

ORIGINAL ARTICLE 



Year : 2013  Volume
: 38
 Issue : 4  Page : 158164 

Monte Carlobased investigation of waterequivalence of solid phantoms at ^{137} Cs energy
Ramkrushna S Vishwakarma, T Palani Selvam, Sridhar Sahoo, Subhalaxmi Mishra, Ghanshyam Chourasiya
Radiological Physics and Advisory Division, Health, Safety and Environment Group, Bhabha Atomic Research Centre, Anushaktinagar, Mumbai, Maharastra, India
Date of Submission  04Jun2013 
Date of Decision  31Jul2013 
Date of Acceptance  01Aug2013 
Date of Web Publication  11Nov2013 
Correspondence Address: Ramkrushna S Vishwakarma Radiological Physics and Advisory Division, Health, Safety and Environment Group, Bhabha Atomic Research Centre, Anushaktinagar, Mumbai  400 094, Maharastra India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/09716203.121192
Abstract   
Investigation of solid phantom materials such as solid water, virtual water, plastic water, RW1, polystyrene, and polymethylmethacrylate (PMMA) for their equivalence to liquid water at ^{137} Cs energy (photon energy of 662 keV) under full scatter conditions is carried out using the EGSnrc Monte Carlo code system. Monte Carlobased EGSnrc code system was used in the work to calculate distancedependent phantom scatter corrections. The study also includes separation of primary and scattered dose components. Monte Carlo simulations are carried out using primary particle histories up to 5 Χ 10 ^{9} to attain less than 0.3% statistical uncertainties in the estimation of dose. Water equivalence of various solid phantoms such as solid water, virtual water, RW1, PMMA, polystyrene, and plastic water materials are investigated at ^{137} Cs energy under full scatter conditions. The investigation reveals that solid water, virtual water, and RW1 phantoms are water equivalent up to 15 cm from the source. Phantom materials such as plastic water, PMMA, and polystyrene phantom materials are water equivalent up to 10 cm. At 15 cm from the source, the phantom scatter corrections are 1.035, 1.050, and 0.949 for the phantoms PMMA, plastic water, and polystyrene, respectively.
Keywords: Brachytherapy; Monte Carlo simulations; solid phantom
How to cite this article: Vishwakarma RS, Selvam T P, Sahoo S, Mishra S, Chourasiya G. Monte Carlobased investigation of waterequivalence of solid phantoms at ^{137} Cs energy. J Med Phys 2013;38:15864 
How to cite this URL: Vishwakarma RS, Selvam T P, Sahoo S, Mishra S, Chourasiya G. Monte Carlobased investigation of waterequivalence of solid phantoms at ^{137} Cs energy. J Med Phys [serial online] 2013 [cited 2019 Aug 25];38:15864. Available from: http://www.jmp.org.in/text.asp?2013/38/4/158/121192 
Introduction   
Brachytherapy refers to a method of treatment in which sealed radioactive sources are used to deliver radiation at short distances by interstitial, intracavitary, or surface mould applications. Brachytherapy delivers a high dose in the tumor and an acceptable low dose to surrounding normal tissue due to rapid dose falloff with distance. American Association of Physicists in Medicine (AAPM) Task Group reports, AAPM TG43 ^{[1]} and TG43U1 ^{[2]} recommend water as a reference medium for dosimetry of interstitial brachytherapy sources. Due to high dose gradients near brachytherapy sources and specification of the dose parameters within few centimetres of the source, sourcedetector distance should be specified very accurately for dosimetric measurements. Precise positioning of detectors, reproducibility of source and detectors in reference liquid water medium, and water proofing of detectors poses a practical problem. Solid phantom materials can be easily machined, to accommodate the source and detectors in a precise geometrical configuration, facilitating an accurate measurement and reproducibility in sourcedetector geometry.
