Skip to main content
SpringerLink
Log in

Neural Tractography Using an Unscented Kalman Filter

  • Conference paper
Information Processing in Medical Imaging (IPMI 2009)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 5636))

Included in the following conference series:

Abstract

We describe a technique to simultaneously estimate a local neural fiber model and trace out its path. Existing techniques estimate the local fiber orientation at each voxel independently so there is no running knowledge of confidence in the estimated fiber model. We formulate fiber tracking as recursive estimation: at each step of tracing the fiber, the current estimate is guided by the previous. To do this we model the signal as a mixture of Gaussian tensors and perform tractography within a filter framework. Starting from a seed point, each fiber is traced to its termination using an unscented Kalman filter to simultaneously fit the local model and propagate in the most consistent direction. Despite the presence of noise and uncertainty, this provides a causal estimate of the local structure at each point along the fiber. Synthetic experiments demonstrate that this approach reduces signal reconstruction error and significantly improves the angular resolution at crossings and branchings. In vivo experiments confirm the ability to trace out fibers in areas known to contain such crossing and branching while providing inherent path regularization.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Basser, P., Jones, D.: Diffusion-tensor MRI: theory, experimental design and data analysis - A technical review. NMR in Biomedicine 25, 456–467 (2002)

    Article  Google Scholar 

  2. Behrens, T., 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. Magnetic Resonance in Medicine 50, 1077–1088 (2003)

    Article  Google Scholar 

  3. Alexander, D., Barker, G., Arridge, S.: Detection and modeling of non-Gaussian apparent diffusion coefficient profiles in human brain data. Magnetic Resonance in Medicine 48, 331–340 (2002)

    Article  Google Scholar 

  4. Frank, L.: Characterization of anisotropy in high angular resolution diffusion-weighted MRI. Magnetic Resonance in Medicine 47, 1083–1099 (2002)

    Article  Google Scholar 

  5. Alexander, A., Hasan, K., Tsuruda, J., Parker, D.: Analysis of partial volume effects in diffusion-tensor MRI. Magnetic Resonance in Medicine 45, 770–780 (2001)

    Article  Google Scholar 

  6. Tuch, D., Reese, T., Wiegell, M., Makris, N., Belliveau, J., Wedeen, V.: High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity. Magnetic Resonance in Medicine 48, 577–582 (2002)

    Article  Google Scholar 

  7. Kreher, B., Schneider, J., Mader, I., Martin, E., Hennig, J., Il’yasov, K.: Multitensor approach for analysis and tracking of complex fiber configurations. Magnetic Resonance in Medicine 54, 1216–1225 (2005)

    Article  Google Scholar 

  8. Peled, S., Friman, O., Jolesz, F., Westin, C.F.: Geometrically constrained two-tensor model for crossing tracts in DWI. Magnetic Resonance in Medicine 24(9), 1263–1270 (2006)

    Google Scholar 

  9. Hlawitschka, M., Scheuermann, G.: HOT-lines: Tracking lines in higher order tensor fields. In: Visualization, pp. 27–34 (2005)

    Google Scholar 

  10. McGraw, T., Vemuri, B., Yezierski, B., Mareci, T.: Von Mises-Fisher mixture model of the diffusion ODF. In: Int. Symp. on Biomedical Imaging, pp. 65–68 (2006)

    Google Scholar 

  11. Kaden, E., Knøsche, T., Anwander, A.: Parametric spherical deconvolution: Inferring anatomical connectivity using diffusion MR imaging. NeuroImage 37, 474–488 (2007)

    Article  Google Scholar 

  12. Rathi, Y., Michailovich, O., Shenton, M., Bouix, S.: Directional functions for orientation distribution estimation. Medical Image Analysis (in press, 2009)

    Google Scholar 

  13. Özarslan, E., Shepherd, T., Vemuri, B., Blackband, S., Mareci, T.: Resolution of complex tissue microarchitecture using the diffusion orientation transform. NeuroImage 31(3) (2006)

    Google Scholar 

  14. Tuch, D.: Q-ball imaging. Magnetic Resonance in Medicine 52, 1358–1372 (2004)

    Article  Google Scholar 

  15. Anderson, A.: Measurement of fiber orientation distributions using high angular resolution diffusion imaging. Magnetic Resonance in Medicine 54(5), 1194–1206 (2005)

    Article  Google Scholar 

  16. Hess, C., Mukherjee, P., Han, E., Xu, D., Vigneron, D.: Q-ball reconstruction of multimodal fiber orientations using the spherical harmonic basis. Magnetic Resonance in Medicine 56, 104–117 (2006)

