Magnetic resonance diffusion tensor imaging(DTI) provides a powerful tool for mapping neural histosrchitecture in vivo. However, DTI can only resolve a single fiber orientation within each imaging voxel due to the contraints of the tensor model. For example, DTI cannot resolve fibers crossing, bending, or twisting within an individual voxel. Intravoxel fiber crossing can be resolved using q-space diffusion imaging, but q-space imaging requires large pulsed field gradients and time-intensive sampling. It is also possible to resolve intravoxel fiber crossing using mixture model decompisition of the high angular resolution diffusion imaging(HARDI) signal, but mixture modeling requires a model of the underlying diffusion process.
Recently, it has been shown that the HARDI signal can be reconstructed model-independently using a spherical tomographic inversion called the Funk-Radon transform, also known as the spherical Radon transform. The resulting imaging method, termed q-ball imaging, can resolve multiple intravoxel fiber orientations and does not require any assumptions on the diffusion process such as Gaussianity or mulri-Gaussianity. The present paer reviews the theory of q-ball imaging anddescribed a simple linear matrix formulation for the q-ball reconstruction based on spherical radial basis function interpolation.
David S. Tuch, “Q-Ball Imaging“, Magn Reson Med 52:1358-1372, 2004.