Adaptive Multi-modal Particle Filtering for Probabilistic White Matter Tractography

  • Aymeric Stamm
  • Olivier Commowick
  • Christian Barillot
  • Patrick Pérez
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7917)


Particle filtering has recently been introduced to perform probabilistic tractography in conjunction with DTI and Q-Ball models to estimate the diffusion information. Particle filters are particularly well adapted to the tractography problem as they offer a way to approximate a probability distribution over all paths originated from a specified voxel, given the diffusion information. In practice however, they often fail at consistently capturing the multi-modality of the target distribution. For brain white matter tractography, this means that multiple fiber pathways are unlikely to be tracked over extended volumes.

We propose to remedy this issue by formulating the filtering distribution as an adaptive M-component non-parametric mixture model. Such a formulation preserves all the properties of a classical particle filter while improving multi-modality capture. We apply this multi-modal particle filter to both DTI and Q-Ball models and propose to estimate dynamically the number of modes of the filtering distribution. We show on synthetic and real data how this algorithm outperforms the previous versions proposed in the literature.


Orientation Distribution Function Local Curvature Phantom Data Proposal Density Order Markov Chain 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aganj, I., Lenglet, C., Sapiro, G., Yacoub, E., Ugurbil, K., Harel, N.: Reconstruction of the orientation distribution function in single- and multiple-shell q-ball imaging within constant solid angle. MRM 64(2), 554–566 (2010)Google Scholar
  2. 2.
    Assaf, Y., Basser, P.: Composite hindered and restricted model of diffusion (CHARMED) MR imaging of the human brain. NeuroImage 27(1), 48–58 (2005)CrossRefGoogle Scholar
  3. 3.
    Assemlal, H., Tschumperlé, D., Brun, L., Siddiqi, K.: Recent advances in diffusion MRI modeling: Angular and radial reconstruction. MedIA (2011)Google Scholar
  4. 4.
    Banerjee, A., Dhillon, I., Ghosh, J., Sra, S.: Clustering on the unit hypersphere using von Mises-Fisher distributions. J. of Machine Learning 6, 1345–1382 (2006)MathSciNetGoogle Scholar
  5. 5.
    Basser, P.J., Pierpaoli, C.: Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. J. Magn. Reson. 111(3), 209–219 (1996)CrossRefGoogle Scholar
  6. 6.
    Basser, P.J., Pajevic, S., Pierpaoli, C., Duda, J., Aldroubi, A.: In vivo fiber tractography using DT-MRI data. MRM 44(4), 625–632 (2000)CrossRefGoogle Scholar
  7. 7.
    Basser, P.J., Mattiello, J., Le Bihan, D.: MR diffusion tensor spectroscopy and imaging. Biophysical Journal 66(1), 259–267 (1994)CrossRefGoogle Scholar
  8. 8.
    Behrens, T.E.J., Woolrich, M., Jenkinson, M., Johansen-Berg, H., Nunes, R., Clare, S., Matthews, P., Brady, J., Smith, S.: Characterization and propagation of uncertainty in diffusion-weighted MR imaging. MRM 50(5), 1077–1088 (2003)CrossRefGoogle Scholar
  9. 9.
    Behrens, T.E.J., Johansen-Berg, H., Jbabdi, S., Rushworth, M.F.S., Woolrich, M.W.: Probabilistic diffusion tractography with multiple fibre orientations: What can we gain? NeuroImage 34(1), 144–155 (2007)CrossRefGoogle Scholar
  10. 10.
    Bhalerao, A., Westin, C.-F.: Hyperspherical von Mises-Fisher mixture (HvMF) modelling of high angular resolution diffusion MRI. In: Ayache, N., Ourselin, S., Maeder, A. (eds.) MICCAI 2007, Part I. LNCS, vol. 4791, pp. 236–243. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    Doucet, A., Godsill, S., Andrieu, C.: On sequential Monte Carlo sampling methods for Bayesian filtering. Statistics and Computing 10(3), 197–208 (2000)CrossRefGoogle Scholar
