Comparison of penh, fluka, and Geant4/topas for absorbed dose calculations in air cavities representing ionization chambers in high-energy photon and proton beams

Abstract

Purpose: The purpose of this work is to analyze whether the Monte Carlo codes penh, fluka, and geant4/topas are suitable to calculate absorbed doses and $f_Q/f_{Q_0}$ ratios in therapeutic high-energy photon and proton beams.

Methods: We used penh, fluka, geant4/topas, and egsnrc to calculate the absorbed dose to water in a reference water cavity and the absorbed dose to air in two air cavities representative of a plane-parallel and a cylindrical ionization chamber in a 1.25 MeV photon beam and a 150 MeV proton beam - egsnrc was only used for the photon beam calculations. The physics and transport settings in each code were adjusted to simulate the particle transport as detailed as reasonably possible. From these absorbed doses, $f_{Q_0}$ factors, $f_Q$ factors, and $f_Q/f_{Q_0}$ ratios (which are the basis of Monte Carlo calculated beam quality correction factors $k_{Q,Q_0}$ ) were calculated and compared between the codes. Additionally, we calculated the spectra of primary particles and secondary electrons in the reference water cavity, as well as the integrated depth-dose curve of 150 MeV protons in water.

Results: The absorbed doses agreed within 1.4% or better between the individual codes for both the photon and proton simulations. The $f_{Q_0}$ and $f_Q$ factors agreed within 0.5% or better for the individual codes for both beam qualities. The resulting $f_Q/f_{Q_0}$ ratios for 150 MeV protons agreed within 0.7% or better. For the 1.25 MeV photon beam, the spectra of photons and secondary electrons agreed almost perfectly. For the 150 MeV proton simulation, we observed differences in the spectra of secondary protons whereas the spectra of primary protons and low-energy delta electrons also agreed almost perfectly. The first 2 mm of the entrance channel of the 150 MeV proton Bragg curve agreed almost perfectly while for greater depths, the differences in the integrated dose were up to 1.5%.

Conclusion: penh, fluka, and geant4/topas are capable of calculating beam quality correction factors in proton beams. The differences in the $f_{Q_0}$ and $f_Q$ factors between the codes are 0.5% at maximum. The differences in the $f_Q/f_{Q_0}$ ratios are 0.7% at maximum.

Keywords: Monte Carlo simulation; beam quality correction factors; dosimetry; high-energy photon and proton radiation; radiation therapy.

Figure 1

Geometries used for the simulations: (a) reference volume: a water‐filled plane‐parallel volume with a diameter of 10 mm and a height of 0.25 mm, (b) air‐filled plane‐parallel volume with a diameter of 10 mm and a height of 2.5 mm and (c) air‐filled cylindrical volume with a height of 20 mm and a diameter of 6 mm. The direction of the broad beam is marked with black arrows on the left. [Color figure can be viewed at http://www.wileyonlinelibrary.com/]

Figure 2

Absorbed dose in Gy per primary scored in each volume from Fig. 1 for all Monte Carlo codes. (a) 1.25 MeV photons, (b) 150 MeV protons. In the bottom graph, the deviations relative to penh are shown (see text for explanation). The statistical uncertainties of the absolute absorbed doses are smaller than the symbol size. The statistical uncertainties represented by bars in the bottom graphs correspond to one standard deviation. [Color figure can be viewed at http://www.wileyonlinelibrary.com/]

Figure 3

Results for $f_{Q_0}$ and $f_Q$ factors: (a) 1.25 MeV photons and (b) 150 MeV protons. (c) The $f_Q/f_{Q_0}$ ratios for 150 MeV protons. The statistical uncertainties represented by bars correspond to one standard deviation. [Color figure can be viewed at http://www.wileyonlinelibrary.com/]

Figure 4

Spectral fluence ${\mathrm{\Phi }}_E(E)$ in water of photons (a) and electrons (b) in the 1.25 MeV photon beam at a depth of 5 cm. [Color figure can be viewed at http://www.wileyonlinelibrary.com/]

Figure 5

Spectral fluence ${\mathrm{\Phi }}_E(E)$ in water of protons (a) and electrons (b) in the 150 MeV proton beam at a depth of 2 cm. [Color figure can be viewed at http://www.wileyonlinelibrary.com/]

Figure 6

(a) Integrated depth–dose curve of 150 MeV protons in water (dose integrated over an area of 100 cm${}^2$). (b) Zoom to the Bragg peak. (c) Zoom to the first 90 mm. (d) Zoom to the first 2 mm while the dose values are normalized to the dose at a depth of 1 mm. The single data points in (d) are connected with lines to guide the eye. No statistical uncertainties are indicated since one standard deviation is smaller than the line width [panels (a)–(c)] or the symbol size [panel (d)]. [Color figure can be viewed at http://www.wileyonlinelibrary.com/]

Figure 7

Electronic mass‐stopping powers of (a) water and (b) air for protons. The data labeled with ICRU90 are taken from Ref. [17]. [Color figure can be viewed at http://www.wileyonlinelibrary.com/]

Figure 8

Absorbed dose in Gy per primary scored in each volume from Fig. 1 for the 1.25 MeV photons (a) and 150 MeV protons (d) calculated with penh and geant4/topas using the physics lists g4em‐standard_opt3 and g4em‐standard_opt4. In (b) and (e), the deviations relative to penh are shown. The statistical uncertainties of the absolute absorbed doses are smaller than the symbol size. The statistical uncertainties represented by bars in panel (b) and (e) correspond to one standard deviation. (c) The results for $f_{Q_0}$ factors for 1.25 MeV photons; (f) the results for $f_Q$ factors for 150 MeV protons. The statistical uncertainties represented by bars correspond to one standard deviation. [Color figure can be viewed at http://www.wileyonlinelibrary.com/]

Figure 9

Energy‐dependent fluence ${\mathrm{\Phi }}_E(E)$ in water of secondary electrons binned by energy in a 1.25 MeV photon beam scored in TOPAS with the self‐programmed scorer (fluence binned by energy the particle had when generating the scoring hit; corresponding to the spectral fluence) and the default scorer fluence implemented in TOPAS (fluence binned by the energy the particle had when entering the scoring volume). [Color figure can be viewed at http://www.wileyonlinelibrary.com/]