Parameter estimation for a tumor invasion PDE model

DAMIÁN FERNÁNDEZ; ANDRÉS A. I. QUIROGA; CRISTINA V. TURNER; GERMÁN A. TORRES

Workshop; XI Brazilian Workshop on Continuous Optimization; 2016

UFAM, IMPA

In this work we introduce a methodology in order to approximate unknown parameters on a non-linear reaction-diffusion model of tumor invasion. These equations consider that tumor-induced alteration of micro-enviromental pH furnishes a mechanism for cancer invasion. The tumor model parameters have a corresponding biological meaning: the reabsorption rate and the destructive influence of H$^+$ ions in the healthy tissue. We solve the direct problem by using the Finite Element Method and minimize an appropriate functional including both the real data and the numerical solution. The gradient of the functional is computed by the adjoint method.