Components Of Diffusion Tensor Research Articles

Long-Range Li-Ion 3D Diffusion in the High-Temperature Hexagonal Phase of LiBH4 Studied by 7Li Pulsed Field Gradient NMR and MD Simulations

Lithium diffusion pathways have been determined in three dimensions using molecular dynamics simulations and 7Li pulsed-field gradient spin-echo (PGSE) NMR diffusometry. Lithium ions arrange in multiple hexagonally arranged and intertwined columns oriented at different angles on (001) surfaces. It has been found that lithium jumps are characterized by zig–zag patterns with the main diffusion tensor axis aligned along the [001] direction. Additional diffusion tensor dimensions appear in the (001) planes through multiple jumps along the [001] direction. The simulation results were confirmed by non-linear spin-echo attenuation in the 7Li PGSE NMR experiment and three-dimensional diffusion model developed for Li+-ion conductivity. The exact values of the main diffusion tensor components D⊥ = (D11 + D22)/2 and D∥ = D33 were derived from the uni-dimensional projection of diffusion tensor under macroscopic powder averaging condition. The single ionic jump in the [001] direction was related to D∥, while translation on the (001) plane required at least two jumps through the zig–zag path and related to D⊥. Lithium diffusion in the [001] direction is faster than that in the (001) planes. The activation energies for D⊥ and D∥ were determined between 105 and 130 °C and varied between 0.47 and 0.51 eV, which suggests that both diffusion coefficients are related to the same mechanism of the jump. Pre-exponential factors for D∥ and D⊥ were also determined and equal to 4.8 × 10–6 m2 s–1 for D∥ and 3.8 × 10–7 m2 s–1 for D⊥, respectively, which confirms that molecular translations between (001) surfaces are not performed in a single jump.

Prospects and Challenges for the Spatial Quantification of the Diffusion of Fluids Containing 1H in the Pore System of Rock Cores

AbstractNuclear magnetic resonance (MR) (NMR) is commonly used for the determination of rock porosity, as well as pore size distribution (PSD) and tortuosity, required to handle hydrocarbon exploitation. Emerging technologies for NMR equipment now enable the visualization of porosity using magnetic resonance imaging (MRI). Currently, single‐point imaging is the most common MRI technique employed, but diffusion‐weighted imaging has been attracting the attention of geologists and geophysicists. In this study, a more advanced technique, diffusion tensor imaging (DTI), is proposed for the characterization of rock core samples. The main purpose of this paper is to demonstrate the usefulness of DTI in the petrophysical characterization of rocks and discuss its strengths. As an example, a carbonate core sample was examined using DTI. The diffusion tensor (DT) was obtained and DT parameters (mean diffusivity, MD; fractional anisotropy, FA; three eigenvalues; DT components; and proton density, PD) were visualized in 2D and 3D. Each parameter was described and its utility in terms of pore space characterization was analyzed. In addition, a new parameter, principal diffusion tracts, was introduced based on the DT tractography performed in the study. The analysis is summarized in a set of DT parameters and a resultant ellipsoid that delivers complementary information about the sample's pore network microgeometry, including referential measurements of anisotropic phantoms. The applications of DTI for the determination of pore size distribution, tortuosity and conductivity are also shown. The study ends with a consideration of the potential prospects and challenges for DTI‐based examination of rock core samples.

Increased intratumoral infiltration in IDH wild-type lower-grade gliomas observed with diffusion tensor imaging.

Diffuse lower grade gliomas (LGG) with isocitrate dehydrogenase (IDH) gene mutations (IDHMUT) have a distinct survival advantage compared with IDH wild-type (IDHWT) cases but the mechanism underlying this disparity is not well understood. Diffusion Tensor Imaging (DTI) has identified infiltrated non-enhancing tumor regions that are characterized by low isotropic (p) and high anisotropic (q) diffusion tensor components that associate with poor survival in glioblastoma. We hypothesized that similar regions are more prevalent in IDHWT (vs. IDHMUT) LGG. p and q maps were reconstructed from preoperative DTI scans in N = 41 LGG patients with known IDH mutation and 1p/19q codeletion status. Enhancing and non-enhancing tumor volumes were autosegmented from standard (non-DTI) MRI scans. Percentage non-enhancing tumor volumes exhibiting low p and high q (Vinf) were then determined using threshold values (p = 2 × 10-3mm2/s, q = 3 × 10-4 mm2/s) and compared between IDHWT and IDHMUT LGG, and between IDHMUT LGG with and without 1p/19q codeletion. Vinf volumes were significantly larger in IDHWT LGG than in IDHMUT LGG (35.4 ± 18.3% vs. 15.9 ± 7.6%, P < 0.001). Vinf volumes did not significantly differ between IDHMUT LGG with and without 1p/19q codeletion (17.1 ± 9.5% vs. 14.8 ± 5.8%, P = 1.0). IDHWT LGG exhibited larger volumes with suppressed isotropic diffusion (p) and high anisotropic diffusion (q) which reflects regions with increased cell density but non-disrupted neuronal structures. This may indicate a greater prevalence of infiltrative tumor in IDHWT LGG.

