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.

In Vivo Myelin Water Quantification Using Diffusion-Relaxation Correlation MRI: A Comparison of 1D and 2D Methods.

Multidimensional Magnetic Resonance Imaging (MRI) is a versatile tool for microstructure mapping. We use a diffusion weighted inversion recovery spin echo (DW-IR-SE) sequence with spiral readouts at ultra-strong gradients to acquire a rich diffusion-relaxation data set with sensitivity to myelin water. We reconstruct 1D and 2D spectra with a two-step convex optimization approach and investigate a variety of multidimensional MRI methods, including 1D multi-component relaxometry, 1D multi-component diffusometry, 2D relaxation correlation imaging, and 2D diffusion-relaxation correlation spectroscopic imaging (DR-CSI), in terms of their potential to quantify tissue microstructure, including the myelin water fraction (MWF). We observe a distinct spectral peak that we attribute to myelin water in multi-component T1 relaxometry, T1-T2 correlation, T1-D correlation, and T2-D correlation imaging. Due to lower achievable echo times compared to diffusometry, MWF maps from relaxometry have higher quality. Whilst 1D multi-component T1 data allows much faster myelin mapping, 2D approaches could offer unique insights into tissue microstructure and especially myelin diffusion.

Microglial morphometric analysis: so many options, so little consistency.

Quantification of microglial activation through morphometric analysis has long been a staple of the neuroimmunologist's toolkit. Microglial morphological phenomics can be conducted through either manual classification or constructing a digital skeleton and extracting morphometric data from it. Multiple open-access and paid software packages are available to generate these skeletons via semi-automated and/or fully automated methods with varying degrees of accuracy. Despite advancements in methods to generate morphometrics (quantitative measures of cellular morphology), there has been limited development of tools to analyze the datasets they generate, in particular those containing parameters from tens of thousands of cells analyzed by fully automated pipelines. In this review, we compare and critique the approaches using cluster analysis and machine learning driven predictive algorithms that have been developed to tackle these large datasets, and propose improvements for these methods. In particular, we highlight the need for a commitment to open science from groups developing these classifiers. Furthermore, we call attention to a need for communication between those with a strong software engineering/computer science background and neuroimmunologists to produce effective analytical tools with simplified operability if we are to see their wide-spread adoption by the glia biology community.

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.

Comprehensive Brain Tumour Characterisation with VERDICT-MRI: Evaluation of Cellular and Vascular Measures Validated by Histology.

The aim of this work was to extend the VERDICT-MRI framework for modelling brain tumours, enabling comprehensive characterisation of both intra- and peritumoural areas with a particular focus on cellular and vascular features. Diffusion MRI data were acquired with multiple b-values (ranging from 50 to 3500 s/mm2), diffusion times, and echo times in 21 patients with brain tumours of different types and with a wide range of cellular and vascular features. We fitted a selection of diffusion models that resulted from the combination of different types of intracellular, extracellular, and vascular compartments to the signal. We compared the models using criteria for parsimony while aiming at good characterisation of all of the key histological brain tumour components. Finally, we evaluated the parameters of the best-performing model in the differentiation of tumour histotypes, using ADC (Apparent Diffusion Coefficient) as a clinical standard reference, and compared them to histopathology and relevant perfusion MRI metrics. The best-performing model for VERDICT in brain tumours was a three-compartment model accounting for anisotropically hindered and isotropically restricted diffusion and isotropic pseudo-diffusion. VERDICT metrics were compatible with the histological appearance of low-grade gliomas and metastases and reflected differences found by histopathology between multiple biopsy samples within tumours. The comparison between histotypes showed that both the intracellular and vascular fractions tended to be higher in tumours with high cellularity (glioblastoma and metastasis), and quantitative analysis showed a trend toward higher values of the intracellular fraction (fic) within the tumour core with increasing glioma grade. We also observed a trend towards a higher free water fraction in vasogenic oedemas around metastases compared to infiltrative oedemas around glioblastomas and WHO 3 gliomas as well as the periphery of low-grade gliomas. In conclusion, we developed and evaluated a multi-compartment diffusion MRI model for brain tumours based on the VERDICT framework, which showed agreement between non-invasive microstructural estimates and histology and encouraging trends for the differentiation of tumour types and sub-regions.

