A biophysical model of tumor invasion

Three-dimensional finite element computations of a cancer invasion model with nonlinear density-dependent diffusion and haptotactic sensitivity function are presented. The nonlinear model includes three key variables, namely the cancer cell density, the extra cellular matrix (ECM) density and the matrix degrading enzymes (MDE) concentration. In order to investigate the effects of tumor growth and invasion on a realistic geometry, the interactions between the cancer cells and the host tissue are incorporated into the model. The convergence study and the validation are first performed for the proposed numerical scheme. Then the effects of nonlinear diffusion and ECM-dependent haptotaxis on tumor growth and invasion in three-dimensional geometries are presented. Finally, several numerical simulations are performed with different combinations of nonlinear diffusion and haptotaxis functions to get an insight into the tumor invasion on a realistic (breast) geometry. The proposed computational model can be used to predict the location and shape of the tumor in realistic geometries at a particular instance.