    Article  Google Scholar 

  17. Descoteaux, M., Angelino, E., Fitzgibbons, S., Deriche, R.: Regularized, fast, and robust analytical Q-ball imaging. Magnetic Resonance in Medicine 58, 497–510 (2007)

    Article  Google Scholar 

  18. Michailovich, O., Rathi, Y.: On approximation of orientation distributions by means of spherical ridgelets. In: Int. Symp. on Biomedical Imaging, pp. 939–942 (2008)

    Google Scholar 

  19. Poupon, C., Roche, A., Dubois, J., Mangin, J.F., Poupon, F.: Real-time MR diffusion tensor and Q-ball imaging using Kalman filtering. Medical Image Analysis 12(5), 527–534 (2008)

    Article  Google Scholar 

  20. Jian, B., Vemuri, B.: A unified computational framework for deconvolution to reconstruct multiple fibers from diffusion weighted MRI. Trans. on Medical Imaging 26(11), 1464–1471 (2007)

    Article  Google Scholar 

  21. Jansons, K., Alexander, D.: Persistent angular structure: New insights from diffusion MRI data. Inverse Problems 19, 1031–1046 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  22. Tournier, J.D., Calamante, F., Gadian, D., Connelly, A.: Direct estimation of the fiber orientation density function from diffusion-weighted MRI data using spherical deconvolution. NeuroImage 23, 1176–1185 (2004)

    Article  Google Scholar 

  23. Kumar, R., Barmpoutis, A., Vemuri, B., Carney, P., Mareci, T.: Multi-fiber reconstruction from DW-MRI using a continuous mixture of von Mises-Fisher distributions. In: Mathematical Methods in Biomedical Image Analysis (MMBIA), pp. 1–8 (2008)

    Google Scholar 

  24. Alexander, D.: Multiple-fiber reconstruction algorithms for diffusion MRI. Annals of the New York Academy of Sciences 1046 (2005)

    Google Scholar 

  25. Descoteaux, M., Deriche, R., Anwander, A.: Deterministic and probabilistic Q-ball tractography: from diffusion to sharp fiber distributions. Technical Report 6273, INRIA (2007)

    Google Scholar 

  26. Basser, P., Pajevic, S., Pierpaoli, C., Duda, J., Aldroubi, A.: In vivo fiber tractography using DT-MRI data. Magnetic Resonance in Medicine 44, 625–632 (2000)

    Article  Google Scholar 

  27. Hagmann, P., Reese, T., Tseng, W.Y., Meuli, R., Thiran, J.P., Wedeen, V.: Diffusion spectrum imaging tractography in complex cerebral white matter: An investigation of the centrum semiovale. In: Int. Symp. on Magnetic Resonance in Medicine (ISMRM), p. 623 (2004)

    Google Scholar 

  28. Guo, W., Zeng, Q., Chen, Y., Liu, Y.: Using multiple tensor deflection to reconstruct white matter fiber traces with branching. In: Int. Symp. on Biomedical Imaging, pp. 69–72 (2006)

    Google Scholar 

  29. Qazi, A., Radmanesh, A., O’Donnell, L., Kindlmann, G., Peled, S., Whalen, S., Westin, C.F., Golby, A.: Resolving crossings in the corticospinal tract by two-tensor streamline tractography: Method and clinical assessment using fMRI. NeuroImage (2008)

    Google Scholar 

  30. Gössl, C., Fahrmeir, L., Putz, B., Auer, L., Auer, D.: Fiber tracking from DTI using linear state space models: Detectability of the pyramidal tract. NeuroImage 16, 378–388 (2002)

    Article  Google Scholar 

  31. Björnemo, M., Brun, A., Kikinis, R., Westin, C.F.: Regularized stochastic white matter tractography using diffusion tensor MRI. In: Dohi, T., Kikinis, R. (eds.) MICCAI 2002. LNCS, vol. 2488, pp. 435–442. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  32. Zhang, F., Goodlett, C., Hancock, E., Gerig, G.: Probabilistic fiber tracking using particle filtering. In: Ayache, N., Ourselin, S., Maeder, A. (eds.) MICCAI 2007, Part II. LNCS, vol. 4792, pp. 144–152. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  33. Zhukov, L., Barr, A.: Oriented tensor reconstruction: Tracing neural pathways from diffusion tensor MRI. In: Visualization, pp. 387–394 (2002)

    Google Scholar 

  34. Parker, G., Alexander, D.: Probabilistic Monte Carlo based mapping of cerebral connections utilizing whole-brain crossing fiber information. In: Taylor, C.J., Noble, J.A. (eds.) IPMI 2003. LNCS, vol. 2732, pp. 684–696. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  35. Campbell, J.W., Siddiqi, K., Rymar, V., Sadikot, A., Pike, G.: Flow-based fiber tracking with diffusion tensor and Q-ball data: Validation and comparison to principal diffusion direction techniques. NeuroImage 27(4), 725–736 (2005)

