Comparison of the hypothetical ⁵⁷Co brachytherapy source with the ¹⁹²Ir source

Introduction

Cancer is the third leading cause of death in developed countries [1]. Three major modalities for the treatment of cancer are surgery, chemotherapy and radiation therapy. Radiation therapy is a method in which ionizing radiation is used to treat or relieve cancer. Almost half of all cancer patients receive radiation therapy during their course of treatment. Radiation therapy is classified into two types: externally delivered radiation therapy (teletherapy) and internally delivered radiation therapy (brachytherapy). From the late 1990s, brachytherapy was widely expanded for treatment of tumours of prostate, breast and cervix [2].
In brachytherapy, a radioactive source (radioisotope) is placed in the vicinity of the tumour or within it during treatment. ¹⁹²Ir is one of the radioisotopes that are widely used in high dose rate (HDR) brachytherapy. ¹⁹²Ir is both a  and  emitter. The emitted gamma radiation from ¹⁹²Ir has an energy range of 201–884 keV, with an average of 360 keV. The average energy for the  particles from ¹⁹²Ir decay is 200 keV. The energy of  and  particles emitted by the ¹⁹²Ir source is relatively high, and therefore it is important to have appropriate protection for radiotherapy staff and enough shielding for the treatment room [3]. Taking into account the relatively high energy of this source and the personnel safety needed, it would be useful to search for other sources with lower energy photons, yet sufficient specific activity.
Nowadays, the ⁵⁷Co radioisotope is used as a source for calibration of gamma cameras and the study of leukaemia, related to B12 vitamin deficiency and its insufficient absorption. ⁵⁷Co can be produced by an accelerator through 55Mn(, 2n)⁵⁷Co nuclear reaction. Based on this reaction  particles interact with 55Mn and the products are neutrons and ⁵⁷Co. This reaction requires  irradiation, which is not commonly available. Therefore, the efficiency of this reaction is not appropriate for therapeutic applications. As an alternative, high energy proton beams can be used. The target material can be natural iron or nickel and the following reactions occur: 26Fe(p, x)⁵⁷Co or 58Ni(p, x)⁵⁷Co. Use of 57Ni can cause the production of a large amount of 56Co nuclides, which are considered as an impurity having a half-life of 79 days. Use of enriched 58Ni as the target and appropriate selection of proton energy can prevent production of this impurity. Carter and Laird [4] described methods for construction of a radioactive stent and reviewed the experimental information on the treatment for enhancement of arterial patency rates after placement of the stent. They declared that with one-year follow-up after implantation of a radioactive stent with combination of - and -emitting 55Co, 56Co, ⁵⁷Co, 52Mg, and 55Fe radionuclides, approximately complete inhibition of neointimal proliferation was observed in a rabbit model. Adequate characteristics of ⁵⁷Co would be a motivation for more evaluation of this radioisotope for application as a brachytherapy source.
Simulation of a source and calculation of dosimetric parameters presented by Task Group No. 43 (TG-43) for a source is one of the methods for verification of dosimetric characteristics of a brachytherapy source before its clinical usage. Task Group No. 43 describes a formalism for calculation of dosimetric parameters for brachytherapy sources. The dosimetric parameters include air kerma strength, dose rate constant, radial dose function and anisotropy function. After verification of the calculations of dosimetric parameters of the ⁵⁷Co source, it can be evaluated whether they are appropriate in comparison with other available brachytherapy sources, then this source may be used in clinical applications.
Up to now, 169Yb and 170Tm radioisotopes, due to their medium energy photons, have been proposed as hypothetical sources for use in brachytherapy, and their dosimetric parameters have been reported. Dosimetric parameters of a hypothetical 170Tm source were studied by Ballester et al. [5]. This radioisotope has high specific activity and a half-life of 128 days. It emits photons with average energy of 66.39 keV. 170Tm has a low photon yield (6 photons per 100 electrons emitted), which is considered a disadvantage for the source. In their simulations, cylindrical and spherical sources were defined inside steel and platinum capsules, respectively. The bremsstrahlung dose contribution had the same order of magnitude as the dose contribution raised from characteristic x-rays and  photons, due to high electron