Monte Carlo simulations of EBT3 film dose deposition for percentage depth dose (PDD) curve evaluation

Abstract Purpose To use Monte Carlo (MC) calculations to evaluate the effects of Gafchromic EBT3 film orientation on percentage depth dose (PDD) curves. Methods Dose deposition in films placed in a water phantom, and oriented either parallel or perpendicular with respect to beam axis, were simulated with MC and compared to PDDs scored in a homogenous water phantom. The effects of introducing 0.01–1.00 mm air gaps on each side of the film as well as a small 1°‐3° tilt for film placed in parallel orientation were studied. PDDs scored based on two published EBT3 film compositions were compared. Three photon beam energies of 120 kVp, 220 kVp, and 6 MV and three field sizes between 1 × 1 and 5 × 5 cm2 were considered. Experimental PDDs for a 6‐MV 3 × 3 cm2 beam were acquired. Results PDD curves for films in perpendicular orientation more closely agreed to water PDDs than films placed in parallel orientation. The maximum difference between film and water PDD for films in parallel orientation was −12.9% for the 220 kVp beam. For the perpendicular film orientation, the maximum difference decreased to 5.7% for the 120 kVp beam. The inclusion of an air gap had the largest effect on the 6‐MV 1 × 1 cm2 beam, for which the dose in the buildup region was underestimated by 21.2% compared to the simulation with no air gap. A 2° film tilt decreased the difference between the parallel film and homogeneous water phantom PDDs from −5.0% to −0.5% for the 6 MV 3 × 3 cm2 beam. The “newer” EBT3 film composition resulted in larger PDD discrepancies than the previous composition. Experimental film data qualitatively agreed with MC simulations. Conclusions PDD measurements with films should either be performed with film in perpendicular orientation to the beam axis or in parallel orientation with a ~ 2º tilt and no air gaps.

collimators, 5 microbeam therapy, 6 and in vivo dosimetry for total body 7 and total electron skin 8 irradiations. Films also find use in particle beams, including for proton 9 or electron 10 beam dosimetry and are considered for the use in MR-guided radiotherapy. 11 Radiochromic films have also been used for diagnostic applications, such as for computed tomography dose measurements. 12,13 An important advantage of film dosimetry over other dosimetry techniques is its high spatial resolution, 2D measurement capabilities, and low-energy dependence. 14 In this work, we focus on the investigation of percentage depth dose (PDD) curves derived from using radiochromic films in a variety of commonly used configurations.
The PDD is an important metric of interest in radiation therapy.
To avoid conducting time-consuming measurements using an ionization chamber in a water tank, PDDs are often measured with radiochromic films placed in a solid water phantom. This is typically achieved with two phantom setups. In the first configuration, a number of film sheets are sandwiched in a phantom in perpendicular orientation with respect to the beam axis and a small number of points for PDD evaluation corresponding to the number of sheets can be obtained. [15][16][17][18] Alternatively, a single sheet of film can be sandwiched in a phantom in parallel orientation with respect to the beam axis, which results in a practically continuous quantification of the PDD curve. [19][20][21] In the present work, the potential differences in accuracy of PDD measurements between these two film phantom setups have been evaluated primarily by means of computer simulation.
Investigations of radiographic film orientation for electron beam isodose distributions date back to the late 1960s. 22 Later in 1981, Williamson et al. investigated how film optical density (OD) changed as a function of film orientation and depth in phantom. 23 The study revealed that radiographic (Kodak V2) film aligned parallel to the beam axis was more sensitive at higher depths compared to the film aligned perpendicularly. The authors developed a stoichiometric procedure to correct for the varying film energy response at depth. In 1999, Suchowerska et al. used experiments and Monte Carlo (MC) simulations to demonstrate that PDD measurements performed using radiographic films (Kodak X Omat-V) in perpendicular orientation matched PDD measurements taken with an ionization chamber. 24 In their study, the authors found that film in parallel orientation over-responded by as much as 14% for a 6-MV beam and an unspecified field size, which was in agreement with the results presented in the study by Williamson  in the parallel orientation compared to perpendicular orientation. 25 They recommended that a gantry tilt of at least 2°should be introduced for accurate dose measurement with films in parallel orientation.
The main goal of this work was to use MC simulations to investigate the effect of Gafchromic TM EBT3 film (ISP, Wayne, NJ) orientation (parallel and perpendicular to beam axis) on PDDs for a number of field sizes and beam energies. For films placed parallel to the beam axis, the effect of a slight 1-3°film tilt and air gaps, which can exist between the film and the phantom, on PDDs was also evaluated.

