MP-PCA denoising for diffusion MRS data: promises and pitfalls

Fast High-Resolution Metabolite Mapping in the rat Brain Using 1H-FID-MRSI at 14.1 T

Magnetic resonance spectroscopic imaging (MRSI) enables the simultaneous noninvasive acquisition of MR spectra from multiple spatial locations inside the brain. Although 1H-MRSI is increasingly used in the human brain, it is not yet widely applied in the preclinical setting, mostly because of difficulties specifically related to very small nominal voxel size in the rat brain and low concentration of brain metabolites, resulting in low signal-to-noise ratio (SNR). In this context, we implemented a free induction decay 1H-MRSI sequence (1H-FID-MRSI) in the rat brain at 14.1 T. We combined the advantages of 1H-FID-MRSI with the ultra-high magnetic field to achieve higher SNR, coverage, and spatial resolution in the rat brain and developed a custom dedicated processing pipeline with a graphical user interface for Bruker 1H-FID-MRSI: MRS4Brain toolbox. LCModel fit, using the simulated metabolite basis set and in vivo measured MM, provided reliable fits for the data at acquisition delays of 1.30 ms. The resulting Cramér-Rao lower bounds were sufficiently low (< 30%) for eight metabolites of interest (total creatine, N-acetylaspartate, N-acetylaspartate + N-acetylaspartylglutamate, total choline, glutamine, glutamate, myo-inositol, and taurine), leading to highly reproducible metabolic maps. Similar spectral quality and metabolic maps were obtained with one and two averages, with slightly better contrast and brain coverage due to increased SNR in the latter case. Furthermore, the obtained metabolic maps were accurate enough to confirm the previously known brain regional distribution of some metabolites. The acquisitions proved high reproducibility over time. We demonstrated that the increased SNR and spectral resolution at 14.1 T can be translated into high spatial resolution in 1H-FID-MRSI of the rat brain in 13 min using the sequence and processing pipeline described herein. High-resolution 1H-FID-MRSI at 14.1 T provided robust, reproducible, and high-quality metabolic mapping of brain metabolites with minimal technical limitations.

Fast 3D 31P B 1 + mapping with a weighted stack of spiral trajectory at 7 T

PURPOSE

Phosphorus MRS (31P MRS) enables noninvasive assessment of energy metabolism, yet its application is hindered by sensitivity limitations. To overcome this, often high magnetic fields are used, leading to challenges such as spatialB 1 + $$ {\mathrm{B}}_1^{+} $$ inhomogeneity and therefore the need for accurate flip-angle determination in accelerated acquisitions with short TRs. In response to these challenges, we propose a novel short TR and look-up table-based double-angle method for fast 3D 31PB 1 + $$ {\mathrm{B}}_1^{+} $$ mapping (fDAM).

METHODS

Our method incorporates 3D weighted stack-of-spiral gradient-echo acquisitions and a frequency-selective pulse to enable efficientB 1 + $$ {\mathrm{B}}_1^{+} $$ mapping based on the phosphocreatine signal at 7 T. Protocols were optimized using simulations and validated through phantom experiments. The method was validated in the human brain using a 31P 1Ch-trasmit/32Ch-receive coil and skeletal muscle using a birdcage 1H/31P volume coil.

RESULTS

The results of fDAM were compared with the classical DAM. A good correlation (r = 0.95) was obtained between the twoB 1 + $$ {\mathrm{B}}_1^{+} $$ maps. A 3D 31PB 1 + $$ {\mathrm{B}}_1^{+} $$ mapping in the human calf muscle was achieved in about 10:50 min using a birdcage volume coil, with a 20% extended coverage (number of voxels with SNR > 3) relative to that of the classical DAM (24 min). fDAM also enabled the first full-brain coverage 31P 3DB 1 + $$ {\mathrm{B}}_1^{+} $$ mapping in approximately 10:15 min using a 1Ch-transmit/32Ch-receive coil.

CONCLUSION

fDAM is an efficient method for 31P 3DB 1 + $$ {\mathrm{B}}_1^{+} $$ mapping, showing promise for future applications in rapid 31P MRSI.

