Additive angle method for fast large-tip-angle RF pulse design in parallel excitation

What can we gain from subpopulation universal pulses? A simulation-based study

PURPOSE

The aim of the study was to explore a novel methodology for designing universal pulses (UPs) that balances the benefits of a calibration-free approach with subject-specific online pulse design.

METHODS

The proposed method involves segmenting the population into subpopulations with variability in anatomical shapes and positions reduced to 75%, 50%, and 25% of their original values while keeping the mean values unchanged. An additional 25% extreme case with a large volume of interest and shifted position was included. For each group, a 5kT-points universal inversion pulse was designed and assessed by the normalized root mean square error (NRMSE) on the target longitudinal magnetization profile. The performance was compared to the conventional one-size-fits-all approach. A total of 132 electromagnetic simulations were executed to generate representative anatomies and specific absorption rate (SAR) distributions in a three-dimensional parameter space comprised of head breadth, head length, and Y-shift. The 99.9th percentile on the peak local SAR distribution was utilized to establish an intersubject variability safety margin.

RESULTS

UPs designed for subpopulations with decreased head shape and position variability reduced the anatomical safety margin by up to 20%. Furthermore, when a head was significantly different to the average case, the proposed approach improved the inversion homogeneity by up to 24%, compared to the conventional one-size-fits-all approach.

CONCLUSION

Subpopulation UPs present an opportunity to improve theB 1 + $$ {\mathrm{B}}_1^{+} $$ homogeneity and reduce anatomical SAR safety margins at 7T without additional acquisition time for calibration.

Stochastic-offset-enhanced restricted slice excitation and 180° refocusing designs with spatially non-linear ΔB0 shim array fields

PURPOSE

Developing a general framework with a novel stochastic offset strategy for the design of optimized RF pulses and time-varying spatially non-linear ΔB0 shim array fields for restricted slice excitation and refocusing with refined magnetization profiles within the intervals of the fixed voxels.

METHODS

Our framework uses the decomposition property of the Bloch equations to enable joint design of RF-pulses and shim array fields for restricted slice excitation and refocusing with auto-differentiation optimization. Bloch simulations are performed independently on orthogonal basis vectors, Mx, My, and Mz, which enables designs for arbitrary initial magnetizations. Requirements for refocusing pulse designs are derived from the extended phase graph formalism obviating time-consuming sub-voxel isochromatic simulations to model the effects of crusher gradients. To refine resultant slice-profiles because of voxelwise optimization functions, we propose an algorithm that stochastically offsets spatial points at which loss is computed during optimization.

RESULTS

We first applied our proposed design framework to standard slice-selective excitation and refocusing pulses in the absence of non-linear ΔB0 shim array fields and compared them against pulses designed with Shinnar-Le Roux algorithm. Next, we demonstrated our technique in a simulated setup of fetal brain imaging in pregnancy for restricted-slice excitation and refocusing of the fetal brain.

CONCLUSIONS

Our proposed framework for optimizing RF pulse and time-varying spatially non-linear ΔB0 shim array fields achieve high fidelity restricted-slice excitation and refocusing for fetal MRI, which could enable zoomed fast-spin-echo-MRI and other applications.

Ultra-high field MRI: parallel-transmit arrays and RF pulse design

This paper reviews the field of multiple or parallel radiofrequency (RF) transmission for magnetic resonance imaging (MRI). Currently the use of ultra-high field (UHF) MRI at 7 tesla and above is gaining popularity, yet faces challenges with non-uniformity of the RF field and higher RF power deposition. Since its introduction in the early 2000s, parallel transmission (pTx) has been recognized as a powerful tool for accelerating spatially selective RF pulses and combating the challenges associated with RF inhomogeneity at UHF. We provide a survey of the types of dedicated RF coils used commonly for pTx and the important modeling of the coil behavior by electromagnetic (EM) field simulations. We also discuss the additional safety considerations involved with pTx such as the specific absorption rate (SAR) and how to manage them. We then describe the application of pTx with RF pulse design, including a practical guide to popular methods. Finally, we conclude with a description of the current and future prospects for pTx, particularly its potential for routine clinical use.

Parallel transmission 2D RARE imaging at 7T with transmit field inhomogeneity mitigation and local SAR control

PURPOSE

We develop and test a parallel transmit (pTx) pulse design framework to mitigate transmit field inhomogeneity with control of local specific absorption rate (SAR) in 2D rapid acquisition with relaxation enhancement (RARE) imaging at 7T.

METHODS

We design large flip angle RF pulses with explicit local SAR constraints by numerical simulation of the Bloch equations. Parallel computation and analytical expressions for the Jacobian and the Hessian matrices are employed to reduce pulse design time. The refocusing-excitation "spokes" pulse pairs are designed to satisfy the Carr-Purcell-Meiboom-Gill (CPMG) condition using a combined magnitude least squares-least squares approach.

RESULTS

In a simulated dataset, the proposed approach reduced peak local SAR by up to 56% for the same level of refocusing uniformity error and reduced refocusing uniformity error by up to 59% (from 32% to 7%) for the same level of peak local SAR compared to the circularly polarized birdcage mode of the pTx array. Using explicit local SAR constraints also reduced peak local SAR by up to 46% compared to an RF peak power constrained design. The excitation and refocusing uniformity error were reduced from 20%-33% to 4%-6% in single slice phantom experiments. Phantom experiments demonstrated good agreement between the simulated excitation and refocusing uniformity profiles and experimental image shading.

