Fast T2 mapping with improved accuracy using undersampled spin-echo MRI and model-based reconstructions with a generating function

Constrained alternating minimization for parameter mapping (CAMP)

OBJECTIVE

To improve image quality in highly accelerated parameter mapping by incorporating a linear constraint that relates consecutive images.

APPROACH

In multi-echo T1 or T2 mapping, scan time is often shortened by acquiring undersampled but complementary measures of k-space at each TE or TI. However, residual undersampling artifacts from the individual images can then degrade the quality of the final parameter maps. In this work, a new reconstruction method, dubbed Constrained Alternating Minimization for Parameter mapping (CAMP), is introduced. This method simultaneously extracts T2 or T1* maps in addition to an image for each TE or TI from accelerated datasets, leveraging the constraints of the decay to improve the reconstructed image quality. The model enforces exponential decay through a linear constraint, resulting in a biconvex objective function that lends itself to alternating minimization. The method was tested in four in vivo volunteer experiments and validated in phantom studies and healthy subjects, using T2 and T1 mapping, with accelerations of up to 12.

MAIN RESULTS

CAMP is demonstrated for accelerated radial and Cartesian acquisitions in T2 and T1 mapping. The method is even applied to generate an entire T2 weighted image series from a single TSE dataset, despite the blockwise k-space sampling at each echo time. Experimental undersampled phantom and in vivo results processed with CAMP exhibit reduced artifacts without introducing bias.

SIGNIFICANCE

For a wide array of applications, CAMP linearizes the model cost function without sacrificing model accuracy so that the well-conditioned and highly efficient reconstruction algorithm improves the image quality of accelerated parameter maps.

MR Neurography and Quantitative Muscle MRI of Parsonage Turner Syndrome Involving the Long Thoracic Nerve

BACKGROUND

Parsonage-Turner syndrome (PTS) is characterized by severe, acute upper extremity pain and subsequent paresis and most commonly involves the long thoracic nerve (LTN). While MR neurography (MRN) can detect LTN hourglass-like constrictions (HGCs), quantitative muscle MRI (qMRI) can quantify serratus anterior muscle (SAM) neurogenic changes.

PURPOSE/HYPOTHESIS

1) To characterize qMRI findings in LTN-involved PTS. 2) To investigate associations between qMRI and clinical assessments of HGCs/electromyography (EMG).

STUDY TYPE

Prospective.

POPULATION

30 PTS subjects (25 M/5 F, mean/range age = 39/15-67 years) with LTN involvement who underwent bilateral chest wall qMRI and unilateral brachial plexus MRN.

FIELD STRENGTH/SEQUENCES

3.0 Tesla/multiecho spin-echo T2-mapping, diffusion-weighted echo-planar-imaging, multiecho gradient echo.

ASSESSMENT

qMRI was performed to obtain T2, muscle diameter fat fraction (FF), and cross-sectional area of the SAM. Clinical reports of MRN and EMG were obtained; from MRN, the number of HGCs; from EMG, SAM measurements of motor unit recruitment levels, fibrillations, and positive sharp waves. qMRI/MRN were performed within 90 days of EMG. EMG was performed on average 185 days from symptom onset (all ≥2 weeks from symptom onset) and 5 days preceding MRI.

STATISTICAL TESTS

Paired t-tests were used to compare qMRI measures in the affected SAM versus the contralateral, unaffected side (P < 0.05 deemed statistically significant). Kendall's tau was used to determine associations between qMRI against HGCs and EMG.

RESULTS

Relative to the unaffected SAM, the affected SAM had increased T2 (50.42 ± 6.62 vs. 39.09 ± 4.23 msec) and FF (8.45 ± 9.69 vs. 4.03% ± 1.97%), and decreased muscle diameter (74.26 ± 21.54 vs. 88.73 ± 17.61 μm) and cross-sectional area (9.21 ± 3.75 vs. 16.77 ± 6.40 mm2). There were weak to negligible associations (tau = -0.229 to <0.001, P = 0.054-1.00) between individual qMRI biomarkers and clinical assessments of HGCs and EMG.

DATA CONCLUSION

qMRI changes in the SAM were observed in subjects with PTS involving the LTN.

LEVEL OF EVIDENCE

2 TECHNICAL EFFICACY: Stage 1.

Joint MAPLE: Accelerated joint T1 and T 2 * $$ {{\mathrm{T}}_2}^{\ast } $$ mapping with scan-specific self-supervised networks

PURPOSE

Quantitative MRI finds important applications in clinical and research studies. However, it is encoding intensive and may suffer from prohibitively long scan times. Accelerated MR parameter mapping techniques have been developed to help address these challenges. Here, an accelerated joint T1,T 2 * $$ {{\mathrm{T}}_2}^{\ast } $$ , frequency and proton density mapping technique with scan-specific self-supervised network reconstruction is proposed to synergistically combine parallel imaging, model-based, and deep learning approaches to speed up parameter mapping.

METHODS

Proposed framework, Joint MAPLE, includes parallel imaging, signal modeling, and data consistency blocks which are optimized jointly in a combined loss function. A scan-specific self-supervised reconstruction is embedded into the framework, which takes advantage of multi-contrast data from a multi-echo, multi-flip angle, gradient echo acquisition.

RESULTS

In comparison with parallel reconstruction techniques powered by low-rank methods, emerging scan specific networks, and model-basedT 2 * $$ {{\mathrm{T}}_2}^{\ast } $$ estimation approaches, the proposed framework reduces the reconstruction error in parameter maps by approximately two-fold on average at acceleration rates as high as R = 16 with uniform sampling. It can outperform evaluated parallel reconstruction techniques up to four-fold on average in the presence of challenging sub-sampling masks. It is observed that Joint MAPLE performs well at extreme acceleration rates of R = 25 and R = 36 with error values less than 20%.

CONCLUSION

Joint MAPLE enables higher fidelity parameter estimation at high acceleration rates by synergistically combining parallel imaging and model-based parameter mapping and exploiting multi-echo, multi-flip angle datasets. Utilizing a scan-specific self-supervised reconstruction obviates the need for large data sets for training while improving the parameter estimation ability.

Quantitative double echo steady state T2 mapping of upper extremity peripheral nerves and muscles

Introduction

T2 mapping can characterize peripheral neuropathy and muscle denervation due to axonal damage. Three-dimensional double echo steady-state (DESS) can simultaneously provide 3D qualitative information and T2 maps with equivalent spatial resolution. However, insufficient signal-to-noise ratio may bias DESS-T2 values. Deep learning reconstruction (DLR) techniques can reduce noise, and hence may improve quantitation of high-resolution DESS-T2. This study aims to (i) evaluate the effect of DLR methods on DESS-T2 values, and (ii) to evaluate the feasibility of using DESS-T2 maps to differentiate abnormal from normal nerves and muscles in the upper extremities, with abnormality as determined by electromyography.

Methods and results

Analysis of images from 25 subjects found that DLR decreased DESS-T2 values in abnormal muscles (DLR = 37.71 ± 9.11 msec, standard reconstruction = 38.56 ± 9.44 msec, p = 0.005) and normal muscles (DLR: 27.18 ± 6.34 msec, standard reconstruction: 27.58 ± 6.34 msec, p < 0.001) consistent with a noise reduction bias. Mean DESS-T2, both with and without DLR, was higher in abnormal nerves (abnormal = 75.99 ± 38.21 msec, normal = 35.10 ± 9.78 msec, p < 0.001) and muscles (abnormal = 37.71 ± 9.11 msec, normal = 27.18 ± 6.34 msec, p < 0.001). A higher DESS-T2 in muscle was associated with electromyography motor unit recruitment (p < 0.001).

Discussion

These results suggest that quantitative DESS-T2 is improved by DLR and can differentiate the nerves and muscles involved in peripheral neuropathies from those uninvolved.