Mapping Activity and Functional Organisation of the Motor and Visual Pathways Using ADC-fMRI in the Human Brain

In contrast to blood-oxygenation level-dependent (BOLD) functional MRI (fMRI), which relies on changes in blood flow and oxygenation levels to infer brain activity, diffusion fMRI (DfMRI) investigates brain dynamics by monitoring alterations in the apparent diffusion coefficient (ADC) of water. These ADC changes may arise from fluctuations in neuronal morphology, providing a distinctive perspective on neural activity. The potential of ADC as an fMRI contrast (ADC-fMRI) lies in its capacity to reveal neural activity independently of neurovascular coupling, thus yielding complementary insights into brain function. To demonstrate the specificity and value of ADC-fMRI, both ADC- and BOLD-fMRI data were collected at 3 T in human subjects during visual stimulation and motor tasks. The first aim of this study was to identify an acquisition design for ADC that minimises BOLD contributions. By examining the timings in responses, we report that ADC 0/1 timeseries (acquired with b values of 0 and 1 ms/μm 2 $$ {\upmu \mathrm{m}}^2 $$ ) exhibit residual vascular contamination, while ADC 0.2/1 timeseries (with b values of 0.2 and 1 ms/μm 2 $$ {\upmu \mathrm{m}}^2 $$ ) show minimal BOLD influence and higher sensitivity to neuromorphological coupling. Second, a general linear model was employed to identify activation clusters for ADC 0.2/1 and BOLD, from which the average ADC and BOLD responses were calculated. The negative ADC response exhibited a significantly reduced delay relative to the task onset and offset as compared to BOLD. This early onset further supports the notion that ADC is sensitive to neuromorphological rather than neurovascular coupling. Remarkably, in the group-level analysis, positive BOLD activation clusters were detected in the visual and motor cortices, while the negative ADC clusters mainly highlighted pathways in white matter connected to the motor cortex. In the averaged individual level analysis, negative ADC activation clusters were also present in the visual cortex. This finding confirmed the reliability of negative ADC as an indicator of brain function, even in regions with lower vascularisation such as white matter. Finally, we established that ADC-fMRI time courses yield the expected functional organisation of the visual system, including both grey and white matter regions of interest. Functional connectivity matrices were used to perform hierarchical clustering of brain regions, where ADC-fMRI successfully reproduced the expected structure of the dorsal and ventral visual pathways. This organisation was not replicated with the b = 0.2 ms/μm 2 $$ {\upmu \mathrm{m}}^2 $$ diffusion-weighted time courses, which can be seen as a proxy for BOLD (via T2-weighting). These findings underscore the robustness of ADC time courses in functional MRI studies, offering complementary insights into BOLD-fMRI regarding brain function and connectivity patterns.

In vivo mapping of postprandial hepatic glucose metabolism using dynamic magnetic resonance spectroscopy combined with stable isotope flux analysis in Roux-en-Y gastric bypass adults and non-operated controls: A case-control study

AIMS

Roux-en-Y gastric bypass (RYGB) surgery alters postprandial glucose profiles, causing post-bariatric hypoglycaemia (PBH) in some individuals. Due to the liver's central role in glucose homeostasis, hepatic glucose handling might differ in RYGB-operated patients with PBH compared to non-operated healthy controls (HC).

MATERIALS AND METHODS

We enrolled RYGB-operated adults with PBH and HCs (n = 10 each). Participants ingested 60 g of [6,6'-2H2]-glucose (d-glucose) after an overnight fast. Deuterium metabolic imaging (DMI) with interleaved 13C magnetic resonance spectroscopy was performed before and until 150 min post-d-glucose intake, with frequent blood sampling to quantify glucose enrichment and gluco-regulatory hormones until 180 min. Glucose fluxes were assessed by mathematical modelling. Outcome trajectories were described using generalized additive models.

RESULTS

In RYGB subjects, the hepatic d-glucose signal increased early, followed by a decrease, whereas HCs exhibited a gradual increase and consecutive stabilization. Postprandial hepatic glycogen accumulation and the suppression of endogenous glucose production were lower in RYGB patients than in HCs, despite higher insulin exposure, indicating lower hepatic insulin sensitivity. The systemic rate of ingested d-glucose was faster in RYGB, leading to a higher, earlier plasma glucose peak and increased insulin secretion. Postprandial glucose disposal increased in RYGB patients, without between-group differences in peripheral insulin sensitivity.

