Nonlinear PDE System as Model of Avascular Tumor Growth

Abstract

In this paper we present the solution of a partial differential equation system to model avascular
tumors growth. A detailed finite-difference numeric algorithm for solving the whole system is presented.
The system, that includes moving boundary condition and a two-point boundary equation, is solved
using a predictor-corrector scheme. The model is sensitive to the used numerical method, so a secondorder
accurate algorithm is necessary rather than a standard first-order accuracy one. A contracting
mesh is also used in order to obtain the solution, as rate of change gets significantly high near tumor
bound. Parameters are swiped to cover a wide range of feasible physiological values. Previous published
works have taken into account the use of a single set of parameter values; therefore a single curve
was calculated. In contrast, we present a range of feasible solutions for tumor growth, covering a more
realistic scenario. A dynamical analysis and local behavior of the system is done. Chaotic situations arise
for particular set of parameter values, showing interesting fixed points where biological experiments may
be triggered.