Inferring Macroscopic Brain Connectomes via Group-Sparse Factorization

Abstract

Mapping the macrostructural connectivity of the living human brain is one of the primary goals of neuroscientists who study connectomics. The reconstruction of a brain's structural connectivity, aka its connectome, typically involves applying expert analysis to diffusion-weighted magnetic resonance imaging (dMRI). A data-driven approach -- inferring the underlying model from data -- could overcome the limitations of such human-based approaches and improve precision mappings for a novel brain. In this work, we explore a framework that facilitates applying learning algorithms to automatically extract brain connectomes. Using a tensor encoding to unify the representation of brain structure and diffusion information, we design a constrained objective function with a group-regularizer that prefers a biologically plausible structure for each bundle of neuronal axons, called a fascicle. We show that the objective is convex and has a unique solution, ensuring identifiable connectomes for an individual brain. We develop an efficient optimization strategy for this extremely high-dimensional sparse problem, by reducing the number of parameters using a greedy algorithm, called GreedyOrientation, designed specifically for the problem. We show that GreedyOrientation significantly improves on a standard greedy algorithm, called Orthogonal Matching Pursuit. We confirm that our method works effectively by reconstructing structural connectivity of two major tracts. We conclude with an analysis of the solutions found by our method, showing it can accurately reconstruct the diffusion information while maintaining contiguous fascicles with smooth direction changes.