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Implementation of output prediction models for a passively double‐scattered proton therapy system
Author(s) -
Ferguson Sven,
Ahmad Salahuddin,
Jin Hosang
Publication year - 2016
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.4965046
Subject(s) - sobp , physics , quartic function , isocenter , proton therapy , inverse , bragg peak , mathematics , mathematical analysis , algorithm , proton , optics , geometry , nuclear physics , imaging phantom , pure mathematics
Purpose Two output (cGy/MU) prediction models (one existing and one newly developed) for a passively double‐scattered proton therapy system are implemented and investigated for clinical use. Variations of each model are tested for accuracy in order to determine the most viable prediction model. Methods The first output prediction model [model (1)] is a semianalytical model proposed by Kooy et al. [Phys. Med. Biol. 50 , 5847–5856 (2005)], which employs three main factors. The first factor (basic output prediction) uses a unique combined parameter [ r = ( R − M )/ M ] of range ( R ) and modulation [ M ; spread‐out Bragg peak (SOBP) width] along with option specific fitting parameters. The second factor takes into account minor source shifts using a linear fit due to varying beamline configurations for different options. The final factor accounts for a condition where the point of measurement is not at the isocenter or away from the middle of the SOBP based on an inverse‐square correction. The second model [model (2)] is a novel quartic polynomial fit of the basic output prediction whose idea was inspired by the first model. Different variations in the definition of R and M at distal ( D ) and proximal ( P ) ends resulted in the exploration of three variations of r for both models: r 1 = ( R D 90 − M D 90− P 95 )/ M D 90− P 95 , r 2 = [( R D 90 + Δ R 1 ) − m × ( M D 90− P 95 + Δ R 1 )]/[ m × ( M D 90− P 95 + Δ R 1 )], where Δ R 1 is an offset between R D 80 and R D 90 and m is a ratio between M D 90− P 95 and theoreticalM D 100 − P 100 ′ , and r 3 = [( R D 90 − 0.305) − 0.801 × M D 90− P 95 ]/(0.801 × M D 90− P 95 ), where 0.305 (Δ R 2 ) is an offset between R D 90 and R D 100 and 0.801 is a ratio between M D 90− P 95 and measured M D 100− P 100 . Output measurements for 177 sets of R and M from all 24 options are compared to outputs predicted by both the models of three variations of r . Results The mean differences between measurements and predictions ([predicted − measured]/measured × 100%) were −0.41% ± 1.78% ( r 1 ), 0.03% ± 1.53% ( r 2 ), and 0.05% ± 1.20% ( r 3 ) for model (1), and 0.27% ± 1.36% ( r 1 ), 0.71% ± 1.51% ( r 2 ), and −0.05% ± 1.20% ( r 3 ) for model (2). For a passing prediction rate with a difference threshold of ±3%, model (1) showed slightly worse results than model (2) using r 1 (91.5% vs 94.4%). In general, small ( M < 4 g/cm 2 ) and close‐to‐full modulations produced larger discrepancies. However, 100% output predictions using r 3 were confined within ±3% of measurements for both models and the difference between the models was not substantial (mean difference: 0.05% vs −0.05%). Conclusions The first existing model has proven to be a successful predictor of output for our compact double‐scattering proton therapy system. The new model performed comparably to the first model and showed better performance in some options due to a great degree of flexibility of a polynomial fit. Both models performed well using r 3 . Either model with r 3 thus can serve well as an output prediction calculator.