Diffusion propagator imaging: a novel technique for reconstructing the diffusion propagator from multiple shell acquisitions

INTRODUCTION: Many recent techniques have been introduced for high angular resolution diffusion imaging (HARDI) [1 and references therein], to infer the diffusion or fiber orientation distribution function (ODF) of the underlying tissue structure. These methods, mostly designed for fiber tractography, are normally based on a single shell acquisition and can only recover some angular information contained in the ensemble average propagator (EAP). The (EAP) describes the full threedimensional (3D) average scattering of water molecules in biological tissue. It can thus provide more information about tissue properties than the ODF. Various methods already exist to estimate the EAP such as [2]-[8], but all have their limitations. Among the most commonly used, diffusion tensor imaging (DTI) [2] is limited by the Gaussian assumption and cannot account for complex fiber configurations, and diffusion spectrum imaging (DSI) [3] is a model-free approach but requires hundreds of diffusion weighted measurements to obtain the EAP. We present diffusion propagator imaging (DPI), a simple and linear analytical EAP reconstruction using Laplace's equation. The solution is computed from only two or more different b-value shells. Robust EAP is possible with less than 100 measurements per shell.