Gender Differences in Cerebral Cortical Folding: Multivariate Complexity-Shape Analysis with Insights into Handling Brain-Volume Differences

This paper presents a study of gender differences in adult human cerebral cortical folding patterns. The study employs a new multivariate statistical descriptor for analyzing folding patterns in a region of interest (ROI) and a rigorous nonparametric permutation-based scheme for hypothesis testing. Unlike typical ROI-based methods that summarize folding complexity or shape by single/few numbers, the proposed descriptor systematically constructs a unified description of complexity and shape in a high-dimensional space (thousands of numbers/dimensions). Furthermore, this paper presents new mathematical insights into the relationship of intra-cranial volume (ICV) with cortical complexity and shows that conventional complexity descriptors implicitly handle ICV differences in different ways, thereby lending different meanings to "complexity". This paper describes two systematic methods for handling ICV changes in folding studies using the proposed descriptor. The clinical study in this paper exploits these theoretical insights to demonstrate that (i) the answer to which gender has higher/lower "complexity" depends on how a folding measure handles ICV differences and (ii) cortical folds in males and females differ significantly in shape as well.