Fast joint design method for parallel excitation radiofrequency pulse and gradient waveforms considering off-resonance

B1 field map synthesis with generative deep learning used in the design of parallel-transmit RF pulses for ultra-high field MRI

Spoke trajectory parallel transmit (pTX) excitation in ultra-high field MRI enables B₁⁺ inhomogeneities arising from the shortened RF wavelength in biological tissue to be mitigated. To this end, current RF excitation pulse design algorithms either employ the acquisition of field maps with subsequent non-linear optimization or a universal approach applying robust pre-computed pulses. We suggest and evaluate an intermediate method that uses a subset of acquired field maps combined with generative machine learning models to reduce the pulse calibration time while offering more tailored excitation than robust pulses (RP). The possibility of employing image-to-image translation and semantic image synthesis machine learning models based on generative adversarial networks (GANs) to deduce the missing field maps is examined. Additionally, an RF pulse design that employs a predictive machine learning model to find solutions for the non-linear (two-spokes) pulse design problem is investigated. As a proof of concept, we present simulation results obtained with the suggested machine learning approaches that were trained on a limited data-set, acquired in vivo. The achieved excitation homogeneity based on a subset of half of the B₁⁺ maps acquired in the calibration scans and half of the B₁⁺ maps synthesized with GANs is comparable with state of the art pulse design methods when using the full set of calibration data while halving the total calibration time. By employing RP dictionaries or machine-learning RF pulse predictions, the total calibration time can be reduced significantly as these methods take only seconds or milliseconds per slice, respectively.

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.

Simultaneous optimization of radio frequency and gradient waveforms with exact Hessians and slew rate constraints applied to kT-points excitation

We consider an excitation pulse with piecewise constant gradient trajectories and radio frequency (RF) waveforms such that the solution of the Bloch equations without relaxation terms can be represented by rotations. Based on this analytic solution we formulate a non-linear program for finding sub-pulse durations, gradient strengths, and complex RF voltages which minimize the deviation between the achieved and desired magnetization. We develop explicit expressions for the first and second order derivatives of the objective function. We extend the non-linear program to precisely account for gradient slew rate constraints. Using an interior point solver we apply the developed theory to simultaneously optimize the positions of k_T-points, their associated RF voltages and durations.

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.

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.

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.

Joint Design of Excitation k-Space Trajectory and RF Pulse for Small-Tip 3D Tailored Excitation in MRI

We propose a new method for the joint design of k-space trajectory and RF pulse in 3D small-tip tailored excitation. Designing time-varying RF and gradient waveforms for a desired 3D target excitation pattern in MRI poses a non-linear, non-convex, constrained optimization problem with relatively large problem size that is difficult to solve directly. Existing joint pulse design approaches are therefore typically restricted to predefined trajectory types such as EPI or stack-of-spirals that intrinsically satisfy the gradient maximum and slew rate constraints and reduce the problem size (dimensionality) dramatically, but lead to suboptimal excitation accuracy for a given pulse duration. Here we use a 2nd-order B-spline basis that can be fitted to an arbitrary k-space trajectory, and allows the gradient constraints to be implemented efficiently. We show that this allows the joint optimization problem to be solved with quite general k-space trajectories. Starting from an arbitrary initial trajectory, we first approximate the trajectory using B-spline basis, and then optimize the corresponding coefficients. We evaluate our method in simulation using four different k-space initializations: stack-of-spirals, SPINS, KT-points, and a new method based on KT-points. In all cases, our approach leads to substantial improvement in excitation accuracy for a given pulse duration. We also validated our method for inner-volume excitation using phantom experiments. The computation is fast enough for online applications.

Rapid inner-volume imaging in the steady-state with 3D selective excitation and small-tip fast recovery imaging

PURPOSE

Develop a method for rapid three-dimensional inner-volume (IV), or reduced field-of-view, steady-state imaging.

