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Global Information Matters in Quantitative Susceptibility Mapping Using 3D Fully Convolutional Neural Networks
Yicheng Chen1,2, Angela Jakary2, Christopher Hess2, and Janine Lupo1,2

1The UC Berkeley - UCSF Graduate Program in Bioengineering, San Francisco, CA, United States, 2Department of Radiology and Biomedical Imaging, University of California, San Francisco, San Francisco, CA, United States

Synopsis

Recent research has shown that deep convolutional neural networks (DCNNs) have the potential to solve the ill-posed dipole inversion problem in quantitative susceptibility mapping (QSM). This study investigates the effects of patch-based QSM reconstruction by modifying a DCNN to take global susceptibility-phase relation into consideration.

Introduction

Quantitative susceptibility mapping (QSM) allows for in vivo quantification of magnetic susceptibility, a tissue parameter that is altered in a variety of neurological disorders.1 Strategies have been developed for solving the dipole inversion problem using single orientation phase images2,3, but these suffer from residual inhomogeneity and inaccurate quantification because of their poor numerical conditioning. Methods like COSMOS partially overcome this issue by using images acquired at multiple head orientations but come at the expense of scan times that are not clinically feasible. Deep convolutional neural networks (DCNNs) have also been recently proposed to solve this inversion4,5. Current DCNN approaches use patch-based methods, which fail to account for global susceptibility in the dipole inversion process. The goal of this study was to examine the effect of increasing the receptive field of the DCNN to incorporate global information and thereby improve the accuracy of the learned QSM reconstruction.

Methods

Data acquisition: 8 healthy volunteers were scanned with a 3D multi-echo gradient sequence (TE=6/9.5/13/16.5ms, TR=50ms, BW=50kHz, FA=20°) using a 32-channel head coil in a 7T GE scanner. The sequence was repeated three times on each volunteer with different head orientations. GRAPPA parallel imaging with R=3 and 16 center auto-calibrating lines was applied with a matrix size of 300x300x190, a 24x24x15cm FOV, and 0.8mm isotropic spatial resolution.

Processing: COSMOS-QSM was reconstructed by: 1) applying GRAPPA reconstruction; 2) combining individual magnitude and phase coil images using the MCPC-3D-S method6; 3) unwrapping phase with a Laplacian-based method2; 4) masking the brain using FSL BET7; 5) removing the background field phase using V-SHARP2; 6) co-registering tissue phase of the three head orientations using the magnitude images and FSL FLIRT7; and 7) solving the dipole field inversion using COSMOS QSM8 as the ground truth in training. iLSQR QSM images were also generated from a single orientation of the test data for comparison.

Network Structure: A 3D patched-based U-Net9 architecture was designed to learn COSMOS susceptibility map reconstruction from tissue phase maps. A cropping layer that saved only the central region of the output was added at the end of the model to increase the receptive field for voxels near the edge of the patch (Figure 1).

Implementation: The DCNNs were implemented using Keras 2.1 with Tensorflow 1.8 as backend and trained using an NVIDIA Titan Xp GPU with 12GB memory. To train the networks, we adopted a mean absolute error (MAE)-based loss function combining gradient loss to preserve edges in QSM. (Equation below) An Adam optimizer was used and the learning rate was gradually reduced from 1e-4 to 1e-6. Models were trained for 100 epochs.

$$Loss=Loss_{MAE} + 0.1\times [|\Delta_x\chi - \Delta_x\bar{\chi}| + |\Delta_y\chi - \Delta_y\bar{\chi}|+|\Delta_z\chi - \Delta_z\bar{\chi}|]$$

Results

Figure 2 shows the validation MAE loss for different combinations of input and output patch sizes. Compared to iLSQR, UNet-based methods significantly lowered the reconstruction error of COSMOS-QSM. Given the same output patch size, lower MAE was achieved when a larger input patch was used, demonstrating the importance of global information. The intermediate output patch size (Wout=48) achieved the lowest error, with the computation time increasing with O(Win3). Differences among iLSQR, UNet with and without global information, and the ground truth (COSMOS-QSM) are illustrated in Figure 3.

