[Mathematical model of tumor evolution in radiotherapy]

The schemes of dose fractionation play an important role in tumor radiotherapy. We used mathematical methods to describe the process of tumor cells evolution during radiotherapy, trying to find how the schemes of dose fractionation affect tumor cells. In clinical radiobiology, linear-quadratic (LQ) model is frequently used to describe radiation effects of tumor cells. We integrated LQ model with effect of oxygen, and with the phenomenon of repopulation and reoxygenation in the theory of radiation biology. While we considered the disappearing progress of doomed cells in tumor, we established the mathematical model of tumor evolution in radiotherapy. We simulated some common treatment schedules, and studied the change role of tumor cells during radiotherapy. These results can serve for the optimization of dose fractionation scheme based on tumor radiobiological characteristics.