Nonparametric Bayes Models of Fiber Curves Connecting Brain Regions

Abstract

In studying structural inter-connections in the human brain, it is common to first estimate fiber bundles connecting different regions of the brain relying on diffusion MRI. These fiber bundles act as highways for neural activity and communication, snaking through the brain and connecting different regions. Current statistical methods for analyzing these fibers reduce the rich information into an adjacency matrix, with the elements containing a count of the number of fibers or a mean diffusion feature (such as fractional anisotropy) along the fibers. The goal of this article is to avoid discarding the rich functional data on the shape, size and orientation of fibers, developing flexible models for characterizing the population distribution of fibers between brain regions of interest within and across different individuals. We start by decomposing each fiber in each individual's brain into a corresponding rotation matrix, shape and translation from a global reference curve. These components can be viewed as data lying on a product space composed of different Euclidean spaces and manifolds. To non-parametrically model the distribution within and across individuals, we rely on a hierarchical mixture of product kernels specific to the component spaces. Taking a Bayesian approach to inference, we develop an efficient method for posterior sampling. The approach automatically produces clusters of fibers within and across individuals, and yields interesting new insights into variation in fiber curves, while providing a useful starting point for more elaborate models relating fibers to covariates and neuropsychiatric traits.