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

Simultaneous multi-transient linear-combination modeling of MRS data improves uncertainty estimation

PURPOSE

The interest in applying and modeling dynamic MRS has recently grown. Two-dimensional modeling yields advantages for the precision of metabolite estimation in interrelated MRS data. However, it is unknown whether including all transients simultaneously in a 2D model without averaging (presuming a stable signal) performs similarly to one-dimensional (1D) modeling of the averaged spectrum. Therefore, we systematically investigated the accuracy, precision, and uncertainty estimation of both described model approaches.

METHODS

Monte Carlo simulations of synthetic MRS data were used to compare the accuracy and uncertainty estimation of simultaneous 2D multitransient linear-combination modeling (LCM) with 1D-LCM of the average. A total of 2,500 data sets per condition with different noise representations of a 64-transient MRS experiment at six signal-to-noise levels for two separate spin systems (scyllo-inositol and gamma-aminobutyric acid) were analyzed. Additional data sets with different levels of noise correlation were also analyzed. Modeling accuracy was assessed by determining the relative bias of the estimated amplitudes against the ground truth, and modeling precision was determined by SDs and Cramér-Rao lower bounds (CRLBs).

RESULTS

Amplitude estimates for 1D- and 2D-LCM agreed well and showed a similar level of bias compared with the ground truth. Estimated CRLBs agreed well between both models and with ground-truth CRLBs. For correlated noise, the estimated CRLBs increased with the correlation strength for the 1D-LCM but remained stable for the 2D-LCM.

CONCLUSION

Our results indicate that the model performance of 2D multitransient LCM is similar to averaged 1D-LCM. This validation on a simplified scenario serves as a necessary basis for further applications of 2D modeling.

Whole-brain deuterium metabolic imaging via concentric ring trajectory readout enables assessment of regional variations in neuronal glucose metabolism

Deuterium metabolic imaging (DMI) is an emerging magnetic resonance technique, for non-invasive mapping of human brain glucose metabolism following oral or intravenous administration of deuterium-labeled glucose. Regional differences in glucose metabolism can be observed in various brain pathologies, such as Alzheimer's disease, cancer, epilepsy or schizophrenia, but the achievable spatial resolution of conventional phase-encoded DMI methods is limited due to prolonged acquisition times rendering submilliliter isotropic spatial resolution for dynamic whole brain DMI not feasible. The purpose of this study was to implement non-Cartesian spatial-spectral sampling schemes for whole-brain 2H FID-MR Spectroscopic Imaging to assess time-resolved metabolic maps with sufficient spatial resolution to reliably detect metabolic differences between healthy gray and white matter regions. Results were compared with lower-resolution DMI maps, conventionally acquired within the same session. Six healthy volunteers (4 m/2 f) were scanned for ~90 min after administration of 0.8 g/kg oral [6,6']-2H glucose. Time-resolved whole brain 2H FID-DMI maps of glucose (Glc) and glutamate + glutamine (Glx) were acquired with 0.75 and 2 mL isotropic spatial resolution using density-weighted concentric ring trajectory (CRT) and conventional phase encoding (PE) readout, respectively, at 7 T. To minimize the effect of decreased signal-to-noise ratios associated with smaller voxels, low-rank denoising of the spatiotemporal data was performed during reconstruction. Sixty-three minutes after oral tracer uptake three-dimensional (3D) CRT-DMI maps featured 19% higher (p = .006) deuterium-labeled Glc concentrations in GM (1.98 ± 0.43 mM) compared with WM (1.66 ± 0.36 mM) dominated regions, across all volunteers. Similarly, 48% higher (p = .01) 2H-Glx concentrations were observed in GM (2.21 ± 0.44 mM) compared with WM (1.49 ± 0.20 mM). Low-resolution PE-DMI maps acquired 70 min after tracer uptake featured smaller regional differences between GM- and WM-dominated areas for 2H-Glc concentrations with 2.00 ± 0.35 mM and 1.71 ± 0.31 mM, respectively (+16%; p = .045), while no regional differences were observed for 2H-Glx concentrations. In this study, we successfully implemented 3D FID-MRSI with fast CRT encoding for dynamic whole-brain DMI at 7 T with 2.5-fold increased spatial resolution compared with conventional whole-brain phase encoded (PE) DMI to visualize regional metabolic differences. The faster metabolic activity represented by 48% higher Glx concentrations was observed in GM- compared with WM-dominated regions, which could not be reproduced using whole-brain DMI with the low spatial resolution protocol. Improved assessment of regional pathologic alterations using a fully non-invasive imaging method is of high clinical relevance and could push DMI one step toward clinical applications.

