Numerical solution of a model for brain cancer progression after therapy

Numerical solution of a model for brain cancer progression after therapy

We present a numerical scheme used to investigate a mathematical model of tumor growth which incorporates multiple disparate timescales. We simulate the model with different initial data. The initial conditions explored herein correspond to a small remnant of tumor tissue left after surgical resect...

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Main Authors: Zdzislaw Jackiewicz, Yang Kuang, Craig Thalhauser, Barbara Zubik-Kowal
Format: Article
Language:English
Published: Vilnius Gediminas Technical University 2009-03-01
Series:Mathematical Modelling and Analysis
Subjects:
theoretical oncology
mathematical models
numerical methods
Online Access:https://journals.vgtu.lt/index.php/MMA/article/view/6516
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spelling doaj-8f9d654145dc4114a1f39a22b691e5192021-07-02T08:03:55ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102009-03-0114110.3846/1392-6292.2009.14.43-56Numerical solution of a model for brain cancer progression after therapyZdzislaw Jackiewicz0Yang Kuang1Craig Thalhauser2Barbara Zubik-Kowal3Arizona State University, 4Boise State University; Department of Mathematics, Tempe, AZ 85287; AGH University of Science and Technology, Kraków, PolandArizona State University, 4Boise State University; Department of Mathematics, Tempe, AZ 85287Arizona State University, 4Boise State University; Department of Mathematics, Tempe, AZ 85287Department of Mathematics, Boise, ID 83725 We present a numerical scheme used to investigate a mathematical model of tumor growth which incorporates multiple disparate timescales. We simulate the model with different initial data. The initial conditions explored herein correspond to a small remnant of tumor tissue left after surgical resection. Our results indicate that tumor regrowth begins at the pre‐surgery tumor‐healthy tissue interface and penetrates back into the original tumor area. This growth is rate‐limited by the reformation of the tumor vascular network. First published online: 14 Oct 2010 https://journals.vgtu.lt/index.php/MMA/article/view/6516theoretical oncologymathematical modelsnumerical methods
collection DOAJ
language English
format Article
sources DOAJ
author Zdzislaw Jackiewicz
Yang Kuang
Craig Thalhauser
Barbara Zubik-Kowal
spellingShingle Zdzislaw Jackiewicz
Yang Kuang
Craig Thalhauser
Barbara Zubik-Kowal
Numerical solution of a model for brain cancer progression after therapy
Mathematical Modelling and Analysis
theoretical oncology
mathematical models
numerical methods
author_facet Zdzislaw Jackiewicz
Yang Kuang
Craig Thalhauser
Barbara Zubik-Kowal
author_sort Zdzislaw Jackiewicz
title Numerical solution of a model for brain cancer progression after therapy
title_short Numerical solution of a model for brain cancer progression after therapy
title_full Numerical solution of a model for brain cancer progression after therapy
title_fullStr Numerical solution of a model for brain cancer progression after therapy
title_full_unstemmed Numerical solution of a model for brain cancer progression after therapy
title_sort numerical solution of a model for brain cancer progression after therapy
publisher Vilnius Gediminas Technical University
series Mathematical Modelling and Analysis
issn 1392-6292
1648-3510
publishDate 2009-03-01
description We present a numerical scheme used to investigate a mathematical model of tumor growth which incorporates multiple disparate timescales. We simulate the model with different initial data. The initial conditions explored herein correspond to a small remnant of tumor tissue left after surgical resection. Our results indicate that tumor regrowth begins at the pre‐surgery tumor‐healthy tissue interface and penetrates back into the original tumor area. This growth is rate‐limited by the reformation of the tumor vascular network. First published online: 14 Oct 2010
topic theoretical oncology
mathematical models
numerical methods
url https://journals.vgtu.lt/index.php/MMA/article/view/6516
work_keys_str_mv AT zdzislawjackiewicz numericalsolutionofamodelforbraincancerprogressionaftertherapy
AT yangkuang numericalsolutionofamodelforbraincancerprogressionaftertherapy
AT craigthalhauser numericalsolutionofamodelforbraincancerprogressionaftertherapy
AT barbarazubikkowal numericalsolutionofamodelforbraincancerprogressionaftertherapy
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