Anisotropic conductivity tensor by analyzing diffusion tensor for electrical brain stimulation (EBS)

Electrical brain stimulation (EBS) is a promising medical treatment method for brain neurological disorders through the direct or indirect excitation by injecting an electric current. At present, it is difficult to directly measure the distribution of the electric current delivered by electrodes inside tissues. By applying low-frequency (1 kHz) external electrical brain stimulation (EBS), the low-frequency conductivity around the cells is uneven due to asymmetric cellular structures. We propose a method of electrical property imaging using the measured one component magnetic flux density by EBS and diffusion tensor imaging (DTI). The low-frequency electrical anisotropic conductivity tensor can be decomposed into the ion concentration and the mobility tensor of charge carriers. By analyzing the role of the diffusion tensor, we reconstruct the apparent anisotropic tensor by EBS using the -component of measured magnetic flux density data and the estimated diffusion tensor. Using only the measured -component of magnetic flux density, the orthotropic conductivity tensor can be approximately recovered. The orthotropic conductivity tensor is not exact, but only reflects the extracellular space (ECS) effects. By comparing the components of orthotropic tensor and diffusion tensor, we stably determine a scale factor which primarily reflects the concentration of total ions in the extracellular space (ECS). Animal experiments verify that the proposed method recovers the anisotropic conductivity tensor which can visualize electrical properties during EBS of the brain. A direct reconstruction method for the apparent anisotropic conductivity tensor imaging during EBS was proposed to analyze unknown effects to brain tissue.

Quantifying white matter tract diffusion parameters in the presence of increased extra-fiber cellularity and vasogenic edema

The effect of extra-fiber structural and pathological components confounding diffusion tensor imaging (DTI) computation was quantitatively investigated using data generated by both Monte-Carlo simulations and tissue phantoms. Increased extent of vasogenic edema, by addition of various amount of gel to fixed normal mouse trigeminal nerves or by increasing non-restricted isotropic diffusion tensor components in Monte-Carlo simulations, significantly decreased fractional anisotropy (FA) and increased radial diffusivity, while less significantly increased axial diffusivity derived by DTI. Increased cellularity, mimicked by graded increase of the restricted isotropic diffusion tensor component in Monte-Carlo simulations, significantly decreased FA and axial diffusivity with limited impact on radial diffusivity derived by DTI. The MC simulation and tissue phantom data were also analyzed by the recently developed diffusion basis spectrum imaging (DBSI) to simultaneously distinguish and quantify the axon/myelin integrity and extra-fiber diffusion components. Results showed that increased cellularity or vasogenic edema did not affect the DBSI-derived fiber FA, axial or radial diffusivity. Importantly, the extent of extra-fiber cellularity and edema estimated by DBSI correlated with experimentally added gel and Monte-Carlo simulations. We also examined the feasibility of applying 25-direction diffusion encoding scheme for DBSI analysis on coherent white matter tracts. Results from both phantom experiments and simulations suggested that the 25-direction diffusion scheme provided comparable DBSI estimation of both fiber diffusion parameters and extra-fiber cellularity/edema extent as those by 99-direction scheme. An in vivo 25-direction DBSI analysis was performed on experimental autoimmune encephalomyelitis (EAE, an animal model of human multiple sclerosis) optic nerve as an example to examine the validity of derived DBSI parameters with post-imaging immunohistochemistry verification. Results support that in vivo DBSI using 25-direction diffusion scheme correctly reflect the underlying axonal injury, demyelination, and inflammation of optic nerves in EAE mice.

Identifiability analysis of rotational diffusion tensor and electronic transition moments measured in time-resolved fluorescence depolarization experiment.