CONCLUSIONS

Exploiting DMI with stable isotope flux analysis, we observed distinct postprandial hepatic glucose trajectories and parameters of glucose-insulin homeostasis in RYGB patients with PBH versus HCs. Despite altered postprandial glucose kinetics and higher insulin exposure, there was no evidence of impaired hepatic glucose uptake or output predisposing to PBH in RYGB patients.

Noise-reduction techniques for 1H-FID-MRSI at 14.1 T: Monte Carlo validation and in vivo application

Proton magnetic resonance spectroscopic imaging (1H-MRSI) is a powerful tool that enables the multidimensional non-invasive mapping of the neurochemical profile at high resolution over the entire brain. The constant demand for higher spatial resolution in 1H-MRSI has led to increased interest in post-processing-based denoising methods aimed at reducing noise variance. The aim of the present study was to implement two noise-reduction techniques, Marchenko-Pastur principal component analysis (MP-PCA) based denoising and low-rank total generalized variation (LR-TGV) reconstruction, and to test their potential with and impact on preclinical 14.1 T fast in vivo 1H-FID-MRSI datasets. Since there is no known ground truth for in vivo metabolite maps, additional evaluations of the performance of both noise-reduction strategies were conducted using Monte Carlo simulations. Results showed that both denoising techniques increased the apparent signal-to-noise ratio (SNR) while preserving noise properties in each spectrum for both in vivo and Monte Carlo datasets. Relative metabolite concentrations were not significantly altered by either method and brain regional differences were preserved in both synthetic and in vivo datasets. Increased precision of metabolite estimates was observed for the two methods, with inconsistencies noted for lower-concentration metabolites. Our study provided a framework for how to evaluate the performance of MP-PCA and LR-TGV methods for preclinical 1H-FID MRSI data at 14.1 T. While gains in apparent SNR and precision were observed, concentration estimations ought to be treated with care, especially for low-concentration metabolites.

Deep learning method with integrated invertible wavelet scattering for improving the quality ofin vivocardiac DTI

Objective.Respiratory motion, cardiac motion and inherently low signal-to-noise ratio (SNR) are major limitations ofin vivocardiac diffusion tensor imaging (DTI). We propose a novel enhancement method that uses unsupervised learning based invertible wavelet scattering (IWS) to improve the quality ofin vivocardiac DTI.Approach.Our method starts by extracting nearly transformation-invariant features from multiple cardiac diffusion-weighted (DW) image acquisitions using multi-scale wavelet scattering (WS). Then, the relationship between the WS coefficients and DW images is learned through a multi-scale encoder and a decoder network. Using the trained encoder, the deep features of WS coefficients of multiple DW image acquisitions are further extracted and then fused using an average rule. Finally, using the fused WS features and trained decoder, the enhanced DW images are derived.Main result.We evaluate the performance of the proposed method by comparing it with several methods on threein vivocardiac DTI datasets in terms of SNR, contrast to noise ratio (CNR), fractional anisotropy (FA), mean diffusivity (MD) and helix angle (HA). Comparing against the best comparison method, SNR/CNR of diastolic, gastric peristalsis influenced, and end-systolic DW images were improved by 1%/16%, 5%/6%, and 56%/30%, respectively. The approach also yielded consistent FA and MD values and more coherent helical fiber structures than the comparison methods used in this work.Significance.The ablation results verify that using the transformation-invariant and noise-robust wavelet scattering features enables us to effectively explore the useful information from the limited data, providing a potential mean to alleviate the dependence of the fusion results on the number of repeated acquisitions, which is beneficial for dealing with the issues of noise and residual motion simultaneously and therefore improving the quality ofinvivocardiac DTI. Code can be found inhttps://github.com/strawberry1996/WS-MCNN.

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.

