A Mathematical Model Of Drug Transport In Tumors

In this paper we study a free boundary problem modelling the growth of an avascular tumor with drug application. The tumor consists of two cell populations: live cells and dead cells. The densities of these cells satisfy a system of nonlinear first order hyperbolic equations. The tumor surface is a moving boundary, which satisfies an integro-differential equation. The nutrient concentration and the drug concentration satisfy nonlinear diffusion equations. The nutrient drives the growth of the tumor, whereas the drug is capable of killing cells with Michaelis-Menten kinetics.We prove that this free boundary problem has a unique global solution. We further investigate the combined effects of a drug and a nutrient on an avascular tumor growth. We prove that the tumor shrinks to a necrotic core with radius Rs > 0 and that the global solution converges to a trivial steady-state solution under some natural assumptions on the model parameters. We also proved that an untreated tumor shrinks to a dead core or continually grows to an infinite size, which depends on the different parameter conditions.