Monte Carlo dosimetry of a new GZP3 60Co high dose rate brachytherapy source

doi:10.21203/rs.3.rs-1626558/v1

Background

The purpose of this work is to obtain the dosimetric parameters of a new GZP3 ⁶⁰Co source currently launched by Nuclear Power Institute of China for use in their high dose rate brachytherapy systems.

Methods

The Monte Carlo software Geant4 and EGSnrc were employed to derive accurate calculations of the dosimetric parameters of the new GZP3 ⁶⁰Co brachytherapy source in the range of 0–10 cm, following the formalism proposed by American Association of Physicists in Medicine (AAPM) reports TG43 and TG43U1. The results were compared with the two Monte Carlo code to verify the accuracy of the data. The source was located in the center of a 30 cm radius theoretical sphere water phantom.

Results

For channel 1 and 2 of the new GZP3 ⁶⁰Co source, the results of dose rate constant (Λ) were 1.115 cGy h^− 1 U^− 1 and 1.112 cGy h^− 1 U^− 1, and for channel 3 were 1.116 cGy h^− 1 U^− 1 and 1.113 cGy h^− 1 U^− 1 by Geant4 and EGSnrc, respectively. The radial dose function in the range of 0.25 ~ 10.0 cm in a longitudinal direction was calculated and the fitting formula for the function were obtained. The polynomial function for the radial dose function and the anisotropy function with a θ of 0°~175° and an r of 0.5 ~ 10.0 cm were obtained. The curves of the radial function and the anisotropy function fit well compared with tow Monte Carlo software.

Conclusion

These dosimetric data sets can be used as input data of the TPS calculations and quality control for the new GZP3 ⁶⁰Co source.

Brachytherapy

60Co source

Monte Carlo

Geant4

EGSnrc

Dosimetry

The use of high dose rate (HDR) brachytherapy is a highly widespread practice around the world. Although not as widespread as ¹⁹²Ir source, ⁶⁰Co source is also available on remote afterloading systems dedicated to HDR brachytherapy, mainly for the treatment of gynaecological cancer [1, 2]. ⁶⁰Co source have the advantage of a longer half time over ¹⁹²Ir source [3], which provides longer duration of clinical use and reduced operating costs.

The GZP3 and GZP6 ⁶⁰Co HDR afterloading systems, manufactured by the Nuclear Power Institute of China (NPIC), which are widely used at home and abroad. Recently, a new GZP3 ⁶⁰Co HDR afterloading system was manufactured by NPIC, has been introduced for brachytherapy procedures. Unlike the HDR ¹⁹²Ir system, the new GZP3 ⁶⁰Co system includes two different sources designs for treatment of cervical, vaginal, rectal, and esophageal. It has three channels in the HDR system, which channel 1 and 2 have the same source but are different with channel 3. These are several studies have been performed on the GZP3 and GZP6 ⁶⁰Co source [4–6]. The dosimetric data for GZP6 ⁶⁰Co source number 3 have been obtained by Lei et al [4] using Monte Carlo (MC) based dosimetry. Wang et al [6] calculated the dosimetric data for GZP3 ⁶⁰Co source by MC simulation EGSnrc.

According to the American Association of Physicist in Medicine (AAPM) and the European Society for Radiotherapy and Oncology (ESTRO) recommendations [7], all brachytherapy sources have to obtain the dosimetric parameters based on the Radiation Therapy Committee Task Group No. 43 (TG43 and TG43U1) formalism before its clinical use, obtained by a method, either experimental or MC [8, 9]. Because of the different source designs, the dose distribution for each source model is different, so the dosimetric data form different sources cannot be used with each other. MC simulation is widely used in brachytherapy, however, for the new GZP3 ⁶⁰Co HDR source there are no dosimetric data available in the literature, based on a comprehensive determination of TG43 and TG43U1.

This study is aimed at obtaining a full dosimetric data (i.e. dose rate constant, radial dose function and anisotropy function) of the new GZP3 ⁶⁰Co source channel1,2 and 3, following the TG43 and TG43U1 using the Monte Carlo simulations Geant4 and EGSnrc. The dosimetric data derived in this work were compared with the available data of the similar ⁶⁰Co sources. These dosimetric data can be used in treatment planning system (TPS) as input data and to validate TPS calculations.

