Monte Carlo‐based investigation of absorbed‐dose energy dependence of radiochromic films in high energy brachytherapy dosimetry

Relative absorbed dose energy response correction, R, for various radiochromic films in water phantom is calculated by the use of the Monte Carlo‐based EGSnrc code system for high energy brachytherapy sources 60Co, 137Cs, 192Ir and 169Yb. The corrections are calculated along the transverse axis of the sources (1‐15 cm). The radiochromic films investigated are EBT, EBT2 (lot 020609 and lot 031109), RTQA, XRT, XRQA, and HS. For the 60Co source, the value of R is about unity and is independent of distance in the water phantom for films other than XRT and XRQA. The XRT and XRQA films showed distance‐dependent R values for this source (the values of R at 15 cm from the source in water are 1.845 and 2.495 for the films XRT and XRQA, respectively). In the case of 137Cs and 192Ir sources, XRT, XRQA, EBT2 (lot 031109), and HS films showed distant‐dependent R values. The rest of the films showed no energy dependence (HS film showed R values less than unity by about 5%, whereas the other films showed R values higher than unity). In the case of 169Yb source, the EBT film showed no energy dependence and EBT2 film (lot 031109) showed a distance‐independent R value of 1.041. The rest of the films showed distance‐dependent R values (increases with distance for the films other than HS). The solid phantoms PMMA and polystyrene enhance the R values for some films when compared the same in the water phantom. PACS number: 87.53.Jw

application, user can chose a suitable radiochromic film. Some films, such as XRT and XRQA, contain high-Z materials in the emulsion and are designed for use in the kilo-voltage range, whereas film HS, which contains low-Z material in the emulsion, is designed for measurement of absorbed dose in high-energy photon beams (above 1 MeV). (14) In a previously published study, Monte Carlo-based relative absorbed-dose energy response correction as a function of depth in water was investigated for solid state detectors such as LiF, Li 2 B 4 O 7 , Si diode, diamond, Al 2 O 3 for 125 I and 169 Yb brachytherapy sources. (15) Influence of solid phantoms, such as polystyrene and polymethyl methacrylate (PMMA), was also investigated in the work. The present study is aimed at calculating relative absorbed-dose energy response correction as a function of depth in water for the various radiochromic films for different brachytherapy sources such as 60 Co, 137 Cs, 192 Ir, and 169 Yb. This study also includes the influence of solid phantoms polystyrene and PMMA on the correction. We have employed the Monte Carlo-based user codes DOSRZnrc and FLURZnrc (16) of the EGSnrc code system (17) in the present work.

B. Energy dependence of the detector
The energy dependence of a detector is composed of two parts: the intrinsic energy dependence (intrinsic beam quality dependence) and the absorbed-dose energy dependence. The intrinsic energy dependence, k bq (Q), is the ratio of the dose to the sensitive element of the detector at a given beam quality D det (Q) to the detector reading at the same beam quality M det (Q): The absorbed-dose energy dependence, ƒ(Q), is the ratio of the dose to the medium at the point of measurement of the detector in the absence of the detector, D med (Q), to the dose to the sensitive material of the detector, D det (Q): In general, Monte Carlo simulation calculates only the absorbed-dose energy dependence of a detector. It varies with different beam quality and also with the location of the detector for a given beam quality. The overall energy dependence of a detector, often referred to as the energy response, is the product of the intrinsic energy dependence and the absorbed-dose energy dependence.
In brachytherapy, quantity of interest is dose to water. The detectors are generally calibrated against a reference beam, which is generally 60 Co. For a given detector material and a beam quality Q, relative absorbed dose energy response correction factor R is defined as: where the numerator presents detector-to-water dose ratio at Q, and the denominator represents the same dose ratio at 60 Co beam energy.
In the presence of charged particle equilibrium, Eq. (3) can be rewritten as:

