Nonlinear PDE System as Model of a a Avascular Tumor Growth

FERNÁNDEZ SLEZAK, DIEGO; SUAREZ, CECILIA; SOBA, ALEJANDRO; RISK, MARCELO; MARSHALL, GUILLERMO

Cordoba

Congreso; ENIEF; 2007

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