Selective RF Pulses Research Articles

Physics-guided self-supervised learning: Demonstration for generalized RF pulse design.

To introduce a new method for generalized RF pulse design using physics-guided self-supervised learning (GPS), which uses the Bloch equations as the guiding physics model. The GPS framework consists of a neural network module and a physics module, where the physics module is a Bloch simulator for MRI applications. For RF pulse design, the neural network module maps an input target profile to an RF pulse, which is subsequently loaded into the physics module. Through the supervision of the physics module, the neural network module designs an RF pulse corresponding to the target profile. GPS was applied to design 1D selective, -insensitive, saturation, and multidimensional RF pulses, each conventionally requiring dedicated design algorithms. We further demonstrate our method's flexibility and versatility by compensating for experimental and scanner imperfections through online adaptation. Both simulations and experiments show that GPS can design a variety of RF pulses with corresponding profiles that agree well with the target input. Despite these verifications, GPS-designed pulses have unique differences compared to conventional designs, such as achieving -insensitivity using different mechanisms and using non-sampled regions of the conventional design to lower its peak power. Experiments, both ex vivo and in vivo, further verify that it can also be used for online adaptation to correct system imperfections, such as / inhomogeneity. This work demonstrates the generalizability, versatility, and flexibility of the GPS method for designing RF pulses and showcases its utility in several applications.

Optimization of the flip angles of narrow-band editing pulses in J-difference edited MRS of lactate at 3T.

Application of highly selective editing RF pulses provides a means of minimizing co-editing of contaminants in J-difference MRS (MEGA), but it causes reduction in editing yield. We examined the flip angles (FAs) of narrow-band editing pulses to maximize the lactate edited signal with minimal co-editing of threonine. The effect of editing-pulse FA on the editing performance was examined, with numerical and phantom analyses, for bandwidths of 17.6-300 Hz in MEGA-PRESS editing of lactate at 3T. The FA and envelope of 46 ms Gaussian editing pulses were tailored to maximize the lactate edited signal at 1.3 ppm and minimize co-editing of threonine. The optimized editing-pulse FA MEGA scheme was tested in brain tumor patients. Simulation and phantom data indicated that the optimum FA of MEGA editing pulses is progressively larger than 180° as the editing-pulse bandwidth decreases. For 46 ms long 17.6 Hz bandwidth Gaussian pulses and other given sequence parameters, the lactate edited signal was maximum at the first and second editing-pulse FAs of 241° and 249°, respectively. The edit-on and difference-edited lactate peak areas of the optimized FA MEGA were greater by 43% and 25% compared to the 180°-FA MEGA, respectively. In-vivo data confirmed the simulation and phantom results. The lesions of the brain tumor patients showed elevated lactate and physiological levels of threonine. The lactate MEGA editing yield is significantly increased with editing-pulse FA much larger than 180° when the editing-pulse bandwidth is comparable to the lactate quartet frequency width.

Pulsed selective excitation theory and design in multiphoton MRI

Excitation in MRI is traditionally done at the Larmor frequency, where the energy of each radiofrequency photon corresponds to the energy difference between two spin states. However, if multiple radiofrequencies are employed, then multiphoton excitation can also occur when the sum or difference of multiple photon frequencies equals the Larmor frequency. Although multiphoton excitation has been known since the early days of NMR, it has been relatively unexplored in MRI. In this work, equations and principles for multiphoton selective RF pulse design in imaging are presented and experimentally demonstrated. In particular, the case where there are radiofrequency fields in both the traditional xy-direction and non-traditional z-direction is considered. To produce the z-direction radiofrequency field, an additional uniform coil was added to a clinical MRI scanner. Using this coil, two-photon slice-selective pulses were designed to be equivalent to traditional pulses, producing similar excitation, slice profiles, and in vivo images. Being the result of a combination of multiple radiofrequency fields instead of just one, two-photon pulses have more flexibility in how their parameters can be changed. Although individual multiphoton excitations are less efficient than their traditional counterparts, when the z-direction radiofrequency field is spatially non-uniform, multiple multiphoton resonances can be simultaneously used at different locations to produce simultaneous multislice excitation with the same pulse duration but less tissue heating than a naive implementation. In particular, non-uniform z-direction radiofrequency fields with negligible added tissue heating provided by oscillating the MRI scanner’s gradient fields at kilohertz frequencies were used to excite multiple slices simultaneously with less high-frequency xy-direction radiofrequency power. For an example three-slice excitation, we achieve half the xy-direction radiofrequency power compared to the naïve approach of adding three single-slice pulses. For conventional or unconventional applications, multiphoton excitation may be of interest when designing new MRI systems.

