An improved approach to calibrating high magnetic field gradients for pulsed field gradient experiments

Probes capable of generating short high intensity pulsed magnetic field gradients are commonly used in diffusion studies of systems with very short T(2). Traditional methods of calibrating magnetic field gradients present unique challenges at ultrahigh field strengths and are often inapplicable. Currently the most accurate method of determining magnetic gradient strength is to use the known diffusion coefficient of a standard sample and determine gradient strength from the echo attenuation plot of a diffusion experiment, however, there are problems with finding suitable standards for high intensity gradients. Here, we show that molecules containing at least two receptive nuclei (i.e. one with high and one with low gyromagnetic ratios) are excellent systems for calibrating high intensity gradients.     

Background gradient suppression in pulsed gradient stimulated echo measurements

Pulsed gradient spin echo (PGSE) experiments can be used to measure the probability distribution of molecular displacements. In homogeneous samples this reports on the molecular diffusion coefficient, and in heterogeneous samples, such as porous media and biological tissue, such measurements provide information about the sample's morphology. In heterogeneous samples however background gradients are also present and prevent an accurate measurement of molecular displacements. The interference of time independent background gradients with the applied magnetic field gradients can be removed through the use of bipolar gradient pulses. However, when the background gradients are spatially non-uniform molecular diffusion introduces a temporal modulation of the background gradients. This defeats simple bipolar gradient suppression of background gradients in diffusion related measurements. Here we introduce a new method that requires the background gradients to be constant over coding intervals only. Since the coding intervals are typically at least an order of magnitude shorter than the storage time, this new method succeeds in suppressing cross-terms for a much wider range of heterogeneous samples.     

One- and Two-Dimensional Pulse Sequences for Diffusion Experiments in the Fringe Field of Superconducting Magnets

The fringe field of superconducting magnets provides extremely strong and stable field gradients which can be used for diffusion experiments. A number of corresponding "supercon fringe-field" variants of the "pulsed-gradient spin-echo" method are presented. These include procedures and pulse sequences for the record of relaxation-independent diffusion decays, multislice excitation, and one- or two-dimensional Fourier-transform evaluation from the k to the z domain. Several test experiments are described. It is demonstrated that reliable diffusion decays are obtained. The one-dimensional z-domain evaluation produces grid patterns analogous to the optical "forced Rayleigh scattering" method. The two-dimensional experiments are suitable for the detection of spatially varying probability densities of diffusion or incoherent flow in heterogeneous media. As the resolution is particularly high, fluids can be studied close to solid surfaces.     

One-Dimensional NOE Experiments Using Pulsed Field Gradients

Previously, it has been shown that the use of pulsed field gradients in one-dimensional NOE experiments results in spectra of much higher quality than it has previously been possible to record. Such high-quality spectra make it possible to measure, with complete confidence, very small NOE enhancements and also make it straightforward to measure NOE buildup curves. In this paper, the spin dynamics behind these NOE experiments with gradients are analyzed in detail; the effects of strong coupling and molecular diffusion are also examined. It is also shown how the basic experiments can be improved upon, in particular how unwanted anti-phase contributions (SPT effects) can be eliminated entirely. Experimental illustrations of the various methods and improvements are given and practical recommendations made as to how the experiments are best performed.     

Velocity distribution of slow fluid flows in bentheimer sandstone: An NMRI and propagator study

This work addresses the special problems of measuring flow velocity distributions in rock by NMR methods. Specifically, these problems are to measure very slow flows as well as flows in the presence of background magnetic field gradients caused by heterogeneities of the rock. We modify a stimulated echo sequence for use in diffusion measurements, in order to maximize velocity sensitivity and minimize background gradient effects. Accurate velocity images of Soltrol 220 oil in sandstone were made for flow velocities up to around 0.04 mm/s with an imager that does not have echo-planar capability. Accurate velocity distributions by the propagator method can be obtained even with stimulated echo delays of 1.9 T₁ by phase cycling combined with suitable crusher gradients.     

