Monte Carlo derivation of AAPM TG-43 dosimetric parameters for GZP6 Co-60 HDR sources

Physica Medica (2012) 28, 153e160

available at www.sciencedirect.com

journal homepage: http://intl.elsevierhealth.com/journals/ejmp

ORIGINAL PAPER

Monte Carlo derivation of AAPM TG-43 dosimetric parameters for GZP6 Co-60 HDR sources Sanaz Hariri Tabrizi*, Alireza Kamali Asl, Zohreh Azma Radiation Medicine Engineering Department, Shahid Beheshti University, Tehran, Iran Received 6 September 2010; received in revised form 19 April 2011; accepted 22 April 2011 Available online 31 May 2011

KEYWORDS HDR brachytherapy; Monte Carlo; TG-43 protocol; Treatment planning software

Abstract Cobalt 60 source is generally available on high dose rate (HDR) afterloading equipment especially for treatment of gynecological lesions. The GZP6 remote afterloader (Nuclear Power Institute of China) utilizes 60Co sources for treatment of intracavitary and intraluminal malignancies. In this study, the AAPM TG-43 dosimetric parameters of three sources in GZP6 system have been studied using MCNP4C Monte Carlo (MC) code; and the results are compared with other available 60 Co HDR sources. The presented parameters consist of air kerma strength, dose rate constant, radial dose function and anisotropy function. They show less than 1% uncertainty. The TG-43 based dosimetry data can be used not only to validate the dedicated treatment planning software (TPS), but also to introduce new complementary software to enhance the system performance in gynecological treatments. ª 2011 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Introduction Although not as widespread as 192Ir, 60Co is a comparable source for high dose rate (HDR) brachytherapy. Clinical examples for intracavitary and interstitial applications show practically identical dose distributions in the treatment volume for the two radioisotopes. However, there are some potential logistical advantages including high specific activity and long half life of 60Co compared to 192Ir [1]. There are some companies which deal with 60Co HDR sources and corresponding dosimetric datasets are available

* Corresponding author. E-mail address: [email protected] (S. Hariri Tabrizi).

[2e5]. Among the older systems is the Ralston remote afterloader (Shimadzu Corporation, Japan) which incorporates two 60Co cylindrical pellets in two of three HDR source designs it manufactures; while one of them has one active pellet with two-fold length [2]. Because Ralston type 2 source design is comparable with GZP6 sources, this type is taken into account in comparisons. The newer system is BEBIG MultiSource remote afterloader (BEBIG GmbH, Germany). Its source is composed of a central cylindrical active core made of metallic 60Co, 3.5 mm in length and 0.6 mm in diameter [3]. Another newer BEBIG Cobalt source has been introduced (model Co0.A86) which differs from the old one (model GK60M21) in that it has a smaller active core and a more rounded capsule tip [5]. Both sources have been studied and their dose rate distribution has been obtained using GEANT4 [5] and EGSnrc MC codes [4].

1120-1797/$ - see front matter ª 2011 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ejmp.2011.04.004

154

S. Hariri Tabrizi et al. agreement with previous studies, the datasets were used to introduce a complementary TPS for the existing dedicated TPS which has been reported elsewhere [17].

Material and methods Brachytherapy sources

Figure 1 Simulated schematic of a) channels 3/4 and b) channel 6 60Co HDR sources of GZP6 brachytherapy system. The coordinate axis used in this study is also shown with its center situated at the geometric center of the active volume. Dimensions are in millimeters.

The GZP6 remote afterloader (Nuclear Power Institute of China) incorporates six braid type 60Co HDR sources. Its widespread use, especially in developing countries, is the result of the low cost which makes it noteworthy among the full option and newer systems. There is no comprehensive documented dosimetric data about this system except some calibration [6] and treatment planning validation [7,8] studies. The use of Monte Carlo method to calculate dosimetric tables of brachytherapy sources, especially near the HDR sources with high dose gradient, is a common practice. Several MC codes including EGSnrc [4,9], GEANT4 [3,5,10,11], PENELOPE [12], PTRAN [13] and MCNP4C [2] have been used to find out the along e away tables and TG-43 parameters for different brachytherapy sources. In this study, the dosimetric datasets for channels 3, 4 and 6 of GZP6 afterloader with 60Co sources were obtained based on AAPM TG-43 formalism [14,15] using the general-purpose Monte Carlo N-Particle transport code version of 4C (MCNP4C) [16]. The along -away table and TG-43 parameters including air kerma strength, dose rate constant, radial dose function and anisotropy function have been calculated and are presented in a tabular and schematic form. In addition, the results have been compared with other investigated 60Co HDR sources [2e5]. Achieving a low uncertainty and good

The GZP6 remote afterloader (Nuclear Power Institute of China) unit comprises six linear braid type sources including one stepping and five non-stepping sources for treatment of intracavitary and intraluminal malignancies such as cervix, rectum, esophagus and nasopharynx [7]. The position of active elements is constant relative to the source braid and it is not changed for different treatments. Each source is positioned in a given channel and loaded independently by a mechanical transport system from a shielded container to applicators to perform the treatment. Because the main purpose of this study is to improve the existing device performance in gynecological treatments, three channels of the unit which are used for these procedures have been selected to be evaluated. All six channels of GZP6 system utilize 60Co sources with different arrangements. The sources of channels 3, 4 and 6 are composed of one active core made of metallic 60Co with 3.5 mm length and 1.5 mm diameter encapsulated in 0.1 mm Titanium [7]. The active core is covered by a cylindrical stainless steel cover of 0.5 mm external diameter and steel balls are arranged along with it. Channels 3 and 4 source designs are identical and the only difference between them is their activity. Channel 6 is different from channels 3/4 source design from the active core position relative to steel balls point of view. The simulated schematic of channels 3/4 and 6 60Co HDR sources in GZP6 system are shown in Fig. 1. In this study, the b particle emission is neglected because of absorption in the source steel cover. Two gamma photons were supposed to be emitted with energy of 1.17 MeV and 1.33 MeV and energy cutoff in the code was set to 10 keV for photons and electrons.

