Fractal dimension (FD) has been widely used to provide a quantitative description of structural complexity in the cerebral cortex. FD is an extremely compact measure of shape complexity, condensing all details into a single numeric value. We interpreted the variation of the FD in the cortical surface of normal controls through multiple regression analysis with cortical thickness, sulcal depth, and folding area related to cortical complexity. We used a cortical surface showing a reliable representation of folded gyri and manually parcellated it into frontal, parietal, temporal, and occipital regions for regional analysis. In both hemispheres the mean cortical thickness and folding area showed significant combination effects on cortical complexity and accounted for about 50% of its variance. The folding area was significant in accounting for the FD of the cortical surface, with positive coefficients in both hemispheres and several lobe regions, while sulcal depth was significant only in the left temporal region. The results may suggest that human cortex develops a complex structure through the thinning of cortical thickness and by increasing the frequency of folds and the convolution of gyral shape rather than by deepening sulcal regions. Through correlation analysis of FD with IQ and the number of years of education, the results showed that a complex shape of the cortical surface has a significant relationship with intelligence and education. Our findings may indicate the structural characteristics that are revealed in the cerebral cortex when the FD in human brain is increased, and provide important information about brain development.

We have examined gender differences of cortical thickness using a 3-D surface-based method that enables more accurate measurement in deep sulci and localized regional mapping compared to volumetric analyses. Cortical thickness was measured using a direct method for calculating the distance between corresponding vertices from inner and outer cortical surfaces. We normalized cortical surfaces using 2-D surface registration and performed diffusion smoothing to reduce the variability of folding patterns and to increase the power of the statistical analysis. In stereotaxic space, significant localized cortical thickening in women was found extensively in frontal, parietal and occipital lobes, including the superior frontal gyrus (SFG), superior parietal gyrus (SPG), inferior frontal gyrus (IFG) and postcentral gyrus (PoCG) in the left hemisphere and mostly in the parietal lobe, including the SPG in the right hemisphere. In the temporal lobe, small regions of the left and right caudal superior temporal gyrus (STG) and the left temporal pole showed significantly greater cortical thickness in women. The temporal lobe shows relatively less significant thickening than other lobes in both hemispheres. In native space, significantly greater cortical thickness in women was detected in left parietal region, including SPG and PoCG. No significant local increases of cortical thickness were observed in men in both spaces. These findings suggest statistically significant cortical thickening in women in localized anatomical regions, which is consistent with several previous studies and may support a hypothesis of sexual dimorphism.