A Physics-Based Algorithm to Universally Standardize Routinely Obtained Clinical T2-Weighted Images

RATIONALE AND OBJECTIVES

MR images can be challenging for machine learning and other large-scale analyses because most clinical images, for example, T2-weighted (T2w) images, reflect not only the biologically relevant T2 of tissue but also hardware and acquisition parameters that vary from site to site. Quantitative T2 mapping avoids these confounds because it quantitatively isolates the biological parameter of interest, thus representing a universal standardization across sites. However, efforts to incorporate quantitative mapping sequences into routine clinical practice have seen slow adoption. Here we show, for the first time, that the routine T2w complex raw dataset can be successfully regarded as a quantitative mapping sequence that can be reconstructed with classical optimization methods and physics-based constraints.

MATERIALS AND METHODS

While previous constrained reconstruction methods are unable to reconstruct a T2 map based on this data, the expanding-constrained alternating minimization for parameter mapping (e-CAMP), which employs stepwise initialization, a linearized version of the exponential model and a phase conjugacy constraint, is demonstrated to provide useful quantitative maps directly from a vendor T2w single image data.

RESULTS

This paper introduces the method and demonstrates its performance using simulations, retrospectively undersampled brain images, and prospectively acquired T2w images taken on both phantom and brain.

CONCLUSION

Because T2w scans are included in nearly every protocol, this approach could open the door to creating large, standardized datasets without requiring widespread changes in clinical protocols.

Latent signal models: Learning compact representations of signal evolution for improved time-resolved, multi-contrast MRI

PURPOSE

To improve time-resolved reconstructions by training auto-encoders to learn compact representations of Bloch-simulated signal evolution and inserting the decoder into the forward model.

METHODS

Building on model-based nonlinear and linear subspace techniques, we train auto-encoders on dictionaries of simulated signal evolution to learn compact, nonlinear, latent representations. The proposed latent signal model framework inserts the decoder portion of the auto-encoder into the forward model and directly reconstructs the latent representation. Latent signal models essentially serve as a proxy for fast and feasible differentiation through the Bloch equations used to simulate signal. This work performs experiments in the context of T₂ -shuffling, gradient echo EPTI, and MPRAGE-shuffling. We compare how efficiently auto-encoders represent signal evolution in comparison to linear subspaces. Simulation and in vivo experiments then evaluate if reducing degrees of freedom by incorporating our proxy for the Bloch equations, the decoder portion of the auto-encoder, into the forward model improves reconstructions in comparison to subspace constraints.

RESULTS

An auto-encoder with 1 real latent variable represents single-tissue fast spin echo, EPTI, and MPRAGE signal evolution to within 0.15% normalized RMS error, enabling reconstruction problems with 3 degrees of freedom per voxel (real latent variable + complex scaling) in comparison to linear models with 4-8 degrees of freedom per voxel. In simulated/in vivo T₂ -shuffling and in vivo EPTI experiments, the proposed framework achieves consistent quantitative normalized RMS error improvement over linear approaches. From qualitative evaluation, the proposed approach yields images with reduced blurring and noise amplification in MPRAGE-shuffling experiments.

CONCLUSION

Directly solving for nonlinear latent representations of signal evolution improves time-resolved MRI reconstructions.

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 Quantitative Parameter Estimation for Prostate T2 Relaxometry using Convolutional Neural Networks

This work seeks to evaluate multiple methods for quantitative parameter estimation from standard T2 mapping acquisitions in the prostate. The T2 estimation performance of methods based on neural networks (NN) was quantitatively compared to that of conventional curve fitting techniques. Large physics-based synthetic datasets simulating T2 mapping acquisitions were generated for training NNs and for quantitative performance comparisons. Ten combinations of different NN architectures, training strategies, and training corpora were implemented and compared with four different curve fitting strategies. All methods were compared quantitatively using synthetic data with known ground truth, and further compared on in vivo test data, with and without noise augmentation, to evaluate feasibility and noise robustness. In the evaluation on synthetic data, a convolutional neural network (CNN), trained in a supervised fashion using synthetic data generated from naturalistic images, showed the highest overall accuracy and precision amongst all the methods. On in vivo data, this best-performing method produced low-noise T2 maps and showed the least deterioration with increasing input noise levels. This study showed that a CNN, trained with synthetic data in a supervised manner, may provide superior T2 estimation performance compared to conventional curve fitting, especially in low signal-to-noise regions.

Synthetic Contrasts in Musculoskeletal MRI: A Review

ABSTRACT

This review summarizes the existing techniques and methods used to generate synthetic contrasts from magnetic resonance imaging data focusing on musculoskeletal magnetic resonance imaging. To that end, the different approaches were categorized into 3 different methodological groups: mathematical image transformation, physics-based, and data-driven approaches. Each group is characterized, followed by examples and a brief overview of their clinical validation, if present. Finally, we will discuss the advantages, disadvantages, and caveats of synthetic contrasts, focusing on the preservation of image information, validation, and aspects of the clinical workflow.

Quantitative MRI Differentiates Electromyography Severity Grades of Denervated Muscle in Neuropathy of the Brachial Plexus

BACKGROUND

Quantitative MRI (qMRI) metrics reflect microstructural skeletal muscle changes secondary to denervation and may correspond to conventional electromyography (EMG) assessments of motor unit recruitment (MUR) and denervation.

HYPOTHESIS

Differences in quantitative T2 , diffusion-based apparent fiber diameter (AFD), and fat fraction (FF) exist between EMG grades, in patients with clinically suspected neuropathy of the brachial plexus.

STUDY TYPE

Prospective.

POPULATION

A total of 30 subjects (age = 37.5 ± 17.5, 21M/9F) with suspected brachial plexopathy.

FIELD STRENGTH/SEQUENCE

3-Tesla; qMRI using fast spin echo (T2 -mapping), multi-b-valued diffusion-weighted echo planar imaging (for AFD), and dual-echo Dixon gradient echo (FF-mapping) sequences.

ASSESSMENT

qMRI values were compared against EMG grades (MUR and denervation). qMRI values (T2 , AFD, and FF) were obtained for five regional shoulder muscles. A 4-point scale was used for MUR/denervation severity.

STATISTICAL TESTS

Linear mixed models and least-squares pairwise comparisons were used to evaluate qMRI differences between EMG grades. Predictive accuracy of EMG grades from qMRI was quantified by 10-fold cross-validated logistic models. A P value < 0.05 was considered statistically significant.

RESULTS

Mean (95% confidence interval) qMRI for "full" MUR were T2  = 39.40 msec (35.72-43.08 msec), AFD = 78.35 μm (72.52-84.19 μm), and FF = 4.54% (2.11-6.97%). Significant T2 increases (+8.36 to +14.67 msec) and significant AFD decreases (-11.04 to -21.58 μm) were observed with all abnormal MUR grades as compared to "full" MUR. Significant changes in both T2 and AFD were observed with increased denervation (+9.59 to +15.04 msec, -16.25 to -18.66 μm). There were significant differences in FF between some MUR grades (-1.45 to +2.96%), but no significant changes were observed with denervation (P = 0.089-0.662). qMRI prediction of abnormal MUR or denervation was strong (mean accuracy = 0.841 and 0.810, respectively) but moderate at predicting individual grades (accuracy = 0.492 and 0.508, respectively).

DATA CONCLUSION

Quantitative T2 and AFD differences were observed between EMG grades in assessing muscle denervation.

