Pattern Formation in Hybrid Models of Cell Populations

Abstract

The paper is devoted to hybrid discrete-continuous models of cell populations dynamics. Cells are considered as individual objects which can divide, die by apoptosis, differentiate and move under external forces. Intra-cellular regulatory networks are described by ordinary differential equations while extracellular species by partial differential equations. We illustrate the application of this approach to some model examples and to the problem of tumor growth. Hybrid models of cell populations present an interesting nonlinear dynamics which is not observed for the conventional continuous models.KeywordsConventional Continuum ModelsHybrid Discrete-continuum ModelModel ExampleIntra-cellular ConcentrationExtracellular ConcentrationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.