Nonlinear optimization for a tumor invasion PDE model : computational and applied mathematics

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–diffusio...

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Autores principales: Quiroga, Andrés Agustín Ignacio, Torres, Germán Ariel, Fernández Ferreyra, Damián Roberto, Turner, Cristina Vilma
Formato: Artículo
Lenguaje:Inglés
Publicado: Sociedade Brasileira de Matemática Aplicada e Computacional 2021
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Acceso en línea:http://repositorio.unne.edu.ar/handle/123456789/30327
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Sumario: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