Introduction

Tissue sodium concentration (TSC) is a biomarker for essential physiological processes^[1] and can be measured non-invasively by quantified ²³Na MRI. In many pathologies – especially in the brain – it was observed that ²³Na MRI can detect additional information on a cellular level^[2,3]. A major limitation of ²³Na MRI is its long measurement time. CNNs are known to enable robust image reconstruction from highly undersampled data^[4]. This study investigates the possibility to reduce ²³Na MRI measurement time for stroke patients by applying CNNs. Grey matter (GM) affection seems to be more prevalent in stroke^[5], but white matter (WM) can be affected as well^[6]. Hence, both tissue types were considered for the evaluation.
Three different CNNs, applied on highly undersampled ²³Na MR images, were evaluated based on their accuracy in GM an WM.

Methods

A standard clinical MRI-protocol for stroke, including the acquisition of a FLAIR image, with an additional 3D radial density-weighted ²³Na sequence^[7] was acquired on a 3T MRI (MAGNETOM Trio, Siemens Healthineers, Erlangen, Germany) using a bird-cage dual-tuned ²³Na/¹H head coil (Rapid Biomedical, Rimpar, Germany)^[8].
This study includes the data from 46 stroke patients ($$$72\pm13$$$ years, 25 female and 21 male). All the acquired k-space data (n=6000 spokes, TA=10mins) were used to reconstruct the full image (FI) which was used as ground truth. Furthermore, an undersampled image (UI) was reconstructed using n=1500 (undersampling factor=4) equidistant spokes to simulate an image with TA=2.5 mins. The image reconstructions were performed in MATLAB 2015a.
Previously, we have evaluated multiple CNN architectures and parameters by calculating the generated SNR and the structural similarity to FI (SSIM). The best performing CNNs were based on a UNet architecture^[9] with residual connections. The networks have four encoding and four decoding stages (each stage 2 to 3 convolutional layers). Training uses an Adam optimizer. The batch size was set to 8 and the training ran for 20 epochs with a learning rate of 0.001. Based on these findings, we implemented three different CNNs:

CNN 1: No batch normalization, filter size of [32, 64, 128, 256, 512], loss function=L2
CNN 2: Usage of batch normalization, filter size of [32, 64, 128, 256, 512], loss function=L1
CNN 3: No batch normalization, filter size of [16, 32, 64, 128, 256], loss function=L1

The networks were implemented in Python 3.5 using Tensorflow 1.10. All CNNs were trained with 64x64voxel patches from the UI as input, and the corresponding patches of the FI as label. The data consisted of 38 training and 8 test datasets. 50 slices per patient (dataset) and 5 patches per slice resulted in 250 samples per training dataset.
For the evaluation of the networks, a segmentation of the brain was performed using the statistical parameter mapping software SPM12 on the acquired FLAIR image resulting in a WM and a GM mask. Furthermore, SPM 12 was also used to coregister the different quantified versions of the ²³Na image (FI, UI, and CNN 1-3) to the FLAIR image with the aim to use the segmentation masks on the ²³Na images. Figure 1 shows one slice of the FLAIR image, the coregistered ²³Na image (FI) and the calculated segmentation masks of WM and GM.
The deviation between UI, CNN and ground truth was evaluated by:

$$AbsoluteError(CNN,UI)=\frac{\sum_{n=1}^{N} |TSC_{CNN,UI}(n)-TSC_{FI}(n)|}{N}$$
with $$$N=\sum{voxels}$$$. Their performances were compared with:
$$RelativeError(CNN)=\frac{AbsoluteError(CNN)}{AbsoluteError(UI)}-1$$

Three neuroradiologists with different levels of experience evaluated the images independently for the clinical relevance. The three images were graded with a scale from 1 (very bad) and 5 (very good). A significance test was performed using the student t-test with alpha=0.05.

Results

CNN 1 and CNN 2 decreased the TSC error compared to UI by >10% for white and grey matter while CNN 3 decreased the TSC error in WM by 2.5% and increased the TSC error in GM by 0.5%. For CNN 1 and 2 the absolute error is similar in WM (5.17 and 5.20 mM) and GM (5.18 and 5.09 mM). Figure 2 shows the error maps in WM and GM. In the exemplary shown slice, especially CNN 1 decreases the quantification error in both WM and GM. Table 1 shows the absolute and the relative averaged error for UI and CNN 1-3 for the whole brain, WM, and GM.
The subjective evaluation of the images from the three neuroradiologists was averaged for all eight test datasets. The results are illustrated as boxplots in figure 3. The UI ($$$\bar{x}=1.88$$$) performed significantly lower than the FI ($$$\bar{x}=4.04$$$) and the CNN ($$$\bar{x}=3.92$$$) while the CNN and the FI had no statistically significant differences.

Discussion

All three CNNs implemented here decreased the TSC quantification error compared to the traditional reconstruction of highly undersampled ²³Na MRI data. CNN 1 and CNN 2 improved the TSC accuracy in WM and GM compared to a traditional reconstruction of highly undersampled data. Furthermore, the diagnosability that was subjectively perceived by the neuroradiologists was improved by the implemented CNN.

Conclusion

The implementation of TSC quantification into the clinical routine might be facilitated by ²³Na MRI acquisition with an acceleration factor of 4 (TA=2.5mins) while keeping its TSC accuracy in WM and GM, and the subjectively perceived diagnosability.

Acknowledgements

The project was funded by Dietmar Hopp Stiftung.