How finite duration inputs are able to change the dynamics of a system:Application to finite duration cancer treatment

In this paper, a new mathematical model is developed to represent the interaction between healthy and cancer cells in the human body, focusing on the role of input on the dynamics of the cancer. Therefore, the effect of input, acted in limited duration, on the dynamics of a system is investigated. It is shown that nonlinearity is a necessary condition for a system in order that its dynamical properties change due to a limited time acted input. Then, based on this new approach, the best radiotherapy protocol is extracted. For this purpose, three aspects of constant radiation are considered. In this study we display consequences for protocols applied, taking into account the sort of fractionation, the dose per fraction, treatment time and the total dose. The simulations were performed with the aim of determining which protocol has minor damage in patients exposed to radiation. In other words, which protocol has the lowest fraction of normal cell kill (FN) and shorter time for the tumor removal. According to theresults, the accelerated fractionation is the best protocol. Also, after removing the radiotherapy the patient become healthy and the cancer do not relapse due to change in the dynamics of the cancer. So, the present analysis suggests that a proper treatment method should change the dynamics of the cancer instead of only reducing the population of cancer cells.

کلیدواژه ها:

Cancer ، stability ، Radiotherapy ، limited durationinput