method is validated against canonical pulsatile and turbulent flows. Finally, it is applied to a clinically relevant configuration, namely the flow downstream of a bioprosthetic valve in an aorta phantom. It is demonstrated how the 4D flow field obtained from experimental observations can be enhanced by the data assimilation algorithm. Results show that the presented method is promising for future use with in vivo data from 4D Flow Magnetic Resonance Imaging (4D Flow MRI). 4D Flow MRI returns spatially and temporally averaged flow fields that are limited by the spatial and the temporal resolution of the tool. These averaged flow fields and the associated uncertainty might be used as observation data in the context of the proposed methodology.

Comparison of Four-Dimensional Flow Magnetic Resonance Imaging and Particle Image Velocimetry to Quantify Velocity and Turbulence Parameters

Although recent advances of four-dimensional (4D) flow magnetic resonance imaging (MRI) has introduced a new way to measure Reynolds stress tensor (RST) in turbulent flows, its measurement accuracy and possible bias have remained to be revealed. The purpose of this study was to compare the turbulent flow measurement of 4D flow MRI and particle image velocimetry (PIV) in terms of velocity and turbulence quantification. Two difference flow rates of 10 and 20 L/min through a 50% stenosis were measured with both PIV and 4D flow MRI. Not only velocity through the stenosis but also the turbulence parameters such as turbulence kinetic energy and turbulence production were quantitatively compared. Results shows that 4D flow MRI velocity measurement well agreed with the that of PIV, showing the linear regression slopes of two methods are 0.94 and 0.89, respectively. Although turbulence mapping of 4D flow MRI was qualitatively agreed with that of PIV, the quantitative comparison shows that the 4D flow MRI overestimates RST showing the linear regression slopes of 1.44 and 1.66, respectively. In this study, we demonstrate that the 4D flow MRI visualize and quantify not only flow velocity and also turbulence tensor. However, further optimization of 4D flow MRI for better accuracy might be remained.

Impact of turbulence-induced asymmetric propagators on the accuracy of phase-contrast velocimetry

Phase-contrast magnetic resonance velocimetry (PC-MRI) has been widely used to investigate flow properties in numerous systems. In a horizontal cylindrical pipe (3 mm diameter), we investigated the accuracy of PC-MRI as the flow transitioned from laminar to turbulent flow (Reynolds number 352-2708). We focus primarily on velocimetry errors introduced by skewed intra-voxel displacement distributions, a consequence of PC-MRI theory assuming symmetric distributions. We demonstrated how rapid fluctuations in the velocity field, can produce broad asymmetric intravoxel displacement distributions near the wall. Depending on the shape of the distribution, this resulted in PC-MRI measurements under-estimating (positive skewness) or over-estimating (negative skewness) the true mean intravoxel velocity, which could have particular importance to clinical wall shear stress measurements. The magnitude of these velocity errors was shown to increase with the variance and decrease with the kurtosis of the intravoxel displacement distribution. These experimental results confirm our previous theoretical analysis, which gives a relationship for PC-MRI velocimetry errors, as a function of the higher moments of the intravoxel displacement distribution (skewness, variance, and kurtosis) and the experimental parameters q and Δ. This suggests that PC-MRI errors in such unsteady/turbulent flow conditions can potentially be reduced by employing lower q values or shorter observation times Δ.

Exploring the Relationships Between Hemodynamic Stresses in the Carotid Arteries

Background: Atherosclerosis manifests as a focal disease, often affecting areas with complex hemodynamics such as the carotid bifurcation. The magnitude and regularity of the hemodynamic shear stresses acting on the vessel wall are thought to generate risk patterns unique to each patient and play a role in the pathogenesis of atherosclerosis. The involvement of different expressions of shear stress in the pathogenesis of carotid atherosclerosis highlights the need to characterize and compare the differential impact of the various expressions of shear stress in the atherosclerotic carotid bifurcation. Therefore, the aim of this study is to characterize and compare hemodynamic wall shear stresses (WSS) in the carotid arteries of subjects with asymptomatic atherosclerotic plaques. Shear stresses were also compared against vessel diameter and bifurcation angle to examine the relationships with the geometry of the carotid bifurcation. Methods: 4D Flow MRI and contrast-enhanced MRA data were acquired for 245 subjects with atherosclerotic plaques of at least 2.7 mm in conjunction with the Swedish CArdioPulmonary bioImage Study (SCAPIS). Following automatic segmentation and geometric analysis, time-resolved WSS and near-wall turbulent kinetic energy (nwTKE) were derived from the 4D Flow data. Whole-cycle parameters including time-averaged WSS and nwTKE, and the oscillatory shear index (OSI) were calculated. Pairwise Spearman rank-correlation analyses were used to investigate relationships among the hemodynamic as well as geometric parameters. Results: One hundred and seventy nine subjects were successfully segmented using automated tools and subsequently geometric and hemodynamic analyses were performed. Temporally resolved WSS and nwTKE were strongly correlated, ρ = 0.64. Cycle-averaged WSS and nwTKE were moderately correlated, ρ = 0.57. Cycle-average nwTKE was weakly correlated to OSI (ρ = -0.273), revealing that nwTKE provides information about disturbed flow on the vessel wall that OSI does not. In this cohort, there was large inter-individual variation for both WSS and nwTKE. Both WSS and nwTKE varied most within the external carotid artery. WSS, nwTKE, and OSI were weakly correlated to vessel diameter and bifurcation angle. Conclusion: The turbulent and mean component of WSS were examined together in vivo for the first time, and a strong correlation was found between them. nwTKE presents the opportunity to quantify turbulent wall stresses in vivo and gain insight into the effects of disturbed flow on the vessel wall. Neither vessel diameter nor bifurcation angle were found to be strongly correlated to the turbulent or mean component of WSS in this cohort.

