The Basal Layer of the Epidermis: A Mathematical Model for Cell Production Under a Surface Density Constraint

An age-structured model for the cell populations of the epidermis basal layer is proposed, with the aim of quantifying the cell production which makes possible epidermis renewal. The model, which extends our previous model [J. Math. Biol., 73 (2016), pp. 1595--1626], describes the dynamics of proliferating cells, differentiated cells, and apoptotic cells under the physical constraint on the total surface cell density imposed by the cell occupancy of a basement membrane. To fulfill this constraint during any dynamics, the surface cell density is assumed to control cell migration toward the epidermis suprabasal region, as well as the balance between production of proliferating and of differentiated cells at cell division. The well-posedness of the model is fully studied, and the unique steady state is characterized. Numerical simulations are provided for realistic values of the parameters, giving some insight into the stability of the equilibrium and into the homeostatic properties of the model.