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Control Theory and Fast Marching Techniques for Brain Connectivity Mapping

Emmanuel Prados 1, 2 Christophe Lenglet 1, 3 Jean-Philippe Pons 1, 4 Nicolas Wotawa 1 Rachid Deriche 1 Olivier Faugeras 1 Stefano Soatto 5
1 ODYSSEE - Computer and biological vision
DI-ENS - Département d'informatique de l'École normale supérieure, CRISAM - Inria Sophia Antipolis - Méditerranée , ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
2 MOVI - Modeling, localization, recognition and interpretation in computer vision
GRAVIR - IMAG - Laboratoire d'informatique GRAphique, VIsion et Robotique de Grenoble, Inria Grenoble - Rhône-Alpes, CNRS - Centre National de la Recherche Scientifique : FR71
3 Siemens Corporate Research
4 CERTIS - Centre d'Enseignement et de Recherche en Technologies de l'Information et Systèmes
5 UCLA-CS - Computer Science Department [UCLA]
Abstract : We propose a novel, fast and robust technique for the computation of anatomical connectivity in the brain. Our approach exploits the information provided by Diffusion Tensor Magnetic Resonance Imaging (or DTI) and models the white matter by using Riemannian geometry and control theory. We show that it is possible, from a region of interest, to compute the geodesic distance to any other point and the associated optimal vector field. The latter can be used to trace shortest paths coinciding with neural fiber bundles. We also demonstrate that no explicit computation of those 3D curves is necessary to assess the degree of connectivity of the region of interest with the rest of the brain. We finally introduce a general local connectivity measure whose statistics along the optimal paths may be used to evaluate the degree of connectivity of any pair of voxels. All those quantities can be computed simultaneously in a Fast Marching framework, directly yielding the connectivity maps. Apart from being extremely fast, this method has other advantages such as the strict respect of the convoluted geometry of white matter, the fact that it is parameter-free, and its robustness to noise. We illustrate our technique by showing results on real and synthetic datasets. Our GCM (Geodesic Connectivity Mapping) algorithm is implemented in C++ and will be soon available on the web.
Keywords : Brownian motion diffusion process control theory partial differential equations Riemannian manifolds HamiltonJacobiBellman equations level set fast marching methods anisotropic Eikonal equation intrinsic distance function brain connectivity mapping diffusion tensor imaging
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Emmanuel Prados, Christophe Lenglet, Jean-Philippe Pons, Nicolas Wotawa, Rachid Deriche, et al.. Control Theory and Fast Marching Techniques for Brain Connectivity Mapping. IEEE Conference on Computer Vision and Pattern Recognition, Jun 2006, New York, United States. pp.1076--1083, ⟨10.1109/CVPR.2006.89⟩. ⟨inria-00377403⟩

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