A mathematical method for parameter estimation in a tumor growth model

Autores
Knopoff, Damián Alejandro; Fernández Ferreyra, Damián Roberto; Torres, German Ariel; Turner, Cristina Vilma
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, we present a methodology for estimating the effectiveness of a drug, an unknown parameter that appears on an avascular, spheric tumor growth model formulated in terms of a coupled system of partial differential equations (PDEs). This model is formulated considering a continuum of live cells that grow by the action of a nutrient. Volume changes occur due to cell birth and death, describing a velocity field. The model assumes that when the drug is applied externally, it diffuses and kills cells. The effectiveness of the drug is obtained by solving an inverse problem which is a PDE-constrained optimization problem. We define suitable objective functions by fitting the modeled and the observed tumor radius and the inverse problem is solved numerically using a Pattern Search method. It is observed that the effectiveness of the drug is retrieved with a reasonable accuracy. Experiments with noised data are also considered and the results are compared and contrasted.
Fil: Knopoff, Damián Alejandro. 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. Politecnico di Torino; Italia
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
Fil: Torres, German Ariel. 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. 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
Avascular Tumor
Inverse Problem
Mathematical Modeling
Pde-Constrained Optimization
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:11336/53097
Acceder
id CONICETDig_921c474debfb2776e14b00d80d54214c
oai_identifier_str oai:ri.conicet.gov.ar:11336/53097
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A mathematical method for parameter estimation in a tumor growth modelKnopoff, Damián AlejandroFernández Ferreyra, Damián RobertoTorres, German ArielTurner, Cristina VilmaAvascular TumorInverse ProblemMathematical ModelingPde-Constrained Optimizationhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper, we present a methodology for estimating the effectiveness of a drug, an unknown parameter that appears on an avascular, spheric tumor growth model formulated in terms of a coupled system of partial differential equations (PDEs). This model is formulated considering a continuum of live cells that grow by the action of a nutrient. Volume changes occur due to cell birth and death, describing a velocity field. The model assumes that when the drug is applied externally, it diffuses and kills cells. The effectiveness of the drug is obtained by solving an inverse problem which is a PDE-constrained optimization problem. We define suitable objective functions by fitting the modeled and the observed tumor radius and the inverse problem is solved numerically using a Pattern Search method. It is observed that the effectiveness of the drug is retrieved with a reasonable accuracy. Experiments with noised data are also considered and the results are compared and contrasted.Fil: Knopoff, Damián Alejandro. 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. Politecnico di Torino; ItaliaFil: 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; ArgentinaFil: Torres, German Ariel. 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. 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; ArgentinaSpringer2017-03-24info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/53097Knopoff, Damián Alejandro; Fernández Ferreyra, Damián Roberto; Torres, German Ariel; Turner, Cristina Vilma; A mathematical method for parameter estimation in a tumor growth model; Springer; Matematica Aplicada E Computacional; 36; 1; 24-3-2017; 733-7480101-82051807-0302CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s40314-015-0259-7info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs40314-015-0259-7info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:47:28Zoai:ri.conicet.gov.ar:11336/53097instacron: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:34982025-10-15 14:47:28.507CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A mathematical method for parameter estimation in a tumor growth model
title A mathematical method for parameter estimation in a tumor growth model
spellingShingle A mathematical method for parameter estimation in a tumor growth model
Knopoff, Damián Alejandro
Avascular Tumor
Inverse Problem
Mathematical Modeling
Pde-Constrained Optimization
title_short A mathematical method for parameter estimation in a tumor growth model
title_full A mathematical method for parameter estimation in a tumor growth model
title_fullStr A mathematical method for parameter estimation in a tumor growth model
title_full_unstemmed A mathematical method for parameter estimation in a tumor growth model
title_sort A mathematical method for parameter estimation in a tumor growth model
dc.creator.none.fl_str_mv Knopoff, Damián Alejandro
Fernández Ferreyra, Damián Roberto
Torres, German Ariel
Turner, Cristina Vilma
author Knopoff, Damián Alejandro
author_facet Knopoff, Damián Alejandro
Fernández Ferreyra, Damián Roberto
Torres, German Ariel
Turner, Cristina Vilma
author_role author
author2 Fernández Ferreyra, Damián Roberto
Torres, German Ariel
Turner, Cristina Vilma
author2_role author
author
author
dc.subject.none.fl_str_mv Avascular Tumor
Inverse Problem
Mathematical Modeling
Pde-Constrained Optimization
topic Avascular Tumor
Inverse Problem
Mathematical Modeling
Pde-Constrained Optimization
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 methodology for estimating the effectiveness of a drug, an unknown parameter that appears on an avascular, spheric tumor growth model formulated in terms of a coupled system of partial differential equations (PDEs). This model is formulated considering a continuum of live cells that grow by the action of a nutrient. Volume changes occur due to cell birth and death, describing a velocity field. The model assumes that when the drug is applied externally, it diffuses and kills cells. The effectiveness of the drug is obtained by solving an inverse problem which is a PDE-constrained optimization problem. We define suitable objective functions by fitting the modeled and the observed tumor radius and the inverse problem is solved numerically using a Pattern Search method. It is observed that the effectiveness of the drug is retrieved with a reasonable accuracy. Experiments with noised data are also considered and the results are compared and contrasted.
Fil: Knopoff, Damián Alejandro. 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. Politecnico di Torino; Italia
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
Fil: Torres, German Ariel. 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. 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 methodology for estimating the effectiveness of a drug, an unknown parameter that appears on an avascular, spheric tumor growth model formulated in terms of a coupled system of partial differential equations (PDEs). This model is formulated considering a continuum of live cells that grow by the action of a nutrient. Volume changes occur due to cell birth and death, describing a velocity field. The model assumes that when the drug is applied externally, it diffuses and kills cells. The effectiveness of the drug is obtained by solving an inverse problem which is a PDE-constrained optimization problem. We define suitable objective functions by fitting the modeled and the observed tumor radius and the inverse problem is solved numerically using a Pattern Search method. It is observed that the effectiveness of the drug is retrieved with a reasonable accuracy. Experiments with noised data are also considered and the results are compared and contrasted.
publishDate 2017
dc.date.none.fl_str_mv 2017-03-24
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/11336/53097
Knopoff, Damián Alejandro; Fernández Ferreyra, Damián Roberto; Torres, German Ariel; Turner, Cristina Vilma; A mathematical method for parameter estimation in a tumor growth model; Springer; Matematica Aplicada E Computacional; 36; 1; 24-3-2017; 733-748
0101-8205
1807-0302
CONICET Digital
CONICET
url http://hdl.handle.net/11336/53097
identifier_str_mv Knopoff, Damián Alejandro; Fernández Ferreyra, Damián Roberto; Torres, German Ariel; Turner, Cristina Vilma; A mathematical method for parameter estimation in a tumor growth model; Springer; Matematica Aplicada E Computacional; 36; 1; 24-3-2017; 733-748
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/doi/10.1007/s40314-015-0259-7
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs40314-015-0259-7
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
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_ 1846082991247327232
score 12.891075

Publicaciones similares