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

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.

Advanced design of MRI inversion pulses for inhomogeneous field conditions by optimal control

Non-selective inversion pulses find widespread use in MRI applications, where requirements on them are increasingly demanding. With the use of high and ultra-high field strength systems, robustness to Δ B 0 and B 1 + inhomogeneities, while tackling SAR and hardware limitations, has rapidly become important. In this work, we propose a time-optimal control framework for the optimization of Δ B 0 - and B 1 + -robust inversion pulses. Robustness is addressed by means of ensemble formulations, while allowing inclusion of hardware and energy limitations. The framework is flexible and performs excellently for various optimization goals. The optimization results are analyzed extensively in numerical experiments. Furthermore, they are validated, and compared with adiabatic RF pulses, in various phantom and in vivo measurements on a 3 T MRI system.

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.

Joint Design of RF and Gradient Waveforms via Auto-differentiation for 3D Tailored Excitation in MRI

This paper proposes a new method for joint design of radiofrequency (RF) and gradient waveforms in Magnetic Resonance Imaging (MRI), and applies it to the design of 3D spatially tailored saturation and inversion pulses. The joint design of both waveforms is characterized by the ODE Bloch equations, to which there is no known direct solution. Existing approaches therefore typically rely on simplified problem formulations based on, e.g., the small-tip approximation or constraining the gradient waveforms to particular shapes, and often apply only to specific objective functions for a narrow set of design goals (e.g., ignoring hardware constraints). This paper develops and exploits an auto-differentiable Bloch simulator to directly compute Jacobians of the (Bloch-simulated) excitation pattern with respect to RF and gradient waveforms. This approach is compatible with arbitrary sub-differentiable loss functions, and optimizes the RF and gradients directly without restricting the waveform shapes. For computational efficiency, we derive and implement explicit Bloch simulator Jacobians (approximately halving computation time and memory usage). To enforce hardware limits (peak RF, gradient, and slew rate), we use a change of variables that makes the 3D pulse design problem effectively unconstrained; we then optimize the resulting problem directly using the proposed auto-differentiation framework. We demonstrate our approach with two kinds of 3D excitation pulses that cannot be easily designed with conventional approaches: Outer-volume saturation (90° flip angle), and inner-volume inversion.

Accuracy and performance analysis for Bloch and Bloch-McConnell simulation methods

PURPOSE

To introduce new solution methods for the Bloch and Bloch-McConnell equations and compare them quantitatively to different known approaches.

THEORY AND METHODS

A new exact solution per time step is derived by means of eigenvalues and generalized eigenvectors. Fast numerical solution methods based on asymmetric and symmetric operator splitting, which are already known for the Bloch equations, are extended to the Bloch-McConnell equations. Those methods are compared to other numerical methods including spin domain, one-step and multi-step methods, and matrix exponential. Error metrics are introduced based on the exact solution method, which allows to assess the accuracy of each solution method quantitatively for arbitrary example data.

RESULTS

Accuracy and performance properties for nine different solution methods are analyzed and compared in extensive numerical experiments including various examples for non-selective and slice-selective MR imaging applications. The accuracy of the methods heavily varies, in particular for short relaxation times and long pulse durations.

CONCLUSION

In absence of relaxation effects, the numerical results confirm the rotation matrices approach as accurate and computationally efficient Bloch solution method. Otherwise, as well as for the Bloch-McConnell equations, symmetric operator splitting methods are recommended due to their excellent numerical accuracy paired with efficient run time.

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.

No need to detune transmitters in 32-channel receiver arrays at 7 T

Ultrahigh field magnetic resonance imaging facilitates high spatiotemporal resolution that benefits from increasing the number of receiver elements. Because high-density receiver arrays have a relatively small element size compared with the transmitter, a side effect is that such setups cause low flux coupling between the transmitter and receiver. Moreover, when transmitters are designed in a multitransmit configuration, their relative size is much smaller than the sample, reducing coupling to the sample and thereby potentially also the coupling to the receivers. Transmitters are traditionally detuned during reception. In this study, we investigate, for a 32-channel receiver head array at 7 T, if transmitter detuning of a quadrature birdcage or of an eight-channel transmit coil can be omitted without substantially sacrificing signal-to-noise ratio (SNR). The transmit elements are operated once with and once without detuning and, in the latter, the received signals are either merged with the array or excluded for image reconstruction. For each of the three measurements, SNR and 1/g-factor maps are investigated. The tuning of the quadrature and eight-channel transmit coils during signal reception introduced a 10.1% and 6.5% penalty in SNR, respectively, relative to the SNR received with detuned transmitters. When also incorporating the signal of the transmit coils, the SNR was regained to 98.5% or 101.4% for the quadrature and eight-channel coil, respectively, relative to the detuned transmitters, while the 1/g-factor maps improved slightly. For the 32-channel receive coil used the SNR penalty can become negligible when omitting detuning of the transmit coils. This not only simplifies transmit coil designs, potentially increasing their efficiency, but also enables the transmitters to be used as receivers in parallel to the receiver array, thus increasing parallel imaging performance.