Radiofrequency magnetic field gradient echoes have reduced sensitivity to susceptibility gradients

The amplitudes of gradient-echoes produced using static field gradients are sensitive to diffusion of tissue water during the echo evolution time. Gradient-echoes have been used to produce MR images in which image intensity is proportional to the self-diffusion coefficient of water. However, such measurements are subject to error due to the presence of background magnetic field gradients caused by variations in local magnetic susceptibility. These local gradients add to the applied gradients. The use of radiofrequency (RF) gradients to produce gradient-echoes may avoid this problem. The RF magnetic field is orthogonal to the offset field produced by local magnetic susceptibility gradients. Thus, the effect of the local gradients on RF gradient-echo amplitude is small if the RF field is strong enough to minimize resonance offset effects. The effects of susceptibility gradients can be further reduced by storing magnetization longitudinally during the echo evolution period. A water phantom was used to evaluate the effects of background gradients on the amplitudes of RF gradient-echoes. A surface coil was used to produce an RF gradient of between 1.3 and 1.6 gauss/cm. Gradient-echoes were detected with and without a 0.16 gauss/cm static magnetic field gradient applied along the same direction as the RF gradient. The background static field gradient had no significant effect on the decay of RF gradient-echo amplitude as a function of echo evolution time. In contrast, the effect of the background gradient on echoes produced using a 1.6 gauss/cm static field gradient is calculated to be significant. This analysis suggests that RF gradient-echoes can produce MR images in which signal intensity is a function of the self-diffusion coefficient of water, but is not significantly affected by background gradients.     

Determination of the defining boundary in nuclear magnetic resonance diffusion experiments

While nuclear magnetic resonance diffusion experiments are widely used to resolve structures confining the diffusion process, it has been elusive whether they can exactly reveal these structures. This question is closely related to x-ray scattering and to Kac's "hear the drum" problem. Although the shape of the drum is not "hearable," we show that the confining boundary of closed pores can indeed be detected using modified Stejskal-Tanner magnetic field gradients that preserve the phase information and enable imaging of the average pore in a porous medium with a largely increased signal-to-noise ratio.     

Effective Gradients in Porous Media Due to Susceptibility Differences

In porous media, magnetic susceptibility differences between the solid phase and the fluid filling the pore space lead to field inhomogeneities inside the pore space. In many cases, diffusion of the spins in the fluid phase through these internal inhomogeneities controls the transverse decay rate of the NMR signal. In disordered porous media such as sedimentary rocks, a detailed evaluation of this process is in practice not possible because the field inhomogeneities depend not only on the susceptibility difference but also on the details of the pore geometry. In this report, the major features of diffusion in internal gradients are analyzed with the concept of effective gradients. Effective gradients are related to the field inhomogeneities over the dephasing length, the typical length over which the spins diffuse before they dephase. For the CPMG sequence, the dependence of relaxation rate on echo spacing can be described to first order by a distribution of effective gradients. It is argued that for a given susceptibility difference, there is a maximum value for these effective gradients,g_max, that depends on only the diffusion coefficient, the Larmor frequency, and the susceptibility difference. This analysis is applied to the case of water-saturated sedimentary rocks. From a set of NMR measurements and a compilation of a large number of susceptibility measurements, we conclude that the effective gradients in carbonates are typically smaller than gradients of current NMR well logging tools, whereas in many sandstones, internal gradients can be comparable to or larger than tool gradients.     