Radioactive source structure

The geometric design and materials of the new GZP3 ⁶⁰Co source were provided by the manufacturer and are shown schematically in Fig. 1. The new GZP3 HDR afterloading system comprises of different two ⁶⁰Co sources affixed to three channels in the system. It is composed of a central cylindrical active core made of ⁶⁰Co with a density of 8.9 g/cm³, 0.5 mm in radius, 1 mm in length for channels 1and 2, and 2 mm in length for channels 3. The radioactive ⁶⁰Co is distributed uniformly throughout the core. The active core is encapsulated in a 2.1 mm in diameter and 5.8 mm in length cylinder made of stainless steel for channels 1 and 2. The mass density and composition of the materials are shown in Table 1.

Table 1

Chemical composition and density of the materials in the Monte Carlo simulations

Material:description	Mass density (g/cm³)	Composition (element/weight fraction)
Cobalt:cobalt−60 source	8.85	Co/1
Stainless steel 1 (0Cr18Ni10Ti): steel spring cover, steel coupling	7.98	C/0.001, Si/0.007, Mn/0.01, Cr/0.18, Ni/0.1, Ti/0.004, Fe/0.698
Stainless steel 2 (0Cr18Ni9):steel wire rope	7.93	C/0.001, Si/0.007, Mn/0.01, Cr/0.18, Ni/0.09, Fe/0.712
Air	0.001205	C/0.00017, N/0.7552, O/0.2318, Ar/0.01283
Water:phantom material	1.0	H/0.111901, O/0.888099
Dose calculation formalism

The dose calculation formalism proposed by AAPM TG43 report has been followed [8]. According to this formalism, the dose rate, Ḋ(r, θ), at point (r, θ) in the medium, where r is the distance in cm form the active source center and θ is the polar angle relative to the longitudinal axis of the source, is expressed as:

$$\dot{\text{D}}\left(\text{r,θ}\right)\text{=}{\text{S}}_{\text{k}}\text{ }\text{Λ}\frac{\text{G(r,θ)}}{\text{G(}{\text{r}}_{\text{0}}\text{,}{\text{θ}}_{\text{0}}\text{)}}\text{g(r)}\text{ }\text{F(r,θ)}$$

Where S_k is the source air kerma strength in units of U (1U = 1µGy m² h^− 1=1cGy cm² h^− 1). The reference distance r₀ and angle θ₀ were 1 cm and π/2, respectively.

Λ is the dose rate constant defined as the ratio of dose rate to water at the reference point (r₀, θ₀) and air kerma strength,

$$\text{Λ=}\dot{\text{D}}\left({\text{r}}_{\text{0}}\text{,}{\text{θ}}_{\text{0}}\right)\text{/}{\text{S}}_{\text{k}}$$

G(r,θ) is the geometry factor, defined as

$$\text{G(r, θ)=}\left\{\begin{array}{c}\frac{\text{1}}{{\text{r}}^{\text{2}}}\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{f}\text{o}\text{r}\text{ }\text{p}\text{o}\text{i}\text{n}\text{t}\text{ }\text{s}\text{o}\text{u}\text{r}\text{c}\text{e}\text{ }\text{a}\text{p}\text{p}\text{r}\text{o}\text{x}\text{i}\text{m}\text{a}\text{t}\text{i}\text{o}\text{n}\text{ }\text{ }\\ \\ \frac{\text{β}}{\text{L}\text{ }\text{r}\text{sin}\text{θ}}\text{ }\text{ }\text{ }\text{ }\text{ }\text{f}\text{o}\text{r}\text{ }\text{l}\text{i}\text{n}\text{e}\text{ }\text{s}\text{o}\text{u}\text{r}\text{c}\text{e}\text{ }\text{a}\text{p}\text{p}\text{r}\text{o}\text{x}\text{i}\text{m}\text{a}\text{t}\text{i}\text{o}\text{n}\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\end{array}\right.$$

where L is the active length of the source, and β is the angle subtended by the active source with respect to the point (r,θ).

