A model of cerebral cortex formation during fetal development using reaction-diffusion-convection equations with Turing space parameters |
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Authors: | Garzón-Alvarado Diego Alexander Martinez Angelica Maria Ramirez Segrera Dorian Luis Linero |
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Affiliation: | aDepartment of Mechanical and Mechatronic Engineering, Universidad Nacional de Colombia, Numerical Modelling and Methods in Engineering Group (GNUM), Colombia;bUniversidad Central de Colombia, Bioengineering Research Group (UCIB), Colombia;cDepartment of Civil and Agricultural Engineering, Universidad Nacional de Colombia, Colombia |
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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 1.25 mm in the occipital lobe to 4 mm 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. |
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Keywords: | Cerebral cortex Polymicrogyria Lissencephaly Turing pattern Numerical solution Finite element Continuum mechanics |
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