Rational approximation of golden angles: Accelerated reconstructions for radial MRI.

PURPOSE: To develop a generic radial sampling scheme that combines the advantages of golden ratio sampling with simplicity of equidistant angular patterns. The irrational angle between consecutive spokes in golden ratio-based sampling schemes enables a flexible retrospective choice of temporal resolution, while preserving good coverage of k-space for each individual bin. Nevertheless, irrational increments prohibit precomputation of the point-spread function (PSF), can lead to numerical problems, and require more complex processing steps. To avoid these problems, a new sampling scheme based on a rational approximation of golden angles (RAGA) is developed. METHODS: The theoretical properties of RAGA sampling are mathematically derived. Sidelobe-to-peak ratios (SPR) are numerically computed and compared to the corresponding golden ratio sampling schemes. The sampling scheme is implemented in the BART toolbox and in a radial gradient-echo sequence. Feasibility is shown for quantitative imaging in a phantom and a cardiac scan of a healthy volunteer. RESULTS: RAGA sampling can accurately approximate golden ratio sampling and has almost identical PSF and SPR. In contrast to golden ratio sampling, each frame can be reconstructed with the same equidistant trajectory using different sampling masks, and the angle of each acquired spoke can be encoded as a small index, which simplifies processing of the acquired data. CONCLUSION: RAGA sampling provides the advantages of golden ratio sampling while simplifying data processing, rendering it a valuable tool for dynamic and quantitative MRI.

Rational Approximation of Golden Angles: Accelerated Reconstructions for Radial MRI.

PURPOSE: To develop a generic radial sampling scheme that combines the advantages of golden ratio sampling with simplicity of equidistant angular patterns. The irrational angle between consecutive spokes in golden ratio based sampling schemes enables a flexible retrospective choice of temporal resolution, while preserving good coverage of k-space for each individual bin. Nevertheless, irrational increments prohibit precomputation of the point-spread function (PSF), can lead to numerical problems, and require more complex processing steps. To avoid these problems, a new sampling scheme based on a rational approximation of golden angles (RAGA) is developed. METHODS: The theoretical properties of RAGA sampling are mathematically derived. Sidelobe-to-peak ratios (SPR) are numerically computed and compared to the corresponding golden ratio sampling schemes. The sampling scheme is implemented in the BART toolbox and in a radial gradient-echo sequence. Feasibility is shown for quantitative imaging in a phantom and a cardiac scan of a healthy volunteer. RESULTS: RAGA sampling can accurately approximate golden ratio sampling and has almost identical PSF and SPR. In contrast to golden ratio sampling, each frame can be reconstructed with the same equidistant trajectory using different sampling masks, and the angle of each acquired spoke can be encoded as a small index, which simplifies processing of the acquired data. CONCLUSION: RAGA sampling provides the advantages of golden ratio sampling while simplifying data processing, rendering it a valuable tool for dynamic and quantitative MRI.

Free-breathing myocardial T1 mapping using inversion-recovery radial FLASH and motion-resolved model-based reconstruction.

PURPOSE: To develop a free-breathing myocardial T 1 $$ {\mathrm{T}}_1 $$ mapping technique using inversion-recovery (IR) radial fast low-angle shot (FLASH) and calibrationless motion-resolved model-based reconstruction. METHODS: Free-running (free-breathing, retrospective cardiac gating) IR radial FLASH is used for data acquisition at 3T. First, to reduce the waiting time between inversions, an analytical formula is derived that takes the incomplete T 1 $$ {\mathrm{T}}_1 $$ recovery into account for an accurate T 1 $$ {\mathrm{T}}_1 $$ calculation. Second, the respiratory motion signal is estimated from the k-space center of the contrast varying acquisition using an adapted singular spectrum analysis (SSA-FARY) technique. Third, a motion-resolved model-based reconstruction is used to estimate both parameter and coil sensitivity maps directly from the sorted k-space data. Thus, spatiotemporal total variation, in addition to the spatial sparsity constraints, can be directly applied to the parameter maps. Validations are performed on an experimental phantom, 11 human subjects, and a young landrace pig with myocardial infarction. RESULTS: In comparison to an IR spin-echo reference, phantom results confirm good T 1 $$ {\mathrm{T}}_1 $$ accuracy, when reducing the waiting time from 5 s to 1 s using the new correction. The motion-resolved model-based reconstruction further improves T 1 $$ {\mathrm{T}}_1 $$ precision compared to the spatial regularization-only reconstruction. Aside from showing that a reliable respiratory motion signal can be estimated using modified SSA-FARY, in vivo studies demonstrate that dynamic myocardial T 1 $$ {\mathrm{T}}_1 $$ maps can be obtained within 2 min with good precision and repeatability. CONCLUSION: Motion-resolved myocardial T 1 $$ {\mathrm{T}}_1 $$ mapping during free-breathing with good accuracy, precision and repeatability can be achieved by combining inversion-recovery radial FLASH, self-gating and a calibrationless motion-resolved model-based reconstruction.