  12. 12.
    Friman, O., Farnebäck, G., Westin, C.: A Bayesian approach for stochastic white matter tractography. IEEE TMI 25(8), 965–978 (2006)Google Scholar
  13. 13.
    Gasser, T., Sroka, L., Jennen-Steinmetz, C.: Residual variance and residual pattern in nonlinear regression. Biometrika 73(3), 625–633 (1986)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Jupp, P., Mardia, K.: A unified view of the theory of directional statistics. International Statistical Review 57(3), 261–294 (1989)zbMATHCrossRefGoogle Scholar
  15. 15.
    Lazar, M.: Mapping brain anatomical connectivity using white matter tractography. NMR in Biomedicine 23(7), 821–835 (2010)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Le Bihan, D.: Looking into the functional architecture of the brain with diffusion MRI. Nature Reviews. Neuroscience 4(6), 469–480 (2003)CrossRefGoogle Scholar
  17. 17.
    McGraw, T., Vemuri, B.: Von Mises-Fisher mixture model of the diffusion ODF. In: IEEE ISBI, pp. 65–68 (2006)Google Scholar
  18. 18.
    Mori, S., Crain, B.J., Chacko, V.P., van Zijl, P.C.: Three-dimensional tracking of axonal projections in the brain by magnetic resonance imaging. Annals of Neurology 45(2), 265–269 (1999)CrossRefGoogle Scholar
  19. 19.
    Ozarslan, E., Mareci, T.: Generalized diffusion tensor imaging and analytical relationships between diffusion tensor imaging and high angular resolution diffusion imaging. MRM 50(5), 955–965 (2003)CrossRefGoogle Scholar
  20. 20.
    Parker, G., Wheeler-Kingshott, C., Barker, G.: Estimating distributed anatomical connectivity using fast marching methods and diffusion tensor imaging. IEEE TMI 21(5), 505–512 (2002)Google Scholar
  21. 21.
    Pontabry, J., Rousseau, F.: Probabilistic tractography using Q-ball modeling and particle filtering. In: Fichtinger, G., Martel, A., Peters, T. (eds.) MICCAI 2011, Part II. LNCS, vol. 6892, pp. 209–216. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  22. 22.
    Staempfli, P., Jaermann, T., Crelier, G.R., Kollias, S., Valavanis, A., Boesiger, P.: Resolving fiber crossing using advanced fast marching tractography based on diffusion tensor imaging. NeuroImage 30(1), 110–120 (2006)CrossRefGoogle Scholar
  23. 23.
    Stamm, A., Pérez, P., Barillot, C.: A new multi-fiber model for low angular resolution diffusion MRI. In: IEEE ISBI, pp. 936–939 (2012)Google Scholar
  24. 24.
    Stejskal, E.O.: Use of spin echoes in a pulsed magnetic-field gradient to study anisotropic, restricted diffusion and flow. J. Chem. Phys. 43, 3597 (1965)CrossRefGoogle Scholar
  25. 25.
    Tuch, D.S.: Q-ball imaging. MRM 52(6), 1358–1372 (2004)CrossRefGoogle Scholar
  26. 26.
    Tuch, D.S., Reese, T., Wiegell, M., Makris, N., Belliveau, J., Wedeen, V.: High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity. MRM 48(4), 577–582 (2002)CrossRefGoogle Scholar
  27. 27.
    Vermaak, J., Doucet, A., Pérez, P.: Maintaining multimodality through mixture tracking. In: IEEE ICCV, vol. 2, pp. 1110–1116 (2003)Google Scholar
  28. 28.
    Zhang, F., Hancock, E., Goodlett, C., Gerig, G.: Probabilistic white matter fiber tracking using particle filtering and von Mises-Fisher sampling. MedIA 13(1), 5–18 (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Aymeric Stamm
    • 1
  • Olivier Commowick
    • 1
  • Christian Barillot
    • 1
  • Patrick Pérez
    • 2
  1. 1.VISAGES: INSERM U746 - CNRS UMR6074 - INRIAUniv. of Rennes IFrance
  2. 2.TechnicolorRennesFrance

Personalised recommendations