Efficient Computation of PDF-Based Characteristics from Diffusion MR Signal

  • Haz-Edine Assemlal
  • David Tschumperlé
  • Luc Brun
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5242)


We present a general method for the computation of PDF-based characteristics of the tissue micro-architecture in MR imaging. The approach relies on the approximation of the MR signal by a series expansion based on Spherical Harmonics and Laguerre-Gaussian functions, followed by a simple projection step that is efficiently done in a finite dimensional space. The resulting algorithm is generic, flexible and is able to compute a large set of useful characteristics of the local tissues structure. We illustrate the effectiveness of this approach by showing results on synthetic and real MR datasets acquired in a clinical time-frame.


Magnetic Resonance Signal High Angular Resolution Single Sphere Spherical Harmonics Basis Nuclear Magnetic Resonance Microscopy 
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.


  1. 1.
    Stejskal, E., Tanner, J.: Spin diffusion measurements: spin echoes in the presence of a time-dependent field gradient. Journal of Chemical Physics 42, 288–292 (1965)CrossRefGoogle Scholar
  2. 2.
    LeBihan, D., Breton, E., Lallemand, D., et al.: Mr imaging of intravoxel incoherent motions: Application to diffusion and perfusion in neurologic disorders. Radiology, 401–407 (1986)Google Scholar
  3. 3.
    Callaghan, P.: Principles of Nuclear Magnetic Resonance Microscopy. Oxford University Press (1991)Google Scholar
  4. 4.
    Basser, P., Mattiello, J., LeBihan, D.: Estimation of the effective self-diffusion tensor from the nmr spin echo. J. Magn. Reson. 103, 247–254 (1994)CrossRefGoogle Scholar
  5. 5.
    Jian, B., Vemuri, B.C., Özarslan, et al.: A novel tensor distribution model for the diffusion-weighted mr signal. NeuroImage 37, 164–176 (2007)CrossRefGoogle Scholar
  6. 6.
    Wedeen, V., Reese, T., Tuch, D., et al.: Mapping fiber orientation spectra in cerebral white matter with fourier transform diffusion mri. In: ISMRM, p. 82 (2000)Google Scholar
  7. 7.
    Tuch, D., Weisskoff, R., Belliveau, J., Wedeen, V.: High angular resolution diffusion imaging of the human brain, p. 321 (1999)Google Scholar
  8. 8.
    Tuch, D.: Q-ball imaging. Magn. Reson. Med. 52, 1358–1372 (2004)CrossRefGoogle Scholar
  9. 9.
    Descoteaux, M., Angelino, E., Fitzgibbons, S., Deriche, R.: Regularized, fast and robust analytical q-ball imaging. Magn. Reson. Med. 58, 497–510 (2007)CrossRefGoogle Scholar
  10. 10.
    Yablonskiy, D.A., Bretthorst, G.L., Ackerman, J.J.: Statistical model for diffusion attenuated mr signal. Magn. Reson. Med. 50, 664–669 (2003)CrossRefGoogle Scholar
  11. 11.
    Tournier, J., Calamante, F., Gadian, D., Connely, A.: Direct estimation of the fiber orientation density function from diffusion-weighted mri data using spherical deconvolution. NeuroImage 23, 1179–1185 (2004)CrossRefGoogle Scholar
  12. 12.
    Liu, C., Bammer, R., Acar, B., Moseley, M.E.: Characterizing non-gaussian diffusion by using generalized diffusion tensors. Magn. Reson. Med. 51, 924–937 (2004)CrossRefGoogle Scholar
  13. 13.
    Özarslan, E., Sherperd, T.M., Vemuri, B.C., et al.: Resolution of complex tissue microarchitecture using the diffusion orientation transform (dot). NeuroImage 31, 1086–1103 (2006)CrossRefGoogle Scholar
  14. 14.
    Assaf, Y., Basser, P.J.: Composite hindered and restricted model of diffusion (charmed) mr imaging of the human brain. NeuroImage 27, 48–58 (2005)CrossRefGoogle Scholar
  15. 15.
    Wu, Y.C., Alexander, A.L.: Hybrid diffusion imaging. NeuroImage 36 (2007)Google Scholar
  16. 16.
    Ritchie, D.W.: High-order analytic translation matrix elements for real-space six-dimensional polar fourier correlations. J. Appl. Cryst. 38, 808–818 (2005)CrossRefGoogle Scholar
  17. 17.
    Frank, L.: Characterization of anisotropy in high angular resolution diffusion-weighted mri. Magn. Reson. Med. 47, 1083–1099 (2002)CrossRefGoogle Scholar
  18. 18.
    Clark, C., Le Bihan, D.: Water diffusion and anisotropy at high b values in the human brain. Magn. Reson. Med. 44, 852–859 (2000)CrossRefGoogle Scholar
  19. 19.
    Cohen, Y., Assaf, Y.: High b-value q-space analyzed diffusion-weighted mrs and mri in neuronal tissues - a technical review. NMR Biomed. 15, 516–542 (2002)CrossRefGoogle Scholar
  20. 20.
    Niendorf, T., Dijkhuizen, R.M., Norris, D.G., van Lookeren, C.M.: Biexponential diffusion attenuation in various states of brain tissue: implications for diffusion-weighted imaging. Magn. Reson. Med. 36, 847–857 (1996)CrossRefGoogle Scholar
  21. 21.
    Assaf, Y., Cohen, Y.: In vivo and in vitro bi-exponential diffusion of n-acetyl aspartate (naa) in rat brain: a potential structural probe? NMR Biomed. 11 (1998)Google Scholar
  22. 22.
    Biedenharn, L.C., Louck, J.D.: Angular momentum in quantum physics. Addison-Wesley Publishing Co., Reading (1981)zbMATHGoogle Scholar
  23. 23.
    Blanco, M.A., Flórez, M., Bermejo, M.: Evaluation of the rotation matrices in the basis of real spherical harmonics. J. Mol. Struct. 419, 19–27 (1997)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Haz-Edine Assemlal
    • 1
  • David Tschumperlé
    • 1
  • Luc Brun
    • 1
  1. 1.GREYC (CNRS UMR 6072)Caen CedexFrance

Personalised recommendations