About the geometry of asymmetric fiber orientation distributions

Fiber orientation distributions (FODs) based on diffusion-sensitized magnetic resonance imaging are usually symmetric, primarily due to the nature of the diffusion. In contrast, the underlying fiber configurations are not, as bending or fanning configurations are inherently asymmetric. We propose to dismiss the symmetry of the FOD to additionally encode the asymmetry of the underlying fiber configuration. This is of particular importance for low resolution images that are common in diffusion weighted imaging. We set up the mathematical foundations and geometric interpretations of asymmetric FODs and show how one can benefit from these considerations. We infer a continuity condition that is used as a prior during FOD estimation by constrained spherical deconvolution. This new prior shows superior performance in comparison to other spatial regularization strategies in reliability and accuracy.