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

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 or spherical deconvolution. 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 ODFs can either be estimated from single q-shell datasets, or exploit the greater information available from multiple q-shell acquisitions. We show that this 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 data and real HARDI volumes.