title: Contour instabilities in early tumor growth models.
abstract: Recent tumor growth models are often based on the multiphase mixture framework. Using bifurcation theory techniques, we show that such models can give contour instabilities. Restricting to a simplified but realistic version of such models, with an elastic cell-to-cell interaction and a growth rate dependent on diffusing nutrients, we prove that the tumor cell concentration at the border acts as a control parameter inducing a bifurcation with loss of the circular symmetry. We show that the finite wavelength at threshold has the size of the proliferating peritumoral zone. We apply our predictions to melanoma growth since contour instabilities are crucial for early diagnosis. Given the generality of the equations, other relevant applications can be envisaged for solving problems of tissue growth and remodeling.
authors.affiliation: Laboratoire de Physique Statistique, Ecole Normale Supérieure, UPMC Univ Paris 06, Université Paris Diderot, CNRS, 24 rue Lhomond, 75005 Paris, France.
authors.forename: M
authors.initials: M
authors.lastname: Ben Amar
authors.forename: C
authors.initials: C
authors.lastname: Chatelain
authors.forename: P
authors.initials: P
authors.lastname: Ciarletta
mesh_terms: D002450:Cell Communication; D049109:Cell Proliferation; D006801:Humans; D008954:Models, Biological; D009369:Neoplasms / Q000473:pathology*