Impact of Gaussian uncertainty assumptions on probabilistic optimization in particle therapy.

Range and setup uncertainties in charged particle therapy may induce a discrepancy between planned and delivered dose. Countermeasures based on probabilistic optimization assume a Gaussian probability density to model the underlying range and setup error. While this assumption is generally taken for granted, this work explicitly investigates dosimetric consequences if the actual errors obey a different probability density function (PDF) over the course of treatment than the one used during probabilistic treatment plan optimization. Discrete random sampling was performed for conventionally and probabilistically optimized proton and carbon ion treatment plans utilizing various probability density functions modeling the setup and range error. This method allowed to assess the treatment plan robustness against different probability density functions of conventional and probabilistic plans, which both explicitly assume Gaussian uncertainties. The induced uncertainty in dose was quantified by estimating the expectation value and standard deviation of the RBE-weighted dose for each probability density function on the basis of 2500/5000 random dose samples. Probabilistic dose metrics and standard deviation volume histograms were computed to quantify treatment plan robustness of both optimization approaches. It was shown that the classical PTV-margin extension concept did not compensate the influence of range and setup errors and consequently resulted in a non-negligible average standard deviation in dose of 7.3% throughout the CTV. In contrast, probabilistic optimization on normally distributed errors yielded treatment plans that were not only robust against normally distributed errors accounted for during optimization but also robust against other symmetric PDFs. It was shown that the influence of an incorrect probability distribution assumption is of lower importance after probabilistic optimization as the average uncertainty in the CTV drops to 3.9%. Probabilistic optimization is an effective tool to create robust particle treatment plans. Normally distributed range and setup error assumptions for probabilistic optimization are a reasonable first approximation and yield treatment plans that are also robust against other PDFs.