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
- Institución
- Universidad Nacional del Nordeste
- OAI Identificador
- oai:repositorio.unne.edu.ar:123456789/30327
Ver los metadatos del registro completo
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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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1844621685949464576 |
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12.891075 |