Pulses with fixed magnitude and variable phase response profiles

Deep Reinforcement Learning Designed Shinnar-Le Roux RF Pulse Using Root-Flipping: DeepRFSLR

A novel approach of applying deep reinforcement learning to an RF pulse design is introduced. This method, which is referred to as DeepRF_SLR, is designed to minimize the peak amplitude or, equivalently, minimize the pulse duration of a multiband refocusing pulse generated by the Shinar Le-Roux (SLR) algorithm. In the method, the root pattern of SLR polynomial, which determines the RF pulse shape, is optimized by iterative applications of deep reinforcement learning and greedy tree search. When tested for the designs of the multiband pulses with three and seven slices, DeepRF_SLR demonstrated improved performance compared to conventional methods, generating shorter duration RF pulses in shorter computational time. In the experiments, the RF pulse from DeepRF_SLR produced a slice profile similar to the minimum-phase SLR RF pulse and the profiles matched to that of the computer simulation. Our approach suggests a new way of designing an RF by applying a machine learning algorithm, demonstrating a "machine-designed" MRI sequence.

Tailored spiral in-out spectral-spatial water suppression pulses for magnetic resonance spectroscopic imaging

PURPOSE

To develop short water suppression sequences for 7 T magnetic resonance spectroscopic imaging, with mitigation of subject-specific transmit RF field ( B1+) inhomogeneity.

METHODS

Patient-tailored spiral in-out spectral-spatial saturation pulses were designed for a three-pulse WET water suppression sequence. The pulses' identical spatial subpulses were designed using patient-specific B1+ maps and a spiral in-out excitation k-space trajectory. The subpulse train was weighted by a spectral envelope that was root-flipped to minimize peak RF demand. The pulses were validated in in vivo experiments that acquired high resolution magnetic resonance spectroscopic imaging data, using a crusher coil for fast lipid suppression. Residual water signals and MR spectra were compared between the proposed tailored sequence and a conventional WET sequence.

RESULTS

Replacing conventional spectrally-selective pulses with tailored spiral in-out spectral-spatial pulses reduced mean water residual from 5.88 to 2.52% (57% improvement). Pulse design time was less then 0.4 s. The pulses' specific absorption rate were compatible with magnetic resonance spectroscopic imaging TRs under 300 ms, which enabled spectra of fine in plane spatial resolution (5 mm) with good quality to be measured in 7.5 min.

CONCLUSION

Tailored spiral in-out spectral-spatial water suppression enables efficient high resolution magnetic resonance spectroscopic imaging in the brain. Magn Reson Med 79:31-40, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

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) (13)C MRI, a dualband saturation RF pulse for (1)H MR spectroscopy, and a pre-saturation pulse for HP (13)C study were developed and tested.

Single voxel localization for dynamic hyperpolarized (13)C MR spectroscopy

The PRESS technique has been widely used to achieve voxel localization for in vivo(1)H MRS acquisitions. However, for dynamic hyperpolarized (13)C MRS experiments, the transition bands of the refocusing pulses may saturate the pre-polarized substrate spins flowing into the voxel. This limitation may be overcome by designing refocusing pulses that do not perturb the resonance of the hyperpolarized substrate, but selectively refocuses the spins of the metabolic products. In this study, a PRESS pulse sequence incorporating spectral-spatial refocusing pulses that have a stop band ('notch') at the substrate resonance is tested in vivo using hyperpolarized [1-(13)C]pyruvate. Higher metabolite SNR was observed in experiments using the spectral-spatial refocusing pulses as compared to conventional refocusing pulses.

Root-flipped multiband refocusing pulses

PURPOSE

To design low peak power multiband refocusing radiofrequency pulses, with application to simultaneous multislice spin echo MRI.

THEORY AND METHODS

Multiband Shinnar-Le Roux β polynomials were designed using convex optimization. A Monte Carlo algorithm was used to determine patterns of β polynomial root flips that minimized the peak power of the resulting refocusing pulses. Phase-matched multiband excitation pulses were also designed to obtain linear-phase spin echoes. Simulations compared the performance of the root-flipped pulses with time-shifted and phase-optimized pulses. Phantom and in vivo experiments at 7T validated the function of the root-flipped pulses and compared them to time-shifted spin echo signal profiles.

