Evaluation of Dosimetric Parameters for Various 192Ir Brachytherapy Sources Under Unbounded Phantom Geometry by Monte Carlo Simulation

Medical Dosimetry, Vol. 32, No. 4, pp. 305-315, 2007 Copyright © 2007 American Association of Medical Dosimetrists Printed in the USA. All rights reserved 0958-3947/07/$–see front matter

doi:10.1016/j.meddos.2007.03.005

EVALUATION OF DOSIMETRIC PARAMETERS FOR VARIOUS 192Ir BRACHYTHERAPY SOURCES UNDER UNBOUNDED PHANTOM GEOMETRY BY MONTE CARLO SIMULATION KRISHNAMURTHY DEVAN, M.SC., PRAKASARAO ARUNA, PH.D., DURAI MANIGANDAN, M.SC., GANESAN BHARANIDHARAN, M.SC., KAMATAM VENKATA SUBBAIAH, PH.D., CHIRAVATH SUNIL SUNNY, PH.D., and SINGARAVELU GANESAN, PH.D. Division of Medical Physics and Lasers, Department of Physics, Anna University, Chennai, India; and Safety Research Institute, Atomic Energy Regulatory Board, Indira Gandhi Centre for Atomic Research, Kalpakkam, India (Received 7 March 2007; accepted 29 March 2007)

Abstract—As per TG-43 dose calculation formalism, it is essential to obtain various dosimetric parameters such as the air-kerma strength, dose rate constant, radial dose function, and anisotropy function, as they account for accurate determination of dose rate distribution around brachytherapy sources. Most of the available reported Monte Carlo simulations were performed in liquid water phantoms with a bounded region of 30-cm diameter. In this context, an attempt was made to report the dosimetric parameters for various commercially available pulsed-dose rate (PDR) and high-dose rate (HDR) sources under unbounded phantom conditions, as the data may be used as input to treatment planning systems (TPSs) for quality control assistance. The air-kerma strength per unit activity, Sk/A, was computed for various Iridium-192 (192Ir) sources in dry air medium. The air-kerma strength and dose rate constant for old PDR is (9.77 ⴞ 0.03) 10ⴚ8 U/Bq and 1.124 ⴞ 0.001 cGyhⴚ1Uⴚ1; for new PDR, the values are (9.96 ⴞ 0.03) 10ⴚ8 U/Bq and 1.124 ⴞ 0.001 cGyhⴚ1Uⴚ1; for old MHDR, the values are (9.80 ⴞ 0.01) 10ⴚ8 U/Bq and 1.115 ⴞ 0.001 cGyhⴚ1Uⴚ1; for new MHDR, (9.80 ⴞ 0.01) 10ⴚ8 U/Bq and 1.112 ⴞ 0.001cGyhⴚ1Uⴚ1; for old VHDR, the values are (10.32 ⴞ 0.01) 10ⴚ8 U/Bq and 1.035 ⴞ 0.002 cGyhⴚ1Uⴚ1; for new VHDR, the values are (10.34 ⴞ 0.02) 10ⴚ8 U/Bq and 1.096 ⴞ 0.001 cGyhⴚ1Uⴚ1. The computed radial dose function values and anisotropy function values are also in good agreement with available data. © 2007 American Association of Medical Dosimetrists. Key Words: Monte Carlo simulation, Brachytherapy, Pulsed-dose rate (PDR), High-dose rate (HDR).

INTRODUCTION

ing small volume ionization chambers, diode detectors, thermoluminescence dosimeters, and film dosimeters, they have the following limitations: ionization chambers are unsuitable for dose measurements around brachytherapy sources due to inferior radiation sensitivity, and lack of the spatial resolution necessary to map high-dose gradients present in the vicinity of brachytherapy sources. The semiconductor diode detector has the advantage of high spatial resolution due to its small size and high radiation sensitivity, but it exhibits enhanced response to low-energy photons emanating from some brachytherapy sources and by Compton interaction in the measuring medium. Thermoluminescence dosimeters are also being employed as a gold standard for brachytherapy dose measurements; however, they need to be corrected for changes in photon spectrum in the medium. A diamond detector is considered to be suitable for the dosimetry of HDR brachytherapy source, provided the seed activity is in the 2 to 20 mCi range, due to sufficient high signal to noise ratio3; hence, it is ideal only for LDR dosimetry. In the case of radiochromic film dosimetry, the dose from the exposed films can only be read after 24 hours. It also involves positional error in finding the dose at a particular point. Further, the absorbed dose from sources of small dimensions used for brachytherapy ap-

There is a wide range of models of radioactive sources commercially available for various brachytherapy applications, for example, low-dose rate (LDR), pulsed-dose rate (PDR) and high-dose rate (HDR). The Iridium-192 (192Ir) radionuclide is commonly and widely used for many brachytherapy applications. Most of the commercially available remote after-loading systems utilize a single cylindrical 192Ir stepping source. The clinical uses of these sources require accurate determination of the air-kerma strength, dose rate constant, radial dose function, and anisotropy function as per TG-43 formalism.1 These parameters are essential, as they account for accurate determination of dose rate distribution around brachytherapy sources. Because of the differences in source design, a specific dataset for each source design should be obtained, for every new source design, to introduce them for clinical practice effectively.2 Although dose rate distributions around any brachytherapy source are being determined experimentally usReprint requests to: Singaravelu Ganesan, Ph.D., Division of Medical Physics and Lasers, Department of Physics, Anna University, Chennai 600 025, India. E-mail: [email protected] 305

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Table 1. Computed values of dose rate constant for various 192 Ir sources Dose Rate Constant (cGy h⫺1U⫺1) No. PDR 1 2 HDR 3 4 5 6

