Logical Foundations and Fast Implementation of Probabilistic Tractography

Abstract

Although tractography can noninvasively map axonal pathways, current approaches are typically incomplete or computationally intensive. Fast, complete maps may serve as a useful clinical tool for assessing neurological disorders stemming from pathological anatomical connections such as epilepsy. We re-frame tractography in terms of logic and conditional probabilities. The formalism inherently includes global constraints and can compute connections between any two arbitrary regions of the brain. The formalism also lends itself to a fast implementation using standard partial differential equation solvers, which makes whole-brain probabilistic maps of anatomical connectivity feasible. We demonstrate results of our implementation on in vivo data and show that it outperforms Monte Carlo approaches in both computation time and identification of pathways.