Velocity and diffusion imaging in dynamic NMR microscopy

The imposition of resolution gradients in a pulsed-gradient spin-echo (PGSE) NMR sequence induces motionally dependent phase and amplitude modulation in the image, a technique which we have termed dynamic NMR microscopy. Fourier analysis of this modulation gives a dynamic displacement profile for each pixel which can then be analyzed to obtain velocity and diffusion maps. The application of this method at high spatial resolution is motivated by a desire to measure vascular flow in living plants and variations in molecular self-diffusion under the influence of velocity shear in narrow capillaries. The theory of dynamic NMR microscopy is presented and potential artifacts discussed, including the effect of slice selection gradients, PGSE gradient nonuniformity, and specific problems associated with the measurement of self-diffusion in the presence of velocity gradients. It is demonstrated that a double-echo PGSE pulse sequence can be used to restore coherent phase shifts associated with steady-state flow, and examples of self-diffusion maps and signed velocity maps from sequences of phase-encoded images obtained by projection reconstruction are given. This method has been applied at 20,um transverse resolution in laminar capillary flow.     

Strategies for Diagnosing and Alleviating Artifactual Attenuation Associated with Large Gradient Pulses in PGSE NMR Diffusion Measurements

The generation of phase-based artifacts resulting from mismatch in the effective areas (i.e., the time integrals) of sequential gradient pulses is discussed in the context of large gradient pulsed-gradient spin-echo (PGSE) NMR diffusion measurements. Such effects result in artifactual attenuation and distortion in the spectra which, in the first instance, are similar to (and commonly mistaken for) the effects of eddy currents. Small degrees of mismatch cause "unphysical" concave downward curvature in PGSE attenuation plots of freely diffusing species. However, larger mismatches can result in artifactual diffraction peaks in the plots which could easily be confused for true restricted diffusion effects. Although "rectangular" gradient pulses are preferable from a theoretical viewpoint, we found that shaped gradient (e.g., half-sine) pulses, which due to their slower rise and fall times were more tractable for the current amplifier, were more sequentially reproducible. As well as generating fewer phase-based artifacts such shaped pulses also decrease the likelihood of vibration problems.     

Inversion of self-diffusion anisotropy by chemical substitution in smectic A liquid crystals as evidenced by PGSE experiment combined with a quadrupole-coil rotation

A technique of pulsed-field-gradient spin-echo (PGSE) NMR combined with a quadrupole-coil rotation was applied to the study of anisotropic self-diffusion in smectic A liquid crystals. Diffusion anisotropy was found to be inverted by chemical substitution of the terminal groups in homologous compounds: Namely, the diffusion across the layer is faster for the cyano compound, whereas the diffusion within the layer is faster for the trifluoromethoxy compound.     

Homogeneous length scale of shear-induced multilamellar vesicles studied by diffusion NMR

A recently developed protocol for pulsed gradient spin echo (PGSE) NMR is applied for the size determination of multilamellar vesicles (MLVs). By monitoring the self-diffusion behavior of water, the technique yields an estimate of the homogeneous length scale λ(hom), i.e. the maximum length scale at which there is local structural heterogeneity in a globally homogeneous material. A cross-over between local non-Gaussian to global Gaussian diffusion is observed by varying the experimentally defined length- and time-scales. Occasional observation of a weak Bragg peak in the PGSE signal attenuation curves permits the direct estimation of the MLV radius in favorable cases, thus yielding the constant of proportionality between λ(hom) and radius. The microstructural origin of the Bragg peak is verified through Brownian dynamics simulations and a theoretical analysis based on the center-of-mass diffusion propagator. λ(hom) is decreasing with increasing shear rate in agreement with theoretical expectations and results from (2)H NMR lineshape analysis.     

