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Brain Connectivity Measures via Direct Sub-Finslerian Front Propagation on the 5D Sphere Bundle of Positions and Directions

  • Jorg Portegies
  • Stephan Meesters
  • Pauly Ossenblok
  • Andrea Fuster
  • Luc Florack
  • Remco DuitsEmail author
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)

Abstract

We propose a novel connectivity measure between brain regions using diffusion-weighted MRI. This connectivity measure is based on optimal sub-Finslerian geodesic front propagation on the 5D base manifold of (3D) positions and (2D) directions, the so-called sphere bundle. The advantage over spatial front propagations is that it prevents leakage at omnipresent crossings. Our optimal fronts on the sphere bundle are geodesically equidistant w.r.t. an asymmetric Finsler metric, and can be computed with existing anisotropic fast-marching methods. Comparisons to ground truth connectivities provided by the ISBI-HARDI challenge reveal promising results, both quantitatively and qualitatively. We also apply the connectivity measures to real data from the Human Connectome Project.

Keywords

Diffusion MRI Brain connectivity Fast-marching Sphere bundle Geodesic fronts Finsler geometry 

Notes

Acknowledgements

Data provided in part by the HCP, WU-Minn Consortium (PI’s: D. Van Essen and K. Ugurbil; 1U54MH091657). We thank S. Mariën for co-developing the rching Tool, available at https://goo.gl/D5Q7dE (Downloads section). We thank J.M. Mirebeau for his Hamiltonian fast-marching C++-code, available at https://www.math.u-psud.fr/~mirebeau. The research leading to these results has received funding from the European Research Council under the European Community’s 7-th Framework Programme (FP7/2007-2013) / ERC grant Lie Analysis, agr. nr. 335555.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Jorg Portegies
    • 1
  • Stephan Meesters
    • 1
    • 2
  • Pauly Ossenblok
    • 1
  • Andrea Fuster
    • 1
  • Luc Florack
    • 1
  • Remco Duits
    • 1
    Email author
  1. 1.Department of Mathematics and Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Academic Center for Epileptology Kempenhaeghe and Maastricht University Medical CenterMaastrichtThe Netherlands

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