Higher order diffusion imaging as a putative index of human sleep-related microstructural changes and glymphatic clearance.

The brain has a unique macroscopic waste clearance system, termed the glymphatic system which utilises perivascular tunnels surrounded by astroglia to promote cerebrospinal-interstitial fluid exchange. Rodent studies have demonstrated a marked increase in glymphatic clearance during sleep which has been linked to a sleep-induced expansion of the extracellular space and concomitant reduction in intracellular volume. However, despite being implicated in the pathophysiology of multiple human neurodegenerative disorders, non-invasive techniques for imaging glymphatic clearance in humans are currently limited. Here we acquired multi-shell diffusion weighted MRI (dwMRI) in twenty-one healthy young participants (6 female, 22.3 ± 3.2 years) each scanned twice, once during wakefulness and once during sleep induced by a combination of one night of sleep deprivation and 10 mg of the hypnotic zolpidem 30 min before scanning. To capture hypothesised sleep-associated changes in intra/extracellular space, dwMRI were analysed using higher order diffusion modelling with the prediction that sleep-associated increases in interstitial (extracellular) fluid volume would result in a decrease in diffusion kurtosis, particularly in areas associated with slow wave generation at the onset of sleep. In line with our hypothesis, we observed a global reduction in diffusion kurtosis (t15=2.82, p = 0.006) during sleep as well as regional reductions in brain areas associated with slow wave generation during early sleep and default mode network areas that are highly metabolically active during wakefulness. Analysis with a higher-order representation of diffusion (MAP-MRI) further indicated that changes within the intra/extracellular domain rather than membrane permeability likely underpin the observed sleep-associated decrease in kurtosis. These findings identify higher-order modelling of dwMRI as a potential new non-invasive method for imaging glymphatic clearance and extend rodent findings to suggest that sleep is also associated with an increase in interstitial fluid volume in humans.

Dysfunction of the hypothalamic-pituitary adrenal axis and its influence on aging: the role of the hypothalamus.

As part of the hypothalamic-pituitary adrenal (HPA) axis, the hypothalamus exerts pivotal influence on metabolic and endocrine homeostasis. With age, these processes are subject to considerable change, resulting in increased prevalence of physical disability and cardiac disorders. Yet, research on the aging human hypothalamus is lacking. To assess detailed hypothalamic microstructure in middle adulthood, 39 healthy participants (35-65 years) underwent comprehensive structural magnetic resonance imaging. In addition, we studied HPA axis dysfunction proxied by hair cortisol and waist circumference as potential risk factors for hypothalamic alterations. We provide first evidence of regionally different hypothalamic microstructure, with age effects in its anterior-superior subunit, a critical area for HPA axis regulation. Further, we report that waist circumference was related to increased free water and decreased iron content in this region. In age, hair cortisol was additionally associated with free water content, such that older participants with higher cortisol levels were more vulnerable to free water content increase than younger participants. Overall, our results suggest no general age-related decline in hypothalamic microstructure. Instead, older individuals could be more susceptible to risk factors of hypothalamic decline especially in the anterior-superior subregion, including HPA axis dysfunction, indicating the importance of endocrine and stress management in age.

Temporal Diffusion Ratio (TDR) for imaging restricted diffusion: Optimisation and pre-clinical demonstration.

