A symmetric probabilistic γ-index for Monte Carlo dose comparisons

The γ-index is a widely used tool to compare two dose distributions, which combines both the dose difference and distance-to-agreement criteria into a single metric. The γ-index passing rate, defined as the percentage of dose points with γ-index value less than one, is often used as an agreement metric. However, the γ-index is not symmetric with respect to the choice of the reference and evaluation distributions. Moreover, the statistical fluctuations present in the dose distributions may have non-negligible effects on γ-passing rates. Fluctuations have opposite effects on the γ-passing rates depending whether they are present in the evaluation or the reference dose distributions. Those discrepancies are analyzed in the case of realistic clinical proton dose distributions. The concept of a probabilistic and symmetric γ-index is introduced to make more robust versus statistical fluctuations.