Introduction

Diffusion tensor imaging (DTI) can quantify tissue microstructure and is useful for tumor classification. The reconstruction of diffusion tensor needs at least seven diffusion-weighted image (DWI) acquisitions since the DTI model has seven free parameters. High-quality DTI usually requires more DWI acquisitions with a series of diffusion directions, which causes a long scan time. Recently, some deep-learning-based methods (e.g., DiffNet¹, DeepDTI², and SuperDTI³) have been proposed to reduce scan time by decreasing the DWI acquisitions, and DTI can keep a high accuracy when only six-direction DWIs are used. In this work, we implemented a deep-learning model combined with multi-slice information sharing to get better performance in modeling DTI, which only used three-direction DWIs every slice, further shortening the scan time. Meanwhile, this method enables higher robustness to noise in fractional anisotropy (FA) mapping by directly modeling the six diffusion tensor parameters.

Methods

Data acquisition: The data were obtained from the Human Connectome Project (HCP).⁴ There are 203 subjects in total, 136 for training, 46 for validation, and 21 for testing. T₁-weighted images and DWIs with two b values (b = 0, 1000 ms/μm²) were used for this study.
Network: The input (Figure 1) of the network has 15 channels from three neighboring slices. Every slice needs a corresponding T₁-weighted image for preventing blurring and offering more structural information⁵, one b = 0 image, and only three b = 1000 ms/μm² DWIs along three diffusion directions for fitting DTI. To share more diffusion information from neighboring slices, the nine DWIs from three neighboring slices are along nine unique diffusion directions, which are the first nine diffusion directions of HCP data for higher robustness to noise⁶ according to the acquisition protocol of HCP data⁷. The diffusion direction of DWIs in all slices is a cycle of the first nine diffusion directions of HCP data. The nine DWIs from three neighboring slices were arranged together according to the order of HCP data, so the spatial order of slices was disrupted. The three channels of the T₁-weighted images or b = 0 images were arranged according to the current slice order of nine DWIs. The network (Figure 2) was improved from U-Net⁸ by adding another encoder to make sure the network models the correct slice. Only the diffusion tensor of the middle slice was reconstructed, and the channel position of the middle slice was not fixed. This method mapped the six parameters ($$$D_{xx}$$$, $$$D_{yy}$$$, $$$D_{yy}$$$ , $$$D_{xy}$$$, $$$D_{xz}$$$, $$$D_{yz}$$$) of diffusion tensor ($$$D$$$):
$$D=\begin{bmatrix}D_{xx}&D_{xy}&D_{xz}\\D_{xy}&D_{yy}&D_{yz}\\D_{xz}&D_{yz}&D_{zz}\end{bmatrix}$$
Evaluation: The averaging of 18 b = 0 images and 90 DWIs were used to obtain the ground-truth by conventional model fitting:
$$S_{i}=S_0exp⁡(-bg_{i}^{T}Dg_i)$$
in which $$$S_{i}$$$ and $$$S_0$$$ are the signal intensities of b = 1000ms/μm² and b = 0 images, respectively. And $$$g_i$$$ is the unit direction vector of diffusion.
Eigen decomposition was applied to the $$$D$$$ to get three parametric maps, fractional anisotropy (FA), mean diffusivity (MD) and directionally encoded colormap (DEC). The mask was applied to FA to remove the noise around the image boundary, which affected the calculation of the index. For comparison, the results of conventional least-squares fitting (LLS), LLS after block-matching and 4D filtering⁹ (LLS-BM4D), and SuperDTI³ using 6-direction DWIs were also given. The peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) were calculated to quantify the reconstruction quality.

Results

Figure 3 shows the reconstruction results of the diffusion tensor. The error images indicate that the six parameter maps reconstructed by our method are very close to the references and obviously better than those obtained by LLS and LLS-BM4D.
The reconstructed results of FA, MD and DEC from different methods are given in Figure 4. Our method outperforms other three methods with less diffusion encoding directions used. It should be noted that MD map has higher PSNR and SSIM compared to the FA and DEC maps because the MD map is relatively robust to noise. The erosion algorithm is applied to the FA and DEC references to avoid the influence of noise at tissue boundary on the evaluation of PSNR and SSIM.
In Figure 5A, a slice with three areas in which obvious noise occurred is shown. Our method illustrates significantly better performance in modeling FA than LLS and LLS-BM4D. In the error images, our method shows similar results to SuperDTI except for the three marked areas. In addition, our method obviously outperforms than all other methods, even the reference at the three ROIs marked in Figure 5A, which are also marked in the b = 0 images from three sections in Figure 5B. Figure 5B indicates that the three ROIs are all at the boundaries of the brain where noise is generated easily during FA modeling. Our method correctly suppresses the noise and enables exact FA mapping, demonstrating its strong robustness to noise in FA mapping.

Discussion and conclusion

In this study, we propose a method for the reconstruction of high-quality diffusion tensor and high-accuracy FA, MD, and DEC maps. The method shows good performance against noise in FA mapping. Meanwhile, the similarity of neighboring slices is utilized so that only 3-direction DWIs are required, which will help to reduce the scan time of DTI.

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