Time-domain quanification of amplitude, chemical shift, apparent relaxation time T2, and phase by wavelet-transform analysis. Application to biomedical magnetic resonance spectroscopy

Noise suppression of proton magnetic resonance spectroscopy improves paediatric brain tumour classification

Proton magnetic resonance spectroscopy (1H-MRS) is increasingly used for clinical brain tumour diagnosis, but suffers from limited spectral quality. This retrospective and comparative study aims at improving paediatric brain tumour classification by performing noise suppression on clinical 1H-MRS. Eighty-three/forty-two children with either an ependymoma (ages 4.6 ± 5.3/9.3 ± 5.4), a medulloblastoma (ages 6.9 ± 3.5/6.5 ± 4.4), or a pilocytic astrocytoma (8.0 ± 3.6/6.3 ± 5.0), recruited from four centres across England, were scanned with 1.5T/3T short-echo-time point-resolved spectroscopy. The acquired raw 1H-MRS was quantified by using Totally Automatic Robust Quantitation in NMR (TARQUIN), assessed by experienced spectroscopists, and processed with adaptive wavelet noise suppression (AWNS). Metabolite concentrations were extracted as features, selected based on multiclass receiver operating characteristics, and finally used for identifying brain tumour types with supervised machine learning. The minority class was oversampled through the synthetic minority oversampling technique for comparison purposes. Post-noise-suppression 1H-MRS showed significantly elevated signal-to-noise ratios (P < .05, Wilcoxon signed-rank test), stable full width at half-maximum (P > .05, Wilcoxon signed-rank test), and significantly higher classification accuracy (P < .05, Wilcoxon signed-rank test). Specifically, the cross-validated overall and balanced classification accuracies can be improved from 81% to 88% overall and 76% to 86% balanced for the 1.5T cohort, whilst for the 3T cohort they can be improved from 62% to 76% overall and 46% to 56%, by applying Naïve Bayes on the oversampled 1H-MRS. The study shows that fitting-based signal-to-noise ratios of clinical 1H-MRS can be significantly improved by using AWNS with insignificantly altered line width, and the post-noise-suppression 1H-MRS may have better diagnostic performance for paediatric brain tumours.

Time-Frequency Analysis of Two-Dimensional Electron Spin Resonance Signals

Two-dimensional electron spin resonance (2D ESR) spectroscopy is a unique experimental technique for probing protein structure and dynamics, including processes that occur at the microsecond time scale. While it provides significant resolution enhancement over the one-dimensional experimental setup, spectral broadening and noise make extraction of spectral information highly challenging. Traditionally, two-dimensional Fourier transform (2D FT) is applied for the analysis of 2D ESR signals, although its efficiency is limited to stationary signals. In addition, it often fails to resolve overlapping peaks in 2D ESR. In this work, we propose a time-frequency analysis of 2D time-domain signals, which identifies all frequency peaks by decoupling a signal into its distinct constituent components via projection on the time-frequency plane. The method utilizes 2D undecimated discrete wavelet transform (2D UDWT) as an intermediate step in the analysis, followed by signal reconstruction and 2D FT. We have applied the method to a simulated 2D double quantum coherence (DQC) signal for validation and a set of experimental 2D ESR signals, demonstrating its efficiency in resolving overlapping peaks in the frequency domain, while displaying frequency evolution with time in case of non-stationary data.

Quantification of 1 H-MRS signals based on sparse metabolite profiles in the time-frequency domain

MRS is an analytical approach used for both quantitative and qualitative analysis of human body metabolites. The accurate and robust quantification capability of proton MRS (¹ H-MRS) enables the accurate estimation of living tissue metabolite concentrations. However, such methods can be efficiently employed for quantification of metabolite concentrations only if the overlapping nature of metabolites, existing static field inhomogeneity and low signal-to-noise ratio (SNR) are taken into consideration. Representation of ¹ H-MRS signals in the time-frequency domain enables us to handle the baseline and noise better. This is possible because the MRS signal of each metabolite is sparsely represented, with only a few peaks, in the frequency domain, but still along with specific time-domain features such as distinct decay constant associated with T₂ relaxation rate. The baseline, however, has a smooth behavior in the frequency domain. In this study, we proposed a quantification method using continuous wavelet transformation of ¹ H-MRS signals in combination with sparse representation of features in the time-frequency domain. Estimation of the sparse representations of MR spectra is performed according to the dictionaries constructed from metabolite profiles. Results on simulated and phantom data show that the proposed method is able to quantify the concentration of metabolites in ¹ H-MRS signals with high accuracy and robustness. This is achieved for both low SNR (5 dB) and low signal-to-baseline ratio (-5 dB) regimes.