RESULTS

Averaged across number of slices, time-bandwidth product, and slice separation, the root-flipped pulses have 46% shorter durations than time-shifted pulses with the same peak radiofrequency amplitude. Unlike time-shifted and phase-optimized pulses, the root-flipped pulses' excitation errors do not increase with decreasing band separation. Experiments showed that the root-flipped pulses excited the desired slices at the target locations, and that for equivalent slice characteristics, the shorter root-flipped pulses allowed shorter echo times, resulting in higher signal than time-shifted pulses.

CONCLUSION

The proposed root-flipped multiband radiofrequency pulse design method produces low peak power pulses for simultaneous multislice spin echo MRI.

Near-contiguous spin echo imaging using matched-phase RF and its application in velocity-selective arterial spin labeling

PURPOSE

The minimum slice spacing in multislice imaging is limited by inter-slice crosstalk due to an imperfect slice profile. This study sought to minimize the slice spacing using matched-phase RF pulses and demonstrate its application in cerebral blood flow imaging using velocity-selective arterial spin labeling.

METHODS

A spin-echo matched-phase 90°-180° RF pair was designed using Shinnar-Le Roux algorithm in order to improve the slice profile of longitudinal magnetization, which plays a more critical role in creating interslice crosstalk than transverse magnetization. Both transverse and longitudinal slice profiles were compared between matched-phase RF and sinc-based RF pulses in simulations and measurements. Velocity-selective arterial spin labeling was performed in normal volunteers using both RF pulses and standard deviation of cerebral blood flow time series was calculated to examine ASL signal stability.

RESULTS

Using designed matched-phase RF, the longitudinal slice profile was sharpened without signal-to-noise ratio loss. In velocity-selective arterial spin labeling imaging, the temporal standard deviation of cerebral blood flow measurements was reduced from 48 mL/100 g/min to 32 mL/100 g/min by 33% using matched-phase RF pulses, and as a result, cerebral blood flow image quality improved.

CONCLUSION

This study reports that near-contiguous multislice imaging can be achieved using matched-phase RF pulses without compromising signal-to-noise ratio and signal stability.

Robust slice-selective broadband refocusing pulses

Slice-selective broadband refocusing pulses are of great interest in localized MR spectroscopy for improving spatial selectivity, reducing chemical-shift displacement errors, and reducing anomalous J modulation. In practice the bandwidth of RF pulses is limited by the maximum available B1 amplitude. The goal of the present work is to design slice-selective and broadband refocusing pulses which are tolerant against B1 deviations. Pulse design is performed by numerical optimization based on optimal control theory. A comprehensive study of different cost functions and their effect on the optimization is given. The optimized slice-selective broadband refocusing pulses are compared to conventional Shinnar-Le Roux (SLR), broadband SLR, and hyperbolic secant pulses. In simulations and experiments optimized pulses were shown to fulfill broadband slice specifications over a range of ±20% B1 scalings. Experimental validation showed a reduction of chemical-shift displacement error by a factor of 3 compared to conventional SLR pulses.

Which pulse sequence is optimal for myo-inositol detection at 3T?

Optimized myo-inositol (mI) detection is important for diagnosing and monitoring a multitude of pathological conditions of the brain. Simulations are presented in this work, performed to decide which pulse sequence has the most significant advantage in terms of improving repeatability and accuracy of mI measurements at 3T over the pulse sequence used typically in the clinic, a TE = 35 ms PRESS sequence. Five classes of pulse sequences, four previously suggested for optimized mI detection (a short TE PRESS, a Carr-Purcell PRESS sequence, an optimized STEAM sequence, an optimized zero quantum filter), and one optimized for mI detection in this work (a single quantum filter) were compared to a standard, TE = 35 ms pulse sequence. While limiting the SNR of an acquisition to the equivalent SNR of a spectrum acquired in 5 min from an 8 cc voxel, it was found through simulations that the most repeatable mI measurements would be obtained with a Carr-Purcell sequence. This sequence was implemented in a clinical scanner, and improved mI measurements were demonstrated in vivo.

Design of phase-modulated broadband refocusing pulses

Broadband linear-phase refocusing pulses were designed with the Shinnar-Le Roux (SLR) transformation and verified experimentally. The design works in several steps: initially, a linear-phase B polynomial is created with the Parks-McClellan/Remez exchange algorithm. The complementary A polynomial required for the SLR transformation is generated with the Hilbert transformation, yielding the minimum-phase response. The phase response of the A polynomial is altered by zero-flipping, which changes the overall pulse shape while retaining its refocusing profile. Optimal pulses in terms of minimal B(1max) and hence broadest bandwidth were found with non-linear optimisation of the zero-flipping pattern. These pulses are generally phase modulated with a time-symmetric amplitude and anti-symmetric phase modulation. In this work, a whole range of pulses were designed to demonstrate the underlying relationships. Five exemplary pulses were implemented into a PRESS sequence and validated by acquiring images of a water-oil phantom and lactate spectra at TE = 144 ms.

