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

Blood Flow Velocities as Determined by Real-Time Phase-Contrast MRI in Patients With Carotid Artery Stenosis

BACKGROUND AND PURPOSE

Real-time phase-contrast (RT-PC) flow MRI can be used to determine quantitative flow parameters throughout the vessel lumen of extracranial, brain-supplying arteries. Its potential value in the diagnostic workup of patients with carotid artery stenosis has not been evaluated.

METHODS

RT-PC flow MRI was performed in 10 patients with carotid stenosis in comparison to conventional neurovascular ultrasound (nvUS). Peak systolic velocity, end-diastolic velocity, mean flow velocity, and flow volumes have been evaluated by RT-PC flow MRI. Measurements have been performed at standardized sites along the common, internal, and external carotid arteries on both sides and at the maximum of the carotid stenosis.

RESULTS

Blood flow velocities were significantly lower with RT-PC flow MRI compared to nvUS and not consistently correlated between both methods. Within the maximum of the carotid stenosis, RT-PC flow MRI showed implausible flow velocity reductions compared to nvUS. In contrast, the flow volumes determined by RT-PC flow MRI-with exception of the stenosis maximum-were comparable with nvUS and significantly correlated in the prestenotic common carotid artery.

CONCLUSION

RT-PC flow MRI does not appear to be suitable for quantifying blood flow velocities and volumes in the patients with carotid stenosis compared to nvUS. Apart from the lower temporal resolution of RT-PC MRI, the lack of correlation of blood flow velocities might be ascribed to the prevalence of nonlaminar flow within and behind the stenosis, which violates a general prerequisite for valid flow velocity measurements by PC MRI.

Free-Breathing Liver Fat, R₂* and B₀ Field Mapping Using Multi-Echo Radial FLASH and Regularized Model-Based Reconstruction

This work introduced a stack-of-radial multi-echo asymmetric-echo MRI sequence for free-breathing liver volumetric acquisition. Regularized model-based reconstruction was implemented in Berkeley Advanced Reconstruction Toolbox (BART) to jointly estimate all physical parameter maps (water, fat, R2∗ , and B0 field inhomogeneity maps) and coil sensitivity maps from self-gated k -space data. Specifically, locally low rank and temporal total variation regularization were employed directly on physical parameter maps. The proposed free-breathing radial technique was tested on a water/fat & iron phantom, a young volunteer, and obesity/diabetes/hepatic steatosis patients. Quantitative fat fraction and R2∗ accuracy were confirmed by comparing our technique with the reference breath-hold Cartesian scan. The multi-echo radial sampling sequence achieves fast k -space coverage and is robust to motion. Moreover, the proposed motion-resolved model-based reconstruction allows for free-breathing liver fat and R2∗ quantification in multiple motion states. Overall, our proposed technique offers a convenient tool for non-invasive liver assessment with no breath holding requirement.

Quantitative MRI by nonlinear inversion of the Bloch equations

PURPOSE

Development of a generic model-based reconstruction framework for multiparametric quantitative MRI that can be used with data from different pulse sequences.

METHODS

Generic nonlinear model-based reconstruction for quantitative MRI estimates parametric maps directly from the acquired k-space by numerical optimization. This requires numerically accurate and efficient methods to solve the Bloch equations and their partial derivatives. In this work, we combine direct sensitivity analysis and pre-computed state-transition matrices into a generic framework for calibrationless model-based reconstruction that can be applied to different pulse sequences. As a proof-of-concept, the method is implemented and validated for quantitative T 1 $$ {\mathrm{T}}_1 $$ and T 2 $$ {\mathrm{T}}_2 $$ mapping with single-shot inversion-recovery (IR) FLASH and IR bSSFP sequences in simulations, phantoms, and the human brain.

RESULTS

The direct sensitivity analysis enables a highly accurate and numerically stable calculation of the derivatives. The state-transition matrices efficiently exploit repeating patterns in pulse sequences, speeding up the calculation by a factor of 10 for the examples considered in this work, while preserving the accuracy of native ordinary differential equations solvers. The generic model-based method reproduces quantitative results of previous model-based reconstructions based on the known analytical solutions for radial IR FLASH. For IR bSFFP it produces accurate T 1 $$ {\mathrm{T}}_1 $$ and T 2 $$ {\mathrm{T}}_2 $$ maps for the National Insitute of Standards and Technology (NIST) phantom in numerical simulations and experiments. Feasibility is also shown for human brain, although results are affected by magnetization transfer effects.

CONCLUSION

By developing efficient tools for numerical optimizations using the Bloch equations as forward model, this work enables generic model-based reconstruction for quantitative MRI.

