SU-E-T-509: Photon Spectrum Modeling of Flattening Filter Free (FFF) Beam and the Optimization of Model Parameters

Purpose: To determine the distribution of photon spectrum on flattening filter free (FFF) beams, novel and fast optimization methods that were applicable on a convolution/superposition dose calculation algorithm were implemented.

Methods: Two-step optimization method was designed to model the virtual photon spectrums for FFF beams. At first, simple functional form of photon spectrums proposed by E. S. M. Ali was modified and used to make rough shapes of photon spectrum. The distributions of photon spectrums were defined at various field sizes (FSs) to consider the changes of the contribution for scattered photons. Percent depth doses (PDDs) at various FSs were used, and collapsed cone convolution (CCC) algorithm was used to calculate PDDs by considering cone-shaped photon fluence in fields. At next, an arbitrary functional form of photon spectrums where the values of photon intensity itself were free parameters was designed. Line search method was used for optimization and gradient terms at each free parameter were derived from CCC algorithm to enhance the speed of iterations.

Results: The mean energies of the optimized spectrums were decreased from 1.40 to 1.21 MeV for 6 MV FFF beams and from 2.45 to 1.27 MeV for 10MV FFF beams as FSs were increased from 3×3 to 40×40 cm² because of the contributions of scattered photons. The shape of the spectrums were not greatly changed with field sizes, but root mean squared differences (RMSDs) between the measured PDDs and the calculated PDDs using optimized spectrums were increased upto 0.87% as the FSs were decreased to 3×3 cm² .

Conclusions: Developed method for spectrum modeling showed good agreements when the PDDs were calculated with the optimized results. Suggested method is proper to the radiation treatment planning systems because it only requires measured PDDs, and based on the analytic dose calculation algorithm. This work was supported by the National Research Foundation of Korea(NRFK)⌉ grant funded by the Korean government (MEST)⌉ (Grant No. K20901000001-09E0100-00110⌉), Varian Medical Systems, NCI Grant No.1R01 CA98523⌉, and NSF Grant No. 0854492⌉.