Uncertainty propagation in absolute metabolite quantification for in vivo MRS of the human brain

PURPOSE

Absolute spectral quantification is the standard method for deriving estimates of the concentration from metabolite signals measured using in vivo proton MRS (1 H-MRS). This method is often reported with minimum variance estimators, specifically the Cramér-Rao lower bound (CRLB) of the metabolite signal amplitude's scaling factor from linear combination modeling. This value serves as a proxy for SD and is commonly reported in MRS experiments. Characterizing the uncertainty of absolute quantification, however, depends on more than simply the CRLB. The uncertainties of metabolite-specific (T1m , T2m ), reference-specific (T1ref , T2ref ), and sequence-specific (TR , TE ) parameters are generally ignored, potentially leading to an overestimation of precision. In this study, the propagation of uncertainty is used to derive a comprehensive estimate of the overall precision of concentrations from an internal reference.

METHODS

The propagated uncertainty is calculated using analytical derivations and Monte Carlo simulations and subsequently analyzed across a set of commonly measured metabolites and macromolecules. The effect of measurement error from experimentally obtained quantification parameters is estimated using published uncertainties and CRLBs from in vivo 1 H-MRS literature.

RESULTS

The additive effect of propagated measurement uncertainty from applied quantification correction factors can result in up to a fourfold increase in the concentration estimate's coefficient of variation compared to the CRLB alone. A case study analysis reveals similar multifold increases across both metabolites and macromolecules.

CONCLUSION

The precision of absolute metabolite concentrations derived from 1 H-MRS experiments is systematically overestimated if the uncertainties of commonly applied corrections are neglected as sources of error.

Diffusion-weighted MR spectroscopy: Consensus, recommendations, and resources from acquisition to modeling

Brain cell structure and function reflect neurodevelopment, plasticity, and aging; and changes can help flag pathological processes such as neurodegeneration and neuroinflammation. Accurate and quantitative methods to noninvasively disentangle cellular structural features are needed and are a substantial focus of brain research. Diffusion-weighted MRS (dMRS) gives access to diffusion properties of endogenous intracellular brain metabolites that are preferentially located inside specific brain cell populations. Despite its great potential, dMRS remains a challenging technique on all levels: from the data acquisition to the analysis, quantification, modeling, and interpretation of results. These challenges were the motivation behind the organization of the Lorentz Center workshop on "Best Practices & Tools for Diffusion MR Spectroscopy" held in Leiden, the Netherlands, in September 2021. During the workshop, the dMRS community established a set of recommendations to execute robust dMRS studies. This paper provides a description of the steps needed for acquiring, processing, fitting, and modeling dMRS data, and provides links to useful resources.

Simultaneous multi-transient linear-combination modeling of MRS data improves uncertainty estimation

Purpose

The interest in applying and modeling dynamic MRS has recently grown. 2D modeling yields advantages for the precision of metabolite estimation in interrelated MRS data. However, it is unknown whether including all transients simultaneously in a 2D model without averaging (presuming a stable signal) performs similarly to 1D modeling of the averaged spectrum. Therefore, we systematically investigated the accuracy, precision, and uncertainty estimation of both described model approaches.

Methods

Monte Carlo simulations of synthetic MRS data were used to compare the accuracy and uncertainty estimation of simultaneous 2D multi-transient LCM with 1D-LCM of the average. 2,500 datasets per condition with different noise representations of a 64-transient MRS experiment at 6 signal-to-noise levels for two separate spin systems (scyllo-inositol and GABA) were analyzed. Additional datasets with different levels of noise correlation were also analyzed. Modeling accuracy was assessed by determining the relative bias of the estimated amplitudes against the ground truth, and modeling precision was determined by standard deviations and Cramér-Rao Lower Bounds (CRLB).

Results

Amplitude estimates for 1D- and 2D-LCM agreed well and showed similar level of bias compared to the ground truth. Estimated CRLBs agreed well between both models and with ground truth CRLBs. For correlated noise the estimated CRLBs increased with the correlation strength for the 1D-LCM but remained stable for the 2D-LCM.

Conclusion

Our results indicate that the model performance of 2D multi-transient LCM is similar to averaged 1D-LCM. This validation on a simplified scenario serves as necessary basis for further applications of 2D modeling.

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.