Improved Image Quality for Static BLADE Magnetic Resonance Imaging Using the Total-Variation Regularized Least Absolute Deviation Solver

In order to improve the image quality of BLADE magnetic resonance imaging (MRI) using the index tensor solvers and to evaluate MRI image quality in a clinical setting, we implemented BLADE MRI reconstructions using two tensor solvers (the least-squares solver and the L1 total-variation regularized least absolute deviation (L1TV-LAD) solver) on a graphics processing unit (GPU). The BLADE raw data were prospectively acquired and presented in random order before being assessed by two independent radiologists. Evaluation scores were examined for consistency and then by repeated measures analysis of variance (ANOVA) to identify the superior algorithm. The simulation showed the structural similarity index (SSIM) of various tensor solvers ranged between 0.995 and 0.999. Inter-reader reliability was high (Intraclass correlation coefficient (ICC) = 0.845, 95% confidence interval: 0.817, 0.87). The image score of L1TV-LAD was significantly higher than that of vendor-provided image and the least-squares method. The image score of the least-squares method was significantly lower than that of the vendor-provided image. No significance was identified in L1TV-LAD with a regularization strength of λ= 0.4–1.0. The L1TV-LAD with a regularization strength of λ= 0.4–0.7 was found consistently better than least-squares and vendor-provided reconstruction in BLADE MRI with a SENSitivity Encoding (SENSE) factor of 2. This warrants further development of the integrated computing system with the scanner.

Physics-based reconstruction methods for magnetic resonance imaging

Conventional magnetic resonance imaging (MRI) is hampered by long scan times and only qualitative image contrasts that prohibit a direct comparison between different systems. To address these limitations, model-based reconstructions explicitly model the physical laws that govern the MRI signal generation. By formulating image reconstruction as an inverse problem, quantitative maps of the underlying physical parameters can then be extracted directly from efficiently acquired k-space signals without intermediate image reconstruction-addressing both shortcomings of conventional MRI at the same time. This review will discuss basic concepts of model-based reconstructions and report on our experience in developing several model-based methods over the last decade using selected examples that are provided complete with data and code. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 1'.

Inferior vena cava revisited - Real-time flow MRI of respiratory maneuvers

Recent MRI studies of blood flow in the inferior vena cava (IVC) resulted in findings which are inconsistent with earlier observations by invasive procedures - most likely because ECG-gated MRI techniques are unable to resolve dynamic adjustments due to respiration. The purpose of this work was to apply real-time phase-contrast MRI at 50 ms resolution to re-evaluate IVC flow in response to normal and deep breathing as well as breath holding and Valsalva maneuver (11 young healthy subjects). Real-time flow MRI relied on highly undersampled radial gradient-echo sequences and a model-based nonlinear inverse reconstruction. A frequency analysis of the predominant pulsatility classified IVC flow in individual subjects as "cardiac", "respiratory" or "mixed" type. Peak flow velocities during free breathing ranged from 30 to 58 cm s^-1 , while flow rates varied from 15 to 37 ml s^-1 . The subject-specific IVC flow pattern persists during deep breathing although the enhanced respiratory influence may shift subjects form "cardiac" to "mixed" or from "mixed" to "respiratory" type. Peak velocities increased relative to normal breathing but led to similar flow rates of 16 to 34 ml s^-1 . Inspiration during deep breathing elicited brief periods of flow reversal in all subjects with mean peak velocities of -21 cm s^-1 . The observation of only mildly flattened parabolic velocity distributions within the IVC indicated mostly laminar flow. Breath holding reduced blood flow velocities and rates by more than 40% on average, while Valsalva maneuvers completely abolished venous return. In conclusion, IVC blood flow is dominated by the acquired respiratory behavior of individual subjects and its pressure-induced alterations relative to cardiac pulsation. The responses to breath holding and Valsalva maneuver are in full agreement with previous invasive observations of reduced or even ceased flow, respectively.

Real-time multi-directional flow MRI using model-based reconstructions of undersampled radial FLASH - A feasibility study

The purpose of this work was to develop an acquisition and reconstruction technique for two- and three-directional (2d and 3d) phase-contrast flow MRI in real time. A previous real-time MRI technique for one-directional (1d) through-plane flow was extended to 2d and 3d flow MRI by introducing in-plane flow sensitivity. The method employs highly undersampled radial FLASH sequences with sequential acquisitions of two or three flow-encoding datasets and one flow-compensated dataset. Echo times are minimized by merging the waveforms of flow-encoding and radial imaging gradients. For each velocity direction individually, model-based reconstructions by regularized nonlinear inversion jointly estimate an anatomical image, a set of coil sensitivities and a phase-contrast velocity map directly. The reconstructions take advantage of a dynamic phase reference obtained by interpolating consecutive flow-compensated acquisitions. Validations include pulsatile flow phantoms as well as in vivo studies of the human aorta at 3 T. The proposed method offers cross-sectional 2d and 3d flow MRI of the human aortic arch at 53 and 67 ms resolution, respectively, without ECG synchronization and during free breathing. The in-plane resolution was 1.5 × 1.5 mm² and the slice thickness 6 mm. In conclusion, real-time multi-directional flow MRI offers new opportunities to study complex human blood flow without the risk of combining differential phase (i.e., velocity) information from multiple heartbeats as for ECG-gated data. The method would benefit from a further reduction of acquisition time and accelerated computing to allow for extended clinical trials.

