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.     

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.     

Improved diffusion measurement in heterogeneous systems using the magic asymmetric gradient stimulated echo (MAGSTE) technique

A magic asymmetric gradient stimulated echo (MAGSTE) sequence was recently proposed to improve molecular diffusion measurements in the presence of spatially varying background gradients. Its effectiveness has been demonstrated previously with simulated background gradients and in phantoms that contain bulk susceptibility differences. In this study, we investigated the MAGSTE technique in microscopically heterogeneous systems, and compared it with the conventional bipolar pulsed gradient stimulated echo (bPGSTE) sequence. We demonstrated that the MASGTE measurements, compared to the bPGSTE method, varied significantly less when the diffusion encoding/decoding interval (delta) was changed. In addition, the MAGSTE technique provided good characterization of the surface area-to-volume ratio for heterogeneous systems investigated in this study. In sum, this study showed that the MAGSTE technique provided diffusion measurements superior to those of the bPGSTE sequence, especially in the presence of severe heterogeneous background gradients.     

Cross-term-compensated pulsed-gradient stimulated echo MR with asymmetric gradient pulse lengths

The magic asymmetric gradient stimulated echo (MAGSTE) sequence developed to compensate background-gradient cross-terms in the preparation and readout interval independently, assumes identical lengths for the two gradient pulses applied in each interval. However, this approach is rather inefficient if some extra delay time is present in one half of an interval, e.g. as required for special RF excitations or spatial encoding prior to the stimulated echo in MR imaging. Therefore, a generalized version of the sequence is presented that considers different gradient pulse lengths within an interval. It is shown theoretically that (i) for any pulse lengths a "magic" amplitude ratio exists which ensures the desired cross-term compensation in each interval and that (ii) prolonging one of the gradients can deliver a considerably higher diffusion weighting efficiency. These results are confirmed in MR imaging experiments on phantoms and in vivo in the human brain at 3T using an echo-planar trajectory. In the examples shown, typically 10 times higher b values can be achieved or an echo time reduction with a 40% signal gain in brain white matter. Thus, in case of asymmetric timing requirements, the generalized MAGSTE sequence with different gradient pulse lengths may help to overcome signal-to-noise limitations in diffusion weighted MR.     

Generalized MAGSTE with bipolar diffusion-weighting gradient pulses

The generalized magic asymmetric gradient stimulated echo (generalized MAGSTE) sequence compensates background gradient cross-terms and can be adjusted to asymmetric timing boundary conditions which for instance are present in echo-planar MR imaging. However, its efficiency is not optimal because one of the two diffusion-weighting gradients applied in each interval usually must have a reduced amplitude to ensure the desired cross-term compensation. In this work, a modification of generalized MAGSTE is investigated where this gradient pulse is replaced by two gradient pulses with full amplitude but opposite polarities. It is shown that with these bipolar gradients (i) the sequence retains the cross-term compensation capability for an appropriate choice of the gradient pulse durations and (ii) the diffusion-weighting efficiency is improved, i.e. higher k and b values can be achieved without prolonging the echo time. These results are confirmed in MR imaging experiments on phantoms and in vivo in the human brain at 3 T using spin-echo and echo-planar MR imaging. In the examples shown, the b value could be increased between about 30% and 200% when using the bipolar gradient pulses. Thus, bipolar gradients may help to improve the applicability of the generalized MAGSTE sequence.     

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.     

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 relaxation and pulsed field gradient study of alginate bead porous media

Experiments are presented, which correlate molecular displacement with the multi-exponential T2 relaxation times of water flowing and diffusing through an alginate bead pack. Three systems were studied comprising beads of 3, 1 or < mm in diameter. T2-resolved propagators were obtained through a combined pulsed gradient stimulated echo (PGSTE) and Carr-Purcell-Meiboom-Gill (CPMG) experiment. Fourier transformation with respect to q produces a propagator for each echo in the CPMG train. Inverse Laplace transformation of the CPMG decays for each point (Z) in the propagator produced a two-dimensional propagator. Analysis of these two-dimensional propagators provided insight into the transport and exchange behaviour of water flowing through this system. This experiment has been simulated in a model bead structure and the resulting T2 relaxation time behaviour and T2-resolved propagators were found to be in good agreement with the experimental data. We also present a theoretical analysis of the response to the combined PGSTE/CPMG sequence in the simple model case of Pouseille flow in a cylindrical capillary, where diffusion to a surface sink is assumed to be the dominant relaxation mechanism.     

