Probabilistic Tractography for Complex Fiber Orientations with Automatic Model Selection

  • Edwin Versteeg
  • Frans M. Vos
  • Gert Kwakkel
  • Frans C. T. van der Helm
  • Joor A. M. Arkesteijn
  • Olena Filatova
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)


Fiber tractography aims to reconstruct white matter (WM) connections in the brain. Challenges in these reconstructions include estimation of the fiber orientations in regions with multiple fiber populations, and the uncertainty in the fiber orientations as a result of noise. In this work, we use a range of multi-tensor models to cope with crossing fibers. The uncertainty in fiber orientation is captured using the Cramér-Rao lower bound. Furthermore, model selection is performed based on model complexity and goodness of fit. The performance of the framework on the fibercup phantom and human data was compared to the open source diffusion MRI toolkit Camino for a range of SNRs. Performance was quantified by using the Tractometer measures in the fibercup phantom and by comparing streamline counts of lateral projections of the corpus callosum (CC) in the human data. On the phantom data, the comparison showed that our method performs similar to Camino in crossing fiber regions, whilst performing better in a region with kissing fibers (median angular error of 0.73 vs 2.7, valid connections of 57% vs 21% when seed is in the corresponding region of interest). Furthermore, the amount of counts in the lateral projections was found to be higher using our method (19–89% increase depending on a subject). Altogether, our method outperforms the reference method on both phantom and human data allowing for in-vivo probabilistic multi fiber tractography with an objective model selection procedure.


