SU-E-P-45: An Analytical Formula for Deriving Mechanical Iso-Center of Rotational Gantry Treatment Unit Rotational Gantry Treatment Unit.

PURPOSE: To present an analytical formula for deriving mechanical isocenter (MIC) of a rotational gantry treatment unit. The input data to the formula is obtained by a custom-made device. The formula has been implemented and used in an operational proton therapy facility since 2005.

METHODS: The custom made device consisted of 3 mutually perpendicular dial indicators and 5 clinometers, to obtain displacement data and gantry angle data simultaneously. During measurement, a steel sphere was affixed to the patient couch, and the device was attached to the snout rotating with the gantry. The displacement data and angle data were obtained simultaneously at angular increments of less than 1 degree. The analytical formula took the displacement and angle as input and derived the positions of dial indicator tips (DIT) position in room-fixed coordinate system. The formula derivation presupposes trigonometry and 3-dimentional coordinate transformations. Due to the symmetry properties of the defining equations, the DIT position can be solved for analytically without using mathematical approximations. We define the mean of all points in the DIT trajectory as the MIC. The formula was implemented in computer code, which has been employed during acceptance test, commissioning, as well as routine QA practice in an operational proton facility since 2005.

RESULTS: It took one minute for the custom-made device to acquire the measurement data for a full gantry rotation. The DIT trajectory and MIS are instantaneously available after the measurement. The MIC Result agrees well with vendor's Result, which came from a different measurement setup, as well as different data analysis algorithm.

CONCLUSION: An analytical formula for deriving mechanical isocenter was developed and validated. The formula is considered to be absolutely accurate mathematically. Be analyzing measured data of radial displacements as function of gantry angle, the formula calculates the MI position in room coordinate.