LEVEL OF EVIDENCE

2 TECHNICAL EFFICACY: Stage 1.

Rapid MR relaxometry using deep learning: An overview of current techniques and emerging trends

Quantitative mapping of MR tissue parameters such as the spin-lattice relaxation time (T₁ ), the spin-spin relaxation time (T₂ ), and the spin-lattice relaxation in the rotating frame (T_1ρ ), referred to as MR relaxometry in general, has demonstrated improved assessment in a wide range of clinical applications. Compared with conventional contrast-weighted (eg T₁ -, T₂ -, or T_1ρ -weighted) MRI, MR relaxometry provides increased sensitivity to pathologies and delivers important information that can be more specific to tissue composition and microenvironment. The rise of deep learning in the past several years has been revolutionizing many aspects of MRI research, including image reconstruction, image analysis, and disease diagnosis and prognosis. Although deep learning has also shown great potential for MR relaxometry and quantitative MRI in general, this research direction has been much less explored to date. The goal of this paper is to discuss the applications of deep learning for rapid MR relaxometry and to review emerging deep-learning-based techniques that can be applied to improve MR relaxometry in terms of imaging speed, image quality, and quantification robustness. The paper is comprised of an introduction and four more sections. Section 2 describes a summary of the imaging models of quantitative MR relaxometry. In Section 3, we review existing "classical" methods for accelerating MR relaxometry, including state-of-the-art spatiotemporal acceleration techniques, model-based reconstruction methods, and efficient parameter generation approaches. Section 4 then presents how deep learning can be used to improve MR relaxometry and how it is linked to conventional techniques. The final section concludes the review by discussing the promise and existing challenges of deep learning for rapid MR relaxometry and potential solutions to address these challenges.

Comparison of T2 Quantification Strategies in the Abdominal-Pelvic Region for Clinical Use

OBJECTIVES

The aim of the study was to compare different magnetic resonance imaging (MRI) acquisition strategies appropriate for T2 quantification in the abdominal-pelvic area. The different techniques targeted in the study were chosen according to 2 main considerations: performing T2 measurement in an acceptable time for clinical use and preventing/correcting respiratory motion.

MATERIALS AND METHODS

Acquisitions were performed at 3 T. To select sequences for in vivo measurements, a phantom experiment was conducted, for which the T2 values obtained with the different techniques of interest were compared with the criterion standard (single-echo SE sequence, multiple acquisitions with varying echo time). Repeatability and temporal reproducibility studies for the different techniques were also conducted on the phantom. Finally, an in vivo study was conducted on 12 volunteers to compare the techniques that offer acceptable acquisition time for clinical use and either address or correct respiratory motion.

RESULTS

For the phantom study, the DESS and T2-preparation techniques presented the lowest precision (ρ2 = 0.9504 and ρ2 = 0.9849 respectively), and showed a poor repeatability/reproducibility compared with the other techniques. The strategy relying on SE-EPI showed the best precision and accuracy (ρ2 = 0.9994 and Cb = 0.9995). GRAPPATINI exhibited a very good precision (ρ2 = 0.9984). For the technique relying on radial TSE, the precision was not as good as GRAPPATINI (ρ2 = 0.9872). The in vivo study demonstrated good respiratory motion management for all of the selected techniques. It also showed that T2 estimate ranges were different from one method to another. For GRAPPATINI and radial TSE techniques, there were significant differences between all the different types of organs of interest.

CONCLUSIONS

To perform T2 measurement in the abdominal-pelvic region, one should favor a technique with acceptable acquisition time for clinical use, with proper respiratory motion management, with good repeatability, reproducibility, and precision. In this study, the techniques relying respectively on SE-EPI, radial TSE, and GRAPPATINI appeared as good candidates.

Diffusion MRI fiber diameter for muscle denervation assessment

BACKGROUND

To develop and evaluate a diffusion MRI-based apparent muscle fiber diameter (AFD) method in patients with muscle denervation. It was hypothesized that AFD differences between denervated, non-denervated and control muscles would be greater than those from standard diffusion metrics.

METHODS

A spin-echo diffusion acquisition with multi-b-valued diffusion sampling was used. An orientation-invariant dictionary approach utilized a cylinder-based forward model and multi-compartment model for obtaining restricted and free fractions. Simulations were performed to determine precision, bias, and optimize dictionary parameters. In all, 18 exams of patients with muscle denervation and 8 exams of healthy subjects were performed at 3T. Six regions of interests (ROIs) within separate shoulder muscles were selected, yielding three groups consisting 47 control (healthy), 36 non-denervated (patients), and 68 denervated (patients) muscle ROIs. Two-sample t-tests (α=0.05) between groups were performed with Holm-Bonferroni correction. T2- and fat fraction (FF)-mapping were acquired for comparison.

RESULTS

Mean AFD was 89.7±13.6 µm in control, 71.6±15.3 µm in non-denervated, and 60.7±15.9 µm in denervated muscles and were significantly different (P<0.001) in paired comparisons and in 10/12 individual muscle region comparisons. Correlation between AFD and FF (-0.331, P<0.001) was low, but correlation between FA and FF was negligible (0.197, P=0.016). Correlation was low between AFD and T2 (-0.395, P<0.001) and between FA and T2 (0.359, P<0.001).

CONCLUSIONS

Diffusion MRI-based AFD complements T2- and FF-mapping techniques to non-invasively assess muscle denervation.

Model-based multi-parameter mapping

Quantitative MR imaging is increasingly favoured for its richer information content and standardised measures. However, computing quantitative parameter maps, such as those encoding longitudinal relaxation rate (R1), apparent transverse relaxation rate (R2*) or magnetisation-transfer saturation (MTsat), involves inverting a highly non-linear function. Many methods for deriving parameter maps assume perfect measurements and do not consider how noise is propagated through the estimation procedure, resulting in needlessly noisy maps. Instead, we propose a probabilistic generative (forward) model of the entire dataset, which is formulated and inverted to jointly recover (log) parameter maps with a well-defined probabilistic interpretation (e.g., maximum likelihood or maximum a posteriori). The second order optimisation we propose for model fitting achieves rapid and stable convergence thanks to a novel approximate Hessian. We demonstrate the utility of our flexible framework in the context of recovering more accurate maps from data acquired using the popular multi-parameter mapping protocol. We also show how to incorporate a joint total variation prior to further decrease the noise in the maps, noting that the probabilistic formulation allows the uncertainty on the recovered parameter maps to be estimated. Our implementation uses a PyTorch backend and benefits from GPU acceleration. It is available at https://github.com/balbasty/nitorch.

Fat-saturated image generation from multi-contrast MRIs using generative adversarial networks with Bloch equation-based autoencoder regularization

Obtaining multiple series of magnetic resonance (MR) images with different contrasts is useful for accurate diagnosis of human spinal conditions. However, this can be time consuming and a burden on both the patient and the hospital. We propose a Bloch equation-based autoencoder regularization generative adversarial network (BlochGAN) to generate a fat saturation T2-weighted (T2 FS) image from T1-weighted (T1-w) and T2-weighted (T2-w) images of human spine. To achieve this, our approach was to utilize the relationship between the contrasts using Bloch equation since it is a fundamental principle of MR physics and serves as a physical basis of each contrasts. BlochGAN properly generated the target-contrast images using the autoencoder regularization based on the Bloch equation to identify the physical basis of the contrasts. BlochGAN consists of four sub-networks: an encoder, a decoder, a generator, and a discriminator. The encoder extracts features from the multi-contrast input images, and the generator creates target T2 FS images using the features extracted from the encoder. The discriminator assists network learning by providing adversarial loss, and the decoder reconstructs the input multi-contrast images and regularizes the learning process by providing reconstruction loss. The discriminator and the decoder are only used in the training process. Our results demonstrate that BlochGAN achieved quantitatively and qualitatively superior performance compared to conventional medical image synthesis methods in generating spine T2 FS images from T1-w, and T2-w images.

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'.

