RF Inhomogeneity Research Articles

Bone mineral (31)P and matrix-bound water densities measured by solid-state (31)P and (1)H MRI.

Bone is a composite material consisting of mineral and hydrated collagen fractions. MRI of bone is challenging because of extremely short transverse relaxation times, but solid-state imaging sequences exist that can acquire the short-lived signal from bone tissue. Previous work to quantify bone density via MRI used powerful experimental scanners. This work seeks to establish the feasibility of MRI-based measurement on clinical scanners of bone mineral and collagen-bound water densities, the latter as a surrogate of matrix density, and to examine the associations of these parameters with porosity and donors' age. Mineral and matrix-bound water images of reference phantoms and cortical bone from 16 human donors, aged 27-97 years, were acquired by zero-echo-time 31-phosphorus ((31)P) and 1-hydrogen ((1)H) MRI on whole body 7T and 3T scanners, respectively. Images were corrected for relaxation and RF inhomogeneity to obtain density maps. Cortical porosity was measured by micro-computed tomography (μCT), and apparent mineral density by peripheral quantitative CT (pQCT). MRI-derived densities were compared to X-ray-based measurements by least-squares regression. Mean bone mineral (31)P density was 6.74 ± 1.22 mol/l (corresponding to 1129 ± 204 mg/cc mineral), and mean bound water (1)H density was 31.3 ± 4.2 mol/l (corresponding to 28.3 ± 3.7 %v/v). Both (31)P and bound water (BW) densities were correlated negatively with porosity ((31)P: R(2) = 0.32, p < 0.005; BW: R(2) = 0.63, p < 0.0005) and age ((31)P: R(2) = 0.39, p < 0.05; BW: R(2) = 0.70, p < 0.0001), and positively with pQCT density ((31)P: R(2) = 0.46, p < 0.05; BW: R(2) = 0.50, p < 0.005). In contrast, the bone mineralization ratio (expressed here as the ratio of (31)P density to bound water density), which is proportional to true bone mineralization, was found to be uncorrelated with porosity, age or pQCT density. This work establishes the feasibility of image-based quantification of bone mineral and bound water densities using clinical hardware.

Adiabatic Rotor-Echo-Short-Pulse-Irradiation mediated cross-polarization

We present a new dipolar recoupling method for efficient and robust heteronuclear polarization transfer in solid-state NMR under magic-angle-spinning (MAS) conditions. The method combines the recent RESPIRATIONCP method with a modulation of the amplitude of the rotor-synchronized pulses at one of the involved rf channels through the recoupling condition. In this manner, it is possible to achieve high transfer efficiencies while maintaining robustness towards rf-field inhomogeneities and resonance offsets. The performance of the so-called adiabatic-RESPIRATIONCP experiment is demonstrated numerically and experimentally using uniformly 13C,15N-labeled samples of alanine and ubiquitin. In particular for cases with relatively high rf inhomogeneity, the scheme offers advantages over the commonly used dipolar recoupling pulse sequences.

Improved Phase-Modulated Homonuclear Dipolar Decoupling for Solid-State NMR Spectroscopy from Symmetry Considerations

We explore the effects of symmetry on the performance of phase-modulated homonuclear dipolar decoupling in (1)H solid-state NMR. We demonstrate that the symmetry of the DUMBO family of decoupling sequences is the result of two well-defined symmetry expansions. The first is an antipalindromic expansion that arises from the symmetrization step that was built into the original architecture of the DUMBO sequence. The second is a mirror-pair expansion that inverts the sign of the phase modulation in the second half of the pulse sequence relative to the first. The combination of these two symmetry expansions generates a sequence of four Lee-Goldburg-type rotations in the rotating frame. The axes of rotation, oriented at the magic angle, are separated in the transverse plane by 2α, where α is chosen to minimize the sensitivity of the sequence to instrument imperfections such as rf inhomogeneity. The efficiency of the DUMBO symmetry for decoupling is demonstrated experimentally, and the effect of the α-phase-shift parameter is investigated. A new decoupling sequence (LG4) that combines the DUMBO symmetry with α = 55° is introduced and is shown to produce very efficient decoupling as well as a nearly 2-fold increase in coherence lifetimes when compared to standard PMLG/FSLG decoupling.

