A Flux-Limited Model for Glioma Patterning with Hypoxia-Induced Angiogenesis
We propose a model for glioma patterns in a microlocal tumor environment under the influence of acidity, angiogenesis, and tissue anisotropy. The bottom-up model deduction eventually leads to a system of reaction–diffusion–taxis equations for glioma and endothelial cell population densities, of whic...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/11/1870 |
| _version_ | 1797547915033444352 |
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| author | Pawan Kumar Christina Surulescu |
| author_facet | Pawan Kumar Christina Surulescu |
| author_sort | Pawan Kumar |
| collection | DOAJ |
| description | We propose a model for glioma patterns in a microlocal tumor environment under the influence of acidity, angiogenesis, and tissue anisotropy. The bottom-up model deduction eventually leads to a system of reaction–diffusion–taxis equations for glioma and endothelial cell population densities, of which the former infers flux limitation both in the self-diffusion and taxis terms. The model extends a recently introduced (Kumar, Li and Surulescu, 2020) description of glioma pseudopalisade formation with the aim of studying the effect of hypoxia-induced tumor vascularization on the establishment and maintenance of these histological patterns which are typical for high-grade brain cancer. Numerical simulations of the population level dynamics are performed to investigate several model scenarios containing this and further effects. |
| first_indexed | 2024-03-10T14:51:53Z |
| format | Article |
| id | doaj.art-7ab6e0d5faee4e08a2b091691a8f342c |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T14:51:53Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-7ab6e0d5faee4e08a2b091691a8f342c2023-11-20T20:55:37ZengMDPI AGSymmetry2073-89942020-11-011211187010.3390/sym12111870A Flux-Limited Model for Glioma Patterning with Hypoxia-Induced AngiogenesisPawan Kumar0Christina Surulescu1Felix-Klein-Zentrum für Mathematik, TU Kaiserslautern, 67663 Kaiserslautern, GermanyFelix-Klein-Zentrum für Mathematik, TU Kaiserslautern, 67663 Kaiserslautern, GermanyWe propose a model for glioma patterns in a microlocal tumor environment under the influence of acidity, angiogenesis, and tissue anisotropy. The bottom-up model deduction eventually leads to a system of reaction–diffusion–taxis equations for glioma and endothelial cell population densities, of which the former infers flux limitation both in the self-diffusion and taxis terms. The model extends a recently introduced (Kumar, Li and Surulescu, 2020) description of glioma pseudopalisade formation with the aim of studying the effect of hypoxia-induced tumor vascularization on the establishment and maintenance of these histological patterns which are typical for high-grade brain cancer. Numerical simulations of the population level dynamics are performed to investigate several model scenarios containing this and further effects.https://www.mdpi.com/2073-8994/12/11/1870glioblastomapseudopalisadeshypoxia-induced angiogenesisflux-limited diffusion and taxiskinetic transport equationsequilibrium-based moment closure |
| spellingShingle | Pawan Kumar Christina Surulescu A Flux-Limited Model for Glioma Patterning with Hypoxia-Induced Angiogenesis Symmetry glioblastoma pseudopalisades hypoxia-induced angiogenesis flux-limited diffusion and taxis kinetic transport equations equilibrium-based moment closure |
| title | A Flux-Limited Model for Glioma Patterning with Hypoxia-Induced Angiogenesis |
| title_full | A Flux-Limited Model for Glioma Patterning with Hypoxia-Induced Angiogenesis |
| title_fullStr | A Flux-Limited Model for Glioma Patterning with Hypoxia-Induced Angiogenesis |
| title_full_unstemmed | A Flux-Limited Model for Glioma Patterning with Hypoxia-Induced Angiogenesis |
| title_short | A Flux-Limited Model for Glioma Patterning with Hypoxia-Induced Angiogenesis |
| title_sort | flux limited model for glioma patterning with hypoxia induced angiogenesis |
| topic | glioblastoma pseudopalisades hypoxia-induced angiogenesis flux-limited diffusion and taxis kinetic transport equations equilibrium-based moment closure |
| url | https://www.mdpi.com/2073-8994/12/11/1870 |
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