Temporal Diffusion Ratio (TDR) is a recently proposed dMRI technique (Dell'Acqua et al., proc. ISMRM 2019) which provides contrast between areas with restricted diffusion and areas either without restricted diffusion or with length scales too small for characterisation. Hence, it has a potential for informing on pore sizes, in particular the presence of large axon diameters or other cellular structures. TDR employs the signal from two dMRI acquisitions obtained with the same, large, b-value but with different diffusion gradient waveforms. TDR is advantageous as it employs standard acquisition sequences, does not make any assumptions on the underlying tissue structure and does not require any model fitting, avoiding issues related to model degeneracy. This work for the first time introduces and optimises the TDR method in simulation for a range of different tissues and scanner constraints and validates it in a pre-clinical demonstration. We consider both substrates containing cylinders and spherical structures, representing cell soma in tissue. Our results show that contrasting an acquisition with short gradient duration, short diffusion time and high gradient strength with an acquisition with long gradient duration, long diffusion time and low gradient strength, maximises the TDR contrast for a wide range of pore configurations. Additionally, in the presence of Rician noise, computing TDR from a subset (50% or fewer) of the acquired diffusion gradients rather than the entire shell as proposed originally further improves the contrast. In the last part of the work the results are demonstrated experimentally on rat spinal cord. In line with simulations, the experimental data shows that optimised TDR improves the contrast compared to non-optimised TDR. Furthermore, we find a strong correlation between TDR and histology measurements of axon diameter. In conclusion, we find that TDR has great potential and is a very promising alternative (or potentially complement) to model-based approaches for informing on pore sizes and restricted diffusion in general.

Joint estimation of relaxation and diffusion tissue parameters for prostate cancer with relaxation-VERDICT MRI.

This work presents a biophysical model of diffusion and relaxation MRI for prostate called relaxation vascular, extracellular and restricted diffusion for cytometry in tumours (rVERDICT). The model includes compartment-specific relaxation effects providing T1/T2 estimates and microstructural parameters unbiased by relaxation properties of the tissue. 44 men with suspected prostate cancer (PCa) underwent multiparametric MRI (mp-MRI) and VERDICT-MRI followed by targeted biopsy. We estimate joint diffusion and relaxation prostate tissue parameters with rVERDICT using deep neural networks for fast fitting. We tested the feasibility of rVERDICT estimates for Gleason grade discrimination and compared with classic VERDICT and the apparent diffusion coefficient (ADC) from mp-MRI. The rVERDICT intracellular volume fraction fic discriminated between Gleason 3 + 3 and 3 + 4 (p = 0.003) and Gleason 3 + 4 and ≥ 4 + 3 (p = 0.040), outperforming classic VERDICT and the ADC from mp-MRI. To evaluate the relaxation estimates we compare against independent multi-TE acquisitions, showing that the rVERDICT T2 values are not significantly different from those estimated with the independent multi-TE acquisition (p > 0.05). Also, rVERDICT parameters exhibited high repeatability when rescanning five patients (R2 = 0.79-0.98; CV = 1-7%; ICC = 92-98%). The rVERDICT model allows for accurate, fast and repeatable estimation of diffusion and relaxation properties of PCa sensitive enough to discriminate Gleason grades 3 + 3, 3 + 4 and ≥ 4 + 3.

Microstructural parameters from DW-MRI for tumour characterization and local recurrence prediction in particle therapy of skull-base chordoma.

BACKGROUND: Quantitative imaging such as Diffusion-Weighted MRI (DW-MRI) can be exploited to non-invasively derive patient-specific tumor microstructure information for tumor characterization and local recurrence risk prediction in radiotherapy. PURPOSE: To characterize tumor microstructure according to proliferative capacity and predict local recurrence through microstructural markers derived from pre-treatment conventional DW-MRI, in skull-base chordoma (SBC) patients treated with proton (PT) and carbon ion (CIRT) radiotherapy. METHODS: Forty-eight patients affected by SBC, who underwent conventional DW-MRI before treatment and were enrolled for CIRT (n = 25) or PT (n = 23), were retrospectively selected. Clinically verified local recurrence information (LR) and histological information (Ki-67, proliferation index) were collected. Apparent diffusion coefficient (ADC) maps were calculated from pre-treatment DW-MRI and, from these, a set of microstructural parameters (cellular radius R, volume fraction vf, diffusion D) were derived by applying a fine-tuning procedure to a framework employing Monte Carlo simulations on synthetic cell substrates. In addition, apparent cellularity (ρapp ) was estimated from vf and R for an easier clinical interpretation. Histogram-based metrics (mean, median, variance, entropy) from estimated parameters were considered to investigate differences (Mann-Whitney U-test, α = 0.05) in estimated tumor microstructure in SBCs characterized by low or high cell proliferation (Ki-67). Recurrence-free survival analyses were also performed to assess the ability of the microstructural parameters to stratify patients according to the risk of local recurrence (Kaplan-Meier curves, log-rank test α = 0.05). RESULTS: Refined microstructural markers revealed optimal capabilities in discriminating patients according to cell proliferation, achieving best results with mean values (p-values were 0.0383, 0.0284, 0.0284, 0.0468, and 0.0088 for ADC, R, vf, D, and ρapp, respectively). Recurrence-free survival analyses showed significant differences between populations at high and low risk of local recurrence as stratified by entropy values of estimated microstructural parameters (p = 0.0110). CONCLUSION: Patient-specific microstructural information was non-invasively derived providing potentially useful tools for SBC treatment personalization and optimization in particle therapy.

