PANDA-T1ρ: Integrating principal component analysis and dictionary learning for fast T1ρ mapping

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.

SPICY: a method for single scan rotating frame relaxometry

T _1ρ is an NMR relaxation mode that is sensitive to low frequency molecular motions, making it an especially valuable tool in biomolecular research. Here, we introduce a new method, SPICY, for measuring T_1ρ relaxation times. In contrast to conventional T_1ρ experiments, in which the sequence is repeated many times to determine the T_1ρ time, the SPICY sequence allows determination of T_1ρ within a single scan, shortening the experiment time remarkably. We demonstrate the method using ¹H T_1ρ relaxation dispersion experiments. Additionally, we combine the sequence with spatial encoding to produce 1D images in a single scan. We show that T_1ρ relaxation times obtained using the single scan approach are in good agreement with those obtained using the traditional experiments.

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.

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

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

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.

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%.

Three-Dimensional GRE T1ρ mapping of the brain using tailored variable flip-angle scheduling

PURPOSE

To introduce a new approach called tailored variable flip-angle (VFA) scheduling for SNR-efficient 3D T_1ρ mapping of the brain using a magnetization-prepared gradient-echo sequence.

METHODS

Simulations were used to assess the relative SNR efficiency, quantitative accuracy, and spatial blurring of tailored VFA scheduling for T_1ρ mapping of brain tissue compared with magnetization-prepared angle-modulated partitioned k-space spoiled gradient-echo snapshots (MAPSS), a state-of-the-art technique for accurate 3D gradient-echo T_1ρ mapping. Simulations were also used to calculate optimal imaging parameters for tailored VFA scheduling versus MAPSS, without and with nulling of CSF. Four participants were imaged at 3T MRI to demonstrate the feasibility of tailored VFA scheduling for T_1ρ mapping of the brain. Using MAPSS as a reference standard, in vivo data were used to validate the relative SNR efficiency and quantitative accuracy of the new approach.

RESULTS

Tailored VFA scheduling can provide a 2-fold to 4-fold gain in the SNR of the resulting T_1ρ map as compared with MAPSS when using identical sequence parameters while limiting T_1ρ quantification errors to 2% or less. In vivo whole-brain 3D T_1ρ maps acquired with tailored VFA scheduling had superior SNR efficiency than is achievable with MAPSS, and the SNR efficiency improved with a greater number of views per segment.

CONCLUSIONS

Tailored VFA scheduling is an SNR-efficient GRE technique for 3D T_1ρ mapping of the brain that provides increased flexibility in choice of imaging parameters compared with MAPSS, which may benefit a variety of applications.

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.

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.

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.

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%.

Compressed sensing in quantitative determination of GAG concentration in cartilage by microscopic MRI

PURPOSE

To evaluate the potentials of compressed sensing (CS) in MRI quantification of glycosaminoglycan (GAG) concentration in articular cartilage at microscopic resolution.

METHODS

T1 -weighted 2D experiments of cartilage were fully sampled in k-space with five inversion times at 17.6 μm resolution. These fully sampled k-space data were re-processed, by undersampling at various 1D and 2D CS undersampling factors (UFs). The undersampled data were reconstructed individually into 2D images using nonlinear reconstruction, which were used to calculate 2D maps of T1 and GAG concentration. The values of T1 and GAG in cartilage were evaluated at different UFs (up to 16, which used 6.25% of the data). K-space sampling pattern and zonal variations were also investigated.

RESULTS

Using 2D variable density sampling pattern, the T1 images at UFs up to eight preserved major visual information and produced negligible artifacts. The GAG concentration remained accurate for different sub-tissue zones at various UFs. The variation of the mean GAG concentration through the whole tissue depth was 1.20%, compared to the fully sampled results. The maximum variation was 2.24% in the deep zone of cartilage. Using 1D variable density sampling pattern, the quantitative T1 mapping and GAG concentration at UFs up to 4 showed negligible variations.

