Aps Shot Range Diagram: Graphic Representation Of Aps-able Shot Coordinates

Yoichi Watanabe, PhD1

1Therapeutic Radiology, University of Minnesota

Keywords: dose delivery, gamma knife, dose planning, physics, Robotic

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     The shot coordinates for a Gamma Knife treatment are defined in the Leksell frame coordinate system (or frame-system).
     To develop a graphic representation showing achievable shot coordinates with the automatic positioning system (APS) for gamma angles (?) of 72°, 110°, and 125°.
      The APS coordinate system (or APS-system) is obtained by translating the frame-system by 79 mm in the negative z-direction. The APS-system is rotated about its X-axis to vary ?. A mathematical relationship between the APS-system and the frame-system was formulated by considering the relative translation and rotation. The equations relate the y and z coordinates of a shot in the frame-system with the Y and Z coordinates of the same shot in the APS-system. The possible ranges of the Y and Z coordinates in the APS-system are 40 160 and 58 142, respectively. These ranges can be represented as a rectangle domain A on Y-Z plane. 
     Applying the transformation equations, we calculated domain B in the frame-system, which corresponds to the domain A of the APS-system for ? = 72°, 110°, and 125°. We developed three illustrative graphs (APS shot range diagrams) by overlaying domain B over domain A so that one can easily visualize the achievable shot coordinates for APS.
     Domain B is identical to domain A for ? = 90°. Domain B has a diamond shape for other ? s. The diagrams indicate that there are possible shot coordinates outside domain A. When ? = 125°, for example, a shot with y = -20 and z = 114 is feasible. One of uses of the diagrams is to change ? or to move the shot position slightly from the original position to alter a trunnion shot to an APS shot. We applied the proposed technique to cases in which LGP automatically sets some of shots in a treatment plan as trunnion shots because of the APS coordinate limit. Applying the diagrams to those cases enabled us to avoid trunnion shots, consequently, to achieve much faster treatment delivery.
     This concept was not tested in prospective patients.
     APS shot range diagrams can be used to achieve more efficient treatment delivery by avoiding unnecessary trunnion shots with a Gamma Knife unit with APS.
     This may make dose planning and delivery more efficient.


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Y. Watanabe ()