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Revista Boliviana de Física

On-line version ISSN 1562-3823

Abstract

CANEZO-GOMEZ, Winder A; RODRIGO, Gloria  and  RAMIREZ-AVILA, Gonzalo Marcelo. Analysis of the dynamics of cancerous cell populations using a Radiosensivity model. Revista Boliviana de Física [online]. 2019, vol.35, n.35, pp. 5-14. ISSN 1562-3823.

Abstract This work describes the population dynamics of cancerous cells when they interact with healthy cells, as well as, effector cells that defend the body in an immune response. The model is based on logistic equations that describe the growth cancerous and healthy cell population. The Lotka-Volterra equation for competitive species includes the radiation effects on both cells and the Michaelis-Menten equation considers the interaction between cancerous and effector cells. The parameters of the model are related to the interactions between the different types of cells. It is crucial to take into account the inactivation of the cancerous cells produced by the action of the other types of cells. On the other hand, it is also essential to consider the transformation of the healthy cells caused by the presence of tumor cells. We also discuss the radiosensitivity of each type of cell. We performed the linear stability analysis of our model, determining stability volumes in several projections of the hypervolume of the parameter space. The model exhibits a great dynamical richness going from fixed points to chaotic behaviors. We took into consideration several regions of the parameter space looking for parameter values leading to the situation in which the radiation tends to eliminate the tumor cells with no or slight modifications on the healthy cells populations. The latter could constitute an essential application for effective radiotherapy treatment.

Keywords : Cancer; radiotherapy; low-dimensional chaos.

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