Controlling the object phase for g-factor reduction in phase-Constrained parallel MRI using spatially selective RF pulses.

Parallel imaging generally entails a reduction in the signal-to-noise ratio of the final image. Phase-constrained methods aim to improve reconstruction quality by using symmetry properties of k-space. Noise amplification in phase-constrained reconstruction depends heavily on the object background phase. The purpose of this work is to present a new approach of using tailored radiofrequency pulses to optimize the object phase distribution in order to maximize the benefit of phase-constrained reconstruction, and to minimize the noise amplification. Intrinsic object phase and coil sensitivity profiles are measured in a prescan. Optimal phase distribution is computed to maximize signal-to-noise ratio in the given setup. Tailored radiofrequency pulses are designed to introduce the optimal phase map in the following accelerated acquisitions, subsequently reconstructed by phase-constrained methods. The potential of the method is demonstrated in vivo with in-plane accelerated (8x) and simultaneous multislice (3x) acquisitions. Mean g-factors are reduced by up to a factor of 2 compared with conventional techniques when an appropriate phase-constrained reconstruction is applied to phase-optimized acquisitions, enhancing the signal-to-noise ratio of the final images and the visibility of small details. Combining phase-constrained reconstruction and phase optimization by tailored radiofrequency pulses can provide notable improvement in the signal-to-noise ratio and reconstruction quality of accelerated MRI. Magn Reson Med 79:2113-2125, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

VERSE-guided parallel RF excitations using dynamic field correction.

In parallel RF pulse design, peak RF magnitudes and specific absorption rate levels are critical concerns in the hardware and safety limits. The variable rate selective excitation (VERSE) method is an efficient technique to limit the peak RF power by applying a local‐only RF and gradient waveform reshaping while retaining the on‐resonance profile. The accuracy of the excitation performed by the VERSEd RF and gradient waveforms strictly depends on the performance of the employed hardware. Any deviation from the nominal gradient fields as a result of frequency dependent system imperfections violates the VERSE condition similarly to off‐resonance effects, leading to significant excitation errors and the RF pulse not converging to the targeted peak RF power. Moreover, for iterative VERSE‐guided RF pulse design (i.e. reVERSE), the k‐space trajectory actually changes at every iteration, which is assumed to be constant. In this work, we show both theoretically and experimentally the effect of gradient system imperfections on iteratively VERSEd parallel RF excitations. In order to improve the excitation accuracy besides limiting the RF power below certain thresholds, we propose to integrate gradient field monitoring or gradient impulse response function (GIRF) estimations of the actual gradient fields into the RF pulse design problem. A third‐order dynamic field camera comprising a set of NMR field sensors and GIRFs was used to measure or estimate the actual gradient waveforms that are involved in the VERSE algorithm respectively. The deviating and variable k‐space is counteracted at each iteration of the VERSE‐guided iterative RF pulse design. The proposed approaches are demonstrated for accelerated multiple‐channel spatially selective RF pulses, and highly improved experimental performance was achieved at both 3 T and 7 T.

