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Quantitative diffusion imaging techniques enable the characterization of tissue microstructural properties of the human brain "in vivo", and are widely used in neuroscientific and clinical contexts. In this review, we present the basic physical principles behind diffusion imaging and provide an overview of the current diffusion techniques, including standard and advanced techniques as well as their main clinical applications. Standard diffusion tensor imaging (DTI) offers sensitivity to changes in microstructure due to diseases and enables the characterization of single fiber distributions within a voxel as well as diffusion anisotropy. Nonetheless, its inability to represent complex intravoxel fiber topologies and the limited biological specificity of its metrics motivated the development of several advanced diffusion MRI techniques. For example, high-angular resolution diffusion imaging (HARDI) techniques enabled the characterization of fiber crossing areas and other complex fiber topologies in a single voxel and supported the development of higher-order signal representations aiming to decompose the diffusion MRI signal into distinct microstructure compartments. Biophysical models, often known by their acronym (e.g., CHARMED, WMTI, NODDI, DBSI, DIAMOND) contributed to capture the diffusion properties from each of such tissue compartments, enabling the computation of voxel-wise maps of axonal density and/or morphology that hold promise as clinically viable biomarkers in several neurological and neuroscientific applications; for example, to quantify tissue alterations due to disease or healthy processes. Current challenges and limitations of state-of-the-art models are discussed, including validation efforts. Finally, novel diffusion encoding approaches (e.g., b-tensor or double diffusion encoding) may increase the biological specificity of diffusion metrics towards intra-voxel diffusion heterogeneity in clinical settings, holding promise in neurological applications.

Formalin fixation has been shown to substantially reduce T2 estimates, primarily driven by the presence of fixative in tissue. Prior to scanning, post‐mortem samples are often placed into a fluid that has more favourable imaging properties. This study investigates whether there is evidence for a change in T2 in regions close to the tissue surface due to fixative outflux into this surrounding fluid. Furthermore, we investigate whether a simulated spatial map of fixative concentration can be used as a confound regressor to reduce T2 inhomogeneity. To achieve this, T2 maps and diffusion tensor estimates were obtained in 14 whole, formalin‐fixed post‐mortem brains placed in Fluorinert approximately 48 hr prior to scanning. Seven brains were fixed with 10% formalin and seven brains were fixed with 10% neutral buffered formalin (NBF). Fixative outflux was modelled using a proposed kinetic tensor (KT) model, which incorporates voxelwise diffusion tensor estimates to account for diffusion anisotropy and tissue‐specific diffusion coefficients. Brains fixed with 10% NBF revealed a spatial T2 pattern consistent with modelled fixative outflux. Confound regression of fixative concentration reduced T2 inhomogeneity across both white and grey matter, with the greatest reduction attributed to the KT model versus simpler models of fixative outflux. No such effect was observed in brains fixed with 10% formalin. Correlations between the transverse relaxation rate R 2 and ferritin/myelin proteolipid protein (PLP) histology lead to an increased similarity for the relationship between R 2 and PLP for the two fixative types after KT correction., Fixed post‐mortem tissue samples are often placed into a fluid with more favourable imaging properties prior to MRI scanning. This study investigates whether there is evidence for a change in T2 in regions close to the tissue surface due to fixative outflux into this surrounding fluid, and whether a simulated spatial map of fixative concentration can be used as a confound regressor to reduce T2 inhomogeneity. Modelling fixative outflux using a proposed kinetic tensor (KT) model, we identified a spatial T2 pattern consistent with modelled fixative outflux, and demonstrated that regressing fixative concentration reduced T2 inhomogeneity across both white and grey matter in brains fixed with 10% neutral buffered formalin (NBF).