In vivo quantification of brain soma and neurite density abnormalities in multiple sclerosis.

BACKGROUND: Soma and neurite density imaging (SANDI) is a new biophysical model that incorporates soma in addition to neurite density, thus possibly providing more specific information about the complex pathological processes of multiple sclerosis (MS). PURPOSE: To discriminate the pathological abnormalities of MS white matter (WM) lesions, normal-appearing (NA) WM and cortex and to evaluate the associations among SANDI-derived measures, clinical disability, and conventional MRI variables. METHODS: Twenty healthy controls (HC) and 23 MS underwent a 3 T brain MRI. Using SANDI on diffusion-weighted sequence, the fractions of neurite (fneurite) and soma (fsoma) were assessed in WM lesions, NAWM, and cortex. RESULTS: Compared to HC WM, MS NAWM showed lower fneurite (false discovery rate [FDR]-p = 0.011). In MS patients, WM lesions showed lower fneurite and fsoma compared to both HC and MS NAWM (FDR-p < 0.001 for all). In the cortex, MS patients had lower fneurite and fsoma compared to HC (FDR-p ≤ 0.009). Compared to both HC and RRMS, PMS patients had lower fneurite in NAWM (vs HC: FDR-p < 0.001; vs RRMS: FDR-p = 0.003) and cortex (vs HC: FDR-p < 0.001; vs RRMS: p = 0.031, not surviving FDR correction), and lower cortical fsoma (vs HC: FDR-p < 0.001; vs RRMS: FDR-p = 0.009). Compared to HC, PMS also showed a higher fsoma in NAWM (FDR-p = 0.015). Fneurite and fsoma in the different brain compartments were correlated with age, phenotype, disease duration, disability, WM lesion volumes, normalized brain, cortical, and WM volumes (r from - 0.761 to 0.821, FDR-p ≤ 0.4). CONCLUSIONS: SANDI may represent a clinically relevant model to discriminate different neurodegenerative phenomena that gradually accumulate through MS disease course.

Minimal number of sampling directions for robust measures of the spherical mean diffusion weighted signal: Effects of sampling directions, b-value, signal-to-noise ratio, hardware, and fitting strategy.

Several recent multi-compartment diffusion MRI investigations and modeling strategies have utilized the orientationally-averaged, or spherical mean, diffusion-weighted signal to study tissue microstructure of the central nervous system. Most experimental designs sample a large number of diffusion weighted directions in order to calculate the spherical mean signal, however, sampling a subset of these directions may increase scanning efficiency and enable either a decrease in scan time or the ability to sample more diffusion weightings. Here, we aim to determine the minimum number of gradient directions needed for a robust measurement of the spherical mean signal. We used computer simulations to characterize the variation of the measured spherical mean signal as a function of the number of gradient directions, while also investigating the effects of diffusion weighting (b-value), signal-to-noise ratio (SNR), available hardware, and spherical mean fitting strategy. We then utilize empirically acquired data in the brain and spinal cord to validate simulations, showing experimental results are in good agreement with simulations. We summarize these results by providing an intuitive lookup table to facilitate the determination of the minimal number of sampling directions needed for robust spherical mean measurements, and give recommendations based on SNR and experimental conditions.