2.A | Phantom and films
To identify and quantify the effect that film orientation has on PDDs, two film orientations inside a 21 × 21 × 30 cm 3 water phantom were considered: a single film parallel to the beam axis and a series of films perpendicular to the beam axis (Fig. 1). One film was placed in the center of the phantom and aligned with the beam axis for the parallel film orientation setup [ Fig. 1(a)]. For the perpendicular film orientation setup, 29 films were simultaneously placed at depths of 1-29 cm in 1-cm increments [ Fig. 1(b)]. The effect of introducing a slight tilt or an air gap in the water phantom for film placed in parallel orientation was also evaluated. The film tilt was modeled by changing the beam incidence angle by 1-3°and the air gap effect was investigated by introducing air gaps of 0.05-1 mm on both sides of the film [ Fig. 1(c)]. As a reference, dose distributions in a 21 × 21 × 30 cm 3 homogeneous water phantom were also evaluated. The geometry of Gafchromic TM EBT3 film studied in this work is depicted in [ Fig. 1(d)]. Two EBT3 film compositions obtained from past studies were considered 26,27 and are listed in Table 1. The composition by Palmer et al., which contains 1.6% of aluminum in the active layer, is considered the "newer" one and it is used in all simulations unless stated otherwise.
Three photon beam energies of 120 kVp, 220 kVp, and 6 MV and three field sizes of 1 × 1 cm 2 , 3 × 3 cm 2 , and 5 × 5 cm 2 were considered in our study. The kilovoltage 120 kVp, the orthovoltage 220 kVp, and the high-energy 6-MV photon beam energies were chosen to represent typical imaging, small animal radiotherapy, and clinical radiotherapy beams, respectively.  26 was used.

2.B | Monte Carlo simulations
The phantom with films in parallel orientation [ Fig. 1(a)] consisted of 109, 105, 150 voxels, in x-, y-, and z-directions, respectively. In the x-direction, the voxel sizes were 0.2 cm in water, 0.0125 cm in the EBT3 polyester layer, and 0.0028 cm for EBT3 active layer, which was centered on the x-axis. The two outermost edge voxels in the x-direction were 0.0861 cm to achieve a total phantom length of 21 cm. The voxel size in the y-and z-directions was 0.2 cm for this phantom.
The phantom with films placed in perpendicular orientation

2.B.3 | Beams
Three photon beam energies of 120 kV, 220 kV, and 6 MV were simulated. The energy spectra were generated by MC based on validated models of a 120-kV microCT imaging beam 29 and a small animal radiotherapy beam. 18 The 6-MV beam was simulated with the default DOSXYZnrc mohan6 spectrum. 30 In most cases, the beam was incident at 0°, as shown in Fig. 1. Parallel rectangular beams with field sizes of 1 × 1 cm 2 , 3 × 3 cm 2 , and 5 × 5 cm 2 were simulated using ISOURCE = 12 for all three beam energies and in each of the phantoms. The effect of EBT3 film elemental composition was only studied for the 220-kVp and 6-MV 1 × 1 cm 2 beams. For the 1-3°film tilt study, the beam was rotated by 1-3°with respect to the z-axis to simulate film tilt. The film tilt was studied for the 220-kVp and 6-MV 3 × 3 cm 2 beams.

