Optimizing spatiotemporally fractionated radiotherapy plans under radio-biological uncertainty

Abstract

Radiotherapy treatments are typically delivered in daily sessions spanning one to several weeks. This is motivated by the clinical observation that irradiated cells tolerate a larger total radiation dose if it is fractionated and delivered in daily sessions - a biological phenomenon known as the fractionation effect. Spatiotemporal fractionation is a relatively new treatment paradigm in radiotherapy planning, which aims at altering the spatial dose distribution across treatment fractions to reduce the fractionation effect in the tumor while still allowing the normal tissue to benefit from it. The design of spatiotemporally fractionated radiotherapy plans requires the use of radio-biological models that quantify the fractionation effect. However, it is difficult to estimate the values of radio-biological parameters for individual cancer patients. In this research, we develop a robust optimization approach to incorporate this radio-biological uncertainty into spatiotemporally fractionated radiotherapy planning. The proposed robust model accounts for all possible realizations of the tumor radio-biological parameter in an uncertainty interval. Using a stylized cancer case, we compare the results obtained by the robust model against those of the deterministic counterpart as well as the conventional fractionation. The results show that in the presence of tumor radio-biological uncertainty, spatiotemporally fractionated treatments yield a potential therapeutic gain (defined as lower deposited dose to the normal tissue) over conventionally fractionated treatments; however, this gain decreases as the uncertainty level increases.