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Direct Glyph-based Visualization of Diffusion MR Data Using Deformed Spheres

  • Martin Domin
  • Sönke Langner
  • Norbert Hosten
  • Lars Linsen
Part of the Mathematics and Visualization book series (MATHVISUAL)

Summary

For visualization of medical diffusion data one typically computes a tensor field from a set of diffusion volume images scanned with different gradient directions. The resulting diffusion tensor field is visualized using glyph- or tracking-based approaches. The derivation of the tensor, in general, involves a loss in information, as the n > 6 diffusion values for the n gradient directions are reduced to six diverse entries of the symmetric 3 × 3 tensor matrix. We propose a direct diffusion visualization approach that does not operate on the diffusion tensor. Instead, we assemble the gradient vectors on a unit sphere and deform the sphere by the measured diffusion values in the respective gradient directions. We compute a continuous deformation model from the few discrete directions by applying several processing steps. First, we compute a triangulation of the spherical domain using a convex hull algorithm. The triangulation leads to neighborhood information for the position vectors of the discrete directions. Using a parameterization over the sphere we perform a Powell-Sabin interpolation, where the surface gradients are computed using least-squares fitting. The resulting triangular mesh is subdivided using a few Loop subdivision steps. The rendering of this subdivided triangular mesh directly leads to a glyph-based visualization of the directional diffusion measured in the respective voxel. In a natural and intuitive fashion, our deformed sphere visualization can exhibit additional, possibly valuable information in comparison to the classical tensor glyph visualization.

