Spatial Autoregressive Model for von-Mises Fisher Distributed Principal Diffusion Directions

The principal diffusion directions are one of the most important statistics derived from diffusion tensor imaging (DTI). It is directional data that depict the anatomical structures of brain tissues. However, only a few approaches are available for covariate-dependent statistical modeling of principal diffusion directions. We thus propose a novel spatial autoregressive model by assuming that the principal diffusion directions are von-Mises Fisher (vMF) distributed directional data. Using a novel link function relying on transformation between Cartesian coordinates and spherical coordinates, we regress the vMF distributed principal diffusion directions on the subject's covariates, measuring how the clinical factors affect the anatomical structures. The spatial residual dependence along fibers is captured by an autoregressive model. Key statistical properties of the model and a comprehensive toolbox for Bayesian inference of the directional data with applications to medical imaging analysis are thoroughly developed. The numerical studies based on synthetic data demonstrate that our model has more accurate estimation of the effects of clinical factors. Applying our regression model to the Alzheimer's Disease Neuroimaging Initiative (ADNI) data, we obtain new insights.