

ORIGINAL ARTICLE 



Year : 2014  Volume
: 39
 Issue : 1  Page : 49 

Monte Carlobased revised values of dose rate constants at discrete photon energies
T Palani Selvam, Vandana Shrivastava, Ghanashyam Chourasiya, D. Appala Raju Babu
Radiological Physics and Advisory Division, Bhabha Atomic Research Centre, Health Safety and Environmental Group, Anushakti Nagar, Mumbai, Maharashtra, India
Date of Submission  07Aug2013 
Date of Decision  03Dec2013 
Date of Acceptance  04Dec2013 
Date of Web Publication  20Jan2014 
Correspondence Address: Vandana Shrivastava Radiological Physics and Advisory Division, Bhabha Atomic Research Centre, CT and CRS Building, Anushakti Nagar 400 094, Mumbai, Maharashtra India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/09716203.125473
Abstract   
Absorbed dose rate to water at 0.2 cm and 1 cm due to a point isotropic photon source as a function of photon energy is calculated using the EDKnrc usercode of the EGSnrc Monte Carlo system. This code system utilized widely used XCOM photon crosssection dataset for the calculation of absorbed dose to water. Using the above dose rates, dose rate constants are calculated. Airkerma strength S _{k} needed for deriving dose rate constant is based on the massenergy absorption coefficient compilations of Hubbell and Seltzer published in the year 1995. A comparison of absorbed dose rates in water at the above distances to the published values reflects the differences in photon crosssection dataset in the lowenergy region (difference is up to 2% in dose rate values at 1 cm in the energy range 3050 keV and up to 4% at 0.2 cm at 30 keV). A maximum difference of about 8% is observed in the dose rate value at 0.2 cm at 1.75 MeV when compared to the published value. S _{k} calculations based on the compilation of Hubbell and Seltzer show a difference of up to 2.5% in the lowenergy region (2050 keV) when compared to the published values. The deviations observed in the values of dose rate and S _{k} affect the values of dose rate constants up to 3%.
Keywords: Absorbed dose rate, airkerma strength, brachytherapy, dose rate constant, TG43
How to cite this article: Selvam T P, Shrivastava V, Chourasiya G, Babu DR. Monte Carlobased revised values of dose rate constants at discrete photon energies. J Med Phys 2014;39:49 
How to cite this URL: Selvam T P, Shrivastava V, Chourasiya G, Babu DR. Monte Carlobased revised values of dose rate constants at discrete photon energies. J Med Phys [serial online] 2014 [cited 2019 Apr 20];39:49. Available from: http://www.jmp.org.in/text.asp?2014/39/1/4/125473 
Introduction   
Brachytherapy is one of the most popular modes of treatment due to its advantage of highly localized tumour dose delivery and at the same time sparing of normal tissues because of rapid dose fall off at various distances from the source. Dose rate constant Λ is one of the key parameters of the dose calculation protocol. ^{[1],[2]} According to AAPM (American Association of Physicists in Medicine) Task Group (TG) 43 and TG43U1, ^{[1],[2]} the dose rate constant is defined as the dose rate to water at a distance of 1 cm on the transverse axis of a unit airkerma strength source in a water phantom. This constant includes the effect of source geometry, the spatial distribution of radioactivity within the source, encapsulation and selffiltration within the source, and scattering in water surrounding the source. In case of intravascular brachytherapy, the distances of interest are much smaller than the conventional brachytherapy reference distance of 1 cm. According to AAPM TG60, ^{[3]} the dose rate constant is defined as the dose rate at a reference distance of 2 mm in water from a source of unit airkerma strength. Luxton and Gabor ^{[4]} calculated the absorbed dose rate to water as a function of distance from monoenergetic point photon sources in a unit density water phantom using the EGS4 Monte Carlo code system. ^{[5]} In their work, airkerma strength S _{k} per unit photon from an isotropic point photon source is obtained as a function of energy using the massenergy absorption coefficient of air published by Hubbell ^{[6]} in the year 1982. The revised data of massenergy absorption coefficients were published by Hubbell and Seltzer ^{[7]} in the year 1995. Using the values of dose rate at 1 cm from the source in water phantom and S _{k}, Luxton and Gabor ^{[4]} calculated Λ as a function of photon energy. Chen and Nath ^{[8]} investigated the general properties of Λ and developed a simple analytical tool to calculate Λ. Selvam et al.^{[9]} published the values of Λ from a point monoenergetic photon source as a function of photon energy (20 keV1 MeV). The authors used Monte Carlobased MCNP code (version 3.1) ^{[10]} which is not capable of transporting secondary electrons produced by the photons.
