Accelerating 3D-T1ρ mapping of cartilage using compressed sensing with different sparse and low rank models

Improved phosphorus MRSI acquisition through compressed sensing acceleration combined with low-rank reconstruction

OBJECTIVES

Phosphorus-31 magnetic resonance spectroscopic imaging (31P-MRSI) is a non-invasive tool for assessing cellular high-energy metabolism in-vivo. However, its acquisition suffers from a low sensitivity, which necessitates large voxel sizes or multiple averages to achieve an acceptable signal-to-noise ratio (SNR), resulting in long scan times.

MATERIALS AND METHODS

To overcome these limitations, we propose an acquisition and reconstruction scheme for FID-MRSI sequences. Specifically, we employed Compressed Sensing (CS) and Low-Rank (LR) with Total Generalized Variation (TGV) regularization in a combined CS-LR framework. Additionally, we used a novel approach to k-space undersampling that utilizes distinct pseudo-random patterns for each average. To evaluate the proposed method's performance, we performed a retrospective analysis on healthy volunteers' brains and ex-vivo perfused kidneys.

RESULTS

The presented method effectively improves the SNR two-to-threefold while preserving spectral and spatial quality even with threefold acceleration. We were able to recover signal attenuation of anatomical information, and the SNR improvement was obtained while maintaining the metabolites peaks linewidth.

CONCLUSIONS

We presented a novel combined CS-LR acceleration and reconstruction method for FID-MRSI sequences, utilizing a unique approach to k-space undersampling. Our proposed method has demonstrated promising results in enhancing the SNR making it applicable for reducing acquisition time.

Measurement of T1ρ dispersion with compressed sensing and magnetization prepared radial balanced steady-state free precession in spontaneous human osteoarthritis

PURPOSE

To assess the potential for accelerating continuous-wave (CW) T1ρ dispersion measurement with compressed sensing approach via studying the effect that the data reduction has on the ability to detect differences between intact and degenerated articular cartilage with different spin-lock amplitudes and to assess quantitative bias due to acceleration.

METHODS

Osteochondral plugs (n = 27, 4 mm diameter) from femur (n = 14) and tibia (n = 13) regions from human cadaver knee joints were obtained from commercial biobank (Science Care, USA) under Ethical permission 134/2015. MRI of specimens was performed at 9.4T with magnetization prepared radial balanced SSFP (bSSFP) readout sequence, and the CWT1ρ relaxation time maps were computed from the measured data. The relaxation time maps were evaluated in the cartilage zones for different acceleration factors. For reference, Osteoarthritis Research Society International (OARSI) grading and biomechanical measurements were performed and correlated with the MRI findings.

RESULTS

Four-fold acceleration of CWT1ρ dispersion measurement by compressed sensing approach was feasible without meaningful loss in the sensitivity to osteoarthritic (OA) changes within the articular cartilage. Differences were significant between intact and OA groups in the superficial and transitional zones, and CWT1ρ correlated moderately with the reference measurements (0.3 < r < 0.7).

CONCLUSION

CWT1ρ was able to differentiate between intact and OA cartilage even with four-fold acceleration. This indicates that acceleration of CWT1ρ dispersion measurement by compressed sensing approach is feasible with negligible loss in the sensitivity to osteoarthritic changes in articular cartilage.

Accelerated Musculoskeletal Magnetic Resonance Imaging

With a substantial growth in the use of musculoskeletal MRI, there has been a growing need to improve MRI workflow, and faster imaging has been suggested as one of the solutions for a more efficient examination process. Consequently, there have been considerable advances in accelerated MRI scanning methods. This article aims to review the basic principles and applications of accelerated musculoskeletal MRI techniques including widely used conventional acceleration methods, more advanced deep learning-based techniques, and new approaches to reduce scan time. Specifically, conventional accelerated MRI techniques, including parallel imaging, compressed sensing, and simultaneous multislice imaging, and deep learning-based accelerated MRI techniques, including undersampled MR image reconstruction, super-resolution imaging, artifact correction, and generation of unacquired contrast images, are discussed. Finally, new approaches to reduce scan time, including synthetic MRI, novel sequences, and new coil setups and designs, are also reviewed. We believe that a deep understanding of these fast MRI techniques and proper use of combined acceleration methods will synergistically improve scan time and MRI workflow in daily practice. EVIDENCE LEVEL: 3 TECHNICAL EFFICACY: Stage 1.

Cartilage compositional MRI-a narrative review of technical development and clinical applications over the past three decades

Articular cartilage damage and degeneration are among hallmark manifestations of joint injuries and arthritis, classically osteoarthritis. Cartilage compositional MRI (Cart-C MRI), a quantitative technique, which aims to detect early-stage cartilage matrix changes that precede macroscopic alterations, began development in the 1990s. However, despite the significant advancements over the past three decades, Cart-C MRI remains predominantly a research tool, hindered by various technical and clinical hurdles. This paper will review the technical evolution of Cart-C MRI, delve into its clinical applications, and conclude by identifying the existing gaps and challenges that need to be addressed to enable even broader clinical application of Cart-C MRI.

MRI-based T1rho and T2 cartilage compositional imaging in osteoarthritis: what have we learned and what is needed to apply it clinically and in a trial setting?

Cartilage MRI-based T1rho and T2 compositional measurements have been developed to characterize cartilage matrix quality and diagnose cartilage damage before irreversible defects are found, allowing intervention at an early, potentially reversible disease stage. Over the last 2 decades, this technology was investigated in numerous studies and was validated using specimen studies and arthroscopy; and longitudinal studies documented its ability to predict progression of degenerative disease and radiographic osteoarthritis (OA). While T1rho and T2 measurements have shown promise in early disease stages, several hurdles have been encountered to apply this technology clinically. These include (i) challenges with cartilage segmentation, (ii) long image acquisition times, (iii) a lack of standardization of imaging, and (iv) an absence of reference databases and definitions of abnormal cut-off values. Progress has been made by developing deep-learning based automatic cartilage segmentation and faster imaging methods, enabling the feasibility of T1rho and T2 imaging for clinical and scientific trial applications. Also, the Radiological Society of North America (RSNA) Quantitative Imaging Biomarker Alliance mechanism was used to establish standardized profiles for compositional T1rho and T2 imaging, and multi-center feasibility testing is work in progress. The last hurdles are the development of reference databases and establishing a definition of normal versus abnormal cartilage T1rho and T2 values. Finally, effective treatments for prevention and slowing progression of OA are required in order to establish T1rho and T2 as imaging biomarkers for initiating and monitoring therapies, analogous to the role of dual X-ray absorptiometry (DXA) bone mineral density measurements in the management of osteoporosis. KEY POINTS: • T1rho and T2 cartilage measurements have been validated in characterizing cartilage degenerative change using histology and arthroscopy as a reference. • They have also been shown to predict progression of cartilage degeneration and incidence of radiographic OA. • Advances have been made to facilitate clinical and trial application of T1rho and T2 by improved standardization of imaging and by establishing deep learning-based automatic cartilage segmentation. • Effective treatments with disease-modifying OA specific drugs may establish T1rho and T2 cartilage compositional measurements as biomarkers to initiate and monitor treatment.

