Monte Carlo modeling of 60 Co HDR brachytherapy source in water and in different solid water phantom materials

The reference medium for brachytherapy dose measurements is water. Accuracy of dose measurements of brachytherapy sources is critically dependent on precise measurement of the source–detector distance. A solid phantom can be precisely machined and hence source–detector distances can be accurately determined. In the present study, four different solid phantom materials such as polymethylmethacrylate (PMMA), polystyrene, Solid Water, and RW1 are modeled using the Monte Carlo methods to investigate the influence of phantom material on dose rate distributions of the new model of BEBIG 60 Co brachytherapy source. The calculated dose rate constant is 1.086 ± 0.06% cGy h − 1 U − 1 for water, PMMA, polystyrene, Solid Water, and RW1. The investigation suggests that the phantom materials RW1 and Solid Water represent water-equivalent up to 20 cm from the source. PMMA and polystyrene are water-equivalent up to 10 cm and 15 cm from the source, respectively, as the differences in the dose data obtained in these phantom materials are not significantly different from the corresponding data obtained in liquid water phantom. At a radial distance of 20 cm from the source, polystyrene overestimates the dose by 3% and PMMA underestimates it by about 8% when compared to the corresponding data obtained in water phantom.


Introduction
A high-dose-rate (HDR) 60 Co source is used for the treatment of gynecological cancers due to its longer half-life as compared with the more conventional 192 Ir source. [1][2][3] The AAPM (American Association of Physicists in Medicine) GEANT4-based Monte Carlo dosimetric parameters have been reported in the literature for the old and new designs of BEBIG 60 Co sources [1,2] using TG-43 protocol. [4,5] The accuracy in dosimetric measurement depends upon precise positioning of the detectors and maintaining correct distances between the source and detector. In order to achieve precision in the positioning of detectors, ease in machining in suitable designs, and convenience in handling, various Solid Water-equivalent phantoms are used. The accuracy in dosimetry data also depends upon the exact chemical composition of the solid materials and their radiation characteristics, i.e., attenuation and scattering in experimental measurement and cross-sectional data accuracy in Monte Carlo codes. There are many published dosimetric studies based on experimental and Monte Carlo methods for 125 I and 103 Pd brachytherapy sources in different phantom materials. [6][7][8][9][10] However, there is no such published data for the 60 Co HDR brachytherapy sources.
The objective of the present study is to investigate the influence of different solid phantom materials such as polymethylmethacrylate (common name: PMMA or Perspex or acrylic), polystyrene, Solid Water, and RW1 on dosimetric parameters of the new model of BEBIG 60 Co HDR source. We have employed the Monte Carlo-based MCNP code for this purpose. [11]

Radioactive source
The geometry of the new BEBIG 60 Co brachytherapy source [1] is slightly different from the old one. [2] The new BEBIG 60 Co source is composed of a cylindrical active core made of metallic 60 Co, with 3.5 mm of active length and an active diameter of 0.5 mm (0.6 mm was the active diameter of the old source), covered by a 0.15-mm thick 316L stainless steel capsule. Note that there is an air gap of 0.1 mm around the active 60 Co pellet. A schematic view of the new BEBIG 60 Co source is shown in Figure 1. The technical details of the source were obtained from the manufacturer.

Monte Carlo simulations
Monte Carlo-based MCNP code [11] is used for modeling of the BEBIG new 60 Co source in different Solid Water phantom materials, including liquid water. The material, mass density data, and geometric details of the new BEBIG 60 Co source needed for Monte Carlo modeling are taken from Granero et al. [1] Tables 1 and 2 present the material  description (density, composition, etc.) for the source and the investigated phantom materials, respectively.
In the Monte Carlo simulations, we have used 1.17 and 1.33 MeV gamma energy lines of 60 Co emission (yield: 2 photons/disintegration) in all calculations. The cutoff energy for photon transport in all calculations was 10 keV. Figure 1 shows the cross-sectional view of the new BEBIG 60 Co HDR source modeled in the Monte Carlo calculations. Also shown in this figure is the coordinate system used in the calculations. In the calculations, the origin coincided with the center of the active part of the sources [ Figure 1]. In the Monte Carlo calculations, the length of the stainless steel cable considered is 2 mm.

