Toward a better understanding of the gamma index: Investigation of parameters with a surface-based distance method

The purpose of this work was to clarify the interactions between the parameters used in the γ index with the surface-based distance method, which itself can be viewed as a generalized version of the γ index. The examined parameters included the distance to agreement (DTA)/dose difference (DD) criteria, the percentage used as a passing criterion, and the passing percentage for given DTA/DD criteria. The specific aims of our work were (1) to understand the relationships between the parameters used in the γ index, (2) to determine the detection limit, or the minimum detectable error, of the γ index with a given set of parameters, and (3) to establish a procedure to determine parameters that are consistent with the capacity of an IMRT QA system.

The surface-based distance technique with dose gradient factor was derived, and then the relationship between surface-based distance and γ index was established. The dose gradient factor for plans and measurements of 10 IMRT patients, 10 spine stereotactic radiosurgery (SRS) patients, and 3 Radiological Physics Center (RPC) head and neck phantom were calculated and evaluated. The detection limits of the surface-based distance and γ index methods were examined by introducing known shifts to the 10 IMRT plans.

The means of the dose gradient factors were 0.434 mm/% and 0.956 mm/% for the SRS and IMRT plans, respectively. Key quantities (including the mean and 90th and 99th percentiles of the distance distribution) of the surface-based distance distribution between two dose distributions were linearly proportional to the actual shifts. However, the passing percentage of the γ index for a given set of DTA/DD criteria was not associated with the actual shift. For IMRT, using the standard quality assurance criteria of 3 mm/3% DTA/DD and a 90% passing rate, we found that the detection limit of the γ index in terms of global shift was 4.07 mm/4.07 % without noise.

Surface-based distance is a direct measure of the difference between two dose distributions and can be used to evaluate or determine parameters for use in calculating the γ index. The dose gradient factor represents the weighting between spatial and dose shift and should be determined before DTA/DD criteria are set. The authors also present a procedure to determine γ index parameters from measurements.