Monte Carlo calculation The dose rate distribution and TG-43 parameters were obtained in an unbounded spherical liquid water phantom with 50 cm radius [1e3]. Based on the TG-43 update [15]

Table 1 Dose rate constants, L, of a point 60Co source [2], BEBIG sources with two models (Co0.A86 and GK60M21) [3e5] and two GZP6 60Co sources (Channels 6 and 3/4). Also, corresponding L to geometry factor, GL(1 cm, 90
), ratios are presented. Sources

L (cGy h1 U1)

Point source [2] BEBIG-GK60M21 Source [3] BEBIG- Co0.A86 Source [5] BEBIG-GK60M21 Source [4] BEBIG- Co0.A86 Source [4] GZP6 Ch. 6 (This study) GZP6 Ch. 3/4 (This study)

1.094 1.084 1.087 1.093 1.097 1.086 1.087

a

      

0.002 0.005 0.011 0.002 0.002 0.005 0.005

Substituting the length of source (L Z 3.5 mm), the GL(1, 90
) has been obtained.

L/(GL(r Z 1 cm, q Z 90
)) (cGy h1 U1 cm2) 1.094 1.095 1.098 1.104 1.108 1.097 1.098

      

0.011 0.005 0.011a 0.002a 0.002a 0.005 0.005

Monte Carlo derivation of AAPM TG-43

155

Table 2 The radial dose function, gL(r), for channels 3/4 and 6 source designs in GZP6 HDR system. Distance (cm)

gL(r) for Ch. 6

gL(r) for Ch. 3/4

0.25 0.5 0.75 1 1.5 2 3 4 5 6 7 8 9 10 12 15 20

0.884 1.003 1.008 1.000 1.008 1.007 0.999 0.987 0.973 0.958 0.942 0.927 0.909 0.890 0.854 0.794 0.698

0.885 0.999 1.006 1.000 1.007 1.007 0.999 0.987 0.972 0.957 0.944 0.924 0.909 0.888 0.853 0.794 0.699

recommendations, liquid water has been assumed to have a density of 0.998 g cm3 (at 22
C). In order to obtain the dose rate in the form of along and away tables as well as dose rate constant and radial dose function, 400  800 cylindrical rings with similar height and thickness of 0.05  0.05 cm2, concentric to the longitudinal source axis was used. Another grid system which was employed to obtain the TG-43 parameters composed of 400  180 concentric spherical sections, 0.05 cm thick with an angular width of 1
in the polar angle q for both source designs. The coordinate center was set to the center of the active core (Fig. 1) [2,3,5].

In contrast with 192Ir and 137Cs sources, dose rate from the Co source cannot be approximated by kerma approximation due to high energy gamma spectrum of it. Therefore, it is reasonable to score both dose and kerma in liquid water up to 1 cm from the source capsule to account for the electronic disequilibrium range like previous studies [2,3,5]. However, it is shown that electronic equilibrium within 1% is reached for 60Co at distances greater than 7 mm from the source center [18]. In this study, the dose and kerma rate values are scored up to 2 cm distance, more conservative than previous studies following with only kerma values. However, kerma rate values were substituted by dose rate values up to 7 mm distance from the source center. The differences between kerma and dose are around 19% at 2 mm from the source, 3.3% at 5 mm and decreasing to 0.1% at 1.9 cm. The widely used dosimetric formalism to report the brachytherapy results in polar coordinates is adopted by the AAPM TG-43 [14]. According to the updated formalism, 2D dose rate in a medium at point P(r,q) relative to a source can be written as [15]: 60

_ qÞZSK ,L, GL ðr; qÞ ,gL ðrÞ,Fðr; qÞ Dðr; GL ðr0 ; q0 Þ

ð1Þ

where the parameters are described in [14,15]. Based on the proximity of the cell under calculation to the active source, 107 up to 1.5  109 photon histories were used to yield an average uncertainty less than 1%. To estimate the air kerma strength, a 4  4  4 m3 air cube was simulated with channel 3/4 and 6 sources in the middle. Based on the updated TG-43 recommendation [15], air with 40% humidity and density of 0.0012 g cm3 was taken into account. The corresponding grid composed of cylindrical rings 1 cm thick and 1 cm high which were scored along the transverse source axis from y Z 5 cm to y Z 150 cm [3,5,11]. 108 photon histories were used in order to obtain

Figure 2 Comparison of the radial dose functions, gL(r), for recent studied 60Co HDR sources [2e5] and GZP6 sources. The fifthorder polynomial curve fitting to GZP6 sources of channel 6 and 3/4 are shown as a solid line.

