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AID-DTI: fast and high-fidelity diffusion tensor imaging with detail-preserving model-based deep learning
Wenxin Fan1,2, Cheng Li1, Jing Yang3,4, Juan Zou5,6, Hairong Zheng1, and Shanshan Wang1,7,8
1Paul C Lauterbur Research Center for Biomedical Imaging, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China, 2University of Chinese Academy of Science, Beijing, China, 3Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China, 4University of Chinese Academy of Science, Beijing, China,, Beijing, China, 5School of Physics and Optoelectronics, Xiangtan University, Xiangtan, China, 6Paul C. Lauterbur Research Center for Biomedical Imaging, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China, 7Guangdong Provincial Key Laboratory of Artificial Intelligence in Medical Image Analysis and Application, Guangzhou, China, 8Peng Cheng Laboratory, Shenzhen, China

Synopsis

Keywords: DWI/DTI/DKI, Diffusion Tensor Imaging, Deep Learning

Motivation: Existing methods tend to suffer from Rician noise, leading to detail loss during the reconstruction of DTI-derived parametric maps. This issue becomes particularly pronounced when sparsely sampled q-space data are used.

Goal(s): Our goal was to facilitate fast and high-fidelity estimation of DTI metrics.

Approach: We propose a novel SVD-based regularizer, which can effectively preserve fine details while suppressing noise during network training.

Results: Experimental results consistently demonstrate that the proposed method estimates DTI parameter maps with finer details, outperforming current state-of-the-art methods.

Impact: The proposed method may facilitate fast and high-fidelity DTI with a newly designed SVD-based regularizer, and it has a potential to become a practical tool in clinical and neuroscientific applications.

Introduction

Diffusion tensor imaging (DTI)1 is the most widely utilized diffusion MRI (dMRI) technique for noninvasively mapping white matter tissue properties and delineating white matter tracts in vivo. The metrics estimated from DTI, such as fractional anisotropy (FA), mean diffusivity (MD), and axial diffusivity (AD)2, have great specificity in mapping the microstructural changes caused by normal aging3, neurodegeneration4 and psychiatric disorders5. However, diffusion MRI data often suffer from Rician noise, which degrades the image quality and leads to detail loss in reconstructing the DTI-derived parametric maps. Additionally, the presence of noise in the diffusion measurements adds to the demand for more data to enable high accuracy in estimating DTI metrics, which is time-consuming and vulnerable to motion artifacts. Consequently, high-quality DTI metrics estimation from sparsely sampled q-space data is urgently needed. Recently, deep learning has shown great potential in accelerating DTI. Despite the achieved promising results6-10, previous research has not fully explored task-oriented loss functions, limiting the quality of estimated DTI metrics. In this study, we proposed a novel method, named AID-DTI (fAst and hIgh fiDelity Diffusion Tensor Imaging), to facilitate fast and high-fidelity DTI with a newly designed singular value decomposition (SVD)-based regularizer.

Method

Given the ability of SVD to extract the most dominant features, we present a novel method called AID-DTI, which leverages an SVD-based regularization term to accurately estimate DTI metrics using only six measurements along uniformly distributed directions instead of the recommended 30 measurements to achieve reliable DTI metrics within the needed clinical accuracy11. The overall framework of AID-DTI is shown in Figure 1. The inputs to the AID-DTI pipeline consist of a single non-diffusion-weighted ($$$b=0$$$) image volume and six DWI volumes sampled along uniform diffusion encoding directions (total of seven input channels). Then, the mapping between the sparse sampling and high-fidelity DTI metrics is directly learned. Generally, after obtaining the output, the $$$L_2$$$ loss is calculated to optimize the network. However, in our method, we additionally performed SVD operation on both the prediction and the ground truth, ensuring data consistency in the singular value matrix as well. Based on the deep supervision structure, we design a detail-preserving SVD-based loss, which constrains the data consistency across the spatial and singular-value domains. Our task-oriented loss function is defined as:
$$\begin{aligned}\text { Loss } & =L_{\text {Data }}+\lambda \cdot L_{\text {Reg }} \\& =\frac{\| \mathrm{GT}-\text { Pred } \|_2^2}{\|\mathrm{GT}\|_2^2}+\lambda \cdot \frac{\left\|\Sigma_{\mathrm{GT}}-\Sigma_{\text {Pred }}\right\|_2^2}{\left\|\Sigma_{\mathrm{GT}}\right\|_2^2}\end{aligned}$$
where $$$\Sigma_{\mathrm{GT}}$$$ and $$$\Sigma_{\mathrm{Pred}}$$$ represent the ground-truth metrics and their singular value diagonal matrix of ground truth metrics and predicted data, respectively. Notably, AID-DTI can utilize any network architecture. The MESC-SD9, a model-based network based on sparse LSTM units with two cascaded stages, is employed here.