Age-Dependent Changes in Knee Cartilage T1 , T2 , and T1p Simultaneously Measured Using MRI Fingerprinting

BACKGROUND

Magnetic resonance fingerprinting (MRF) techniques have been recently described for simultaneous multiparameter cartilage mapping of the knee although investigation of their ability to detect early cartilage degeneration remains limited.

PURPOSE

To investigate age-dependent changes in knee cartilage T1 , T2 , and T1p relaxation times measured using a three-dimensional (3D) MRF sequence in healthy volunteers.

STUDY TYPE

Prospective.

SUBJECTS

The study group consisted of 24 healthy asymptomatic human volunteers (15 males with mean age 34.9 ± 14.4 years and 9 females with mean age 44.5 ± 13.1 years).

FIELD STRENGTH/SEQUENCE

A 3.0 T gradient-echo-based 3D-MRF sequence was used to simultaneously create proton density-weighted images and T1 , T2 , and T1p maps of knee cartilage.

ASSESSMENT

Mean global cartilage and regional cartilage (lateral femur, lateral tibia, medial femur, medial tibia, and patella) T1 , T2 , and T1ρ relaxation times of the knee were measured.

STATISTICAL TESTS

Kruskal-Wallis tests were used to compared cartilage T1 , T2 , and T1ρ relaxation times between different age groups, while Spearman correlation coefficients was used to determine the association between age and cartilage T1 , T2 , and T1ρ relaxation times. The value of P < 0.05 was considered statistically significant.

RESULTS

Higher age groups showed higher global and regional cartilage T1 , T2 , and T1ρ . There was a significant difference between age groups in global cartilage T2 and T1ρ but no significant difference (P = 0.13) in global cartilage T1. Significant difference was also present between age groups in cartilage T2 and T1ρ for medial femur cartilage and medial tibia cartilage. There were significant moderate correlations between age and T2 and T1ρ for global cartilage (R2  = 0.63-0.64), medial femur cartilage (R2  = 0.50-0.56), and medial tibia cartilage (R2  = 0.54-0.66).

CONCLUSION

Cartilage T2 and T1p relaxation times simultaneously measured using a 3D-MRF sequence in healthy volunteers showed age-dependent changes in knee cartilage, primarily within the medial compartment.

Assessing post-traumatic changes in cartilage using T1ρ dispersion parameters

Degeneration of cartilage can be studied non-invasively with quantitative MRI. A promising parameter for detecting early osteoarthritis in articular cartilage is T_1ρ, which can be tuned via the amplitude of the spin-lock pulse. By measuring T_1ρ at several spin-lock amplitudes, the dispersion of T_1ρ is obtained. The aim of this study is to find out if the dispersion contains diagnostically relevant information complementary to a T_1ρ measurement at a single spin-lock amplitude. To this end, five differently acquired dispersion parameters are utilized; A, B, τ_c, T_1ρ/T₂, and R₂ - R_1ρ. An open dataset of an equine model of post-traumatic cartilage was utilized to assess the T_1ρ dispersion parameters for the evaluation of cartilage degeneration. Firstly, the parameters were compared for their sensitivity in detecting degenerative changes. Secondly, the relationship of the dispersion parameters to histological and biomechanical reference parameters was studied. Parameters A, T_1ρ/T₂, and R₂ - R_1ρ were found to be sensitive to lesion-induced changes in the cartilage within sample. Strong correlations of several dispersion parameters with optical density, as well as with collagen fibril angle were found. Most of the dispersion parameters correlated strongly with individual T_1ρ values. The results suggest that dispersion parameters can in some cases provide a more accurate description of the biochemical composition of cartilage as compared to conventional MRI parameters. However, in most cases the information given by the dispersion parameters is more of a refinement than complementary to conventional quantitative MRI.

Single breath-hold three-dimensional whole-heart T2 mapping with low-rank plus sparse reconstruction

The purpose of the current study was to develop and evaluate a three-dimensional single Breath-hOLd cardiac T₂ mapping sequence (3D BOLT) with low-rank plus sparse (L + S) reconstruction for rapid whole-heart T₂ measurement. 3D BOLT collects three highly accelerated electrocardiogram-triggered volumes with whole-heart coverage, all within a single 12-heartbeat breath-hold. Saturation pulses are performed every heartbeat to prepare longitudinal magnetization before T₂ preparation (T₂ -prep) or readout, and the echo time of T₂ -prep is varied per volume for variable T₂ weighting. Accelerated volumes are reconstructed jointly by an L + S algorithm. 3D BOLT was optimized and validated against gradient spin echo (GraSE) and a previously published approach (three-dimensional free-breathing cardiac T₂ mapping [3DFBT2]) in both phantoms and human subjects (11 healthy subjects and 10 patients). The repeatability of 3D BOLT was validated on healthy subjects. Retrospective experiments indicated that 3D BOLT with 4.2-fold acceleration achieved T₂ measurements comparable with those obtained with fully sampled data. T₂ measured in phantoms using 3D BOLT demonstrated good accuracy and precision compared with the reference (R²  > 0.99). All in vivo imaging was successful and the average left ventricle T₂ s measured by GraSE, 3DFBT2, and 3D BOLT were comparable and consistent for all healthy subjects (47.0 ± 2.3 vs. 47.7 ± 2.7 vs. 48.4 ± 1.8 ms) and patients (50.8 ± 3.0 vs. 48.6 ± 3.9 vs. 49.1 ± 3.7 ms), respectively. Myocardial T₂ measured by 3D BOLT had excellent agreement with 3DFBT2 and there was no significant difference in mean, standard deviation, and coefficient of variation. 3D BOLT showed excellent repeatability (intraclass correlation coefficient: 0.938). The proposed 3D BOLT achieved whole-heart T₂ mapping in a single breath-hold with good accuracy, precision, and repeatability on T₂ measurements.

