Derivation of equations to define inflection point and its analysis in flattening filter free photon beams based on the principle of polynomial function

Simplified sigmoidal curve fitting for a 6 MV FFF photon beam of the Halcyon 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 that contains representative information such as the percent depth dose, profile and output factor for commissioning and quality assurance. However, because it does not provide information about 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 mathematical definition of the SCF using four coefficients, the defined curves were fitted to both the reference data (RD) and the measured data (MD). For good 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 and 20 cm). The field size results from the RD were compared with the results from the MD using the same condition.

Results

All fitting curves show goodness of fit, R², values that are greater than 0.99. The differences in field size between the RD and the MD were within the range of 0 to 0.2 cm. The smallest difference in the field sizes at a depth of 10 cm, which is a surface-to-axis distance, was reported.

Conclusion

Application of the SCF method has been proven to accurately capture the field size of the preconfigured RD and 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 RD in the treatment planning system of a newly installed Halcyon system and for routine quality assurance to ascertain the correctness of field sizes for clinical use of the Halcyon system.