Constrained Magnetic Resonance Spectroscopic Imaging by Learning Nonlinear Low-Dimensional Models

One for multiple: Physics-informed synthetic data boosts generalizable deep learning for fast MRI reconstruction

Magnetic resonance imaging (MRI) is a widely used radiological modality renowned for its radiation-free, comprehensive insights into the human body, facilitating medical diagnoses. However, the drawback of prolonged scan times hinders its accessibility. The k-space undersampling offers a solution, yet the resultant artifacts necessitate meticulous removal during image reconstruction. Although deep learning (DL) has proven effective for fast MRI image reconstruction, its broader applicability across various imaging scenarios has been constrained. Challenges include the high cost and privacy restrictions associated with acquiring large-scale, diverse training data, coupled with the inherent difficulty of addressing mismatches between training and target data in existing DL methodologies. Here, we present a novel Physics-Informed Synthetic data learning Framework for fast MRI, called PISF. PISF marks a breakthrough by enabling generalizable DL for multi-scenario MRI reconstruction through a single trained model. Our approach separates the reconstruction of a 2D image into many 1D basic problems, commencing with 1D data synthesis to facilitate generalization. We demonstrate that training DL models on synthetic data, coupled with enhanced learning techniques, yields in vivo MRI reconstructions comparable to or surpassing those of models trained on matched realistic datasets, reducing the reliance on real-world MRI data by up to 96 %. With a single trained model, our PISF supports the high-quality reconstruction under 4 sampling patterns, 5 anatomies, 6 contrasts, 5 vendors, and 7 centers, exhibiting remarkable generalizability. Its adaptability to 2 neuro and 2 cardiovascular patient populations has been validated through evaluations by 10 experienced medical professionals. In summary, PISF presents a feasible and cost-effective way to significantly boost the widespread adoption of DL in various fast MRI applications.

WALINET: A water and lipid identification convolutional neural network for nuisance signal removal in 1 H $$ {}^1\mathrm{H} $$ MR spectroscopic imaging

PURPOSE

Proton magnetic resonance spectroscopic imaging (  1 H $$ {}^1\mathrm{H} $$ -MRSI) provides noninvasive spectral-spatial mapping of metabolism. However, long-standing problems in whole-brain  1 H $$ {}^1\mathrm{H} $$ -MRSI are spectral overlap of metabolite peaks with large lipid signal from scalp, and overwhelming water signal that distorts spectra. Fast and effective methods are needed for high-resolution  1 H $$ {}^1\mathrm{H} $$ -MRSI to accurately remove lipid and water signals while preserving the metabolite signal. The potential of supervised neural networks for this task remains unexplored, despite their success for other MRSI processing.

METHODS

We introduce a deep learning method based on a modified Y-NET network for water and lipid removal in whole-brain  1 H $$ {}^1\mathrm{H} $$ -MRSI. The WALINET (WAter and LIpid neural NETwork) was compared with conventional methods such as the state-of-the-art lipid L2 regularization and Hankel-Lanczos singular value decomposition (HLSVD) water suppression. Methods were evaluated on simulated models and in vivo whole-brain MRSI using NMRSE, SNR, CRLB, and FWHM metrics.

RESULTS

WALINET is significantly faster and needs 8s for high-resolution whole-brain MRSI, compared with 42min for conventional HLSVD+L2. WALINET suppresses lipid and water in the brain by 25-45 and 34-53-fold, respectively. WALINET has better performance than HLSVD+L2, providing: (1) more lipid removal with 41% lower NRMSE; (2) better metabolite signal preservation with 71% lower NRMSE in simulated data; 155% higher SNR and 50% lower CRLB in in vivo data. Metabolic maps obtained by WALINET in healthy subjects and patients show better gray-/white-matter contrast with more visible structural details.

CONCLUSIONS

WALINET has superior performance for nuisance signal removal and metabolite quantification on whole-brain  1 H $$ {}^1\mathrm{H} $$ -MRSI compared with conventional state-of-the-art techniques. This represents a new application of deep learning for MRSI processing, with potential for automated high-throughput workflow.

Deep-ER: Deep Learning ECCENTRIC Reconstruction for fast high-resolution neurometabolic imaging

INTRODUCTION

Altered neurometabolism is an important pathological mechanism in many neurological diseases and brain cancer, which can be mapped non-invasively by Magnetic Resonance Spectroscopic Imaging (MRSI). Advanced MRSI using non-cartesian compressed-sense acquisition enables fast high-resolution metabolic imaging but has lengthy reconstruction times that limits throughput and needs expert user interaction. Here, we present a robust and efficient Deep Learning reconstruction embedded in a physical model within an end-to-end automated processing pipeline to obtain high-quality metabolic maps.

METHODS

Fast high-resolution whole-brain metabolic imaging was performed at 3.4 mm3 isotropic resolution with acquisition times between 4:11-9:21 min:s using ECCENTRIC pulse sequence on a 7T MRI scanner. Data were acquired in a high-resolution phantom and 27 human participants, including 22 healthy volunteers and 5 glioma patients. A deep neural network using recurring interlaced convolutional layers with joint dual-space feature representation was developed for deep learning ECCENTRIC reconstruction (Deep-ER). 21 subjects were used for training and 6 subjects for testing. Deep-ER performance was compared to iterative compressed sensing Total Generalized Variation reconstruction using image and spectral quality metrics.

RESULTS

Deep-ER demonstrated 600-fold faster reconstruction than conventional methods, providing improved spatial-spectral quality and metabolite quantification with 12%-45% (P<0.05) higher signal-to-noise and 8%-50% (P<0.05) smaller Cramer-Rao lower bounds. Metabolic images clearly visualize glioma tumor heterogeneity and boundary. Deep-ER generalizes reliably to unseen data.

