Introduction

In MRI, scan parameters (e.g., TR, FA) are selected for a desired objective by considering properties of interests (e.g., T₁, noises). Previously, a few optimization methods have been utilized to select the scan parameters¹. However, these methods typically require assumptions such as an unbiased network based on noisy measurement, limiting their applications. Recently, deep-learning methods have been proposed to design MRI sequences^{2, 3}, which focus on the development of new sequences, not optimizing sequence parameters of an existing sequence. In this study, we proposed a new automation method that jointly optimizes both sequence parameters and a neural network that extracts information for an objective (AutoSON). This new method allows flexible optimization to any objective (e.g. T₁ mapping, classification of tissues) that can be modeled as a loss function in the network.

Methods

[AutoSON]
AutoSON jointly optimized scan parameters and a neural network (Fig. 1). The MR simulator generated signals corresponding to the scan parameters from a dataset that consists of tissue properties. The neural network utilized the simulated-signals as inputs in order to extract information of a desired objective (e.g., T₁ mapping, tissue classification). The loss function of the neural network was back-propagated to the network parameters and sequence parameters, jointly optimizing the network and the sequence. The network structure was a multi-layer perceptron⁴. The training dataset was constructed for the objective (see Experiment 1-3).

[Experiment 1: T₁ mapping using DESPOT1]
To verify the performance of AutoSON, we utilized DESPOT1⁵, which has a simple analytic signal equation, as a test sequence to optimize scan parameters for T₁ mapping⁶. In DESPOT1, two data with two FAs (α₁, α₂) are utilized. AutoSON optimized these two flip angles to provide high accuracy in T₁ estimation for noise corrupted signals. The input for the network was magnitude signals from the DESPOT1 equation, and the output was a T₁ value. Training signals are generated using the following parameters: T₁=159 ms to 1695ms, T₂=50ms, α₁, α₁=5°-40°, M₀=0.5-1.0, TR/TE=10/5ms, and noise SD=2e-5. L2 loss was utilized. The optimization results were compared with the analytic solutions for T₁=1645ms.

[Experiment 2: Tissue classification using DESPOT1]
To demonstrate flexibility in optimization, the FAs for DESPOT1 were re-optimized to classify white matter and gray matter. The network input was the same but the output was modified to generate gray matter signal as 0 and white matter signal as 1. Two datasets, T₁=1288±67ms and T₂=76±5 ms for gray matter, and T₁=917±32ms and T₂=67±4ms for white matter, were generated with M₀=0.5-1.0, noise SD=1e-3 and initial =25°,20°. The cross-entropy loss was utilized.

[Experiment3: T2 mapping using Partially spoiled SSFP]
To demonstrate that AutoSON can optimize a sequence with no simple analytic form, we optimized phase-based T₂ mapping⁷. This method uses two partially spoiled SSFP images with different RF phase increment. AutoSON optimized 3 parameters: FA, RF phase increment, and TR. The input of the network was the real and imaginary parts of the ratio of two complex signals. The output was a T₂ value. For the training, the dataset was set to be results of M₀, T₁, and T₂ of in-vivo data⁸. Large T₂ (>200 ms; CSF) were excluded. The initial parameters were chosen from Wang et al. (FA=18°, phase increment=2°, TR=10ms). L2 loss was utilized. For MR signal simulator, a numerical simulation using Bloch equation was performed for 500 repetitions for steady-state. The 100 spins were induced a 2π phase dispersion in each repetition. Gaussian noises (SD:2e-4) were added to real and imaginary axes. Evaluation was performed for the scan parameters of AutoSON vs. Wang et al. by using the T₂ mapping method from Wang et al. for a fair comparison of the sequence parameter optimization. The T₂ mapping results of in-vivo data (another subject data from ref.8) were compared using normalized-root-mean-squared error (NRMSE).

Results

Figure 2 shows the optimization results of DESPOT1. When started with various initial points, all results converged to FAs of α₁=2.6±0.0° and α₂=16.5±0.2°. These results are close to the optimum FAs from the analytic equation (α₁=2.6°, α₂=15.1°). For the task of classifying gray and white matter, the results are illustrated in Figure 3. The optimized FAs (α₁=3.2°, α₂=18.6°) were located in-between the optimal angles of white matter (α₁=3.5°, α₂=20.2°) and gray matter (α₁=3.0°, α₂=17.1°), showing reasonable results. As the optimization progresses, the separation of the two signals becomes clear (Figure 3b). The T₂ mapping results are summarized in Figure 4. The optimized scan parameters (FA=74.2°, phase increment=2.4°, TR=6.7ms) yielded reduced NRMSE than the original parameters (NRMSE from 8.6±13.5% to 2.6±3.3%). When the signals are plotted for the two scan parameters (original vs AutoSON), the newly optimized results show a signal separation depending on T_2, demonstrating successful optimization (Figure 5).

Discussion and Conclusion

In this work, a new sequence optimization method that jointly optimizes scan parameters and a neural network was proposed. Our results demonstrates feasibility and some of the results (e.g. T₂ mapping) may not be feasible (FA too large). Still, the proposed method is flexible in its optimization target. The optimization is performed as long as the target can be formulated as a loss function. Additionally, the method does not require any assumptions (e.g. unbiased estimator) and analytic equation, and therefore flexible.

Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2018R1A2B3008445).