Suitable solid phantom material should be selected to mimic the absorption and scattering of radiation as that in liquid water. ^{[3]} Constantinou et al., ^{[4]} had studied the radiation characteristic of solid water, polystyrene, and lucite [polymethylmethacrylate (PMMA)] in the energy range 0.01100 MeV for radiotherapy xray and gamma ray beam calibration and found that solid water is superior to the polystyrene and lucite phantom materials. Sahoo et al., ^{[5]} investigated water equivalence of various solid phantom materials for ^{60} Co brachytherapy source using the Monte Carlo methods. The authors concluded that the phantom materials RW1 and solid water represent water equivalent up to 20 cm from the source. Whereas, PMMA and polystyrene are water equivalent up to 10 and 15 cm from the source, respectively.
Meli et al., ^{[6]} studied dosimetric characteristics of solid water, polystyrene, and PMMA phantom materials using experimental and Monte Carlo methods in a bounded phantom material for ^{192} Ir brachytherapy source. The authors concluded that, under full scatter conditions, PMMA, polystyrene, and solid water are equivalent to water up to 10 cm distance. They also concluded that PMMA is not a suitable phantom material in the absence of full scatter, whereas polystyrene and solid water are suitable phantom materials even in the absence of full scatter. Tedgren and Carlsson ^{[7]} also studied the influence of PMMA, solid water, and polystyrene phantom material and dimensions on ^{192} Ir source dosimetry. The authors concluded that water equivalence at a specified distance from the source depends not only on the size of the plastic phantom but also on the size of the water phantom used for comparison. Compared to equally sized water phantoms, polystyrene is less water equivalent than PMMA and solid water, but compared to larger water phantoms, polystyrene is most water equivalent. Water equivalence of solid phantom materials for ^{125} I brachytherapy source was studied by Meigooni et al. ^{[8]} Dosimetric study for solid phantom material for ^{125} I and ^{103} Pd energies was studied by Meigooni et al., ^{[9]} Luxton, ^{[10]} and Reniers et al. ^{[11]}
To our knowledge, limited information is available on phantom scatter corrections at the ^{137} Cs energy. The study by PιrezCalatyud et al., ^{[12]} is only limited to comparison of Monte Carlobased dose distributions in a PMMA phantom to thermoluminescent dosimeter TLDbased measurements in a PMMA phantom. Meigooni et al., ^{[13]} studied the dosimetric properties of plastic water and solid water for photon energies in the range 20 keV ^{60} Co including 662 keV using the Monte Carlo methods. The authors presented ratio of dose rate in medium to water only up to a distance of 5 cm for 662 keV photons.
The objective of the present study is to examine water equivalence of several solid phantom materials such as solid water ^{TM} (Gammex RMI, USA), virtual water ^{TM} (MEDCAL, Inc., Wisconsin, USA), plastic water ^{TM} (Computerized Imaging Reference Systems, Inc., Virginia, USA), PMMA, polystyrene, and RW1 ^{TM} (PTWFreiburg) ^{[13]} at the ^{137} Cs energy. The study also includes separation of primary and scatter components of absorbed dose to water. We have used EGSnrcbased Monte Carlo system for this purpose. ^{[14]}
Materials and Methods   
Phantom materials
The atomic composition and density of the investigated phantom materials are given in [Table 1]. The electron density (ρ_{e} ) of a phantom material was calculated from its mass density (ρ_{m} ) and atomic composition according to equation 1 as presented by Shrimpton in his publication ^{[15]} as below:  Table 1: Elemental composition, mass fraction, mass density, < Z/A >, and average atomic number of water and solid phantom materials
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Where, a _{1} , a _{2} , a _{3} , ....a _{n} are the fractional contributions of each element to the total number of electrons in the mixture. Z _{1} , Z _{2} , ... Z _{n} are the atomic number of each element.