Optimising time-varying gradient orientation for microstructure sensitivity in diffusion-weighted MR

Here we investigate whether varying the diffusion-gradient orientation during a general waveform single pulsed-field gradient sequence improves sensitivity to the size of coherently oriented pores over having a fixed orientation. The experiment optimises the shape and the orientation of the gradient waveform in each of a set of measurements to minimise the expected variance of estimates of the parameters of a simple model. A key application motivating the work is measuring the size of axons in white matter. Thus, we use a two compartment white matter model with impermeable, single-radius cylinders, and search for waveforms that maximise the sensitivity to axon radius, intra-cellular volume fraction and diffusion constants. Output of the optimisation suggests the only benefit of allowing the gradient orientation to vary in the plane perpendicular to the cylinders is that we can gain perpendicular gradient strength by maximising two orthogonal gradients simultaneously. This suggests that varying orientation in itself does not increase the sensitivity to model parameters. On the other hand, the variation in a plane containing the parallel direction increases the sensitivity significantly because parallel sensitivity improves the diffusion constant estimates. However, we also find that similar improvement in the estimates can be achieved without optimising the orientation, but by having one measurement in the parallel and the rest in the perpendicular direction. The optimisation searches a very large space where it cannot hope to find the global minimum so we cannot make a categorical conclusion. However, given the consistency of the results in multiple reruns and variations of the experiments reported here, we can suggest that for probing coherently oriented systems, pulse sequences with variable orientation, such as double-wave vector sequences, do not offer more advantage than fixed orientation sequences with optimised shape. The advantage of varying orientation is however likely to emerge for more complex systems with dispersed pore orientation.     

Macroscopic background gradient and radiation damping effects on high-field PGSE NMR diffusion measurements

The effects of macroscopic background gradients due to susceptibility differences at the sample interfaces and of radiation damping on pulsed-gradient spin-echo (PGSE) experiments are examined. Both phenomena can lead to the seemingly strange effect of the echo signal growing as the gradient strength increases at low applied gradient strengths. For a freely diffusing species, background gradients manifest themselves as slight concave or convex inflections in the linearized PGSE attenuation curve, depending on the polarity of the applied gradient. The various means of overcoming macroscopic background gradient problems, including bipolar gradients, and their efficacy are examined experimentally and discussed. The effects of radiation damping can also result in the attenuation curve being nonlinear but, different from the effect of background gradients, the nonlinearity does not change with the polarity of the applied gradient. The vulnerability of the stimulated echo-based PGSE sequence and variations of Hahn-based PGSE sequences is investigated. Both background gradients and radiation damping have serious implications for accurate diffusion measurement determination.     

Combining PGSE NMR with homonuclear dipolar decoupling

A new robust approach for combining multiple-pulse homonuclear decoupling and PGSE NMR is introduced for accurately measuring molecular diffusion coefficients in systems with nonvanishing static homonuclear dipolar couplings. Homonuclear decoupling suppresses dipolar dephasing during the gradient pulses but its efficiency and scaling factor for the effective gradient vary across the sample because of the large variation of the frequency offset caused by the gradient. The resulting artifacts are reduced by introducing a slice selection scheme. The method is demonstrated by (19)F PGSE NMR experiments in a lyotropic liquid crystal.     

Purpose-designed probes and their applications for dynamic NMR microscopy in an electromagnet.

The electromagnet provides a favorable environment for certain applications of NMR microscopy. These include plant imaging experiments and measurements of slow molecular diffusion, where high magnetic field gradients for the pulsed gradient spin echo (PGSE) technique are required. In this paper, two probes designed specifically for these two applications are described. In the first case, the open space within the probe has been maximized in order to incorporate environmental support systems for the plant, while in the second the smallest possible PGSE gradient coil former has been used to maximize the gradient strength. Examples are given of Dynamic NMR Microscopy experiments on a castor bean stem and on poly(ethylene oxide)/water solutions under shear thinning conditions.     

13C PGSE NMR experiment with heteronuclear dipolar decoupling to measure diffusion in liquid crystals and solids

A new PGSE NMR experiment, designed to measure molecular diffusion coefficients in systems with nonvanishing static dipolar coupling, is described. The fast static dipolar dephasing of the single-quantum (13)C coherences is removed by multiple-pulse heteronuclear decoupling. The resulting slow dephasing of the (13)C coherences allows for inserting appropriate gradient pulses into the pulse sequence. The presence of the large magnetic field gradient reduces the efficiency of the decoupling sequences which is compensated for by introducing a scheme of sequential slice selection across the sample. The method is demonstrated by (19)F-decoupled (13)C PGSE NMR experiments in a lyotropic nematic and lamellar liquid crystal.     

