Parameter estimation for a tumor invasion PDE model

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

Tandil

Workshop; 5º Latin American Workshop on Optimization and Control; 2016

UNCPBA

In this work we introduce a methodology in order to approximateunknown parameters on a non-linear reaction-diffusion model of tumorinvasion. 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: thereabsorption rate and the destructive influence of H$^+$ ions in thehealthy tissue. We solve the direct problem by using the Finite ElementMethod 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.