Objective: Focused ultrasound (FUS) has emerged as a non-invasive technique to locally and reversibly disrupt the blood-brain barrier (BBB). Here, we investigate the use of diffusion tensor imaging (DTI) as a means of detecting FUS-induced BBB opening at the absence of an MRI contrast agent. A non-human primate (NHP) was repeatedly treated with FUS and preformed circulating microbubbles to transiently disrupt the BBB (n = 4). T1- and diffusion-weighted MRI scans were acquired after the ultrasound treatment, with and without gadolinium-based contrast agent, respectively. Both scans were registered with a high-resolution T1-weighted scan of the NHP to investigate signal correlations. DTI detected an increase in fractional anisotropy from 0.21 ± 0.02 to 0.38 ± 0.03 (82.6 ± 5.2% change) within the targeted area one hour after BBB opening. Enhanced DTI contrast overlapped by 77.22 ± 9.2% with hyper-intense areas of gadolinium-enhanced T1-weighted scans, indicating diffusion anisotropy enhancement only within the BBB opening volume. Diffusion was highly anisotropic and unidirectional within the treated brain region, as indicated by the direction of the principal diffusion eigenvectors. Polar and azimuthal angle ranges decreased by 35.6% and 82.4%, respectively, following BBB opening. Evaluation of the detection methodology on a second NHP (n = 1) confirmed the across-animal feasibility of the technique. In conclusion, DTI may be used as a contrast-free MR imaging modality in lieu of contrast-enhanced T1 mapping for detecting BBB opening during focused-ultrasound treatment or evaluating BBB integrity in brain-related pathologies.

Zeolite morphology is crucial in determining their catalytic activity, selectivity and stability, but quantitative descriptors of such a morphology effect are challenging to define. Here we introduce a descriptor that accounts for the morphology effect in the catalytic performances of H-ZSM-5 zeolite for C4 olefin catalytic cracking. A series of H-ZSM-5 zeolites with similar sheet-like morphology but different c-axis lengths were synthesized. We found that the catalytic activity and stability is improved in samples with longer c-axis. Combining time-resolved in-situ FT-IR spectroscopy with molecular dynamics simulations, we show that the difference in catalytic performance can be attributed to the anisotropy of the intracrystalline diffusive propensity of the olefins in different channels. Our descriptor offers mechanistic insight for the design of highly effective zeolite catalysts for olefin cracking. The morphology of zeolites influences their catalytic activity, but defining descriptors to link morphology and activity is challenging. Here, time-resolved in situ FT-IR spectroscopy and MD simulations reveal that the difference in the catalytic performance of a series of H-ZSM-5 zeolites with similar sheet-like morphology can be attributed to intracrystalline diffusive propensities in different channels.

Labeling in diffusion measurements by pulsed field gradient (PFG) NMR is based on the observation of the phase of nuclear spins acquired in a constant magnetic field with purposefully superimposed field gradients. This labeling does in no way affect microdynamics and provides information about the probability distribution of molecular displacements as a function of time. An introduction of the measuring principle is followed by a detailed description of the ranges of measurements and their limitation. Particular emphasis is given to an explanation of possible pitfalls in the measurements and the ways to circumvent them. Showcases presented for illustrating the wealth of information provided by PFG NMR include a survey on the various patterns of concentration dependence of intra-particle diffusion and examples of transport inhibition by additional transport resistances within the nanoporous particles and on their external surface. The latter information is attained by combination with the outcome of tracer exchange experiments, which are shown to become possible via a special formalism of PFG NMR data analysis. Further evidence provided by PFG NMR concerns diffusion enhancement in pore hierarchies, diffusion anisotropy and the impact of diffusion on chemical conversion in porous catalysts. A compilation of the specifics of PFG NMR and of the parallels with other measurement techniques concludes the paper.

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.

Objective Delineation of malformations of cortical development (MCD) is central in presurgical evaluation of drug-resistant epilepsy. Delineation using magnetic resonance imaging (MRI) can be ambiguous, however, because the conventional T1 - and T2 -weighted contrasts depend strongly on myelin for differentiation of cortical tissue and white matter. Variations in myelin content within both cortex and white matter may cause MCD findings on MRI to change size, become undetectable, or disagree with histopathology. The novel tensor-valued diffusion MRI (dMRI) technique maps microscopic diffusion anisotropy, which is sensitive to axons rather than myelin. This work investigated whether tensor-valued dMRI may improve differentiation of cortex and white matter in the delineation of MCD. Methods Tensor-valued dMRI was performed on a 7 T MRI scanner in 13 MCD patients (age = 32 ± 13 years) featuring periventricular heterotopia, subcortical heterotopia, focal cortical dysplasia, and polymicrogyria. Data analysis yielded maps of microscopic anisotropy that were compared with T1 -weighted and T2 -fluid-attenuated inversion recovery images and with the fractional anisotropy from diffusion tensor imaging. Results Maps of microscopic anisotropy revealed large white matter-like regions within MCD that were uniformly cortex-like in the conventional MRI contrasts. These regions were seen particularly in the deep white matter parts of subcortical heterotopias and near the gray-white boundaries of focal cortical dysplasias and polymicrogyrias. Significance By being sensitive to axons rather than myelin, mapping of microscopic anisotropy may yield a more robust differentiation of cortex and white matter and improve MCD delineation in presurgical evaluation of epilepsy.