2.B.4 | Simulation setup
All relevant processes for high-and low-energy photon and electron transport, such as Rayleigh scattering, electron-impact ionization and  pair production were included in the simulations and the XCOM cross-section data were used. The electron and photon cutoff kinetic energies were 5 keV and no variance reduction techniques were used. For simulations of phantoms with films, the dose to the film active layer was reported. For the water phantom simulation, the dose to water was reported. The number of simulated histories were 7 × 10 8 , 7 × 10 9 , and 1.95 × 10 10 for the 1 × 1 cm 2 , 3 × 3 cm 2 and 5 × 5 cm 2 field sizes, respectively, in order to achieve a central-axis dose uncertainty of < 1%. The simulations were run in parallel on a 64-bit Linux computer with 64 AMD Opteron 6738 cores and took between~80 and~1700 CPU hours to run, depending on the beam energy and field size.  To complement the film data, relative ionization chamber measurements were taken using a PTW Pinpoint chamber (PTW, Freiburg, Germany) together with a PTW UNIDOS E Electrometer and a −300 V bias applied. The chamber was positioned at the center of the 3x3cm 2 beam and irradiated at various effective depths between 0.53 and 23.53 cm, in 0.5 to 5 cm intervals, within the same solid water phantom described previously; the raw electrometer reading was then taken and normalized to provide the relative depth dose data. The raw chamber response data were normalized to the dose at a depth of 1.6 cm, interpolated from the point nearest to d max , thereby providing a secondary reference measurement for comparison with the normalized film data.

2.D | Data analysis
The MC 3D dose distributions were analyzed in MATLAB and central axis PDDs were plotted. Unless stated otherwise, 120 kVp and 220 kVp PDD curves were normalized to dose scored at 1-cm depth while 6-MV PDD curves were normalized to dose scored at d max = q .

| RESULTS
Sample normalized 2D dose distributions for a 6-MV 5 × 5 cm 2 beam in the homogeneous water phantom and the phantoms with film oriented parallel and perpendicular to the beam axis are shown in Fig. 2. Comparisons of PDD curves for the two different film orientations as a function of field size and beam energy, as well as a function of air gap size for the parallel film orientation, are discussed below. Note that [ Fig. 2(a)] indicates that the dose to water is lower than the dose to the EBT3 film polyester and active layers. This is due to the difference in mass energy-absorption coefficients µ en /ρ of these two materials: at 2 MeV, the ratio of µ en /ρof polyester to water is 1.22, which corresponds to the 1.25 dose ratio of the film polyester layer to water at 1.6-cm depth. | 317 studied photon beam energies and field sizes. The maximum differences between the PDDs for the water phantom and those calculated for phantoms with films in parallel and perpendicular orientation are summarized in Table 2.

3.A | The effect of film orientation on PDD
For all beam energies and field sizes, the parallel film orientation resulted in poorer agreement with the water phantom simulations.
Moreover, smaller field sizes generally resulted in larger dose discrepancies. For the parallel film simulations, the dose differences were largest for the 220-kV beam, up to −12.9% at 6.2-cm depth for the 1 × 1 cm 2 field size. Dose with film in parallel orientation was underestimated by −7.7% at 13.6-cm depth for the 6-MV 1 × 1 cm 2 beam. For the film in perpendicular orientation, increasing the beam energy resulted in a better agreement with the water phantom PDD, where the largest difference was found to be −5.7% at 5-cm depth for the 120-kVp 1 × 1 cm 2 beam.

3.B | The effect of air gap on PDD
Parallel orientation film PDDs with varying air gaps for all beam energies and field sizes are plotted in Fig. 4. In most cases, the dose difference relative to a PDD with no air gap increased with increasing air gap size and decreasing field size.

3.C | Film elemental composition
The results of investigating dose distribution differences for two different EBT3 film compositions by Palmer et al. 26 and Bekerat et al. 27 for the 220-kVp and 6-MV 1 × 1 cm 2 beams are presented in Fig. 5.
When comparing to the homogeneous water phantom PDD, the film composition from the study by Bekerat et

3.D | Film tilt
The effect of introducing a slight tilt when films are placed in parallel orientation for the 220-kVp and 6-MV 3 × 3 cm 2 beams is demonstrated in Fig. 6. Evidently, even a small tilt of 1°resulted in notably improved agreement between film and water phantom PDD. The mean absolute difference between the water and 1°-tilt PDD decreased to 1.7% from 4.7% for 0°-tilt in the 220-kVp beam. The improvement for larger tilt angles was negligible. For the 6-MV beam, the mean dose difference between water and film PDD for 1°, 2°, and 3°-tilt was 0.8%, 0.5%, and 0.2%, respectively, which was an improvement over the 5% dose difference found with a 0°-tilt.