Source Type

Present Study

Literature

Old PDR New PDR

1.124 ⫾ 0.001 1.124 ⫾ 0.001

1.128 ⫾ 0.00520 1.121 ⫾ 0.00610

Old MHDR New MHDR Old VHDR New VHDR

1.115 ⫾ 0.001 1.112 ⫾ 0.001 1.035 ⫾ 0.002 1.096 ⫾ 0.001

1.115 ⫾ 0.00521 1.109 ⫾ 0.00521 1.043 ⫾ 0.00521 1.101⫾ 0.00621

plications is found to be highly nonuniform due to the steep dose gradient in the vicinity of the sources.4 The dose rate around a cylindrical brachytherapy source is partially expected to vary with angle, as a result of the variation of the photon energy spectrum due to oblique filtration and source self-absorption.5 In addition to the primary photon spectrum and medium, the dose distribution is also found to depend significantly on the geometric characteristics of the source and encapsulation materials.6 In this regard, commercially available treatment planning systems (TPS) make use of different input data for their dose rate calculations. Most of the TPS requires tabular entry of 2-dimensional distribution of data, termed as the traditional “along and away” table. Therefore, it is recommended that dose rate distribution data should be obtained accurately by any of the appropriate methods, based on a realistic geometry and on the mechanical characteristics of the source. The data set thus obtained can be used as input data to verify the TPS. Thus, the treatment quality can be improved by means of accurate dose delivery. In this context, the Monte Carlo simulation technique has been recognized as one of the techniques in the clinical radiation dosimetry of radioac-

Volume 32, Number 4, 2007

tive sources.7 Further, the Monte Carlo method has also been utilized to calculate absolute dose rate in water around sources and to estimate its statistical errors. This is because Monte Carlo simulation is limited neither by the complexity of the underlying physics of radiation interactions nor by the geometric complexity of clinical brachytherapy sources and applicators that are possible in the experimental methods.8 This approach is made feasible by the availability of more and accurate photon cross-section libraries. Further, the actual or realistic source geometry has to be taken into consideration for accurate dosimetry in a medium. Most of the available reported Monte Carlo simulations were performed in liquid water phantoms with a bounded region of 30-cm diameter. In this regard, only limited data9 –11 are available for 192Ir brachytherapy sources under unbounded phantom conditions using Monte Carlo simulation. Williamson9 calculated the dose rate constant for LDR steel-clad seed both under unbounded liquid water and solid water phantom, and Nath et al.12 solid water phantom. He reported the dose rate constant (⌳) values, 1.110 ⫾ 0.2%, 1.121 ⫾ 0.3%, 1.119 ⫾ 0.2% cGyh⫺1U⫺1 under unbounded liquid water phantom, unbounded solid water phantom, and Nath et al.12 solid water phantom, respectively. He also reported the radial dose function values under unbounded liquid-water medium for the seed. He observed that the phantom geometry significantly influenced the radial dose distribution at long distances (5 to 15 cm) from the seed. Karaiskos et al.10 calculated the radial dose function for the new MicroSelectron PDR source design and for an isotropic point 192Ir source under unbounded liquid water phantom condition. They observed a significant difference between the distance of source-to-body surface and source-to-phantom boundary for different phantom geometry. They also reported that for bounded and unbounded phantom, the radial dose function values

Table 2. Radial dose function values computed for various

192

Ir sources

Radial Dose Function g(r) Distance Along Transverse Axis (cm)

Old PDR

New PDR

Old MHDR

New MDHR

Old VHDR

New VHDR

0.25 0.50 0.75 1 1.5 2 3 4 5 6 7 8 10 12 15 20

0.992 0.996 1.003 1.000 1.007 1.009 1.013 1.013 1.012 1.006 0.998 0.988 0.957 0.917 0.844 0.704

0.991 0.997 0.998 1.000 1.005 1.009 1.016 1.015 1.012 1.007 0.999 0.987 0.958 0.919 0.845 0.704

0.992 0.996 0.997 1.000 1.004 1.007 1.008 1.011 1.006 1.001 0.992 0.981 0.949 0.910 0.836 0.695

0.991 0.995 0.996 1.000 1.003 1.007 1.011 1.010 1.008 0.999 0.992 0.979 0.948 0.908 0.836 0.693

0.979 0.985 0.992 1.000 1.001 1.004 1.008 1.011 1.007 1.003 0.993 0.986 0.950 0.910 0.837 0.697

0.982 0.991 0.993 1.000 1.001 1.005 1.009 1.012 1.006 1.001 0.994 0.982 0.951 0.913 0.838 0.698

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Fig. 1. (a) Comparison of radial dose function for old PDR with Williamson et al.20 (b) Comparison of radial dose function for new PDR with Karaiskos et al.10 (c) Comparison of radial dose function for old MHDR with Williamson et al.20 (d) Comparison of radial dose function for old VHDR with Karaiskos et al.10 (e) Comparison of radial dose function for new VHDR with Angelopoulos et al.6

increase with that of radial distance (over 3% for r ⬎ 7 cm and reaching up to 23%). This was attributed to the lack of backscatter at points nearer to the boundary of liquid water phantom (radius ⫽ 15 cm). To the best of our knowledge, Ballester et al.11 only reported the detailed dosimetric parameters for Alpha Omega and Best Industries LDR 192Ir seed sources under unbounded liquid water phantom conditions, i.e., phantom with a maximum radius of 40 cm. They computed the complete set of TG-43 dosimetry data under unbounded liquid water phantom conditions using GEANT4 Monte Carlo code for both the LDR seeds. However, not much of Monte Carlo computed dosimetric

data are available for other commercial PDR and HDR 192 Ir sources under unbounded phantom conditions. Based on these, an attempt was made to obtain the dosimetric data (air-kerma strength, dose rate constant, radial dose function, and anisotropy function) under unbounded phantom conditions for various commercially available brachytherapy sources at greater distances (up to 14 cm) from the source using the MCNP4B code. It is also aimed to provide 2D rectangular away and along dose rate table for various PDR and HDR sources compatible to TG-43, as it may be used as an input to treatment planning systems for accurate dose estimation purpose and quality control assistance. The computed

