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.     

PFG NMR and internal magnetic field gradients in plant-based materials

In this contribution, it is demonstrated that inner magnetic field gradients can seriously affect the results of stimulated echo PFG NMR experiments on plant-based materials even if there is no notable content of paramagnetic substances. Such effects could be observed both in experiments on water in pharmaceutical grade cellulose powder materials and on eggplant fruit tissue. In both cases, it was observed that the effects of internal magnetic field gradients led to different relative values of the diffusion coefficient compared to values obtained with a gradient-compensating pulse sequence.     

Determination of genuine diffusivities in heterogeneous media using stimulated echo pulsed field gradient NMR

Pulsed field gradient (PFG) NMR diffusion measurements in heterogeneous media may lead to erroneous results due to the disturbing influence of internal magnetic field gradients. Here, we present a simple theoretical model which allows one to interpret data obtained by stimulated spin echo PFG NMR in the presence of spatially varying internal field gradients. Using the results of this theory, the genuine self-diffusion coefficients in heterogeneous media may be extrapolated from the dependence of the apparent diffusivities on the dephasing time of the simulated echo PFG NMR sequence. Experimental evidence that such extrapolation yields satisfactory results for self-diffusion of hexadecane in natural sediments (sand) and of n-octanol in doped MgO pastes is provided.     

MAG-PGSTE: a new STE-based PGSE NMR sequence for the determination of diffusion in magnetically inhomogeneous samples

A new stimulated echo based pulsed gradient spin-echo sequence, MAG-PGSTE, has been developed for the determination of self-diffusion in magnetically inhomogeneous samples. The sequence was tested on two glass bead samples (i.e., 212-300 and <106 microm glass bead packs). The MAG-PGSTE sequence was compared to the MAGSTE (or MPFG) (P.Z. Sun, J.G. Seland, D. Cory, Background gradient suppression in pulsed gradient stimulated echo measurements, J. Magn. Reson. 161 (2003) 168-173; P.Z. Sun, S.A. Smith, J. Zhou, Analysis of the magic asymmetric gradient stimulated echo sequence with shaped gradients, J. Magn. Reson. 171 (2004) 324-329; P.Z. Sun, Improved diffusion measurement in heterogeneous systems using the magic asymmetric gradient stimulated echo (MAGSTE) technique, J. Magn. Reson. 187 (2007) 177-183; P. Galvosas, F. Stallmach, J. K?rger, Background gradient suppression in stimulated echo NMR diffusion studies using magic pulsed field gradient ratios, J. Magn. Reson. 166 (2004) 164-173, P. Galvosas, PFG NMR-Diffusionsuntersuchungen mit ultra-hohen gepulsten magnetischen Feldgradienten an mikropor?sen Materialien, Ph.D. Thesis, Universit?t Leipzig, 2003, P.Z. Sun, Nuclear Magnetic Resonance Microscopy and Diffusion, Ph.D. Thesis, Massachusetts Institute of Technology, 2003] sequence and Cotts 13-interval [R.M. Cotts, M.J.R. Hoch, T. Sun, J.T. Marker, Pulsed field gradient stimulated echo methods for improved NMR diffusion measurements in heterogeneous systems, J. Magn. Reson. 83 (1989) 252-266] sequence using both glass bead samples. The MAG-PGSTE and MAGSTE (or MPFG) sequences outperformed the Cotts 13-interval sequence in the measurement of diffusion coefficients; more interestingly, for the sample with higher background gradients (i.e., the <106 microm glass bead sample), the MAG-PGSTE sequence provided higher signal-to-noise ratios and thus better diffusion measurements than the MAGSTE and Cotts 13-interval sequences. In addition, the MAG-PGSTE sequence provided good characterization of the surface-to-volume ratio for the glass bead samples.     