Deep model-based magnetic resonance parameter mapping network (DOPAMINE) for fast T1 mapping using variable flip angle method

Quantitative tissue characteristics, which provide valuable diagnostic information, can be represented by magnetic resonance (MR) parameter maps using magnetic resonance imaging (MRI); however, a long scan time is necessary to acquire them, which prevents the application of quantitative MR parameter mapping to real clinical protocols. For fast MR parameter mapping, we propose a deep model-based MR parameter mapping network called DOPAMINE that combines a deep learning network with a model-based method to reconstruct MR parameter maps from undersampled multi-channel k-space data. DOPAMINE consists of two networks: 1) an MR parameter mapping network that uses a deep convolutional neural network (CNN) that estimates initial parameter maps from undersampled k-space data (CNN-based mapping), and 2) a reconstruction network that removes aliasing artifacts in the parameter maps with a deep CNN (CNN-based reconstruction) and an interleaved data consistency layer by an embedded MR model-based optimization procedure. We demonstrated the performance of DOPAMINE in brain T₁ map reconstruction with a variable flip angle (VFA) model. To evaluate the performance of DOPAMINE, we compared it with conventional parallel imaging, low-rank based reconstruction, model-based reconstruction, and state-of-the-art deep-learning-based mapping methods for three different reduction factors (R = 3, 5, and 7) and two different sampling patterns (1D Cartesian and 2D Poisson-disk). Quantitative metrics indicated that DOPAMINE outperformed other methods in reconstructing T₁ maps for all sampling patterns and reduction factors. DOPAMINE exhibited quantitatively and qualitatively superior performance to that of conventional methods in reconstructing MR parameter maps from undersampled multi-channel k-space data. The proposed method can thus reduce the scan time of quantitative MR parameter mapping that uses a VFA model.

Quantitative T2 -mapping magnetic resonance imaging for assessment of muscle motor unit recruitment patterns

INTRODUCTION

In this study, we aimed to determine whether muscle transverse relaxation time (T₂ ) magnetic resonance (MR) mapping results correlate with motor unit loss, as defined by motor unit recruitment patterns on electromyography (EMG).

METHODS

EMG and 3-Tesla MRI exams were acquired no more than 31 days apart in subjects referred for peripheral nerve MRI. Two musculoskeletal radiologists qualitatively graded T₂ -weighted, fat-suppressed sequences for severity of muscle edema-like patterns and manually placed regions of interest within muscles to obtain T₂ values from T₂ -mapping sequences. Concordance was calculated between qualitative and quantitative MR grades and EMG recruitment categories (none, discrete, decreased) as well as interobserver agreement for both MR grades.

RESULTS

Thirty-four muscles (21 abnormal, 13 control) were assessed in 13 subjects (5 females and 8 males; mean age, 46 years) with 14 EMG-MRI pairs. T₂ -relaxation times were significantly (P < .001) increased in all EMG recruitment categories compared with control muscles. T₂ differences were not significant between EMG grades of motor unit recruitment (P = .151-.702). T₂ and EMG score concordance was acceptable (Harrell's concordance index [c index]: rater A, 0.71; 95% confidence interval [CI], 0.51-0.87; rater B, 0.77; 95% CI, 0.57-0.91). Qualitative MRI and EMG score concordance was poor to acceptable (c index: rater A, 0.60; 95% CI, 0.50-0.79; rater B, 0.72; 95% CI, 0.55-0.89). T₂ values had moderate-to-substantial ability to distinguish between absent vs incomplete (ie, decreased or discrete) motor unit recruitment (c index: rater A, 0.78; 95% CI, 0.50-1.00; rater B, 0.86; 95% CI, 0.57-1.00).

DISCUSSION

Quantitative T₂ MR muscle mapping is a promising tool for noninvasive evaluation of the degree of motor unit recruitment loss.

Accelerated T2 Mapping of the Lumbar Intervertebral Disc: Highly Undersampled K-Space Data for Robust T2 Relaxation Time Measurement in Clinically Feasible Acquisition Times

T2 mapping of the intervertebral disc (IVD) can depict quantitative changes reflecting biochemical change due to loss of glycosaminoglycan content. Conventional T2 mapping is usually performed using a 2-dimensional multi-echo-spin echo sequence (2D-MESE) with long acquisition times that are generally not compatible with clinical routine. This study investigates the applicability of GRAPPATINI, a T2 mapping sequence combining undersampling, model-based reconstruction, and parallel imaging, to offer clinically feasible acquisition times in T2 mapping of the lumbar IVD.

MATERIALS AND METHODS

Fifty-eight individuals (26 female; mean age, 23.3 ± 8.1 years) were prospectively studied at 3 T. GRAPPATINI was conducted with the same parameters as the 2D-MESE while shortening the acquisition time from 13:18 to 2:27 minutes. The setup was also validated in a phantom experiment using a 6.48-hour-long single echo-spin echo sequence as reference. The IVDs were manually segmented on 4 central slices.

RESULTS

The median nucleus pulposus showed a strong Pearson correlation coefficient between T2GRAPPATINI and T2MESE (rp = 0.919; P < 0.001). There was also a significant correlation for the ventral (rp = 0.241; P < 0.001) and posterior (rp = 0.418; P < 0.001) annular regions.In the single spin-echo phantom experiment, the most accurate T2 estimation was achieved using T2GRAPPATINI with a median absolute deviation of 15.3 milliseconds as compared with T2MESE with 26.5 milliseconds.

CONCLUSIONS

GRAPPATINI facilitates precise T2 mapping at 3 T in accordance with clinical standards and reference methods using the same parameters while shortening acquisition times from 13:18 to 2:27 minutes with the same parameters.

Echo planar time-resolved imaging with subspace reconstruction and optimized spatiotemporal encoding

PURPOSE

To develop new encoding and reconstruction techniques for fast multi-contrast/quantitative imaging.

METHODS

The recently proposed Echo Planar Time-resolved Imaging (EPTI) technique can achieve fast distortion- and blurring-free multi-contrast/quantitative imaging. In this work, a subspace reconstruction framework is developed to improve the reconstruction accuracy of EPTI at high encoding accelerations. The number of unknowns in the reconstruction is significantly reduced by modeling the temporal signal evolutions using low-rank subspace. As part of the proposed reconstruction approach, a B₀ -update algorithm and a shot-to-shot B₀ variation correction method are developed to enable the reconstruction of high-resolution tissue phase images and to mitigate artifacts from shot-to-shot phase variations. Moreover, the EPTI concept is extended to 3D k-space for 3D GE-EPTI, where a new "temporal-variant" of CAIPI encoding is proposed to further improve performance.

RESULTS

The effectiveness of the proposed subspace reconstruction was demonstrated first in 2D GESE EPTI, where the reconstruction achieved higher accuracy when compared to conventional B₀ -informed GRAPPA. For 3D GE-EPTI, a retrospective undersampling experiment demonstrates that the new temporal-variant CAIPI encoding can achieve up to 72× acceleration with close to 2× reduction in reconstruction error when compared to conventional spatiotemporal-CAIPI encoding. In a prospective undersampling experiment, high-quality whole-brain T 2 ∗ and tissue phase maps at 1 mm isotropic resolution were acquired in 52 seconds at 3T using 3D GE-EPTI with temporal-variant CAIPI encoding.

CONCLUSION

The proposed subspace reconstruction and optimized temporal-variant CAIPI encoding can further improve the performance of EPTI for fast quantitative mapping.