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Table 3. Dose rate in water per unit air-kerma strength (cGy/hU) around old PDR source (origin taken at geometric center of the source) Distance Along z (cm) 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

Distance Away y (cm) 0

0.25

0.5

0.75

1

1.5

2

2.5

3

4

5

6

8

10

14

0.0050 0.0050 0.0050 0.0050 0.0049 0.0049 0.0049 0.0048 0.0047 0.0045 0.0043 0.0040 0.0035 0.0030 0.0020 0.0106 0.0107 0.0106 0.0106 0.0105 0.0104 0.0102 0.0100 0.0097 0.0091 0.0084 0.0076 0.0062 0.0049 0.0030 0.0172 0.0171 0.0172 0.0171 0.0170 0.0166 0.0162 0.0156 0.0150 0.0137 0.0122 0.0108 0.0082 0.0062 0.0035 0.0308 0.0309 0.0310 0.0306 0.0304 0.0294 0.0281 0.0267 0.0250 0.0215 0.0182 0.0153 0.0108 0.0077 0.0041 0.0449 0.0448 0.0445 0.0442 0.0434 0.0415 0.0391 0.0363 0.0333 0.0276 0.0225 0.0183 0.0123 0.0084 0.0043 0.0703 0.0702 0.0697 0.0686 0.0667 0.0622 0.0569 0.0512 0.0457 0.0355 0.0277 0.0216 0.0138 0.0092 0.0046 0.1248 0.1244 0.1224 0.1189 0.1140 0.1014 0.0881 0.0752 0.0637 0.0457 0.0335 0.0252 0.0151 0.0098 0.0047 0.1803 0.1794 0.1750 0.1674 0.1579 0.1344 0.1118 0.0918 0.0753 0.0516 0.0366 0.0268 0.0158 0.0101 0.0048 0.2824 0.2793 0.2687 0.2503 0.2289 0.1830 0.1435 0.1122 0.0886 0.0574 0.0394 0.0284 0.0163 0.0103 0.0049 0.5042 0.4951 0.4611 0.4083 0.3533 0.2555 0.1848 0.1357 0.1024 0.0629 0.0420 0.0297 0.0168 0.0105 0.0049 1.1535 1.0936 0.9298 0.7401 0.5771 0.3542 0.2303 0.1586 0.1149 0.0675 0.0440 0.0307 0.0171 0.0107 0.0050 2.0904 1.8882 1.4454 1.0337 0.7400 0.4093 0.2515 0.1684 0.1202 0.0692 0.0447 0.0310 0.0172 0.0107 0.0050 4.9108 3.8889 2.3687 1.4344 0.9241 0.4586 0.2691 0.1762 0.1237 0.0705 0.0452 0.0312 0.0173 0.0107 0.0050 15.8896 10.0401 3.7754 1.8426 1.0765 0.4928 0.2809 0.1811 0.1261 0.0712 0.0454 0.0314 0.0173 0.0107 0.0050 —– 17.6881 4.4694 1.9956 1.1240 0.5011 0.2836 0.1824 0.1263 0.0712 0.0454 0.0314 0.0173 0.0107 0.0050 10.0486 7.4930 3.3558 1.7390 1.0375 0.4834 0.2771 0.1797 0.1253 0.0708 0.0453 0.0313 0.0173 0.0107 0.0050 2.5541 2.8056 2.0050 1.2973 0.8645 0.4429 0.2641 0.1736 0.1222 0.0699 0.0448 0.0311 0.0172 0.0107 0.0050 1.1749 1.3461 1.1878 0.9124 0.6777 0.3899 0.2437 0.1645 0.1179 0.0684 0.0443 0.0308 0.0173 0.0107 0.0050 0.6814 0.7654 0.7444 0.6404 0.5197 0.3337 0.2208 0.1541 0.1123 0.0663 0.0434 0.0304 0.0170 0.0106 0.0049 0.3158 0.3374 0.3553 0.3408 0.3092 0.2352 0.1736 0.1301 0.0989 0.0615 0.0413 0.0294 0.0166 0.0104 0.0049 0.1835 0.1900 0.2043 0.2063 0.1945 0.1654 0.1334 0.1064 0.0849 0.0559 0.0386 0.0279 0.0161 0.0102 0.0049 0.1207 0.1227 0.1304 0.1337 0.1316 0.1188 0.1024 0.0859 0.0714 0.0497 0.0356 0.0263 0.0156 0.0100 0.0048 0.0855 0.0867 0.0909 0.0937 0.0939 0.0884 0.0793 0.0694 0.0599 0.0439 0.0325 0.0245 0.0149 0.0097 0.0047 0.0502 0.0503 0.0516 0.0529 0.0538 0.0528 0.0505 0.0463 0.0421 0.0336 0.0265 0.0209 0.0134 0.0090 0.0045 0.0330 0.0329 0.0335 0.0339 0.0347 0.0348 0.0337 0.0322 0.0302 0.0257 0.0214 0.0176 0.0119 0.0083 0.0043 0.0230 0.0232 0.0234 0.0237 0.0241 0.0243 0.0240 0.0233 0.0223 0.0199 0.0172 0.0146 0.0104 0.0075 0.0040 0.0133 0.0133 0.0133 0.0134 0.0135 0.0137 0.0137 0.0135 0.0132 0.0123 0.0113 0.0101 0.0078 0.0060 0.0035 0.0086 0.0085 0.0085 0.0085 0.0085 0.0086 0.0086 0.0086 0.0085 0.0081 0.0076 0.0071 0.0058 0.0047 0.0029 0.0042 0.0041 0.0041 0.0041 0.0041 0.0041 0.0041 0.0041 0.0041 0.0040 0.0039 0.0037 0.0033 0.0028 0.0020