Improved convection compensating pulsed field gradient spin-echo and stimulated-echo methods

The need for convection compensating methods in NMR has been manifested through an increasing number of publications related to the subject over the past few years (J. Magn. Reson. 125, 372 (1997); 132, 13 (1998); 131, 126 (1998); 118, 50 (1996); 133, 379 (1998)). When performing measurements at elevated temperature, small convection currents may give rise to erroneous values of the diffusion coefficient. In work with high resolution NMR spectroscopy, the application of magnetic field gradients also introduces an eddy-current magnetic field which may result in errors in phase and baseline in the FFT-spectra. The eddy current field has been greatly suppressed by the application of bipolar magnetic field gradients. However, when introducing bipolar magnetic field gradients, the pulse sequence is lengthened significantly. This has recently been pointed out as a major drawback because of the loss of coherence and of NMR-signal due to transverse relaxation processes. Here we present modified convection compensating pulsed field gradient double spin echo and double stimulated echo sequences which suppress the eddy-current magnetic field without increasing the duration of the pulse sequences.     

Analysis of the magic asymmetric gradient stimulated echo sequence with shaped gradients

Recently a 13-interval magic asymmetrical gradient stimulated echo (MAGSTE) sequence has been proposed for accurate displacement measurements in the presence of spatially varying background gradients. In this paper, the commonly used trapezoidal and sine shaped gradients are studied for the MAGSTE sequence, and the magic asymmetrical gradient ratio and b-factor are provided. The derivation enables the MAGSTE sequence to be implemented on systems with non-negligible gradient rise times.     

Diffusion measurements at long observation times in the presence of spatially variable internal magnetic field gradients

Diffusion measurements in heterogeneous media may contain a significant source of error, the influence of the coupling between the applied and internal magnetic field gradients on the attenuation of the NMR signal. The application of bipolar magnetic field gradients has been introduced to suppress this error. The basic assumption for the successful removal of the coupling is that the diffusing molecules are experiencing a constant internal gradient during the experiment. We will provide theoretical and experimental evidence that the application of bipolar magnetic field gradients may fail to suppress the effect from all the cross terms between internal and applied gradients effectively at long observation times. It will be shown experimentally that a successful suppression of the cross terms is strongly dependent on the observation time, and on the tau value in the bipolar pulsed field gradient stimulated echo experiment. Copyright 2000 Academic Press.     

Constant time steady gradient NMR diffusometry using the secondary stimulated echo

A pulse sequence producing a second stimulated echo is suggested for the compensation of relaxation and residual dipolar interaction effects in steady gradient spin echo diffusometry. Steady field gradients of considerable strength exist in the fringe field of NMR magnets, for instance. While the absolute echo time of the second stimulated echo is kept constant throughout the experiment, the interval between the first two radiofrequency pulses is augmented leading to a modulation of the amplitude of that second stimulated echo by self-diffusion only. The unique feature of this technique is that it is of a single-scan/single-echo-signal nature. That is, no reference signals neither of the same pulse sequence nor of separate experiments are needed. The new method was tested with poly(ethylene oxide) melts and proved to provide reliable data for (time dependent) self-diffusion coefficients down to the physical limit (D approximately 10(-15)m(2)/s) when flip-flop spin diffusion starts to become effective.     

The elimination of magnetic susceptibility artifacts in the micro-image of liquid-solid interfaces: internal gradient modulation by the CPMG RF train

Distortions of magnetic resonance images near solid-liquid interface appear as the result of the restriction to spin self-diffusion in the proximity of impermeable boundary as well as of a susceptibility difference. The spectral analysis of spin echo enables to resolve, in a simple way, how various RF-gradient pulse sequences reduce the effect of the internal magnetic field induced by the susceptibility difference at interfaces. The 1D diffusion-weighted imaging of water in the narrow notch tested efficiency of some sequence. The notch was milled in a piece of Plexiglas. The method can be used to distinguish the susceptibility effect from the effects of applied gradients when investigating the transport of fluid through a porous structure.     

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.     

Microscopic imaging of slow flow and diffusion: a pulsed field gradient stimulated echo sequence combined with turbo spin echo imaging.

