Rotational gradient field for interpolation of fiber orientation distribution in connectivity analysis

Advances in diffusion weighted MR imaging have made it possible to non-invasively study the structral connectivity of human brains at high resolution. To model crossing fibers in white matter, a popular choice is the reconstruction of fiber orientation distributions (FODs) from diffusion data. For this sophiscated image representation of brain connectivity, classical image operations such as differentiation and interpolation must be redefined. In this paper, we introduce rotational gradient fields (RGF) as the spatial differential of FODs´ orientations. By taking into accout the rotational effect of traveling in the RGF, an FOD at one location can be transported and aligned with the FOD at the target location. We propose a method for inducing RGFs with FOD metrics. We also show how RGFs can be used for interpolation, yielding intuitively more reasonable results than the Frechet mean on the unit sphere in a Hilbert space [1].