Apparent Intravoxel Fibre Population Dispersion (FPD) Using Spherical Harmonics

  • Haz-Edine Assemlal
  • Jennifer Campbell
  • Bruce Pike
  • Kaleem Siddiqi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6892)

Abstract

The vast majority of High Angular Resolution Diffusion Imaging (HARDI) modeling methods recover networks of neuronal fibres, using a heuristic extraction of their local orientation. In this paper, we present a method for computing the apparent intravoxel Fibre Population Dispersion (FPD), which conveys the manner in which distinct fibre populations are partitioned within the same voxel. We provide a statistical analysis, without any prior assumptions on the number or size of these fibre populations, using an analytical formulation of the diffusion signal autocorrelation function in the spherical harmonics basis. We also propose to extract features of the FPD obtained in the group of rotations, using several metrics based on unit quaternions. We show results on simulated data and on physical phantoms, that demonstrate the effectiveness of the FPD to reveal regions with crossing tracts, in contrast to the standard anisotropy measures.

Keywords

Probability Density Function Spherical Harmonic Euler Angle Unit Quaternion Spherical Harmonic Basis 
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.

References

  1. 1.
    Stejskal, E., Tanner, J.: Spin diffusion measurements: spin echoes in the presence of a time-dependent field gradient. J. Chem. Phys. 42, 288–292 (1965)CrossRefGoogle Scholar
  2. 2.
    Stejskal, E.: Use of spin echoes in a pulsed magnetic-field gradient to study anisotropic, restricted diffusion and flow. J. Chem. Phys. 43(10), 3597–3603 (1965)CrossRefGoogle Scholar
  3. 3.
    Assemlal, H.E., Tschumperlé, D., Brun, L.: Efficient and robust computation of PDF features from diffusion MR signal. Med. Image Anal. 13(5), 715–729 (2009)CrossRefGoogle Scholar
  4. 4.
    Cheng, J., Ghosh, A., Deriche, R., Jiang, T.: Model-free, regularized, fast, and robust analytical orientation distribution function estimation. In: Jiang, T., Navab, N., Pluim, J.P.W., Viergever, M.A. (eds.) MICCAI 2010. LNCS, vol. 6361, pp. 648–656. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Seunarine, K.K., Cook, P.A., Hall, M.G., Embleton, K.V., Parker, G.J.M., Alexander, D.C.: Exploiting peak anisotropy for tracking through complex structures. In: ICCV, pp. 1–8. IEEE, Los Alamitos (2007)Google Scholar
  6. 6.
    Savadjiev, P., Campbell, J., Descoteaux, M., Deriche, R., Pike, G., Siddiqi, K.: Labeling of ambiguous subvoxel fibre bundle configurations in high angular resolution diffusion MRI. NeuroImage 41(1), 58–68 (2008)CrossRefGoogle Scholar
  7. 7.
    Savadjiev, P., Kindlmann, G., Bouix, S., Shenton, M., Westin, C.: Local white matter geometry from diffusion tensor gradients. NeuroImage 49(4), 3175–3186 (2010)CrossRefGoogle Scholar
  8. 8.
    Su, Z., Coppens, P.: Rotation of real spherical harmonics. Found. Cryst. 50(5), 7673 (1994)MathSciNetMATHGoogle Scholar
  9. 9.
    Anderson, A.: Measurement of fiber orientation distributions using high angular resolution diffusion imaging. Magn. Reson. Med. 54(5) (2005)Google Scholar
  10. 10.
    Özarslan, E., Sherperd, T.M., Vemuri, B.C., Blackband, S.J., Mareci, T.H.: Resolution of complex tissue microarchitecture using the diffusion orientation transform (DOT). NeuroImage 31, 1086–1103 (2006)CrossRefGoogle Scholar
  11. 11.
    Descoteaux, M., Deriche, R., Bihan, D., Mangin, J., Poupon, C.: Multiple q-Shell Diffusion Propagator Imaging. Med. Image Anal. (2010)Google Scholar
  12. 12.
    Shoemake, K.: Graphics gems IV. In: Euler Angle Conversion, pp. 222–229. Academic Press Professional, Inc., London (1994)Google Scholar
  13. 13.
    Poupon, C., Rieul, B., Kezele, I., Perrin, M., Poupon, F., Mangin, J.F.: New diffusion phantoms dedicated to the study and validation of high-angular-resolution diffusion imaging (HARDI) models. Magn. Reson. Med. 60(6), 1276–1283 (2008)CrossRefGoogle Scholar
  14. 14.
    Tuch, D.: Q-ball imaging. Magnetic Resonance in Medicine 52, 1358–1372 (2004)CrossRefGoogle Scholar
  15. 15.
    Campbell, J., 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)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Haz-Edine Assemlal
    • 1
  • Jennifer Campbell
    • 2
  • Bruce Pike
    • 2
  • Kaleem Siddiqi
    • 1
  1. 1.Centre for Intelligent MachinesMcGill UniversityMontréalCanada
  2. 2.Montreal Neurological InstituteMcConnell Brain Imaging CentreMontréalCanada

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