Nonlinear stability of a heterogeneous state in a PDE-ODE model for acid-mediated tumor invasion
This work studies a general reaction-diffusion model foracid-mediated tumor invasion, where tumor cells produce excess acidthat primarily kills healthy cells, and thereby invade the microenvironment. The acid diffuses and could be cleared byvasculature, and the healthy and tumor...
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AIMS Press
2015-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2016.13.193 |
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| author | Youshan Tao J. Ignacio Tello |
| author_facet | Youshan Tao J. Ignacio Tello |
| author_sort | Youshan Tao |
| collection | DOAJ |
| description | This work studies a general reaction-diffusion model foracid-mediated tumor invasion, where tumor cells produce excess acidthat primarily kills healthy cells, and thereby invade the microenvironment. The acid diffuses and could be cleared byvasculature, and the healthy and tumor cells are viewed as twospecies following logistic growth with mutual competition. A keyfeature of this model is the density-limited diffusion for tumorcells, reflecting that a healthy tissue will spatially constrain atumor unless shrunk. Under appropriate assumptions on modelparameters and on initial data, it is shown that the uniqueheterogeneous state is nonlinearly stable, which implies a long-term coexistence of the healthy and tumor cells in certainparameter space. Our theoretical result suggests that acidity mayplay a significant role in heterogeneous tumor progression. |
| format | Article |
| id | doaj-art-1c4d6c9197504a3f9d61873e55842f0c |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2015-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-1c4d6c9197504a3f9d61873e55842f0c2025-01-24T02:34:05ZengAIMS PressMathematical Biosciences and Engineering1551-00182015-09-0113119320710.3934/mbe.2016.13.193Nonlinear stability of a heterogeneous state in a PDE-ODE model for acid-mediated tumor invasionYoushan Tao0J. Ignacio Tello1Department of Applied Mathematics, Dong Hua University, Shanghai 200051Departamento de Matemática Aplicada, E.T.S.I. Sistemas Informáticos, Universidad Politécnica de Madrid, 28031 MadridThis work studies a general reaction-diffusion model foracid-mediated tumor invasion, where tumor cells produce excess acidthat primarily kills healthy cells, and thereby invade the microenvironment. The acid diffuses and could be cleared byvasculature, and the healthy and tumor cells are viewed as twospecies following logistic growth with mutual competition. A keyfeature of this model is the density-limited diffusion for tumorcells, reflecting that a healthy tissue will spatially constrain atumor unless shrunk. Under appropriate assumptions on modelparameters and on initial data, it is shown that the uniqueheterogeneous state is nonlinearly stable, which implies a long-term coexistence of the healthy and tumor cells in certainparameter space. Our theoretical result suggests that acidity mayplay a significant role in heterogeneous tumor progression.https://www.aimspress.com/article/doi/10.3934/mbe.2016.13.193numerical simulations.existence of solutionssteady statesreaction diffusion equationsmorphogenesis |
| spellingShingle | Youshan Tao J. Ignacio Tello Nonlinear stability of a heterogeneous state in a PDE-ODE model for acid-mediated tumor invasion Mathematical Biosciences and Engineering numerical simulations. existence of solutions steady states reaction diffusion equations morphogenesis |
| title | Nonlinear stability of a heterogeneous state in a PDE-ODE model for acid-mediated tumor invasion |
| title_full | Nonlinear stability of a heterogeneous state in a PDE-ODE model for acid-mediated tumor invasion |
| title_fullStr | Nonlinear stability of a heterogeneous state in a PDE-ODE model for acid-mediated tumor invasion |
| title_full_unstemmed | Nonlinear stability of a heterogeneous state in a PDE-ODE model for acid-mediated tumor invasion |
| title_short | Nonlinear stability of a heterogeneous state in a PDE-ODE model for acid-mediated tumor invasion |
| title_sort | nonlinear stability of a heterogeneous state in a pde ode model for acid mediated tumor invasion |
| topic | numerical simulations. existence of solutions steady states reaction diffusion equations morphogenesis |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2016.13.193 |
| work_keys_str_mv | AT youshantao nonlinearstabilityofaheterogeneousstateinapdeodemodelforacidmediatedtumorinvasion AT jignaciotello nonlinearstabilityofaheterogeneousstateinapdeodemodelforacidmediatedtumorinvasion |