Brain Parcellation and Connectivity Mapping Using Wasserstein Geometry

Abstract

Several studies have used structural connectivity information to parcellate brain areas like the corpus callosum, thalamus, substantia nigra or motor cortex, which is otherwise difficult to achieve using conventional MRI techniques. They typically employ diffusion MRI (dMRI) tractography and compare connectivity profiles from individual voxels using correlation. However, this is potentially limiting since the profile signals (e.g. probabilistic connectivity maps) have non-zero values only in restricted areas of the brain, and correlation coefficients do not fully capture differences between connectivity profiles . Our first contribution is to introduce the Wasserstein distance as a metric to compare connectivity profiles, viewed as distributions. The Wasserstein metric (also known as Optimal Mass Transport cost or, Earth Mover’s distance) is natural as it allows a global comparison between probability distributions. Thereby, it relies not only on non-zero values but also takes into account their spatial pattern, which is crucial for the comparison of the brain connectivity profiles. Once a brain area is parcellated into anatomically relevant sub-regions, it is of interest to determine how voxels within each sub-region are collectively connected to the rest of the brain. The commonly used arithmetic mean of connectivity profiles fails to account for anatomical features and can easily over-emphasize spurious pathways. Therefore, our second contribution is to introduce the concept of Wasserstein barycenters of distributions, to estimate “average” connectivity profiles, and assess whether these are more representative of the neuroanatomy. We demonstrate the benefits of using the Wasserstein geometry to parcellate and “average” probabilistic tractography results from a realistic phantom dataset, as well as in vivo data from the Human Connectome Project.