3.E | Experimental data
The results from the experimental measurements for a 6-MV the films were assumed to be perfectly flat and geometrically uniform and we did not take into account the spectral changes of the beam that would affect the measurements of film OD and therefore F I G . 3. PDD plot comparison between parallel and perpendicular EBT3 film orientations in a water phantom and PDDs simulated for a water phantom for all three studied beam energies and field sizes. The dose difference line of AE 5% is indicated.
T A B L E 2 Maximum differences between PDDs calculated for the parallel or perpendicular film orientation phantoms and thewater phantom PDD (film-water) for all three beam energies and field sizes. First, it was demonstrated that dose calculated in EBT3 films oriented perpendicular to the beam axis more closely agreed with dose to water when compared to the films in parallel orientation (Fig. 3).
The largest differences were found for the smallest 1 × 1 cm 2 beam size for all beam energies. For example, when orthovoltage beam PDDs were normalized to 1-cm depth, the 220-kV photon beam suffered from the largest overall dose discrepancy of −12.9% at 6. T A B L E 3 Maximum differences between PDDs calculated for a phantom with film in parallel orientation without an air gap and with a 0.10mm or 1.00-mm air gap (no air gap-air gap) for all three beam energies and field sizes. increasing field size. Altogether, the largest PDD differences between films in parallel orientation and the homogeneous water phantom were observed for the 220-kVp beam. This can be explained by the large energy dependence for films in this beam (similar to the 120-kVp beam) combined with the increased beam attenuation, relative to water, when compared to the 120-kVp beam ( Fig. 9). For energies lower than 60 keV, x-ray beam attenuation in the film active layer is lower than beam attenuation in water, which will result in lower 120-kVp beam attenuation compared to the 220-kVp beam.
Second, it was demonstrated that the presence of air gaps on the side of film placed in parallel orientation altered the magnitude of the absorbed dose (Fig. 4). The dose discrepancy increased with increasing air gap and beam energy. Even for a small 0.10-mm air gap, doses were underestimated by up to 4% in the buildup region for the 6-MV 1 × 1 cm 2 beam. For the largest studied 1.00-mm air gap, the film dose was underestimated by 21.2% in the buildup region for the same beam. The other beam energies were less affected by the air gap; for example, using the 1.00-mm air gap, doses were underestimated by up to 6% for the 120-kVp and 220-kVp beams. Note that the maximum differences between simulations with and without air gaps, for all PDDs normalized to their respective maximum dose, were found to be less than 3% beyond the buildup region for all beam energies and field sizes. For the 1.00-mm (a) (b) F I G . 5. PDD curve comparison for films oriented parallel to the beam axis for two different compositions of Gafchromic EBT3 films for the 220-kV 1 × 1 cm 2 (a) and 6-MV 1 × 1 cm 2 beam (b). The dose difference line of AE 5% is indicated.

