### Introduction

### Materials and Methods

### 1. LINAC head modeling based on the Geant4 toolkit

### 2. Evaluation of the dosimetric effect according to initial electron beam parameters

_{max}) on the PDD and profile dose flatness, the PDDs and lateral dose profiles were calculated and analyzed with different initial electron beam conditions.

#### 1) Mean energy of the initial electron pencil beam

#### 2) Radial intensity distribution of the initial electron beam

#### 3) Energy spread of the initial electron pencil beam

#### 4) Normalization and comparison of PDDs and profiles

_{max}and the distribution center, respectively. The PDD was assessed at 2 mm intervals at depths ranging from 0 to 50 mm to observe the dose distribution in build-up region and dose distribution nearby d

_{max}. For depths greater than 50 mm, the depth dose was assessed at 15 mm intervals for depths greater than 50 mm to reduce the statistical fluctuation. The depth before d

_{max}was not considered in the PDD comparison for treatment beam modeling because electron equilibrium was not reached, and statistically significant fluctuation occurs in that region. Moreover, electron contamination affects the dose distribution before d

_{max}.

### 3. Simulation conditions for dose calculation

^{9}initial electrons was recorded in the phase space files and then used repeatedly four times to obtain the dose distribution with reduced statistical fluctuation.

^{3}. Each voxel measured 5×5×2 mm

^{3}.

^{2}, which is generally considered to be the reference size for assessing the effects of initial electron parameters, while the profile was calculated at d

_{max}with a field size of 40×40 cm

^{2}. Since the profile with the larger beam field is more heavily impacted by changes to the initial electron conditions such as mean electron energy, energy spread, and beam radial width [10], the largest field size was selected for the profile assessment. Finally, the optimal parameters were determined by comparing the PDDs and profiles of golden beam data (GBD) achieved with beams of 4×4 cm

^{2}, 10×10 cm

^{2}, and 30×30 cm

^{2}fields.

### Results

### 1. Effects of the initial electron beam on the PDD and profile

#### 1) Mean energy of the initial electron pencil beam

_{max}. Specifically, the dose values increased on average by 4.36%, while the mean energy increased from 5.6 to 6.4 MeV. This finding indicates that the overall PDD curve moved toward the beam direction with the higher electron energy, even though the reference parameters of the initial electron beam were the same.

#### 2) Radial intensity distribution of the initial electron beam

_{max}of 0.49% from the reference condition. Moreover, the minimum dose difference from the reference beam (0.26%) was observed with the beam with a 3 mm radial width at the FWHM. In addition, no significant difference was observed between the PDD curves with respect to beam radial width (Figure 3).

#### 3) Energy spread of the initial electron pencil beam

_{max}increased as the energy spread broadened. The electron beam with an energy spread of 1.019 MeV at the FWHM showed the largest average difference from the reference beam, 2.77%. The minimum difference was 0.17% and was found with an energy spread of 0.127 MeV at the FWHM.

### 2. MC commissioning of the photon beam

^{2}, 10×10 cm

^{2}, and 30×30 cm

^{2}. A total of 2.8×10

^{8}, 5.6×10

^{8}and 5.6×10

^{8}initial electrons, respectively, were generated by beams with field sizes of 4×4 cm

^{2}, 10×10 cm

^{2}, and 30×30 cm

^{2}. The calculation of the dose distributions for the three field sizes required 39, 270, and 860 hours, respectively, with a single CPU.

### Discussion

_{max}, PDD increased when the mean electron energy and the FWHM of the energy spread increased. The higher mean energy of the initial electron generates higher bremsstrahlung photon energy in the target, enabling the photons to produce secondary electrons that penetrate water more efficiently and can deliver their energy to deeper locations along the beam direction. Depths shallower then d

_{max}, which corresponded to the dose difference from the reference condition, showed larger statistical uncertainty compared to deeper locations. In the case of the energy spread, larger energy spread indicates a higher likelihood of producing electrons with both higher and lower energies. Electrons with lower energies produce relatively low energy bremsstrahlung photons in the target that consists of tungsten. They showed less effect on the PDD compared to the photons generated by higher energy electrons because most of them cannot penetrate the target and reach the phantom, even though larger energy spread results in electron production with much broader energy variation than smaller energy spread. With this respect, a larger energy spread results in increased PDD values only in the region deeper than d

_{max}. However, the dose differences from the reference condition as the energy spread was varied were smaller than those observed when the mean electron energy was varied, even though the mean energy was not varied in a wider range than that of the energy spread. Potential explanations for the findings include: (a) the energy spread follows a Gaussian distribution; (b) the majority of electrons had energy near the mean value; and (c) the mean electron energy of the spread was not changed, although the standard deviation of the energy distribution changed. The PDD was changed insignificantly according to the change of the intensity distribution of the electron beam. While changing the initial electron distribution on the target surface results in changes of the treatment beam width, it does not affect the energy of the bremsstrahlung photons produced in the target. Since the depth dose distribution is mainly affected by the bremsstrahlung photon energy, the radial intensity distribution of the initial electron beam could not have any significant effect on the PDD.