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Accelerating Acquisition for the Reconstruction of Fiber Orientation Distribution Function Using Convolutional Neural Network

Ting Gong¹, Hongjian He¹, Zhichao Lin², Zhiwei Li², Feng Yu², and Jianhui Zhong^1,3

¹Center for Brain Imaging Science and Technology, Key Laboratory for Biomedical Engineering of Ministry of Education, College of Biomedical Engineering and Instrumental Science, Zhejiang University, Hangzhou, China, ²Department of Instrument Science & Technology, Zhejiang University, Hangzhou, China, ³Department of Imaging Sciences, University of Rochester, Rochester, NY, United States

Synopsis

Fiber orientation distribution function (fODF) is one of the key components for establishing brain connectivity maps. However, its reliable reconstruction usually requires a large number of diffusion weighted image (DWI) volumes leading to long acquisition time. Our previous study has shown the potential of multi-layer perceptron in recovering fODF directly from a small number of DWIs. In this study, we proposed a 3-dimentional convolution neural network to take the spatial correlation into consideration, allowing robust fODF reconstruction with up to eleven-fold reduction of number of DWIs. This method offers a new approach for fast fODF reconstruction which could facilitate its clinical applications.

Introduction

The Fiber Orientation Distribution Function (fODF) can be more reliably reconstructed by multi-shell, multi-tissue, constrained spherical deconvolution (MSMT-CSD)¹, at the cost of long acquisition time. Inspired by the strong inference ability of neural network, our earlier study applied the multi-layer perceptron (MLP) to exploit down-sampled DWIs to directly reconstruct the fODF voxel-by-voxel, with promising preliminary results.² However, the voxel-wise method may confront a constraint of low signal-to-noise ratio when a limited number of DWIs are used. Since there is spatial continuity, the spatial correlations may provide additional information for network learning. We herein propose to apply 3-dimentional convolution neural network (3D-CNN) in a regression manner to take the spatial information into consideration, improving the performance of the deep-learning based method for direct reconstruction of fODF.

Method

The method treats spherical harmonics (SH)-represented diffusion-weighted image (DWI) signals and fODF coefficients as inputs and outputs, respectively. A highest recommended order of 8 leading to 45 SH coefficients ³ was adopted for the output fODF. For input DWI signals, the highest order was utilized for each shell, and the SH coefficients were concatenated for all shells to generate as many coefficients as possible. The detailed network structure is depicted in Figure 1. The network width and depth were chosen as the setting of 1024-512-512-256, achieving a balance between the performance and the cost of time and space.

We conducted experiments on 30 randomly selected datasets from the database of the Human Connectome Project (HCP). The HCP datasets were acquired at a 1.25 mm isotropic resolution with the diffusion weighting of b = 1000, 2000, and 3000 s/mm² applied in 90 directions in each shell, and additionally 18 b=0 s/mm² images, resulting in a total of 288 DWIs.⁴ To evaluate the generalization capability of the proposed method, 24 subject datasets were used for training and the remaining 6 subjects were reserved for testing.

The performance of the proposed method was primarily compared to the super-resolved MSMT-CSD¹ with decreasing number of DWIs. All MSMT-CSD reconstruction was performed in MRtrix (http://www.mrtrix.org/) using an unsupervised method.⁵ The fODFs reconstructed by MSMT-CSD from all available 288 DWIs were used as training labels and reference standard. The performance was quantitatively measured by the angular correlation coefficient (ACC)⁶ and the mean angular error (MAE) of all peaks. Finally, to validate the effectiveness of the learned fODFs, fiber tractography was conducted using extracted peaks from fODFs.⁷

Results

In general, the proposed method outperformed the MSMT-CSD in all investigated cases, with its advantage more obvious when a smaller number of DWIs were used.

Figure 2: From average of the six subjects, the median ACC ranges from 0.96 to 0.91 for CNN, and 0.93 to 0.77 for MSMT-CSD (with perfect score of 1) when the number of DWIs was reduced from 95 to 25. The CNN reached a more concentrated average interquartile range (IQR) ranging from 0.20 to 0.12, whereas the MSMT-CSD reached 0.39 to 0.18.

Figure 3: The average MAE for the CNN method in regions containing one, two, three fibers was respectively 1.09°, 2.75°, and 8.35° smaller than the MSMT-CSD method. The visual inception of the fODF further confirmed this superiority.

Figure 4: For multi-tissue assessment, the boxplots in pure white matter region and partial volume region show similar patterns to those of the whole brain ACC (Figure 2), with better performance in white matter region for all methods. Comparing to our previous study using MLP, 3D-CNN shows huge improvements especially when a limited number of DWIs were available.