Multiband RF pulses with improved performance via convex optimization

Selective RF pulses are commonly designed with the desired profile as a low pass filter frequency response. However, for many MRI and NMR applications, the spectrum is sparse with signals existing at a few discrete resonant frequencies. By specifying a multiband profile and releasing the constraint on “don’t-care” regions, the RF pulse performance can be improved to enable a shorter duration, sharper transition, or lower peak B1 amplitude. In this project, a framework for designing multiband RF pulses with improved performance was developed based on the Shinnar–Le Roux (SLR) algorithm and convex optimization. It can create several types of RF pulses with multiband magnitude profiles, arbitrary phase profiles and generalized flip angles. The advantage of this framework with a convex optimization approach is the flexible trade-off of different pulse characteristics. Designs for specialized selective RF pulses for balanced SSFP hyperpolarized (HP) 13C MRI, a dualband saturation RF pulse for 1H MR spectroscopy, and a pre-saturation pulse for HP 13C study were developed and tested.

Preserving the excitation profile of small flip angle RF pulses in the presence of rapid transverse relaxation

Degradation of excitation profile of selective RF pulses by rapid transverse relaxation has been a long-standing concern. In this report we demonstrate that transverse relaxation can be incorporated into small flip angle RF pulse design based on the linear response theory. Small flip angle pulses that were designed without considering transverse relaxation effects can be transformed for a predefined pulse duration/T2 ratio. The transformed pulses, within the realm of the linear response theory, produce the same transverse frequency response as if there were no relaxation.

Fast numerical design of spatial-selective rf pulses in MRI using Krotov and quasi-Newton based optimal control methods

The use of increasingly strong magnetic fields in magnetic resonance imaging (MRI) improves sensitivity, susceptibility contrast, and spatial or spectral resolution for functional and localized spectroscopic imaging applications. However, along with these benefits come the challenges of increasing static field (B(0)) and rf field (B(1)) inhomogeneities induced by radial field susceptibility differences and poorer dielectric properties of objects in the scanner. Increasing fields also impose the need for rf irradiation at higher frequencies which may lead to elevated patient energy absorption, eventually posing a safety risk. These reasons have motivated the use of multidimensional rf pulses and parallel rf transmission, and their combination with tailoring of rf pulses for fast and low-power rf performance. For the latter application, analytical and approximate solutions are well-established in linear regimes, however, with increasing nonlinearities and constraints on the rf pulses, numerical iterative methods become attractive. Among such procedures, optimal control methods have recently demonstrated great potential. Here, we present a Krotov-based optimal control approach which as compared to earlier approaches provides very fast, monotonic convergence even without educated initial guesses. This is essential for in vivo MRI applications. The method is compared to a second-order gradient ascent method relying on the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method, and a hybrid scheme Krotov-BFGS is also introduced in this study. These optimal control approaches are demonstrated by the design of a 2D spatial selective rf pulse exciting the letters "JCP" in a water phantom.

Parallel transmission RF pulse design for eddy current correction at ultra high field

Multidimensional spatially selective RF pulses have been used in MRI applications such as B1 and B0 inhomogeneities mitigation. However, the long pulse duration has limited their practical applications. Recently, theoretical and experimental studies have shown that parallel transmission can effectively shorten pulse duration without sacrificing the quality of the excitation pattern. Nonetheless, parallel transmission with accelerated pulses can be severely impeded by hardware and/or system imperfections. One of such imperfections is the effect of the eddy current field. In this paper, we first show the effects of the eddy current field on the excitation pattern and then report an RF pulse the design method to correct eddy current fields caused by the RF coil and the gradient system. Experimental results on a 7T human eight-channel parallel transmit system show substantial improvements on excitation patterns with the use of eddy current correction. Moreover, the proposed model-based correction method not only demonstrates comparable excitation patterns as the trajectory measurement method, but also significantly improves time efficiency.

