Rotationally-invariant mapping of scalar and orientational metrics of neuronal microstructure with diffusion MRI

We develop a general analytical and numerical framework for estimating intra- and extra-neurite water fractions and diffusion coefficients, as well as neurite orientational dispersion, in each imaging voxel. By employing a set of rotational invariants and their expansion in the powers of diffusion weighting, we analytically uncover the nontrivial topology of the parameter estimation landscape, showing that multiple branches of parameters describe the measurement almost equally well, with only one of them corresponding to the biophysical reality. A comprehensive acquisition shows that the branch choice varies across the brain. Our framework reveals hidden degeneracies in MRI parameter estimation for neuronal tissue, provides microstructural and orientational maps in the whole brain without constraints or priors, and connects modern biophysical modeling with clinical MRI.Comment: 25 pages, 12 figures, elsarticle two-colum

Intra- and extra-axonal axial diffusivities in the white matter: which one is faster?

A two-compartment model of diffusion in white matter, which accounts for intra- and extra-axonal spaces, is associated with two plausible mathematical scenarios: either the intra-axonal axial diffusivity is higher than the extra-axonal (Branch 1), or the opposite (Branch 2). This duality calls for an independent validation of compartment axial diffusivities, to determine which of the two cases holds. The aim of the present study was to use an intracerebroventricular injection of a gadolinium-based contrast agent to selectively reduce the extracellular water signal in the rat brain, and compare diffusion metrics in the genu of the corpus callosum before and after gadolinium infusion. The diffusion metrics considered were diffusion and kurtosis tensor metrics, as well as compartment-specific estimates of the WMTI-Watson two-compartment model. A strong decrease in genu T1 and T2 relaxation times post-Gd was observed (p < 0.001), as well as an increase of 48% in radial kurtosis (p < 0.05), which implies that the relative fraction of extracellular water signal was selectively decreased. This was further supported by a significant increase in intra-axonal water fraction as estimated from the two-compartment model, for both branches (p < 0.01 for Branch 1, p < 0.05 for Branch 2). However, pre-Gd estimates of axon dispersion in Branch 1 agreed better with literature than those of Branch 2. Furthermore, comparison of post-Gd changes in diffusivity and dispersion between data and simulations further supported Branch 1 as the biologically plausible solution, i.e. the intra-axonal axial diffusivity is higher than the extra-axonal one. This result is fully consistent with other recent measurements of compartment axial diffusivities that used entirely different approaches, such as diffusion tensor encoding

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

Diffusion-weighted (DW) magnetic resonance spectroscopy (MRS) suffers from a lower signal to noise ratio (SNR) compared to conventional MRS owing to the addition of diffusion attenuation. This technique can therefore strongly benefit from noise reduction strategies. In the present work, the Marchenko-Pastur principal component analysis (MP-PCA) denoising is tested on Monte Carlo simulations and on in vivo DW-MRS data acquired at 9.4T in the rat brain. We provide a descriptive study of the effects observed following different MP-PCA denoising strategies (denoising the entire matrix versus using a sliding window), in terms of apparent SNR, rank selection, noise correlation within and across b-values and quantification of metabolite concentrations and fitted diffusion coefficients. MP-PCA denoising yielded an increased apparent SNR, a more accurate B0 drift correction between shots, and similar estimates of metabolite concentrations and diffusivities compared to the raw data. No spectral residuals on individual shots were observed but correlations in the noise level across shells were introduced, an effect which was mitigated using a sliding window, but which should be carefully considered.Comment: Cristina Cudalbu and Ileana O. Jelescu have contributed equally to this manuscrip

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

Diffusion-weighted (DW) magnetic resonance spectroscopy (MRS) suffers from a lower signal to noise ratio (SNR) compared to conventional MRS owing to the addition of diffusion attenuation. This technique can therefore strongly benefit from noise reduction strategies. In the present work, Marchenko-Pastur principal component analysis (MP-PCA) denoising is tested on Monte Carlo simulations and on in vivo DW-MRS data acquired at 9.4T in rat brain and at 3T in human brain. We provide a descriptive study of the effects observed following different MP-PCA denoising strategies (denoising the entire matrix versus using a sliding window), in terms of apparent SNR, rank selection, noise correlation within and across b-values and quantification of metabolite concentrations and fitted diffusion coefficients. MP-PCA denoising yielded an increased apparent SNR, a more accurate B0 drift correction between shots, and similar estimates of metabolite concentrations and diffusivities compared to the raw data. No spectral residuals on individual shots were observed but correlations in the noise level across shells were introduced, an effect which was mitigated using a sliding window, but which should be carefully considered

Diffusion of brain metabolites highlights altered brain microstructure in type C hepatic encephalopathy: a 9.4 T preliminary study

