Brain Parcellation and Connectivity Mapping Using Wasserstein Geometry

  • Hamza Farooq
  • Yongxin Chen
  • Tryphon Georgiou
  • Christophe Lenglet
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)


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.



Data were provided in part by the Human Connectome Project, WU-Minn Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil 1U54MH091657) funded by the 16 NIH Institutes and Centers that support the NIH Blueprint for Neuroscience Research; and by the McDonnell Center for Systems Neuroscience at Washington University. The work was partly supported by NIH grants P41 EB015894, P30 NS076408, and Fulbright Program.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Hamza Farooq
    • 1
  • Yongxin Chen
    • 2
  • Tryphon Georgiou
    • 3
  • Christophe Lenglet
    • 4
  1. 1.Department of Electrical and Computer EngineeringUniversity of MinnesotaMinneapolisUSA
  2. 2.Department of Medical PhysicsMemorial Sloan Kettering Cancer CenterNew YorkUSA
  3. 3.Department of Mechanical and Aerospace EngineeringUniversity of CaliforniaIrvineUSA
  4. 4.Center for Magnetic Resonance Research, Department of RadiologyUniversity of MinnesotaMinneapolisUSA

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