Reconstruction of the orientation distribution function in single- and multiple-shell q-ball imaging within constant solid angle

Iman Aganj, Christophe Lenglet, Guillermo Sapiro, Essa Yacoub, Kamil Ugurbil, Noam Harel
2010 Magnetic Resonance in Medicine  
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
more » ... 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. Key words: Orientation distribution function (ODF), q-ball imaging (QBI), high angular resolution diffusion imaging (HARDI), solid angle. normalized and dimensionless expression. In addition, we illustrate through our experiments that the ODFs are naturally sharp and that multiple fiber orientations are thus better resolved. We also provide a general formulation for multiple q-shell QBI, and demonstrate the improvement achieved by considering the information from multiple q-shells and using richer multi-exponential models. Furthermore, by making use of the spherical harmonic basis, we demonstrate that the implementation of the new, mathematically correct expression is as straightforward as that of the original formula, or maybe even simpler, considering that further sharpening (post-processing) is not necessary. This paper extends our previous conference versions for single (10) and multiple q-shells (11). In particular, we provide complete mathematical proofs, a regularization scheme, and additional validation and comparisons. 1
doi:10.1002/mrm.22365 pmid:20535807 pmcid:PMC2911516 fatcat:xqid4hwn2rfidd6ls5hrsxcwrq