Representing diffusion MRI in 5D for segmentation of white matter tracts with a level set method

Abstract

We present a method for segmenting white matter tracts from high angular resolution diffusion MR images by representing the data in a 5 dimensional space of position and orientation. Whereas crossing fiber tracts cannot be separated in 3D position space, they clearly disentangle in 5D position-orientation space. The segmentation is done using a 5D level set method applied to hyper-surfaces evolving in 5D position-orientation space. In this paper we present a methodology for constructing the position-orientation space. We then show how to implement the standard level set method in such a non-Euclidean high dimensional space. The level set theory is basically defined for N-dimensions but there are several practical implementation details to consider, such as mean curvature. Finally, we will show results from a synthetic model and a few preliminary results on real data of a human brain acquired by high angular resolution diffusion MRI. © Springer-Verlag Berlin Heidelberg 2005.