Mesoscopic structure of neuronal tracts from time-dependent diffusion

g-Ratio weighted imaging of the human spinal cord in vivo

The fiber g-ratio is defined as the ratio of the inner to the outer diameter of the myelin sheath. This ratio provides a measure of the myelin thickness that complements axon morphology (diameter and density) for assessment of demyelination in diseases such as multiple sclerosis. Previous work has shown that an aggregate g-ratio map can be computed using a formula that combines axon and myelin density measured with quantitative MRI. In this work, we computed g-ratio weighted maps in the cervical spinal cord of nine healthy subjects. We utilized the 300mT/m gradients from the CONNECTOM scanner to estimate the fraction of restricted water (fr) with high accuracy, using the CHARMED model. Myelin density was estimated using the lipid and macromolecular tissue volume (MTV) method, derived from normalized proton density (PD) mapping. The variability across spinal level, laterality and subject were assessed using a three-way ANOVA. The average g-ratio value obtained in the white matter was 0.76+/-0.03, consistent with previous histology work. Coefficients of variation of fr and MTV were respectively 4.3% and 13.7%. fr and myelin density were significantly different across spinal tracts (p=3×10-7 and 0.004 respectively) and were positively correlated in the white matter (r=0.42), suggesting shared microstructural information. The aggregate g-ratio did not show significant differences across tracts (p=0.6). This study suggests that fr and myelin density can be measured in vivo with high precision and that they can be combined to produce a g-ratio-weighted map robust to free water pool contamination from cerebrospinal fluid or veins. Potential applications include the study of early demyelination in multiple sclerosis, and the quantitative assessment of remyelination drugs.

Assessing White Matter Microstructure in Brain Regions with Different Myelin Architecture Using MRI

OBJECTIVE

We investigate how known differences in myelin architecture between regions along the cortico-spinal tract and frontal white matter (WM) in 19 healthy adolescents are reflected in several quantitative MRI parameters that have been proposed to non-invasively probe WM microstructure. In a clinically feasible scan time, both conventional imaging sequences as well as microstructural MRI parameters were assessed in order to quantitatively characterise WM regions that are known to differ in the thickness of their myelin sheaths, and in the presence of crossing or parallel fibre organisation.

RESULTS

We found that diffusion imaging, MR spectroscopy (MRS), myelin water fraction (MWF), Magnetization Transfer Imaging, and Quantitative Susceptibility Mapping were myelin-sensitive in different ways, giving complementary information for characterising WM microstructure with different underlying fibre architecture. From the diffusion parameters, neurite density (NODDI) was found to be more sensitive than fractional anisotropy (FA), underlining the limitation of FA in WM crossing fibre regions. In terms of sensitivity to different myelin content, we found that MWF, the mean diffusivity and chemical-shift imaging based MRS yielded the best discrimination between areas.

CONCLUSION

Multimodal assessment of WM microstructure was possible within clinically feasible scan times using a broad combination of quantitative microstructural MRI sequences. By assessing new microstructural WM parameters we were able to provide normative data and discuss their interpretation in regions with different myelin architecture, as well as their possible application as biomarker for WM disorders.

Disordered hyperuniform heterogeneous materials

Disordered hyperuniform many-body systems are distinguishable states of matter that lie between a crystal and liquid: they are like perfect crystals in the way they suppress large-scale density fluctuations and yet are like liquids or glasses in that they are statistically isotropic with no Bragg peaks. These systems play a vital role in a number of fundamental and applied problems: glass formation, jamming, rigidity, photonic and electronic band structure, localization of waves and excitations, self-organization, fluid dynamics, quantum systems, and pure mathematics. Much of what we know theoretically about disordered hyperuniform states of matter involves many-particle systems. In this paper, we derive new rigorous criteria that disordered hyperuniform two-phase heterogeneous materials must obey and explore their consequences. Two-phase heterogeneous media are ubiquitous; examples include composites and porous media, biological media, foams, polymer blends, granular media, cellular solids, and colloids. We begin by obtaining some results that apply to hyperuniform two-phase media in which one phase is a sphere packing in d-dimensional Euclidean space [Formula: see text]. Among other results, we rigorously establish the requirements for packings of spheres of different sizes to be 'multihyperuniform'. We then consider hyperuniformity for general two-phase media in [Formula: see text]. Here we apply realizability conditions for an autocovariance function and its associated spectral density of a two-phase medium, and then incorporate hyperuniformity as a constraint in order to derive new conditions. We show that some functional forms can immediately be eliminated from consideration and identify other forms that are allowable. Specific examples and counterexamples are described. Contact is made with well-known microstructural models (e.g. overlapping spheres and checkerboards) as well as irregular phase-separation and Turing-type patterns. We also ascertain a family of autocovariance functions (or spectral densities) that are realizable by disordered hyperuniform two-phase media in any space dimension, and present select explicit constructions of realizations. These studies provide insight into the nature of disordered hyperuniformity in the context of heterogeneous materials and have implications for the design of such novel amorphous materials.