CONCLUSION

This study demonstrates that CS could be beneficial in microscopic MRI (µMRI) studies of cartilage by acquiring less data, without losing significant accuracy in the quantification of GAG concentration. Magn Reson Med 79:3163-3171, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

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

PURPOSE

To evaluate the feasibility of using compressed sensing (CS) to accelerate 3D-T_1ρ mapping of cartilage and to reduce total scan times without degrading the estimation of T_1ρ relaxation times.

METHODS

Fully sampled 3D-T_1ρ datasets were retrospectively undersampled by factors 2-10. CS reconstruction using 12 different sparsifying transforms were compared, including finite differences, temporal and spatial wavelets, learned transforms using principal component analysis (PCA) and K-means singular value decomposition (K-SVD), explicit exponential models, low rank and low rank plus sparse models. Spatial filtering prior to T_1ρ parameter estimation was also tested. Synthetic phantom (n = 6) and in vivo human knee cartilage datasets (n = 7) were included.

RESULTS

Most CS methods performed satisfactorily for an acceleration factor (AF) of 2, with relative T_1ρ error lower than 4.5%. Some sparsifying transforms, such as spatiotemporal finite difference (STFD), exponential dictionaries (EXP) and low rank combined with spatial finite difference (L+S SFD) significantly improved this performance, reaching average relative T_1ρ error below 6.5% on T_1ρ relaxation times with AF up to 10, when spatial filtering was used before T_1ρ fitting, at the expense of smoothing the T_1ρ maps. The STFD achieved 5.1% error at AF = 10 with spatial filtering prior to T_1ρ fitting.

CONCLUSION

Accelerating 3D-T_1ρ mapping of cartilage with CS is feasible up to AF of 10 when using STFD, EXP or L+S SFD regularizers. These three best CS methods performed satisfactorily on synthetic phantom and in vivo knee cartilage for AFs up to 10, with T_1ρ error of 6.5%.

Recovery of Damped Exponentials Using Structured Low Rank Matrix Completion

We introduce a structured low rank matrix completion algorithm to recover a series of images from their under-sampled measurements, where the signal along the parameter dimension at every pixel is described by a linear combination of exponentials. We exploit the exponential behavior of the signal at every pixel, along with the spatial smoothness of the exponential parameters to derive an annihilation relation in the Fourier domain. This relation translates to a low-rank property on a structured matrix constructed from the Fourier samples. We enforce the low-rank property of the structured matrix as a regularization prior to recover the images. Since the direct use of current low rank matrix recovery schemes to this problem is associated with high computational complexity and memory demand, we adopt an iterative re-weighted least squares algorithm, which facilitates the exploitation of the convolutional structure of the matrix. Novel approximations involving 2-D fast Fourier transforms are introduced to drastically reduce the memory demand and computational complexity, which facilitates the extension of structured low-rank methods to large scale 3-D problems. We demonstrate our algorithm in the MR parameter mapping setting and show improvement over the state-of-the-art methods.

Improved Computational Efficiency of Locally Low Rank MRI Reconstruction Using Iterative Random Patch Adjustments

This paper presents and analyzes an alternative formulation of the locally low-rank (LLR) regularization framework for magnetic resonance image (MRI) reconstruction. Generally, LLR-based MRI reconstruction techniques operate by dividing the underlying image into a collection of matrices formed from image patches. Each of these matrices is assumed to have low rank due to the inherent correlations among the data, whether along the coil, temporal, or multi-contrast dimensions. The LLR regularization has been successful for various MRI applications, such as parallel imaging and accelerated quantitative parameter mapping. However, a major limitation of most conventional implementations of the LLR regularization is the use of multiple sets of overlapping patches. Although the use of overlapping patches leads to effective shift-invariance, it also results in high-computational load, which limits the practical utility of the LLR regularization for MRI. To circumvent this problem, alternative LLR-based algorithms instead shift a single set of non-overlapping patches at each iteration, thereby achieving shift-invariance and avoiding block artifacts. A novel contribution of this paper is to provide a mathematical framework and justification of LLR regularization with iterative random patch adjustments (LLR-IRPA). This method is compared with a state-of-the-art LLR regularization algorithm based on overlapping patches, and it is shown experimentally that results are similar but with the advantage of much reduced computational load. We also present theoretical results demonstrating the effective shift invariance of the LLR-IRPA approach, and we show reconstruction examples and comparisons in both retrospectively and prospectively undersampled MRI acquisitions, and in T1 parameter mapping.