Measurement of the principal values of the anisotropic diffusion tensor in an unoriented sample by exploiting the chemical shift anisotropy: (19)F PGSE NMR with homonuclear decoupling

NMR methods (S. V. Dvinskikh et al., J. Magn. Reson. 142, 102-110 (2000) and S. V. Dvinskikh and I. Furó, J. Magn. Reson. 144, 142-149 (2000)) that combine PGSE with dipolar decoupling are extended to polycrystalline solids and unoriented liquid crystals. Decoupling suppresses dipolar dephasing not only during the gradient pulses but also under signal acquisition so that the detected spectral shape is dominated by the chemical shift tensor of the selected nucleus. The decay of the spectral intensity at different positions in the powder spectrum provides the diffusion coefficient in sample regions with their crystal axes oriented differently with respect to the direction of the field gradient. Hence, one can obtain the principal values of the diffusion tensor. The method is demonstrated by (19)F PGSE NMR with homonuclear decoupling in a lyotropic lamellar liquid crystal.     

Applications of Nuclear Magnetic Resonance Imaging in Particle Technology

During the past decade, the application of Nuclear Magnetic Resonance (NMR) imaging techniques to problems of relevance to the process industries has been identified. In the context of particle technology, NMR imaging, in addition to the more routinely used techniques of Pulsed Gradient Spin Echo (PGSE) NMR and NMR spectroscopy, offer new methods of characterising pore structure, adsorption and diffusion processes within particles and packed beds of particles, as well as enabling time-resolved in-situ study of processes such as twophase flow, aggregation, polymerisation, crystallisation and phase separation phenomena. This paper reviews recent work in these areas, and also highlights the new insights NMR imaging can give us regarding the characterisation of porous materials, and the influence of the structure of the pore space on the transport processes occuring within a given porous solid.     

Evaluation of diffusional anisotropy and microscopic structure in skeletal muscles using magnetic resonance

The pulsed-gradient spin-echo (PGSE) nuclear magnetic resonance (NMR) method is used for detecting the diffusion of water molecules in biological tissues. Because tissues generally have diffusional anisotropy, their diffusion properties are denoted by a tensor. In this study, we evaluated the diffusional anisotropy and microscopic structure in atrophied skeletal muscles using the PGSE NMR method. The left sciatic nerve was severed in twelve 9-week-old rats. Neurotomy caused neurogenic muscular atrophy at the left gastrocnemius. At 2, 4 and 8 weeks after neurotomy, magnetic resonance signals were selectively acquired from a 2 x 2 x 2 mm(3) voxel, which was located on the left gastrocnemius. The diffusion tensor, the mean diffusivity (MD) and the fractional anisotropy (FA) were calculated from the signals. A theoretical model of the diffusion in muscles was derived from Tanner's equation. The muscle fiber diameter was estimated by fitting the model to the measured signals. The measurements were also performed for normal rats as controls. No significant difference was found in the MD and the estimated intracellular diffusion coefficient between the control group and the denervated group. The denervated group had significantly higher FA compared with the control group (P<.05). The estimated muscle fiber diameter of the denervated group was significantly smaller than the estimated value of the control group (P<.05). These differences were found at 8 weeks after neurotomy. The proposed method is effective for evaluating changes in the microscopic structure of skeletal muscles.     