Keywords

Fractional Anisotropy Triangular Mesh Gradient Direction Subdivision Scheme High Angular Resolution 
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. [Aur91]
    F. Aurenhammer. Voronoi diagrams - a survey of a fundamental geometric data structure. ACM Computing Surveys, 23:345–405, 1991.CrossRefGoogle Scholar
  2. [Bar81]
    A. Barr. Superquadrics and angle-preserving transformations. IEEE Computer Graphics and Applications, 18(1):11–23, 1981.CrossRefGoogle Scholar
  3. [Bar96]
    C.B. Barber. The quickhull algorithm for convex hulls. ACM Transactions on Mathematical Software, 22(4):469–483, 1996.CrossRefMathSciNetzbMATHGoogle Scholar
  4. [BBKW02a]
    Mats Bjornemo, Anders Brun, Ron Kikinis, and Carl-Fredrik Westin. Regularized stochastic white matter tractography using diffusion tensor mri. In MICCAI 2002, 2002.Google Scholar
  5. [BBKW02b]
    A. Brun, M. Bjornemo, R. Kikinis, and C.-F. Westin. White matter tractography using sequential importance sampling. In ISMRM 2002, 2002.Google Scholar
  6. [BPP+00]
    Peter J. Basser, Sinisa Pajevic, Carlo Pierpaoli, Jeffrey Duda, and Akram Aldroubi. In vivo fiber tractography using dt-mri data. Magnetic Resonance in Medicine, 44:625–632, 2000.CrossRefGoogle Scholar
  7. [HS05]
    Mario Hlawitschka and Gerik Scheuermann. Hot-lines - tracking lines in higher order tensor fields. In Cláudio T. Silva, Eduard Gröller, and Holly Rushmeier, editors, Proceedings of IEEE Conference on Visualization 2005, pages 27-34, 2005.Google Scholar
  8. [KW99]
    Gordon Kindlmann and David Weinstein. Hue-balls and lit-tensors for direct volume rendering of diffusion tensor fields. In Proceedings of IEEE Conference on Visualization ’99, pages 183-189, Los Alamitos, CA, USA, 1999. IEEE Computer Society Press.Google Scholar
  9. [LeB01]
    D. LeBihan. Diffusion tensor imaging: Concepts and applications. Journal of Magnetic Resonance Imaging, 13:534–546, 2001.CrossRefGoogle Scholar
  10. [Loo87]
    C.T. Loop. Smooth subdivision surfaces based on triangles. Master’s thesis, Department of Mathematics, University of Utah, 1987.Google Scholar
  11. [OAS02]
    O.Coulon, D.C. Alex, and S.R.Arridge. Tensor field regularisation for dt-mr images. In Proceedings of British Conference on Medical Image Understanding and Analysis 2002, 2002.Google Scholar
  12. [PB96]
    C. Pierpaoli and P. J. Basser. Toward a quantitative assessment of diffusion anisotropy. Magn Reson Med., 36(6):893–906, 1996.CrossRefGoogle Scholar
  13. [PCF+00]
    C. Poupon, C. A. Clark, V. Frouin, J. Regis, I. Block, D. Le Behan, and J.-F. Mangin. Regularization of diffusion-based direction maps for the tracking of brain white matter fascicles. NeuroImage, 12:184–195, 2000.CrossRefGoogle Scholar
  14. [PDD+02]
    P.G.Batchelor, D.L.G.Hill, D.Atkinson, F.Calamanten, and A.Connellyn.Fibre-tracking by solving the diffusion-convection equation. In ISMRM 2002, 2002.Google Scholar
  15. [PP99]
    Sinisa Pajevic and Carl Pierpaoli. Color schemes to represent the orientation of anisotropic tissues from diffusion tensor data: Application to white matter fiber tract mapping in the human brain. Magnetic Resonance in Medicine, 42:526–540, 1999.CrossRefGoogle Scholar
  16. [PS77]
    M.J.D. Powell and M.A. Sabin. Piecewise quadratic approximation on triangles. ACM Transactions on Mathematical Software, 3(4):316–325, 1977.CrossRefMathSciNetzbMATHGoogle Scholar
  17. [PSB+02]
    Geoffrey J.M. Parker Klaas, E. Stephan, Gareth J. Barker, James B. Rowe, David, G. MacManus Claudia A. M. Wheeler-Kingshott, Olga Ciccarelli, Richard E. Passingham, Rachel, L. Spinks, Roger, N. D. Lemon, and Robert Turner. Initial demonstration of in vivo tracing of axonal projections in the macaque brain and comparison with the human brain using diffusion tensor imaging and fast marching tractography. NeuroImage, 15:797–809, 2002.CrossRefGoogle Scholar
  18. [TRW+02]
    D. S. Tuch, T. G. Reese, M. R. Wiegell, N. Makris, J. W. Belliveau, and V. J. Wedeen. High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity. Magn. Reson. Med., 48(4):577–582, 2002.CrossRefGoogle Scholar
  19. [Tuc04a]
    David S. Tuch. High angular resolution diffusion imaging reveals in-travoxel white matter fiber heterogeneity. Magnetic Resonance in Medicine, 48:577–582, 2004.Google Scholar
  20. [Tuc04b]
    David S. Tuch. Q-ball imaging. Magnetic Resonance in Medicine, 52:1358–1372, 2004.CrossRefGoogle Scholar
  21. [TWBW99]
    D. S. Tuch, R. M. Weisskoff, J. W. Belliveau, and V. J. Wedeen. High angular resolution diffusion imaging of the human brain. In Proceedings of the 7th Annual Meeting of ISMRM, page 321, 1999.Google Scholar
  22. [WKL99]
    David M. Weinstein, Gordon L. Kindlmann, and Eric C. Lundberg. Tensorlines: Advection-diffusion based propagation through diffusion tensor fields. In IEEE Visualization ’99, pages 249-254, 1999.Google Scholar
  23. [WMM+02]
    C.-F. Westin, S. E. Maier, H. Mamata, A. Nabavi, F. A. Jolesz, and R. Kikinis. Processing and visualization for diffusion tensor mri. Medical Image Analysis, 6:93–108, 2002.CrossRefGoogle Scholar
  24. [ZB02] L. Zhukov and A. Barr. Oriented tensor reconstruction: tracing neural pathways from diffusion tensor mri. In Proceedings of the conference on Visualization 2002, pages 387-394, 2002.Google Scholar
  25. [ZDL03]
    Song Zhang, Cagatay Demiralp, and David H. Laidlaw. Visualizing diffusion tensor mr images using streamtubes and streamsurfaces. IEEE Transactions on Visualization and Computer Graphics, 2003.Google Scholar

Copyright information

© Springer 2008

Authors and Affiliations

  • Martin Domin
    • 1
  • Sönke Langner
    • 1
  • Norbert Hosten
    • 1
  • Lars Linsen
    • 2
  1. 1.Department of Diagnostic Radiology and NeuroradiologyErnst-Moritz-Arndt-Universität GreifswaldGreifswaldGermany
  2. 2.Computational Science and Computer Science School of Engineering and ScienceJacobs UniversityBremenGermany

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