values were also compared with the already reported experimental values. METHODS AND MATERIALS Brachytherapy sources Calculations were performed around (a) the 2 microSelectron-PDR brachytherapy sources (old and new design)10; (b) the 2 microSelectron-HDR brachytherapy sources (old and new design)4,13 (Nucletron B.V., Veenendaal, The Netherlands); and (c) the 2 VariSourceHDR brachytherapy sources (old and new design)4,6 (Varian Oncology Systems, Palo Alto, CA). The compositional data for all the sources modeled in this study were taken from Baltas et al.4 Two MicroSelectron PDR (old and new design) sources manufactured by Nucletron International are commercially available. The internal construction and dimensions of the old and new PDR sources used for our simulation were taken from Karaiskos et al.10 The old design consists of 2 cylindrical Iridium pellets of 0.6 mm length and 0.6 mm diameter each, with only distal most being radioactive. The new design consists of 2 cylindrical radioactive Iridium pellets of 0.5 mm length and 0.5 mm diameter each. Overall, the new PDR design presents an active core length increase of 0.4 mm and an active core diameter decrease of 0.1 mm. Both sources are encapsulated with an AISI 316L stainless steel cyl-

inder that is 1.1 mm in the outer diameter and bears a cavity of 1.2 mm length and 0.6 mm diameter. In the new source design, an air gap exists between the active pellet and the encapsulation that was modeled as 0.1 mm thick in the longitudinal axis direction and 0.05 mm thick in the transverse axis direction. The encapsulation end is semi spherically shaped and the distance from its tip to pellet is 0.55 mm for the old and 0.5 mm for the new PDR design. These sources will henceforth be referred to as old PDR and new PDR sources, respectively. Two MicroSelectron HDR (old and new design) sources manufactured by Nucletron International are commercially available. The internal construction and dimensions of the old and new HDR sources used for our simulation was taken from Daskalov et al.13 and Baltas et al.,4 respectively. The old MicroSelectron HDR source design is 0.6 mm in diameter by 3.5 mm long, and the new MicroSelectron HDR source design is a 0.65 mm diameter by 3.6 mm long cylinder of pure Iridium metal, within which the radioactive 192Ir is uniformly distributed. The old source is encapsulated in an AISI 316L stainless steel capsule with an outer diameter of 1.1 mm and a spherical distal end with a radius of curvature of 0.55 mm, welded to a steel cable having a total length of approximately 6.85 mm. The distance from the distal face of the active source core to the physical source tip is 0.35 mm. The new source is also encapsulated in an AISI

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Table 4. Dose rate in water per unit air-kerma strength (cGy/hU) around new PDR source (origin taken at geometric center of source) Distance Along z (cm) 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

Distance Away y (cm) 0

0.25

0.5

0.75

1

1.5

2

2.5

3

4

5

6

8

10

14

0.0047 0.0047 0.0047 0.0047 0.0047 0.0046 0.0046 0.0046 0.0045 0.0043 0.0041 0.0039 0.0034 0.0029 0.0020 0.0098 0.0102 0.0100 0.0099 0.0099 0.0098 0.0097 0.0095 0.0092 0.0087 0.0081 0.0074 0.0060 0.0048 0.0030 0.0157 0.0159 0.0159 0.0158 0.0158 0.0156 0.0153 0.0149 0.0144 0.0131 0.0118 0.0105 0.0080 0.0061 0.0035 0.0284 0.0286 0.0287 0.0286 0.0281 0.0277 0.0265 0.0254 0.0239 0.0209 0.0178 0.0150 0.0106 0.0076 0.0041 0.0410 0.0415 0.0415 0.0411 0.0405 0.0392 0.0369 0.0346 0.0321 0.0269 0.0221 0.0180 0.0121 0.0083 0.0043 0.0637 0.0647 0.0639 0.0635 0.0620 0.0591 0.0540 0.0493 0.0442 0.0348 0.0272 0.0214 0.0136 0.0091 0.0045 0.1123 0.1140 0.1121 0.1097 0.1058 0.0962 0.0843 0.0725 0.0618 0.0449 0.0331 0.0249 0.0150 0.0098 0.0047 0.1620 0.1629 0.1594 0.1542 0.1464 0.1282 0.1076 0.0893 0.0733 0.0508 0.0361 0.0266 0.0157 0.0101 0.0048 0.2512 0.2519 0.2445 0.2318 0.2135 0.1755 0.1391 0.1093 0.0868 0.0566 0.0390 0.0281 0.0162 0.0103 0.0049 0.4445 0.4412 0.4164 0.3797 0.3330 0.2463 0.1794 0.1327 0.1008 0.0623 0.0416 0.0295 0.0167 0.0106 0.0049 0.9887 0.9658 0.8460 0.6940 0.5503 0.3444 0.2256 0.1565 0.1136 0.0667 0.0436 0.0305 0.0170 0.0106 0.0050 1.7563 1.6547 1.3303 0.9757 0.7109 0.4000 0.2479 0.1667 0.1192 0.0689 0.0445 0.0309 0.0171 0.0106 0.0050 3.9785 3.3796 2.1848 1.3654 0.8941 0.4504 0.2663 0.1751 0.1233 0.0703 0.0449 0.0313 0.0172 0.0107 0.0050 16.7434 8.7817 3.5555 1.7897 1.0581 0.4877 0.2791 0.1804 0.1255 0.0710 0.0453 0.0314 0.0173 0.0107 0.0050 —– 17.7628 4.4610 1.9913 1.1244 0.5023 0.2834 0.1826 0.1262 0.0711 0.0455 0.0313 0.0173 0.0107 0.0050 —– 8.7812 3.5646 1.7921 1.0587 0.4878 0.2793 0.1799 0.1257 0.0709 0.0453 0.0313 0.0172 0.0107 0.0050 3.4349 3.3415 2.1887 1.3664 0.8941 0.4505 0.2671 0.1750 0.1232 0.0701 0.0450 0.0312 0.0172 0.0107 0.0050 1.4999 1.5986 1.3174 0.9762 0.7108 0.4001 0.2476 0.1665 0.1187 0.0688 0.0444 0.0309 0.0172 0.0107 0.0050 0.8456 0.9062 0.8353 0.6929 0.5504 0.3445 0.2260 0.1567 0.1140 0.0671 0.0437 0.0305 0.0170 0.0107 0.0050 0.3808 0.3931 0.4016 0.3729 0.3319 0.2459 0.1790 0.1330 0.1007 0.0623 0.0416 0.0295 0.0167 0.0105 0.0049 0.2158 0.2194 0.2293 0.2249 0.2116 0.1746 0.1386 0.1094 0.0868 0.0567 0.0390 0.0282 0.0162 0.0103 0.0049 0.1409 0.1412 0.1464 0.1483 0.1440 0.1268 0.1073 0.0888 0.0733 0.0507 0.0361 0.0266 0.0157 0.0101 0.0048 0.0989 0.0987 0.1013 0.1036 0.1025 0.0945 0.0837 0.0724 0.0619 0.0450 0.0330 0.0249 0.0150 0.0098 0.0047 0.0572 0.0574 0.0573 0.0583 0.0587 0.0570 0.0533 0.0487 0.0439 0.0347 0.0270 0.0213 0.0137 0.0091 0.0045 0.0366 0.0370 0.0371 0.0375 0.0380 0.0376 0.0360 0.0317 0.0266 0.0219 0.0180 0.0121 0.0084 0.0059 0.0043 0.0261 0.0259 0.0258 0.0258 0.0262 0.0263 0.0257 0.0235 0.0206 0.0177 0.0149 0.0106 0.0076 0.0055 0.0041 0.0146 0.0147 0.0146 0.0147 0.0146 0.0148 0.0146 0.0144 0.0141 0.0129 0.0117 0.0106 0.0080 0.0061 0.0035 0.0092 0.0091 0.0091 0.0092 0.0092 0.0092 0.0092 0.0092 0.0090 0.0085 0.0080 0.0073 0.0060 0.0048 0.0029 0.0044 0.0044 0.0044 0.0044 0.0044 0.0044 0.0044 0.0043 0.0043 0.0042 0.0040 0.0039 0.0034 0.0029 0.0020

