• Deep learning tractography method
  • Predicts the parameters for a unimodal distribution on the sphere (Fisher von Mises)
  • Uncertainty quantification
  • Maximum-entropy regularization as loss function instead of NLL to enforce non-zero uncertainty and robustness to noise


Model: Simple Multi-Layer perceptron


  • Block of 3x3x3 voxels of DWI data fitted with spherical harmonics of order 4 (15 values per voxel = 405 features)
  • 4 last directions (3 values per direction = 12 features)

Prediction: Parameters of a Fisher von Mises distribution:

(Taken from Wikipedia)

(Taken from [1])

The Fisher von Mises distribution is analogous to a Gaussian on the Sphere. It has a mean parameter \(\mu\) and a concentration parameter \(\kappa\).

Loss function: Total free energy given the predicted distribution parameters (and a temperature hyper-parameter \(T\)), which can be calculated analytically for the Fisher von Mises distribution

The model is optimized using SGD and gradient clipping.


  • Training: 1 HCP subject, tracked using a probabilistic algorithm.

  • Testing: Tractometer tool (synthetic signal, 25 GT bundles to reconstruct)

    • Output metrics: Valid Bundles (VB), Invalid Bundles (IB), Valid Connections (VC), Overlap (OL), Overreach (OR), F1-score (using overlap + overreach)


The Entrack model achieves scores comparable to the other works, indicating its usefulness as predictive model for fiber tracking, in addition to its benefits of uncertainty quantification, and outlier detection.

  • See figure 6: The model is also trained on the tractometer data and used to color the training streamlines according to the total probability ((a) and (b) or local uncertainty ((c) and (d)).


[1]: Plis, S., McCracken, S., Lane, T., & Calhoun, V. (2011, June). Directional statistics on permutations. In Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics (pp. 600-608).