Body coil reference for inverse reconstructions of multi-coil data-the case for real-time MRI

Real-time magnetic resonance imaging (MRI) or model-based MRI reconstructions of parametric maps require the solution of an ill-posed nonlinear inverse problem. Respective algorithms, e.g., the iteratively regularized Gauss-Newton method, implicitly combine datasets from multiple receive coils. Because these local coils may exhibit complex sensitivity profiles with rather different phase offsets, the numerical optimization may lead to phase singularities which in turn cause "black holes" in magnitude images. The purpose of this work is to develop a method for inverse reconstructions of multi-coil MRI data which avoids the generation of such spatially selective phase singularities. It is proposed to use volumetric body coil data and start the iterative reconstruction of multi-coil data with a reference image which offers proper phase information. In more detail, inverse reconstructions of multi-coil data are initialized with a complex "seed" image which is obtained by a Fast Fourier Transform (FFT) reconstruction of data from a single body coil element. This is accomplished at no additional cost as only very few body coil scans with identical conditions as the multi-coil acquisitions are needed as part of the regular prep scan period. The method is evaluated for anatomical real-time MRI and model-based phase-contrast flow MRI in real-time at 3 T. The proposed method overcomes phase singularities in all cases for arbitrary sets of receive coils. In conclusion, the automatic use of a single body coil reference image is simple, robust, and further improves the reliability of advanced MRI reconstructions from multi-coil data.

Dynamic water/fat separation and B 0 inhomogeneity mapping-joint estimation using undersampled triple-echo multi-spoke radial FLASH

PURPOSE

To achieve dynamic water/fat separation and B 0 field inhomogeneity mapping via model-based reconstructions of undersampled triple-echo multi-spoke radial FLASH acquisitions.

METHODS

This work introduces an undersampled triple-echo multi-spoke radial FLASH sequence, which uses (i) complementary radial spokes per echo train for faster spatial encoding, (ii) asymmetric echoes for flexible and nonuniform echo spacing, and (iii) a golden angle increment across frames for optimal k-space coverage. Joint estimation of water, fat, B 0 inhomogeneity, and coil sensitivity maps from undersampled triple-echo data poses a nonlinear and non-convex inverse problem which is solved by a model-based reconstruction with suitable regularization. The developed methods are validated using phantom experiments with different degrees of undersampling. Real-time MRI studies of the knee, liver, and heart are conducted without prospective gating or retrospective data sorting at temporal resolutions of 70, 158, and 40 ms, respectively.

RESULTS

Up to 18-fold undersampling is achieved in this work. Even in the presence of rapid physiological motion, large B 0 field inhomogeneities, and phase wrapping, the model-based reconstruction yields reliably separated water/fat maps in conjunction with spatially smooth inhomogeneity maps.

CONCLUSIONS

The combination of a triple-echo acquisition and joint reconstruction technique provides a practical solution to time-resolved and motion robust water/fat separation at high spatial and temporal resolution.

Carotid artery flow as determined by real-time phase-contrast flow MRI and neurovascular ultrasound: A comparative study of healthy subjects

BACKGROUND

The assessment of carotid artery flow by neurovascular ultrasound (nvUS) can be complemented by real-time phase-contrast (RT-PC) flow MRI which apart from quantitative flow parameters offers velocity distributions across the entire vessel lumen.

MATERIALS AND METHODS

The feasibility and diagnostic potential of RT-PC flow MRI was evaluated in 20 healthy volunteers in comparison to conventional nvUS. RT-PC flow MRI at 40 ms temporal resolution and 0.8 mm in-plane resolution resulted in velocity maps with low phase noise and high spatiotemporal accuracy by exploiting respective advances of a recent nonlinear inverse model-based reconstruction. Peak-systolic velocities (PSV), end-diastolic velocities (EDV), flow volumes and comprehensive velocity profiles were determined in the common, internal and external carotid artery on both sides.

RESULTS

Flow characteristics such as pulsatility and individual abnormalities shown on nvUS could be reproduced and visualized in detail by RT-PC flow MRI. PSV to EDV differences revealed good agreement between both techniques, mean PSV and EDV were significantly lower and flow volumes were higher for MRI.

CONCLUSION

Our findings suggest that RT-PC flow MRI adds to clinical diagnostics, e.g. by alterations of dynamic velocity distributions in patients with carotid stenosis. Lower PSV and EDV values than for nvUS mainly reflect the longer MRI acquisition time which attenuates short peak velocities, while higher flow volumes benefit from a proper assessment of the true vessel lumen.