Spatial Autoregressive von-Mises Fisher Regression for Diffusion Tensor Imaging

The principal diffusion directions, representing the tissue fiber orientations, are one of the most important markers derived from diffusion tensor imaging (DTI). They are frequently analyzed in several medical studies. However, only a few approaches are available for covariate-dependent statistical analysis for the principal diffusion direction data. To address this gap, we propose a novel generalized linear model to analyze such that using a von Mises Fisher (vMF) distributed error structure. Using a novel link function that relies on the transformation between Cartesian and spherical coordinates, we regress the vMF distributed principal diffusion directions on the subject's covariates. This regression model allows us to measure the importance of the clinical factors on fiber orientations. Furthermore, we impose the spatial dependence to be supported along a given fiber using an autoregressive model. This novel specification renders computational efficiency and flexibility. For Bayesian inference of the directional data, a comprehensive toolbox is thoroughly developed with applications to neuroimaging analysis. We first show the method's empirical efficacy through simulation experiments. Subsequently, applying our regression model to the Alzheimer's Disease Neuroimaging Initiative (ADNI) data, we acquire new insights related to the progression of cognitive impairment.