Diffusion nuclear magnetic resonance (NMR) is a powerful technique for studying porous media, but yields ambiguous results when the sample comprises multiple regions with different pore sizes, shapes, and orientations. Inspired by solid-state NMR techniques for correlating isotropic and anisotropic chemical shifts, we propose a diffusion NMR method to resolve said ambiguity. Numerical data inversion relies on sparse representation of the data in a basis of radial and axial diffusivities. Experiments are performed on a composite sample with a cell suspension and a liquid crystal. DOI: 10.1103/PhysRevLett.116.087601 Many porous materials of biological, geological, and synthetic origin contain water in a range of microscopic environments with different local pore geometries. Information about the structure of the pore space can be inferred from nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) measurements of the self-diffusion of the pore water [1,2]. The diffusion MRI approach has been especially powerful for noninvasive studies of the living human brain [3], allowing for quantification of axon diameter [4], mean orientation [5], and orientation distribution [6]. Although useful, classical diffusion MRI protocols relying on the Stejskal-Tanner experiment [7] suffer from the fact that the effects of distributions in pore size, anisotropy, and orientation are intrinsically entangled. A partial solution to this problem is provided by the double diffusion encoding (DDE) family of NMR methods [8], which can give estimates of the pore size and shape even in the presence of orientational disorder [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Current in vivo versions of DDE permit detection of anisotropy in areas of the human brain that are macroscopically isotropic [24] and the assignment of metabolitespecific compartment shapes in animal models [25]. Despite these impressive feats, DDE yields ambiguous results if the investigated volume element comprises several types of water environments, the presence of which has been inferred by fitting multicomponent biophysical models [26][27][28][29] to in vivo data acquired with the StejskalTanner method [30,31]. Selection of a single model from all the ones that are able to reproduce the experimental data remains a challenge [29]. The key to future progress in diffusion NMR and MRI of heterogeneous anisotropic materials lies in designing a method to unambiguously resolve and quantify water compartments with respect to their size and anisotropy, irrespective of the details of their orientations. Once this goal has been achieved, the obtained information could be used as input for existing methods to estimate distributions of axon diameters [4] and orientations [32][33][34].In solid-state NMR spectroscopy [35], the eigenvalues and eigenvectors of the chemical shift tensors can be determined through the dependence of the nuclear spin Hamiltonian on the orientation of the tensors with respect to the static magnetic field. We have recently poin...

Despite their widespread use in non-invasive studies of porous materials, conventional MRI methods yield ambiguous results for microscopically heterogeneous materials such as brain tissue. While the forward link between microstructure and MRI observables is well understood, the inverse problem of separating the signal contributions from different microscopic pores is notoriously difficult. Here, we introduce an experimental protocol where heterogeneity is resolved by establishing 6D correlations between the individual values of isotropic diffusivity, diffusion anisotropy, orientation of the diffusion tensor, and relaxation rates of distinct populations. Such procedure renders the acquired signal highly specific to the sample’s microstructure, and allows characterization of the underlying pore space without prior assumptions on the number and nature of distinct microscopic environments. The experimental feasibility of the suggested method is demonstrated on a sample designed to mimic the properties of nerve tissue. If matched to the constraints of whole body scanners, this protocol could allow for the unconstrained determination of the different types of tissue that compose the living human brain.

Abstract. Magnetic resonance imaging (MRI) is the primary method for noninvasive investigations of the human brain in health, disease, and development but yields data that are difficult to interpret whenever the millimeter-scale voxels contain multiple microscopic tissue environments with different chemical and structural properties. We propose a novel MRI framework to quantify the microscopic heterogeneity of the living human brain as spatially resolved five-dimensional relaxation–diffusion distributions by augmenting a conventional diffusion-weighted imaging sequence with signal encoding principles from multidimensional solid-state nuclear magnetic resonance (NMR) spectroscopy, relaxation–diffusion correlation methods from Laplace NMR of porous media, and Monte Carlo data inversion. The high dimensionality of the distribution space allows resolution of multiple microscopic environments within each heterogeneous voxel as well as their individual characterization with novel statistical measures that combine the chemical sensitivity of the relaxation rates with the link between microstructure and the anisotropic diffusivity of tissue water. The proposed framework is demonstrated on a healthy volunteer using both exhaustive and clinically viable acquisition protocols.

