Diffusion Propagator Imaging (DPI): an alternative to Diffusion Spectrum Imaging (DSI)

INTRODUCTION: The quest of diffusion-weighted (DW) imaging is to non-invasively obtain information about the average diffusion of water molecules in biological tissue. Many recent high angular resolution diffusion imaging (HARDI) [1, and references therein] techniques are proposed to infer the diffusion or fiber orientation distribution function (ODF), but this ODF only captures the angular structure of the diffusion process. In this work, we are interested in the reconstruction of the full three-dimensional (3D) ensemble average propagator (EAP) describing the diffusion process. Under the narrow pulse assumption, the relationship between the diffusion signal attenuation, E(q), in q-space and the EAP in real space, P(R), is given by an Fourier transform (FT), P(R) = FT[ E(q) ]. Diffusion Spectrum Imaging (DSI) [2] is currently the only established method exploiting this relation in order to reconstruct a model-free EAP in the human brain. DSI measures DW images along as many directions and as many q-values as possible on a 3D Cartesian grid before computing the FT giving the EAP. More recently, another technique was proposed to perform measurements along many radial lines before computing 1D tomographic projections to reconstruct the 3D EAP [3]. Other techniques suggest using multiple spherical shells sampling, but reconstruct other functions than the EAP, such as generalized high order tensors [4] or the diffusion orientation transform (DOT) [5] or the Kurtosis [6] or a better diffusion ODF [7]. As of today, most methods for EAP reconstruction ([2,3]) unfortunately need to use more than 200 DW measurements, considerably limiting their application. We present diffusion propagator imaging (DPI), a novel technique for simple and linear analytical EAP reconstruction using Laplace's equation. We show that EAP reconstruction from DPI is similar to the established DSI reconstruction from the same subject, and is, thus, an alternative.