Introduction

Diffusion-weighted imaging (DWI) can probe tissue microstructural alterations in many disease processes, which has been demonstrated over a broad range of b-values with different diffusion models^1–5. The widely used sequence in DWI – single-shot EPI – is subject to geometric distortion despite its rapid scan speed and resilience to motion. Multi-shot sequences have been proposed to mitigate this problem. However, they often prolong the acquisition times and/or accentuate the SAR issue⁶. An alternative strategy is to substantially undersample k-space data, as in parallel imaging and recently emerging deep learning techniques^7,8. Among the many deep learning neural networks, a convolutional recurrent neural network (CRNN)⁹ is of particular interest because it combines convolutional neural network (CNN) and recurrent neural network (RNN), thereby providing better image quality through exploiting spatio-temporal redundancy in a series of images, such as the time series in dynamic imaging. Recognizing that the image series can be generalized to a set of diffusion images with different b-value and/or different diffusion directions, we hypothesize that the CRNN approach can be applied to reconstructing highly undersampled multi-b-value DWI data. Herein, we employ a novel neural network – CRNN-DWI – and demonstrate its ability to achieve up to six-fold undersampling in DWI without degrading the image quality.

Methods

CRNN-DWI:
Multi-b-value DWI series exhibit similar image features (i.e., edges, anatomy) among differing b-values and diffusion directions (Figure 1). Exploiting this information in a neural network can effectively train it to reconstruct highly undersampled k-space data. The formulation of the proposed CRNN-DWI is expressed as:
$$X_{rec}=f_{N}(f_{N-1}(...(f_{1}(X_{u})))), (1)$$
where $$$X_{rec}$$$ is the image to be reconstructed, $$$X_{u}$$$ is the input image series from direct Fourier Transform of the under-sampled k-space data, and $$$f_{i}$$$ is the network function including model parameters such as weights and bias of each iteration, and $$$N$$$ is the number of iterations.
During each iteration, the network function performs:
$$X_{rnn}^{(i)}=X_{rec}^{(i-1)}+CRNN(X_{rec}^{(i-1)}), (2a) $$
$$X_{rec}^{(i)}=DC(X_{rec}^{(i-1)};{\bf{y}}), (2b)$$
where CRNN is the learnable box that consists of five layers (Figure 2A), DC represents data consistency operation, and y is the acquired k-space data.
Figure 2B shows the unfolded CRNN box, which consists of one CRNN-b-i (evolving over both b-value and iteration) layer, three CRNN-i (evolving over iteration only) layers, and one conventional CNN layer.
CRNN-i:
For the CRNN-i layer, let $$$H_{l}^{(i)}$$$ be the feature representation at layer $$$l$$$ and iteration step $$$i$$$, $$$W_{c}$$$ and $$$W_{r}$$$ represent the filters of input-to-hidden convolutions and hidden-to-hidden recurrent convolutions evolving over iterations, respectively, and $$$B_{l}$$$ denote a bias term. We then have:
$$H_{l}^{(i)}=ReLU(W_{c}*H_{l-1}^{(i)}+W_{r}*H_{l}^{(i-1)}+B_{l}). (3)$$
CRNN-b-i:
In this layer, both the iteration and the b-value information are propagated. Specifically, for each b in the b-value series, the feature representation $$$H_{l, b}^{(i)}$$$ is formulated as (Figure 2C):
$${H_{l,b}^{(i)}}=\overrightarrow{H_{l,b}^{(i)}}+\overleftarrow{H_{l,b}^{(i)}}, (4a)$$
$$\overrightarrow{H_{l,b}^{(i)}}=ReLU(W_{c}*H_{l-1,b}^{(i)}+W_{b}*\overrightarrow{H_{l,b-1}^{(i)}}+W_{r}*H_{l,b}^{(i-1)}+\overrightarrow{B_{l}}), (4b)$$
$$\overleftarrow{H_{l,b}^{(i)}}=ReLU(W_{c}*H_{l-1,b}^{(i)}+W_{b}*\overleftarrow{H_{l,b-1}^{(i)}}+W_{r}*H_{l,b}^{(i+1)}+\overleftarrow{B_{l}}), (4c)$$
where $$$\overrightarrow{H_{l,b}^{(i)}}$$$ and $$$\overleftarrow{H_{l,b}^{(i)}}$$$ are the feature representation calculated along forward and backward directions, respectively, and other parameters are defined in Figure 2C.

Training Data and Image Analysis:
With IRB approval, multi-b-value DWI data were acquired on a 3T GE MR750 scanner from ten subjects. The key acquisition parameters were: slice thickness=5mm, FOV=22cm×22cm, matrix=256×256, slice number=25, 14 b-values from 0 to 4000 s/mm², and acquisition time of ~6’30’’. The acquired images were transformed back to k-space before fed to the neural network. Seven datasets were used for training, two for validation and one for testing. The datasets were also reconstructed with zero padding and 3D-CNN for comparison. The experiment was repeated with undersampling rate (R) of 4 and 6, respectively. The network was trained on a NVIDIA Titan Xp 64GB graphics card. Standard image quality metrics (SSIM and PSNR) were calculated to provide quantitative assessments of the reconstructed image quality. Signal decay curves from trace-weighted image in the two randomly selected ROI were plotted for comparison.

Results

Figures 3 and 4 show a set of diffusion images using CRNN-DWI with R = 4 and 6, respectively. The average SSIM and PSNR of CRNN-DWI were 0.750±0.016 and 28.32±0.69 (R=4), and 0.675±0.023 and 24.16±0.77 (R=6), respectively, both of which were much higher than those using zero-padding or 3D-CNN reconstruction. The trace-weighted images and the signal decay curves from two randomly selected regions of interest agreed well between the images from CRNN-DWI (R=6) and those from fully sampled data (Figure 5).

Discussion and Conclusion

A novel neural network – CRNN-DWI – has been successfully applied to the reconstruction of highly undersampled multi-b-value DWI dataset. The redundant image features among different b-values and diffusion directions allow for exploiting correlations within the dataset. With an up to six-fold reduction in data acquisition, CRNN-DWI worked well without noticeably compromising the image quality or diffusion signal quantification. The same approach can be extended to a larger number of b-values and/or diffusion directions (e.g., >60 in a typical DTI dataset). One limitation of CRNN-DWI is the extensive GPU memory required compared with other neural networks due to the large number of parameters to be stored during the training process. Utilizing deep subspace based network may mitigate this problem by reconstructing a simpler set of basis functions¹⁰. To conclude, the CRNN-DWI is a viable approach to reconstructing highly undersampled DWI data, providing opportunities to relieve the data acquisition burden and mitigate image distortion.

Acknowledgements

No acknowledgement found.

References

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