CONCLUSION

Deep-ER provides efficient and robust reconstruction for sparse-sampled MRSI. The accelerated acquisition-reconstruction MRSI is compatible with high-throughput imaging workflow. It is expected that such improved performance will facilitate basic and clinical MRSI applications for neuroscience and precision medicine.

Joint learning of nonlinear representation and projection for fast constrained MRSI reconstruction

PURPOSE

To develop and evaluate a novel method for computationally efficient reconstruction from noisy MR spectroscopic imaging (MRSI) data.

METHODS

The proposed method features (a) a novel strategy that jointly learns a nonlinear low-dimensional representation of high-dimensional spectroscopic signals and a neural-network-based projector to recover the low-dimensional embeddings from noisy/limited data; (b) a formulation that integrates the forward encoding model, a regularizer exploiting the learned representation, and a complementary spatial constraint; and (c) a highly efficient algorithm enabled by the learned projector within an alternating direction method of multipliers (ADMM) framework, circumventing the computationally expensive network inversion subproblem.

RESULTS

The proposed method has been evaluated using simulations as well as in vivo  1 $$ {}^1 $$ H and  31 $$ {}^{31} $$ P MRSI data, demonstrating improved performance over state-of-the-art methods, with about 6× $$ \times $$ fewer averages needed than standard Fourier reconstruction for similar metabolite estimation variances and up to 100× $$ \times $$ reduction in processing time compared to a prior neural network constrained reconstruction method. Computational and theoretical analyses were performed to offer further insights into the effectiveness of the proposed method.

CONCLUSION

A novel method was developed for fast, high-SNR spatiospectral reconstruction from noisy MRSI data. We expect our method to be useful for enhancing the quality of MRSI or other high-dimensional spatiospectral imaging data.

Improving Brain Metabolite Detection with a Combined Low-Rank Approximation and Denoising Diffusion Probabilistic Model Approach

In vivo proton magnetic resonance spectroscopy (MRS) is a noninvasive technique for monitoring brain metabolites. However, it is challenged by a low signal-to-noise ratio (SNR), often necessitating extended scan times to compensate. One of the conventional techniques for noise reduction is signal averaging, which is inherently time-consuming and can lead to participant discomfort, thus posing limitations in clinical settings. This study aimed to develop a hybrid denoising strategy that integrates low-rank approximation and denoising diffusion probabilistic model (DDPM) to enhance MRS data quality and shorten scan times. Using publicly available 1H MRS datasets from 15 subjects, we applied the Casorati SVD and DDPM to obtain baseline and functional data during a pain stimulation task. This method significantly improved SNR, resulting in outcomes comparable to or better than averaging over 32 signals. It also provided the most consistent metabolite measurements and adequately tracked temporal changes in glutamate levels, correlating with pain intensity ratings after heating. These findings demonstrate that our approach enhances MRS data quality, offering a more efficient alternative to conventional methods and expanding the potential for the real-time monitoring of neurochemical changes. This contribution has the potential to advance MRS techniques by integrating advanced denoising methods to increase the acquisition speed and enhance the precision of brain metabolite analyses.

Multi-Parametric Molecular Imaging of the Brain Using Optimized Multi-TE Subspace MRSI

OBJECTIVE

To develop a novel multi-TE MR spectroscopic imaging (MRSI) approach to enable label-free, simultaneous, high-resolution mapping of several molecules and their biophysical parameters in the brain.

METHODS

The proposed method uniquely integrated an augmented molecular-component-specific subspace model for multi-TE 1H-MRSI signals, an estimation-theoretic experiment optimization (nonuniform TE selection) for molecule separation and parameter estimation, a physics-driven subspace learning strategy for spatiospectral reconstruction and molecular quantification, and a new accelerated multi-TE MRSI acquisition for generating high-resolution data in clinically relevant times. Numerical studies, phantom and in vivo experiments were conducted to validate the optimized experiment design and demonstrate the imaging capability offered by the proposed method.

RESULTS

The proposed TE optimization improved estimation of metabolites, neurotransmitters and their T2's over conventional TE choices, e.g., reducing variances of neurotransmitter concentration by  ∼  40% and metabolite T2 by  ∼  60%. Simultaneous metabolite and neurotransmitter mapping of the brain can be achieved at a nominal resolution of 3.4 × 3.4 × 6.4 mm 3. High-resolution, 3D metabolite T2 mapping was made possible for the first time. The translational potential of the proposed method was demonstrated by mapping biochemical abnormality in a post-traumatic epilepsy (PTE) patient.

CONCLUSION

The feasibility for high-resolution mapping of metabolites/neurotransmitters and metabolite T2's within clinically relevant time was demonstrated. We expect our method to offer richer information for revealing and understanding metabolic alterations in neurological diseases.

SIGNIFICANCE

A novel multi-TE MRSI approach was presented that enhanced the technological capability of multi-parametric molecular imaging of the brain. The proposed method presents new technology development and application opportunities for providing richer molecular level information to uncover and comprehend metabolic changes relevant in various neurological applications.

Magnetic Resonance Spectroscopy Quantification Aided by Deep Estimations of Imperfection Factors and Macromolecular Signal

OBJECTIVE

Magnetic Resonance Spectroscopy (MRS) is an important technique for biomedical detection. However, it is challenging to accurately quantify metabolites with proton MRS due to serious overlaps of metabolite signals, imperfections because of non-ideal acquisition conditions, and interference with strong background signals mainly from macromolecules. The most popular method, LCModel, adopts complicated non-linear least square to quantify metabolites and addresses these problems by designing empirical priors such as basis-sets, imperfection factors. However, when the signal-to-noise ratio of MRS signal is low, the solution may have large deviation.