Spatio-spectral regularization to improve magnetic resonance spectroscopic imaging quantification

Magnetic resonance spectroscopic imaging (MRSI) is a non-invasive technique able to provide the spatial distribution of relevant biochemical compounds commonly used as biomarkers of disease. Information provided by MRSI can be used as a valuable insight for the diagnosis, treatment and follow-up of several diseases such as cancer or neurological disorders. Obtaining accurate metabolite concentrations from in vivo MRSI signals is a crucial requirement for the clinical utility of this technique. Despite the numerous publications on the topic, accurate quantification is still a challenging problem due to the low signal-to-noise ratio of the data, overlap of spectral lines and the presence of nuisance components. We propose a novel quantification method, which alleviates these limitations by exploiting a spatio-spectral regularization scheme. In contrast to previous methods, the regularization terms are not expressed directly on the parameters being sought, but on appropriate transformed domains. In order to quantify all signals simultaneously in the MRSI grid, while introducing prior information, a fast proximal optimization algorithm is proposed. Experiments on synthetic MRSI data demonstrate that the error in the estimated metabolite concentrations is reduced by a mean of 41% with the proposed scheme. Results on in vivo brain MRSI data show the benefit of the proposed approach, which is able to fit overlapping peaks correctly and to capture metabolites that are missed by single-voxel methods due to their lower concentrations. Copyright © 2016 John Wiley & Sons, Ltd.

Compressive sensing could accelerate 1H MR metabolic imaging in the clinic

PURPOSE

To retrospectively evaluate the fidelity of magnetic resonance (MR) spectroscopic imaging data preservation at a range of accelerations by using compressed sensing.

MATERIALS AND METHODS

The protocols were approved by the institutional review board of the university, and written informed consent to acquire and analyze MR spectroscopic imaging data was obtained from the subjects prior to the acquisitions. This study was HIPAA compliant. Retrospective application of compressed sensing was performed on 10 clinical MR spectroscopic imaging data sets, yielding 600 voxels from six normal brain data sets, 163 voxels from two brain tumor data sets, and 36 voxels from two prostate cancer data sets for analysis. The reconstructions were performed at acceleration factors of two, three, four, five, and 10 and were evaluated by using the root mean square error (RMSE) metric, metabolite maps (choline, creatine, N-acetylaspartate [NAA], and/or citrate), and statistical analysis involving a voxelwise paired t test and one-way analysis of variance for metabolite maps and ratios for comparison of the accelerated reconstruction with the original case.

RESULTS

The reconstructions showed high fidelity for accelerations up to 10 as determined by the low RMSE (< 0.05). Similar means of the metabolite intensities and hot-spot localization on metabolite maps were observed up to a factor of five, with lack of statistically significant differences compared with the original data. The metabolite ratios of choline to NAA and choline plus creatine to citrate did not show significant differences from the original data for up to an acceleration factor of five in all cases and up to that of 10 for some cases.

CONCLUSION

A reduction of acquisition time by up to 80%, with negligible loss of information as evaluated with clinically relevant metrics, has been successfully demonstrated for hydrogen 1 MR spectroscopic imaging.

MRS signal quantitation: a review of time- and frequency-domain methods

In this paper an overview of time-domain and frequency-domain quantitation methods is given. Advantages and drawbacks of these two families of quantitation methods are discussed. An overview of preprocessing methods, such as lineshape correction methods or unwanted component removal methods, is also given. The choice of the quantitation method depends on the data under investigation and the pursued objectives.

