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

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.

High-resolution 1H-MRSI at 9.4 T by integrating relaxation enhancement and subspace imaging

Achieving high-resolution and high signal-to-noise ratio (SNR) in vivo metabolic imaging via fast magnetic resonance spectroscopic imaging (MRSI) has been a longstanding challenge. This study combines the methods of relaxation enhancement (RE) and subspace imaging for the first time, enabling high-resolution and high-SNR in vivo MRSI of rodent brains at 9.4 T. Specifically, an RE-based chemical shift imaging sequence, which combines a frequency-selective pulse to excite only the metabolite frequencies with minimum perturbation of the water spins and a pair of adiabatic pulses to spatially localize the slice of interest, is designed and evaluated in vivo. This strategy effectively shortens the apparent T1 of metabolites, thereby increasing the SNR during relatively short repetition time ((TR) compared with acquisitions with only spatially selective wideband excitations, and does not require water suppression. The SNR was further enhanced via a state-of-the-art subspace reconstruction method. A novel subspace learning strategy tailored for 9.4 T and RE acquisitions is developed. In vivo, high-resolution (e.g., voxel size of 0.6 × 0.6 × 1.5 mm3) MRSI of both healthy mouse brains and a glioma-bearing mouse brain in 12.5 min has been demonstrated.

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 Sparse Model-Inspired Deep Thresholding Network for Exponential Signal Reconstruction-Application in Fast Biological Spectroscopy

The nonuniform sampling (NUS) is a powerful approach to enable fast acquisition but requires sophisticated reconstruction algorithms. Faithful reconstruction from partially sampled exponentials is highly expected in general signal processing and many applications. Deep learning (DL) has shown astonishing potential in this field, but many existing problems, such as lack of robustness and explainability, greatly limit its applications. In this work, by combining the merits of the sparse model-based optimization method and data-driven DL, we propose a DL architecture for spectra reconstruction from undersampled data, called MoDern. It follows the iterative reconstruction in solving a sparse model to build the neural network, and we elaborately design a learnable soft-thresholding to adaptively eliminate the spectrum artifacts introduced by undersampling. Extensive results on both synthetic and biological data show that MoDern enables more robust, high-fidelity, and ultrafast reconstruction than the state-of-the-art methods. Remarkably, MoDern has a small number of network parameters and is trained on solely synthetic data while generalizing well to biological data in various scenarios. Furthermore, we extend it to an open-access and easy-to-use cloud computing platform (XCloud-MoDern), contributing a promising strategy for further development of biological applications.

Quantification of spatially localized MRS by a novel deep learning approach without spectral fitting

PURPOSE

To propose a novel end-to-end deep learning model to quantify absolute metabolite concentrations from in vivo J-point resolved spectroscopy (JPRESS) without using spectral fitting.

METHODS

A novel encoder-decoder-style neural network was created, which was trained to predict metabolite concentrations and individual component signals concurrently from 3T JPRESS data in the time domain. The training data set contained 100 000 samples created by spin-density simulations using experimentally used RF pulses. Concentrations, phase, frequencies, linewidths, and T2 relaxation times in the training data set were varied over a large range with uniform distributions. Random synthesized noise and extraneous signals were added to the data set. Two thousand validation samples were created similarly to the training data set but with mean concentrations close to in vivo values. An in vivo test was conducted with 20 samples acquired from the human brain.

RESULTS

Both validation and in vivo test results showed that the proposed model successfully predicted metabolite concentrations as well as individual metabolite signals without involving spectral fitting, while extraneous peaks or unregistered signals were filtered out. Compared with the short-TE spectral fitting by LCModel, the proposed method had the advantage that the undesired correlations between the estimated concentrations and noise levels and between metabolites were eliminated or substantially reduced.

CONCLUSION

The proposed method provides a working deep learning model that directly maps in vivo JPRESS data to metabolite concentrations. Because spectral fitting is not used, the trained model does not depend on the assumptions associated with parameter tuning when applied to in vivo data.

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

PURPOSE

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

METHODS

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

RESULTS

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

CONCLUSION

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

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.

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.

Variational Manifold Learning From Incomplete Data: Application to Multislice Dynamic MRI

Current deep learning-based manifold learning algorithms such as the variational autoencoder (VAE) require fully sampled data to learn the probability density of real-world datasets. However, fully sampled data is often unavailable in a variety of problems, including the recovery of dynamic and high-resolution magnetic resonance imaging (MRI). We introduce a novel variational approach to learn a manifold from undersampled data. The VAE uses a decoder fed by latent vectors, drawn from a conditional density estimated from the fully sampled images using an encoder. Since fully sampled images are not available in our setting, we approximate the conditional density of the latent vectors by a parametric model whose parameters are estimated from the undersampled measurements using back-propagation. We use the framework for the joint alignment and recovery of multi-slice free breathing and ungated cardiac MRI data from highly undersampled measurements. Experimental results demonstrate the utility of the proposed scheme in dynamic imaging alignment and reconstructions.

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.

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.

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.