A gyrification analysis approach based on Laplace Beltrami eigenfunction level sets

Abstract

An accurate measure of the complexity of patterns of cortical folding or gyrification is necessary for understanding normal brain development and neurodevelopmental disorders. Conventional gyrification indices (GIs) are calculated based on surface curvature (curvature-based GI) or an outer hull surface of the cortex (outer surface-based GI). The latter is dependent on the definition of the outer hull surface and a corresponding function between surfaces. In the present study, we propose the Laplace Beltrami-based gyrification index (LB-GI). This is a new curvature-based local GI computed using the first three Laplace Beltrami eigenfunction level sets. As with outer surface-based GI methods, this method is based on the hypothesis that gyrification stems from a flat surface during development. However, instead of quantifying gyrification with reference to corresponding points on an outer hull surface, LB-GI quantifies the gyrification at each point on the cortical surface with reference to their surrounding gyral points, overcoming several shortcomings of existing methods. The LB-GI was applied to investigate the cortical maturation profile of the human brain from preschool to early adulthood using the PING database. The results revealed more detail in patterns of cortical folding than conventional curvature-based methods, especially on frontal and posterior tips of the brain, such as the frontal pole, lateral occipital, lateral cuneus, and lingual. Negative associations of cortical folding with age were observed at cortical regions, including bilateral lingual, lateral occipital, precentral gyrus, postcentral gyrus, and superior frontal gyrus. The results also indicated positive significant associations between age and the LB-GI of bilateral insula, the medial orbitofrontal, frontal pole and rostral anterior cingulate regions. It is anticipated that the LB-GI will be advantageous in providing further insights in the understanding of brain development and degeneration in large clinical neuroimaging studies.

Keywords

• Cortical folding
• Local gyrification index
• Laplace Beltrami operator
• Curvature
• Brain development