Abstract

RAMIREZ, Angélica; DUQUE-DAZA, Carlos A  and  GARZON-ALVARADO, Diego A. Preliminary computation form of the cerebral surface development. Rev Cubana Invest Bioméd [online]. 2011, vol.30, n.3, pp. 412-423. ISSN 0864-0300.

Cerebral cortex is a gray layer including neuron bodies covering the cerebral hemispheres and whose thickness fluctuates from 1.25 mm in the occipital lobule to 4 mm in the anterior lobule. Due to the many folds present, la cerebral surface is a thirty times greater than the cranial surface. These folds create the cerebral convolutions, grooves and fissures defining areas with determined functions, divided into five lobules. La convolutions formation may to vary among subjects and are an important characteristic of brain formation. These patterns may be represented in a mathematical way like Turing patterns. The aim of present paper was to design a phenomenological model describing the formation of convolutions patterns occurring in the cerebral cortex by means of diffusion reaction equations with parameters in the Turing space. To study la formation of patterns it is necessary to solve some numerical examples on simplified geometries of a brain. For numerical solution authors used the finite elements method together with the Newton-Raphson method. The numerical examples demonstrate that this model may to represent the folds formation in the cerebral cortex and to reproduce pathologies of the convolutions formation, such as the polymicrogyria and lissencephalous.

Keywords : Neocortex; continuous medium; mathematical models.

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