Combined simulated annealing and Shinnar-Le Roux pulse design of slice-multiplexed RF pulses for multi-slice imaging

Slice-multiplexed RF pulses have recently been introduced for simultaneous multi-slice imaging. Their novel aspect is that each slice is given a different linear phase profile, and hence a different slice-rephasing requirement, by the pulse. During readout, extra slice gradients are applied such that when one slice is rephased, the others are dephased to prevent aliasing. In this paper, an improved method of designing slice-multiplexed RF pulses is presented: component pulses which are optimized with simulated annealing for a specific rephasing are combined using Shinnar-Le Roux methods. In this way, non-linearities at higher flip angles are taken into account and more slices can be excited. Bloch simulations show the phase and amplitude profile of component pulses are faithfully preserved in the multiplexed pulse. Three- and four-slice multiplex pulses are demonstrated in gradient- and spin-echo in-vivo imaging.

Sequence design for magnetic resonance spectroscopic imaging of prostate cancer at 3 T

Magnetic resonance spectroscopic imaging (MRSI) has proven to be a powerful tool for the metabolic characterization of prostate cancer in patients before and following therapy. The metabolites that are of particular interest are citrate and choline because an increased choline-to-citrate ratio can be used as a marker for cancer. High-field systems offer the advantage of improved spectral resolution as well as increased magnetization. Initial attempts at extending MRSI methods to 3 T have been confounded by the J-modulation of the citrate resonances. A new pulse sequence is presented that controls the J-modulation of citrate at 3 T such that citrate is upright, with high amplitude, at a practical echo time. The design of short (14 ms) spectral-spatial refocusing pulses and trains of nonselective refocusing pulses are described. Phantom studies and simulations showed that upright citrate with negligible sidebands is observed at an echo time of 85 ms. Studies in a human subject verified that this behavior is reproduced in vivo and demonstrated that the water and lipid suppression of the new pulse sequence are sufficient for application in prostate cancer patients.

Reduction of blurring in view angle tilting MRI

Magnetic resonance imaging (MRI) in the presence of metallic objects suffers from slice-selection errors and in-plane distortions. View angle tilting (VAT) corrects for in-plane distortions by adding a gradient on the slice-select axis during readout, but can suffer from image blurring. This work demonstrates that the major source of blurring is a slice profile modulation of the data, and proposes several solutions to prevent such blurring. Multiple high-bandwidth readouts are demonstrated to reduce the blurring while improving the signal-to-noise ratio (SNR) over a single high-bandwidth readout.

Practical pulse synthesis via the discrete inverse scattering transform

This paper provides the practical details required to use the inverse scattering (IST) approach to design selective RF-pulses. As in the Shinnar-Le Roux (SLR) approach, we use a hard pulse approximation to actually design the pulse. Unlike SLR, the pulse is designed using the full inverse scattering data (the reflection coefficient and the bound states) rather than the flip angle profile. We explain how to approximate the reflection coefficient to obtain a pulse with a prescribed rephasing time. In contrast to the SLR approach, we retain direct control on the phase of the magnetization profile throughout the design process. We give explicit recursive algorithms for computing the hard pulse from the inverse scattering data. These algorithms are quite different from the SLR recursion, being essentially discretizations of the Marchenko equations. We call our approach the discrete inverse scattering transform or DIST. Overall, it is as fast as the SLR approach. When bound states are present, we use both the left and right Marchenko equations to improve the numerical stability of the algorithm. We compute a variety of examples and consider the effect of amplitude errors on the magnetization profile.