g(r) is the radial dose function, defined as

$$\text{g(r)=}\frac{\dot{\text{D}}\text{(r,}{\text{θ}}_{\text{0}}\text{)}\text{ }\text{G(}{\text{r}}_{\text{0}}\text{,}{\text{θ}}_{\text{0}}\text{)}}{\dot{\text{D}}\text{(}{\text{r}}_{\text{0}}\text{,}{\text{θ}}_{\text{0}}\text{)}\text{ }\text{G(r,}{\text{θ}}_{\text{0}}\text{)}}$$

and F(r,θ) is the dose anisotropy function, defined as

$$\text{F(r,θ)=}\frac{\dot{\text{D}}\text{(r,θ)}\text{ }\text{G(r,}{\text{θ}}_{\text{0}}\text{)}}{\dot{\text{D}}\text{(r,}{\text{θ}}_{\text{0}}\text{)}\text{ }\text{G(r,θ)}}$$

Monte Carlo calculations

In this study, we employed the Monte Carlo codes Geant4 (version 10.4) [10] and EGSnrc [11] to derive all dosimetric parameters of the new GZP3 ⁶⁰Co source, following the formalism described by TG43 and TG43U1. These MC codes, which have been successfully and widely used in dosimetric studies of brachytherapy [12–15]. Different MC codes used different physics models, different cross sections data in the transport of electrons. The low energy physics model of Geant4 has been used. This physics model uses the EPDL97 cross sections [16] for photons and EEDL [17] for electrons. For the EGSnrc, the photon cross sections from the XCOM database [18] are used. The cutoff energy was set to 10 keV for both photons and electrons. The ⁶⁰Co spectrum was obtained form NuDat database, taking only the two gamma photons with 1.17 and 1.33 MeV energies in the simulation [19]. The contribution of the β spectrum to the dose was not considered in the simulation due to the absorption with stainless steel cover around the metallic ⁶⁰Co, which the total dose of electrons to be less than 1% at distances greater than 1.0 mm from the source [20, 21].

In order to obtain the dose distribution in water, the ⁶⁰Co source was located at the center of a spherical liquid water phantom with a 30 cm radius in the simulation, which acts as an unbounded phantom [22]. Three different grid sizes were used to score the absorbed dose at distances from the center of the source r (ranging from 0.25 to 10.0 cm) and polar angle (ranging from 5˚ to 180˚). The first one, composed of cylindrical rings with 0.025 cm thick and 0.005 cm high, for 0 cm < r ≤ 1.0 cm, the second one, composed of cylindrical rings with 0.05 cm thick and 0.05 cm high, for 1 cm < r < 3.0 cm and the second one, and the third one, composed of cylindrical rings with 0.1 cm thick and 0.1 cm high, for 3.0 cm ≤ r ≤ 10.0 cm. In the coordinate system, θ, y, and z are representative of the polar angle, radial and axial coordinates, respectively. The coordinate axis used are shown in Fig. 1. The absorbed dose to the water was calculated in Geant4 using the function of GetTotalEnergyDeposit, whereas in EGSnrc it was used the tally afforded within the DOSRZnrc package. The absorbed dose were calculated to obtained for radial dose function and anisotropy function in spherical (r, θ) and cylindrical (y, z) coordinates. When z = 0, we set up the cylindrical rings at y in the ranging from 0.25 cm to 10 cm to obtain the dose, and then used equation g(r) to calculated the radial dose function. Simultaneously, we obtained the dose for 5˚ ≤ θ ≤ 180˚ and 0.25 cm ≤ r ≤ 10.0 cm, and then calculated the anisotropy function by equation F(r, θ).

Due to the high energy of the ⁶⁰Co, electronic equilibrium is reached up a distance of about 1.0 cm. The differences between dose and kerma are 1.5% at 0.5 cm from the source, less than 0.5% at 0.7 cm and negligible at distances greater than 1.0 cm [20]. Thus, the dose cannot be approximated by kerma at very small distances (< 0.5 cm), unlike ¹⁹²Ir and ¹³⁷Cs sources. In order to speed up calculations and to reduce statistical uncertainty and the computation time, kerma has been obtained for r > 0.7 cm. To estimate the air-kerma strength the ⁶⁰Co source was located in the center of a 3 × 3 × 3 m³ air phantom. As TG43U1 recommended [9], the air used in this simulation is composition with 40% humidity. The cylindrical ring was used to scored for kerma of 0.1 cm in height and 0.1 cm in diameter.

The number of photon histories was 5 × 10⁹ to obtain dose values and 2 × 10⁹ photon histories to obtain kerma values.

