Abstract
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.
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Notes
- 1.
It is important to distinguish between white matter fibers (fascicles) and observed “tracts.” In this paper we use “tracts” to denote the 3D-curves recovered from diffusion-weighted imaging via tractography algorithms.
- 2.
The largest study to date aims to have 100,000 subjects participating in the imaging cohort [15]. By our back-of-the-envelope estimate, 100,000 subjects with 10,000,000 tracts each would require about 1.5 petabytes of disk space, just for the tractograms.
- 3.
In short, we are asserting that \(\hat{P}\) converges as the number of samples used to construct it increases. This does not guarantee that \(\hat{P}\) converges to P.
- 4.
Please contact the authors to access the code.
- 5.
The definition of complete noise is actually tricky, but we could use a proxy of “drawing a tract length uniformly at random between 1 and the number of voxels, and filling its sequence with points drawn uniformly from the domain of the image”.
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Acknowledgements
This work was supported by NIH Grant U54 EB020403 and DARPA grant W911NF-16-1-0575, as well as the NSF Graduate Research Fellowship Program Grant Number DGE-1418060.
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Moyer, D.C., Thompson, P., Steeg, G.V. (2019). Measures of Tractography Convergence. In: Bonet-Carne, E., Grussu, F., Ning, L., Sepehrband, F., Tax, C. (eds) Computational Diffusion MRI. MICCAI 2019. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-030-05831-9_23
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