
ORIGINAL ARTICLE 



Year : 2010  Volume
: 35
 Issue : 1  Page : 1522 

Monte Carlo modeling of ^{ 60} Co HDR brachytherapy source in water and in different solid water phantom materials
S Sahoo, T Palani Selvam, RS Vishwakarma, G Chourasiya
Radiological Physics and Advisory Division, Health Safety, and Environment Group, Bhabha Atomic Research Centre, Mumbai  400 094, India
Date of Submission  28Aug2009 
Date of Decision  01Oct2009 
Date of Acceptance  15Oct2009 
Date of Web Publication  7Jan2010 
Correspondence Address: S Sahoo Room204, CTCRS Building, Bhabha Atomic Research Centre, Anushaktinagar, Mumbai400 094 India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/09716203.58779
Abstract   
The reference medium for brachytherapy dose measurements is water. Accuracy of dose measurements of brachytherapy sources is critically dependent on precise measurement of the sourcedetector distance. A solid phantom can be precisely machined and hence sourcedetector 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 waterequivalent up to 20 cm from the source. PMMA and polystyrene are waterequivalent 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.
Keywords: Brachytherapy, Cobalt60, highdoserate, Monte Carlo simulation, solid phantom
How to cite this article: Sahoo S, Selvam T P, Vishwakarma R S, Chourasiya G. Monte Carlo modeling of ^{ 60} Co HDR brachytherapy source in water and in different solid water phantom materials. J Med Phys 2010;35:1522 
How to cite this URL: Sahoo S, Selvam T P, Vishwakarma R S, Chourasiya G. Monte Carlo modeling of ^{ 60} Co HDR brachytherapy source in water and in different solid water phantom materials. J Med Phys [serial online] 2010 [cited 2019 Nov 21];35:1522. Available from: http://www.jmp.org.in/text.asp?2010/35/1/15/58779 
Introduction   
A highdoserate (HDR) ^{ 60} Co source is used for the treatment of gynecological cancers due to its longer halflife as compared with the more conventional ^{ 192} Ir source.^{[1],[2],[3]} The AAPM (American Association of Physicists in Medicine) GEANT4based Monte Carlo dosimetric parameters have been reported in the literature for the old and new designs of BEBIG ^{ 60} Co sources^{ [1],[2] } using TG43 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 Waterequivalent 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 crosssectional 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 Carlobased MCNP code for this purpose.^{ [11]}
Materials and Methods   
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 0.15mm 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 Carlobased 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]} [Table 1] and [Table 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 crosssectional 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.
Airkerma strength   
To estimate the value of airkerma strength, S_{ k} , the source was positioned at the center of a 5m 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 airkerma per initial photon, k_{ air} (Gy/initial photon) using the massenergyabsorption coefficient of air. ^{[12]} The k_{ air} (y) values were then converted to airkerma 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 buildup of scattered photons. The density of air is 1.2 Χ 10^{−3 } g cm^{−3} and the elemental composition of air corresponds to 40% humidity. This is consistent with the updated TG43U1 formalism.^{ [4]}
Waterkerma 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 50cm 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 100cm diameter and 100cm 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 TG43 update.^{ [4]}
A grid system was set up with cells defined as symmetrical rings around zaxis with rectangular crosssection δy − δz (δy = δz = 0.5 mm) in the yz 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 massenergyabsorption coefficients of water. ^{[12]} Using the collision kerma values scored in the phantom materials, dose rate constant (Λ) and radial dose function [g_{L}(r)] were calculated. We used the line sourcebased geometry function, G_{L}(r,θ), for calculating g_{L}(r). This is consistent with the TG43 update.^{ [4]}
Depending upon the simulation, up to 5 Χ 10^{ 7 } primary photon histories are simulated. The simulations are run on a Dualcore 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 100cm 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 lowenergy 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 scattering. In normal circumstances, all scattering angles will occur in the detector, yielding a continuum of scattered photons with energies ranging from 1.25 MeV down to the minimum possible energy, , which occurs when an incident photon is backscattered through an angle of 180°; this is given by , where hv is the energy of the incident primary photon, , and m_{ o} c^{ 2} is the rest mass energy of the electron (511 keV). For a primary photon of energy 1.25 MeV, the is 212 keV, which is consistent with [Figure 2], with the dropoff in the number of photons below the 210 keV energy bin.
Airkerma strength and dose rate constant
The calculated value of S_{ K} /A_{ } for the BEBIG ^{ 60} Co source is found to be 3.04 Χ 10^{−7 }± 0.05% cGy cm^{ 2 } h^{−1 } Bq^{−1} . The source is also simulated at the center of a 5m diameter vacuum sphere and the values of S_{ k} obtained is found to be same as that obtained in air.
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 Carlobased 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 sourcebased 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 }Χ 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 thirdorder 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 Χ 10^{−4} cm^{−2} ,^{ } and a_{ 3 } = 3.9995 Χ 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
[Table 4],[Table 5],[Table 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 waterequivalent 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 waterequivalent 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 airkerma 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 waterequivalent at all distances from the source. PMMA and polystyrene are waterequivalent 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 waterequivalent up to 10 cm from the source.
Acknowledgments   
The authors are grateful to Dr. Y. S. Mayya, Head, Radiological Physics and Advisory Division, Bhabha Atomic Research Centre (BARC), and Shri H. S. Kushwaha, Director, Health, Safety, and Environment Group, BARC, for their constant encouragement throughout the project.
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[Figure 1], [Figure 2], [Figure 3]
[Table 1], [Table 2], [Table 3], [Table 4], [Table 5], [Table 6]
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