Simulating Solid Tumor Growth Using Multigrid Algorithms

In mathematical cancer modeling, the growth of solid tumors combines the mechanics of cell-cell adhesion, cell growth velocity and angiogenesis amongst numerous others. This project simulates solid tumoral growth with the use of a coupled system of Cahn-Hilliard-type convection-reaction-diffusion equations. This mathematical model uses a two-cellular tumoral structure of viable, or proliferating, cells and dead cells in the necrotic core. The nonlinear system is then discretized in space using a finite difference approximation and in time using a Crank-Nicolson-type algorithm to account for the stiffness in the fourth order diffusion term of the equation. In order to solve the discretized system, a multigrid scheme with uniform square grids is then implemented. Finally, the growth of solid tumors is simulated with varying initial conditions. The University of Maryland, College Park