Artifacts correction for T1rho imaging with constant amplitude spin-lock

T1rho imaging with constant amplitude spin-lock is prone to artifacts in the presence of B1 RF and B0 field inhomogeneity. Despite significant technological progress, improvements on the robustness of constant amplitude spin-lock are necessary in order to use it for routine clinical practice. This work proposes methods to simultaneously correct for B1 RF and B0 field inhomogeneity in constant amplitude spin-lock. By setting the maximum B1 amplitude of the excitation adiabatic pulses equal to the expected constant amplitude spin-lock frequency, the spins become aligned along the effective field throughout the spin-lock process. This results in T1rho-weighted images free of artifacts, despite the spatial variation of the effective field caused by B1 RF and B0 field inhomogeneity. When the pulse is long, the relaxation effect during the adiabatic half passage may result in a non-negligible error in the mono-exponential relaxation model. A two-acquisition approach is presented to solve this issue. Simulation, phantom, and in-vivo scans demonstrate the proposed methods achieve superior image quality compared to existing methods, and that the two-acquisition method is effective in resolving the relaxation effect during the adiabatic half passage.

Chemical Exchange Saturation Transfer (CEST) MR Technique for Liver Imaging at 3.0 Tesla: an Evaluation of Different Offset Number and an After-Meal and Over-Night-Fast Comparison

PURPOSE

This study seeks to explore whether chemical exchange saturation transfer (CEST) magnetic resonance imaging (MRI) can detect liver composition changes between after-meal and over-night-fast statuses.

PROCEDURES

Fifteen healthy volunteers were scanned on a 3.0-T human MRI scanner in the evening 1.5-2 h after dinner and in the morning after over-night (12-h) fasting. Among them, seven volunteers were scanned twice to assess the scan-rescan reproducibility. Images were acquired at offsets (n = 41, increment = 0.25 ppm) from -5 to 5 ppm using a turbo spin echo (TSE) sequence with a continuous rectangular saturation pulse. Amide proton transfer-weighted (APTw) and GlycoCEST signals were quantified with the asymmetric magnetization transfer ratio (MTRasym) at 3.5 ppm and the total MTRasym integrated from 0.5 to 1.5 ppm from the corrected Z-spectrum, respectively. To explore scan time reduction, CEST images were reconstructed using 31 offsets (with 20% time reduction) and 21 offsets (with 40% time reduction), respectively.

RESULTS

For reproducibility, GlycoCEST measurements in 41 offsets showed the smallest scan-rescan mean measurements variability, indicated by the lowest mean difference of -0.049% (95% limits of agreement, -0.209 to 0.111%); for APTw, the smallest mean difference was found to be 0.112% (95% limits of agreement, -0.698 to 0.921%) in 41 offsets. Compared with after-meal, both GlycoCEST measurement and APTw measurement under different offset number decreased after 12-h fasting. However, as the offsets number decreased (41 offsets vs. 31 offsets vs. 21 offsets), GlycoCEST map and APTw map became more heterogeneous and noisier.

CONCLUSION

Our results show that CEST liver imaging at 3.0 T has high sensitivity for fasting.

Black blood T1rho MR imaging may diagnose early stage liver fibrosis: a proof-of-principle study with rat biliary duct ligation model

BACKGROUND

To explore black blood T1rho (T1ρ) liver imaging and investigate the earliest stage when biliary duct ligation (BDL) induced liver fibrosis can be diagnosed.

