Name
Abstract | ||
|---|---|---|
We introduce an original approach for the cerebral white matter connectivity mapping from diffusion tensor imaging (DTI). Our method relies on a global modeling of the acquired magnetic resonance imaging volume as a Riemannian manifold whose metric directly derives from the diffusion tensor. These tensors will be used to measure physical three-dimensional distances between different locations of a brain diffusion tensor image. The key concept is the notion of geodesic distance that will allow us to find optimal paths in the white matter. We claim that such optimal paths are reasonable approximations of neural fiber bundles. The geodesic distance function can be seen as the solution of two theoretically equivalent but, in practice, significantly different problems in the partial differential equation framework: an initial value problem which is intrinsically dynamic, and a boundary value problem which is, on the contrary, intrinsically stationary. The two approaches have very different properties which make them more or less adequate for our problem and more or less computationally efficient. The dynamic formulation is quite easy to implement but has several practical drawbacks. On the contrary, the stationary formulation is much more tedious to implement; we will show, however, that it has many virtues which make it more suitable for our connectivity mapping problem. Finally, we will present different possible measures of connectivity, reflecting the degree of connectivity between different regions of the brain. We will illustrate these notions on synthetic and real DTI datasets. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1137/070710986 | SIAM J. Imaging Sciences |
Keywords | Field | DocType |
riemannianmanifolds,different location,anisotropic eikonal equation,different region,different problem,brownian motion,initial value problem,partial differen- tial equations,optimal path,different property,control theory,diffusion process,level set,boundary value problem,different possible measure,brain connectivity mapping,riemannian geometry,diffusion tensor imaging,hamilton-jacobi-bellman equations,connectivity mapping problem,fast marching methods,cerebral white matter connectivity,intrinsic distance function,fast marching method,eikonal equation,magnetic resonance image,three dimensional,hamilton jacobi bellman equation,partial differential equations,geodesic distance,distance function,diffusion tensor | Topology,Boundary value problem,Mathematical optimization,Diffusion MRI,Tensor,Mathematical analysis,Riemannian manifold,Initial value problem,Riemannian geometry,Partial differential equation,Mathematics,Geodesic | Journal |
Volume | Issue | ISSN |
2 | 2 | 1936-4954 |
Citations | PageRank | References |
10 | 0.59 | 35 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Christophe Lenglet | 1 | 880 | 56.06 |
| Emmanuel Prados | 2 | 450 | 20.47 |
| Jean-Philippe Pons | 3 | 915 | 46.17 |
| Rachid Deriche | 4 | 4903 | 633.65 |
| Olivier D. Faugeras | 5 | 9364 | 2568.69 |