An Analysis of a Mathematical Model Describing Acid-mediated Tumor Invasion
This is a theoretical analysis of a known model for cancer invasion, providing mathematical rigor but no new biological insights or performance improvements.
The paper analyzes a reaction-diffusion model for acid-mediated tumor invasion, proving existence and uniqueness of solutions under Neumann and Dirichlet boundary conditions, and providing numerical simulations.
We present a mathematical analysis of a reaction-diffusion model describing acid-mediated tumor invasion. The model describes the spatial distribution and temporal evolution of tumor cells, normal cells, and excess lactic acid concentration. The model assumes that tumor-induced alteration of microenvironmental pH provides a simple but complete mechanism for cancer invasion. We provide results on the existence and uniqueness of a solution considering Neumann and Dirichlet boundary conditions. We also provide numerical simulations to the solutions considering both boundary conditions.