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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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Formato: | Online Artículo Texto |
Lenguaje: | English |
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Hindawi Publishing Corporation
2013
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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. |
format | Online Article Text |
id | pubmed-3762161 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2013 |
publisher | Hindawi Publishing Corporation |
record_format | MEDLINE/PubMed |
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 |
work_keys_str_mv | AT pamukserdal solutionsofalinearizedmathematicalmodelforcapillaryformationintumorangiogenesisaninitialdataperturbationapproximation |