156

S. Hariri Tabrizi et al.

the air kerma strength with a standard deviation of K_ d ðdÞ of less than 0.2% (k Z 1).

the values divided by their geometrical factors (GL(r Z 1, q Z 90
)) are presented. Although Papagiannis et al [2] have used the “exact” geometry factor, Granero et al [5] and Ballester et al [3] have estimated the geometric function with the line source geometry approximation. In this study line source approximation with source length of L Z 0.35 cm was used, as well. Ratios in Table 1 reveal that L values for 60Co sources are proportional to the corresponding geometry factors and can be calculated, within clinically acceptable accuracy (2%), for any 60Co source design following the equation [2]:   L cGyh1 U1 ZLpoint  GL ð1 cm; 90+ ÞZ1:094   cGyh1 U1 cm2  GL ð1 cm; 90+ Þ ð2Þ

Results and discussion The air kerma obtained along the transverse axis of the sources was fitted to the linear equation kair(y)y2 Z Sk þ by, where Sk is the air kerma strength and b describes the buildup of scattered photons [19]. The air kerma strength for channel 6 source equals to 10 706  18 U per unit Curie activity and 10 716  18 U/Ci for channels 3/4 consistent with the Selvam et al [4] study. The bigger value for channels 3/4 can be attributed to the enclosed active capsule between steel balls from both sides which can backscatter the emitted gamma radiation to the evaluated cells. Table 1 shows the dose rate constants for previous studies on 60Co HDR sources [2e5] and compares them with the two source designs of GZP6 system (this study). Also, Table 3

The anisotropy function, F(r, q), for the channel 6

Table 2 presents the radial dose function, gL(r), for channels 3/4 and 6 60Co sources of GZP6 HDR system. The radial dose function has been fitted to a fifth-order polynomial based on TG-43 revised protocol [15] with coefficients 60

Co HDR source of GZP6 brachytherapy system.

q (
)

r (cm) 0.25

0.5

0.75

1

1.5

2

3

4

5

6

8

10

12

15

20

179 178 177 176 175 174 172 170 160 150 140 130 120 110 100 90 80 70 60 55 50 45 40 35 30 25 20 15 10 8 6 5 4 3 2 1

0.792 0.879 0.925 0.969 0.999 1.000 0.999 0.984 0.939 0.892 0.881 0.829 0.783 0.720 -

0.926 0.953 0.982 0.999 0.987 1.019 1.026 1.000 1.011 0.985 0.997 0.991 0.982 0.973 0.976 0.965 0.944 0.939 0.923 0.927 0.914 0.919 0.930 0.918 0.913 0.921 0.929 0.914

0.973 0.993 0.971 0.996 1.005 1.013 1.005 1.000 1.013 0.999 0.990 1.008 0.984 0.992 0.997 0.986 0.972 0.976 0.984 0.977 0.960 0.971 0.979 0.982 0.968 0.970 0.977 0.959

0.950 0.970 0.956 0.998 0.989 0.986 0.989 0.985 1.000 0.994 0.982 0.996 0.985 0.963 0.989 0.981 0.966 0.976 0.970 0.966 0.966 0.984 0.975 0.979 0.959 0.961 0.962 0.980 0.980

0.943 0.942 0.944 0.965 0.989 0.976 0.974 0.999 0.981 0.998 1.000 0.986 0.997 0.992 0.990 0.984 0.984 0.989 0.954 0.970 0.971 0.980 0.963 0.961 0.956 0.965 0.946 0.954 0.966 0.962 0.976

0.954 0.966 0.963 0.953 0.994 0.993 1.009 0.972 1.011 1.002 0.998 1.000 0.993 1.001 1.009 1.013 1.007 0.993 0.982 0.996 0.989 1.009 0.986 1.011 0.976 0.981 0.982 0.999 0.977 0.992 0.997 1.009

0.933 0.936 0.945 0.932 0.949 0.954 0.974 0.973 0.970 0.988 0.988 0.988 0.994 0.996 1.000 1.000 0.999 0.997 1.005 0.978 0.986 0.985 0.985 0.976 0.989 0.971 0.974 0.962 0.980 0.978 0.981 0.973 0.966 0.972 0.965

0.932 0.934 0.941 0.941 0.951 0.964 0.968 0.976 0.973 0.982 0.980 0.986 0.996 0.989 1.000 0.997 0.990 1.003 0.992 0.992 0.987 0.983 0.985 0.977 0.987 0.971 0.976 0.970 0.979 0.979 0.983 0.971 0.969 0.976 0.970

0.949 0.946 0.939 0.950 0.941 0.961 0.965 0.975 0.986 0.976 0.996 0.988 0.998 1.012 1.001 1.000 1.000 1.007 0.995 1.004 0.994 1.004 0.983 0.997 0.988 0.989 0.976 0.978 0.976 0.987 0.985 0.990 0.986 0.967 0.974 0.979

0.949 0.942 0.941 0.945 0.949 0.960 0.965 0.975 0.987 0.968 0.995 0.989 1.004 1.013 1.001 1.000 0.997 1.011 0.998 1.002 0.999 1.001 0.986 0.991 0.993 0.994 0.976 0.987 0.984 0.989 0.983 0.991 0.985 0.967 0.980 0.977

0.949 0.937 0.944 0.948 0.950 0.957 0.968 0.970 0.987 0.970 0.992 0.988 0.996 1.012 1.003 1.000 0.996 0.999 0.995 0.997 0.996 1.001 0.980 0.982 0.987 0.990 0.978 0.978 0.986 0.984 0.983 0.990 0.982 0.961 0.985 0.969