Air-kerma strength
To estimate the value of air-kerma strength, S k , the source was positioned at the center of a 5-m diameter air phantom. The photon fluence spectra at every 10 keV interval were scored along the transverse axis at y = 25, 50, 75, and 100 cm, using a point detector tally; this was subsequently converted into air-kerma per initial photon, k air (Gy/initial photon) using the mass-energy-absorption coefficient of air. [12] The k air (y) values were then converted to air-kerma rate per unit activity, (in cGy h −1 Bq −1 ). The value of S K is calculated using the linear equation fitting, i.e.,   where S k /A is S K per unit source activity A (in cGy cm 2 h −1 Bq −1 or U Bq −1 ) and b describes the build-up of scattered photons. The density of air is 1.2 × 10 −3 g cm −3 and the elemental composition of air corresponds to 40% humidity. This is consistent with the updated TG-43U1 formalism. [4] Water-kerma calculations in water and solid phantoms Due to the high energy of the 60 Co gamma source, electronic disequilibrium exists up to 1 cm from the source. [2] A significant difference in dose and kerma values (up to 20% at 2 mm), was observed at distances less than 5 mm. [3] In our calculations, we have ignored transport of secondary electrons. In our calculations, we have scored collision kerma and, in the presence of charged particle equilibrium, collision kerma may be approximated to the absorbed dose.

( )
Previous published studies suggest that spherical water phantom of 50-cm radius acts as an unbound phantom for BEBIG 60 Co sources up to a distance of 20 cm. [2,3] In order to calculate dose rate distribution in water as well as in solid phantom materials, the source was located in the center of a cylindrical phantom of 100-cm diameter and 100-cm height to get full scatter conditions up to a distance of 20 cm from the source. The density of water was taken 0.998 g cm −3 (at 22°C) as recommended in the TG-43 update. [4] A grid system was set up with cells defined as symmetrical rings around z-axis with rectangular cross-section δy − δz (δy = δz = 0.5 mm) in the y-z plane. Initially, photon energy fluence spectra were calculated as functions of Cartesian coordinates y and z (z is distance along source axis, y is distance away from the source) for all the investigated phantom materials. We used the F4 tallying feature of the MCNP code for this purpose. The photon spectrum at each position (y,z) was subsequently converted to collision kerma by using the mass-energy-absorption coefficients of water. [12] Using the collision kerma values scored in the phantom materials, dose rate constant (Λ) and radial dose function [ ) (r g L ] were calculated. We used the line sourcebased geometry function, This is consistent with the TG-43 update. [4] Depending upon the simulation, up to 5 × 10 7 primary photon histories are simulated. The simulations are run on a Dual-core CPU, 3.4 GHz machine. Depending upon the scoring regions positioned with respect to the origin of the coordinate system used, the 1 σ statistical uncertainties on collision kerma values vary between 0.04% and 2%.

Results and Discussion
Photon energy spectrum Figure 2 presents the normalized photon fluence spectra calculated for the BEBIG new HDR 60 Co source at 1 cm, 5 cm, and 20 cm along the transverse axis of the source in the spherical water phantom with dimensions of 100-cm radius. Also presented in Figure 2 is the spectrum obtained at 50 cm along the transverse axis of the source in a 500cm radius air and vacuum sphere. In the Monte Carlo calculations, the photon fluence spectra were scored in a 20 keV energy bin. The bin width at 60 Co energies, 1.17 MeV and 1.33 MeV, was chosen at 2 keV. The photon fluence in each energy bin was normalized to the total photon fluence. Figure 2 demonstrates the influence of the water medium on the photon fluence spectrum. As the distance increases, the relative fluence of low-energy photons increases due to multiple scattering of photons in the water medium.
Following is the analysis of the distribution of the energy spectrum of photons exiting the source capsule in a vacuum. The predominant mode of photon interaction at 60 Co energies (average energy = 1.25 MeV) is through Compton

