A robust optimisation approach accounting for the effect of fractionation on setup uncertainties

Proton plans are subject to a number of uncertainties which must be accounted for to ensure that they are delivered safely. Misalignment resulting from residual errors in daily patient positioning can result in both a displacement and distortion of dose distributions. This can be particularly important for intensity modulated proton therapy treatments where the accurate alignment of highly modulated fields may be required to deliver the intended treatment. A number of methods to generate plans that are robust to these uncertainties exist. These include robust optimisation approaches which account for the effect of uncertainties on the dose distribution within the optimisation process. However, robustness to uncertainty comes at the cost of plan quality. For this reason, it is important that the uncertainties considered are realistic. Existing approaches to robust optimisation have neglected the role of fractionated treatment deliveries in reducing the uncertainties that result from random setup errors. Here, a method of robust optimisation which accounts for this effect is presented and is evaluated using a 2D planning environment. The optimisation algorithm considers the dose in the estimated upper and lower bounds of the dose distribution under the effect of setup and range errors. A comparison with plans robustly optimised without consideration of the effect of fractionation and conventionally optimised plans is presented. Fractionation incorporated robust optimisation demonstrates a reduced sensitivity to uncertainty compared to conventionally optimised plans and a reduced integral dose compared to robustly optimised plans.