Publicação
Mathematical modeling of efficient protocols to control glioma growth
| Resumo: | In this paper we propose a mathematical model to describe the evolution of glioma cells taking into account the viscoelastic properties of brain tissue. The mathematical model is established considering that the glioma cells are of two phenotypes: migratory and proliferative. The evolution of the migratory cells is described by a diffusion-reaction equation of non Fickian type deduced considering a mass conservation law with a non Fickian migratory mass flux. The evolution of the proliferative cells is described by a reaction equation. A stability analysis that leads to the design of efficient protocols is presented. Numerical simulations that illustrate the behavior of the mathematical model are included. |
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| Autores principais: | Branco, João |
| Outros Autores: | Ferreira, José Augusto; Oliveira, Paula de |
| Assunto: | Antineoplastic Agents Brain Neoplasms Cell Proliferation Clinical Protocols Computer Simulation Elasticity Glioma Humans Mathematical Concepts Neoplasm Invasiveness Viscosity Models, Biological |
| Ano: | 2014 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso embargado |
| Instituição associada: | Universidade de Coimbra |
| Idioma: | inglês |
| Origem: | Estudo Geral - Universidade de Coimbra |
| Resumo: | In this paper we propose a mathematical model to describe the evolution of glioma cells taking into account the viscoelastic properties of brain tissue. The mathematical model is established considering that the glioma cells are of two phenotypes: migratory and proliferative. The evolution of the migratory cells is described by a diffusion-reaction equation of non Fickian type deduced considering a mass conservation law with a non Fickian migratory mass flux. The evolution of the proliferative cells is described by a reaction equation. A stability analysis that leads to the design of efficient protocols is presented. Numerical simulations that illustrate the behavior of the mathematical model are included. |
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