Oncogenic transformation of tubular epithelial ducts: how mechanics affects morphology

We derive a continuum mechanical model to capture the morphological changes occurring at the pre-tumoral stage of epithelial tissues. The mathematical model, derived from first principles, accounts for the competition between the bulk elasticity of the epithelium and the surface tension of the apical and basal boundaries. The variation of the energy functional yields the Euler-Lagrange equations to be numerically integrated. The numerical results reproduce a variety of morphological shapes, from invagination to evagination, depending on the ratio between bulk and surface energy at variance of the length of the section. In particular, using parameters independently measured, we are able to reproduce experimental data reported for a ring partially made of transformed cells.