Quantifying in vivo MR spectra with circles

Accurate and robust quantification of in vivo magnetic resonance spectroscopy (MRS) data is essential to its application in research and medicine. The performance of existing analysis methods is problematic for in vivo studies where low signal-to-noise ratio, overlapping peaks and intense artefacts are endemic. Here, a new frequency-domain technique for MRS data analysis is introduced wherein the circular trajectories which result when spectral peaks are projected onto the complex plane, are fitted with active circle models. The use of active contour strategies naturally allows incorporation of prior knowledge as constraint energy terms. The problem of phasing spectra is eliminated, and baseline artefacts are dealt with using active contours-snakes. The stability and accuracy of the new technique, CFIT, is compared with a standard time-domain fitting tool, using simulated 31P data with varying amounts of noise and 98 real human chest and heart 31P MRS data sets. The real data were also analyzed by our standard frequency-domain absorption-mode technique. On the real data, CFIT demonstrated the least fitting failures of all methods and an accuracy similar to the latter method, with both these techniques outperforming the time-domain approach. Contrasting results from simulations argue that performance relative to Cramer-Rao Bounds may not be a suitable indicator of fitting performance with typical in vivo data such as these. We conclude that CFIT is a stable, accurate alternative to the best existing methods of fitting in vivo data.

NMR spectroscopy in inhomogeneous B0 and B1 fields with non-linear correlation

Resolved NMR spectra from samples in inhomogeneous B0 and B1 fields can be obtained with the so-called "ex situ" methodology, employing a train of composite or adiabatic z-rotation RF pulses to periodically refocus the inhomogeneous broadening during the detection of the time-domain signal. Earlier schemes relied on a linear correlation between the inhomogeneous B0 and B1 fields. Here the pulse length, bandwidth, and amplitude of the adiabatic pulses of the hyperbolic secant type are adjusted to improve the refocusing for a setup with non-linear correlation. The field correlation is measured using a two-dimensional nutation experiment augmented with a third dimension with varying RF carrier frequency accounting for off-resonance effects. The pulse optimization is performed with a computer algorithm using the experimentally determined field correlation and a standard adiabatic z-rotation pulse as a starting point for the iterative optimization procedure. The shape of the z-rotation RF pulse is manipulated to provide refocusing for the conditions given by the sample-, magnet-, and RF-coil geometry.

Lactate doublet quantification and lipid signal suppression using a new biexponential decay filter: application to simulated and 1H MRS brain tumor time-domain data

A new postprocessing filter based on the continuous wavelet transform (CWT) method modeled as a biexponential decay function to isolate the lactate doublet from overlapping lipid resonance(s) and estimate its magnetic resonance spectroscopy (MRS) parameters (signal amplitude, resonance frequencies, and apparent relaxation time (T(*) (2))) is proposed. The new filter employs the same iterative process used in the previously single exponential decay filter. A comparison of the results obtained from application of both filters to simulated data and real (1)H MRS data collected from human blood plasma and brain tumors demonstrates that the new filter provides a better estimate of MRS parameters of lactate, with less computation time. Furthermore, the results show that the new filter is less sensitive to noise and provides a direct estimate of J-coupling value of the lactate doublet.

Spectral restoration from low signal-to-noise, distorted NMR signals: application to hyphenated capillary electrophoresis-NMR

In capillary electrophoresis separations coupled to NMR signal detection using small solenoidal coils, electrophoretic currents cause substantial distortion in the NMR spectral linewidths and peak heights, distortions which cannot be fully counteracted through shimming. The NMR spectra also have a low signal-to-noise ratio due to the small amounts of material, typically <1nmol, associated with such microseparations. This study proposes a two-step, signal processing method to restore spectral lines from the distorted NMR spectrum. First, a reference signal is acquired to estimate the broadening function, as a combination of several Lorentzian functions, using a gradient descent method. Then multi-resolution wavelet analysis is applied to the distorted spectrum to determine an initial estimate of the frequencies of the spectral lines. Convergence to the final spectrum, a second set of Lorentzians, involves deconvolution with the estimated broadening function using a gradient descent method. Experimental CE-NMR data show that considerable improvements in spectral quality are possible using this approach, although fine splittings can not be resolved if the broadening function is large.

