2010/05/03 by Clairambault, Jean, Flores, Vladimir, Perthame, Benoit +3
#Analysis of PDEs (math.AP) #Cell Behavior (q-bio.CB) #FOS: Biological sciences #FOS: Mathematics #Tissues and Organs (q-bio.TO)
paper · doi:10.48550/arxiv.1005.0207
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.