DeMarco et al., ^{[11]} in their Monte Carlo study using the MCNP4C code, ^{[12]} emphasized that the photon crosssection dataset has to be updated to a modern tabulation such as DLC146 or XCOM while simulating photons in the energy range 20100 keV in materials of low atomic number such as water. Because, differences of up to 10% are observed in the photoelectric cross section for water at 30 keV between the standard MCNP crosssection dataset (DLC200) and the most recent XCOM or NIST (National Institute of Standards and Technology) tabulation.
The aim of this work is to calculate the dose rate to water and Λ at 0.2 cm and 1 cm distances from an isotropic point photon source as a function of photon energy (20 keV2 MeV) and compare the same with the published values. The Monte Carlo calculations are carried out using the EGSnrc code system ^{[13],[14]} which utilizes the widely used XCOM photon crosssection dataset. ^{[15]} The study also includes comparison of published values of S _{k} by Luxton and Gabor ^{[4]} against the values based on massenergy absorption coefficient of air by Hubbell and Seltzer. ^{[7]}
Materials and Methods   
Calculation of S _{k}
According to TG43U1 ^{[1],[2]} formalism, S _{k} is defined as airkerma rate at the point along the transverse axis of the source in free space. In this study, the general formula proposed by Luxton and Gabor ^{[4]} is used to calculate S _{k} (μGy m ^{2} /h) as a function of energy E (keV) for a point source of activity A (MBq).
coefficient (m ^{2} /kg) of air and C = 0.5768 μGy kg/h/keV/MBq. The point source is in vacuum, and therefore, exponential attenuation and scattering by air is not required.
Monte Carlo calculations
In the present study, point photon source is positioned at the center of the water sphere of diameter 1 m for energy below 500 keV and 1.3 m for energy of 500 keV and above. The dimensions of the water phantom considered are consistent with the approach adopted by Luxton and Gabor. ^{[4]} The absorbed dose rate per photon is scored in spherical shell of water of thickness 0.1 mm centered at distances of 0.2 cm and 1 cm from the point source. Density of water is taken as 0.998 g/cm ^{3} . The Monte Carlobased usercode EDKnrc of the EGSnrc ^{[14]} code system is used for this purpose. The PEGS4 dataset needed for Monte Carlo calculations described above is based on XCOM ^{[15]} compilations. We set AE = 0.512 MeV (1 keV kinetic energy) and AP = 0.001 MeV while generating the PEGS4 dataset, where the parameters AE and AP are the lowenergy thresholds for the production of knockon electrons and secondary bremsstrahlung photons, respectively. All the calculations utilized the PRESTAII 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 cutoff energy, PCUT, is chosen at 1 keV in all calculations. In EDKnrc calculations, we set AE = ECUT = 0.512 MeV (1 keV kinetic energy). We included bound Compton scattering and Rayleigh scattering in the calculations. Up to 10 ^{8} photon histories are simulated. Depending upon the photon energy, the 1ó statistical uncertainties on the calculated EDKnrcbased dose values are generally in the range 0.10.4%.
Calculation of Λ
Using the absorbed dose rate values at 1 cm and 0.2 cm from the point sources, dose rate constants at these distances are calculated as a function of photon energy E as below.
