Morphological stability of an elastic tumor–host interface

Abstract

Abstract The ability of tumors to metastasize is preceded by morphological instabilities such as chains or fingers that invade the host environment. Therefore, parameters that control the morphology of the tumor may also contribute to its invasive ability. Previous analyses on morphological changes were performed using surface energy of the tumor–host interface. In an effort to understand the role the interface stiffness plays on tumor evolution, here we model the tumor–host interface as an elastic membrane governed by the Helfrich bending energy. Using an energy variation approach, we derive a modified Laplace–Young condition for the stress jump across the interface in the Stokes equation. We then perform a linear stability analysis and investigate how physical parameters such as viscosity, bending rigidity, and apoptosis affect the morphological instability. Results show that increased bending rigidity versus mitosis rate contributes to a more stable morphological tumor behavior. On the other hand, increasing tumor viscosity or apoptosis may lead to invasive fingering morphologies. Comparison with experimental data on glioblastoma spheroids shows good agreement especially for tumors with high adhesion and low proliferation.