Probing four orders of magnitude of the diffusion time in porous silica glass with unconventional NMR techniques

The combined use of two unconventional NMR diffusometry techniques permits measurements of the self-diffusion coefficient of fluids confined in porous media in the time range from 100 microseconds to seconds. The fringe field stimulated echo technique (FFStE) exploits the strong steady gradient in the fringe field of a superconducting magnet. Using a standard 9.4 T (400 MHz) wide-bore magnet, for example, the gradient is 22 T/m at 375 MHz proton resonance and reaches 60 T/m at 200 MHz. Extremely short diffusion times can be probed on this basis. The magnetization grid rotating frame imaging technique (MAGROFI) is based on gradients of the radio frequency (RF) field. The RF gradients not necessarily need be constant since the data are acquired with spatial resolution along the RF gradient direction. MAGROFI is also well suited for unilateral NMR applications where all fields are intrinsically inhomogeneous. The RF gradients reached depend largely on the RF coil diameter and geometry. Using a conic shape, a value of at least 0.3 T/m can be reached which is suitable for long-time diffusion measurements. Both techniques do not require any special hardware and can be implemented on standard high RF power NMR spectrometers. As an application, the influence of the tortuosity increasing with the diffusion time is examined in a saturated porous silica glass.     

COIL亚声速段横向喷流混合流场数值分析

 COIL是一个气体动力学、化学反应动力学以及光学相互耦合的复杂过程。作为高总压COIL系统研究的第一步,利用三维CFD技术对传统的COIL亚声速段横向射流混合过程进行了数值分析,讨论了包括压力梯度驱动项的分子扩散机制,得到了横向射流的较精细的结构,如马蹄形射流界面、逆旋涡对以及射流剪切层。结果表明,压力梯度驱动项对重、轻组分的扩散作用相反,重组分沿压力梯度正向扩散,轻组分逆压力梯度方向扩散。在射流穿透不足的情况下,仍然在喷管出口得到了约为0.01 cm^-1的小信号增益系数。     

Earlier detection of tumor treatment response using magnetic resonance diffusion imaging with oscillating gradients

An improved method for detecting early changes in tumors in response to treatment, based on a modification of diffusion-weighted magnetic resonance imaging, has been demonstrated in an animal model. Early detection of therapeutic response in tumors is important both clinically and in pre-clinical assessments of novel treatments. Noninvasive imaging methods that can detect and assess tumor response early in the course of treatment, and before frank changes in tumor morphology are evident, are of considerable interest as potential biomarkers of treatment efficacy. Diffusion-weighted magnetic resonance imaging is sensitive to changes in water diffusion rates in tissues that result from structural variations in the local cellular environment, but conventional methods mainly reflect changes in tissue cellularity and do not convey information specific to microstructural variations at sub-cellular scales. We implemented a modified imaging technique using oscillating gradients of the magnetic field for evaluating water diffusion rates over very short spatial scales that are more specific for detecting changes in intracellular structure that may precede changes in cellularity. Results from a study of orthotopic 9L gliomas in rat brains indicate that this method can detect changes as early as 24 h following treatment with 1,3-bis(2-chloroethyl)-1-nitrosourea, when conventional approaches do not find significant effects. These studies suggest that diffusion imaging using oscillating gradients may be used to obtain an earlier indication of treatment efficacy than previous magnetic resonance imaging methods.     

A unilateral magnet with an extended constant magnetic field gradient

Unilateral magnetic resonance (UMR) has become, in different research areas, a powerful tool to interrogate samples of arbitrary size. Numerous designs have been suggested in the literature to produce the desired magnetic field distributions, including designs which feature constant magnetic field gradients suitable for diffusion and profiling experiments. This work presents a new approach which features extended constant magnetic field gradients with a three magnet array. Constant gradients of more than 3cm extent can be achieved in a very simple, compact and safe design. Diffusion measurements from different positions over the magnet are presented in addition to practical applications for reservoir core plug characterization. The idea of a solenoid as a probe for specific measurements in UMR is introduced. Simple profiling experiments are also presented.     