0.947 0.946 0.949 0.948 0.950 0.954 0.962 0.961 0.986 0.974 1.000 0.991 0.999 1.006 0.999 1.000 1.005 1.001 1.002 0.992 0.996 1.006 0.989 0.984 0.985 0.987 0.991 0.978 0.986 0.990 0.978 0.973 0.992 0.987 0.980 0.972

0.945 0.947 0.948 0.941 0.955 0.960 0.965 0.956 0.988 0.976 0.992 0.987 0.991 0.996 1.001 1.000 0.997 0.998 1.003 0.998 0.998 0.999 0.997 0.988 0.982 0.993 0.990 0.975 0.978 0.991 0.978 0.979 0.984 0.987 0.983 0.980

0.957 0.944 0.950 0.956 0.956 0.965 0.967 0.964 0.988 0.979 0.996 1.002 1.003 1.008 0.996 1.000 1.006 0.994 0.993 0.994 1.005 0.994 1.000 0.987 0.990 0.988 0.983 0.984 0.982 0.990 0.978 0.979 0.989 0.981 0.980 0.973

0.943 0.951 0.950 0.951 0.962 0.959 0.966 0.958 0.979 0.970 0.989 0.988 0.984 0.995 0.991 1.000 1.000 0.995 0.987 0.986 0.981 0.987 0.995 0.980 0.979 0.980 0.984 0.981 0.975 0.979 0.965 0.976 0.974 0.970 0.978 0.974

Monte Carlo derivation of AAPM TG-43

157

a0 Z 9.8228^-1, a1 Z 3.198^-2 cm1, a2 Z 1.144^-2 cm2, a3 Z 1.23^-3 cm3, a4 Z 6.13387^-5 cm4 and a5 Z 1.13181^-6 cm5 for channel 6 and coefficients a0 Z 9.7985^-1, a1 Z 3.403^-2 cm1, a2 Z 1.207^-2 cm2, a3 Z 1.3^-3 cm3, a4 Z 6.45427^-5 cm4 and a5 Z 1.18417^-6 cm5 for channels 3/4 sources between 0.3 and 20 cm from the source surface. The R-square values for these two fittings are 0.9913 and 0.9897 for channel 6 and channels 3/4 sources, respectively. Figure. 2 shows a comparison between radial dose functions of GZP6 60Co sources in channels 3/4 and 6 with comparable HDR 60Co source designs of previous studies [2e5]. The fitted fifth-order polynomial curve to the data points of channel 6 and channels 3/4 sources are shown, as well. The figure shows that there is a negligible difference between dose fall-off in the 60Co source designs of channels 3/4 and 6 in GZP6 system and other similar studies. Also, the most significant disagreement (z30%) is seen between BEBIG source model Co0.A86 [4]

Table 4

with GZP6 system at 0.15 cm distance from the source on the transverse axis. It is due to the different source design which especially appears in the most vicinity of the source. Tables 3 and 4 present reduced data of anisotropy function, F(r, q), for the GZP6 channels 6 and 3/4 60Co HDR sources, respectively. Full tables with high resolution are available from the authors upon request. Origin is taken at the active center of the source and the origin of the polar angle is on the side of the source tip. The values show that there is a variance from unit value near the source braid but at larger distances and on the central axis it approaches to 1. Also, there is almost symmetry on the transverse axis of the sources. The mean anisotropy values of two source designs up to 10 cm distance from the active cores are 0.983  0.019 and 0.985  0.023 for channels 3/4 and 6, respectively. Less variance in anisotropy factor for sources of channels 3/4 is because they are surrounded by steel balls which make uniform scatterers around them.

The anisotropy function, F(r, q), for the channels 3 / 4

60

Co HDR sources of GZP6 brachytherapy system.

q (
)

r (cm) 0.25

0.5

0.75

1

1.5

2

3

4

5

6

8

10

12

15

20

179 178 177 176 175 174 172 170 160 150 140 130 120 110 100 90 80 70 60 55 50 45 40 35 30 25 20 15 10 8 6 5 4 3 2 1

0.785 0.877 0.927 0.970 0.995 1.000 0.983 0.981 0.927 0.899 0.882 0.831 0.786 0.739 -

0.923 0.952 0.973 0.991 0.986 1.001 1.019 1.000 1.008 0.996 1.001 0.988 0.987 0.977 0.972 0.969 0.937 0.942 0.907 -

0.970 0.972 0.965 0.995 0.998 0.999 1.004 1.000 1.006 1.005 0.985 0.993 0.990 0.979 0.981 0.973 0.974 0.972 0.954 0.953 0.943 0.936 -

0.936 0.967 0.953 0.980 0.970 0.999 0.977 0.981 1.000 0.979 0.987 0.981 0.974 0.968 0.972 0.961 0.968 0.950 0.966 0.960 0.942 0.947 0.937 0.932 0.932 0.926 0.930 0.949 0.939

0.926 0.945 0.941 0.960 0.972 0.963 0.970 0.987 0.986 0.989 1.000 0.976 0.976 1.000 0.982 0.975 0.986 0.965 0.956 0.969 0.946 0.971 0.945 0.947 0.932 0.936 0.937 0.934 0.938 0.927 0.946