A new type of sample tube for reducing convection effects in PGSE-NMR measurements of self-diffusion coefficients of liquid samples

Pulsed gradient spin-echo (PGSE) NMR measurements of the self-diffusion coefficients of low viscosity liquids are greatly hampered by the effects of convection especially away from ambient temperature. Here we report on a new NMR tube designed to minimize the deleterious effects of convection. In this tube, which derives from a Shigemi symmetrical NMR tube, the sample is contained in an annulus formed from a concentric cylinder of susceptibility matched glass. The performance of this tube was demonstrated by conducting measurements on the electrochemically important LiN(SO3CF3)2 (LiTFSI)-diglyme (DG) system. Calibrations were first made using DG at column heights of 2, 3, and 4-mm in the temperature range between -40 and 100 degrees C. Measurements of the diffusion coefficients of the lithium, anion, and DG were then performed to probe the solvent-ion and ion-ion interactions in the DG doped with LiTFSI. Changes in the 1H, 7Li, and 19F PGSE-NMR attenuation curves at -40 degrees C provided clear evidence of interactions between the DG and lithium ion.     

Removal of J-coupling peak distortion in PGSE experiments

Peak distortion caused by homonuclear J-coupling is a major problem that limits the utility of the pulsed-field gradient spin–echo (PGSE) method for studying translational diffusion. This unwanted effect can be removed by incorporation of anti-phase magnetization purging pulse elements at the end of the spin–echo sequence. Three methods, namely, trim-pulse, homospoil pulse gradient and chirp based z-filter were evaluated as potential candidates for an improved NMR diffusion method that is less sensitive to J-coupling peak distortion. The chirp based z-filter was found to be excellent in suppressing anti-phase magnetization while leaving the in-phase magnetization basically intact in spin–echo and stimulated-echo based experiments. The incorporation of chirp based z-filter into PGSE could allow diffusion analysis that would otherwise be impossible by conventional means.     

Measurements of restricted diffusion using an oscillating gradient spin-echo sequence

An oscillating gradient spin-echo (OGSE) pulse sequence was used to measure the apparent diffusion coefficient (D(app)) of water in the short diffusion time regime in the presence of restrictions. The diffusion coefficients of water in a simple water sample and a water and oil mixture were measured to be the same for different periods of the gradient oscillation, as expected when there are no restriction effects. The D(app) of water in the spaces between closely packed beads was also measured as a function of the gradient oscillation periods in the range 11 to 80 ms. The D(app) of water in restricted systems varies with the period of the gradient oscillation and the dispersion depends on the scale of the restriction. For a sample of packed beads of diameter 9.1 +/- 0.7 microm, the pore surface-to-volume ratio was estimated experimentally by this method to be 1.3 +/- 0.1 microm(-1), corresponding to a mean pore diameter of 6.4 +/- 0.7 microm. A Monte Carlo computer simulation of the NMR OGSE signal from the spins diffusing in a system of compartments was also implemented and the D(app) demonstrated similar behavior with gradient oscillation periods.     

The narrow pulse approximation and long length scale determination in xenon gas diffusion NMR studies of model porous media

We report a systematic study of xenon gas diffusion NMR in simple model porous media, random packs of mono-sized glass beads, and focus on three specific areas peculiar to gas-phase diffusion. These topics are: (i) diffusion of spins on the order of the pore dimensions during the application of the diffusion encoding gradient pulses in a PGSE experiment (breakdown of the narrow pulse approximation and imperfect background gradient cancellation), (ii) the ability to derive long length scale structural information, and (iii) effects of finite sample size. We find that the time-dependent diffusion coefficient, D(t), of the imbibed xenon gas at short diffusion times in small beads is significantly affected by the gas pressure. In particular, as expected, we find smaller deviations between measured D(t) and theoretical predictions as the gas pressure is increased, resulting from reduced diffusion during the application of the gradient pulse. The deviations are then completely removed when water D(t) is observed in the same samples. The use of gas also allows us to probe D(t) over a wide range of length scales and observe the long time asymptotic limit which is proportional to the inverse tortuosity of the sample, as well as the diffusion distance where this limit takes effect (approximately 1-1.5 bead diameters). The Padé approximation can be used as a reference for expected xenon D(t) data between the short and the long time limits, allowing us to explore deviations from the expected behavior at intermediate times as a result of finite sample size effects. Finally, the application of the Padé interpolation between the long and the short time asymptotic limits yields a fitted length scale (the Padé length), which is found to be approximately 0.13b for all bead packs, where b is the bead diameter.     

