Accelerated Parameter Mapping of Multiple-Echo Gradient-Echo Data Using Model-Based Iterative Reconstruction

QRAGE-Simultaneous multiparametric quantitative MRI of water content, T1, T2*, and magnetic susceptibility at ultrahigh field strength

PURPOSE

To introduce quantitative rapid gradient-echo (QRAGE), a novel approach for the simultaneous mapping of multiple quantitative MRI parameters, including water content, T1, T2*, and magnetic susceptibility at ultrahigh field strength.

METHODS

QRAGE leverages a newly developed multi-echo MPnRAGE sequence, facilitating the acquisition of 171 distinct contrast images across a range of TI and TE points. To maintain a short acquisition time, we introduce MIRAGE2, a novel model-based reconstruction method that exploits prior knowledge of temporal signal evolution, represented as damped complex exponentials. MIRAGE2 minimizes local Block-Hankel and Casorati matrices. Parameter maps are derived from the reconstructed contrast images through postprocessing steps. We validate QRAGE through extensive simulations, phantom studies, and in vivo experiments, demonstrating its capability for high-precision imaging.

RESULTS

In vivo brain measurements show the promising performance of QRAGE, with test-retest SDs and deviations from reference methods of < 0.8% for water content, < 17 ms for T1, and < 0.7 ms for T2*. QRAGE achieves whole-brain coverage at a 1-mm isotropic resolution in just 7 min and 15 s, comparable to the acquisition time of an MP2RAGE scan. In addition, QRAGE generates a contrast image akin to the UNI image produced by MP2RAGE.

CONCLUSION

QRAGE is a new, successful approach for simultaneously mapping multiple MR parameters at ultrahigh field.

Highly accelerated parameter mapping using model-based alternating reconstruction coupling fitting

Objective.A model-based alternating reconstruction coupling fitting, termed Model-based Alternating Reconstruction COupling fitting (MARCO), is proposed for accurate and fast magnetic resonance parameter mapping.Approach.MARCO utilizes the signal model as a regularization by minimizing the bias between the image series and the signal produced by the suitable signal model based on iteratively updated parameter maps when reconstructing. The technique can incorporate prior knowledge of both image series and parameters by adding sparsity constraints. The optimization problem is decomposed into three subproblems and solved through three alternating steps involving reconstruction and nonlinear least-square fitting, which can produce both contrast-weighted images and parameter maps simultaneously.Main results.The algorithm is applied toT2mapping with extended phase graph algorithm integrated and validated on undersampled multi-echo spin-echo data from both phantom and in vivo sources. Compared with traditional compressed sensing and model-based methods, the proposed approach yields more accurateT2maps with more details at high acceleration factors.Significance.The proposed method provides a basic framework for quantitative MR relaxometry, theoretically applicable to all quantitative MR relaxometry. It has the potential to improve the diagnostic utility of quantitative imaging techniques.

Accelerated multiple-quantum-filtered sodium magnetic resonance imaging using compressed sensing at 7 T

PURPOSE

Multiple-quantum-filtered (MQF) sodium magnetic resonance imaging (MRI), such as enhanced single-quantum and triple-quantum-filtered imaging of 23Na (eSISTINA), enables images to be weighted towards restricted sodium, a promising biomarker in clinical practice, but often suffers from clinically infeasible acquisition times and low image quality. This study aims to mitigate the above limitation by implementing a novel eSISTINA sequence at 7 T with the application of compressed sensing (CS) to accelerate eSISTINA acquisitions without a noticeable loss of information.

METHODS

A novel eSISTINA sequence with a 3D spiral-based sampling scheme was implemented at 7 T for the application of CS. Fully sampled datasets were obtained from one phantom and ten healthy subjects, and were then retrospectively undersampled by various undersampling factors. CS undersampled reconstructions were compared to fully sampled and undersampled nonuniform fast Fourier transform (NUFFT) reconstructions. Reconstruction performance was evaluated based on structural similarity (SSIM), signal-to-noise ratio (SNR), weightings towards total and compartmental sodium, and in vivo quantitative estimates.

RESULTS

CS-based phantom and in vivo images have less noise and better structural delineation while maintaining the weightings towards total, non-restricted (predominantly extracellular), and restricted (primarily intracellular) sodium. CS generally outperforms NUFFT with a higher SNR and a better SSIM, except for the SSIM in TQ brain images, which is likely due to substantial noise contamination. CS enables in vivo quantitative estimates with <15% errors at an undersampling factor of up to two.