0.924 0.953 0.950 0.943 0.958 0.948 0.980 0.993 0.987 0.984 0.995 1.004 0.990 1.000 1.001 1.003 1.003 1.001 0.996 0.987 0.989 0.992 0.985 1.002 0.987 0.979 0.944 0.969 0.964 0.961 0.950 0.964 0.976 0.991

0.936 0.941 0.947 0.933 0.949 0.953 0.973 0.973 0.969 0.988 0.987 0.988 0.994 0.997 1.000 1.001 1.000 0.997 1.006 0.978 0.986 0.983 0.983 0.971 0.984 0.963 0.959 0.944 0.958 0.960 0.957 0.951 0.942 0.949 0.946

0.937 0.938 0.943 0.941 0.951 0.965 0.967 0.976 0.973 0.982 0.980 0.988 0.997 0.988 1.000 0.998 0.993 1.004 0.994 0.991 0.987 0.984 0.984 0.974 0.983 0.967 0.962 0.955 0.957 0.961 0.963 0.951 0.944 0.952 0.948

0.950 0.947 0.941 0.949 0.940 0.960 0.964 0.973 0.984 0.975 0.994 0.987 0.996 1.010 1.000 1.000 0.999 1.005 0.995 1.002 0.994 1.006 0.984 0.996 0.986 0.982 0.968 0.968 0.961 0.963 0.966 0.973 0.963 0.944 0.954 0.957

0.951 0.945 0.947 0.947 0.951 0.961 0.966 0.975 0.987 0.970 0.995 0.990 1.005 1.016 1.002 1.000 1.000 1.013 0.999 1.003 1.000 1.003 0.989 0.990 0.989 0.994 0.970 0.975 0.966 0.969 0.967 0.974 0.963 0.947 0.959 0.958

0.953 0.940 0.947 0.951 0.951 0.959 0.969 0.971 0.989 0.970 0.995 0.989 0.997 1.014 1.005 1.000 0.998 1.000 0.997 0.997 1.000 1.003 0.983 0.982 0.990 0.985 0.972 0.963 0.969 0.965 0.969 0.972 0.962 0.945 0.964 0.950

0.949 0.948 0.952 0.949 0.951 0.954 0.962 0.962 0.985 0.974 1.000 0.991 0.999 1.006 1.000 1.000 1.006 1.001 1.003 0.992 0.997 1.004 0.990 0.982 0.983 0.984 0.981 0.971 0.971 0.968 0.961 0.958 0.972 0.963 0.961 0.948

0.947 0.948 0.950 0.943 0.957 0.960 0.965 0.957 0.987 0.976 0.992 0.987 0.992 0.997 1.001 1.000 0.997 0.998 1.003 1.000 0.997 0.997 0.996 0.989 0.979 0.990 0.981 0.967 0.963 0.972 0.967 0.960 0.967 0.963 0.963 0.958

0.959 0.946 0.951 0.957 0.958 0.965 0.967 0.964 0.988 0.980 0.996 1.001 1.003 1.008 0.997 1.000 1.007 0.994 0.993 0.995 1.001 0.992 0.999 0.985 0.986 0.982 0.974 0.974 0.968 0.968 0.962 0.966 0.971 0.963 0.964 0.953

0.946 0.952 0.953 0.953 0.964 0.961 0.967 0.959 0.979 0.970 0.989 0.989 0.985 0.996 0.992 1.000 1.001 0.995 0.986 0.984 0.982 0.987 0.998 0.977 0.979 0.975 0.974 0.970 0.961 0.964 0.960 0.956 0.954 0.957 0.964 0.953

158

Table 5 Dose rate in an unbounded liquid water phantom per unit air kerma strength (cGy h1 U1) around the GZP6 defined in Fig. 1.

60

Co source of channel 6. The coordinate axes are

Distance away, y (cm) 0

0.25

0.5

0.75

1

1.5

2

2.5

3

4

5

6

8

10

14

14 10 8 6 5 4 3 2.5 2 1.5 1 0.75 0.5 0.25 0 0.25 0.5 0.75 1 1.5 2 2.5 3 4 5 6 8 10 14

e e e e e e e e e e e e e e e e 4.706 2.033 1.113 0.4884 0.2716 0.1734 0.1201 0.0648 0.0399 0.027 0.0147 0.0089 0.0042

0.0025 0.0057 0.0100 0.0192 0.0277 0.0433 0.0808 0.1254 0.2136 0.4088 0.9732 1.7671 3.6404 8.6800 14.9342 9.0159 3.8162 1.8340 1.0568 0.4776 0.2689 0.1706 0.1184 0.0655 0.0409 0.0281 0.0153 0.0094 0.0044

0.0032 0.0068 0.0107 0.0198 0.0308 0.0517 0.0989 0.1479 0.2365 0.4211 0.8776 1.3990 2.3301 3.7555 4.6400 3.7675 2.3255 1.4065 0.8972 0.4418 0.2579 0.1666 0.1162 0.0646 0.0409 0.0280 0.0152 0.0094 0.0044

0.0032 0.0068 0.0114 0.0224 0.0341 0.0560 0.1033 0.1493 0.2310 0.3851 0.7113 1.0048 1.4080 1.8348 2.0275 1.8320 1.4069 1.0064 0.7191 0.3934 0.2397 0.1594 0.1127 0.0635 0.0408 0.0280 0.0152 0.0093 0.0044

