Loss of local control due to tumor displacement as a function of margin size, dose–response slope, and number of fractions




Geometric uncertainties are inevitable in radiotherapy. To account for these uncertainties, a margin is added to the clinical target volume (CTV) to create the planning target volume (PTV), and its size is critical for obtaining an optimal treatment plan. Dose-based (i.e., physical) margin recipes have been published and widely used, but it is important to consider fractionation and the radiobiological characteristics of the tumor when deriving margins. Hence a tumor control probability (TCP)-based margin is arguably more appropriate.


Margins required for ≤1% loss in mean population TCP (relative to a static tumor) for varying numbers of fractions, varying slope of the dose–response curve (γ50) and varying degrees of dose distribution conformity are investigated for spherical and four-field (4F)-brick dose distributions. To simulate geometric uncertainties, systematic (Σ) and random (σ) tumor displacements were sampled from Gaussian distributions and applied to each fraction for a spherical CTV. Interfraction tumor motion was simulated and the dose accumulated from fraction to fraction on a voxel-by-voxel basis to calculate TCP. PTV margins derived from this work for various fraction numbers and dose–response slopes (γ50) for different degrees of geometric uncertainties are compared with margins calculated using published physical-dose- and TCP-based recipes.


Larger margins are required for a decrease in the number of fractions and for an increase in γ50 for both spherical and 4F-brick dose distributions. However, the margins can be close to zero for the 4F-brick distribution for small geometric uncertainties (Σ = 1, σ = 1 mm) irrespective of the number of fractions and the magnitude of γ50 due to the higher “incidental” dose outside the tumor. For Σ = 1 mm and σ = 3 mm, physical-dose-based recipes underestimate the margin only for the combination of hypofractionated treatments and tumors with a high γ50. For all other situations TCP-based margins are smaller than physical-dose-based recipes.


Margins depend on the number of fractions and γ50 in addition to Σ and σ. Dose conformity should also be considered since the required margin increases with increasing dose conformity. Ideally margins should be anisotropic and individualized, taking into account γ50, number of fractions, and the dose distribution, as well as estimates of Σ and σ. No single “recipe” can adequately account for all these variables.