Using mDixon to remove motion artifacts in carotid artery vessel wall MRI

Background Black blood carotid artery wall imaging can evaluate not just atherosclerotic plaque burden but also high risk components like lipid core and intraplaque hemorrhage. A current limitation in its clinical application, however, is its susceptibility to motion artifacts caused by involuntary motions like swallowing, coughing and breathing. Due to the natural bright signal from subcutaneous fat, unsuppressed fat signal contributes to the majority of motion artifacts in the carotid artery wall region. The fat signal cannot always be properly suppressed using spectrally selective RF pulses due to magnetic field inhomogeneities. Modified Dixon (mDixon) technique, however, is less susceptible to field inhomogeneities because it can separate fat signal without relying on the absolute frequency of the fat spectral. The aim of this study is to explore the feasibility of using mDixon techniques to better separate the strong fat signal and thus reduce motion artifacts near carotid wall region. Methods

Simultaneous investigation of cardiac pyruvate dehydrogenase flux, Krebs cycle metabolism and pH, using hyperpolarized [1,2‐13C2]pyruvate in vivo

(13)C MR spectroscopy studies performed on hearts ex vivo and in vivo following perfusion of prepolarized [1-(13)C]pyruvate have shown that changes in pyruvate dehydrogenase (PDH) flux may be monitored non-invasively. However, to allow investigation of Krebs cycle metabolism, the (13)C label must be placed on the C2 position of pyruvate. Thus, the utilization of either C1 or C2 labeled prepolarized pyruvate as a tracer can only afford a partial view of cardiac pyruvate metabolism in health and disease. If the prepolarized pyruvate molecules were labeled at both C1 and C2 positions, then it would be possible to observe the downstream metabolites that were the results of both PDH flux ((13)CO(2) and H(13)CO(3)(-)) and Krebs cycle flux ([5-(13)C]glutamate) with a single dose of the agent. Cardiac pH could also be monitored in the same experiment, but adequate SNR of the (13)CO(2) resonance may be difficult to obtain in vivo. Using an interleaved selective RF pulse acquisition scheme to improve (13)CO(2) detection, the feasibility of using dual-labeled hyperpolarized [1,2-(13)C(2)]pyruvate as a substrate for dynamic cardiac metabolic MRS studies to allow simultaneous investigation of PDH flux, Krebs cycle flux and pH, was demonstrated in vivo.

Slice profile correction for transmit sensitivity mapping using actual flip angle imaging

To enable clinical use of parallel transmission technology, it is necessary to rapidly produce transmit sensitivity (σ) maps. Actual flip angle imaging is an efficient mapping technique, which is accurate when used with 3D encoding and nonselective RF pulses. Mapping single slices is quicker, but 2D encoding leads to systematic errors due to slice profile effects. By simulating steady-state slice profiles, we computed the relationship between σ and the signals received from the actual flip angle imaging sequence for arbitrarily chosen slice selective RF pulses. Pulse specific lookup tables were then used for reconstruction. The resulting σ-maps are sensitive to T(1) in a manner that depends strongly on the specific pulse, for example a precision of ±3% can be achieved by using a 3-lobe sinc pulse. The method is applicable to any RF pulse; simulations must be performed once and thereafter fast reconstruction of σ-maps is possible.

Acoustic noise‐optimized verse pulses

Variable-rate selective excitation RF pulses modulate the slice selection gradients during RF transmission, especially to reduce the total RF power. Amplitude-modulated slice selection gradients can lead to increased gradient noise, in particular in high-field MRI where variable-rate selective excitation techniques are often used. In this work, an algorithm is presented that calculates a variable-rate selective excitation pulse modulation from given RF pulses with constant slice selection gradient. The algorithm avoids the known acoustic resonance frequencies of the gradient system to minimize sound pressure levels. It was tested with four different slice-selective RF pulse shapes (Sinc, Gaussian, and two Shinnar-LeRoux). Sound measurements revealed a reduction of the mean sound pressure level by up to 13 dB, and simultaneously, the specific absorption rate was reduced by 55%.