METHODS

Linear Least Squares (LLS) is integrated with deep learning to reduce the complexity of solving this overall quantification. First, a neural network is designed to explicitly predict the imperfection factors and the overall signal from macromolecules. Then, metabolite quantification is solved analytically with the introduced LLS. In our Quantification Network (QNet), LLS takes part in the backpropagation of network training, which allows the feedback of the quantification error into metabolite spectrum estimation. This scheme greatly improves the generalization to metabolite concentrations unseen in training compared to the end-to-end deep learning method.

RESULTS

Experiments show that compared with LCModel, the proposed QNet, has smaller quantification errors for simulated data, and presents more stable quantification for 20 healthy in vivo data at a wide range of signal-to-noise ratio. QNet also outperforms other end-to-end deep learning methods.

CONCLUSION

This study provides an intelligent, reliable and robust MRS quantification.

SIGNIFICANCE

QNet is the first LLS quantification aided by deep learning.

A user independent denoising method for x-nuclei MRI and MRS

PURPOSE

X-nuclei (also called non-proton MRI) MRI and spectroscopy are limited by the intrinsic low SNR as compared to conventional proton imaging. Clinical translation of x-nuclei examination warrants the need of a robust and versatile tool improving image quality for diagnostic use. In this work, we compare a novel denoising method with fewer inputs to the current state-of-the-art denoising method.

METHODS

Denoising approaches were compared on human acquisitions of sodium (23 Na) brain, deuterium (2 H) brain, carbon (13 C) heart and brain, and simulated dynamic hyperpolarized 13 C brain scans, with and without additional noise. The current state-of-the-art denoising method Global-local higher order singular value decomposition (GL-HOSVD) was compared to the few-input method tensor Marchenko-Pastur principal component analysis (tMPPCA). Noise-removal was quantified by residual distributions, and statistical analyses evaluated the differences in mean-square-error and Bland-Altman analysis to quantify agreement between original and denoised results of noise-added data.

RESULTS

GL-HOSVD and tMPPCA showed similar performance for the variety of x-nuclei data analyzed in this work, with tMPPCA removing ˜5% more noise on average over GL-HOSVD. The mean ratio between noise-added and denoising reproducibility coefficients of the Bland-Altman analysis when compared to the original are also similar for the two methods with 3.09 ± 1.03 and 2.83 ± 0.79 for GL-HOSVD and tMPPCA, respectively.

CONCLUSION

The strength of tMPPCA lies in the few-input approach, which generalizes well to different data sources. This makes the use of tMPPCA denoising a robust and versatile tool in x-nuclei imaging improvements and the preferred denoising method.

Denoising single MR spectra by deep learning: Miracle or mirage?

PURPOSE

The inherently poor SNR of MRS measurements presents a significant hurdle to its clinical application. Denoising by machine or deep learning (DL) was proposed as a remedy. It is investigated whether such denoising leads to lower estimate uncertainties or whether it essentially reduces noise in signal-free areas only.

METHODS

Noise removal based on supervised DL with U-nets was implemented using simulated 1 H MR spectra of human brain in two approaches: (1) via time-frequency domain spectrograms and (2) using 1D spectra as input. Quality of denoising was evaluated in three ways: (1) by an adapted fit quality score, (2) by traditional model fitting, and (3) by quantification via neural networks.

RESULTS

Visually appealing spectra were obtained; hinting that denoising is well-suited for MRS. However, an adapted denoising score showed that noise removal is inhomogeneous and more efficient for signal-free areas. This was confirmed by quantitative analysis of traditional fit results as well as DL quantitation following DL denoising. DL denoising, although apparently successful as judged by mean squared errors, led to substantially biased estimates in both implementations.

CONCLUSION

The implemented DL-based denoising techniques may be useful for display purposes, but do not help quantitative evaluations, confirming expectations based on estimation theory: Cramér Rao lower bounds defined by the original data and the appropriate fitting model cannot be circumvented in an unbiased way for single data sets, unless additional prior knowledge can be incurred in the form of parameter restrictions/relations or applicable substates.

Quantification of MR spectra by deep learning in an idealized setting: Investigation of forms of input, network architectures, optimization by ensembles of networks, and training bias

PURPOSE

The aims of this work are (1) to explore deep learning (DL) architectures, spectroscopic input types, and learning designs toward optimal quantification in MR spectroscopy of simulated pathological spectra; and (2) to demonstrate accuracy and precision of DL predictions in view of inherent bias toward the training distribution.

METHODS

Simulated 1D spectra and 2D spectrograms that mimic an extensive range of pathological in vivo conditions are used to train and test 24 different DL architectures. Active learning through altered training and testing data distributions is probed to optimize quantification performance. Ensembles of networks are explored to improve DL robustness and reduce the variance of estimates. A set of scores compares performances of DL predictions and traditional model fitting (MF).

RESULTS

Ensembles of heterogeneous networks that combine 1D frequency-domain and 2D time-frequency domain spectrograms as input perform best. Dataset augmentation with active learning can improve performance, but gains are limited. MF is more accurate, although DL appears to be more precise at low SNR. However, this overall improved precision originates from a strong bias for cases with high uncertainty toward the dataset the network has been trained with, tending toward its average value.