A time domain signal equation for multi-echo spin-echo sequences with arbitrary excitation and refocusing angle and phase

Accurate T₂ mapping using multi-echo spin-echo is usually impaired by non-ideal refocusing due to B₁+ inhomogeneities and slice profile effects. Incomplete refocusing gives rise to stimulated echo and so called "T₁-mixing" and consequently a non-exponential signal decay. Here we present a time domain formula that incorporates all relaxation and pulse parameters and enables accurate and realistic modelling of the magnetization decay curve. By pulse parameters here we specifically mean the actual refocusing angle and axis, and phase angle of both the excitation and refocusing pulse. The method used for derivation comprises the so called Generating functions approach with subsequent back-transformation to the time domain. The proposed approach was validated by simulations using realistic RF pulse shapes as well as by comparison to phantom measurements. Excellent agreement between simulations and measurements underpin the validity of the presented approach. Conclusively, we here present a complete time domain formula ready to use for accurate T₂ mapping with multi-echo spin-echo sequences.

Bio-SCOPE: fast biexponential T1ρ mapping of the brain using signal-compensated low-rank plus sparse matrix decomposition

PURPOSE

To develop and evaluate a fast imaging method based on signal-compensated low-rank plus sparse matrix decomposition to accelerate data acquisition for biexponential brain T_1ρ mapping (Bio-SCOPE).

METHODS

Two novel strategies were proposed to improve reconstruction performance. A variable-rate undersampling scheme was used with a varied acceleration factor for each k-space along the spin-lock time direction, and a modified nonlinear thresholding scheme combined with a feature descriptor was used for Bio-SCOPE reconstruction. In vivo brain T_1ρ mappings were acquired from 4 volunteers. The fully sampled k-space data acquired from 3 volunteers were retrospectively undersampled by net acceleration rates (R) of 4.6 and 6.1. Reference values were obtained from the fully sampled data. The agreement between the accelerated T_1ρ measurements and reference values was assessed with Bland-Altman analyses. Prospectively undersampled data with R = 4.6 and R = 6.1 were acquired from 1 volunteer.

RESULTS

T_1ρ -weighted images were successfully reconstructed using Bio-SCOPE for R = 4.6 and 6.1 with signal-to-noise ratio variations <1 dB and normalized root mean square errors <4%. Accelerated and reference T_1ρ measurements were in good agreement for R = 4.6 (T_{1ρ s} : 18.6651 ± 1.7786 ms; T_{1ρ l} : 88.9603 ± 1.7331 ms) and R = 6.1 (T_{1ρ s} : 17.8403 ± 3.3302 ms; T_{1ρ l} : 88.0275 ± 4.9606 ms) in the Bland-Altman analyses. T_1ρ parameter maps from prospectively undersampled data also show reasonable image quality using the Bio-SCOPE method.

CONCLUSION

Bio-SCOPE achieves a high net acceleration rate for biexponential T_1ρ mapping and improves reconstruction quality by using a variable-rate undersampling data acquisition scheme and a modified soft-thresholding algorithm in image reconstruction.

MRI T2 Mapping of the Knee Providing Synthetic Morphologic Images: Comparison to Conventional Turbo Spin-Echo MRI

Background Use of a T2 mapping sequence in addition to the conventional knee MRI protocol increases sensitivity to early cartilage lesions but is time consuming. Purpose To test the in vitro validity of quantitative data from an accelerated parallel T2 mapping sequence (combined generalized autocalibrating partially parallel acquisition and model-based accelerated relaxometry by iterative nonlinear inversion [GRAPPATINI]) of the knee and to compare in vivo synthetic images generated with this sequence with those generated with conventional morphologic sequences. Materials and Methods T2 estimations with GRAPPATINI were validated in vitro in comparison with T2 estimations with routine multisection multiecho and reference standard single-section single-echo spin-echo T2 mapping sequences by using a Bland-Altman plot. Synthetic morphologic images (intermediate-weighted sequence, 34-msec echo time; T2-weighted sequence, 80-msec echo time) were compared in vivo with corresponding conventional morphologic turbo spin-echo 3-T sequences by three readers in consecutive patients recruited retrospectively from February to May 2018. Synthetic and conventional morphologic images were compared by using rates of interreader agreement, κ statistics, and rates of findings. Results T2 values with GRAPPATINI were accurate compared with those obtained with the reference single-section single-echo sequence, with slight T2 overestimation (2.7 msec). Sixty-one patients (mean age, 43 years ± 16 [standard deviation]; 32 men) were included. The rate of agreement when one reader used synthetic morphologic images and the other used conventional sequences was not inferior to the rate of agreement when all readers used conventional sequences (upper bounds of 95% confidence intervals of differences between rates of agreement ≤ 4.8%). Interreader agreement was similar for the conventional set alone, the synthetic set alone, and when readers used different sets (two-by-two differences between κ values for all items ≤ 0.15). The rates of findings were not different between synthetic and conventional image sets (all P ≥ .07) except for two items (femoral trochlear cartilage [3.0% vs 0.3%, P = .006] and joint effusion [0.3% vs 2.7%, P = .005]). Conclusion This T2 mapping sequence yields, in one acquisition, accurate T2 values and synthetic morphologic images that are comparable with those obtained with conventional turbo spin-echo sequences. © RSNA, 2019 Online supplemental material is available for this article. See also the editorial by Fritz in this issue.

Model-based myocardial T1 mapping with sparsity constraints using single-shot inversion-recovery radial FLASH cardiovascular magnetic resonance

BACKGROUND

This study develops a model-based myocardial T1 mapping technique with sparsity constraints which employs a single-shot inversion-recovery (IR) radial fast low angle shot (FLASH) cardiovascular magnetic resonance (CMR) acquisition. The method should offer high resolution, accuracy, precision and reproducibility.

METHODS

The proposed reconstruction estimates myocardial parameter maps directly from undersampled k-space which is continuously measured by IR radial FLASH with a 4 s breathhold and retrospectively sorted based on a cardiac trigger signal. Joint sparsity constraints are imposed on the parameter maps to further improve T1 precision. Validations involved studies of an experimental phantom and 8 healthy adult subjects.

RESULTS

In comparison to an IR spin-echo reference method, phantom experiments with T1 values ranging from 300 to 1500 ms revealed good accuracy and precision at simulated heart rates between 40 and 100 bpm. In vivo T1 maps achieved better precision and qualitatively better preservation of image features for the proposed method than a real-time CMR approach followed by pixelwise fitting. Apart from good inter-observer reproducibility (0.6% of the mean), in vivo results confirmed good intra-subject reproducibility (1.05% of the mean for intra-scan and 1.17, 1.51% of the means for the two inter-scans, respectively) of the proposed method.

CONCLUSION

Model-based reconstructions with sparsity constraints allow for single-shot myocardial T1 maps with high spatial resolution, accuracy, precision and reproducibility within a 4 s breathhold. Clinical trials are warranted.

Model-based super-resolution reconstruction of T2 maps

PURPOSE

High-resolution isotropic T₂ mapping of the human brain with multi-echo spin-echo (MESE) acquisitions is challenging. When using a 2D sequence, the resolution is limited by the slice thickness. If used as a 3D acquisition, specific absorption rate limits are easily exceeded due to the high power deposition of nonselective refocusing pulses. A method to reconstruct 1-mm³ isotropic T₂ maps is proposed based on multiple 2D MESE acquisitions. Data were undersampled (10-fold) to compensate for the prolonged scan time stemming from the super-resolution acquisition.

THEORY AND METHODS

The proposed method integrates a classical super-resolution with an iterative model-based approach to reconstruct quantitative maps from a set of undersampled low-resolution data. The method was tested on numerical and multipurpose phantoms, and in vivo data. T₂ values were assessed with a region-of-interest analysis using a single-slice spin-echo and a fully sampled MESE acquisition in a phantom, and a MESE acquisition in healthy volunteers.

RESULTS

Numerical simulations showed that the best trade-off between acceleration and number of low-resolution datasets is 10-fold acceleration with 4 acquisitions (acquisition time = 18 min). The proposed approach showed improved resolution over low-resolution images for both phantom and brain. Region-of-interest analysis of the phantom compartments revealed that at shorter T₂ , the proposed method was comparable with the fully sampled MESE. For the volunteer data, the T₂ values found in the brain structures were consistent across subjects (8.5-13.1 ms standard deviation).

