Nonlinear optimization for a tumor invasion PDE model

ANDRÉS AGUSTÍN IGNACIO QUIROGA; CRISTINA TURNER; GERMÁN ARIEL TORRES; DAMIÁN FERNÁNDEZ

COMPUTATIONAL AND APPLIED MATHEMATICS

Springer

Año: 2016 p. 1 - 15

In this work we introduce a methodology in order to approximate unknown parameters that appear 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. A coupled system reaction-diffusion explaining this model is given by three partial differential equations for the  non-dimensional spatial distribution and temporal evolution of the density of normal tissue, the neoplastic tissue growth and the excess concentration of H + ions. The tumor model parameters have a corresponding biological meaning: the reabsorption rate, the destructive influence of H+ ions in the healthy tissue, the growth rate of tumor tissue and the diffusion coefficient. We propose to solve the direct problem by using the Finite Element Method (FEM) and minimize an appropriate functional including both the real data (obtained via in-vitro experiments and fluorescence ratio imaging microscopy) and the numerical solution. The gradient of the functional is computed by the adjoint method.