Tissue microstructure features derived from anomalous diffusion measurements in magnetic resonance imaging

OBJECTIVES

Tissue microstructure features, namely axon radius and volume fraction, provide important information on the function of white matter pathways. These parameters vary on the scale much smaller than imaging voxels (microscale) yet influence the magnetic resonance imaging diffusion signal at the image voxel scale (macroscale) in an anomalous manner. Researchers have already mapped anomalous diffusion parameters from magnetic resonance imaging data, but macroscopic variations have not been related to microscale influences. With the aid of a tissue model, we aimed to connect anomalous diffusion parameters to axon radius and volume fraction using diffusion-weighted magnetic resonance imaging measurements.

EXPERIMENTAL DESIGN

An ex vivo human brain experiment was performed to directly validate axon radius and volume fraction measurements in the human brain. These findings were validated using electron microscopy. Additionally, we performed an in vivo study on nine healthy participants to map axon radius and volume fraction along different regions of the corpus callosum projecting into various cortical areas identified using tractography.

PRINCIPAL OBSERVATIONS

We found a clear relationship between anomalous diffusion parameters and axon radius and volume fraction. We were also able to map accurately the trend in axon radius along the corpus callosum, and in vivo findings resembled the low-high-low-high behaviour in axon radius demonstrated previously.

CONCLUSIONS

Axon radius and volume fraction measurements can potentially be used in brain connectivity studies and to understand the implications of white matter structure in brain diseases and disorders. Hum Brain Mapp 38:1068-1081, 2017. © 2016 Wiley Periodicals, Inc.

Precise Inference and Characterization of Structural Organization (PICASO) of tissue from molecular diffusion

Inferring the microstructure of complex media from the diffusive motion of molecules is a challenging problem in diffusion physics. In this paper, we introduce a novel representation of diffusion MRI (dMRI) signal from tissue with spatially-varying diffusivity using a diffusion disturbance function. This disturbance function contains information about the (intra-voxel) spatial fluctuations in diffusivity due to restrictions, hindrances and tissue heterogeneity of the underlying tissue substrate. We derive the short- and long-range disturbance coefficients from this disturbance function to characterize the tissue structure and organization. Moreover, we provide an exact relation between the disturbance coefficients and the time-varying moments of the diffusion propagator, as well as their relation to specific tissue microstructural information such as the intra-axonal volume fraction and the apparent axon radius. The proposed approach is quite general and can model dMRI signal for any type of gradient sequence (rectangular, oscillating, etc.) without using the Gaussian phase approximation. The relevance of the proposed PICASO model is explored using Monte-Carlo simulations and in-vivo dMRI data. The results show that the estimated disturbance coefficients can distinguish different types of microstructural organization of axons.

Pulsed and oscillating gradient MRI for assessment of cell size and extracellular space (POMACE) in mouse gliomas