The elemental composition of phantom materials for Monte Carlo simulation should be considered carefully. Meigooni et al., ^{[9]} have indicated that the discrepancies in phantom material composition can significantly affect the conversion factors estimated for water equivalent phantom materials used in low energy brachytherapy sources. In present study, the atomic composition and density of solid water was adapted from the work of Meigooni et al. ^{[9]} The composition and density of water, PMMA, and polystyrene are adapted from work of Hubbell and Seltzer. ^{[17]} Similarly, the composition and density details of RW1, plastic water, and virtual water are adapted from ICRU44 ^{3} , Meigooni et al., ^{[13]} and Reniers et al., ^{[11]} respectively. [Table 2] presents the values of linear attenuation coefficient and meanfree path in different phantom materials at ^{137} Cs energy (0.662 MeV). These data are adapted from Hubbell and Seltzer compilations. ^{[17]}  Table 2: Linear attenuation coefficient μ(cm^{1}) and mean free path τ (cm) of 0.662 MeV photon for water and solid phantom materials
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Analysis of photon interaction crosssection
[Figure 1] shows the ratio of mass attenuation coefficient of solid phantom materials to that of liquid water, (μ/ρ) _{Phant} /(μ/ρ) _{Wat} as a function of photon energy, where the suffice "Phant" refers to phantom material other than water. The values of mass attenuation coefficient of solid water, virtual water, and RW1 are comparable to that of water for photons in the energy range 15 keV1.5 MeV (maximum deviation is less than about 3%). For PMMA and polystyrene, for photon energies less than 100 keV, (μ/ρ) _{Phant} value is less compared with (μ/ρ) _{Water} . For plastic water, the (μ/ρ) _{Phant} value is significantly higher than that of water for photon energies below 100 keV. Above 100 keV, the (μ/ρ) _{Phant} values of PMMA, polystyrene and plastic water are comparable within 3% when compared with that of liquid water.  Figure 1: Ratio of massattenuation coefficient of solid phantoms to liquid water presented as a function of photon energy
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Contribution of photoelectric effect and Compton scattering (CS) to total mass attenuation coefficient was studied by using the stateofthe art XCOM ^{[18]} photon interaction data set. The ratio of photoelectric crosssection to the total crosssection of the phantom material (σ_{PE, Phant} /σ_{Tot,Phant} ) is presented in [Figure 2]. As seen from the figure, the ratio σ_{PE,Phant} /σ_{Tot,Phant} for photons in the energy range 10200 keV in solid water, virtual water, and RW1 is comparable to that of water. In phantom material having smaller Z _{eff} such as polystyrene (Z _{eff} = 5.70) and PMMA (Z _{eff} = 6.47) as compared with water (Z _{eff} = 7.42), the contribution of photoelectric effect to total interaction crosssection in material is less than that of water. Whereas, for the materials with Z _{eff} values more than that of water, such as Plastic Water (Z _{eff} = 9.37), larger contribution of photoelectric effect to the total crosssection of the phantom material is observed.  Figure 2: Ratio of photoelectric crosssection to total crosssection presented for water and solid phantoms as a function of photon energy
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The ratio of CS crosssection to the total crosssection of phantom material (σ_{CS,Phant} /σ_{Tot,Phant} ) as a function of photon energy is shown in [Figure 3]. This ratio for Solid Water, Virtual Water and RW1 are comparable to that of water. Polystyrene and PMMA show more contribution of CS to the total crosssection as compared to that of water. For plastic water, the contribution of CS to total crosssection is less than that of water for photon energies less than 200 keV.  Figure 3: Ratio of Compton scattering crosssection to total crosssection presented for water and solid phantoms as a function of photon energy
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Monte Carlo calculations
In the Monte Carlo calculations, the absorbed dose to water is scored for radial distances r = 115 cm in the liquid water and solid phantom materials in spherical shells of thickness 0.1 mm using the EGSnrcMPbased ^{[14]} EDKnrc ^{[19]} user code. In the case of solid phantom materials, the 0.1 mm thick spherical scoring region was filled with water. The radius of the material phantom is 50 cm, which provides full scatter up to 20 cm. This approach is based on the study of Granero et al., ^{[20]} on the impact of phantom size and shape in brachytherapy dosimetry and PeérezCalatayud et al., ^{[21]} that a spherical phantom 40 cm in radius mimics an unbounded phantom for ^{137} Cs for full scatter conditions within 1% for distances less than 20 cm from the source. The density of water considered is 0.998 g/cm ^{3} at 22°C. ^{[2]} For Monte Carlo calculations, we have considered only 662 keV gamma energy of ^{137} Cs emission (yield of 662 keV: 0.851 photon/disintegration. ^{[22]} In the Monte Carlo calculations, we ignored xrays from ^{137} Ba, as in a previously published study by Selvam et al., ^{[23]} it was demonstrated that these xrays were not important.
