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

TL;DR

This paper introduces a deterministic mathematical model using PDEs to describe spatial cell proliferation in the developing central nervous system, validated with experimental data from chick embryo optic tectum development.

Contribution

It presents a novel PDE-based model for spatial cell proliferation and provides initial validation with experimental data, advancing understanding of neurodevelopmental processes.

Findings

Model accurately describes spatial proliferation patterns

Numerical tests support model validity

First experimental validation of PDE model in this context

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.