Results

We used 77 subjects from the publicly available Human Connectome Project (HCP) dataset in this study12. Among the 77 subjects, 60 were selected as training data, and the remaining 17 as test data. HCP data were acquired with four b-values (0, 1000, 2000, 3000$$$s/mm^2$$$). For each non-zero b-value, there are 90 DWI volumes along uniformly distributed diffusion-encoding directions13. To obtain the input data of AID-DTI, DWI volumes acquired along six uniform directions at $$$b=1000s/mm^2$$$ of each subject were selected. To obtain the ground-truth DTI metrics, diffusion tensor fitting was performed on all the diffusion data using ordinary linear squares fitting implemented in the DIPY software package (https://github.com/dipy/dipy#id1). The experimental results are summarized in Table 1. We can observe that results using SVD-based regularization outperform those obtained using the non-regularized methods, q-DL and 2D-CNN, by a large margin. Moreover, we investigated the impact of different learning rates on the performance of each method. AID-DTI consistently outperforms other methods across all learning rates, further supporting its superiority. Example visualization results are provided in Figure 2.

Discussion

As shown in Figure 3, most values in the singular value matrix $$$\Sigma$$$ are close to 0. According to the Eckart–Young theorem14, in an informal sense, the dominant singular subspaces capture the majority of the informational content. It is presumed that components with larger absolute singular values encompass more detailed structural information, whereas singular values closer to zero are more likely to contain noise. Therefore, aligning the primary singular values can effectively preserve fine details while removing a certain degree of noise.

Conclusion

In this study, we develop a novel model-driven deep learning approach entitled AID-DTI for fast and high-fidelity DTI parametric maps estimation employing an SVD-based regularization. The proposed method exhibits simplicity, interpretability, and flexibility, and it has a high potential to become a practical tool in clinical and neuroscientific applications.

Acknowledgements

This research was partly supported by the National Natural Science Foundation of China (62222118, U22A2040), Guangdong Provincial Key Laboratory of Artificial Intelligence in Medical Image Analysis and Application (2022B1212010011), Shenzhen Science and Technology Program (RCYX20210706092104034, JCYJ20220531100213029), and Key Laboratory for Magnetic Resonance and Multimodality Imaging of Guangdong Province (2023B1212060052).

