Q‐ball reconstruction of multimodal fiber orientations using the spherical harmonic basis

Diffusion tensor imaging (DTI) accurately delineates white matter pathways when the Gaussian model of diffusion is valid. However, DTI yields erroneous results when diffusion takes on a more complex distribution, as is the case in the brain when fiber tracts cross. High angular resolution diffusion imaging (HARDI) overcomes this limitation of DTI by more fully characterizing the angular dependence of intravoxel diffusion. Among the various HARDI methods that have been proposed, QBI offers advantages such as linearity, model independence, and relatively easy implementation. In this work, reconstruction of the q-ball orientation distribution function (ODF) is reformulated in terms of spherical harmonic basis functions, yielding an analytic solution with useful properties of a frequency domain representation. The harmonic basis is parsimonious for typical b-values, which enables the ODF to be synthesized from a relatively small number of noisy measurements and thus brings the technique closer to clinical feasibility from the standpoint of total imaging time. The proposed method is assessed using Monte Carlo computer simulations and compared with conventional q-ball reconstruction using spherical RBFs. In vivo results from 3T whole-brain HARDI of adult volunteers are also provided to verify the underlying mathematical theory.