Air-kerma strength and dose rate constant
The calculated value of S K /A for the BEBIG 60 Co source is found to be 3.04 × 10 −7 ± 0.05% cGy cm 2 h −1 Bq −1 . The source is also simulated at the center of a 5-m diameter vacuum sphere and the values of S k obtained is found to be same as that obtained in air. The radial dose function of BEBIG new HDR 60 Co source in water has been fi tted to a 3 rd order polynomial between r = 0.2 -20 cm. The co-effi cients obtained as a 0 = 1.0118, a 1 = −0.01225 cm −1 , a 2 = −3.39297 × 10 −4 cm −2 and a 3 = 3.9995 × 10 −6 cm −3 .      The value of Λ is 1.086 ± 0.06% cGy h −1 U −1 for water, PMMA, polystyrene, Solid Water, and RW1 phantom materials. This is in good agreement with GEANT Monte Carlo-based published value 1.087 ± 0.011 cGy h −1 U −1 in the water medium. [1] It has been shown by Papagiannis et al, [3] that Λ, for any source design of 60 Co, can be accurately determined using the corresponding point source-based dose rate constant, Λ point , (Λ point = 1.094 cGy h −1 U −1 ). The Λ of real source is dictated by the spatial distribution of radioactivity addressed by the exact geometry factor and, at 1 cm along transverse axis from the source, the line source based geometry factor may well be approximated to the exact geometry factor. The value of Λ obtained for the BEBIG 60 Co source, using the equation Λ = Λ point × G L (r = 1 cm, θ = 90°) is 1.083 cGy h −1 U −1 .

Radial dose function, g L (r)
The Monte Carlo calculated values of g L (r) for the new BEBIG 60 Co source are presented in Table 3 for water, PMMA, polystyrene, Solid Water, and RW1 phantom materials. In Figure 3, these g L (r) results are plotted vs radial distance, r. The values of g L (r) in water has been fitted to a third-order polynomial for r = 0.2 cm to 20 cm. The coefficients obtained as a 0 = 1.0118, a 1 = −0.01225 cm −1 , a 2 = −3.39297 × 10 −4 cm −2 , and a 3 = 3.9995 × 10 −6 cm −3 . The fitted values of g L (r) agree with the corresponding Monte Carlo calculated values obtained in the present work as well as with the published values. [1]

Dose variation in different phantoms
Tables 4-6 present dose rate distributions in the Cartesian format (in cGy h −1 U −1 ) around the BEBIG new 60 Co source in water, PMMA, and polystyrene phantom materials, respectively. The dosimetric data in RW1 and Solid Water is not presented because these two phantoms produced the same dose results as that of water. For radial distances up to 10 cm, PMMA is water-equivalent as PMMA underestimates dose by about only 3% at 10 cm. At radial distances 15 cm and 20 cm, PMMA underestimates the dose by about 5% and 8%, respectively. A similar comparison of dose values in the polystyrene phantom suggests that polystyrene is water-equivalent up to a radial distance of 10 cm from the source. At radial distances 15 cm and 20 cm, polystyrene overestimates the dose by less than 2% and 3%, respectively.

Conclusions
The dose rate per unit air-kerma strength around the new BEBIG HDR 60 Co source in water, PMMA, and polystyrene materials are calculated using the Monte Carlo methods. The investigation suggests that the phantom materials RW1 and Solid Water represent water-equivalent at all distances from the source. PMMA and polystyrene are water-equivalent up to 10 cm and 15 cm from the source, respectively, as the differences in the dose data obtained in these phantom materials are not significant when compared to the corresponding data in water. In general, all the investigated phantom materials are water-equivalent up to 10 cm from the source.