Solid tumor microstructure is related to the aggressiveness of the tumor, interstitial pressure and drug delivery pathways, which are closely associated with treatment response, metastatic spread and prognosis. In this study, we introduce a novel diffusion MRI data analysis framework, pulsed and oscillating gradient MRI for assessment of cell size and extracellular space (POMACE), and demonstrate its feasibility in a mouse tumor model. In vivo and ex vivo POMACE experiments were performed on mice bearing the GL261 murine glioma model (n = 8). Since the complete diffusion time dependence is in general non-analytical, the tumor microstructure was modeled in an appropriate time/frequency regime by impermeable spheres (radius Rcell , intracellular diffusivity Dics ) surrounded by extracellular space (ECS) (approximated by constant apparent diffusivity Decs in volume fraction ECS). POMACE parametric maps (ECS, Rcell , Dics , Decs ) were compared with conventional diffusion-weighted imaging metrics, electron microscopy (EM), alternative ECS determination based on effective medium theory (EMT), and optical microscopy performed on the same samples. It was shown that Decs can be approximated by its long time tortuosity limit in the range [1/(88 Hz)-31 ms]. ECS estimations (44 ± 7% in vivo and 54 ± 11% ex vivo) were in agreement with EMT-based ECS and literature on brain gliomas. Ex vivo, ECS maps correlated well with optical microscopy. Cell sizes (Rcell  = 4.8 ± 1.3 in vivo and 4.3 ± 1.4 µm ex vivo) were consistent with EM measurements (4.7 ± 1.8 µm). In conclusion, Rcell and ECS can be quantified and mapped in vivo and ex vivo in brain tumors using the proposed POMACE method. Our experimental results support the view that POMACE provides a way to interpret the frequency or time dependence of the diffusion coefficient in tumors in terms of objective biophysical parameters of neuronal tissue, which can be used for non-invasive monitoring of preclinical cancer studies and treatment efficacy. Copyright © 2016 John Wiley & Sons, Ltd.

New insights about time-varying diffusivity and its estimation from diffusion MRI

PURPOSE

Characterizing the relation between the applied gradient sequences and the measured diffusion MRI signal is important for estimating the time-dependent diffusivity, which provides important information about the microscopic tissue structure.

THEORY AND METHODS

In this article, we extend the classical theory of Stepišnik for measuring time-dependent diffusivity under the Gaussian phase approximation. In particular, we derive three novel expressions which represent the diffusion MRI signal in terms of the mean-squared displacement, the instantaneous diffusivity, and the velocity autocorrelation function. We present the explicit signal expressions for the case of single diffusion encoding and oscillating gradient spin-echo sequences. Additionally, we also propose three different models to represent time-varying diffusivity and test them using Monte-Carlo simulations and in vivo human brain data.

RESULTS

The time-varying diffusivities are able to distinguish the synthetic structures in the Monte-Carlo simulations. There is also strong statistical evidence about time-varying diffusivity from the in vivo human data set.

CONCLUSION

The proposed theory provides new insights into our understanding of the time-varying diffusivity using different gradient sequences. The proposed models for representing time-varying diffusivity can be utilized to study time-varying diffusivity using in vivo human brain diffusion MRI data. Magn Reson Med 78:763-774, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Double oscillating diffusion encoding and sensitivity to microscopic anisotropy

Purpose

To introduce a novel diffusion pulse sequence, namely double oscillating diffusion encoding (DODE), and to investigate whether it adds sensitivity to microscopic diffusion anisotropy (µA) compared to the well‐established double diffusion encoding (DDE) methodology.

Methods

We simulate measurements from DODE and DDE sequences for different types of microstructures exhibiting restricted diffusion. First, we compare the effect of varying pulse sequence parameters on the DODE and DDE signal. Then, we analyse the sensitivity of the two sequences to the microstructural parameters (pore diameter and length) which determine µA. Finally, we investigate specificity of measurements to particular substrate configurations.

Results

Simulations show that DODE sequences exhibit similar signal dependence on the relative angle between the two gradients as DDE sequences, however, the effect of varying the mixing time is less pronounced. The sensitivity analysis shows that in substrates with elongated pores and various orientations, DODE sequences increase the sensitivity to pore diameter, while DDE sequences are more sensitive to pore length. Moreover, DDE and DODE sequence parameters can be tailored to enhance/suppress the signal from a particular range of substrates.

Conclusions

A combination of DODE and DDE sequences maximize sensitivity to µA, compared to using just the DDE method. Magn Reson Med 78:550–564, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Hyperuniformity and its generalizations