yield and energetic  particles. The dose rate constant was reported to be 1.23 cGyh–1U–1 for the cylindrical source. The results showed that brachytherapy with 170Tm needs longer treatment duration in comparison with other sources. On the other hand, this source provides a more uniform dose distribution. Enger et al. [6] calculated dosimetric parameters for a hypothetical 170Tm source by means of the Monte Carlo (MC) method. They evaluated the effect of the capsule material on emitted photons’ and electrons’ energy spectra. In the study, a cylindrical 170Tm source was designed with active length of 3.5 mm and diameter of 0.6 mm, the same as the Flexisource ¹⁹²Ir source. Furthermore, the radial dose function for various materials (stainless steel, gold and platinum) was calculated. The results showed that gold and platinum capsules not only can absorb the emitted  particles but also attenuate low energy photons. The average photon energy transmitted through the source core and the stainless steel capsule was about 113 keV, whereas the average energy transmitted via the gold and platinum capsules was about 160 keV and 165 keV, respectively. Enger et al. [7] presented dosimetric characteristics of a hypothetical 153Gd source. This source is a photon emitting source with 40–100 keV photons and a half-life of 242 days. They simulated the hypothetical 153Gd source with 0.84 mm diameter and 10 mm length in a stainless steel encapsulation. The results imply that this source would be adequate as a low dose rate or pulsed dose rate brachytherapy source. The  particles emitted by this source are low energy and are absorbed in the source’s capsule. An increasing radial dose function was observed due to multiple scattering of low energy photons of the source. It was concluded that this source can provide brachytherapy treatments with patient-specific shielding and reduced personnel shielding compared to ¹⁹²Ir. In order to predict physical parameters useful in treatment planning and radiation protection, Mason et al. [8] studied characteristics of a 169Yb source by Monte Carlo simulation. This radioisotope emits photons with mean energy of 93 keV, and its half-life is 32 days. The air kerma rate constant and dose rate constant for this radioisotope were reported as 0.427 cGycm²h–1MBq–1 and 1.8 Rcm²mCi–1h–1, respectively. The results showed that 169Yb provides a more uniform dose distribution relative to ¹⁹²Ir and 137Cs sources. Additionally, due to the short half-life of 169Yb this source is more adequate for interstitial brachytherapy.
Ninkovic et al. [9] calculated the air kerma rate constant for point sources of various radionuclides which are practically used. The radionuclides were 35 radionuclides including ⁵⁷Co. The calculations were based on corrections for internal conversion of X and  rays and the generation of the K and L series X rays from internal conversion and electron capture. Air kerma rate constants were calculated for each discrete energy in the photon spectrum of the radionuclides with yield per decay more than 0.01% and with energy higher than 20 keV. They used the latest energy spectrum and mass energy transfer coefficient data and therefore were able to calculate the most accurate air kerma rate constants for the 35 radionuclides. In a study by Enger et al. [3] the radial dose function and anisotropy function for a hypothetical ⁵⁷Co source were calculated using the Monte Carlo method, and the results were compared with those of 125I and ¹⁹²Ir sources, which are routinely used in brachytherapy. 125I and ¹⁹²Ir have lower and higher average photon energies relative to ⁵⁷Co, respectively. An increase in radial dose function was observed for the hypothetical ⁵⁷Co source due to an increase in scattered photons resulting from low energy photons. Furthermore, the ⁵⁷Co source can provide a more uniform dose distribution relative to the ¹⁹²Ir source. However, anisotropy functions of both sources do not differ significantly.
Although some dosimetric parameters of a hypothetical ⁵⁷Co source were reported by Enger et al. [3], to the best of our knowledge there is not a comprehensive comparison of the data to a ¹⁹²Ir source. In the study by Enger et al. [3] radial dose function and anisotropy function data were presented only in the form of plots, and the anisotropy function was only calculated for one distance. The aim of this study is to evaluate the ⁵⁷Co radioisotope as a source for use in brachytherapy. For this purpose, dosimetric parameters of a hypothetical ⁵⁷Co source are calculated by Monte Carlo method and are compared with those of a corresponding ¹⁹²Ir source.