CONCLUSIONS

Successful implementation of an eSISTINA sequence with an incoherent sampling scheme at 7 T was demonstrated. CS can accelerate eSISTINA by up to twofold at 7 T with reduced noise levels compared to NUFFT, while maintaining major structural information, reasonable weightings towards total and compartmental sodium, and relatively reliable in vivo quantification. The associated reduction in acquisition time has the potential to facilitate the clinical applicability of MQF sodium MRI.

Acceleration Strategies for MR-STAT: Achieving High-Resolution Reconstructions on a Desktop PC Within 3 Minutes

MR-STAT is an emerging quantitative magnetic resonance imaging technique which aims at obtaining multi-parametric tissue parameter maps from single short scans. It describes the relationship between the spatial-domain tissue parameters and the time-domain measured signal by using a comprehensive, volumetric forward model. The MR-STAT reconstruction solves a large-scale nonlinear problem, thus is very computationally challenging. In previous work, MR-STAT reconstruction using Cartesian readout data was accelerated by approximating the Hessian matrix with sparse, banded blocks, and can be done on high performance CPU clusters with tens of minutes. In the current work, we propose an accelerated Cartesian MR-STAT algorithm incorporating two different strategies: firstly, a neural network is trained as a fast surrogate to learn the magnetization signal not only in the full time-domain but also in the compressed low-rank domain; secondly, based on the surrogate model, the Cartesian MR-STAT problem is re-formulated and split into smaller sub-problems by the alternating direction method of multipliers. The proposed method substantially reduces the computational requirements for runtime and memory. Simulated and in-vivo balanced MR-STAT experiments show similar reconstruction results using the proposed algorithm compared to the previous sparse Hessian method, and the reconstruction times are at least 40 times shorter. Incorporating sensitivity encoding and regularization terms is straightforward, and allows for better image quality with a negligible increase in reconstruction time. The proposed algorithm could reconstruct both balanced and gradient-spoiled in-vivo data within 3 minutes on a desktop PC, and could thereby facilitate the translation of MR-STAT in clinical settings.

Accelerated MRI Reconstruction With Separable and Enhanced Low-Rank Hankel Regularization

Magnetic resonance imaging serves as an essential tool for clinical diagnosis, however, suffers from a long acquisition time. Sparse sampling effectively saves this time but images need to be faithfully reconstructed from undersampled data. Among the existing reconstruction methods, the structured low-rank methods have advantages in robustness to the sampling patterns and lower error. However, the structured low-rank methods use the 2D or higher dimension k-space data to build a huge block Hankel matrix, leading to considerable time and memory consumption. To reduce the size of the Hankel matrix, we proposed to separably construct multiple small Hankel matrices from rows and columns of the k-space and then constrain the low-rankness on these small matrices. This separable model can significantly reduce the computational time but ignores the correlation existed in inter- and intra-row or column, resulting in increased reconstruction error. To improve the reconstructed image without obviously increasing the computation, we further introduced the self-consistency of k-space and virtual coil prior. Besides, the proposed separable model can be extended into other imaging scenarios which hold exponential characteristics in the parameter dimension. The in vivo experimental results demonstrated that the proposed method permits the lowest reconstruction error with a fast reconstruction. The proposed approach requires only 4% of the state-of-the-art STDLR-SPIRiT runtime for parallel imaging reconstruction, and achieves the fastest computational speed in parameter imaging reconstruction.

A simultaneous multi-slice T2 mapping framework based on overlapping-echo detachment planar imaging and deep learning reconstruction

PURPOSE

Quantitative MRI (qMRI) is of great importance to clinical medicine and scientific research. However, most qMRI techniques are time-consuming and sensitive to motion, especially when a large 3D volume is imaged. To accelerate the acquisition, a framework is proposed to realize reliable simultaneous multi-slice T₂ mapping.

METHODS

The simultaneous multi-slice T₂ mapping framework is based on overlapping-echo detachment (OLED) planar imaging (dubbed SMS-OLED). Multi-slice overlapping-echo signals were generated by multiple excitation pulses together with echo-shifting gradients. The signals were excited and acquired with a single-channel coil. U-Net was used to reconstruct T₂ maps from the acquired overlapping-echo image.

RESULTS

Single-shot double-slice and two-shot triple-slice SMS-OLED scan schemes were designed according to the framework for evaluation. Simulations, water phantom, and in vivo rat brain experiments were carried out. Overlapping-echo signals were acquired, and T₂ maps were reconstructed and compared with references. The results demonstrate the superior performance of our method.

CONCLUSION

Two slices of T₂ maps can be obtained in a single shot within hundreds of milliseconds. Higher quality multi-slice T₂ maps can be obtained via multiple shots. SMS-OLED provides a lower specific absorption rate scheme compared with conventional SMS methods with a coil with only a single receiver channel. The new method is of potential in dynamic qMRI and functional qMRI where temporal resolution is vital.