METHODS

Tailored radiofrequency pulses for exciting a three-dimensional IV were designed using a recently proposed algorithm and used in three different sequences: spoiled gradient echo, balanced steady-state free precession, and "small-tip fast recovery" (STFR) which uses a "tip-up" RF pulse after the readout to fast recover spins to the longitudinal axis. The inner- and outer-volume (OV) steady-state signals were analyzed. To demonstrate the potential utility of the proposed method, segmented stack-of-spirals reduced field-of-view images in a volunteer were acquired.

RESULTS

For a given three-dimensional IV excitation pulse, STFR can achieve higher IV/OV signal ratio compared with spoiled gradient echo and balanced steady-state free precession. For spoiled gradient echo and balanced steady-state free precession, this ratio is significantly lower than that produced by a single IV excitation. For STFR, this ratio exceeds that produced by a single IV excitation, due to partial OV saturation produced by the nonspatially selective tip-up pulse. Reduced FOV STFR stack-of-spirals imaging with 2-fold under-sampling in both x-y and z is demonstrated.

CONCLUSION

STFR provides an effective mechanism for OV suppression in steady-state IV imaging. The recently proposed joint pulse design method can be used in the STFR sequence to achieve fast reduced field-of-view imaging. Magn Reson Med 76:1217-1223, 2016. © 2015 Wiley Periodicals, Inc.

Comparison of RF body coils for MRI at 3 T: a simulation study using parallel transmission on various anatomical targets

The performance of multichannel transmit coil layouts and parallel transmission (pTx) RF pulse design was evaluated with respect to transmit B1 (B1 (+)) homogeneity and specific absorption rate (SAR) at 3 T for a whole body coil. Five specific coils were modeled and compared: a 32-rung birdcage body coil (driven either in a fixed quadrature mode or a two-channel transmit mode), two single-ring stripline arrays (with either 8 or 16 elements), and two multi-ring stripline arrays (with two or three identical rings, stacked in the z axis and each comprising eight azimuthally distributed elements). Three anatomical targets were considered, each defined by a 3D volume representative of a meaningful region of interest (ROI) in routine clinical applications. For a given anatomical target, global or local SAR controlled pTx pulses were designed to homogenize RF excitation within the ROI. At the B1 (+) homogeneity achieved by the quadrature driven birdcage design, pTx pulses with multichannel transmit coils achieved up to about eightfold reduction in local and global SAR. When used for imaging head and cervical spine or imaging thoracic spine, the double-ring array outperformed all coils, including the single-ring arrays. While the advantage of the double-ring array became much less pronounced for pelvic imaging, with a substantially larger ROI, the pTx approach still provided significant gains over the quadrature birdcage coil. For all design scenarios, using the three-ring array did not necessarily improve the RF performance. Our results suggest that pTx pulses with multichannel transmit coils can reduce local and global SAR substantially for body coils while attaining improved B1 (+) homogeneity, particularly for a "z-stacked" double-ring design with coil elements arranged on two transaxial rings.

Two-spoke placement optimization under explicit specific absorption rate and power constraints in parallel transmission at ultra-high field

The spokes method combined with parallel transmission is a promising technique to mitigate the B1(+) inhomogeneity at ultra-high field in 2D imaging. To date however, the spokes placement optimization combined with the magnitude least squares pulse design has never been done in direct conjunction with the explicit Specific Absorption Rate (SAR) and hardware constraints. In this work, the joint optimization of 2-spoke trajectories and RF subpulse weights is performed under these constraints explicitly and in the small tip angle regime. The problem is first considerably simplified by making the observation that only the vector between the 2 spokes is relevant in the magnitude least squares cost-function, thereby reducing the size of the parameter space and allowing a more exhaustive search. The algorithm starts from a set of initial k-space candidates and performs in parallel for all of them optimizations of the RF subpulse weights and the k-space locations simultaneously, under explicit SAR and power constraints, using an active-set algorithm. The dimensionality of the spoke placement parameter space being low, the RF pulse performance is computed for every location in k-space to study the robustness of the proposed approach with respect to initialization, by looking at the probability to converge towards a possible global minimum. Moreover, the optimization of the spoke placement is repeated with an increased pulse bandwidth in order to investigate the impact of the constraints on the result. Bloch simulations and in vivo T2(∗)-weighted images acquired at 7 T validate the approach. The algorithm returns simulated normalized root mean square errors systematically smaller than 5% in 10 s.

