Efficient optimization of R50% when planning multiple cranial metastases simultaneously in single isocenter SRS/SRT

Simultaneous optimization of multiple Planning Target Volumes (PTVs) of varying size and location in the cranium is a non-trivial task. The rate of dose falloff around PTV structures is variable and depends on PTV characteristics such as the volume. The metric R50% is one parameter that can be used to quantify dose falloff achieved in a given treatment plan. An important treatment planning question is how to construct optimization conditions that result in the efficient production of acceptable plan outcomes considering metrics such as R50%. Guidance provided in literature suggests generating multiple shell control structures around each PTV. The constraints applied to these shells can vary significantly depending on PTV volume. Additionally, there is no clear guidance on how to prospectively determine objective constraints for the optimization shells to achieve a specified goal of R50%. Based on physical principles and empirical evidence, we provide clear quantitative guidance on how to translate the desired R50% outcome into appropriately sized optimization structures around PTVs via an equation that depends on a desired goal for R50% and the volume of PTV. Optimization schema are also provided that allow the goal R50% to be approached or achieved for all PTVs individually. We demonstrate the application of the methodology using commercially available treatment planning software and radiotherapy treatment equipment.