Parameterization of metabolite and macromolecule contributions in interrelated MR spectra of human brain using multidimensional modeling

Model-based frequency-and-phase correction of 1H MRS data with 2D linear-combination modeling

PURPOSE

Retrospective frequency-and-phase correction (FPC) methods attempt to remove frequency-and-phase variations between transients to improve the quality of the averaged MR spectrum. However, traditional FPC methods like spectral registration struggle at low SNR. Here, we propose a method that directly integrates FPC into a 2D linear-combination model (2D-LCM) of individual transients ("model-based FPC"). We investigated how model-based FPC performs compared to the traditional approach, i.e., spectral registration followed by 1D-LCM in estimating frequency-and-phase drifts and, consequentially, metabolite level estimates.

METHODS

We created synthetic in-vivo-like 64-transient short-TE sLASER datasets with 100 noise realizations at 5 SNR levels and added randomly sampled frequency and phase variations. We then used this synthetic dataset to compare the performance of 2D-LCM with the traditional approach (spectral registration, averaging, then 1D-LCM). Outcome measures were the frequency/phase/amplitude errors, the SD of those ground-truth errors, and amplitude Cramér Rao lower bounds (CRLBs). We further tested the proposed method on publicly available in-vivo short-TE PRESS data.

RESULTS

2D-LCM estimates (and accounts for) frequency-and-phase variations directly from uncorrected data with equivalent or better fidelity than the conventional approach. Furthermore, 2D-LCM metabolite amplitude estimates were at least as accurate, precise, and certain as the conventionally derived estimates. 2D-LCM estimation of FPC and amplitudes performed substantially better at low-to-very-low SNR.

CONCLUSION

Model-based FPC with 2D linear-combination modeling is feasible and has great potential to improve metabolite level estimation for conventional and dynamic MRS data, especially for low-SNR conditions, for example, long TEs or strong diffusion weighting.

GABA-edited MEGA-PRESS at 3 T: Does a measured macromolecule background improve linear combination modeling?

PURPOSE

The J-difference edited γ-aminobutyric acid (GABA) signal is contaminated by other co-edited signals-the largest of which originates from co-edited macromolecules (MMs)-and is consequently often reported as "GABA+." MM signals are broader and less well-characterized than the metabolites, and are commonly approximated using a Gaussian model parameterization. Experimentally measured MM signals are a consensus-recommended alternative to parameterized modeling; however, they are relatively under-studied in the context of edited MRS.

METHODS

To address this limitation in the literature, we have acquired GABA-edited MEGA-PRESS data with pre-inversion to null metabolite signals in 13 healthy controls. An experimental MM basis function was derived from the mean across subjects. We further derived a new parameterization of the MM signals from the experimental data, using multiple Gaussians to accurately represent their observed asymmetry. The previous single-Gaussian parameterization, mean experimental MM spectrum and new multi-Gaussian parameterization were compared in a three-way analysis of a public MEGA-PRESS dataset of 61 healthy participants.

RESULTS

Both the experimental MMs and the multi-Gaussian parameterization exhibited reduced fit residuals compared to the single-Gaussian approach (p = 0.034 and p = 0.031, respectively), suggesting they better represent the underlying data than the single-Gaussian parameterization. Furthermore, both experimentally derived models estimated larger MM fractional contribution to the GABA+ signal for the experimental MMs (58%) and multi-Gaussian parameterization (58%), compared to the single-Gaussian approach (50%).

CONCLUSIONS

Our results indicate that single-Gaussian parameterization of edited MM signals is insufficient and that both experimentally derived GABA+ spectra and their parameterized replicas improve the modeling of GABA+ spectra.

Universal dynamic fitting of magnetic resonance spectroscopy

PURPOSE

Dynamic (2D) MRS is a collection of techniques where acquisitions of spectra are repeated under varying experimental or physiological conditions. Dynamic MRS comprises a rich set of contrasts, including diffusion-weighted, relaxation-weighted, functional, edited, or hyperpolarized spectroscopy, leading to quantitative insights into multiple physiological or microstructural processes. Conventional approaches to dynamic MRS analysis ignore the shared information between spectra, and instead proceed by independently fitting noisy individual spectra before modeling temporal changes in the parameters. Here, we propose a universal dynamic MRS toolbox which allows simultaneous fitting of dynamic spectra of arbitrary type.

