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

Purpose: The purpose of this work was to clarify the interactions between the parameters used in the index with the surface-based distance method, which itself can be viewed as a generalized version of the 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 index, (2) to determine the detection limit, or the minimum detectable error, of the 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. Methods: The surface-based distance technique with dose gradient factor was derived, and then the relationship between surface-based distance and 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 index methods were examined by introducing known shifts to the 10 IMRT plans. Results: 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 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 index in terms of global shift was 4.07 mm/4.07 without noise. Conclusions: 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 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 index parameters from measurements.