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

Jean Clairambault (1) , Vladimir Flores (2) , Benoît Perthame (1, 3) , Melina Rapacioli (2) , Edmundo Rofman (4) , Rafael Verdes (5)

1 BANG - Nonlinear Analysis for Biology and Geophysical flows
2 Department of Biostructural Sciences
3 LJLL - Laboratoire Jacques-Louis Lions
4 IAM - Instituto Argentino de Matemática
5 Instituto de Matemática Beppo Levi

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.

Mots clés: developmental neurobiology; cell proliferation; structured partial differential equations; spatial organization; optical tectum

Domaines: Equations aux dérivées partielles [math.AP]; Biologie du développement

Jean Clairambault, Vladimir Flores, Benoît Perthame, Melina Rapacioli, Edmundo Rofman, et al.. Modelling the spatial organization of cell proliferation in the developing central nervous system. [Research Report] 2010, pp.33. ⟨inria-00476695⟩