Steady-state functional MRI using spoiled small-tip fast recovery imaging

PURPOSE

To determine whether a recently proposed steady-state magnetic resonance imaging (MRI) sequence, "small-tip fast recovery" (STFR), can be used for functional brain imaging. Compared to existing functional MRI (fMRI) based on T2*-contrast and long echo time, STFR has the potential for high-resolution imaging with reduced B0 artifacts such as geometric distortions, blurring, or local signal dropout.

METHODS

We used Monte Carlo Bloch simulations to calculate the voxel-averaged steady-state signal during rest and activation, for blood oxygen level dependent (BOLD) and STFR. STFR relies on a tailored "tip-up" radiofrequency pulse to align the spins with the longitudinal axis after each data readout segment, and here we performed proof-of-concept in vivo STFR fMRI experiments using a tip-up pulse tailored to a two-dimensional region-of-interest in motor cortex. Experiments were performed on multiple subjects to test reliability of the functional activation maps.

RESULTS

Bloch simulations predict a detectable functional signal that depends mainly on intravoxel dephasing, and only weakly on spin diffusion. STFR produces similar activation maps and signal change as BOLD in finger-tapping experiments, and shows reliability comparable to BOLD.

CONCLUSION

STFR can produce functional contrast (even with short TE), and is a potential alternative to long-TE ( T2*) fMRI. The functional contrast arises primarily from the interaction between T2*-like dephasing and the tailored tip-up pulse, and not from spin diffusion.

Quadrature transmit array design using single-feed circularly polarized patch antenna for parallel transmission in MR imaging

Quadrature coils are often desired in MR applications because they can improve MR sensitivity and also reduce excitation power. In this work, we propose, for the first time, a quadrature array design strategy for parallel transmission at 298 MHz using single-feed circularly polarized (CP) patch antenna technique. Each array element is a nearly square ring microstrip antenna and is fed at a point on the diagonal of the antenna to generate quadrature magnetic fields. Compared with conventional quadrature coils, the single-feed structure is much simple and compact, making the quadrature coil array design practical. Numerical simulations demonstrate that the decoupling between elements is better than -35 dB for all the elements and the RF fields are homogeneous with deep penetration and quadrature behavior in the area of interest. Bloch equation simulation is also performed to simulate the excitation procedure by using an 8-element quadrature planar patch array to demonstrate its feasibility in parallel transmission at the ultrahigh field of 7 Tesla.

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.

B0-informed variable density trajectory design for enhanced correction of off-resonance effects in parallel transmission

PURPOSE

To improve B1 and B0 inhomogeneity mitigation performance of spatially selective radio-frequency (RF) pulses in parallel transmission while decreasing RF pulse power. Further enhancement of off-resonance correction for rectilinear spoke-trajectory-based RF pulses with known residual geometric distortions after optimization.

METHODS

The appropriate definition of the target magnetization pattern is discussed regarding the maximum physical excitation resolution. Furthermore, a novel variable-density trajectory design is introduced, which subsamples accrued B0 phase error elevations in k-space. A simulation study (echo-planar and spiral 2DRF) at different off-resonance levels and pulse acceleration factors was pursued using data from a whole-body 2-channel parallel transmit 3T MRI system. The new trajectory design for echo-planar 2DRF was validated in human in-vivo experiments.

RESULTS

Proper target pattern definition can require spatial filtering, such that RF pulse optimization is prevented from lower excitation performance with significant higher RF power level. The new trajectory design proposed can considerably improve off-resonance compensation, while further reducing the RF power, e.g., 43% less RMSE with 79% less RF power for spoke based pulses.

CONCLUSION

The proposed methods offer significant improvements of the excitation performance (homogeneity and acceleration), while significantly decreasing the RF power. Furthermore, single-channel transmit RF pulse performance can be similarly improved.