A model of cerebral cortex formation during fetal development using reaction-diffusion-convection equations with Turing space parameters

Authors:
Diego Alexander Garzón-Alvarado;Angelica Maria Ramirez Martinez;Dorian Luis Linero Segrera
Affiliations:
Department of Mechanical and Mechatronic Engineering, Universidad Nacional de Colombia, Numerical Modelling and Methods in Engineering Group (GNUM), Colombia;Universidad Central de Colombia, Bioengineering Research Group (UCIB), Colombia;Department of Civil and Agricultural Engineering, Universidad Nacional de Colombia, Colombia
Venue:
Computer Methods and Programs in Biomedicine
Year:
2011

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Abstract

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 Newton-Raphson 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.