Control Theory and Fast Marching Techniques for Brain Connectivity Mapping

  • Authors:

  • Emmanuel Prados;Stefano Soatto;Christophe Lenglet;Jean-Philippe Pons;Nicolas Wotawa;Rachid Deriche;Olivier Faugeras

  • Affiliations:

  • UCLA Vision Lab., USA;UCLA Vision Lab., USA;Odyssee Lab., INRIA, France;Odyssee Lab., INRIA, France;Odyssee Lab., INRIA, France;Odyssee Lab., INRIA, France;Odyssee Lab., INRIA, France

  • Venue:
  • CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
  • Year:
  • 2006

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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. OurGCM(Geodesic Connectivity Mapping) algorithm is implemented in C++ and will be soon available on the web.