One of the most intriguing phenomena under radiation is the self-organization of defects, such as the void superlattices, which have been observed in a list of bcc and fcc metals and alloys when the irradiation conditions fall into certain windows defined by temperature and dose rate. A superlattice features a lattice parameter and a crystal structure. Previously, it has been shown that the superlattice parameter is given by the wavelength of vacancy concentration waves that develop when the uniform concentration field becomes unstable. This instability is driven thermodynamically by vacancy concentration supersaturation and affected by the irradiation condition. However, a theory that predicts the superlattice symmetry, i.e., the selection of superlattice structure, has remained missing decades after the first report of superlattices. By analyzing the nonlinear recombination between vacancies and self-interstitial-atoms (SIAs) in the discrete lattice space, this work establishes the physical connection between symmetry breaking and anisotropic SIA diffusion, allowing for predictions of void ordering during defect self-organization. The results suggest that while the instability is driven thermodynamically by vacancy supersaturation, the symmetry development is kinetically rather than thermodynamically driven. The significance of SIA diffusion anisotropy in affecting superlattice formation under irradiation is also indicated. Various superlattice structures can be predicted based on different SIA diffusion modes, and the predictions are in good agreement with atomistic simulations and previous experimental observations.

PURPOSE: A new method for enhancing the sensitivity of diffusion MRI (dMRI) by combining the data from single (sPFG) and double (dPFG) pulsed field gradient experiments is presented. METHODS: This method uses our JESTER framework to combine microscopic anisotropy information from dFPG experiments using a new method called diffusion tensor subspace imaging (DiTSI) to augment the macroscopic anisotropy information from sPFG data analyzed using our guided by entropy spectrum pathways method. This new method, called joint estimation diffusion imaging (JEDI), combines the sensitivity to macroscopic diffusion anisotropy of sPFG with the sensitivity to microscopic diffusion anisotropy of dPFG methods. RESULTS: Its ability to produce significantly more detailed anisotropy maps and more complete fiber tracts than existing methods within both brain white matter (WM) and gray matter (GM) is demonstrated on normal human subjects on data collected using a novel fast, robust, and clinically feasible sPFG/dPFG acquisition. CONCLUSIONS: The potential utility of this method is suggested by an initial demonstration of its ability to mitigate the problem of gyral bias. The capability of more completely characterizing the tissue structure and connectivity throughout the entire brain has broad implications for the utility and scope of dMRI in a wide range of research and clinical applications.

Polycrystalline thin films and single crystals of hybrid perovskites – a material group successfully used for photovoltaic and optoelectronic applications – reportedly display heterogeneous charge carrier dynamics often attributed to grain boundaries or crystalline strain. Here, we locally resolved the carrier diffusion in large, isolated methylammonium lead iodide (MAPbI3) grains via spatial- and time-resolved photoluminescence microscopy. We found that the anisotropic carrier dynamics directly correlate with the arrangement of ferroelastic twin domains. Comparing diffusion constants parallel and perpendicular to the domains showed carriers diffuse around 50–60% faster along the parallel direction. Extensive piezoresponse force microscopy experiments on the nature of the domain pattern suggest that the diffusion anisotropy most likely originates from structural and electrical anomalies at ferroelastic domain walls. We believe that the domain walls act as shallow energetic barriers, which delay the transversal diffusion of carriers. Furthermore, we demonstrate a rearrangement of the domains via heat treatment above the cubic-tetragnal phase transition. Together with the previously reported strain engineering via external stress, our findings promise additional routes to tailor the directionality of the charge carrier diffusion in MAPbI3-based photovoltaics and optoelectronics as well as other ferroelastic materials for optoelectronic applications.