Multi-task convolutional neural network-based design of radio frequency pulse and the accompanying gradients for magnetic resonance imaging

Modern MRI systems usually load the predesigned RFs and the accompanying gradients during clinical scans, with minimal adaption to the specific requirements of each scan. Here, we describe a neural network-based method for real-time design of excitation RF pulses and the accompanying gradients' waveforms to achieve spatially two-dimensional selectivity. Nine thousand sets of radio frequency (RF) and gradient waveforms with two-dimensional spatial selectivity were generated as the training dataset using the Shinnar-Le Roux (SLR) method. Neural networks were created and trained with five strategies (TS-1 to TS-5). The neural network-designed RF and gradients were compared with their SLR-designed counterparts and underwent Bloch simulation and phantom imaging to investigate their performances in spin manipulations. We demonstrate a convolutional neural network (TS-5) with multi-task learning to yield both the RF pulses and the accompanying two channels of gradient waveforms that comply with the SLR design, and these design results also provide excitation spatial profiles comparable with SLR pulses in both simulation (normalized root mean square error [NRMSE] of 0.0075 ± 0.0038 over the 400 sets of testing data between TS-5 and SLR) and phantom imaging. The output RF and gradient waveforms between the neural network and SLR methods were also compared, and the joint NRMSE, with both RF and the two channels of gradient waveforms considered, was 0.0098 ± 0.0024 between TS-5 and SLR. The RF and gradients were generated on a commercially available workstation, which took ~130 ms for TS-5. In conclusion, we present a convolutional neural network with multi-task learning, trained with SLR transformation pairs, that is capable of simultaneously generating RF and two channels of gradient waveforms, given the desired spatially two-dimensional excitation profiles.

Application of Evolution Strategies to the Design of SAR Efficient Parallel Transmit Multi-Spoke Pulses for Ultra-High Field MRI

We present an evolution-strategy based approach to solve the magnitude least squares (MLS) design problem of low flip-angle slice-selective parallel transmit RF pulses for ultra-high field MRI using SAR and peak-RF-constraints. A combined transmit k-space trajectory and RF pulse weight optimization is proposed in two algorithmic steps. The first step is a coarse grid search to find an initial solution that fulfills all constraints for the subsequent multistage optimization. This avoids convergence to the next nearest local minimum. The second step attempts to refine the results using multiple evolution strategies. We compare the performance of our approach with the non-convex optimization methods described in the literature. The proposed algorithm converges for phantom and in vivo data and only requires an initial estimate of the range of suitable regularization parameters. It demonstrates improved excitation homogeneity compared to published spoke-design methods and allows optimization for homogeneity with a subsequent reduction in the SAR burden. Moreover, excitation homogeneity and the SAR burden can be balanced against each other, enabling a further reduction in SAR at the cost of minor relaxations in excitation homogeneity. This feature makes the algorithm a good candidate for SAR limited sequences in ultra-high field imaging. The algorithm is validated using phantom and in vivo measurements obtained with a 16-channel transmit array at 9.4T.

Global and peak local specific absorption rate control on parallel transmit systems using k-means SAR compression model

PURPOSE

To improve the specific absorption rate (SAR) compression model capability in parallel transmission (pTx) MRI systems.

METHODS

A k-means clustering method is proposed to group voxels with similar SAR behaviors in the scanned object, providing a controlled upper-bounded estimation of peak local SARs. This k-means compression model and the conventional virtual observation point (VOP) model were tested in a pTx MRI framework. The pTx pulse design with different SAR controlling schemes was simulated using a numerical human head model and an eight-channel 7T coil array. Multiple criteria (including RF power, global and peak local SARs, and excitation accuracy) were compared for the performance testing.

RESULTS

The k-means compression model generated a narrower overestimation bound, leading to a more accurate local SAR estimation. Among different pTx pulse design approaches, the k-means compression model showed the best trade-off between the SAR and excitation accuracy.

CONCLUSIONS

The developed SAR compression model is advantageous for pTx framework given the narrower overestimation bound and control over the compression ratio. Results also illustrate that a moderate increase of maximum RF power can be useful for reducing the maximum local SAR deposition.

Universal nonselective excitation and refocusing pulses with improved robustness to off-resonance for Magnetic Resonance Imaging at 7 Tesla with parallel transmission

PURPOSE

In MRI at ultra-high field, the k T -point and spiral nonselective (SPINS) pulse design techniques can be advantageously combined with the parallel transmission (pTX) and universal pulse techniques to create uniform excitation in a calibration-free manner. However, in these approaches, pulse duration is typically increased as compared to standard hard pulses, and excitation quality in regions exhibiting large resonance frequency offsets often suffer. This limitation is inherent to structure of k T -point or SPINS pulse, and likely can be mitigated using parameterization-free pulse design approaches.

