Philippe Poulin^{1}, Francois Rheault^{1}, Etienne St-Onge^{1}, Pierre-Marc Jodoin^{1}, and Maxime Descoteaux^{1}

We propose a novel bundle-wise tracking algorithm based on deep learning and recurrent neural networks. This allows bundle-specific features to be learned directly from the diffusion signal without the need to reconstruct a fiber orientation distribution. With a high amount of examples, the proposed method improves classic algorithms for several quantitative measures such as tracking efficiency, number of valid streamlines, and volume coverage.

Building on the architecture of *Learn-to-Track*^{1}, we propose the *Bundle-Wise Deep Tracker* (BWDT), a Recurrent Neural Network (RNN) trained to predict tracking directions using bundle-wise input data. GRU^{7} was chosen as the RNN implementation, using a hidden layer of size 512 with layer normalization^{8}. Optimization was done with the Adam^{9} optimizer, an initial learning rate of 0.0001 and gradient clipping of norm 5. During training, an L2 reconstruction error was minimized between normalized predictions and targets, with early stopping of 10 epochs. Models were regularized using a variant of Dropout called Zoneout^{10} with a drop probability of 0.3, and random 3D gaussian noise was added to the streamline coordinates (0.03mm) across all batches.

Reference streamlines were generated using particle filtered probabilistic BST^{4,11}, segmented by a neuroanatomy expert and resampled to a constant step size of 1.0mm. Model inputs were interpolated at reference positions from raw DWIs fitted with spherical harmonics of order 8^{12}.

Three algorithms were evaluated as baseline results:

- Deterministic (DET) tracking
^{13} - DET BST
^{4} - Probabilistic (PROB) BST
^{4}with particle filtering^{11}

All methods tracked five bundles of the randomly chosen 12 test subjects (Arcuate Fasciculus left/right, Corpus Callosum, Corticospinal Tract left/right). After initial tracking, automatic segmentation was done using the same procedure as in BST^{4} to extract valid streamlines. Across all test subjects, 5 metrics were computed in template space: number of streamlines, volume coverage, valid streamline ratio, efficiency ratio (number of valid tracking steps over total number of tracking steps), and weighted dice score.

A model was trained for each bundle using an Nvidia TITAN Xp GPU, which took between 6 and 12 hours per model (depending on the number of streamlines in a bundle’s training set). Results are detailed in Table 1.

When enough training data is provided (AF Left/Right, CC), BWDT provides a sharp increase in valid and efficiency ratios. In other words, less streamlines are rejected, and rejected streamlines are generally shorter, which leads to faster tracking when generating the same number of valid streamlines. Note that even though BWDT is a deterministic model, its volume coverage is better or comparable to a state-of-the-art probabilistic tracking with particle filtering, and is much better than other deterministic methods, as seen in Figures 1, 2 and 3. Visually, BWDT also generates a much smoother streamlines than probabilistic tracking while keeping a high volume coverage. It also runs on a GPU implementation instead of CPU, and can track 200,000 streamlines in about 3 minutes, compared to 2 hours for PROB and 4 hours for DET (all on CPU).

Compared to other methods, BWDT is much easier to use, as it uses only DWI as input and does not need standard pre-processing steps to be robust to noise and motion artefacts. It also does not require registration as in BST^{4}.

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[4] Rheault, F., St-Onge, E., Chenot Q., Petit L., Descoteaux M., 2017. Bundle-Specific Tractography. Computational Diffusion MRI, MICCAI Workshop. Springer, CDMRI'17. - (Accepted)

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[11] Girard, G., Whittingstall, K., Deriche, R. and Descoteaux, M., 2014. Towards quantitative connectivity analysis: reducing tractography biases. Neuroimage, 98, pp.266-278.

[12] Descoteaux, M., Angelino, E., Fitzgibbons, S. and Deriche, R., 2006. Apparent diffusion coefficients from high angular resolution diffusion imaging: Estimation and applications. Magnetic Resonance in Medicine, 56(2), pp.395-410.

[13] Garyfallidis, E., Brett, M., Amirbekian, B., Rokem, A., Van Der Walt, S., Descoteaux, M., Nimmo-Smith, I. and Contributors, D., 2014. Dipy, a library for the analysis of diffusion MRI data. Frontiers in neuroinformatics, 8.

Table 1: Evaluation metrics on the test set, with means and standard deviations computed across 12 subjects.

A: DET; B: DET-BST; C: PROB-BST + PFT; D: BWDT

Figure 1: Tracking results for all methods on both AFs

Figure 2: Tracking results for all methods on the CC

Figure 3: Tracking results for all methods on both CSTs