Removing the effect of statistical uncertainty on dose-volume histograms from Monte Carlo dose calculations

Dose-volume histograms (DVHs) of the dose distributions calculated by the Monte Carlo method contain statistical uncertainties. The Monte Carlo DVH can be considered as blurred from the noiseless DVH by the statistical uncertainty. The focus of the present work is on the removal of the statistical uncertainty effect on the Monte Carlo DVHs and the reconstruction of the noiseless DVHs. We first study the effect of statistical uncertainty. It is found that the steeper the DVH, the more significant the effect. For typical critical structure DVHs the effect is usually negligible. For the target DVHs the effect could be clinically significant, depending on the value of uncertainty and the slope of the DVH. We then propose an iterative reconstruction algorithm. Using the DVHs and statistical uncertainties from the Monte Carlo simulations, we are able to reconstruct the noiseless DVHs. A hypothetical example and a number of clinical cases have been used to test the proposed algorithm. For each clinical case, two Monte Carlo simulations (denoted A and B) were performed. Simulation A has very large statistical uncertainties (about 10% of dose in the target volume) while simulation B has very small uncertainties (about 1%). DVHs from simulation B were used to approximate the noiseless DVHs. Using the proposed algorithm, the effect of statistical uncertainty can be removed from the DVHs of simulation A. The reconstructed DVHs were in good agreement with the DVHs from simulation B. The proposed approach is expected to be useful in removing the blurring effect on a quickly calculated Monte Carlo DVH when performing the iterative forward treatment planning.