316L stainless steel capsule with an outer diameter of 0.9 mm and a spherical distal end with radius of curvature of 0.495 mm and is welded to a steel cable and has a total length of approximately 6.85 mm. In this study, the cable for both old and new source design was approximated by AISI 316L material. These sources will henceforth be referred to as old MHDR and new MHDR sources, respectively. Two Varian HDR (old and new design) sources manufactured by Varian Associates are commercially available. The internal construction and dimensions of the old and new HDR sources used for our simulation was taken from Baltas et al.4 and Angelopulos et al., respectively.6 The old design consists of an active source of a 0.34 mm diameter by 10 mm long cylinder of pure Iridium metal, within which the radioactive material is uniformly distributed. The source is encapsulated at the end of a 150 mm long titanium/nickel wire cylinder of 0.59 mm in outer diameter, with a composition of 44% Ti and 56% Ni by weight. The encapsulation extends 1 mm beyond the distal end of the active source and can be approximated by a 0.59 mm diameter and 0.705 mm long cylinder with a semispherical end of 0.295 mm radius. The new design differs from the old design in the total length of the active source, which is about 5 mm compared to a length of 10 mm for the old Varian HDR source design. These sources will henceforth be referred to as old VHDR and new VHDR sources, respectively.

Monte Carlo simulation code (MCNP4B) In the present work, the computation of dose rate was done using the Monte Carlo N-Particle transport code System (MCNP) version 4B computer program.14 MCNP4B is a general-purpose code for calculating the time-dependant, continuous-energy transport of neutrons, photons, and/or electrons in 3-dimensional (3D) geometry. The detailed photon physics treatment accounts for incoherent and coherent scattering, photoelectric absorption (with fluorescent emission), and pair production. MCNP4B supports a wide variety of tally/ scoring features and variance reduction schemes. For photons, the code takes into account incoherent and coherent scattering, the possibility of fluorescent emission after photoelectric absorption, absorption in pair production with local emission of annihilation, and bremsstrahlung radiation.15–17 Point-wise cross-section data were used in this study. Point detectors (F5 tally) and ring detectors (F5a tally) were used to compute flux at various points of interest, where “a” can be either X-, Y-, or Z-axis, the coordinates of the detector location. The radius of a point detector should be about 1/8 to 1/2 of mean free path of average energy of the particles. The relative error (R) for a point detector should be less than 0.10 to produce generally reliable confidence intervals. A smaller value of R (⬍ 0.05) should be used to have larger third and fourth moments of the individual tally distributions.13 The absorbed dose is computed from the es-

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Table 5. Dose rate in water per unit air-kerma strength (cGy/hU) around old MHDR source (origin taken at geometric center of source) Distance Along z (cm) 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