K2S Challenge: From Undersampled K-Space to Automatic Segmentation

Magnetic Resonance Imaging (MRI) offers strong soft tissue contrast but suffers from long acquisition times and requires tedious annotation from radiologists. Traditionally, these challenges have been addressed separately with reconstruction and image analysis algorithms. To see if performance could be improved by treating both as end-to-end, we hosted the K2S challenge, in which challenge participants segmented knee bones and cartilage from 8× undersampled k-space. We curated the 300-patient K2S dataset of multicoil raw k-space and radiologist quality-checked segmentations. 87 teams registered for the challenge and there were 12 submissions, varying in methodologies from serial reconstruction and segmentation to end-to-end networks to another that eschewed a reconstruction algorithm altogether. Four teams produced strong submissions, with the winner having a weighted Dice Similarity Coefficient of 0.910 ± 0.021 across knee bones and cartilage. Interestingly, there was no correlation between reconstruction and segmentation metrics. Further analysis showed the top four submissions were suitable for downstream biomarker analysis, largely preserving cartilage thicknesses and key bone shape features with respect to ground truth. K2S thus showed the value in considering reconstruction and image analysis as end-to-end tasks, as this leaves room for optimization while more realistically reflecting the long-term use case of tools being developed by the MR community.

Data-driven optimization of sampling patterns for MR brain T1ρ mapping

PURPOSE

The goal of this study was to apply a fast data-driven optimization algorithm, called bias-accelerated subset selection, for MR brain T1ρ mapping to generate optimized sampling patterns (SPs) for compressed sensing reconstruction of brain 3D-T1ρ MRI.

METHODS

Five healthy volunteers were recruited, and fully sampled Cartesian 3D-T1ρ MRIs were obtained. Variable density (VD) and Poisson disc (PD) undersampling was used as the input to SP optimization process. The reconstruction used 3 compressed sensing methods: spatiotemporal finite differences, low-rank plus sparse with spatial finite differences, and low rank. The performance of images and T1ρ maps using PD-SP and VD-SP and their optimized sampling patterns (PD-OSP and VD-OSP) were compared to the fully sampled reference using normalized root mean square error (NRMSE).

RESULTS

The VD-OSP with spatiotemporal finite differences reconstruction (NRMSE = 0.078) and the PD-OSP with spatiotemporal finite differences reconstruction (NRMSE = 0.079) at the highest acceleration factors (AF = 30) showed the largest improvement compared to the respective nonoptimized SPs (VD NRMSE = 0.087 and PD NRMSE = 0.149). Prospective undersampling was tested at AF = 4, with VD-OSP NRMSE = 0.057 versus PD-OSP NRMSE = 0.060, with optimized sampling performing better that input PD or VD sampling. For brain T1ρ mapping, the VD-OSP with low rank reconstruction for AFs <10 and VD-OSP with spatiotemporal finite differences for AFs >10 perform better.

CONCLUSIONS

The study demonstrated that the appropriate use of data-driven optimized sampling and suitable compressed sensing reconstruction technique can be employed to potentially accelerate 3D T1ρ mapping for brain imaging applications.

Latest advancements in imaging techniques in OA

The osteoarthritis (OA) research community has been advocating a shift from radiography-based screening criteria and outcome measures in OA clinical trials to a magnetic resonance imaging (MRI)-based definition of eligibility and endpoint. For conventional morphological MRI, various semiquantitative evaluation tools are available. We have lately witnessed a remarkable technological advance in MRI techniques, including compositional/physiologic imaging and automated quantitative analyses of articular and periarticular structures. More recently, additional technologies were introduced, including positron emission tomography (PET)-MRI, weight-bearing computed tomography (CT), photon-counting spectral CT, shear wave elastography, contrast-enhanced ultrasound, multiscale X-ray phase contrast imaging, and spectroscopic photoacoustic imaging of cartilage. On top of these, we now live in an era in which artificial intelligence is increasingly utilized in medicine. Osteoarthritis imaging is no exception. Successful implementation of artificial intelligence (AI) will hopefully improve the workflow of radiologists, as well as the level of precision and reproducibility in the interpretation of images.

Region of interest-specific loss functions improve T2 quantification with ultrafast T2 mapping MRI sequences in knee, hip and lumbar spine

MRI T2 mapping sequences quantitatively assess tissue health and depict early degenerative changes in musculoskeletal (MSK) tissues like cartilage and intervertebral discs (IVDs) but require long acquisition times. In MSK imaging, small features in cartilage and IVDs are crucial for diagnoses and must be preserved when reconstructing accelerated data. To these ends, we propose region of interest-specific postprocessing of accelerated acquisitions: a recurrent UNet deep learning architecture that provides T2 maps in knee cartilage, hip cartilage, and lumbar spine IVDs from accelerated T2-prepared snapshot gradient-echo acquisitions, optimizing for cartilage and IVD performance with a multi-component loss function that most heavily penalizes errors in those regions. Quantification errors in knee and hip cartilage were under 10% and 9% from acceleration factors R = 2 through 10, respectively, with bias for both under 3 ms for most of R = 2 through 12. In IVDs, mean quantification errors were under 12% from R = 2 through 6. A Gray Level Co-Occurrence Matrix-based scheme showed knee and hip pipelines outperformed state-of-the-art models, retaining smooth textures for most R and sharper ones through moderate R. Our methodology yields robust T2 maps while offering new approaches for optimizing and evaluating reconstruction algorithms to facilitate better preservation of small, clinically relevant features.

Highly accelerated MR parametric mapping by undersampling the k-space and reducing the contrast number simultaneously with deep learning

Introduction. To propose a novel deep learning-based method called RG-Net (reconstruction and generation network) for highly accelerated MR parametric mapping by undersampling k-space and reducing the acquired contrast number simultaneously. Methods. The proposed framework consists of a reconstruction module and a generative module. The reconstruction module reconstructs MR images from the acquired few undersampled k-space data with the help of a data prior. The generative module then synthesizes the remaining multi-contrast images from the reconstructed images, where the exponential model is implicitly incorporated into the image generation through the supervision of fully sampled labels. The RG-Net was trained and tested on the T1ρ mapping data from 8 volunteers at net acceleration rates of 17, respectively. Regional T1ρ analysis for cartilage and the brain was performed to assess the performance of RG-Net. Results. RG-Net yields a high-quality T1ρ map at a high acceleration rate of 17. Compared with the competing methods that only undersample k-space, our framework achieves better performance in T1ρ value analysis. Conclusion. The proposed RG-Net can achieve a high acceleration rate while maintaining good reconstruction quality by undersampling k-space and reducing the contrast number simultaneously for fast MR parametric mapping. The generative module of our framework can also be used as an insertable module in other fast MR parametric mapping methods.