IntroductionType C hepatic encephalopathy (HE) is a decompensating event of chronic liver disease leading to severe motor and cognitive impairment. The progression of type C HE is associated with changes in brain metabolite concentrations measured by 1H magnetic resonance spectroscopy (MRS), most noticeably a strong increase in glutamine to detoxify brain ammonia. In addition, alterations of brain cellular architecture have been measured ex vivo by histology in a rat model of type C HE. The aim of this study was to assess the potential of diffusion-weighted MRS (dMRS) for probing these cellular shape alterations in vivo by monitoring the diffusion properties of the major brain metabolites.MethodsThe bile duct-ligated (BDL) rat model of type C HE was used. Five animals were scanned before surgery and 6- to 7-week post-BDL surgery, with each animal being used as its own control. 1H-MRS was performed in the hippocampus (SPECIAL, TE = 2.8 ms) and dMRS in a voxel encompassing the entire brain (DW-STEAM, TE = 15 ms, diffusion time = 120 ms, maximum b-value = 25 ms/μm2) on a 9.4 T scanner. The in vivo MRS acquisitions were further validated with histological measures (immunohistochemistry, Golgi-Cox, electron microscopy).ResultsThe characteristic 1H-MRS pattern of type C HE, i.e., a gradual increase of brain glutamine and a decrease of the main organic osmolytes, was observed in the hippocampus of BDL rats. Overall increased metabolite diffusivities (apparent diffusion coefficient and intra-stick diffusivity—Callaghan’s model, significant for glutamine, myo-inositol, and taurine) and decreased kurtosis coefficients were observed in BDL rats compared to control, highlighting the presence of osmotic stress and possibly of astrocytic and neuronal alterations. These results were consistent with the microstructure depicted by histology and represented by a decline in dendritic spines density in neurons, a shortening and decreased number of astrocytic processes, and extracellular edema.DiscussiondMRS enables non-invasive and longitudinal monitoring of the diffusion behavior of brain metabolites, reflecting in the present study the globally altered brain microstructure in BDL rats, as confirmed ex vivo by histology. These findings give new insights into metabolic and microstructural abnormalities associated with high brain glutamine and its consequences in type C HE

Quantifying human gray matter microstructure using neurite exchange imaging (NEXI) and 300 mT/m gradients

Biophysical models of diffusion tailored to quantify gray matter microstructure are gathering increasing interest. The two-compartment Neurite EXchange Imaging (NEXI) model has been proposed recently to account for neurites, extra-cellular space, and exchange across the cell membrane. NEXI parameter estimation requires multi-shell multi-diffusion time data and has so far only been implemented experimentally on animal data collected on a preclinical magnetic resonance imaging (MRI) set-up. In this work, the translation of NEXI to the human cortex in vivo was achieved using a 3 T Connectom MRI system with 300 mT/m gradients, that enables the acquisition of a broad range of b-values (0 – 7.5 ms/µm²) with a window covering short to intermediate diffusion times (20 – 49 ms) suitable for the characteristic exchange times (10 – 50 ms). Microstructure estimates of four model variants: NEXI, NEXIdot (its extension with the addition of a dot compartment), and their respective versions that correct for the Rician noise floor (NEXIRM and NEXIdot,RM) that particularly impacts high b-value signal, were compared. The reliability of estimates in each model variant was evaluated in synthetic and human in vivo data. In the latter, the intra-subject (scan-rescan) versus between-subjects variability of microstructure estimates was compared in the cortex. The better performance of NEXIRM highlights the importance of correcting for Rician bias in the NEXI model to obtain accurate estimates of microstructure parameters in the human cortex, and the sensitivity of the NEXI framework to individual differences in cortical microstructure. This application of NEXI in humans represents a significant step, unlocking new avenues for studying neurodevelopment, aging, and various neurodegenerative disorders

Cellular EXchange Imaging (CEXI): Evaluation of a diffusion model including water exchange in cells using numerical phantoms of permeable spheres

Purpose: Biophysical models of diffusion MRI have been developed to characterize microstructure in various tissues, but existing models are not suitable for tissue composed of permeable spherical cells. In this study we introduce Cellular Exchange Imaging (CEXI), a model tailored for permeable spherical cells, and compares its performance to a related Ball \& Sphere (BS) model that neglects permeability. Methods: We generated DW-MRI signals using Monte-Carlo simulations with a PGSE sequence in numerical substrates made of spherical cells and their extracellular space for a range of membrane permeability. From these signals, the properties of the substrates were inferred using both BS and CEXI models. Results: CEXI outperformed the impermeable model by providing more stable estimates cell size and intracellular volume fraction that were diffusion time-independent. Notably, CEXI accurately estimated the exchange time for low to moderate permeability levels previously reported in other studies ($\kappa<25\mu m/s$). However, in highly permeable substrates ($\kappa=50\mu m/s$), the estimated parameters were less stable, particularly the diffusion coefficients. Conclusion: This study highlights the importance of modeling the exchange time to accurately quantify microstructure properties in permeable cellular substrates. Future studies should evaluate CEXI in clinical applications such as lymph nodes, investigate exchange time as a potential biomarker of tumor severity, and develop more appropriate tissue models that account for anisotropic diffusion and highly permeable membranes.Comment: 7 figures, 2 tables, 21 pages, under revie

Orientation-Dispersed Apparent Axon Diameter via Multi-Stage Spherical Mean Optimization

The estimation of the apparent axon diameter (AAD) via diffusion MRI is affected by the incoherent alignment of single axons around its axon bundle direction, also known as orientational dispersion. The simultaneous estimation of AAD and dispersion is challenging and requires the optimization of many parameters at the same time. We propose to reduce the complexity of the estimation with an multi-stage approach, inspired to alternate convex search, that separates the estimation problem into simpler ones, thus avoiding the estimation of all the relevant model parameters at once. The method is composed of three optimization stages that are iterated, where we separately estimate the volume fractions, diffusivities, dispersion, and mean AAD, using a Cylinder and Zeppelin model. First, we use multi-shell data to estimate the undispersed axon micro-environment’s signal fractions and diffusivities using the spherical mean technique; then, to account for dispersion, we use the obtained micro-environment parameters to estimate a Watson axon orientation distribution; finally, we use data acquired perpendicularly to the axon bundle direction to estimate the mean AAD and updated signal fractions, while fixing the previously estimated diffusivity and dispersion parameters. We use the estimated mean AAD to initiate the following iteration. We show that our approach converges to good estimates while being more efficient than optimizing all model parameters at once. We apply our method to ex-vivo spinal cord data, showing that including dispersion effects results in mean apparent axon diameter estimates that are closer to their measured histological values

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

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