Pulsed Gradient Spin Echo Data Research Articles

Axial and radial axonal diffusivities and radii from single encoding strongly diffusion-weighted MRI.

We enable the estimation of the per-axon axial diffusivity from single encoding, strongly diffusion-weighted, pulsed gradient spin echo data. Additionally, we improve the estimation of the per-axon radial diffusivity compared to estimates based on spherical averaging. The use of strong diffusion weightings in magnetic resonance imaging (MRI) allows to approximate the signal in white matter as the sum of the contributions from only axons. At the same time, spherical averaging leads to a major simplification of the modeling by removing the need to explicitly account for the unknown distribution of axonal orientations. However, the spherically averaged signal acquired at strong diffusion weightings is not sensitive to the axial diffusivity, which cannot therefore be estimated although needed for modeling axons - especially in the context of multi-compartmental modeling. We introduce a new general method for the estimation of both the axial and radial axonal diffusivities at strong diffusion weightings based on kernel zonal modeling. The method could lead to estimates that are free from partial volume bias with gray matter or other isotropic compartments. The method is tested on publicly available data from the MGH Adult Diffusion Human Connectome project. We report reference values of axonal diffusivities based on 34 subjects, and derive estimates of axonal radii from only two shells. The estimation problem is also addressed from the angle of the required data preprocessing, the presence of biases related to modeling assumptions, current limitations, and future possibilities.

Oscillating and pulsed gradient diffusion magnetic resonance microscopy over an extendedb‐value range: Implications for the characterization of tissue microstructure

Oscillating gradient spin-echo (OGSE) pulse sequences have been proposed for acquiring diffusion data with very short diffusion times, which probe tissue structure at the subcellular scale. OGSE sequences are an alternative to pulsed gradient spin echo measurements, which typically probe longer diffusion times due to gradient limitations. In this investigation, a high-strength (6600 G/cm) gradient designed for small-sample microscopy was used to acquire OGSE and pulsed gradient spin echo data in a rat hippocampal specimen at microscopic resolution. Measurements covered a broad range of diffusion times (TDeff = 1.2-15.0 ms), frequencies (ω = 67-1000 Hz), and b-values (b = 0-3.2 ms/μm2). Variations in apparent diffusion coefficient with frequency and diffusion time provided microstructural information at a scale much smaller than the imaging resolution. For a more direct comparison of the techniques, OGSE and pulsed gradient spin echo data were acquired with similar effective diffusion times. Measurements with similar TDeff were consistent at low b-value (b < 1 ms/μm(2) ), but diverged at higher b-values. Experimental observations suggest that the effective diffusion time can be helpful in the interpretation of low b-value OGSE data. However, caution is required at higher b, where enhanced sensitivity to restriction and exchange render the effective diffusion time an unsuitable representation. Oscillating and pulsed gradient diffusion techniques offer unique, complementary information. In combination, the two methods provide a powerful tool for characterizing complex diffusion within biological tissues.

Molecular Weight Determination of Block Copolymers by Pulsed Gradient Spin Echo NMR

Matrix-assisted laser desorption/ionization (MALDI) time-of-flight (TOF) mass spectrometry (MS) is the technique of choice to achieve molecular weight data for synthetic polymers. Because the success of a MALDI-MS analysis critically depends on a proper matrix and cation selection, which in turn relates closely to the polymer chemical nature and size, prior estimation of the polymer size range strongly helps in rationalizing MALDI sample preparation. We recently showed how pulsed gradient spin echo (PGSE) nuclear magnetic resonance could be used as an advantageous alternative to size exclusion chromatography, to rationalize MALDI sample preparation and confidently interpret MALDI mass spectra for homopolymers. Our aim here is to extend this methodology to the demanding case of amphiphilic block copolymers, for which obtaining prior estimates on the Mw values appears as an even more stringent prerequisite. Specifically, by studying poly(ethylene oxide) polystyrene block copolymers of distinct molecular weights and relative block weight fractions, we show how PGSE data can be used to derive the block Mw values. In contrast to homopolymers, such determination requires not only properly recorded calibration curves for each of the polymers constituting the block copolymers but also an appropriate hydrodynamic model to correctly interpret the diffusion data.

A PGSE diffusion and electrophoretic NMR study of Cs+ and Na+ dynamics in aqueous crown ether systems

Multinuclear pulsed gradient spin-echo (PGSE) NMR diffusion and linewidth measurements were used to probe binding and transport in aqueous Na+-15-crown-5, Na+-18-crown-6, Cs+-15-crown-5 and Cs+-18-crown-6 systems. Since direct PGSE observation of many alkali cations is precluded by either low inherent sensitivity or rapid relaxation (or both), the feasibility of proton-detected electrophoretic NMR (ENMR) measurements to complement PGSE data was investigated. ENMR measurements were performed on aqueous Cs+-, Li+-, Na+-, K+-, and Rb+- 18-crown-6 systems. The data analysis is based on a two-site binding model and its corresponding association constants. Cs+ was found to bind considerably more tightly to 18-crown-6 (K=8 M-1) than to 15-crown-5 (K approximately 2 M-1), whereas Na+ had almost equal affinity (K approximately 4.5 M-1) for 15-crown-5 and 18-crown-6. The difficulties encountered in analysing the NMR parameters, methodological limitations and the implied need for more complicated binding models are discussed.