The development of improved zeolite materials for applications in separation and catalysis requires understanding of mass transport. Herein, diffusion of single molecules is tracked in the straight and sinusoidal channels of the industrially relevant ZSM-5 zeolites using a combination of single-molecule localization microscopy and uniformly oriented zeolite thin films. Distinct motion behaviors are observed in zeolite channels with the same geometry, suggesting heterogeneous guest-host interactions. Quantification of the diffusion heterogeneities in the sinusoidal and straight channels suggests that the geometry of zeolite channels dictates the mobility and motion behavior of the guest molecules, resulting in diffusion anisotropy. The study of hierarchical zeolites shows that the addition of secondary pore networks primarily enhances the diffusivity of sinusoidal zeolite channels, and thus alleviating the diffusion limitations of microporous zeolites.

OBJECTIVES: The objectives of this exploratory study were to investigate the feasibility of multidimensional diffusion magnetic resonance imaging (MddMRI) in assessing diffusion heterogeneity at both a macroscopic and microscopic level in prostate cancer (PCa). MATERIALS AND METHODS: Informed consent was obtained from 46 subjects who underwent 3.0-T prostate multiparametric MRI, complemented with a prototype spin echo–based MddMRI sequence in this institutional review board–approved study. Prostate cancer tumors and comparative normal tissue from each patient were contoured on both apparent diffusion coefficient and MddMRI-derived mean diffusivity (MD) maps (from which microscopic diffusion heterogeneity [MKi] and microscopic diffusion anisotropy were derived) using 3D Slicer. The discriminative ability of MddMRI-derived parameters to differentiate PCa from normal tissue was determined using the Friedman test. To determine if tumor diffusion heterogeneity is similar on macroscopic and microscopic scales, the linear association between SD of MD and mean MKi was estimated using robust regression (bisquare weighting). Hypothesis testing was 2 tailed; P values less than 0.05 were considered statistically significant. RESULTS: All MddMRI-derived parameters could distinguish tumor from normal tissue in the fixed-effects analysis (P < 0.0001). Tumor MKi was higher (P < 0.05) compared with normal tissue (median, 0.40; interquartile range, 0.29–0.52 vs 0.20–0.18; 0.25), as was tumor microscopic diffusion anisotropy (0.55; 0.36–0.81 vs 0.20–0.15; 0.28). The MKi could not be predicted (no significant association) by SD of MD. There was a significant correlation between tumor volume and SD of MD (R(2) = 0.50, slope = 0.008 μm(2)/ms per millimeter, P < 0.001) but not between tumor volume and MKi. CONCLUSIONS: This explorative study demonstrates that MddMRI provides novel information on MKi and microscopic anisotropy, which differ from measures at the macroscopic level. MddMRI has the potential to characterize tumor tissue heterogeneity at different spatial scales.

PURPOSE Several neurological conditions are associated with microstructural changes in the hippocampus that can be observed using DWI. Imaging studies often use protocols with whole-brain coverage, imposing limits on image resolution and worsening partial-volume effects. Also, conventional single-diffusion-encoding methods confound microscopic diffusion anisotropy with size variance of microscopic diffusion environments. This study addresses these issues by implementing a multidimensional diffusion-encoding protocol for microstructural imaging of the hippocampus at high resolution. METHODS The hippocampus of 8 healthy volunteers was imaged at 1.5-mm isotropic resolution with a multidimensional diffusion-encoding sequence developed in house. Microscopic fractional anisotropy (µFA) and normalized size variance (CMD ) were estimated using q-space trajectory imaging, and their values were compared with DTI metrics. The overall scan time was 1 hour. The reproducibility of the protocol was confirmed with scan-rescan experiments, and a shorter protocol (14 minutes) was defined for situations with time constraints. RESULTS Mean µFA (0.47) was greater than mean FA (0.20), indicating orientation dispersion in hippocampal tissue microstructure. Mean CMD was 0.17. The reproducibility of q-space trajectory imaging metrics was comparable to DTI, and microstructural metrics in the healthy hippocampus are reported. CONCLUSION This work shows the feasibility of high-resolution microscopic anisotropy imaging in the human hippocampus at 3 T and provides reference values for microstructural metrics in a healthy hippocampus.