Deep, deep learning with BART.

PURPOSE: To develop a deep-learning-based image reconstruction framework for reproducible research in MRI. METHODS: The BART toolbox offers a rich set of implementations of calibration and reconstruction algorithms for parallel imaging and compressed sensing. In this work, BART was extended by a nonlinear operator framework that provides automatic differentiation to allow computation of gradients. Existing MRI-specific operators of BART, such as the nonuniform fast Fourier transform, are directly integrated into this framework and are complemented by common building blocks used in neural networks. To evaluate the use of the framework for advanced deep-learning-based reconstruction, two state-of-the-art unrolled reconstruction networks, namely the Variational Network and MoDL, were implemented. RESULTS: State-of-the-art deep image-reconstruction networks can be constructed and trained using BART's gradient-based optimization algorithms. The BART implementation achieves a similar performance in terms of training time and reconstruction quality compared to the original implementations based on TensorFlow. CONCLUSION: By integrating nonlinear operators and neural networks into BART, we provide a general framework for deep-learning-based reconstruction in MRI.

Model-based reconstruction for simultaneous multi-slice T1 mapping using single-shot inversion-recovery radial FLASH.

PURPOSE: To develop a single-shot multi-slice T1 mapping method by combing simultaneous multi-slice (SMS) excitations, single-shot inversion-recovery (IR) radial fast low-angle shot (FLASH), and a nonlinear model-based reconstruction method. METHODS: SMS excitations are combined with a single-shot IR radial FLASH sequence for data acquisition. A previously developed single-slice calibrationless model-based reconstruction is extended to SMS, formulating the estimation of parameter maps and coil sensitivities from all slices as a single nonlinear inverse problem. Joint-sparsity constraints are further applied to the parameter maps to improve T1 precision. Validations of the proposed method are performed for a phantom and for the human brain and liver in 6 healthy adult subjects. RESULTS: Phantom results confirm good T1 accuracy and precision of the simultaneously acquired multi-slice T1 maps in comparison to single-slice references. In vivo human brain studies demonstrate the better performance of SMS acquisitions compared to the conventional spoke-interleaved multi-slice acquisition using model-based reconstruction. Aside from good accuracy and precision, the results of 6 healthy subjects in both brain and abdominal studies confirm good repeatability between scan and re-scans. The proposed method can simultaneously acquire T1 maps for 5 slices of a human brain ( 0.75×0.75×5mm3 ) or 3 slices of the abdomen ( 1.25×1.25×6mm3 ) within 4 seconds. CONCLUSIONS: The IR SMS radial FLASH acquisition together with a nonlinear model-based reconstruction enable rapid high-resolution multi-slice T1 mapping with good accuracy, precision, and repeatability.

Cardiac and Respiratory Self-Gating in Radial MRI Using an Adapted Singular Spectrum Analysis (SSA-FARY).

