In vivo NMR spectral parameter estimation: a comparison between time and frequency domain methods

Key concepts in MR spectroscopy and practical approaches to gaining biochemical information in children

Magnetic resonance spectroscopy (MRS) provides independent biochemical information and has become an invaluable adjunct to MRI and other imaging modalities. This review introduces key concepts and presents basic methodological steps regarding the acquisition and the interpretation of proton MRS. We review major brain metabolites and discuss MRS dependence on age, location, echo time and field strength.

MR spectroscopy and spectroscopic imaging of the brain

Magnetic resonance spectroscopy (MRS) and the related technique of magnetic resonance spectroscopic imaging (MRSI) are widely used in both clinical and preclinical research for the non-invasive evaluation of brain metabolism. They are also used in medical practice, although their ultimate clinical value continues to be a source of discussion. This chapter reviews the general information content of brain spectra and commonly used protocols for both MRS and MRSI and also touches on data analysis methods and quantitation. The main focus is on proton MRS for application in humans, but many of the methods are also applicable to other nuclei and studies of animal models as well.

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.

New denoising scheme for magnetic resonance spectroscopy signals

A new scheme for denoising magnetic resonance spectroscopy (MRS) signals is presented. This scheme is based on projecting noisy MRS signals in different domains, consecutively, and performing noise filtering operations in these domains. The domains are chosen such that the noise portion, which is inseparable from the desired signal in one domain, is separable in the other. A set of stable, linear, time-frequency (SLTF) transforms with different resolutions was selected for these projections as an example. Scheme evaluation was performed using extensive MRS signals with various noise levels. Compared with one domain denoising, it was observed that the proposed scheme gives superior results that compensate for the excess computational requirements. The proposed scheme supersedes also the wavelet packet denoising schemes.

Quantitative magnetic resonance spectroscopy: Semi-parametric modeling and determination of uncertainties

A semi-parametric approach for the quantitative analysis of magnetic resonance (MR) spectra is proposed and an uncertainty analysis is given. Single resonances are described by parametric models or by parametrized in vitro spectra and the baseline is determined nonparametrically by regularization. By viewing baseline estimation in a reproducing kernel Hilbert space, an explicit parametric solution for the baseline is derived. A Bayesian point of view is adopted to derive uncertainties, and the many parameters associated with the baseline solution are treated as nuisance parameters. The derived uncertainties formally reduce to Cramér-Rao lower bounds for the parametric part of the model in the case of a vanishing baseline. The proposed uncertainty calculation was applied to simulated and measured MR spectra and the results were compared to Cramér-Rao lower bounds derived after the nonparametrically estimated baselines were subtracted from the spectra. In particular, for high SNR and strong baseline contributions the proposed procedure yields a more appropriate characterization of the accuracy of parameter estimates than Crémer-Rao lower bounds, which tend to overestimate accuracy.

NMR signal enhancement via a new time-frequency transform

In this paper, a reliable method to reduce the noise from nuclear magnetic resonance (NMR) signals using a recently developed linear critically sampled time-frequency transform is proposed. In addition to its low computational requirements, this transform has many theoretical advantages that make it a good candidate for NMR signal enhancement. NMR signals in the transform domain are concentrated in a few coefficients while the noise is well distributed. Performing a thresholding technique in the transform domain, therefore, significantly enhances the signal. A comparison with other signal enhancement techniques shows that this technique has a superior performance, thus confirming the theoretical expectations.

Correction of MR kappa-space data corrupted by spike noise

Magnetic resonance images are reconstructed from digitized raw data, which are collected in the spatial-frequency domain (also called kappa-space). Occasionally, single or multiple data points in the k-space data are corrupted by spike noise, causing striation artifacts in images. Thresholding methods for detecting corrupted data points can fail because of small alterations, especially for data points in the low spatial frequency area where the k-space variation is large. Restoration of corrupted data points using interpolations of neighboring pixels can give incorrect results. We propose a Fourier transform method for detecting and restoring corrupted data points using a window filter derived from the striation-artifact structure in an image or an intermediate domain. The method provides an analytical solution for the alteration at each corrupted data point. It can effectively restore corrupted kappa-space data, removing striation artifacts in images, provided that the following three conditions are satisfied. First, a region of known signal distribution (for example, air background) is visible in either the image or the intermediate domain so that it can be selected using a window filter. Second, multiple spikes are separated by the full-width at half-maximum of the point spread function for the window filter. Third, the magnitude of a spike is larger than the minimum detectable value determined by the window filter and the standard deviation of kappa-space random noise.

