Introduction

In MR imaging, a high specific absorption rate (SAR) of a radiofrequency (RF) pulse is a significant problem in clinical use, particularly for high field systems. To reduce SAR, a variable-rate selective excitation (VERSE) method, which remaps uniform slice-selective gradient into the time-varying gradient, was introduced¹. As reported, however, VERSE pulses are vulnerable to off-resonance frequency, limiting the applicability of the method. Recently, deep reinforcement learning (DRL)-powered RF pulse design has been proposed, demonstrating improved performance in SAR^2,3. In this work, we extended the dimension of the design space in DeepRF³ to include both RF pulse and slice-selective gradient waveform (G_z). This new method is named DeepRF-Grad (Fig 1) and is tested to generate i) SAR-reduced design and ii) SAR-reduced and off-resonance robust design, while satisfying hardware constraints (i.e., gradient slew rate and max gradient limits).

Methods

For a conventional RF pulse, a slice-selective linear-phase inversion pulse is designed using Shinnar-Le-Roux (SLR)^4,5. The parameters are as follows: pulse duration = 3.873 ms, time-bandwidth product = 2.711, stopband ripple = 1%, and passband ripple = 1%. This pulse is redesigned using the VERSE algorithm to reduce SAR⁶.
In DeepRF-Grad, the pulse duration is the same and the ripple conditions are designed to match the conventional RF pulse. The design process of DeepRF-Grad is as follows: first, magnitude and phase parts of the RF pulse and slice selective gradient waveform (G_z) are simultaneously designed using DRL (3x256 points). Secondly, these designs are jointly updated using gradient descent until they converged to an optimal point (Fig 2).
To design a slice-selective inversion pulse while regularizing SAR, the reward of DRL is devised as follows:
$$reward=-\frac{1}{N}\sum_{z_p\in{Z_{pass}}}M_z(RF,G_z,z_p)+\frac{1}{M}\sum_{z_s\in{Z_{stop}}}M_z(RF,G_z,z_s)-c_{SAR}SAR$$
where N (= 24) is the number of z-positions in the passband (Z_pass), and M (= 86) is the number of z-positions in the stopband (Z_stop), M_z is the longitudinal magnetization, and c_SAR (= 0.3) is a coefficient for the SAR regularizer term. Each training of the DRL agent consists of 1000 epochs. After training, RF pulses and G_z generated with the top 1000 highest rewards are selected as seeds for the second part of DeepRF-Grad, gradient descent.
The objective of the gradient descent step is to match the slice profile to that of the SLR-designed result while minimizing SAR and keeping the slew rate under the limit. Two types of designs are developed: i) SAR minimized design with off-resonance sensitivity comparable to that of VERSE, and ii) off-resonance robust design with reduced SAR. The loss function, which is minimized via gradient descent, is designed as follows:
$$loss=\sum_{w_o\in{W}}\parallel{M_z(RF,G)-M_z(SLR)}\parallel+c_1SAR+c_2\sum_{i=1}^{256}u(slew_i-slew_{max})$$
where w_o means off-resonance frequencies, c₁ and c₂ are coefficients, u is a unit step function, slew_i is a gradient slew rate for each time step, slew_max is the slew rate limit (= 170 mT/(m*ms)). The off-resonance frequencies are included only for the off-resonance robust design. The derivatives of the loss function with respect to each of the RF pulse and G_z are computed via automatic differentiation. The gradient descent is repeated until the RF pulse and G_z converge.
The SLR, VERSE, DeepRF, and DeepRF-Grad designs are evaluated in terms of their slice profile and SAR. Additionally, the slice profiles of the VERSE and DeepRF-Grad designs are compared at two additional off-resonance frequencies (200 Hz, and 400 Hz). For a fair comparison, a VERSE designed pulse that has a similar SAR to the DeepRF-Grad pulse is produced. Lastly, an additional DeepRF-Grad design is produced for a low slew rate condition (135 mT/(m*ms); 20% lower slew rate), comparing for the SAR and slice profile.

Results

[SAR minimized design]
The SARs of the four designs are 13.2mG²s for SLR, 6.37 mG²s for VERSE, 11.3mG²s for DeepRF, and 5.00 mG²s for DeepRF-Grad, demonstrating a reduction of 62% in SAR when comparing the DeepRF-Grad result with that of SLR (Fig. 3). The slice profiles (last column in Fig. 3) reveal comparable results in all designs. In DeepRF-Grad, the mean Mz in the passband is -0.97 (SLR: -0.99), and the stopband ripple is 1.19% (SLR: 0.21%). No hardware constraint is violated. When the off-resonance profiles are compared, both VERSE and DeepRF-Grad results show similar profiles (Fig. 3e).
[Off-resonance robust design]
The SARs are 8.81mG²s for DeepRF-Grad, and 8.40 mG²s for VERSE. Figure 4 illustrates the VERSE and off-resonance robust DeepRF-Grad designs with similar SAR. DeepRF-Grad reveals an improved off-resonance profile, particularly at a high off-resonance frequency (400Hz).

Conclusion and Discussion

In this study, we propose a deep learning method that simultaneously designs RF pulse and slice-selective gradient waveform. The results show that DeepRF-Grad can reduce SAR by 62% when compared to the SLR pulse. Additionally, DeepRF-Grad can be utilized to design an off-resonance robust RF/Gz design that has 35% lower SAR than the SLR pulse. Since DeepRF-Grad designed gradient shows a high slew rate at the edges, an eddy-current-induced artifact could exist. This may be mitigated by setting a lower limit to the slew rate, which resulted in a similar pulse while maintaining SAR reduction performance (60% reduction) (Fig. 5).

Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF- 2018R1A2B3008445), and Brain Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2019M3C7A1031994).