We have also calculated phantom scatter corrections for the PMMA phantom for the commercial ^{137} Cs source of Radiation Therapy Resources Inc., Valencia, CA (RTR) ^{[24]} to compare with the point sourcebased phantom corrections. For simulation of ^{137} Cs RTR brachytherapy source, we have used the FLURZnrc user code. ^{[19]} The phantom dimensions considered are 50 cm diameter × 50 cm height. In the calculations photon fluence spectrum was initially scored which was subsequently converted to waterkerma by using the massenergyabsorption coefficients of water from Hubbell and Setlzer. ^{[17]}
Monte Carlo parameters and statistical uncertainties
The PEGS4 data set needed for the Monte Carlo calculations is based on widely used XCOM compilations. ^{[18]} The lowenergy threshold for the production of knockon electrons (AE) is set to 521 keV for an electron with 10 keV kinetic energy, and the threshold for secondary bremsstrahlung photons (AP) is set to 10 keV.
All Monte Carlo simulations utilized the PRESTAII electron step length and EXACT boundarycrossing algorithms. The electron step size parameter, ESTEP is set to 0.25. To increase the speed of the calculations, for all simulations, electron range rejection technique is used by setting ESAVE = 2 MeV. The value of photon transport cutoff parameter PCUT used in all simulations is 10 keV. The value of ECUT used in EDKnrc and FLURZnrc calculations is 2 MeV. This means detailed electron transport is not necessary as waterkerma may be approximated to absorbed dose at ^{137} Cs energy.
Up to 5 × 10 ^{9} primary photon histories are simulated. The statistical uncertainties on the calculated estimates have a coverage factor k = 1. Uncertainties on the dose values from the EDKnrc simulations are less than 0.3%.
Results and Discussion   
Reference dose rates
[Table 3] compares dose rate per unit activity (cGy h ^{1} mCi ^{1} ) in liquid water phantom at 1 cm from the ^{137} Cs point isotropic source calculated in the present study against Melhus and Rivard. ^{[25]} The dose rate values calculated by including Barium xrays compare well.  Table 3: Dose rate per unit activity (cGy h^{1} mCi^{1}) in the liquid water phantom at 1 cm for the ^{137}Cs point source
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Analysis of dose components
The primary component of waterkerma at a radial distance r (in Gy/photon) due to a monoenergetic point photon source is given by:
where, k is the unit conversion constant from MeV/g to J/kg, μ_{phant} (E) is the linear attenuation coefficient of the phantom material at photon energy E, and [μ_{en }/ρ(E)] _{w} is massenergyabsorptioncoefficient of water at E. For ^{137} Cs source, E = 0.662 MeV.