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'.

Improving subspace constrained radial fast spin echo MRI using block matching driven non-local low rank regularization

Subspace-constrained reconstruction methods restrict the relaxation signals (of size M) in the scene to a pre-determined subspace (of size K≪M) and allow multi-contrast imaging and parameter mapping from accelerated acquisitions. However, these constraints yield poor image quality at some imaging contrasts, which can impact the parameter mapping performance. Additional regularization such as the use of joint-sparse (JS) or locally-low-rank (LLR) constraints can help improve the recovery of these images but are not sufficient when operating at high acceleration rates. We propose a method, non-local rank 3D (NLR3D), that is built on block matching and transform domain low rank constraints to allow high quality recovery of subspace-coefficient images (SCI) and subsequent multi-contrast imaging and parameter mapping. The performance of NLR3D was evaluated using Monte-Carlo (MC) simulations and compared against the JS and LLR methods. In vivo T 2 mapping results are presented on brain and knee datasets. MC results demonstrate improved bias, variance, and MSE behavior in both the multi-contrast images and parameter maps when compared to the JS and LLR methods. In vivo brain and knee results at moderate and high acceleration rates demonstrate improved recovery of high SNR early TE images as well as parameter maps. No significant difference was found in the T2 values measured in ROIs between the NLR3D reconstructions and the reference images (Wilcoxon signed rank test). The proposed method, NLR3D, enables recovery of high-quality SCI and, consequently, the associated multi-contrast images and parameter maps.

Efficient eddy current characterization using a 2D image-based sampling scheme and a model-based fitting approach

PURPOSE

To propose two innovations to existing eddy current characterization techniques, which include (1) an efficient spatio-temporal sampling scheme and (2) a model-based fitting of spherical harmonic eddy current components.

THEORY AND METHODS

This work introduces a three-plane 2D image-based acquisition scheme to efficiently sample eddy current fields. Additionally, a model-based spherical harmonic decomposition is presented, which reduces fitting noise using a rank minimization to impose an exponential decay on the eddy current amplitude evolution. Both techniques are applied in combination and analyzed in simulations for their applicability in reconstructing suitable pre-emphasis parameters. In a proof-of-concept measurement, the routine is tested for its propriety to correctly quantify user-defined field dynamics. Furthermore, based on acquired precompensation and postcompensation eddy current data, the suitability of pre-emphasis parameters calculated based on the proposed technique is evaluated.

RESULTS

Simulation results derived from 500 data sets demonstrate the applicability of the acquisition scheme for the spatio-temporal sampling of eddy current fields. Compared with a conventional data processing strategy, the proposed model-based approach yields pre-emphasis parameters that reduce the average maximum residual field offset within a 10-cm-diameter spherical volume from 3.17 Hz to 0.58 Hz. Experimental data prove the proposed routine to be suitable to measure and effectively compensate for eddy currents within 10 minutes of acquisition time.

CONCLUSION

The proposed framework was found to be well-suited to efficiently characterize and compensate for eddy current fields in a one-time calibration effort. It can be applied to facilitate pre-emphasis implementations, such as for dynamic B₀ shimming applications.

Blind Source Separation for Myelin Water Fraction Mapping Using Multi-Echo Gradient Echo Imaging

In conventional gradient-echo myelin water imaging (GRE-MWI), myelin water fraction (MWF) is estimated by fitting the multi-echo gradient recalled echo (mGRE) signal to a pre-assumed numerical model (e.g., multi-component exponential curves or three component exponential curves). However, in mGRE, imaging artifacts (e.g., voxel spread function and physiological noise) and noise render the signal to deviate from the numerical model, leading to misfit of the model parameters. Here, as an alternative to the model-based GRE-MWI, a blind source separation (BSS) technique for the separation of multi-exponential mGRE signal is proposed. Among the various BSS techniques, a modified robust principal component analysis (rPCA) is presented to separate signal sources by enforcing the data-driven properties such as "low rankness" and "sparsity." Considering the signal evolution of T₂^∗ relaxation (i.e., non-negative exponential decay), low rankness of exponential decay was enforced by nonnegative matrix factorization (NMF) and hankelization. This method provides the separation of slow-decaying, fast-decaying exponential components and artifact components from mGRE images. After the separation, MWF map is reconstructed as the ratio of the fast-decaying component to the total decaying components. The proposed method was demonstrated in numerical simulations and in vivo scans. The method provided a robust estimation of MWF in the presence of statistical noise and imaging artifacts.