Reproducibility of 3D MRSI for imaging human brain glucose metabolism using direct (2H) and indirect (1H) detection of deuterium labeled compounds at 7T and clinical 3T

INTRODUCTION

Deuterium metabolic imaging (DMI) and quantitative exchange label turnover (QELT) are novel MR spectroscopy techniques for non-invasive imaging of human brain glucose and neurotransmitter metabolism with high clinical potential. Following oral or intravenous administration of non-ionizing [6,6'-2H2]-glucose, its uptake and synthesis of downstream metabolites can be mapped via direct or indirect detection of deuterium resonances using 2H MRSI (DMI) and 1H MRSI (QELT), respectively. The purpose of this study was to compare the dynamics of spatially resolved brain glucose metabolism, i.e., estimated concentration enrichment of deuterium labeled Glx (glutamate+glutamine) and Glc (glucose) acquired repeatedly in the same cohort of subjects using DMI at 7T and QELT at clinical 3T.

METHODS

Five volunteers (4 m/1f) were scanned in repeated sessions for 60 min after overnight fasting and 0.8 g/kg oral [6,6'-2H2]-glucose administration using time-resolved 3D 2H FID-MRSI with elliptical phase encoding at 7T and 3D 1H FID-MRSI with a non-Cartesian concentric ring trajectory readout at clinical 3T.

RESULTS

One hour after oral tracer administration regionally averaged deuterium labeled Glx4 concentrations and the dynamics were not significantly different over all participants between 7T 2H DMI and 3T 1H QELT data for GM (1.29±0.15 vs. 1.38±0.26 mM, p=0.65 & 21±3 vs. 26±3 µM/min, p=0.22) and WM (1.10±0.13 vs. 0.91±0.24 mM, p=0.34 & 19±2 vs. 17±3 µM/min, p=0.48). Also, the observed time constants of dynamic Glc6 data in GM (24±14 vs. 19±7 min, p=0.65) and WM (28±19 vs. 18±9 min, p=0.43) dominated regions showed no significant differences. Between individual 2H and 1H data points a weak to moderate negative correlation was observed for Glx4 concentrations in GM (r=-0.52, p<0.001), and WM (r=-0.3, p<0.001) dominated regions, while a strong negative correlation was observed for Glc6 data GM (r=-0.61, p<0.001) and WM (r=-0.70, p<0.001).

CONCLUSION

This study demonstrates that indirect detection of deuterium labeled compounds using 1H QELT MRSI at widely available clinical 3T without additional hardware is able to reproduce absolute concentration estimates of downstream glucose metabolites and the dynamics of glucose uptake compared to 2H DMI data acquired at 7T. This suggests significant potential for widespread application in clinical settings especially in environments with limited access to ultra-high field scanners and dedicated RF hardware.

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.

The Psychosis Human Connectome Project: Design and rationale for studies of visual neurophysiology

Visual perception is abnormal in psychotic disorders such as schizophrenia. In addition to hallucinations, laboratory tests show differences in fundamental visual processes including contrast sensitivity, center-surround interactions, and perceptual organization. A number of hypotheses have been proposed to explain visual dysfunction in psychotic disorders, including an imbalance between excitation and inhibition. However, the precise neural basis of abnormal visual perception in people with psychotic psychopathology (PwPP) remains unknown. Here, we describe the behavioral and 7 tesla MRI methods we used to interrogate visual neurophysiology in PwPP as part of the Psychosis Human Connectome Project (HCP). In addition to PwPP (n = 66) and healthy controls (n = 43), we also recruited first-degree biological relatives (n = 44) in order to examine the role of genetic liability for psychosis in visual perception. Our visual tasks were designed to assess fundamental visual processes in PwPP, whereas MR spectroscopy enabled us to examine neurochemistry, including excitatory and inhibitory markers. We show that it is feasible to collect high-quality data across multiple psychophysical, functional MRI, and MR spectroscopy experiments with a sizable number of participants at a single research site. These data, in addition to those from our previously described 3 tesla experiments, will be made publicly available in order to facilitate further investigations by other research groups. By combining visual neuroscience techniques and HCP brain imaging methods, our experiments offer new opportunities to investigate the neural basis of abnormal visual perception in PwPP.

Quantification of GABA concentration measured noninvasively in the human posterior cingulate cortex with 7 T ultra-short-TE MR spectroscopy

PURPOSE

The increased spectral dispersion achieved at ultra-high field permits quantification of γ-aminobutyric acid (GABA) concentrations at ultra-short-TE without editing. This work investigated the influence of spectral quality and different LCModel fitting approaches on quantification of GABA. Additionally, the sensitivity with which cross-sectional and longitudinal variations in GABA concentrations can be observed was characterized.