Neurite Exchange Imaging (NEXI): A minimal model of diffusion in gray matter with inter-compartment water exchange.

Biophysical models of diffusion in white matter have been center-stage over the past two decades and are essentially based on what is now commonly referred to as the "Standard Model" (SM) of non-exchanging anisotropic compartments with Gaussian diffusion. In this work, we focus on diffusion MRI in gray matter, which requires rethinking basic microstructure modeling blocks. In particular, at least three contributions beyond the SM need to be considered for gray matter: water exchange across the cell membrane - between neurites and the extracellular space; non-Gaussian diffusion along neuronal and glial processes - resulting from structural disorder; and signal contribution from soma. For the first contribution, we propose Neurite Exchange Imaging (NEXI) as an extension of the SM of diffusion, which builds on the anisotropic Kärger model of two exchanging compartments. Using datasets acquired at multiple diffusion weightings (b) and diffusion times (t) in the rat brain in vivo, we investigate the suitability of NEXI to describe the diffusion signal in the gray matter, compared to the other two possible contributions. Our results for the diffusion time window 20-45 ms show minimal diffusivity time-dependence and more pronounced kurtosis decay with time, which is well fit by the exchange model. Moreover, we observe lower signal for longer diffusion times at high b. In light of these observations, we identify exchange as the mechanism that best explains these signal signatures in both low-b and high-b regime, and thereby propose NEXI as the minimal model for gray matter microstructure mapping. We finally highlight multi-b multi-t acquisition protocols as being best suited to estimate NEXI model parameters reliably. Using this approach, we estimate the inter-compartment water exchange time to be 15 - 60 ms in the rat cortex and hippocampus in vivo, which is of the same order or shorter than the diffusion time in typical diffusion MRI acquisitions. This suggests water exchange as an essential component for interpreting diffusion MRI measurements in gray matter.

Soma and Neurite Density MRI (SANDI) of the in-vivo mouse brain and comparison with the Allen Brain Atlas.

Diffusion MRI (dMRI) provides unique insights into the neural tissue milieu by probing interactions between diffusing molecules and tissue microstructure. Most dMRI techniques focus on white matter (WM) tissues, nevertheless, interest in gray matter characterizations is growing. The Soma and Neurite Density MRI (SANDI) methodology harnesses a model incorporating water diffusion in spherical objects (assumed to be associated with cell bodies) and in impermeable "sticks" (assumed to represent neurites), which potentially enables the characterization of cellular and neurite densities. Recognising the importance of rodents in animal models of development, aging, plasticity, and disease, we here employ SANDI for in-vivo preclinical imaging and provide a first validation of the methodology by comparing SANDI metrics with cellular density reflected by the Allen mouse brain atlas. SANDI was implemented on a 9.4T scanner equipped with a cryogenic coil, and in-vivo experiments were carried out on N = 6 mice. Pixelwise, ROI-based, and atlas comparisons were performed, magnitude vs. real-valued analyses were compared, and shorter acquisitions with reduced the number of b-value shells were investigated. Our findings reveal good reproducibility of the SANDI parameters, including the sphere and stick fractions, as well as sphere size (CoV < 7%, 12% and 3%, respectively). Additionally, we find a very good rank correlation between SANDI-driven sphere fraction and Allen mouse brain atlas contrast that represents cellular density. We conclude that SANDI is a viable preclinical MRI technique that can greatly contribute to research on brain tissue microstructure.

Both Gender and Agonistic Experience Affect Perceived Pain during the Cold Pressor Test.

