Restricted diffusion within a single pore

Self-diffusion in polycrystalline Li1+x Ti2-x Al x (PO4)3 (0.2 ≤ x ≤ 0.4) samples followed by 7Li PFG (pulse field gradient) NMR spectroscopy

Short and long range lithium motions in powder Li_1+x Ti_2-x Al _x (PO₄)₃ (LTAP) NASICON compounds prepared by ceramic (x = 0.2 and 0.4) and sol-gel (x = 0.3 and 0.4) routes are discussed. ND diffraction and MAS-NMR spectroscopy were previously used to investigate structural features of these compounds. In particular, Fourier map differences showed that the amount of Li atoms allocated at M3 increases at the expense of M1 sites when the Li content increases. In this work, PFG-NMR results show that diffusion coefficients rise with the amount of lithium and temperature. The restricted diffusion inside NASICON particles is compared with "free" diffusion processes. At 300 K, diffusion coefficients D _PFG ∼ 5 × 10^-12 m² s^-1 have been deduced in ceramic x = 0.2 and 0.4 samples, decreasing with diffusion time Δ used in PFG experiments. In sol-gel samples, diffusion coefficients are near those of ceramic samples, but decrease faster with diffusion Δ times, as a consequence of the Li confinement inside sub-micrometric crystallites. The NMR spin-echo signal displays minima at specific q(γgδ) values that are related to the crystallite size. From R _dif ∼ q _m ^-1 distances, calculated from the position of minima, and from diffusion coefficients deduced for high Δ values, the mean crystallite size was estimated. Finally, from the temperature dependence of conductivity and diffusion coefficients, the activation energy and charge carriers concentrations were determined.

Investigation of different boundary treatment methods in Monte-Carlo simulations of diffusion NMR

PURPOSE

To enrich and develop more convenient and effective boundary treatment method in Monte-Carlo simulation of restricted diffusion nuclear magnetic resonance.

METHODS

The conventional approach used in treating boundary behaviors of restricted diffusion is the elastic boundary reflection. Because random walk is not dynamic process, other boundary treatments such as inelastic reflection are acceptable and probably simplify the programming of diffusion nuclear magnetic resonance simulation. The present study simulated the pulse gradient spin echo nuclear magnetic resonance by employing three boundary models, i.e., the elastic boundary reflection, the non-elastic boundary reflection, and the equal-step-length random leap. Their effects on precision, convergence, and calculation efficiency were investigated, as well as the effects of non-fixed boundary reflection step-length drawn from a Gaussian distribution in barrier-crossing steps.

RESULTS

The results show no obvious difference in convergences and precisions for different methods when the relative step-length is sufficiently small. Compared with the traditional approach, the required computation time of the latter two was reduced in some degree.

CONCLUSION

Boundary treatments based on inelastic reflection are a feasible choice in Monte-Carlo simulation of nuclear magnetic resonance, and in comparison with the conventional approach, it not only renders programming more convenience but also possibly lead to higher calculating efficiency.

Mapping of (3) He apparent diffusion coefficient anisotropy at sub-millisecond diffusion times in an elastase-instilled rat model of emphysema

Hyperpolarized (3) He gas can provide detailed anatomical maps of the macroscopic airways in the lungs (i.e., ventilation) as well as insight into the lung microstructure through the apparent diffusion coefficient. In particular, the apparent diffusion coefficient of (3) He in the lung exhibits anisotropic effects that depend on diffusion time (δ), and it has been shown to be extraordinarily sensitive to enlargement in terminal airways and alveoli associated with emphysema. In this study, the anisotropic nature of the (3) He apparent diffusion coefficient is studied in a rat model of emphysema, based on elastase instillation, specifically for δ values less than one millisecond. Longitudinal (D(L) ) and transverse (D(T) ) diffusion coefficients were mapped at δ = 360 μs and δ = 800 μs based on a cylinder model of lung structure and correlated with histological measurement of alveolar damage based on mean linear intercept (L(m) ). Whole-lung mean D(T) measured at δ = 360 μs in the elastase-instilled rat lungs (0.14 ± 0.09 cm(2) /s) demonstrated the most significant increase (p = 0.00195) compared to the sham-instilled cohort (0.06 ± 0.06 cm(2) /s) and had a strong linear correlation with L(m) (Pearson's correlation coefficient of 0.9). These results suggest that measurement of (3) He apparent diffusion coefficient anisotropy, specifically D(T) , can provide a sensitive indicator of emphysema, particularly at very short diffusion times (δ = 360 μs).

