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 neurodegenerative 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.

Measuring Asymmetric Interactions in Resting State Brain Networks.

Directed graph representations of brain networks are increasingly being used to indicate the direction and level of influence among brain regions. Most of the existing techniques for directed graph representations are based on time series analysis and the concept of causality, and use time lag information in the brain signals. These time lag-based techniques can be inadequate for functional magnetic resonance imaging (fMRI) signal analysis due to the limited time resolution of fMRI as well as the low frequency hemodynamic response. The aim of this paper is to present a novel measure of necessity that uses asymmetry in the joint distribution of brain activations to infer the direction and level of interaction among brain regions. We present a mathematical formula for computing necessity and extend this measure to partial necessity, which can potentially distinguish between direct and indirect interactions. These measures do not depend on time lag for directed modeling of brain interactions and therefore are more suitable for fMRI signal analysis. The necessity measures were used to analyze resting state fMRI data to determine the presence of hierarchy and asymmetry of brain interactions during resting state. We performed ROI-wise analysis using the proposed necessity measures to study the default mode network. The empirical joint distribution of the fMRI signals was determined using kernel density estimation, and was used for computation of the necessity and partial necessity measures. The significance of these measures was determined using a one-sided Wilcoxon rank-sum test. Our results are consistent with the hypothesis that the posterior cingulate cortex plays a central role in the default mode network.