Effects of experimental imperfections on a spin counting experiment

Spin counting NMR is an experimental technique that allows a determination of the size and time evolution of networks of dipolar coupled nuclear spins. This work reports on an average Hamiltonian treatment of two spin counting sequences and compares the efficiency of the two cycles in the presence of flip errors, RF inhomogeneity, phase transients, phase errors, and offset interactions commonly present in NMR experiments. Simulations on small quantum systems performed using the two cycles reveal the effects of pulse imperfections on the resulting multiple quantum spectra, in qualitative agreement with the average Hamiltonian calculations. Experimental results on adamantane are presented, demonstrating differences in the two sequences in the presence of pulse errors.

Refocused continuous-wave decoupling: A new approach to heteronuclear dipolar decoupling in solid-state NMR spectroscopy

A novel strategy for heteronuclear dipolar decoupling in magic-angle spinning solid-state nuclear magnetic resonance (NMR) spectroscopy is presented, which eliminates residual static high-order terms in the effective Hamiltonian originating from interactions between oscillating dipolar and anisotropic shielding tensors. The method, called refocused continuous-wave (rCW) decoupling, is systematically established by interleaving continuous wave decoupling with appropriately inserted rotor-synchronized high-power π refocusing pulses of alternating phases. The effect of the refocusing pulses in eliminating residual effects from dipolar coupling in heteronuclear spin systems is rationalized by effective Hamiltonian calculations to third order. In some variants the π pulse refocusing is supplemented by insertion of rotor-synchronized π/2 purging pulses to further reduce the residual dipolar coupling effects. Five different rCW decoupling sequences are presented and their performance is compared to state-of-the-art decoupling methods. The rCW decoupling sequences benefit from extreme broadbandedness, tolerance towards rf inhomogeneity, and improved potential for decoupling at relatively low average rf field strengths. In numerical simulations, the rCW schemes clearly reveal superior characteristics relative to the best decoupling schemes presented so far, which we to some extent also are capable of demonstrating experimentally. A major advantage of the rCW decoupling methods is that they are easy to set up and optimize experimentally.

Designing optimal universal pulses using second-order, large-scale, non-linear optimization

Recently, RF pulse design using first-order and quasi-second-order pulses has been actively investigated. We present a full second-order design method capable of incorporating relaxation, inhomogeneity in B0 and B1. Our model is formulated as a generic optimization problem making it easy to incorporate diverse pulse sequence features. To tame the computational cost, we present a method of calculating second derivatives in at most a constant multiple of the first derivative calculation time, this is further accelerated by using symbolic solutions of the Bloch equations. We illustrate the relative merits and performance of quasi-Newton and full second-order optimization with a series of examples, showing that even a pulse already optimized using other methods can be visibly improved.To be useful in CPMG experiments, a universal refocusing pulse should be independent of the delay time and insensitive of the relaxation time and RF inhomogeneity. We design such a pulse and show that, using it, we can obtain reliable R2 measurements for offsets within ±γB1. Finally, we compare our optimal refocusing pulse with other published refocusing pulses by doing CPMG experiments.

Efficient and Robust Heteronuclear Cross-Polarization for High-Speed-Spinning Biological Solid-State NMR Spectroscopy.

