Nonlinear optimization for a tumor invasion PDE model

Autores
Quiroga, Andrés Agustin Ignacio; Torres, German Ariel; Fernández Ferreyra, Damián Roberto; Turner, Cristina Vilma
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this work, we introduce a methodology to approximate unknown parameters that appear on a non-linear reaction–diffusion model 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.
Fil: Quiroga, Andrés Agustin Ignacio. Comision Nacional de Energia Atomica. Gerencia de Area de Aplicaciones de la Tecnología Nuclear. Gerencia de Investigación Aplicada. Grupo de Mecanica Computacional; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Torres, German Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Modelado e Innovación Tecnológica. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Instituto de Modelado e Innovación Tecnológica; Argentina
Fil: Fernández Ferreyra, Damián Roberto. 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. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Fil: Turner, Cristina Vilma. 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. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Materia
REACTION DIFFUSION EQUATION
TUMOR INVASION
PDE-CONSTRAINED OPTIMIZATION
ADJOINT METHOD
FINITE ELEMENT METHOD
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:11336/31530
Acceder
id CONICETDig_be918689efd5dc801695c2fc251d5eac
oai_identifier_str oai:ri.conicet.gov.ar:11336/31530
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Nonlinear optimization for a tumor invasion PDE modelQuiroga, Andrés Agustin IgnacioTorres, German ArielFernández Ferreyra, Damián RobertoTurner, Cristina VilmaREACTION DIFFUSION EQUATIONTUMOR INVASIONPDE-CONSTRAINED OPTIMIZATIONADJOINT METHODFINITE ELEMENT METHODhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this work, we introduce a methodology to approximate unknown parameters that appear on a non-linear reaction–diffusion model 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.Fil: Quiroga, Andrés Agustin Ignacio. Comision Nacional de Energia Atomica. Gerencia de Area de Aplicaciones de la Tecnología Nuclear. Gerencia de Investigación Aplicada. Grupo de Mecanica Computacional; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Torres, German Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Modelado e Innovación Tecnológica. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Instituto de Modelado e Innovación Tecnológica; ArgentinaFil: Fernández Ferreyra, Damián Roberto. 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. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Turner, Cristina Vilma. 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. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaSpringer2016-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/31530Fernández Ferreyra, Damián Roberto; Torres, German Ariel; Quiroga, Andrés Agustin Ignacio; Turner, Cristina Vilma; Nonlinear optimization for a tumor invasion PDE model; Springer; Computational And Applied Mathematics; 6-2016; 1-150101-82051807-0302CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/10.1007/s40314-016-0356-2info:eu-repo/semantics/altIdentifier/doi/10.1007/s40314-016-0356-2info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-17T11:14:05Zoai:ri.conicet.gov.ar:11336/31530instacron: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:34982025-09-17 11:14:05.634CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Nonlinear optimization for a tumor invasion PDE model
title Nonlinear optimization for a tumor invasion PDE model
spellingShingle Nonlinear optimization for a tumor invasion PDE model
Quiroga, Andrés Agustin Ignacio
REACTION DIFFUSION EQUATION
TUMOR INVASION
PDE-CONSTRAINED OPTIMIZATION
ADJOINT METHOD
FINITE ELEMENT METHOD
title_short Nonlinear optimization for a tumor invasion PDE model
title_full Nonlinear optimization for a tumor invasion PDE model
title_fullStr Nonlinear optimization for a tumor invasion PDE model
title_full_unstemmed Nonlinear optimization for a tumor invasion PDE model
title_sort Nonlinear optimization for a tumor invasion PDE model
dc.creator.none.fl_str_mv Quiroga, Andrés Agustin Ignacio
Torres, German Ariel
Fernández Ferreyra, Damián Roberto
Turner, Cristina Vilma
author Quiroga, Andrés Agustin Ignacio
author_facet Quiroga, Andrés Agustin Ignacio
Torres, German Ariel
Fernández Ferreyra, Damián Roberto
Turner, Cristina Vilma
author_role author
author2 Torres, German Ariel
Fernández Ferreyra, Damián Roberto
Turner, Cristina Vilma
author2_role author
author
author
dc.subject.none.fl_str_mv REACTION DIFFUSION EQUATION
TUMOR INVASION
PDE-CONSTRAINED OPTIMIZATION
ADJOINT METHOD
FINITE ELEMENT METHOD
topic REACTION DIFFUSION EQUATION
TUMOR INVASION
PDE-CONSTRAINED OPTIMIZATION
ADJOINT METHOD
FINITE ELEMENT METHOD
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 work, we introduce a methodology to approximate unknown parameters that appear on a non-linear reaction–diffusion model 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.
Fil: Quiroga, Andrés Agustin Ignacio. Comision Nacional de Energia Atomica. Gerencia de Area de Aplicaciones de la Tecnología Nuclear. Gerencia de Investigación Aplicada. Grupo de Mecanica Computacional; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Torres, German Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Modelado e Innovación Tecnológica. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Instituto de Modelado e Innovación Tecnológica; Argentina
Fil: Fernández Ferreyra, Damián Roberto. 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. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Fil: Turner, Cristina Vilma. 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. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
description In this work, we introduce a methodology to approximate unknown parameters that appear on a non-linear reaction–diffusion model 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.
publishDate 2016
dc.date.none.fl_str_mv 2016-06
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/11336/31530
Fernández Ferreyra, Damián Roberto; Torres, German Ariel; Quiroga, Andrés Agustin Ignacio; Turner, Cristina Vilma; Nonlinear optimization for a tumor invasion PDE model; Springer; Computational And Applied Mathematics; 6-2016; 1-15
0101-8205
1807-0302
CONICET Digital
CONICET
url http://hdl.handle.net/11336/31530
identifier_str_mv Fernández Ferreyra, Damián Roberto; Torres, German Ariel; Quiroga, Andrés Agustin Ignacio; Turner, Cristina Vilma; Nonlinear optimization for a tumor invasion PDE model; Springer; Computational And Applied Mathematics; 6-2016; 1-15
0101-8205
1807-0302
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://link.springer.com/10.1007/s40314-016-0356-2
info:eu-repo/semantics/altIdentifier/doi/10.1007/s40314-016-0356-2
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
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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
_version_ 1843606476738789376
score 13.001348

Publicaciones similares