Material and methods

Geometry of hypothetical ⁵⁷Co and Flexisource ¹⁹²Ir sources In this study the geometry of a hypothetical ⁵⁷Co source was considered similar to that of the Flexisource ¹⁹²Ir source model. In the study by Enger et al. [3] on the ⁵⁷Co hypothetical source, this geometry was also used. Based on this geometry, the active part of the source was assumed as pure ⁵⁷Co, instead of active ¹⁹²Ir. The active part was simulated as a cylinder with 3.5 mm length and 0.6 mm diameter located inside a capsule by MCNPX Monte Carlo code (version 2.6.0) [10] (Fig. 1). Herein the density of the ⁵⁷Co source was considered the same as 60Co (8.86 g/cm³). The source’s capsule is made of stainless steel with density of 8 g/cm³, and its elemental composition includes: Fe (67.92%), Cr (19%), Ni (10%), Mn (2%), Si (1%) and C (0.08%). The cylindrical part of the source encapsulation has inner and outer radiuses of 0.335 mm and 0.425 mm, respectively. An air gap with density of 0.001205 g/cm³ was considered in the space between the active part and the capsule. There are two truncated cones with lengths of 0.108 mm and 0.4 mm at the two ends of the cylindrical part of the capsule. The source cable was modelled as a cylinder with length of 5 mm and radius of 0.25 mm. These parameters which were simulated in this study are based on the studies by Enger et al. [3] and Granero et al. [11] on a hypothetical ⁵⁷Co source and the Flexisource ¹⁹²Ir source, respectively.
In the present study, the Flexisource ¹⁹²Ir source was also simulated. The geometry of the Flexisource ¹⁹²Ir source is similar to that of ⁵⁷Co which was described in the previous paragraph with the difference that the active parts of the sources are different. The density of the ¹⁹²Ir active core was considered as 22.42 g/cm³.
In order to simulate the hypothetical ⁵⁷Co source, the three most probable  photons in the spectrum emitted by the radioisotope with energies of 136.47 keV (10.68%), 122.06 keV (85.6%) and 14.41 keV (9.16%) were defined (Table 1). Based on this spectrum, the average energy of photons emitted by ⁵⁷Co is 114.17 keV. The spectrum of the ¹⁹²Ir photons was considered based on the study by Medich et al. [12] (Table 2).
In order to verify the Flexisource ¹⁹²Ir simulations, the dose rate constant and radial dose function for the ¹⁹²Ir source were calculated and compared with those reported by Granero et al. on this source model [11].

