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

Autores
Quiroga, Andrés Agustín Ignacio; Torres, Germán Ariel; Fernández Ferreyra, Damián Roberto; Turner, Cristina Vilma
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Fil: Quiroga, Andrés Agustín Ignacio. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina.
Fil: Torres, Germán Ariel. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura; Argentina.
Fil: Torres, Germán Ariel. Consejo Nacional de Investigaciones Científicas y Técnica. Instituto de Modelado e Innovación Tecnológica; Argentina.
Fil: Fernández Ferreyra, Damián Roberto. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.
Fil: Fernández Ferreyra, Damián Roberto. Consejo Nacional de Investigaciones Científicas y Técnica. Centro de Investigación y Estudios de Matemática; Argentina.
Fil: Turner, Cristina Vilma. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.
Fil: Turner, Cristina Vilma. Consejo Nacional de Investigaciones Científicas y Técnica. Centro de Investigación y Estudios de Matemática; Argentina.
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
Fuente
Computational And Applied Mathematics, 2018, vol. 37, no. 1, p. 485-499.
Materia
Reaction–diffusion equation
Tumor invasión
PDE-constrained optimization
Adjoint method
Finite element method
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
Repositorio Institucional de la Universidad Nacional del Nordeste (UNNE)
Institución
Universidad Nacional del Nordeste
OAI Identificador
oai:repositorio.unne.edu.ar:123456789/30327

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network_name_str Repositorio Institucional de la Universidad Nacional del Nordeste (UNNE)
spelling Nonlinear optimization for a tumor invasion PDE model : computational and applied mathematicsQuiroga, Andrés Agustín IgnacioTorres, Germán ArielFernández Ferreyra, Damián RobertoTurner, Cristina VilmaReaction–diffusion equationTumor invasiónPDE-constrained optimizationAdjoint methodFinite element methodFil: Quiroga, Andrés Agustín Ignacio. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina.Fil: Torres, Germán Ariel. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura; Argentina.Fil: Torres, Germán Ariel. Consejo Nacional de Investigaciones Científicas y Técnica. Instituto de Modelado e Innovación Tecnológica; Argentina.Fil: Fernández Ferreyra, Damián Roberto. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Fernández Ferreyra, Damián Roberto. Consejo Nacional de Investigaciones Científicas y Técnica. Centro de Investigación y Estudios de Matemática; Argentina.Fil: Turner, Cristina Vilma. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Turner, Cristina Vilma. Consejo Nacional de Investigaciones Científicas y Técnica. Centro de Investigación y Estudios de Matemática; Argentina.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 methodSociedade Brasileira de Matemática Aplicada e Computacional2018info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfQuiroga, 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 2238-3603.2238-3603http://repositorio.unne.edu.ar/handle/123456789/30327Computational And Applied Mathematics, 2018, vol. 37, no. 1, p. 485-499.reponame:Repositorio Institucional de la Universidad Nacional del Nordeste (UNNE)instname:Universidad Nacional del Nordesteenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-nd/2.5/ar/Atribución-NoComercial-SinDerivadas 2.5 Argentina2025-09-29T14:30:16Zoai:repositorio.unne.edu.ar:123456789/30327instacron:UNNEInstitucionalhttp://repositorio.unne.edu.ar/Universidad públicaNo correspondehttp://repositorio.unne.edu.ar/oaiososa@bib.unne.edu.ar;sergio.alegria@unne.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:48712025-09-29 14:30:16.582Repositorio Institucional de la Universidad Nacional del Nordeste (UNNE) - Universidad Nacional del Nordestefalse
dc.title.none.fl_str_mv Nonlinear optimization for a tumor invasion PDE model : computational and applied mathematics
title Nonlinear optimization for a tumor invasion PDE model : computational and applied mathematics
spellingShingle Nonlinear optimization for a tumor invasion PDE model : computational and applied mathematics
Quiroga, Andrés Agustín Ignacio
Reaction–diffusion equation
Tumor invasión
PDE-constrained optimization
Adjoint method
Finite element method
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
dc.creator.none.fl_str_mv Quiroga, Andrés Agustín Ignacio
Torres, Germán Ariel
Fernández Ferreyra, Damián Roberto
Turner, Cristina Vilma
author Quiroga, Andrés Agustín Ignacio
author_facet Quiroga, Andrés Agustín Ignacio
Torres, Germán Ariel
Fernández Ferreyra, Damián Roberto
Turner, Cristina Vilma
author_role author
author2 Torres, Germán Ariel
Fernández Ferreyra, Damián Roberto
Turner, Cristina Vilma
author2_role author
author
author
dc.subject.none.fl_str_mv Reaction–diffusion equation
Tumor invasión
PDE-constrained optimization
Adjoint method
Finite element method
topic Reaction–diffusion equation
Tumor invasión
PDE-constrained optimization
Adjoint method
Finite element method
dc.description.none.fl_txt_mv Fil: Quiroga, Andrés Agustín Ignacio. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina.
Fil: Torres, Germán Ariel. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura; Argentina.
Fil: Torres, Germán Ariel. Consejo Nacional de Investigaciones Científicas y Técnica. Instituto de Modelado e Innovación Tecnológica; Argentina.
Fil: Fernández Ferreyra, Damián Roberto. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.
Fil: Fernández Ferreyra, Damián Roberto. Consejo Nacional de Investigaciones Científicas y Técnica. Centro de Investigación y Estudios de Matemática; Argentina.
Fil: Turner, Cristina Vilma. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.
Fil: Turner, Cristina Vilma. Consejo Nacional de Investigaciones Científicas y Técnica. Centro de Investigación y Estudios de Matemática; Argentina.
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
description Fil: Quiroga, Andrés Agustín Ignacio. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina.
publishDate 2018
dc.date.none.fl_str_mv 2018
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv 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
identifier_str_mv 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
url http://repositorio.unne.edu.ar/handle/123456789/30327
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Atribución-NoComercial-SinDerivadas 2.5 Argentina
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Atribución-NoComercial-SinDerivadas 2.5 Argentina
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv Computational And Applied Mathematics, 2018, vol. 37, no. 1, p. 485-499.
reponame:Repositorio Institucional de la Universidad Nacional del Nordeste (UNNE)
instname:Universidad Nacional del Nordeste
reponame_str Repositorio Institucional de la Universidad Nacional del Nordeste (UNNE)
collection Repositorio Institucional de la Universidad Nacional del Nordeste (UNNE)
instname_str Universidad Nacional del Nordeste
repository.name.fl_str_mv Repositorio Institucional de la Universidad Nacional del Nordeste (UNNE) - Universidad Nacional del Nordeste
repository.mail.fl_str_mv ososa@bib.unne.edu.ar;sergio.alegria@unne.edu.ar
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