CONCLUSION

PTx-designed excitation and refocusing CPMG pulse pairs can mitigate transmit field inhomogeneity in the 2D RARE sequence. Moreover, local SAR can be decreased significantly using pTx, potentially leading to better slice coverage, enabling larger flip angles or faster imaging.

Parallel transmit pulse design for saturation homogeneity (PUSH) for magnetization transfer imaging at 7T

PURPOSE

This work proposes a novel RF pulse design for parallel transmit (pTx) systems to obtain uniform saturation of semisolid magnetization for magnetization transfer (MT) contrast in the presence of transmit field B1+ inhomogeneities. The semisolid magnetization is usually modeled as being purely longitudinal, with the applied B1+ field saturating but not rotating its magnetization; thus, standard pTx pulse design methods do not apply.

THEORY AND METHODS

Pulse design for saturation homogeneity (PUSH) optimizes pTx RF pulses by considering uniformity of root-mean squared B1+ , B1rms , which relates to the rate of semisolid saturation. Here we considered designs consisting of a small number of spatially non-selective sub-pulses optimized over either a single 2D plane or 3D. Simulations and in vivo experiments on a 7T Terra system with an 8-TX Nova head coil in five subjects were carried out to study the homogenization of B1rms and of the MT contrast by acquiring MT ratio maps.

RESULTS

Simulations and in vivo experiments showed up to six and two times more uniform B1rms compared to circular polarized (CP) mode for 2D and 3D optimizations, respectively. This translated into 4 and 1.25 times more uniform MT contrast, consistently for all subjects, where two sub-pulses were enough for the implementation and coil used.

CONCLUSION

The proposed PUSH method obtains more uniform and higher MT contrast than CP mode within the same specific absorption rate (SAR) budget.

Selective RF excitation designs enabled by time-varying spatially non-linear ΔB0 fields with applications in fetal MRI

PURPOSE

To demonstrate, through numerical simulations, novel designs of spatially selective radiofrequency (RF) excitations of the fetal brain by both a restricted 2D slice and 3D inner-volume selection. These designs exploit a single-channel RF pulse, conventional gradient fields, and the spatially non-linear ΔB₀ fields of a multi-coil shim array, using an auto-differentiation optimization algorithm.

METHODS

The design algorithm jointly optimizes the RF pulse and the time-varying ΔB₀ fields, which is produced by a 64-channel multi-coil ΔB₀ body array to augment the RF and the linear gradient fields, using an auto-differentiation approach. Two design targets were specified, one a 4-mm thick slice with a limited in-slice extent in one dimension ("restricted slice"), and the other a 3D inner-volume selection encompassing the fetal brain ("inner volume"). The RF duration was limited to 2 ms for the restricted slice excitation and 6 ms for the inner-volume excitation.

RESULTS

Excitation profiles were achieved for both the restricted slice excitation task (one-minus-minimum magnitude, 8%) within the region of interest (ROI) and (maximum-minus-zero magnitude, 8%) in the suppressed regions and the fetal brain volume excitation task (13% and 9%, respectively).

CONCLUSIONS

The proposed joint design of RF and time-varying, spatially non-linear ΔB₀ fields achieves the target excitation profiles with short RF pulse durations and demonstrates the potential to enhance fetal MRI with multi-channel body shim arrays.

Parallel transmit optimized 3D composite adiabatic spectral-spatial pulse for spectroscopy

PURPOSE

To develop a 3D composite adiabatic spectral-spatial pulse for refocusing in spin-echo spectroscopy acquisitions and to compare its performance against standard acquisition methods.

METHODS

A 3D composite adiabatic pulse was designed by modulating a train of parallel transmit-optimized 2D subpulses with an adiabatic envelope. The spatial and spectral profiles were simulated and validated by experiments to demonstrate the feasibility of the design in both single and double spin-echo spectroscopy acquisitions. Phantom and in vivo studies were performed to evaluate the pulse performance and compared with semi-LASER with respect to localization performance, sequence timing, signal suppression, and specific absorption rate.

RESULTS

Simultaneous 2D spatial localization with water and lipid suppression was achieved with the designed refocusing pulse, allowing high-quality spectra to be acquired with shorter minimum TE/TR, reduced SAR, as well as adaptation to spatially varying B0 and B 1 + field inhomogeneities in both prostate and brain studies.

CONCLUSION

The proposed composite pulse can serve as a more SAR efficient alternative to conventional localization methods such as semi-LASER at ultrahigh field for spin echo-based spectroscopy studies. Subpulse parallel-transmit optimization provides the flexibility to manage the tradeoff among multiple design criteria to accommodate different field strengths and applications.

k-Space Domain Parallel Transmit Pulse Design

PURPOSE

To accelerate the design of (under- or oversampled) multidimensional parallel transmission pulses.

METHODS

A k-space domain parallel transmission pulse design algorithm was proposed that produces a sparse matrix relating a complex-valued target excitation pattern to the pulses that produce it, and can be finely parallelized. The algorithm was applied in simulations to the design of 3D SPINS pulses for inner volume excitation in the brain at 7 Tesla. It was characterized in terms of the dependence of computation time, excitation error, and required memory on algorithm parameters, and it was compared to an iterative spatial domain pulse design method in terms of computation time, excitation error, Gibbs ringing, and ability to compensate off-resonance.

