Derivation and application of effective interface conditions for continuum mechanical models of cell invasion through thin membranes

摘要: We consider a continuum mechanical model of cell invasion through thin membranes. The consists transmission problem for volume fraction complemented with continuity stresses and mass flux across the surfaces reduce original to limiting whereby each membrane is replaced by an effective interface, we develop formal asymptotic method that enables derivation set biophysically consistent conditions close problem. results obtained are validated via numerical simulations showing relative error between solutions vanishes when thickness membranes tends zero. In order show potential applications our interface conditions, employ cancer basement metastatic spread ovarian carcinoma.