Disordered many-particle hyperuniform systems are exotic amorphous states of matter that lie between crystal and liquid: They are like perfect crystals in the way they suppress large-scale density fluctuations and yet are like liquids or glasses in that they are statistically isotropic with no Bragg peaks. These exotic states of matter play a vital role in a number of problems across the physical, mathematical as well as biological sciences and, because they are endowed with novel physical properties, have technological importance. Given the fundamental as well as practical importance of disordered hyperuniform systems elucidated thus far, it is natural to explore the generalizations of the hyperuniformity notion and its consequences. In this paper, we substantially broaden the hyperuniformity concept along four different directions. This includes generalizations to treat fluctuations in the interfacial area (one of the Minkowski functionals) in heterogeneous media and surface-area driven evolving microstructures, random scalar fields, divergence-free random vector fields, and statistically anisotropic many-particle systems and two-phase media. In all cases, the relevant mathematical underpinnings are formulated and illustrative calculations are provided. Interfacial-area fluctuations play a major role in characterizing the microstructure of two-phase systems (e.g., fluid-saturated porous media), physical properties that intimately depend on the geometry of the interface, and evolving two-phase microstructures that depend on interfacial energies (e.g., spinodal decomposition). In the instances of random vector fields and statistically anisotropic structures, we show that the standard definition of hyperuniformity must be generalized such that it accounts for the dependence of the relevant spectral functions on the direction in which the origin in Fourier space is approached (nonanalyticities at the origin). Using this analysis, we place some well-known energy spectra from the theory of isotropic turbulence in the context of this generalization of hyperuniformity. Among other results, we show that there exist many-particle ground-state configurations in which directional hyperuniformity imparts exotic anisotropic physical properties (e.g., elastic, optical, and acoustic characteristics) to these states of matter. Such tunability could have technological relevance for manipulating light and sound waves in ways heretofore not thought possible. We show that disordered many-particle systems that respond to external fields (e.g., magnetic and electric fields) are a natural class of materials to look for directional hyperuniformity. The generalizations of hyperuniformity introduced here provide theoreticians and experimentalists new avenues to understand a very broad range of phenomena across a variety of fields through the hyperuniformity "lens."

White matter microstructure from nonparametric axon diameter distribution mapping

We report the development of a double diffusion encoding (DDE) MRI method to estimate and map the axon diameter distribution (ADD) within an imaging volume. A variety of biological processes, ranging from development to disease and trauma, may lead to changes in the ADD in the central and peripheral nervous systems. Unlike previously proposed methods, this ADD experimental design and estimation framework employs a more general, nonparametric approach, without a priori assumptions about the underlying form of the ADD, making it suitable to analyze abnormal tissue. In the current study, this framework was used on an ex vivo ferret spinal cord, while emphasizing the way in which the ADD can be weighted by either the number or the volume of the axons. The different weightings, which result in different spatial contrasts, were considered throughout this work. DDE data were analyzed to derive spatially resolved maps of average axon diameter, ADD variance, and extra-axonal volume fraction, along with a novel sub-micron restricted structures map. The morphological information contained in these maps was then used to segment white matter into distinct domains by using a proposed k-means clustering algorithm with spatial contiguity and left-right symmetry constraints, resulting in identifiable white matter tracks. The method was validated by comparing histological measures to the estimated ADDs using a quantitative similarity metric, resulting in good agreement. With further acquisition acceleration and experimental parameters adjustments, this ADD estimation framework could be first used preclinically, and eventually clinically, enabling a wide range of neuroimaging applications for improved understanding of neurodegenerative pathologies and assessing microstructural changes resulting from trauma.

MAPL: Tissue microstructure estimation using Laplacian-regularized MAP-MRI and its application to HCP data

The recovery of microstructure-related features of the brain's white matter is a current challenge in diffusion MRI. To robustly estimate these important features from multi-shell diffusion MRI data, we propose to analytically regularize the coefficient estimation of the Mean Apparent Propagator (MAP)-MRI method using the norm of the Laplacian of the reconstructed signal. We first compare our approach, which we call MAPL, with competing, state-of-the-art functional basis approaches. We show that it outperforms the original MAP-MRI implementation and the recently proposed modified Spherical Polar Fourier (mSPF) basis with respect to signal fitting and reconstruction of the Ensemble Average Propagator (EAP) and Orientation Distribution Function (ODF) in noisy, sparsely sampled data of a physical phantom with reference gold standard data. Then, to reduce the variance of parameter estimation using multi-compartment tissue models, we propose to use MAPL's signal fitting and extrapolation as a preprocessing step. We study the effect of MAPL on the estimation of axon diameter using a simplified Axcaliber model and axonal dispersion using the Neurite Orientation Dispersion and Density Imaging (NODDI) model. We show the positive effect of using it as a preprocessing step in estimating and reducing the variances of these parameters in the Corpus Callosum of six different subjects of the MGH Human Connectome Project. Finally, we correlate the estimated axon diameter, dispersion and restricted volume fractions with Fractional Anisotropy (FA) and clearly show that changes in FA significantly correlate with changes in all estimated parameters. Overall, we illustrate the potential of using a well-regularized functional basis together with multi-compartment approaches to recover important microstructure tissue parameters with much less variability, thus contributing to the challenge of better understanding microstructure-related features of the brain's white matter.

