A mean-field theory of cellular growth
Centro de Ciências Exatas e Tecnológicas, Universidade
do Vale do Rio dos Sinos 93022-000 São Leopoldo, RS, Brazil
2 Instituto de Física, Universidade Federal do Rio Grande do Sul 91501-970 Porto Alegre, RS, Brazil
Accepted: 28 June 2002
We present a unified model for the growth of a population of cells. We propose that sigmoidal growth in cellular systems is a self-organised process due to long-range interactions among the cells. The interaction is mediated through diffusive substances produced by them. The model considers a competition between cell drive to replicate and inhibitory interactions that are modeled by a power law of the distance between the cells. The different classes of solutions (Logistic, Richards-like, Gompertz, and Exponential) are determined by a relation between the interaction length and the fractal dimension of the cellular structure.
PACS: 87.17.Ee – Growth and division
© EDP Sciences, 2002