Simplified sigmoidal curve fitting for a 6 MV FFF photon beam of Halcyon system to determine the field size for beam commissioning and quality assurance

Background: An O-ring gantry-type linear accelerator (Linac) with a 6 MV flattening filter-free (FFF) photon beam, Halcyon, includes a reference beam containing the representative information regarding the percent depth dose, profile, output factor, etc. for commissioning and quality assurance. However, because it does not provide the information of the field size, we proposed a method to determine all field sizes according to all depths for radiation therapy using simplified sigmoidal curve fitting (SCF).Methods: After a mathematical definition of the SCF using four coefficients, the defined curves were fitted to both the reference and measured data. For a high agreement between the fitting curve and the profiles in each data set, the field sizes were determined by identifying the maximum point along the third derivative of the fitting curve. The curve fitting included the field sizes for beam profiles of 2 × 2, 4 × 4, 6 × 6, 8 × 8, 10 × 10, 20 × 20 and 28 × 28 cm2 as a function of depth (at 1.3, 5, 10, 20 cm). The results of the field size from the reference data were compared with the results in the measured data using the same condition.Results: All fitting curves show values of goodness of fit, R2, better than 0.99. The differences in the field size between the reference data and the measured data were within the range of 0 to 0.2 cm. The lowest difference in the field sizes at a depth of 10 cm, which is a surface-to-axis distance, was reported. Conclusion: The application of the SCF has been proven to accurately obtain the field size of the preconfigured reference and of the measured FFF photon beam data for the Halcyon system. The current work can be useful for beam commissioning as a countercheck methodology to determine the field size from the reference data in the treatment planning system of a newly installed Halcyon system and for the routine quality assurance to ascertain the correctness of field sizes clinically used with the Halcyon system.