Uma generalização da equação logística no crescimento do tumor avascular

Abstract

The origin of tumor cells is related to the regulation of the cell cycle and the loss of control of cell division by mitosis, promoting an aceted and disordered occurrence of cell divisions. This group of cells can be considered as a far from equilibrium thermodynamic equilibrium, non-linear dynamical system, self-organized in time and space, exhibiting high complexity, robustness and adaptability. During avascular growth, the dynamics between healthy and malignant cells can be described by a set of network model of chemical reactions representing the populations of these two types of cells, governed by the dynamics processes of cell division by mitosis and cell death by apoptosis.As a consequence, a fractal morphology is observed in this region owing to the stochastic nature of these processes. Studies in the literature have described this dynamics, at the level of individual cells, through the logistic equation or Gompertz dynamics. In this work, from a generalization of the logistic equation characterized by a q index, we studied the relationship between the fractal dimension of the set of malignant cells and the q parameter and analyzed the consequences for the properties related to the growth of the tumor, associated with its aggressiveness.