METHODS

A simple user-interface allows information to be shared and precisely modeled across spectra to make inferences on both spectral and dynamic processes. We demonstrate and thoroughly evaluate our approach in three types of dynamic MRS techniques. Simulations of functional and edited MRS are used to demonstrate the advantages of dynamic fitting.

RESULTS

Analysis of synthetic functional 1H-MRS data shows a marked decrease in parameter uncertainty as predicted by prior work. Analysis with our tool replicates the results of two previously published studies using the original in vivo functional and diffusion-weighted data. Finally, joint spectral fitting with diffusion orientation models is demonstrated in synthetic data.

CONCLUSION

A toolbox for generalized and universal fitting of dynamic, interrelated MR spectra has been released and validated. The toolbox is shared as a fully open-source software with comprehensive documentation, example data, and tutorials.

Model-based frequency-and-phase correction of 1H MRS data with 2D linear-combination modeling

Purpose

Retrospective frequency-and-phase correction (FPC) methods attempt to remove frequency-and-phase variations between transients to improve the quality of the averaged MR spectrum. However, traditional FPC methods like spectral registration struggle at low SNR. Here, we propose a method that directly integrates FPC into a two-dimensional linear-combination model (2D-LCM) of individual transients ('model-based FPC'). We investigated how model-based FPC performs compared to the traditional approach, i.e., spectral registration followed by 1D-LCM in estimating frequency-and-phase drifts and, consequentially, metabolite level estimates.

Methods

We created synthetic in-vivo-like 64-transient short-TE sLASER datasets with 100 noise realizations at 5 SNR levels and added randomly sampled frequency and phase variations. We then used this synthetic dataset to compare the performance of 2D-LCM with the traditional approach (spectral registration, averaging, then 1D-LCM). Outcome measures were the frequency/phase/amplitude errors, the standard deviation of those ground-truth errors, and amplitude Cramér Rao Lower Bounds (CRLBs). We further tested the proposed method on publicly available in-vivo short-TE PRESS data.

Results

2D-LCM estimates (and accounts for) frequency-and-phase variations directly from uncorrected data with equivalent or better fidelity than the conventional approach. Furthermore, 2D-LCM metabolite amplitude estimates were at least as accurate, precise, and certain as the conventionally derived estimates. 2D-LCM estimation of frequency and phase correction and amplitudes performed substantially better at low-to-very-low SNR.

Conclusion

Model-based FPC with 2D linear-combination modeling is feasible and has great potential to improve metabolite level estimation for conventional and dynamic MRS data, especially for low-SNR conditions, e.g., long TEs or strong diffusion weighting.

Multi-echo single-shot spectroscopy combined with simultaneous 2D model fitting for fast and accurate measurement of metabolite-specific concentrations and T2 relaxation times

The purpose of the current study was to develop a novel single-voxel MR spectroscopy acquisition scheme to simultaneously determine metabolite-specific concentrations and transverse relaxation times within realistic clinical scan times. Partly truncated multi-TE data are acquired as an echo train in a single acquisition (multi-echo single-shot [MESS]). A 2D multiparametric model fitting approach combines truncated, low-resolved short TE data with fully sampled, highly resolved, longer TE data to yield concentration and T2 estimates for major brain metabolites simultaneously. Cramer-Rao lower bounds (CRLB) are used as a measure of performance. The novel scheme was compared with traditional multi-echo multi-shot methods. In silico, in vitro, and in vivo experiments support the findings. MESS schemes, requiring only 2 min 12 s for the acquisition of three echo times, provide valid concentration and relaxation estimates for multiple metabolites and outperform traditional methods for simultaneous determinations of metabolite-specific T2 s and concentrations, with improvements ranging from 5% to 30% for T2 s and from 10% to 50% for concentrations. However, substantial unsuppressed residual water signals may hamper the method's reproducibility, as observed in an initial experiment setup that prioritizes short TEs with severely truncated acquisition for the benefit of signal-to-noise ratio (SNR). Nevertheless, CRLB have been confirmed to be well suited as design criteria, and within-session repeatability approaches CRLB when residual water is removed in postprocessing by exploiting longer and less truncated data recordings. MESS MRS combined with 2D model fitting promises comparable accuracy, increased precision, or inversely shorter experimental times compared with traditional approaches. However, the optimal design must be investigated as a trade-off between SNR, the truncation factor, and TE batch selections, all of which influence the robustness of estimations.

