Adjoint method for a tumor growth PDE-constrained optimization problem

Autores
Knopoff, Damián Alejandro; Fernández Ferreyra, Damián Roberto; Torres, Germán Ariel; Turner, Cristina Vilma
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we present a method for estimating unknown parameters that appear on an avascular, spheric tumor growth model. The model for the tumor is based on nutrient driven growth of a continuum of live cells, whose birth and death generate volume changes described by a velocity field. The model consists of a coupled system of partial differential equations whose spatial domain is the tumor, that changes in size over time. Thus, the situation can be formulated as a free boundary problem. After solving the direct problem properly, we use the model for the estimation of parameters by fitting the numerical solution with real data, obtained via in vitro experiments and medical imaging. We define an appropriate functional to compare both the real data and the numerical solution. We use the adjoint method for the minimization of this functional.
Fil: Knopoff, Damián Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina
Fil: Fernández Ferreyra, Damián Roberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina
Fil: Torres, Germán Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina
Fil: Turner, Cristina Vilma. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina
Materia
Avascular Tumor
Pde Constrained Optimization
Inverse Problem
Mathematical Modeling
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:11336/13481
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Adjoint method for a tumor growth PDE-constrained optimization problemKnopoff, Damián AlejandroFernández Ferreyra, Damián RobertoTorres, Germán ArielTurner, Cristina VilmaAvascular TumorPde Constrained OptimizationInverse ProblemMathematical Modelinghttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we present a method for estimating unknown parameters that appear on an avascular, spheric tumor growth model. The model for the tumor is based on nutrient driven growth of a continuum of live cells, whose birth and death generate volume changes described by a velocity field. The model consists of a coupled system of partial differential equations whose spatial domain is the tumor, that changes in size over time. Thus, the situation can be formulated as a free boundary problem. After solving the direct problem properly, we use the model for the estimation of parameters by fitting the numerical solution with real data, obtained via <em>in vitro</em> experiments and medical imaging. We define an appropriate functional to compare both the real data and the numerical solution. We use the adjoint method for the minimization of this functional.Fil: Knopoff, Damián Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); ArgentinaFil: Fernández Ferreyra, Damián Roberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); ArgentinaFil: Torres, Germán Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); ArgentinaFil: Turner, Cristina Vilma. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); ArgentinaPergamon-elsevier Science Ltd2013-10info: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/11336/13481Knopoff, Damián Alejandro; Fernández Ferreyra, Damián Roberto; Torres, Germán Ariel; Turner, Cristina Vilma; Adjoint method for a tumor growth PDE-constrained optimization problem; Pergamon-elsevier Science Ltd; Computers & Mathematics With Applications (1987); 66; 6; 10-2013; 1104-11190898-1221enginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.camwa.2013.05.028info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/journal/08981221info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:14:04Zoai:ri.conicet.gov.ar:11336/13481instacron: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:34982025-09-10 13:14:04.632CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Adjoint method for a tumor growth PDE-constrained optimization problem
title Adjoint method for a tumor growth PDE-constrained optimization problem
spellingShingle Adjoint method for a tumor growth PDE-constrained optimization problem
Knopoff, Damián Alejandro
Avascular Tumor
Pde Constrained Optimization
Inverse Problem
Mathematical Modeling
title_short Adjoint method for a tumor growth PDE-constrained optimization problem
title_full Adjoint method for a tumor growth PDE-constrained optimization problem
title_fullStr Adjoint method for a tumor growth PDE-constrained optimization problem
title_full_unstemmed Adjoint method for a tumor growth PDE-constrained optimization problem
title_sort Adjoint method for a tumor growth PDE-constrained optimization problem
dc.creator.none.fl_str_mv Knopoff, Damián Alejandro
Fernández Ferreyra, Damián Roberto
Torres, Germán Ariel
Turner, Cristina Vilma
author Knopoff, Damián Alejandro
author_facet Knopoff, Damián Alejandro
Fernández Ferreyra, Damián Roberto
Torres, Germán Ariel
Turner, Cristina Vilma
author_role author
author2 Fernández Ferreyra, Damián Roberto
Torres, Germán Ariel
Turner, Cristina Vilma
author2_role author
author
author
dc.subject.none.fl_str_mv Avascular Tumor
Pde Constrained Optimization
Inverse Problem
Mathematical Modeling
topic Avascular Tumor
Pde Constrained Optimization
Inverse Problem
Mathematical Modeling
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 unknown parameters that appear on an avascular, spheric tumor growth model. The model for the tumor is based on nutrient driven growth of a continuum of live cells, whose birth and death generate volume changes described by a velocity field. The model consists of a coupled system of partial differential equations whose spatial domain is the tumor, that changes in size over time. Thus, the situation can be formulated as a free boundary problem. After solving the direct problem properly, we use the model for the estimation of parameters by fitting the numerical solution with real data, obtained via <em>in vitro</em> experiments and medical imaging. We define an appropriate functional to compare both the real data and the numerical solution. We use the adjoint method for the minimization of this functional.
Fil: Knopoff, Damián Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina
Fil: Fernández Ferreyra, Damián Roberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina
Fil: Torres, Germán Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina
Fil: Turner, Cristina Vilma. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina
description In this paper we present a method for estimating unknown parameters that appear on an avascular, spheric tumor growth model. The model for the tumor is based on nutrient driven growth of a continuum of live cells, whose birth and death generate volume changes described by a velocity field. The model consists of a coupled system of partial differential equations whose spatial domain is the tumor, that changes in size over time. Thus, the situation can be formulated as a free boundary problem. After solving the direct problem properly, we use the model for the estimation of parameters by fitting the numerical solution with real data, obtained via <em>in vitro</em> experiments and medical imaging. We define an appropriate functional to compare both the real data and the numerical solution. We use the adjoint method for the minimization of this functional.
publishDate 2013
dc.date.none.fl_str_mv 2013-10
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/11336/13481
Knopoff, Damián Alejandro; Fernández Ferreyra, Damián Roberto; Torres, Germán Ariel; Turner, Cristina Vilma; Adjoint method for a tumor growth PDE-constrained optimization problem; Pergamon-elsevier Science Ltd; Computers & Mathematics With Applications (1987); 66; 6; 10-2013; 1104-1119
0898-1221
url http://hdl.handle.net/11336/13481
identifier_str_mv Knopoff, Damián Alejandro; Fernández Ferreyra, Damián Roberto; Torres, Germán Ariel; Turner, Cristina Vilma; Adjoint method for a tumor growth PDE-constrained optimization problem; Pergamon-elsevier Science Ltd; Computers & Mathematics With Applications (1987); 66; 6; 10-2013; 1104-1119
0898-1221
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.camwa.2013.05.028
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/journal/08981221
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 Pergamon-elsevier Science Ltd
publisher.none.fl_str_mv Pergamon-elsevier Science Ltd
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 12.993085

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