(a) (b)
F I G . 6. PDD curve comparison for films oriented at a slight tilt with respect to the beam axis for the 220-kV 3 × 3 cm 2 (a) and 6-MV 3 × 3 cm 2 beam (b). film in parallel orientation can likely be attributed to the increased attenuation within the film active layer compared to water, as indicated by the linear attenuation coefficient ratio of film active layer to water being consistently higher than 1.0 (Fig. 9).
Fourth, it was demonstrated that a slight film tilt improved the accuracy of central axis depth doses (Fig. 6). Interestingly, for the 220-kVp beam the film PDD was overestimated relative to the water PDD even for the smallest 1°-tilt and no further improvement for 2°-or 3°-tilts was observed. For the 6-MV beam, however, the dose accuracy was the maximized using a 3°-tilt and did not improve further for a 4°-tilt (data not shown). The improvement in PDD agreement for a film slightly tilted with respect to the beam axis can be attributed to the increased beam attenuation in the film active layer relative to water. When a slight film tilt α is introduced, the path length through the active layer is significantly decreased from the measurement depth to d al /sin(α), where d al is the thickness of active layer of 28 µm. For example, for a film tilt of 2°the path length reduces from the measurement depth to only 0.8 mm.
While most of the presented results are based on MC simulations, experimental data acquired for a 6-MV 3 × 3 cm 2 beam and presented in Fig. 7 and Fig. 8 qualitatively support the results of MC simulations. The PDD curve for a 0.9-mm air gap in [ Fig. 8(a)] shows the largest difference between measurements with no air gap at depths between 10 and 15 cm, suggesting that the air gap between the film and the solid water was likely inconsistent and largest at these depths.
For films in parallel orientation, the dose deposition is affected by the increased attenuation of the beam within the active layer F I G . 9. The ratio of the linear attenuation coefficient µ and the mass energy-absorption coefficient µ en /ρ of the film active layer to water for the two different compositions of Gafchromic EBT3 films studied in this work. Data are derived from the NIST database. compared to water, as well as different lateral scatter contributions from the adjacent polyester layer. Central axis PDDs are more sensitive to lateral scattering contributions as field size increases. For phantoms with films in perpendicular orientation, the attenuation difference in the thin active layer as well as in the polyester layer has a smaller effect on the PDD than for phantoms with films in parallel orientation. In the case where air gaps are introduced for films in parallel orientation, the lateral scatter from air contributes less to the central axis dose than would be the case for water.
As mentioned above, our study design did not include the response of EBT3 Gafchromic TM films as a function of beam energy, which changes as the beam travels through the phantom. Thankfully EBT3 film has been shown to be less energy dependent than its previous generations. 14,[33][34][35] Including the film energy response in our investigation would likely have minor implications on our findings for the 6-MV photon beam, which is supported by the experimental results presented in Fig. 7 and Fig. 8 This silver-based film placed in parallel orientation resulted in up to 15% and 14% overestimation of dose at 25-cm depth for a 60 Co and a 6-MV beam, respectively, compared to the perpendicular orientation which had agreed with ionization chamber measurements. The overestimation of dose for films in parallel orientation was explained by the increased film-to-water ratio of µ en /ρ at lower energies, raising rapidly for energies below 550 keV, exceeding a factor of 2 at~150 keV. EBT3 films, on the other hand, are more tissue equivalent and the µ en /ρ ratio of film to water decreases by less than 1.5% from 2 MeV to 150 keV (Fig. 9). The lower absorbed doses observed in this tudy for EBT3 film in parallel orientation can be explained by the increased beam attenuation in the film active layer compared to water.
Due to the presence of the film in the perpendicular orientation, beams, the difference between the actual film depth and the effective film depths was decreased, and thus the film depths were considered to be equal to the actual film depths in this study.
Based on our MC study, we present a short list of recommendations for PDD measurements with Gafchromic TM EBT3 films.
1. If possible, use a number of films in perpendicular orientation with respect to beam axis. While dose measurement accuracy for high-energy photon beams could be within 2%, dose measurement accuracy for kilovoltage and orthovoltage beams might be only 4-5%.
2. If a parallel film orientation is used, tilt the film at a small~2°a ngle. This should improve dose measurement accuracy, especially for high-energy photon beams. The dose at depth for kilovoltage and orthovoltage beams might be overestimated by~3%.

3.
Ensure that there are no air gaps between the film and the phantom. This is most critical for dose measurement accuracy in highenergy photon beams and using small field sizes. Air gaps might result in an underestimation of absolute dose as well as a shift in d max .

| CONCLUSION
We have presented a Monte Carlo study that highlighted some chal-

CONFLI CT OF INTEREST
The authors have no conflict of interest.