Anisotropy Measure from Three Diffusion-Encoding Gradient Directions

PurposeWe propose a method that can provide information about the anisotropy and orientation of diffusion in the brain from only 3 orthogonal gradient directions without imposing additional assumptions.MethodsThe method is based on the Diffusion Anisotropy (DiA) that measures the distance from a diffusion signal to its isotropic equivalent. The original formulation based on a Spherical Harmonics basis allows to go down to only 3 orthogonal directions in order to estimate the measure. In addition, an alternative simplification and a color-coding representation are also proposed.ResultsAcquisitions from a publicly available database are used to test the viability of the proposal. The DiA succeeded in providing anisotropy information from the white matter using only 3 diffusion-encoding directions. The price to pay for such reduced acquisition is an increment in the variability of the data and a subestimation of the metric.ConclusionsThe calculation of anisotropy information from DMRI is feasible using fewer than 6 gradient directions by using DiA. The method is totally compatible with existing acquisition protocols and it may provide complementary information about orientation in fast diffusion acquisitions.

Diffusion anisotropy descriptor revealing morphology effect of H-ZSM-5 zeolite for olefin catalytic cracking

Zeolite morphology is vital in determining catalytic activity, selectivity and stability in zeolite catalysis, while quantitative description of morphology effect is great challenging but highly desirable. Herein, a descriptor to elucidate the morphology effect is proposed by revealing the diffusion anisotropy in straight and sinusoidal channels of H-ZSM-5 zeolite for olefin catalytic cracking. A series of H-ZSM-5 zeolites with similar nano-sheet morphology were precisely synthesized in which only the length in c-axis varies. It is unexpectedly demonstrated that the catalytic activity and stability can be obviously improved by employing samples with longer length in c-axis. Combining time-resolved in-situ FT-IR spectroscopy with molecular dynamic simulations, we revealed that the difference in catalytic performance can be attributed to the intracrystalline diffusive propensity in different channels. This work not only provides a clear descriptor revealing morphology effect, but also offers deep insight into design of highly effective zeolite catalysts for olefin catalytic cracking.

On a role of anisotropy and nonlinear diffusive effects during the construction of waveguides in the lithium niobate

Direct numerical simulation of a process of hydrogen diffusive intrusion into the lithium niobate monocrystal is fulfilled with reference to the manufacturing two-channel system of waveguides. The calculations were carried out according to the technology of waveguides production, taking into account the presence of several stages, which at first include the material saturation with the protons by treating the working surface with the melt of benzoic acid, and then annealing the sample. The contribution of the nonlinear diffusion to the process of the waveguide shaping is analyzed. It is shown that the formation of a stepped waveguide boundary is significantly influenced by the procedure of monocrystal annealing. Heretofore, the annealing stage was not quantitatively investigated. It can be emphasized that the attention has not been paid to the possible role of the annealing on formation of the sharper boundary between the waveguide and its mother substrate. A theoretical model of anisotropic diffusion in a solid material is constructed on the basis of experimental data, which indicate the presence of a transitional surface layer with pronounced regular mesostructural directions in the polished lithium niobate monocrystal. Based on the derived equations, the waveguides shape in a cross-section was simulated numerically for different values of inclination angle of the main axes with respect to the cut lines of the crystal. It is demonstrated that in the region of the waveguide bifurcation, when at the stage of protons intrusion the interaction of diffusive fluxes is possible, the diffusion anisotropy can lead to a breakdown of the waveguides symmetry, which can affect their optical properties.