BACKGROUND: Differences in pain perception in athletes have recently been highlighted in the literature. OBJECTIVES: To compare gender ratings of perceived pain in athletes with low and high agonistic experiences (N = 200) using the Cold Pressor Test (CPT). METHODS: A three-way repeated measures ANOVA to assess both the effects of the athletes' gender and lower vs. higher agonistic experiences in the intensity of perceived pain at the beginning of the cold box hand immersion (L0) and after a 90 s interval (L1). RESULTS: There was a statistically significant interaction effect between the level of the agonistic experience and gender in the two moments: p < 0.001; ηp2 = 0.266; F(1,49) = 9.771. Simple main effects analysis showed a significative difference for females at L0: F(1,99) = 93.567, p < 0.025, partial η2 = 0.302) and for males at L1: F(1,99) = 173.420, p < 0.025, partial η2 = 0.666. At the initial moment of CPT, the female athletes showed significantly higher perceived intensity than males, regardless of their experience level. After a 90 s interval, a significantly lower pain perception effect associated with the increased competitive experience of male athletes was observed. Female athletes did not appear to benefit from the experience effect on their pain tolerance. CONCLUSIONS: The study confirmed a significant difference in pain perception associated with the athletes' gender and agonistic experience. Separate explanations related to the pattern of pain inhibition and the acquired reduction in pain sensitivity are reported.

Longitudinal multimodal MRI characterization of a knock-in mouse model of Huntington's disease reveals early gray and white matter alterations.

Pathogenesis of the inherited neurodegenerative disorder Huntington's disease (HD) is progressive with a long presymptomatic phase in which subtle changes occur up to 15 years before the onset of symptoms. Thus, there is a need for early, functional biomarker to better understand disease progression and to evaluate treatment efficacy far from onset. Recent studies have shown that white matter may be affected early in mutant HTT gene carriers. A previous study performed on 12 months old Ki140CAG mice showed reduced glutamate level measured by Chemical Exchange Saturation Transfer of glutamate (gluCEST), especially in the corpus callosum. In this study, we scanned longitudinally Ki140CAG mice with structural MRI, diffusion tensor imaging, gluCEST and magnetization transfer imaging, in order to assess white matter integrity over the life of this mouse model characterized by slow progression of symptoms. Our results show early defects of diffusion properties in the anterior part of the corpus callosum at 5 months of age, preceding gluCEST defects in the same region at 8 and 12 months that spread to adjacent regions. At 12 months, frontal and piriform cortices showed reduced gluCEST, as well as the pallidum. MT imaging showed reduced signal in the septum at 12 months. Cortical and striatal atrophy then appear at 18 months. Vulnerability of the striatum and motor cortex, combined with alterations of anterior corpus callosum, seems to point out the potential role of white matter in the brain dysfunction that characterizes HD and the pertinence of gluCEST and DTI as biomarkers in HD.

Transient Anomalous Diffusion MRI Measurement Discriminates Porous Polymeric Matrices Characterized by Different Sub-Microstructures and Fractal Dimension.

Considering the current development of new nanostructured and complex materials and gels, it is critical to develop a sub-micro-scale sensitivity tool to quantify experimentally new parameters describing sub-microstructured porous systems. Diffusion NMR, based on the measurement of endogenous water's diffusion displacement, offers unique information on the structural features of materials and tissues. In this paper, we applied anomalous diffusion NMR protocols to quantify the subdiffusion of water and to measure, in an alternative, non-destructive and non-invasive modality, the fractal dimension dw of systems characterized by micro and sub-micro geometrical structures. To this end, three highly heterogeneous porous-polymeric matrices were studied. All the three matrices composed of glycidylmethacrylate-divynilbenzene porous monoliths obtained through the High Internal Phase Emulsion technique were characterized by pores of approximately spherical symmetry, with diameters in the range of 2-10 µm. Pores were interconnected by a plurality of window holes present on pore walls, which were characterized by size coverings in the range of 0.5-2 µm. The walls were characterized by a different degree of surface roughness. Moreover, complementary techniques, namely Field Emission Scanning Electron Microscopy (FE-SEM) and dielectric spectroscopy, were used to corroborate the NMR results. The experimental results showed that the anomalous diffusion α parameter that quantifies subdiffusion and dw = 2/α changed in parallel to the specific surface area S (or the surface roughness) of the porous matrices, showing a submicroscopic sensitivity. The results reported here suggest that the anomalous diffusion NMR method tested may be a valid experimental tool to corroborate theoretical and simulation results developed and performed for describing highly heterogeneous and complex systems. On the other hand, non-invasive and non-destructive anomalous subdiffusion NMR may be a useful tool to study the characteristic features of new highly heterogeneous nanostructured and complex functional materials and gels useful in cultural heritage applications, as well as scaffolds useful in tissue engineering.

