Robust 4D flow denoising using divergence-free wavelet transform

Implicit neural representations for unsupervised super-resolution and denoising of 4D flow MRI

BACKGROUND AND OBJECTIVE

4D flow magnetic resonance imaging provides time-resolved blood flow velocity measurements, but suffers from limitations in spatio-temporal resolution and noise. In this study, we investigated the use of sinusoidal representation networks (SIRENs) to improve denoising and super-resolution of velocity fields measured by 4D flow MRI in the thoracic aorta.

METHODS

Efficient training of SIRENs in 4D was achieved by sampling voxel coordinates and enforcing the no-slip condition at the vessel wall. A set of synthetic measurements were generated from computational fluid dynamics simulations, reproducing different noise levels. The influence of SIREN architecture was systematically investigated, and the performance of our method was compared to existing approaches for 4D flow denoising and super-resolution.

RESULTS

Compared to existing techniques, a SIREN with 300 neurons per layer and 20 layers achieved lower errors (up to 50% lower vector normalized root mean square error, 42% lower magnitude normalized root mean square error, and 15% lower direction error) in velocity and wall shear stress fields. Applied to real 4D flow velocity measurements in a patient-specific aortic aneurysm, our method produced denoised and super-resolved velocity fields while maintaining accurate macroscopic flow measurements.

CONCLUSIONS

This study demonstrates the feasibility of using SIRENs for complex blood flow velocity representation from clinical 4D flow, with quick execution and straightforward implementation.

Physics-informed compressed sensing for PC-MRI: an inverse Navier-Stokes problem

We formulate a physics-informed compressed sensing (PICS) method for the reconstruction of velocity fields from noisy and sparse phase-contrast magnetic resonance signals. The method solves an inverse Navier-Stokes boundary value problem, which permits us to jointly reconstruct and segment the velocity field, and at the same time infer hidden quantities such as the hydrodynamic pressure and the wall shear stress. Using a Bayesian framework, we regularize the problem by introducing a priori information about the unknown parameters in the form of Gaussian random fields. This prior information is updated using the Navier-Stokes problem, an energy-based segmentation functional, and by requiring that the reconstruction is consistent with the k-space signals. We create an algorithm that solves this inverse problem, and test it for noisy and sparse k-space signals of the flow through a converging nozzle. We find that the method is capable of reconstructing and segmenting the velocity fields from sparsely-sampled (15% k-space coverage), low (~10) signal-to-noise ratio (SNR) signals, and that the reconstructed velocity field compares well with that derived from fully-sampled (100% k-space coverage) high (>40) SNR signals of the same flow.

Wall Shear Stress Estimation for 4D Flow MRI Using Navier-Stokes Equation Correction

This study introduces a novel wall shear stress (WSS) estimation method for 4D flow MRI. The method improves the WSS accuracy by using the reconstructed pressure gradient and the flow-physics constraints to correct velocity gradient estimation. The method was tested on synthetic 4D flow data of analytical Womersley flow and flow in cerebral aneurysms and applied to in vivo 4D flow data acquired in cerebral aneurysms and aortas. The proposed method's performance was compared to the state-of-the-art method based on smooth-spline fitting of velocity profile and the WSS calculated from uncorrected velocity gradient. The proposed method improved the WSS accuracy by as much as 100% for the Womersley flow and reduced the underestimation of mean WSS by 39 to 50% for the synthetic aneurysmal flow. The predicted mean WSS from the in vivo aneurysmal data using the proposed method was 31 to 50% higher than the other methods. The predicted aortic WSS using the proposed method was 3 to 6 times higher than the other methods and was consistent with previous CFD studies and the results from recently developed methods that take into account the limited spatial resolution of 4D flow MRI. The proposed method improves the accuracy of WSS estimation from 4D flow MRI, which can help predict blood vessel remodeling and progression of cardiovascular diseases.

SRflow: Deep learning based super-resolution of 4D-flow MRI data

Exploiting 4D-flow magnetic resonance imaging (MRI) data to quantify hemodynamics requires an adequate spatio-temporal vector field resolution at a low noise level. To address this challenge, we provide a learned solution to super-resolve in vivo 4D-flow MRI data at a post-processing level. We propose a deep convolutional neural network (CNN) that learns the inter-scale relationship of the velocity vector map and leverages an efficient residual learning scheme to make it computationally feasible. A novel, direction-sensitive, and robust loss function is crucial to learning vector-field data. We present a detailed comparative study between the proposed super-resolution and the conventional cubic B-spline based vector-field super-resolution. Our method improves the peak-velocity to noise ratio of the flow field by 10 and 30% for in vivo cardiovascular and cerebrovascular data, respectively, for 4 × super-resolution over the state-of-the-art cubic B-spline. Significantly, our method offers 10x faster inference over the cubic B-spline. The proposed approach for super-resolution of 4D-flow data would potentially improve the subsequent calculation of hemodynamic quantities.