We present a new and highly efficient approach for heteronuclear coherence transfer in solid-state NMR spectroscopy under high-speed spinning conditions. The so-called (RESPIRATION)CP experiment exploits phase-alternated recoupling on only one of the two rf channels intertwined in a synchronized train of short rf pulses on both channels. The method provides significantly higher efficiencies than state-of-the art techniques including ramped and adiabatic cross-polarization experiments with long durations of intense rf irradiation. At the same time, it is easier to setup experimentally and significantly more robust toward imperfections such as rf inhomogeneity, misadjustments, and sample-induced variations in the rf tuning. The method is described analytically, numerically, and experimentally for biological solids. We demonstrate sensitivity gains of factors of 1.3 and 1.8 for typical (1)H→(15)N and (15)N→(13)C transfers and a combined gain of a factor of 2-4 for a typical NCA experiment for biological solid-state NMR.

Optimal control design of band-selective excitation pulses that accommodate relaxation and RF inhomogeneity

Existing optimal control protocols for mitigating the effects of relaxation and/or RF inhomogeneity on broadband pulse performance are extended to the more difficult problem of designing robust, refocused, frequency selective excitation pulses. For the demanding case of T1 and T2 equal to the pulse length, anticipated signal losses can be significantly reduced while achieving nearly ideal frequency selectivity. Improvements in performance are the result of allowing residual unrefocused magnetization after applying relaxation-compensated selective excitation by optimized pulses (RC-SEBOPs). We demonstrate simple pulse sequence elements for eliminating this unwanted residual signal.

Inverse field-based approach for simultaneous B1 mapping at high fields – A phantom based study

Based on computational electromagnetics and multi-level optimization, an inverse approach of attaining accurate mapping of both transmit and receive sensitivity of radiofrequency coils is presented. This paper extends our previous study of inverse methods of receptivity mapping at low fields, to allow accurate mapping of RF magnetic fields (B1) for high-field applications. Accurate receive sensitivity mapping is essential to image domain parallel imaging methods, such as sensitivity encoding (SENSE), to reconstruct high quality images. Accurate transmit sensitivity mapping will facilitate RF-shimming and parallel transmission techniques that directly address the RF inhomogeneity issue, arguably the most challenging issue of high-field magnetic resonance imaging (MRI). The inverse field-based approach proposed herein is based on computational electromagnetics and iterative optimization. It fits an experimental image to the numerically calculated signal intensity by iteratively optimizing the coil-subject geometry to better resemble the experiments. Accurate transmit and receive sensitivities are derived as intermediate results of the optimization process. The method is validated by imaging studies using homogeneous saline phantom at 7T. A simulation study at 300MHz demonstrates that the proposed method is able to obtain receptivity mapping with errors an order of magnitude less than that of the conventional method. The more accurate receptivity mapping and simultaneously obtained transmit sensitivity mapping could enable artefact-reduced and intensity-corrected image reconstructions. It is hoped that by providing an approach to the accurate mapping of both transmit and receive sensitivity, the proposed method will facilitate a range of applications in high-field MRI and parallel imaging.

Gradient Echo Plural Contrast Imaging — Signal model and derived contrasts: T2*, T1, Phase, SWI, T1f, FST2*and T2*-SWI

Gradient Echo Plural Contrast Imaging (GEPCI) is a post processing technique that, based on a widely available multiple gradient echo sequence, allows simultaneous generation of naturally co-registered images with various contrasts: T1 weighted, R2*=1/T2* maps and frequency (f) maps. Herein, we present results demonstrating the capability of GEPCI technique to generate image sets with additional contrast characteristics obtained by combing the information from these three basic contrast maps. Specifically, we report its ability to generate GEPCI-susceptibility weighted images (GEPCI-SWI) with improved SWI contrast that is free of T1 weighting and RF inhomogeneities; GEPCI-SWI-like images with the contrast similar to original SWI; T1f images that offer superior GM/WM matter contrast obtained by combining the GEPCI T1 and frequency map data; Fluid Suppressed T2* (FST2*) images that utilize GEPCI T1 data to suppress CSF signal in T2* maps and provide contrast similar to FLAIR T2 weighted images; and T2*-SWI images that combine SWI contrast with quantitative T2* map and offer advantages of visualizing venous structure with hyperintense T2* lesions (e.g. MS lesions). To analyze GEPCI images we use an improved algorithm for combining data from multi-channel RF coils and a method for unwrapping phase/frequency maps that takes advantage of the information on phase evolution as a function of gradient echo time in GEPCI echo train.

