Introduction

In quantitative MRI, parameters (e.g., T₁, T₂, B₁, ΔB₀, etc.) are typically estimated by dictionary matching¹ or deep learning^2-4. Both methods require a substantial time (~days; depending on # of parameters, range, resolution, etc) for the generation of precomputed MR signals from discretely dividing parameters either for the dictionary or network training, which may not be a big burden because it needs to be generated (and trained) once. In dynamic imaging (e.g., cardiac imaging using MRF with gating and sequence optimization), however, data for dictionary or network training may need to be regenerated for different scan parameters, hindering its applications.³ These dictionary generation or deep-learning training explores the whole search space and, therefore, has unnecessity, considering parameters under investigation often has limited variability. In this study, we propose a novel parameter mapping method with a highly reduced computation by using AI-guiding dictionary learning to search the expected target properties (Fig. 1).

Methods

Active dictionary learning trains a neural network for parameter estimation by active dataset generation based on the target MR signals to reduce unnecessary simulation. The efficient training was performed using an active learning approach, which is learning a rough problem space with a few initial training data and then adaptively generating data for additional training.⁵ To explore potential parameters, a probabilistic network model was utilized, which was autoregressive flow.⁶

[Active learning]
Our network was trained progressively by iterations of data recommendation and training (Fig. 2a). At first, the network is trained with a small size of a randomly generated dataset. After that, the inference was performed for a target signal, producing putative parameters as output. Then, these outputs were randomly sampled by using estimation quality from the autoregressive model for data recommendation. Finally, these sampled outputs were applied to the simulator to generate corresponding signals which were utilized for network training. As this process repeated, the estimation results became more accurate and the whole process worked as a coarse-to-fine search (Fig. 2b).

[Experiments]
For demonstration of the whole quantification process from dictionary generation stage, a FISP MRF sequence⁷ was used to estimate for M₀, T₁, T₂, B₁, and ΔB₀. The MRF simulation was conducted with extended phase graph (EPG) with GPU acceleration.⁸
The target MR signals were generated by voxel-wise simulation using M₀, T₁, and T₂ mapping results from in-vivo data. Additionally, gaussian-shaped B₁ and horizontal-striped ΔB₀ were assumed. MR signals were corrupted by Gaussian noise. The total size of the target data was 542,381 voxels with mean SNR of 7.
For comparison, dictionary matching results and computational time were calculated. The dictionary matching was performed in both cases using a full dictionary and a compressed dictionary by SVD compression⁹ to 100 values on different B1 values. The dictionary ranges were T₁=[20:20:3000, 3000:200:5000] ms, T₂=[10:5:300, 300:50:500, 500:200:2000] ms, B₁=0.7:0.05:1.3, and ΔB₀=-200:10:200 Hz, resulting in a total of 5,099,120 atoms.^2,6,10

Experiment 1: For validation, the proposed method was tested for B1 and ΔB0 range from 0.7 to 1.2 and from -200 to 200 Hz, respectively.
Experiment 2: To demonstrate the adaptive estimation of the proposed method, the parameters were out of ranges from Experiment 1: B1 from 1.2 to 1.7 and ΔB0 from 0 to 400 Hz.
Experiment 3: A computationally expensive signal model with 64 points of a slice profile was evaluated. In this setting, dictionary generation using the model took over 1 month in our environment, therefore, the same dictionary with Experiments 1-2 was used.

For active dictionary learning, initial training data were randomly generated in the same ranges as the dictionary. The target signals were normalized to have standard deviations of 0.1. The number of initial data was 20,000, the additional dataset per iteration was 2,000, and the data addition process was repeated 20 times.
All experiments were conducted with i7-9800X CPU and an Nvidia TITAN Xp GPU.

Results

In Experiment 1 (Fig. 3), the proposed active dictionary learning showed successful estimation of the parameters using only 60,000 simulations. The performance was comparable to the full dictionary matching while taking only 30 min for the entire process (ours: 30 min for whole process; Full dictionary matching: 6 hours for generation and 36 hours for matching; SVD-compressed dictionary matching: 6.5 hours for generation and 3 hours for matching). In Experiment 2, out method demonstrated successful adaptation to the out-of-initial parameters range (Fig. 4). Experiment 3 also demonstrate successful estimations with much higher accuracy than the conventional method, while taking only 3 hours despite the need for simulating the slice profile (Fig. 5).

Discussion and Conclusion

In this work, a novel parameter mapping method, active dictionary learning, is proposed for fast and adaptive mapping of parameters. This method may be valuable for dynamic imaging such as cardiac MRF, which changes the scan parameters for each subject, requiring dictionary generation for each case and, therefore, taking substantial computation and time when the conventional method is used. Additionally, our adaptation to out-of-range parameters indicates benefit in imaging targets of unknown or unexpected parameter ranges. Similar to the dictionary methods requiring only one time of generation, our method may be further improved or reused by pretraining the network to expected target range data, reducing the iteration time.

Acknowledgements

This work has been supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2022R1A4A1030579 and No. NRF-2019M3C7A1031994).