    Article  Google Scholar 

  36. Hosey, T., Williams, G., Ansorge, R.: Inference of multiple fiber orientations in high angular resolution diffusion imaging. Magnetic Resonance in Medicine 54, 1480–1489 (2005)

    Article  Google Scholar 

  37. Behrens, T., Johansen-Berg, H., Jbabdi, S., Rushworth, M., Woolrich, M.: Probabilistic diffusion tractography with multiple fibre orientations: What can we gain? NeuroImage 34, 144–155 (2007)

    Article  Google Scholar 

  38. Zhan, W., Yang, Y.: How accurately can the diffusion profiles indicate multiple fiber orientations? A study on general fiber crossings in diffusion MRI. J. of Magnetic Resonance 183, 193–202 (2006)

    Article  Google Scholar 

  39. Seunarine, K., Cook, P., Hall, M., Embleton, K., Parker, G., Alexander, D.: Exploiting peak anisotropy for tracking through complex structures. In: Mathematical Methods in Biomedical Image Analysis (MMBIA), pp. 1–8 (2007)

    Google Scholar 

  40. Bloy, L., Verma, R.: On computing the underlying fiber directions from the diffusion orientation distribution function. In: Metaxas, D., Axel, L., Fichtinger, G., Székely, G. (eds.) MICCAI 2008, Part I. LNCS, vol. 5241, pp. 1–8. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  41. Schultz, T., Seidel, H.: Estimating crossing fibers: A tensor decomposition approach. Trans. on Visualization and Computer Graphics 14(6), 1635–1642 (2008)

    Article  Google Scholar 

  42. Ramirez-Manzanares, A., Cook, P., Gee, J.: A comparison of methods for recovering intra-voxel white matter fiber architecture from clinical diffusion imaging scans. In: Metaxas, D., Axel, L., Fichtinger, G., Székely, G. (eds.) MICCAI 2008, Part I. LNCS, vol. 5241, pp. 305–312. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  43. Friman, O., Farnebäck, G., Westin, C.F.: A Bayesian approach for stochastic white matter tractography. Trans. on Medical Imaging 25(8), 965–978 (2006)

    Article  Google Scholar 

  44. Parker, G., Alexander, D.: Probabilistic anatomical connectivity derived from the microscopic persistent angular structure of cerebral tissue. Phil. Trans. R. Soc. B 360, 893–902 (2005)

    Article  Google Scholar 

  45. Julier, S., Uhlmann, J.: Unscented filtering and nonlinear estimation. IEEE 92(3), 401–422 (2004)

    Article  Google Scholar 

  46. van der Merwe, R., Wan, E.: Sigma-point Kalman filters for probabilistic inference in dynamic state-space models. In: Workshop on Advances in Machine Learning (2003)

    Google Scholar 

  47. Mallat, S., Zhang, Z.: Matching pursuits with time-frequency dictionaries. Trans. on Signal Processing 41, 3397–3415 (1993)

    Article  MATH  Google Scholar 

  48. Anwander, A., Descoteaux, M., Deriche, R.: Probabilistic Q-Ball tractography solves crossings of the callosal fibers. In: Human Brain Mapping, p. 342 (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Psychiatry Neuroimaging Laboratory, Harvard Medical School, Boston, MA, USA

    James G. Malcolm, Martha E. Shenton & Yogesh Rathi

  2. Brockton Division, VA Boston Healthcare System, Brockton, MA, USA

    Martha E. Shenton

Authors
  1. James G. Malcolm
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Martha E. Shenton
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yogesh Rathi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, Johns Hopkins University, 3400 North Charles Street, MD 21218, Baltimore, USA

    Jerry L. Prince

  2. Department of Radiology, Johns Hopkins University, 600 North Wolfe Street, MD 21287, Baltimore, USA

    Dzung L. Pham

  3. Division of Imaging and Applied Mathematics, OSEL, U.S. Food and Drug Administration, 10903 New Hampshire Avenue, MD 20993, Silver Spring, USA

    Kyle J. Myers

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Malcolm, J.G., Shenton, M.E., Rathi, Y. (2009). Neural Tractography Using an Unscented Kalman Filter. In: Prince, J.L., Pham, D.L., Myers, K.J. (eds) Information Processing in Medical Imaging. IPMI 2009. Lecture Notes in Computer Science, vol 5636. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02498-6_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02498-6_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02497-9

  • Online ISBN: 978-3-642-02498-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation