Multiband RF pulse design for realistic gradient performance

A magnitude-least-squares radiofrequency pulse design algorithm is reported which uses interleaved exact and stochastically-generated inexact updates to escape local minima and find low-cost solutions. Inexact updates are performed using a small randomly selected minibatch of the available measurements to update RF pulse weights, which perturbs the sequence of alternating projections. Applications to RF shimming, parallel transmit spokes RF pulse design, and spectral-spatial RF pulse design are considered. Numerical and simulation studies characterized the optimal minibatch size, which was found to consistently produce lower power and lower RMSE solutions across subjects, coil geometries, resolutions and orientations. The method was validated in-vivo at 7 Tesla and produced improvements in image quality in a slice-by-slice RF-shimmed imaging sequence. Compared to conventional methods, the pulse design method can more robustly design RF pulses that correct for inhomogeneities at ultra-high field strengths, and enable pulse designs to be completed with increased computational efficiency.

Purpose: Exception gating and dynamic MLC tracking on MRI-gRT systems require segmentation of high temporal resolution images. Multi-band excitation is an emerging MRI acceleration technique that simultaneously excites a short comb of 2D slices, thereby increasing effective temporal resolution. However, the design of multiband RF pulses imposes tradeoffs between slice profiles and the temporal duration of the pulse. The goal of this study was to determine whether slice profiles of shorter duration multiband RF pulses affect organ tracking accuracy for MRI-gRT. Methods: Three-band Shinnar-Le Roux (SLR) RF pulses were designed with slice bandwidths of 1.5kHz and durations ranging from 750 to 3000 µs. The pulses were implemented into a golden angle radial pulse sequence of our own design. Time series of dynamic 2D sagittal cine images of an MRI-compatible dynamic phantom (Model 008M, CIRS) with 2.5 cm superior/inferior target motion were acquired at 3T using each of the RF pulse durations. Images were reconstructed offline in Matlab. The target was contoured on the last image of the time series and tracked through the time series using normalized cross-correlation with a Powell optimizer and B-spline interpolator. Peak-to-peak (P2P) centroid displacements along the superior/inferior dimension were estimated and compared against the phantom motion trajectory. Results: Transition band sizes of the multiband RF slice profiles ranged from 2.1 to 4.6 mm for intended 5 mm slices. P2P centroid displacements ranged from 2.3 to 2.6 cm, demonstrating good agreement with the 2.5 cm phantom displacement, and indicating that slice profile has minimal effect on tracking ability. Conclusion: Slice profile does not affect tracking ability, permitting the use of shorter duration RF pulses to increase temporal resolution during MRI-gRT. Future work will investigate the advantages of multiband excitation for 2D/3D image registration and will combine multiband excitation with in-plane acceleration to further improve temporal resolution. Elekta Instruments, AB

Some advanced RF pulses, like multidimensional RF pulses, are often long and require substantial computation time because of a number of constraints and requirements, sometimes hampering clinical use. However, the pulses offer opportunities of reduced-FOV imaging, regional flip-angle homogenization, and localized spectroscopy, e.g., of hyperpolarized metabolites. Proposed herein is a novel deep learning approach to ultrafast design of multidimensional RF pulses with intention of real-time pulse updates. The proposed neural network considers input maps of the desired excitation region of interest and outputs a single-channel, multidimensional RF pulse. The training library is, e.g., retrieved from a large image database, and the target RF pulses trained upon are calculated with a method of choice. A relatively simple neural network is enough to produce reliable 2D spatial-selective RF pulses of comparable performance to the teaching method. For binary regions of interest, the training library does not need to be vast; hence, reestablishment of the training library is not necessarily cumbersome. The predicted pulses were tested numerically and experimentally at 3 T. Relatively effortless training of multidimensional RF pulses, based on non-MRI-related inputs, but working in an MRI setting still, has been demonstrated. The prediction time of a few milliseconds renders real-time updates of advanced RF pulses possible.

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

Current methods for parallel excitation RF pulse design are based on the small-tip-angle approximation, which provides a computationally efficient means of pulse calculation. In general, pulses designed with those methods are inaccurate when scaled to produce large-tip angles, and methods for large-tip-angle pulse design are more computationally demanding. This paper introduces a fast iterative method for large-tip-angle parallel pulse design that is formulated as a small number of Bloch equation simulations and fast small-tip-angle pulse designs, the results of which add to produce large-tip-angle pulses. Simulations and a phantom experiment demonstrate that the method is effective in designing multidimensional large-tip-angle pulses of high excitation accuracy, compared to pulses designed with small-tip-angle methods.

Equi-ripple design of quadratic-phase RF pulses

Joint design of minimum duration RF pulses and slice-selective gradient shapes for MRI via time optimal control with strict physical constraints, and its application to simultaneous multislice imaging. The minimization of the pulse duration is cast as a time optimal control problem with inequality constraints describing the refocusing quality and physical constraints. It is solved with a bilevel method, where the pulse length is minimized in the upper level, and the constraints are satisfied in the lower level. To address the inherent nonconvexity of the optimization problem, the upper level is enhanced with new heuristics for finding a near global optimizer based on a second optimization problem. A large set of optimized examples shows an average temporal reduction of 87.1% for double diffusion and 74% for turbo spin echo pulses compared to power independent number of slices pulses. The optimized results are validated on a 3T scanner with phantom measurements. The presented design method computes minimum duration RF pulse and slice-selective gradient shapes subject to physical constraints. The shorter pulse duration can be used to decrease the effective echo time in existing echo-planar imaging or echo spacing in turbo spin echo sequences.