Results and Discussion   
Dose rate
[Table 1] compares the values of absorbed dose rate to water per disintegration at 1 cm from the source times square of the distance from the source (nGy cm ^{2} /h/Bq) calculated using the EDKnrc and those published by Luxton and Gabor. ^{[4]} The comparison shows that the values calculated in the present study are higher by about 2% than the published values in the energy range 3050 keV. This difference is due to the most recent XCOM/NIST crosssection dataset used in the EDKnrcbased calculations. In the rest of energy region, the agreement is within 0.5%.  Table 1: Comparison of absorbed dose rate to water per disintegration at 1 cm times square of the distance (nGy cm2/h/Bq) due to a point isotropic photon source in liquid water
Click here to view 
[Table 2] compares the values of absorbed dose rate to water per disintegration at 0.2 cm from the source times square of the distance from the source (nGy cm ^{2} /h/Bq) calculated using the EDKnrc and those published by Luxton and Gabor ^{[4]} and Selvam et al.^{[9]} The comparison (see column 5) against the values published by Selvam et al.^{[9]} shows about 4% difference at high energies (800 and 1000 keV). This is due to the fact that MCNP (version 3.1) ^{[10]} calculations did not include detailed electron transport and, therefore, collision kerma was approximated to the absorbed dose. Auxiliary simulations by setting ECUT = 2 MeV in the EDKnrc usercode produced comparable dose rate values at photon energies E = 600, 800, and 1000 keV against the values reported by Selvam et al.^{[9]} Note that calculation using ECUT = 2 MeV in the EDKnrc usercode is equivalent to scoring waterkerma, as the secondary electrons will deposit their energy where they are generated. The last column of [Table 2] shows the comparison of dose rate values calculated in the present study and those by Luxton and Gabor. ^{[4]} The differences are significant at both lowenergy and highenergy regions. In the lowenergy region, the difference is up to 4% (at 30 keV). In the highenergy region, the difference is between 2% and 8% (8% at 1750 keV). At 2 MeV, the comparison is within about 1%.  Table 2: Comparison of absorbed dose rate to water per disintegration at 0.2 cm times square of the distance (nGy cm2/h/Bq) due to a point isotropic photon source in liquid water
Click here to view 
Airkerma strength
[Table 3] compares the values of S _{k} calculated in the present study against the values published by Luxton and Gabor. ^{[4]} In lower energy range (up to 60 keV), the variation in the S _{k} is about 2%. This difference is because the calculation of S _{k} by Luxton and Gabor ^{[4]} was based on massenergy absorption coefficient of air published by Hubbell ^{[6]} in 1982, whereas the present study utilized the massenergy absorption coefficient of air published by Hubbell and Seltzer ^{[7]} in 1995.  Table 3: Comparison of airkerma strength Sk per Bq (nGy cm2/h/Bq) (1 Bq=1 photon/s)
Click here to view 
Dose rate constant
Note that the differences in the values of absorbed dose to water and S _{k} as discussed above will directly affect the value of Λ. [Table 4] compares the values of Λ in the present work against the values published by Luxton and Gabor ^{[4]} and Chen and Nath. ^{[8]} Λ is based on dose rate to water at 1 cm from a point isotropic photon source. The values reported by Luxton and Gabor ^{[4]} show agreement at all energies except at 20 keV where the overestimation is 2.4%. This is because the dose rate values at 1 cm and S _{k} obtained in the present study are higher by 2% in the energy range 3050 keV when compared to the corresponding values reported by Luxton and Gabor. ^{[4]} Hence, there is no variation in the Λ values. Whereas at 20 keV, the dose rates at 1 cm compare well [Table 1], and hence, a difference of about 2% in the Λ value is observed.
The analytical calculation of Λ by Chen and Nath ^{[8]} utilized the Monte Carlobased energy absorption buildup factors reported by Angeloupos et al.^{[16]} These buildup factors may not be accurate in the lowenergy region as the calculations were based on old crosssection dataset. Hence, the values of Λ calculated in the present study are higher in the lower energy region (higher by about 3% at 50 and 60 keV).
[Table 5] compares the values of Λ in the present work against those published by Selvam et al.^{[9]} and Luxton and Gabor. ^{[4]} Λ is based on dose rate to water at 0.2 cm from a point isotropic photon source. The differences in the values reflect the differences observed in the dose rate values, as the present study and the work by Selvam et al.^{[9]} utilized the same massenergy absorption coefficient of air. ^{[7]} Differences shown in the last column of the [Table 5] (present work vs. Luxton and Gabor ^{[4]} ) reflect the combined effect of differences observed in the dose rate values [Table 2] and the different dataset used for calculating S _{k}. Dose rate calculations using ECUT = 2 MeV in the EDKnrc produced Λ values of 27.64, 27.81, and 27.73 cGy cm ^{2} /h at photon energies E = 600, 800, and 1000 keV, respectively, which compare well with the corresponding values reported by Selvam et al. ^{[9]}
Conclusion   
EDKnrcbased calculations show that dose rate values in water at 1 cm from the point photon sources are higher by about 2% than the published values in the energy range 3050 keV. This difference is attributed to the most recent XCOM/NIST crosssection dataset used in the EDKnrc calculations. Regarding dose rate values at 0.2 cm from the source, the differences are significant at both lowenergy and highenergy regions when compared to the published values. In the lowenergy region, the difference is up to 4% (at 30 keV) and at 1.75 MeV, the difference is about 8%. The study suggests that the recent compilation of massenergy absorption coefficient of air by Hubbell and Seltzer ^{[7]} is important for airkerma strength calculations, as a difference of up to 2.5% is observed in the lowenergy photons (2050 keV). The deviations observed in the values of dose rate and airkerma strength affect dose rate constants up to 3%.
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[Table 1], [Table 2], [Table 3], [Table 4], [Table 5]