The subject of this paper is studies of the deterministic identifiability of molecular parameters, such as rotational diffusion tensor components and orientation of electronic transition moments, resulting from the time-resolved fluorescence anisotropy experiment. In the most general case considered, a pair of perpendicularly polarized emissions enables the unique determination of all the rotational diffusion tensor's principal components. The influence of the tensor's symmetry and the associated degeneration of its eigenvalues on the identifiability of the electronic transitions moments is systematically investigated. The analysis reveals that independently of the rotational diffusion tensor's symmetry, the transition moments involved in photoselection and emission processes cannot be uniquely identified without a priori information about their mutual orientation or their orientation with respect to the principal axes of the tensor. Moreover, it is shown that increasing the symmetry of the rotational diffusion tensor deteriorates the degree of the transition moments identifiability. To obtain these results analytically, a novel approach to solve bilinear system of equations for Markov parameters is applied. The effect of the additional information, obtained from fluorescence measurements for different molecular mobilities, to improve the identifiability at various levels of analysis is shown. The effectiveness and reliability of the target analysis method for experimental determination of the molecular parameters is also discussed.

An atomistic description of the nematic and smectic phases of 4-n-octyl-4′ cyanobiphenyl (8CB)

We report the results of atomistic molecular dynamics simulations of 4-n-octyl-4' cyanobiphenyl (8CB) on samples of 750 and 3000 molecules showing the spontaneous formation of the nematic phase and then of smectic layers by gradually cooling down from the isotropic phase. Orientational, positional, and mixed order parameters, layer spacing, translational diffusion tensor components and their temperature dependence are reported. A detailed comparison with available experimental data validates the model and force field employed and clarifies the molecular organization of this important liquid crystal often used as reference smectic material.

Incorporating Human Ventricular Fiber Architecture in Patient‐Specific Computational Models

Patient‐specific models of the cardiac ventricles require a realistic representation of the myofiber architecture to accurately simulate mechanical and electrical properties of healthy and failing hearts. Diffusion tensor magnetic resonance imaging (DT‐MRI) techniques have made it possible to reconstruct the fiber anatomy of the ventricles. However, in vivo DT‐MRI scans are still impractical to obtain for individual patients. The aim of this study develops a method to register DT‐MRI measurements from an explanted human heart into an anatomical model and warping the result to patient‐specific anatomies using large deformation diffeomorphic mapping.An explanted human organ donor heart was subjected to a DT‐MRI scan. The raw tensor data was registered into an anatomical model of the ventricles by fitting the measured diffusion tensor components in log‐Euclidean space. A material coordinate transformation model defined a local orthogonal coordinate system representing the fiber, sheet, and sheet‐normal directions of the myocardium from the eigenvectors of a locally interpolated diffusion tensor. Diffeomorphic maps of the deformation F between the donor and patient models were computed and used to warp the donor fiber architecture into the patient models. The registration error between the eigenvectors of the measured tensor and its interpolated tensor was quantified by a scalar metric of axes overlap. It found 74% of the registered DT‐MRI data (112,419 of 152,651 voxels) had mean angular errors of 12.5°±7° (SD) in the fiber, 20°±11.5° (SD) in the sheet, and 18°±11.6° (SD) in the sheet normal axes.

The computational simulation of brain connectivity using diffusion tensor MRI

Water molecule diffusion in the brain is measured using a magnetic resonance imaging method. The anisotropy of the diffusion tensor is of particular interest in brain images, as it relates to white matter fibre tracts. Depending on the interrelation of eigenvalues, diffusion can be divided into the three cases of linear diffusion, planar diffusion and spherical diffusion. We present additional information from the (brain image) diffusion tensor magnetic resonance imaging of a patient with Parkinson's disease. This information includes maps of diffusion tensor components, fractional anisotropy and an fractional anisotropy weighted colour coded orientation. We also investigate linear diffusion, time fractional diffusion, and space fractional diffusion, as well as proposing computational simulations of connectivity in the brain using numerical methods for the analysis of diffusion tensor magnetic resonance imaging.

Linear dielectric relaxation of dipolar, rigid, non-interacting and asymmetric-top molecules in Smoluchowski-Debye approach

Assuming the low molecular reorientation approximation, the formulae for linear electric polarization induced in liquids composed of rigid, noninteracting, dipolar and asymmetric-top molecules in spherical solvents were derived. The Kalmykov's equation [Phys.Rev., E 65 (021101) 2001] - equivalent to the classical, noninertial Smoluchowski-Debye model of rotational diffusion was applied. In order to highlight the influence of the anisotropy of rotational diffusion tensor components and the orientation of permanent dipole moment of the molecule on the complex linear electric susceptibility, we present three-dimensional plots of the dispersion and absorption spectra, Cole-Cole diagrams for different values of the anisotropies of rotational diffusion tensor components and different frequencies of an ac electric field.

