Motion-robust free-running volumetric cardiovascular MRI.

PURPOSE: To present and assess an outlier mitigation method that makes free-running volumetric cardiovascular MRI (CMR) more robust to motion. METHODS: The proposed method, called compressive recovery with outlier rejection (CORe), models outliers in the measured data as an additive auxiliary variable. We enforce MR physics-guided group sparsity on the auxiliary variable, and jointly estimate it along with the image using an iterative algorithm. For evaluation, CORe is first compared to traditional compressed sensing (CS), robust regression (RR), and an existing outlier rejection method using two simulation studies. Then, CORe is compared to CS using seven three-dimensional (3D) cine, 12 rest four-dimensional (4D) flow, and eight stress 4D flow imaging datasets. RESULTS: Our simulation studies show that CORe outperforms CS, RR, and the existing outlier rejection method in terms of normalized mean square error and structural similarity index across 55 different realizations. The expert reader evaluation of 3D cine images demonstrates that CORe is more effective in suppressing artifacts while maintaining or improving image sharpness. Finally, 4D flow images show that CORe yields more reliable and consistent flow measurements, especially in the presence of involuntary subject motion or exercise stress. CONCLUSION: An outlier rejection method is presented and tested using simulated and measured data. This method can help suppress motion artifacts in a wide range of free-running CMR applications.

Maximum Likelihood Estimation in Mixed Integer Linear Models.

We consider the maximum likelihood (ML) parameter estimation problem for mixed integer linear models with arbitrary noise covariance. This problem appears in applications such as single frequency estimation, phase contrast imaging, and direction of arrival (DoA) estimation. Parameter estimates are found by solving a closest lattice point problem, which requires a lattice basis. In this letter, we present a lattice basis construction for ML parameter estimation and conclude with simulated results from DoA estimation and phase contrast imaging.

Alias-Free Arrays.

Nonuniform array geometries provide freedom for increased aperture and reduced mutual coupling. A necessary and sufficient condition is given for an array of isotropic sensor elements to be unambiguous for any specified set of directions of arrival. The set of unambiguous spatial frequencies is shown to be a parallelepiped, admitting simple geometrical interpretation. Results are used in design of linear, planar, and 3D arrays.

High-dimensional fast convolutional framework (HICU) for calibrationless MRI.

PURPOSE: To present a computational procedure for accelerated, calibrationless magnetic resonance image (Cl-MRI) reconstruction that is fast, memory efficient, and scales to high-dimensional imaging. THEORY AND METHODS: Cl-MRI methods can enable high acceleration rates and flexible sampling patterns, but their clinical application is limited by computational complexity and large memory footprint. The proposed computational procedure, HIgh-dimensional fast convolutional framework (HICU), provides fast, memory-efficient recovery of unsampled k-space points. For demonstration, HICU is applied to 6 2D T2-weighted brain, 7 2D cardiac cine, 5 3D knee, and 1 multi-shot diffusion weighted imaging (MSDWI) datasets. RESULTS: The 2D imaging results show that HICU can offer 1-2 orders of magnitude computation speedup compared to other Cl-MRI methods without sacrificing imaging quality. The 2D cine and 3D imaging results show that the computational acceleration techniques included in HICU yield computing time on par with SENSE-based compressed sensing methods with up to 3 dB improvement in signal-to-error ratio and better perceptual quality. The MSDWI results demonstrate the feasibility of HICU for a challenging multi-shot echo-planar imaging application. CONCLUSIONS: The presented method, HICU, offers efficient computation and scalability as well as extendibility to a wide variety of MRI applications.

Patient-Adaptive Magnetic Resonance Oximetry: Comparison With Invasive Catheter Measurement of Blood Oxygen Saturation in Patients With Cardiovascular Disease.