  1. 1.
    Basser, P.J., Mattiello, J., LeBihan, D.: MR diffusion tensor spectroscopy and imaging. Biophys. J. 66(1), 259–267 (1994)CrossRefGoogle Scholar
  2. 2.
    Alexander, D.C., Hubbard, P.L., Hall, M.G., Moore, E.A., Ptito, M., Parker, G.J., Dyrby, T.B.: Orientationally invariant indices of axon diameter and density from diffusion MRI. Neuroimage 52(4), 1374–1389 (2010)CrossRefGoogle Scholar
  3. 3.
    Mori, S., van Zijl, P.: Fiber tracking: principles and strategies–a technical review. NMR Biomed. 15(7–8), 468–480 (2002)CrossRefGoogle Scholar
  4. 4.
    Jones, D.K.: Determining and visualizing uncertainty in estimates of fiber orientation from diffusion tensor MRI. Magn. Reson. Med. 49(1), 7–12 (2003)CrossRefGoogle Scholar
  5. 5.
    Behrens, T.E., Woolrich, M., Jenkinson, M., Johansen-Berg, H., Nunes, R., Clare, S., Matthews, P., Brady, J.M., Smith, S.M.: Characterization and propagation of uncertainty in diffusion-weighted MR imaging. Magn. Reson. Med. 50(5), 1077–1088 (2003)CrossRefGoogle Scholar
  6. 6.
    Tuch, D.S., Reese, T.G., Wiegell, M.R., Makris, N., Belliveau, J.W., Wedeen, V.J.: High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity. Magn. Reson. Med. 48(4), 577–582 (2002)CrossRefGoogle Scholar
  7. 7.
    Behrens, T.E., Berg, H.J., Jbabdi, S., Rushworth, M., Woolrich, M.: Probabilistic diffusion tractography with multiple fibre orientations: what can we gain? Neuroimage 34(1), 144–155 (2007)CrossRefGoogle Scholar
  8. 8.
    Jeurissen, B., Leemans, A., Tournier, J.D., Jones, D.K., Sijbers, J.: Investigating the prevalence of complex fiber configurations in white matter tissue with diffusion magnetic resonance imaging. Hum. Brain Mapp. 34(11), 2747–2766 (2013)CrossRefGoogle Scholar
  9. 9.
    Wedeen, V.J., Hagmann, P., Tseng, W.Y.I., Reese, T.G., Weisskoff, R.M.: Mapping complex tissue architecture with diffusion spectrum magnetic resonance imaging. Magn. Reson. Med. 54(6), 1377–1386 (2005)CrossRefGoogle Scholar
  10. 10.
    Tuch, D.S.: Q-ball imaging. Magn. Reson. Med. 52(6), 1358–1372 (2004)CrossRefGoogle Scholar
  11. 11.
    Jansons, K.M., Alexander, D.C.: Persistent angular structure: new insights from diffusion magnetic resonance imaging data. Inverse Prob. 19(5), 1031 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Kreher, B., Schneider, J., Mader, I., Martin, E., Hennig, J., Il’Yasov, K.: Multitensor approach for analysis and tracking of complex fiber configurations. Magn. Reson. Med. 54(5), 1216–1225 (2005)CrossRefGoogle Scholar
  13. 13.
    Taquet, M., Scherrer, B., Commowick, O., Peters, J.M., Sahin, M., Macq, B., Warfield, S.K.: A mathematical framework for the registration and analysis of multi-fascicle models for population studies of the brain microstructure. IEEE Trans. Med. Imag. 33(2), 504–517 (2014)CrossRefGoogle Scholar
  14. 14.
    Parker, G.J., Haroon, H.A., Wheeler-Kingshott, C.A.: A framework for a streamline-based probabilistic index of connectivity (pico) using a structural interpretation of MRI diffusion measurements. J. Magn. Reson. Imag. 18(2), 242–254 (2003)CrossRefGoogle Scholar
  15. 15.
    Jones, D.K.: Tractography gone wild: probabilistic fibre tracking using the wild bootstrap with diffusion tensor MRI. IEEE Trans. Med. Imag. 27(9), 1268–1274 (2008)CrossRefGoogle Scholar
  16. 16.
    Jeurissen, B., Leemans, A., Jones, D.K., Tournier, J.D., Sijbers, J.: Probabilistic fiber tracking using the residual bootstrap with constrained spherical deconvolution. Hum. Brain Mapp. 32(3), 461–479 (2011)CrossRefGoogle Scholar
  17. 17.
    Chung, H.W., Chou, M.C., Chen, C.Y.: Principles and limitations of computational algorithms in clinical diffusion tensor MR tractography. Am. J. Neuroradiol. 32(1), 3–13 (2011)Google Scholar
  18. 18.
    Yang, J., Poot, D.H., Caan, M.W., Su, T., Majoie, C.B., van Vliet, L.J., Vos, F.M.: Reliable dual tensor model estimation in single and crossing fibers based on jeffreys prior. PloS One 11(10), e0164336 (2016)CrossRefGoogle Scholar
  19. 19.
    Alexander, D., Barker, G., Arridge, S.: Detection and modeling of non-gaussian apparent diffusion coefficient profiles in human brain data. Magn. Reson. Med. 48(2), 331–340 (2002)CrossRefGoogle Scholar
  20. 20.
    Freidlin, R.Z., Ozarslan, E., Komlosh, M.E., Chang, L.C., Koay, C.G., Jones, D.K., Basser, P.J.: Parsimonious model selection for tissue segmentation and classification applications: a study using simulated and experimental DTI data. IEEE Trans. Med. Imag. 26(11), 1576–1584 (2007)CrossRefGoogle Scholar
  21. 21.
    Caan, M.W., Khedoe, H.G., Poot, D.H., Arjan, J., Olabarriaga, S.D., Grimbergen, K.A., Van Vliet, L.J., Vos, F.M.: Estimation of diffusion properties in crossing fiber bundles. IEEE Trans. Med. Imag. 29(8), 1504–1515 (2010)CrossRefGoogle Scholar
  22. 22.
    Poot, D.H., Klein, S.: Detecting statistically significant differences in quantitative MRI experiments, applied to diffusion tensor imaging. IEEE Trans. Med. Imag. 34(5), 1164–1176 (2015)CrossRefGoogle Scholar
  23. 23.
    Yang, J., Poot, D.H., Caan, M.W., Vos, F.M., van Vliet, L.J.: Rank-2 model-order selection in diffusion tensor MRI: information complexity based on the total Kullback-Leibler divergence. In: 2015 IEEE 12th International Symposium on Biomedical Imaging (ISBI), pp. 926–929. IEEE, New York (2015)Google Scholar
  24. 24.
    Bozdogan, H.: Akaike’s information criterion and recent developments in information complexity. J. Math. Psychol. 44(1), 62–91 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Vemuri, B.C., Liu, M., Amari, S.I., Nielsen, F.: Total bregman divergence and its applications to dti analysis. IEEE Trans. Med. Imag. 30(2), 475–483 (2011)CrossRefGoogle Scholar
  26. 26.
    Yang, J., Poot, D.H., Van Vliet, L.J., Vos, F.M.: Estimation of diffusion properties in three-way fiber crossings without overfitting. Phys. Med. Biol. 60(23), 9123 (2015)CrossRefGoogle Scholar
  27. 27.
    Sid, F.A., Abed-Meraim, K., Harba, R., Oulebsir-Boumghar, F.: Analytical performance bounds for multi-tensor diffusion-MRI. Magn. Reson. Imag. 36, 146–158 (2017)CrossRefGoogle Scholar
  28. 28.
    Cook, P., Bai, Y., Nedjati-Gilani, S., Seunarine, K., Hall, M., Parker, G., Alexander, D.: Camino: open-source diffusion-mri reconstruction and processing. In: 14th Scientific Meeting of the International Society for Magnetic Resonance in Medicine, vol. 2759, Seattle, WA (2006)Google Scholar
  29. 29.
    Neher, P.F., Descoteaux, M., Houde, J.C., Stieltjes, B., Maier-Hein, K.H.: Strengths and weaknesses of state of the art fiber tractography pipelines–a comprehensive in-vivo and phantom evaluation study using tractometer. Med. Image Anal. 26(1), 287–305 (2015)CrossRefGoogle Scholar
  30. 30.
    Côté, M.A., Girard, G., Boré, A., Garyfallidis, E., Houde, J.C., Descoteaux, M.: Tractometer: towards validation of tractography pipelines. Med. Image Anal. 17(7), 844–857 (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Edwin Versteeg
    • 1
  • Frans M. Vos
    • 1
    • 2
  • Gert Kwakkel
    • 3
  • Frans C. T. van der Helm
    • 4
  • Joor A. M. Arkesteijn
    • 1
  • Olena Filatova
    • 1
    • 4
  1. 1.Imaging PhysicsDelft University of TechnologyDelftThe Netherlands
  2. 2.Department of RadiologyAcademic Medical CenterAmsterdamThe Netherlands
  3. 3.Department of Rehabilitation MedicineVU University Medical CenterAmsterdamThe Netherlands
  4. 4.BioMechanical Engineering DepartmentDelft University of TechnologyDelftThe Netherlands

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