Inference of brain connectivity

C. Poupon, C. A. Clark, V. Frouin, J. Régis,
I. Bloch, D. Le Bihan, and J.-F. Mangin
Regularization of Diffusion-based direction maps
for the tracking of brain white matter fascicles
Neuroimage,
12(2):184--195,
2000

Magnetic resonance diffusion tensor imaging (DTI) provides information about fiber local directions in brain white matter. This paper addresses inference of the connectivity induced by fascicles made up of numerous fibers from such diffusion data. The usual fascicle tracking idea, which consists of following locally the direction of highest diffusion, is prone to erroneous forks because of problems induced by fiber crossing. In this paper, this difficulty is partly overcomed by the use of a priori knowledge of the low curvature of most of the fascicles. This knowledge is embedded in a model of the bending energy of a spaghetti plate representation of the white matter used to compute a regularized fascicle direction map. A new tracking algorithm is then proposed to highlight putative fascicle trajectories from this direction map. This algorithm takes into account potential fan shaped junctions between fascicles. A study of the tracking behavior according to the influence given to the a priori knowledge is proposed and concrete tracking results obtained with in vivo human brain data are illustrated. These results include putative trajectories of some pyramidal, commissural and various association fibers.

J.-F. Mangin, C. Poupon, Y. Cointepas,
D. Rivière, D. Papadopoulos-Orfanos,
C. A. Clark, J. Régis, and D. Le Bihan
A framework based on spin glass models
for the inference of anatomical connectivity
from diffusion-weighted MR data
NMR in Biomedicine,
15:481--492,
2002

A family of methods aiming at the reconstruction of a putative fascicle map from any diffusion-weighted dataset is proposed. This fascicle map is defined as a trade-off between local information on voxel micro-structure provided by diffusion data and a priori information on the low curvature of plausible fascicles. The optimal fascicle map is the minimum energy configuration of a simulated spin glass in which each spin represents a fascicle piece. This spin glass is embedded into a simulated magnetic external field that tends to align the spins along the more probable fiber orientations according to diffusion models. A model of spin interactions related to the curvature of the underlying fascicles introduces a low bending potential constraint. Hence, the optimal configuration is a trade-off between these two kind of forces acting on the spins. Experimental results are presented for the simplest spin glass model made up of compass needles located in the center of each voxel of a tensor based acquisition.

Y. Cointepas, C. Poupon, D. Le Bihan, and J.-F. Mangin
A spin glass based framework
to untangle fiber crossing
in MR diffusion based tracking
In Proc. 5th MICCAI, Tokyo, Japan,
pages 475--482,
LNCS 2488 (Part I), Springer Verlag,
2002

We propose a general approach to the reconstruction of brain white matter geometry from diffusion-weighted data. This approach is based on an inverse problem framework. The optimal geometry corresponds to the lowest energy configuration of a spin glass. These spins represent pieces of fascicles that orient themselves according to diffusion data and interact in order to create low curvature fascicles. Simulated diffusion-weighted datasets corresponding to the crossing of two fascicle bundles are used to validate the method