In this paper we present a pulse sequence that combines a displacement-encoded stimulated echo with rapid sampling of k-space by means of turbo spin echo imaging. The stimulated echo enables the use of long observation times between the two pulsed field gradients that sample q-space completely. Propagators, constructed with long observation times, could discriminate slowly flowing protons from diffusing protons, as shown in a phantom in which a plug flow with linear velocity of 50microm/s could clearly be distinguished from stationary water. As a biological application the apparent diffusion constant in longitudinal direction of a transverse image of a maize plant stem had been measured as a function of observation time. Increasing contrast in the apparent diffusion constant image with increasing observation times were caused by differences in plant tissue: although the plant stem did not take up any water, the vascular bundles, concentrated in the outer ring of the stem, could still be discerned because of their longer unrestricted diffusional pathways for water in the longitudinal direction compared to cells in the parenchymal tissue. In the xylem region of a tomato pedicel flowing water could be distinguished from a large amount of stationary water. Linear flow velocities up to 0.67 mm/s were measured with an observation time of 180 ms.     

Fast measurements of average flow velocity by Low-Field ¹H NMR

In this paper, we describe a method for measuring the average flow velocity of a sample by means of Nuclear Magnetic Resonance. This method is based on the Carr-Purcell-Meiboom-Gill (CPMG) sequence and does not require the application of any additional static or pulsed magnetic field gradients to the background magnetic field. The technique is based on analyzing the early-time behavior of the echo amplitudes of the CPMG sequence. Measurements of average flow velocity of water are presented. The experimental results show a linear relationship between the slope/y-intercept ratio of a linear fit of the first echoes in the CPMG sequence, and the average flow velocity of the flowing fluid. The proposed method can be implemented in low-cost Low-Field NMR spectrometers allowing a continuous monitoring of the average velocity of a fluid in almost real-time, even if the flow velocity changes rapidly.     

A computer algorithm for the simulation of any nuclear magnetic resonance (NMR) imaging method

More than a dozen Nuclear Magnetic Resonance (NMR) imaging methods have been described using different radio-frequency pulse sequences, magnetic field gradient variations, and data processing. In order to have a theoretical understanding in the most general case, we have conceived a computer program for the simulation of NMR imaging techniques. The algorithm uses the solution of the Bloch equations at each point of a simulated object. The direction of every elementary magnetic moment is computed at each instant, and stored in an array giving the global signal to be processed, whatever the pulse and gradient sequence. To test the validity of this program, we have simulated some well-known experimental results. Some applications are presented which contribute to the understanding of image distortions and to techniques such as selective radio-frequency pulse or oscillating gradients. This program can be used to unravel physical and technological causes of image distortions, to have a "microscopic" look at any parameter of an experiment, and to study the contrast given by various NMR imaging techniques as a function of the three NMR parameters, i.e., the hydrogen nuclei density rho and the relaxation times T1 and T2.     

Investigation of two phase flow and phase trapping by secondary imbibition within Fontainebleau sandstone

Pulsed magnetic field gradient stimulated echo NMR is used to investigate the simultaneous flow of two phases (an aqueous phase and an hydrocarbon phase) within a strongly water-wet sample of Fontainebleau sandstone. The Fontainebleau sandstone is prepared in increasing steady-state water saturations by a secondary imbibition process. The increase in the water saturation causes an increasing fraction of the oil phase (non-wetting phase) to become trapped within the sample. The stimulated echo dependence on the gradient pulse area, q, is used to derive the displacement probability, PX, for a fixed observation time. These displacement probabilities clearly show the progressive trapping of the hydrocarbon phase with increasing steady-state water saturations. Quantitative measurements of the fraction of the oil phase trapped were made from the echo attenuation function Edelta(q), both as a function of water saturation and observation time.     

NMR studies of water diffusion and relaxation in hydrating slag-based construction materials.

The NMR relaxation properties of hydrating blast-furnace slag cements have recently been shown to be dominated by the effect of water self-diffusion in internal magnetic field gradients in the pastes. While this was suggested on the basis of NMR relaxometry and magnetic susceptibility data, we report here the results from first direct studies of the water self-diffusion in the hydrating paste using a specialized PFG sequence and very intensive magnetic field gradient pulses.     

Categories of coherence pathways for the CPMG sequence

The CPMG sequence has been extremely useful for efficient measurements of NMR signal, spin-spin relaxation, and diffusion, particularly in inhomogeneous magnetic fields, such as when samples are outside the magnet and RF coil. Due to the inaccuracy of the pulses and the off-resonance effects, the CPMG echoes have contributions from the Hahn echo as well as signals that are similar to stimulated echoes. The systematic understanding of the CPMG pulse sequence requires decomposing the magnetization dynamics into different coherence pathways. In this paper, we describe a method to classify the CPMG coherence pathways and illustrate the nature of these types of pathways. This classification shows that direct echo and stimulated echoes are the major contribution to the CPMG signal. It also provides a clear understanding of the effect of restricted diffusion in porous media.     