BACKGROUND: The current standard method to measure intracardiac oxygen (O2 ) saturation is by invasive catheterization. Accurate noninvasive blood O2 saturation by MRI could potentially reduce the duration and risk of invasive diagnostic procedures. PURPOSE: To noninvasively determine blood oxygen saturation in the heart with MRI and compare the accuracy with catheter measurements. STUDY TYPE: Prospective. SUBJECTS: Thirty-two patients referred for right heart catheterization (RHC) and five healthy subjects. FIELD STRENGTH/SEQUENCE: T2-prepared single-shot balanced steady-state free-precession at 1.5T. ASSESSMENT: MR signals in venous and arterial blood, hematocrit, and arterial O2 saturation from a pulse oximeter were jointly processed to fit the Luz-Meiboom model and estimate blood O2 saturation in the right heart. Interstudy reproducibility was evaluated in volunteers and patients. Interobserver reproducibility among three readers was assessed using data from volunteers and 10 patients. Accuracy of MR oximetry was compared to RHC in all patients. STATISTICAL TESTS: Coefficient of variation, intraclass correlation coefficient, Bland-Altman analysis, Pearson's correlation. RESULTS: The coefficient of variation for interstudy reproducibility of O2 saturation was 2.6% on average in volunteers and 3.2% in patients. Interobserver reproducibility among three observers yielded intraclass correlation coefficients of 0.81 and 0.87 respectively for RV and MPA O2 saturation. O2 saturation (y = 0.85x + 0.13, R = 0.78) and (a-v)O2 difference (y = 0.71x + 0.90, R = 0.69) by MR and RHC were significantly correlated (N = 32, P < 0.05 in both cases) in patients. MR slightly overestimated O2 saturation compared to RHC with 2% ± 5% bias and limits of agreement between -7% and 12%. DATA CONCLUSION: MR oximetry is repeatable and reproducible. Good agreement was shown between MR and catheter venous O2 saturation and (a-v)O2 difference in a cohort whose venous O2 ranged from abnormally low to high levels, with most values in the normal physiological range. LEVEL OF EVIDENCE: 2. TECHNICAL EFFICACY STAGE: 2.

A Bayesian approach for 4D flow imaging of aortic valve in a single breath-hold.

PURPOSE: To develop and validate a data processing technique that allows phase-contrast MRI-based 4D flow imaging of the aortic valve in a single breath-hold. THEORY AND METHODS: To regularize the ill-posed inverse problem, we extend a recently proposed 2D phase-contrast MRI method to 4D flow imaging. Adopting an empirical Bayes approach, spatial and temporal redundancies are exploited via sparsity in the wavelet domain, and the voxel-wise magnitude and phase structure across encodings is captured in a conditional mixture prior that applies regularizing constraints based on the presence of flow. We validate the proposed technique using data from a mechanical flow phantom and five healthy volunteers. RESULTS: The flow parameters derived from the proposed technique are in good agreement with those derived from reference datasets for both in vivo and mechanical flow experiments at accelerations rates as high as R = 27. Additionally, the proposed technique outperforms kt SPARSE-SENSE and a method that exploits spatio-temporal sparsity but does not utilize signal structure across encodings. CONCLUSIONS: Using the proposed technique, it is feasible to highly accelerate 4D flow acquisition and thus enable aortic valve imaging within a single breath-hold.

CMR-based blood oximetry via multi-parametric estimation using multiple T2 measurements.

BACKGROUND: Measurement of blood oxygen saturation (O2 saturation) is of great importance for evaluation of patients with many cardiovascular diseases, but currently there are no established non-invasive methods to measure blood O2 saturation in the heart. While T2-based CMR oximetry methods have been previously described, these approaches rely on technique-specific calibration factors that may not generalize across patient populations and are impractical to obtain in individual patients. We present a solution that utilizes multiple T2 measurements made using different inter-echo pulse spacings. These data are jointly processed to estimate all unknown parameters, including O2 saturation, in the Luz-Meiboom (L-M) model. We evaluated the accuracy of the proposed method against invasive catheterization in a porcine hypoxemia model. METHODS: Sufficient data diversity to estimate the various unknown parameters of the L-M model, including O2 saturation, was achieved by acquiring four T2 maps, each at a different τ 180 (12, 15, 20, and 25 ms). Venous and arterial blood T2 values from these maps, together with hematocrit and arterial O2 saturation, were jointly processed to derive estimates for venous O2 saturation and other nuisance parameters in the L-M model. The technique was validated by a progressive graded hypoxemia experiment in seven pigs. CMR estimates of O2 saturation in the right ventricle were compared against a reference O2 saturation obtained by invasive catheterization from the right atrium in each pig, at each hypoxemia stage. O2 saturation derived from the proposed technique was also compared against the previously described method of applying a global calibration factor (K) to the simplified L-M model. RESULTS: Venous O2 saturation results obtained using the proposed CMR oximetry method exhibited better agreement (y = 0.84× + 12.29, R2 = 0.89) with invasive blood gas analysis when compared to O2 saturation estimated by a global calibration method (y = 0.69× + 27.52, R2 = 0.73). CONCLUSIONS: We have demonstrated a novel, non-invasive method to estimate O2 saturation using quantitative T2 mapping. This technique may provide a valuable addition to the diagnostic utility of CMR in patients with congenital heart disease, heart failure, and pulmonary hypertension.