CONCLUSION

MF mostly performs better compared to the faster DL approach. Potential intrinsic biases on training sets are dangerous in a clinical context that requires the algorithm to be unbiased to outliers (i.e., pathological data). Active learning and ensemble of networks are good strategies to improve prediction performances. However, data quality (sufficient SNR) has proven as a bottleneck for adequate unbiased performance-like in the case of MF.

Physics-informed deep learning approach to quantification of human brain metabolites from magnetic resonance spectroscopy data

PURPOSE

While the recommended analysis method for magnetic resonance spectroscopy data is linear combination model (LCM) fitting, the supervised deep learning (DL) approach for quantification of MR spectroscopy (MRS) and MR spectroscopic imaging (MRSI) data recently showed encouraging results; however, supervised learning requires ground truth fitted spectra, which is not practical. Moreover, this work investigates the feasibility and efficiency of the LCM-based self-supervised DL method for the analysis of MRS data.

METHOD

We present a novel DL-based method for the quantification of relative metabolite concentrations, using quantum-mechanics simulated metabolite responses and neural networks. We trained, validated, and evaluated the proposed networks with simulated and publicly accessible in-vivo human brain MRS data and compared the performance with traditional methods. A novel adaptive macromolecule fitting algorithm is included. We investigated the performance of the proposed methods in a Monte Carlo (MC) study.

RESULT

The validation using low-SNR simulated data demonstrated that the proposed methods could perform quantification comparably to other methods. The applicability of the proposed method for the quantification of in-vivo MRS data was demonstrated. Our proposed networks have the potential to reduce computation time significantly.

CONCLUSION

The proposed model-constrained deep neural networks trained in a self-supervised manner can offer fast and efficient quantification of MRS and MRSI data. Our proposed method has the potential to facilitate clinical practice by enabling faster processing of large datasets such as high-resolution MRSI datasets, which may have thousands of spectra.

Joint spectral quantification of MR spectroscopic imaging using linear tangent space alignment-based manifold learning

PURPOSE

To develop a manifold learning-based method that leverages the intrinsic low-dimensional structure of MR Spectroscopic Imaging (MRSI) signals for joint spectral quantification.

METHODS

A linear tangent space alignment (LTSA) model was proposed to represent MRSI signals. In the proposed model, the signals of each metabolite were represented using a subspace model and the local coordinates of the subspaces were aligned to the global coordinates of the underlying low-dimensional manifold via linear transform. With the basis functions of the subspaces predetermined via quantum mechanics simulations, the global coordinates and the matrices for the local-to-global coordinate alignment were estimated by fitting the proposed LTSA model to noisy MRSI data with a spatial smoothness constraint on the global coordinates and a sparsity constraint on the matrices.

RESULTS

The performance of the proposed method was validated using numerical simulation data and in vivo proton-MRSI experimental data acquired on healthy volunteers at 3T. The results of the proposed method were compared with the QUEST method and the subspace-based method. In all the compared cases, the proposed method achieved superior performance over the QUEST and the subspace-based methods both qualitatively in terms of noise and artifacts in the estimated metabolite concentration maps, and quantitatively in terms of spectral quantification accuracy measured by normalized root mean square errors.

CONCLUSION

Joint spectral quantification using linear tangent space alignment-based manifold learning improves the accuracy of MRSI spectral quantification.

JSENSE-Pro: Joint sensitivity estimation and image reconstruction in parallel imaging using pre-learned subspaces of coil sensitivity functions

PURPOSE

To improve calibrationless parallel imaging using pre-learned subspaces of coil sensitivity functions.

THEORY AND METHODS

A subspace-based joint sensitivity estimation and image reconstruction method was developed for improved parallel imaging with no calibration data. Specifically, we proposed to use a probabilistic subspace model to capture prior information of the coil sensitivity functions from previous scans acquired using the same receiver system. Both the subspace basis and coefficient distributions were learned from a small set of training data. The learned subspace model was then incorporated into the regularized reconstruction formalism that includes a sparsity prior. The nonlinear optimization problem was solved using alternating minimization algorithm. Public fastMRI brain dataset was retrospectively undersampled by different schemes for performance evaluation of the proposed method.

RESULTS

With no calibration data, the proposed method consistently produced the most accurate coil sensitivity estimation and highest quality image reconstructions at all acceleration factors tested in comparison with state-of-the-art methods including JSENSE, DeepSENSE, P-LORAKS, and Sparse BLIP. Our results are comparable to or even better than those from SparseSENSE, which used calibration data for sensitivity estimation. The work also demonstrated that the probabilistic subspace model learned from T₂ w data can be generalized to aiding the reconstruction of FLAIR data acquired from the same receiver system.

CONCLUSION

A subspace-based method named JSENSE-Pro has been proposed for accelerated parallel imaging without the acquisition of companion calibration data. The method is expected to further enhance the practical utility of parallel imaging, especially in applications where calibration data acquisition is not desirable or limited.

High-Dimensional MR Spatiospectral Imaging by Integrating Physics-Based Modeling and Data-Driven Machine Learning: Current progress and future directions

Magnetic resonance spectroscopic imaging (MRSI) offers a unique molecular window into the physiological and pathological processes in the human body. However, the applications of MRSI have been limited by a number of long-standing technical challenges due to high dimensionality and low signal-to-noise ratio (SNR). Recent technological developments integrating physics-based modeling and data-driven machine learning that exploit unique physical and mathematical properties of MRSI signals have demonstrated impressive performance in addressing these challenges for rapid, high-resolution, quantitative MRSI. This paper provides a systematic review of these progresses in the context of MRSI physics and offers perspectives on promising future directions.