METHODS

The Gradient Ascent Pulse Engineering (GRAPE) algorithm was used to design parameterization-free RF and magnetic field gradient (MFG) waveforms for creating 8 ∘ excitation, up to 105 ∘ scalable refocusing and inversion, nonselectively across the brain. Simulations were performed to provide flip angle normalized root-mean-squares error (FA-NRMSE) estimations for the 8 ∘ and the 180 ∘ k T -point, SPINS, and GRAPE pulses. GRAPE pulses were tested experimentally with anatomical head scans at 7T.

RESULTS

As compared to k T -points and SPINS, GRAPE provided substantial improvement of excitation, refocusing, and inversion quality at off-resonance while at least preserving the same global FA-NRMSE performance. As compared to k T -points, GRAPE allowed for a substantial reduction of the pulse duration for the 8 ∘ excitation and the 105 ∘ refocusing.

CONCLUSIONS

Parameterization-free universal nonselective pTX-pulses were successfully computed using GRAPE. Performance gains as compared to k T -points were validated numerically and experimentally for three imaging protocols. In its current implementation, the computational burden of GRAPE limits its use to applications where pulse computations are not subject to time constraints.

Solving the Time- and Frequency-Multiplexed Problem of Constrained Radiofrequency Induced Hyperthermia

Targeted radiofrequency (RF) heating induced hyperthermia has a wide range of applications, ranging from adjunct anti-cancer treatment to localized release of drugs. Focal RF heating is usually approached using time-consuming nonconvex optimization procedures or approximations, which significantly hampers its application. To address this limitation, this work presents an algorithm that recasts the problem as a semidefinite program and quickly solves it to global optimality, even for very large (human voxel) models. The target region and a desired RF power deposition pattern as well as constraints can be freely defined on a voxel level, and the optimum application RF frequencies and time-multiplexed RF excitations are automatically determined. 2D and 3D example applications conducted for test objects containing pure water (r_target = 19 mm, frequency range: 500–2000 MHz) and for human brain models including brain tumors of various size (r₁ = 20 mm, r₂ = 30 mm, frequency range 100–1000 MHz) and locations (center, off-center, disjoint) demonstrate the applicability and capabilities of the proposed approach. Due to its high performance, the algorithm can solve typical clinical problems in a few seconds, making the presented approach ideally suited for interactive hyperthermia treatment planning, thermal dose and safety management, and the design, rapid evaluation, and comparison of RF applicator configurations.

Multiple-Input Multiple-Output (MIMO) MRI: Combining Parallel Excitation and Parallel Reception for Enhanced Imaging

Magnetic resonance imaging (MRI) plays a critical role in visualizing the structure and functions of the human body. In order to accelerate imaging time and improve image quality, radio-frequency (RF) coil receive arrays are commonly employed to acquire the magnetic resonance (MR) signal. Similarly, multiple transmit coils have been shown to accelerate and refine RF excitation. In this work, we investigate the optimization of total imaging time and image accuracy when considering both the transmit and receive coil arrays; we term this strategy multiple-input multiple-output (MIMO) MRI. Our RF pulse design method is modeled by minimizing the excitation errors while simultaneously maximizing the signal-to-noise ratio (SNR) of the reconstructed MR image. It further allows a key tradeoff between the two optimizers. Additionally, multiple acceleration factors, varying numbers of receive coils used, maximum excitation error tolerance, and different excitation patterns are simulated and analyzed in this model. For a given excitation pattern, our method is shown to improve the SNR by 18-130% under certain acceleration schemes, as compared to conventional parallel transmission methods, while simultaneously controlling the excitation error within a desired scope (NRMSE ≤ 0.12).

A simplified framework to optimize MRI contrast preparation

PURPOSE

This article proposes a rigorous optimal control framework for the design of preparation schemes that optimize MRI contrast based on relaxation time differences.

METHODS

Compared to previous optimal contrast preparation schemes, a drastic reduction of the optimization parameter number is performed. The preparation scheme is defined as a combination of several block pulses whose flip angles, phase terms and inter-pulse delays are optimized to control the magnetization evolution.

RESULTS

The proposed approach reduces the computation time of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>B</mml:mi> <mml:mn>0</mml:mn></mml:msub> </mml:math> -robust preparation schemes to around a minute (whereas several hours were required with previous schemes), with negligible performance loss. The chosen parameterization allows to formulate the total preparation duration as a constraint, which improves the overall compromise between contrast performance and preparation time. Simulation, in vitro and in vivo results validate this improvement, illustrate the straightforward applicability of the proposed approach, and point out its flexibility in terms of achievable contrasts. Major improvement is especially achieved for short-T₂ enhancement, as shown by the acquisition of a non-trivial contrast on a rat brain, where a short-T₂ white matter structure (corpus callosum) is enhanced compared to surrounding gray matter tissues (hippocampus and neocortex).

CONCLUSIONS

This approach proposes key advances for the design of optimal contrast preparation sequences, that emphasize their ability to generate non-standard contrasts, their potential benefit in a clinical context, and their straightforward applicability on any MR system.

