Steady-State Analysis of Necrotic Core Formation for Solid Avascular Tumors with Time Delays in Regulatory Apoptosis

A mathematical model for the growth of solid avascular tumor with time delays in regulatory apoptosis is studied. The existence of stationary solutions and the mechanism of formation of necrotic cores in the growth of the tumors are studied. The results show that if the natural death rate of the tum...

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Detalles Bibliográficos
Autores principales: Zhang, Fangwei, Xu, Shihe
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4211211/
https://www.ncbi.nlm.nih.gov/pubmed/25667597
http://dx.doi.org/10.1155/2014/467158
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author Zhang, Fangwei
Xu, Shihe
author_facet Zhang, Fangwei
Xu, Shihe
author_sort Zhang, Fangwei
collection PubMed
description A mathematical model for the growth of solid avascular tumor with time delays in regulatory apoptosis is studied. The existence of stationary solutions and the mechanism of formation of necrotic cores in the growth of the tumors are studied. The results show that if the natural death rate of the tumor cell exceeds a fixed positive constant, then the dormant tumor is nonnecrotic; otherwise, the dormant tumor is necrotic.
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spelling pubmed-42112112015-02-09 Steady-State Analysis of Necrotic Core Formation for Solid Avascular Tumors with Time Delays in Regulatory Apoptosis Zhang, Fangwei Xu, Shihe Comput Math Methods Med Research Article A mathematical model for the growth of solid avascular tumor with time delays in regulatory apoptosis is studied. The existence of stationary solutions and the mechanism of formation of necrotic cores in the growth of the tumors are studied. The results show that if the natural death rate of the tumor cell exceeds a fixed positive constant, then the dormant tumor is nonnecrotic; otherwise, the dormant tumor is necrotic. Hindawi Publishing Corporation 2014 2014-10-13 /pmc/articles/PMC4211211/ /pubmed/25667597 http://dx.doi.org/10.1155/2014/467158 Text en Copyright © 2014 F. Zhang and S. Xu. 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
Zhang, Fangwei
Xu, Shihe
Steady-State Analysis of Necrotic Core Formation for Solid Avascular Tumors with Time Delays in Regulatory Apoptosis
title Steady-State Analysis of Necrotic Core Formation for Solid Avascular Tumors with Time Delays in Regulatory Apoptosis
title_full Steady-State Analysis of Necrotic Core Formation for Solid Avascular Tumors with Time Delays in Regulatory Apoptosis
title_fullStr Steady-State Analysis of Necrotic Core Formation for Solid Avascular Tumors with Time Delays in Regulatory Apoptosis
title_full_unstemmed Steady-State Analysis of Necrotic Core Formation for Solid Avascular Tumors with Time Delays in Regulatory Apoptosis
title_short Steady-State Analysis of Necrotic Core Formation for Solid Avascular Tumors with Time Delays in Regulatory Apoptosis
title_sort steady-state analysis of necrotic core formation for solid avascular tumors with time delays in regulatory apoptosis
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4211211/
https://www.ncbi.nlm.nih.gov/pubmed/25667597
http://dx.doi.org/10.1155/2014/467158
work_keys_str_mv AT zhangfangwei steadystateanalysisofnecroticcoreformationforsolidavasculartumorswithtimedelaysinregulatoryapoptosis
AT xushihe steadystateanalysisofnecroticcoreformationforsolidavasculartumorswithtimedelaysinregulatoryapoptosis

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