Dose rate constant

The air-kerma strength, S_k was calculated by using Geant4 and EGSnrc and it were to be 2.985 × 10^-7 and 2.981 × 10^-7 cGy cm² h^-1 Bq^-1 for channel 1 and 2, and 2.975 × 10^-7 and 2.969 × 10^-7 cGy cm² h^-1 Bq^-1 for channel 3. The dose rate constant for the ⁶⁰Co source was found to be equal to 1.115± 0.004 and 1.112 ± 0.004 cGy h^-1 U^-1for channel 1 and 2, and 1.116± 0.004 and 1.113 ± 0.004 cGy h^-1 U^-1for channel 3, which are presented in Table 2, along with the corresponding values calculated for the similar ⁶⁰Co HDR sources. The different between dose rate constant of channel 1, 2 and 3 with two Monte Carlo codes are 0.27% and 0.27%, respectively. Furthermore, Table 2 show that all the dose rate constant values with different source match closely (within 2.87%) and the values of GZP ⁶⁰Co sources are slight higher than other types.

Table 2

Comparison of dose rate constant values for similar ⁶⁰Co sources

Source design	Λ (cGy h^-1 U^-1)
New GZP3 ⁶⁰Co Channel 1 and 2 (This work by Geant4)	1.115± 0.004
New GZP3 ⁶⁰Co Channel 1 and 2 (This work by EGSnrc)	1.112 ± 0.004
New GZP3 ⁶⁰Co Channel 3 (This work by Geant4)	1.116± 0.004
New GZP3 ⁶⁰Co Channel 3 (This work by EGSnrc)	1.113 ± 0.004
GZP6 ⁶⁰Co (MCNP) [5]	1.104 ± 0.003
BEBIG ⁶⁰Co (Geant4) [21]	1.084 ± 0.005
Flexisource ⁶⁰Co (Geant4) [23]	1.085 ± 0.003

Radial dose functions and anisotropy functions

The values of radial dose function g(r) of new GZP3 ⁶⁰Co source for radial distances from 0.25 to 10.0 cm by two MC codes are presented in Table 3. Table 3 and Fig.2 show that g(r) values between two MC codes match well, the differences less than 0.55% for channel 1 and 2 and less than 0.58% for channel 3. The radial dose function obtained for the new GZP3 ⁶⁰Co source has been compared with similar sources from the relevant literature in Fig.3. This comparison shows that the curves of the g(r) are very similar at r > 1 cm, and small differences at r < 1 cm. The results of our calculations of channel 1 and 2 were compared with Ballester et al [21] for the BEBIG ⁶⁰Co source by Geant4, for 0.25 ≤ r ≤ 1.0 cm, the different less than 4.64%, and for 1 < r ≤ 10.0 cm, the different less than 0.32%. These differences are due to varying degrees of photon scattering and absorption in the sources and the different dimensions and encapsulation designs of sources are negligible [24, 25].

Table 3

Radial dose function calculated for the new GZP3 ⁶⁰Co source by Geant4 and EGSnrc

r (cm)	g(r)
	Channel 1 and 2		Channel 3
	Geant4	EGSnrc	Geant4	EGSnrc
0.25	0.963	0.965	0.964	0.969
0.5	1.037	1.035	1.033	1.039
0.75	1.015	1.010	1.011	1.015
1	1.000	1.000	1.000	1.000
1.5	0.991	0.991	0.989	0.994
2	0.981	0.982	0.981	0.985
2.5	0.971	0.973	0.972	0.976
3	0.966	0.965	0.963	0.967
4	0.950	0.947	0.947	0.950
5	0.936	0.931	0.935	0.933
6	0.917	0.914	0.921	0.916
7	0.898	0.898	0.901	0.900
8	0.883	0.882	0.885	0.884
10	0.852	0.850	0.849	0.853

The radial dose function (by Geant4) were fitted to a fifth-order polynomial function, over the range of 0.25 ≤ r ≤ 10.0 cm, fitted according to:

g(r)=(a0r^-2+a1r^-1+a2+a3r+a4r²) e^-a5r

The values of the fitted parameters are as follows: (a) for channel 1 and 2, R²=0.995, a0=-0.023, a1=0.112, a2=0.885, a3=-0.112, a4=0.004, a5=0.149; and (b) for channel 3, R²=0.995, a0=-0.022, a1=0.102, a2=0.895, a3=-0.11, a4=0.004, a5=0.142. The overall accuracy of the fits were excellent, the maximum deviations were less than 0.46% and 0.41% for channel 1 and 2, and 3, respectively.

