Diffusion Propagator Estimation Using Radial Basis Functions

  • Yogesh Rathi
  • Marc Niethammer
  • Frederik Laun
  • Kawin Setsompop
  • Oleg Michailovich
  • P. Ellen Grant
  • C.-F. Westin
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)


The average diffusion propagator (ADP) obtained from diffusion MRI (dMRI) data encapsulates important structural properties of the underlying tissue. Measures derived from the ADP can be potentially used as markers of tissue integrity in characterizing several mental disorders. Thus, accurate estimation of the ADP is imperative for its use in neuroimaging studies. In this work, we propose a simple method for estimating the ADP by representing the acquired diffusion signal in the entire q-space using radial basis functions (RBF). We demonstrate our technique using two different RBF’s (generalized inverse multiquadric and Gaussian) and derive analytical expressions for the corresponding ADP’s. We also derive expressions for computing the solid angle orientation distribution function (ODF) for each of the RBF’s. Estimation of the weights of the RBF’s is done by enforcing positivity constraint on the estimated ADP or ODF. Finally, we validate our method on data obtained from a physical phantom with known fiber crossing of 45 degrees and also show comparison with the solid spherical harmonics method of Descoteaux et al. (Med Image Anal 2010). We also demonstrate our method on in-vivo human brain data.



This work has been supported by NIH grants: R01MH097979 (YR), R01MH074794 (CFW), P41RR013218, P41EB015902 and Swedish VR grant 2012-3682(CFW).


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Yogesh Rathi
    • 1
  • Marc Niethammer
    • 2
  • Frederik Laun
    • 3
  • Kawin Setsompop
    • 4
  • Oleg Michailovich
    • 5
  • P. Ellen Grant
    • 6
  • C.-F. Westin
    • 1
  1. 1.Brigham and Women’s Hospital, Harvard Medical SchoolBostonUSA
  2. 2.University of North CarolinaChapel HillUSA
  3. 3.German Cancer Research CenterHeidelbergGermany
  4. 4.Massachusetts General Hospital, Harvard Medical SchoolBostonUSA
  5. 5.University of WaterlooWaterlooCanada
  6. 6.Boston Children’s Hospital, Harvard Medical SchoolBostonUSA

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