Monte Carlo (MC) codes are currently used to verify brachytherapy sources while utilizing the photon energy spectrum of a specific radionuclide for calculations. There exist some common energy spectrum databases which are used by researchers. Some use the recommendation of the American Association of Physicists in Medicine (AAPM) from task group No. 43 updated report (TG-43 U1) which was prepared for low energy photon emitting radionuclides such as 125I and 103Pd.1 In a report by the AAPM and the European Society for Therapeutic Radiology and Oncology (ESTRO)2, the use of the energy spectrum database of the National Nuclear Data Center (NNDC)3 was recommended for photon emitting radionuclides higher than 50 keV.
There are various methods to determine the energy spectra of photon emitting radionuclides. One widely used technique is high-purity germanium detectors, especially for low energy sources.4-6 Chen
It is necessary to implement TG-43 dosimetric parameters in treatment planning systems.10125I brachytherapy source models are widely used in prostate cancer treatments wherein the dose received by organs at risk such as rectum and urinary bladder is important. To quantify the dose to these organs, treatment planning systems use the appropriate TG-43 dosimetric parameters which were reported in the literature. Treatment planning systems do not use energy spectrum directly, but they use TG-43 parameters reported by a published study. Therefore, the energy spectrum used in that study can effect on the calculation accuracy of the treatment planning systems indirectly. So the precision of energy spectrum of the radionuclide can have influences on the calculated dose to the tumor and the related organs at risk. Therefore, it is important to provide accurate energy spectra of radionuclides. In the previously mentioned studies, only some dosimetric parameters were evaluated from the energy spectrum point of view. To the best of our knowledge, a comprehensive study considering the influence of photon energy spectrum on the dosimetric parameters of brachytherapy sources was not performed.
The aim of this study is to evaluate the influence of photon energy spectrum on TG-43 dosimetric parameters and isodose curves for three common photon energy spectra; for 125I, 103Pd, 169Yb, and 192Ir brachytherapy sources.
In this study, MCNPX code (version 2.4.0) was used to simulate brachytherapy sources.11 Four brachytherapy sources were studied: MED 3631-A/M 125I, Optiseed 103Pd, a hypothetical 169Yb, and Flexisource 192Ir sources. In the selection of these radionuclides, there was an attempt to evaluate various brachytherapy sources within a relatively wide range of photon energies. The MED 3631-A/M 125I source consists of four polystyrene spheres coated with active 125I with an active length of 4.2 mm. The Optiseed 103Pd is composed of two polystyrene cylinders containing active 103Pd. The active length of 103Pd is assumed to be 3.8 mm. The 169Yb and 192Ir sources have the same geometries with 3.5 mm active core, including radioactive 169Yb and 192Ir, respectively. The geometry properties of simulated sources were described in details in the previous published article.12 The simulations of the sources were verified in that study and the same input files were applied for the mentioned brachytherapy sources in the current study. In that study12 the verification was based on calculation and comparison of dose rate constant and radial dose function with the corresponding published data on these source models.
The updated report of TG-43U11 was followed to calculate the dosimetric parameters of low energy brachytherapy sources. For higher energy brachytherapy sources the recommendations by the report of AAPM and ESTRO2 were applied. Based on the report of TG-43 U1, dose rate is calculated from the following formula:
Geometry function with line-source approximation (
where
MCNPX code (version 2.4.0) was used for the simulations. MCNPX is a general purpose Monte Carlo code and is able to transport neutrons, photons, electrons and other particles in various geometries. It includes a geometry modeling tool and various tallies related to energy deposition, particle current, and particle flux. The 2.4.0 version of this code, which was used in the present study, uses MCPLIB02 cross section library for transport of photons.13-14 In the MC calculations both photons and electrons were transported. Line-source approximation was used in the MC simulations. The energy cut-off for photons and electrons was considered 1 keV for 125I and 103Pd sources and 5 keV for 169Yb and 192Ir sources in all input files. No other variance reduction method was applied in this study.
