Reporting and analyzing statistical uncertainties in Monte Carlo-based treatment planning

Purpose: To investigate methods of reporting and analyzing statistical uncertainties in doses to targets and normal tissues in Monte Carlo (MC)-based treatment planning. Methods and Materials: Methods for quantifying statistical uncertainties in dose, such as uncertainty specification to specific dose points, or to volume-based regions, were analyzed in MC-based treatment planning for 5 lung cancer patients. The effect of statistical uncertainties on target and normal tissue dose indices was evaluated. The concept of uncertainty volume histograms for targets and organs at risk was examined, along with its utility, in conjunction with dose volume histograms, in assessing the acceptability of the statistical precision in dose distributions. The uncertainty evaluation tools were extended to four-dimensional planning for application on multiple instances of the patient geometry. All calculations were performed using the Dose Planning Method MC code. Results: For targets, generalized equivalent uniform doses and mean target doses converged at 150 million simulated histories, corresponding to relative uncertainties of less than 2% in the mean target doses. For the normal lung tissue (a volume-effect organ), mean lung dose and normal tissue complication probability converged at 150 million histories despite the large range in the relative organ uncertainty volume histograms. For "serial" normal tissues such as the spinal cord, large fluctuations exist in point dose relative uncertainties. Conclusions: The tools presented here provide useful means for evaluating statistical precision in MC-based dose distributions. Tradeoffs between uncertainties in doses to targets, volume-effect organs, and "serial" normal tissues must be considered carefully in determining acceptable levels of statistical precision in MC-computed dose distributions.