Practical considerations of diffusion-weighted MRS with ultra-strong diffusion gradients

Introduction

Diffusion-weighted magnetic resonance spectroscopy (DW-MRS) offers improved cellular specificity to microstructure-compared to water-based methods alone-but spatial resolution and SNR is severely reduced and slow-diffusing metabolites necessitate higher b-values to accurately characterize their diffusion properties. Ultra-strong gradients allow access to higher b-values per-unit time, higher SNR for a given b-value, and shorter diffusion times, but introduce additional challenges such as eddy-current artefacts, gradient non-uniformity, and mechanical vibrations.

Methods

In this work, we present initial DW-MRS data acquired on a 3T Siemens Connectom scanner equipped with ultra-strong (300 mT/m) gradients. We explore the practical issues associated with this manner of acquisition, the steps that may be taken to mitigate their impact on the data, and the potential benefits of ultra-strong gradients for DW-MRS. An in-house DW-PRESS sequence and data processing pipeline were developed to mitigate the impact of these confounds. The interaction of TE, b-value, and maximum gradient amplitude was investigated using simulations and pilot data, whereby maximum gradient amplitude was restricted. Furthermore, two DW-MRS voxels in grey and white matter were acquired using ultra-strong gradients and high b-values.

Results

Simulations suggest T2-based SNR gains that are experimentally confirmed. Ultra-strong gradient acquisitions exhibit similar artefact profiles to those of lower gradient amplitude, suggesting adequate performance of artefact mitigation strategies. Gradient field non-uniformity influenced ADC estimates by up to 4% when left uncorrected. ADC and Kurtosis estimates for tNAA, tCho, and tCr align with previously published literature.

Discussion

In conclusion, we successfully implemented acquisition and data processing strategies for ultra-strong gradient DW-MRS and results indicate that confounding effects of the strong gradient system can be ameliorated, while achieving shorter diffusion times and improved metabolite SNR.

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.

Singular vectors of sums of rectangular random matrices and optimal estimation of high-rank signals: The extensive spike model

Across many disciplines spanning from neuroscience and genomics to machine learning, atmospheric science, and finance, the problems of denoising large data matrices to recover hidden signals obscured by noise, and of estimating the structure of these signals, is of fundamental importance. A key to solving these problems lies in understanding how the singular value structure of a signal is deformed by noise. This question has been thoroughly studied in the well-known spiked matrix model, in which data matrices originate from low-rank signal matrices perturbed by additive noise matrices, in an asymptotic limit where matrix size tends to infinity but the signal rank remains finite. We first show, strikingly, that the singular value structure of large finite matrices (of size ∼1000) with even moderate-rank signals, as low as 10, is not accurately predicted by the finite-rank theory, thereby limiting the application of this theory to real data. To address these deficiencies, we analytically compute how the singular values and vectors of an arbitrary high-rank signal matrix are deformed by additive noise. We focus on an asymptotic limit corresponding to an extensive spike model, in which both the signal rank and the size of the data matrix tend to infinity at a constant ratio. We map out the phase diagram of the singular value structure of the extensive spike model as a joint function of signal strength and rank. We further exploit these analytics to derive optimal rotationally invariant denoisers to recover the hidden high-rank signal from the data, as well as optimal invariant estimators of the signal covariance structure. Our extensive-rank results yield several conceptual differences compared to the finite-rank case: (1) as signal strength increases, the singular value spectrum does not directly transition from a unimodal bulk phase to a disconnected phase, but instead there is a bimodal connected regime separating them; (2) the signal singular vectors can be partially estimated even in the unimodal bulk regime, and thus the transitions in the data singular value spectrum do not coincide with a detectability threshold for the signal singular vectors, unlike in the finite-rank theory; (3) signal singular values interact nontrivially to generate data singular values in the extensive-rank model, whereas they are noninteracting in the finite-rank theory; and (4) as a result, the more sophisticated data denoisers and signal covariance estimators we derive, which take into account these nontrivial extensive-rank interactions, significantly outperform their simpler, noninteracting, finite-rank counterparts, even on data matrices of only moderate rank. Overall, our results provide fundamental theory governing how high-dimensional signals are deformed by additive noise, together with practical formulas for optimal denoising and covariance estimation.