Cardiac Magnetic Resonance Imaging (MRI) is time-consuming and error-prone. To ease the patient's burden and to increase the efficiency and robustness of cardiac exams, interest in methods based on continuous steady-state acquisition and self-gating has been growing in recent years. Self-gating methods extract the cardiac and respiratory signals from the measurement data and then retrospectively sort the data into cardiac and respiratory phases. Repeated breathholds and synchronization with the heart beat using some external device as required in conventional MRI are then not necessary. In this work, we introduce a novel self-gating method for radially acquired data based on a dimensionality reduction technique for time-series analysis (SSA-FARY). Building on Singular Spectrum Analysis, a zero-padded, time-delayed embedding of the auto-calibration data is analyzed using Principle Component Analysis. We demonstrate the basic functionality of SSA-FARY using numerical simulations and apply it to in-vivo cardiac radial single-slice bSSFP and Simultaneous Multi-Slice radiofrequency-spoiled gradient-echo measurements, as well as to Stack-of-Stars bSSFP measurements. SSA-FARY reliably detects the cardiac and respiratory motion and separates it from noise. We utilize the generated signals for high-dimensional image reconstruction using parallel imaging and compressed sensing with in-plane wavelet and (spatio-)temporal total-variation regularization.

ENLIVE: An Efficient Nonlinear Method for Calibrationless and Robust Parallel Imaging.

Robustness against data inconsistencies, imaging artifacts and acquisition speed are crucial factors limiting the possible range of applications for magnetic resonance imaging (MRI). Therefore, we report a novel calibrationless parallel imaging technique which simultaneously estimates coil profiles and image content in a relaxed forward model. Our method is robust against a wide class of data inconsistencies, minimizes imaging artifacts and is comparably fast, combining important advantages of many conceptually different state-of-the-art parallel imaging approaches. Depending on the experimental setting, data can be undersampled well below the Nyquist limit. Here, even high acceleration factors yield excellent imaging results while being robust to noise and the occurrence of phase singularities in the image domain, as we show on different data. Moreover, our method successfully reconstructs acquisitions with insufficient field-of-view. We further compare our approach to ESPIRiT and SAKE using spin-echo and gradient echo MRI data from the human head and knee. In addition, we show its applicability to non-Cartesian imaging on radial FLASH cardiac MRI data. Using theoretical considerations, we show that ENLIVE can be related to a low-rank formulation of blind multi-channel deconvolution, explaining why it inherently promotes low-rank solutions.

Simple auto-calibrated gradient delay estimation from few spokes using Radial Intersections (RING).

PURPOSE: To develop a simple and robust tool for the estimation of gradient delays from highly undersampled radial k-space data. THEORY: In radial imaging gradient delays induce parallel and orthogonal trajectory shifts, which can be described using an ellipse model. The intersection points of the radial spokes, which can be estimated by spoke-by-spoke comparison of k-space samples, distinctly determine the parameters of the ellipse. Using the proposed method (RING), these parameters can be obtained using a least-squares fit and utilized for the correction of gradient delays. METHODS: The functionality and accuracy of the proposed RING method is validated and compared to correlation-based gradient-delay estimation from opposing spokes using numerical simulations, phantom and in vivo heart measurements. RESULTS: In all experiments, RING robustly provides accurate gradient delay estimations even for as few as three radial spokes. CONCLUSIONS: The simple and straightforward to implement RING method provides accurate gradient delay estimation for highly undersampled radial imaging.

Frequency-modulated SSFP with radial sampling and subspace reconstruction: A time-efficient alternative to phase-cycled bSSFP.

PURPOSE: A novel subspace-based reconstruction method for frequency-modulated balanced steady-state free precession (fmSSFP) MRI is presented. In this work, suitable data acquisition schemes, subspace sizes, and efficiencies for banding removal are investigated. THEORY AND METHODS: By combining a fmSSFP MRI sequence with a 3D stack-of-stars trajectory, scan efficiency is maximized as spectral information is obtained without intermediate preparation phases. A memory-efficient reconstruction routine is implemented by introducing the low-frequency Fourier transform as a subspace which allows for the formulation of a convex reconstruction problem. The removal of banding artifacts is investigated by comparing the proposed acquisition and reconstruction technique to phase-cycled bSSFP MRI. Aliasing properties of different undersampling schemes are analyzed and water/fat separation is demonstrated by reweighting the reconstructed subspace coefficients to generate virtual spectral responses in a post-processing step. RESULTS: A simple root-of-sum-of-squares combination of the reconstructed subspace coefficients yields high-SNR images with the characteristic bSSFP contrast but without banding artifacts. Compared to Golden-Angle trajectories, turn-based sampling schemes were superior in minimizing aliasing across reconstructed subspace coefficients. Water/fat separated images of the human knee were obtained by reweighting subspace coefficients. CONCLUSIONS: The novel subspace-based fmSSFP MRI technique emerges as a time-efficient alternative to phase-cycled bSFFP. The method does not need intermediate preparation phases, offers high SNR and avoids banding artifacts. Reweighting of the reconstructed subspace coefficients allows for generating virtual spectral responses with applications to water/fat separation.

