Gompertz Model: resolution and analysis for tumors

摘要

It is called cancer a wide range of diseases that has in common an unusual cells proliferation of the organism itself. This uncontrolled proliferation provokes the formation of a cellular mass named tumor. In order to enable the tumor develop beyond a given volume it needs to develop the capacity to promote the growth of new blood vases towards itself. Those new vases will proportionate the blood irrigation of the tumor, supplying its needs of nutrition and oxygenation. If this vascularization does not happen, the tumor`s cells enters in degeneration and necrosis. The formation process of these new blood vases is called angiogenesis or neovascularization. The main objective of this paper is to use the Gompertz equation in order to study the development of blood irrigated solid tumors, using parameters defined in some important bibliographic references about the mathematical modelling of this biological phenomenon. Thus, It is showed a simple introduction of the Gompertz Equation history, its detailed resolution, and also the analysis of its equilibrium conditions, using important parameters of the tumors evolution, related to the growth rate and also to the maximum number of tumor`s cells that the organism can stand. As results, it was obtained the possibility of better understand the development behavior of a tumor mass, even modeling the standard behavior of sigmoidal growth. In addition to that, it was verified that this research can be used as support for observation and understanding of the practical application of differentials equations on teaching and on research in graduation and post-graduation of several areas.