TG-43 dosimetric parameters calculation

Dosimetric parameters introduced by TG-43U1 formalism [13] were calculated for the ⁵⁷Co source. For this purpose, after source simulations, air kerma strength, dose rate constant, radial dose function and anisotropy function of the ⁵⁷Co source were calculated. In order to have an accurate comparison of the ⁵⁷Co and ¹⁹²Ir sources, the obtained data were reported as tables and figures for both sources. Finally, isodose curves around the ⁵⁷Co and ¹⁹²Ir sources were plotted in a single plot in order to compare the dose distributions of the sources. In the current study, MCNPX code (version 2.6.0) was utilized for all simulations [10]. The advantages of Monte Carlo simulation technique in dosimetry in external beam radiation therapy and brachytherapy have been demonstrated for many years. Nowadays, the use of Monte Carlo simulation in radiotherapy applications is increasing because of the availability of high-speed computers and new Monte Carlo codes [14].
In order to calculate air kerma strength for the ⁵⁷Co source, a number of 1 mm thick tori were defined at various radial distances ranging from 1 cm to 49 cm in free space, in the form of 50 cm radius spherical volume. Air was considered inside the tori. Electron and photon energy cut-offs were defined as equal to 250 eV, as adopted by Enger et al. [3]. The outputs were scored in the torus cells using F6 tally. The product of air kerma rate and the square of radial distance (air kerma rate ×d2) was plotted versus radial distance. The average value of this product in the relatively flat portion of the plot was used for calculation of air kerma strength. The calculation method of air kerma strength for the ¹⁹²Ir source was the same as that of the ⁵⁷Co source, except that the energy cut-off was set to 5 keV, because of its higher energy photons relative to ⁵⁷Co. To calculate the air kerma strength for ⁵⁷Co, 3 × 108 particles were run and the maximum type A MC statistical uncertainty was 0.2%. The calculation method for the ¹⁹²Ir source is similar to ⁵⁷Co, with the difference that the input file was run for 4 × 108 particles and the maximum type A MC statistical uncertainty was 0.2% in calculation of air kerma strength.
For calculation of the dose rate constant, dose rate was calculated by means of a 0.1 cm thick torus at a distance of 1 cm from the source using *F8 tally in a water phantom ( = 0.998 g/cm³) with 50 cm radius. Energy cut-off was defined as the same as that for air kerma strength. Dry air up to the radius of 200 cm was defined outside of the spherical water phantom. The output of *F8 tally was divided by the mass of the torus, then the dose rate constant was calculated by division of the dose rate value at 1 cm distance and air kerma strength. The input programs for ⁵⁷Co and ¹⁹²Ir sources were run for 2 × 108 and 3 × 108 particles, respectively, and the maximum type A MC statistical uncertainty was 0.1% in both calculations.
Radial dose functions were calculated at distances of 0.1–15 cm from the source in a water phantom with 50 cm radius. The thickness of the tori was 0.04 cm at distances lower than 1 cm, and after 1 cm the thickness was 0.1 cm. Outside the water sphere there was dry air up to a radius of 200 cm. The energy cut-off for particles in the case of ⁵⁷Co was 250 eV. The outputs of *F8 tally were divided by the masses of the tori. The energy cut-off for the ¹⁹²Ir source was defined as 10 keV. A number of 108 particles were scored for ⁵⁷Co and the maximum type A MC uncertainty was 1.77%. For the ¹⁹²Ir source, 8.5 × 107 particles were scored and the maximum uncertainty was 2.13% in the simulations.
In calculation of the anisotropy function for ⁵⁷Co and ¹⁹²Ir sources, 0.1 cm thickness tori were defined with 10-degrees intervals at various distances ranging from 0.5 to 10 cm inside a 40 cm radius spherical water phantom. The energy cut-off for this calculation was similar to that in radial dose function calculation and the output was obtained by F6 tally. Anisotropy function values were obtained using the outputs and geometric functions of the sources by use of linear source approximation. To calculate the anisotropy function, an active length of 3.5 mm was used for both ⁵⁷Co and ¹⁹²Ir sources in calculation of the geometric function with linear source approximation. A number of 5 × 107 photons were scored for both sources and the maximum type A MC uncertainty for ⁵⁷Co and ¹⁹²Ir was 4.86% and 6.33%, respectively.
Finally, dosimetric parameters of the ¹⁹²Ir source were compared with the corresponding published data. Dosimetric parameters of the ⁵⁷Co source were compared with those of the ¹⁹²Ir source.

Isodose curves

In order to obtain the dose distribution around the ⁵⁷Co and ¹⁹²Ir sources, MCNPX code (version 2.6.0) was used. Type 1 mesh tally with the “pedep” option in Cartesian coordinates was utilized. The mesh cells were defined in the form of voxels with 2 × 2 × 2 mm3 dimensions, from –7 cm to +7 cm along the x- and y-axes. The input programs were run for 2 × 109 particles, and the maximum type A MC statistical uncertainty was 0.3%. After running both programs, the output files, “mdata” files, were saved. These files are binary, and their contents are not directly accessible by a user. The outputs were converted to text files by means of “gridconv” command in MCNPX. The outputs were converted to matrices and the isodose curves were plotted using MATLAB software (version 7.8.0.347, Math Works Inc., Natwick, MA). The output of type 1 mesh tally was in terms of MeV/cm³, while the isodose curves were plotted in terms of cGyh–1U–1. In the first step of this conversion, the mesh tallies were divided by the density of the phantom and then were multiplied by other appropriate conversion factors to obtain the dose rate terms of cGyh-1U–1. Some of these conversion factors include unit conversion factors, source activities, source yields, etc. The yield values for ¹⁹²Ir and ⁵⁷Co radioisotopes are 2.3012 photons/disintegration and 1.0544 photons/disintegration, respectively. These values were calculated from the spectra data of these two sources in Tables 1 and 2.