WAVEWAT-improved solvent suppression in NMR spectra employing wavelet transforms

WAVEWAT is a new processing algorithm to suppress the on-resonance water signal in NMR spectra. It is based on a multiresolution analysis (MRA) of the free induction decay (FID) using a dyadic discrete wavelet transform (DWT). The width of the suppressed signal can be adjusted so that signals close to water are recovered without distortion of the signal shape and intensity. Computational efficiency is comparable to that of convolution filters employing a Fourier transform.

A wavelet packets decomposition algorithm for quantification of in vivo (1)H-MRS parameters

In this paper a novel method for the extraction of magnetic resonance spectroscopy (MRS) parameters is presented. The method applies the traditional time-domain linear prediction singular value decomposition (LPSVD) on the set of orthonormal sub-signals obtained by wavelet packets (WP) decomposition of the original free induction decay (FID) signal. Using the properties of WP the desired, optimal, sub-band FID decomposition is obtained and used to progressively separate the different metabolic components in distinct sub-bands. A pseudo-optimal WP tree is obtained using the minimum description length (MDL) criteria. The proposed algorithm preserves all the advantages of the traditional LPSVD method, but the WP decomposition considerably improves the LPSVD performances in the presence of noise. The paper addresses this aspect in details by comparing the innovative sub-band and the traditional full-band approaches. Algorithms are tested on simulated signals that mimic real MRS data.

Wavelets and related time-frequency techniques in magnetic resonance spectroscopy

We survey the various applications in MRS of the wavelet transform and related time-frequency methods. For the sake of completeness, we first quickly review the mathematical tools needed.

Water modeled signal removal and data quantification in localized MR spectroscopy using a time-scale postacquistion method

We have previously shown the continuous wavelet transform (CWT), a signal-processing tool, which is based upon an iterative algorithm using a lorentzian signal model, to be useful as a postacquisition water suppression technique. To further exploit this tool we show its usefulness in accurately quantifying the signal metabolites after water removal. However, due to the static field inhomogeneities, eddy currents, and "radiation damping," the water signal and the metabolites may no longer have a lorentzian lineshape. Therefore, another signal model must be used. As the CWT is a flexible method, we have developed a new algorithm using a gaussian model and found that it fits the signal components, especially the water resonance, better than the lorentzian model in most cases. A new framework, which uses the two models, is proposed. The framework iteratively extracts each resonance, starting by the water peak, from the raw signal and adjusts its envelope to both the lorentzian and the gaussian models. The model giving the best fit is selected. As a consequence, the small signals originating from metabolites when selecting, removing, and quantifying the dominant water resonance from the raw time domain signal are preserved and an accurate estimation of their concentrations is obtained. This is demonstrated by analyzing (1H) magnetic resonance spectroscopy unsuppressed water data collected from a phantom with known concentrations at two different field strengths and data collected from normal volunteers using two different localization methods.

NMRLAB-Advanced NMR data processing in matlab

NMRLAB is a toolbox for NMR data processing in MATLAB (The Mathworks). MATLAB is a matrix-oriented high-level programming environment which gives access to fast algorithms for a large number of numerical tasks on many common computer platforms. To take advantage of fast matrix operations in MATLAB most processing commands in NMRLAB have been vectorized. Data processing can be achieved either by scripts or by a user-friendly command structure. An interface to WaveLab enables spectral denoising employing wavelet transforms. The use of wavelet denoising is demonstrated for one- and two-dimensional data. Copyright 2000 Academic Press.

Water peak suppression: time-frequency vs time-scale approach

Wavelets are the most popular time-scale analysis tool. A well-known application of wavelets in nuclear magnetic resonance spectroscopy is water peak extraction/suppression. However, spectroscopists are more familiar with frequency than scale. So, from a spectroscopist point of view, a time-scale analysis tool (i.e., wavelets) is not natural and a time-frequency approach would be much more satisfactory. We explain a time-frequency solution to this problem based on Gabor analysis. As the two formalisms are closely linked together we continuously emphasize their similarities and differences. In particular we show that, here, the Gabor method is as efficient as the wavelet approach, and we give some examples. Those remarks also apply to other NMR problems solved previously with the continuous wavelet transform, such as quantification or dynamical phase correction.

