  In the present work, we use information theory to understand the empirical
convergence rate of tractography, a widely-used approach to reconstruct
anatomical fiber pathways in the living brain. Based on diffusion MRI data,
tractography is the starting point for many methods to study brain
connectivity. Of the available methods to perform tractography, most
reconstruct a finite set of streamlines, or 3D curves, representing probable
connections between anatomical regions, yet relatively little is known about
how the sampling of this set of streamlines affects downstream results, and how
exhaustive the sampling should be. Here we provide a method to measure the
information theoretic surprise (self-cross entropy) for tract sampling schema.
We then empirically assess four streamline methods. We demonstrate that the
relative information gain is very low after a moderate number of streamlines
have been generated for each tested method. The results give rise to several
guidelines for optimal sampling in brain connectivity analyses.
