^{1,a)}, Jomar Frengen

^{2}, Arve Kylling

^{3,b)}and Tore Lindmo

^{4}

### Abstract

**Purpose**

: To individually benchmark the incident electron parameters in a Monte Carlo model of an Elekta linear accelerator operating at 6 and 15 MV. The main objective is to establish a simplified but still precise benchmarking procedure that allows accurate dose calculations of advanced treatment techniques.

**Methods**

: TheEGSnrc Monte Carlo user codes BEAMnrc and DOSXYZnrc are used for photon beam simulations and dose calculations, respectively. A 5 × 5 cm^{2} field is used to determine both the incident electron energy and the electron radial intensity. First, the electron energy is adjusted to match the calculated depth dose to the measured one. Second, the electron radial intensity is adjusted to make the calculated dose profile in the penumbrae region match the penumbrae measured by GafChromic EBT film. Finally, the mean angular spread of the incident electron beam is determined by matching calculated and measured cross-field profiles of large fields. The beam parameters are verified for various field sizes and shapes.

**Results**

: The penumbrae measurements revealed a non-circular electron radial intensity distribution for the 6 MV beam, while a circular electron radial intensity distribution could best describe the 15 MV beam. These electron radial intensity distributions, given as the standard deviation of a Gaussian distribution, were found to be 0.25 mm (in-plane) and 1.0 mm (cross-plane) for the 6 MV beam and 0.5 mm (both in-plane and cross-plane) for the 15 MV beam. Introducing a small mean angular spread of the incident electron beam has a considerable impact on the lateral dose profiles of large fields. The mean angular spread was found to be 0.7° and 0.5° for the 6 and 15 MV beams, respectively.

**Conclusions**

: The incident electron beam parameters in a Monte Carlo model of a linear accelerator could be precisely and independently determined by the benchmarking procedure proposed. As the dose distribution in the penumbra region is insensitive to moderate changes in electron energy and angular spread, accurate penumbra measurements is feasible for benchmarking the electron radial intensity distribution. This parameter is particularly important for accurate dosimetry of mlc-shaped fields and small fields.

The study was made possible by the financial support from the Strategic Research Area Medical Technology at the Norwegian University of Science and Technology.

I. INTRODUCTION

II. MATERIALS AND METHODS

II.A. BEAMnrc accelerator model

II.B. Phantom simulations in DOSXYZnrc

II.B.1. Depth doses

II.B.2. Penumbra profiles

II.B.3. Cross-field profiles of large fields

II.C. Dosimetric measurements

II.C.1. Depth and cross-field dose profile measurements

II.C.2. Penumbra, buildup, and MLC-field measurements

III. RESULTS

III.A. Depth doses

III.B. Penumbra profiles

III.C. Cross-field profiles

III.D. Build-up region

III.E. MLC-shaped fields

IV. DISCUSSION

V. CONCLUSION

### Key Topics

- Dosimetry
- 17.0
- Linear accelerators
- 14.0
- Electron beams
- 13.0
- Photons
- 11.0
- Field size
- 7.0

## Figures

Measured (ionization chamber; CC13) and calculated depth doses for optimal electron energies, all normalized at 10 cm depth. (a) The 6 MV beam. (b) The 15 MV beam. The radial intensity of the electron beam (given by the standard deviation of a Gaussian distribution), σ, was 1.0 mm in the BEAMnrc simulations. Field size: 5 × 5 cm^{2}, SSD = 90 cm. The insets show relative deviations between simulations and measurements for various incident electron energies.

Measured (ionization chamber; CC13) and calculated depth doses for optimal electron energies, all normalized at 10 cm depth. (a) The 6 MV beam. (b) The 15 MV beam. The radial intensity of the electron beam (given by the standard deviation of a Gaussian distribution), σ, was 1.0 mm in the BEAMnrc simulations. Field size: 5 × 5 cm^{2}, SSD = 90 cm. The insets show relative deviations between simulations and measurements for various incident electron energies.

Calculated penumbrae for (a) the 6 MV beam and (b) the 15 MV beam, for different electron radial intensities (field size: 5 × 5 cm^{2}, depth: 10 cm, SSD: 90 cm). The field borders are defined by the jaws in both in-plane and cross-plane directions by using different collimator rotations. Penumbra profiles for σ = 0.0, 0.5, 1.0, and 1.5 mm are shown (calculations based on σ = 0.25, 0.75, and 1.25 mm were also performed, but are omitted for clarity). In (c) and (d), the measured penumbrae in both directions, for the 6 MV beam and the 15 MV beam, respectively, are shown together with the simulations that best fitted the measured data (see Fig. 3).

Calculated penumbrae for (a) the 6 MV beam and (b) the 15 MV beam, for different electron radial intensities (field size: 5 × 5 cm^{2}, depth: 10 cm, SSD: 90 cm). The field borders are defined by the jaws in both in-plane and cross-plane directions by using different collimator rotations. Penumbra profiles for σ = 0.0, 0.5, 1.0, and 1.5 mm are shown (calculations based on σ = 0.25, 0.75, and 1.25 mm were also performed, but are omitted for clarity). In (c) and (d), the measured penumbrae in both directions, for the 6 MV beam and the 15 MV beam, respectively, are shown together with the simulations that best fitted the measured data (see Fig. 3).

Root mean squared difference between simulations and measurements in the penumbra region for different values of the incident electron intensity distribution (sigma). Field size: 5 × 5 cm^{2}, SSD = 90 cm. (a) The 6 MV beam (simulated with 6.45 MeV electrons). (b) The 15 MV beam (simulated with 13.35 MeV electrons).