References

  1. P. J. Basser, J. Mattiello, and D. LeBihan, “MR diffusion tensor spectroscopy and imaging,” Biophys. J., vol. 66, no. 1, pp. 259–267, Jan. 1994, doi: 10.1016/S0006-3495(94)80775-1.
  2. K. M. Curran, L. Emsell, and A. Leemans, “Quantitative DTI Measures,” in Diffusion Tensor Imaging: A Practical Handbook, W. Van Hecke, L. Emsell, and S. Sunaert, Eds., New York, NY: Springer, 2016, pp. 65–87. doi: 10.1007/978-1-4939-3118-7_5.
  3. D. H. Salat et al., “Age-Related Changes in Prefrontal White Matter Measured by Diffusion Tensor Imaging,” Ann. N. Y. Acad. Sci., vol. 1064, no. 1, pp. 37–49, 2005, doi: 10.1196/annals.1340.009.
  4. T. M. Nir et al., “Effectiveness of regional DTI measures in distinguishing Alzheimer’s disease, MCI, and normal aging,” NeuroImage Clin., vol. 3, pp. 180–195, 2013, doi: 10.1016/j.nicl.2013.07.006.
  5. Zhong Zheng et al., “DTI correlates of distinct cognitive impairments in Parkinson’s disease,” Hum. Brain Mapp., vol. 35, no. 4, pp. 1325–1333, Jan. 2014, doi: 10.1002/hbm.22256.
  6. V. Golkov et al., “q-Space Deep Learning: Twelve-Fold Shorter and Model-Free Diffusion MRI Scans,” IEEE Trans. Med. Imaging, vol. 35, no. 5, pp. 1344–1351, 2016, doi: 10.1109/TMI.2016.2551324.
  7. E. K. Gibbons et al., “Simultaneous NODDI and GFA parameter map generation from subsampled q-space imaging using deep learning,” Magn. Reson. Med., vol. 81, no. 4, pp. 2399–2411, 2019, doi: 10.1002/mrm.27568.
  8. C. Ye, X. Li, and J. Chen, “A deep network for tissue microstructure estimation using modified LSTM units,” Med. Image Anal., vol. 55, pp. 49–64, Jul. 2019, doi: 10.1016/j.media.2019.04.006.
  9. C. Ye, Y. Li, and X. Zeng, “An improved deep network for tissue microstructure estimation with uncertainty quantification,” Med. Image Anal., vol. 61, p. 101650, Apr. 2020, doi: 10.1016/j.media.2020.101650.
  10. G. Chen et al., “Hybrid Graph Transformer for Tissue Microstructure Estimation with Undersampled Diffusion MRI Data,” in Medical Image Computing and Computer Assisted Intervention – MICCAI 2022, L. Wang, Q. Dou, P. T. Fletcher, S. Speidel, and S. Li, Eds., in Lecture Notes in Computer Science. Cham: Springer Nature Switzerland, 2022, pp. 113–122. doi: 10.1007/978-3-031-16431-6_11.
  11. D. K. Jones, T. R. Knösche, and R. Turner, “White matter integrity, fiber count, and other fallacies: The do’s and don’ts of diffusion MRI,” NeuroImage, vol. 73, pp. 239–254, Jun. 2013, doi: 10.1016/j.neuroimage.2012.06.081.
  12. D. C. Van Essen, S. M. Smith, D. M. Barch, T. E. J. Behrens, E. Yacoub, and K. Ugurbil, “The WU-Minn Human Connectome Project: An overview,” NeuroImage, vol. 80, pp. 62–79, Oct. 2013, doi: 10.1016/j.neuroimage.2013.05.041.
  13. E. Caruyer, C. Lenglet, G. Sapiro, and R. Deriche, “Design of multishell sampling schemes with uniform coverage in diffusion MRI,” Magn. Reson. Med., vol. 69, no. 6, pp. 1534–1540, 2013, doi: 10.1002/mrm.24736.
  14. C. Eckart and G. Young, “The approximation of one matrix by another of lower rank,” Psychometrika, vol. 1, no. 3, pp. 211–218, Sep. 1936, doi: 10.1007/BF02288367.

Figures

Figure 1. The proposed AID-DTI pipeline. The input consists of a single image and six diffusion-weighted image volumes sampled along uniform diffusion-encoding directions. The output is the high-quality volume of DTI metrics estimation.

Table 1. A comprehensive comparison of the performance among different methods at various learning rates.

Figure 2. The Ground Truth, estimated DTI parameters FA, AD, and MD, and corresponding residual maps based on q-DL, MESC-SD, and AID-DTI (ours) in a test subject with 6 diffusion directions at b-values of 1000s/mm2.

Figure 3. The plot of the singular values sorted in descending order.

Proc. Intl. Soc. Mag. Reson. Med. 32 (2024)
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DOI: https://doi.org/10.58530/2024/1141