Purpose To characterize the magnetic susceptibility changes of liver fibrosis using susceptibility tensor imaging. Methods Liver biopsy tissue samples of patients with liver fibrosis were obtained. Three-dimensional gradient-echo and diffusion-weighted images were acquired at 9.4 T. Susceptibility tensors of the samples were calculated using the gradient-echo phase signal acquired at 12 different orientations relative to the B0 field. Susceptibility anisotropy of the liver collagen fibers was quantified and compared with diffusion anisotropy, measured by DTI. For validation, a comparison was made to histology including hematoxylin and eosin staining, iron staining, and Masson's trichrome staining. Results Areas with strong diamagnetic susceptibility were observed in the tissue samples forming fibrous patterns. This diamagnetic susceptibility was highly anisotropic. Both the mean magnetic susceptibility and susceptibility anisotropy of collagen fibers exhibited a strong contrast against the surrounding nonfibrotic tissues. The same regions also showed an elevated diffusion anisotropy but with much lower tissue contrast. Masson's trichrome staining identified concentrated collagens in the fibrous regions with high susceptibility anisotropy, and a linear correlation was found between the susceptibility anisotropy and the histology-based staging. Conclusion Diamagnetic susceptibility indicates the presence of collagen in the fibrotic liver tissues. Mapping magnetic susceptibility anisotropy may serve as a potential marker to quantify collagen fiber changes in patients with liver fibrosis.

Connectivity-based parcellation of subcortical structures using diffusion tractography is now a common paradigm in neuroscience. These analyses often imply voxel-level specificity of connectivity, and the formation of compact, spatially coherent clusters is often taken as strong imaging-based evidence for anatomically distinct subnuclei in an individual. In this study, we demonstrate that internal structure in diffusion anisotropy is not necessary for a plausible parcellation to be obtained, by spatially permuting diffusion parameters within the thalami and repeating the parcellation. Moreover, we show that, in a winner-takes-all paradigm, most voxels receive the same label before and after this shuffling process-a finding that is stable across image acquisitions and tractography algorithms. We therefore suggest that such parcellations should be interpreted with caution.

The ongoing myelination of white-matter fiber bundles plays a significant role in brain development. However, reliable and consistent identification of these bundles from infant brain MRIs is often challenging due to inherently low diffusion anisotropy, as well as motion and other artifacts. In this paper we introduce a new tool for automated probabilistic tractography specifically designed for newborn infants. Our tool incorporates prior information about the anatomical neighborhood of white-matter pathways from a training data set. In our experiments, we evaluate this tool on data from both full-term and prematurely born infants and demonstrate that it can reconstruct known white-matter tracts in both groups robustly, even in the presence of differences between the training set and study subjects. Additionally, we evaluate it on a publicly available large data set of healthy term infants (UNC Early Brain Development Program). This paves the way for performing a host of sophisticated analyses in newborns that we have previously implemented for the adult brain, such as pointwise analysis along tracts and longitudinal analysis, in both health and disease.

The recent experimental observation of twist-bend nematic phases has kindled interest on this new class of materials. The natural twist-bend deformations of the director results in a nanoscale pitch (pseudo-layers) probed by freeze-fracture transmission electron microscopy (FFTEM) and very recently it was verified by resonant soft x-ray scattering (RSoXS) technique. It is pivotal that other mechanisms arise to certify the recent experiments and corroborate the theoretical models. Impedance spectroscopy is a method commonly used to investigate the dynamics of bound or mobile charge in the bulk or interfacial regions of materials in the vast field of condensed matter. Here we use impedance spectroscopy technique to investigate the electrical transport properties of twist-bend nematic phase in a dimeric liquid crystal mixture. The experimental data is analyzed in the framework of an anomalous diffusion equation coupled with Poisson’s equation where bulk and surface contributions are taken into account. Our fitting results agree well with the impedance measurements in the nematic (N) and the twist-bend ( N tb ) phase and indicate that strong subdiffusive regimes take place in the system. We also find a large diffusion anisotropy depending on the imposed orientation, which is associated with motions along or through the pseudo-layers, showing that the impedance technique can be used to explore the molecular arrangement of N tb phases.

Ordering and self-organization are critical in determining the dynamics of reaction-diffusion systems. Here we show a unique pattern formation mechanism, dictated by the coupling of thermodynamic instability and kinetic anisotropy. Intrinsically different from the physical origin of Turing instability and patterning, the ordered patterns we obtained are caused by the interplay of the instability from uphill diffusion, the symmetry breaking from anisotropic diffusion, and the reactions. To understand the formation of the void/gas bubble superlattices in crystals under irradiation, we establish a general theoretical framework to predict the symmetry selection of superlattice structures associated with anisotropic diffusion. Through analytical study and phase field simulations, we found that the symmetry of a superlattice is determined by the coupling of diffusion anisotropy and the reaction rate, which indicates a new type of bifurcation phenomenon. Our discovery suggests a means for designing target experiments to tailor different microstructural patterns.