Assessment of 4D flow MRI's quality by verifying its Navier-Stokes compatibility

4D Flow Magnetic Resonance Imaging (MRI) is the state-of-the-art technique to comprehensively measure the complex spatio-temporal and multidirectional patterns of blood flow. However, it is subject to artifacts such as noise and aliasing, which due to the 3D and dynamic structure is difficult to detect in clinical practice. In this work, a new mathematical and computational model to determine the quality of 4D Flow MRI is presented. The model is derived by assuming the true velocity satisfies the incompressible Navier-Stokes equations and that can be decomposed by the measurements u→meas plus an extra field w→ . Therefore, a non-linear problem with w→ as unknown arises, which serves as a measure of data quality. A stabilized finite element formulation tailored to this problem is proposed and analyzed. Then, extensive numerical examples-using synthetic 4D Flow MRI data as well as real measurements on experimental phantom and subjects-illustrate the ability to use w→ for assessing the quality of 4D Flow MRI measurements over space and time.

Virtual injections using 4D flow MRI with displacement corrections and constrained probabilistic streamlines

PURPOSE

Streamlines from 4D-flow MRI have been used clinically for intracranial blood-flow tracking. However, deterministic and stochastic errors degrade streamline quality. The purpose of this study is to integrate displacement corrections, probabilistic streamlines, and novel fluid constraints to improve selective blood-flow tracking and emulate "virtual bolus injections."

METHODS

Both displacement artifacts (deterministic) and velocity noise (stochastic) inherently occur during phase-contrast MRI acquisitions. Here, two displacement correction methods, single-step and iterative, were tested in silico with simulated displacements and were compared with ground-truth velocity fields. Next, the effects of combining displacement corrections and constrained probabilistic streamlines were performed in 10 healthy volunteers using time-averaged 4D-flow data. Measures of streamline length and depth into vasculature were then compared with streamlines generated with no corrections and displacement correction alone using one-way repeated-measures analysis of variance and Friedman's tests. Finally, virtual injections with improved streamlines were generated for three intracranial pathology cases.

RESULTS

Iterative displacement correction outperformed the single-step method in silico. In volunteers, the combination of displacement corrections and constrained probabilistic streamlines allowed for significant improvements in streamline length and increased the number of streamlines entering the circle of Willis relative to streamlines with no corrections and displacement correction alone. In the pathology cases, virtual injections with improved streamlines were qualitatively similar to dynamic arterial spin labeling images and allowed for forward/reverse selective flow tracking to characterize cerebrovascular malformations.

CONCLUSION

Virtual injections with improved streamlines from 4D-flow MRI allow for flexible, robust, intracranial flow tracking.

Divergence-Free Constrained Phase Unwrapping and Denoising for 4D Flow MRI Using Weighted Least-Squares

A novel divergence-free constrained phase unwrapping method was proposed and evaluated for 4D flow MRI. The unwrapped phase field was obtained by integrating the phase variations estimated from the wrapped phase data using weighted least-squares. The divergence-free constraint for incompressible blood flow was incorporated to regulate and denoise the resulting phase field. The proposed method was tested on synthetic phase data of left ventricular flow and in vitro 4D flow measurement of Poiseuille flow. The method was additionally applied to in vivo 4D flow measurements in the thoracic aorta from 30 human subjects. The performance of the proposed method was compared to the state-of-the-art 4D single-step Laplacian algorithm. The synthetic phase data were completely unwrapped by the proposed method for all the cases with velocity encoding (venc) as low as 20% of the maximum velocity and signal-to-noise ratio as low as 5. The in vitro Poiseuille flow data were completely unwrapped with a 60% increase in the velocity-to-noise ratio. For the in-vivo aortic datasets with venc ratio less than 0.4, the proposed method significantly improved the success rate by as much as 40% and reduced the velocity error levels by a factor of 10 compared to the state-of-the-art method. The divergence-free constrained method exhibits reliability and robustness on phase unwrapping and shows improved accuracy of velocity and hemodynamic quantities by unwrapping the low-venc 4D flow MRI data.

Left atrial 4D flow cardiovascular magnetic resonance: a reproducibility study in sinus rhythm and atrial fibrillation

BACKGROUND

Four-dimensional (4D) flow cardiovascular magnetic resonance (CMR) allows sophisticated quantification of left atrial (LA) blood flow, and could yield novel biomarkers of propensity for intra-cardiac thrombus formation and embolic stroke. As reproducibility is critically important to diagnostic performance, we systematically investigated technical and temporal variation of LA 4D flow in atrial fibrillation (AF) and sinus rhythm (SR).

