A MODEL OF THE FORMATION OF THE CEREBRAL CORTEX THROUGH A MIXED APPROACH OF REACTION DIFFUSION EQUATIONS AND MECHANICAL STRAIN

Abstract

During fetal development the morphology and function of the organs and tissues is determined. An example occurs with the formation of the cerebral cortex. On the external surface of the brain there are numerous folds (gyri, sulci, and fissures) that determine brain function. The exact cause for the formation of patterns of these folds is unknown. This article proposes a reaction-diffusion model in conjunction with a process of surface mechanical strain to explain the morphogenesis of the superficial structure of the brain.The model is solved using finite elements. There have been tests done on the formation of brain patterns through the reaction-diffusion equations with parameters in the space of Turing and by random mechanical strain. Several numerical examples have been developed that show an acceptable correlation between the results and clinical reality. With the model we can represent, qualitatively, the formation of the cerebral cortex by the proposed model. The model can approximate, and explain, lissencephaly and polymicrogyria, diseases that develop in the cerebral cortex and lead to medical complications to sufferers.