In Table 4 and Table 5 full data for the anisotropy functions by Geant4, F(r, θ), are presented at radial distances r=0 - 10.0 cm, and at polar angles θ= 0° - 175°. F(r, θ) values for selected radial distances of ?, ?, and ? are presented in Figure 4. In this figure it can be seen that at the polar angles close to the long axis the curves of the F(r, θ) present an unsmooth shape with F(r, θ) values significantly less than other angles (30° ≤ θ ≤ 150°), which is due to the oblique filtration within the source design.

Table 4

Anisotropy function calculated for the new GZP3 ⁶⁰Co source of Channel 1 and 2 by Geant4

θ(°)	r (cm)
θ(°)	0.25	0.5	0.75	1.0	1.5	2.0	2.5	3.0	4.0	5.0	6.0	7.0	8.0	10.0
0	0.717	0.945	0.951	0.950	0.954	0.928	0.932	0.969	0.952	0.936	0.940	0.968	0.946	0.935
5	0.711	0.941	0.954	0.960	0.961	0.954	0.975	0.965	0.978	0.964	0.949	0.970	0.946	0.958
10	0.705	0.948	0.956	0.967	0.965	0.970	0.973	0.971	0.964	0.969	0.968	0.978	0.955	0.960
15	0.787	0.942	0.953	0.963	0.963	0.964	0.967	0.968	0.968	0.966	0.970	0.973	0.962	0.968
20	0.760	0.942	0.967	0.972	0.962	0.966	0.969	0.963	0.961	0.959	0.967	0.974	0.969	0.967
25	0.733	0.947	0.960	0.972	0.963	0.969	0.961	0.970	0.970	0.961	0.973	0.977	0.970	0.965
30	0.774	0.948	0.970	0.977	0.964	0.974	0.973	0.969	0.975	0.970	0.968	0.975	0.976	0.981
40	0.803	0.972	0.983	0.990	0.980	0.979	0.984	0.979	0.986	0.985	0.977	0.982	0.991	0.984
50	0.884	0.984	0.987	0.987	0.988	0.994	0.987	0.991	0.988	0.991	0.991	0.986	0.993	0.990
60	0.941	0.994	0.994	0.994	0.992	0.996	0.992	0.996	0.993	0.993	0.995	0.996	1.000	0.994
70	0.972	0.998	0.991	1.002	0.992	0.993	0.999	0.998	1.002	0.995	1.000	0.994	1.002	1.000
80	0.991	1.002	0.995	1.000	0.995	0.998	1.002	1.001	1.000	0.997	0.998	1.000	1.000	1.000
90	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
100	0.995	0.997	0.996	1.004	0.999	0.998	1.001	1.000	1.003	0.999	0.999	1.001	1.003	0.998
110	0.978	0.998	1.000	0.995	0.996	0.997	0.999	1.001	0.998	0.993	0.999	0.994	1.002	1.002
120	0.949	0.994	0.994	0.998	0.993	0.994	0.994	0.995	0.998	0.998	0.995	0.998	0.994	0.995
130	0.921	0.983	0.991	0.993	0.987	0.995	0.990	0.994	0.991	0.987	0.990	0.994	0.995	0.994
140	0.834	0.977	0.979	0.992	0.982	0.983	0.984	0.983	0.985	0.981	0.981	0.985	0.985	0.983
150	0.825	0.945	0.968	0.969	0.967	0.975	0.975	0.972	0.973	0.968	0.973	0.975	0.973	0.972
155	-	0.912	0.950	0.959	0.954	0.962	0.963	0.961	0.961	0.961	0.960	0.959	0.962	0.969
160	-	0.859	0.947	0.946	0.937	0.945	0.949	0.948	0.941	0.949	0.945	0.947	0.943	0.939
165	-	0.802	0.921	0.927	0.921	0.922	0.924	0.927	0.932	0.931	0.928	0.935	0.932	0.933
170	-	-	0.915	0.923	0.907	0.915	0.918	0.920	0.925	0.925	0.919	0.917	0.927	0.924
175	-	-	-	-	-	0.929	0.922	0.920	0.920	0.923	0.927	0.928	0.907	0.931

Table 5 Anisotropy function calculated for the new GZP3 ⁶⁰Co source of Channel 3 by Geant4

