A mathematical model to identify the output variations of TrueBeam linear accelerators using Machine Performance Check evaluations

Abstract

The aim of this work is to find an effective mathematical model to identify the output variations of TrueBeam (Varian Medical Systems, Palo Alto, CA, U.S.A.) linear accelerators (Linacs), using the daily output measurements performed with Machine Performance Check (MPC) tool. All daily output data, measured with MPC from July 2020 to October 2021, were exported and plotted for all energies investigated. After identifying the dates of dose calibration, the measurement period was divided into four and three sub-periods for photon and electron beams, respectively, common to the three Linacs; straight lines were applied to the data and slopes were analysed. Finally, all the output data were merged and a parameters optimisation process was performed that minimised the differences between output values measured by MPC and output values calculated by model. The output of Linacs under examination showed an increase for all photon and electron energies in agreement with the literature findings. MPC output trends were well represented by means of a linear mathematical model and the angular coefficients of the regression lines characterized the rate of daily output increase. The optimisation of the model provided an optimised angular coefficient for photon (0.0126% per day) and electron (0.0128% per day) beams. In this study, linear regression analysis is used to identify the TrueBeam output drift. The proposed model fitting daily MPC output data allows to define the right timing for preventive beams calibrations offering a tool to improve dose control.