Embedded Quantitative MRI T1ρ Mapping Using Non-Linear Primal-Dual Proximal Splitting

Quantitative MRI (qMRI) methods allow reducing the subjectivity of clinical MRI by providing numerical values on which diagnostic assessment or predictions of tissue properties can be based. However, qMRI measurements typically take more time than anatomical imaging due to requiring multiple measurements with varying contrasts for, e.g., relaxation time mapping. To reduce the scanning time, undersampled data may be combined with compressed sensing (CS) reconstruction techniques. Typical CS reconstructions first reconstruct a complex-valued set of images corresponding to the varying contrasts, followed by a non-linear signal model fit to obtain the parameter maps. We propose a direct, embedded reconstruction method for T1ρ mapping. The proposed method capitalizes on a known signal model to directly reconstruct the desired parameter map using a non-linear optimization model. The proposed reconstruction method also allows directly regularizing the parameter map of interest and greatly reduces the number of unknowns in the reconstruction, which are key factors in the performance of the reconstruction method. We test the proposed model using simulated radially sampled data from a 2D phantom and 2D cartesian ex vivo measurements of a mouse kidney specimen. We compare the embedded reconstruction model to two CS reconstruction models and in the cartesian test case also the direct inverse fast Fourier transform. The T1ρ RMSE of the embedded reconstructions was reduced by 37–76% compared to the CS reconstructions when using undersampled simulated data with the reduction growing with larger acceleration factors. The proposed, embedded model outperformed the reference methods on the experimental test case as well, especially providing robustness with higher acceleration factors.

Accelerating MR Parameter Mapping Using Nonlinear Compressive Manifold Learning and Regularized Pre-Imaging

In this study, we presented a novel method to reconstruct the MR parametric maps from highly undersampled k-space data. Specifically, we utilized a nonlinear model to sparsely represent the unknown MR parameter-weighted images in high-dimensional feature space. Each image at a specific time point is assumed to belong to a low-dimensional manifold which is learned from training images created based on the parametric model. The final reconstruction is carried out by venturing the sparse representation of the images in the feature space back to the input space, using the pre-imaging technique. Particularly, among an infinite number of solutions that satisfy the data consistency, the one that is closest to the manifold is selected as the desired solution. The underlying optimization problem is solved using kernel trick, sparse coding, and split Bregman iteration algorithm. In addition, both spatial and temporal regularizations were utilized to further improve the reconstruction quality. The proposed method was validated on both phantom and in vivo human brain T2 mapping data. Results showed the proposed method was superior to the conventional linear model-based reconstruction methods, in terms of artifact removal and quantitative estimate accuracy. The proposed method could be potentially beneficial for quantitative MR applications.

Alternating Learning Approach for Variational Networks and Undersampling Pattern in Parallel MRI Applications

This work proposes an alternating learning approach to learn the sampling pattern (SP) and the parameters of variational networks (VN) in accelerated parallel magnetic resonance imaging (MRI). We investigate four variations of the learning approach, that alternates between improving the SP, using bias-accelerated subset selection, and improving parameters of the VN, using ADAM. The variations include the use of monotone or non-monotone alternating steps and systematic reduction of learning rates. The algorithms learn an effective pair to be used in future scans, including an SP that captures fewer k-space samples in which the generated undersampling artifacts are removed by the VN reconstruction. The quality of the VNs and SPs obtained by the proposed approaches is compared against different methods, including other kinds of joint learning methods and state-of-art reconstructions, on two different datasets at various acceleration factors (AF). We observed improvements visually and in three different figures of merit commonly used in deep learning (RMSE, SSIM, and HFEN) on AFs from 2 to 20 with brain and knee joint datasets when compared to the other approaches. The improvements ranged from 1% to 62% over the next best approach tested with VNs. The proposed approach has shown stable performance, obtaining similar learned SPs under different initial training conditions. We observe that the improvement is not only due to the learned sampling density, it is also due to the learned position of samples in k-space. The proposed approach was able to learn effective pairs of SPs and reconstruction VNs, improving 3D Cartesian accelerated parallel MRI applications.

Fast data-driven learning of parallel MRI sampling patterns for large scale problems

In this study, a fast data-driven optimization approach, named bias-accelerated subset selection (BASS), is proposed for learning efficacious sampling patterns (SPs) with the purpose of reducing scan time in large-dimensional parallel MRI. BASS is applicable when Cartesian fully-sampled k-space measurements of specific anatomy are available for training and the reconstruction method for undersampled measurements is specified; such information is used to define the efficacy of any SP for recovering the values at the non-sampled k-space points. BASS produces a sequence of SPs with the aim of finding one of a specified size with (near) optimal efficacy. BASS was tested with five reconstruction methods for parallel MRI based on low-rankness and sparsity that allow a free choice of the SP. Three datasets were used for testing, two of high-resolution brain images ([Formula: see text]-weighted images and, respectively, [Formula: see text]-weighted images) and another of knee images for quantitative mapping of the cartilage. The proposed approach has low computational cost and fast convergence; in the tested cases it obtained SPs up to 50 times faster than the currently best greedy approach. Reconstruction quality increased by up to 45% over that provided by variable density and Poisson disk SPs, for the same scan time. Optionally, the scan time can be nearly halved without loss of reconstruction quality. Quantitative MRI and prospective accelerated MRI results show improvements. Compared with greedy approaches, BASS rapidly learns effective SPs for various reconstruction methods, using larger SPs and larger datasets; enabling better selection of sampling-reconstruction pairs for specific MRI problems.

Accelerating the 3D T1ρ mapping of cartilage using a signal-compensated robust tensor principal component analysis model

Background

Magnetic resonance (MR) quantitative T_1ρ imaging has been increasingly used to detect the early stages of osteoarthritis. The small volume and curved surface of articular cartilage necessitate imaging with high in-plane resolution and thin slices for accurate T_1ρ measurement. Compared with 2D T_1ρ mapping, 3D T_1ρ mapping is free from artifacts caused by slice cross-talk and has a thinner slice thickness and full volume coverage. However, this technique needs to acquire multiple T_1ρ-weighted images with different spin-lock times, which results in a very long scan duration. It is highly expected that the scan time can be reduced in 3D T_1ρ mapping without compromising the T_1ρ quantification accuracy and precision.

Methods

To accelerate the acquisition of 3D T_1ρ mapping without compromising the T_1ρ quantification accuracy and precision, a signal-compensated robust tensor principal component analysis method was proposed in this paper. The 3D T_1ρ-weighted images compensated at different spin-lock times were decomposed as a low-rank high-order tensor plus a sparse component. Poisson-disk random undersampling patterns were applied to k-space data in the phase- and partition-encoding directions in both retrospective and prospective experiments. Five volunteers were involved in this study. The fully sampled k-space data acquired from 3 volunteers were retrospectively undersampled at R=5.2, 7.7, and 9.7, respectively. Reference values were obtained from the fully sampled data. Prospectively undersampled data for R=5 and R=7 were acquired from 2 volunteers. Bland-Altman analyses were used to assess the agreement between the accelerated and reference T_1ρ measurements. The reconstruction performance was evaluated using the normalized root mean square error and the median of the normalized absolute deviation (MNAD) of the reconstructed T_1ρ-weighted images and the corresponding T_1ρ maps.