7Li, 31P, and 1H Pulsed Gradient Spin‐Echo (PGSE) Diffusion NMR Spectroscopy and Ion Pairing: On the Temperature Dependence of the Ion Pairing in Li(CPh3), Fluorenyllithium, and Li[N(SiMe3)2] amongst Other Salts

7Li, 31P, and 1H variable-temperature pulsed gradient spin-echo (PGSE) diffusion methods have been used to study ion pairing and aggregation states for a range of lithium salts such as lithium halides, lithium carbanions, and a lithium amide in THF solutions. For trityllithium (2) and fluorenyllithium (9), it is shown that ion pairing is favored at 299 K but the ions are well separated at 155 K. For 2-lithio-1,3-dithiane (13) and lithium hexamethyldisilazane (LiHMDS 16), low-temperature data show that the ions remain together. For the dithio anion 13, a mononuclear species has been established, whereas for the lithium amide 16, the PGSE results allow two different aggregation states to be readily recognized. For the lithium halides LiX (X = Br, Cl, I) in THF, the 7Li PGSE data show that all three salts can be described as well-separated ions at ambient temperature. The solid state structure of trityllithium (2) is described and reveals a solvent-separated ion pair formed by a [Li(thf)4]+ ion and a bare triphenylmethide anion.

Enhanced Ligand Affinity for Receptors in which Components of the Binding Site Are Independently Mobile

Using calmodulin antagonism as a model, it is demonstrated that, under circumstances in which binding sites are motionally independent, it is possible to create bifunctional ligands that bind with significant affinity enhancement over their monofunctional counterparts. Suitable head groups were identified by using a semiquantitative screen of monofunctional tryptophan analogs. Two bifunctional ligands, which contained two copies of the highest-affinity head group tethered by rigid linkers, were synthesized. The bifunctional ligands bound to calmodulin with a stoichiometry of 1:1 and with an affinity enhancement over their monofunctional counterparts; the latter bound with a stoichiometry of 2:1 ligand:protein. A lower limit to the effective concentrations of the domains of calmodulin relative to each other (0.2-2 mM) was determined. A comparable effective concentration was achieved for bifunctional ligands based on higher-affinity naphthalene sulphonamide derivatives.

Time domain analysis: an alternative way to interpret PGSE experiment

We report a theoretical development which aims at interpreting Pulsed Gradient Spin Echo data for diffusing fluids in saturated porous media. It consists in analyzing the time dependence of PGSE amplitudes for each single gradient strength, and introduces a new diffusion coefficient D( q ) as being continuously dependent on the length scale in the material. Both experimental measurements on water saturated bead packings and simulated experiments in 2D and 3D model systems are interpreted with this approach. D( q ) is shown to give a new insight in the micro-macro transition. Its evolution vs. the length scale is non trivial, and can be sensitive to local slow kinetic effects.

An earth’s field nuclear magnetic resonance apparatus suitable for pulsed gradient spin echo measurements of self-diffusion under Antarctic conditions

We describe an earth’s field nuclear magnetic resonance apparatus which can be used to carry out pulsed gradient spin echo (PGSE) diffusion measurements. The instrument is portable and incorporates automated process control, allowing direct measurement of the Larmor precession. The use of a common clock for pulse sequencing, excitation pulse synthesis, and detection, results in a phase stability sufficient for accurate signal averaging. The analysis of PGSE data under the conditions of a weak detection field is discussed and measurements of diffusion are presented under both New Zealand and Antarctic conditions. The Antarctic results include an example of restricted diffusion of brine water in McMurdo Sound sea ice.

An analytical model of restricted diffusion in bovine optic nerve.

An analytical model of restricted diffusion in bovine optic nerve is presented. The nerve tissue model is composed of two different objects: prolate ellipsoids (axons) and spheres (glial cells) surrounded by partially permeable membranes. The free diffusion coefficients of intracellular and extracellular water may differ. Analytical formulas for signal loss due to diffusion in the pulsed gradient spin echo (PGSE) experiment for this tissue model are derived. The model is fitted to experimental data for bovine optic nerve. The obtained model parameters are shown to be reasonable. The model describes all of the characteristics of the PGSE data: anisotropy, upward curvature of decay curves, and diffusion time dependence. The validity and sensitivity of the model are also discussed.

Transport heterogeneity in porous pellets—I. PGSE NMR studies

This paper is the first in a series of reports describing Nuclear Magnetic Resonance (NMR) and numerical modelling studies of the representation of the structure of porous media and associated transport phenomena. In this paper the interpretation of Pulsed Gradient Spin Echo (PGSE) NMR data are considered. In extending earlier studies in which the porous medium is assumed to be macroscopically homogeneous, we have considered the effect of spatial variations in both the diffusivity and relaxation properties within the porous medium, occurring over lengthscales of order > 100 μm. Expressions for the log-attenuation plot and the diffusivity are derived. The theory gives excellent agreement with experimental PGSE data obtained for a variety of porous catalyst support pellets, and both the effective diffusivity of the materials and an indication of the degree of heterogeneity of diffusion are obtained. Sample tortuosities are found to be in the range 1.3–4.3. The results suggest that macroscopically heterogeneous materials have a greater tortuosity than more homogeneous materials.