Quantification of aortic stenosis diagnostic parameters: comparison of fast 3 direction and 1 direction phase contrast CMR and transthoracic echocardiography.

BACKGROUND: Aortic stenosis (AS) is a common valvular disorder, and disease severity is currently assessed by transthoracic echocardiography (TTE). However, TTE results can be inconsistent in some patients, thus other diagnostic modalities such as cardiovascular magnetic resonance (CMR) are demanded. While traditional unidirectional phase-contrast CMR (1Dir PC-CMR) underestimates velocity if the imaging plane is misaligned to the flow direction, multi-directional acquisitions are expected to improve velocity measurement accuracy. Nonetheless, clinical use of multidirectional techniques has been hindered by long acquisition times. Our goal was to quantify flow parameters in patients using 1Dir PC-CMR and a faster multi-directional technique (3Dir PC-CMR), and compare to TTE. METHODS: Twenty-three patients were prospectively assessed with TTE and CMR. Slices above the aortic valve were acquired for both PC-CMR techniques and cine SSFP images were acquired to quantify left ventricular stroke volume. 3Dir PC-CMR implementation included a variable density sampling pattern with acceleration rate of 8 and a reconstruction method called ReVEAL, to significantly accelerate acquisition. 3Dir PC-CMR reconstruction was performed offline and ReVEAL-based image recovery was performed on the three (x, y, z) encoding pairs. 1Dir PC-CMR was acquired with GRAPPA acceleration rate of 2 and reconstructed online. CMR derived flow parameters and aortic valve area estimates were compared to TTE. RESULTS: ReVEAL based 3Dir PC-CMR derived parameters correlated better with TTE than 1Dir PC-CMR. Correlations ranged from 0.61 to 0.81 between TTE and 1Dir PC-CMR and from 0.61 to 0.87 between TTE and 3Dir-PC-CMR. The correlation coefficients between TTE, 1Dir and 3Dir PC-CMR Vpeakwere 0.81 and 0.87, respectively. In comparison to ReVEAL, TTE slightly underestimates peak velocities, which is not surprising as TTE is only sensitive to flow that is parallel to the acoustic beam. CONCLUSIONS: By exploiting structure unique to PC-CMR, ReVEAL enables multi-directional flow imaging in clinically feasible acquisition times. Results support the hypothesis that ReVEAL-based 3Dir PC-CMR provides better estimation of hemodynamic parameters in AS patients in comparison to 1Dir PC-CMR. While TTE can accurately measure velocity parallel to the acoustic beam, it is not sensitive to the other directions of flow. Therefore, multi-directional flow imaging, which encodes all three components of the velocity vector, can potentially outperform TTE in patients with eccentric or multiple jets.

A subspace-based coil combination method for phased-array magnetic resonance imaging.

PURPOSE: Coil-by-coil reconstruction methods are followed by coil combination to obtain a single image representing a spin density map. Typical coil combination methods, such as square-root sum-of-squares and adaptive coil combining, yield images that exhibit spatially varying modulation of image intensity. Existing practice is to first combine coils according to a signal-to-noise criterion, then postprocess to correct intensity inhomogeneity. If inhomogeneity is severe, however, intensity correction methods can yield poor results. The purpose of this article is to present an alternative optimality criterion for coil combination; the resulting procedure yields reduced intensity inhomogeneity while preserving contrast. THEORY AND METHODS: A minimum mean squared error criterion is adopted for combining coils via a subspace decomposition. Techniques are compared using both simulated and in vivo data. RESULTS: Experimental results for simulated and in vivo data demonstrate lower bias, higher signal-to-noise ratio (about 7×) and contrast-to-noise ratio (about 2×), compared to existing coil combination techniques. CONCLUSION: The proposed coil combination method is noniterative and does not require estimation of coil sensitivity maps or image mask; the method is particularly suited to cases where intensity inhomogeneity is too severe for existing approaches.

A Bayesian model for highly accelerated phase-contrast MRI.