θ(°)	r (cm)
θ(°)	0.25	0.5	0.75	1.0	1.5	2.0	2.5	3.0	4.0	5.0	6.0	7.0	8.0	10.0
0	0.698	0.943	0.954	0.965	0.951	0.930	0.930	0.962	0.937	0.957	0.949	0.957	0.946	0.932
5	0.697	0.944	0.968	0.968	0.961	0.960	0.965	0.963	0.970	0.961	0.958	0.956	0.951	0.955
10	0.687	0.947	0.966	0.975	0.974	0.968	0.962	0.968	0.966	0.963	0.956	0.966	0.952	0.972
15	0.771	0.952	0.973	0.973	0.966	0.962	0.964	0.973	0.971	0.969	0.961	0.960	0.961	0.973
20	0.741	0.945	0.969	0.970	0.969	0.971	0.974	0.963	0.975	0.961	0.966	0.980	0.965	0.972
25	0.799	0.951	0.975	0.980	0.972	0.975	0.971	0.974	0.970	0.972	0.970	0.984	0.972	0.972
30	0.770	0.959	0.977	0.981	0.977	0.981	0.979	0.978	0.980	0.975	0.972	0.981	0.976	0.969
40	0.806	0.973	0.984	0.984	0.986	0.984	0.986	0.986	0.991	0.983	0.978	0.988	0.985	0.988
50	0.892	0.992	0.988	0.986	0.997	0.995	0.993	0.994	0.995	0.993	0.984	0.991	0.989	0.992
60	0.945	0.996	0.991	0.996	1.001	1.005	0.993	0.998	1.000	0.996	0.989	0.995	0.993	0.995
70	0.978	1.000	0.999	0.998	1.000	1.000	0.998	1.001	1.000	0.992	0.990	0.991	0.993	0.993
80	0.995	1.004	1.000	0.999	1.006	1.331	1.002	1.002	1.001	1.000	0.992	0.994	1.000	1.000
90	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
100	0.994	1.001	1.000	1.003	1.001	1.332	1.004	1.002	1.001	0.996	0.994	0.998	0.995	0.997
110	0.980	0.998	0.995	0.998	1.001	1.004	1.000	1.002	1.002	0.996	0.987	0.991	0.998	0.999
120	0.951	0.999	0.991	0.994	0.997	1.000	0.999	0.999	0.996	0.995	0.990	0.995	0.995	0.993
130	0.931	0.995	0.991	0.989	0.995	0.996	0.993	0.997	0.996	0.994	0.983	0.996	0.993	0.988
140	0.839	0.985	0.988	0.986	0.992	0.996	0.992	0.989	0.987	0.988	0.981	0.986	0.982	0.988
150	0.835	0.958	0.978	0.973	0.976	0.980	0.979	0.975	0.977	0.976	0.971	0.981	0.973	0.977
155		0.923	0.958	0.964	0.966	0.966	0.969	0.966	0.968	0.959	0.959	0.966	0.966	0.966
160		0.864	0.952	0.942	0.949	0.951	0.947	0.948	0.950	0.943	0.949	0.950	0.947	0.953
165		0.774	0.919	0.920	0.921	0.934	0.929	0.926	0.929	0.921	0.923	0.936	0.934	0.937
170			0.899	0.907	0.905	0.910	0.911	0.906	0.912	0.913	0.903	0.911	0.916	0.937
175					0.896	0.902	0.904	0.911	0.904	0.902	0.895	0.908	0.906	0.913

Dose rate distribution and Uncertainties

The along-away 2D dose rate results (cGy h^-1 U^-1), for the channel 1 and 2, and 3 ⁶⁰Co source for quality assurance (QA) purposes is presented in Table 6 and Table 7, respectively. The QA values were tabulated over the range of -10 cm ≤ z ≤ 10 cm and 0 ≤ y ≤ 10 cm.

The uncertainties in the final dose rate distributions for ⁶⁰Co sources, including statistical uncertainty (type A) and systematic uncertainty (type B), have been calculated as is recommended by TG43U1.⁹ The systematic uncertainty is more difficult to obtain such as source design uncertainties, cross-section uncertainties. Thus, the systematic uncertainty is negligible for ⁶⁰Co source.^21,26 For the statistical uncertainty of ⁶⁰Co source depended on the axial position z and the longitudinal position y. In this study, the systematic uncertainty is less than 0.72% and 0.73% for the points located or very near to the longitudinal axis, and less than 1.21% and 1.19% for the other points, for channel 1 and 2, and 3 by Geant4, respectively.

