Introduction

Sodium (²³Na) MRI has been proposed as a means to gain unique information about brain physiology in vivo¹. Sodium MRI in the human brain is, however, difficult due to the lower average brain tissue sodium concentration and the challenging NMR properties of the ²³Na nucleus, which include a lower gyromagnetic ratio, and fast biexponential relaxation behavior. These NMR properties limit the maximum resolution and Signal-to-Noise Ratio (SNR) that can be achieved using conventional image reconstruction means. To address these challenges, iterative Anatomically-Guided Reconstructions (AGR) have been used, resulting in higher SNR and spatial resolution at the expense of long (>1 hour) image reconstruction times². In this work, we demonstrate the use of conventional and AGR sodium images for training a Convolutional Neural Network (CNN) to perform AGR reconstructions in a very short computational time (seconds). Our results indicate that convolutional neural networks can quickly and accurately approximate sodium AGR reconstructions, which could enable the use of high-resolution sodium MRI in clinical environments.

Methods

Iterative ²³Na AGR reconstruction requires the solution of the following non-linear optimization problem for sodium data acquired at two different echo times:$$L = \frac{1}{2}\bigg\lVert\overline{S}_{TE1}(\rho,\Gamma)-S_{TE1}\bigg\rVert^2_2+\frac{1}{2}\bigg\lVert\overline{S}_{TE2}(\rho,\Gamma)-S_{TE2}\bigg\rVert^2_2+\beta_pR_{Bow}(\rho,\Theta)+\beta_{\Gamma}R_{Bow}(\Gamma,\Theta). $$Here, $$$\rho$$$ is the desired sodium concentration, $$$S_{TE}$$$ is the measured signal at a given TE, $$$\overline{S}_{TE}$$$ is the predicted MR signal at a given TE (forward model) and $$$\Gamma$$$ is the spatially dependent magnetization decay function, which is defined as:$$\large \Gamma(x) = e^{\frac{TE1-TE2}{T^*_2(x)}} = e^{\frac{{\Delta}TE}{T^*_2(x)}},$$where $$$T^*_2(x)$$$ is a mono-exponential decay rate used to approximate the bi-exponential transverse relaxation decay of a voxel’s NMR signal and $$$R_{Bow}(x,\Theta)$$$ is the image-based Bowsher prior.

Although the iterative solution to the problem is effective, it is computationally prohibitive for routine use in clinical environments. To address this issue, we evaluate the use of a convolutional neural network (CNN) to achieve clinically compatible computational times as previously demonstrated in the context of PET reconstruction³.

The proposed CNN (shown in Figure 1) was implemented using a U-Net architecture and was designed to predict an AGR using input images consisting of two low-resolution ²³Na MRI images ($$${4}\times{4}\times{4}$$$mm$$$^3$$$) acquired at 3 Tesla (TR=100ms), corresponding to two echo times (0.5 and 5.0ms; respectively), and one high-resolution ¹H MRI image ($$${1}\times{1}\times{1}$$$mm$$$^3$$$). It was trained on $$${48}\times{48}\times{48}$$$ image patches from 13 subjects, which were split into eight, two, and three for training, validation, and testing; respectively.

Computational times were recorded and the quality of the CNN reconstructions relative to the iterative AGRs was assessed using the Structural Similarity Index Measure (SSIM) and Peak Signal-to-Noise Ratio (PSNR). Segmentation maps for the AGR images were generated using FreeSurfer so that the accuracy of specific regions of interest in the brain could be evaluated⁴.

Results

To quantify the ability of the CNN to approximate iterative AGRs, we calculated SSIM and PSNR between the two reconstructions. Figure 2 shows a summary of these results for several anatomical regions of the brain. Our results indicate high SSIM and PSNR scores for all ROIs, reflecting the CNN’s ability to approximate AGRs with high fidelity, as shown in Figure 3. Finally, by using the CNN, computational times are reduced from 1-2 hours to a few seconds (<1 second on GPU devices).

Discussion

In addition to achieving a considerable reduction in computational times, the CNN’s accuracy in reconstructing ²³Na MRI images is still comparable to that of iterative AGR methods. Therefore, it stands as a promising approach for accelerating ²³Na MRI image reconstruction, warranting further exploration and validation in clinical settings. Notably, the CNN’s performance appears to be more robust in image areas with lower SNR, as seen in Figure 3's sub-tentorial spaces (bottom half of the coronal slice). This seems to suggest that the non-stochastic nature of the CNN’s inference is less sensitive to noise, which will be further investigated using a larger cohort of subjects and including images at higher field strength to assess the role of image SNR on the reconstructions.

Conclusion

Our findings suggest that a CNN approach to anatomically-guided reconstruction could offer a feasible solution for obtaining high-resolution and high-SNR sodium images in clinical settings, owing to its accuracy and reduced computational requirements. Consequently, this would better facilitate the integration of Sodium MRI into clinical domains.

Acknowledgements

Supported in part by PHS Grants R01 EB031199, R01 NS113517, and NIH RF1 AG067502.