METHODS

MR was performed at 3 Tesla. A T1ρ prepared 2D fast spin echo (FSE) sequence with acquisition of four spin lock times (TSLs: 1, 10, 30, and 50 msec) and spin-lock frequency of 500 Hz was applied. Inherent black blood effect of FSE and double inversion recovery (DIR) achieved blood signal suppression, and 3 axial sections per liver were obtained. Male Sprague-Dawley rats were scanned at baseline (n=32), and on day-3 (n=13), day-5 (n=11), day-7 (n=10), day-10 (n=4) respectively after BDL. Hematoxylin-eosin (HE) and picrosirius red staining liver histology was obtained at these time points.

RESULTS

The physiological liver parenchyma T1ρ was 38.38±1.53 msec (range, 36.05-41.53 msec). Liver T1ρ value elevated progressively after BDL. On day-10 after BDL all experimental animals can be separated from normal liver based on T1ρ measurement with lowest value being 42.82 msec. Day-7 and day-10 liver resembled METAVIR stage-F1/F2 fibrosis, and fibrous area counted for 0.22%±0.13% and 0.38%±0.44% of liver parenchyma area, respectively.

CONCLUSIONS

This study provides the first proof-of-principle that T1ρ might diagnose early stage liver fibrosis.

Accelerated exponential parameterization of T2 relaxation with model-driven low rank and sparsity priors (MORASA)

PURPOSE

This work is to develop a novel image reconstruction method from highly undersampled multichannel acquisition to reduce the scan time of exponential parameterization of T2 relaxation.

THEORY AND METHODS

On top of the low-rank and joint-sparsity constraints, we propose to exploit the linear predictability of the T2 exponential decay to further improve the reconstruction of the T2-weighted images from undersampled acquisitions. Specifically, the exact rank prior (i.e., number of non-zero singular values) is adopted to enforce the spatiotemporal low rankness, while the mixed L2-L1 norm of the wavelet coefficients is used to promote joint sparsity, and the Hankel low-rank approximation is used to impose linear predictability, which integrates the exponential behavior of the temporal signal into the reconstruction process. An efficient algorithm is adopted to solve the reconstruction problem, where corresponding nonlinear filtering operations are performed to enforce corresponding priors in an iterative manner.

RESULTS

Both simulated and in vivo datasets with multichannel acquisition were used to demonstrate the feasibility of the proposed method. Experimental results have shown that the newly introduced linear predictability prior improves the reconstruction quality of the T2-weighted images and benefits the subsequent T2 mapping by achieving high-speed, high-quality T2 mapping compared with the existing fast T2 mapping methods.

CONCLUSION

This work proposes a novel fast T2 mapping method integrating the linear predictable property of the exponential decay into the reconstruction process. The proposed technique can effectively improve the reconstruction quality of the state-of-the-art fast imaging method exploiting image sparsity and spatiotemporal low rankness. Magn Reson Med 76:1865-1878, 2016. © 2016 International Society for Magnetic Resonance in Medicine.

Acceleration of MR parameter mapping using annihilating filter-based low rank hankel matrix (ALOHA)

PURPOSE

MR parameter mapping is one of clinically valuable MR imaging techniques. However, increased scan time makes it difficult for routine clinical use. This article aims at developing an accelerated MR parameter mapping technique using annihilating filter based low-rank Hankel matrix approach (ALOHA).

THEORY

When a dynamic sequence can be sparsified using spatial wavelet and temporal Fourier transform, this results in a rank-deficient Hankel structured matrix that is constructed using weighted k-t measurements. ALOHA then utilizes the low rank matrix completion algorithm combined with a multiscale pyramidal decomposition to estimate the missing k-space data.

METHODS

Spin-echo inversion recovery and multiecho spin echo pulse sequences for T₁ and T₂ mapping, respectively, were redesigned to perform undersampling along the phase encoding direction according to Gaussian distribution. The missing k-space is reconstructed using ALOHA. Then, the parameter maps were constructed using nonlinear regression.

RESULTS

Experimental results confirmed that ALOHA outperformed the existing compressed sensing algorithms. Compared with the existing methods, the reconstruction errors appeared scattered throughout the entire images rather than exhibiting systematic distortion along edges and the parameter maps.

