چكيده به لاتين
Cancer is one of the most important causes of mortality in human society. Therefore, scientists are always looking for new ways to cope with the disease. Understanding the activity of cancerous tumors in the body can help this research. Thus, finding accurate models for tumor growth is very important.
For the growth dynamic of cancer cells, various growth models have been proposed. In some models the interaction between cancerous cell's and the other cell's type in the body is considered. In cancerous systems usually there are tumor, normal and effector immune cells. Previous models which are base on these three type of cells, cannot simulate chaotic behavior. Whereas biology of cancer has confirmed chaos in cancerous systems.
This study is started from a three-state cancer model (TEN_L) and the role of model parameters in the system dynamics is interpreted via bifurcation diagram. This analysis has shown that the parameter of immune system has the least effect in the dynamic of model. In the following with developing the previous model, a new model is presented which is called TEN_G. In this model, the tumor cell growth is consider as Gompertz. Then by considering the lyapanuov exponent and due to the Schilinikov teory it has shown that the new model have the ability of chaotic behavior. The role of parameter in the dynamic of this model considered and the biological relivance due to model parameter has discussed. At the end a comparison between two models has performed. Some differences between the attractors can be seen. In TEN_L the attractor is narrower. Also in TEN_L the tumor cells can reach their maximum whereas in TEN_G the immune system cells reach their maximum.
The analysis in this study has shown that adjusting some parameters can change the chaotic behavior of system and driven it to the desire fix point which is tumor free. Adjusting some other parameters can simulate malignant tumor growth. This result can help to propose or choosing the best therapy for cancer. Finally, as an application of the TEN_G model, radiotherapy was applied to control the disease and reach the desired fix point. The results showed that the therapeutic method should be such that in addition to reducing the number of tumor cells, the damage to the surrounding tissue would be minimal. Accordingly, a range of radiation dose for radiotherapy was presented.