To calculate air kerma strength, air toroid cells were defined in a 100 cm radius vacuum sphere. The brachytherapy source was located at the center of this sphere. The torus cells were in the range of 1–50 cm and their thickness was assumed 1 mm. An F6 tally was scored in these torus cells and the outputs were multiplied by
To obtain the dose rate constant, an *F4 tally was calculated at
The 2D anisotropy function was calculated at 0°–180° with a degree interval of 10° at radial distances of 0.5, 1, 5, 10, and 15 cm. The source was located at the center of a spherical water phantom with a 50 cm radius and an *F4 tally was calculated. Spherical cells were used for 0°and 180°polar angles while torus cells were defined for the other polar angles. The number of particles for this section was assumed as 2 × 108 for 169Yb and 192Ir sources; 9 × 108 for 125I source; and 2 × 109 for 103Pd source. In all of the data points, the Type A statistical uncertainty was less than 4.18%, with exceptions for two points with 13.8% uncertainty at 0
To plot isodose curves for a source, a mesh grid was defined in a 50 cm spherical water phantom. The sources were defined in the phantom, separately. For the purpose of output calculation, “pedep” option of type 1 mesh tally type in MCNP was applied in the grid. In MCNP, there are various mesh tallies (including type 1, type 2, type 3, etc.) which can be used to score different dosimetric variables in a grid. Each mesh tally has various options, by which the user defines that which variable should be scored by the code. As an example, type 1 tally is track-average mesh tally. With “pedep” option in this mesh tally type, the average energy deposition per unit volume (in terms of MeV/cm per source particle) for a specified particle type is calculated. This option allows the user to score the equivalent of F6 tally. The grid included 2 × 2 × 2 mm3 and the obtained data was plotted in the
The effect of energy spectrum on dosimetric parameters of 125I, 103Pd, 169Yb, and 192Ir radionuclides was evaluated for three different spectra. As the first spectrum and via a common method in brachytherapy Monte Carlo studies, the reported photon energy spectra by previous papers were used for the radionuclides.1,16-18 As the second spectrum database, Lawrence Berkeley National Laboratory (LBNL) was chosen.19 We applied version 2.1 (January 2004) for all radionuclides in the LBNL database. The third spectrum applied for each radionuclide was extracted from the National Nuclear Data Center (NNDC) database3 as it was suggested by the report of AAPM and ESTRO.2 The NNDC database reports a number of energy spectra for a radionuclide. In the present study, these numbers of datasets were chosen from NNDC database: dataset No. 1 for 125I20, dataset No. 1 for 103Pd21, dataset No. 2 for 169Yb22 and dataset No. 4 for 192Ir23 radionuclides.
The photon energy spectra of 125I, 103Pd, 169Yb, and 192Ir radionuclides reported by various databases are listed in Table 1. The photon energy spectra applied for the 125I source are: AAPM TG-43 U1 report1, LBNL database19, and NNDC database.20 For the 103Pd source, the photon energy spectra reported by a study by Rivard16, LBNL database19, and NNDC database21 were used. The photon energy spectra applied for the 169Yb source are: the study by Cazeca
Information on photon energy spectra of the 125I and 103Pd, 169Yb, and 192Ir radionuclides reported by different databases
Reference | TG-43 U11 | LBNL19 | NNDC20 | Rivard16 | LBNL19 | NNDC21 |
Energy range (keV) | 27.202-35492 | 3.335-35.4919 | 3.77-35.4925 | 22.074-497.054 | 2.377-497.08 | 2.7-487.08 |
Total photons per disintegration | 1.4757 | 1.60482 | 1.5767 | 0.7713825 | 0.851569801 | 0.857582605 |
Average energy (keV) | 28.370 | 27.541 | 26.059 | 21.319 | 19.038 | 18.889 |
Reference | Cazeca | LBNL19 | NNDC22 | Medich and Munro18 | LBNL19 | NNDC23 |
Energy range (keV) | 49.77-307.74 | 6.341-781.64 | 7.18-781.64 | 61.49-884.54 | 7.822-1378.3 | 9.44-1378.50 |
Total photons per disintegration | 3.322 | 3.779 | 3.771 | 2.301 | 2.359 | 2.214 |
Average energy (keV) | 92.797 | 82.622 | 82.781 | 354.356 | 346.736 | 369.525 |
LBNL = Lawrence Berkeley National Laboratory; NNDC = National Nuclear Data Center; TG-43 U1 = Recommendation of the American Association of Physicists in Medicine from task group No. 43 updated report
In MCNPX code, the photon energy spectrum should be introduced for a source in terms of energies of photons (MeV) emitted by the radionuclide and their intensities. For the four sources, it was not feasible to list all the energies and the related probabilities in a single table or figure. Therefore, some information including the energy range, total intensity, and average energy are listed in Table 1. TG-43 parameters were calculated for 125I, 103Pd, 169Yb, and 192Ir sources with three specific photon energy spectra to evaluate whether the photon energy spectrum effect the dosimetric parameters.