Apparent diffusion behaviors of spins in the presence of distant dipolar field in two-component solution NMR

The diffusion behaviors of spins in the presence of distant dipolar field in two-component spin systems during the second evolution period of a modified CRAZED sequence before acquisition were investigated. Theoretical formulas were deduced based on the distant dipolar field model. The simulation results and experimental observations are consistent with the theoretical predictions. This study shows that the relative intensities of signals from intermolecular zero-quantum coherences (iZQCs) and intermolecular double-quantum coherences (iDQCs) have the same diffusion attenuation characteristic under the combined effect of diffusion weighting gradients and distant dipolar field during the second evolution period. This diffusion attenuation may be different from that of conventional single-quantum coherence signal, depending on the relative orientation of the diffusion weighting gradients to the coherence selection gradients. The results presented herein are helpful for understanding the effect of distant dipolar field from a spin system on the diffusion behavior of other spin system and the signal properties in the iZQC or iDQC magnetic resonance imaging.     

Magnetic field anisotropy based MR tractography

Non-invasive measurements of structural orientation provide unique information regarding the connectivity and functionality of fiber materials. In the present study, we use a capillary model to demonstrate that the direction of fiber structure can be obtained from susceptibility-induced magnetic field anisotropy. The interference pattern between internal and external magnetic field gradients carries the signature of the underlying anisotropic structure and can be measured by MRI-based water diffusion measurements. Through both numerical simulation and experiments, we found that this technique can determine the capillary orientation within 3°. Therefore, susceptibility-induced magnetic field anisotropy may be useful for an alternative tractography method when diffusion anisotropy is small at higher magnetic field strength without the need to rotate the subject inside the scanner.     

A continuous tensor field approximation of discrete DT-MRI data for extracting microstructural and architectural features of tissue

The effective diffusion tensor of water, D, measured by diffusion tensor MRI (DT-MRI), is inherently a discrete, noisy, voxel-averaged sample of an underlying macroscopic effective diffusion tensor field, D(x). Within fibrous tissues this field is presumed to be continuous and smooth at a gross anatomical length scale. Here a new, general mathematical framework is proposed that uses measured DT-MRI data to produce a continuous approximation to D(x). One essential finding is that the continuous tensor field representation can be constructed by repeatedly performing one-dimensional B-spline transforms of the DT-MRI data. The fidelity and noise-immunity of this approximation are tested using a set of synthetically generated tensor fields to which background noise is added via Monte Carlo methods. Generally, these tensor field templates are reproduced faithfully except at boundaries where diffusion properties change discontinuously or where the tensor field is not microscopically homogeneous. Away from such regions, the tensor field approximation does not introduce bias in useful DT-MRI parameters, such as Trace(D(x)). It also facilitates the calculation of several new parameters, particularly differential quantities obtained from the tensor of spatial gradients of D(x). As an example, we show that they can identify tissue boundaries across which diffusion properties change rapidly using in vivo human brain data. One important application of this methodology is to improve the reliability and robustness of DT-MRI fiber tractography.     

Diffusion measurements using the nonlinear stimulated echo

The nonlinear stimulated echo that is generated by a sequence of three radiofrequency pulses, 90 degrees-tau(1)-90 degrees-tau(2)-45 degrees, in high magnetic fields (or at low temperatures) in the presence of pulsed or steady field gradients can be applied for measurements of the diffusion coefficient. Corresponding test experiments are reported. Steady gradients can be used without knowledge of the relaxation times. Remarkably the attenuation of the nonlinear stimulated echo by diffusion is substantially stronger than in the case of the ordinary stimulated echo.     

