A robustness analysis method with fast estimation of dose uncertainty distributions for carbon-ion therapy treatment planning

A simple and efficient approach is needed for robustness evaluation and optimization of treatment planning in routine clinical particle therapy. Here we propose a robustness analysis method using dose standard deviation (SD) in possible scenarios such as the robustness indicator and a fast dose warping method, i.e. deformation of dose distributions, taking into account the setup and range errors in carbon-ion therapy. The dose warping method is based on the nominal dose distribution and the water-equivalent path length obtained from planning computed tomography data with a clinically commissioned treatment planning system (TPS). We compared, in a limited number of scenarios at the extreme boundaries of the assumed error, the dose SD distributions obtained by the warping method with those obtained using the TPS dose recalculations. The accuracy of the warping method was examined by the standard-deviation-volume histograms (SDVHs) for varying degrees of setup and range errors for three different tumor sites. Furthermore, the influence of dose fractionation on the combined dose uncertainty, taking into consideration the correlation of setup and range errors between fractions, was evaluated with simple equations using the SDVHs and the mean value of SDs in the defined volume of interest. The results of the proposed method agreed well with those obtained with the dose recalculations in these comparisons, and the effectiveness of dose SD evaluations at the extreme boundaries of given errors was confirmed from the responsivity and DVH analysis of relative SD values for each error. The combined dose uncertainties depended heavily on the number of fractions, assumed errors and tumor sites. The typical computation time of the warping method is approximately 60 times less than that of the full dose calculation method using the TPS. The dose SD distributions and SDVHs with the fractionation effect will be useful indicators for robustness analysis in treatment planning, and the results of our comparative study show that the proposed analysis method would be beneficial in routine clinical use. (paper)