Generalised finite volume strategies for simulating transport in strongly orthotropic porous media

In this work two different finite volume computational strategies for solving a representative two-dimensional diffusion equation in an orthotropic medium are considered. When the diffusivity tensor is treated as linear, this problem admits an analytic solution used for analysing the accuracy of the proposed numerical methods. In the first method, the gradient approximation techniques discussed by Jayantha and Turner [Numerical Heat Transfer, Part B: Fundamentals, 40, pp.367–390, 2001] are applied directly to the

Transport coefficients for the shear dynamo problem at small Reynolds numbers

We build on the formulation developed in S. Sridhar and N. K. Singh J. Fluid Mech. 664, 265 (2010)] and present a theory of the shear dynamo problem for small magnetic and fluid Reynolds numbers, but for arbitrary values of the shear parameter. Specializing to the case of a mean magnetic field that is slowly varying in time, explicit expressions for the transport coefficients alpha(il) and eta(iml) are derived. We prove that when the velocity field is nonhelical, the transport coefficient alpha(il) vanishes. We then consider forced, stochastic dynamics for the incompressible velocity field at low Reynolds number. An exact, explicit solution for the velocity field is derived, and the velocity spectrum tensor is calculated in terms of the Galilean-invariant forcing statistics. We consider forcing statistics that are nonhelical, isotropic, and delta correlated in time, and specialize to the case when the mean field is a function only of the spatial coordinate X-3 and time tau; this reduction is necessary for comparison with the numerical experiments of A. Brandenburg, K. H. Radler, M. Rheinhardt, and P. J. Kapyla Astrophys. J. 676, 740 (2008)]. Explicit expressions are derived for all four components of the magnetic diffusivity tensor eta(ij) (tau). These are used to prove that the shear-current effect cannot be responsible for dynamo action at small Re and Rm, but for all values of the shear parameter.

Characterisation of the micro-architecture of direct writing melt electrospun tissue engineering scaffolds using diffusion tensor and computed tomography microimaging

This article describes the first steps toward comprehensive characterization of molecular transport within scaffolds for tissue engineering. The scaffolds were fabricated using a novel melt electrospinning technique capable of constructing 3D lattices of layered polymer fibers with well - defined internal microarchitectures. The general morphology and structure order was then determined using T 2 - weighted magnetic resonance imaging and X - ray microcomputed tomography. Diffusion tensor microimaging was used to measure the time - dependent diffusivity and diffusion anisotropy within the scaffolds. The measured diffusion tensors were anisotropic and consistent with the cross - hatched geometry of the scaffolds: diffusion was least restricted in the direction perpendicular to the fiber layers. The results demonstrate that the cross - hatched scaffold structure preferentially promotes molecular transport vertically through the layers ( z - axis), with more restricted diffusion in the directions of the fiber layers ( x – y plane). Diffusivity in the x – y plane was observed to be invariant to the fiber thickness. The characteristic pore size of the fiber scaffolds can be probed by sampling the diffusion tensor at multiple diffusion times. Prospective application of diffusion tensor imaging for the real - time monitoring of tissue maturation and nutrient transport pathways within tissue engineering scaffolds is discussed.

Fluid registration of diffusion tensor images using information theory

We apply an information-theoretic cost metric, the symmetrized Kullback-Leibler (sKL) divergence, or $J$-divergence, to fluid registration of diffusion tensor images. The difference between diffusion tensors is quantified based on the sKL-divergence of their associated probability density functions (PDFs). Three-dimensional DTI data from 34 subjects were fluidly registered to an optimized target image. To allow large image deformations but preserve image topology, we regularized the flow with a large-deformation diffeomorphic mapping based on the kinematics of a Navier-Stokes fluid. A driving force was developed to minimize the $J$-divergence between the deforming source and target diffusion functions, while reorienting the flowing tensors to preserve fiber topography. In initial experiments, we showed that the sKL-divergence based on full diffusion PDFs is adaptable to higher-order diffusion models, such as high angular resolution diffusion imaging (HARDI). The sKL-divergence was sensitive to subtle differences between two diffusivity profiles, showing promise for nonlinear registration applications and multisubject statistical analysis of HARDI data.