We propose and evaluate multiphoton parallel transmission (MP-pTx) to mitigate flip angle inhomogeneities in high-field MRI. MP-pTx is an excitation method that utilizes a single, conventional birdcage coil supplemented with low-frequency (kHz) irradiation from a multichannel shim array and/or gradient channels. SAR analysis is simplified to that of a conventional birdcage coil, because only the radiofrequency (RF) field from the birdcage coil produces significant SAR. MP-pTx employs an off-resonance RF pulse from a conventional birdcage coil supplemented with oscillating -directed fields from a multichannel shim array and/or the gradient coils. We simulate the ability of MP-pTx to create uniform nonselective brain excitations at 7 T using realistic and field maps. The RF, shim array, and gradient waveform's amplitudes and phases are optimized using a genetic algorithm followed by sequential quadratic programming. A 1 ms MP-pTx excitation using a 32-channel shim array with current constrained to less than 50 Amp-turns reduced the transverse magnetization's normalized root-mean-squared error from 29% for a conventional birdcage excitation to 6.6% and was nearly 40% better than a 1 ms birdcage coil 5 kT-point excitation with optimized kT-point locations and comparable pulse power. The MP-pTx method resembles conventional pTx in its goals and approach but replaces the parallel RF channels with cheaper, low-frequency shim channels. The method mitigates high-field flip angle inhomogeneities to a level better than 3 T CP-mode and comparable to 7 T pTx while retaining the straightforward SAR characteristics of conventional birdcage excitations, as low-frequency shim array fields produce negligible SAR.

Develop a general radiofrequency (RF) pulse design algorithm for the design of three-dimensional (3D) spatially selective refocusing pulses and explore their potential applications in reduced field-of-view imaging. Spin-domain representation was used to describe the effect of RF pulses and to formulate the optimization problem. The implementation was based on an auto-differentiable simulator. Spatially selective excitation and refocusing pulses for a small regions of interest were designed with consideration of hardware limits and B0 and B1 + inhomogeneities. The designed RF pulses were validated in simulation as well as in vivo experiments in brain and prostate on a 3T scanner. Pulses of short duration (4.15 ms) were designed for 3D tailored excitation and refocusing accounting for B0 and B1 + inhomogeneities. The computation time for each design was approximately 7 min. Improved outer-volume signal suppression in phantom and in vivo spin-echo imaging experiments was achieved by combining 3D excitation and refocusing pulses compared with using only one 3D pulse. The potential of using tailored 3D pulses to obtain images with higher spatial resolution (1 1 3 mm3) and less distortion with the same scan time was demonstrated by acquiring reduced field-of-view 3D images of brain and prostate. The proposed algorithm jointly optimizes the RF and gradient waveforms given an initial pulse and a desired spin-domain target pattern. Our approach is broadly applicable to the design of excitation and refocusing pulses and complements existing methods based on describing individual spin isochromatic behavior. Combining 3D excitation and 3D refocusing pulses produced better spatial selectivity than using a combination of one-dimensional and 3D pulses.

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.

Improving excitation and inversion accuracy by optimized RF pulse using genetic algorithm

Multi-Slice T2-weighted MR imaging is a fundamental technique in brain imaging but suffers from field inhomogeneities at ultra-high field systems. In this work we present a pulse design method which provides slab-selective universal pulses with phase-coherent excitation profiles over selected brain regions. Applied in a 3D variable flip angle turbo-spin-echo (TSE) sequence, the pulses achieve superior SNR compared to multi-slice TSE imaging and B1 + field inhomogeneity mitigation.

Pulsed selective excitation theory and design in multiphoton MRI

This paper proposes a new pulse design method to improve spectrum utilization rate and reduce the outage probability in ultra wide band (UWB) system. Several third derivative Gaussian waveforms are employed to generate the pulse based on the bandwidth constraint set by the US Federal Communications Commission (FCC) mask. The genetic algorithm (GA) is used to find the optimal pulse parameter. This method is an easy way to achieve in practical circuit implementation compared to one pulse generator, since COMS circuit is hard to produce one pulse with short duration and complex pulse shape. Comparisons with the traditional Gaussian pulse, the synthesis pulse by GA not only satisfy the FCC emission mask but also have high spectrum utilization rate. Simulation results show that the performances in indoor UWB system using the synthesis pulse by GA is better than that using traditional Gaussian pulse. Numerical results show that the synthesis pulse by GA is higher 30 percent of spectrum utilization rate and lower 65 percent of outage probability for the same transmission power, as well as lower 21 percent of outage probability for fixed signal-to-noise ratio (SNR)at the receiver comparing with traditional Gaussian pulse. This proposed method not only use in indoor UWB system but also can extend to different communication system just changing the system object function.

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.