METHODS

Eighty-six subjects (SR, n = 64; AF, n = 22) with wide-ranging stroke risk (CHA2DS2VASc 0-6) underwent LA 4D flow assessment of peak and mean velocity, vorticity, vortex volume, and stasis. Eighty-five (99%) underwent a second acquisition within the same session, and 74 (86%) also returned at 30 (27-35) days for an interval scan. We assessed variability attributable to manual contouring (intra- and inter-observer), and subject repositioning and reacquisition of data, both within the same session (same-day scan-rescan), and over time (interval scan). Within-subject coefficients of variation (CV) and bootstrapped 95% CIs were calculated and compared.

RESULTS

Same-day scan-rescan CVs were 6% for peak velocity, 5% for mean velocity, 7% for vorticity, 9% for vortex volume, and 10% for stasis, and were similar between SR and AF subjects (all p > 0.05). Interval-scan variability was similar to same-day scan-rescan variability for peak velocity, vorticity, and vortex volume (all p > 0.05), and higher for stasis and mean velocity (interval scan CVs of 14% and 8%, respectively, both p < 0.05). Longitudinal changes in heart rate and blood pressure at the interval scan in the same subjects were associated with significantly higher variability for LA stasis (p = 0.024), but not for the remaining flow parameters (all p > 0.05). SR subjects showed significantly greater interval-scan variability than AF patients for mean velocity, vortex volume, and stasis (all p < 0.05), but not peak velocity or vorticity (both p > 0.05).

CONCLUSIONS

LA peak velocity and vorticity are the most reproducible and temporally stable novel LA 4D flow biomarkers, and are robust to changes in heart rate, blood pressure, and differences in heart rhythm.

Modeling and Reducing the Effect of Geometric Uncertainties in Intracranial Aneurysms with Polynomial Chaos Expansion, Data Decomposition, and 4D-Flow MRI

PURPOSE

Variations in the vessel radius of segmented surfaces of intracranial aneurysms significantly influence the fluid velocities given by computer simulations. It is important to generate models that capture the effect of these variations in order to have a better interpretation of the numerically predicted hemodynamics. Also, it is highly relevant to develop methods that combine experimental observations with uncertainty modeling to get a closer approximation to the blood flow behavior.

METHODS

This work applies polynomial chaos expansion to model the effect of geometric uncertainties on the simulated fluid velocities of intracranial aneurysms. The radius of the vessel is defined as the uncertainty variable. Proper orthogonal decomposition is applied to characterize the solution space of fluid velocities. Next, a process of projecting the 4D-Flow MRI velocities on the basis vectors followed by coefficient mapping using generalized dynamic mode decomposition enables the merging of 4D-Flow MRI with the uncertainty propagated fluid velocities.

RESULTS

Polynomial chaos expansion propagates the fluid velocities with an error of 2% in velocity magnitude relative to computer simulations. Also, the bifurcation region (or impingement location) shows a standard deviation of 0.17 m/s (since an available reported variance in the vessel radius is adopted to model the uncertainty, the expected standard deviation may be different). Numerical phantom experiments indicate that the proposed approach reconstructs the fluid velocities with 0.3% relative error in presence of geometric uncertainties.

CONCLUSION

Polynomial chaos expansion is an effective approach to propagate the effect of the uncertainty variable in the blood flow velocities of intracranial aneurysms. Merging 4D-Flow MRI and uncertainty propagated fluid velocities leads to more realistic flow trends relative to ignoring the uncertainty in the vessel radius.

Amplified Flow Imaging (aFlow): A Novel MRI-Based Tool to Unravel the Coupled Dynamics Between the Human Brain and Cerebrovasculature

With each heartbeat, periodic variations in arterial blood pressure are transmitted along the vasculature, resulting in localized deformations of the arterial wall and its surrounding tissue. Quantification of such motions may help understand various cerebrovascular conditions, yet it has proven technically challenging thus far. We introduce a new image processing algorithm called amplified Flow (aFlow) which allows to study the coupled brain-blood flow motion by combining the amplification of cine and 4D flow MRI. By incorporating a modal analysis technique known as dynamic mode decomposition into the algorithm, aFlow is able to capture the characteristics of transient events present in the brain and arterial wall deformation. Validating aFlow, we tested it on phantom simulations mimicking arterial walls motion and observed that aFlow displays almost twice higher SNR than its predecessor amplified MRI (aMRI). We then applied aFlow to 4D flow and cine MRI datasets of 5 healthy subjects, finding high correlations between blood flow velocity and tissue deformation in selected brain regions, with correlation values r = 0.61 , 0.59, 0.52 for the pons, frontal and occipital lobe ( ). Finally, we explored the potential diagnostic applicability of aFlow by studying intracranial aneurysm dynamics, which seems to be indicative of rupture risk. In two patients, aFlow successfully visualized the imperceptible aneurysm wall motion, additionally quantifying the increase in the high frequency wall displacement after a one-year follow-up period (20%, 76%). These preliminary data suggest that aFlow may provide a novel imaging biomarker for the assessment of aneurysms evolution, with important potential diagnostic implications.