Computer simulation study of rotational diffusion in polar liquids of different types

Rotational diffusion in liquid acetonitrile, dimethylsulphoxide (DMSO), water, and methanol is studied with molecular dynamics simulations. The effects of hydrogen bonding and local dipole-dipole correlations (Kirkwood g-factor) on the relationship between the single molecule and collective relaxation are examined. The first rank single molecule dipole moment autocorrelation functions (ACFs) are constructed in the molecule-fixed coordinate frame and the principal components of rotation diffusion tensor are reported. Higher rank orientational ACFs are computed. These ACFs, as a rule, are strongly nonexponential (at least not single exponential) at longer times and the decomposition of these functions into a series of single exponentials results in broad distributions of relaxation times, with the broadening being particularly prominent in the case of higher rank ACFs. The rank dependence of characteristic times calculated as weighted averages over the relaxation time distributions does not follow the pattern of small angle (Debye) diffusion model for all liquids studied in this work except methanol. In contradiction, the same rank dependence computed by direct integration of ACFs leads to good agreement with the Debye diffusion model in the case of acetonitrile, DMSO, and water (but not methanol). The linear-angular momentum cross correlation functions are also computed and the effect of rototranslational coupling on reorientaional relaxation at longer times (>1.0 ps) is found to be small.

Unified continuum description for sub-diffusion random walks on multi-dimensional comb model

The anisotropic sub-diffusion random walks on multi-dimensional comb structure model have been studied in the continuum approximation. The problem is that in the considered model mean square displacements on different directions have different power temporal dependencies. So this case essentially differs from usual anisotropic diffusion case and it is not obviously how to describe such a diffusion by a unified way. Nevertheless the unified continuum description for such random walks has been developed. As result the new generalization of Fick’s law for diffusion current has been obtained for anisotropic anomalous sub-diffusion random walks in multi-dimensional case. Namely, it has been shown that the effective diffusion coefficient in the generalized Fick’s law has new operator form: components of diffusion tensor instead of constant values have the fractional order temporal derivatives.

Using the Experimentally Determined Components of the Overall Rotational Diffusion Tensor To Restrain Molecular Shape and Size in NMR Structure Determination of Globular Proteins and Protein−Protein Complexes

This paper describes an approach for making use of the components of the experimentally determined rotational diffusion tensor derived from NMR relaxation measurements in macromolecular structure determination. The parameters of the rotational diffusion tensor describe the shape and size of the macromolecule or macromolecular complex, and are therefore complementary to traditional NMR restraints. The structural information contained in the rotational diffusion tensor is not dissimilar to that present in the small-angle region of solution X-ray scattering profiles. We demonstrate the utility of rotational diffusion tensor restraints for protein structure refinement using the N-terminal domain of enzyme I (EIN) as an example and validate the results by solution small-angle X-ray scattering. We also show how rotational diffusion tensor restraints can be used for docking complexes using the dimeric HIV-1 protease and the EIN-HPr complexes as examples. In the former case, the rotational diffusion tensor restraints are sufficient in their own right to determine the position of one subunit relative to another. In the latter case, rotational diffusion tensor restraints complemented by highly ambiguous distance restraints derived from chemical shift perturbation mapping and a hydrophobic contact potential are sufficient to correctly dock EIN to HPr. In each case, the cluster containing the lowest-energy structure corresponds to the correct solution.

Kinetic Theory of the Langevin Saturation in Dilute Solution of Dipolar Symmetric-Top Molecules in Spherical Solvents

Assuming the low molecular reorientation approximation, the formulae for the third-order electric polarization induced in liquids composed of rigid noninteracting dipolar, symmetric-top molecules in spherical solvents were derived. Our medium is acted on by a strong external dc bias electric field superimposed on a weak ac electric field, and the classical Smoluchowski– Debye equation for rotational diffusion of the symmetric-top molecules is applied. In order to highlight the influence of the anisotropy of rotational diffusion tensor components and the orientation of permanent dipole moment of the molecule on the complex linear and nonlinear electric susceptibilities, we present three-dimensional plots of the linear and nonlinear dispersion and absorption spectra, for different values of the frequency of ac electric field.