Constant gradient elastography with optimal control RF pulses

This article presents a new motion encoding strategy to perform magnetic resonance elastography (MRE). Instead of using standard motion encoding gradients, a tailored RF pulse is designed to simultaneously perform selective excitation and motion encoding in presence of a constant gradient. The RF pulse is designed with a numerical optimal control algorithm, in order to obtain a magnetization phase distribution that depends on the displacement characteristics inside each voxel. As a consequence, no post-excitation encoding gradients are required. This offers numerous advantages, such as reducing eddy current artifacts, and relaxing the constraint on the gradients maximum switch rate. It also allows to perform MRE with ultra-short TE acquisition schemes, which limits T₂ decay and optimizes signal-to-noise ratio. The pulse design strategy is developed and analytically analyzed to clarify the encoding mechanism. Finally, simulations, phantom and ex vivo experiments show that phase-to-noise ratios are improved when compared to standard MRE encoding strategies.

Rotation relaxation splitting for optimizing parallel RF excitation pulses with T1- and T2-relaxations in MRI

Exact solutions of the Bloch equations with T₁- and T₂-relaxation terms for piecewise constant magnetic fields are numerically challenging. We therefore investigate an approximation for the achieved magnetization in which rotations and relaxations are split into separate operations. We develop an estimate for its accuracy and explicit first and second order derivatives with respect to the complex excitation radio frequency voltages. In practice, the deviation between an exact solution of the Bloch equations and this rotation relaxation splitting approximation seems negligible. Its computation times are similar to exact solutions without relaxation terms. We apply the developed theory to numerically optimize radio frequency excitation waveforms with T₁- and T₂-relaxations in several examples.

Boosting the SNR by adding a receive-only endorectal monopole to an external antenna array for high-resolution, T2 -weighted imaging of early-stage cervical cancer with 7-T MRI

The aim of this study was to investigate the signal-to-noise ratio (SNR) gain in early-stage cervical cancer at ultrahigh-field MRI (e.g. 7 T) using a combination of multiple external antennas and a single endorectal antenna. In particular, we used an endorectal monopole antenna to increase the SNR in cervical magnetic resonance imaging (MRI). This should allow high-resolution, T₂ -weighted imaging and magnetic resonance spectroscopy (MRS) for metabolic staging, which could facilitate the local tumor status assessment. In a prospective feasibility study, five healthy female volunteers and six patients with histologically proven stage IB1-IIB cervical cancer were scanned at 7 T. We used seven external fractionated dipole antennas for transmit-receive (transceive) and an endorectally placed monopole antenna for reception only. A region of interest, containing both normal cervix and tumor tissue, was selected for the SNR measurement. Separated signal and noise measurements were obtained in the region of the cervix for each element and in the near field of the monopole antenna (radius < 30 mm) to calculate the SNR gain of the endorectal antenna in each patient. We obtained high-resolution, T₂ -weighted images with a voxel size of 0.7 × 0.8 × 3.0 mm³ . In four cases with optimal placement of the endorectal antenna (verified on the T₂ -weighted images), a mean gain of 2.2 in SNR was obtained at the overall cervix and tumor tissue area. Within a radius of 30 mm from the monopole antenna, a mean SNR gain of 3.7 was achieved in the four optimal cases. Overlap between the two different regions of the SNR calculations was around 24%. We have demonstrated that the use of an endorectal monopole antenna substantially increases the SNR of 7-T MRI at the cervical anatomy. Combined with the intrinsically high SNR of ultrahigh-field MRI, this gain may be employed to obtain metabolic information using MRS and to enhance spatial resolutions to assess tumor invasion.

Optimal control design of preparation pulses for contrast optimization in MRI

This work investigates the use of MRI radio-frequency (RF) pulses designed within the framework of optimal control theory for image contrast optimization. The magnetization evolution is modeled with Bloch equations, which defines a dynamic system that can be controlled via the application of the Pontryagin Maximum Principle (PMP). This framework allows the computation of optimal RF pulses that bring the magnetization to a given state to obtain the desired contrast after acquisition. Creating contrast through the optimal manipulation of Bloch equations is a new way of handling contrast in MRI, which can explore the theoretical limits of the system. Simulation experiments carried out on-resonance quantify the contrast improvement when compared to standard T₁ or T₂ weighting strategies. The use of optimal pulses is also validated for the first time in both in vitro and in vivo experiments on a small-animal 4.7T MR system. Results demonstrate their robustness to static field inhomogeneities as well as the fact that they can be embedded in standard imaging sequences without affecting standard parameters such as slice selection or echo type. In vivo results on rat and mouse brains illustrate the ability of optimal contrast pulses to create non-trivial contrasts on well-studied structures (white matter versus gray matter).

Local SAR, global SAR, and power-constrained large-flip-angle pulses with optimal control and virtual observation points

PURPOSE

To present a constrained optimal-control (OC) framework for designing large-flip-angle parallel-transmit (pTx) pulses satisfying hardware peak-power as well as regulatory local and global specific-absorption-rate (SAR) limits. The application is 2D and 3D spatial-selective 90° and 180° pulses.