Long component time constant of 23Na T*2 relaxation in healthy human brain

Signal intensity in 23Na images is altered in pathologic conditions such as ischemia and may provide information regarding tissue viability complementary to MR diffusion and perfusion imaging. However, the multicomponent transverse relaxation of 23Na (spin 3/2) complicates the determination of tissue sodium concentration from 23Na images with nonzero echo-time. The purpose of this study was to measure the long component time constant of tissue sodium T*2 relaxation in the healthy human brain at 4 T. Multiecho gradient-echo 23Na images (10 echo-times ranging from 3.8-68.7 ms) were acquired in five healthy human volunteers. T*2 was quantified on a pixel-by-pixel basis using a nonnegative least squares fitting routine using 100 equally spaced bins between 0.5-99.5 ms and parametric maps were produced representing components between 0.5-3, 3.1-50, 50.1-98, and 98.1-99.5 ms. The long T*2 component of tissue sodium (average +/- standard deviation) varied between cortex (occipital = 22.0 +/- 2.4 ms), white matter (parietal = 18.2 +/- 1.9 ms), and subcortical gray matter (thalamus = 16.9 +/- 2.4 ms). These results demonstrate considerable regional variability and establish a foundation for future characterization of 23Na T*2 in conditions such as cerebral ischemia and cancer.

Minimum energy pulse synthesis via the inverse scattering transform

This paper considers a variety of problems in the design of selective RF-pulses. We apply a formula of Zakharov and Manakov to directly relate the energy of an RF-envelope to the magnetization profile and certain auxiliary parameters used in the inverse scattering transform (IST) approach to RF-pulse synthesis. This allows a determination of the minimum possible energy for a given magnetization profile. We give an algorithm to construct both the minimum energy RF-envelope as well as any other envelope that produces a given magnetization profile. This includes an algorithm for solving the Gel'fand-Levitan-Marchenko equations with bound states. The SLR method is analyzed in terms of traditional scattering data, and shown to be a special (singular) case of the IST approach. RF-envelopes are computed for a variety of examples.

Design of symmetric-sweep spectral-spatial RF pulses for spectral editing

Spectral-spatial RF (SSRF) pulses allow simultaneous selection in both frequency and spatial domains. These pulses are particularly important for clinical and research MR spectroscopy (MRS) applications for suppression of large water and lipid resonances. Also, the high bandwidth of the subpulses (5-10 kHz) greatly reduces the spatial-shift errors associated with different chemical shifts. However, the use of high-bandwidth subpulses along with enough spectral bandwidth to measure a typical range of metabolite frequencies (e.g., 300 Hz at 3 T) can require RF amplitudes beyond the limits of the RF amplifier of a typical scanner. In this article, a new method is described for designing nonlinear-phase 180 degrees SSRF pulses that can be used for spectral editing. The novel feature of the pulses is that the spectral profile develops as a symmetric sweep, from the outside edges of the spectral window towards the middle, so that coupled components are tipped simultaneously and over a short interval. Pulses were designed for lactate editing at 1.5 T and 3 T. The spectral and spatial spin-echo profiles of the new pulses were measured experimentally. Spectra acquired in phantom experiments showed a well-resolved, edited lactate doublet, with 91% to 93% editing efficiency.

Variable-rate selective excitation for rapid MRI sequences

Balanced steady-state free precession (SSFP) imaging sequences require short repetition times (TRs) to avoid off-resonance artifacts. The use of slab-selective excitations is common, as this can improve imaging speed by limiting the field of view (FOV). However, the necessarily short-duration excitations have poor slab profiles. This results in unusable slices at the slab edge due to significant flip-angle variations or aliasing in the slab direction. Variable-rate selective excitation (VERSE) is a technique by which a time-varying gradient waveform is combined with a modified RF waveform to provide the same excitation profile with different RF power and duration characteristics. With the use of VERSE, it is possible to design short-duration pulses with dramatically improved slab profiles. These pulses achieve high flip angles with only minor off-resonance sensitivity, while meeting SAR limits at 1.5 T. The improved slab profiles will enable more rapid 3D imaging of limited volumes, with more consistent image contrast across the excited slab.

Dualband spectral-spatial RF pulses for prostate MR spectroscopic imaging

Although MR spectroscopic imaging (MRSI) of the prostate has demonstrated clinical utility for the staging and monitoring of cancer extent, current acquisition methods are often inadequate in several aspects. Conventional 180 degrees pulses can suffer from chemical shift misregistration, and have high peak-power requirements that can exceed hardware limits in many prostate MRSI studies. Optimal water and lipid suppression are also critical to obtain interpretable spectra. While complete suppression of the periprostatic lipid resonance is desired, controlled partial suppression of water can provide a valuable phase and frequency reference for data analysis and an assessment of experimental success in cases in which all other resonances are undetectable following treatment. In this study, new spectral-spatial RF pulses were developed to negate chemical shift misregistration errors and to provide dualband excitation with partial excitation of the water resonance and full excitation of the metabolites of interest. Optimal phase modulation was also included in the pulse design to provide 40% reduction in peak RF power. Patient studies using the new pulses demonstrated both feasibility and clear benefits in the reliability and applicability of prostate cancer MRSI.