Model-informed unsupervised deep learning approaches to frequency and phase correction of MRS signals

PURPOSE

A supervised deep learning (DL) approach for frequency and phase correction (FPC) of MRS data recently showed encouraging results, but obtaining transients with labels for supervised learning is challenging. This work investigates the feasibility and efficiency of unsupervised deep learning-based FPC.

METHODS

Two novel deep learning-based FPC methods (deep learning-based Cr referencing and deep learning-based spectral registration), which use a priori physics domain knowledge, are presented. The proposed networks were trained, validated, and evaluated using simulated, phantom, and publicly accessible in vivo MEGA-edited MRS data. The performance of our proposed FPC methods was compared with other generally used FPC methods, in terms of precision and time efficiency. A new measure was proposed in this study to evaluate the FPC method performance. The ability of each of our methods to carry out FPC at varying SNR levels was evaluated. A Monte Carlo study was carried out to investigate the performance of our proposed methods.

RESULTS

The validation using low-SNR manipulated simulated data demonstrated that the proposed methods could perform FPC comparably with other methods. The evaluation showed that the deep learning-based spectral registration over a limited frequency range method achieved the highest performance in phantom data. The applicability of the proposed method for FPC of GABA-edited in vivo MRS data was demonstrated. Our proposed networks have the potential to reduce computation time significantly.

CONCLUSIONS

The proposed physics-informed deep neural networks trained in an unsupervised manner with complex data can offer efficient FPC of large MRS data in a shorter time.

In vivo magnetic resonance 31 P-Spectral Analysis With Neural Networks: 31P-SPAWNN

PURPOSE

We have introduced an artificial intelligence framework, 31P-SPAWNN, in order to fully analyze phosphorus-31 (31 $$ {}^{31} $$ P) magnetic resonance spectra. The flexibility and speed of the technique rival traditional least-square fitting methods, with the performance of the two approaches, are compared in this work.

THEORY AND METHODS

Convolutional neural network architectures have been proposed for the analysis and quantification of31 $$ {}^{31} $$ P-spectroscopy. The generation of training and test data using a fully parameterized model is presented herein. In vivo unlocalized free induction decay and three-dimensional31 $$ {}^{31} $$ P-magnetic resonance spectroscopy imaging data were acquired from healthy volunteers before being quantified using either 31P-SPAWNN or traditional least-square fitting techniques.

RESULTS

The presented experiment has demonstrated both the reliability and accuracy of 31P-SPAWNN for estimating metabolite concentrations and spectral parameters. Simulated test data showed improved quantification using 31P-SPAWNN compared with LCModel. In vivo data analysis revealed higher accuracy at low signal-to-noise ratio using 31P-SPAWNN, yet with equivalent precision. Processing time using 31P-SPAWNN can be further shortened up to two orders of magnitude.

CONCLUSION

The accuracy, reliability, and computational speed of the method open new perspectives for integrating these applications in a clinical setting.

Signal-to-Noise Ratio Enhancement of Single-Voxel In Vivo 31P and 1H Magnetic Resonance Spectroscopy in Mice Brain Data Using Low-Rank Denoising

Magnetic resonance spectroscopy (MRS) is a noninvasive technique for measuring metabolite concentration. It can be used for preclinical small animal brain studies using rodents to provide information about neurodegenerative diseases and metabolic disorders. However, data acquisition from small volumes in a limited scan time is technically challenging due to its inherently low sensitivity. To mitigate this problem, this study investigated the feasibility of a low-rank denoising method in enhancing the quality of single voxel multinuclei (³¹P and ¹H) MRS data at 9.4 T. Performance was evaluated using in vivo MRS data from a normal mouse brain (³¹P and ¹H) and stroke mouse model (¹H) by comparison with signal-to-noise ratios (SNRs), Cramer-Rao lower bounds (CRLBs), and metabolite concentrations of a linear combination of model analysis results. In ³¹P MRS data, low-rank denoising resulted in improved SNRs and reduced metabolite quantification uncertainty compared with the original data. In ¹H MRS data, the method also improved the SNRs, CRLBs, but it performed better for ³¹P MRS data with relatively simpler patterns compared to the ¹H MRS data. Therefore, we suggest that the low-rank denoising method can improve spectra SNR and metabolite quantification uncertainty in single-voxel in vivo ³¹P and ¹H MRS data, and it might be more effective for ³¹P MRS data. The main contribution of this study is that we demonstrated the effectiveness of the low-rank denoising method on small-volume single-voxel MRS data. We anticipate that our results will be useful for the precise quantification of low-concentration metabolites, further reducing data acquisition voxel size, and scan time in preclinical MRS studies.

MR image reconstruction from undersampled data for image-guided radiation therapy using a patient-specific deep manifold image prior

Introduction

Recent advancements in radiotherapy (RT) have allowed for the integration of a Magnetic Resonance (MR) imaging scanner with a medical linear accelerator to use MR images for image guidance to position tumors against the treatment beam. Undersampling in MR acquisition is desired to accelerate the imaging process, but unavoidably deteriorates the reconstructed image quality. In RT, a high-quality MR image of a patient is available for treatment planning. In light of this unique clinical scenario, we proposed to exploit the patient-specific image prior to facilitate high-quality MR image reconstruction.

Methods

Utilizing the planning MR image, we established a deep auto-encoder to form a manifold of image patches of the patient. The trained manifold was then incorporated as a regularization to restore MR images of the same patient from undersampled data. We performed a simulation study using a patient case, a real patient study with three liver cancer patient cases, and a phantom experimental study using data acquired on an in-house small animal MR scanner. We compared the performance of the proposed method with those of the Fourier transform method, a tight-frame based Compressive Sensing method, and a deep learning method with a patient-generic manifold as the image prior.

