A mathematical model for cell differentiation, as an evolutionary and regulated process

Last modified: 2014-06-09

#### Abstract

We propose a model where cell plasticity is considered for the simulation of tissue regeneration. Opposed to many classical models, cell differentiation is considered as a gradual process which evolves in time. The model regulates cell differentiation by a means of a differentiation state variable where cells are assumed to have the ability to differentiate to several cell types. The differentiation path is treated as reversible as long as cell differentiation has not completed completely. In the mathematical model, an additional differentiation state–space is added in the sense that the governing partial differential equations are enrichted with an additional differentiation state–dimension. In this way, differentiation is treated as a gradual process which is close to biology. This cannot be done in the classical models where a reaction–like terms is added to the governing partial differential equations. An application that we consider is peri–implant osseo–integration. Numerical results will be compared to experimental data and the formalism has been applied to a moving boundary model for osseo–integration.