SU‐F‐BRD‐04: Robustness Analysis of Proton Breast Treatments Using An Alpha‐Stable Distribution Parameterization

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.