title: The steady state of epidermis: mathematical modeling and numerical simulations.
abstract: We consider a model with age and space structure for the epidermis evolution. The model, previously presented and analyzed with respect to the suprabasal epidermis, includes different types of cells (proliferating cells, differentiated cells, corneous cells, and apoptotic cells) moving with the same velocity, under the constraint that the local volume fraction occupied by the cells is constant in space and time. Here, we complete the model proposing a mechanism regulating the cell production in the basal layer and we focus on the stationary case of the problem, i.e. on the case corresponding to the normal status of the skin. A numerical scheme to compute the solution of the model is proposed and its convergence is studied. Simulations are provided for realistic values of the parameters, showing the possibility of reproducing the structure of both "thin" and "thick" epidermis.
authors.affiliation: Istituto di Analisi dei Sistemi ed Informatica "A. Ruberti"-CNR, Via dei Taurini 19, 00185, Rome, Italy. alberto.gandolfi@iasi.cnr.it.
authors.forename: Alberto
authors.initials: A
authors.lastname: Gandolfi
authors.affiliation: Department of Mathematics, University of Trento, Via Sommarive 14, Povo, 38123, Trento, Italy.
authors.forename: Mimmo
authors.initials: M
authors.lastname: Iannelli
authors.affiliation: Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, Calea 13 Septembrie 13, 050711, Bucharest, Romania.
authors.forename: Gabriela
authors.initials: G
authors.lastname: Marinoschi
mesh_terms: D002454:Cell Differentiation; D049109:Cell Proliferation; D003198:Computer Simulation; D000078404:Epidermal Cells; D004817:Epidermis / Q000502:physiology*; D006801:Humans; D008954:Models, Biological
keywords: Age structure; Nonlinear PDE; Numerical methods; Population dynamics; Stratified epithelium