Dependence of planning target volume margins on degrees of freedom and correlations of uncertainties

BACKGROUND: The aim of this paper is to describe and extend the analytical framework from the original van Herk margin recipe to deal with more complex situations, which are typical in the current era where accuracy in radiotherapy delivery has dramatically improved. This new framework deals with movement ranging from rigid motion to multiple independent CTVs, deformable CTVs, and delineation variation. METHODS: Margins for random errors could be described by dose blurring using the local uncertainty. Margins for systematic errors depend on the number of CTVs and their motion correlation, and in general cannot be derived from the local uncertainty, because uncorrelated motion requires larger margins than correlated motion. RESULTS: Analytical derivations and simulations were compared and were generally in good agreement. Increasing motion correlation shows a gradual transition between the margin required for uncorrelated CTVs towards the margin for a single rigid CTV. However, motion correlations below 0.5 behave as uncorrelated for margin derivation. Margins for both level set and independent region representations of deformation and/or delineation uncertainty were found to have similar behaviour. CONCLUSIONS: By accounting for multiple targets and by including simple representations of target deformation or delineation uncertainty, this updated framework provides a toolset to allow the reader to define analytical margin estimates for a variety of situations.