C.1 DOSRZnrc simulations of dose ratios for 60 Co beam
Film-to-water dose ratio, D film D wat 60 Co , is calculated in the water phantom for each of the investigated films for 60 Co beam using the DOSRZnrc user code of EGSnrc code system. Here, D film and D wat represent the dose to active region of the film and dose to water, respectively. In the Monte Carlo calculation, a realistic 60 Co spectrum from a telecobalt unit is used. The 60 Co beam is parallel and has a radius of 5.64 cm at the front face of the phantom (equivalent field size is 10 × 10 cm 2 ). The beam is incident on a unity density cylindrical water phantom of 20 cm radius and 40 cm height. In the Monte Carlo calculations, the active layer of films is positioned at 0.5 cm depth along the central axis of the water phantom. All layers of the films are modeled as cylindrical discs with radius 0.5 cm. The thicknesses of the films are detailed in Table 2.

C.2 FLURZnrc simulations of collision kerma for brachytherapy sources
As described in the published work, (15) calculation of dose ratio of film to water for the 60 Co, 137 Cs, 192 Ir, and 169 Yb sources (numerator of Eq. (3)) is based on FLURZnrc user code. (16) In the calculations, the photon fluence spectrum is scored in 0.5 mm thick and 0.5 mm high cylindrical shells, along the transverse axis of the sources (distances, 1 cm-15 cm) in 20 cm radius × 40 cm high cylindrical phantoms (liquid water, PMMA, and polystyrene). The fluence spectrum is converted to collision kerma to water and collision kerma to films by using the mass energyabsorption coefficients of water and active materials of the films, respectively. (27) Using the values of collision kerma to water and collision kerma to films, the numerator of Eq. (3) is obtained for the 60 Co, 137 Cs, 192 Ir, and 169 Yb sources. In the calculation of collision kerma to films, no film is present. We have assumed that the presence of the film does not affect the photon fluence spectrum and the collision kerma may be approximated to absorbed dose. In order to verify this, auxiliary simulations are carried out using the DOSRZnrc user code in which all the layers of the XRT film are modeled as cylinders. The active layer of the film is positioned at 1 cm along the transverse axis of the 169 Yb source. The height of the layers of the XRT film considered is 1 mm. In another similar simulation, the active layer of the film is positioned at 15 cm along the transverse axis of the 169 Yb source. The values of absorbed dose to active part of the XRT film obtained at 1 cm and 15 cm compare well to the values of collision kerma to the active part of XRT film obtained in the absence of the XRT film (agreement is within 0.2%).

C.3 Monte Carlo parameters and statistical uncertainties
The PEGS4 dataset needed for Monte Carlo calculations described above is based on the XCOM (28) compilations. We set AE = 0.521 MeV (kinetic energy of the electron is 0.01 MeV) and AP = 0.01 MeV while generating the PEGS4 dataset, where the parameters AE and AP are the low-energy thresholds for the production of knock-on electrons and secondary bremsstrahlung photons, respectively. All the calculations utilized the PRESTA-II step length and EXACT boundary crossing algorithms. In all calculations, electron range rejection technique is used to save computation time. We set ESAVE = 2 MeV for this purpose. The photon transport cut off energy PCUT is chosen at 10 keV in all calculations. In DOSRZnrc calculations, we set AE = ECUT = 0.521 MeV (10 keV kinetic energy). In the FLURZnrc calculations, electrons are not transported by setting electron transport cutoff parameter ECUT = 2 MeV (kinetic energy). Up to 10 9 photon histories are simulated. The 1 σ statistical uncertainties on the calculated DOSRZnrc-based dose values are generally within 0.3%. The 1 σ statistical uncertainties on the calculated FLURZnrc-based collision kerma values are less than 0.2%. The statistical uncertainties on the calculated values of R are less than 0.6%. Figure 1 presents the mass energy-absorption coefficient ratio of film to water for the investigated films as a function of photon energy (from 10 keV-1.25 MeV). Figure 2 presents the values of R as a function of photon energy (from 10 keV-1.25 MeV) for the investigated radiochromic films. Both figures are based on the mass energy-absorption coefficient data from Hubbell and Selzter. (27) Figure 3 presents the calculated values of R as a function of distance along the transverse axis of the 60 Co source in water phantom for the XRT and XRQA films. For the films other than XRT and XRQA, the value of R in water phantom is about unity and independent of distance for this source. The value of R increases from 1.027 to 1.845 for the XRT film and from 1.046 to 2.495 for the XRQA film when the distance is varied from 1 cm to 15 cm along the transverse axis of the 60 Co source (Fig. 3).