Figure 5: Finally, the tractography results were consistent with the previous fODF inspection in that more spurious and rotated peaks led to more meaningless tracts.

Discussion

The proposed method derives the SH representation of the DWI signals by least-squares linear fitting the amplitude data, which alleviates possible effect of inconsistent gradient schemes between training and testing dataset. However, this additional step may yield inevitable errors when very limited DWIs are used. One possible improvement is to obtain the SH representations by deep learning also. Hence, the network could learn the fODF from the raw DWI signals and the related b-values and DW directions directly in an end-to-end manner. The related research is ongoing.

Conclusion

Experiments on HCP datasets demonstrated the feasibility of the proposed method in recovering fODFs from up to eleven-fold reduced number of DWIs. In terms of acquisition time in HCP protocol, this implies a reduction of scan time from approximately 59 minutes to 5 minutes. The proposed method exhibits promising potential in acquisition acceleration for the reconstruction of fODFs with good accuracy.

Acknowledgements

We would like to acknowledge the support from National Key R&D Program of China (2017YFC0909200), NSFC (81871428, 91632109) and Shanghai Key Laboratory of Psychotic Disorders(13dz2260500).

References

1. Jeurissen B, Tournier J, Dhollander T, et al. Multi-tissue constrained spherical deconvolution for improved analysis of multi-shell diffusion MRI data. NeuroImage, 2014: 411-426.

2. Gong T, He H, Lin Z, et al. Direct and Fast Learning of Fiber Orientation Distribution Function for Tractography. In: Joint Annual Meeting ISMRM-ESMRMB. Paris, France; 2018:6-8.

3. Tournier J, Calamante F, Connelly A, et al. Determination of the appropriate b value and number of gradient directions for high-angular-resolution diffusion-weighted imaging. NMR Biomed. 2013;26(12):1775-1786.

4. Van Essen DC, Ugurbil K, Auerbach E, et al. The Human Connectome Project: a data acquisition perspective. Neuroimage. 2012;62(4):2222-2231.

5. Dhollander T, Raffelt D, Connelly A. Unsupervised 3-tissue response function estimation from single-shell or multi-shell diffusion MR data without a co-registered T1 image. Proc. ISMRM Workshop on Breaking the Barriers of Diffusion MRI, vol. 5, 2016.

6. Anderson AW. Measurement of fiber orientation distributions using high angular resolution diffusion imaging. Magn Reson Med An Off J Int Soc Magn Reson Med. 2005;54(5):1194-1206.

7. Yeh F-C, Verstynen TD, Wang Y, et al. Deterministic diffusion fiber tracking improved by quantitative anisotropy. PLoS One. 2013;8(11).

Figures

Figure 1. Network architecture used in this work, composed of two convolutional (conv) layers with kernels of size 2×2×2 and three fully-connected (FC) layers. The first convolutional layer used the 3×3×3 patch as the input to utilize the spatial information. The generated fODF corresponds to the central voxel in the input cube.

Figure 2. Boxplot of overall ACC from 3D CNN method and MSMT-CSD in whole-brain WM voxels including partial volume region for the 6 test subjects. The box represents the interquartile range (IQR) and the whiskers indicate the highest and lowest values within 1.5 IQR of the nearer quartile. The Reference standard is model reconstruction result using 288 DWIs. The CNN method (red) outperforms model reconstruction (blue) in all cases.

Figure 3. fODFs (lmax=8) of one typical subject from ROIs containing (a) single, (b) two, and (c) three fiber population (k=1, 2, 3). (left) Reference standards from the model reconstruction with all 288 DWIs, (middle) model-reconstructed and 3D CNN results for reduced n, and (right) the mean angular error (MAE (degree)) of existing peaks in each ROI from 25 to 95 DWIs. The blue curve representing MSMT-CSD is much higher than the red curve representing 3D CNN and is highly unstable.

Figure 4. Angular correlation coefficient comparison of 3D CNN, MSMT-CSD and MLP in pure white matter region (a) and partial volume region (b) from one typical subject. In both regions, the MLP method (green) gains a slight advantage over model reconstruction. The 3D CNN method (red) remarkably outperformances them in all situations.

Figure 5. Fiber tractography comparison (200 tracks for each situation). (a-d) results from 288, 85, 55, 25 DWIs by MSMT-CSD; (e-g) results from 85, 55, 25 DWIs by 3D CNN. The 3D CNN reconstruction generated a relatively stable track volume (TV) and mean track length (mTL). The super-resolved reconstruction generated some extra fibers of changed direction when the number of DWIs was fewer than 85 and even mussy fibers of increased track length and track volume with fewer than 55 DWIs (yellow circles); all the major branching fibers were kept with 25 DWIs for 3D-CNN.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)

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