Diffusion Propagator Estimation Using Radial Basis Functions

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 Yogesh Rathi Brigham and Women’s Hospital, Harvard Medical School, Boston, MA, e-mail: [email protected] Marc Niethammer Universtiy of North Carolina, Chapel Hill, NC, e-mail: [email protected] Frederik Laun German Cancer Research Center, Heidelberg, Germany, e-mail: F.Laun@ dkfz-heidelberg.de Kawin Setsompop Massachusetts General Hospital, Harvard Medical School, Boston, MA, e-mail: [email protected] Oleg Michailovich University of Waterloo, Canada, e-mail: [email protected] P. Ellen Grant Boston Children’s Hospital, Harvard Medical School, Boston, MA, e-mail: Ellen.Grant@ childrens.harvard.edu C-F Westin Brigham and Women’s Hospital, Harvard Medical School, Boston, MA, e-mail: [email protected]