Nonlinear waves in a simple model of high-grade glioma
We present an analysis of a mathematical model describing the key features of the most frequent and aggressive type of primary brain tumor: glioblastoma. The model captures the salient physiopathological characteristics of this type of tumor: invasion of the normal brain tissue, cell proliferation a...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Sciendo
2016-10-01
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| Series: | Applied Mathematics and Nonlinear Sciences |
| Subjects: | |
| Online Access: | https://doi.org/10.21042/AMNS.2016.2.00035 |
| _version_ | 1818755230839341056 |
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| author | Álvarez-Arenas Arturo Belmonte-Beitia Juan Calvo Gabriel F. |
| author_facet | Álvarez-Arenas Arturo Belmonte-Beitia Juan Calvo Gabriel F. |
| author_sort | Álvarez-Arenas Arturo |
| collection | DOAJ |
| description | We present an analysis of a mathematical model describing the key features of the most frequent and aggressive type of primary brain tumor: glioblastoma. The model captures the salient physiopathological characteristics of this type of tumor: invasion of the normal brain tissue, cell proliferation and the formation of a necrotic core. Our study, based on phase space analysis, geometric perturbation theory, exact solutions and numerical simulations, proves the existence of bright solitary waves in the tumor coupled with kink and anti-kink fronts for the normal tissue and the necrotic core. Finally, we study the linear stability of the solutions to calculate the time of tumor recurrence. |
| first_indexed | 2024-12-18T05:35:51Z |
| format | Article |
| id | doaj.art-a1909b3e78a944a39ff975e0bc4d3bf4 |
| institution | Directory Open Access Journal |
| issn | 2444-8656 |
| language | English |
| last_indexed | 2024-12-18T05:35:51Z |
| publishDate | 2016-10-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Applied Mathematics and Nonlinear Sciences |
| spelling | doaj.art-a1909b3e78a944a39ff975e0bc4d3bf42022-12-21T21:19:19ZengSciendoApplied Mathematics and Nonlinear Sciences2444-86562016-10-011240542210.21042/AMNS.2016.2.00035Nonlinear waves in a simple model of high-grade gliomaÁlvarez-Arenas Arturo0Belmonte-Beitia Juan1Calvo Gabriel F.2Department of Mathematics and Mathematical Oncology Laboratory, University of Castilla-La Mancha, 13071, Ciudad Real, SpainDepartment of Mathematics and Mathematical Oncology Laboratory, University of Castilla-La Mancha, 13071, Ciudad Real, SpainDepartment of Mathematics and Mathematical Oncology Laboratory, University of Castilla-La Mancha, 13071, Ciudad Real, SpainWe present an analysis of a mathematical model describing the key features of the most frequent and aggressive type of primary brain tumor: glioblastoma. The model captures the salient physiopathological characteristics of this type of tumor: invasion of the normal brain tissue, cell proliferation and the formation of a necrotic core. Our study, based on phase space analysis, geometric perturbation theory, exact solutions and numerical simulations, proves the existence of bright solitary waves in the tumor coupled with kink and anti-kink fronts for the normal tissue and the necrotic core. Finally, we study the linear stability of the solutions to calculate the time of tumor recurrence.https://doi.org/10.21042/AMNS.2016.2.00035solitary wavesbright solitonsdark solitonsmathematical oncology92b0535c0735c0834d1035b35 |
| spellingShingle | Álvarez-Arenas Arturo Belmonte-Beitia Juan Calvo Gabriel F. Nonlinear waves in a simple model of high-grade glioma Applied Mathematics and Nonlinear Sciences solitary waves bright solitons dark solitons mathematical oncology 92b05 35c07 35c08 34d10 35b35 |
| title | Nonlinear waves in a simple model of high-grade glioma |
| title_full | Nonlinear waves in a simple model of high-grade glioma |
| title_fullStr | Nonlinear waves in a simple model of high-grade glioma |
| title_full_unstemmed | Nonlinear waves in a simple model of high-grade glioma |
| title_short | Nonlinear waves in a simple model of high-grade glioma |
| title_sort | nonlinear waves in a simple model of high grade glioma |
| topic | solitary waves bright solitons dark solitons mathematical oncology 92b05 35c07 35c08 34d10 35b35 |
| url | https://doi.org/10.21042/AMNS.2016.2.00035 |
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