ALE: Anisotropic Laplace Equation Method for Estimation of Cortical Thickness using Partial Tissue Fractions
Abstract
Automatic computation of cortical thickness based on T1 MR images is a critical step for neuroanatomical population studies. Limited spatial
resolution and partial volume effects, in which more than one tissue
type is represented in each voxel, have a significant impact on the
accuracy of thickness estimates, particularly if a hard intensity
threshold is used to delineate cortical boundaries. This paper describes a
novel method based on the anisotropic heat equation that explicitly
accounts for the presence of partial tissue fraction maps to more
accurately estimate cortical thickness. The anisotropic term uses
gray matter fractions to incorporate partial tissue voxels into the
thickness calculation, as demonstrated through simulations and experiments.
It is also shown that the proposed method is robust to the effects
of finite voxel resolution and blurring by a unit integral kernel.
In comparison to methods based on hard intensity thresholds, the heat
equation based method yields results with in-vivo data that are more
consistent with histological findings reported in literature. We also
performed test-retest study across scanners and sessions. The proposed
method showed good reliability in these studies indicating robustness
to scanner differences.