PURPOSE: Phase-contrast magnetic resonance imaging is a noninvasive tool to assess cardiovascular disease by quantifying blood flow; however, low data acquisition efficiency limits the spatial and temporal resolutions, real-time application, and extensions to four-dimensional flow imaging in clinical settings. We propose a new data processing approach called Reconstructing Velocity Encoded MRI with Approximate message passing aLgorithms (ReVEAL) that accelerates the acquisition by exploiting data structure unique to phase-contrast magnetic resonance imaging. THEORY AND METHODS: The proposed approach models physical correlations across space, time, and velocity encodings. The proposed Bayesian approach exploits the relationships in both magnitude and phase among velocity encodings. A fast iterative recovery algorithm is introduced based on message passing. For validation, prospectively undersampled data are processed from a pulsatile flow phantom and five healthy volunteers. RESULTS: The proposed approach is in good agreement, quantified by peak velocity and stroke volume (SV), with reference data for acceleration rates R≤10. For SV, Pearson r≥0.99 for phantom imaging (n = 24) and r≥0.96 for prospectively accelerated in vivo imaging (n = 10) for R≤10. CONCLUSION: The proposed approach enables accurate quantification of blood flow from highly undersampled data. The technique is extensible to four-dimensional flow imaging, where higher acceleration may be possible due to additional redundancy. Magn Reson Med 76:689-701, 2016. © 2015 Wiley Periodicals, Inc.

Pitfalls and possibilities of radar compressive sensing.

In this paper, we consider the application of compressive sensing (CS) to radar remote sensing applications. We survey a suite of practical system-level issues related to the compression of radar measurements, and we advocate the consideration of these issues by researchers exploring potential gains of CS in radar applications. We also give abbreviated examples of decades-old radio-frequency (RF) practices that already embody elements of CS for relevant applications. In addition to the cautionary implications of system-level issues and historical precedents, we identify several promising results that RF practitioners may gain from the recent explosion of CS literature.

MAXIMIZING UNAMBIGUOUS VELOCITY RANGE IN PHASE-CONTRAST MRI WITH MULTIPOINT ENCODING.

In phase-contrast magnetic resonance imaging (PC-MRI), the velocity of spins at a voxel is encoded in the image phase. The strength of the velocity encoding gradient offers a trade-off between the velocity-to-noise ratio (VNR) and the extent of phase aliasing. Phase differences provide invariance to an unknown background phase. Existing literature proposes processing a reduced set of phase difference equations, simplifying the phase unwrapping problem at the expense of VNR or unaliased range of velocities, or both. Here, we demonstrate that the fullest unambiguous range of velocities is a parallelepiped, which can be accessed by jointly processing all phase differences. The joint processing also maximizes the velocity-to-noise ratio. The simple understanding of the unambiguous parallelepiped provides the potential for analyzing new multi-point acquisitions for an enhanced range of unaliased velocities; two examples are given.

Venc Design and Velocity Estimation for Phase Contrast MRI.

In phase-contrast magnetic resonance imaging (PC-MRI), spin velocity contributes to the phase measured at each voxel. Therefore, estimating velocity from potentially wrapped phase measurements is the task of solving a system of noisy congruence equations. We propose Phase Recovery from Multiple Wrapped Measurements (PRoM) as a fast, approximate maximum likelihood estimator of velocity from multi-coil data with possible amplitude attenuation due to dephasing. The estimator can recover the fullest possible extent of unambiguous velocities, which can greatly exceed twice the highest venc. The estimator uses all pairwise phase differences and the inherent correlations among them to minimize the estimation error. Correlations are directly estimated from multi-coil data without requiring knowledge of coil sensitivity maps, dephasing factors, or the actual per-voxel signal-to-noise ratio. Derivation of the estimator yields explicit probabilities of unwrapping errors and the probability distribution for the velocity estimate; this, in turn, allows for optimized design of the phase-encoded acquisition. These probabilities are also incorporated into spatial post-processing to further mitigate wrapping errors. Simulation, phantom, and in vivo results for three-point PC-MRI acquisitions validate the benefits of reduced estimation error, increased recovered velocity range, optimized acquisition, and fast computation. A phantom study at 1.5T demonstrates 48.5% decrease in root mean squared error using PRoM with post-processing versus a conventional "dual-venc" technique. Simulation and 3T in vivo results likewise demonstrate the proposed benefits.

CALIBRATIONLESS MRI RECONSTRUCTION WITH A PLUG-IN DENOISER.

