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.     

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.     

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.     

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.     

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.     

Magic Echo Solid-State NMR Imaging without a Rapidly Switchable Field Gradient

To relax the high-speed requirement imposed on the gradient system used in solid-state proton imaging, we propose two simple modifications of the magic echo imaging sequence, TREV-16TS. In the first modification, the applied gradient is inverted in the middle of the RF irradiation; the second modification utilizes a sinusoidal gradient synchronized with the RF sequence. It is estimated by experiments that as long as the RF amplitude is at least about 10 times stronger than the resonance offset induced by the gradient, the spatial resolution is not degraded significantly by the line narrowing deterioration due to the gradient applied during the on-resonance RF irradiation. The modifications allow commercially available standard gradients to be used for the magic echo imaging of solids.     

Magnetic field gradients in solid state magic angle spinning NMR.

Magnetic field gradients have proven useful in NMR for coherence pathway selection, diffusion studies, and imaging. Recently they have been combined with magic angle spinning to permit high-resolution measurements of semi-solids, where magic angle spinning averages any residual dipolar couplings and local variations in the bulk magnetic susceptibility. Here we show the first examples of coherence pathway selection by gradients in dipolar coupled solids. When the gradient evolution competes with dipolar evolution the experiment design must take into account both the strength of the dipolar couplings and the means to refocus it. Examples of both homonuclear and heteronuclear experiments are shown in which gradients have been used to eliminate the need for phase cycling.     

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.     

Combination of magic-echo and single-point imaging techniques for solid-state MRI

Due to reduced molecular motion the transverse relaxation timeT ₂ in solid materials is typically shorter by a factor of 10³ to 10⁵ in comparison to those in liquids, resulting in a large intrinsic nuclear magnetic resonance line-width that can be well above 20 kHz. Therefore high-resolution solid-state magnetic resonance imaging requires either very strong gradients or special line-narrowing techniques. Single-point imaging (SPI) is a successful pure phase encoding sequence in imaging soft-solid materials; however, when used to study rigid solid materials it still suffers from a very long acquisition time and large gradients. On the other hand, magic echo is a technique that can be used to effectively refocus dipolar interaction, thus achieving a line narrowing. Therefore, the aim of this work is to improve the signal intensity with the combination of the magic echo technique and the SPI sequence. In this paper first applications and a comparison of the SPI sequence with a combination of the magic echo and the SPI sequence to image structures of solid-state materials are presented.     

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.     

Symmetric echo acquisition for absolute-value display in solid-state NMR imaging

A method of solid-state NMR imaging that permits echo Fourier transformation (FT) has been devised using a magic echo train. The echo FT imaging can be implemented simply by modifying the gradient pulse sequence in the previous magic echo imaging (TREV-16TS) so that the one-dimensional k-space trajectory follows the sampling points which are symmetric about the k origin. The implemented ability of echo FT improves the performance of the magic echo imaging: the sensitivity gained by radical2, the phase correction is made unnecessary, and the digital resolution is doubled. One- and two-dimensional imaging experiments have been conducted on some solid samples, confirming the improved performance and revealing a TREV-16TS adjustment parameter that is critical for the successful echo FT imaging.     

Improved diffusion-weighting efficiency of pulsed gradient stimulated echo MR measurements with background gradient cross-term suppression

Accurate diffusion measurements with pulsed gradient NMR are hampered by cross-terms of the diffusion-weighting and background gradients. For experiments based on a stimulated echo pulse sequence, that is preferred for samples with a T2 short compared to the diffusion time, a diffusion-weighting scheme has been presented that avoids these cross-terms in each of the en- and decoding periods separately. However, this approach suffers from a reduced diffusion-weighting efficiency because the two gradients applied in each of the periods have effectively opposite polarities leading to a partial cancellation. An extension of this scheme is presented that involves an additional gradient pulse in each period and delivers an improved diffusion-weighting efficiency without sacrificing the cross-term compensation. Analytical expressions for the gradient pulse lengths and amplitudes are given for arbitrary timing parameters. MR measurements with artificial (switched) background gradients were performed to test the cross-term compensation capability of the proposed extension. The results show that considerably higher q and b values can be achieved with the extension without changing the timing parameters. The MR measurements yielded identical diffusion coefficients without, with the same, and with different background gradients in the en- and decoding periods demonstrating the cross-term compensation of the presented approach.     

A band-selective composite gradient: application to DQF-COSY

We describe a unique band-selective method that utilizes a selective composite gradient to simultaneously achieve band selection and coherence pathway selection. This element is similar to the composite gradient known as the CLUB sandwich except the original broadband pulses have been replaced with selective pulses and the strengths of the antipolar gradients have been unbalanced. In this way, only the signals within the inversion band will continue to dephase throughout the duration of the element and satisfy the proper encoding-to-decoding gradient ratio necessary for coherence selection. Apart from the inverted polarity and asymmetry of the gradients, the band-selective CLUB sandwich is identical to the DPFGSE sequence and provides many of its desirable characteristics. We have successfully incorporated the band-selective CLUB into the DQF-COSY pulse sequence to create a band-selective experiment that offers the selectivity desired for resolution enhancement while maintaining excellent phase behavior. This is demonstrated on the congested aliphatic region of the ionophorous antibiotic Lasalocid A.     

