GCM - Geodesic Connectivity Mapping

About / Introduction

What is the GCM Algorithm ?

In Short :

The GCM algorithm is "Fast Marching" based Algorithm for computing the anatomical connectivity in the brain. The algorithm computes the anisotropic geodesic distance map, the associated "gradients" and some connectivity measures with their statistics along the geodesics.

Detailed description :

The GCM Library (Geodesic Connectivity Mapping) is the C++ implementation of the GCM algorithm proposed by E. Prados, C. Lenglet, J.-P. Pons, Etal. in 2006 (see "Publications"). The GCM algorithm is a fast and robust algorithm for the computation of anatomical connectivity in the brain. It exploits the whole information provided by Diffusion Tensor Magnetic Resonance Imaging (or DTI) and it is based on some models of the white matter using Riemannian geometry and the control theory. The GCM algorithm allows, 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. The GCM algorithm also allows to compute the degree of connectivity of the region of interest with the rest of the brain without the need of explicit computation of the 3D geodesic curves. This degree of connectivity is based on a general local connectivity measure whose the algorithm computes the statistics along the optimal paths (geodesics). All those quantities are computed simultaneously in a process of the type "Fast Marching". Apart from being extremely fast, this algorithm 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. For some theoretical/algoritmics/implementation details, some samples of results and experimental validations, we refer to the associated publications (see "Publications").

Keywords :

• Control Theory, Fast Marching Methods, Partial Differential Equations (PDE),
  
• Anisotropic Distance Map, Anisotropic Geodesic Distances, Riemanian Manifold,
  
• Brain Connectivity Mapping, White Matter Fibers, Diffusion Tensor Images (DTI),
  
• Connectivity Measures, Statistics along the Geodesics,
  
• C++ source code.

Authors :

Christophe Lenglet , Jean-Philipe Pons , Emmanuel Prados

License :

The GCM Library is distributed and governed by an (LGPL-like) open source license: CeCILL-C License. The source code has been registered to the APP (French Agency for the Protection of Programs) by the INRIA and UCLA.