0.0033 0.0072 0.0123 0.0236 0.0356 0.0571 0.1021 0.1445 0.2144 0.3364 0.5577 0.7188 0.9021 1.0632 1.1278 1.0636 0.9031 0.7209 0.5602 0.3412 0.2190 0.1496 0.1074 0.0622 0.0399 0.0275 0.0152 0.0093 0.0043

0.0035 0.0078 0.0130 0.0245 0.0357 0.0556 0.0936 0.1262 0.1739 0.2449 0.3425 0.3975 0.4483 0.4854 0.4989 0.4853 0.4484 0.3980 0.3433 0.2456 0.1756 0.1276 0.0956 0.0578 0.0381 0.0267 0.0148 0.0092 0.0043

0.0037 0.0081 0.0133 0.0241 0.0345 0.0516 0.0814 0.1050 0.1363 0.1760 0.2216 0.2435 0.2619 0.2744 0.2788 0.2739 0.2618 0.2435 0.2217 0.1766 0.1367 0.1058 0.0826 0.0528 0.0357 0.0254 0.0144 0.0091 0.0043

0.0037 0.0082 0.0132 0.0233 0.0325 0.0468 0.0699 0.0864 0.1060 0.1288 0.1517 0.1620 0.1701 0.1752 0.1771 0.1750 0.1700 0.1623 0.1521 0.1286 0.1063 0.0864 0.0706 0.0471 0.0333 0.0241 0.0140 0.0088 0.0043

0.0038 0.0081 0.0128 0.0220 0.0300 0.0415 0.0592 0.0704 0.0832 0.0968 0.1094 0.1145 0.1187 0.1211 0.1220 0.1212 0.1186 0.1145 0.1095 0.0968 0.0834 0.0704 0.0592 0.0421 0.0303 0.0226 0.0134 0.0086 0.0042

0.0038 0.0078 0.0119 0.0191 0.0249 0.0326 0.0423 0.0476 0.0534 0.0589 0.0634 0.0651 0.0664 0.0672 0.0676 0.0673 0.0662 0.0652 0.0633 0.0587 0.0535 0.0479 0.0424 0.0326 0.0250 0.0194 0.0121 0.0081 0.0040

0.0037 0.0072 0.0107 0.0162 0.0203 0.0251 0.0306 0.0335 0.0363 0.0388 0.0408 0.0414 0.0421 0.0424 0.0425 0.0425 0.0421 0.0415 0.0408 0.0388 0.0364 0.0336 0.0307 0.0252 0.0203 0.0164 0.0108 0.0074 0.0038

0.0035 0.0066 0.0095 0.0137 0.0164 0.0196 0.0228 0.0244 0.0259 0.0271 0.0282 0.0285 0.0288 0.0289 0.0290 0.0289 0.0289 0.0284 0.0282 0.0272 0.0258 0.0244 0.0229 0.0195 0.0165 0.0137 0.0096 0.0068 0.0036

0.0031 0.0054 0.0073 0.0096 0.0109 0.0123 0.0135 0.0142 0.0147 0.0151 0.0154 0.0156 0.0156 0.0157 0.0157 0.0157 0.0156 0.0156 0.0154 0.0151 0.0147 0.0142 0.0136 0.0123 0.0110 0.0096 0.0073 0.0055 0.0032

0.0027 0.0043 0.0055 0.0068 0.0075 0.0082 0.0088 0.0090 0.0092 0.0094 0.0095 0.0096 0.0096 0.0096 0.0097 0.0097 0.0097 0.0096 0.0095 0.0094 0.0093 0.0090 0.0088 0.0081 0.0075 0.0068 0.0055 0.0044 0.0027

0.0019 0.0027 0.0032 0.0037 0.0039 0.0041 0.0043 0.0044 0.0044 0.0044 0.0045 0.0045 0.0045 0.0045 0.0045 0.0045 0.0045 0.0045 0.0045 0.0044 0.0044 0.0043 0.0043 0.0041 0.0039 0.0037 0.0032 0.0027 0.0019

S. Hariri Tabrizi et al.

Distance along, x (cm)

Distance along, x (cm)

Distance away, y (cm) 0

0.25

0.5

0.75

1

1.5

2

2.5

3

4

5

6

8

10

14

14 10 8 6 5 4 3 2.5 2 1.5 1 0.75 0.5 0.25 0 0.25 0.5 0.75 1 1.5 2 2.5 3 4 5 6 8 10 14

e e e e e e e e e e e e e e e e e 1.5470 1.0330 0.4460 0.2479 0.1584 0.1092 0.0610 0.0382 0.0260 0.0143 0.0087 0.0040

0.0028 0.0063 0.0108 0.0212 0.0321 0.0521 0.0945 0.1385 0.2268 0.4291 1.0115 1.8572 3.8615 9.4063 15.1768 9.4274 3.8588 1.8121 1.0095 0.4456 0.2491 0.1587 0.1096 0.0610 0.0384 0.0263 0.0142 0.0088 0.0042

0.0034 0.0075 0.0124 0.0229 0.0338 0.0551 0.1037 0.1531 0.2431 0.4302 0.8948 1.4315 2.3559 3.7663 4.5845 3.7625 2.3518 1.4241 0.8934 0.4283 0.2432 0.1554 0.1079 0.0600 0.0380 0.0260 0.0142 0.0088 0.0041