Technical feasibility of magnetic resonance fingerprinting on a 1.5T MRI-linac

Hybrid MRI-linac (MRL) systems enable daily multiparametric quantitative MRI to assess tumor response to radiotherapy. Magnetic resonance fingerprinting (MRF) may provide time efficient means of rapid multiparametric quantitative MRI. The accuracy of MRF, however, relies on adequate control over system imperfections, such as eddy currents and [Formula: see text], which are different and not as well established on MRL systems compared to diagnostic systems. In this study we investigate the technical feasibility of gradient spoiled 2D MRF on a 1.5T MRL. We show with phantom experiments that the MRL generates reliable MRF signals that are temporally stable during the day and have good agreement with spin-echo reference measurements. Subsequent in-vivo MRF scans in healthy volunteers and a patient with a colorectal liver metastasis showed good image quality, where the quantitative values of selected organs corresponded with the values reported in literature. Therefore we conclude that gradient spoiled 2D MRF is feasible on a 1.5T MRL with similar performance as on a diagnostic system. The precision and accuracy of the parametric maps are sufficient for further investigation of the clinical utility of MRF for online quantitatively MRI-guided radiotherapy.

Towards multi-modal data fusion for super-resolution and denoising of 4D-Flow MRI

4D-Flow magnetic resonance imaging (MRI) has enabled in vivo time-resolved measurement of three-dimensional blood flow velocities in the human vascular system. However, its clinical use has been hampered by two main issues, namely, low spatio-temporal resolution and acquisition noise. While patient-specific computational fluid dynamics (CFD) simulations can address the resolution and noise issues, its fidelity is impacted by accuracy of estimation of boundary conditions, model parameters, vascular geometry, and flow model assumptions. In this paper a scheme to address limitations of both modalities through data-fusion is presented. The solutions of the patient-specific CFD simulation are characterized using proper orthogonal decomposition (POD). Next, a process of projecting the 4D-Flow MRI data onto the POD basis and projection coefficient mapping using generalized dynamic mode decomposition (DMD) enables simultaneous super-resolution and denoising of 4D-Flow MRI. The method has been tested using numerical phantoms derived from patient-specific aneurysmal geometries and applied to in vivo 4D-Flow MRI data.

Accelerated aortic 4D flow cardiovascular magnetic resonance using compressed sensing: applicability, validation and clinical integration

BACKGROUND

Three-dimensional time-resolved phase-contrast cardiovascular magnetic resonance (4D flow CMR) enables the quantification and visualisation of blood flow, but its clinical applicability remains hampered by its long scan time. The aim of this study was to evaluate the use of compressed sensing (CS) with on-line reconstruction to accelerate the acquisition and reconstruction of 4D flow CMR of the thoracic aorta.

METHODS

4D flow CMR of the thoracic aorta was acquired in 20 healthy subjects using CS with acceleration factors ranging from 4 to 10. As a reference, conventional parallel imaging (SENSE) with acceleration factor 2 was used. Flow curves, net flows, peak flows and peak velocities were extracted from six contours along the aorta. To measure internal data consistency, a quantitative particle trace analysis was performed. Additionally, scan-rescan, inter- and intraobserver reproducibility were assessed. Subsequently, 4D flow CMR with CS factor 6 was acquired in 3 patients with differing aortopathies. The flow patterns resulting from particle trace visualisation were qualitatively analysed.

RESULTS

All collected data were successfully acquired and reconstructed on-line. The average acquisition time including respiratory navigator efficiency with CS factor 6 was 5:02 ± 2:23 min while reconstruction took approximately 9 min. For CS factors of 8 or less, mean differences in net flow, peak flow and peak velocity as compared to SENSE were below 2.2 ± 7.8 ml/cycle, 4.6 ± 25.2 ml/s and - 7.9 ± 13.0 cm/s, respectively. For a CS factor of 10 differences reached 5.4 ± 8.0 ml/cycle, 14.4 ± 28.3 ml/s and - 4.0 ± 12.2 cm/s. Scan-rescan analysis yielded mean differences in net flow of - 0.7 ± 4.9 ml/cycle for SENSE and - 0.2 ± 8.5 ml/cycle for CS factor of 6.

CONCLUSIONS

A six- to eightfold acceleration of 4D flow CMR using CS is feasible. Up to a CS acceleration rate of 6, no statistically significant differences in measured flow parameters could be observed with respect to the reference technique. Acquisitions in patients with aortopathies confirm the potential to integrate the proposed method in a clinical routine setting, whereby its main benefits are scan-time savings and direct on-line reconstruction.

