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

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Computational Diffusion MRI (MICCAI 2019)

Part of the book series: Mathematics and Visualization ((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.

Jorg Portegies, Stephan Meesters and Remco Duits: Joint main authors.

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Notes

  1. 1.

    ‘Quasi’ pertains to its asymmetrical nature.

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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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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands

    Jorg Portegies, Stephan Meesters, Pauly Ossenblok, Andrea Fuster, Luc Florack & Remco Duits

  2. Academic Center for Epileptology Kempenhaeghe and Maastricht University Medical Center, Maastricht, The Netherlands

    Stephan Meesters

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  1. Jorg Portegies
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Correspondence to Remco Duits .

Editor information

Editors and Affiliations

  1. Centre for Medical Image Computing, University College London, London, UK

    Elisenda Bonet-Carne

  2. Queen Square Institute of Neurology and Centre for Medical Image Computing, University College London, London, UK

    Francesco Grussu

  3. Psychiatry Neuroimaging Laboratory, Brigham and Women’s Hospital, Harvard Medical School, Boston, MA, USA

    Lipeng Ning

  4. Laboratory of Neuro Imaging (LONI), Stevens Neuroimaging and Informatics Institute, Keck School of Medicine, University of Southern California, Los Angeles, CA, USA

    Farshid Sepehrband

  5. Cardiff University Brain Research Imaging Centre (CUBRIC), Cardiff University, Cardiff, UK

    Chantal M. W. Tax

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Portegies, J., Meesters, S., Ossenblok, P., Fuster, A., Florack, L., Duits, R. (2019). Brain Connectivity Measures via Direct Sub-Finslerian Front Propagation on the 5D Sphere Bundle of Positions and Directions. 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_24

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