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Solutions of a Linearized Mathematical Model for Capillary Formation in Tumor Angiogenesis: An Initial Data Perturbation Approximation

We present a mathematical model for capillary formation in tumor angiogenesis and solve it by linearizing it using an initial data perturbation method. This method is highly effective to obtain solutions of nonlinear coupled differential equations. We also provide a specific example resulting, that...

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Detalles Bibliográficos
Autor principal: Pamuk, Serdal
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2013
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3762161/
https://www.ncbi.nlm.nih.gov/pubmed/24027602
http://dx.doi.org/10.1155/2013/789402
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author Pamuk, Serdal
author_facet Pamuk, Serdal
author_sort Pamuk, Serdal
collection PubMed
description We present a mathematical model for capillary formation in tumor angiogenesis and solve it by linearizing it using an initial data perturbation method. This method is highly effective to obtain solutions of nonlinear coupled differential equations. We also provide a specific example resulting, that even a few terms of the obtained series solutions are enough to have an idea for the endothelial cell movement in a capillary. MATLAB-generated figures are provided, and the stability criteria are determined for the steady-state solution of the cell equation.
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spelling pubmed-37621612013-09-11 Solutions of a Linearized Mathematical Model for Capillary Formation in Tumor Angiogenesis: An Initial Data Perturbation Approximation Pamuk, Serdal Comput Math Methods Med Research Article We present a mathematical model for capillary formation in tumor angiogenesis and solve it by linearizing it using an initial data perturbation method. This method is highly effective to obtain solutions of nonlinear coupled differential equations. We also provide a specific example resulting, that even a few terms of the obtained series solutions are enough to have an idea for the endothelial cell movement in a capillary. MATLAB-generated figures are provided, and the stability criteria are determined for the steady-state solution of the cell equation. Hindawi Publishing Corporation 2013 2013-08-18 /pmc/articles/PMC3762161/ /pubmed/24027602 http://dx.doi.org/10.1155/2013/789402 Text en Copyright © 2013 Serdal Pamuk. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Pamuk, Serdal
Solutions of a Linearized Mathematical Model for Capillary Formation in Tumor Angiogenesis: An Initial Data Perturbation Approximation
title Solutions of a Linearized Mathematical Model for Capillary Formation in Tumor Angiogenesis: An Initial Data Perturbation Approximation
title_full Solutions of a Linearized Mathematical Model for Capillary Formation in Tumor Angiogenesis: An Initial Data Perturbation Approximation
title_fullStr Solutions of a Linearized Mathematical Model for Capillary Formation in Tumor Angiogenesis: An Initial Data Perturbation Approximation
title_full_unstemmed Solutions of a Linearized Mathematical Model for Capillary Formation in Tumor Angiogenesis: An Initial Data Perturbation Approximation
title_short Solutions of a Linearized Mathematical Model for Capillary Formation in Tumor Angiogenesis: An Initial Data Perturbation Approximation
title_sort solutions of a linearized mathematical model for capillary formation in tumor angiogenesis: an initial data perturbation approximation
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3762161/
https://www.ncbi.nlm.nih.gov/pubmed/24027602
http://dx.doi.org/10.1155/2013/789402
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