Quantitative Assessment of Injury in Rat Spinal Cords In Vivo by MRI of Water Diffusion Tensor

Magnetic resonance diffusion tensor imaging (DTI) of control and injured spinal cord of rats in vivo during first 6 h after the trauma was reported. DTI and histopathological results were compared. The aim of this work was to correlate the presence of damage of rat spinal cord with statistically significant changes in the apparent diffusion tensor components, in order to find the parameters that are useful in the visualization of the injury. Apparent diffusion tensor weighted data were measured in vivo 1 h after traumatic injury induced by a controlled weight drop on healthy and injured rat spinal cords for defined dozen regions of interest. Significant alternations in the injured regions of gray matter and white matter were detected. The differences in gray matter can be explained on the basis of cytotoxic edema due to ischemia and they are confirmed by the histological observations of neurons. The white matter changes in diffusional attributes are associated with the destruction of the nerve microstructure by the mechanical implant.

Generalized Fick law for anomalous diffusion in the multidimensional comb model

The problem of multidimensional diffusion is considered within the framework of the comb model. It is shown that the diffusion current for the case of anomalous subdiffusion random walks is described by the generalized Fick law containing the diffusion tensor instead of the usual coefficient. The form of the diffusion tensor components is an unusual form of operator as fractional time derivatives. The orders of the fractional exponents are different for different directions.

Structural Assembly of Multidomain Proteins and Protein Complexes Guided by the Overall Rotational Diffusion Tensor

We present a simple and robust approach that uses the overall rotational diffusion tensor as a structural constraint for domain positioning in multidomain proteins and protein-protein complexes. This method offers the possibility to use NMR relaxation data for detailed structure characterization of such systems provided the structures of individual domains are available. The proposed approach extends the concept of using long-range information contained in the overall rotational diffusion tensor. In contrast to the existing approaches, we use both the principal axes and principal values of protein's rotational diffusion tensor to determine not only the orientation but also the relative positioning of the individual domains in a protein. This is achieved by finding the domain arrangement in a molecule that provides the best possible agreement with all components of the overall rotational diffusion tensor derived from experimental data. The accuracy of the proposed approach is demonstrated for two protein systems with known domain arrangement and parameters of the overall tumbling: the HIV-1 protease homodimer and Maltose Binding Protein. The accuracy of the method and its sensitivity to domain positioning are also tested using computer-generated data for three protein complexes, for which the experimental diffusion tensors are not available. In addition, the proposed method is applied here to determine, for the first time, the structure of both open and closed conformations of a Lys48-linked diubiquitin chain, where domain motions render impossible accurate structure determination by other methods. The proposed method opens new avenues for improving structure characterization of proteins in solution.

Quantifying Human Brain Connectivity from Diffusion Tensor MRI

A new approach for quantifying the degree of connectivity between human brain regions from Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) data is presented. To this aim, a functional is proposed and its theoretical properties are shown. The connectivity between pairs of white matter points is quantified by minimizing the weighted length of the curves within white matter connecting the points to each other. The weighting factor is a decreasing function of the diffusion coefficient along the curve tangent. This coefficient is a linear function of the diffusion tensor components, which are estimated from DT-MRI data. As a by-product of the analysis, the minimizing curves connecting the two points are provided. The solution of the minimization problem is obtained numerically by approximating the functional on a lattice and then solving a shortest path problem on an undirected weighted graph. The presented method is global and therefore not affected by problems due to fiber branching and crossing. It is also automatic and fast. Some results obtained from the implementation of this method on real data in physiological and simulated pathological conditions are illustrated.

A104 拡散トラクトグラフィ法による脳内神経線維の可視化

In this paper, we present a new visualization method, called diffusion based tractography (DBT), for diffusion tensor magnetic resonance imaging (DT-MRI). The DBT method generates 3D textures similar to the line integral convolution (LIC) by smearing 3D random dot textures. In contrast to LIC, which only traces a single direction, DBT takes into account both linear and planar diffusion components and suppresses excessive blur due to spherical diffusion, by an analysis of the diffusion tensor components. We will demonstrate that DBT is effective for visualizing dense white matter connectivity to be found in human brain.

Intrinsic trapping of stochastic sheared magnetic field lines

The decorrelation trajectory method is applied to the diffusion of magnetic field lines in a perturbed sheared slab magnetic configuration. Some interesting decorrelation trajectories for several values of the magnetic Kubo number and of the shear parameter are exhibited. The asymmetry of the decorrelation trajectories appears in comparison with those obtained in the purely electrostatic case studied in earlier work. The running and asymptotic diffusion tensor components are calculated and displayed.