Implementation of output prediction models for a passively double-scattered proton therapy system

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.

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 = (R_D90 - M_D90-P95)/M_D90-P95, r₂ = [(R_D90 + ΔR₁) - m × (M_D90-P95 + ΔR₁)]/[m × (M_D90-P95 + ΔR₁)], where ΔR₁ is an offset between R_D80 and R_D90 and m is a ratio between M_D90-P95 and theoretical M_D100-P100^', and r₃ = [(R_D90 - 0.305) - 0.801 × M_D90-P95]/(0.801 × M_D90-P95), where 0.305 (ΔR₂) is an offset between R_D90 and R_D100 and 0.801 is a ratio between M_D90-P95 and measured M_D100-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.

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%).

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.