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

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.

Fast Compressed Sensing of 3D Radial T1 Mapping with Different Sparse and Low-Rank Models

Knowledge of the relative performance of the well-known sparse and low-rank compressed sensing models with 3D radial quantitative magnetic resonance imaging acquisitions is limited. We use 3D radial T1 relaxation time mapping data to compare the total variation, low-rank, and Huber penalty function approaches to regularization to provide insights into the relative performance of these image reconstruction models. Simulation and ex vivo specimen data were used to determine the best compressed sensing model as measured by normalized root mean squared error and structural similarity index. The large-scale compressed sensing models were solved by combining a GPU implementation of a preconditioned primal-dual proximal splitting algorithm to provide high-quality T1 maps within a feasible computation time. The model combining spatial total variation and locally low-rank regularization yielded the best performance, followed closely by the model combining spatial and contrast dimension total variation. Computation times ranged from 2 to 113 min, with the low-rank approaches taking the most time. The differences between the compressed sensing models are not necessarily large, but the overall performance is heavily dependent on the imaged object.

Efficient phase-cycling strategy for high-resolution 3D gradient-echo quantitative parameter mapping

Magnetization-prepared (MP) gradient-echo (GRE) sequences suffer from signal contaminations from T₁ recovery during the readout train, which can be eliminated by paired RF phase cycling (PC) at the cost of doubling the scan time. The objective of this study was to develop and validate a novel unpaired PC strategy to eliminate the time penalty for high-resolution quantitative parameter mapping in 3D MP-GRE sequences. Based on the observation that the contaminating T₁ recovery signal along the GRE readout train is independent of magnetization preparation, its impact can be eliminated using a novel curve-fitting approach with complex-valued data without needing paired PC acquisitions. Four new unpaired PC schemes were compared with two traditional paired PC schemes in both phantom and in vivo human knee studies at 3 T using a MP angle-modulated partitioned k-space spoiled gradient-echo snapshots (MAPSS) T_1ρ mapping sequence. In the phantom study, all methods resulted in consistent T_1ρ measurements (∆T_1ρ  < 0.5%) at the center slice when B₀ /B₁ values were uniform. Results were not consistent when off-center slices with nonideal B₀ /B₁ were included. Two unpaired PC schemes had comparable or significantly improved quantitative accuracy and scan-rescan reproducibility compared with the paired PC schemes. There was no significant T_1ρ quantitative variability increase or spatial fidelity loss using the new unpaired PC schemes. Unpaired PC schemes also had different T_1ρ spectral responses at different B₀ frequency offsets, which can potentially be exploited to reduce sensitivity to B₀ field inhomogeneities. The human knee study results were consistent with the phantom study findings. In conclusion, an unpaired PC strategy potentially allows more accurate quantitative parameter mapping with halved scan time compared with the paired PC approach to eliminate signal contaminations from T₁ recovery. It therefore offers additional flexibility in SNR optimization, spatial resolution improvement, and choice of imaging sampling points to obtain more accurate quantitative parameter mapping.

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.

Optimization of spin-lock times in T1ρ mapping of knee cartilage: Cramér-Rao bounds versus matched sampling-fitting

PURPOSE

To compare different optimization approaches for choosing the spin-lock times (TSLs), in spin-lattice relaxation time in the rotating frame (T_1ρ ) mapping.

METHODS

Optimization criteria for TSLs based on Cramér-Rao lower bounds (CRLB) are compared with matched sampling-fitting (MSF) approaches for T_1ρ mapping on synthetic data, model phantoms, and knee cartilage. The MSF approaches are optimized using robust methods for noisy cost functions. The MSF approaches assume that optimal TSLs depend on the chosen fitting method. An iterative non-linear least squares (NLS) and artificial neural networks (ANN) are tested as two possible T_1ρ fitting methods for MSF approaches.

RESULTS

All optimized criteria were better than non-optimized ones. However, we observe that a modified CRLB and an MSF based on the mean of the normalized absolute error (MNAE) were more robust optimization approaches, performing well in all tested cases. The optimized TSLs obtained the best performance with synthetic data (3.5-8.0% error), model phantoms (1.5-2.8% error), and healthy volunteers (7.7-21.1% error), showing stable and improved quality results, comparing to non-optimized approaches (4.2-13.3% error on synthetic data, 2.1-6.2% error on model phantoms, 9.8-27.8% error on healthy volunteers).