METHODS

In - vivo spectra were acquired in the posterior cingulate cortex of 10 volunteers at 7 T using a STEAM sequence. Synthetically altered spectra with different levels of GABA signals were used to investigate the reliability of GABA quantification with different LCModel fitting approaches and different realizations of SNR. The synthetically altered spectra were also used to characterize the sensitivity of GABA quantification.

RESULTS

The best LCModel fitting approach used stiff spline baseline, no soft constraints, and measured macromolecules in the basis set. With lower SNR, coefficients of variation increased dramatically. Longitudinal and cross-sectional variations in GABA of 10% could be detected with 79 and 48 participants per group, respectively. However, the small cohort may bias the calculation of the coefficients of variation and of the sample size that would be needed to detect variations in GABA.

CONCLUSION

Reliable quantification of normal and abnormal GABA concentrations was achieved for high quality 7 T spectra using LCModel fitting.

Does the change in glutamate to GABA ratio correlate with change in depression severity? A randomized, double-blind clinical trial

Previous proton magnetic resonance spectroscopy (¹H-MRS) studies suggest a perturbation in glutamate and/or GABA in Major Depressive Disorder (MDD). However, no studies examine the ratio of glutamate and glutamine (Glx) to GABA (Glx/GABA) as it relates to depressive symptoms, which may be more sensitive than either single metabolite. Using a within-subject design, we hypothesized that reduction in depressive symptoms correlates with reduction in Glx/GABA in the anterior cingulate cortex (ACC). The present trial is a randomized clinical trial that utilized ¹H-MRS to examine Glx/GABA before and after 8 weeks of escitalopram or placebo. Participants completed the 17-item Hamilton Depression Rating Scale (HDRS₁₇) and underwent magnetic resonance spectroscopy before and after treatment. Two GABA-edited MEGA-PRESS acquisitions were interleaved with a water unsuppressed reference scan. GABA and Glx were quantified from the average difference spectrum, with preprocessing using Gannet and spectral fitting using TARQUIN. Linear mixed models were utilized to evaluate relationships between change in HDRS₁₇ and change in Glx/GABA using a univariate linear regression model, multiple linear regression incorporating treatment type as a covariate, and Bayes Factor (BF) hypothesis testing to examine strength of evidence. No significant relationship was detected between percent change in Glx, GABA, or Glx/GABA and percent change in HDRS₁₇, regardless of treatment type. Further, MDD severity before/after treatment did not correlate with ACC Glx/GABA. In light of variable findings in the literature and lack of association in our investigation, future directions should include evaluating glutamate and glutamine individually to shed light on the underpinnings of MDD severity. Advancing Personalized Antidepressant Treatment Using PET/MRI, ClinicalTrials.gov, NCT02623205.

Comparison of seven modelling algorithms for γ-aminobutyric acid-edited proton magnetic resonance spectroscopy

Edited MRS sequences are widely used for studying γ-aminobutyric acid (GABA) in the human brain. Several algorithms are available for modelling these data, deriving metabolite concentration estimates through peak fitting or a linear combination of basis spectra. The present study compares seven such algorithms, using data obtained in a large multisite study. GABA-edited (GABA+, TE = 68 ms MEGA-PRESS) data from 222 subjects at 20 sites were processed via a standardised pipeline, before modelling with FSL-MRS, Gannet, AMARES, QUEST, LCModel, Osprey and Tarquin, using standardised vendor-specific basis sets (for GE, Philips and Siemens) where appropriate. After referencing metabolite estimates (to water or creatine), systematic differences in scale were observed between datasets acquired on different vendors' hardware, presenting across algorithms. Scale differences across algorithms were also observed. Using the correlation between metabolite estimates and voxel tissue fraction as a benchmark, most algorithms were found to be similarly effective in detecting differences in GABA+. An interclass correlation across all algorithms showed single-rater consistency for GABA+ estimates of around 0.38, indicating moderate agreement. Upon inclusion of a basis set component explicitly modelling the macromolecule signal underlying the observed 3.0 ppm GABA peaks, single-rater consistency improved to 0.44. Correlation between discrete pairs of algorithms varied, and was concerningly weak in some cases. Our findings highlight the need for consensus on appropriate modelling parameters across different algorithms, and for detailed reporting of the parameters adopted in individual studies to ensure reproducibility and meaningful comparison of outcomes between different studies.

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.