Discussion and Conclusions

We demonstrated that including global information in the input is necessary for accurate susceptibility mapping when training DCNNs to learn the dipole inversion. When the output patch size is the same as the input patch size (no cropping, local phase only), the validation MAE loss is much higher than with cropping. This is because the susceptibility effect extends beyond the local region, so gathering global phase information from a larger receptive field helps to solves the dipole inversion problem. Figure 4 provides a graphic depiction of the receptive field with respect to the received/missing information of output voxels. The benefit of a larger receptive field that includes more global information comes at the cost of higher training difficulty and inference complexity. To train the largest input patch size (Win=192), the batch size had to be reduced from 8 to 2 to fit on a single GPU. The ratio of training to inference time also significantly increased because the cropping permits only (Wout/Win)3 of computation. Although ideally the output size would equal the entire image as in Rasmussen et al5, in practice we were limited by: 1) GPU memory; 2) the small number of training samples that results from larger output patches that can cause overfitting; 3) difficulties in learning subtle details that lead to higher error rates).

Acknowledgements

Research reported in this publication was funded by NIH NINDS Grant R01-NS099564.

References

  1. Wang Y, Spincemaille P, et al. Clinical quantitative susceptibility mapping (QSM): biometal imaging and its emerging roles in patient care. Journal of Magnetic Resonance Imaging. 2017 Oct;46(4):951-71.
  2. Li W, Wang N, et al. A method for estimating and removing streaking artifacts in quantitative susceptibility mapping. Neuroimage. 2015 Mar 1;108:111-22.
  3. Liu J, Liu T, et al. Morphology enabled dipole inversion for quantitative susceptibility mapping using structural consistency between the magnitude image and the susceptibility map. Neuroimage. 2012 Feb 1;59(3):2560-8.
  4. Yoon J, Gong E, et al. Quantitative susceptibility mapping using deep neural network: QSMnet. NeuroImage. 2018 Jun 15.
  5. Rasmussen KG, Kristensen MJ, et al. DeepQSM-Using Deep Learning to Solve the Dipole Inversion for MRI Susceptibility Mapping. Biorxiv. 2018 Jan 1:278036.
  6. Eckstein K, Dymerska B, et al. Computationally Efficient Combination of Multi‐channel Phase Data From Multi‐echo Acquisitions (ASPIRE). Magnetic resonance in medicine. 2018 Jun;79(6):2996-3006.
  7. Jenkinson M, Beckmann CF, et al. Fsl. Neuroimage. 2012 Aug 15;62(2):782-90.
  8. Liu T, Spincemaille P, et al. Calculation of susceptibility through multiple orientation sampling (COSMOS): a method for conditioning the inverse problem from measured magnetic field map to susceptibility source image in MRI. Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine. 2009 Jan;61(1):196-204.
  9. Ronneberger O, Fischer P, et al. In International Conference on Medical image computing and computer-assisted intervention 2015 Oct 5 (pp. 234-241). Springer, Cham.

Figures

Figure 1. 3D UNet architecture used to learn the dipole inversion relationship to reconstruct QSM. Win and Wout represent the size of the input and output patches respectively. The cropping layer was added to the end of the model to include global information.

Figure 2. Network performance on the validation set. (a) Inference time per scan of different input/output patch size combinations where time ~ O((Win/Wout)3). (b) MAE of validation data of different input/output patch size combinations. MAE of iLSQR is also listed for comparison. (c) Bar plot of MAE in (b).

Figure 3. Visual comparison of reconstructed QSM of test subjects. Rows 1 and 3: QSM. Rows 2 and 4: error map. Numbers listed at the bottom of the error map show the MAE of the slice.

Figure 4. Visualization of receptive field and phase information received for voxels in a patch. (a) A voxel at the center (red circle) receives both local and global information (orange box). (b) When Win=Wout, part of the phase information (gray) is missing for voxels near the edge. (c) When Win>Wout (using our cropping layer), voxels near the edge also receive the full information.

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