In biological tissues, typical MRI voxels comprise multiple microscopic environments, the local organization of which can be captured by microscopic diffusion tensors. The measured diffusion MRI signal can, therefore, be written as the multidimensional Laplace transform of an intravoxel diffusion tensor distribution (DTD). Tensor-valued diffusion encoding schemes have been designed to probe specific features of the DTD, and several algorithms have been introduced to invert such data and estimate statistical descriptors of the DTD, such as the mean diffusivity, the variance of isotropic diffusivities, and the mean squared diffusion anisotropy. However, the accuracy and precision of these estimations have not been assessed systematically and compared across methods. In this article, we perform and compare such estimations in silico for a one-dimensional Gamma fit, a generalized two-term cumulant approach, and two-dimensional and four-dimensional Monte-Carlo-based inversion techniques, using a clinically feasible tensor-valued acquisition scheme. In particular, we compare their performance at different signal-to-noise ratios (SNRs) for voxel contents varying in terms of the aforementioned statistical descriptors, orientational order, and fractions of isotropic and anisotropic components. We find that all inversion techniques share similar precision (except for a lower precision of the two-dimensional Monte Carlo inversion) but differ in terms of accuracy. While the Gamma fit exhibits infinite-SNR biases when the signal deviates strongly from monoexponentiality and is unaffected by orientational order, the generalized cumulant approach shows infinite-SNR biases when this deviation originates from the variance in isotropic diffusivities or from the low orientational order of anisotropic diffusion components. The two-dimensional Monte Carlo inversion shows remarkable accuracy in all systems studied, given that the acquisition scheme possesses enough directions to yield a rotationally invariant powder average. The four-dimensional Monte Carlo inversion presents no infinite-SNR bias, but suffers significantly from noise in the data, while preserving good contrast in most systems investigated. KEYWORDS diffusion MRI, in silico validation, Laplace inversion, microstructure, tensor-valued diffusion encoding 1 INTRODUCTION Diffusion magnetic resonance imaging (dMRI) allows the characterization of living tissues below the millimeter scale set by typical imaging voxel sizes. The basic principle of dMRI techniques is to use magnetic field gradients to encode the acquired signal with information about the

Diffusion MRI techniques are used widely to study the characteristics of the human brain connectome in vivo. However, to resolve and characterise white matter (WM) fibres in heterogeneous MRI voxels remains a challenging problem typically approached with signal models that rely on prior information and constraints. We have recently introduced a 5D relaxation-diffusion correlation framework wherein multidimensional diffusion encoding strategies are used to acquire data at multiple echotimes to increase the amount of information encoded into the signal and ease the constraints needed for signal inversion. Nonparametric Monte Carlo inversion of the resulting datasets yields 5D relaxation-diffusion distributions where contributions from different sub-voxel tissue environments are separated with minimal assumptions on their microscopic properties. Here, we build on the 5D correlation approach to derive fibre-specific metrics that can be mapped throughout the imaged brain volume. Distribution components ascribed to fibrous tissues are resolved, and subsequently mapped to a dense mesh of overlapping orientation bins to define a smooth orientation distribution function (ODF). Moreover, relaxation and diffusion measures are correlated to each independent ODF coordinate, thereby allowing the estimation of orientation-specific relaxation rates and diffusivities. The proposed method is tested on a healthy volunteer, where the estimated ODFs were observed to capture major WM tracts, resolve fibre crossings, and, more importantly, inform on the relaxation and diffusion features along with distinct fibre bundles. If combined with fibre-tracking algorithms, the methodology presented in this work has potential for increasing the depth of characterisation of microstructural properties along individual WM pathways.

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