THEORY AND METHODS

The OC gradient-ascent-pulse-engineering method with exact gradients and the limited-memory Broyden-Fletcher-Goldfarb-Shanno method is proposed. Local SAR is constrained by the virtual-observation-points method. Two numerical models facilitated the optimizations, a torso at 3 T and a head at 7 T, both in eight-channel pTx coils and acceleration-factors up to 4.

RESULTS

The proposed approach yielded excellent flip-angle distributions. Enforcing the local-SAR constraint, as opposed to peak power alone, reduced the local SAR 7 and 5-fold with the 2D torso excitation and inversion pulse, respectively. The root-mean-square errors of the magnetization profiles increased less than 5% with the acceleration factor of 4.

CONCLUSION

A local and global SAR, and peak-power constrained OC large-flip-angle pTx pulse design was presented, and numerically validated for 2D and 3D spatial-selective 90° and 180° pulses at 3 T and 7 T. Magn Reson Med 77:374-384, 2017. © 2015 Wiley Periodicals, Inc.

In vivo demonstration of whole-brain multislice multispoke parallel transmit radiofrequency pulse design in the small and large flip angle regimes at 7 Tesla

PURPOSE

A multispoke specific absorption rate (SAR) -aware pulse design approach for homogeneous multiple-slice small and large flip angle (FA) excitations with parallel transmission is proposed. The approach aims at optimizing in a slice-specific manner the spokes locations and radiofrequency pulses.

METHODS

The problem is posed as a set of slice-specific magnitude-least-squares problems, linked together by hardware and SAR constraints, and solved jointly using an active-set algorithm. Average Hamiltonian theory is exploited in the large FA case to greatly reduce the computational burden. The approach is validated numerically by means of simulations and experimentally on two volunteers at 7 Tesla through application of a high-resolution T2*-weighted brain imaging protocol.

RESULTS

The optimization of up to 1300 variables under 745 explicit constraints could be performed in less than 1 and 4 min for the small and large FA cases, respectively. The joint design proves valuable for SAR demanding protocols. Compared with the conventional circularly polarized mode, the designed pulses increased the signal by more than 40% in 70% of the voxels.

CONCLUSION

The B1+ inhomogeneity problem was mitigated efficiently in a multislice near whole-brain coverage protocol in the small and large FA regimes using a rapid slice-specific pulse design algorithm where the pulses were optimized jointly. Magn Reson Med 78:1009-1019, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Toward imaging the body at 10.5 tesla

PURPOSE

To explore the potential of performing body imaging at 10.5 Tesla (T) compared with 7.0T through evaluating the transmit/receive performance of similarly configured dipole antenna arrays.

METHODS

Fractionated dipole antenna elements for 10.5T body imaging were designed and evaluated using numerical simulations. Transmit performance of antenna arrays inside the prostate, kidneys and heart were investigated and compared with those at 7.0T using both phase-only radiofrequency (RF) shimming and multi-spoke pulses. Signal-to-noise ratio (SNR) comparisons were also performed. A 10-channel antenna array was constructed to image the abdomen of a swine at 10.5T. Numerical methods were validated with phantom studies at both field strengths.

RESULTS

Similar power efficiencies were observed inside target organs with phase-only shimming, but RF nonuniformity was significantly higher at 10.5T. Spokes RF pulses allowed similar transmit performance with accompanying local specific absorption rate increases of 25-90% compared with 7.0T. Relative SNR gains inside the target anatomies were calculated to be >two-fold higher at 10.5T, and 2.2-fold SNR gain was measured in a phantom. Gradient echo and fast spin echo imaging demonstrated the feasibility of body imaging at 10.5T with the designed array.

CONCLUSION

While comparable power efficiencies can be achieved using dipole antenna arrays with static shimming at 10.5T; increasing RF nonuniformities underscore the need for efficient, robust, and safe parallel transmission methods. Magn Reson Med 77:434-443, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

gr-MRI: A software package for magnetic resonance imaging using software defined radios

The goal of this work is to develop software that enables the rapid implementation of custom MRI spectrometers using commercially-available software defined radios (SDRs). The developed gr-MRI software package comprises a set of Python scripts, flowgraphs, and signal generation and recording blocks for GNU Radio, an open-source SDR software package that is widely used in communications research. gr-MRI implements basic event sequencing functionality, and tools for system calibrations, multi-radio synchronization, and MR signal processing and image reconstruction. It includes four pulse sequences: a single-pulse sequence to record free induction signals, a gradient-recalled echo imaging sequence, a spin echo imaging sequence, and an inversion recovery spin echo imaging sequence. The sequences were used to perform phantom imaging scans with a 0.5Tesla tabletop MRI scanner and two commercially-available SDRs. One SDR was used for RF excitation and reception, and the other for gradient pulse generation. The total SDR hardware cost was approximately $2000. The frequency of radio desynchronization events and the frequency with which the software recovered from those events was also measured, and the SDR's ability to generate frequency-swept RF waveforms was validated and compared to the scanner's commercial spectrometer. The spin echo images geometrically matched those acquired using the commercial spectrometer, with no unexpected distortions. Desynchronization events were more likely to occur at the very beginning of an imaging scan, but were nearly eliminated if the user invoked the sequence for a short period before beginning data recording. The SDR produced a 500kHz bandwidth frequency-swept pulse with high fidelity, while the commercial spectrometer produced a waveform with large frequency spike errors. In conclusion, the developed gr-MRI software can be used to develop high-fidelity, low-cost custom MRI spectrometers using commercially-available SDRs.

