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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Detalles Bibliográficos
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
Materias:
Reaction–diffusion equation
Tumor invasión
PDE-constrained optimization
Adjoint method
Finite element method
Acceso en línea:http://repositorio.unne.edu.ar/handle/123456789/30327
Aporte de:
RIUNNE - Repositorio Institucional de la Universidad Nacional del Nordeste (UNNE) de Universidad Nacional del Nordeste
id I48-R184-123456789-30327
record_format dspace
spelling I48-R184-123456789-303272025-03-06T11:02:37Z Nonlinear optimization for a tumor invasion PDE model : computational and applied mathematics Quiroga, Andrés Agustín Ignacio Torres, Germán Ariel Fernández Ferreyra, Damián Roberto Turner, Cristina Vilma Reaction–diffusion equation Tumor invasión PDE-constrained optimization Adjoint method Finite element method 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 2021-12-09T15:35:11Z 2021-12-09T15:35:11Z 2018 Artículo 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 http://repositorio.unne.edu.ar/handle/123456789/30327 eng openAccess http://creativecommons.org/licenses/by-nc-nd/2.5/ar/ application/pdf application/pdf Sociedade Brasileira de Matemática Aplicada e Computacional Computational And Applied Mathematics, 2018, vol. 37, no. 1, p. 485-499.
institution Universidad Nacional del Nordeste
institution_str I-48
repository_str R-184
collection RIUNNE - Repositorio Institucional de la Universidad Nacional del Nordeste (UNNE)
language Inglés
topic Reaction–diffusion equation
Tumor invasión
PDE-constrained optimization
Adjoint method
Finite element method
spellingShingle Reaction–diffusion equation
Tumor invasión
PDE-constrained optimization
Adjoint method
Finite element method
Quiroga, Andrés Agustín Ignacio
Torres, Germán Ariel
Fernández Ferreyra, Damián Roberto
Turner, Cristina Vilma
Nonlinear optimization for a tumor invasion PDE model : computational and applied mathematics
topic_facet Reaction–diffusion equation
Tumor invasión
PDE-constrained optimization
Adjoint method
Finite element method
description 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
format Artículo
author Quiroga, Andrés Agustín Ignacio
Torres, Germán Ariel
Fernández Ferreyra, Damián Roberto
Turner, Cristina Vilma
author_facet Quiroga, Andrés Agustín Ignacio
Torres, Germán Ariel
Fernández Ferreyra, Damián Roberto
Turner, Cristina Vilma
author_sort Quiroga, Andrés Agustín Ignacio
title Nonlinear optimization for a tumor invasion PDE model : computational and applied mathematics
title_short Nonlinear optimization for a tumor invasion PDE model : computational and applied mathematics
title_full Nonlinear optimization for a tumor invasion PDE model : computational and applied mathematics
title_fullStr Nonlinear optimization for a tumor invasion PDE model : computational and applied mathematics
title_full_unstemmed Nonlinear optimization for a tumor invasion PDE model : computational and applied mathematics
title_sort nonlinear optimization for a tumor invasion pde model : computational and applied mathematics
publisher Sociedade Brasileira de Matemática Aplicada e Computacional
publishDate 2021
url http://repositorio.unne.edu.ar/handle/123456789/30327
work_keys_str_mv AT quirogaandresagustinignacio nonlinearoptimizationforatumorinvasionpdemodelcomputationalandappliedmathematics
AT torresgermanariel nonlinearoptimizationforatumorinvasionpdemodelcomputationalandappliedmathematics
AT fernandezferreyradamianroberto nonlinearoptimizationforatumorinvasionpdemodelcomputationalandappliedmathematics
AT turnercristinavilma nonlinearoptimizationforatumorinvasionpdemodelcomputationalandappliedmathematics
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