Statistical analysis of the gamma evaluation acceptance criteria: A simulation study of 2D dose distributions under error free conditions

Purpose: To investigate the statistical distribution of the gamma value under error-free conditions, in order to study the relation between the gamma evaluation failure rate and statistically significant deviations in the general situation. Methods: The 2D absorbed dose distribution for 30 clinical head-and-neck IMRT fields were calculated in a QC phantom. For the same fields, dose measurements were simulated by assuming that the calculated value represented the expectation value, and by adding a random spatial uncertainty of 1–9 mm (1SD) and a random dose uncertainty of 1%–3% (1SD). The simulated measurements were then compared to the calculated dose using the gamma evaluation, and the distribution of the failure rate (i.e. the probability of gamma values above unity) was analysed. Results: For a wide range of the random measurement uncertainty, a distinct peak in the failure rate distribution was observed. The presence of higher failure rates was associated with large values of the second order derivative of the dose distribution. For spatial uncertainties larger than or equal to the resolution of the dose matrix, and for reasonable dose uncertainties, the median value of the failure rate distribution was fairly constant. Conclusions: Simulations showed, in the general case, that the probability of having a gamma value above unity under error-free conditions was not spatially uniform. We believe that this shortcoming may be partly responsible for the limited ability of the gamma evaluation method to detect errors in clinically relevant situations.