Free Boundary Problem of Cell Deformation and Invasion

Abstract

A novel approach of free boundary problem of invadopodia formation and invasion is proposed in this paper. The modeling of invadopodia formation and invasion of cell involving the interaction across plasma membrane is considered. The formation is formulated by Stefan problem approach which is known as free boundary problem where the boundary membrane is priori unknown. Changes in cell membrane will lead to protrusions of cell membrane. A normal growing cell in tissue on an organ will be altered into cancerous cells after some processes of mutation in genes. We proposed level set method to indicate the moving plasma membrane and to represent the behavior of the cell interface. An efficient and a straightforward enthalpy method (phase change problem) is then used to provide the description of the cell membrane diffusion. We successfully show the formation of invadopodia and migration of a single cell modeling.