Comput Methods Programs Biomed - A model of cerebral cortex formation during fetal development using reaction-diffusion-convection equations with Turing space parameters.

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Resumo

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 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.

Resumo Limpo

cerebr cortex gray lamina form bodi neuron cover cerebr hemispher vari thick mm occipit lobe mm anterior lobe brain surfac time greater skull mani fold fold form gyri sulci fissur mark area specif function divid five lobe convolut format may vari individu import featur brain format pattern can mathemat repres ture pattern articl describ phenomenolog model develop describ format pattern gyri occur cerebr cortex reaction diffus equat ture space paramet numer exampl simplifi geometri brain solv studi pattern format finit element method use numer solut conjunct newtonraphson method numer exampl show model can repres cerebr cortex fold format reproduc patholog relat gyri format polymicrogyria lissencephali

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