Sinogram-based coil selection for streak artifact reduction in undersampled radial real-time magnetic resonance imaging.

BACKGROUND: Streak artifacts are a common problem in radial magnetic resonance imaging (MRI). We therefore developed a method for automatically excluding receiver coil elements which lead to these artifacts. METHODS: The proposed coil selection relates to real-time MRI data based on highly undersampled radial acquisitions. It exploits differences between high- and low-resolution sinograms reconstructed from datasets acquired during preparatory scans. Apart from phantom validations, the performance was assessed for real-time MRI studies of different human organ systems in vivo. RESULTS: The algorithm greatly reduces streak artifact strength without compromising image quality in other parts of the image. It is robust with respect to different experimental settings and fast to be included in the online reconstruction pipeline for real-time MRI. CONCLUSIONS: The proposed method enables a fast reduction of streak artifacts in radial real-time MRI.

Determination of enzymatic hydrolysis specificity of partially N-acetylated chitosans.

A new method for determining the specificity of hydrolysis of the linear binary heteropolysaccharide chitosan composed of (1-->4)-linked 2-acetamido-2-deoxy-beta-D-glucopyranose (GlcNAc; A-unit) and 2-amino-2-deoxy-beta-D-glucopyranose (GlcN; D-unit) residues is described. The method is based on the assignments of the 13C chemical shifts of the identity (A- or D-units) of the new reducing and non-reducing ends and the variation in their nearest neighbours, using low molecular weight chitosans with known random distribution of A- and D-units as substrate. A highly N-acetylated chitosan with fraction of acetylated units (FA) of 0.68 and a number-average degree of polymerization (DPn) of 30 was hydrolysed with hen egg-white lysozyme, showing that both the new reducing and non-reducing ends consisted exclusively of A-units, indicating a high specificity for A-units in subsites DL and EL on lysozyme. Our data suggests that the preceding unit of the reducing A-units, is invariable, and based on earlier studies, most probably an A-unit, while the unit following the non-reducing A-units can be either an A- or a D-unit. A more detailed study of the specificity of lysozyme at subsite DL was performed by hydrolyzing a more deacetylated chitosan (FA = 0.35 and DPn of 20) to a DPn of 9, showing that even for this chitosan more than 90% of the new reducing ends were acetylated units. Thus, lysozyme depolymerizes partially N-acetylated chitosans by preferentially hydrolyzing sequences of acetylated units bound to site CL, DL and EL of the active cleft, while there is no specificity between acetylated and deacetylated units to site FL. In addition, a moderately N-acetylated chitosan with fraction of acetylated units (FA) of 0.35 and a DPn of 20 was hydrolysed with Bacillus sp. No. 7-M chitosanase, showing that both the new reducing and non-reducing ends consisted exclusively of D-units. Our data suggests that the nearest neigbour to the D-unit at the reducing end is invariable, and based on earlier studies, most probably a D-unit, while the unit following the non-reducing D-units can be either an A- or a D-unit. We conclude that the Bacillus chitosanase hydrolyzes partially N-acetylated chitosan by preferentially attacking sequences of three consecutive deacetylated units, hypothetical subsites CC, DC and EC, where the cleavage occur between sugar units bound to subsites DC and EC. A hypothetical subsite FC on the chitosanase show no specificity with respect to A- and D-units. The new NMR method described herein offers a time and labour-saving alternative to the procedure of extensive hydrolysis of the binary heteropolysaccharide chitosan and subsequent isolation and characterization of the oligosaccharides.