Distance Away y (cm) 0

0.25

0.5

0.75

1

1.5

2

2.5

3

4

5

6

8

10

14

0.0040 0.0040 0.0042 0.0040 0.0041 0.0041 0.0041 0.0041 0.0041 0.0040 0.0039 0.0037 0.0033 0.0028 0.0020 0.0085 0.0084 0.0085 0.0086 0.0086 0.0087 0.0088 0.0087 0.0086 0.0082 0.0077 0.0071 0.0059 0.0047 0.0029 0.0130 0.0131 0.0133 0.0135 0.0136 0.0138 0.0138 0.0136 0.0133 0.0124 0.0113 0.0101 0.0079 0.0060 0.0034 0.0224 0.0229 0.0234 0.0239 0.0242 0.0246 0.0243 0.0237 0.0227 0.0201 0.0173 0.0148 0.0105 0.0075 0.0040 0.0319 0.0326 0.0338 0.0344 0.0351 0.0352 0.0344 0.0328 0.0307 0.0261 0.0215 0.0176 0.0119 0.0082 0.0042 0.0490 0.0503 0.0524 0.0538 0.0544 0.0540 0.0512 0.0472 0.0427 0.0340 0.0267 0.0211 0.0135 0.0090 0.0045 0.0838 0.0881 0.0930 0.0957 0.0960 0.0906 0.0813 0.0707 0.0607 0.0442 0.0326 0.0246 0.0149 0.0097 0.0047 0.1188 0.1269 0.1345 0.1376 0.1354 0.1225 0.1047 0.0873 0.0724 0.0501 0.0357 0.0263 0.0155 0.0099 0.0047 0.1826 0.1992 0.2121 0.2124 0.2027 0.1704 0.1361 0.1076 0.0857 0.0560 0.0386 0.0279 0.0161 0.0102 0.0048 0.3223 0.3618 0.3790 0.3586 0.3291 0.2415 0.1772 0.1315 0.0997 0.0616 0.0413 0.0292 0.0166 0.0104 0.0049 0.7348 0.8547 0.8133 0.6772 0.5416 0.3404 0.2234 0.1550 0.1128 0.0665 0.0434 0.0304 0.0169 0.0105 0.0049 1.3548 1.5486 1.3030 0.9634 0.7030 0.3961 0.2459 0.1653 0.1180 0.0682 0.0441 0.0308 0.0171 0.0106 0.0049 3.4127 3.4217 2.1907 1.3522 0.8872 0.4471 0.2645 0.1744 0.1225 0.0696 0.0447 0.0310 0.0171 0.0106 0.0049 15.7066 9.1953 3.5072 1.7648 1.0437 0.4852 0.2772 0.1793 0.1250 0.0704 0.0450 0.0311 0.0171 0.0106 0.0049 — 15.5377 4.3064 1.9610 1.1146 0.4980 0.2816 0.1810 0.1258 0.0709 0.0452 0.0312 0.0172 0.0106 0.0050 13.1842 9.2129 3.5095 1.7640 1.0464 0.4839 0.2767 0.1789 0.1251 0.0706 0.0451 0.0311 0.0172 0.0107 0.0049 3.0067 3.4187 2.1908 1.3566 0.8856 0.4469 0.2653 0.1737 0.1223 0.0696 0.0447 0.0310 0.0171 0.0106 0.0049 1.1755 1.5256 1.3050 0.9640 0.7030 0.3957 0.2455 0.1653 0.1180 0.0682 0.0441 0.0307 0.0170 0.0106 0.0049 0.6794 0.7632 0.7422 0.6386 0.5182 0.3327 0.2202 0.1537 0.1120 0.0661 0.0433 0.0303 0.0169 0.0106 0.0049 0.2820 0.3385 0.3741 0.3572 0.3218 0.2414 0.1765 0.1312 0.0996 0.0617 0.0413 0.0292 0.0165 0.0104 0.0049 0.1615 0.1819 0.2067 0.2099 0.2011 0.1699 0.1360 0.1077 0.0854 0.0561 0.0386 0.0279 0.0160 0.0102 0.0048 0.1061 0.1149 0.1295 0.1351 0.1348 0.1223 0.1046 0.0872 0.0722 0.0500 0.0356 0.0263 0.0155 0.0100 0.0047 0.0752 0.0796 0.0883 0.0932 0.0950 0.0902 0.0811 0.0707 0.0605 0.0442 0.0328 0.0246 0.0148 0.0097 0.0047 0.0441 0.0458 0.0487 0.0516 0.0535 0.0536 0.0511 0.0471 0.0427 0.0339 0.0267 0.0210 0.0135 0.0090 0.0045 0.0295 0.0301 0.0313 0.0325 0.0338 0.0348 0.0341 0.0326 0.0305 0.0260 0.0215 0.0176 0.0119 0.0083 0.0043 0.0208 0.0212 0.0218 0.0226 0.0232 0.0241 0.0241 0.0235 0.0226 0.0200 0.0173 0.0147 0.0104 0.0075 0.0040 0.0121 0.0123 0.0124 0.0127 0.0129 0.0133 0.0135 0.0134 0.0132 0.0124 0.0113 0.0102 0.0078 0.0060 0.0035 0.0078 0.0079 0.0080 0.0081 0.0082 0.0083 0.0084 0.0085 0.0084 0.0082 0.0077 0.0071 0.0058 0.0047 0.0029 0.0039 0.0038 0.0039 0.0039 0.0039 0.0039 0.0040 0.0040 0.0040 0.0039 0.0038 0.0037 0.0033 0.0028 0.0020

timated flux multiplied by mass absorption coefficient. The values of mass absorption coefficients were taken from the published data of Hubbell and Seltzer.18 The decay photon energy spectrum of 192Ir used in this study was taken from Watanabe.19 It consists of 31 lines, with energy ranging from 8.91 keV to 1.061 MeV. Total photon yield is 2.363 photons per decay. Each photon history originates at a random position and direction inside the source core. The simulations were done for 106 photon histories to obtain statistically acceptable results. Each photon history was traced down to 1 keV, a default cutoff energy set by MCNP.

