Parameter estimation in a model of cancer invasion

ANDRÉS QUIROGA; CRISTINA TURNER; GERMÁN TORRES; DAMIÁN FERNANDEZ FERREYRA

Cabo Frio

Workshop; Mathematical Methods and Modeling of Biophysical Phenomena; 2013

IMPA

We present a method for estimating unknown parameters that appear on an non-linear reaction-diffusion model of cancer invasion. This model consider that tumor-induced alteration of microenviromental pH provides a mechanism for cancer invasion . A coupled system reaction-diffusion describing the spatial distribution and temporal development of tumor tissue, normal tissue, and excess H^+ ion concentration. After solving the direct problem, we use the model for the estimation of parameters by fitting the numerical solution with experimental data. We define an appropriate functional to compare both the "real" data and the numerical solution. We use the adjoint method for the minimization of this functional.