Evaluation of 4D flow MRI-based non-invasive pressure assessment in aortic coarctations

Severity of aortic coarctation (CoA) is currently assessed by estimating trans-coarctation pressure drops through cardiac catheterization or echocardiography. In principle, more detailed information could be obtained non-invasively based on space- and time-resolved magnetic resonance imaging (4D flow) data. Yet the limitations of this imaging technique require testing the accuracy of 4D flow-derived hemodynamic quantities against other methodologies. With the objective of assessing the feasibility and accuracy of this non-invasive method to support the clinical diagnosis of CoA, we developed an algorithm (4DF-FEPPE) to obtain relative pressure distributions from 4D flow data by solving the Poisson pressure equation. 4DF-FEPPE was tested against results from a patient-specific fluid-structure interaction (FSI) simulation, whose patient-specific boundary conditions were prescribed based on 4D flow data. Since numerical simulations provide noise-free pressure fields on fine spatial and temporal scales, our analysis allowed to assess the uncertainties related to 4D flow noise and limited resolution. 4DF-FEPPE and FSI results were compared on a series of cross-sections along the aorta. Bland-Altman analysis revealed very good agreement between the two methodologies in terms of instantaneous data at peak systole, end-diastole and time-averaged values: biases (means of differences) were +0.4 mmHg, -1.1 mmHg and +0.6 mmHg, respectively. Limits of agreement (2 SD) were ±0.978 mmHg, ±1.06 mmHg and ±1.97 mmHg, respectively. Peak-to-peak and maximum trans-coarctation pressure drops obtained with 4DF-FEPPE differed from FSI results by 0.75 mmHg and -1.34 mmHg respectively. The present study considers important validation aspects of non-invasive pressure difference estimation based on 4D flow MRI, showing the potential of this technology to be more broadly applied to the clinical practice.

Fast Robust Dejitter and Interslice Discontinuity Removal in MRI Phase Acquisitions: Application to Magnetic Resonance Elastography

MRI phase contrast imaging methods that assemble slice-wise acquisitions into volumes can contain interslice phase discontinuities (IPDs) over the course of the scan from sources, including unavoidable physiological activity. In magnetic resonance elastography (MRE), this can alter wavelength and tissue stiffness estimates, invalidating the analysis. We first model this behavior as jitter along the z-axis of the phase of 3D complex-valued wave volumes. A two-step image processing pipeline is then proposed that removes IPDs. First, constant slicewise phase shift is removed with a novel, non-convex dejittering algorithm. Then, regional physiological noise artifacts are removed with novel filtering of 3D wavelet coefficients. Calibration of two pipeline coefficients, the dejitter parameter α and the wavelet band high-pass coefficient ω_c , was first performed on a finite-element method brain phantom. A comparative investigation was then performed, on a cohort of 48 brain acquisitions, of four approaches to IPDs: 1) the proposed method; 2) a "control" condition of neglect of IPDs; 3) an anisotropic wavelet-based method; and 4) a method of in-plane (2D) processing. The present method showed medians of [Formula: see text] Pa for a multifrequency wave inversion centered at 40 Hz which was within 6% of methods 3) and 4), while neglect produced [Formula: see text] estimates a mean of 17% lower. The proposed method reduced the value range of the cohort against methods 3) and 4) by 29% and 31%, respectively. Such reduction in variance enhances the ability of brain MRE to predict subtler physiological changes. Our theoretical approach further enables more powerful applications of fundamental findings in noise and denoising to MRE.

Reduced Cycle Spinning Method for the Undecimated Wavelet Transform

The Undecimated Wavelet Transform is commonly used for signal processing due to its advantages over other wavelet techniques, but it is limited for some applications because of its computational cost. One of the methods utilized for the implementation of the Undecimated Wavelet Transform is the one known as Cycle Spinning. This paper introduces an alternative Cycle Spinning implementation method that divides the computational cost by a factor close to 2. This work develops the mathematical background of the proposed method, shows the block diagrams for its implementation and validates the method by applying it to the denoising of ultrasonic signals. The evaluation of the denoising results shows that the new method produces similar denoising qualities than other Cycle Spinning implementations, with a reduced computational cost.

Coil combination methods for multi-channel hyperpolarized 13C imaging data from human studies

Effective coil combination methods for human hyperpolarized ¹³C spectroscopy multi-channel data had been relatively unexplored. This study implemented and tested several coil combination methods, including (1) the sum-of-squares (SOS), (2) singular value decomposition (SVD), (3) Roemer method by using reference peak area as a sensitivity map (RefPeak), and (4) Roemer method by using ESPIRiT-derived sensitivity map (ESPIRiT). These methods were evaluated by numerical simulation, thermal phantom experiments, and human cancer patient studies. Overall, the SVD, RefPeak, and ESPIRiT methods demonstrated better accuracy and robustness than the SOS method. Extracting complex pyruvate signal provides an easy and excellent approximation of the coil sensitivity map while maintaining valuable phase information of the coil-combined data.

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.

