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 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.