A novel measure of fractional anisotropy based on the tensor distribution function

Fractional anisotropy (FA), a very widely used measure of fiber integrity based on diffusion tensor imaging (DTI), is a problematic concept as it is influenced by several quantities including the number of dominant fiber directions within each voxel, each fiber's anisotropy, and partial volume effects from neighboring gray matter. With High-angular resolution diffusion imaging (HARDI) and the tensor distribution function (TDF), one can reconstruct multiple underlying fibers per voxel and their individual anisotropy measures by representing the diffusion profile as a probabilistic mixture of tensors. We found that FA, when compared with TDF-derived anisotropy measures, correlates poorly with individual fiber anisotropy, and may sub-optimally detect disease processes that affect myelination. By contrast, mean diffusivity (MD) as defined in standard DTI appears to be more accurate. Overall, we argue that novel measures derived from the TDF approach may yield more sensitive and accurate information than DTI-derived measures.

Analysis of diffusion tensor magnetic resonance imaging data using principal component analysis

An analysis method for diffusion tensor (DT) magnetic resonance imaging data is described, which, contrary to the standard method (multivariate fitting), does not require a specific functional model for diffusion-weighted (DW) signals. The method uses principal component analysis (PCA) under the assumption of a single fibre per pixel. PCA and the standard method were compared using simulations and human brain data. The two methods were equivalent in determining fibre orientation. PCA-derived fractional anisotropy and DT relative anisotropy had similar signal-to-noise ratio (SNR) and dependence on fibre shape. PCA-derived mean diffusivity had similar SNR to the respective DT scalar, and it depended on fibre anisotropy. Appropriate scaling of the PCA measures resulted in very good agreement between PCA and DT maps. In conclusion, the assumption of a specific functional model for DW signals is not necessary for characterization of anisotropic diffusion in a single fibre.

Diffusion tensor imaging reveals no white matter impairments among adults with autism spectrum disorder

Abnormalities within white matter (WM) have been identified in autism spectrum disorder (ASD). Although there is some support for greater neurobiological deficits among females with ASD, there is little research investigating sex differences in WM in ASD. We used diffusion tensor imaging (DTI) to investigate WM aberration in 25 adults with high-functioning ASD and 24 age-, sex- and IQ-matched controls. Tract-based spatial statistics (TBSS) was used to explore differences in WM in major tract bundles. The effects of biological sex were also investigated. TBSS revealed no differences in fractional anisotropy (FA), mean diffusivity (MD), radial diffusivity (RD), or axial diffusivity (AD) between groups. There were no effects of biological sex. We consider whether methodological differences between past studies have contributed to the highly heterogeneous findings in the literature. Finally, we suggest that, among a high-functioning sample of adults with ASD, differences in WM microstructure may not be related to clinical impairment.

Imagem de tensor de difusão na epilesia de lobo temporal mesial

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Characterization of white matter alterations in phenylketonuria by magnetic resonance relaxometry and diffusion tensor imaging

A multimodal MR study including relaxometry, diffusion tensor imaging (DTI), and MR spectroscopy was performed on patients with classical phenylketonuria (PKU) and matched controls, to improve our understanding of white matter (WM) lesions. Relaxometry yields information on myelin loss or malformation and may substantiate results from DTI attributed to myelin changes. Relaxometry was used to determine four brain compartments in normal-appearing brain tissue (NABT) and in lesions: water in myelin bilayers (myelin water, MW), water in gray matter (GM), water in WM, and water with long relaxation times (cerebrospinal fluid [CSF]-like signals). DTI yielded apparent diffusion coefficients (ADCs) and fractional anisotropies. MW and WM content were reduced in NABT and in lesions of PKU patients, while CSF-like signals were significantly increased. ADC values were reduced in PKU lesions, but also in the corpus callosum. Diffusion anisotropy was reduced in lesions because of a stronger decrease in the longitudinal than in the transverse diffusion. WM content and CSF-like components in lesions correlated with anisotropy and ADC. ADC values in lesions and in the corpus callosum correlated negatively with blood and brain phenylalanine (Phe) concentrations. Intramyelinic edema combined with vacuolization is a likely cause of the WM alterations. Correlations between diffusivity and Phe concentrations confirm vulnerability of WM to high Phe concentrations.