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.

Toward 20 T magnetic resonance for human brain studies: opportunities for discovery and neuroscience rationale

An initiative to design and build magnetic resonance imaging (MRI) and spectroscopy (MRS) instruments at 14 T and beyond to 20 T has been underway since 2012. This initiative has been supported by 22 interested participants from the USA and Europe, of which 15 are authors of this review. Advances in high temperature superconductor materials, advances in cryocooling engineering, prospects for non-persistent mode stable magnets, and experiences gained from large-bore, high-field magnet engineering for the nuclear fusion endeavors support the feasibility of a human brain MRI and MRS system with 1 ppm homogeneity over at least a 16-cm diameter volume and a bore size of 68 cm. Twelve neuroscience opportunities are presented as well as an analysis of the biophysical and physiological effects to be investigated before exposing human subjects to the high fields of 14 T and beyond.

Joint design of large-tip-angle parallel RF pulses and blipped gradient trajectories

PURPOSE

To design multichannel large-tip-angle kT-points and spokes radiofrequency (RF) pulses and gradient waveforms for transmit field inhomogeneity compensation in high field magnetic resonance imaging.

THEORY AND METHODS

An algorithm to design RF subpulse weights and gradient blip areas is proposed to minimize a magnitude least-squares cost function that measures the difference between realized and desired state parameters in the spin domain, and penalizes integrated RF power. The minimization problem is solved iteratively with interleaved target phase updates, RF subpulse weights updates using the conjugate gradient method with optimal control-based derivatives, and gradient blip area updates using the conjugate gradient method. Two-channel parallel transmit simulations and experiments were conducted in phantoms and human subjects at 7 T to demonstrate the method and compare it to small-tip-angle-designed pulses and circularly polarized excitations.

RESULTS

The proposed algorithm designed more homogeneous and accurate 180° inversion and refocusing pulses than other methods. It also designed large-tip-angle pulses on multiple frequency bands with independent and joint phase relaxation. Pulses designed by the method improved specificity and contrast-to-noise ratio in a finger-tapping spin echo blood oxygen level dependent functional magnetic resonance imaging study, compared with circularly polarized mode refocusing.

CONCLUSION

A joint RF and gradient waveform design algorithm was proposed and validated to improve large-tip-angle inversion and refocusing at ultrahigh field.

Efficient high-resolution RF pulse design applied to simultaneous multi-slice excitation

RF pulse design via optimal control is typically based on gradient and quasi-Newton approaches and therefore suffers from slow convergence. We present a flexible and highly efficient method that uses exact second-order information within a globally convergent trust-region CG-Newton method to yield an improved convergence rate. The approach is applied to the design of RF pulses for single- and simultaneous multi-slice (SMS) excitation and validated using phantom and in vivo experiments on a 3T scanner using a modified gradient echo sequence.

Balanced SSFP-like steady-state imaging using small-tip fast recovery with a spectral prewinding pulse

PURPOSE

Small-tip fast recovery (STFR) imaging has been proposed recently as a potential alternative to balanced steady-state free precession (bSSFP). STFR relies on a tailored "tip-up" radio-frequency pulse to achieve comparable signal level as bSSFP, but with reduced banding artifacts and transient oscillations, and is compatible with magnetization-preparation pulses. Previous STFR implementations used two-dimensional or three-dimensional pulses spatially tailored to the accumulated phase calculated from a B0 field map, making the steady-state STFR signal contain some T2* weighting. Here, we propose to replace the spatially tailored pulse with a recently introduced spectrally selective "pre-winding" pulse that is precomputed to a target frequency range. The proposed "spectral-STFR" sequence produces T2/T1-weighted images similar to bSSFP, but with reduced banding and potentially other benefits.

THEORY AND METHODS

We investigated the steady-state signal properties of spectral-STFR using simulations, and phantom and human volunteer experiments.

RESULTS

Our simulation and experimental results showed that the spectral-STFR sequence has similar signal level and tissue contrast as bSSFP, but has a wider passband and more consistent banding profiles across different tissues (e.g., less hyperintense signal at band edges for low flip angles). Care is needed in designing the spectral radio-frequency pulse to ensure that the small tip angle approximation holds during radio-frequency transmission.

CONCLUSION

Spectral-STFR has similar tissue contrast as bSSFP but a wider passband and more consistent cerebrospinal fluid/brain tissue contrast across the passband. The spectral-STFR sequence is a potential alternative to bSSFP in some applications. Compared to a spatially tailored STFR sequence, spectral-STFR can be precomputed, is easier to implement in practice, and potentially has more uniform image contrast and minimal T2* weighting.