RESULTS

The proposed algorithm achieved approximately 80% faster pulse design compared to the spatial domain method with the same number of parallel threads, with the tradeoff of increased excitation error and RMS RF amplitude. It reduced the memory required to store the design matrix by 99% compared to a full matrix solution. Even with a coarse design grid, the algorithm produced patterns that were free of Gibbs ringing. It was similarly sensitive to k-space undersampling as the spatial domain method, and was similarly capable of compensating for off-resonance.

CONCLUSIONS

The proposed k-space domain algorithm accelerates and finely parallelizes parallel transmission pulse design, with a modest tradeoff of excitation error and RMS RF amplitude.

IMPULSE: A scalable algorithm for design of minimum specific absorption rate parallel transmit RF pulses

PURPOSE

Managing local specific absorption rate (SAR) in parallel transmission requires ensuring that the peak SAR over a large number of voxels (> 10 5 ) is below the regulatory limit. The safety risk to the patient depends on cumulative (not instantaneous) SAR thus making a joint design of all RF pulses in a sequence desirable. We propose the Iterative Minimization Procedure with Uncompressed Local SAR Estimate (IMPULSE), an efficient optimization formulation and algorithm that can handle uncompressed SAR matrices and optimize pulses for all slices jointly within a practical time frame.

THEORY AND METHODS

IMPULSE optimizes parallel transmit pulses for small-tip-angle slice selective excitation to minimize a single cost function incorporating multiple quantities (local SAR, global SAR, and per-channel power) averaged over the entire multislice scan subject to a strict constraint on excitation accuracy. Pulses for an 8-channel 7T head coil were designed with IMPULSE and compared with pulses designed using generic optimization algorithms and VOPs to assess the computation time and SAR performance benefits.

RESULTS

IMPULSE achieves lower SAR and shorter computation time compared with a VOP approach. Compared with the generic sequential quadratic programming algorithm, computation time is reduced by a factor of 5-6 by using IMPULSE. Using as many as 6 million local SAR terms, up to 120 slices can be designed jointly with IMPULSE within 45 s.

CONCLUSIONS

IMPULSE can handle significantly larger number of SAR matrices and slices than conventional optimization algorithms, enabling the use of uncompressed or partially compressed SAR matrices to design pulses for a multislice scan in a practical time frame.

Squeezed Trajectory Design for Peak RF and Integrated RF Power Reduction in Parallel Transmission MRI

High peak RF amplitude and excessive specific absorption rate (SAR) are two critical concerns for hardware implementation and patient safety in scientific and clinical research for high field MRI using parallel transmissions (pTX). In this paper, we introduce a squeezing strategy to reduce peak RF amplitude and integrated RF power via direct reshaping of the k-space trajectory. In the existing peak RF / integrated RF power optimization methods gradient amplitude or slew rate is reduced, but the k-space trajectory remains unchanged. Unlike these traditional methods, we worked directly in the excitation k-space to reshape k-space traversal by a squeezing vector in order to achieve peak RF and total RF power optimization, using a particle swarm optimization algorithm. The squeezing strategy was applied to the conventional variable density spiral (CVDS) and the variable rate selective excitation (VERSE) trajectories, dubbed SVDS (squeezed variable density spiral) and SVERSE (squeezing trajectory with VERSE), respectively, for different excitation profiles of small or large tip angles. Pulse acceleration and off-resonance effects were evaluated for an 8-ch pTX via Bloch simulation. CVDS, VERSE, SVDS, and SVERSE pulses were implemented on a 3T scanner with a 2-ch pTX. Phantom and in vivo experiments were performed for reduced FOV (rFOV) imaging. The results show that SVDS pulses simultaneously reduce integrated RF power and peak RF by about 30% on average compared to CVDS pulses for a square pattern ( $80\times80$ mm2) with flip angles of 30°, 90°, and 180°. Compared with the VERSE method under the same peak RF constraints, the SVDS method reduces integrated RF power by an average of 20% for small tip excitations for profiles of slice, rectangular, square, and circle, and has slightly reduced excitation accuracy slightly (about 0.6%, from 6.8% to 7.4%). The SVERSE method shortens the duration of the VERSE pulse by 12.8% at large ti p angle (180°). Feasibility for rFOV imaging was demonstrated with phantom and in vivo experiments with squeezed pulses.

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.

Parallel transmission for ultrahigh-field imaging

The development of MRI systems operating at or above 7 T has provided researchers with a new window into the human body, yielding improved imaging speed, resolution and signal-to-noise ratio. In order to fully realise the potential of ultrahigh-field MRI, a range of technical hurdles must be overcome. The non-uniformity of the transmit field is one of such issues, as it leads to non-uniform images with spatially varying contrast. Parallel transmission (i.e. the use of multiple independent transmission channels) provides previously unavailable degrees of freedom that allow full spatial and temporal control of the radiofrequency (RF) fields. This review discusses the many ways in which these degrees of freedom can be used, ranging from making more uniform transmit fields to the design of subject-tailored RF pulses for both uniform excitation and spatial selection, and also the control of the specific absorption rate. © 2015 The Authors. NMR in Biomedicine published by John Wiley & Sons Ltd.

Phase relaxed localized excitation pulses for inner volume fast spin echo imaging

PURPOSE

To design multidimensional spatially selective radiofrequency (RF) pulses for inner volume imaging (IVI) with three-dimensional (3D) fast spin echo (FSE) sequences. Enhanced background suppression is achieved by exploiting particular signal properties of FSE sequences.

