Diffusion Propagator Estimation Using Gaussians Scattered in q-Space

  • Lipeng Ning
  • Oleg Michailovich
  • Carl-Fredrik Westin
  • Yogesh Rathi
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)


The ensemble average diffusion propagator (EAP) obtained from diffusion MRI (dMRI) data captures important structural properties of the underlying tissue. As such, it is imperative to derive accurate estimate of the EAP from the acquired diffusion data. Taking inspiration from the theory of radial basis functions, we propose a method for estimating the EAP by representing the diffusion signal as a linear combination of 3D anisotropic Gaussian basis functions centered at the sample points in the q-space. This is in contrast to other methods, that always center the Gaussians at the origin in q-space. We also derive analytical expressions for the estimated diffusion orientation distribution function (ODF), the return-to-the-origin probability (RTOP) and the mean-squared-displacement (MSD). We validate our method on data obtained from a physical phantom with known crossing angle and on in-vivo human brain data. The performance is compared with the 3D-SHORE method of [4, 9] and radial basis function based method of [15].



This work has been supported by NIH grants: R01MH097979 (Rathi), R01MH074794 (Westin), P41RR013218, P41EB015902 (Kikinis, Core PI: Westin), and Swedish research grant VR 2012-3682 (Westin).


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Lipeng Ning
    • 1
  • Oleg Michailovich
    • 2
  • Carl-Fredrik Westin
    • 1
  • Yogesh Rathi
    • 1
  1. 1.Brigham and Women’s Hospital, Harvard Medical SchoolBostonUSA
  2. 2.University of WaterlooWaterlooCanada

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