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 relying on diffusion MRI. These fiber bundles act as highways for neural activity. Current statistical methods reduce the rich information into an adjacency matrix, with the elements containing a count of fibers or a mean diffusion feature along the fibers. The goal of this article is to avoid discarding the rich geometric information 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 into a rotation matrix, shape and translation from a global reference curve. These components are viewed as data lying on a product space composed of different Euclidean spaces and manifolds. To nonparametrically 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 efficient methods for posterior sampling. The approach automatically produces clusters of fibers within and across individuals. Applying the method to Human Connectome Project data, we find interesting relationships between brain fiber geometry and reading ability. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

Keywords:

• Brain connectomics
• Connectome geometry
• Functional data analysis
• Mixture model
• Shape analysis

Acknowledgments

We want to thank the anonymous reviewers for their comments to improve our rotation matrix embedding procedure and sensitivity analysis of shape component representation.

Additional information

Funding

The research of Z. Zhang is partially supported by grants MH118020 and MH118927 of the United States National Institute of Health. The research of D. Dunson is partially supported by grant MH118927 of the United States National Institute of Health, W911NF from the Army Research Institute, and N00014 from the Office of Naval Research. M. Descoteaux is thankful to his Institutional Research Chair in NeuroInformatics and his NSERC Discovery grants. We thank Kevin Whittingstall, Michael Bernier, Maxime Chamberland, Gabriel Girard, and Jean-Christophe Houde for acquiring the test-retest database (supported by the CHU Sherbrooke and the NeuroInformatics Research Chair jointly funded by the Medical and Science faculties). We thank the Human Connectome Project, WU-Minn Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil; 1U54MH091657) funded by the 16 NIH Institutes and Centers that support the NIH Blueprint for Neuroscience Research; and by the McDonnell Center for Systems Neuroscience at Washington University.