Observation of intramyocellular lipids by means of 1H magnetic resonance spectroscopy

Magnetic resonance imaging (MRI) and magnetic resonance spectroscopy (MRS) are being increasingly used for investigations of human muscle physiology. While MRI reveals the morphology of muscles in great detail (e.g. for the determination of muscle volumes), MRS provides information on the chemical composition of the tissue. Depending on the observed nucleus, MRS allows the monitoring of high-energy phosphates (31P MRS), glycogen (13C MRS), or intramyocellular lipids (1H MRS), to give only a few examples. The observation of intramyocellular lipids (IMCL) by means of 1H MRS is non-invasive and, therefore, can be repeated many times and with a high temporal resolution. MRS has the potential to replace the biopsy for the monitoring of IMCL levels; however, the biopsy still has the advantage that other methods such as those used in molecular biology can be applied to the sample. The present study describes variations in the IMCL levels (expressed in mmol/kg wet weight and ml/100 ml) in three different muscles before and after (0, 1, 2, and 5 d) marathon runs for a well-trained individual who followed two different recovery protocols varying mainly in the diet. It was shown that the repletion of IMCL levels is strongly dependent on the diet post exercise. The monitoring of IMCL levels by means of 1H MRS is extremely promising, but several methodological limitations and pitfalls need to be considered, and these are addressed in the present revie

In vivo1H-MR spectroscopy of the human heart

4. Conclusions: Combined respiratory and cardiac triggering improves the localization accuracy and spectral quality in cardiac1H-MRS dramatically leading to substantially increased spectral reproducibility. The best practical realization of double triggering turned out to be the use of the ECG amplitude when making use of the fact that it is modulated by respiration. In spite of the spectral quality achieved in most subjects, we still fail to record satisfactory spectra in a minority of subjects. The reasons for this are not understood at present but must be some particulars of either a given subject or the experimental setup. The cardiac1H-MR spectra contain quantifiable contributions from creatine, TMA, lipids, and probably taurine. It is possible that the spectral contributions of creatine are subject to dipolar coupling similar to the observations for skeletal muscl

Observation of intramyocellular lipids by means of 1H magnetic resonance spectroscopy

Magnetic resonance imaging (MRI) and magnetic resonance spectroscopy (MRS) are being increasingly used for investigations of human muscle physiology. While MRI reveals the morphology of muscles in great detail (e.g. for the determination of muscle volumes), MRS provides information on the chemical composition of the tissue. Depending on the observed nucleus, MRS allows the monitoring of high-energy phosphates (31P MRS), glycogen (13C MRS), or intramyocellular lipids (1H MRS), to give only a few examples. The observation of intramyocellular lipids (IMCL) by means of 1H MRS is non-invasive and, therefore, can be repeated many times and with a high temporal resolution. MRS has the potential to replace the biopsy for the monitoring of IMCL levels; however, the biopsy still has the advantage that other methods such as those used in molecular biology can be applied to the sample. The present study describes variations in the IMCL levels (expressed in mmol/kg wet weight and ml/100 ml) in three different muscles before and after (0, 1, 2, and 5 d) marathon runs for a well-trained individual who followed two different recovery protocols varying mainly in the diet. It was shown that the repletion of IMCL levels is strongly dependent on the diet post exercise. The monitoring of IMCL levels by means of 1H MRS is extremely promising, but several methodological limitations and pitfalls need to be considered, and these are addressed in the present review

Frobenius-Type Norms and Inner Products of Matrices and Linear Maps with Applications to Neural Network Training

The Frobenius norm is a frequent choice of norm for matrices. In particular, the underlying Frobenius inner product is typically used to evaluate the gradient of an objective with respect to matrix variable, such as those occuring in the training of neural networks. We provide a broader view on the Frobenius norm and inner product for linear maps or matrices, and establish their dependence on inner products in the domain and co-domain spaces. This shows that the classical Frobenius norm is merely one special element of a family of more general Frobenius-type norms. The significant extra freedom furnished by this realization can be used, among other things, to precondition neural network training