ESTIMATION OF DOMAIN SIZE IN NANO-FERROELECTRICS FROM NMR T1 MEASUREMENTS

ABSTRACT The spin lattice relaxation of I = 3/2 quadrupolar spin system due to domain walls in order-disorder ferroelectrics has been studied and a general method is proposed for the measurement of domain width in nano ferroelectrics. Based on the fact that electric polarization undergoes spiral orientation as one moves from one domain to the other, it is assumed that at low temperatures the spins at and near domain walls undergo relaxation due to possible easy reorientation of electric polarization in domain walls even though such a relaxation in the main body of the domain has almost ceased. The spins present inside the domain undergo relaxation through transfer of magnetization to the domain walls through a spin diffusion process by nearest neighbour interaction. Rate equations for spin populations are formed by representing the ferroelectric domain by a one-dimensional chain of equidistant spins having dipolar coupling. Spin populations are calculated as a function of time for different ratios of quadrupolar to dipolar transition probabilities for a sample subjected to selective rf pulse. Expression for spin- lattice relaxation time T 1 is derived in terms of domain width and ratio of quadrupolar to dipolar transition probabilities. It is found that the domain width can be estimated provided the value of spin lattice relaxation time T 1 is known for the corresponding crystal with normal sized grains. The results are quite general and can be applied to any order disorder ferroelectric with nano sized domains and having spin I = 3/2 nuclei.

Intermolecular double-quantum coherence NMR spectroscopy in moderate inhomogeneous fields

Intermolecular multiple-quantum coherences (iMQCs) can be utilized to retrieve high-resolution NMR spectra in inhomogeneous magnetic fields. The application of selective pulses in pulse sequences can greatly simplify 2D iMQC spectra. However, so far high-resolution iMQC methods are mainly used in relatively small field inhomogeneities. In this paper, we took the IDEAL-II sequence as an example to study their applicability in moderate inhomogeneous magnetic fields. The experimental and simulation results show that high-resolution NMR spectra can be obtained in moderate inhomogeneous fields if the excitation range of selective pulse is properly set. Once the field inhomogeneity reaches a certain degree, the appearance of undesirable intermolecular cross-peaks due to the distant dipolar field produced by solute spins is inevitable. The spectral quality may vary with sample even in the same moderate inhomogeneous fields, depending on the chemical shift distributions and the J coupling networks of the components under study. The conclusions drawn in this paper are generally applicable to all high-resolution iMQC methods utilizing selective RF pulses.

Numerical simulations of localized high field 1H MR spectroscopy

The limited bandwidths of volume selective RF pulses in localized in vivo MRS experiments introduce spatial artifacts that complicate spectral quantification of J-coupled metabolites. These effects are commonly referred to as a spatial interference or “four compartment” artifacts and are more pronounced at higher field strengths. The main focus of this study is to develop a generalized approach to numerical simulations that combines full density matrix calculations with 3D localization to investigate the spatial artifacts and to provide accurate prior knowledge for spectral fitting. Full density matrix calculations with 3D localization using experimental pulses were carried out for PRESS (TE = 20, 70 ms), STEAM (TE = 20, 70 ms) and LASER (TE = 70 ms) pulse sequences and compared to non-localized simulations and to phantom solution data at 4 T. Additional simulations at 1.5 and 7 T were carried out for STEAM and PRESS (TE = 20 ms). Four brain metabolites that represented a range from weak to strong J-coupling networks were included in the simulations (lactate, N-acetylaspartate, glutamate and myo-inositol). For longer TE, full 3D localization was necessary to achieve agreement between the simulations and phantom solution spectra for the majority of cases in all pulse sequence simulations. For short echo time (TE = 20 ms), ideal pulses without localizing gradients gave results that were in agreement with phantom results at 4 T for STEAM, but not for PRESS (TE = 20). Numerical simulations that incorporate volume localization using experimental RF pulses are shown to be a powerful tool for generation of accurate metabolic basis sets for spectral fitting and for optimization of experimental parameters.