Model Verification and Error Sensitivity of Turbulence-Related Tensor Characteristics in Pulsatile Blood Flow Simulations

Model verification, validation, and uncertainty quantification are essential procedures to estimate errors within cardiovascular flow modeling, where acceptable confidence levels are needed for clinical reliability. While more turbulent-like studies are frequently observed within the biofluid community, practical modeling guidelines are scarce. Verification procedures determine the agreement between the conceptual model and its numerical solution by comparing for example, discretization and phase-averaging-related errors of specific output parameters. This computational fluid dynamics (CFD) study presents a comprehensive and practical verification approach for pulsatile turbulent-like blood flow predictions by considering the amplitude and shape of the turbulence-related tensor field using anisotropic invariant mapping. These procedures were demonstrated by investigating the Reynolds stress tensor characteristics in a patient-specific aortic coarctation model, focusing on modeling-related errors associated with the spatiotemporal resolution and phase-averaging sampling size. Findings in this work suggest that attention should also be put on reducing phase-averaging related errors, as these could easily outweigh the errors associated with the spatiotemporal resolution when including too few cardiac cycles. Also, substantially more cycles are likely needed than typically reported for these flow regimes to sufficiently converge the phase-instant tensor characteristics. Here, higher degrees of active fluctuating directions, especially of lower amplitudes, appeared to be the most sensitive turbulence characteristics.

On the limitations of echo planar 4D flow MRI

PURPOSE

To compare EPI and GRE readout in high-flow velocity regimes and evaluate their impact on measurement accuracy in silico and in vitro.

THEORY AND METHODS

Phase-contrast sequences for EPI and GRE were simulated using CFD velocity data to assess displacement artifacts as well as effective spatial resolution. In silico findings were validated experimentally using a steady flow phantom.

RESULTS

For EPI factor 5 and simulated stenotic flow with peak velocity of 2.2 m s - 1 , displacement artifacts resulted in misregistration of 7.3 mm at echo time and the effective resolution was locally reduced by factors 5 and 8 compared to GRE for flow along phase and frequency encoding directions, respectively. In vitro, a maximum velocity difference between EPI factor 5 and GRE of 0.97 m s - 1 was found.

CONCLUSIONS

Four-dimensional flow MRI using EPI readout results not only in considerable velocity misregistration but also in spatially varying degradation of resolution. The proposed work indicates that EPI is inferior to standard GRE for 4D flow MRI.

Experimental Insight into the Hemodynamics and Perfusion of Radiological Contrast in Patent and Non-patent Aortic Dissection Models

PURPOSE

In a curved vessel such as the aortic arch, the velocity profile closer to the aortic root is normally skewed towards the inner curvature wall, while further downstream along the curve, the velocity profile becomes skewed towards the outer wall. In an aortic dissection (AD) disease, blood velocities in the true lumen (TL) and false lumen (FL) are hypothesized to depend on the proximity of the entry tear to the root of aortic arch. Faster velocity in the FL can lead to higher hemodynamic loading, and pose tearing risk. Furthermore, the luminal velocities control the perfusion rate of radiological contrast media during diagnostic imaging. The objective in this study is to investigate the effect of AD disease morphology and configuration on the blood velocity field in the TL and FL, and on the relative perfusion of radiological enhancement agents through the dissection.

METHODS

Eight in vitro models were studied, including patent and non-patent FL configurations. Particle image velocimetry (PIV) was used to quantify the AD velocity field, while laser-induced fluorescence (LIF) was implemented to visualize dynamical flow phenomena and to quantify the perfusion of injected dye, in mimicry of contrast-enhanced computed tomography (CT).

RESULTS

The location of the proximal entry tear along the aortic arch in a patent FL had a dramatic impact on whether the blood velocity was higher in the TL or FL. The luminal velocities were dependent on the entry/reentry tear size combination, with the smaller tear (whether distal or proximal) setting the upper limit on the maximal flow velocity in the FL. Upon merging near the distal reentry tear, the TL/FL velocity differential gave rise to the roll up and shedding of shear layer vortices that convected downstream in close proximity to the wall of the non-dissected aorta. In a non-patent FL, the flow velocity was practically null with all the blood passing through the TL. LIF imaging showed much slower perfusion of contrast dye in the FL compared to the TL. In a patent FL, however, dye had a comparable perfusion rate appearing around the same time as in the TL.

