Validating a double Gaussian source model for small proton fields in a commercial Monte-Carlo dose calculation engine

Abstract

Purpose

The primary fluence of a proton pencil beam exiting the accelerator is enveloped by a region of secondaries, commonly called “spray”. Although small in magnitude, this spray may affect dose distributions in pencil beam scanning mode e.g., in the calculation of the small field output, if not modelled properly in a treatment planning system (TPS). The purpose of this study was to dosimetrically benchmark the Monte Carlo (MC) dose engine of the RayStation TPS (v.10A) in small proton fields and systematically compare single Gaussian (SG) and double Gaussian (DG) modeling of initial proton fluence providing a more accurate representation of the nozzle spray.

Methods

The initial proton fluence distribution for SG/DG beam modeling was deduced from two-dimensional measurements in air with a scintillation screen with electronic readout. The DG model was either based on direct fits of the two Gaussians to the measured profiles, or by an iterative optimization procedure, which uses the measured profiles to mimic in-air scan-field factor (SF) measurements. To validate the DG beam models SFs, i.e. relative doses to a 10 × 10 cm² field, were measured in water for three different initial proton energies ($100MeV$, $160MeV$, $226.7MeV$) and square field sizes from $1\times 1{cm}^2$ to $10\times 10{cm}^2$ using a small field ionization chamber (IBA CC01) and an IBA ProteusPlus system (universal nozzle). Furthermore, the dose to the center of spherical target volumes (diameters: $1cm$ to $10cm$) was determined using the same small volume ionization chamber (IC). A comprehensive uncertainty analysis was performed, including estimates of influence factors typical for small field dosimetry deduced from a simple two-dimensional analytical model of the relative fluence distribution. Measurements were compared to the predictions of the RayStation TPS.

Results

SFs deviated by more than $2\%$ from TPS predictions in all fields $<4\times 4{cm}^2$ with a maximum deviation of $5.8\%$ for SG modeling. In contrast, deviations were smaller than $2\%$ for all field-sizes and proton energies when using the directly fitted DG model. The optimized DG model performed similarly except for slightly larger deviations in the $1\times 1{cm}^2$ scan-fields. The uncertainty estimates showed a significant impact of pencil beam size variations ($\pm 5\%$) resulting in up to $5.0\%$ standard uncertainty. The point doses within spherical irradiation volumes deviated from calculations by up to $3.3\%$ for the SG model and $2.0\%$ for the DG model.

Conclusion

Properly representing nozzle spray in RayStation’s MC-based dose engine using a DG beam model was found to reduce the deviation to measurements in small spherical targets to below $2\%$. A thorough uncertainty analysis shows a similar magnitude for the combined standard uncertainty of such measurements.