SIMULATION OF A MATHEMATICAL MODEL OF TUMORAL GROWTH
Palavras-chave:
Mathematical model, Numerical simulations, Breast geometry, Non-regular domainResumo
The work presents a study of the non-linear mathematical model of tumor growth, proposed by Kolev
and Zubik-Kowal [1]. The model is described by a system composed of four partial differential equations that
represent the evolution of the density of cancer cells, density of the extracellular matrix (ECM), concentration of
matrix-degrading enzyme (MDE) and concentration of tissue metalloproteinase inhibitors. For numerical simu-
lations, the finite difference method is used, in which the temporal terms of the equations are discretized using a
two-stage method. In spatial terms, finite central differences are used. A study of numerical convergence for the
proposed scheme is presented, using analytical solutions manufactured in a rectangular geometry. Finally, simula-
tions of the tumor growth model are performed, using a non-regular mesh that represents the geometry of a female
breast. To simulate the model in non-regular geometry, the technique used is to approximate the contour of the
physical domain by mesh segments. The simulations showed that the model has important characteristics of the
interactions between tumor cells and the surrounding tissue.
