Publicación: Aproximación a los modelos matemáticos basados en ecuaciones diferenciales ordinarias usados en quimioterapia. Aplicaciones y limitaciones
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2017-10-11
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info:eu-repo/semantics/openAccess
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Universidad Nacional de Educación a Distancia (España). Facultad de Ciencias
Resumen
La modelización matemática del crecimiento tumoral bajo quimioterapia usando ecuaciones diferenciales ordinarias (EDO) es un procedimiento que se ha convertido en habitual, a la par de práctico y relativamente simple. En este trabajo se revisarán los usos y restricciones de algunos de los modelos matemáticos basados en ecuaciones diferenciales ordinarias utilizados en el tratamiento matemático de tumores con quimioterapia. Para ello se comenzará explicando lo que es el cáncer, sus tratamientos, focalizando en el tratamiento por quimioterapia, tanto en tratamiento único como junto a otros tratamientos complementarios, para finalizar viendo algunos de los modelos matemáticos básicos que se utilizan en esta terapia, con sus principales aplicaciones y limitaciones. Estos modelos más básicos nos permiten entender otros más complicados que derivan de ellos, más realistas pero, por su complejidad, menos prácticos.
The mathematical modeling of tumor growth under chemotherapy using ordinary differential equations (ODE) is a procedure that has become common, as well as practical and relatively simple. In this paper we describe the uses and restrictions of some of the mathematical models based on ordinary differential equations used in the mathematical treatment of tumors with chemotherapy. We discuss what cancer is as well as its treatments, focusing on treatment by chemotherapy, either in single or complementary treatments. We finish by describing some of the basic mathematical models used in these therapies, with their main applications and limitations. These more basic models allow us to understand the more complicated ones that derive from them. More complicated models are more realistic but, due to their complexity, less practical.
The mathematical modeling of tumor growth under chemotherapy using ordinary differential equations (ODE) is a procedure that has become common, as well as practical and relatively simple. In this paper we describe the uses and restrictions of some of the mathematical models based on ordinary differential equations used in the mathematical treatment of tumors with chemotherapy. We discuss what cancer is as well as its treatments, focusing on treatment by chemotherapy, either in single or complementary treatments. We finish by describing some of the basic mathematical models used in these therapies, with their main applications and limitations. These more basic models allow us to understand the more complicated ones that derive from them. More complicated models are more realistic but, due to their complexity, less practical.
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Categorías UNESCO
Palabras clave
cáncer, quimioterapia, modelos matemáticos, ecuaciones diferenciales ordinarias, EDO, cancer, chemotherapy, mathematical models, ordinary differential equations, ODE
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Centro
Facultades y escuelas::Facultad de Ciencias
Departamento
Física Matemática y de Fluídos