Fast and simplified mapping of mean axon diameter using temporal diffusion spectroscopy

Mapping axon diameter is of interest for the potential diagnosis and monitoring of various neuronal pathologies. Advanced diffusion-weighted MRI methods have been developed to measure mean axon diameters non-invasively, but suffer major drawbacks that prevent their direct translation into clinical practice, such as complex non-linear data fitting and, more importantly, long scanning times that are usually not tolerable for most human subjects. In the current study, temporal diffusion spectroscopy using oscillating diffusion gradients was used to measure mean axon diameters with high sensitivity to small axons in the central nervous system. Axon diameters have been found to be correlated with a novel metric, DDR⊥ (the rate of dispersion of the perpendicular diffusion coefficient with gradient frequency), which is a model-free quantity that does not require complex data analyses and can be obtained from two diffusion coefficient measurements in clinically relevant times with conventional MRI machines. A comprehensive investigation including computer simulations and animal experiments ex vivo showed that measurements of DDR⊥ agree closely with histological data. In humans in vivo, DDR⊥ was also found to correlate well with reported mean axon diameters in human corpus callosum, and the total scan time was only about 8 min. In conclusion, DDR⊥ may have potential to serve as a fast, simple and model-free approach to map the mean axon diameter of white matter in clinics for assessing axon diameter changes.

Estimation of Bounded and Unbounded Trajectories in Diffusion MRI

Disentangling the tissue microstructural information from the diffusion magnetic resonance imaging (dMRI) measurements is quite important for extracting brain tissue specific measures. The autocorrelation function of diffusing spins is key for understanding the relation between dMRI signals and the acquisition gradient sequences. In this paper, we demonstrate that the autocorrelation of diffusion in restricted or bounded spaces can be well approximated by exponential functions. To this end, we propose to use the multivariate Ornstein-Uhlenbeck (OU) process to model the matrix-valued exponential autocorrelation function of three-dimensional diffusion processes with bounded trajectories. We present detailed analysis on the relation between the model parameters and the time-dependent apparent axon radius and provide a general model for dMRI signals from the frequency domain perspective. For our experimental setup, we model the diffusion signal as a mixture of two compartments that correspond to diffusing spins with bounded and unbounded trajectories, and analyze the corpus-callosum in an ex-vivo data set of a monkey brain.

Towards higher sensitivity and stability of axon diameter estimation with diffusion-weighted MRI

Diffusion-weighted MRI is an important tool for in vivo and non-invasive axon morphometry. The ActiveAx technique utilises an optimised acquisition protocol to infer orientationally invariant indices of axon diameter and density by fitting a model of white matter to the acquired data. In this study, we investigated the factors that influence the sensitivity to small-diameter axons, namely the gradient strength of the acquisition protocol and the model fitting routine. Diffusion-weighted ex. vivo images of the mouse brain were acquired using 16.4-T MRI with high (Gmax of 300 mT/m) and ultra-high (Gmax of 1350 mT/m) gradient strength acquisitions. The estimated axon diameter indices of the mid-sagittal corpus callosum were validated using electron microscopy. In addition, a dictionary-based fitting routine was employed and evaluated. Axon diameter indices were closer to electron microscopy measures when higher gradient strengths were employed. Despite the improvement, estimated axon diameter indices (a lower bound of ~ 1.8 μm) remained higher than the measurements obtained using electron microscopy (~1.2 μm). We further observed that limitations of pulsed gradient spin echo (PGSE) acquisition sequences and axonal dispersion could also influence the sensitivity with which axon diameter indices could be estimated. Our results highlight the influence of acquisition protocol, tissue model and model fitting, in addition to gradient strength, on advanced microstructural diffusion-weighted imaging techniques. © 2016 The Authors. NMR in Biomedicine published by John Wiley & Sons Ltd.