THEORY AND METHODS

The CPMG condition dictates that echo amplitudes will rapidly decrease if a 90° phase difference between excitation and refocusing pulses is not present, and refocusing flip angles are not precisely 180°. This mechanism is proposed as a means for generating additional background suppression for spatially selective excitation, by biasing residual excitation errors toward violating the CPMG condition. 3D RF pulses were designed using this method with a 3D spherical spiral trajectory, under-sampled by factor 5.6 for an eight-channel PTx system, at 3 Tesla.

RESULTS

3D-FSE IVI with pulse durations of approximately 12 ms was demonstrated in phantoms and for T2 -weighted brain imaging in vivo. Good image quality was obtained, with mean background suppression factors of 103 and 82 ± 6 in phantoms and in vivo, respectively.

CONCLUSION

Inner Volume Imaging with 3D-FSE has been demonstrated in vivo with tailored 3D-RF pulses. The proposed design methods are also applicable to 2D pulses. Magn Reson Med 76:848-861, 2016. © 2015 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine.

First and second order derivatives for optimizing parallel RF excitation waveforms

For piecewise constant magnetic fields, the Bloch equations (without relaxation terms) can be solved explicitly. This way the magnetization created by an excitation pulse can be written as a concatenation of rotations applied to the initial magnetization. For fixed gradient trajectories, the problem of finding parallel RF waveforms, which minimize the difference between achieved and desired magnetization on a number of voxels, can thus be represented as a finite-dimensional minimization problem. We use quaternion calculus to formulate this optimization problem in the magnitude least squares variant and specify first and second order derivatives of the objective function. We obtain a small tip angle approximation as first order Taylor development from the first order derivatives and also develop algorithms for first and second order derivatives for this small tip angle approximation. All algorithms are accompanied by precise floating point operation counts to assess and compare the computational efforts. We have implemented these algorithms as callback functions of an interior-point solver. We have applied this numerical optimization method to example problems from the literature and report key observations.

General design approach and practical realization of decoupling matrices for parallel transmission coils

PURPOSE

In a coupled parallel transmit (pTx) array, the power delivered to a channel is partially distributed to other channels because of coupling. This power is dissipated in circulators resulting in a significant reduction in power efficiency. In this study, a technique for designing robust decoupling matrices interfaced between the RF amplifiers and the coils is proposed. The decoupling matrices ensure that most forward power is delivered to the load without loss of encoding capabilities of the pTx array.

THEORY AND METHODS

The decoupling condition requires that the impedance matrix seen by the power amplifiers is a diagonal matrix whose entries match the characteristic impedance of the power amplifiers. In this work, the impedance matrix of the coupled coils is diagonalized by a successive multiplication by its eigenvectors. A general design procedure and software are developed to generate automatically the hardware that implements diagonalization using passive components.

RESULTS

The general design method is demonstrated by decoupling two example parallel transmit arrays. Our decoupling matrices achieve better than -20 db decoupling in both cases.

CONCLUSION

A robust framework for designing decoupling matrices for pTx arrays is presented and validated. The proposed decoupling strategy theoretically scales to any arbitrary number of channels. Magn Reson Med 76:329-339, 2016. © 2015 Wiley Periodicals, Inc.

Real-time 2D spatially selective MRI experiments: Comparative analysis of optimal control design methods

There is an increasing need for development of advanced radio-frequency (RF) pulse techniques in modern magnetic resonance imaging (MRI) systems driven by recent advancements in ultra-high magnetic field systems, new parallel transmit/receive coil designs, and accessible powerful computational facilities. 2D spatially selective RF pulses are an example of advanced pulses that have many applications of clinical relevance, e.g., reduced field of view imaging, and MR spectroscopy. The 2D spatially selective RF pulses are mostly generated and optimised with numerical methods that can handle vast controls and multiple constraints. With this study we aim at demonstrating that numerical, optimal control (OC) algorithms are efficient for the design of 2D spatially selective MRI experiments, when robustness towards e.g. field inhomogeneity is in focus. We have chosen three popular OC algorithms; two which are gradient-based, concurrent methods using first- and second-order derivatives, respectively; and a third that belongs to the sequential, monotonically convergent family. We used two experimental models: a water phantom, and an in vivo human head. Taking into consideration the challenging experimental setup, our analysis suggests the use of the sequential, monotonic approach and the second-order gradient-based approach as computational speed, experimental robustness, and image quality is key. All algorithms used in this work were implemented in the MATLAB environment and are freely available to the MRI community.

Clinical applications of dual-channel transmit MRI: A review

This article reviews the principle of dual-channel transmit MRI and highlights current clinical applications which are performed primarily at 3 Tesla. The main benefits of dual-channel transmit compared with single-transmit systems are the increased image contrast homogeneity and the decreased scanning time due to the more accurate local specific absorption ratio estimation, meaning that less conservative safety limits are needed. The dual-transmit approach has been particularly beneficial in body imaging applications, and is also promising in terms of cardiac, spine, and fetal imaging. Future advances in transmit SENSE, the combination of dual-channel transmit with high permittivity pads, as well as the potential increase in the number of transmit channels are also discussed.