Results

In the simulation study with 12.5% radial undersampling and 15% increase in noise, our method improved peak-signal-to-noise ratio by 4.46dB and structural similarity index measure by 28% compared to the patient-generic manifold method. In the experimental study, our method outperformed others by producing reconstructions of visually improved image quality.

Assessment of higher-order singular value decomposition denoising methods on dynamic hyperpolarized [1-13C]pyruvate MRI data from patients with glioma

BACKGROUND

Real-time metabolic conversion of intravenously-injected hyperpolarized [1-13C]pyruvate to [1-13C]lactate and [13C]bicarbonate in the brain can be measured using dynamic hyperpolarized carbon-13 (HP-13C) MRI. However, voxel-wise evaluation of metabolism in patients with glioma is challenged by the limited signal-to-noise ratio (SNR) of downstream 13C metabolites, especially within lesions. The purpose of this study was to evaluate the ability of higher-order singular value decomposition (HOSVD) denoising methods to enhance dynamic HP [1-13C]pyruvate MRI data acquired from patients with glioma.

METHODS

Dynamic HP-13C MRI were acquired from 14 patients with glioma. The effects of two HOSVD denoising techniques, tensor rank truncation-image enhancement (TRI) and global-local HOSVD (GL-HOSVD), on the SNR and kinetic modeling were analyzed in [1-13C]lactate data with simulated noise that matched the levels of [13C]bicarbonate signals. Both methods were then evaluated in patient data based on their ability to improve [1-13C]pyruvate, [1-13C]lactate and [13C]bicarbonate SNR. The effects of denoising on voxel-wise kinetic modeling of kPL and kPB was also evaluated. The number of voxels with reliable kinetic modeling of pyruvate-to-lactate (kPL) and pyruvate-to-bicarbonate (kPB) conversion rates within regions of interest (ROIs) before and after denoising was then compared.

RESULTS

Both denoising methods improved metabolite SNR and regional signal coverage. In patient data, the average increase in peak dynamic metabolite SNR was 2-fold using TRI and 4-5 folds using GL-HOSVD denoising compared to acquired data. Denoising reduced kPL modeling errors from a native average of 23% to 16% (TRI) and 15% (GL-HOSVD); and kPB error from 42% to 34% (TRI) and 37% (GL-HOSVD) (values were averaged voxelwise over all datasets). In contrast-enhancing lesions, the average number of voxels demonstrating within-tolerance kPL modeling error relative to the total voxels increased from 48% in the original data to 84% (TRI) and 90% (GL-HOSVD), while the number of voxels showing within-tolerance kPB modeling error increased from 0% to 15% (TRI) and 8% (GL-HOSVD).

CONCLUSION

Post-processing denoising methods significantly improved the SNR of dynamic HP-13C imaging data, resulting in a greater number of voxels satisfying minimum SNR criteria and maximum kinetic modeling errors in tumor lesions. This enhancement can aid in the voxel-wise analysis of HP-13C data and thereby improve monitoring of metabolic changes in patients with glioma following treatment.

Improved Balanced Steady-State Free Precession Based MR Fingerprinting with Deep Autoencoders

Magnetic Resonance (MR) Fingerprinting is an emerging transient-state imaging paradigm, which enables the quantization of multiple MR tissue parameters in a single experiment. Balanced steady-state free precession (bSSFP)-based MR Fingerprinting has excellent signal-to-noise characteristics and also allows for acquiring both tissue parameter maps and field inhomogeneity maps. However, field inhomogeneity often results in complex magnetization evolutions in bSSFP-based MR Fingerprinting, which creates significant challenges in image reconstruction. In this paper, we introduce a new method to address the image reconstruction problem. The proposed method incorporates a low-dimensional nonlinear manifold learned from an ensemble of magnetization evolutions using a deep autoencoder. It provides much better representation power than a low-dimensional linear subspace in capturing complex magnetization evolutions. We formulate the image reconstruction problem with this nonlinear model and solve the resulting optimization problem using an algorithm based on variable splitting and the alternating direction method of multipliers. We evaluate the performance of the proposed method using numerical experiments and demonstrate that it significantly outperforms the state-of-art method using a linear subspace model.

SNR Enhancement for Multi-TE MRSI Using Joint Low-Dimensional Model and Spatial Constraints

We present a novel method to enhance the SNR for multi-TE MR spectroscopic imaging (MRSI) data by integrating learned nonlinear low-dimensional model and spatial constraints. A deep complex convolutional autoen-coder (DCCAE) was developed to learn a nonlinear low-dimensional representation of the high-dimensional multi-TE 1 H spectroscopy signals. The learned model significantly reduces the data dimension thus serving as an effective constraint for noise reduction. A reconstruction formulation was proposed to integrate the spatiospectral encoding model, the learned model, and a spatial constraint for an SNR-enhancing reconstruction from multi-TE data. The proposed method has been evaluated using both numerical simulations and in vivo brain MRSI experiments. The superior denoising performance of the proposed over alternative methods was demonstrated, both qualitatively and quantitatively. In vivo multi-TE data was used to assess the improved metabolite quantification reproducibility and accuracy achieved by the proposed method. We expect the proposed SNR-enhancing reconstruction to enable faster and/or higher-resolution multi-TE 1 H-MRSI of the brain, potentially useful for various clinical applications.