Including diffusion time dependence in the extra-axonal space improves in vivo estimates of axonal diameter and density in human white matter

Axonal density and diameter are two fundamental properties of brain white matter. Recently, advanced diffusion MRI techniques have made these two parameters accessible in vivo. However, the techniques available to estimate such parameters are still under development. For example, current methods to map axonal diameters capture relative trends over different structures, but consistently over-estimate absolute diameters. Axonal density estimates are more accessible experimentally, but different modeling approaches exist and the impact of the experimental parameters has not been thoroughly quantified, potentially leading to incompatibility of results obtained in different studies using different techniques. Here, we characterise the impact of diffusion time on axonal density and diameter estimates using Monte Carlo simulations and STEAM diffusion MRI at 7 T on 9 healthy volunteers. We show that axonal density and diameter estimates strongly depend on diffusion time, with diameters almost invariably overestimated and density both over and underestimated for some commonly used models. Crucially, we also demonstrate that these biases are reduced when the model accounts for diffusion time dependency in the extra-axonal space. For axonal density estimates, both upward and downward bias in different situations are removed by modeling extra-axonal time-dependence, showing increased accuracy in these estimates. For axonal diameter estimates, we report increased accuracy in ground truth simulations and axonal diameter estimates decreased away from high values given by earlier models and towards known values in the human corpus callosum when modeling extra-axonal time-dependence. Axonal diameter feasibility under both advanced and clinical settings is discussed in the light of the proposed advances.

In vivo observation and biophysical interpretation of time-dependent diffusion in human white matter

The presence of micrometer-level restrictions leads to a decrease of diffusion coefficient with diffusion time. Here we investigate this effect in human white matter in vivo. We focus on a broad range of diffusion times, up to 600 ms, covering diffusion length scales up to about 30 μm. We perform stimulated echo diffusion tensor imaging on 5 healthy volunteers and observe a relatively weak time-dependence in diffusion transverse to major fiber tracts. Remarkably, we also find notable time-dependence in the longitudinal direction. Comparing models of diffusion in ordered, confined and disordered media, we argue that the time-dependence in both directions can arise due to structural disorder, such as axonal beads in the longitudinal direction, and the random packing geometry of fibers within a bundle in the transverse direction. These time-dependent effects extend beyond a simple picture of Gaussian compartments, and may lead to novel markers that are specific to neuronal fiber geometry at the micrometer scale.

Detection of acute nervous system injury with advanced diffusion-weighted MRI: a simulation and sensitivity analysis

Diffusion-weighted imaging (DWI) is a powerful tool to investigate the microscopic structure of the central nervous system (CNS). Diffusion tensor imaging (DTI), a common model of the DWI signal, has a demonstrated sensitivity to detect microscopic changes as a result of injury or disease. However, DTI and other similar models have inherent limitations that reduce their specificity for certain pathological features, particularly in tissues with complex fiber arrangements. Methods such as double pulsed field gradient (dPFG) and q-vector magic angle spinning (qMAS) have been proposed to specifically probe the underlying microscopic anisotropy without interference from the macroscopic tissue organization. This is particularly important for the study of acute injury, where abrupt changes in the microscopic morphology of axons and dendrites manifest as focal enlargements known as beading. The purpose of this work was to assess the relative sensitivity of DWI measures to beading in the context of macroscopic fiber organization and edema. Computational simulations of DWI experiments in normal and beaded axons demonstrated that, although DWI models can be highly specific for the simulated pathologies of beading and volume fraction changes in coherent fiber pathways, their sensitivity to a single idealized pathology is considerably reduced in crossing and dispersed fibers. However, dPFG and qMAS have a high sensitivity for beading, even in complex fiber tracts. Moreover, in tissues with coherent arrangements, such as the spinal cord or nerve fibers in which tract orientation is known a priori, a specific dPFG sequence variant decreases the effects of edema and improves specificity for beading. Collectively, the simulation results demonstrate that advanced DWI methods, particularly those which sample diffusion along multiple directions within a single acquisition, have improved sensitivity to acute axonal injury over conventional DTI metrics and hold promise for more informative clinical diagnostic use in CNS injury evaluation.

