Dosimetric characterizations of GZP6 60Co high dose rate brachytherapy sources: application of superimposition method

Background Dosimetric characteristics of a high dose rate (HDR) GZP6 Co-60 brachytherapy source have been evaluated following American Association of Physicists in MedicineTask Group 43U1 (AAPM TG-43U1) recommendations for their clinical applications. Materials and methods MCNP-4C and MCNPX Monte Carlo codes were utilized to calculate dose rate constant, two dimensional (2D) dose distribution, radial dose function and 2D anisotropy function of the source. These parameters of this source are compared with the available data for Ralstron 60Co and microSelectron192Ir sources. Besides, a superimposition method was developed to extend the obtained results for the GZP6 source No. 3 to other GZP6 sources. Results The simulated value for dose rate constant for GZP6 source was 1.104±0.03 cGyh-1U-1. The graphical and tabulated radial dose function and 2D anisotropy function of this source are presented here. The results of these investigations show that the dosimetric parameters of GZP6 source are comparable to those for the Ralstron source. While dose rate constant for the two 60Co sources are similar to that for the microSelectron192Ir source, there are differences between radial dose function and anisotropy functions. Radial dose function of the 192Ir source is less steep than both 60Co source models. In addition, the 60Co sources are showing more isotropic dose distribution than the 192Ir source. Conclusions The superimposition method is applicable to produce dose distributions for other source arrangements from the dose distribution of a single source. The calculated dosimetric quantities of this new source can be introduced as input data to the GZP6 treatment planning system (TPS) and to validate the performance of the TPS.


Introduction
culations around these implants were performed using the traditional dose calculation technique. However, presently, the Task Group 43 (TG-43) report of American Association of Physicists in Medicine(AAPM) has recommended determination of dosimetric parameters, such as radial dose function, anisotropy function (ANF), etc., of any brachytherapy sourcebefore its clinical use. 9 Also according to the AAPM TG-56 such parameters are required as input data and for verification of the treatment planning system. 10 The newly designed GZP6 HDR 60 Co brachytherapy unit has been recently employed for the clinical practice in Iran. Unlike the HDR 192 Ir systems, which contain one source, the GZP6 unit includes six different sources ( Figure 1). Each source is designated to a separate channel in the HDR unit. Five of these six sources are stationary, and the 6 th source (i.e. source number 6) has stepping (dwelling) capability that could be used for treatment of patients with longer active length. As shown in Figure 1, each source is composed of a source-braid or packing, consist of 1, 2, 3 or 4 radioactive source pellets as well as a number of non active steel pellets. In order to make these source FIGURE 1. Schematic diagram illustrating six GZP6 source braids, containing active and nonactive pellets. Each source is allocated to one separate channel. The sources 1-5 are stationary while the source No. 6 is stepper.

FIGURE 2.
A schematic view of the GZP6 source braid number 3 illustrating the dimensions of active cylindrical 60 Co and non-active steel pellets as well as TG43U1 coordinate systems. This diagram is schematic and is not to scale.
geometries reproducible, at the same time flexible as it moves within the transfer tube and applicator, the active and non-active pellets are fitted within a steel spring cover. Dimensions and components of the active and non-active pellets of these sources are provided in the schematic diagram of source number 3 ( Figure 2). In their first publication on this system, Mesbahi et al. measured the air kerma strengthsof source numbers 1, 2 and 5. 11 In a separate investigation, Mesbahi has also calculated radial dose function for these three sources. 12 Naseri et al. have examined the accuracy of the dose distributions calculated by the GZP6 treatment planning system by Monte Carlo simulation of these sources. 13 Monte Carlo simulation is widely used in radiophysics 14 , however, to our knowledge the GZP6 unit has not been studied before, based on a comprehensive determination of TG-43U1 dosimetric parameters. 15 Since the GZP6 unit has six sources with different fixed configurations, each source has been individually evaluated for their clinical applications.
The goal of this project is to investigate the dosimetric parameters (i.e. dose rate constant, radial dose function and anisotropy function) of source number 3, which has not been studied before, following the TG-43U1 recommendation through Monte Carlo simulations. The results of these investigations will be compared with the corresponding data available for Ralstron (type 2) 60 Co and microSelectron 192 Ir sources. 4,16 The dose distribution for the source No. 3 is used to produce dose distributions for the other GZP6 sources using a superimposition method developed in this study.

