In this article, we demonstrate a single-scan method to measure an average flow velocity vector along an arbitrary direction. This method is based on the MMME sequence and utilizes static and pulsed magnetic field gradients along multiple directions for the optimal determination of flow velocity components in three-dimensional space.
In this article, the authors demonstrate a rapid NMR method to measure a full three-dimensional diffusion tensor. This method is based on a multiple modulation multiple echo sequence and utilizes static and pulsed magnetic field gradients to measure diffusion along multiple directions simultaneously. The pulse sequence was optimized using a well-known linear inversion metric (condition number) and successfully tested on both isotropic (water) and anisotropic (asparagus) diffusion systems.
Laplace inversion has been widely used in analyzing nuclear magnetic resonance data to obtain a spectrum of decay time constant, such as the T(2) spectrum. However, due to the ill-conditioned nature of such inversion, it is difficult to determine the reliability and error of the resulting spectrum. This article describes methods used to analyze resolution and to obtain bounds of integral quantities of the spectrum.
The structure factor provides a fundamental characterization of porous and granular materials as it is the key for solid crystals via measurements of x-ray and neutron scattering. Here, we demonstrate that the structure factor of the granular and porous media can be approximated by the pair correlation function of the inhomogeneous internal magnetic field, which arises from the susceptibility difference between the pore filling liquid and the solid matrix.
Relaxation and diffusion data are often analyzed using a Laplace inversion algorithm that incorporates regularization. Regularization is used because Laplace inversion with finite and noisy data is an ill-conditioned problem for which many solutions exist for a given data set. This paper reports a different approach. Instead of finding a "best" solution by some ad hoc criterion, we developed an efficient Monte Carlo algorithm that generates thousands of probable solutions from which the statistical properties of the solution can be analyzed.
NMR relaxation and diffusion data analysis commonly uses a wide range of methods from simple exponential fitting to Laplace inversions. The pros and cons of these methods are often the subject of intense debate. We show that the ill-conditioned nature of such analysis gives rise to a range of solutions for every method resulting in uncertainty in the spectral solution. Such uncertainty is in fact characteristic of the inversion method. We show a simple method of sparse spectral representation can be used to improve the statistics of multiple-exponential-based inversion schemes.
Diffusion in porous media has been used as a probe of pore geometry in various NMR techniques. We will examine the effect of time-dependent diffusion in CPMG by showing that the diffusion time in CPMG is approximately the echo time, even in grossly inhomogeneous magnetic fields. Extension of the diffusion time in modified CPMG sequences is discussed. Diffusion in the susceptibility-contrast induced internal field is discussed as a means to probe pore size and pore shape.
We present new NMR techniques to characterize food products that are based on the measurement of two-dimensional diffusion-T2 relaxation and T1-T2 relaxation distribution functions. These measurements can be performed in magnets of modest strength and low homogeneity and do not require pulsed gradients. As an illustration, we present measurements on a range of dairy products that include milks, yogurt, cream, and cheeses. The two-dimensional distribution functions generally exhibit two distinct components that correspond to the aqueous phase and the liquid fat content.
Spin-lattice relaxation time (T(1)) measurements are often time-consuming due to the need to measure the full equilibrium magnetization with a long wait time. However, any magnetization recovery can be decomposed into pure recovery and pure decay components, the latter of which lends itself to a much simpler and faster extraction of T(1). We demonstrate several pulse sequences that accomplish this decomposition experimentally and illustrate its applications in a steady magnetic field gradient, and in materials possessing a broad distribution of T(1).
This paper reviews a recently reported NMR method capable of determining the diffusion constant within milliseconds and without the need of multiple scans. The method can be used with static or pulsed magnetic field gradients.