C.2 137 Cs brachytherapy source
For 137 Cs source, the value of R is constant and is close to unity (with in 3%) for all the films except for EBT2 (lot 020609), XRT, and XRQA films. Figure 4 presents the values of R as a function of distance along the transverse axis of the 137 Cs source in water phantom for EBT2 (lot 020609), XRT, and XRQA films. The value of R increases from 1.004 to 1.075 for the EBT2 (lot 020609) film, from 1.142 to 3.155 for the XRT film, and from 1.249 to 4.816 for XRQA film when the distance is varied from 1 cm to 15 cm.

C.3 192 Ir brachytherapy source
For 192 Ir source, the values of R are unity (within 1%) and are distance independent for the films EBT and EBT2 (lot03119). Figure 5 presents the values of R as a function of distance along the transverse axis of the source in water phantom for the 192 Ir source for the films, EBT2 (lot020609), XRT, XRQA, RTQA, and HS. The value of R increases from 1.017 to 1.169, 1.007 to 1.085, 1.586 to 5.761, and 2.035 to 9.437 for EBT2 (lot 020609), RTQA, XRT, and XRQA films, respectively, when the distance is varied from 1 cm to 15 cm along the transverse axis of the source. For the HS film, the value decreases from 0.997 to 0.954 in the above distance range.

C.4 169 Yb brachytherapy source
For 169 Yb source, the value of R is distant independent for the films EBT and EBT2 (lot 031109). For the EBT film, the value is about unity (within 1%) and about 1.040 for EBT2 (lot 031109). Figure 6 presents the values of R for the 169 Yb (model 4140) source as a function of distance along the transverse axis of the source in water phantom for the films, EBT2 (lot020609), XRT, XRQA, RTQA, and HS.

IV. dISCuSSIon
Z eff values of active materials the films and the fluence-weighted mean energy (hereafter referred to as mean energy) of photons in the phantoms play a role on the values of R. The mean energy calculated using the FLURZnrc (16) user code decreases as the distance along the transverse axis of the sources increases. For example, for the 60 Co source, the mean energy in water phantom decreases from 1.150 MeV to 0.520 MeV when the distance is increased from 1 to 15 cm. In this distance range, the mean energy decreases from 0. The energy degradation of photons in the PMMA and polystyrene phantoms is different when compared to the water phantom. This affects the values of R, and the change in R is significant for the XRT and XRQA films for the 60 Co, 137 Cs, and 192 Ir sources (see Results section D above). In the distance range of 1-15 cm, the mean energy decreases from 1. The values of R calculated in the present study are applicable along the transverse axis of the sources (1-15 cm). As the investigated sources exhibit anisotropy in the dose profiles, there is a possibility that the R values may exhibit angular dependence for some films, which is beyond the scope of present study.

V. ConCLuSIonS
Relative absorbed-dose energy response correction R for various radiochromic films in water phantom is calculated by the use of the Monte Carlo-based EGSnrc code system for high energy brachytherapy sources 60 Co, 137 Cs, 192 Ir, and 169 Yb. For 60 Co source, the value of R is about unity and is independent of distance in water phantom for the films other than XRT and XRQA. The XRT and XRQA films showed distance-dependent R values for this source. In the case of 137 Cs and 192 Ir sources, XRT, XRQA, EBT2 (lot 031109), and HS films showed distantdependent R values, and the rest showed no energy dependence. HS film showed R values less than unity by about 5%, whereas the other films showed R values higher than unity for these sources. In the case of 169 Yb source, the EBT film showed no energy dependence and EBT2 film (lot 031109) showed a distance-independent R value of 1.041. The rest showed distancedependent R values (increases with distance for the films other than HS). The solid phantoms, such as PMMA and polystyrene, enhance the R values for some film materials when compared the same in water phantom.