A margin recipe for the management of intra-fraction target motion in radiotherapy

Background and purpose: Strategies to limit the impact of intra-fraction motion during treatment are common in radiotherapy. Margin recipes, however, are not designed to incorporate these strategies. This work aimed to provide a framework to determine how motion management strategies influence treatment margins. Materials and methods: Two models of intra-fraction motion were considered. In model 1 motion was instanta-neous, before treatment starts and in model 2 motion was a continuous drift during treatment. Motion man-agement strategies were modelled by truncating the underlying error distribution at ca, with a the standard deviation of the distribution and c a free parameter. Using Monte Carlo simulations, we determined how motion management changed the required margin. The analysis was performed for different number of treatment fractions and different standard deviations of the underlying random and systematic errors.Results: The required margin for a continuous drift was found to be well approximated by an average position of the target at3/4 of the drift. Introducing a truncation at ca, the relative change in the margin was equal to 0.3c. This result held for both models, was independent of a or the number of fractions and naturally generalizes to the situation with a residual (systematic) error. Conclusion: Treatment margins can be determined when motion management strategies are applied. Moreover, our analysis can be used to study the potential benefit of different motion management strategies. This allows to discuss and determine the most appropriate strategy for margin reduction.