Magnetic Resonance Imaging (MRI) is a noninvasive imaging technique that provides excellent soft-tissue contrast without using ionizing radiation. MRI's clinical application may be limited by long data acquisition time; therefore, MR image reconstruction from highly under-sampled k-space data has been an active research area. Calibrationless MRI not only enables a higher acceleration rate but also increases flexibility for sampling pattern design. To leverage non-linear machine learning priors, we pair our High-dimensional Fast Convolutional Framework (HICU) [1] with a plug-in denoiser and demonstrate its feasibility using 2D brain data.

CONVOLUTIONAL FRAMEWORK FOR ACCELERATED MAGNETIC RESONANCE IMAGING.

Magnetic Resonance Imaging (MRI) is a noninvasive imaging technique that provides exquisite soft-tissue contrast without using ionizing radiation. The clinical application of MRI may be limited by long data acquisition times; therefore, MR image reconstruction from highly undersampled k-space data has been an active area of research. Many works exploit rank deficiency in a Hankel data matrix to recover unobserved k-space samples; the resulting problem is non-convex, so the choice of numerical algorithm can significantly affect performance, computation, and memory. We present a simple, scalable approach called Convolutional Framework (CF). We demonstrate the feasibility and versatility of CF using measured data from 2D, 3D, and dynamic applications.

Estimation of mean and median pO2 values for a composite EPR spectrum.

Electron paramagnetic resonance (EPR)-based oximetry is capable of quantifying oxygen content in samples. However, for a heterogeneous environment with multiple pO2 values, peak-to-peak linewidth of the composite EPR lineshape does not provide a reliable estimate of the overall pO2 in the sample. The estimate, depending on the heterogeneity, can be severely biased towards narrow components. To address this issue, we suggest a postprocessing method to recover the linewidth histogram which can be used in estimating meaningful parameters, such as the mean and median pO2 values. This information, although not as comprehensive as obtained by EPR spectral-spatial imaging, goes beyond what can be generally achieved with conventional EPR spectroscopy. Substantially shorter acquisition times, in comparison to EPR imaging, may prompt its use in clinically relevant models. For validation, simulation and EPR experiment data are presented.

A parametric approach to spectral-spatial EPR imaging.

Continuous wave electron paramagnetic resonance imaging for in vivo mapping of spin distribution and spectral shape requires rapid data acquisition. A spectral-spatial imaging technique is presented that provides an order of magnitude reduction in acquisition time, compared to iterative tomographic reprojection. The proposed approach assumes that spectral shapes in the sample are well-approximated by members from a parametric family of functions. A model is developed for the spectra measured with magnetic field modulation. Parameters defining the spin distribution and spectral shapes are then determined directly from the measurements using maximum a posteriori probability estimation. The approach does not suffer approximation error from limited sweep width of the main magnetic field and explicitly incorporates the variability in signal-to-noise ratio versus strength of magnetic field gradient. The processing technique is experimentally demonstrated on a one-dimensional phantom containing a nitroxide spin label with constant g-factor. Using an L-band EPR spectrometer, spectral shapes and spin distribution are accurately recovered from two projections and a spectral window which is comparable to the maximum linewidth of the sample.

Uniform distribution of projection data for improved reconstruction quality of 4D EPR imaging.

In continuous wave (CW) electron paramagnetic resonance imaging (EPRI), high quality of reconstruction in a limited acquisition time is a high priority. It has been shown for the case of 3D EPRI, that a uniform distribution of the projection data generally enhances reconstruction quality. In this work, we have suggested two data acquisition techniques for which the gradient orientations are more evenly distributed over the 4D acquisition space as compared to the existing methods. The first sampling technique is based on equal solid angle partitioning of 4D space, while the second technique is based on Fekete points estimation in 4D to generate a more uniform distribution of data. After acquisition, filtered backprojection (FBP) is applied to carry out the reconstruction in a single stage. The single-stage reconstruction improves the spatial resolution by eliminating the necessity of data interpolation in multi-stage reconstructions. For the proposed data distributions, the simulations and experimental results indicate a higher fidelity to the true object configuration. Using the uniform distribution, we expect about 50% reduction in the acquisition time over the traditional method of equal linear angle acquisition.

Multivariate MIMO FIR inverses.

The problem of computing exact finite impulse response (FIR) inverses for multivariate multiple-input multiple-output (MIMO) FIR systems is considered. Necessary and sufficient conditions for invertibility are given, along with computation techniques. Random systems and structured systems are defined. Necessary and sufficient conditions for the almost sure invertibility of structured random systems are derived. Bounds on the orders of the inverse filters are computed.