New strategies for designing robust universal rotation pulses: Application to broadband refocusing at low power

Optimizing pulse performance often requires a compromise between maximizing signal amplitude and minimizing spectral phase errors. We consider methods for the de novo design of universal rotation pulses, applied specifically but not limited to refocusing pulses. Broadband inversion pulses that rotate all magnetization components 180° about a given fixed axis are necessary for refocusing and mixing in high-resolution NMR spectroscopy. The relative merits of various methodologies for generating pulses suitable for broadband refocusing are considered. The de novo design of 180° universal rotation pulses 180UR° using optimal control can provide improved performance compared to schemes which construct refocusing pulses as composites of existing pulses. The advantages of broadband universal rotation by optimized pulses (BURBOP) are most evident for pulse design that includes tolerance to RF inhomogeneity or miscalibration. Nearly ideal refocusing is possible over a resonance offset range of ± 170% relative to the nominal pulse B1 field, concurrent with tolerance to B1 inhomogeneity/miscalibration of ± 33%. We present new modifications of the optimal control algorithm that incorporate symmetry principles (S-BURBOP) and relax conservative limits on peak RF pulse amplitude for short time periods that pose no threat to the probe. We apply them to generate a set of low-power 180BURBOP°pulses suitable for widespread use in 13C spectroscopy on the majority of available probes. A quantitative measure for the reduced spectral phase error provided by these symmetry principles is also derived. For pulses designed according to this symmetry, refocusing phase errors are virtually eliminated upon application of EXORCYCLE or an equivalent G–180S-BURBOP°–G gradient sandwich, independent of resonance offset and RF inhomogeneity. The magnitude of the refocused component is not significantly compromised in achieving such ideal phase performance.

A common theory for phase-modulated homonuclear decoupling in solid-state NMR

We propose a new framework for homonuclear dipolar decoupling in solid-state NMR that provides a theoretical link between the FSLG, PMLG and DUMBO families. We show that through the use of a Legendre polynomial basis, the phase modulation of these decoupling schemes can be described by the same set of parameters, permitting for the first time a direct theoretical comparison between these methods. Use of this common basis reveals that the central decoupling mechanism is the same for DUMBO and FSLG/PMLG and that a similar vector picture can be used to describe both methods. In addition to the common root of decoupling efficiency, this new analysis highlights two major points of difference between the methods. First, the DUMBO phase modulation consists not only of a linear change in phase with time à la PMLG but also smaller high-order oscillations, which act to improve line-narrowing performance. Second, we show how the DUMBO phase waveforms are generated from a four-step permutation of a single asymmetric unit, in contrast to the two-step permutation of PMLG. Numerical simulations and experimental results suggest that this latter point of difference is responsible for the superior performance of DUMBO in the presence of significant RF inhomogeneity.

Slice-selective excitation with [formula omitted]-insensitive composite pulses

Spatially selective excitation pulses have been designed to produce uniform flip angles in the presence of the RF and static field inhomogeneities typically encountered in MRI studies of the human brain at 7 T. Pulse designs are based upon non-selective, composite pulses numerically optimized for the desired performance over prescribed ranges of field inhomogeneities. The non-selective pulses are subsequently transformed into spatially selective pulses with the same field-insensitive properties through modification of the spectral composition of the individual sub-pulses which are then executed in conjunction with an oscillating gradient waveform. An in-depth analysis of the performance of these RF pulses is presented in terms of total pulse durations, slice profiles, linearity of in-slice magnetization phase, sensitivity to RF and static field variations, and signal loss due to T 2 ∗ effects. Both simulations and measurements in phantoms and in the human brain are used to evaluate pulses with nominal flip angles of 45° and 90°. Target slice thickness in all cases is 2 mm. Results indicate that the described class of field-insensitive RF pulses is capable of improving flip-angle uniformity in 7 T human brain imaging. There appears to be a subset of pulses with durations ≲10 ms for which non-linearities in the magnetization phase are minimal and signal loss due to T 2 ∗ decay is not prohibitive. Such pulses represent practical solutions for achieving uniform flip angles in the presence of the large field inhomogeneities common to high-field human imaging and help to better establish the performance limits of high-field imaging systems with single-channel transmission.