0.0036 0.0078 0.0126 0.0239 0.0358 0.0581 0.1061 0.1529 0.2343 0.3904 0.7195 1.0156 1.4129 1.8246 2.0122 1.8258 1.4099 1.0155 0.7190 0.3895 0.2335 0.1523 0.1060 0.0594 0.0376 0.0258 0.0141 0.0088 0.0041

0.0037 0.0079 0.0130 0.0247 0.0366 0.0586 0.1040 0.1463 0.2168 0.3400 0.5615 0.7226 0.9042 1.0614 1.1240 1.0617 0.9037 0.7222 0.5615 0.3397 0.2163 0.1459 0.1037 0.0588 0.0374 0.0257 0.0141 0.0087 0.0041

0.0038 0.0082 0.0135 0.0252 0.0365 0.0563 0.0944 0.1270 0.1750 0.2460 0.3436 0.3984 0.4485 0.4851 0.4981 0.4850 0.4486 0.3981 0.3436 0.2460 0.1748 0.1268 0.0943 0.0563 0.0365 0.0252 0.0139 0.0086 0.0041

0.0038 0.0084 0.0136 0.0246 0.0349 0.0521 0.0823 0.1055 0.1367 0.1766 0.2221 0.2438 0.2620 0.2742 0.2785 0.2743 0.2621 0.2439 0.2220 0.1765 0.1367 0.1054 0.0822 0.0520 0.0349 0.0245 0.0137 0.0085 0.0041

0.0039 0.0084 0.0134 0.0236 0.0326 0.0470 0.0702 0.0865 0.1064 0.1292 0.1521 0.1621 0.1702 0.1752 0.1770 0.1752 0.1701 0.1621 0.1521 0.1291 0.1063 0.0864 0.0701 0.0470 0.0326 0.0235 0.0134 0.0084 0.0041

0.0039 0.0083 0.0130 0.0222 0.0301 0.0418 0.0593 0.0706 0.0834 0.0970 0.1095 0.1147 0.1186 0.1211 0.1220 0.1211 0.1186 0.1147 0.1095 0.0969 0.0834 0.0705 0.0593 0.0419 0.0302 0.0222 0.0130 0.0083 0.0040

0.0039 0.0079 0.0120 0.0193 0.0249 0.0326 0.0424 0.0479 0.0535 0.0589 0.0634 0.0652 0.0664 0.0673 0.0675 0.0673 0.0664 0.0652 0.0635 0.0589 0.0535 0.0480 0.0423 0.0325 0.0249 0.0193 0.0120 0.0078 0.0039

0.0037 0.0073 0.0108 0.0164 0.0203 0.0252 0.0307 0.0336 0.0364 0.0388 0.0408 0.0415 0.0421 0.0424 0.0425 0.0424 0.0421 0.0415 0.0408 0.0388 0.0364 0.0335 0.0307 0.0251 0.0203 0.0163 0.0107 0.0073 0.0038

0.0036 0.0067 0.0095 0.0137 0.0165 0.0195 0.0229 0.0244 0.0259 0.0272 0.0282 0.0285 0.0288 0.0289 0.0290 0.0289 0.0288 0.0285 0.0282 0.0272 0.0259 0.0245 0.0228 0.0196 0.0165 0.0137 0.0095 0.0067 0.0036

0.0032 0.0055 0.0073 0.0096 0.0110 0.0123 0.0136 0.0142 0.0147 0.0151 0.0155 0.0156 0.0156 0.0157 0.0157 0.0157 0.0157 0.0156 0.0155 0.0151 0.0147 0.0142 0.0136 0.0123 0.0110 0.0096 0.0073 0.0055 0.0031

0.0027 0.0044 0.0055 0.0068 0.0075 0.0082 0.0088 0.0090 0.0093 0.0094 0.0096 0.0096 0.0096 0.0097 0.0097 0.0097 0.0096 0.0096 0.0096 0.0094 0.0093 0.0090 0.0088 0.0082 0.0075 0.0068 0.0055 0.0044 0.0027

0.0019 0.0027 0.0032 0.0037 0.0039 0.0041 0.0043 0.0043 0.0044 0.0044 0.0045 0.0045 0.0045 0.0045 0.0045 0.0045 0.0045 0.0045 0.0045 0.0044 0.0044 0.0043 0.0043 0.0041 0.0039 0.0037 0.0032 0.0027 0.0019

Monte Carlo derivation of AAPM TG-43

Table 6 Dose rate in an unbounded liquid water phantom per unit air kerma strength (cGy h1 U1) around the GZP6 60Co sources of channels 3/4. The coordinate axes are defined in Fig. 1.

159

160 Tables 5 and 6 summarize the along e away dose rate for channel 6 and channels 3/4 sources of GZP6 afterloader, respectively. Based on the updated AAPM TG-43 protocol [15], uncertainty analysis of the obtained results includes statistical (A) and systemic uncertainty (B). All the statistical (type A) uncertainties in water phantom calculations are limited to less than 0.6% (k Z 1) except in the grid elements so near to the source where it is about 1.0% (k Z 1). The air kerma strength uncertainty is less than 0.2% (k Z 1). The quadrature sum of these two terms gives a total statistical uncertainty of 0.6% (k Z 1), except at points located near to the longitudinal axis with about 1.0% (k Z 1) value. The type B uncertainty is difficult to evaluate and negligible for 60Co sources [3]. Thus, the total uncertainty of TG-43 parameters can be attributed to A type and it is less than or about 1.0%.