CONCLUSIONS

Blood velocities in the TL and FL were highly sensitive to the exact dissection configuration. Geometric case A1R, which had its proximal entry tear located further downstream along the aortic arch, and had its entry and reentry tears sufficiently sized, exhibited the highest FL flow velocity among the tested models, and it was also higher than in the TL, which suggest that this configuration had elevated hemodynamic loading and risk for tearing. In contrast-enhanced diagnostic imaging, a time-delayed acquisition protocol is recommended to improve the detection of suspected cases with a non-patent FL.

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

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

Age-Related Vascular Changes Affect Turbulence in Aortic Blood Flow

Turbulent blood flow is implicated in the pathogenesis of several aortic diseases but the extent and degree of turbulent blood flow in the normal aorta is unknown. We aimed to quantify the extent and degree of turbulece in the normal aorta and to assess whether age impacts the degree of turbulence. 22 young normal males (23.7 ± 3.0 y.o.) and 20 old normal males (70.9 ± 3.5 y.o.) were examined using four dimensional flow magnetic resonance imaging (4D Flow MRI) to quantify the turbulent kinetic energy (TKE), a measure of the intensity of turbulence, in the aorta. All healthy subjects developed turbulent flow in the aorta, with total TKE of 3–19 mJ. The overall degree of turbulence in the entire aorta was similar between the groups, although the old subjects had about 73% more total TKE in the ascending aorta compared to the young subjects (young = 3.7 ± 1.8 mJ, old = 6.4 ± 2.4 mJ, p < 0.001). This increase in ascending aorta TKE in old subjects was associated with age-related dilation of the ascending aorta which increases the volume available for turbulence development. Conversely, age-related dilation of the descending and abdominal aorta decreased the average flow velocity and suppressed the development of turbulence. In conclusion, turbulent blood flow develops in the aorta of normal subjects and is impacted by age-related geometric changes. Non-invasive assessment enables the determination of normal levels of turbulent flow in the aorta which is a prerequisite for understanding the role of turbulence in the pathophysiology of cardiovascular disease.

Estimating the irreversible pressure drop across a stenosis by quantifying turbulence production using 4D Flow MRI

The pressure drop across a stenotic vessel is an important parameter in medicine, providing a commonly used and intuitive metric for evaluating the severity of the stenosis. However, non-invasive estimation of the pressure drop under pathological conditions has remained difficult. This study demonstrates a novel method to quantify the irreversible pressure drop across a stenosis using 4D Flow MRI by calculating the total turbulence production of the flow. Simulation MRI acquisitions showed that the energy lost to turbulence production can be accurately quantified with 4D Flow MRI within a range of practical spatial resolutions (1-3 mm; regression slope = 0.91, R2 = 0.96). The quantification of the turbulence production was not substantially influenced by the signal-to-noise ratio (SNR), resulting in less than 2% mean bias at SNR > 10. Pressure drop estimation based on turbulence production robustly predicted the irreversible pressure drop, regardless of the stenosis severity and post-stenosis dilatation (regression slope = 0.956, R2 = 0.96). In vitro validation of the technique in a 75% stenosis channel confirmed that pressure drop prediction based on the turbulence production agreed with the measured pressure drop (regression slope = 1.15, R2 = 0.999, Bland-Altman agreement = 0.75 ± 3.93 mmHg).

Assessment of turbulent viscous stress using ICOSA 4D Flow MRI for prediction of hemodynamic blood damage

Flow-induced blood damage plays an important role in determining the hemodynamic impact of abnormal blood flow, but quantifying of these effects, which are dominated by shear stresses in highly fluctuating turbulent flow, has not been feasible. This study evaluated the novel application of turbulence tensor measurements using simulated 4D Flow MRI data with six-directional velocity encoding for assessing hemodynamic stresses and corresponding blood damage index (BDI) in stenotic turbulent blood flow. The results showed that 4D Flow MRI underestimates the maximum principal shear stress of laminar viscous stress (PLVS), and overestimates the maximum principal shear stress of Reynolds stress (PRSS) with increasing voxel size. PLVS and PRSS were also overestimated by about 1.2 and 4.6 times at medium signal to noise ratio (SNR) = 20. In contrast, the square sum of the turbulent viscous shear stress (TVSS), which is used for blood damage index (BDI) estimation, was not severely affected by SNR and voxel size. The square sum of TVSS and the BDI at SNR >20 were underestimated by less than 1% and 10%, respectively. In conclusion, this study demonstrated the feasibility of 4D Flow MRI based quantification of TVSS and BDI which are closely linked to blood damage.