Strategies for improved 3D small-tip fast recovery imaging

PURPOSE

Small-tip fast recovery (STFR) imaging is a recently proposed steady-state sequence that has similar image contrast as balanced steady-state free precession but has the potential to simultaneously remove banding artifacts and transient fluctuation. STFR relies on a "tip-up" radiofrequency (RF) pulse tailored to the accumulated phase during the free precession (data acquisition) interval, designed to bring spins back to the longitudinal axis, thereby preserving transverse magnetization as longitudinal magnetization for the next pulse repetition time. We recently proposed an RF-spoiled STFR sequence suitable for thin slab imaging, however, in many applications, e.g., functional magnetic resonance imaging or isotropic-resolution structural imaging, three-dimensional (3D) steady-state imaging is desirable. Unfortunately, 3D STFR imaging is challenging due to the need for 3D tailored RF pulses. Here, we propose new strategies for improved 3D STFR imaging, based on (i) unspoiled imaging, and (ii) joint design of nonslice-selective tip-down/tip-up RF pulses.

THEORY AND METHODS

We derive an analytic signal model for the proposed unspoiled STFR sequence, and propose two strategies for designing the 3D tailored tip-down/tip-up RF pulses. We validate the analytic results using phantom and in vivo imaging experiments.

RESULTS

Our analytic model and imaging experiments demonstrate that the proposed unspoiled STFR sequence is less sensitive to tip-up excitation error compared to the corresponding spoiled sequence, and may, therefore, be an attractive candidate for 3D imaging. The proposed "joint" RF pulse design method, in which we formulate the tip-down/tip-up RF pulse design task as a magnitude least squares problem, produces modest improvement over a simpler "Separate" design approach. Using the proposed unspoiled sequence and joint RF pulse design, we demonstrate proof-of-principle 3D STFR brain images with balanced steady-state free precession-like signal properties but with reduced banding.

CONCLUSION

Using the proposed unspoiled sequence and joint RF pulse design, STFR brain images in a 3D region of interest with balanced steady-state free precession-like signal properties but with reduced banding can be obtained.

Four dimensional spectral-spatial fat saturation pulse design

PURPOSE

The conventional spectrally selective fat saturation pulse may perform poorly with inhomogeneous amplitude of static (polarizing) field (B0 ) and/or amplitude of (excitation) radiofrequency field (B1 ) fields. We propose a four dimensional spectral-spatial fat saturation pulse that is more robust to B0/B1 inhomogeneity and also shorter than the conventional fat saturation pulse.

THEORY

The proposed pulse is tailored for local B0 inhomogeneity, which avoids the need of a sharp transition band in the spectral domain, so it improves both performance and pulse length. Furthermore, it can also compensate for B1 inhomogeneity. The pulse is designed sequentially by small-tip-angle approximation design and an automatic rescaling procedure.

METHODS

The proposed method is compared to the conventional fat saturation in phantom experiments and in vivo knee imaging at 3 T for both single-channel and parallel excitation versions.

RESULTS

Compared to the conventional method, the proposed method produces superior fat suppression in the presence of B0 and B1 inhomogeneity and reduces pulse length by up to half of the standard length.

CONCLUSION

The proposed four dimensional spectral-spatial fat saturation suppresses fat more robustly with shorter pulse length than the conventional fat saturation in the presence of B0 and B1 inhomogeneity.

Improving T2 -weighted imaging at high field through the use of kT -points

PURPOSE

At high magnetic field strengths (B(0) ≥ 3 T), the shorter radiofrequency wavelength produces an inhomogeneous distribution of the transmit magnetic field. This can lead to variable contrast across the brain which is particularly pronounced in T(2) -weighted imaging that requires multiple radiofrequency pulses. To obtain T(2) -weighted images with uniform contrast throughout the whole brain at 7 T, short (2-3 ms) 3D tailored radiofrequency pulses (kT -points) were integrated into a 3D variable flip angle turbo spin echo sequence.

METHODS

The excitation and refocusing "hard" pulses of a variable flip angle turbo spin echo sequence were replaced with kT -point pulses. Spatially resolved extended phase graph simulations and in vivo acquisitions at 7 T, utilizing both single channel and parallel-transmit systems, were used to test different kT -point configurations.

RESULTS

Simulations indicated that an extended optimized k-space trajectory ensured a more homogeneous signal throughout images. In vivo experiments showed that high quality T(2) -weighted brain images with uniform signal and contrast were obtained at 7 T by using the proposed methodology.

CONCLUSION

This work demonstrates that T(2) -weighted images devoid of artifacts resulting from B(1)(+) inhomogeneity can be obtained at high field through the optimization of extended kT -point pulses.

Design of non-selective refocusing pulses with phase-free rotation axis by gradient ascent pulse engineering algorithm in parallel transmission at 7T

At ultra-high magnetic field (≥ 7T), B1 and ΔB0 non-uniformities cause undesired inhomogeneities in image signal and contrast. Tailored radiofrequency pulses exploiting parallel transmission have been shown to mitigate these phenomena. However, the design of large flip angle excitations, a prerequisite for many clinical applications, remains challenging due the non-linearity of the Bloch equation. In this work, we explore the potential of gradient ascent pulse engineering to design non-selective spin-echo refocusing pulses that simultaneously mitigate severe B1 and ΔB0 non-uniformities. The originality of the method lays in the optimization of the rotation matrices themselves as opposed to magnetization states. Consequently, the commonly used linear class of large tip angle approximation can be eliminated from the optimization procedure. This approach, combined with optimal control, provides additional degrees of freedom by relaxing the phase constraint on the rotation axis, and allows the derivative of the performance criterion to be found analytically. The method was experimentally validated on an 8-channel transmit array at 7T, using a water phantom with B1 and ΔB0 inhomogeneities similar to those encountered in the human brain. For the first time in MRI, the rotation matrix itself on every voxel was measured by using Quantum Process Tomography. The results are complemented with a series of spin-echo measurements comparing the proposed method against commonly used alternatives. Both experiments confirm very good performance, while simultaneously maintaining a low energy deposition and pulse duration compared to well-known adiabatic solutions.