Lactate editing and lipid suppression by continuous wavelet transform analysis: application to simulated and (1)H MRS brain tumor time-domain data

Determination of lactate concentrations in vivo is required in the noninvasive diagnosis, staging, and therapeutic monitoring of diseases such as cancer, heart disease, and stroke. An iterative filtering process based on the continuous wavelet transform (CWT) method in the time domain is proposed to isolate the lactate doublet signal from overlapping lipid resonances and estimate the magnetic resonance spectroscopy (MRS) parameters of the lactate methyl signal (signal amplitude, chemical shift, J-coupling and apparent transverse relaxation time (T*(2))). This method offers a number of advantages over the multiple quantum (MQ) and difference spectroscopy approaches, including: 1) full recovery of the lactate methyl signal, whereas the MQ methods usually detect 50% of the signal intensity; 2) in contrast to MQ methods, the lipid signal is retained together with J-coupling data on the lactate peak; 3) the CWT method is much less sensitive to motion artifacts than difference spectroscopy. Application of the method to simulated and real (1)H MRS data collected from human blood plasma and brain tumors demonstrated that this filter provides accurate estimates of the MRS parameters of the lactate doublet and efficiently removes lipid contributions.

Time-domain quantification of multiple-quantum-filtered (23)Na signal using continuous wavelet transform analysis

The application of continuous wavelet transform (CWT) analysis technique is presented to analyze multiple-quantum-filtered (MQF) (23)Na magnetic resonance spectroscopy (MRS) data. CWT acts on the free-induction-decay (FID) signal as a time-frequency variable filter. The signal-to-noise ratio (SNR) and frequency resolution of the output filter are locally increased. As a result, MQF equilibrium longitudinal magnetization and the apparent fast and slow transverse relaxation times are accurately estimated. A developed iterative algorithm based on frequency signal detection and components extraction, already proposed, was used to estimate the values of the signal parameters by analyzing simulated time-domain MQF signals and data from an agarose gel. The results obtained were compared to those obtained by measurement of signal height in frequency domain as a function of MQF preparation time and those obtained by a simple time-domain curve fitting. The comparison indicates that the CWT approach provides better results than the other tested methods that are generally used for MQF (23)Na MRS data analysis, especially when the SNR is low. The mean error on the estimated values of the amplitude signal and the apparent fast and slow transverse relaxation times for the simulated data were 2.19, 6. 63, and 16.17% for CWT, signal height in frequency domain, and time-domain curve fitting methods, respectively. Another major advantage of the proposed technique is that it allows quantification of MQF (23)Na signal from a single FID and, thus, reduces the experiment time dramatically.

Quantification of plasma lipoprotein fractions by wavelet transform time-domain data processing of the proton nuclear magnetic resonance methylene spectral region

Quantitative analysis of lipoprotein major fractions, LDL, VLDL and HDL, is of great interest for medical purposes, for instance in liver or heart diseases, diet management or cancer. The presently available biochemical methods require time consuming ultracentrifugation. A potentially automated method is proposed, using time domain quantification by Wavelet Transform (WT-NMR) method. The aim of the present study was to evaluate, on a preliminary series of nine human plasmas, the potential interest of WT-NMR in the quantification of both NMR-visible lipids and total lipoprotein fractions. The correlation coefficients between low and intermediate density (LDL+IDL), very low density (VLDL) and high density (HDL) lipoprotein visible lipid quantifications, obtained on nine human plasmas with WT-NMR and standard biochemical methods, were 0.79, 0.84 and 0.92, respectively. For the total lipoprotein assay, i.e. including an estimation of non NMR-visible protein and free cholesterol, the correlation between WT-NMR and the biochemistry were 0.87 for LDL+IDL, 0.81 for VLDL and 0.88 for HDL.