Improved Multi-Echo Gradient-Echo-Based Myelin Water Fraction Mapping Using Dimensionality Reduction

Multi-echo gradient-echo (mGRE)-based myelin water fraction (MWF) mapping is a promising myelin water imaging (MWI) modality but is vulnerable to noise and artifact corruption. The linear dimensionality reduction (LDR) method has recently shown improvements with regard to these challenges. However, the magnitude value based low rank operators have been shown to misestimate the MWF for regions with [Formula: see text] anisotropy. This paper presents a nonlinear dimensionality reduction (NLDR) method to estimate the MWF map better by encouraging nonlinear low dimensionality of mGRE signal sources. Specifically, we implemented a fully connected deep autoencoder to extract the low-dimensional features of complex-valued signals and incorporated a sparse regularization to separate the anomaly sources that do not reside in the low-dimensional manifold. Simulations and in vivo experiments were performed to evaluate the accuracy of the MWF map under various situations. The proposed NLDR-based MWF improves the accuracy of the MWF map over the conventional nonlinear least-squares method and the LDR-based MWF and maintains robustness against noise and artifact corruption.

Machine Learning-Enabled High-Resolution Dynamic Deuterium MR Spectroscopic Imaging

Deuterium magnetic resonance spectroscopic imaging (DMRSI) has recently been recognized as a potentially powerful tool for noninvasive imaging of brain energy metabolism and tumor. However, the low sensitivity of DMRSI has significantly limited its utility for both research and clinical applications. This work presents a novel machine learning-based method to address this limitation. The proposed method synergistically integrates physics-based subspace modeling and data-driven deep learning for effective denoising, making high-resolution dynamic DMRSI possible. Specifically, a novel subspace model was used to represent the dynamic DMRSI signals; deep neural networks were trained to capture the low-dimensional manifolds of the spectral and temporal distributions of practical dynamic DMRSI data. The learned subspace and manifold structures were integrated via a regularization formulation to remove measurement noise. Theoretical analysis, computer simulations, and in vivo experiments have been conducted to demonstrate the denoising efficacy of the proposed method which enabled high-resolution imaging capability. The translational potential was demonstrated in tumor-bearing rats, where the Warburg effect associated with cancer metabolism and tumor heterogeneity were successfully captured. The new method may not only provide an effective tool to enhance the sensitivity of DMRSI for basic research and clinical applications but also provide a framework for denoising other spatiospectral data.

DeepSENSE: Learning coil sensitivity functions for SENSE reconstruction using deep learning

PURPOSE

To improve the estimation of coil sensitivity functions from limited auto-calibration signals (ACS) in SENSE-based reconstruction for brain imaging.

METHODS

We propose to use deep learning to estimate coil sensitivity functions by leveraging information from previous scans obtained using the same RF receiver system. Specifically, deep convolutional neural networks were designed to learn an end-to-end mapping from the initial sensitivity to the high-resolution counterpart. Sensitivity alignment was further proposed to reduce the geometric variation caused by different subject positions and imaging FOVs. Cross-validation with a small set of datasets was performed to validate the learned neural network. Iterative SENSE reconstruction was adopted to evaluate the utility of the sensitivity functions from the proposed and conventional methods.

RESULTS

The proposed method produced improved sensitivity estimates and SENSE reconstructions compared to the conventional methods in terms of aliasing and noise suppression with very limited ACS data. Cross-validation with a small set of data demonstrated the feasibility of learning coil sensitivity functions for brain imaging. The network learned on the spoiled GRE data can be applied to predict sensitivity functions for spin-echo and MPRAGE datasets.

CONCLUSION

A deep learning-based method has been proposed for improving the estimation of coil sensitivity functions. Experimental results have demonstrated the feasibility and potential of the proposed method for improving SENSE-based reconstructions especially when the ACS data are limited.

High-resolution, 3D multi-TE 1 H MRSI using fast spatiospectral encoding and subspace imaging

PURPOSE

To develop a novel method to achieve fast, high-resolution, 3D multi-TE ¹ H-MRSI of the brain.

METHODS

A new multi-TE MRSI acquisition strategy was developed that integrates slab selective excitation with adiabatic refocusing for better volume coverage, rapid spatiospectral encoding, sparse multi-TE sampling, and interleaved water navigators for field mapping and calibration. Special data processing strategies were developed to interpolate the sparsely sampled data, remove nuisance signals, and reconstruct multi-TE spatiospectral distributions with high SNR. Phantom and in vivo experiments have been carried out to demonstrate the capability of the proposed method.

RESULTS

The proposed acquisition can produce multi-TE ¹ H-MRSI data with three TEs at a nominal spatial resolution of 3.4 × 3.4 × 5.3 mm³ in around 20 min. High-SNR brain metabolite spatiospectral reconstructions can be obtained from both a metabolite phantom and in vivo experiments by the proposed method.

CONCLUSION

High-resolution, 3D multi-TE ¹ H-MRSI of the brain can be achieved within clinically feasible time. This capability, with further optimizations, could be translated to clinical applications and neuroscience studies where simultaneously mapping metabolites and neurotransmitters and TE-dependent molecular spectral changes are of interest.

Achieving high-resolution 1H-MRSI of the human brain with compressed-sensing and low-rank reconstruction at 7 Tesla

Low sensitivity MR techniques such as magnetic resonance spectroscopic imaging (MRSI) greatly benefit from the gain in signal-to-noise provided by ultra-high field MR. High-resolution and whole-slab brain MRSI remains however very challenging due to lengthy acquisition, low signal, lipid contamination and field inhomogeneity. In this study, we propose an acquisition-reconstruction scheme that combines 1H free-induction-decay (FID)-MRSI sequence, short TR acquisition, compressed sensing acceleration and low-rank modeling with total-generalized-variation constraint to achieve metabolite imaging in two and three dimensions at 7 Tesla. The resulting images and volumes reveal highly detailed distributions that are specific to each metabolite and follow the underlying brain anatomy. The MRSI method was validated in a high-resolution phantom containing fine metabolite structures, and in five healthy volunteers. This new application of compressed sensing acceleration paves the way for high-resolution MRSI in clinical setting with acquisition times of 5 min for 2D MRSI at 2.5 mm and of 20 min for 3D MRSI at 3.3 mm isotropic.