SOGGY: solvent-optimized double gradient spectroscopy for water suppression. A comparison with some existing techniques

Excitation sculpting, a general method to suppress unwanted magnetization while controlling the phase of the retained signal [T.L. Hwang, A.J. Shaka, Water suppression that works. Excitation sculpting using arbitrary waveforms and pulsed field gradients, J. Magn. Reson. Ser. A 112 (1995) 275-279] is a highly effective method of water suppression for both biological and small molecule NMR spectroscopy. In excitation sculpting, a double pulsed field gradient spin echo forms the core of the sequence and pairing a low-power soft 180 degrees (-x) pulse with a high-power 180 degrees (x) all resonances except the water are flipped and retained, while the water peak is attenuated. By replacing the hard 180 degrees pulse in the double echo with a new phase-alternating composite pulse, broadband and adjustable excitation of large bandwidths with simultaneous high water suppression is obtained. This "Solvent-Optimized Gradient-Gradient Spectroscopy" (SOGGY) sequence is a reliable workhorse method for a wide range of practical situations in NMR spectroscopy, optimizing both solute sensitivity and water suppression.     

NMR imaging of solids by Jeener-Broekaert phase encoding

A method for imaging of spectral parameters of solid samples is presented. The detected NMR signals are Jeener-Broekaert echoes. No read field gradient is applied during the acquisition, so that wide-line spectral parameters can be evaluated and be transferred to image contrasts. On the other hand, multipulse line-narrowing sequences can be applied during the echoes in order to obtain high-resolution spectra. The imaging principle is a pure phase-encoding Fourier technique in two or three dimensions. The phase-encoding gradients are active in the interval between the first two pulses of the Jeener-Broekaert three-pulse sequence. Between the second and the third pulse, the information is conserved in the dipolar (or quadrupolar) order state which is insensitive to field gradients and governed by the relatively slow dipolar (or quadrupolar) relaxation. This interval therefore can be chosen to be long enough to switch the gradients off. The third pulse “reads” the information of the spin-state order and produces an echo under homogeneous field conditions. In the case of two-dimensional imaging, a slice is preselected prior to the whole Jeener-Broekaert sequence by the aid of a LOSY slice-selection pulse. Test experiments are reported, and applications to polymer and biological materials are discussed.     

A modified PGSE for measuring diffusion in the presence of static magnetic field gradients

With a proper timing of pi pulses, it is possible to reduce the effect of the static internal magnetic field gradient on the measurement of diffusion with the pulsed gradient spin echo (PGSE). A pulse sequence that in the first order eliminates the effect of weak internal static gradients in a standard PGSE experiment is introduced. The method should be applied in the cases, where strong and short magnetic gradient pulses are used to investigate the motion of liquid in heterogeneous samples with large susceptibility differences such as porous media.     

Investigation of the correlation between internal gradients and dephasing effect in inhomogeneous field

Internal magnetic gradient plays a significant role in Nuclear Magnetic Resonance (NMR) measurements of fluid saturated porous media. The quantitative characterization and application of this physical phenomenon could effectively improve the accuracy of NMR measurements and interpretations. In this paper, by using the equivalent magnetic dipole method, the three-dimensional distribution of internal induced magnetic field and its gradients in the randomly packed water saturated glass beads are quantitatively characterized. By simulating the diffusive motion of water molecules in porous media with random walk method, the computational dephasing effects equation related to internal gradients is deduced. Thereafter, the echo amplitudes are obtained and the corresponding T ₂-G spectrum is also inverted. For the sake of verifying the simulation results, an experiment is carried out using the Halbach core analyzing system (B ₀=0.18 T, G=2.3 T/m) to detect the induced internal field and gradients. The simulation results indicate the equivalent internal gradient is a distribution of 0.12–0.3 T/m, which matched well with the experimental results.