Results

T_1ρ parameter maps were successfully estimated from T_1ρ-weighted images reconstructed using the proposed method for all accelerations. The accelerated T_1ρ measurements and reference values were in good agreement for R=5.2 (T_1ρ: 40.4±1.4 ms), R=7.7 (T_1ρ: 40.4±2.1 ms), and R=9.7 (T_1ρ: 40.9±2.2 ms) in the Bland-Altman analyses. The T_1ρ parameter maps reconstructed from the prospectively undersampled data also showed promising image quality using the proposed method.

Conclusions

The proposed method achieves the 3D T_1ρ mapping of in vivo knee cartilage in eight minutes using a signal-compensated robust tensor principal component analysis method in image reconstruction.

Whole Brain Myelin Water Mapping in One Minute Using Tensor Dictionary Learning With Low-Rank Plus Sparse Regularization

The quantification of myelin water content in the brain can be obtained by the multi-echo [Formula: see text] weighted images ( [Formula: see text]WIs). To accelerate the long acquisition, a novel tensor dictionary learning algorithm with low-rank and sparse regularization (TDLLS) is proposed to reconstruct the [Formula: see text]WIs from the undersampled data. The proposed algorithm explores the local and nonlocal similarity and the global temporal redundancy in the real and imaginary parts of the complex relaxation signals. The joint application of the low-rank constraints on the dictionaries and the sparse constraints on the core coefficient tensors improves the performance of the tensor-based recovery. Parallel imaging is incorporated into the TDLLS algorithm (pTDLLS) for further acceleration. A pulse sequence is proposed to prospectively undersample the Ky-t space to obtain the whole brain high-quality myelin water fraction (MWF) maps within 1 minute at an undersampling rate (R) of 6.

Measurement of Three-Dimensional Internal Dynamic Strains in the Intervertebral Disc of the Lumbar Spine With Mechanical Loading and Golden-Angle Radial Sparse Parallel-Magnetic Resonance Imaging

BACKGROUND

Noninvasive measurement of internal dynamic strain can be potentially useful to characterize spine intervertebral disc (IVD) in the setting of injury or degenerative disease.

PURPOSE

To develop and demonstrate a noninvasive technique to quantify three-dimensional (3D) internal dynamic strains in the IVD using a combination of static mechanical loading of the IVD using a magnetic resonance imaging (MRI)-compatible ergometer.

STUDY TYPE

Prospective.

SUBJECTS

Silicone gel phantom studies were conducted to assess strain variation with load and repeatability. Mechanical testing was done on the phantoms to confirm MR results. Eight healthy human volunteers (four men and four woman, age = 29 ± 5 years) underwent MRI using a rest, static loading, and recovery paradigm. Repeatability tests were conducted in three subjects.

FIELD STRENGTH/SEQUENCE

MRI (3 T) with 3D continuous golden-angle radial sparse parallel (GRASP) and compressed sensing (CS) reconstruction.

ASSESSMENT

CS reconstruction of the images, motion deformation, and Lagrangian strain maps were calculated for five IVD segments from L1/L2 to L5/S1.

STATISTICAL TESTS

Ranges of displacement and strain in each subject and the resulting mean and standard deviation were calculated. Student t-tests were used to calculate changes in strain from loading to recovery. The correlation coefficient (CC) in the repeatability study was calculated.

RESULTS

The most compressive strain experienced by the IVD segments under loaded conditions was in the L4/L5 segment (-7.5 ± 2.9%). The change in minimum strain from load to recovery was the most for the L4/L5 segment (-7.5% to -5.0%, P = 0.026) and the least for the L1/L2 segment (-4.4% to -3.9%, P = 0.51). In vivo repeatability in three subjects shows strong correlation between scans in subjects done 6 months apart, with CCs equal to 0.86, 0.94, and 0.94 along principal directions.

DATA CONCLUSION

This study shows the feasibility of using static mechanical loading with continuous GRASP-MRI acquisition with CS reconstruction to measure 3D internal dynamic strains in the spine IVD.

LEVEL OF EVIDENCE

2 TECHNICAL EFFICACY STAGE: 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.

A guaranteed convergence analysis for the projected fast iterative soft-thresholding algorithm in parallel MRI

Sparse sampling and parallel imaging techniques are two effective approaches to alleviate the lengthy magnetic resonance imaging (MRI) data acquisition problem. Promising data recoveries can be obtained from a few MRI samples with the help of sparse reconstruction models. To solve the optimization models, proper algorithms are indispensable. The pFISTA, a simple and efficient algorithm, has been successfully extended to parallel imaging. However, its convergence criterion is still an open question. Besides, the existing convergence criterion of single-coil pFISTA cannot be applied to the parallel imaging pFISTA, which, therefore, imposes confusions and difficulties on users about determining the only parameter - step size. In this work, we provide the guaranteed convergence analysis of the parallel imaging version pFISTA to solve the two well-known parallel imaging reconstruction models, SENSE and SPIRiT. Along with the convergence analysis, we provide recommended step size values for SENSE and SPIRiT reconstructions to obtain fast and promising reconstructions. Experiments on in vivo brain images demonstrate the validity of the convergence criterion.

A 4-minute solution for submillimeter whole-brain T1ρ quantification

PURPOSE

To develop a robust, accurate, and accelerated T_1ρ quantification solution for submillimeter in vivo whole-brain imaging.

METHODS

A multislice T_1ρ mapping solution (MS-T_1ρ ) was developed based on a two-acquisition scheme using turbo spin echo with RF cycling to allow for whole-brain coverage with 0.8-mm in-plane resolution. A compressed sensing-based fast imaging method, SCOPE, was used to accelerate the MS-T_1ρ acquisition time to a total scan time of 3 minutes 31 seconds. A phantom experiment was conducted to assess the accuracy of MS-T_1ρ by comparing the T_1ρ value obtained using MS-T_1ρ with the reference value obtained using the standard single-slice T_1ρ mapping method. In vivo scans of 13 volunteers were acquired prospectively to validate the robustness of MS-T_1ρ .

RESULTS

In the phantom study, the T_1ρ values obtained with MS-T_1ρ were in good agreement with the reference T_1ρ values (R² = 0.9991) and showed high consistency throughout all slices (coefficient of variation = 2.2 ± 2.43%). In the in vivo experiments, T_1ρ maps were successfully acquired for all volunteers with no visually noticeable artifacts. There was no significant difference in T_1ρ values between MS-T_1ρ acquisitions and fully sampled acquisitions for all brain tissues (p-value > .05). In the intraclass correlation coefficient and Bland-Altman analyses, the accelerated T_1ρ measurements show moderate to good agreement to the fully sampled reference values.

CONCLUSION

The proposed MS-T_1ρ solution allows for high-resolution whole-brain T_1ρ mapping within 4 minutes and may provide a potential tool for investigating neural diseases.