Dynamic Denoising and Gappy Data Reconstruction Based on Dynamic Mode Decomposition and Discrete Cosine Transform

Dynamic Mode Decomposition (DMD) is a data-driven method to analyze the dynamics, first applied to fluid dynamics. It extracts modes and their corresponding eigenvalues, where the modes are spatial fields that identify coherent structures in the flow and the eigenvalues describe the temporal growth/decay rates and oscillation frequencies for each mode. The recently introduced compressed sensing DMD (csDMD) reduces computation times and also has the ability to deal with sub-sampled datasets. In this paper, we present a similar technique based on discrete cosine transform to reconstruct the fully-sampled dataset (as opposed to DMD modes as in csDMD) from sub-sampled noisy and gappy data using l 1 minimization. The proposed method was benchmarked against csDMD in terms of denoising and gap-filling using three datasets. The first was the 2-D time-resolved plot of a double gyre oscillator which has about nine oscillatory modes. The second dataset was derived from a Duffing oscillator. This dataset has several modes associated with complex eigenvalues which makes them oscillatory. The third dataset was taken from the 2-D simulation of a wake behind a cylinder at Re = 100 and was used for investigating the effect of changing various parameters on reconstruction error. The Duffing and 2-D wake datasets were tested in presence of noise and rectangular gaps. While the performance for the double-gyre dataset is comparable to csDMD, the proposed method performs substantially better (lower reconstruction error) for the dataset derived from the Duffing equation and also, the 2-D wake dataset according to the defined reconstruction error metrics.

Development of the MRI Flow Phantom System Focused on Low Speed Flows in Fluid Machinery

At present, magnetic resonance imaging (MRI), which is one of the noninvasive diagnostic imaging techniques for medical use, has been applied to industrial product inspection. In this study, a hydraulic model test system, called the “flow phantom system,” which can generate steady flow and oscillating flow for time-resolved MRI, was developed to aid optimum design of fluid machinery. Simple flow phantoms are tested under laminar flow or oscillating flow to evaluate the validity and effectiveness of the proposed system. In this article, the test results of double cylindrical pipe flow, elbow pipe flow, cylindrical valve flow, and jet pump flow, which are often seen in fluid machines, are tested using the 2D time-spatial labeling inversion pulse (Time-SLIP) method, which can track a labeled water mass and visualize it using two-dimensional images. MRI-detected flow patterns were compared with particle image velocimetry (PIV) or numerical simulation.

General phase regularized reconstruction using phase cycling

PURPOSE

To develop a general phase regularized image reconstruction method, with applications to partial Fourier imaging, water-fat imaging and flow imaging.

THEORY AND METHODS

The problem of enforcing phase constraints in reconstruction was studied under a regularized inverse problem framework. A general phase regularized reconstruction algorithm was proposed to enable various joint reconstruction of partial Fourier imaging, water-fat imaging and flow imaging, along with parallel imaging (PI) and compressed sensing (CS). Since phase regularized reconstruction is inherently non-convex and sensitive to phase wraps in the initial solution, a reconstruction technique, named phase cycling, was proposed to render the overall algorithm invariant to phase wraps. The proposed method was applied to retrospectively under-sampled in vivo datasets and compared with state of the art reconstruction methods.

RESULTS

Phase cycling reconstructions showed reduction of artifacts compared to reconstructions without phase cycling and achieved similar performances as state of the art results in partial Fourier, water-fat and divergence-free regularized flow reconstruction. Joint reconstruction of partial Fourier + water-fat imaging + PI + CS, and partial Fourier + divergence-free regularized flow imaging + PI + CS were demonstrated.

CONCLUSION

The proposed phase cycling reconstruction provides an alternative way to perform phase regularized reconstruction, without the need to perform phase unwrapping. It is robust to the choice of initial solutions and encourages the joint reconstruction of phase imaging applications. Magn Reson Med 80:112-125, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Curvelet Transform-based volume fusion for correcting signal loss artifacts in Time-of-Flight Magnetic Resonance Angiography data

Flow fields in cerebral aneurysms can be measured in vivo with phase-contrast MRI (4D Flow MRI), providing 3D anatomical magnitude images as well as 3-directional velocities through the cardiac cycle. The low spatial resolution of the 4D Flow MRI data, however, requires the images to be co-registered with higher resolution angiographic data for better segmentation of the blood vessel geometries to adequately quantify relevant flow descriptors such as wall shear stress or flow residence time. Time-of-Flight Magnetic Resonance Angiography (TOF MRA) is a non-invasive technique for visualizing blood vessels without the need to administer contrast agent. Instead TOF uses the blood flow-related enhancement of unsaturated spins entering into an imaging slice as means to generate contrast between the stationary tissue and the moving blood. Because of the higher resolutions, TOF data are often used to assist with the segmentation process needed for the flow analysis and Computational Fluid Dynamics (CFD) modeling. However, presence of slow moving and recirculating blood flow such as in brain aneurysms, especially regions where the blood flow is not perpendicular to the image plane, causes signal loss in these regions. In this work a 3D Curvelet Transform-based image fusion approach is proposed for signal loss artifact reduction of TOF volume data. Experiments show the superiority of the proposed approach in comparison to other multi-resolution 3D Wavelet-based image fusion methodologies. The proposed approach can further facilitate model-based fluid analysis and pre/post-operative treatment of patients with brain aneurysms.