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.

Feasibility and implications of using subject-specific macromolecular spectra to model short echo time magnetic resonance spectroscopy data

Expert consensus recommends linear-combination modeling (LCM) of 1 H MR spectra with sequence-specific simulated metabolite basis function and experimentally derived macromolecular (MM) basis functions. Measured MM basis functions are usually derived from metabolite-nulled spectra averaged across a small cohort. The use of subject-specific instead of cohort-averaged measured MM basis functions has not been studied widely. Furthermore, measured MM basis functions are not widely available to non-expert users, who commonly rely on parameterized MM signals internally simulated by LCM software. To investigate the impact of the choice of MM modeling, this study, therefore, compares metabolite level estimates between different MM modeling strategies (cohort-mean measured; subject-specific measured; parameterized) in a lifespan cohort and characterizes its impact on metabolite-age associations. 100 conventional (TE = 30 ms) and metabolite-nulled (TI = 650 ms) PRESS datasets, acquired from the medial parietal lobe in a lifespan cohort (20-70 years of age), were analyzed in Osprey. Short-TE spectra were modeled in Osprey using six different strategies to consider the MM baseline. Fully tissue- and relaxation-corrected metabolite levels were compared between MM strategies. Model performance was evaluated by model residuals, the Akaike information criterion (AIC), and the impact on metabolite-age associations. The choice of MM strategy had a significant impact on the mean metabolite level estimates and no major impact on variance. Correlation analysis revealed moderate-to-strong agreement between different MM strategies (r > 0.6). The lowest relative model residuals and AIC values were found for the cohort-mean measured MM. Metabolite-age associations were consistently found for two major singlet signals (total creatine (tCr])and total choline (tCho)) for all MM strategies; however, findings for metabolites that are less distinguishable from the background signals associations depended on the MM strategy. A variance partition analysis indicated that up to 44% of the total variance was related to the choice of MM strategy. Additionally, the variance partition analysis reproduced the metabolite-age association for tCr and tCho found in the simpler correlation analysis. In summary, the inclusion of a single high signal-to-noise ratio MM basis function (cohort-mean) in the short-TE LCM leads to more lower model residuals and AIC values compared with MM strategies with more degrees of freedom (Gaussian parametrization) or subject-specific MM information. Integration of multiple LCM analyses into a single statistical model potentially allows to identify the robustness in the detection of underlying effects (e.g., metabolite vs. age), reduces algorithm-based bias, and estimates algorithm-related variance.

Macromolecular background signal and non-Gaussian metabolite diffusion determined in human brain using ultra-high diffusion weighting

Purpose

Definition of a macromolecular MR spectrum based on diffusion properties rather than relaxation time differences and characterization of non‐Gaussian diffusion of brain metabolites with strongly diffusion‐weighted MR spectroscopy.

Methods

Short echo time MRS with strong diffusion‐weighting with b‐values up to 25 ms/μm² at two diffusion times was implemented on a Connectom system and applied in combination with simultaneous spectral and diffusion decay modeling. Motion‐compensation was performed with a combined method based on the simultaneously acquired water and a macromolecular signal.

Results

The motion compensation scheme prevented spurious signal decay reflected in very small apparent diffusion constants for macromolecular signal. Macromolecular background signal patterns were determined using multiple fit strategies. Signal decay corresponding to non‐Gaussian metabolite diffusion was represented by biexponential fit models yielding parameter estimates for human gray matter that are in line with published rodent data. The optimal fit strategies used constraints for the signal decay of metabolites with limited signal contributions to the overall spectrum.

Conclusion

The determined macromolecular spectrum based on diffusion properties deviates from the conventional one derived from longitudinal relaxation time differences calling for further investigation before use as experimental basis spectrum when fitting clinical MR spectra. The biexponential characterization of metabolite signal decay is the basis for investigations into pathologic alterations of microstructure.