Fast multicomponent 3D-T1ρ relaxometry

NMR relaxometry can provide information about the relaxation of the magnetization in different tissues, increasing our understanding of molecular dynamics and biochemical composition in biological systems. In general, tissues have complex and heterogeneous structures composed of multiple pools. As a result, bulk magnetization returns to its original state with different relaxation times, in a multicomponent relaxation. Recovering the distribution of relaxation times in each voxel is a difficult inverse problem; it is usually unstable and requires long acquisition time, especially on clinical scanners. MRI can also be viewed as an inverse problem, especially when compressed sensing (CS) is used. The solution of these two inverse problems, CS and relaxometry, can be obtained very efficiently in a synergistically combined manner, leading to a more stable multicomponent relaxometry obtained with short scan times. In this paper, we will discuss the details of this technique from the viewpoint of inverse problems.

Resolution-dependent influences of compressed sensing in quantitative T2 mapping of articular cartilage

This study evaluates the resolution-dependent influences of compressed sensing (CS) in MRI quantification of T2 mapping in articular cartilage with osteoarthritis (OA). T2-weighed 2D experiments of healthy and OA cartilage were fully sampled in k-space with five echo times at both 17.6 μm and 195.3 μm in-plane resolutions; termed as microscopic MRI (μMRI) and macroscopic MRI (mMRI) respectively. These fully sampled k-space data were under-sampled at various 2D CS accelerating factors (AF = 4-32). The under-sampled data were reconstructed individually into 2D images using nonlinear reconstruction, which were used to calculate the T2 maps. The bulk and zonal variations of T2 values in cartilage were evaluated at different AFs. The study finds that the T2 images at AFs up to 8 preserved major visual information and produced negligible artifacts for μMRI. The T2 values remained accurate for different sub-tissue zones at various AFs. The absolute difference between the CS (AF up to 32) and the Ground Truth (i.e., using 100% of the k-space data) of the mean T2 values through the whole tissue depth was higher in mMRI versus μMRI. For mMRI (where the resolution mimics the clinical MRI of human cartilage), the quantitative T2 mapping at AFs up to 4 showed negligible variations. This study demonstrates that both clinical MRI and μMRI can benefit from the use of CS in image acquisition, and μMRI benefits more from the use of CS by acquiring much less data, without losing significant accuracy in the quantification of T2 maps in osteoarthritic cartilage.

Performance Comparison of Compressed Sensing Algorithms for Accelerating T1ρ Mapping of Human Brain

BACKGROUND

3D-T_1ρ mapping is useful to quantify various neurologic disorders, but data are currently time-consuming to acquire.

PURPOSE

To compare the performance of five compressed sensing (CS) algorithms-spatiotemporal finite differences (STFD), exponential dictionary (EXP), 3D-wavelet transform (WAV), low-rank (LOW) and low-rank plus sparse model with spatial finite differences (L + S SFD)-for 3D-T_1ρ mapping of the human brain with acceleration factors (AFs) of 2, 5, and 10.

STUDY TYPE

Retrospective.

SUBJECTS

Eight healthy volunteers underwent T_1ρ imaging of the whole brain.

FIELD STRENGTH/SEQUENCE

The sequence was fully sampled 3D Cartesian ultrafast gradient echo sequence with a customized T_1ρ preparation module on a clinical 3T scanner.

ASSESSMENT

The fully sampled data was undersampled by factors of 2, 5, and 10 and reconstructed with the five CS algorithms. Image reconstruction quality was evaluated and compared to the SENSE reconstruction of the fully sampled data (reference) and T_1ρ estimation errors were assessed as a function of AF.

STATISTICAL TESTS

Normalized root mean squared errors (nRMSE) and median normalized absolute deviation (MNAD) errors were calculated to compare image reconstruction errors and T_1ρ estimation errors, respectively. Linear regression plots, Bland-Altman plots, and Pearson correlation coefficients (CC) are shown.

RESULTS

For image reconstruction quality, at AF = 2, EXP transforms had the lowest mRMSE (1.56%). At higher AF values, STFD performed better, with the smallest errors (3.16% at AF = 5, 4.32% at AF = 10). For whole-brain quantitative T_1ρ mapping, at AF = 2, EXP performed best (MNAD error = 1.62%). At higher AF values (AF = 5, 10), the STFD technique had the least errors (2.96% at AF = 5, 4.24% at AF = 10) and the smallest variance from the reference T_1ρ estimates.

DATA CONCLUSION

This study demonstrates the use of different CS algorithms that may be useful in reducing the scan time required to perform volumetric T_1ρ mapping of the brain.

LEVEL OF EVIDENCE

2.

TECHNICAL EFFICACY STAGE

1.

Rapid mono and biexponential 3D-T1ρ mapping of knee cartilage using variational networks

In this study we use undersampled MRI acquisition methods to obtain accelerated 3D mono and biexponential spin-lattice relaxation time in the rotating frame (T1ρ) mapping of knee cartilage, reducing the usual long scan time. We compare the accelerated T1ρ maps obtained by deep learning-based variational network (VN) and compressed sensing (CS). Both methods were compared with spatial (S) and spatio-temporal (ST) filters. Complex-valued fitting was used for T1ρ parameters estimation. We tested with seven in vivo and six synthetic datasets, with acceleration factors (AF) from 2 to 10. Median normalized absolute deviation (MNAD), analysis of variance (ANOVA), and coefficient of variation (CV) were used for analysis. The methods CS-ST, VN-S, and VN-ST performed well for accelerating monoexponential T1ρ mapping, with MNAD around 5% for AF = 2, which increases almost linearly with the AF to an MNAD of 13% for AF = 8, with all methods. For biexponential mapping, the VN-ST was the best method starting with MNAD of 7.4% for AF = 2 and reaching MNAD of 13.1% for AF = 8. The VN was able to produce 3D-T1ρ mapping of knee cartilage with lower error than CS. The best results were obtained by VN-ST, improving CS-ST method by nearly 7.5%.

Rapid Knee MRI Acquisition and Analysis Techniques for Imaging Osteoarthritis

Osteoarthritis (OA) of the knee is a major source of disability that has no known treatment or cure. Morphological and compositional MRI is commonly used for assessing the bone and soft tissues in the knee to enhance the understanding of OA pathophysiology. However, it is challenging to extend these imaging methods and their subsequent analysis techniques to study large population cohorts due to slow and inefficient imaging acquisition and postprocessing tools. This can create a bottleneck in assessing early OA changes and evaluating the responses of novel therapeutics. The purpose of this review article is to highlight recent developments in tools for enhancing the efficiency of knee MRI methods useful to study OA. Advances in efficient MRI data acquisition and reconstruction tools for morphological and compositional imaging, efficient automated image analysis tools, and hardware improvements to further drive efficient imaging are discussed in this review. For each topic, we discuss the current challenges as well as potential future opportunities to alleviate these challenges. LEVEL OF EVIDENCE: 5 TECHNICAL EFFICACY STAGE: 3.