An eigenvalue approach for the automatic scaling of unknowns in model-based reconstructions: Application to real-time phase-contrast flow MRI

The purpose of this work is to develop an automatic method for the scaling of unknowns in model-based nonlinear inverse reconstructions and to evaluate its application to real-time phase-contrast (RT-PC) flow magnetic resonance imaging (MRI). Model-based MRI reconstructions of parametric maps which describe a physical or physiological function require the solution of a nonlinear inverse problem, because the list of unknowns in the extended MRI signal equation comprises multiple functional parameters and all coil sensitivity profiles. Iterative solutions therefore rely on an appropriate scaling of unknowns to numerically balance partial derivatives and regularization terms. The scaling of unknowns emerges as a self-adjoint and positive-definite matrix which is expressible by its maximal eigenvalue and solved by power iterations. The proposed method is applied to RT-PC flow MRI based on highly undersampled acquisitions. Experimental validations include numerical phantoms providing ground truth and a wide range of human studies in the ascending aorta, carotid arteries, deep veins during muscular exercise and cerebrospinal fluid during deep respiration. For RT-PC flow MRI, model-based reconstructions with automatic scaling not only offer velocity maps with high spatiotemporal acuity and much reduced phase noise, but also ensure fast convergence as well as accurate and precise velocities for all conditions tested, i.e. for different velocity ranges, vessel sizes and the simultaneous presence of signals with velocity aliasing. In summary, the proposed automatic scaling of unknowns in model-based MRI reconstructions yields quantitatively reliable velocities for RT-PC flow MRI in various experimental scenarios.

Merging computational fluid dynamics and 4D Flow MRI using proper orthogonal decomposition and ridge regression

Time resolved phase-contrast magnetic resonance imaging 4D-PCMR (also called 4D Flow MRI) data while capable of non-invasively measuring blood velocities, can be affected by acquisition noise, flow artifacts, and resolution limits. In this paper, we present a novel method for merging 4D Flow MRI with computational fluid dynamics (CFD) to address these limitations and to reconstruct de-noised, divergence-free high-resolution flow-fields. Proper orthogonal decomposition (POD) is used to construct the orthonormal basis of the local sampling of the space of all possible solutions to the flow equations both at the low-resolution level of the 4D Flow MRI grid and the high-level resolution of the CFD mesh. Low-resolution, de-noised flow is obtained by projecting in vivo 4D Flow MRI data onto the low-resolution basis vectors. Ridge regression is then used to reconstruct high-resolution de-noised divergence-free solution. The effects of 4D Flow MRI grid resolution, and noise levels on the resulting velocity fields are further investigated. A numerical phantom of the flow through a cerebral aneurysm was used to compare the results obtained using the POD method with those obtained with the state-of-the-art de-noising methods. At the 4D Flow MRI grid resolution, the POD method was shown to preserve the small flow structures better than the other methods, while eliminating noise. Furthermore, the method was shown to successfully reconstruct details at the CFD mesh resolution not discernible at the 4D Flow MRI grid resolution. This method will improve the accuracy of the clinically relevant flow-derived parameters, such as pressure gradients and wall shear stresses, computed from in vivo 4D Flow MRI data.

Mitigation of partial volume effects in susceptibility-based oxygenation measurements by joint utilization of magnitude and phase (JUMP)

PURPOSE

Susceptibility-based blood oxygenation measurements in small vessels of the brain derive from gradient echo (GRE) phase and can provide localized assessment of brain function and pathology. However, when vessel diameter becomes smaller than the acquisition voxel size, partial volume effects compromise these measurements. The purpose of this study was to develop a technique to improve the reliability of vessel oxygenation estimates in the presence of partial volume effects.

METHODS

Intravoxel susceptibility variations are present when a vessel and parenchyma experience partial volume effects, modifying the voxel's GRE phase signal and attenuating the GRE magnitude signal. Using joint utilization of magnitude and phase (JUMP), both vessel susceptibility and voxel partial volume fraction can be estimated, providing measurements of venous oxygen saturation ( Yv) in straight, nearly vertical vessels that have improved robustness to partial volume effects.

RESULTS

JUMP was demonstrated by estimating vessel Yv in numerical and in vivo experiments. Deviations from ground truth of Yv measurements in vessels tilted up to 30° from B0 were reduced by over 50% when using JUMP compared with phase-only techniques.

