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Probabilistic Shortest Path Tractography in DTI Using Gaussian Process ODE Solvers

  • Michael Schober
  • Niklas Kasenburg
  • Aasa Feragen
  • Philipp Hennig
  • Søren Hauberg
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8675)

Abstract

Tractography in diffusion tensor imaging estimates connectivity in the brain through observations of local diffusivity. These observations are noisy and of low resolution and, as a consequence, connections cannot be found with high precision. We use probabilistic numerics to estimate connectivity between regions of interest and contribute a Gaussian Process tractography algorithm which allows for both quantification and visualization of its posterior uncertainty. We use the uncertainty both in visualization of individual tracts as well as in heat maps of tract locations. Finally, we provide a quantitative evaluation of different metrics and algorithms showing that the adjoint metric [8] combined with our algorithm produces paths which agree most often with experts.

Keywords

Short Path Short Path Problem Gaussian Process Regression Human Connectome Project Moment Match Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Basser, P.J., Mattiello, J., LeBihan, D.: Estimation of the effective self-diffusion tensor from the NMR spin echo. J. Magn. Reson. B 103(3), 247–254 (1994)CrossRefGoogle Scholar
  2. 2.
    Basser, P.J., Pajevic, S., Pierpaoli, C., Duda, J., Aldroubi, A.: In vivo fiber tractography using DT-MRI data. Magnetic Resonance in Medicine 44(4), 625–632 (2000)CrossRefGoogle Scholar
  3. 3.
    Catani, M., de Schotten, M.T.: A diffusion tensor imaging tractography atlas for virtual in vivo dissections. Cortex 44(8), 1105–1132 (2008)CrossRefGoogle Scholar
  4. 4.
    Chkrebtii, O., Campbell, D., Girolami, M., Calderhead, B.: Bayesian uncertainty quantification for differential equations. arXiv stat.ME 1306.2365 (June 2013)Google Scholar
  5. 5.
    Desikan, R.S., et al.: An automated labeling system for subdividing the human cerebral cortex on MRI scans into gyral based regions of interest. NeuroImage 31(3), 968–980 (2006)CrossRefGoogle Scholar
  6. 6.
    van Essen, D., et al.: The Human Connectome Project: a data acquisition perspective. NeuroImage 62(4), 2222–2231 (2012)CrossRefGoogle Scholar
  7. 7.
    van Essen, D., et al.: The WU-Minn Human Connectome Project: an overview. NeuroImage 80, 62–79 (2013)CrossRefGoogle Scholar
  8. 8.
    Fuster, A., et al.: A novel Riemannian metric for geodesic tractography in DTI. In: Computational Diffusion MRI and Brain Connectivity. Mathematics and Visualization, pp. 97–104 (2014)Google Scholar
  9. 9.
    Glasser, M., et al.: The minimal preprocessing pipelines for the human connectome project. NeuroImage 80, 105–124 (2013)CrossRefGoogle Scholar
  10. 10.
    Hairer, E., Nørsett, S., Wanner, G.: Solving Ordinary Differential Equations I – Nonstiff Problems. Springer (1987)Google Scholar
  11. 11.
    Hao, X., Whitaker, R.T., Fletcher, P.T.: Adaptive Riemannian metrics for improved geodesic tracking of white matter. In: Székely, G., Hahn, H.K. (eds.) IPMI 2011. LNCS, vol. 6801, pp. 13–24. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  12. 12.
    Hennig, P., Hauberg, S.: Probabilistic solutions to differential equations and their application to Riemannian statistics. In: AISTATS. JMLR, W&CP, vol. 33 (2014)Google Scholar
  13. 13.
    Lenglet, C., Deriche, R., Faugeras, O.: Inferring white matter geometry from diffusion tensor MRI: Application to connectivity mapping. In: Pajdla, T., Matas, J.(G.) (eds.) ECCV 2004. LNCS, vol. 3024, pp. 127–140. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  14. 14.
    O’Donnell, L., Haker, S., Westin, C.-F.: New approaches to estimation of white matter connectivity in diffusion tensor MRI: Elliptic PDEs and geodesics in a tensor-warped space. In: Dohi, T., Kikinis, R. (eds.) MICCAI 2002, Part I. LNCS, vol. 2488, pp. 459–466. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  15. 15.
    Parker, G., et al.: A framework for a streamline-based probabilistic index of connectivity (PICo) using a structural interpretation of MRI diffusion measurements. J. Magn. Reson. Imaging 18(2), 242–254 (2003)CrossRefGoogle Scholar
  16. 16.
    Prados, E., et al.: Control theory and fast marching techniques for brain connectivity mapping. In: CVPR, pp. 1076–1083 (2006)Google Scholar
  17. 17.
    Rasmussen, C., Williams, C.: GPs for Machine Learning. MIT Press (2006)Google Scholar
  18. 18.
    Schultz, T., et al.: Fuzzy fibers: Uncertainty in dMRI tractography. arXiv cs.CV 1307.3271 (2013)Google Scholar
  19. 19.
    Skilling, J.: Bayesian solution of ordinary differential equations. Maximum Entropy and Bayesian Methods, Seattle (1991)Google Scholar
  20. 20.
    Sotiropoulos, S.N., et al.: Effects of image reconstruction on fiber orientation mapping from multichannel diffusion MRI: reducing the noise floor using SENSE. Magn. Reson. Med. 70(6), 1682–1689 (2013)CrossRefGoogle Scholar
  21. 21.
    Wassermann, D., Rathi, Y., Bouix, S., Kubicki, M., Kikinis, R., Shenton, M., Westin, C.-F.: White matter bundle registration and population analysis based on gaussian processes. In: Székely, G., Hahn, H.K. (eds.) IPMI 2011. LNCS, vol. 6801, pp. 320–332. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  22. 22.
    Zhang, Y., et al.: Segmentation of brain MR images through a hidden Markov random field model and the expectation-maximization algorithm. IEEE TMI 20(1), 45–57 (2001)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Michael Schober
    • 1
  • Niklas Kasenburg
    • 1
    • 2
  • Aasa Feragen
    • 1
    • 2
  • Philipp Hennig
    • 1
  • Søren Hauberg
    • 3
  1. 1.Max Planck Institute for Intelligent SystemsTübingenGermany
  2. 2.Department of Computer ScienceUniversity of CopenhagenDenmark
  3. 3.Technical University of DenmarkDenmark

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