Fiber Density Estimation from Single Q-shell Diffusion Imaging by Tensor Divergence

Diffusion-weighted magnetic resonance imaging provides information about the nerve fiber bundle geometry of the human brain. While the inference of the underlying fiber bundle orientation only requires single q-shell measurements, the absolute determination of their volume fractions is much more challenging with respect to measurement techniques and analysis. Unfortunately, the usually employed multi-compartment models cannot be applied to single q-shell measurements, because the compartment's diffusivities cannot be resolved. This work proposes an equation for fiber orientation densities that can infer the absolute fraction up to a global factor. This equation, which is inspired by the classical mass preservation law in fluid dynamics, expresses the fiber conservation associated with the assumption that fibers do not terminate in white matter. Simulations on synthetic phantoms show that the approach is able to derive the densities correctly for various configurations. Experiments with a pseudo ground truth phantom show that even for complex, brain-like geometries the method is able to infer the densities correctly. In-vivo results with 81 healthy volunteers are plausible and consistent. A group analysis with respect to age and gender show significant differences, such that the proposed maps can be used as a quantitative measure for group and longitudinal analysis.