B1 inhomogeneity effect reduction for 2D spatial selective RF pulse using simulated annealing

AbstractWith the development of the high‐field MRI system, the RF field inhomogeneity becomes a challenging problem in high flip angle excitation. In this study, a new RF pulse design method is proposed, which combines the simulated annealing (SA) algorithm and the k‐space method to attain a pulse which can compensate the RF field inhomogeneity effect. The RF pulse envelope is firstly initiated using the k‐space method and a cost function which contains the passband error and stopband error is defined. Then the SA is applied to refine the RF pulse shape to achieve low‐cost value. Finally, under inhomogeneous RF field an optimized RF pulse with improved flip angle accuracy can be obtained. Simulation results show that when compared with the pulse designed only using the k‐space method, the passband error can be decreased by 28%, 40%, and 75% for 90° excitation pulse, refocusing pulse, and 180° inversion pulse, respectively. © 2008 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 33B: 75–83, 2008

T1 relaxation measurement with solvent suppression

Three solvent-suppression pulse sequences of varying complexity were incorporated into the standard inversion recovery pulse program and experimentally evaluated. The least complex suppression sequence involves a composite 90 degrees pulse. A more complex sequence utilizes an excitation sculpting sequence requiring pulsed field gradients, and the most complex sequence incorporates an excitation sculpting sequence with selective rf pulses and gradient pulses. The quality of the spectral data and the accuracy of T(1) measurements of the investigated suppression schemes were evaluated using three aqueous samples with increasing proton content in the water solvent, i.e. by volume 100% D(2)O, 80/20% D(2)O/H(2)O, and 100% H(2)O. For lines removed from the water resonance the T(1) values were generally very consistent between all pulse sequences tested. For lines less than about 200 Hz from the water signal the T(1) measurements become less reliable but are still possible for most of the tested pulse programs.

Simultaneously Cycled NMR Spectroscopy

Simultaneously cycled (SC) NMR was introduced and exemplified by implementing a set of 2-D [1H,1H] SC exclusive COSY (E.COSY) NMR experiments, that is, rf pulse flip-angle cycled (SFC), rf pulse phase cycled (SPC), and pulsed field gradient (PFG) strength cycled (SGC) E.COSY. Spatially selective 1H rf pulses were applied as composite pulses such that all steps of the respective cycles were affected simultaneously in different slices of the sample. This increased the data acquisition speed for an n-step cycle n-fold. A high intrinsic sensitivity was achieved by defining the cycles in a manner that the receiver phase remains constant for all steps of the cycle. Then, the signal resulting from applying the cycle corresponded to the sum of the signals from all steps of the cycle. Hence, the detected free induction decay did not have to be separated into the contributions arising from different slices, and read-out PFGs, which not only greatly reduce sensitivity but also negatively impact lineshapes in the direct dimension, were avoided. The current implementation of SFC E.COSY reached approximately 65% of the intrinsic sensitivity of the conventional phase cycled congener, making this experiment highly attractive whenever conventional data acquisition is sampling limited. Highly resolved SC E.COSY yielding accurate 3J-coupling values was recorded for the 416 Da plant alkaloid tomatidine within 80 min, that is, 12 times faster than with conventional phase cycled E.COSY. SC NMR is applicable for a large variety of NMR experiments and thus promises to be a valuable addition to the arsenal of approaches for tackling the NMR sampling problem to avoid sampling limited data acquisition.

An alternative approach for recording of multidimensional NMR data based on frequency dependent folding mechanism

A new scheme for obtaining HSQC spectra with improved resolution or in a shorter time called SHARC (Shaped Arrayed data aCquisition protocol) is proposed, which uses region selective RF pulses and allows the sweep width to be adjusted individually for each region. It thus bypasses the problems with the Nyquist theorem associated with other method suggested for this purpose. Assignment of the cross-peaks to their respective region is achieved by manipulating the phases of the RF pulses and/or their frequencies. SHARC NMR can be applied without any previous knowledge of the chemical shift distribution, but can be further optimized on the basis of a quick overview spectrum.