A comparison of NCO and NCA transfer methods for biological solid-state NMR spectroscopy

Three different techniques (adiabatic passage Hartman-Hahn cross-polarization, optimal control designed pulses, and EXPORT) are compared for transferring 15N magnetization to 13C in solid-state NMR experiments under magic-angle-spinning conditions. We demonstrate that, in comparison to adiabatic passage Hartman-Hahn cross-polarization, optimal control transfer pulses achieve similar or better transfer efficiencies for uniformly- 13C, 15N labeled samples and are generally superior for samples with non-uniform labeling schemes (such as 1,3- and 2- 13C glycerol labeling). In addition, the optimal control pulses typically use substantially lower average RF field strengths and are more robust with respect to experimental variation and RF inhomogeneity. Consequently, they are better suited for demanding samples.

NMR quantitation: influence of RF inhomogeneity.

The NMR peak integral is ideally linearly dependent on the sine of excitation angle (θ), which has provided unsurpassed flexibility in quantitative NMR by allowing the use of a signal of any concentration as the internal concentration reference. Controlling the excitation angle is particularly critical for solvent proton concentration referencing to minimize the negative impact of radiation damping, and to reduce the risk of receiver gain compression. In practice, due to the influence of RF inhomogeneity for any given probe, the observed peak integral is not exactly proportional to sin θ. To evaluate the impact quantitatively, we introduce a RF inhomogeneity factor I(θ) as a function of the nominal pulse excitation angle and propose a simple calibration procedure. Alternatively, I(θ) can be calculated from the probe's RF profile, which can be readily obtained as a gradient image of an aqueous sample. Our results show that without consideration of I(θ), even for a probe with good RF homogeneity, up to 5% error can be introduced due to different excitation pulse angles used for the analyte and the reference. Hence, a simple calibration of I(θ) can eliminate such errors and allow an accurate description of the observed NMR signal's dependence on the excitation angle in quantitative analysis.

Repetitive cross-polarization contacts via equilibration-re-equilibration of the proton bath: Sensitivity enhancement for NMR of membrane proteins reconstituted in magnetically aligned bicelles

Thermodynamic limit of magnetization corresponding to the intact proton bath usually cannot be transferred in a single cross-polarization contact. This is mainly due to the finite ratio between the number densities of the high- and low-gamma nuclei, quantum–mechanical bounds on spin dynamics, and Hartmann–Hahn mismatches due to rf field inhomogeneity. Moreover, for fully hydrated membrane proteins refolded in magnetically oriented bicelles, short spin-lock relaxation times ( T 1 ρ ) and rf heating can further decrease cross polarization efficiency. Here we show that multiple equilibrations-re-equilibrations of the high- and low-spin reservoirs during the preparation period yield an over twofold gain in the magnetization transfer as compared to a single-contact cross polarization (CP), and up to 45% enhancement as compared to the mismatch-optimized CP-MOIST scheme for bicelle-reconstituted membrane proteins. This enhancement is achieved by employing the differences between the spin–lattice relaxation times for the high- and low-gamma spins. The new technique is applicable to systems with short T 1 ρ ’s, and speeds up acquisition of the multidimensional solid-state NMR spectra of oriented membrane proteins for their subsequent structural and dynamic studies.

Optimal (2)H rf Pulses and (2)H-(13)C Cross-Polarization Methods for Solid-State (2)H MAS NMR of Perdeuterated Proteins.