N-acetyl-aspartate levels correlate with intra-axonal compartment parameters from diffusion MRI

Diffusion MRI combined with biophysical modeling allows for the description of a white matter (WM) fiber bundle in terms of compartment specific white matter tract integrity (WMTI) metrics, which include intra-axonal diffusivity (Daxon), extra-axonal axial diffusivity (De||), extra-axonal radial diffusivity (De┴), axonal water fraction (AWF), and tortuosity (α) of extra-axonal space. Here we derive these parameters from diffusion kurtosis imaging to examine their relationship to concentrations of global WM N-acetyl-aspartate (NAA), creatine (Cr), choline (Cho) and myo-Inositol (mI), as measured with proton MR spectroscopy ((1)H-MRS), in a cohort of 25 patients with mild traumatic brain injury (MTBI). We found statistically significant (p<0.05) positive correlations between NAA and Daxon, AWF, α, and fractional anisotropy; negative correlations between NAA and De,┴ and the overall radial diffusivity (D┴). These correlations were supported by similar findings in regional analysis of the genu and splenium of the corpus callosum. Furthermore, a positive correlation in global WM was noted between Daxon and Cr, as well as a positive correlation between De|| and Cho, and a positive trend between De|| and mI. The specific correlations between NAA, an endogenous probe of the neuronal intracellular space, and WMTI metrics related to the intra-axonal space, combined with the specific correlations of De|| with mI and Cho, both predominantly present extra-axonally, corroborate the overarching assumption of many advanced modeling approaches that diffusion imaging can disentangle between the intra- and extra-axonal compartments in WM fiber bundles. Our findings are also generally consistent with what is known about the pathophysiology of MTBI, which appears to involve both intra-axonal injury (as reflected by a positive trend between NAA and Daxon) as well as axonal shrinkage, demyelination, degeneration, and/or loss (as reflected by correlations between NAA and De┴, AWF, and α).

Surface-to-volume ratio mapping of tumor microstructure using oscillating gradient diffusion weighted imaging

PURPOSE

To disentangle the free diffusivity (D0 ) and cellular membrane restrictions, by means of their surface-to-volume ratio (S/V), using the frequency-dependence of the diffusion coefficient D(ω), measured in brain tumors in the short diffusion-time regime using oscillating gradients (OGSE).

METHODS

In vivo and ex vivo OGSE experiments were performed on mice bearing the GL261 murine glioma model (n = 10) to identify the relevant time/frequency (t/ω) domain where D(ω) linearly decreases with ω(-1/2) . Parametric maps (S/V, D0 ) are compared with conventional DWI metrics. The impact of frequency range and temperature (20°C versus 37°C) on S/V and D0 is investigated ex vivo.

RESULTS

The validity of the short diffusion-time regime is demonstrated in vivo and ex vivo. Ex vivo measurements confirm that the purely geometric restrictions embodied in S/V are independent from temperature and frequency range, while the temperature dependence of the free diffusivity D0 is similar to that of pure water.

CONCLUSION

Our results suggest that D(ω) in the short diffusion-time regime can be used to uncouple the purely geometric restriction effect, such as S/V, from the intrinsic medium diffusivity properties, and provides a nonempirical and objective way to interpret frequency/time-dependent diffusion changes in tumors in terms of objective biophysical tissue parameters. Magn Reson Med 76:237-247, 2016. © 2015 Wiley Periodicals, Inc.

In vivo mapping of human spinal cord microstructure at 300mT/m

The ability to characterize white matter microstructure non-invasively has important applications for the diagnosis and follow-up of several neurological diseases. There exists a family of diffusion MRI techniques, such as AxCaliber, that provide indices of axon microstructure, such as axon diameter and density. However, to obtain accurate measurements of axons with small diameters (<5μm), these techniques require strong gradients, i.e. an order of magnitude higher than the 40-80mT/m currently available in clinical systems. In this study we acquired AxCaliber diffusion data at a variety of different q-values and diffusion times in the spinal cord of five healthy subjects using a 300mT/m whole body gradient system. Acquisition and processing were optimized using state-of-the-art methods (e.g., 64-channel coil, template-based analysis). Results consistently show an average axon diameter of 4.5+/-1.1μm in the spinal cord white matter. Diameters ranged from 3.0μm (gracilis) to 5.9μm (spinocerebellar tracts). Values were similar across laterality (left-right), but statistically different across spinal cord pathways (p<10(-5)). The observed trends are similar to those observed in animal histology. This study shows, for the first time, in vivo mapping of axon diameter in the spinal cord at 300mT/m, thus creating opportunities for applications in spinal cord diseases.