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The role of thickness inhomogeneities in hierarchical cortical folding

For long it has been known that specific patterns of folding are necessary for an optimally functioning brain. For instance, lissencephaly and polymicrogyria can lead to severe mental retardation, short life expectancy, epileptic seizures, and tetraplegia. The construction of a quantitative model on how and why these folds appear is the first step in understanding the cause of these conditions. In recent years, there have been various attempts to understand and model the mechanisms of brain folding. Previous works have shown that mechanical instabilities play a crucial role in the formation of brain folds, and that the geometry of the fetal brain is one of the main factors in dictating the folding characteristics. However, modeling higher-order folding, one of the main characteristics of the human brain, has not been fully tackled. The effects of thickness inhomogeneity in the gyrogenesis of the mammalian brain are studied through finite-element simulations of rectangular slabs. The slabs are divided into two distinct regions, where the outer layer mimics the gray matter, and the inner layer the underlying white matter. Differential growth is introduced by only growing the top layer. The brain tissue is modeled as a neo-Hookean hyperelastic material. Simulations are performed with both, homogeneous and inhomogeneous cortical thickness. The homogeneous cortex is shown to fold into a single wavelength, as common for bilayered materials, while the inhomogeneous cortex folds into more complex conformations: In their early stages of development, structures reminiscent of the deep sulci in the brain are obtained. As the cortex continues to develop, secondary undulations, which are shallower and more variable than the structures obtained in earlier gyrification stage emerge, reproducing well-known characteristics of higher-order folding in the mammalian, and particularly the human, brain.