Title: Director Field Analysis (DFA): Exploring Local White Matter Geometric Structure in diffusion MRI,
Abstract: In Diffusion Tensor Imaging (DTI) or High Angular Resolution Diffusion
Imaging (HARDI), a tensor field or a spherical function field (e.g., an
orientation distribution function field), can be estimated from measured
diffusion weighted images. In this paper, inspired by the microscopic
theoretical treatment of phases in liquid crystals, we introduce a novel
mathematical framework, called Director Field Analysis (DFA), to study local
geometric structural information of white matter based on the reconstructed
tensor field or spherical function field: 1) We propose a set of mathematical
tools to process general director data, which consists of dyadic tensors that
have orientations but no direction. 2) We propose Orientational Order (OO) and
Orientational Dispersion (OD) indices to describe the degree of alignment and
dispersion of a spherical function in a single voxel or in a region,
respectively; 3) We also show how to construct a local orthogonal coordinate
frame in each voxel exhibiting anisotropic diffusion; 4) Finally, we define
three indices to describe three types of orientational distortion (splay, bend,
and twist) in a local spatial neighborhood, and a total distortion index to
describe distortions of all three types. To our knowledge, this is the first
work to quantitatively describe orientational distortion (splay, bend, and
twist) in general spherical function fields from DTI or HARDI data. The
proposed DFA and its related mathematical tools can be used to process not only
diffusion MRI data but also general director field data, and the proposed
scalar indices are useful for detecting local geometric changes of white matter
for voxel-based or tract-based analysis in both DTI and HARDI acquisitions. The
related codes and a tutorial for DFA will be released in DMRITool.