Radioactive source structure
The GZP6 high dose rate afterloading unit comprises of different six 60 Co sources affixed to six different channels in the system. In this study dosimetric characteristic of the source number 3 of the unit, which is a non-stepping source and includes one active cylindrical 60 Co pellet, is being evaluated. As illustrated schematically in Figure 2, this source braid consists of an active nickel-plated cobalt pellet and a number of inactive spherical pellets which are made of steel. The active 60 Co cylinder has a radius of 0.5 mm and length of 2 mm (including the nickel-plating), in which the 60 Co radionuclide was distributed uniformly throughout the core. The nickel plating has a thickness of 0.05 mm, which has not been illustrated in the Figure 2. The active cobalt pellet is additionally encapsulated in a titanium capsule, with 0.25 mm in thickness and consisting of two hemispheres with 0.75 mm in radius at the two ends, sealed by Argon arc welding. The whole pellets are accommodated in a steel spring cover with an external diameter of 2.7 mm. 60 Co is emitting two gamma photons with 1.17 and 1.33 MeV energies and βparticles with E max =0.318 MeV. It has a half-life of 5.271 years. The latter particle is attenuated effectively with the titanium capsule.

TG 43 formalism
The formalism of TG-43U1 was followed to compute the dosimetric parameters of the source. 15 According to this formalism the dose rate at the point P(r, θ) from the source center is defined by the following equation (as illustrated in Figure 2): Where r is the radial distance (in cm) from the source center and θ is the polar angle. r 0 is the reference radial distance of 1 cm and θ 0 is the reference polar angle of 90º. S k is air kerma strength of the source (in U, where 1 U=1 μGym 2 h -1 ), Λ is dose rate constant, G(r,θ) is geometry function, g(r,θ) is radial dose function and F(r,θ) is two-dimensional (2D) anisotropy function.
The dose rate constant is the ratio of dose rate at the reference point (r 0 ,θ 0 ) and air kerma strength: [2] Dose rate constant has a unit of cGyh -1 U -1 . In this study the line-source approximation was used for calculation of geometry function. By using this approximation, for the geometry function can be obtained from the following equation: [3] If the geometry function is obtained from equation [4]: [4] As denoted by Awan et al. 17 , considering the source active length L, the radial distance r and the angles θ and ß as showed in the Figure 2, equation [5] can be resulted from the above equation: [5] Thus if , the geometry function can be calculated directly in terms of r and θ from equation [5].
The radial dose function, g(r), and anisotropy function, F(r, θ) are defined as: [6] [7] In which denotes the dose rate at the point P(r, θ) from the source.

Monte Carlo calculations
The MCNP-4C Monte Carlo code was employed to estimate absorbed dose towards obtaining TG-43U1 parameters. 18 Since it has the option of defining the mesh grids, the MCNPX version 2.4.0 Monte Carlo code was also utilized to obtain 2D dose distribution for the source. 19 When this option is used it would be easier to score tally values in a large number of scoring volumes. Table 1 lists the mass density and chemical composition of the materials used in our Monte Carlo calculations.
In calculations of dose rate constant and 2D dose distributions, the value of air kerma strength was taken from our previous work. 20 The source braid was centered in a cylindrical water of dimensions R=25 cm and L=50 cm in the simulations. A cutoff energy of 10 keV was used for both photons and electrons. To speed up the Monte Carlo calculations, the absorbed dose was approximated as kerma to estimate dose at points where the electronic equilibrium exists. For a 60 Co source, the dose build up region affects only points in close vicinity from the 60 Co pellet. The f6 tally was used to score collision kerma (in MeV/g/photon). At the points in the vicinity of the source, in which the electronic equilibrium may not exist, dose was scored using *f8  16 To obtain 2D dose rate table, a cylindrical grid of 14 cm14 cm in y-z plane, with resolution of 0.05 cm in both longitudinal and radial directions was overlaid on the geometry. The thin grid was used to reduce the Monte Carlo computation time. 3.510 8 photon histories were followed, resulting an average error of 0.44% over the mesh cells. MCNPX tally type 1 with the option of depth for photons was used to determine energy deposition per volume per photon in terms of per photon. The tally value then was converted to the dose rate per U by introducing the activity, air kerma strength of the source and appropriate conversion factors in the calculations.