CONCLUSION

The proposed method addresses the inherent limitations associated with high-resolution T₂ mapping and enables the reconstruction of 1 mm³ isotropic relaxation maps with a 10 times faster acquisition.

Evaluation of principal component analysis image denoising on multi-exponential MRI relaxometry

PURPOSE

Multi-exponential relaxometry is a powerful tool for characterizing tissue, but generally requires high image signal-to-noise ratio (SNR). This work evaluates the use of principal-component-analysis (PCA) denoising to mitigate these SNR demands and improve the precision of relaxometry measures.

METHODS

PCA denoising was evaluated using both simulated and experimental MRI data. Bi-exponential transverse relaxation signals were simulated for a wide range of acquisition and sample parameters, and experimental data were acquired from three excised and fixed mouse brains. In both cases, standard relaxometry analysis was performed on both original and denoised image data, and resulting estimated signal parameters were compared.

RESULTS

Denoising reduced the root-mean-square-error of parameters estimated from multi-exponential relaxometry by factors of ≈3×, for typical acquisition and sample parameters. Denoised images and subsequent parameter maps showed little or no signs of spatial artifact or loss of resolution.

CONCLUSION

Experimental studies and simulations demonstrate that PCA denoising of MRI relaxometry data is an effective method of improving parameter precision without sacrificing image resolution. This simple yet important processing step thus paves the way for broader applicability of multi-exponential MRI relaxometry.

Rapid compositional mapping of knee cartilage with compressed sensing MRI

More than a decade after the introduction of compressed sensing (CS) in MRI, researchers are still working on ways to translate it into different research and clinical applications. The greatest advantage of CS in MRI is the reduced amount of k-space data needed to reconstruct images, which can be exploited to reduce scan time or to improve spatial resolution and volumetric coverage. Efficient data acquisition using CS is extremely important for compositional mapping of the musculoskeletal system in general and knee cartilage mapping techniques in particular. High-resolution quantitative information about tissue biochemical composition could be obtained in just a few minutes using CS MRI. However, in order to make this goal a reality, some issues still need to be addressed. In this article we review the current state of the art of CS methods for rapid compositional mapping of knee cartilage. Specifically, data acquisition strategies, image reconstruction algorithms, and data fitting models are discussed. Different CS studies for T2 and T1ρ mapping of knee cartilage are reviewed, with illustrative results. Future directions, opportunities, and challenges of rapid compositional mapping techniques are also discussed. Level of Evidence: 4 Technical Efficacy: Stage 6 J. Magn. Reson. Imaging 2018;47:1185-1198.

Rapid T1 quantification from high resolution 3D data with model-based reconstruction

Purpose

Magnetic resonance imaging protocols for the assessment of quantitative information suffer from long acquisition times since multiple measurements in a parametric dimension are required. To facilitate the clinical applicability, accelerating the acquisition is of high importance. To this end, we propose a model‐based optimization framework in conjunction with undersampling 3D radial stack‐of‐stars data.

Theory and Methods

High resolution 3D T₁ maps are generated from subsampled data by employing model‐based reconstruction combined with a regularization functional, coupling information from the spatial and parametric dimension, to exploit redundancies in the acquired parameter encodings and across parameter maps. To cope with the resulting non‐linear, non‐differentiable optimization problem, we propose a solution strategy based on the iteratively regularized Gauss‐Newton method. The importance of 3D‐spectral regularization is demonstrated by a comparison to 2D‐spectral regularized results. The algorithm is validated for the variable flip angle (VFA) and inversion recovery Look‐Locker (IRLL) method on numerical simulated data, MRI phantoms, and in vivo data.

Results

Evaluation of the proposed method using numerical simulations and phantom scans shows excellent quantitative agreement and image quality. T₁ maps from accelerated 3D in vivo measurements, e.g. 1.8 s/slice with the VFA method, are in high accordance with fully sampled reference reconstructions.

Conclusions

The proposed algorithm is able to recover T₁ maps with an isotropic resolution of 1 mm³ from highly undersampled radial data by exploiting structural similarities in the imaging volume and across parameter maps.

Rapid and accurate dictionary-based T2 mapping from multi-echo turbo spin echo data at 7 Tesla

BACKGROUND

Using lower refocusing flip angles in multi-echo turbo spin echo (ME-TSE) sequences at ultra-high magnetic field leads to non-monoexponential signal decay and overestimation of T₂ values due to stimulated and secondary echoes.

PURPOSE

To investigate the feasibility of a fast and accurate reconstruction of quantitative T₂ values using an ME-TSE sequence with reduced refocusing flip angles at 7 Tesla, a dictionary-based reconstruction method was developed and is presented in this work.

STUDY TYPE

Prospective.

SUBJECTS

Phantom measurements with relaxation phantom, four healthy volunteers.

FIELD STRENGTH/SEQUENCE

7 Tesla MRI, multi-echo turbo spin echo (ME-TSE), spin echo (SE), and B₁ mapping.

ASSESSMENT

Based on Bloch simulations and the extended phase graph model, signal decay curves were calculated to account for nonrectangular slice profile, B₁ inhomogeneity, and reduced refocusing flip angles and stored in a dictionary. Data obtained with an ME-TSE sequence at 7 Tesla were matched to this dictionary to obtain T₂ values. To compare the proposed method to reference T₂ values, a spin echo sequence with different echo times was used.

STATISTICAL TESTS

Welch's t-test was used to compare T₂ values in phantom measurements.

RESULTS

T₂ values obtained with the proposed ME-TSE method coincided with the T₂ values from the spin echo experiment in phantom measurements (P = 0.89 for 120° flip angle, P = 0.75 for 180° flip angle). Only for very low B₁ transmit fields, a slight overestimation of T₂ values was observed. In vivo measurements showed lower T₂ values in gray matter (55 ± 2 millisecond) and white matter (39 ± 5 millisecond) compared with literature values of 3 Tesla data.

DATA CONCLUSIONS

The proposed dictionary-based ME-TSE approach provided accurate T₂ values in short measurement time at 7 Tesla with low specific absorption rate burden due to the reduction of refocusing flip angles. Therefore, it can provide new opportunities in clinical high-field MRI to further improve radiographic diagnosis by using quantitative imaging.

LEVEL OF EVIDENCE

1 Technical Efficacy: Stage 1 J. Magn. Reson. Imaging 2019;49:1253-1262.

SCOPE: signal compensation for low-rank plus sparse matrix decomposition for fast parameter mapping

Magnetic resonance (MR) parameter mapping is useful for many clinical applications. However, its practical utility is limited by the long scan time. To address this problem, this paper developed a novel image reconstruction method for fast MR parameter mapping. The proposed method (SCOPE) used a low-rank plus sparse model to reconstruct the parameter-weighted images from highly undersampled acquisitions. A signal compensation strategy was introduced to promote low rankness along the parametric direction and thus improve the reconstruction accuracy. Specifically, compensation was performed by multiplying the original signal by the inversion of the mono-exponential decay at each voxel. The performance of SCOPE was evaluated via quantitative T _1ρ mapping. The results of the simulation and in vivo experiments with acceleration factors from 3 to 5 are shown. The performance of SCOPE was verified via comparisons with several low-rank and sparsity-based methods. The experimental results showed that the T _1ρ maps obtained using SCOPE were more accurate than those obtained using competing methods and were comparable to the reference, even when the acceleration factor reached 5. SCOPE can greatly reduce the scan time of parameter mapping while still achieving high accuracy. This technique might therefore help facilitate fast MR parameter mapping in clinical use.