MQ-PGSTE: A new multi-quantum STE-based PGSE NMR sequence

A new multi-quantum stimulated echo based pulsed gradient spin-echo sequence, MQ-PGSTE, has been developed for measuring translational diffusion. The new sequence provides a higher signal-to-noise ratio than the (Hahn spin-echo based) MAXY-D sequence at long diffusion times, and thus potentially affords better diffusion measurements on macromolecule samples. Based on multi-quantum coherence encoding, the MQ-PGSTE sequence needs considerably lower gradient strengths for diffusion characterization compared to standard single quantum pulsed gradient spin-echo sequences. By using the new sequence, the diffusion coefficient of l-[3-¹³C]-alanine was found to be 8.1 ± 0.1 × 10⁻¹⁰ m² s⁻¹, which is in line with the value obtained by the use of the standard stimulated echo based pulsed gradient spin-echo sequence.     

Spin Echo Analysis of Restricted Diffusion under Generalized Gradient Waveforms: Planar, Cylindrical, and Spherical Pores with Wall Relaxivity

A simple matrix formalism presented by Callaghan [J. Magn. Reson.129, 74–84 (1997)], and based on the multiple propagator approach of Caprihanet al.[J. Magn. Reson. A118, 94–102 (1996)], allows for the calculation of the echo attenuation,E(q), in spin echo diffusion experiments, for practically all gradient waveforms. We have extended the method to the treatment of restricted diffusion in parallel plate, cylindrical, and spherical geometries, including the effects of fluid–surface interactions. In particular, theq-space coherence curves are presented for the finite-width gradient pulse PGSE experiment and the results of the matrix calculations compare precisely with published computer simulations. It is shown that the use of long gradient pulses (δ a²/D) create the illusion of smaller pores if a narrow pulse approximation is assumed, while ignoring the presence of significant wall relaxation can lead to both an underestimation of the pore dimensions and a misidentification of the pore geometry.     

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.     

Spectral simulations incorporating gradient coherence selection.

Computer-aided methods can considerably simplify the use of the product operator formalism for theoretical analysis of NMR phenomena, which otherwise becomes unwieldy for anything but simple spin systems and pulse sequences. In this report, two previously available programming approaches using symbolic algebra (J. Shriver, Concepts Magn. Reson. 4, 1-33, 1992) and numerical simulation using object-oriented programming (S. A. Smith, T. O. Levante, B. H. Meier, and R. R. Ernst, J. Magn. Reson. A 106, 75-105, 1994) have been extended to include the use of gradient operators for simulation of spatially localized NMR spectroscopy and gradient coherence selection. These methods are demonstrated using an analysis of the response of an AX(3) spin system to the STEAM pulse sequence and verified with experimental measurements on lactate.     

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.     

Unwanted signal leakage in excitation sculpting with single axis gradients

Excitation sculpting (T-L. Hwang and A. J. Shaka, J. Magn. Reson. A 112, 275-279 (1995)) used for solvent suppression and selective excitation in NMR bases its success on the ability to remove baseline and phase errors created by the application of selective rf pulses. This is achieved by the application of two pulsed field gradient (PFG) echoes in sequence. It is essential that the two pairs of PFGs select the coherence transfer steps independently of each other, which is conveniently achieved if they are applied along orthogonal spatial axes. Here, the much more common case where both PFG pairs must be applied along a single axis is investigated. This is shown to lead to complications for certain ratios of PFG strengths. The original theory of excitation sculpting is restated in the spherical basis for convenience. Some of the effects can only be explained by invoking the dipolar demagnetizing field.     

Diffusion studies in porous media with the "inside-out" technique

Diffusion measurements of water in a glass beads porous media were carried out by the "One-Sided Access" sensor. An approach to determine the long time mean square displacement of hydrogen molecules by measuring the ratio of stimulated echo to primary echo in a three pulse sequence in the presence of permanent static field gradient is analysed. The difference between the apparent diffusion coefficient in a pure water sample and in water/glass beads mixtures becomes visible.     