T1rho Fractional-order Relaxation of Human Articular Cartilage

T1rho imaging is a promising non-invasive diagnostic tool for early detection of articular cartilage degeneration. A mono-exponential model is normally used to describe the T1rho relaxation process. However, mono-exponentials may not adequately to describe NMR relaxation in complex, heterogeneous, and anisotropic materials, such as articular cartilage. Fractional-order models have been used successfully to describe complex relaxation phenomena in the laboratory frame in cartilage matrix components. In this paper, we develop a time-fractional order (T-FACT) model for T1rho fitting in human articular cartilage. Representative results demonstrate that the proposed method is able to fit the experimental data with smaller root mean squared error than the one from conventional mono-exponential relaxation model in human articular cartilage.

Improvement of Fast Model-Based Acceleration of Parameter Look-Locker T1 Mapping

Quantitative mapping is desirable in many scientific and clinical magneric resonance imaging (MRI) applications. Recent inverse recovery-look locker sequence enables single-shot T₁ mapping with a time of a few seconds but the main computational load is directed into offline reconstruction, which can take from several minutes up to few hours. In this study we proposed improvement of model-based approach for T₁-mapping by introduction of two steps fitting procedure. We provided analysis of further reduction of k-space data, which lead us to decrease of computational time and perform simulation of multi-slice development. The region of interest (ROI) analysis of human brain measurements with two different initial models shows that the differences between mean values with respect to a reference approach are in white matter-0.3% and 1.1%, grey matter-0.4% and 1.78% and cerebrospinal fluid-2.8% and 11.1% respectively. With further improvements we were able to decrease the time of computational of single slice to 6.5 min and 23.5 min for different initial models, which has been already not achieved by any other algorithm. In result we obtained an accelerated novel method of model-based image reconstruction in which single iteration can be performed within few seconds on home computer.

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.

Accelerated mono- and biexponential 3D-T1ρ relaxation mapping of knee cartilage using golden angle radial acquisitions and compressed sensing

PURPOSE

To use golden-angle radial sampling and compressed sensing (CS) for accelerating mono- and biexponential 3D spin-lattice relaxation time in the rotating frame (T_1ρ ) mapping of knee cartilage.

METHODS

Golden-angle radial stack-of-stars and Cartesian 3D-T_1ρ -weighted knee cartilage datasets (n = 12) were retrospectively undersampled by acceleration factors (AFs) 2-10. CS-based reconstruction using 8 different sparsifying transforms were compared for mono- and biexponential T_1ρ -mapping of knee cartilage, including spatio-temporal finite differences, wavelets, dictionary from principal component analysis, and exponential decay models, and also low rank and low rank plus sparse models (L+S). Complex-valued fitting was used and Marchenko-Pastur principal component analysis filtering also tested.

RESULTS

Most CS methods performed well for an AF of 2, with relative median normalized absolute deviation below 10% for monoexponential and biexponential mapping. For monoexponential mapping, radial sampling obtained a median normalized absolute deviation below 10% up to AF of 10, while Cartesian obtained this level of error only up to AF of 4. Radial sampling was also better with biexponential T_1ρ mapping, with median normalized absolute deviation below 10% up to AF of 6.

CONCLUSION

Golden-angle radial acquisitions combined with CS outperformed Cartesian acquisitions for 3D-T_1ρ mapping of knee cartilage, being it is a good alternative to Cartesian sampling for reducing scan time and/or improving image and mapping quality. The methods exponential decay models, spatio-temporal finite differences, and low rank obtained the best results for radial sampling patterns.

In vivo tibiofemoral cartilage strain mapping under static mechanical loading using continuous GRASP-MRI

BACKGROUND

Quantification of dynamic biomechanical strain in articular cartilage in vivo; in situ using noninvasive MRI techniques is desirable and may potentially be used to assess joint pathology.

PURPOSE

To demonstrate the use of static mechanical loading and continuous 3D-MRI acquisition of the human knee joint in vivo to measure the strain in the tibiofemoral articular cartilage.

STUDY TYPE

Prospective.

SUBJECTS

Five healthy human volunteers (four women, one man; age 25.6 ± 1.7) underwent MRI at rest, under static mechanical loading condition, and during recovery.

FIELD STRENGTH/SEQUENCE

A field strength of 3T was used. The sequence used was 3D-continuous golden angle radial sparse parallel (GRASP) MRI and compressed sensing (CS) reconstruction.

ASSESSMENT

Tibiofemoral cartilage deformation maps under loading and during recovery were calculated using an optical flow algorithm. The corresponding Lagrangian strain was calculated in the articular cartilage.

STATISTICAL TESTS

Range of displacement and strain in each subject, and the resulting mean and standard deviation, were calculated.

RESULTS

During the loading condition, the cartilage displacement in the direction of loading ranged from a minimum of -673.6 ± 121.9 μm to a maximum of 726.5 ± 169.5 μm. Corresponding strain ranged from a minimum of -7.0 ± 4.2% to a maximum of 5.4 ± 1.6%. During the recovery condition, the cartilage displacement in the same direction reduced to a minimum of -613.0 ± 129.5 μm and a maximum of 555.7 ± 311.4 μm. The corresponding strain range reduced to a minimum of -1.6 ± 7.5% to a maximum of 4.2 ± 2.6%.

DATA CONCLUSION

This study shows the feasibility of using static mechanical loading with continuous GRASP-MRI acquisition to measure the strain in the articular cartilage. By measuring strain during the loading and recovery phases, dynamic strain information in the articular cartilage might be able to be investigated.

LEVEL OF EVIDENCE

2 Technical Efficacy: Stage 1 J. Magn. Reson. Imaging 2020;51:426-434.

Monotone FISTA with Variable Acceleration for Compressed Sensing Magnetic Resonance Imaging

An improvement of the monotone fast iterative shrinkage-thresholding algorithm (MFISTA) for faster convergence is proposed. Our motivation is to reduce the reconstruction time of compressed sensing problems in magnetic resonance imaging. The proposed modification introduces an extra term, which is a multiple of the proximal-gradient step, into the so-called momentum formula used for the computation of the next iterate in MFISTA. In addition, the modified algorithm selects the next iterate as a possibly-improved point obtained by any other procedure, such as an arbitrary shift, a line search, or other methods. As an example, an arbitrary-length shift in the direction from the previous iterate to the output of the proximal-gradient step is considered. The resulting algorithm accelerates MFISTA in a manner that varies with the iterative steps. Convergence analysis shows that the proposed modification provides improved theoretical convergence bounds, and that it has more flexibility in its parameters than the original MFISTA. Since such problems need to be studied in the context of functions of several complex variables, a careful extension of FISTA-like methods to complex variables is provided.