Accelerated T2 mapping combining parallel MRI and model-based reconstruction: GRAPPATINI

BACKGROUND

Quantitative T₂ measurements are sensitive to intra- and extracellular water accumulation and myelin loss. Therefore, quantitative T₂ promises to be a good biomarker of disease. However, T₂ measurements require long acquisition times.

PURPOSE

To accelerate T₂ quantification and subsequent generation of synthetic T₂ -weighted (T₂ -w) image contrast for clinical research and routine. To that end, a recently developed model-based approach for rapid T₂ and M₀ quantification (MARTINI) based on undersampling k-space, was extended by parallel imaging (GRAPPA) to enable high-resolution T₂ mapping with access to T₂ -w images in less than 2 minutes acquisition time for the entire brain.

STUDY TYPE

Prospective cross-sectional study.

SUBJECTS/PHANTOM

Fourteen healthy subjects and a multipurpose phantom.

FIELD STRENGTH/SEQUENCE

Carr-Purcell-Meiboom-Gill sequence at a 3T scanner.

ASSESSMENT

The accuracy and reproducibility of the accelerated T₂ quantification was assessed. Validations comprised MRI studies on a phantom as well as the brain, knee, prostate, and liver from healthy volunteers. Synthetic T₂ -w images were generated from computed T₂ and M₀ maps and compared to conventional fast spin-echo (SE) images.

STATISTICAL TESTS

Root mean square distance (RMSD) to the reference method and region of interest analysis.

RESULTS

The combination of MARTINI and GRAPPA (GRAPPATINI) lead to a 10-fold accelerated T₂ mapping protocol with 1:44 minutes acquisition time and full brain coverage. The RMSD of GRAPPATINI increases less (4.3%) than a 10-fold MARTINI reconstruction (37.6%) in comparison to the reference. Reproducibility tests showed low standard deviation (SD) of T₂ values in regions of interest between scan and rescan (<0.4 msec) and across subjects (<4 msec).

DATA CONCLUSION

GRAPPATINI provides highly reproducible and fast whole-brain T₂ maps and arbitrary synthetic T₂ -w images in clinically compatible acquisition times of less than 2 minutes. These abilities are expected to support more widespread clinical applications of quantitative T₂ mapping.

LEVEL OF EVIDENCE

2 Technical Efficacy: Stage 1 J. MAGN. RESON. IMAGING 2018;48:359-368.

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

A new reconstruction method, coined MIRAGE, is presented for accurate, fast, and robust parameter mapping of multiple-echo gradient-echo (MEGE) imaging, the basis sequence of novel quantitative magnetic resonance imaging techniques such as water content and susceptibility mapping. Assuming that the temporal signal can be modeled as a sum of damped complex exponentials, MIRAGE performs model-based reconstruction of undersampled data by minimizing the rank of local Hankel matrices. It further incorporates multi-channel information and spatial prior knowledge. Finally, the parameter maps are estimated using nonlinear regression. Simulations and retrospective undersampling of phantom and in vivo data affirm robustness, e.g., to strong inhomogeneity of the static magnetic field and partial volume effects. MIRAGE is compared with a state-of-the-art compressed sensing method, -ESPIRiT. Parameter maps estimated from reconstructed data using MIRAGE are shown to be accurate, with the mean absolute error reduced by up to 50% for in vivo results. The proposed method has the potential to improve the diagnostic utility of quantitative imaging techniques that rely on MEGE data.

Inferring brain tissue composition and microstructure via MR relaxometry

MRI relaxometry is sensitive to a variety of tissue characteristics in a complex manner, which makes it both attractive and challenging for characterizing tissue. This article reviews the most common water proton relaxometry measures, T₁, T₂, and T₂^*, and reports on their development and current potential to probe the composition and microstructure of brain tissue. The development of these relaxometry measures is challenged by the need for suitably accurate tissue models, as well as robust acquisition and analysis methodologies. MRI relaxometry has been established as a tool for characterizing neural tissue, particular with respect to myelination, and the potential for further development exists.

Low rank alternating direction method of multipliers reconstruction for MR fingerprinting

PURPOSE

The proposed reconstruction framework addresses the reconstruction accuracy, noise propagation and computation time for magnetic resonance fingerprinting.

METHODS

Based on a singular value decomposition of the signal evolution, magnetic resonance fingerprinting is formulated as a low rank (LR) inverse problem in which one image is reconstructed for each singular value under consideration. This LR approximation of the signal evolution reduces the computational burden by reducing the number of Fourier transformations. Also, the LR approximation improves the conditioning of the problem, which is further improved by extending the LR inverse problem to an augmented Lagrangian that is solved by the alternating direction method of multipliers. The root mean square error and the noise propagation are analyzed in simulations. For verification, in vivo examples are provided.

RESULTS

The proposed LR alternating direction method of multipliers approach shows a reduced root mean square error compared to the original fingerprinting reconstruction, to a LR approximation alone and to an alternating direction method of multipliers approach without a LR approximation. Incorporating sensitivity encoding allows for further artifact reduction.

CONCLUSION

The proposed reconstruction provides robust convergence, reduced computational burden and improved image quality compared to other magnetic resonance fingerprinting reconstruction approaches evaluated in this study. Magn Reson Med 79:83-96, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

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.

Propagation of error from parameter constraints in quantitative MRI: Example application of multiple spin echo T2 mapping

PURPOSE

Quantitative MRI may require correcting for nuisance parameters which can or must be constrained to independently measured or assumed values. The noise and/or bias in these constraints propagate to fitted parameters. For example, the case of refocusing pulse flip angle constraint in multiple spin echo T₂ mapping is explored.

METHODS

An analytical expression for the mean-squared error of a parameter of interest was derived as a function of the accuracy and precision of an independent estimate of a nuisance parameter. The expression was validated by simulations and then used to evaluate the effects of flip angle (θ) constraint on the accuracy and precision of T⁁2 for a variety of multi-echo T₂ mapping protocols.

RESULTS

Constraining θ improved T⁁2 precision when the θ-map signal-to-noise ratio was greater than approximately one-half that of the first spin echo image. For many practical scenarios, constrained fitting was calculated to reduce not just the variance but the full mean-squared error of T⁁2, for bias in θ⁁≲6%.

CONCLUSION

The analytical expression derived in this work can be applied to inform experimental design in quantitative MRI. The example application to T₂ mapping provided specific cases, depending on θ⁁ accuracy and precision, in which θ⁁ measurement and constraint would be beneficial to T⁁2 variance or mean-squared error. Magn Reson Med 79:673-682, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

T2 shuffling: Sharp, multicontrast, volumetric fast spin-echo imaging

PURPOSE

A new acquisition and reconstruction method called T2 Shuffling is presented for volumetric fast spin-echo (three-dimensional [3D] FSE) imaging. T2 Shuffling reduces blurring and recovers many images at multiple T2 contrasts from a single acquisition at clinically feasible scan times (6-7 min).

THEORY AND METHODS

The parallel imaging forward model is modified to account for temporal signal relaxation during the echo train. Scan efficiency is improved by acquiring data during the transient signal decay and by increasing echo train lengths without loss in signal-to-noise ratio (SNR). By (1) randomly shuffling the phase encode view ordering, (2) constraining the temporal signal evolution to a low-dimensional subspace, and (3) promoting spatio-temporal correlations through locally low rank regularization, a time series of virtual echo time images is recovered from a single scan. A convex formulation is presented that is robust to partial voluming and radiofrequency field inhomogeneity.

RESULTS

Retrospective undersampling and in vivo scans confirm the increase in sharpness afforded by T2 Shuffling. Multiple image contrasts are recovered and used to highlight pathology in pediatric patients. A proof-of-principle method is integrated into a clinical musculoskeletal imaging workflow.

