Reconstruction of the Orientation Distribution Function in Single and Multiple Shell Q-Ball Imaging within Constant Solid Angle

Abstract

Q-ball imaging (QBI) is a high angular resolution diffusion imaging (HARDI) technique which has been proven very successful in resolving multiple intravoxel fiber orientations in MR images. The standard computation of the orientation distribution function (ODF, the probability of diffusion in a given direction) from q-ball data uses linear radial projection, neglecting the change in the volume element along each direction. This results in spherical distributions that are different from the true ODFs. For instance, they are neither normalized nor as sharp as expected, and generally require post-processing, such as artificial sharpening. In this paper, a new technique is proposed that, by considering the solid angle factor, uses the mathematically correct definition of the ODF and results in a dimensionless and normalized ODF expression. Our model is flexible enough so that ODFs can be estimated either from single q-shell datasets, or by exploiting the greater information available from multiple q-shell acquisitions. We show that the latter can be achieved by using a more accurate multi-exponential model for the diffusion signal. The improved performance of the proposed method is demonstrated on artificial examples and high-resolution HARDI data acquired on a 7T magnet.