CONCLUSION

Given that many diagnostic errors are caused by the systematic distortion of images, ALOHA may have a great potential for clinical applications. Magn Reson Med 76:1848-1864, 2016. © 2016 International Society for Magnetic Resonance in Medicine.

T1ρ magnetic resonance: basic physics principles and applications in knee and intervertebral disc imaging

T1ρ relaxation time provides a new contrast mechanism that differs from T1- and T2-weighted contrast, and is useful to study low-frequency motional processes and chemical exchange in biological tissues. T1ρ imaging can be performed in the forms of T1ρ-weighted image, T1ρ mapping and T1ρ dispersion. T1ρ imaging, particularly at low spin-lock frequency, is sensitive to B0 and B1 inhomogeneity. Various composite spin-lock pulses have been proposed to alleviate the influence of field inhomogeneity so as to reduce the banding-like spin-lock artifacts. T1ρ imaging could be specific absorption rate (SAR) intensive and time consuming. Efforts to address these issues and speed-up data acquisition are being explored to facilitate wider clinical applications. This paper reviews the T1ρ imaging's basic physic principles, as well as its application for cartilage imaging and intervertebral disc imaging. Compared to more established T2 relaxation time, it has been shown that T1ρ provides more sensitive detection of proteoglycan (PG) loss at early stages of cartilage degeneration. T1ρ has also been shown to provide more sensitive evaluation of annulus fibrosis (AF) degeneration of the discs.

T1ρ relaxation time in brain regions increases with ageing: an experimental MRI observation in rats

OBJECTIVE

T1ρ variation is associated with neurodegenerative diseases. This study aims to observe T1ρ relaxation time changes in rat brains associated with normal ageing in Sprague-Dawley (SD) rats, Wistar Kyoto (WKY) rats and spontaneously hypertension rats (SHRs).

METHODS

18 male SD rats, 11 male WKY rats and 11 male SHRs were used. T1ρ measurement was performed at 3-T MR with a spin-lock frequency of 500 Hz. SD rats were scanned at the ages of 5, 8, 10 and 15 months. SHRs and WKY rats were scanned at the ages of 6, 9 and 12 months.

RESULTS

For SD rats, T1ρ at the thalamus, hippocampus and frontal cortices increased significantly from 5 to 15 months (p < 0.05). For the WKY rats and SHRs, the T1ρ values in the thalamus, hippocampus and frontal cortices also increased significantly from 6 to 12 months (p < 0.05). Furthermore, T1ρ in the thalamus, hippocampus and frontal cortices of SHRs were consistently higher than those of WKY rats at the ages of 6, 9 and 12 months (p < 0.05). The percentage regional T1ρ differences between WKY rats and SHRs did not change during ageing.

CONCLUSION

An increase in T1ρ was associated with age-related changes of the rat brain.

ADVANCES IN KNOWLEDGE

An age-related and hypertension-related T1ρ increase in rat brain regions was observed in the thalamus, hippocampus and frontal cortical regions of the rat brain.

Chemical exchange saturation transfer (CEST) MR technique for in-vivo liver imaging at 3.0 tesla

PURPOSE

To evaluate Chemical Exchange Saturation Transfer (CEST) MRI for liver imaging at 3.0-T.

MATERIALS AND METHODS

Images were acquired at offsets (n = 41, increment = 0.25 ppm) from -5 to 5 ppm using a TSE sequence with a continuous rectangular saturation pulse. Amide proton transfer-weighted (APTw) and GlycoCEST signals were quantified as the asymmetric magnetization transfer ratio (MTRasym) at 3.5 ppm and the total MTRasym integrated from 0.5 to 1.5 ppm, respectively, from the corrected Z-spectrum. Reproducibility was assessed for rats and humans. Eight rats were devoid of chow for 24 hours and scanned before and after fasting. Eleven rats were scanned before and after one-time CCl4 intoxication.

