Decomposition of the weight fractions for modelling ridge filters in a proton wobbling nozzle

In proton therapy, the width of a pristine Bragg peak is too narrow to cover the entire tumor volume, and should be spread out using the Spread out Bragg peak (SOBP) techniques such as energy stacking, range modulator wheel and ridge filter. The main purpose of this study was to demonstrate feasibility of using a simple least square technique to decompose the simulated weight fractions of elemental Bragg peaks of ridge filters used in a clinical wobbling beam nozzle. First, initial simulated beam parameters including mean energy and energy spread at the nozzle entrance for all available clinical energies were commissioned against measurements for the open middle wobbling field at the Proton and Radiation Center of the Linkou Chang Gung Memorial Hospital (LCGMH) using the Particle Therapy Simulation Framework (PTSim) Monte Carlo package. Material composition and geometry of nozzle components were provided by the vendor. Depth dose distribution of beam energies from 70 to 230 MeV at 20-MeV increment were simulated and validated with measurement. Curve fitting to those beam parameters was performed to extend simulation energy range to all available clinical energies. For the reconstructed ridge filter simulation, elemental Bragg peaks (BPs) with layer filters corresponding to ridge filter step thicknesses were obtained as bases of the weight factor decomposition. The least square technique was implemented to decompose weight factors for individual ridge filter at a selected beam energy within its applicable energy range. Finally, the reconstructed ridge filters using decomposed weight factors were tested at one other energy to validate the study design. Four different ridge filters (5 cm-LE, 5 cm-HE, 10 cm and 11 cm SOBP) were examined in this study. Commission results for tuned beam parameter settings showed maximum disagreement of BP characteristics, represented by the 80% dose depth (R80d) and width of distal fall-off (W80-20), occurred at 230 MeV and was smaller than 0.2 and 0.5 mm respectively. Furthermore, analyzed outcome for SOBPs from the four ridge filters revealed general improvement of agreement to measurement with decomposition and satisfactory agreement between measurements and those with least square technique. Deviation from measurement of SOBP characteristics evaluated for R90d, W80-20 and SOBP flatness after weight decomposition showed values smaller than 1mm/1%. Similar evaluation of SOBP width generated larger difference with maximum value of 2.7 mm for the 11-cm ridge filter. Results of the validation testes were similar with maximum deviation of 1.4 mm, 0.6 mm, 0.2% and 3.8 mm for R90d, W80-20, flatness and width respectively.