Accelerated MR spectroscopic imaging-a review of current and emerging techniques

Over more than 30 years in vivo MR spectroscopic imaging (MRSI) has undergone an enormous evolution from theoretical concepts in the early 1980s to the robust imaging technique that it is today. The development of both fast and efficient sampling and reconstruction techniques has played a fundamental role in this process. State-of-the-art MRSI has grown from a slow purely phase-encoded acquisition technique to a method that today combines the benefits of different acceleration techniques. These include shortening of repetition times, spatial-spectral encoding, undersampling of k-space and time domain, and use of spatial-spectral prior knowledge in the reconstruction. In this way in vivo MRSI has considerably advanced in terms of spatial coverage, spatial resolution, acquisition speed, artifact suppression, number of detectable metabolites and quantification precision. Acceleration not only has been the enabling factor in high-resolution whole-brain 1 H-MRSI, but today is also common in non-proton MRSI (31 P, 2 H and 13 C) and applied in many different organs. In this process, MRSI techniques had to constantly adapt, but have also benefitted from the significant increase of magnetic field strength boosting the signal-to-noise ratio along with high gradient fidelity and high-density receive arrays. In combination with recent trends in image reconstruction and much improved computation power, these advances led to a number of novel developments with respect to MRSI acceleration. Today MRSI allows for non-invasive and non-ionizing mapping of the spatial distribution of various metabolites' tissue concentrations in animals or humans, is applied for clinical diagnostics and has been established as an important tool for neuro-scientific and metabolism research. This review highlights the developments of the last five years and puts them into the context of earlier MRSI acceleration techniques. In addition to 1 H-MRSI it also includes other relevant nuclei and is not limited to certain body regions or specific applications.

Separation of Metabolites and Macromolecules for Short-TE 1H-MRSI Using Learned Component-Specific Representations

Short-echo-time (TE) proton magnetic resonance spectroscopic imaging (MRSI) allows for simultaneously mapping a number of molecules in the brain, and has been recognized as an important tool for studying in vivo biochemistry in various neuroscience and disease applications. However, separation of the metabolite and macromolecule (MM) signals present in the short-TE data with significant spectral overlaps remains a major technical challenge. This work introduces a new approach to solve this problem by integrating imaging physics and representation learning. Specifically, a mixed unsupervised and supervised learning-based strategy was developed to learn the metabolite and MM-specific low-dimensional representations using deep autoencoders. A constrained reconstruction formulation is proposed to integrate the MRSI spatiospectral encoding model and the learned representations as effective constraints for signal separation. An efficient algorithm was developed to solve the resulting optimization problem with provable convergence. Simulation and experimental results have been obtained to demonstrate the component-specific representation power of the learned models and the capability of the proposed method in separating metabolite and MM signals for practical short-TE [Formula: see text]-MRSI data.

Tensor image enhancement and optimal multichannel receiver combination analyses for human hyperpolarized 13 C MRSI

PURPOSE

With the initiation of human hyperpolarized ¹³ C (HP-¹³ C) trials at multiple sites and the development of improved acquisition methods, there is an imminent need to maximally extract diagnostic information to facilitate clinical interpretation. This study aims to improve human HP-¹³ C MR spectroscopic imaging through means of Tensor Rank truncation-Image enhancement (TRI) and optimal receiver combination (ORC).

METHODS

A data-driven processing framework for dynamic HP ¹³ C MR spectroscopic imaging (MRSI) was developed. Using patient data sets acquired with both multichannel arrays and single-element receivers from the brain, abdomen, and pelvis, we examined the theory and application of TRI, as well as 2 ORC techniques: whitened singular value decomposition (WSVD) and first-point phasing. Optimal conditions for TRI were derived based on bias-variance trade-off.

RESULTS

TRI and ORC techniques together provided a 63-fold mean apparent signal-to-noise ratio (aSNR) gain for receiver arrays and a 31-fold gain for single-element configurations, which particularly improved quantification of the lower-SNR-[¹³ C]bicarbonate and [1-¹³ C]alanine signals that were otherwise not detectable in many cases. Substantial SNR enhancements were observed for data sets that were acquired even with suboptimal experimental conditions, including delayed (114 s) injection (8× aSNR gain solely by TRI), or from challenging anatomy or geometry, as in the case of a pediatric patient with brainstem tumor (597× using combined TRI and WSVD). Improved correlation between elevated pyruvate-to-lactate conversion, biopsy-confirmed cancer, and mp-MRI lesions demonstrated that TRI recovered quantitative diagnostic information.

CONCLUSION

Overall, this combined approach was effective across imaging targets and receiver configurations and could greatly benefit ongoing and future HP ¹³ C MRI research through major aSNR improvements.

Review and Prospect: Deep Learning in Nuclear Magnetic Resonance Spectroscopy

Since the concept of deep learning (DL) was formally proposed in 2006, it has had a major impact on academic research and industry. Nowadays, DL provides an unprecedented way to analyze and process data with demonstrated great results in computer vision, medical imaging, natural language processing, and so forth. Herein, applications of DL in NMR spectroscopy are summarized, and a perspective for DL as an entirely new approach that is likely to transform NMR spectroscopy into a much more efficient and powerful technique in chemistry and life sciences is outlined.