Dose calculation formalism The dose calculation formalism proposed by AAPM Task Group 431 was followed in this study. According to this, the dose distribution around a cylindrical symmetric brachytherapy source in a medium at a radial distance r from the center of the source at an angle ␪ relative to the longitudinal axis should be expressed as D共r, ␪兲 ⫽ Sk ⌳ G共r, ␪兲 ⁄ G共r0, ␪0兲 F共r, ␪兲 g共r兲

(1)

The dose rate constant ⌳ is defined as the dose rate in the medium per unit air kerma strength (Sk) at radial distance r0 ⫽ 1 cm along the transverse axis, ␪0 ⫽ 90° is given by

⌳ ⫽ D共r0, ␪0兲 ⁄ Sk

(2)

The radial dose function was determined from the dose rate value evaluated on the transverse axis D(r, ⌳) using the equation g共r兲 ⫽ D共r, ␪0兲 G共r0, ␪0兲 ⁄ D共r0, ␪0兲 G共r, ␪0兲

(3)

Where g(r) is the radial dose function (dimensionless), which accounts for photon attenuation and scattering in the medium and encapsulation along the transverse axis of the source. F(r, ␪) is the anisotropy function (dimensionless), which accounts for photon attenuation and scattering at any polar angle ⌳ and is given by F共r, ␪兲 ⫽ D共r, ␪兲 G共r, ␪0兲 ⁄ D共r, ␪0兲 G共r, ␪兲

(4)

Where G(r, ␪) is the geometry factor. In this study, geometry factor was calculated using linear source model. Air-kerma strength of the sources Air-kerma strength per unit contained activity Sk (cGy cm2 h⫺1mCi⫺1) is the quantity used to normalize the absorbed dose rates (cGy h⫺1 U⫺1) in water to be estimated by the Monte Carlo simulation.20 Monte Carlo code was used to calculate air-kerma rates per contained mCi, Kl (l), for distances, l, ranging from 5 to 100 cm

Evaluation of dosimetric parameters ● S. GANESAN et al.

311

Table 6. Dose rate in water per unit air-kerma strength (cGy/hU) around new MHDR source (origin taken at geometric center of source) Distance Along z (cm) 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

Distance Away y (cm) 0

0.25

0.5

0.75

1

1.5

2

2.5

3

4

5

6

8

10

14

0.0041 0.0041 0.0042 0.0041 0.0041 0.0041 0.0041 0.0041 0.0041 0.0040 0.0038 0.0037 0.0033 0.0028 0.0020 0.0085 0.0084 0.0085 0.0085 0.0086 0.0086 0.0088 0.0086 0.0085 0.0082 0.0077 0.0071 0.0058 0.0047 0.0029 0.0129 0.0131 0.0132 0.0133 0.0134 0.0137 0.0137 0.0136 0.0133 0.0124 0.0113 0.0101 0.0079 0.0060 0.0034 0.0224 0.0229 0.0234 0.0238 0.0241 0.0245 0.0242 0.0236 0.0226 0.0200 0.0172 0.0147 0.0104 0.0075 0.0040 0.0317 0.0323 0.0335 0.0341 0.0347 0.0350 0.0342 0.0326 0.0306 0.0260 0.0214 0.0176 0.0119 0.0082 0.0042 0.0485 0.0500 0.0521 0.0534 0.0541 0.0537 0.0510 0.0471 0.0427 0.0339 0.0267 0.0210 0.0135 0.0090 0.0045 0.0836 0.0875 0.0923 0.0951 0.0953 0.0902 0.0810 0.0704 0.0606 0.0442 0.0326 0.0245 0.0149 0.0096 0.0047 0.1184 0.1258 0.1333 0.1369 0.1348 0.1220 0.1044 0.0872 0.0722 0.0501 0.0357 0.0263 0.0155 0.0099 0.0047 0.1818 0.1976 0.2103 0.2117 0.2017 0.1699 0.1357 0.1074 0.0855 0.0560 0.0386 0.0278 0.0161 0.0102 0.0048 0.3205 0.3590 0.3764 0.3570 0.3269 0.2412 0.1768 0.1312 0.0996 0.0616 0.0412 0.0292 0.0166 0.0104 0.0049 0.7350 0.8491 0.8089 0.6769 0.5398 0.3393 0.2231 0.1547 0.1125 0.0665 0.0433 0.0302 0.0169 0.0105 0.0049 1.3578 1.5416 1.2970 0.9632 0.7013 0.3953 0.2454 0.1654 0.1179 0.0681 0.0441 0.0307 0.0170 0.0106 0.0049 3.4389 3.4217 2.1870 1.3502 0.8855 0.4469 0.2643 0.1735 0.1223 0.0696 0.0447 0.0310 0.0171 0.0106 0.0049 16.6890 9.2036 3.5050 1.7629 1.0438 0.4850 0.2772 0.1787 0.1247 0.0703 0.0451 0.0312 0.0172 0.0106 0.0049 —– 15.4288 4.2990 1.9603 1.1116 0.4981 0.2815 0.1810 0.1257 0.0708 0.0452 0.0312 0.0172 0.0106 0.0049 —– 9.2331 3.5056 1.7617 1.0447 0.4834 0.2764 0.1787 0.1248 0.0705 0.0450 0.0311 0.0171 0.0106 0.0049 3.0492 3.4244 2.1894 1.3537 0.8844 0.4466 0.2644 0.1735 0.1221 0.0696 0.0446 0.0309 0.0171 0.0106 0.0049 1.1817 1.5289 1.3051 0.9623 0.7016 0.3955 0.2454 0.1652 0.1181 0.0681 0.0441 0.0306 0.0170 0.0106 0.0049 0.6400 0.8173 0.8075 0.6761 0.5397 0.3403 0.2231 0.1550 0.1125 0.0664 0.0433 0.0303 0.0169 0.0105 0.0049 0.2820 0.3367 0.3715 0.3555 0.3206 0.2411 0.1762 0.1310 0.0996 0.0617 0.0412 0.0292 0.0165 0.0104 0.0049 0.1614 0.1812 0.2053 0.2085 0.2000 0.1694 0.1356 0.1074 0.0854 0.0559 0.0385 0.0278 0.0160 0.0102 0.0048 0.1060 0.1145 0.1285 0.1341 0.1341 0.1217 0.1042 0.0871 0.0721 0.0500 0.0356 0.0262 0.0154 0.0099 0.0047 0.0752 0.0793 0.0876 0.0925 0.0944 0.0898 0.0809 0.0705 0.0604 0.0441 0.0328 0.0247 0.0148 0.0097 0.0047 0.0440 0.0457 0.0485 0.0512 0.0529 0.0533 0.0508 0.0470 0.0426 0.0338 0.0266 0.0210 0.0134 0.0090 0.0045 0.0294 0.0300 0.0313 0.0324 0.0336 0.0345 0.0340 0.0324 0.0305 0.0260 0.0215 0.0176 0.0119 0.0082 0.0042 0.0209 0.0212 0.0219 0.0225 0.0232 0.0239 0.0240 0.0234 0.0225 0.0199 0.0173 0.0147 0.0104 0.0075 0.0040 0.0121 0.0123 0.0124 0.0126 0.0129 0.0132 0.0134 0.0133 0.0132 0.0124 0.0113 0.0101 0.0078 0.0060 0.0035 0.0078 0.0079 0.0079 0.0081 0.0081 0.0083 0.0084 0.0084 0.0084 0.0081 0.0077 0.0071 0.0058 0.0047 0.0029 0.0039 0.0039 0.0039 0.0039 0.0039 0.0039 0.0040 0.0040 0.0040 0.0039 0.0038 0.0036 0.0033 0.0028 0.0019

