Modelling the spatial organization of cell proliferation in the developing central nervous system

Jean Clairambault; Vladimir Flores; Benoit Perthame; Melina Rapacioli; Edmundo Rofman; Rafael Verdes

inria-00476695, version 1

Modelling the spatial organization of cell proliferation in the developing central nervous system

Jean Clairambault ()^a^, 1, Vladimir Flores^b^, 2, Benoit Perthame ( Auteur à contacter de préférence ) ^1, 3, Melina Rapacioli^b^, 2, Edmundo Rofman ⁴, Rafael Verdes^c^, 5

(2010)

Résumé : 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.

a – INRIA
b – Universidad Favaloro, Department of Biostructural Sciences
c – Universidad Nacional de Rosario
1 : BANG (INRIA Rocquencourt)
INRIA – Laboratoire Jacques-Louis Lions
2 : Department of Biostructural Sciences
Universidad Favaloro
3 : Laboratoire Jacques-Louis Lions (LJLL)
CNRS : UMR7598 – Université Pierre et Marie Curie [UPMC] - Paris VI
4 : Instituto Argentino de Matemática (IAM)
Consejo Nacional de Investigaciones Científicas y Técnicas
5 : Instituto de Matemática Beppo Levi
Universidad Nacional de Rosario

inria-00476695, version 1
http://hal.inria.fr/inria-00476695
oai:hal.inria.fr:inria-00476695
Contributeur : Benoit Perthame <>
Soumis le : Mardi 27 Avril 2010, 09:33:12
Dernière modification le : Vendredi 7 Mai 2010, 15:53:06

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arXiv : 1005.0207

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