Training data distribution significantly impacts the estimation of tissue microstructure with machine learning.

PURPOSE: Supervised machine learning (ML) provides a compelling alternative to traditional model fitting for parameter mapping in quantitative MRI. The aim of this work is to demonstrate and quantify the effect of different training data distributions on the accuracy and precision of parameter estimates when supervised ML is used for fitting. METHODS: We fit a two- and three-compartment biophysical model to diffusion measurements from in-vivo human brain, as well as simulated diffusion data, using both traditional model fitting and supervised ML. For supervised ML, we train several artificial neural networks, as well as random forest regressors, on different distributions of ground truth parameters. We compare the accuracy and precision of parameter estimates obtained from the different estimation approaches using synthetic test data. RESULTS: When the distribution of parameter combinations in the training set matches those observed in healthy human data sets, we observe high precision, but inaccurate estimates for atypical parameter combinations. In contrast, when training data is sampled uniformly from the entire plausible parameter space, estimates tend to be more accurate for atypical parameter combinations but may have lower precision for typical parameter combinations. CONCLUSION: This work highlights that estimation of model parameters using supervised ML depends strongly on the training-set distribution. We show that high precision obtained using ML may mask strong bias, and visual assessment of the parameter maps is not sufficient for evaluating the quality of the estimates.

Neural networks for parameter estimation in microstructural MRI: Application to a diffusion-relaxation model of white matter.

Specific features of white matter microstructure can be investigated by using biophysical models to interpret relaxation-diffusion MRI brain data. Although more intricate models have the potential to reveal more details of the tissue, they also incur time-consuming parameter estimation that may converge to inaccurate solutions due to a prevalence of local minima in a degenerate fitting landscape. Machine-learning fitting algorithms have been proposed to accelerate the parameter estimation and increase the robustness of the attained estimates. So far, learning-based fitting approaches have been restricted to microstructural models with a reduced number of independent model parameters where dense sets of training data are easy to generate. Moreover, the degree to which machine learning can alleviate the degeneracy problem is poorly understood. For conventional least-squares solvers, it has been shown that degeneracy can be avoided by acquisition with optimized relaxation-diffusion-correlation protocols that include tensor-valued diffusion encoding. Whether machine-learning techniques can offset these acquisition requirements remains to be tested. In this work, we employ artificial neural networks to vastly accelerate the parameter estimation for a recently introduced relaxation-diffusion model of white matter microstructure. We also develop strategies for assessing the accuracy and sensitivity of function fitting networks and use those strategies to explore the impact of the acquisition protocol. The developed learning-based fitting pipelines were tested on relaxation-diffusion data acquired with optimal and sub-optimal acquisition protocols. Networks trained with an optimized protocol were observed to provide accurate parameter estimates within short computational times. Comparing neural networks and least-squares solvers, we found the performance of the former to be less affected by sub-optimal protocols; however, model fitting networks were still susceptible to degeneracy issues and their use could not fully replace a careful design of the acquisition protocol.

Combined diffusion-relaxometry microstructure imaging: Current status and future prospects.

Microstructure imaging seeks to noninvasively measure and map microscopic tissue features by pairing mathematical modeling with tailored MRI protocols. This article reviews an emerging paradigm that has the potential to provide a more detailed assessment of tissue microstructure-combined diffusion-relaxometry imaging. Combined diffusion-relaxometry acquisitions vary multiple MR contrast encodings-such as b-value, gradient direction, inversion time, and echo time-in a multidimensional acquisition space. When paired with suitable analysis techniques, this enables quantification of correlations and coupling between multiple MR parameters-such as diffusivity, T1 , T2 , and T2∗ . This opens the possibility of disentangling multiple tissue compartments (within voxels) that are indistinguishable with single-contrast scans, enabling a new generation of microstructural maps with improved biological sensitivity and specificity.