Proton diffusion tensor spectroscopy of metabolites in human muscle in vivo

PURPOSE To study the apparent diffusivity and its directionality for metabolites of skeletal muscle in humans in vivo by (1) H magnetic resonance spectroscopy. METHODS The diffusion tensors were determined on a 3 Tesla MR system using optimized acquisition and processing methods including an adapted STEAM sequence with orientation-dependent diffusion weighting, pulse-triggering with individually adapted delays, eddy-current correction schemes, median filtering, and simultaneous prior-knowledge fitting of all related spectra. RESULTS The average apparent diffusivities, as well as the fractional anisotropies of taurine (ADCav  = 0.74 × 10(-3) s/mm(2) , FA = 0.46), creatine (ADCav  = 0.41 × 10(-3)  s/mm(2) , FA = 0.33), trimethylammonium compounds (ADCav  = 0.48 × 10(-3)  s/mm(2) , FA = 0.34), carnosine (ADCav  = 0.46 × 10(-3)  s/mm(2) , FA = 0.47), and water (ADCav  = 1.5 × 10(-3)  s/mm(2) , FA = 0.36) were estimated. The diffusivities of most metabolites and water were significantly different from each other. Diffusion was found to be anisotropic and the diffusion tensors showed tensor correlation coefficients close to 1 and were hence found to be essentially coaligned. The magnitudes of apparent metabolite diffusivities were largely ordered according to molecular weight, with taurine as the smallest molecule diffusing fastest, both along and across the fiber direction. CONCLUSION Diffusivities, directional dependence of diffusion and fractional anisotropies of (1) H MRS-visible muscle metabolites were presented. It was shown that metabolites share diffusion directionality with water and have similar fractional anisotropies, hinting at similar diffusion barriers. Magn Reson Med, 2014. © 2014 Wiley Periodicals, Inc.

Synchrotron x ray induced axonal transections in the brain of rats assessed by high-field diffusion tensor imaging tractography

Since approximately two thirds of epileptic patients are non-eligible for surgery, local axonal fiber transections might be of particular interest for them. Micrometer to millimeter wide synchrotron-generated X-ray beamlets produced by spatial fractionation of the main beam could generate such fiber disruptions non-invasively. The aim of this work was to optimize irradiation parameters for the induction of fiber transections in the rat brain white matter by exposure to such beamlets. For this purpose, we irradiated cortex and external capsule of normal rats in the antero-posterior direction with a 4 mm×4 mm array of 25 to 1000 µm wide beamlets and entrance doses of 150 Gy to 500 Gy. Axonal fiber responses were assessed with diffusion tensor imaging and fiber tractography; myelin fibers were examined histopathologically. Our study suggests that high radiation doses (500 Gy) are required to interrupt axons and myelin sheaths. However, a radiation dose of 500 Gy delivered by wide minibeams (1000 µm) induced macroscopic brain damage, depicted by a massive loss of matter in fiber tractography maps. With the same radiation dose, the damage induced by thinner microbeams (50 to 100 µm) was limited to their paths. No macroscopic necrosis was observed in the irradiated target while overt transections of myelin were detected histopathologically. Diffusivity values were found to be significantly reduced. A radiation dose ≤ 500 Gy associated with a beamlet size of < 50 µm did not cause visible transections, neither on diffusion maps nor on sections stained for myelin. We conclude that a peak dose of 500 Gy combined with a microbeam width of 100 µm optimally induced axonal transections in the white matter of the brain.

Focal white matter changes in spasmodic dysphonia: a combined diffusion tensor imaging and neuropathological study.

Spasmodic dysphonia is a neurological disorder characterized by involuntary spasms in the laryngeal muscles during speech production. Although the clinical symptoms are well characterized, the pathophysiology of this voice disorder is unknown. We describe here, for the first time to our knowledge, disorder-specific brain abnormalities in these patients as determined by a combined approach of diffusion tensor imaging (DTI) and postmortem histopathology. We used DTI to identify brain changes and to target those brain regions for neuropathological examination. DTI showed right-sided decrease of fractional anisotropy in the genu of the internal capsule and bilateral increase of overall water diffusivity in the white matter along the corticobulbar/corticospinal tract in 20 spasmodic dysphonia patients compared to 20 healthy subjects. In addition, water diffusivity was bilaterally increased in the lentiform nucleus, ventral thalamus and cerebellar white and grey matter in the patients. These brain changes were substantiated with focal histopathological abnormalities presented as a loss of axonal density and myelin content in the right genu of the internal capsule and clusters of mineral depositions, containing calcium, phosphorus and iron, in the parenchyma and vessel walls of the posterior limb of the internal capsule, putamen, globus pallidus and cerebellum in the postmortem brain tissue from one patient compared to three controls. The specificity of these brain abnormalities is confirmed by their localization, limited only to the corticobulbar/corticospinal tract and its main input/output structures. We also found positive correlation between the diffusivity changes and clinical symptoms of spasmodic dysphonia (r = 0.509, P = 0.037). These brain abnormalities may alter the central control of voluntary voice production and, therefore, may underlie the pathophysiology of this disorder.

