On a skin tumor growth modeling by the surface finite element methods combined with the phase field approach

The phase field model is a popular mathematical tool for studying tumor growth. It describes the tumor growth via marking the tumor area. Since skin tumors are usually accompanied by the raised growth of skin tumor area, such as the keloid, the simulation is requested to simultaneously mark the tumor area and the height of the skin bulge. This paper combines the phase field model with the evolving surface partial differential equations to complete the above simulation requirements. The identification of the height of skin tumor bulge is realized by setting the appropriate tumor area related velocity of the evolving surface. Since the bulge of skin tumor does not involve large geometric deformations, the Lagrangian evolving surface finite element method is considered as the space-time discretization approach for the proposed model and the corresponding stability analysis is shown. For long-time stable numerical simulations, the stabilizing approach is employed to improve the numerical scheme. Based on the proposed model and numerical method, several numerical simulations of real keloids are performed. Simulations of skin tumor growth on human limbs are also presented. In addition, the effect of chemotaxis on skin tumor growth is investigated.