[Figure 4] presents the ratio of primary component of waterkerma in a solid phantom material to that in liquid water as a function of r from the ^{137} Cs point source (calculated using equation (3)). Deviation of this ratio from unity is due to differences in the values of linear attenuation coefficients of the phantom materials (difference is up to 18% at 15 cm for PMMA).  Figure 4: Ratio of primary component of dose in solid phantoms to that in liquid water phantom presented as a function of radial distance r from ^{137}Cs point source
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The scatter component of the absorbed dose, D _{s} (r) was obtained by subtracting D _{p} (r) from the EDKnrccalculated total dose. The scattertoprimary ratio D _{s} (r)/D _{p} (r) helps in understanding the differences in the scattering of photons in different phantom materials. This ratio is plotted in [Figure 5] for the investigated phantom materials. Although the absolute values of D _{s} (r) decrease with r, the ratio D _{s} (r)/Dp (r) increases because of the inverse square fall of Dp (r). [Table 4] presents the distance at which Ds (r) equals Dp (r) for the investigated phantom materials. [Figure 6] presents dose per unit energy multiplied by 4πr^{2} per source photon as a function of r from the ^{137} Cs point source.  Table 4: Distance (in cm) from the ^{137}Cs point source at which scatter to primary ratio, D_{s}(r)/D_{P}(r) is unity for water and solid phantom materials
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 Figure 5: Ratio of scattertoprimary component of absorbed dose in water and solid phantoms as a function of radial distance r from ^{137}Cs point source
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 Figure 6: The dependence of primary, scattered, and total dose in water multiplied by 4πr^{2} per unit mean energy versus radial distance r from ^{137}Cs point source in water
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Phantom scatter correction factor
The measurementbased absorbed dose to water in solid water phantoms is required to be corrected for differences in attenuation and scattering between solid phantom materials and liquid water to obtain absorbed dose to water in liquid water phantom. The distancedependent phantom scatter correction K(r) is given below:
[Table 5] presents the values of K(r) for select distances of r = 5 cm, 10 cm, and 15 cm from the source in solid phantom materials. The statistical uncertainty in the calculated phantom scatter corrections is less than 0.4%. The values of K(r) calculated for PMMA phantom based on the point source compare within 0.5% with that of the ^{137} Cs RTR brachytherapy for distances up to 15 cm from the source. [Figure 7] represents phantom scatter correction K(r) for solid phantoms as a function of radial distance r from ^{137} Cs point source. At 5 cm from the source, all the investigated phantoms are waterequivalent. This observation is consistent with the study carried by Meigooni, et al., ^{[13]} for the solid water and plastic water phantoms. Solid water, virtual water, and RW1 are suitable phantom materials for the dosimetry up to a distance of 15 cm from the source. Phantom materials such as plastic water, PMMA and polystyrene phantom materials are waterequivalent for distances up to 10 cm. At 15 cm, the phantom scatter corrections are 1.035, 1.050, and 0.949 for the phantoms PMMA, plastic water, and polystyrene, respectively.  Table 5: Phantom scatter corrections for solid phantom materials at distances of 5, 10, and 15 cm from the ^{137}Cs point source
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 Figure 7: The phantom scatter correction K(r) for solid phantoms as a function of radial distance r from ^{137}Cs point source
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Conclusion   
Water equivalence of solid phantoms such as solid water, virtual water, RW1, PMMA, polystyrene, and plastic water materials are investigated at ^{137} Cs energy for distances up to 15 cm from the source. The Monte Carlobased investigation suggests that the phantom materials such as virtual water, RW1, and solid water are water equivalent up to 15 cm from the source. Polystyrene phantom demonstrates that the corrections are always smaller than unity and the deviation from unity is larger as the distance from the source increases. For example, the corrections at 10 and 15 cm for this phantom are about 2.5% and 5% smaller than unity, respectively. For PMMA phantom the phantom scatter correction is less 1% for distances up to 8 cm and it increases to about 3.4% at 15 cm. The corrections for the plastic phantom are about 2.5% and 5% larger than unity at distances 10 and 15 cm, respectively. The corrections obtained for the phantoms virtual water and solid water are comparable at all distances. The investigation demonstrates the importance of evaluation of water equivalence of a solid phantom material prior to its use in dosimetric measurements.
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[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7]
[Table 1], [Table 2], [Table 3], [Table 4], [Table 5]
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