Table 6

Dose rate results (cGy h ^-1 U ^-1), for the new GZP3 ⁶⁰Co source of Channel 1 and 2 by Geant4

z(cm)	y(cm)
z(cm)	0	0.25	0.5	0.75	1.0	1.5	2.0	3.0	4.0	5.0	6.0	7.0	8.0	10.0
-10	0.030	0.030	0.030	0.030	0.030	0.030	0.030	0.028	0.027	0.024	0.022	0.020	0.018	0.014
-8	0.051	0.050	0.050	0.050	0.048	0.048	0.047	0.044	0.039	0.035	0.031	0.027	0.024	0.018
-7	0.066	0.066	0.066	0.066	0.064	0.064	0.061	0.056	0.050	0.043	0.038	0.032	0.028	0.020
-6	0.096	0.092	0.092	0.091	0.088	0.088	0.083	0.073	0.063	0.054	0.045	0.038	0.032	0.023
-5	0.135	0.135	0.135	0.134	0.128	0.124	0.116	0.099	0.082	0.067	0.054	0.044	0.036	0.025
-4	0.218	0.213	0.214	0.208	0.198	0.189	0.172	0.138	0.107	0.083	0.064	0.051	0.041	0.027
-3	0.377	0.386	0.376	0.365	0.348	0.312	0.269	0.196	0.139	0.102	0.076	0.057	0.045	0.029
-2	0.854	0.883	0.840	0.771	0.716	0.571	0.449	0.274	0.177	0.120	0.085	0.064	0.048	0.031
-1.5	1.600	1.545	1.429	1.275	1.113	0.809	0.578	0.319	0.194	0.127	0.090	0.066	0.050	0.031
-1	3.451	0.851	2.899	2.336	1.845	1.124	0.731	0.362	0.209	0.135	0.093	0.067	0.051	0.031
-0.75	6.703	1.456	4.517	3.321	2.385	1.309	0.807	0.380	0.216	0.137	0.095	0.068	0.052	0.032
-0.5	14.964	2.971	7.533	4.627	2.987	1.481	0.862	0.389	0.220	0.139	0.095	0.069	0.052	0.032
0	-	14.258	15.555	6.778	3.749	1.656	0.919	0.402	0.223	0.140	0.096	0.069	0.052	0.032
0.5	-	2.913	7.534	4.643	3.001	1.483	0.868	0.393	0.220	0.139	0.095	0.069	0.052	0.032
0.75	-	1.418	4.537	3.316	2.386	1.314	0.805	0.379	0.215	0.137	0.094	0.068	0.051	0.032
1	-	0.828	2.891	2.360	1.838	1.130	0.733	0.362	0.210	0.135	0.093	0.068	0.051	0.032
1.5	-	1.488	1.395	1.270	1.111	0.807	0.578	0.321	0.194	0.128	0.090	0.066	0.050	0.031
2	-	0.831	0.798	0.764	0.704	0.577	0.450	0.273	0.176	0.120	0.085	0.064	0.049	0.031
3	-	0.368	0.364	0.346	0.342	0.311	0.270	0.193	0.140	0.101	0.075	0.058	0.045	0.029
4	-	0.206	0.202	0.198	0.145	0.184	0.171	0.138	0.107	0.083	0.065	0.051	0.041	0.027
5	-	0.127	0.126	0.126	0.093	0.120	0.114	0.198	0.083	0.067	0.054	0.044	0.036	0.025
6	-	0.087	0.087	0.087	0.064	0.083	0.080	0.073	0.063	0.054	0.045	0.038	0.032	0.023
7	-	0.065	0.064	0.062	0.047	0.061	0.059	0.055	0.050	0.044	0.038	0.032	0.027	0.020

