Spatiotemporal dynamics of a glioma immune interaction model
Abstract We report a mathematical model which depicts the spatiotemporal dynamics of glioma cells, macrophages, cytotoxic-T-lymphocytes, immuno-suppressive cytokine TGF-β and immuno-stimulatory cytokine IFN-γ through a system of five coupled reaction-diffusion equations. We performed local stability...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2021-11-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-021-00985-1 |
| _version_ | 1818823525671108608 |
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| author | Subhas Khajanchi Juan J. Nieto |
| author_facet | Subhas Khajanchi Juan J. Nieto |
| author_sort | Subhas Khajanchi |
| collection | DOAJ |
| description | Abstract We report a mathematical model which depicts the spatiotemporal dynamics of glioma cells, macrophages, cytotoxic-T-lymphocytes, immuno-suppressive cytokine TGF-β and immuno-stimulatory cytokine IFN-γ through a system of five coupled reaction-diffusion equations. We performed local stability analysis of the biologically based mathematical model for the growth of glioma cell population and their environment. The presented stability analysis of the model system demonstrates that the temporally stable positive interior steady state remains stable under the small inhomogeneous spatiotemporal perturbations. The irregular spatiotemporal dynamics of gliomas, macrophages and cytotoxic T-lymphocytes are discussed extensively and some numerical simulations are presented. Performed some numerical simulations in both one and two dimensional spaces. The occurrence of heterogeneous pattern formation of the system has both biological and mathematical implications and the concepts of glioma cell progression and invasion are considered. Simulation of the model shows that by increasing the value of time, the glioma cell population, macrophages and cytotoxic-T-lymphocytes spread throughout the domain. |
| first_indexed | 2024-12-18T23:41:22Z |
| format | Article |
| id | doaj.art-2ff4cd1146fe4a12a6b33b3cb1e9bc83 |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-12-18T23:41:22Z |
| publishDate | 2021-11-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-2ff4cd1146fe4a12a6b33b3cb1e9bc832022-12-21T20:47:22ZengNature PortfolioScientific Reports2045-23222021-11-0111111710.1038/s41598-021-00985-1Spatiotemporal dynamics of a glioma immune interaction modelSubhas Khajanchi0Juan J. Nieto1Department of Mathematics, Presidency UniversityInstituto de Matem\acute{a}ticas, Universidade de Santiago de CompostelaAbstract We report a mathematical model which depicts the spatiotemporal dynamics of glioma cells, macrophages, cytotoxic-T-lymphocytes, immuno-suppressive cytokine TGF-β and immuno-stimulatory cytokine IFN-γ through a system of five coupled reaction-diffusion equations. We performed local stability analysis of the biologically based mathematical model for the growth of glioma cell population and their environment. The presented stability analysis of the model system demonstrates that the temporally stable positive interior steady state remains stable under the small inhomogeneous spatiotemporal perturbations. The irregular spatiotemporal dynamics of gliomas, macrophages and cytotoxic T-lymphocytes are discussed extensively and some numerical simulations are presented. Performed some numerical simulations in both one and two dimensional spaces. The occurrence of heterogeneous pattern formation of the system has both biological and mathematical implications and the concepts of glioma cell progression and invasion are considered. Simulation of the model shows that by increasing the value of time, the glioma cell population, macrophages and cytotoxic-T-lymphocytes spread throughout the domain.https://doi.org/10.1038/s41598-021-00985-1 |
| spellingShingle | Subhas Khajanchi Juan J. Nieto Spatiotemporal dynamics of a glioma immune interaction model Scientific Reports |
| title | Spatiotemporal dynamics of a glioma immune interaction model |
| title_full | Spatiotemporal dynamics of a glioma immune interaction model |
| title_fullStr | Spatiotemporal dynamics of a glioma immune interaction model |
| title_full_unstemmed | Spatiotemporal dynamics of a glioma immune interaction model |
| title_short | Spatiotemporal dynamics of a glioma immune interaction model |
| title_sort | spatiotemporal dynamics of a glioma immune interaction model |
| url | https://doi.org/10.1038/s41598-021-00985-1 |
| work_keys_str_mv | AT subhaskhajanchi spatiotemporaldynamicsofagliomaimmuneinteractionmodel AT juanjnieto spatiotemporaldynamicsofagliomaimmuneinteractionmodel |