Optimal weekly scheduling in fractionated radiotherapy: effect of an upper bound on the dose fraction size

This work concerns the optimization of the dose fractionation for cancer radiotherapy schedules of the kind one fraction/day, five fractions/week, assuming a fixed overall treatment time. Constraints are set to limit the radiation damages to surrounding normal tissues, as well as the daily fraction size. The response to radiation of tumour and normal tissues is represented by the classical LQ model, including the exponential repopulation term. We provide a framework to analytically determine the optimal weekly scheme of radiation doses as a function of the tumour type, the fraction upper bound and the normal tissue parameters. For a comparison with the literature, we present some numerical examples of optimal treatment schedules for specific tumour types.