Super-resolution Y-Net for simultaneous ¹H MRF/²³Na MRI

Introduction

Sodium (²³Na) MRI can reveal valuable metabolic information¹. However, its low natural abundance in the human body and low gyromagnetic ratio practically prohibits the acquisition of high-resolution (HR) ²³Na images. Therefore, developing post-processing methods to increase sodium resolution is critical for translating sodium MRI into clinical practice. In this work, we introduce a Y-Net super-resolution method that generates HR sodium images from simultaneously acquired ¹H MRF/²³Na MRI data².

Methods

Dataset

The method was tested on simultaneously-acquired low-resolution (LR) sodium and HR proton density, T₁ and T₂ maps². The images were acquired at 7T (MAGNETOM, Siemens) using an in-house developed 16-channel-Tx/Rx dual-tuned head coil³. Eight volunteers were scanned (2 females, 32±12 years old) after informed consent, in accordance with the relevant institutional and national guidelines.

The 3D simultaneous ¹H MRF/²³Na MRI sequence² parameters were: FOV 240´240´280 mm³,¹H 160´160´56/²³Na 84´84´56 matrix, ¹H 1.5´1.5´5/²³Na 2.85´2.85´5 mm³ resolution, ¹H 7.5ms/²³Na 15ms TR, 30º constant FA for ²³Na, pulse train of 500 FAs for ¹H, 1 slab, 6 shots per slab, ¹H full radial/²³Na center-out radial trajectories, scan time 21 min. Ground truth HR ²³Na images were acquired using a 3D stack-of-stars GRE sequence, with the acquisition parameters adjusted to match the LR ²³Na image contrast (2 averages, and scan time 42 min). The resolution ratio between the HR and LR is 1.9 in both in-plane directions.

Y-Net super-resolution

The Y-Net is a deep convolutional neural network architecture like a U-Net but with two encoder paths⁴. It is composed of two contracting paths, an expanding path, and skip connections that allow the network to retain low-level features. We modified the Y-Net to use multi-contrast images in the ¹H path and only sodium density in the ²³Na path. Additionally, a second Y-Net was cascaded to the first one to refine the result, taking as input the ²³Na output from the first Y-Net and the ¹H images.

The network was trained using 160×160 ¹H images and ²³Na images interpolated to match the ¹H images as input and 160×160 ²³Na images as targets. The images from 7 healthy volunteers (22 images per volunteer) were augmented using rotation and additive Gaussian noise, generating a set of 1540 images used for training (1386) and validation (154). The dataset from volunteer #8 was used for testing (19). The network was trained using AdamW with a learning rate of 0.01, decreasing by 20% every 10 epochs for a total of 300 epochs. The loss function used was the structural-similarity-index-measure (SSIM)⁵. Fig.1 shows a schematic diagram of the network architecture.

The performance of the method was compared with a super-resolution method based on partial-least-squares-regression⁶ (PLS) and with bi-cubic interpolation.

Methods evaluation

To evaluate the method’s performance, the SSIM, the root-mean-square error (RMSE), and the peak-signal-to-noise ratio (PSNR) between ground truth and generated HR ²³Na images were computed over the 3D volume of volunteer #8.

Results & Discussion

Fig. 2 shows the center slice of the initial ¹H and ²³Na data acquired with 3D simultaneous ¹H MRF/²³Na MRI and the ground truth HR ²³Na acquired with 3D stack-of-stars GRE. Fig. 3 shows the acquired LR and HR (ground truth) ²³Na images, the generated HR ²³Na images, and the differences between ground truth and the generated HR images for the four central slices of volunteer #8 (test dataset). Fig. 4 shows the comparison between the Y-Net, PLS and bi-cubic interpolation methods for the central slice of volunteer #8. Table 1 shows the statistical parameters calculated for each method over the 3D volume.

The results for the Y-Net over 3D volume of the test subject show a SSIM=0.935, RMSE=0.034, and PSNR=28.8. The results from the PLS method are SSIM=0.916, RMSE=0.040, and PSNR=28.0 and for the bi-cubic interpolation SSIM=0.928, RMSE=0.058, and PSNR=24.3. The Y-Net outperforms both methods for all the statistical parameters, with a small difference in the RMSE and PSNR compared with the PLS method.

Although the PLS method does not need any training, it takes a long time to be executed (≈616s), while the Y-Net running on a regular CPU takes ≈51s. Even with the high computational cost of training the Y-Net, the difference in running time can potentially allow for online implementation. When running the Y-Net on a A100 GPU, the prediction time falls to ≈1.2s.

Conclusion

We introduced a super-resolution Y-Net method to generate HR ²³Na images. The final HR sodium image showed high similarity to the HR sodium ground truth image (SSIM=0.935). The performance of the Y-Net method was found superior to the performance of the bi-cubic interpolation and the super-resolution PLS method⁶.

References

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