Results

Air kerma strength values per 1 mCi activity for the hypothetical ⁵⁷Co source and Flexisource ¹⁹²Ir source are 0.46 cGycm²h–1mCi–1 and 3.62 cGycm²h–1mCi–1, respectively.
Dose rate constant values for the hypothetical ⁵⁷Co and ¹⁹²Ir sources are 1.215 cGyh–1U–1 and 1.114 cGyh–1U–1, respectively. This quantity for the Flexisource ¹⁹²Ir source reported by Granero et al. [11] is 1.109 cGyh–1U–1, which is 0.46% lower than the result presented above.
Radial dose function values from the current study and those reported by Granero et al. [11] for the Flexisource ¹⁹²Ir source are presented in Table 3. Based on a comparison of these two data sets, it is evident that the Flexisource ¹⁹²Ir simulation in this study is validated. The blank cells in this table represent those points which have no value reported by Granero et al. [11]; therefore, no comparison of these data points was performed. The maximum difference between these two data sets was 4.26%.
Radial dose function values for the hypothetical ⁵⁷Co source are presented in Table 4. In order to compare radial dose function values of the two sources, radial dose function diagrams are presented in a single figure (Fig. 2).
Anisotropy function data for the hypothetical ⁵⁷Co and ¹⁹²Ir sources are listed in Tables 5 and 6, respectively. To compare anisotropy function values of these sources, the corresponding diagrams are plotted in Fig. 3 for four distances of 0.5, 1, 5 and 10 cm.
A comparison of isodose curves for these two sources may be interesting. Isodose curves of the two sources are plotted in Fig. 4. The dose rate values in these figures were obtained using mesh tallies in MCNPX code and were plotted in the MATLAB software environment.