CONCLUSION

JUMP exploits both magnitude and phase data in GRE imaging to mitigate partial volume effects in estimation of vessel oxygenation. Magn Reson Med 77:1713-1727, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

The manifestation of vortical and secondary flow in the cerebral venous outflow tract: An in vivo MR velocimetry study

Aberrations in flow in the cerebral venous outflow tract (CVOT) have been implicated as the cause of several pathologic conditions including idiopathic intracranial hypertension (IIH), multiple sclerosis (MS), and pulsatile tinnitus (PT). The advent of 4D flow magnetic resonance imaging (4D-flow MRI) has recently allowed researchers to evaluate blood flow patterns in the arterial structures with great success. We utilized similar imaging techniques and found several distinct flow characteristics in the CVOT of subjects with and without lumenal irregularities. We present the flow patterns of 8 out of 38 subjects who have varying heights of the internal jugular bulb and varying lumenal irregularities including stenosis and diverticulum. In the internal jugular vein (IJV) with an elevated jugular bulb (JB), 4Dflow MRI revealed a characteristic spiral flow that was dependent on the level of JB elevation. Vortical flow was also observed in the diverticula of the venous sinuses and IJV. The diversity of flow complexity in the CVOT illustrates the potential importance of hemodynamic investigations in elucidating venous pathologies.

Accuracy of 4D Flow Measurement of Cerebrospinal Fluid Dynamics in the Cervical Spine: An In Vitro Verification Against Numerical Simulation

Abnormal alterations in cerebrospinal fluid (CSF) flow are thought to play an important role in pathophysiology of various craniospinal disorders such as hydrocephalus and Chiari malformation. Three directional phase contrast MRI (4D Flow) has been proposed as one method for quantification of the CSF dynamics in healthy and disease states, but prior to further implementation of this technique, its accuracy in measuring CSF velocity magnitude and distribution must be evaluated. In this study, an MR-compatible experimental platform was developed based on an anatomically detailed 3D printed model of the cervical subarachnoid space and subject specific flow boundary conditions. Accuracy of 4D Flow measurements was assessed by comparison of CSF velocities obtained within the in vitro model with the numerically predicted velocities calculated from a spatially averaged computational fluid dynamics (CFD) model based on the same geometry and flow boundary conditions. Good agreement was observed between CFD and 4D Flow in terms of spatial distribution and peak magnitude of through-plane velocities with an average difference of 7.5 and 10.6% for peak systolic and diastolic velocities, respectively. Regression analysis showed lower accuracy of 4D Flow measurement at the timeframes corresponding to low CSF flow rate and poor correlation between CFD and 4D Flow in-plane velocities.

Enhancing the Velocity Data From 4D Flow MR Images by Reducing its Divergence

Velocity measurements from 4D flow MRI are prone to be affected by several imperfections of the MR system. Assuming that blood is incompressible, we propose a novel method for enhancing the velocity field by reducing its divergence. To enhance the velocity data, we added a corrector velocity to each voxel such that the divergence is minimized. The method was validated using an analytical Womersley flow model for different settings of resolution and noise levels. The performance of the proposed method was also assessed in volunteers and patients. Results demonstrated a significant reduction of the divergence depending on the size of the regularization term, obtaining a reduction close to 50% of the mean divergence with negligible modification of flow parameters. Remarkably, we found that the reduction of the divergence, in percentage, was independent of volunteers, resolution or noise.

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.

Cardiovascular magnetic resonance phase contrast imaging

Cardiovascular magnetic resonance (CMR) phase contrast imaging has undergone a wide range of changes with the development and availability of improved calibration procedures, visualization tools, and analysis methods. This article provides a comprehensive review of the current state-of-the-art in CMR phase contrast imaging methodology, clinical applications including summaries of past clinical performance, and emerging research and clinical applications that utilize today's latest technology.

Accelerating 4D flow MRI by exploiting vector field divergence regularization

PURPOSE

To improve velocity vector field reconstruction from undersampled four-dimensional (4D) flow MRI by penalizing divergence of the measured flow field.

THEORY AND METHODS

Iterative image reconstruction in which magnitude and phase are regularized separately in alternating iterations was implemented. The approach allows incorporating prior knowledge of the flow field being imaged. In the present work, velocity data were regularized to reduce divergence, using either divergence-free wavelets (DFW) or a finite difference (FD) method using the ℓ1-norm of divergence and curl. The reconstruction methods were tested on a numerical phantom and in vivo data. Results of the DFW and FD approaches were compared with data obtained with standard compressed sensing (CS) reconstruction.

RESULTS

Relative to standard CS, directional errors of vector fields and divergence were reduced by 55-60% and 38-48% for three- and six-fold undersampled data with the DFW and FD methods. Velocity vector displays of the numerical phantom and in vivo data were found to be improved upon DFW or FD reconstruction.

CONCLUSION

Regularization of vector field divergence in image reconstruction from undersampled 4D flow data is a valuable approach to improve reconstruction accuracy of velocity vector fields.