Monte Carlo Simulations of PAC-Spectra as a General Approach to Dynamic Interactions

Time Dependent Perturbed Angular Correlations of -rays (PAC) can be used to study hyperfine interactions of a dynamic nature. However, the exact effect of the dynamic interaction on the PAC-spectrum is sometimes difficult to derive analytically. A new approach based on Monte Carlo simulations is therefore suggested, here implemented as a Fortran 90 program for simulating PAC spectra of dynamic electric field gradients of any origin. The program is designed for the most common experimental condition where the intermediate level has spin 5/2, but the approach can equally well be used for other spin states. Codes for 4 different situations have been developed: (1) Rotational diffusion by jumps; used as a test case. (2) Jumps between two states with different electric field gradients, different lifetimes and different orientations of the electric field gradient principal axes. (3) Relaxation of one state to another. (4) Molecules adhering to a surface with random rotational jumps around the axis perpendicular to the surface. To illustrate how this approach can be used to improve data-interpretation, previously published data on ^111mCd-plastocyanin and ¹¹¹Ag-plastocyanin are re-considered. The strength of this novel approach is its simplicity and generality so that other dynamic processes can easily be included by only adding new program units describing the random process behind the dynamics. The program is hereby made publicly available.     

Electric field gradient effects in raman spectroscopy

Raman spectra of materials subject to strong electric field gradients, such as those present near a metal surface, can show significantly altered selection rules. We describe a new mechanism by which the field gradients can produce Raman-like lines. We develop a theoretical model for this "gradient-field Raman" effect, discuss selection rules, and compare to other mechanisms that produce Raman-like lines in the presence of strong field gradients. The mechanism can explain the origin and intensity of some Raman modes observed in SERS and through a near-field optical microscope (NSOM-Raman).     

Relationship between susceptibility induced field inhomogeneities, restricted diffusion, and relaxation in sedimentary rocks

Low field relaxation and diffusion measurements have become essential tools to study the pore space of sedimentary rocks with important practical applications in the field of well logging and hydrocarbon extractions. Even at Larmor frequencies below 2 MHz, diffusion measurements are often affected noticeably by internal field inhomogeneities. These field inhomogeneities are induced by susceptibility contrast between the rock and the fluid and are evident in most sandstones. Using sets of two-dimensional diffusion-relaxation measurements in applied and internal gradients, we study in detail the correlation between the field inhomogeneities, restricted diffusion, and relaxation time in three rocks of different susceptibility. We find that in the sandstone cores, the field inhomogeneities in large pores can be described by a local gradient that scales inversely with relaxation time above 250 ms. At shorter relaxation times, the extracted internal gradients deviate from this scaling relationship and we observe a dependence on diffusion time. This demonstrates that in this case, the internal field has structure on a length scale of a few microns.     

Background gradient suppression in stimulated echo NMR diffusion studies using magic pulsed field gradient ratios

By evaluating the spin echo attenuation for a generalized 13-interval PFG NMR sequence consisting of pulsed field gradients with four different effective intensities (F(p/r) and G(p/r)), magic pulsed field gradient (MPFG) ratios for the prepare (G(p)/F(p)) and the read (G(r)/F(r)) interval are derived, which suppress the cross term between background field gradients and the pulsed field gradients even in the cases where the background field gradients may change during the z-store interval of the pulse sequence. These MPFG ratios depend only on the timing of the pulsed gradients in the pulse sequence and allow a convenient experimental approach to background gradient suppression in NMR diffusion studies with heterogeneous systems, where the local properties of the (internal) background gradients are often unknown. If the pulsed field gradients are centered in the tau-intervals between the pi and pi/2 rf pulses, these two MPFG ratios coincide to eta=G(p/r)/F(p/r)=1-8/[1+(1/3)(delta/tau)(2)]. Since the width of the pulsed field gradients (delta) is bounded by 0< or =delta< or =tau, eta can only be in the range of 5< or =-eta< or =7. The predicted suppression of the unwanted cross terms is demonstrated experimentally using time-dependent external gradients which are controlled in the NMR experiment as well as spatially dependent internal background gradients generated by the magnetic properties of the sample itself. The theoretical and experimental results confirm and extend the approach of Sun et al. (J. Magn. Reson. 161 (2003) 168), who recently introduced a 13-interval type PFG NMR sequence with two asymmetric pulsed magnetic field gradients suitable to suppress unwanted cross terms with spatially dependent background field gradients.