On the selection of gantry and collimator angles for isocenter localization using Winston-Lutz tests

In Winston-Lutz (WL) tests, the isocenter of a linear accelerator (linac) is determined as the intersection of radiation central axes (CAX) from multiple gantry, collimator, and couch angles. It is well known that the CAX can wobble due to mechanical imperfections of the linac. Previous studies suggested that the wobble varies with gantry and collimator angles. Therefore, the isocenter determined in the WL tests has a profound dependence on the gantry and collimator angles at which CAX are sampled. In this study, we evaluated the systematic and random errors in the isocenters determined with different CAX sampling schemes. Digital WL tests were performed on six linacs. For each WL test, 63 CAX were sampled at nine gantry angles and seven collimator angles. Subsets of these data were used to simulate the effects of various CAX sampling schemes. An isocenter was calculated from each subset of CAX and compared against the reference isocenter, which was calculated from 48 opposing CAX. The differences between the calculated isocenters and the reference isocenters ranged from 0 to 0.8 mm. The differences diminished to less than 0.2 mm when 24 or more CAX were sampled. Isocenters determined with collimator 0° were vertically lower than those determined with collimator 90° and 270°. Isocenter localization errors in the longitudinal direction (along the axis of gantry rotation) showed a strong dependence on the collimator angle selected. The errors in all directions were significantly reduced when opposing collimator angles and opposing gantry angles were employed. The isocenter localization errors were less than 0.2 mm with the common CAX sampling scheme, which used four cardinal gantry angles and two opposing collimator angles. Reproducibility studies on one linac showed that the mean and maximum variations of CAX during the WL tests were 0.053 mm and 0.30 mm, respectively. The maximal variation in the resulting isocenters was 0.068 mm if 48 CAX were used, or 0.13 mm if four CAX were used. Quantitative results from this study are useful for understanding and minimizing the isocenter uncertainty in WL tests.