Joint design of kT-points trajectories and RF pulses under explicit SAR and power constraints in the large flip angle regime

In Magnetic Resonance Imaging at ultra-high field, kT-points radiofrequency pulses combined with parallel transmission are a promising technique to mitigate the B1 field inhomogeneity in 3D imaging applications. The optimization of the corresponding k-space trajectory for its slice-selective counterpart, i.e. the spokes method, has been shown in various studies to be very valuable but also dependent on the hardware and specific absorption rate constraints. Due to the larger number of degrees of freedom than for spokes excitations, joint design techniques based on the fine discretization (gridding) of the parameter space become hardly tractable for kT-points pulses. In this article, we thus investigate the simultaneous optimization of the 3D blipped k-space trajectory and of the kT-points RF pulses, using a magnitude least squares cost-function, with explicit constraints and in the large flip angle regime. A second-order active-set algorithm is employed due to its demonstrated success and robustness in similar problems. An analysis of global optimality and of the structure of the returned trajectories is proposed. The improvement provided by the k-space trajectory optimization is validated experimentally by measuring the flip angle on a spherical water phantom at 7T and via Quantum Process Tomography.

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.

Multichannel compressive sensing MRI using noiselet encoding

The incoherence between measurement and sparsifying transform matrices and the restricted isometry property (RIP) of measurement matrix are two of the key factors in determining the performance of compressive sensing (CS). In CS-MRI, the randomly under-sampled Fourier matrix is used as the measurement matrix and the wavelet transform is usually used as sparsifying transform matrix. However, the incoherence between the randomly under-sampled Fourier matrix and the wavelet matrix is not optimal, which can deteriorate the performance of CS-MRI. Using the mathematical result that noiselets are maximally incoherent with wavelets, this paper introduces the noiselet unitary bases as the measurement matrix to improve the incoherence and RIP in CS-MRI. Based on an empirical RIP analysis that compares the multichannel noiselet and multichannel Fourier measurement matrices in CS-MRI, we propose a multichannel compressive sensing (MCS) framework to take the advantage of multichannel data acquisition used in MRI scanners. Simulations are presented in the MCS framework to compare the performance of noiselet encoding reconstructions and Fourier encoding reconstructions at different acceleration factors. The comparisons indicate that multichannel noiselet measurement matrix has better RIP than that of its Fourier counterpart, and that noiselet encoded MCS-MRI outperforms Fourier encoded MCS-MRI in preserving image resolution and can achieve higher acceleration factors. To demonstrate the feasibility of the proposed noiselet encoding scheme, a pulse sequences with tailored spatially selective RF excitation pulses was designed and implemented on a 3T scanner to acquire the data in the noiselet domain from a phantom and a human brain. The results indicate that noislet encoding preserves image resolution better than Fouirer encoding.

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.

Design of multidimensional Shinnar-Le Roux radiofrequency pulses

PURPOSE

To generalize the conventional Shinnar-Le Roux method for the design of multidimensional radiofrequency pulses.

METHODS

Using echo-planar gradients, the multidimensional radiofrequency pulse design problem was converted into a series of one-dimensional polynomial design problems. Each of the one-dimensional polynomial design problems was solved efficiently. B0 inhomogeneity compensation and design of spatial-spectral pulses were also considered.

RESULTS

The proposed method was used to design two-dimensional excitation and refocusing pulses. The results were validated through Bloch equation simulation and experiments on a 3.0 T scanner. Large-tip-angle, equiripple-error, multidimensional excitation was achieved with ripple levels closely matching the design specifications.

CONCLUSION

The conventional Shinnar-Le Roux method can be extended to design multidimensional radiofrequency pulses. The proposed method achieves almost equiripple excitation errors, allows easy control of the tradeoff among design parameters, and is computationally efficient.

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.

Dynamic nuclear polarization and optimal control spatial-selective 13C MRI and MRS

Aimed at (13)C metabolic magnetic resonance imaging (MRI) and spectroscopy (MRS) applications, we demonstrate that dynamic nuclear polarization (DNP) may be combined with optimal control 2D spatial selection to simultaneously obtain high sensitivity and well-defined spatial restriction. This is achieved through the development of spatial-selective single-shot spiral-readout MRI and MRS experiments combined with dynamic nuclear polarization hyperpolarized [1-(13)C]pyruvate on a 4.7 T pre-clinical MR scanner. The method stands out from related techniques by facilitating anatomic shaped region-of-interest (ROI) single metabolite signals available for higher image resolution or single-peak spectra. The 2D spatial-selective rf pulses were designed using a novel Krotov-based optimal control approach capable of iteratively fast providing successful pulse sequences in the absence of qualified initial guesses. The technique may be important for early detection of abnormal metabolism, monitoring disease progression, and drug research.

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.