We present a novel concept for rf pulses and optimal control designed cross-polarization experiments for quadrupolar nuclei. The methods are demonstrated for (2)H CP-MAS and (2)H multiple-pulse NMR of perdeuterated proteins, for which sensitivity enhancements up to an order of magnitude are presented relative to commonly used approaches. The so-called RESPIRATION rf pulses combines the concept of short broad-band pulses with generation of pulses with large flip angles through distribution of the rf pulse over several rotor echoes. This lead to close-to-ideal rf pulses, facilitating implementation of experiments relying on the ability to realize high-performance 90 and 180° pulses, as, for example, in refocused INEPT and double-to-single quantum coherence experiments, or just pulses that provide a true representation of the quadrupolar powder pattern to extract information about the structure or dynamics. The optimal control (2)H → (13)C CP-MAS method demonstrates transfer efficiencies up to around 85% while being extremely robust toward rf inhomogeneity and resonance offsets.

Correction of inhomogeneous magnetic resonance images using multiscale retinex for segmentation accuracy improvement

The purpose of this study was to improve the accuracy of tissue segmentation on brain magnetic resonance (MR) images preprocessed by multiscale retinex (MSR), segmented with a combined boosted decision tree (BDT) and MSR algorithm (hereinafter referred to as the MSRBDT algorithm). Simulated brain MR (SBMR) T1-weighted images of different noise levels and RF inhomogeneities were adopted to evaluate the outcome of the proposed method; the MSRBDT algorithm was used to identify the gray matter (GM), white matter (WM), and cerebral-spinal fluid (CSF) in the brain tissues. The accuracy rates of GM, WM, and CSF segmentation, with spatial features (G,x,y,r,θ), were respectively greater than 0.9805, 0.9817, and 0.9871. In addition, images segmented with the MSRBDT algorithm were better than those obtained with the expectation maximization (EM) algorithm; brain tissue segmentation in MR images was significantly more precise. The proposed MSRBDT algorithm could be beneficial in clinical image segmentation.

Quantitative T1ρ imaging using phase cycling for B0 and B1 field inhomogeneity compensation

T 1 ρ imaging is useful in a number of clinical applications. T 1 ρ preparation methods, however, are sensitive to non-uniformities of the B 0 magnetic field and the B 1 RF field. These common system imperfections can result in image artifacts and quantification errors in T 1 ρ imaging. We report on a phase-cycling method which can eliminate B 1 RF inhomogeneity effects in T 1 ρ imaging. This method does not only correct for image artifacts but also for T 2 ρ contamination caused by B 1 RF inhomogeneity. The presence of B 0 magnetic field inhomogeneity can compromise the effectiveness of this method for B 1 RF inhomogeneity correction. We demonstrate that, by combining the spin-locking scheme reported by Dixon et al. (Myocardial suppression in vivo by spin locking with composite pulses. Magn Reson Med 1996; 36:90–94) with phase cycling, we can simultaneously correct B 0 magnetic field inhomogeneity effects and B 1 RF inhomogeneity effects in T 1 ρ imaging. Phantom and in vivo data sets are used to demonstrate the proposed methods and to compare them with other existing T 1 ρ preparation methods.

Slice with angulated non-parallel boundaries

Adiabatic pulses are widely used for spatial localization in magnetic resonance spectroscopy because of their high immunity to RF inhomogeneity and excellent slice profiles. Since non-rectangular volume is often preferred in localized spectroscopy, we propose a scheme for selecting a trapezoidal slice using adiabatic π pulses. In this scheme, a time-varying gradient orthogonal to a stationary slice selection gradient is used to change the boundaries of the slice profile from parallel to non-parallel. Numerical simulation results for the transverse and longitudinal magnetization using different RF and gradient waveforms are presented for non-parallel slice selection. Phantom imaging and in vivo 1H MRS of rat brain using non-parallel slices are demonstrated.