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

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 fold...

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Bibliographic Details
Published in:Computer methods and programs in biomedicine 2011-12, Vol.104 (3), p.489-497
Main Authors: Garzón-Alvarado, Diego Alexander, Martinez, Angelica Maria Ramirez, Segrera, Dorian Luis Linero
Format: Article
Language:English
Subjects:
Biological and medical sciences
Cerebral cortex
Cerebral Cortex - embryology
Continuum mechanics
Diffusion
Female
Fetal Development
Finite element
Humans
Internal Medicine
Lissencephaly
Medical sciences
Models, Biological
Numerical solution
Other
Polymicrogyria
Pregnancy
Radiotherapy. Instrumental treatment. Physiotherapy. Reeducation. Rehabilitation, orthophony, crenotherapy. Diet therapy and various other treatments (general aspects)
Technology. Biomaterials. Equipments. Material. Instrumentation
Turing pattern
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Summary: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.
ISSN:0169-2607
1872-7565
DOI:10.1016/j.cmpb.2011.07.001