Diagrams for the Leksell Gamma Knife 4C automatic positioning system accessible shot coordinates

We have developed a graphic representation (APS shot-range diagrams) of achievable shot coordinates with the automatic positioning system (APS) for Gamma Knife stereotactic radiosurgery. We formulated a mathematical relationship between the APS coordinate system and the Leksell frame coordinate system (frame-system) by considering the relative translation and rotation. Using the transformation equations, we calculated the Y-Z coordinate domain in the frame-system (domain B), which corresponds to the known coordinate domain achievable in the APS coordinate system (domain A). APS shot-range diagrams were presented by overlaying of domain B over domain A so that one can easily visualize the achievable shot coordinates with APS for various gamma angles. Domains A and B are identical for a 90° gamma angle, but they are different for other gamma angles. Applications of the diagrams to clinical cases, in which Leksell GammaPlan treatment planning software automatically set some of the shots in a treatment plan as trunnion shots because of the APS coordinate limit, enabled us to avoid the trunnion shots, and consequently to achieve much faster treatment delivery. In conclusion, APS shot-range diagrams can be used for achieving more efficient treatment delivery by avoiding unnecessary trunnion shots with a Gamma Knife unit equipped with the APS.