Nonlinear PDE System as Model of Avascular Tumor Growth

D. FERNANDEZ SLEZAK, C. SUAREZ, A. SOBA, M. RISK AND G. MARSHALL

Cordoba, Argentina

Congreso; ENIEF 2007 - XVI Congreso sobre Métodos Numéricos y sus Aplicaciones & MACI 2007 - I Congreso de Matemática Aplicada, Computacional e Industrial; 2007

Asociación Argentina de Mecánica Computacional y SIAM Sección Argentina

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 second- order 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.