Adaptive Step Sizes for Preconditioned Stochastic Gradient Descent

This paper proposes a novel approach to adaptive step sizes in stochastic gradient descent (SGD) by utilizing quantities that we have identified as numerically traceable -- the Lipschitz constant for gradients and a concept of the local variance in search directions. Our findings yield a nearly hyperparameter-free algorithm for stochastic optimization, which has provable convergence properties when applied to quadratic problems and exhibits truly problem adaptive behavior on classical image classification tasks. Our framework enables the potential inclusion of a preconditioner, thereby enabling the implementation of adaptive step sizes for stochastic second-order optimization methods

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

Erratum to: Two-dimensional linear-combination model fitting of magnetic resonance spectra to define the macromolecule baseline using FiTAID, a fitting tool for arrays of interrelated datasets

Object: To propose the determination of the macromolecular baseline (MMBL) in clinical 1H MR spectra based on T1 and T2 differentiation using 2D fitting in FiTAID, a general Fitting Tool for Arrays of Interrelated Datasets. Materials and methods: Series of localized inversion-recovery (IR) and 2DJ separation spectra of the brain were recorded at 3T. The MMBL was determined by three 2D evaluation methods based on (1) IR spectra only, (2) 2DJ spectra only, (3) both IR and 2DJ spectra (2DJ-IR). Their performance was compared using synthetic spectra and based on variability and reproducibility as obtained in vivo from 12 subjects in 20 examinations. Results: All methods performed well for synthetic data. In vivo, 2DJ-only yielded larger variations than the other methods. IR-only and 2DJ-IR yielded similar performance. FiTAID is illustrated with further applications where linear-combination model fitting of interrelated arrays of spectra is advantageous. Conclusion: 2D-Fitting offers the possibility to determine the MMBL based on a range of complementary experimental spectra not relying on smoothness criteria or global assumptions on T1. Since 2DJ-IR includes information from spectra with different inversion and echo times, it is expected to be more robust in cases with more variable data quality and overlap with lipid resonance

Sensitivity-Based Layer Insertion for Residual and Feedforward Neural Networks

The training of neural networks requires tedious and often manual tuning of the network architecture. We propose a systematic method to insert new layers during the training process, which eliminates the need to choose a fixed network size before training. Our technique borrows techniques from constrained optimization and is based on first-order sensitivity information of the objective with respect to the virtual parameters that additional layers, if inserted, would offer. We consider fully connected feedforward networks with selected activation functions as well as residual neural networks. In numerical experiments, the proposed sensitivity-based layer insertion technique exhibits improved training decay, compared to not inserting the layer. Furthermore, the computational effort is reduced in comparison to inserting the layer from the beginning. The code is available at \url{https://github.com/LeonieKreis/layer_insertion_sensitivity_based}

Forecasting the quality of water-suppressed (1) H MR spectra based on a single-shot water scan.

PURPOSE To investigate whether an initial non-water-suppressed acquisition that provides information about the signal-to-noise ratio (SNR) and linewidth is enough to forecast the maximally achievable final spectral quality and thus inform the operator whether the foreseen number of averages and achieved field homogeneity is adequate. METHODS A large range of spectra with varying SNR and linewidth was simulated and fitted with popular fitting programs to determine the dependence of fitting errors on linewidth and SNR. A tool to forecast variance based on a single acquisition was developed and its performance evaluated on simulated and in vivo data obtained at 3 Tesla from various brain regions and acquisition settings. RESULTS A strong correlation to real uncertainties in estimated metabolite contents was found for the forecast values and the Cramer-Rao lower bounds obtained from the water-suppressed spectra. CONCLUSION It appears to be possible to forecast the best-case errors associated with specific metabolites to be found in model fits of water-suppressed spectra based on a single water scan. Thus, nonspecialist operators will be able to judge ahead of time whether the planned acquisition can possibly be of sufficient quality to answer the targeted clinical question or whether it needs more averages or improved shimming. Magn Reson Med, 2016. © 2016 International Society for Magnetic Resonance in Medicine

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