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Results and interpretation of a fitting challenge for MR spectroscopy set up by the MRS study group of ISMRM

PURPOSE

Fitting of MRS data plays an important role in the quantification of metabolite concentrations. Many different spectral fitting packages are used by the MRS community. A fitting challenge was set up to allow comparison of fitting methods on the basis of performance and robustness.

METHODS

Synthetic data were generated for 28 datasets. Short-echo time PRESS spectra were simulated using ideal pulses for the common metabolites at mostly near-normal brain concentrations. Macromolecular contributions were also included. Modulations of signal-to-noise ratio (SNR); lineshape type and width; concentrations of γ-aminobutyric acid, glutathione, and macromolecules; and inclusion of artifacts and lipid signals to mimic tumor spectra were included as challenges to be coped with.

RESULTS

Twenty-six submissions were evaluated. Visually, most fit packages performed well with mostly noise-like residuals. However, striking differences in fit performance were found with bias problems also evident for well-known packages. In addition, often error bounds were not appropriately estimated and deduced confidence limits misleading. Soft constraints as used in LCModel were found to substantially influence the fitting results and their dependence on SNR.

CONCLUSIONS

Substantial differences were found for accuracy and precision of fit results obtained by the multiple fit packages.

The macromolecular MR spectrum does not change with healthy aging

PURPOSE

To acquire the mobile macromolecule (MM) spectrum from healthy participants, and to investigate changes in the signals with age and sex.

METHODS

102 volunteers (49 M/53 F) between 20 and 69 years were recruited for in vivo data acquisition in the centrum semiovale (CSO) and posterior cingulate cortex (PCC). Spectral data were acquired at 3T using PRESS localization with a voxel size of 30 × 26 × 26 mm³ , pre-inversion (TR/TI 2000/600 ms) and CHESS water suppression. Metabolite-nulled spectra were modeled to eliminate residual metabolite signals, which were then subtracted out to yield a "clean" MM spectrum using the Osprey software. Pearson's correlation coefficient was calculated between integrals and age for the 14 MM signals. One-way ANOVA was performed to determine differences between age groups. An independent t-test was carried out to determine differences between sexes.

RESULTS

MM spectra were successfully acquired in 99 (CSO) and 96 (PCC) of 102 subjects. No significant correlations were seen between age and MM signals. One-way ANOVA also suggested no age-group differences for any MM peak (all p > .004). No differences were observed between sex groups. WM and GM voxel fractions showed a significant (p < .05) negative linear association with age in the WM-predominant CSO (R = -0.29) and GM-predominant PCC regions (R = -0.57) respectively while CSF increased significantly with age in both regions.

CONCLUSION

Our findings suggest that a pre-defined MM basis function can be used for linear combination modeling of metabolite data from different age and sex groups.

In vivo macromolecule signals in rat brain 1 H-MR spectra at 9.4T: Parametrization, spline baseline estimation, and T2 relaxation times

PURPOSE

Reliable detection and fitting of macromolecules (MM) are crucial for accurate quantification of brain short-echo time (TE) ¹ H-MR spectra. An experimentally acquired single MM spectrum is commonly used. Higher spectral resolution at ultra-high field (UHF) led to increased interest in using a parametrized MM spectrum together with flexible spline baselines to address unpredicted spectroscopic components. Herein, we aimed to: (1) implement an advanced methodological approach for post-processing, fitting, and parametrization of 9.4T rat brain MM spectra; (2) assess the concomitant impact of the LCModel baseline and MM model (ie, single vs parametrized); and (3) estimate the apparent T₂ relaxation times for seven MM components.

METHODS

A single inversion recovery sequence combined with advanced AMARES prior knowledge was used to eliminate the metabolite residuals, fit, and parametrize 10 MM components directly from 9.4T rat brain in vivo ¹ H-MR spectra at different TEs. Monte Carlo simulations were also used to assess the concomitant influence of parametrized MM and DKNTMN parameter in LCModel.

RESULTS

A very stiff baseline (DKNTMN ≥ 1 ppm) in combination with a single MM spectrum led to deviations in metabolite concentrations. For some metabolites the parametrized MM showed deviations from the ground truth for all DKNTMN values. Adding prior knowledge on parametrized MM improved MM and metabolite quantification. The apparent T₂ ranged between 12 and 24 ms for seven MM peaks.

