To present the implementation and validation of a geometrical based variance reduction technique for the calculation of phase space data for proton therapy dose calculation.
The treatment heads at the Francis H Burr Proton Therapy Center were modeled with a new Monte Carlo tool (TOPAS based on Geant4). For variance reduction purposes, two particle-splitting planes were implemented. First, the particles were split upstream of the second scatterer or at the second ionization chamber. Then, particles reaching another plane immediately upstream of the field specific aperture were split again. In each case, particles were split by a factor of 8. At the second ionization chamber and at the latter plane, the cylindrical symmetry of the proton beam was exploited to position the split particles at randomly spaced locations rotated around the beam axis. Phase space data in IAEA format were recorded at the treatment head exit and the computational efficiency was calculated. Depth–dose curves and beam profiles were analyzed. Dose distributions were compared for a voxelized water phantom for different treatment fields for both the reference and optimized simulations. In addition, dose in two patients was simulated with and without particle splitting to compare the efficiency and accuracy of the technique.
A normalized computational efficiency gain of a factor of 10–20.3 was reached for phase space calculations for the different treatment head options simulated. Depth–dose curves and beam profiles were in reasonable agreement with the simulation done without splitting: within 1% for depth–dose with an average difference of (0.2 ± 0.4)%, 1 standard deviation, and a 0.3% statistical uncertainty of the simulations in the high dose region; 1.6% for planar fluence with an average difference of (0.4 ± 0.5)% and a statistical uncertainty of 0.3% in the high fluence region. The percentage differences between dose distributions in water for simulations done with and without particle splitting were within the accepted clinical tolerance of 2%, with a 0.4% statistical uncertainty. For the two patient geometries considered, head and prostate, the efficiency gain was 20.9 and 14.7, respectively, with the percentages of voxels with gamma indices lower than unity 98.9% and 99.7%, respectively, using 2% and 2 mm criteria.
The authors have implemented an efficient variance reduction technique with significant speed improvements for proton Monte Carlo simulations. The method can be transferred to other codes and other treatment heads.
J.R.M. acknowledges the Consejo Nacional de Ciencia y Tecnología (México) and H. Salazar-Ibargüen (Benemérita Universidad Autónoma de Puebla) for financial supporting for his visit to the Massachusetts General Hospital. J.R.M. thanks J. Shin (University of California San Francisco) for discussions on Geant4 topics. This work was supported by National Institutes of Health/National Cancer Institute (NIH/NCI) under R01 CA 140735-01.
II. MATERIALS AND METHODS
II.A. The TOPAS code
II.B. The treatment head
II.C. Patient geometries
II.D. The geometrical particle splitting technique
II.E. Computational efficiency
III.A. Computational efficiency
III.B. Phase space analysis
III.C. Comparison of dose profiles
III.D. Patient calculations
III.D.1. Head treatment field
III.D.2. Prostate treatment field
V. SUMMARY AND CONCLUSIONS
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