Conclusions The TG-43 parameters of three GZP6 60Co HDR sources with two different designs were calculated by Monte Carlo method (channels 6, 3 and 4). The parameters consist of air kerma strength, dose rate constant, radial dose function and anisotropy function. Also, the along e away table of dose rate for these sources are presented for data validation purpose. The obtained TG-43 dosimetric parameters are consistent with other 60Co HDR system datasets [2e5] and they have an uncertainty less than 1%. As a result, they can be used to validate the current TPS as well as to develop a complementary TPS. The existing GZP6 HDR system utilizes a treatment planning software which has some deficiencies including lack of a comprehensive treatment planning software for nonpredefined treatments and uncommon anatomies, lack of ability to adapt the gradually changeable dosimetric variables and using the point source estimation in dose calculation. They can be overcome by introduction of a complementary TPS using the obtained dosimetric parameters [17].

Acknowledgments The authors acknowledge Prof. M. Shahriari for his useful comments and Mr. A. Jabbari for supporting the system datasets. This research is supported by Research and Technology office of Shahid Beheshti University, grant number 600/1399.

References [1] Richter J, Baier K, Flentje M. Comparison of 60Cobalt and 192 Iridium sources in high dose rate afterloading brachytherapy. Strahlenther Onkol 2008;184:187e92.

S. Hariri Tabrizi et al. [2] Papagiannis P, Angelopoulos A, Pantelis E, Sakelliou L, Karaiskos P, Shimizu Y. Monte Carlo dosimetry of 60Co HDR brachytherapy sources. Med Phys 2003;30:712e21. [3] Ballester F, Granero D, Pe ´rez-Calatayud J, Casal E, Agramunt S, Cases R. Monte Carlo dosimetric study of the BEBIG Co-60 HDR source. Phys Med Biol 2005;50:N309e16. [4] Selvam T, Bhola S. Technical note: EGSnrc-based dosimetric study of the BEBIG 60Co HDR brachytherapy sources. Med Phys 2010;37(3):1365e70. [5] Granero D, Pe ´rez-Calatayud J, Ballester F. Technical note: dosimetric study of a new Co-60 source used in brachytherapy. Med Phys 2007;34(9):3485e8. [6] Mesbahi A, Naseri A. In-air calibration of new high dose rate 60 Co brachytherapy sources: results of measurements on a GZP6 brachytherapy afterloading unit. Rep Pract Oncol Radiother 2008;13:69e73. [7] Mesbahi A. Radial dose functions of GZP6 intracavitary brachytherapy 60Co sources: treatment planning system versus Monte Carlo calculations. Iran J Radiat Res 2008;5:181e6. [8] Naseri A, Mesbahi A. Application of Monte Carlo calculations for validation of a treatment planning system in high dose rate brachytherapy. Rep Pract Oncol Radiother 2010;14:200e4. [9] Taylor R, Rogers D. EGSnrc Monte Carlo calculated dosimetry parameters for 192Ir and 169Yb brachytherapy sources. Med Phys 2008;35(11):4933e44. [10] Pe ´rez-Calatayud J, Granero D, Casal E, Ballester F, Puchades V. Monte Carlo and experimental derivation of TG43 dosimetric parameters for CSM-type Cs-137 sources. Med Phys 2005;32(1):28e36. [11] Ballester F, Granero D, Perez-Calatayud J, Casal E, Puchades V. Monte Carlo dosimetric study of best industries and alpha omega Ir-192 brachytherapy seeds. Med Phys 2004; 31:3298e305. [12] Casado F, Garcı´a-Pareja S, Cenizo E, Mateo B, Bodineau C, Gala ´n P. Dosimetric characterization of an 192Ir brachytherapy source with the Monte Carlo code PENELOPE. Physica Med 2010;26:132e9. [13] Williamson J, Li Z. Monte Carlo aided dosimetry of the microselectron pulsed and high dose-rate 192Ir sources. Am Assoc Phys Med 1995;22(6):809e19. [14] Nath R, Anderson L, Luxton G, Weaver K, Williamson J, Meigooni A. Dosimetry of interstitial brachytherapy sources: recommendations of the AAPM radiation therapy committee task group no. 43. Med Phys 1995;22:209e34. [15] Rivard M, Coursey B, DeWerd L, Hanson WF, Huq MS, Ibbott GS, et al. Update of AAPM task group no. 43 report: a revised AAPM protocol for brachytherapy dose calculations. Med Phys 2004;31:633e74. [16] Briesmeister J. MCNP-A general Monte Carlo N-particle transport code. Version 4C. Los Alamos National Laboratory; 2000. [17] Hariri S, Kamali Asl A. Introducing a complementary treatment planning software for GZP6 brachytherapy system. Paper presented at: 3rd International Conference on Biomedical Engineering and Informatics (BMEI). Yantai, China; 2010. [18] Ballestera F, Granero D, Pe ´rez-Calatayud J, Melhus CS, Rivard MJ. Evaluation of high-energy brachytherapy source electronic disequilibrium and dose from emitted electrons. Med Phys 2009;36(9):4250e6. [19] Williamson J. Monte Carlo evaluation of kerma at a point for photon transport problems. Am Assoc Phys Med 1987;14(4): 567e76.