Multi-slice parallel transmission three-dimensional tailored RF (PTX 3DTRF) pulse design for signal recovery in ultra high field functional MRI

T(2)(∗) weighted fMRI at high and ultra high field (UHF) is often hampered by susceptibility-induced, through-plane, signal loss. Three-dimensional tailored RF (3DTRF) pulses have been shown to be an effective approach for mitigating through-plane signal loss at UHF. However, the required RF pulse lengths are too long for practical applications. Recently, parallel transmission (PTX) has emerged as a very effective means for shortening the RF pulse duration for 3DTRF without sacrificing the excitation performance. In this article, we demonstrate a RF pulse design strategy for 3DTRF based on the use of multi-slice PTX 3DTRF to simultaneously and precisely recover signal with whole-brain coverage. Phantom and human experiments are used to demonstrate the effectiveness and robustness of the proposed method on three subjects using an eight-channel whole body parallel transmission system.

Precompensation for mutual coupling between array elements in parallel excitation

Parallel transmission or excitation has been suggested to perform multi-dimensional spatial selective excitation to shorten the pulse width using a coil array and the sensitivity information. The mutual coupling between array elements has been a critical technical issue in RF array designs, which can cause artifacts on the excitation profile, leading to degraded excitation performance and image quality. In this work, a precompensation method is proposed to address the mutual coupling effect in parallel transmission by introducing the mutual coupling coefficient matrix into the RF pulses design procedure of the parallel transmission. 90° RF pulses have been designed using both the original transmit SENSE method and the proposed precompensation method for RF arrays with non-negligible mutual coupling, and their excitation profiles are generated by simulating the Bloch equation. The results show that the mutual coupling effect can be effectively compensated by using the proposed method, yielding enhanced tolerance to insufficient mutual decoupling of RF arrays in parallel excitation, ultimately, providing improved performance and accuracy of parallel excitation.

Parallel excitation for B-field insensitive fat-saturation preparation

Multichannel transmission has the potential to improve many aspects of MRI through a new paradigm in excitation. In this study, multichannel transmission is used to address the effects that variations in B(0) homogeneity have on fat-saturation preparation through the use of the frequency, phase, and amplitude degrees of freedom afforded by independent transmission channels. B(1) homogeneity is intrinsically included via use of coil sensitivities in calculations. A new method, parallel excitation for B-field insensitive fat-saturation preparation, can achieve fat saturation in 89% of voxels with M(z) ≤ 0.1 in the presence of ± 4 ppm B(0) variation, where traditional CHESS methods achieve only 40% in the same conditions. While there has been much progress to apply multichannel transmission at high field strengths, particular focus is given here to application of these methods at 1.5 T.

Advanced three-dimensional tailored RF pulse design in volume selective parallel excitation

Volume selective excitation has a variety of uses in clinical magnetic resonance imaging, but can suffer from insufficient excitation accuracy and impractically long pulse duration in ultra-high field applications. Based on recently-developed parallel transmission techniques, an optimized 3D tailored radio-frequency RF (TRF) pulse, designed with a novel 3D adaptive trajectory, is proposed to improve and accelerate volume selective excitation. The trajectory is designed to be regular-shaped and adaptively stretched according to the size of a 3D k-space "trajectory container." The container is designed to hold most of the RF energy deposition responsible for the desired pattern in the excitation k-space in the use of the blurring patterns caused by the multichannel sensitivity maps. The proposed method can also be used to reduce both global and peak RF energy required during excitation. The feasibility of this method is confirmed by simulations of ultra-high field cases.

Experimental demonstration of diffusion signal enhancement in 2D DESIRE images

In magnetic resonance microscopy based on conventional Fourier encoding techniques, molecular self-diffusion leads to a loss in signal to noise ratio while also limiting the spatial resolution. As opposed to standard diffusion-weighted sequences, the DESIRE (Diffusion Enhancement of SIgnal and REsolution) method gains signal through diffusion via a signal difference measurement, corresponding to the total number of spins saturated by a localized pulse applied for a given amount of time. The higher the diffusion coefficient at that location, the larger the number of spins effectively saturated and thus the higher the difference in signal. While the method has been previously demonstrated in 1D, the availability of higher magnetic fields and gradient strengths has recently brought its development within reach in 2D. Here we report the implementation of 2D DESIRE and the first experimental evaluation of enhancements in water and thin silicone oil. Enhancement levels obtained by saturating a 60 μm diameter region (effectively ~140 μm) and allowing diffusion lengths of 28 μm or 7 μm, respectively, are consistent with theoretical predictions. The typical enhancement values are 100% in water and 20% in silicone oil.

