Using the anisotropic laplace equation to compute cortical thickness

Automatic computation of cortical thickness is a critical step when investigating neuroanatomical population differences and changes associated with normal development and aging, as well as in neuro-degenerative diseases including Alzheimer’s and Parkinson’s. 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. We describe a novel method based on the anisotropic heat equation that explicitly accounts for the presence of partial tissue volumes 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. We also show that the proposed method is robust to the effects of finite voxel resolution and blurring. 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 the literature. We also performed a test-retest study across scanners that indicated improved consistency and robustness to scanner differences.