The values of air kerma strength per activity were calculated for MED 3631-A/M 125I, Optiseed 103Pd, a hypothetical 169Yb, and Flexisource 192Ir sources. These values are presented in Table 2 for three photon energy spectra for each of these sources. Furthermore, dose rate constant and dose rate at
Air kerma strength, dose rate constant, and dose rate at 1 cm for 125I, 103Pd, 169Yb, and 192Ir sources based on different photon energy spectra reported by other studies, LBNL, and NNDC databases
1.035 | 1.169 | 1.121 | -7.67 | 4.28 | |
1.132 | 1.428 | 1.404 | -19.37 | 1.71 | |
1.094 | 1.094 | 1.097 | -0.27 | -0.27 | |
3.622 | 3.631 | 3.496 | 3.60 | 3.86 | |
1.115 | 0.961 | 1.013 | 10.07 | -5.13 | |
0.830 | 0.658 | 0.669 | 24.06 | -1.64 | |
1.222 | 1.226 | 1.222 | 0.00 | 0.33 | |
1.117 | 1.117 | 1.117 | 0.00 | 0.00 | |
1.154 | 1.123 | 1.136 | 1.60 | -1.07 | |
0.939 | 0.940 | 0.939 | 0.00 | 0.09 | |
1.338 | 1.341 | 1.341 | -0.23 | 0.00 | |
4.045 | 4.054 | 3.904 | 3.59 | 3.84 |
LBNL = Lawrence Berkeley National Laboratory; NNDC = National Nuclear Data Center
Radial dose function for 125I, 103Pd, 169Yb, and 192Ir sources based on different photon energy spectra reported by other studies1,16-18, Lawrence Berkeley National Laboratory (LBNL)19, and National Nuclear Data Center (NNDC)20-23 databases
125 | 0.5 | 0.996 | 0.996 | 0.996 | 0.00 | 0.00 | 103 | 1.196 | 1.196 | 1.196 | 0.00 | 0.00 |
1 | 1.000 | 1.000 | 1.000 | 0.00 | 0.00 | 1.000 | 1.000 | 1.000 | 0.00 | 0.00 | ||
1.5 | 0.955 | 0.955 | 0.954 | 0.11 | 0.10 | 0.789 | 0.789 | 0.789 | 0.00 | 0.00 | ||
2 | 0.890 | 0.890 | 0.890 | 0.00 | 0.00 | 0.609 | 0.609 | 0.608 | 0.16 | 0.16 | ||
2.5 | 0.816 | 0.815 | 0.816 | 0.00 | -0.12 | 0.465 | 0.465 | 0.464 | 0.22 | 0.22 | ||
3 | 0.740 | 0.740 | 0.740 | 0.00 | 0.00 | 0.352 | 0.352 | 0.352 | 0.00 | 0.00 | ||
3.5 | 0.667 | 0.666 | 0.667 | 0.00 | -0.15 | 0.265 | 0.265 | 0.264 | 0.38 | 0.38 | ||
4 | 0.596 | 0.596 | 0.595 | 0.17 | 0.17 | 0.199 | 0.199 | 0.198 | 0.50 | 0.51 | ||
4.5 | 0.530 | 0.530 | 0.530 | 0.00 | 0.00 | 0.150 | 0.150 | 0.149 | 0.67 | 0.68 | ||
5 | 0.470 | 0.469 | 0.470 | 0.00 | -0.21 | 0.112 | 0.112 | 0.112 | 0.00 | 0.00 | ||
5.5 | 0.415 | 0.415 | 0.415 | 0.00 | 0.00 | 0.084 | 0.084 | 0.083 | 1.20 | 1.21 | ||
6 | 0.365 | 0.365 | 0.365 | 0.00 | 0.00 | 0.063 | 0.062 | 0.062 | 1.61 | 0.00 | ||
6.5 | 0.320 | 0.319 | 0.319 | 0.31 | 0.00 | 0.047 | 0.047 | 0.047 | 0.00 | 0.00 | ||
7 | 0.279 | 0.279 | 0.279 | 0.00 | 0.00 | 0.035 | 0.035 | 0.035 | 0.00 | 0.00 | ||
10 | 0.120 | 0.120 | 0.120 | 0.00 | 0.00 | 0.0066 | 0.0066 | 0.0065 | 1.54 | 1.54 | ||
15 | 0.029 | 0.029 | 0.029 | 0.00 | 0.00 | 0.0010 | 0.0010 | 0.0010 | 0.00 | 0.00 | ||
169 | 0.5 | 0.950 | 0.949 | 0.951 | -0.11 | -0.21 | 192 | 0.996 | 0.996 | 0.996 | 0.00 | 0.00 |
1 | 1.000 | 1.000 | 1.000 | 0.00 | 0.00 | 1.000 | 1.000 | 1.000 | 0.00 | 0.00 | ||
1.5 | 1.042 | 1.041 | 1.041 | 0.10 | 0.00 | 1.003 | 1.003 | 1.003 | 0.00 | 0.00 | ||
2 | 1.079 | 1.079 | 1.077 | 0.19 | 0.19 | 1.006 | 1.006 | 1.006 | 0.00 | 0.00 | ||
2.5 | 1.113 | 1.111 | 1.110 | 0.27 | 0.09 | 1.008 | 1.008 | 1.008 | 0.00 | 0.00 | ||
3 | 1.136 | 1.137 | 1.133 | 0.27 | 0.35 | 1.010 | 1.010 | 1.009 | 0.10 | 0.10 | ||
3.5 | 1.157 | 1.156 | 1.155 | 0.17 | 0.09 | 1.011 | 1.011 | 1.010 | 0.10 | 0.01 | ||
4 | 1.169 | 1.171 | 1.168 | 0.09 | 0.26 | 1.011 | 1.011 | 1.010 | 0.10 | 0.10 | ||