Tailored excitation using nonlinear B0-shims

In high-field MRI, RF flip angle inhomogeneity due to wavelength effects can lead to spatial variations in contrast and sensitivity. Improved flip angle homogeneity can be achieved through multidimensional excitation, but long RF pulse durations limit practical application. A recent approach to reduce RF pulse duration is based on parallel excitation through multiple RF channels. Here, an alternative approach to shorten multidimensional excitation is proposed that makes use of nonlinear spatial variations in the stationary (B(0)) magnetic field during a B(0)-sensitive excitation pulse. As initial demonstration, the method was applied to 2D gradient echo (GE) MRI of human brain at 7 T. Using B(0) shims with up to second-order spatial dependence, it is demonstrated that root-mean-squared flip angle variation can be reduced from 20 to 11% with RF pulse lengths that are practical for general GE imaging applications without requiring parallel excitation. The method is expected to improve contrast and sensitivity in GE MRI of human brain at high field.

VERSE-guided numerical RF pulse design: a fast method for peak RF power control

In parallel excitation, the computational speed of numerical radiofrequency (RF) pulse design methods is critical when subject dependencies and system nonidealities need to be incorporated on-the-fly. One important concern with optimization-based methods is high peak RF power exceeding hardware or safety limits. Hence, online controllability of the peak RF power is essential. Variable-rate selective excitation pulse reshaping is ideally suited to this problem due to its simplicity and low computational cost. In this work, we first improve the fidelity of variable-rate selective excitation implementation for discrete-time waveforms through waveform oversampling such that variable-rate selective excitation can be robustly applied to numerically designed RF pulses. Then, a variable-rate selective excitation-guided numerical RF pulse design is suggested as an online RF pulse design framework, aiming to simultaneously control peak RF power and compensate for off-resonance.

Specific absorption rate benefits of including measured electric field interactions in parallel excitation pulse design

Specific absorption rate management and excitation fidelity are key aspects of radiofrequency pulse design for parallel transmission at ultra-high magnetic field strength. The design of radiofrequency pulses for multiple channels is often based on the solution of regularized least-squares optimization problems for which a regularization term is typically selected to control the integrated or peak pulse waveform amplitude. Unlike single-channel transmission, the specific absorption rate of parallel transmission is significantly influenced by interferences between the electric fields associated with the individual transmission elements, which a conventional regularization term does not take into account. This work explores the effects upon specific absorption rate of incorporating experimentally measurable electric field interactions into parallel transmission pulse design. Results of numerical simulations and phantom experiments show that the global specific absorption rate during parallel transmission decreases when electric field interactions are incorporated into pulse design optimization. The results also show that knowledge of electric field interactions enables robust prediction of the net power delivered to the sample or subject by parallel radiofrequency pulses before they are played out on a scanner.

Improved large tip angle parallel transmission pulse design through a perturbation analysis of the Bloch equation

Parallel transmission has emerged as an efficient means for implementing multidimensional spatially selective radiofrequency excitation pulses. To date, most theoretical and experimental work on parallel transmission radiofrequency (RF) pulse design is based on the small-tip-angle approximation to the Bloch equation. The small-tip-angle, while mathematically compact, is not an exact solution and leads to significant errors when large-tip-angle pulses are designed. Methods have been proposed to overcome the limitations of the small-tip-angle using regularized least-square optimization or optimal control algorithms. These methods, however, are based on further approximations to the Bloch equation or require the use of general purpose algorithms that do not capitalize fully on the dynamics of the physical model at hand. In this article, a novel algorithm for large-tip-angle parallel transmission pulse design is proposed. The algorithm relies on a perturbation analysis of the Bloch equation and it depicts the relationship between the excited magnetization, its deviation from the target pattern and the desired pulses. Simulations and experiments are used to validate the proposed method on a 7 T 8-channel transmit array. The results demonstrate that the perturbation analysis algorithm provides a fast and accurate approach for multidimensional large-tip-angle pulse design, especially when large acceleration factors and/or echo-planar trajectories are used.

kT -points: short three-dimensional tailored RF pulses for flip-angle homogenization over an extended volume

With Transmit SENSE, we demonstrate the feasibility of uniformly exciting a volume such as the human brain at 7T through the use of an original minimalist transmit k-space coverage, referred to as "k(T) -points." Radio-frequency energy is deposited only at a limited number of k-space locations in the vicinity of the center to counteract transmit sensitivity inhomogeneities. The resulting nonselective pulses are short and need little energy compared to adiabatic or other B 1+-robust pulses available in the literature, making them good candidates for short-repetition time 3D sequences at high field. Experimental verification was performed on three human volunteers at 7T by means of an 8-channel transmit array system. On average, whereas the standard circularly polarized excitation resulted in a 33%-flip angle spread (standard deviation over mean) throughout the brain, and a static radio-frequency shim showed flip angle variations of 17% and up, application of k(T) -point-based excitations demonstrated excellent flip angle uniformity (8%) for a small target flip angle and with sub-millisecond durations.

Local SAR reduction in parallel excitation based on channel-dependent Tikhonov parameters

PURPOSE

To reduce the local specific absorption rate (SAR) obtained with tailored pulses using parallel transmission while obtaining homogenous flip angle distributions.