CONCLUSION

The proposed T2 Shuffling method improves the diagnostic utility of 3D FSE by reducing blurring and producing multiple image contrasts from a single scan. Magn Reson Med 77:180-195, 2017. © 2016 Wiley Periodicals, Inc.

An in vivo study of the orientation-dependent and independent components of transverse relaxation rates in white matter

Diffusion-weighted imaging (DWI) provides information that allows the estimation of white-matter (WM) fibre orientation and distribution, but it does not provide information about myelin density, fibre concentration or fibre size within each voxel. On the other hand, quantitative relaxation contrasts (like the apparent transverse relaxation, R2∗) offer iron and myelin-related contrast, but their dependence on the orientation of microstructure with respect to the applied magnetic field, B₀ , is often neglected. The aim of this work was to combine the fibre orientation information retrieved from the DWI acquisition and the sensitivity to microstructural information from quantitative relaxation parameters. The in vivo measured quantitative transverse relaxation maps (R₂ and R2∗) were decomposed into their orientation-dependent and independent components, using the DWI fibre orientation information as prior knowledge. The analysis focused on major WM fibre bundles such as the forceps major (FMj), forceps minor (FMn), cingulum (CG) and corticospinal tracts (CST). The orientation-dependent R₂ parameters, despite their small size (0-1.5 Hz), showed higher variability across different fibre populations, while those derived from R2∗, although larger (3.1-4.5 Hz), were mostly bundle-independent. With this article, we have, for the first time, attempted the in vivo characterization of the orientation-(in)dependent components of the transverse relaxation rates and demonstrated that the orientation of WM fibres influences both R₂ and R2∗ contrasts.

High-resolution myocardial T1 mapping using single-shot inversion recovery fast low-angle shot MRI with radial undersampling and iterative reconstruction

OBJECTIVE

To develop a novel method for rapid myocardial T₁ mapping at high spatial resolution.

METHODS

The proposed strategy represents a single-shot inversion recovery experiment triggered to early diastole during a brief breath-hold. The measurement combines an adiabatic inversion pulse with a real-time readout by highly undersampled radial FLASH, iterative image reconstruction and T₁ fitting with automatic deletion of systolic frames. The method was implemented on a 3-T MRI system using a graphics processing unit-equipped bypass computer for online application. Validations employed a T₁ reference phantom including analyses at simulated heart rates from 40 to 100 beats per minute. In vivo applications involved myocardial T₁ mapping in short-axis views of healthy young volunteers.

RESULTS

At 1-mm in-plane resolution and 6-mm section thickness, the inversion recovery measurement could be shortened to 3 s without compromising T₁ quantitation. Phantom studies demonstrated T₁ accuracy and high precision for values ranging from 300 to 1500 ms and up to a heart rate of 100 beats per minute. Similar results were obtained in vivo yielding septal T₁ values of 1246 ± 24 ms (base), 1256 ± 33 ms (mid-ventricular) and 1288 ± 30 ms (apex), respectively (mean ± standard deviation, n = 6).

CONCLUSION

Diastolic myocardial T₁ mapping with use of single-shot inversion recovery FLASH offers high spatial resolution, T₁ accuracy and precision, and practical robustness and speed. Advances in knowledge: The proposed method will be beneficial for clinical applications relying on native and post-contrast T₁ quantitation.

Maximum Likelihood Reconstruction for Magnetic Resonance Fingerprinting

This paper introduces a statistical estimation framework for magnetic resonance (MR) fingerprinting, a recently proposed quantitative imaging paradigm. Within this framework, we present a maximum likelihood (ML) formalism to estimate multiple MR tissue parameter maps directly from highly undersampled, noisy k-space data. A novel algorithm, based on variable splitting, the alternating direction method of multipliers, and the variable projection method, is developed to solve the resulting optimization problem. Representative results from both simulations and in vivo experiments demonstrate that the proposed approach yields significantly improved accuracy in parameter estimation, compared to the conventional MR fingerprinting reconstruction. Moreover, the proposed framework provides new theoretical insights into the conventional approach. We show analytically that the conventional approach is an approximation to the ML reconstruction; more precisely, it is exactly equivalent to the first iteration of the proposed algorithm for the ML reconstruction, provided that a gridding reconstruction is used as an initialization.

Sparse Reconstruction Techniques in Magnetic Resonance Imaging: Methods, Applications, and Challenges to Clinical Adoption

The family of sparse reconstruction techniques, including the recently introduced compressed sensing framework, has been extensively explored to reduce scan times in magnetic resonance imaging (MRI). While there are many different methods that fall under the general umbrella of sparse reconstructions, they all rely on the idea that a priori information about the sparsity of MR images can be used to reconstruct full images from undersampled data. This review describes the basic ideas behind sparse reconstruction techniques, how they could be applied to improve MRI, and the open challenges to their general adoption in a clinical setting. The fundamental principles underlying different classes of sparse reconstructions techniques are examined, and the requirements that each make on the undersampled data outlined. Applications that could potentially benefit from the accelerations that sparse reconstructions could provide are described, and clinical studies using sparse reconstructions reviewed. Lastly, technical and clinical challenges to widespread implementation of sparse reconstruction techniques, including optimization, reconstruction times, artifact appearance, and comparison with current gold standards, are discussed.

Direct and accelerated parameter mapping using the unscented Kalman filter

PURPOSE

To accelerate parameter mapping using a new paradigm that combines image reconstruction and model regression as a parameter state-tracking problem.

METHODS

In T2 mapping, the T2 map is first encoded in parameter space by multi-TE measurements and then encoded by Fourier transformation with readout/phase encoding gradients. Using a state transition function and a measurement function, the unscented Kalman filter can describe T2 mapping as a dynamic system and directly estimate the T2 map from the k-space data. The proposed method was validated with a numerical brain phantom and volunteer experiments with a multiple-contrast spin echo sequence. Its performance was compared with a conjugate-gradient nonlinear inversion method at undersampling factors of 2 to 8. An accelerated pulse sequence was developed based on this method to achieve prospective undersampling.

RESULTS

Compared with the nonlinear inversion reconstruction, the proposed method had higher precision, improved structural similarity and reduced normalized root mean squared error, with acceleration factors up to 8 in numerical phantom and volunteer studies.

CONCLUSION

This work describes a new perspective on parameter mapping by state tracking. The unscented Kalman filter provides a highly accelerated and efficient paradigm for T2 mapping.

Model-based reconstruction for real-time phase-contrast flow MRI: Improved spatiotemporal accuracy

PURPOSE

To develop a model-based reconstruction technique for real-time phase-contrast flow MRI with improved spatiotemporal accuracy in comparison to methods using phase differences of two separately reconstructed images with differential flow encodings.

METHODS

The proposed method jointly computes a common image, a phase-contrast map, and a set of coil sensitivities from every pair of flow-compensated and flow-encoded datasets obtained by highly undersampled radial FLASH. Real-time acquisitions with five and seven radial spokes per image resulted in 25.6 and 35.7 ms measuring time per phase-contrast map, respectively. The signal model for phase-contrast flow MRI requires the solution of a nonlinear inverse problem, which is accomplished by an iteratively regularized Gauss-Newton method. Aspects of regularization and scaling are discussed. The model-based reconstruction was validated for a numerical and experimental flow phantom and applied to real-time phase-contrast MRI of the human aorta for 10 healthy subjects and 2 patients.

RESULTS

Under all conditions, and compared with a previously developed real-time flow MRI method, the proposed method yields quantitatively accurate phase-contrast maps (i.e., flow velocities) with improved spatial acuity, reduced phase noise and reduced streaking artifacts.

CONCLUSION

This novel model-based reconstruction technique may become a new tool for clinical flow MRI in real time. Magn Reson Med 77:1082-1093, 2017. © 2016 International Society for Magnetic Resonance in Medicine.