Quantitative MRS: comparison of time domain and time domain frequency domain methods using a novel test procedure

For quantitative analysis of in vivo MR spectra, a state-of-the-art time domain method was compared with a recently reported time domain frequency domain method which uses wavelets for background characterization. The comparison was made on the basis of results for simulated test problems that were constructed by combining measured and simulated MRS data at different signal-to-noise ratios in order to simultaneously reflect real world difficulties, in particular the overlapping background problem, and to allow for quantitative judgment of a method's accuracy. Incorporating prior knowledge was also considered. The results obtained give insight into the accuracy of the methods when applied to measured MRS data. Due to the improved background characterization, the time domain frequency domain method outperformed the time domain method in some of the test cases. Both methods were also applied to serial brain MR spectra of a healthy volunteer on 10 occasions.

Factors affecting the quantification of short echo in-vivo 1H MR spectra: prior knowledge, peak elimination, and filtering

Short echo 1H in-vivo brain MR spectra are difficult to quantify for several reasons: low signal to noise ratio, the severe overlap of spectral lines, the presence of macromolecule resonances beneath the resonances of interest, and the effect of resonances adjacent to the spectral region of interest (SRI). This paper outlines several different quantification strategies and the effect of each on the precision of in-vivo metabolite measurements. In-vivo spectra were quantified with no operator interaction using a template of prior knowledge determined by mathematically modeling separate in-vitro metabolite spectra. Metabolite level estimates and associated precision were compared before and after the inclusion of macromolecule resonances as part of the prior knowledge, and following two different methods of handling resonances adjacent to the SRI. The effects of rectangular and exponential filters were also investigated. All methods were tested using repeated in-vivo spectra from one individual acquired at 1.5 T using stimulated echo acquisition mode (STEAM, TE = 20 ms) localization. The results showed that the inclusion of macromolecules in the prior knowledge was necessary to obtain metabolite levels consistent with the literature, while the fitting of resonances adjacent to the SRI concurrent with modeled metabolites optimized the precision of metabolite estimates. Metabolite levels and precision were also affected by rectangular and exponential filtering, suggesting caution must be taken when such filters are used.

Versatile frequency domain fitting using time domain models and prior knowledge

An iterative nonlinear least-squares fitting algorithm in the frequency domain using time domain models for quantification of complex frequency domain MR spectra is presented. The algorithm allows incorporation of prior knowledge and has both the advantage of time-domain fitting with respect to handling the problem of missing data points and truncated data sets and of frequency-domain fitting with respect to multiple frequency-selective fitting. The described algorithm can handle, in addition to Lorentzian and Gaussian lineshapes, Voigt and nonanalytic lineshapes. The program allows the user the design of his own fitting strategy to optimize the probability of reaching the global least-squares minimum. The application of the fitting program is illustrated with examples from in vivo 1H-, 31P-, and 13C-MR spectroscopy.

Sodium TQF NMR and intracellular sodium in isolated crystalloid perfused rat heart

The feasibility of monitoring intracellular sodium changes using Na triple quantum filtered NMR without a chemical shift reagent (SR) was investigated in an isolated rat heart during a variety of interventions for Na(i) loading. Perfusion with 1 mM ouabain or without K+ present in the perfusate for 30 min produced a rise of the Na TQF signal with a plateau of approximately 190% and approximately 228% relative to the preintervention level, respectively. Stop-flow ischemia for 30 min resulted in a TQF signal growth of approximately 147%. The maximal Na TQF signal increase of 460% was achieved by perfusion without K+/Ca2+, corresponding to an elimination of the Na transmembrane gradient. The observed values of Na NMR TQF growth in the physiological and pathological ranges are in agreement with reported data by other methods and have a linear correlation with intracellular sodium content as determined in this study by Co-EDTA method and by sucrose-histidine washout of the extracellular space. Our data indicate that the increase in Na TQF NMR signal is determined by the growth of Na(i), and the extracellular Na contribution to the total TQF signal is unchanged at approximately 64%. In conclusion, Na TQF NMR without using SR offers a unique and noninvasive opportunity to monitor alterations of intracellular sodium. It may provide valuable insights for developing cardioprotective strategies and for observing the effects of pharmaceutical treatments on sodium homeostasis.