PGSTE-WATERGATE: an STE-based PGSE NMR sequence with excellent solvent suppression

A new stimulated-echo based pulsed gradient spin-echo NMR diffusion sequence incorporating WATERGATE solvent suppression, PGSTE-WATERGATE, is presented. The sequence provides superb solvent suppression without any phase distortions. The sequence is simple to set up and particularly suited to measuring diffusion coefficients in aqueous solution such as is commonly required in pharmaceutical and combinatorial applications. The utility of the sequence is demonstrated on samples containing lysozyme and sucrose. Importantly, the high degree of phase-distortion suppression allows more complicated selective pi pulses to be used to enhance the selectivity of solvent suppression.     

Accurate measurement of translational diffusion coefficients: a practical method to account for nonlinear gradients

For NMR probes equipped with pulsed field gradient coils, which are not optimized for gradient linearity, the precision and accuracy of experimentally measured translational diffusion coefficients are limited by the linearity of the gradient pulses over the sample volume. This study shows that the accuracy and precision of measured diffusion coefficients by the Stejskal--Tanner spin-echo pulsed field gradient experiment can be significantly improved by mapping the gradient z-profile and by using the mapped calibration parameters in the data analysis. For practical applications the gradient distribution may be approximated by a truncated linear distribution defined by minimum and maximum values of the gradient. By including the truncated linear gradient distribution function in the Stejskal--Tanner equation, the systematic deviation between the fitted curve and the experimental attenuation curve decreases by an order of magnitude. The gradient distribution may be calibrated using an intense NMR signal from a sample with a known diffusion coefficient. The diffusion coefficient of an unknown sample may then be determined from a two-parameter fit, using the known gradient distribution function.     

Influential Factors of Internal Magnetic Field Gradient in Reservoir Rock and Its Effects on NMR Response

Nuclear magnetic resonance (NMR) plays a significant role in porous media analysis and petroleum exploration, but its response is significantly influenced by the internal magnetic field gradient in fluid saturated porous medium, which obviously limits the accuracy of rock core analysis and logging interpretation. The influential factors of the internal magnetic field gradient in formation and its influences on NMR response are studied in this paper, based on NMR mechanism through one- and two-dimensional core NMR experiments. The results indicate that the internal magnetic field gradient is positively correlated with the static magnetic field strength and the magnetic susceptibility difference between pore fluid and solid grains, while it presents negative correlation with pore radius. The internal magnetic field gradient produces an additional diffusion relaxation in hydrogen relaxation system and accelerates the attenuation of magnetization vector. As a result, T₂ spectrum shifts to the left and NMR porosity and diffusion coefficient of the fluid could be inaccurate. This research sets a foundation for the NMR porosity correction and fluid distribution on T₂-G maps based on the internal magnetic field gradient correction.     

A PFG NMR experiment for translational diffusion measurements in low-viscosity solvents containing multiple resonances

Pulsed gradient simulated-echo (PGSE) NMR diffusion measurements provide a facile and accurate means for determining the self-diffusion coefficients for molecules over a wide range of sizes and conditions. The measurement of diffusion in solvents of low intrinsic viscosity is particularly challenging, due to the persistent presence of convection. Although convection can occur in most solvent systems at elevated temperatures, in lower viscosity solvents (e.g., short chain alkanes), convection may manifest itself even at ambient laboratory temperatures. In most circumstances, solvent suppression will also be required, and for solvents that have multiple resonances, effective suppression can likewise represent a substantial challenge. In this article, we report an NMR experiment that combines a double-stimulated echo PFG approach with a WET-based solvent suppression scheme that effectively and simultaneously address the issues of dynamic range and the deleterious effects of convection. The experiment described will be of general benefit to studies aimed at the characterization of diffusion of single molecules directly dissolved in low-viscosity solvents, and should also be of substantial utility in studies of supramolecular assemblies such as reverse-micelles dissolved in apolar solvents.