A Single-Scan, Rapid Whole-Brain Protocol for Quantitative Water Content Mapping With Neurobiological Implications

Water concentration is tightly regulated in the healthy human brain and changes only slightly with age and gender in healthy subjects. Consequently, changes in water content are important for the characterization of disease. MRI can be used to measure changes in brain water content, but as these changes are usually in the low percentage range, highly accurate and precise methods are required for detection. The method proposed here is based on a long-TR (10 s) multiple-echo gradient-echo measurement with an acquisition time of 7:21 min. Using such a long TR ensures that there is no T₁ weighting, meaning that the image intensity at zero echo time is only proportional to the water content, the transmit field, and to the receive field. The receive and transmit corrections, which are increasingly large at higher field strengths and for highly segmented coil arrays, are multiplicative and can be approached heuristically using a bias field correction. The method was tested on 21 healthy volunteers at 3T field strength. Calibration using cerebral-spinal fluid values (~100% water content) resulted in mean values and standard deviations of the water content distribution in white matter and gray matter of 69.1% (1.7%) and 83.7% (1.2%), respectively. Measured distributions were coil-independent, as seen by using either a 12-channel receiver coil or a 32-channel receiver coil. In a test-retest investigation using 12 scans on one volunteer, the variation in the mean value of water content for different tissue types was ~0.3% and the mean voxel variability was ~1%. Robustness against reduced SNR was assessed by comparing results for 5 additional volunteers at 1.5T and 3T. Furthermore, water content distribution in gray matter is investigated and regional contrast reported for the first time. Clinical applicability is illustrated with data from one stroke patient and one brain tumor patient. It is anticipated that this fast, stable, easy-to-use, high-quality mapping method will facilitate routine quantitative MR imaging of water content.

Multi-Exponential Relaxometry Using l1 -Regularized Iterative NNLS (MERLIN) With Application to Myelin Water Fraction Imaging

A new parameter estimation algorithm, MERLIN, is presented for accurate and robust multi-exponential relaxometry using magnetic resonance imaging, a tool that can provide valuable insight into the tissue microstructure of the brain. Multi-exponential relaxometry is used to analyze the myelin water fraction and can help to detect related diseases. However, the underlying problem is ill-conditioned, and as such, is extremely sensitive to noise and measurement imperfections, which can lead to less precise and more biased parameter estimates. MERLIN is a fully automated, multi-voxel approach that incorporates state-of-the-art l₁ -regularization to enforce sparsity and spatial consistency of the estimated distributions. The proposed method is validated in simulations and in vivo experiments, using a multi-echo gradient-echo (MEGE) sequence at 3 T. MERLIN is compared to the conventional single-voxel l₂ -regularized NNLS (rNNLS) and a multi-voxel extension with spatial priors (rNNLS + SP), where it consistently showed lower root mean squared errors of up to 70 percent for all parameters of interest in these simulations.

Sub-millimeter T1 mapping of rapidly relaxing compartments with gradient delay corrected spiral TAPIR and compressed sensing at 3T

PURPOSE

The TAPIR sequence is an accurate and efficient method for T₁ mapping. It combines a slice-interleaving Look-Locker read-out with an acquisition of multiple k-space lines in 1 shot. Whereas the acquisition of multiple lines per excitation increases imaging speed, the corresponding increase in TR and TE is detrimental to the T₁ fitting performance. This is especially problematic for substances exhibiting rapid T₂ ^* relaxation (e.g., myelin water).

METHODS

The T₁ fitting performance of TAPIR is enhanced by using an interleaved spiral read-out with shorter TE and TR. Furthermore, an improvement to a method for fast gradient delay estimation is presented. Whereas previous methods assume the gradient delay to be stationary, the presented approach corrects the spiral k-space trajectory by using a polynomial fit of the measured gradient delays.

RESULTS

Gradient delay artifacts are largely eliminated, requiring very little additional scanning time. The sampling efficiency of the spiral read-out allows for a significant reduction of the acquisition time in comparison to Cartesian TAPIR. Spiral TAPIR enables the sampling of more slices and an accurate measurement of rapidly relaxing compartments. Over a wide T₁ range (448-3115 ms), spiral TAPIR reduces the mean fitting error from -2.5% to -0.1%. Combining 50% undersampling with the shorter TR of spiral TAPIR, an increase in imaging speed by a factor of up to 3.3 was achieved.

CONCLUSION

Using a spiral read-out trajectory, the established TAPIR sequence enables measurement of rapidly relaxing T₁ compartments, while improving T₁ mapping performance and imaging speed.