Discussion

In the current study, TG-43 dosimetric parameters and dose distributions for a hypothetical ⁵⁷Co source and Flexisource ¹⁹²Ir source were calculated and reported. The geometries of the ⁵⁷Co and ¹⁹²Ir sources were the same, except for the compositions of the active parts of the sources. Some criteria which should be considered in radiation therapy are appropriate accuracy in dose calculations, dose delivery and adequate dose distribution relative to the expected situation. Air kerma strength per mCi activity for the hypothetical ⁵⁷Co source is less than that of the ¹⁹²Ir source (0.46 cGycm²h–1mCi–1 for ⁵⁷Co and 3.62 cGycm²h–1mCi–1 for ¹⁹²Ir). This effect is due to the difference in the photon yields and photon energy spectra emitted by these two sources. The average photon energy for ⁵⁷Co and ¹⁹²Ir is 114.17 keV and 360 keV, respectively. From the air kerma strength data of the two sources it can be concluded that in the same conditions, air kerma strength for ¹⁹²Ir is greater than that of ⁵⁷Co, which is considered an advantage for the ¹⁹²Ir source over ⁵⁷Co. However, if both sources have the same initial activities, due to the lower half-life of ¹⁹²Ir, its air kerma strength will decrease at a faster rate. With the same initial activities, after about four half-lives of ¹⁹²Ir, the air kerma strength of ⁵⁷Co will be equal to that of the ¹⁹²Ir source, which can be considered as an advantage of the ⁵⁷Co source. By comparison between the dose rate constant values (1.215 cGyh–1U–1 and 1.114 cGyh–1U–1 for ⁵⁷Co and ¹⁹²Ir, respectively) it can be seen that per U of air kerma strength, ⁵⁷Co can produce a higher dose rate at the reference distance (1 cm) from the source in water medium.
In order to compare the radial dose function values of the two sources (Fig. 2), the photon interactions in phantom material should be interpreted. The energies of the emitted photons from the brachytherapy sources affect photon absorption in the phantom. For relatively high energy brachytherapy sources such as ¹⁹²Ir, the total dose distribution is not mainly from the scattered photons in the typical brachytherapy range. However, the photon absorption in the phantom material is compensated by scattering of low energy photons. As can be seen from the data in Fig. 2, the radial dose function for the ¹⁹²Ir source is more uniform due to build up of the scattering component of the dose. For sources with medium energy, such as ⁵⁷Co, dose distribution is mainly influenced by multiple scattered low energy photons. Therefore, as shown in Fig. 2, this source has an increase in radial dose function which is specific for this energy range. From this point of view, the ¹⁹²Ir source has a more uniform dose distribution at various radial distances from the source, compared to the ⁵⁷Co source. The same effect for the radial dose function of these two sources was reported by Enger et al. [3].
In the study by Enger et al. [3] the anisotropy function was reported only at a distance of 1 cm from the hypothetical ⁵⁷Co source in the form of a diagram. In the current study, in addition to the diagram presentation of the anisotropy function for various distances (Fig. 3), the tabulated data for various distances are also presented for this source (Table 5). Due to the lack of any tabulated data, it is not possible to make a comparison between the data from this study and other studies for the hypothetical ⁵⁷Co source. The anisotropy function diagram by Enger et al. [3] contains some fluctuations. The shape of the tally cells used in calculation of the anisotropy function was not described in the materials and methods section of that study. It can be guessed that spherical or cubic cells were used. This may be the origin of fluctuations in anisotropy function values of the source. In this study, tori were used in order to preserve the cylindrical symmetry. As demonstrated in Fig. 3, there is no fluctuation in anisotropy function data in the current study. At all distances and various angles, anisotropy function data for ⁵⁷Co are closer to 1.00 relative to the data for ¹⁹²Ir. This effect may be considered as an advantage of ⁵⁷Co versus the ¹⁹²Ir source.
Isodose curves for the ⁵⁷Co and ¹⁹²Ir sources are plotted in Fig. 4. When one considers these curves, isodose curves of ⁵⁷Co for the same dose contour values are located outside the corresponding contours of the ¹⁹²Ir source, except for the 300 cGyh–1U–1 contour. This effect implies that at the same points, the dose rate of ⁵⁷Co is higher than ¹⁹²Ir. From Fig. 2, the same results are expected for the radial dose function. Also, except for distances less than 1 cm, the radial dose function curve of ⁵⁷Co is greater than that of ¹⁹²Ir. This is another advantage of the ⁵⁷Co source. In Fig. 4, the cable of the source is located at the left side of the plot. At the left end of the sources, in the position of the cables, the magnitude of the dose contour dip for ⁵⁷Co and ¹⁹²Ir in the isodose curves are the same. However, at the right end of the sources, in the position of the tip of the sources, the amount of dip in the contours of the ⁵⁷Co isodose curves are somewhat less than for ¹⁹²Ir. This provides a more uniform dose distribution for the ⁵⁷Co source. The same results are evident from the anisotropy function comparisons of ⁵⁷Co and ¹⁹²Ir sources in Fig. 3.
In conclusions the hypothetical ⁵⁷Co source were to be made available commercially, with the same geometry as designed in this study, the data presented herein could be used as input data for a treatment planning system and also in verification of the system calculations after commissioning of the unit including this radioisotope.
The beneficial characteristics of the ⁵⁷Co radioisotope make it a possible future brachytherapy source. This source has a combination of possible high specific activity (312 TBq/g [15]), relatively medium energy photon emission and an appropriate half-life (272 days). ⁵⁷Co decays by electron capture, and it is converted to 57Fe by gamma emission. The half-life of ⁵⁷Co is about four times longer than that of the ¹⁹²Ir source (74 days). Therefore, due to the longer half-life of the ⁵⁷Co radioisotope in comparison to other available brachytherapy sources, it needs fewer source calibrations and exchanges, which may reduce costs. Half-value layers for ⁵⁷Co and ¹⁹²Ir are 0.145 mm and 2.5 mm, respectively. Therefore, lower shielding thickness is needed around a ⁵⁷Co source compared to ¹⁹²Ir. The higher dose rate constant and more isotropic anisotropy functions and more uniform dose distributions relative to ¹⁹²Ir are other advantages of the ⁵⁷Co source relative to ¹⁹²Ir. However, the initial air kerma strength for ¹⁹²Ir is higher than that of ⁵⁷Co, and the radial dose function of ¹⁹²Ir is more uniform than that of ⁵⁷Co. The two latter points can be considered as advantages of ¹⁹²Ir over ⁵⁷Co.