NMR velocimetry with 13-interval stimulated echo multi-slice imaging in natural porous media under low flow rates

Characterization and quantification of root water uptake processes play a key role in understanding and managing the effects of global climate change on agricultural production and ecosystem dynamics. Part of this understanding is related to the flow of water towards plant roots in soils. In this study we demonstrate for the first time, to our knowledge, that fluid flow in the voids of the pore space of a model soil system (natural sand) can be detected and mapped to an NMR image for mean flows as low as 0.06 mm/s even under the influence of internal magnetic field gradients. To accomplish this we combined multi-slice imaging with a 13-interval pulse sequence to the NMR pulse sequence 13-interval stimulated echo multi-slice imaging (13-interval STEMSI). The result is a largely reduced influence of the internal magnetic field gradients, leading to an improved signal-to-noise ratio which in turn enables one to acquire velocity maps where conventional stimulated echo methods fail.     

Rapid surface-to-volume ratio and tortuosity measurement using Difftrain

Analysis of diffusion measurements as a function of observation time (Delta), to calculate surface-to-volume ratios (S/V) and tortuosities (kappa), is a useful tool in the characterisation of porous media using NMR. However, using conventional pulsed field gradient (PFG) measurements, this requires long total experiment times (typically hours). Here, we show how the rapid diffusion measurement pulse sequence, Difftrain, can be used to provide the required experimental data much more rapidly (typically within minutes) with a consequential reduction in total experiment time of typically over an order of magnitude. Several novel modifications to the Difftrain pulse sequence are also presented to tailor it to this particular application; these include a variable delay between echoes (to ensure optimal echo position with respect to Delta) and a variable tip angle for the refocusing pulse (to ensure optimal use of available signal). Difftrain is applied to measure both S/V and kappa for a model glass bead pack; excellent agreement is found with both a conventional PFG measurement and with a bulk gravimetric measurement of S/V.     

Nuclear longitudinal relaxation time images by radiofrequency field gradients.

Combination of the Super Fast Inversion Recovery (SUFIR) method (D. Canet, J. Brondeau, and K. Elbayed, J. Magn. Reson. 77, 483 (1988)) and imaging procedures by radiofrequency field gradients (P. Maffei, P. Mutzenhardt, A. Retournard, B. Diter, R. Raulet, J. Brondeau, and D. Canet, J. Magn. Reson. A 107, 40 (1994)) provides spatially resolved maps of longitudinal relaxation times (T1). In addition to accurate T1 values, enhanced spatial resolution is obtained.     

Short-time restricted diffusion in a static gradient and the attenuation of individual coherence pathways

We experimentally explore some of the implications of a recent theoretical study [J. Magn. Reson. 64 (2003) 145] for the measurement of restricted diffusion in connected porous media in a static gradient. In particular, we examine how restriction affects the short-time attenuation of different coherence pathways, all excited with the same sequence of slice-selective radiofrequency (RF) pulses, and how the various pathways make the transition to the long-time or tortuosity regime. We confirm that every pathway contains equivalent diffusional information and, for short times, yields the surface-to-volume ratio (S/V) of the confining space. We find also, in agreement with the theoretical predictions, that different pathways are controlled by different time scales and, thus, exhibit different sensitivity to restriction. This property might be exploited when designing optimal sequences to study restricted motion.     

Volume selective detection by weighted averaging of constant tip angle scans

We propose a method to improve the sensitivity in volume selective detection based on the CARVE excitation sequence (I. Sersa and S. Macura, J. Magn. Reson. 135, 466-477 (1998)) which consists of signal acquisition with constant tip angle excitation and a short phase-encoding gradient pulse. Volume selectivity is achieved using the weighted average of a number of scans whose weights and gradient steps are determined by the shape of the excitation profile. The method is particularly useful for broadband volume selective detection of insensitive spins where the volume selection can be merged with the standard signal averaging process, without compromising the excitation bandwidth or sensitivity.