CONCLUSION

Moderate flexibility in the spline baseline was required for reliable quantification of real/experimental spectra based on in vivo and Monte Carlo data. Prior knowledge on parametrized MM improved MM and metabolite quantification.

Are Cramér-Rao lower bounds an accurate estimate for standard deviations in in vivo magnetic resonance spectroscopy?

Due to inherent time constraints for in vivo experiments, it is infeasible to repeat multiple MRS scans to estimate standard deviations on the desired measured parameters. As such, the Cramér-Rao lower bounds (CRLBs) have become the routine method to approximate standard deviations for in vivo experiments. Cramér-Rao lower bounds, however, as the name suggests, are theoretically a lower bound on the standard deviation and it is not clear if and under what circumstances this approximation is valid. Realistic synthetic 3 T spectra were used to investigate the relationship between estimated CRLBs, true CRLBs and standard deviations. Here we demonstrate that, although the CRLBs are theoretically truly a lower bound on the standard deviation (not an equality) for the problem typically encountered in quantification, they are still an adequate approximation to standard deviation as long as the model perfectly characterizes the data. In the case when the macromolecule basis deviates from the measured macromolecules it was shown that the CRLBs can deviate from standard deviations by approximately 50% for N-acetylaspartic acid, creatine and glutamate and of the order of 100% or more for myo-inositol and γ-aminobutyric acid. In the case when the model perfectly reflects the data the CRLBs are within approximately 10% of standard deviations for all metabolites. The result of the CRLB being within 10% of standard deviations means that, for an accurate model, novel quantification methods such as machine learning or deep learning will not be able to obtain substantially more precise estimates for the desired parameters than traditional maximum-likelihood estimation.

Contribution of macromolecules to brain 1 H MR spectra: Experts' consensus recommendations

Proton MR spectra of the brain, especially those measured at short and intermediate echo times, contain signals from mobile macromolecules (MM). A description of the main MM is provided in this consensus paper. These broad peaks of MM underlie the narrower peaks of metabolites and often complicate their quantification but they also may have potential importance as biomarkers in specific diseases. Thus, separation of broad MM signals from low molecular weight metabolites enables accurate determination of metabolite concentrations and is of primary interest in many studies. Other studies attempt to understand the origin of the MM spectrum, to decompose it into individual spectral regions or peaks and to use the components of the MM spectrum as markers of various physiological or pathological conditions in biomedical research or clinical practice. The aim of this consensus paper is to provide an overview and some recommendations on how to handle the MM signals in different types of studies together with a list of open issues in the field, which are all summarized at the end of the paper.

A novel method to measure T1 -relaxation times of macromolecules and quantification of the macromolecular resonances

PURPOSE

Macromolecular peaks underlying metabolite spectra influence the quantification of metabolites. Therefore, it is important to understand the extent of contribution from macromolecules (MMs) in metabolite quantification. However, to model MMs more accurately in spectral fitting, differences in T₁ relaxation times among individual MM peaks must be considered. Characterization of T₁ -relaxation times for all individual MM peaks using a single inversion recovery technique is difficult due to eventual contributions from metabolites. On the contrary, a double inversion recovery (DIR) technique provided flexibility to acquire MM spectra spanning a range of longitudinal magnetizations with minimal metabolite influence. Thus, a novel method to determine T₁ -relaxation times of individual MM peaks is reported in this work.

METHODS

Extensive Bloch simulations were performed to determine inversion time combinations for a DIR technique that yielded adequate MM signal with varying longitudinal magnetizations while minimizing metabolite contributions. MM spectra were acquired using DIR-metabolite-cycled semi-LASER sequence. LCModel concentrations were fitted to the DIR signal equation to calculate T₁ -relaxation times.

RESULTS

T₁ -relaxation times of MMs range from 204 to 510 ms and 253 to 564 ms in gray- and white-matter rich voxels respectively at 9.4T. Additionally, concentrations of 13 MM peaks are reported.

CONCLUSION

A novel DIR method is reported in this work to calculate T₁ -relaxation times of MMs in the human brain. T₁ -relaxation times and relaxation time corrected concentrations of individual MMs are reported in gray- and white-matter rich voxels for the first time at 9.4T.