Incorporation of delivery times in stereotactic radiosurgery treatment optimization

Although the use of mathematical optimization techniques can greatly improve the quality of treatment plans in various radiation therapy treatment settings, one complication is the potentially clinically unrealistic nature of optimized treatments. The difficulty arises from two factors: (1) machine limitations that govern the minimum amount of radiation delivery time, and (2) long treatment times due to the complexity of optimized treatments. In the first scenario, if a particular configuration of the radiation delivery device is used, then it typically must deliver radiation for a minimum length of time. Incorporation of such requirements in a mathematical model generally requires additional constraints and binary variables, increasing the difficulty of the optimization. In the second scenario, mathematically optimized treatments commonly assign (small amounts of) radiation to be delivered from many configurations, drastically increasing the time needed to deliver the treatment (beam-on time). We examine these two issues within the penalty-based sector duration optimization model for Leksell Gamma Knife\(^{\textregistered }\) Perfexion\(^{\mathrm{TM}}\) (Elekta, Stockholm, Sweden) and the combined sector duration and isocentre optimization model to reduce beam-on time and to ensure that machine limitations regarding delivery times are met.