MATERIALS AND METHODS

Finite-element simulations on a human head model were performed to obtain the individual magnetic and electric field maps for each channel of a parallel transmit array. From those maps, SAR calculations were carried out for "spoke" pulses designed to homogenize the flip angle in an axial slice of a human brain at 7 T. Based on the assumption that the coil element nearest to the maximum local energy deposition is the dominant contributor to the corresponding hot spot, a set of channel-dependent Tikhonov parameters is optimized. Resulting SAR distributions are compared to the ones obtained when using standard pulse design approaches based on a single Tikhonov parameter.

RESULTS

In both the small- and large-tip-angle domain, the simulations show local SAR reductions by over a factor of 2 (4) for a well-centered (off-centered) head model at the expense of roughly 1% increment in flip-angle spread over the slice.

CONCLUSION

Significant SAR reductions can be obtained by optimizing channel-dependent Tikhonov parameters based on the relation between coil elements and SAR hot spot positions.

Accelerated multidimensional radiofrequency pulse design for parallel transmission using concurrent computation on multiple graphics processing units

Multidimensional radiofrequency (RF) pulses are of current interest because of their promise for improving high-field imaging and for optimizing parallel transmission methods. One major drawback is that the computation time of numerically designed multidimensional RF pulses increases rapidly with their resolution and number of transmitters. This is critical because the construction of multidimensional RF pulses often needs to be in real time. The use of graphics processing units for computations is a recent approach for accelerating image reconstruction applications. We propose the use of graphics processing units for the design of multidimensional RF pulses including the utilization of parallel transmitters. Using a desktop computer with four NVIDIA Tesla C1060 computing processors, we found acceleration factors on the order of 20 for standard eight-transmitter two-dimensional spiral RF pulses with a 64 × 64 excitation resolution and a 10-μsec dwell time. We also show that even greater acceleration factors can be achieved for more complex RF pulses.

An electromagnetic reverse method of coil sensitivity mapping for parallel MRI - theoretical framework

In this paper, a novel sensitivity mapping method is proposed for the image domain parallel MRI (pMRI) technique. Instead of refining raw sensitivity maps by means of conventional image processing operations such as polynomial fitting, the presented method determines coil sensitivity profiles through an iterative optimization process. During the algorithm implementation the optimization cost function is defined as the difference between the raw sensitivity profile and the desired profile. The minimization is governed by the physics of low-frequency electromagnetic and reciprocity theories. The performance of the method was theoretically investigated and compared with that of a traditional polynomial fitting, against a range of system noise levels. It was found that, the new method produces high-fidelity sensitivity profiles with noise amplitudes, measured as root mean square deviation an order of magnitude less than that of the polynomial fitting method. Using the sensitivity profiles generated by our method, SENSE (sensitivity encoding) reconstructions produce significantly less image artefacts than conventional methods. The successful implementation of this method has far-reaching implications that accurate sensitivity mapping is not only important for parallel reconstruction, but also essential for its transmission analogy, such as Transmit SENSE.

B1 and B0 inhomogeneity mitigation in the human brain at 7 T with selective pulses by using average Hamiltonian theory

A novel method based on average Hamiltonian theory to design selective pulses is reported. With this tool, it is first shown how to shape the radiofrequency and gradient pulses to generate a desired rotation matrix, which is independent of the position through the slice of interest. After theoretical examination of the concept, it is applied to the strongly modulating pulses' recipe developed by the same authors and initially designed to be nonselective, to mitigate the amplitude of (excitation) radiofrequency field and amplitude of static (polarizing) field inhomogeneity problems at high field. Two in vivo human brain imaging experiments at 7 T are reported to prove the validity of the technique.

Fast large-tip-angle multidimensional and parallel RF pulse design in MRI

Large-tip-angle multidimensional radio-frequency (RF) pulse design is a difficult problem, due to the nonlinear response of magnetization to applied RF at large tip-angles. In parallel excitation, multidimensional RF pulse design is further complicated by the possibility for transmit field patterns to change between subjects, requiring pulses to be designed rapidly while a subject lies in the scanner. To accelerate pulse design, we introduce a fast version of the optimal control method for large-tip-angle parallel excitation. The new method is based on a novel approach to analytically linearizing the Bloch equation about a large-tip-angle RF pulse, which results in an approximate linear model for the perturbations created by adding a small-tip-angle pulse to a large-tip-angle pulse. The linear model can be evaluated rapidly using nonuniform fast Fourier transforms, and we apply it iteratively to produce a sequence of pulse updates that improve excitation accuracy. We achieve drastic reductions in design time and memory requirements compared to conventional optimal control, while producing pulses of similar accuracy. The new method can also compensate for nonidealities such as main field inhomogeneties.

Time-optimal design for multidimensional and parallel transmit variable-rate selective excitation

Variable-rate selective excitation (VERSE) is a radio frequency (RF) pulse reshaping technique. It is most commonly used to reduce the peak magnitude and specific absorption rate (SAR) of RF pulses by reshaping pulses and gradient waveforms to reduce RF magnitude while preserving excitation profiles. In this work, a general time-optimal VERSE algorithm for multidimensional and parallel transmit pulses is presented. Time optimality is achieved by translating peak RF limits to gradient upper bounds in excitation k-space. The limits are fed into a time-optimal gradient waveform design technique. Effective SAR reduction is achieved by reducing peak RF subject to a fixed pulse length. The presented method is different from other VERSE techniques in that it provides a noniterative time-optimal multidimensional solution, which drastically simplifies VERSE designs. Examples are given for 1D and 2D single channel and 2D parallel transmit pulses.