Modelling the spatial organization of cell proliferation in the developing central nervous system
Abstract
How far is neuroepithelial cell proliferation in the developing central nervous system a deterministic process? Or, to put it in a more precise way, how accurately can it be described by a deterministic mathematical model? To provide tracks to answer this question, a deterministic system of transport and diffusion partial differential equations, both physiologically and spatially structured, is introduced as a model to describe the spatially organized process of cell proliferation during the development of the central nervous system. As an initial step towards dealing with the three-dimensional case, a unidimensional version of the model is presented. Numerical analysis and numerical tests are performed. In this work we also achieve a first experimental validation of the proposed model, by using cell proliferation data recorded from histological sections obtained during the development of the optic tectum in the chick embryo.
Cite
@article{arxiv.1005.0207,
title = {Modelling the spatial organization of cell proliferation in the developing central nervous system},
author = {Jean Clairambault and Vladimir Flores and Benoit Perthame and Melina Rapacioli and Edmundo Rofman and Rafael Verdes},
journal= {arXiv preprint arXiv:1005.0207},
year = {2010}
}