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: r1 = (RD90 - MD90-P95)/MD90-P95, r2 = [(RD90 + ΔR1) - m × (MD90-P95 + ΔR1)]/[m × (MD90-P95 + ΔR1)], where ΔR1 is an offset between RD80 and RD90 and m is a ratio between MD90-P95 and theoretical MD100-P100', and r3 = [(RD90 - 0.305) - 0.801 × MD90-P95]/(0.801 × MD90-P95), where 0.305 (ΔR2) is an offset between RD90 and RD100 and 0.801 is a ratio between MD90-P95 and measured MD100-P100. 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% (r1), 0.03% ± 1.53% (r2), and 0.05% ± 1.20% (r3) for model (1), and 0.27% ± 1.36% (r1), 0.71% ± 1.51% (r2), and -0.05% ± 1.20% (r3) for model (2). For a passing prediction rate with a difference threshold of ±3%, model (1) showed slightly worse results than model (2) using r1 (91.5% vs 94.4%). In general, small (M < 4 g/cm2) and close-to-full modulations produced larger discrepancies. However, 100% output predictions using r3 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 r3. Either model with r3 thus can serve well as an output prediction calculator.