CONCLUSION

A modified CRLB and the MSF based on MNAE are robust optimization approaches for choosing TSLs in T_1ρ mapping. All optimized criteria allowed good results even using rapid scans with two TSLs when a complex-valued fitting is done with iterative NLS or ANN.

Single point imaging with radial acquisition and compressed sensing

PURPOSE

To accelerate the Pointwise Encoding Time Reduction with Radial Acquisition (PETRA) sequence using compressed sensing while preserving the image quality for high-resolution MRI of tissue with ultra-short T 2 ∗ values.

METHODS

Compressed sensing was introduced in the PETRA sequence (csPETRA) to accelerate the time-consuming single point acquisition of the k-space center data. Random undersampling was applied to achieve acceleration factors up to Acc = 32. Phantom and in vivo images of the knee joint of six volunteers were measured at 3T using csPETRA sequence with Acc = 4, 8, 12, 16, 24, and 32. Images were compared against fully sampled PETRA data (Acc = 1) for structural similarity and normalized-mean-square-error. Qualitative and semi-quantitative analyses were performed to assess the effect of the acceleration on image artifacts, image quality, and delineation of anatomical structures at the knee.

RESULTS

Even at high acceleration factors of Acc = 16 no aliasing artifacts were observed, and the anatomical details were preserved compared with the fully sampled data. The normalized-mean-square-error was less than 1% for Acc = 16, in which single point imaging acquisition time was reduced from 165 to 10 s, reducing the total scan time from 7.8 to 5.2 min. Semi-quantitative analyses suggest that Acc = 16 yields comparable diagnostic quality as the fully sampled data for knee imaging at a scan time of 5.2 min.

CONCLUSION

csPETRA allows for ultra-short T 2 ∗ imaging of the knee joint in clinically acceptable scan times while maintaining the image quality of original non-accelerated PETRA sequence.

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.

Pilot study quantifying muscle glycosaminoglycan using bi-exponential T1ρ mapping in patients with muscle stiffness after stroke

Post stroke muscle stiffness is a common problem, which left untreated can lead to disabling muscle contractures. The purpose of this pilot study was to evaluate the feasibility of bi-exponential T1ρ mapping in patients with arm muscle stiffness after stroke and its ability to measure treatment related changes in muscle glycosaminoglycans (GAGs). Five patients with muscle stiffness after stroke and 5 healthy controls were recruited for imaging of the upper arm with 3D-T1ρ mapping. Patients were scanned before and after treatment with hyaluronidase injections, whereas the controls were scanned once. Wilcoxon Mann-Whitney tests compared patients vs. controls and patients pre-treatment vs. post-treatment. With bi-exponential modeling, the long component, T1ρl was significantly longer in the patients (biceps P = 0.01; triceps P = 0.004) compared to controls. There was also a significant difference in the signal fractions of the long and short components (biceps P = 0.03, triceps P = 0.04). The results suggest that muscle stiffness is characterized by increased muscle free water and GAG content. Post-treatment, the T1ρ parameters shifted toward control values. This pilot study demonstrates the application of bi-exponential T1ρ mapping as a marker for GAG content in muscle and as a potential treatment monitoring tool for patients with muscle stiffness after stroke.

Optimal acceleration factor for image acquisition in turbo spin echo: diffusion-weighted imaging with compressed sensing

In this study, the change in the image quality and apparent diffusion coefficient (ADC) with increase in the acceleration factor (AF) was analyzed and the most optimal AF was determined to reduce the scan time while preserving the image quality. The AF was changed from 2 to 20 in the MR acquisitions. The similarities between the accelerated and reference images were determined based on the structural similarity (SSIM) index for DWI image and coefficient of variation (%CV) for ADC. The SSIM index decreased significantly when the AF ≥ 8 compared with when the AF = 2 (p < 0.05). In the reference image, the %CV of the ADC increased significantly when the AF ≥ 10 (p < 0.01). In conclusion, a remarkable decrease in the image quality and ADC was observed when the AF was > 8. Thus, an AF < 8 would be optimal for reducing the scan time while preserving the image quality.

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.

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%.