Entrack: A Data-Driven Maximum-Entropy Approach to Fiber Tractography
- 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 )
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)).
: 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).