T1ρ mapping for assessment of renal allograft fibrosis

BACKGROUND

There is an unmet need for noninvasive methods to diagnose and stage renal allograft fibrosis.

PURPOSE

To investigate the utility of T_1ρ measured with MRI for the assessment of fibrosis in renal allografts.

STUDY TYPE

Institutional Review Board (IRB)-approved prospective.

SUBJECTS

Fifteen patients with stable functional allograft (M/F 9/6, mean age 56 years) and 12 patients with allograft dysfunction and established fibrosis (M/F 6/6, mean age 51 years).

FIELD STRENGTH/SEQUENCE

T_1ρ imaging at 1.5T using a custom-developed sequence.

ASSESSMENT

Average T_1ρ in the cortex and medulla was quantified and T_1ρ repeatability (expressed by the coefficient of variation [CV]) was measured in four patients.

STATISTICAL TESTS

Differences in T_1ρ values between the 2 groups were assessed using Mann-Whitney U-tests. Diagnostic performance of T_1ρ for differentiation between functional and fibrotic allografts was evaluated using receiver operating characteristic (ROC) analysis. Spearman correlations of T_1ρ with Masson's trichrome-stained fractions and serum estimated glomerular filtration rate (eGFR) were assessed.

RESULTS

Higher T_1ρ repeatability was found for cortex compared with medulla (mean CV T_1ρ cortex 7.4%, medulla 13.3%). T_1ρ values were significantly higher in the cortex of fibrotic vs. functional allografts (111.8 ± 17.2 msec vs. 99.0 ± 11.0 msec, P = 0.027), while there was no difference in medullary T_1ρ values (122.6 ± 20.8 msec vs. 124.3 ± 20.8 msec, P = 0.789). Cortical T_1ρ significantly correlated with Masson's trichrome-stained fractions (r = 0.515, P = 0.044) and eGFR (r = -0.546, P = 0.004), and demonstrated an area under the curve (AUC) of 0.77 for differentiating between functional and fibrotic allografts (sensitivity and specificity of 75.0% and 86.7%, using threshold of 106.9 msec).

DATA CONCLUSION

Our preliminary results suggest that T_1ρ is a potential imaging biomarker of renal allograft fibrosis. These results should be verified in a larger study.

LEVEL OF EVIDENCE

1 Technical Efficacy: Stage 1 J. Magn. Reson. Imaging 2019;50:1085-1091.

Accelerated free-breathing 3D T1ρ cardiovascular magnetic resonance using multicoil compressed sensing

BACKGROUND

Endogenous contrast T1ρ cardiovascular magnetic resonance (CMR) can detect scar or infiltrative fibrosis in patients with ischemic or non-ischemic cardiomyopathy. Existing 2D T1ρ techniques have limited spatial coverage or require multiple breath-holds. The purpose of this project was to develop an accelerated, free-breathing 3D T1ρ mapping sequence with whole left ventricle coverage using a multicoil, compressed sensing (CS) reconstruction technique for rapid reconstruction of undersampled k-space data.

METHODS

We developed a cardiac- and respiratory-gated, free-breathing 3D T1ρ sequence and acquired data using a variable-density k-space sampling pattern (A = 3). The effect of the transient magnetization trajectory, incomplete recovery of magnetization between T1ρ-preparations (heart rate dependence), and k-space sampling pattern on T1ρ relaxation time error and edge blurring was analyzed using Bloch simulations for normal and chronically infarcted myocardium. Sequence accuracy and repeatability was evaluated using MnCl2 phantoms with different T1ρ relaxation times and compared to 2D measurements. We further assessed accuracy and repeatability in healthy subjects and compared these results to 2D breath-held measurements.

RESULTS

The error in T1ρ due to incomplete recovery of magnetization between T1ρ-preparations was T1ρhealthy = 6.1% and T1ρinfarct = 10.8% at 60 bpm and T1ρhealthy = 13.2% and T1ρinfarct = 19.6% at 90 bpm. At a heart rate of 60 bpm, error from the combined effects of readout-dependent magnetization transients, k-space undersampling and reordering was T1ρhealthy = 12.6% and T1ρinfarct = 5.8%. CS reconstructions had improved edge sharpness (blur metric = 0.15) compared to inverse Fourier transform reconstructions (blur metric = 0.48). There was strong agreement between the mean T1ρ estimated from the 2D and accelerated 3D data (R2 = 0.99; P < 0.05) acquired on the MnCl2 phantoms. The mean R1ρ estimated from the accelerated 3D sequence was highly correlated with MnCl2 concentration (R2 = 0.99; P < 0.05). 3D T1ρ acquisitions were successful in all human subjects. There was no significant bias between undersampled 3D T1ρ and breath-held 2D T1ρ (mean bias = 0.87) and the measurements had good repeatability (COV2D = 6.4% and COV3D = 7.1%).

CONCLUSIONS

This is the first report of an accelerated, free-breathing 3D T1ρ mapping of the left ventricle. This technique may improve non-contrast myocardial tissue characterization in patients with heart disease in a scan time appropriate for patients.

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.

Compressed sensing acceleration of biexponential 3D-T1ρ relaxation mapping of knee cartilage

PURPOSE

Use compressed sensing (CS) for 3D biexponential spin-lattice relaxation time in the rotating frame (T_1ρ ) mapping of knee cartilage, reducing the total scan time and maintaining the quality of estimated biexponential T_1ρ parameters (short and long relaxation times and corresponding fractions) comparable to fully sampled scans.

METHODS

Fully sampled 3D-T_1ρ -weighted data sets were retrospectively undersampled by factors 2-10. CS reconstruction using 12 different sparsifying transforms were compared for biexponential T_1ρ -mapping of knee cartilage, including temporal and spatial wavelets and finite differences, dictionary from principal component analysis (PCA), k-means singular value decomposition (K-SVD), exponential decay models, and also low rank and low rank plus sparse models. Synthetic phantom (N = 6) and in vivo human knee cartilage data sets (N = 7) were included in the experiments. Spatial filtering before biexponential T_1ρ parameter estimation was also tested.

RESULTS

Most CS methods performed satisfactorily for an acceleration factor (AF) of 2, with relative median normalized absolute deviation (MNAD) around 10%. Some sparsifying transforms, such as low rank with spatial finite difference (L + S SFD), spatiotemporal finite difference (STFD), and exponential dictionaries (EXP) significantly improved this performance, reaching MNAD below 15% with AF up to 10, when spatial filtering was used.

CONCLUSION

Accelerating biexponential 3D-T_1ρ mapping of knee cartilage with CS is feasible. The best results were obtained by STFD, EXP, and L + S SFD regularizers combined with spatial prefiltering. These 3 CS methods performed satisfactorily on synthetic phantom as well as in vivo knee cartilage for AFs up to 10, with median error below 15%.

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.