Dynamics of water in polyelectrolyte multilayers: restricted diffusion and cross-relaxation

The diffusion properties of water in polyelectrolyte multilayers (PEM) are investigated by pulsed field gradient diffusion NMR. The dependence of the mean-square displacement on the observation time does not agree to Gaussian diffusion, suggesting restricted diffusion in a porous structure. However, the extraction of a pore size in a model of restricted diffusion yields a very large pore size of several micrometers. The additional influence of cross-relaxation of water and polymer spins is investigated in Goldman-Shen experiments. These demonstrate a strong influence of cross-relaxation rates on diffusion echo decays, such that pore sizes obtained from the model of restricted diffusion have to be corrected. Corrected pore sizes are about 4 microm and reflect the existence of domains of lower polymer density and thus faster water diffusion. These heterogeneities occur upon PEM preparation at high salt content for large layer numbers and are detected in the surface morphology, too.

Experimental investigation and numerical simulation of 3He gas diffusion in simple geometries: implications for analytical models of 3He MR lung morphometry

Models of lung acinar geometry have been proposed to analytically describe the diffusion of (3)He in the lung (as measured with pulsed gradient spin echo (PGSE) methods) as a possible means of characterizing lung microstructure from measurement of the (3)He ADC. In this work, major limitations in these analytical models are highlighted in simple diffusion weighted experiments with (3)He in cylindrical models of known geometry. The findings are substantiated with numerical simulations based on the same geometry using finite difference representation of the Bloch-Torrey equation. The validity of the existing "cylinder model" is discussed in terms of the physical diffusion regimes experienced and the basic reliance of the cylinder model and other ADC-based approaches on a Gaussian diffusion behaviour is highlighted. The results presented here demonstrate that physical assumptions of the cylinder model are not valid for large diffusion gradient strengths (above approximately 15 mT/m), which are commonly used for (3)He ADC measurements in human lungs.

Self-diffusion anisotropy of water in sheep Achilles tendon

The principal values of the diffusion tensor of free water in the pores of sheep Achilles tendon were determined. For this purpose, the azimuthally angular dependence of the self-diffusion coefficient was measured using a radiofrequency tilt coil and pulsed-field-gradient stimulated-echo (PFGSE) NMR. Combining the PFGSE with multiple acquisitions of Hahn echoes using the Carr-Purcell-Meiboom-Gill pulse sequence reduced the measuring time. The diffusion measurements revealed two diffusion process characterized by a fast and a slow effective diffusion coefficient. A model which describes the stimulated-echo amplitude, encoded by the water diffusion and magnetization transfer, was used for evaluation of the fast diffusion coefficients. The fast diffusion process characterizes the water molecules in pores surrounding the collagen fibrils. The diffusion coefficients characterizing the fast process show a well-defined anisotropy. The principal values of the diffusion tensors were determined assuming the elongated pores to be oriented parallel to the tendon fibrils and thus the orientation distribution function of the pores followed that of the collagen fibrils. The average aspect ratio of pores was estimated from the principal values of the water diffusion tensor and is suitable to characterize quantitatively the changes in tendon morphology due to healing or aging. The methods in this investigation can also be applied to measurements of the diffusion anisotropy using ex situ NMR sensors.

Active shielding of cylindrical saddle-shaped coils: application to wire-wound RF coils for very low field NMR and MRI

We provide an exact expression for the magnetic field produced by cylindrical saddle-shaped coils and their ideal shield currents in the low-frequency limit. The stream function associated with the shield surface current is also determined. The results of the analysis are useful for the design of actively shielded radio-frequency (RF) coils. Examples pertinent to very low field nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) are presented and discussed.

NMR measurements of hyperpolarized He3 gas diffusion in high porosity silica aerogels

Hyperpolarized 3He is used to non-destructively probe by NMR the structure of custom-made and commercial silica aerogels (97% and 98.5% porous). Large spin-echo signals are obtained at room temperature and very low magnetic field (2 mT) even with small amounts of gas. Attenuation induced by applied field gradients results from the combined effects of gas diffusion and confinement by the porous medium on atomic motion. Nitrogen is used as a buffer gas to reach equivalent 3He pressures ranging from 5 mbars to 3.5 bars. The observed pressure dependence suggests a nonuniform structure of the aerogels on length scales up to tens of micrometers. A description by broad phenomenological distributions of mean free paths is proposed, and quantitatively discussed by comparison to numerical calculations. The investigated aerogel samples exhibit different effective diffusion characteristics despite comparable nominal porosities.

Composite hindered and restricted model of diffusion (CHARMED) MR imaging of the human brain

High b value diffusion-weighted images sampled at high angular resolution were analyzed using a composite hindered and restricted model of diffusion (CHARMED). Measurements and simulations of diffusion in white matter using CHARMED provide an unbiased estimate of fiber orientation with consistently smaller angular uncertainty than when calculated using a DTI model or with a dual tensor model for any given signal-to-noise level. Images based on the population fraction of the restricted compartment provide a new contrast mechanism that enhances white matter like DTI. Nevertheless, it is assumed that these images might be more sensitive than DTI to white matter disorders. We also provide here an experimental design and analysis framework to implement CHARMED MRI that is feasible on human clinical scanners.