Adjoint method for a tumor invasion PDE-constrained optimization problem in 2D using adaptive finite element method

Autores
Quiroga, Andrés Agustin Ignacio; Fernández, Damián Andrés; Turner, Cristina Vilma; Torres, German Ariel
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we present a method for estimating an unknown parameter that appears in a two dimensional non-linear reaction-diffusion model of cancer invasion. This model considers that tumor-induced alteration of micro-environmental pH provides a mechanism for cancer invasion. A coupled system reaction-diffusion describing this model is given by three partial differential equations for the 2D non-dimensional spatial distribution and temporal evolution of the density of normal tissue, the neoplastic tissue growth and the excess H+ ion concentration. Each of the model parameters has a corresponding biological interpretation, for instance, the growth rate of neoplastic tissue, the diffusion coefficient, the re-absorption rate and the destructive influence of H+ ions in the healthy tissue. The parameter is estimated by solving a minimization problem, in which the objective function is defined in order to compare both the real data and the numerical solution of the cancer invasion model. The real data can be obtained by, for example, fluorescence ratio imaging microscopy. We apply a splitting strategy joint with the adaptive finite element method to numerically solve the model. The minimization problem (the inverse problem) is solved by using a gradient-based optimization method, in which the functional derivative is provided through an adjoint approach.
Fil: Quiroga, Andrés Agustin Ignacio. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Fil: Fernández, Damián Andrés. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Fil: Turner, Cristina Vilma. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Fil: Torres, German Ariel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Materia
ADAPTIVE FINITE ELEMENT METHOD
ADJOINT METHOD
PDE-CONSTRAINED OPTIMIZATION
REACTION-DIFFUSION 2D EQUATION
SPLITTING METHOD
TUMOR INVASION
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/111144
Acceder
id CONICETDig_1575eac13e4220b08a8ba6665402fdf5
oai_identifier_str oai:ri.conicet.gov.ar:11336/111144
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Adjoint method for a tumor invasion PDE-constrained optimization problem in 2D using adaptive finite element methodQuiroga, Andrés Agustin IgnacioFernández, Damián AndrésTurner, Cristina VilmaTorres, German ArielADAPTIVE FINITE ELEMENT METHODADJOINT METHODPDE-CONSTRAINED OPTIMIZATIONREACTION-DIFFUSION 2D EQUATIONSPLITTING METHODTUMOR INVASIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we present a method for estimating an unknown parameter that appears in a two dimensional non-linear reaction-diffusion model of cancer invasion. This model considers that tumor-induced alteration of micro-environmental pH provides a mechanism for cancer invasion. A coupled system reaction-diffusion describing this model is given by three partial differential equations for the 2D non-dimensional spatial distribution and temporal evolution of the density of normal tissue, the neoplastic tissue growth and the excess H+ ion concentration. Each of the model parameters has a corresponding biological interpretation, for instance, the growth rate of neoplastic tissue, the diffusion coefficient, the re-absorption rate and the destructive influence of H+ ions in the healthy tissue. The parameter is estimated by solving a minimization problem, in which the objective function is defined in order to compare both the real data and the numerical solution of the cancer invasion model. The real data can be obtained by, for example, fluorescence ratio imaging microscopy. We apply a splitting strategy joint with the adaptive finite element method to numerically solve the model. The minimization problem (the inverse problem) is solved by using a gradient-based optimization method, in which the functional derivative is provided through an adjoint approach.Fil: Quiroga, Andrés Agustin Ignacio. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaFil: Fernández, Damián Andrés. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaFil: Turner, Cristina Vilma. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaFil: Torres, German Ariel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaElsevier Science Inc2015-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/111144Quiroga, Andrés Agustin Ignacio; Fernández, Damián Andrés; Turner, Cristina Vilma; Torres, German Ariel; Adjoint method for a tumor invasion PDE-constrained optimization problem in 2D using adaptive finite element method; Elsevier Science Inc; Applied Mathematics and Computation; 270; 11-2015; 358-3680096-3003CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0096300315010930info:eu-repo/semantics/altIdentifier/doi/10.1016/j.amc.2015.08.038info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:59:44Zoai:ri.conicet.gov.ar:11336/111144instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:59:44.641CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Adjoint method for a tumor invasion PDE-constrained optimization problem in 2D using adaptive finite element method
title Adjoint method for a tumor invasion PDE-constrained optimization problem in 2D using adaptive finite element method
spellingShingle Adjoint method for a tumor invasion PDE-constrained optimization problem in 2D using adaptive finite element method
Quiroga, Andrés Agustin Ignacio
ADAPTIVE FINITE ELEMENT METHOD
ADJOINT METHOD
PDE-CONSTRAINED OPTIMIZATION
REACTION-DIFFUSION 2D EQUATION
SPLITTING METHOD
