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

Bayesian optimization of gradient trajectory for parallel-transmit pulse design

PURPOSE

Spoke pulses improve excitation homogeneity in parallel-transmit MRI. We propose an efficient global optimization algorithm, Bayesian optimization of gradient trajectory (BOGAT), for single-slice and simultaneous multislice imaging.

THEORY AND METHODS

BOGAT adds an outer loop to optimize kT-space positions. For each position, the RF coefficients are optimized (e.g., with magnitude least squares) and the cost function evaluated. Bayesian optimization progressively estimates the cost function. It automatically chooses the kT-space positions to sample, to achieve fast convergence, often coming close to the globally optimal spoke positions. We investigated the typical features of spokes cost functions by a grid search with field maps comprising 85 slabs from 14 volunteers. We tested BOGAT in this database, and prospectively in a phantom and in vivo. We compared the vendor-provided Fourier transform approach with the same magnitude least squares RF optimizer.

RESULTS

The cost function is nonconvex and seen empirically to be piecewise smooth with discontinuities where the underlying RF optimum changes sharply. BOGAT converged to within 10% of the global minimum cost within 30 iterations in 93% of slices in our database. BOGAT achieved up to 56% lower flip angle RMS error (RMSE) or 55% lower pulse energy in phantoms versus the Fourier transform approach, and up to 30% lower RMSE and 29% lower energy in vivo with 7.8 s extra computation.

CONCLUSION

BOGAT efficiently estimated near-global optimum spoke positions for the two-spoke tests, reducing flip-angle RMSE and/or pulse energy in a computation time (˜10 s), which is suitable for online optimization.

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

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

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.

Robust RF shimming and small-tip-angle multispoke pulse design with finite-difference regularization

PURPOSE

A new regularizer is proposed for the magnitude least-squares optimization algorithm, to ensure robust parallel transmit RF shimming and small-tip-angle multispoke pulse designs for ultrahigh-field MRI.

METHODS

A finite-difference regularization term is activated as an additional regularizer in the iterative magnitude-least-squares based pulse design algorithm when an unwanted flip angle null distribution is detected. Both simulated and experimental B 1 + maps from different transmit arrays and different human subjects at 7 T were used to evaluate the proposed algorithm. The algorithm was further demonstrated in experiment with dynamic multislice RF shimming for a single-shot gradient-echo EPI for human functional MRI at 7 T.

RESULTS

The proposed finite-difference regularizer effectively prevented excitation null to be formed for RF shimming and small-tip-angle multispoke pulses, and improved the latter with a monotonic trade-off relationship between flip angle error and RF power. The proposed algorithm was demonstrated to be effective with several head-array geometries by simulation and with a commercial head array with 12 healthy human subjects by experiment. During a functional MRI scan at 7 T with dynamic RF shimming, the proposed algorithm ensured high image SNR throughout the human brain, compared with near-complete local signal loss by the conventional magnitude-least-squares algorithm.

CONCLUSION

Using finite-difference regularization to avoid unwanted solutions, the robustness of RF shimming and small-tip-angle multispoke pulse design algorithms are improved, with better flip angle homogeneity and a monotonic trade-off relationship between flip angle error and RF power.