Artículo
Nonlinear optimization for a tumor invasion PDE model : computational and applied mathematics
Fecha
2018Registro en:
Quiroga, Andrés Agustín Ignacio, et al., 2018. Nonlinear optimization for a tumor invasion PDE model : computational and applied mathematics. San Pablo: Sociedade Brasileira de Matemática Aplicada e Computacional, vol. 37, no. 1, p. 485-499. ISSN 2238-3603.
2238-3603
Autor
Quiroga, Andrés Agustín Ignacio
Torres, Germán Ariel
Fernández Ferreyra, Damián Roberto
Turner, Cristina Vilma
Institución
Resumen
In thiswork,we introduce amethodology to approximate unknownparameters that appear on a non-linear reaction–diffusionmodel of tumor invasion. These equations consider that tumor-induced alteration of micro-environmental 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 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