PURPOSE: Currently, planning systems allow robustness calculations to be performed, but a generalized assessment methodology is not yet available. We introduce and evaluate a methodology to quantify the robustness of a plan on an individual patient basis. METHODS: We introduce the notion of characterizing a treatment instance (i.e. one single fraction delivery) by describing the dose distribution within an organ as an alpha-stable distribution. The parameters of the distribution (shape(α), scale(γ), position(δ), and symmetry(β)), will vary continuously (in a mathematical sense) as the distributions change with the different positions. The rate of change of the parameters provides a measure of the robustness of the treatment. The methodology is tested in a planning study of 25 patients with known residual errors at each fraction. Each patient was planned using Eclipse with an IBA-proton beam model. The residual error space for every patient was sampled 30 times, yielding 31 treatment plans for each patient and dose distributions in 5 organs. The parameters' change rate as a function of Euclidean distance from the original plan was analyzed. RESULTS: More than 1,000 dose distributions were analyzed. For 4 of the 25 patients the change in scale rate (γ) was considerably higher than the lowest change rate, indicating a lack of robustness. The sign of the shape change rate (α) also seemed indicative but the experiment lacked the power to prove significance. CONCLUSION: There are indications that this robustness measure is a valuable tool to allow a more patient individualized approach to the determination of margins. In a further study we will also evaluate this robustness measure using photon treatments, and evaluate the impact of using breath hold techniques, and the a Monte Carlo based dose deposition calculation. A principle component analysis is also planned.

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