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%).

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.

On the limitations of partial Fourier acquisition in phase-contrast MRI of turbulent kinetic energy.

PURPOSE: To investigate limitations of partial Fourier acquisition in phase-contrast MRI of turbulent kinetic energy (TKE). METHODS: To assess the validity of partial Fourier reconstruction of TKE and phase images, computational fluid dynamics data of mean and turbulent velocities in a stenotic U-bend phantom was used. Partial Fourier acquisition with 75% k-space coverage was simulated and TKE data were reconstructed using zero-filling, homodyne reconstruction, and the method of projections onto convex sets (POCS). Results were compared to data from fully sampled k-space and 75% symmetric sampling. In addition, compressed sensing (CS) reconstruction was compared for a standard variable density sampling pattern and a variable density sampling pattern combined with 75% partial Fourier. For illustration purposes, in vivo examples of velocity magnitude and TKE maps of aortic flow reconstructed with the different methods are provided. RESULTS: In accordance with theory, partial Fourier reconstruction of TKE maps from phase-contrast data results in artifacts relative to fully sampled data. It is demonstrated that neither homodyne reconstruction nor POCS can improve reconstruction of TKE data with respect to zero-filling reconstruction when compared to ground-truth (RMS error: 4.70%, 4.34%, and 2.45% for homodyne, POCS, and zero-filling reconstruction of in vivo data, respectively). CS reconstruction from data acquired with partial Fourier did not recover the resolution loss incurred by partial Fourier sampling. CONCLUSION: Partial Fourier reconstruction of TKE maps from phase-contrast data does not yield a benefit over zero-filling reconstruction. In consequence, symmetric sampling is preferred over partial Fourier acquisition for a given number of phase-encodes in phase-contrast MRI.

Multipoint 5D flow cardiovascular magnetic resonance - accelerated cardiac- and respiratory-motion resolved mapping of mean and turbulent velocities.

BACKGROUND: Volumetric quantification of mean and fluctuating velocity components of transient and turbulent flows promises a comprehensive characterization of valvular and aortic flow characteristics. Data acquisition using standard navigator-gated 4D Flow cardiovascular magnetic resonance (CMR) is time-consuming and actual scan times depend on the breathing pattern of the subject, limiting the applicability of the method in a clinical setting. We sought to develop a 5D Flow CMR framework which combines undersampled data acquisition including multipoint velocity encoding with low-rank image reconstruction to provide cardiac- and respiratory-motion resolved assessment of velocity maps and turbulent kinetic energy in fixed scan times. METHODS: Data acquisition and data-driven motion state detection was performed using an undersampled Cartesian tiny Golden angle approach. Locally low-rank (LLR) reconstruction was implemented to exploit correlations among heart phases and respiratory motion states. To ensure accurate quantification of mean and turbulent velocities, a multipoint encoding scheme with two velocity encodings per direction was incorporated. Velocity-vector fields and turbulent kinetic energy (TKE) were obtained using a Bayesian approach maximizing the posterior probability given the measured data. The scan time of 5D Flow CMR was set to 4 min. 5D Flow CMR with acceleration factors of 19 .0 ± 0.21 (mean ± std) and velocity encodings (VENC) of 0.5 m/s and 1.5 m/s per axis was compared to navigator-gated 2x SENSE accelerated 4D Flow CMR with VENC = 1.5 m/s in 9 subjects. Peak velocities and peak flow were compared and magnitude images, velocity and TKE maps were assessed. RESULTS: While net scan time of 5D Flow CMR was 4 min independent of individual breathing patterns, the scan times of the standard 4D Flow CMR protocol varied depending on the actual navigator gating efficiency and were 17.8 ± 3.9 min on average. Velocity vector fields derived from 5D Flow CMR in the end-expiratory state agreed well with data obtained from the navigated 4D protocol (normalized root-mean-square error 8.9 ± 2.1%). On average, peak velocities assessed with 5D Flow CMR were higher than for the 4D protocol (3.1 ± 4.4%). CONCLUSIONS: Respiratory-motion resolved multipoint 5D Flow CMR allows mapping of mean and turbulent velocities in the aorta in 4 min.

5D Flow Tensor MRI to Efficiently Map Reynolds Stresses of Aortic Blood Flow In-Vivo.

Diseased heart valves perturb normal blood flow with a range of hemodynamic and pathologic consequences. In order to better stratify patients with heart valve disease, a comprehensive characterization of blood flow including turbulent contributions is desired. In this work we present a framework to efficiently quantify velocities and Reynolds stresses in the aorta in-vivo. Using a highly undersampled 5D Flow MRI acquisition scheme with locally low-rank image reconstruction, multipoint flow tensor encoding in short and predictable scan times becomes feasible (here, 10 minutes), enabling incorporation of the protocol into clinical workflows. Based on computer simulations, a 19-point 5D Flow Tensor MRI encoding approach is proposed. It is demonstrated that, for in-vivo resolution and signal-to-noise ratios, sufficient accuracy and precision of velocity and turbulent shear stress quantification is achievable. In-vivo proof of concept is demonstrated on patients with a bio-prosthetic heart valve and healthy controls. Results demonstrate that aortic turbulent shear stresses and turbulent kinetic energy are elevated in the patients compared to the healthy subjects. Based on these data, it is concluded that 5D Flow Tensor MRI holds promise to provide comprehensive flow assessment in patients with heart valve diseases.