TUMOR INVASION
title_short Adjoint method for a tumor invasion PDE-constrained optimization problem in 2D using adaptive finite element method
title_full Adjoint method for a tumor invasion PDE-constrained optimization problem in 2D using adaptive finite element method
title_fullStr Adjoint method for a tumor invasion PDE-constrained optimization problem in 2D using adaptive finite element method
title_full_unstemmed Adjoint method for a tumor invasion PDE-constrained optimization problem in 2D using adaptive finite element method
title_sort Adjoint method for a tumor invasion PDE-constrained optimization problem in 2D using adaptive finite element method
dc.creator.none.fl_str_mv Quiroga, Andrés Agustin Ignacio
Fernández, Damián Andrés
Turner, Cristina Vilma
Torres, German Ariel
author Quiroga, Andrés Agustin Ignacio
author_facet Quiroga, Andrés Agustin Ignacio
Fernández, Damián Andrés
Turner, Cristina Vilma
Torres, German Ariel
author_role author
author2 Fernández, Damián Andrés
Turner, Cristina Vilma
Torres, German Ariel
author2_role author
author
author
dc.subject.none.fl_str_mv ADAPTIVE FINITE ELEMENT METHOD
ADJOINT METHOD
PDE-CONSTRAINED OPTIMIZATION
REACTION-DIFFUSION 2D EQUATION
SPLITTING METHOD
TUMOR INVASION
topic ADAPTIVE FINITE ELEMENT METHOD
ADJOINT METHOD
PDE-CONSTRAINED OPTIMIZATION
REACTION-DIFFUSION 2D EQUATION
SPLITTING METHOD
TUMOR INVASION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper we present a method for estimating an unknown parameter that appears in a two dimensional non-linear reaction-diffusion model of cancer invasion. This model considers that tumor-induced alteration of micro-environmental pH provides a mechanism for cancer invasion. A coupled system reaction-diffusion describing this model is given by three partial differential equations for the 2D non-dimensional spatial distribution and temporal evolution of the density of normal tissue, the neoplastic tissue growth and the excess H+ ion concentration. Each of the model parameters has a corresponding biological interpretation, for instance, the growth rate of neoplastic tissue, the diffusion coefficient, the re-absorption rate and the destructive influence of H+ ions in the healthy tissue. The parameter is estimated by solving a minimization problem, in which the objective function is defined in order to compare both the real data and the numerical solution of the cancer invasion model. The real data can be obtained by, for example, fluorescence ratio imaging microscopy. We apply a splitting strategy joint with the adaptive finite element method to numerically solve the model. The minimization problem (the inverse problem) is solved by using a gradient-based optimization method, in which the functional derivative is provided through an adjoint approach.
Fil: Quiroga, Andrés Agustin Ignacio. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Fil: Fernández, Damián Andrés. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Fil: Turner, Cristina Vilma. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Fil: Torres, German Ariel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
description In this paper we present a method for estimating an unknown parameter that appears in a two dimensional non-linear reaction-diffusion model of cancer invasion. This model considers that tumor-induced alteration of micro-environmental pH provides a mechanism for cancer invasion. A coupled system reaction-diffusion describing this model is given by three partial differential equations for the 2D non-dimensional spatial distribution and temporal evolution of the density of normal tissue, the neoplastic tissue growth and the excess H+ ion concentration. Each of the model parameters has a corresponding biological interpretation, for instance, the growth rate of neoplastic tissue, the diffusion coefficient, the re-absorption rate and the destructive influence of H+ ions in the healthy tissue. The parameter is estimated by solving a minimization problem, in which the objective function is defined in order to compare both the real data and the numerical solution of the cancer invasion model. The real data can be obtained by, for example, fluorescence ratio imaging microscopy. We apply a splitting strategy joint with the adaptive finite element method to numerically solve the model. The minimization problem (the inverse problem) is solved by using a gradient-based optimization method, in which the functional derivative is provided through an adjoint approach.
publishDate 2015
dc.date.none.fl_str_mv 2015-11
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 http://hdl.handle.net/11336/111144
Quiroga, Andrés Agustin Ignacio; Fernández, Damián Andrés; Turner, Cristina Vilma; Torres, German Ariel; Adjoint method for a tumor invasion PDE-constrained optimization problem in 2D using adaptive finite element method; Elsevier Science Inc; Applied Mathematics and Computation; 270; 11-2015; 358-368
0096-3003
CONICET Digital
CONICET
url http://hdl.handle.net/11336/111144
identifier_str_mv Quiroga, Andrés Agustin Ignacio; Fernández, Damián Andrés; Turner, Cristina Vilma; Torres, German Ariel; Adjoint method for a tumor invasion PDE-constrained optimization problem in 2D using adaptive finite element method; Elsevier Science Inc; Applied Mathematics and Computation; 270; 11-2015; 358-368
0096-3003
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0096300315010930
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.amc.2015.08.038
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science Inc
publisher.none.fl_str_mv Elsevier Science Inc
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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