Effect of statistical fluctuation in Monte Carlo based photon beam dose calculation on gamma index evaluation

The γ-index test has been commonly adopted to quantify the degree of agreement between a reference dose distribution and an evaluation dose distribution. Monte Carlo (MC) simulation has been widely used for the radiotherapy dose calculation for both clinical and research purposes. The goal of this work is to investigate both theoretically and experimentally the impact of the MC statistical fluctuation on the γ-index test when the fluctuation exists in the reference, the evaluation, or both dose distributions. To the first order approximation, we theoretically demonstrated in a simplified model that the statistical fluctuation tends to overestimate γ-index values when existing in the reference dose distribution and underestimate γ-index values when existing in the evaluation dose distribution given the original γ-index is relatively large for the statistical fluctuation. Our numerical experiments using realistic clinical photon radiation therapy cases have shown that (1) when performing a γ-index test between an MC reference dose and a non-MC evaluation dose, the average γ-index is overestimated and the gamma passing rate decreases with the increase of the statistical noise level in the reference dose; (2) when performing a γ-index test between a non-MC reference dose and an MC evaluation dose, the average γ-index is underestimated when they are within the clinically relevant range and the gamma passing rate increases with the increase of the statistical noise level in the evaluation dose; (3) when performing a γ-index test between an MC reference dose and an MC evaluation dose, the gamma passing rate is overestimated due to the statistical noise in the evaluation dose and underestimated due to the statistical noise in the reference dose. We conclude that the γ-index test should be used with caution when comparing dose distributions computed with MC simulation.