Fo and Ni Relations in Olivine Differentiate between Crystallization and Diffusion Trends

Nickel is a strongly compatible element in olivine, and thus fractional crystallization of olivine typically results in a concave-up trend on a Fo–Ni diagram. ‘Ni-enriched’ olivine compositions are considered those that fall above such a crystallization trend. To explain Ni-enriched olivine crystals, we develop a set of theoretical and computational models to describe how primitive olivine phenocrysts from a parent (high-Mg, high-Ni) basalt re-equilibrate with an evolved (low-Mg, low-Ni) melt through diffusion. These models describe the progressive loss of Fo and Ni in olivine cores during protracted diffusion for various crystal shapes and different relative diffusivities for Ni and Fe–Mg. In the case when the diffusivity of Ni is lower than that for Fe–Mg interdiffusion, then olivine phenocrysts affected by protracted diffusion form a concave-down trend that contrasts with the concave-up crystallization trend. Models for different simple geometries show that the concavity of the diffusion trend does not depend on the size of the crystals and only weakly depends on their shape. We also find that the effect of diffusion anisotropy on trend concavity is of the same magnitude as the effect of crystal shape. Thus, both diffusion anisotropy and crystal shape do not significantly change the concave-down diffusion trend. Three-dimensional numerical diffusion models using a range of more complex, realistic olivine morphologies with anisotropy corroborate this conclusion. Thus, the curvature of the concave-down diffusion trend is mainly determined by the ratio of Ni and Fe–Mg diffusion coefficients. The initial and final points of the diffusion trend are in turn determined by the compositional contrast between mafic and more evolved melts that have mixed to cause disequilibrium between olivine cores and surrounding melt. We present several examples of measurements on olivine from arc basalts from Kamchatka, and published olivine datasets from mafic magmas from non-subduction settings (lamproites and kimberlites) that are consistent with diffusion-controlled Fo–Ni behaviour. In each case the ratio of Ni and Fe–Mg diffusion coefficients is indicated to be <1. These examples show that crystallization and diffusion can be distinguished by concave-up and concave-down trends in Fo–Ni diagrams.

Rapid Microscopic Fractional Anisotropy Imaging via an Optimized Kurtosis Formulation

Water diffusion anisotropy in the human brain is affected by disease, trauma, and development. Microscopic fractional anisotropy (μFA) is a diffusion MRI (dMRI) metric that can quantify water diffusion anisotropy independent of neuron fiber orientation dispersion. However, there are several different techniques to estimate μFA and few have demonstrated full brain imaging capabilities within clinically viable scan times and resolutions. Here, we present an optimized spherical tensor encoding (STE) technique to acquire μFA directly from the 2nd order cumulant expansion of the dMRI signal (i.e. diffusion kurtosis) which requires fewer powder-averaged signals than other STE fitting techniques and can be rapidly computed. We found that the optimal dMRI parameters for white matter μFA imaging were a maximum b-value of 2000 s/mm2 and a ratio of isotropic to linear tensor encoded acquisitions of 1.7 for our system specifications. We then compared two implementations of the direct approach to the well-established gamma model in 4 healthy volunteers on a 3 Tesla system. One implementation of the direct cumulant approach used mean diffusivity (D) obtained from a 2nd order fit of the cumulant expansion, while the other used a linear estimation of D from the low b-values. Both implementations of the direct approach showed strong linear correlations with the gamma model (ρ=0.97 and ρ=0.90) but mean biases of −0.11 and −0.02 relative to the gamma model were also observed, respectively. All three μFA measurements showed good test-retest reliability (ρ≥0.79 and bias=0). To demonstrate the potential scan time advantage of the direct approach, 2 mm isotropic resolution μFA was demonstrated over a 10 cm slab using a subsampled data set with fewer powder-averaged signals that would correspond to a 3.3-minute scan. Accordingly, our results introduce an optimization procedure that has enabled clinically relevant, nearly full brain μFA in only several minutes.HighlightsDemonstrated method to acquire optimal parameters for regression μFA imagingμFA measured using an optimized linear regression method at 3TFirst μFA comparison between direct regression approach and the gamma modelBoth approaches correlated strongly in white matter in healthy volunteersNearly full brain μFA demonstrated in a 3.3-minute scan at 2 mm isotropic resolution