Root mean squared difference between simulations and measurements in the penumbra region for different values of the incident electron intensity distribution (sigma). Field size: 5 × 5 cm^{2}, SSD = 90 cm. (a) The 6 MV beam (simulated with 6.45 MeV electrons). (b) The 15 MV beam (simulated with 13.35 MeV electrons).

Measured and calculated in-plane dose profiles of 40 × 40 cm^{2} fields with parameters based on the results from Secs. III A and III B (without angular spread of the incident electrons). (a) The 6 MV beam (electron energy = 6.45 MeV; σ_{in-plane} = 0.25 mm; σ_{cross-plane} = 1.0 mm). (b) The 15 MV beam (electron energy = 13.35 MeV; σ_{in-plane} = σ_{cross-plane} = 0.5 mm). Similar results were found for the cross-plane direction, and are therefore not shown.

Measured and calculated in-plane dose profiles of 40 × 40 cm^{2} fields with parameters based on the results from Secs. III A and III B (without angular spread of the incident electrons). (a) The 6 MV beam (electron energy = 6.45 MeV; σ_{in-plane} = 0.25 mm; σ_{cross-plane} = 1.0 mm). (b) The 15 MV beam (electron energy = 13.35 MeV; σ_{in-plane} = σ_{cross-plane} = 0.5 mm). Similar results were found for the cross-plane direction, and are therefore not shown.

Measured and calculated cross-field dose profiles for square fields at 1.5 cm depth (6 MV beam), 3 cm depth (15 MV beam), and 10 cm depth (both beams). [(a) and (c)] The 6 MV beam in in-plane and cross-plane directions, respectively. Electron energy = 6.45 MeV; σ_{in-plane} = 0.25 mm; σ_{cross-plane} = 1.0 mm; mean angular spread = 0.7°. [(b) and (d)] The 15 MV beam in in-plane and cross-plane directions, respectively. Electron energy = 13.35 MeV; σ_{in-plane} = σ_{cross-plane} = 0.5 mm; mean angular spread = 0.5°. The field sizes are 5 × 5, 10 × 10, 20 × 20, and 40 × 40 cm^{2}. Curves represent ionization chamber measurements, symbols represent Monte Carlo simulations.

Measured and calculated cross-field dose profiles for square fields at 1.5 cm depth (6 MV beam), 3 cm depth (15 MV beam), and 10 cm depth (both beams). [(a) and (c)] The 6 MV beam in in-plane and cross-plane directions, respectively. Electron energy = 6.45 MeV; σ_{in-plane} = 0.25 mm; σ_{cross-plane} = 1.0 mm; mean angular spread = 0.7°. [(b) and (d)] The 15 MV beam in in-plane and cross-plane directions, respectively. Electron energy = 13.35 MeV; σ_{in-plane} = σ_{cross-plane} = 0.5 mm; mean angular spread = 0.5°. The field sizes are 5 × 5, 10 × 10, 20 × 20, and 40 × 40 cm^{2}. Curves represent ionization chamber measurements, symbols represent Monte Carlo simulations.

Measured and calculated build-up doses for 5 × 5 cm^{2} fields. Parameters for the 6 MV beam were: electron energy = 6.45 MeV; σ_{in-plane} = 0.25 mm; σ_{cross-plane} = 1.0 mm; mean angular spread = 0.7°. Parameters for the 15 MV beam were: electron energy = 13.35 MeV; σ_{in-plane} = σ_{cross-plane} = 0.5 mm; mean angular spread = 0.5°.

Measured and calculated build-up doses for 5 × 5 cm^{2} fields. Parameters for the 6 MV beam were: electron energy = 6.45 MeV; σ_{in-plane} = 0.25 mm; σ_{cross-plane} = 1.0 mm; mean angular spread = 0.7°. Parameters for the 15 MV beam were: electron energy = 13.35 MeV; σ_{in-plane} = σ_{cross-plane} = 0.5 mm; mean angular spread = 0.5°.

(a) An MLC-shaped field used for verification of the radial intensity of the incident electron beam. Dose profiles were extracted in the direction perpendicular to the leaf motion, as depicted by the red line. The field was used with 0° and 90° collimator rotation, thus profiles in the in-plane and cross-plane direction were obtained. The doses are normalized to the dose at 1.75 cm off-axis, as depicted by the red cross. (b) Measured and calculated dose profiles for the 6 MV beam. Monte Carlo parameters: electron energy = 6.45 MeV; σ_{in-plane} = 0.25 mm; σ_{cross-plane} = 1.0 mm; mean angular spread = 0.7°. (c) Measured and calculated dose profiles for the 15 MV beam. Monte Carlo parameters: electron energy = 13.35 MeV; σ_{in-plane} = σ_{cross-plane} = 0.5 mm; mean angular spread = 0.5°. Standard deviations in the simulations were <0.57% of normalization dose.

(a) An MLC-shaped field used for verification of the radial intensity of the incident electron beam. Dose profiles were extracted in the direction perpendicular to the leaf motion, as depicted by the red line. The field was used with 0° and 90° collimator rotation, thus profiles in the in-plane and cross-plane direction were obtained. The doses are normalized to the dose at 1.75 cm off-axis, as depicted by the red cross. (b) Measured and calculated dose profiles for the 6 MV beam. Monte Carlo parameters: electron energy = 6.45 MeV; σ_{in-plane} = 0.25 mm; σ_{cross-plane} = 1.0 mm; mean angular spread = 0.7°. (c) Measured and calculated dose profiles for the 15 MV beam. Monte Carlo parameters: electron energy = 13.35 MeV; σ_{in-plane} = σ_{cross-plane} = 0.5 mm; mean angular spread = 0.5°. Standard deviations in the simulations were <0.57% of normalization dose.

## Tables

The incident electron beam parameters and their influence on dose distributions.

The incident electron beam parameters and their influence on dose distributions.

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