Synopsis

Keywords: Pulse Sequence Design, Machine Learning/Artificial Intelligence

DeepRF¹ is a recently proposed RF pulse design method^2-5 using deep reinforcement learning and optimization, generating an RF pulse defined by a reward (e.g., slice profile and energy constraint) from self-learning. Here, we proposed an improved algorithm for DeepRF that incorporates a modulation function to design an simultaneous multislice⁶ RF pulse. The new algorithm is tested and compared with the original multiband⁹ pulses, reporting reduced RF energy while preserving the characteristics of the original slice profile. Additionally, a multiPINS⁸ like inversion pulse is designed to demonstrate the usefulness of DeepRF for a non-constant slice selective gradient.

Introduction

Simultaneous multislice (SMS) imaging⁶, which acquires multiple slices simultaneously, is widely used in MR imaging to reduce the scan time. Despite this advantage, SMS RF pulses have higher RF energy deposition compared to single-slice pulses, suffering from a high specific absorption rate (SAR). A recently proposed deep reinforcement learning (DRL)-powered RF design method, DeepRF¹, has successfully designed diverse types of RF pulses with reduced RF energy (ENG). DeepRF is able to design various type of pulses because the algorithm is driven only by a user-defined reward that includes slice profile specifications and RF energy. In this work, we utilize DeepRF to design a simultaneous multislice RF design pulse. To improve the performance, we propose to incorporate a modulation function in the RF generation step of DeepRF. Multiband (MB) factors 2 and 3 pulses are designed. Additionally, a multiPINS–like inversion pulse is designed to demonstrate the usefulness of DeepRF for a non-constant slice selective gradient.

Methods

Conventional RF pulse design
The SMS inversion pulses are designed using multiband⁷ (MB factor = 2, 3) and multiPINS⁸ (MB factor = 3). For the multiband RF pulse with MB = 2, the parameters are as follows: pulse duration = 2.36 ms, time-bandwidth product = 1.94, slice thickness = 0.3 mm. The parameters for the multiband RF pulse with MB = 3 are as follows: pulse duration = 3.0 ms, time-bandwidth product = 1.3, and slice thickness = 0.3 mm. For the multiPINS RF pulse (MB =3), the parameters are pulse duration = 2.10 ms, time-bandwidth product = 1.3, and slice thickness = 0.3 mm.

SMS pulse design using DeepRF
DeepRF consists of two steps: The DRL step designing a large number of seed RFs and the gradient descent step optimizing top-scored seed pulses for performance improvement. For the multiband-like pulse design, we added a modulation function into the DRL step: When the DRL agent designs the magnitude and phase of an RF pulse, the RF pulse is translated to the complex domain and the pre-defined modulation function is multiplied (Fig 1a). The pre-defined modulation function is determined by the sum of sinusoidal functions whose frequencies ($$$f_{mod}$$$ ) are of which the modulation frequency of the original multiband pulse ($$$cos(f_{mod}t)$$$; $$$f_{mod}=2\pi\gamma G_{ss}z$$$ where $$$G_{ss}$$$: slice selection gradient and $$$z$$$: physical offset). To measure the effect size of modulation function, another RF pulse is also designed using the original DeepRF without a modulation function. For the multiPINS-like pulse design, DeepRF is used with the zig-zag slice-selective gradient of the multiPINS pulse instead of a uniform gradient (Fig 1b). An RF energy term and $$$L_2$$$ loss of $$$M_z$$$ between the designed RF and original SMS are used as a reward function for all pulse designs. The target inversion frequency range is -13000 Hz to 13000 Hz, excluding the frequency range out of field-of-view (don’t care region). DeepRF is implemented using PyTorch¹⁰ in Nvidia RTX 8000 GPUs (Nvidia Corp., Santa Clara, CA).

Ablation study: Optimizing original RF pulse using gradient descent
To illustrate the necessity of the DRL step of DeepRF, an ablation study is carried out. The conventional method-designed RF pulses are further optimized using gradient descent. The reward functions, which are minimized via gradient descent, are the same as those of DeepRF.

Results

For the multiband-like pulses, DeepRF with modulation function results show the ENG reduction of 4.5% and 4.4% for MB = 2 and MB = 3, respectively with comparable or slightly degraded slice profiles when compared to the multiband pulses. The RF pulses designed by DeepRF with no modulation function show slightly increased ENG and more degraded slice profiles, demonstrating the advantages of applying the modulation functions in DeepRF. On the other hand, the multiband RF pulses with optimization using gradient descent do not show substantial reductions in ENG (Figs. 2, 3).
In Figure 4, the results of the multiPINS-like RF pulse design are shown. The RF ENG of DeepRF and optimized multiPINS RF pulses with gradient descent report a reduction of 11.9% and 4.2% for DeepRF and multiPINS with gradient descent, respectively when compared to the conventional multiPINS pulse, demonstrating the advantage of DeepRF. The slice profiles are similar but DeepRF shows a slightly increased stopband ripple.

Conclusion and Discussion

In this study, we modified DeepRF to design simultaneous-multislice inversion RF pulses. The results showed that designing multiband- and multiPINS-like RF pulses with reduced energy is possible using DeepRF. Adding the modulation function into the DeepRF algorithm seems to help to reduce the computational complexity of DeepRF, producing better results. However, the original DeepRF results still show similar-shaped pulses despite the fact that DeepRF had no knowledge of the multiband- or multiPINS RF pulses. In the slice profiles, DeepRF and DeepRF with modulation designed pulses had additional ripples in the don’t care region, which may be the origin of the degree of freedom in DeepRF. The slight degradation of the slice profiles was difficult to control both in DeepRF and conventional methods because they are at the boundary of the condition (e.g., maximum of TBW). DeepRF may be applied to design other types of RF pulse such as parallel transmit pulses, that have more degree of freedom for optimization.

Acknowledgements

This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. NRF-2022R1A4A1030579) and BK21 FOUR program of the Education and Research Program for Future ICT Pioneers, Seoul National University.

References

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