A novel technique for imaging with inhomogeneous fields

We introduce a simple, efficient, low-SAR method for magnetic resonance imaging in the presence of a static field with a permanent, and possibly large gradient. The technique, which is called slant-slice imaging is essentially a spin-echo imaging sequence except that the imaging slice is oriented such that the static field gradient can be used in conjunction with applied gradients during readout. Data are collected for 2D slices. Unlike single point imaging techniques, entire lines of k-space are acquired with each readout. The slant-slice pulse sequence is used to obtain high quality images, using a clinical scanner to simulate a static field with a large permanent gradient. The effects of the inhomogeneity are quantified by two parameters nu and q, which are useful for assessing the utility of a magnet design for 3D-MR imaging.     

Different magic number behaviors in supported metal clusters

Two different magic number behaviors in supported metal clusters, which contain several to hundreds of atoms, are revealed on a series of fcc(001) metal surfaces based on the calculations with the tight-binding potential. The magic number sequence persists on some surfaces while gradually disappears on the others with the increasing cluster size. A theory is proposed to explain these behaviors in terms of atomic interactions. We find in surprise that the different magic number behaviors are triggered by the relatively weak adatom–adatom interactions between next nearest-neighbor (NNN) atoms, although the closed shell of the magic cluster is enhanced by nearest-neighbor interactions. For an attractive NNN interaction, the closed shell of the magic cluster is gradually destabilized and eventually broken, leading to the disappearance of the magic number sequence with increasing cluster size. For a repulsive one, the closed shell and magic number sequence persists. Besides, our theory also allows a good understanding of the equilibrium shape of Cu islands on the Cu(001) surface.     

Sensitivity enhancement of a two-dimensional experiment for the measurement of heteronuclear long-range coupling constants, by a new scheme of coherence selection by gradients

In this work we present a new pulse sequence for the measurement of long-range heteronuclear coupling constants in which the optimization of coherence selection by pulsed field gradients offers a net increase in sensitivity. This type of experiments is extremely valuable for conformational studies of molecules in natural abundance and in this context the use of gradients is essential for an efficient suppression of (12)C bound proton signals. A comparative analysis of the different gradient schemes available is presented with a conclusive elucidation of the relative sensitivities. Our gradient scheme could be advantageous as a building block for other related experiments.     

Dynamic NMR q-space studies of microstructure with the multigrade CPMG sequence

A new approach to q-space studies of microstructure is proposed, which exploits the combined information contained in the water proton transverse relaxation time distribution and the frequency dependence of the apparent water diffusivity in heterogeneous systems. Using an automated two-dimensional multigrade CPMG sequence, both the pulse spacing and the amplitude of the applied field gradient are varied systematically and used to measure the frequency and wave vector dependence of the multiple exponential echo decay constants and amplitudes. Undesirable crossterms in the applied and background field gradients are eliminated by a simple procedure involving a sign reversal in the applied gradient. Nonlinear, local susceptibility-induced field gradients are shown to lead to enhanced, frequency-dependent apparent water diffusivities that are sensitive to the local microstructure.     

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.     

Density-Matrix Calculations of the 1.5 T Citrate Signal Acquired with Volume-Localized STEAM Sequences

Citrate detection and quantitation with proton spectroscopic methods are of current interest as potential tools in the diagnosis and staging of prostate cancer. Thestimulatedechoacquisitionmode (STEAM) sequence is a commonly used volume-localization method for detecting citrate signal. Since the¹H citrate resonance at clinically available field strengths arises from a strongly coupled two-spin system, the 90° RF pulses and localizing gradients used in STEAM sequences result in a complicated dependence of signal intensity on timing intervals and gradient amplitudes. The density-matrix formalism has been applied to arrive at a general solution to this problem. Citrate-signal properties at 1.5 T for different gradient localization schemes are examined with the solution. Optimal interpulse delays, deleterious gradient balances, zero-quantum oscillations with mixing time, and a low-frequency, large-amplitude oscillation with echo time are identified for signals acquired with the standard disposition of gradients in STEAM. The generality of the solution also allows for an examination of nonstandard gradient disposition schemes for enhancing citrate signal and for quantifying the sensitivity of such approaches to both field inhomogeneities and off-resonance effects.     

Correction of concomitant gradient artifacts in experimental microtesla MRI

Magnetic resonance imaging (MRI) suffers from artifacts caused by concomitant gradients when the product of the magnetic field gradient and the dimension of the sample becomes comparable to the static magnetic field. To investigate and correct for these artifacts at very low magnetic fields, we have acquired MR images of a 165-mm phantom in a 66-microT field using gradients up to 350 microT/m. We prepolarize the protons in a field of about 100 mT, apply a spin-echo pulse sequence, and detect the precessing spins using a superconducting gradiometer coupled to a superconducting quantum interference device (SQUID). Distortion and blurring are readily apparent at the edges of the images; by comparing the experimental images to computer simulations, we show that concomitant gradients cause these artifacts. We develop a non-perturbative, post-acquisition phase correction algorithm that eliminates the effects of concomitant gradients in both the simulated and the experimental images. This algorithm assumes that the switching time of the phase-encoding gradient is long compared to the spin precession period. In a second technique, we demonstrate that raising the precession field during phase encoding can also eliminate blurring caused by concomitant phase-encoding gradients; this technique enables one to correct concomitant gradient artifacts even when the detector has a restricted bandwidth that sets an upper limit on the precession frequency. In particular, the combination of phase correction and precession field cycling should allow one to add MRI capabilities to existing 300-channel SQUID systems used to detect neuronal currents in the brain because frequency encoding could be performed within the 1-2 kHz bandwidth of the readout system.