Noise reduction for NMR FID signals via Gabor expansion

The parameters in a nuclear magnetic resonance (NMR) free induction decay (FID) signal contain information that is useful in biological and biomedical applications and research. A real time-sampled FID signal is well modeled as a finite mixture of modulated exponential sequences plus noise. We propose to use the generalized Gabor expansion for noise reduction, where the generalized Gabor expansion represents a signal in terms of a collection of time-shifted and frequency-modulated versions of a single sequence (prototype sequence). For FID signal-fitting, we choose the exponential sequence as the prototype function. Using the generalized Gabor expansion and exponential prototype sequences for FID model-fitting, an NMR FID signal can be well represented by the Gabor coefficients distributed in the joint time-frequency domain (JTFD). The Gabor coefficients reflect the weights of modulated exponential sequences in a signal. One of the important features is that the nonzero Gabor coefficients of a modulated exponential sequence will span a very small area in the JTFD, whereas the Gabor coefficients of the noise will not. If the exponent constant of the prototype sequence in the generalized Gabor expansion matches that of a modulated exponential sequence in the signal, then only one of the Gabor coefficients is nonzero in the JTFD. This is a very important property since it can be exploited to separate a signal from noise and to estimate modulated exponential sequence parameters.

In vivo 31P MRS: absolute concentrations, signal-to-noise and prior knowledge

Absolute metabolite concentrations have been estimated for nucleoside triphosphate and P(i) from in vivo 31P MR measurements using ISIS localization in a rat tumour model, and the results have been compared to those obtained from acid extracts of the tumours. The aim of the experiment was to assess the performance of four different spectral analysis techniques used for absolute quantitation. The spectral analysis techniques used were two frequency domain methods (peak area integration and Lorentzian fitting--FITSPEC) and two time domain methods (VARPRO and HLSVD). The spectra were acquired in blocks so that the degradation in performance of the four spectral analysis methods with decreasing signal-to-noise ratio (SNR) could be compared and referenced. This and the inclusion of a sophisticated method incorporating prior knowledge yields a more realistic and comprehensive protocol than previously published comparisons. The results suggest that VARPRO is the method of choice for quantitative analysis of tumour 31P MR spectra, giving the most reliable results at low SNR.

Simultaneous 31P NMR spectroscopy and EMG in exercising and recovering human skeletal muscle: technical aspects

The bioenergetics of human skeletal muscle can be studied by 31P NMR spectroscopy (31P-MRS) and by surface electromyography (SEMG). Simultaneous 31P-MRS and SEMG permit accurate and noninvasive studies of the correlation between metabolic and electrical changes in exercising and recovering human skeletal muscle, a relationship that is still poorly understood. This study describes the optimization of skeletal muscle 31P-MRS in a whole-body magnet, involving surface coil design, utilization of adiabatic radio frequency pulses and advanced time-domain fitting, to the technical design of SEMG. A nonmagnetic ergometer was used for ankle dorsiflexions that activated only the anterior tibial muscle as verified by post exercise imaging. The coil design and the adiabatic sech/tanh pulse improved sensitivity by 45% and 56% respectively, compared with standard techniques. Simultaneous electromyographic recordings did not deteriorate the NMR spectra. The VARPRO time domain fitting routine was very suitable for estimating 31P muscle spectra. With these methods it was possible to accurately estimate parameters describing metabolic and electrical changes during rest, exercise and the entire recovery period with a 20-s time resolution on a standard 1.5 T whole-body NMR scanner.

Automatic in vivo NMR data processing based on an enhancement procedure and linear prediction method

A new data processing method for in vivo NMR data quantitation is presented. This method (EPLPSVD) is based on the enhancement procedure (EP) proposed by J. A. Cadzow (IEEE Trans. Acoust. Speech Signal Process. 36, 49, 1988) followed by the usual linear prediction method using the singular value decomposition (LPSVD). The evaluation of this protocol is performed using synthesized 31P signals with different signal-to-noise ratios. A Monte-Carlo simulation as a function of signal-to-noise ratio (SNR) has proved that EPLPSVD leads to unbiased estimated values of parameters. Then the Cramer-Rao method yields reliable confidence intervals for the estimated parameters. The estimates of NMR parameters using EPLPSVD are reliable and accurate for SNR > or = 1.2 while the LPSVD method failed for SNR < or = 4. This protocol is applied to analyze automatically a series of 31P free induction decays obtained from the human gastrocnemius muscle during exercise. Spectral parameters with their confidence intervals, curves of relative intensity variations in phosphocreatine and inorganic phosphate, and pH curves are automatically provided.

Improving data acquisition parameters of 31P in vivo spectra for signal analysis in the time domain

To obtain reliable NMR quantitation, experimental cautions concerning data acquisition must be taken when using automatic predictive calculations. For this study, 2000 31P in vitro and in vivo spectra were processed, using the enhancement procedure with linear prediction using singular value decomposition (EPLPSVD) method, and analyzed. The effects of quadrature detection modes (simultaneous or sequential), of the number of time-domain samples used are investigated and experimental conditions such as sample motions and spectral width are discussed.