Quantification of the spatiotemporal microstructural organization of the human brain association, projection and commissural pathways across the lifespan using diffusion tensor tractography.

Using diffusion tensor tractography, we quantified the microstructural changes in the association, projection, and commissural compact white matter pathways of the human brain over the lifespan in a cohort of healthy right-handed children and adults aged 6-68 years. In both males and females, the diffusion tensor radial diffusivity of the bilateral arcuate fasciculus, inferior longitudinal fasciculus, inferior fronto-occipital fasciculus, uncinate fasciculus, corticospinal, somatosensory tracts, and the corpus callosum followed a U-curve with advancing age; fractional anisotropy in the same pathways followed an inverted U-curve. Our study provides useful baseline data for the interpretation of data collected from patients.

Quantitative diffusion tensor imaging detects dopaminergic neuronal degeneration in a murine model of Parkinson's disease.

Early diagnosis of Parkinson's disease (PD) is required to improve therapeutic responses. Indeed, a clinical diagnosis of resting tremor, rigidity, movement and postural deficiencies usually reflect >50% loss of the nigrostriatal system in disease. In a step to address this, quantitative diffusion tensor magnetic resonance imaging (DTI) was used to assess nigrostriatal degeneration in the 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP) intoxication model of dopaminergic nigral degeneration. We now demonstrate increased average diffusion (p<0.005) and decreased fractional anisotropy (p<0.03) in the substantia nigra (SN) of 5- to 7-day MPTP-treated animals when compared to saline controls. Transverse diffusivity demonstrated the most significant differences (p < or = 0.002) and correlated with the numbers of SN dopaminergic neurons (r=-0.75, p=0.012). No differences were found in the striatum, corpus callosum, cerebral cortex, or ventricles. These results demonstrate that DTI may be used as a surrogate biomarker of nigral dopaminergic neuronal degeneration.

Accelerated magnetic resonance diffusion tensor imaging of the median nerve using simultaneous multi-slice echo planar imaging with blipped CAIPIRINHA.

PURPOSE To investigate the feasibility of MR diffusion tensor imaging (DTI) of the median nerve using simultaneous multi-slice echo planar imaging (EPI) with blipped CAIPIRINHA. MATERIALS AND METHODS After federal ethics board approval, MR imaging of the median nerves of eight healthy volunteers (mean age, 29.4 years; range, 25-32) was performed at 3 T using a 16-channel hand/wrist coil. An EPI sequence (b-value, 1,000 s/mm(2); 20 gradient directions) was acquired without acceleration as well as with twofold and threefold slice acceleration. Fractional anisotropy (FA), mean diffusivity (MD) and quality of nerve tractography (number of tracks, average track length, track homogeneity, anatomical accuracy) were compared between the acquisitions using multivariate ANOVA and the Kruskal-Wallis test. RESULTS Acquisition time was 6:08 min for standard DTI, 3:38 min for twofold and 2:31 min for threefold acceleration. No differences were found regarding FA (standard DTI: 0.620 ± 0.058; twofold acceleration: 0.642 ± 0.058; threefold acceleration: 0.644 ± 0.061; p ≥ 0.217) and MD (standard DTI: 1.076 ± 0.080 mm(2)/s; twofold acceleration: 1.016 ± 0.123 mm(2)/s; threefold acceleration: 0.979 ± 0.153 mm(2)/s; p ≥ 0.074). Twofold acceleration yielded similar tractography quality compared to standard DTI (p > 0.05). With threefold acceleration, however, average track length and track homogeneity decreased (p = 0.004-0.021). CONCLUSION Accelerated DTI of the median nerve is feasible. Twofold acceleration yields similar results to standard DTI. KEY POINTS • Standard DTI of the median nerve is limited by its long acquisition time. • Simultaneous multi-slice acquisition is a new technique for accelerated DTI. • Accelerated DTI of the median nerve yields similar results to standard DTI.