Vishwesh Nath^{1}, Kurt G Schilling^{2}, Prasanna Parvathaneni^{3}, Allison E Hainline^{4}, Colin B Hansen^{1}, Camilo Bermudez^{2}, Andrew J Plassard^{1}, Justin A Blaber^{1}, Vaibhav Janve^{2}, Yurui Gao^{2}, Iwona Stepniewska^{5}, Adam W Anderson^{2}, and Bennett A Landman^{3}

Confocal histology provides an opportunity to establish intra-voxel fiber orientation distributions that can be used to quantitatively assess the biological relevance of diffusion-weighted MRI models, e.g., constrained spherical deconvolution (CSD). Here, we apply deep learning to investigate the potential of single shell diffusion-weighted MRI to explain histologically observed fiber orientation distributions (FOD) and compare the derived deep learning model with a leading CSD approach. This study (1) demonstrates that there exists additional information in the diffusion signal that is not currently exploited by CSD, and (2) provides an illustrative data-driven model that makes use of this information.

Introduction

Three ex vivo squirrel monkey brains were imaged on a Varian 9.4T scanner. Briefly, data were acquired with a 3D diffusion-weighted EPI sequence (b-value=6,000 s/mm2, 100 directions) at 300um isotropic resolution. After scanning, the tissue was sectioned, stained with the fluorescent DiI, and imaged on an LSM710 Confocal microscope following the procedures outlined in [6]. The histological FOD was extracted using structure tensor analysis. Finally, a multi-step registration procedure [6] was used to determine the corresponding diffusion MRI signal. A total of 567 histological voxels were processed, and a hundred random rotations were applied to each one of them for both the MR signal and the histology FOD to augment the data bringing the total to 57267 voxels [7].

For qualitative validation, a single healthy human volunteer was scanned for a single session using a 3T (Achieva, Philips Medical Systems, Best, The Netherlands) with a 32-channel head coil. Four scans acquired were at a b-value of 2000 s/mm2 (which approximates the diffusion contrast of a fixed ex vivo scan at a b-value of 6000 s/mm2) with 96 gradient directions and an additional b0 per scan (2.5mm isotropic resolution, matrix of 96x96, 38 slices, Multi-Band=2; SENSE=2.2;TR= 2650 ms; TE=94 ms; partial Fourier=0.7). Standard pre-processing with FSL (topup, eddy correction, registration, averaging across scans) was performed before analysis.

1.) Tournier, J-Donald, et al. "Resolving crossing fibres using constrained spherical deconvolution: validation using diffusion-weighted imaging phantom data." Neuroimage 42.2 (2008): 617-625.

2.) Anderson, Adam W. "Measurement of fiber orientation distributions using high angular resolution diffusion imaging." Magnetic Resonance in Medicine 54.5 (2005): 1194-1206.

3.)Descoteaux, Maxime, et al. "Regularized, fast, and robust analytical Q‐ball imaging." Magnetic resonance in medicine 58.3 (2007): 497-510.

4.) Jansons, Kalvis M., and Daniel C. Alexander. "Persistent angular structure: new insights from diffusion magnetic resonance imaging data." Inverse problems 19.5 (2003): 1031.

5.) Koppers, Simon, Christoph Haarburger, and Dorit Merhof. "Diffusion MRI Signal Augmentation: From Single Shell to Multi Shell with Deep Learning." International Conference on Medical Image Computing and Computer-Assisted Intervention. Springer, Cham, 2016.

6.) Schilling, Kurt, et al. "Comparison of 3D orientation distribution functions measured with confocal microscopy and diffusion MRI." Neuroimage 129 (2016): 185-197.

7.) Krizhevsky, Alex, Ilya Sutskever, and Geoffrey E. Hinton. "Imagenet classification with deep convolutional neural networks." Advances in neural information processing systems. 2012.

8.) Tieleman, Tijmen, and Geoffrey Hinton. "Lecture 6.5-rmsprop: Divide the gradient by a running average of its recent magnitude." COURSERA: Neural networks for machine learning 4.2 (2012): 26-31.

Figure 1: Confocal histological data provides a ground truth basis for fiber orientation distributions. The truth data was split into a training set and a testing set. Once trained, the deep learning approach was applied to both the testing set and a separate human dataset.

Figure 2: A) Histogram of MSE across all voxels between histology and DNN predicted FOD’s. B) Histogram of ACC across all voxels from the test set of histology and DNN predicted FOD’s. Media ACC is 0.817 C) Histogram of ACC across all voxels from the test set of histology and CSD predicted FOD’s. Median ACC is 0.797

Figure 3: Qualitative visualizations of the MRI fitted to 8th order SH, Histology FOD 10th order SH, CSD 8th order SH, DNN prediction 10th order SH (in order per row). A) 75th percentile (0.936) of ACC for DNN. B) 50th percentile (0.817) of ACC for DNN. C) 25th percentile (0.740) of ACC for DNN.

Figure 4: A.) Prediction of deep learning model on human in vivo data at a b-value of 2000 s/mm shown on a middle axial slice. B.) deep learning model predictions zoomed region of interest in the pons of corpus callosum. C) CSD predictions zoomed region of interest in the pons of corpus callosum. D) Predictions of CSD on human in vivo data at a b-value of 2000 s/mm shown on a middle axial slice.