We report controlled fractal growth of atomically thin transition metal dichalcogenides (TMDCs) by chemical vapor deposition, with morphological evolution from dendritic to triangular. Several important growth parameters controlling the fractal dimensions were identified, including the relaxation rate, adhesion coefficient, diffusion anisotropy and growth time. A model based on nucleation, diffusion limited aggregation and relaxation was proposed to explain the morphological evolution. The results of the computational simulation based on this model are in good agreement with the experimental results. Our study sheds light on the growth mechanism of TMDCs and paves the way for growth of TMDCs with improved controllability.

Purpose\ud \ud The apparent propagator anisotropy (APA) is a new diffusion MRI metric that, while drawing on the benefits of the ensemble averaged propagator anisotropy (PA) compared to the fractional anisotropy (FA), can be estimated from single‐shell data.\ud Theory and Methods\ud \ud Computation of the full PA requires acquisition of large datasets with many diffusion directions and different b‐values, and results in extremely long processing times. This has hindered adoption of the PA by the community, despite evidence that it provides meaningful information beyond the FA. Calculation of the complete propagator can be avoided under the hypothesis that a similar sensitivity/specificity may be achieved from apparent measurements at a given shell. Assuming that diffusion anisotropy (DiA) is nondependent on the b‐value, a closed‐form expression using information from one single shell (ie, b‐value) is reported.\ud Results\ud \ud Publicly available databases with healthy and diseased subjects are used to compare the APA against other anisotropy measures. The structural information provided by the APA correlates with that provided by the PA for healthy subjects, while it also reveals statistically relevant differences in white matter regions for two pathologies, with a higher reliability than the FA. Additionally, APA has a computational complexity similar to the FA, with processing‐times several orders of magnitude below the PA.\ud Conclusions\ud \ud The APA can extract more relevant white matter information than the FA, without any additional demands on data acquisition. This makes APA an attractive option for adoption into existing diffusion MRI analysis pipelines.

Diffusion magnetic resonance imaging (MRI) offers a wealth of information regarding the neonatal brain. Diffusion anisotropy values reflect changes in the microstructure that accompany early maturation of white and gray matter. In term neonates with neonatal encephalopathy, diffusion imaging provides a useful means of assessing brain injury during the first week of life. In preterm neonates, measures of white matter anisotropy provide information on the nature and extent of white matter disruption. Subsequently, diffusion MRI plays an important role in illuminating fundamental elements of brain development and fulfilling the clinical need to develop prognostic indicators for term and preterm infants.

Microscopic diffusion anisotropy imaging using diffusion-weighted MRI and multidimensional diffusion encoding is a promising method for quantifying clinically and scientifically relevant microstructural properties of neural tissue. Several methods for estimating microscopic fractional anisotropy (µFA), a normalized measure of microscopic diffusion anisotropy, have been introduced but the differences between the methods have received little attention thus far. In this study, the accuracy and precision of µFA estimation using q-space trajectory encoding and different signal models were assessed using imaging experiments and simulations. Three healthy volunteers and a microfibre phantom were imaged with five non-zero b-values and gradient waveforms encoding linear and spherical b-tensors. Since the ground-truth µFA was unknown in the imaging experiments, Monte Carlo random walk simulations were performed using axon-mimicking fibres for which the ground truth was known. Furthermore, parameter bias due to time-dependent diffusion was quantified by repeating the simulations with tuned waveforms, which have similar power spectra, and with triple diffusion encoding, which, unlike q-space trajectory encoding, is not based on the assumption of time-independent diffusion. The truncated cumulant expansion of the powder-averaged signal, gamma-distributed diffusivities assumption, and q-space trajectory imaging, a generalization of the truncated cumulant expansion to individual signals, were used to estimate µFA. The gamma-distributed diffusivities assumption consistently resulted in greater µFA values than the second order cumulant expansion, 0.1 greater when averaged over the whole brain. In the simulations, the generalized cumulant expansion provided the most accurate estimates. Importantly, although time-dependent diffusion caused significant overestimation of µFA using all the studied methods, the simulations suggest that the resulting bias in µFA is less than 0.1 in human white matter.

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.