RESULTS

For reproducibility, rat liver APTw and GlycoCEST measurements had 95 % limits of agreement of -1.49 % to 1.28 % and -0.317 % to 0.345 %. Human liver APTw and GlycoCEST measurements had 95 % limits of agreement of -0.842 % to 0.899 % and -0.344 % to 0.164 %. After 24 hours, fasting rat liver APTw and GlycoCEST signals decreased from 2.38 ± 0.86 % to 0.67 ± 1.12 % and from 0.34 ± 0.26 % to -0.18 ± 0.37 % respectively (p < 0.05). After CCl4 intoxication rat liver APTw and GlycoCEST signals decreased from 2.46 ± 0.48 % to 1.10 ± 0.77 %, and from 0.34 ± 0.23 % to -0.16 ± 0.51 % respectively (p < 0.05).

CONCLUSION

CEST liver imaging at 3.0-T showed high sensitivity for fasting as well as CCl4 intoxication.

KEY POINTS

• CEST MRI of in-vivo liver was demonstrated at clinical 3 T field strength. • After 24-hour fasting, rat liver APTw and GlycoCEST signals decreased significantly. • After CCl4 intoxication both rat liver APTw and GlycoCEST signals decreased significantly. • Good scan-rescan reproducibility of liver CEST MRI was shown in healthy volunteers.

Accelerating T1ρ cartilage imaging using compressed sensing with iterative locally adapted support detection and JSENSE

PURPOSE

To accelerate T1ρ quantification in cartilage imaging using combined compressed sensing with iterative locally adaptive support detection and JSENSE.

METHODS

To reconstruct T1ρ images from accelerated acquisition at different time of spin-lock (TSLs), we propose an approach to combine an advanced compressed sensing (CS) based reconstruction technique, LAISD (locally adaptive iterative support detection), and an advanced parallel imaging technique, JSENSE. Specifically, the reconstruction process alternates iteratively among local support detection in the domain of principal component analysis, compressed sensing reconstruction of the image sequence, and sensitivity estimation with JSENSE. T1ρ quantification results from accelerated scans using the proposed method are evaluated using in vivo knee cartilage data from bilateral scans of three healthy volunteers.

RESULTS

T1ρ maps obtained from accelerated scans (acceleration factors of 3 and 3.5) using the proposed method showed results comparable to conventional full scans. The T1ρ errors in all compartments are below 1%, which is well below the in vivo reproducibility of cartilage T1ρ reported from previous studies.

CONCLUSION

The proposed method can significantly accelerate the acquisition process of T1ρ quantification on human cartilage imaging without sacrificing accuracy, which will greatly facilitate the clinical translation of quantitative cartilage MRI.

Accelerated T1ρ acquisition for knee cartilage quantification using compressed sensing and data-driven parallel imaging: A feasibility study

PURPOSE

Quantitative T1ρ imaging is beneficial for early detection for osteoarthritis but has seen limited clinical use due to long scan times. In this study, we evaluated the feasibility of accelerated T1ρ mapping for knee cartilage quantification using a combination of compressed sensing (CS) and data-driven parallel imaging (ARC-Autocalibrating Reconstruction for Cartesian sampling).

METHODS

A sequential combination of ARC and CS, both during data acquisition and reconstruction, was used to accelerate the acquisition of T1ρ maps. Phantom, ex vivo (porcine knee), and in vivo (human knee) imaging was performed on a GE 3T MR750 scanner. T1ρ quantification after CS-accelerated acquisition was compared with non CS-accelerated acquisition for various cartilage compartments.

RESULTS

Accelerating image acquisition using CS did not introduce major deviations in quantification. The coefficient of variation for the root mean squared error increased with increasing acceleration, but for in vivo measurements, it stayed under 5% for a net acceleration factor up to 2, where the acquisition was 25% faster than the reference (only ARC).

CONCLUSION

To the best of our knowledge, this is the first implementation of CS for in vivo T1ρ quantification. These early results show that this technique holds great promise in making quantitative imaging techniques more accessible for clinical applications.