Optimization of irradiation interval for fractionated stereotactic radiosurgery by a cellular automata model with reoxygenation effects

The current study aims to determine the optimal irradiation interval of fractionated stereotactic radiosurgery (SRS) by using an improved cellular automata (CA) model. The tumor growth process was simulated by considering the amount of oxygen and the density of blood vessels, which supplied oxygen and nutrient required for cell growth. Cancer cells died by the mitotic death process due to radiation, which was quantified by the LQ-model, or the apoptosis due to the lack of nutrients. The radiation caused increased permeation of plasma protein through the blood vessel or the breakdown of the vasculature. Consequently, these changes lead to a change in radiation sensitivity of cancer cells and tumor growth rate after irradiation. The optimal model parameters were determined with experimental data of the rat tumor volume. The tumor control probability (TCP) was defined as the ratio of the number of histories in which all cancer cells died after the irradiation to the total number of the histories per simulation. The optimal irradiation interval was defined as the irradiation interval that TCP was the maximum. For one fractionation treatment, the ratio of hypoxic cells to the total number of cancer cells kept decreasing until day 16th after irradiation; whereas the number of surviving cancer cells begun increasing immediately after irradiation. This intricate relationship between the hypoxia (or reoxygenation) and the number of cancer cells lead to an optimal irradiation interval for the second irradiation. The optimal irradiation interval for two-fraction SRS was six days. The optimum intervals for the first-second irradiations and the second-third irradiations were five and two days, respectively, for three fraction SRS. For 4 and 5-fraction treatments, the optimum first-interval was five days, which was similar to three fraction treatment. The remaining intervals should be one day. We showed that the improved CA model could be used to optimize the irradiation interval by explicitly including the reoxygenation after irradiation in the model.