Superimposition method
A superimposition algorithm was developed to produce the dose distributions of the GZP6 sources No. 1, 2 and 5 from the dose distribution data of the source No. 3. The algorithm was consisted of four steps: (a) The dose distribution data for each pellet in the sources 1, 2 and 5 was obtained from the dose distribution matrix of source 3 through application of matrix shift method. 21 The shifting distance was equal to the inter-pellets distance (6.5 mm).
(b) The dose distribution data for each pellet was multiplied by normalized activity of that pellet to the activity of source No. 3.
(c) A summation was then performed over the matrixes of all pellets in each source of 1, 2 ad 5.
(d) Dose contours were plotted from the dose distribution matrix of sources 1, 2 and 5.
The results of the mentioned algorithm were verified to examine its accuracy. For this purpose the sources 1, 2 and 5 were simulated separately and the obtained dose distributions were compared by the dose distributions resulted from the above algorithm.

TG-43 dosimetric parameters
The calculated values of geometry function for 0.5-5 cm radial distance and 0°-90° angles are presented in the Table 2. The calculated values for geometry function were equal to unity at 6-10 cm distance. To summarize the results, these values were not presented in the Table 2. The geometry function is symmetrical with reference to the angle of 90°. On the other hand the angular values of the on the either side of the 90° angle, for the angles 100°-180°, are mirror images of the values for 80°-0° angles. 22 So as showed in Table 2, the two dimensional geometry function is presented only for angles 0°-90°.
Monte Carlo calculated value of air kerma strength is S k= 17240.01 cGyh -1 U -1 as worked out earlier for the GZP6 source number three. 20 The value was used for the calculation of dose rate constant in the present study. Monte Carlo calculated dose rate constants for GZP6 and Ralstron (type 2) and microSelectron sources are presented in Table 3.
The dose rate results, in terms of cGyh -1 U -1 , in Cartesian away (y) and along (z) coordinates are presented in the Table 4. It should be noted that the source center is assumed to be in the origin of the Cartesian coordinates.
A graphical representation of g(r) values for the GZP6 source is presented in Figure 3 and com-

B C A
Our results are indicating that the dose rate constant, radial dose function and anisotropy function for GZP6 and Ralstron (type 2) 60 Co sources are comparable. While the value of dose rate constant for the GZP6 and Ralstron (type 2) 60 Co sources are close to that for the microSelectron 192 Ir source (Table 3), radial dose function fall off for the 192 Ir source is less steep compared to the cobalt sourc-es especially for lower radial distances from the source ( in Figure 3). It can be also noticed from the Figure 4 that the two cobalt sources have more isotropic anisotropy functions than the iridium source.
The dosimetric data presented in this study for GZP6 source (number 3) can be utilized in clinical practice of the source and towards the improvement of its treatment planning system.

Dose distributions from the superimposition method
The dose distributions for the GZP6 source No. 1, 2 and 5 which was obtained by MC simulations of the sources and the superimposition method described are presented in the Figure 5. The dose contours of 1, 2, 5, 10, 15 and 20 Gy were plotted. As it can be observed the dose distributions obtained by the two methods for the sources 1, 2 and 5 are equal.
The superimposition algorithm developed in this study is able to produce dose distributions for the GZP6 sources No. 1, 2 and 5 from the dose distribution of the source No. 3. The algorithm is also applicable for other bracytherapy units in which an arrangement of sources is used in the treatment process. These results may provide comprehensive dosimetric information that could be clinically more applicable for dose calculations around different implants by superimposition method.