The authors would like to thank the Iran National Science Foundation (INSF) for financial support of this work.
The authors declare no conflict of interest.

References

1. Cai W, Gao T, Hong H, Sun J. Applications of gold nanoparticles in cancer nanotechnology. Nanotechnol Sci Appl 2008; 1: 17-32.
2. Awan SB, Dini SA, Hussain M, Meigooni DS, Meigooni AS. Cylindrical coordinate based TG-43U1 parameters for dose calculation around elongated brachytherapy sources. J Appl Clin Med Phys 2008; 9: 123-42.
3. Enger SA, Lundqvist H, D’Amours M, Beaulieu L. Exploring ⁵⁷Co as a new isotope for brachytherapy applications. Med Phys 2012; 39: 2342-5.
4. Carter AJ, Laird JR. Experimental results with endovascular irradiation via a radioactive stent. Int J Radiat Oncol Biol Phys 1996; 36: 797-803.
5. Ballester F, Granero D, Perez-Calatayud J, Venselaar JL, Rivard MJ. Study of encapsulated 170Tm sources for their potential use in brachytherapy. Med Phys 2010; 37: 1629-37.
6. Enger SA, D’Amours M, Beaulieu L. Modeling a hypothetical 170Tm source for brachytherapy applications. Med Phys 2011; 38: 5307-10.
7. Enger SA, Fisher DR, Flynn RT. Gadolinium-153 as a brachytherapy isotope. Phys Med Biol 2013; 58: 957-64.
8. Mason DL, Battista JJ, Barnett RB, Porter AT. Ytterbium-169: Calculated physical properties of a new radiation source for brachytherapy. Med Phys 1992; 19: 695-703.
9. Ninkovic MM, Raicevic JJ, Adrovic F. Air kerma rate constants for gamma emitters used most often in practice. Radiat Prot Dosimetry 2005; 115: 247-50.
10. Pelowitz D. MCNPX users manual, LA-CP-07-1473 Version 2.6.0, 2008, Los Alamos National Laboratory.
11. Granero D, Pérez-Calatayud J, Casal E, Ballester F, Venselaar J. A dosimetric study on the Ir-192 high dose rate Flexisource. Med Phys 2006; 33: 4578-82.
12. Medich DC, Munro JJ 3rd. Monte Carlo characterization of the M-19 high dose rate Iridium-192 brachytherapy source. Med Phys 2007; 34: 1999-2006.
13. Rivard MJ, Coursey BM, DeWerd LA, et al. Update of AAPM Task Group No. 43 Report: A revised AAPM protocol for brachytherapy dose calculations. Med Phys 2004; 31: 633-74.
14. Zhang H, Baker C, McKinsey R, Meigooni A. Dose verification with Monte Carlo technique for prostate brachytherapy implants with 125I sources. Med Dosim 2005; 30: 85-91.
15. Enger SA, Beauliue L. Modeling a hypothetical ⁵⁷Co source for brachytherapy application. Brachytherapy 2011; 10 (Suppl 1): S33. '

Address for correspondence

Mahdi Ghorbani, PhD
Medical Physics Department, Faculty of Medicine
Mashhad University of Medical Sciences
Pardise Daneshgah, Vakil Abad Blvd., Mashhad, Iran
Postal zip code: 9177948564
e-mail: mhdghorbani@gmail.com
tel. +98 51 38002316
fax +98 51 38002320

Submitted: 6.04.2015
Accepted: 30.11.2015