Mapping tissue microstructure across the human brain on a clinical scanner with soma and neurite density image metrics

Soma and neurite density image (SANDI) is an advanced diffusion magnetic resonance imaging biophysical signal model devised to probe in vivo microstructural information in the gray matter (GM). This model requires acquisitions that include b values that are at least six times higher than those used in clinical practice. Such high b values are required to disentangle the signal contribution of water diffusing in soma from that diffusing in neurites and extracellular space, while keeping the diffusion time as short as possible to minimize potential bias due to water exchange. These requirements have limited the use of SANDI only to preclinical or cutting-edge human scanners. Here, we investigate the potential impact of neglecting water exchange in the SANDI model and present a 10-min acquisition protocol that enables to characterize both GM and white matter (WM) on 3 T scanners. We implemented analytical simulations to (i) evaluate the stability of the fitting of SANDI parameters when diminishing the number of shells; (ii) estimate the bias due to potential exchange between neurites and extracellular space in such reduced acquisition scheme, comparing it with the bias due to experimental noise. Then, we demonstrated the feasibility and assessed the repeatability and reproducibility of our approach by computing microstructural metrics of SANDI with AMICO toolbox and other state-of-the-art models on five healthy subjects. Finally, we applied our protocol to five multiple sclerosis patients. Results suggest that SANDI is a practical method to characterize WM and GM tissues in vivo on performant clinical scanners.

Artificial intelligence for diffusion MRI-based tissue microstructure estimation in the human brain: an overview

Artificial intelligence (AI) has made significant advances in the field of diffusion magnetic resonance imaging (dMRI) and other neuroimaging modalities. These techniques have been applied to various areas such as image reconstruction, denoising, detecting and removing artifacts, segmentation, tissue microstructure modeling, brain connectivity analysis, and diagnosis support. State-of-the-art AI algorithms have the potential to leverage optimization techniques in dMRI to advance sensitivity and inference through biophysical models. While the use of AI in brain microstructures has the potential to revolutionize the way we study the brain and understand brain disorders, we need to be aware of the pitfalls and emerging best practices that can further advance this field. Additionally, since dMRI scans rely on sampling of the q-space geometry, it leaves room for creativity in data engineering in such a way that it maximizes the prior inference. Utilization of the inherent geometry has been shown to improve general inference quality and might be more reliable in identifying pathological differences. We acknowledge and classify AI-based approaches for dMRI using these unifying characteristics. This article also highlighted and reviewed general practices and pitfalls involving tissue microstructure estimation through data-driven techniques and provided directions for building on them.

MP-PCA denoising of fMRI time-series data can lead to artificial activation "spreading"

MP-PCA denoising has become the method of choice for denoising MRI data since it provides an objective threshold to separate the signal components from unwanted thermal noise components. In rodents, thermal noise in the coils is an important source of noise that can reduce the accuracy of activation mapping in fMRI. Further confounding this problem, vendor data often contains zero-filling and other post-processing steps that may violate MP-PCA assumptions. Here, we develop an approach to denoise vendor data and assess activation "spreading" caused by MP-PCA denoising in rodent task-based fMRI data. Data was obtained from N = 3 mice using conventional multislice and ultrafast acquisitions (1 s and 50 ms temporal resolution, respectively), during visual stimulation. MP-PCA denoising produced SNR gains of 64% and 39% and Fourier Spectral Amplitude (FSA) increases in BOLD maps of 9% and 7% for multislice and ultrafast data, respectively, when using a small [2 2] denoising window. Larger windows provided higher SNR and FSA gains with increased spatial extent of activation that may or may not represent real activation. Simulations showed that MP-PCA denoising can incur activation "spreading" with increased false positive rate and smoother functional maps due to local "bleeding" of principal components, and that the optimal denoising window for improved specificity of functional mapping, based on Dice score calculations, depends on the data's tSNR and functional CNR. This "spreading" effect applies also to another recently proposed low-rank denoising method (NORDIC), although to a lesser degree. Our results bode well for enhancing spatial and/or temporal resolution in future fMRI work, while taking into account the sensitivity/specificity trade-offs of low-rank denoising methods.