A model of cerebral cortex formation during fetal development using reactiondiffusionconvection equations with Turing space parameters
The cerebral cortex is a gray lamina formed by bodies of neurons covering the cerebral hemispheres, varying in thickness from 1.25mm in the occipital lobe to 4mm in the anterior lobe. The brain's surface is about 30 times greater that of the skull because of its many folds; such folds form the gyri, sulci and fissures and mark out areas having specific functions, divided into five lobes. Convolution formation may vary between individuals and is an important feature of brain formation; such patterns can be mathematically represented as Turing patterns. This article describes how a phenomenological model was developed by describing the formation pattern for the gyri occurring in the cerebral cortex by reaction diffusion equations with Turing space parameters. Numerical examples for simplified geometries of a brain were solved to study pattern formation. The finite element method was used for the numerical solution, in conjunction with the NewtonRaphson method. The numerical examples showed that the model can represent cerebral cortex fold formation and reproduce pathologies related to gyri formation, such as polymicrogyria and lissencephaly.
cerebral cortex turing pattern finite element numerical solution polymicrogyria lissencephaly continuum mechanics