An analytical formalism to calculate phantom scatter factors for flattening filter free (FFF) mode photon beams

Phantom Scatter Factors, Sp in the Khan formalism (Khan et al 1980 J. Radiat. Oncol. Biol. Phys. 6 745-51) describe medium-induced changes in photon-beam intensity as a function of size of the beam. According to the British Journal of Radiology, Supplement 25, megavoltage phantom scatter factors are invariant as a function of photon-beam energy. However, during the commissioning of an accelerator with flattening filter free (FFF) photon beams (Varian TrueBeam(TM) 6-MV FFF and 10-MV FFF), differences were noted in phantom scatter between the filtered beams and FFF-mode beams. The purpose of this work was to evaluate this difference and provide an analytical formalism to explain the phantom scatter differences between FFF-mode and the filtered mode. An analytical formalism was devised to demonstrate the source of phantom scatter differences between the filtered and the FFF-mode beams. The reason for the differences in the phantom scatter factors between the filtered and the FFF-mode beams is hypothesized to be the non-uniform beam profiles of the FFF-mode beams. The analytical formalism proposed here is based on this idea, taking the product of the filtered phantom scatter factors and the ratio of the off-axis ratio between the FFF-mode and the filtered beams. All measurements were performed using a Varian TrueBeam(TM) linear accelerator with photon energies of 6-MV and 10-MV in both filtered and FFF-modes. For all measurements, a PTW Farmer type chamber and a Scanditronix CC04 cylindrical ionization were used. The in-water measurements were made at depth dose maximum and 100 cm source-to-axis distance. The in-air measurements were done at 100 cm source-to-axis distance with appropriate build-up cap. From these measurements, the phantom scatter factors were derived for the filtered beams and the FFF-mode beams for both energies to be evaluated against the phantoms scatter factors calculated using the proposed algorithm. For 6-MV, the difference between the measured and the calculated FFF-mode phantom scatter factors ranged from -0.34% to 0.73%. The average per cent difference was -0.17% (1σ = 0.25%). For 10-MV, the difference ranged from -0.19% to 0.24%. The average per cent difference was -0.17% (1σ = 0.13%). An analytical formalism was presented to calculate the phantom scatter factors for FFF-mode beams using filtered phantom scatter factors as a basis. The overall differences between measurements and calculations were within ± 0.5% for 6-MV and ± 0.25% for 10-MV.