Table 7

Dose rate results (cGy h ^-1 U ^-1), for the new GZP3 ⁶⁰Co source of Channel 3 by Geant4

z(cm)	y(cm)
z(cm)	0	0.25	0.5	0.75	1.0	1.5	2.0	3.0	4.0	5.0	6.0	7.0	8.0	10.0
-10	0.032	0.032	0.031	0.030	0.030	0.030	0.030	0.028	0.026	0.024	0.022	0.020	0.018	0.014
-8	0.048	0.050	0.049	0.049	0.048	0.048	0.047	0.044	0.040	0.036	0.032	0.027	0.024	0.018
-7	0.065	0.068	0.066	0.066	0.064	0.064	0.062	0.056	0.050	0.044	0.038	0.032	0.028	0.020
-6	0.089	0.093	0.093	0.091	0.087	0.087	0.083	0.074	0.063	0.054	0.045	0.038	0.032	0.023
-5	0.133	0.134	0.133	0.133	0.127	0.125	0.116	0.100	0.082	0.067	0.054	0.044	0.036	0.025
-4	0.216	0.215	0.212	0.208	0.197	0.189	0.174	0.138	0.107	0.083	0.064	0.051	0.041	0.027
-3	0.347	0.387	0.380	0.365	0.351	0.313	0.272	0.196	0.139	0.101	0.076	0.058	0.045	0.029
-2	0.850	0.876	0.836	0.779	0.716	0.575	0.449	0.274	0.177	0.120	0.086	0.063	0.048	0.031
-1.5	1.568	1.561	1.439	1.288	1.114	0.812	0.580	0.319	0.194	0.128	0.090	0.066	0.050	0.031
-1	3.695	0.850	2.959	2.385	1.870	1.131	0.731	0.361	0.209	0.135	0.093	0.067	0.051	0.032
-0.75	6.433	1.487	4.595	3.305	2.382	1.310	0.803	0.376	0.214	0.137	0.094	0.068	0.051	0.032
-0.5	15.054	3.063	7.608	4.589	3.006	1.484	0.865	0.391	0.220	0.139	0.095	0.069	0.052	0.032
0	-	13.767	15.334	6.716	3.775	1.649	0.918	0.403	0.223	0.141	0.096	0.069	0.052	0.032
0.5	-	3.006	7.606	4.602	2.995	1.483	0.864	0.391	0.220	0.139	0.095	0.069	0.052	0.032
0.75	-	1.466	4.605	3.334	2.395	1.313	0.802	0.378	0.215	0.137	0.094	0.068	0.051	0.032
1	-	0.814	2.920	2.378	1.871	1.129	0.736	0.359	0.209	0.135	0.093	0.068	0.051	0.032
1.5	-	1.472	1.396	1.274	1.123	0.809	0.582	0.319	0.194	0.127	0.090	0.066	0.050	0.031
2	-	0.826	0.798	0.763	0.712	0.577	0.450	0.275	0.176	0.120	0.086	0.063	0.048	0.030
3	-	0.367	0.354	0.349	0.342	0.311	0.271	0.195	0.140	0.102	0.075	0.058	0.045	0.029
4	-	0.199	0.198	0.196	0.144	0.184	0.173	0.139	0.107	0.083	0.065	0.051	0.040	0.027
5	-	0.128	0.125	0.125	0.090	0.120	0.115	0.198	0.082	0.067	0.054	0.044	0.036	0.025
6	-	0.086	0.086	0.085	0.063	0.083	0.081	0.074	0.064	0.054	0.045	0.038	0.032	0.022
7	-	0.062	0.063	0.063	0.046	0.061	0.059	0.055	0.050	0.044	0.038	0.032	0.028	0.020

In this study, a full dosimetric parameters for the new GZP3 ⁶⁰Co source was obtained using the Monte Carlo Geant4 and EGSnrc codes, based on the dose calculation formalism recommended by the AAPM TG43 and TG43U1 reports. The dose rate constant, radial dose function, anisotropy function and away-along dose rate distributions were calculated for the new GZP3 ⁶⁰Co source. Furthermore, these dosimetric parameters of the new GZP3 ⁶⁰Co source did not previously publish. These dosimetric datasets can be used as input data and to quality control the TPS calculations.

Acknowledgements

None.

Authors’ contributions

Design of the Research: JXW, XLW; Monte Carlo codes: SWK, JL, PW; Elaboration of the data: JXW. All authors read and approved the final manuscript.

Funding

The authors did not receive any funding for this work.

Availability of data and material

The data are fully available without restriction in a public repository (Dryad). The reference treatment plans and corresponding perturbed plans were archived in the Informatic System of Sichuan Cancer Hospital.

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

None of the authors have any competing interests (financial and nonfinancial) in the manuscript.

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Monte Carlo dosimetry of a new GZP3 60Co high dose rate brachytherapy source

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