Very selective suppression pulses for clinical MRSI studies of brain and prostate cancer

Focal three-dimensional magnetic resonance spectroscopic imaging (3D MRSI) methods based on conventional point resolved spectroscopy (PRESS) localization are compromised by the geometric restrictions in volume prescription and by chemical shift registration errors. Outer volume saturation (OVS) pulses have been applied to address the geometric limits, but conventional OVS pulses do little to overcome chemical shift registration error, are not particularly selective, and often leave substantial signals that can degrade the spectra of interest. In this paper, an optimized sequence of quadratic phase pulses is introduced to provide very selective spatial suppression with improved B1 and T1 insensitivity. This method was then validated in volunteer studies and in clinical 3D MRSI exams of brain tumors and prostate cancer.

Optimized outer volume suppression for single-shot fast spin-echo cardiac imaging

Among the ultrafast MRI techniques, the single-shot fast spin-echo sequence offers a robust alternative to echo planar imaging, essentially because of a much reduced sensitivity to B0 inhomogeneity. This property is particularly appealing in situations in which B0 inhomogeneities can be severe and difficult to correct, such as in cardiac imaging. With single-shot cardiac imaging, however, achieving high resolution over the necessarily large field of views without introducing back-folding artifacts is problematic. One option is to use multishot sequences. However, then issues related to cardiac gating arise. Another solution is to use, optimized presaturation slabs with quadratic phase pulses generated by the Shinnar-LeRoux algorithm. These can be set to reduce the field of view in the phase-encoding direction, resulting in a reduction in the number of phase-encoding steps. For instance, for a 1 x 2-mm spatial resolution, over a rectangular, 250 x 125-mm field of view, and using a half Fourier acquisition, an echo-train length of only 40 is required. With a 4.5-msec echo spacing, the total imaging time is approximately 180 msec. The efficacy of this solution on phantoms and volunteers is demonstrated. Multislice short-axis examinations of the whole heart, realized within a single short breath-hold of approximately 10 seconds, are shown. The possibility of investigating not only cardiac anatomy but also both contractility and myocardial perfusion is discussed.

3D multivoxel proton spectroscopy of human brain using a hybrid of 8th-order Hadamard encoding with 2D chemical shift imaging

Multivoxel 3D localized proton spectroscopy using a hybrid of 1D 8th-order transverse Hadamard spectroscopic imaging (HSI) with 2D chemical shift imaging (CSI) is demonstrated in human brain. The spatially selective HSI pulse incorporates naturally into the PRESS sequence (TE = 135 ms), which then both excites an 8 x 8 x 6 cm parallelepiped volume of interest (VOI) and subdivides it into eight slices. The planes of these slices are further partitioned into 16 x 16 voxel arrays using 2D CSI to yield 8 x 8 x 8 voxels within the VOI. Simultaneous 3D coverage yields good voxel signal-to-noise (8, 12, and 22 for choline, creatine, and N-acetylaspartate, respectively) from these 0.75-ml voxels, in approximately 45 min. The high spatial isolation allows localization to within less than 1 cm from the skull without fat contamination.

Efficient design of pulses with trapezoidal magnitude and linear phase response profiles

A variation of the Shinnar-Le Roux (SLR) method of pulse envelope design that allows for control of the phase of the frequency response profile has been developed. The method makes use of the fact that a knowledge of one of the SLR polynomials in combination with a root inversion pattern for the other polynomial is sufficient to fully define the second polynomial. Optimization of the first polynomial, when cast in this form, remains nonlinear. However, it was demonstrated that the relationship between the SLR polynomials and the frequency response profile may be used to generate an initial guess for the SLR polynomials that is sufficiently accurate to allow for the application of linear optimization techniques in most cases. In practice several pulse envelopes having different root inversion patterns are investigated for each target profile. The resulting collection of pulses allows the user to trade off pulse power for profile accuracy. The proposed technique was used to design a large number of amplitude modulated excitation pulses having trapezoidal magnitude and linear phase frequency response profiles. A few examples of the resulting pulses and their response profiles are presented.