Two-Dimensional Correlation of Isotropic and Directional Diffusion Using NMR

Abstract

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...

Axon Diameters and Myelin Content Modulate Microscopic Fractional Anisotropy at Short Diffusion Times in Fixed Rat Spinal Cord

“…Methods other than D(O)DE, targeting µFA such as tailoring b-tensor shapes are emerging, with many potential applications [77][78][79][80]. However, such methods may be confounded by time-dependent diffusion effects [27,[81][82][83], whereas D(O)DE at long mixing times naturally avoids these confounds [43].…”

Magnetic resonance microdynamic imaging reveals distinct tissue microenvironments

“…However, these strategies would not help to distinguish between dispersed axons or dendrites that exhibit identical diffusion profiles as a heterogeneous distribution of isotropic tissue components (Mitra, 1995). The difference between such cases can be fully captured by estimating the 2D correlation of isotropic and directional diffusion (de Almeida Martins and Topgaard, 2016). Although still limited to NMR applications, this method may be used in conjunction with the MADCO framework to significantly reduce the number of acquisitions in the densely sampled 2D parameter space, thereby permitting measurements within the time frame of clinical MRI.…”

Characterizing intra‐axonal water diffusion with direction‐averaged triple diffusion encoding MRI

“…Our TDE sequence is identical to the Stejskal‐Tanner sequence, except with additional diffusion encoding gradients that are oriented in directions orthogonal to the primary gradients in a manner so as to make the b ‐matrix axially symmetric. Similar sequences have been previously applied to characterize microstructure of diffusive media in several prior studies . For gradient strengths of 80 mT/m and a radial b ‐value of 500 s/mm 2 , it would take about 50 ms to play out the full set of radial diffusion encoding gradients.…”

“…This new approach requires data from a specific triple diffusion encoding (TDE) MRI pulse sequence, which augments the usual Stejskal‐Tanner pulse sequence by adding a set of weak diffusion encoding gradients oriented orthogonally to the direction of the main gradients that provide the primary diffusion weighting. This unconventional pulse sequence is not typically available on commercial MRI systems, and it is inspired by recent work showing the value of dMRI sequences with complex gradient waveforms . Here we present the theory for this new method, describe numerical simulations that illustrate its application, and discuss practical considerations relevant to the implementation the TDE pulse sequence.…”