PexLoc-Parallel excitation using local encoding magnetic fields with nonlinear and nonbijective spatial profiles

With the recent proposal of using magnetic fields that are nonlinear by design for spatial encoding, new flexibility has been introduced to MR imaging. The new degrees of freedom in shaping the spatially encoding magnetic fields (SEMs) can be used to locally adapt the imaging resolution to features of the imaged object, e.g., anatomical structures, to reduce peripheral nerve stimulation during in vivo experiments or to increase the gradient switching speed by reducing the inductance of the coils producing the SEMs and thus accelerate the imaging process. In this work, the potential of nonlinear and nonbijective SEMs for spatial encoding during transmission in multidimensional spatially selective excitation is explored. Methods for multidimensional spatially selective excitation radiofrequency pulse design based on nonlinear encoding fields are introduced, and it is shown how encoding ambiguities can be resolved using parallel transmission. In simulations and phantom experiments, the feasibility of selective excitation using nonlinear, nonbijective SEMs is demonstrated, and it is shown that the spatial resolution with which the target distribution of the transverse magnetization can be realized varies locally. Thus, the resolution of the target pattern can be increased in some regions compared with conventional linear encoding. Furthermore, experimental proof of principle of accelerated two-dimensional spatially selective excitation using nonlinear SEMs is provided in this study.

Field shaping arrays: a means to address shading in high field breast MRI

PURPOSE

To develop a simple correction approach to mitigate shading in 3 Tesla (T) breast MRI.

MATERIALS AND METHODS

A slightly modified breast receive (Rx) array, which we termed field shaping array (FSA), was shown to mitigate breast shading at 3T. In this FSA, one Rx element was selectively unblocked and tuned off the Larmor frequency during the transmit (Tx) phase. The current flowing in this element during Tx created a secondary transmit field; the vector addition of this field and the one created directly by the body coil resulted in a more uniform excitation profile over the entire breast area. The receive Rx element was returned to its intended tuning during the Rx phase, ensuring unperturbed signal reception.

RESULTS

Using the FSA, improved Tx field uniformity, better fat suppression, increased image homogeneity and reduced power deposition was seen in all volunteers studied.

CONCLUSION

A simple modification of a standard breast Rx array, converting it to a field shaping array, was shown to mitigate breast shading in all volunteers studied.

Local SAR in parallel transmission pulse design

The management of local and global power deposition in human subjects (specific absorption rate, SAR) is a fundamental constraint to the application of parallel transmission (pTx) systems. Even though the pTx and single channel have to meet the same SAR requirements, the complex behavior of the spatial distribution of local SAR for transmission arrays poses problems that are not encountered in conventional single-channel systems and places additional requirements on pTx radio frequency pulse design. We propose a pTx pulse design method which builds on recent work to capture the spatial distribution of local SAR in numerical tissue models in a compressed parameterization in order to incorporate local SAR constraints within computation times that accommodate pTx pulse design during an in vivo magnetic resonance imaging scan. Additionally, the algorithm yields a protocol-specific ultimate peak in local SAR, which is shown to bound the achievable peak local SAR for a given excitation profile fidelity. The performance of the approach was demonstrated using a numerical human head model and a 7 Tesla eight-channel transmit array. The method reduced peak local 10 g SAR by 14-66% for slice-selective pTx excitations and 2D selective pTx excitations compared to a pTx pulse design constrained only by global SAR. The primary tradeoff incurred for reducing peak local SAR was an increase in global SAR, up to 34% for the evaluated examples, which is favorable in cases where local SAR constraints dominate the pulse applications.

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.

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.

Nonuniform and multidimensional Shinnar-Le Roux RF pulse design method

The Shinnar-Le Roux (SLR) radiofrequency (RF) pulse design algorithm is widely used for designing slice-selective RF pulses due to its intuitiveness, optimality, and speed. SLR is limited, however, in that it is only capable of designing one-dimensional pulses played along constant gradients. We present a nonuniform SLR RF pulse design framework that extends most of the capabilities of classical SLR to nonuniform gradient trajectories and multiple dimensions. Specifically, like classical SLR, the new method is a hard pulse approximation-based technique that uses filter design relationships to produce the lowest power RF pulse that satisfies target magnetization ripple levels. The new method is validated and compared with methods conventionally used for nonuniform and multidimensional large-tip-angle RF pulse design.

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.

Minimum envelope roughness pulse design for reduced amplifier distortion in parallel excitation

Parallel excitation uses multiple transmit channels and coils, each driven by independent waveforms, to afford the pulse designer an additional spatial encoding mechanism that complements gradient encoding. In contrast to parallel reception, parallel excitation requires individual power amplifiers for each transmit channel, which can be cost prohibitive. Several groups have explored the use of low-cost power amplifiers for parallel excitation; however, such amplifiers commonly exhibit nonlinear memory effects that distort radio frequency pulses. This is especially true for pulses with rapidly varying envelopes, which are common in parallel excitation. To overcome this problem, we introduce a technique for parallel excitation pulse design that yields pulses with smoother envelopes. We demonstrate experimentally that pulses designed with the new technique suffer less amplifier distortion than unregularized pulses and pulses designed with conventional regularization.