4.5 | 1.183 | 1.181 | 1.180 | 0.25 | 0.09 | 1.010 | 1.010 | 1.010 | 0.00 | 0.00 | ||
5 | 1.189 | 1.185 | 1.185 | 0.34 | 0.00 | 1.008 | 1.008 | 1.007 | 0.10 | 0.10 | ||
5.5 | 1.193 | 1.191 | 1.191 | 0.17 | 0.00 | 1.005 | 1.005 | 1.005 | 0.00 | 0.00 | ||
6 | 1.195 | 1.189 | 1.190 | 0.42 | -0.08 | 1.002 | 1.002 | 1.001 | 0.10 | 0.10 | ||
6.5 | 1.189 | 1.185 | 1.186 | 0.25 | -0.08 | 0.998 | 0.998 | 0.998 | 0.00 | 0.00 | ||
7 | 1.182 | 1.181 | 1.181 | 0.09 | 0.00 | 0.995 | 0.994 | 0.994 | 0.10 | 0.00 | ||
10 | 1.089 | 1.091 | 1.090 | -0.09 | 0.09 | 0.949 | 0.949 | 0.949 | 0.00 | 0.00 | ||
15 | 0.860 | 0.865 | 0.862 | -0.23 | 0.35 | 0.836 | 0.836 | 0.835 | 0.12 | 0.12 |
2D anisotropy function calculated at
In the current study, the influence of photon energy spectrum on dosimetric parameters of 125I, 103Pd, 169Yb, and 192Ir brachytherapy sources was evaluated. Dose rate constant is the ratio of dose rate at 1 cm to air kerma strength. All these quantities are presented in Table 2 for the considered sources. The relative difference values of dose rate constant with regard to NNDC based data, shows a maximum value of 24.06% and 10.07% for the 103Pd and 125I brachytherapy sources, respectively (Table 2). These percentage differences are related to the photon energy spectra by TG-43 U1 protocol1 and NNDC20 database for the 125I source; and LBNL19 and NNDC database21 for the 103Pd source. There are non-negligible differences between the dose rate constant values obtained by different photon energy spectra databases for the 125I and 103Pd sources. Table 2 demonstrates that the cause of these differences is due to air kerma strengths. The effect for air kerma strength to the differences in total number of photons per disintegration (Table 1) and the differences in photon energy in various spectra demonstrate their main cause is air kerma strength. In other words, for calculation of air kerma strength the environment is void and minor differences in photon energy have a major effect on the kerma rate. This effect is not seen for dose rate at 1 cm in which the media is water.
The radial dose function calculated by different photon energy spectra does not show a considerable difference between brachytherapy sources. The differences do not show a general trend with distance. The minor effect of energy spectrum on radial dose function is in agreement with the results by Rivard
As it is seen in Figure 3, there is no observable difference in isodose curves of 125I, 103Pd, 169Yb, and 192Ir sources with different photon energy spectra. However, this doesn’t mean that the photon energy spectrum choice for a radionuclide doesn’t affect dose distribution around the source. As it was implied from the obtained data of TG-43 dosimetric parameters, such as air kerma strength and dose rate constant values, this effect is not negligible. On the other hand, isodose contours cannot show such differences. Relying only on isodose curves for clinical application of brachytherapy sources may induce some errors in quantification of dose values.
For different photon energy spectra the calculated mean energies were in relatively good agreement for both LBNL and NNDC databases. A maximum of 24.06% difference was observed between dose rate constant of different energy databases. Ignoring the differences in the anisotropy function values at