Estimation of Anatomical Connectivity by Anisotropic Front Propagation and Diffusion Tensor Imaging

  • Marcel Jackowski
  • Chiu Yen Kao
  • Maolin Qiu
  • R. Todd Constable
  • Lawrence H. Staib
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3217)


Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) allows one to capture the restricted diffusion of water molecules in fibrous tissues which can be used to infer their structural organization. In this paper, we propose a novel wavefront propagation method for estimating the connectivity in the white matter of the brain using DT-MRI. First, an anisotropic version of the static Hamilton-Jacobi equation is solved by a sweeping method in order to obtain accurate front arrival times and determine connectivity. Our wavefront then propagates using the diffusion tensor rather than its principal eigenvector, which is prone to misclassification in oblate tensor regions. Furthermore, we show that our method is robust to noise and can estimate connectivity pathways across regions where singularities, such as fiber crossings, are present. Preliminary connectivity results on synthetic data and on a normal human brain are illustrated and discussed.


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  1. 1.
    Alexander, A.L., Hasan, K.M., Lazar, M., Tsuruda, J.S., Parker, D.L.: Analysis of partial volume effects in diffusion-tensor MRI. Mag. Res. Medicine 45(5), 770–780 (2001)CrossRefGoogle Scholar
  2. 2.
    Basser, P.J., Pierpaoli, C.: Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. J. Mag. Res. Series B 111(3), 209–219 (1996)CrossRefGoogle Scholar
  3. 3.
    Basser, P.J., Pajevic, S., PierPaoli, C., Duda, J., Aldroubi, A.: In-vivo fiber tractography using DT-MRI data. Mag. Res. Medicine 44, 625–632 (2000)CrossRefGoogle Scholar
  4. 4.
    Jones, D.K., Simmons, A., Williams, S.C., Horsfield, M.A.: Noninvasive assessment of axonal fiber connectivity in the human brain via diffusion tensor MRI. Mag. Res. Medicine 42, 37–41 (1999)CrossRefGoogle Scholar
  5. 5.
    Kao, C., Osher, S., Qian, J.: Lax-Friedrichs Sweeping scheme for static Hamilton- Jacobi equations. Journal of Computational Physics (2003) (in press)Google Scholar
  6. 6.
    Kao, C., Osher, S., Tsai,Y.: Fast Sweeping Methods for static Hamilton Jacobi equations. Technical report, University of California Los Angeles (2002),
  7. 7.
    Lenglet, C., Deriche, R., Faugeras, O.: Diffusion tensor magnetic resonance imaging: Brain connectivity mapping. Research Report 4983, INRIA (2003) Google Scholar
  8. 8.
    Lori, N.F., Akbudak, E., Shimony, J.S., Cull, T.S., Snyder, A.Z., Guillory, R.K., Conturo, T.E.: Diffusion tensor fiber tracking of human brain connectivity: aquisition methods, reliability analysis and biological results. NMR in Biomedicine 15(7-8), 494–515 (2002)CrossRefGoogle Scholar
  9. 9.
    Mori, S., van Zijl, P.C.M.: Fiber tracking: principles and strategies - a technical review. NMR in Biomedicine 15(7-8), 468–480 (2002)CrossRefGoogle Scholar
  10. 10.
    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. LNCS, vol. 2488, pp. 459–466. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  11. 11.
    Osher, S., Fedkiw, R.: Level Set Methods and Dynamic Implicit Surfaces, 1st edn. Springer, New York (2003)MATHGoogle Scholar
  12. 12.
    Parker, G.J.M., Wheeler-Kingshott, C.A.M., Barker, G.J.: Estimating distributed anatomical connectivity using fast marching methods and diffusion tensor imaging. IEEE Trans. Med. Imaging 21(5), 505–512 (2002)CrossRefGoogle Scholar
  13. 13.
    Sethian, J.A., Vladimirsky, A.: Ordered Upwind Methods for static HamiltonJacobi equations. PNAS 98(20) (September 2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Marcel Jackowski
    • 1
  • Chiu Yen Kao
    • 3
  • Maolin Qiu
    • 1
  • R. Todd Constable
    • 2
  • Lawrence H. Staib
    • 2
  1. 1.Dept. of Diagnostic RadiologyYale School of MedicineNew HavenUSA
  2. 2.Dept. of Diagnostic Radiology and Biomedical EngineeringYale School of MedicineNew HavenUSA
  3. 3.Dept. of MathematicsUniversity of California Los AngelesLos AngelesUSA

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