along the transverse source bisector for all the sources immersed in a 5 m sphere of dry air. These data were fitted to a linear equation, Kl (l) l2 ⫽ Sk ⫹ b (l), Where “b” is the slope, describing the deviation in Kl (l) l2 due to buildup of scattered photons in air. The intercept is the product of the air-kerma rate and square of the distance. Simulation of absorbed dose in water To obtain the dose rate in the form of along-andaway tables, as given by TG-43 formalism, all the 192Ir sources have been located in an unbounded liquid water phantom. For 192Ir, a spherical water phantom with a radius of 40 cm is equivalent to an unbounded phantom up to a distance of 20 cm from the source.11 Because bounded or unbounded medium implies the accuracy in the dose determination at greater distances (⬎ 5 cm) from the source, in this work, we have used unbounded phantom to verify the dose distribution at greater distances from the sources. The origin of the reference system is taken at the geometric center of the sources, where the y-axis is the transverse axis and the z-axis is the longitudinal axis of the sources. RESULTS AND DISCUSSION Air-kerma strength The air-kerma strength per unit activity, Sk/A, was computed for various 192Ir sources in dry air medium, as

suggested by Williamson and Li,20 and is found to be (9.77 ⫾ 0.03) 10⫺8 U/Bq, (9.96 ⫾ 0.03) 10⫺8 U/Bq, (9.80 ⫾ 0.01) 10⫺8 U/Bq, (9.80 ⫾ 0.01) 10⫺8 U/Bq, (10.32 ⫾ 0.01) 10⫺8 U/Bq and (10.34 ⫾ 0.02) 10⫺8 U/Bq the old PDR, new PDR, old MHDR, new MHDR, old VHDR, and new VHDR sources, respectively. Dose rate constant The dose rate constant, ⌳, was computed for various 192Ir sources using Eq. (2). The dose rate constant values for the investigated 192Ir sources along with corresponding values available in the literature10,20,21 are presented in Table 1. It is observed that the computed values of ⌳ for old PDR and new PDR of this work is in good agreement (0.35% for old PDR and ⫺0.27% for new PDR) with the reported values of Williamson and Li20 and Karaiskos et al.,10 respectively. It is also observed that the computed values of ⌳ for old MHDR, new MHDR, old VHDR, and new VHDR of this work is in good agreement (⫺0.27% for new MHDR, 0.77% for old VHDR, and 0.45% for new VHDR) with the computed values of Papagiannis et al.21 The dose rate constant value of 1.115 ⫾ 0.1% cGy h⫺1U⫺1 for old MHDR obtained in this study has been compared with the reported value of 1.134 ⫾ 2.9% cGy h⫺1U⫺1 by Anctil et al.,22 who had performed TLD measurement in water equivalent phantom. There is a difference of 1.68% with respect to the reported values and this difference may be

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Table 7. Dose rate in water per unit air-kerma strength (cGy/hU) around old VHDR source (origin taken at geometric center of source) Distance Away y (cm)

Distance Along z (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

0.0048 0.0106 0.0171 0.0312 0.0453 0.0706 0.1244 0.0810 0.2754 0.4811 1.0324 1.7399 3.4682 9.6300 —– —– —– —– —– —– —– —– —– —– —– —– —– —– —–

0.0037 0.0074 0.0114 0.0197 0.0282 0.0444 0.0819 0.1232 0.2062 0.4106 1.1299 2.3732 5.6742 8.8662 9.6510 8.8502 5.6927 2.3774 1.1320 0.4097 0.2058 0.1222 0.0810 0.0431 0.0271 0.0188 0.0107 0.0070 0.0034

0.0038 0.0077 0.0122 0.0222 0.0325 0.0520 0.0966 0.1435 0.2332 0.4310 0.9659 1.5560 2.4183 3.1946 3.4746 3.1893 2.4225 1.5555 0.9669 0.4307 0.2346 0.1441 0.0967 0.0519 0.0321 0.0218 0.0120 0.0076 0.0036

0.0039 0.0081 0.0130 0.0238 0.0348 0.0559 0.1015 0.1477 0.2316 0.3948 0.7433 1.0284 1.3611 1.6375 1.7408 1.6339 1.3624 1.0329 0.7429 0.3939 0.2305 0.1481 0.1018 0.0556 0.0346 0.0237 0.0128 0.0080 0.0038

0.0040 0.0084 0.0135 0.0247 0.0361 0.0571 0.1017 0.1445 0.2162 0.3438 0.5674 0.7176 0.8723 0.9908 1.0347 0.9899 0.8712 0.7177 0.5672 0.3438 0.2165 0.1449 0.1024 0.0572 0.0360 0.0247 0.0135 0.0083 0.0039

0.0041 0.0087 0.0140 0.0255 0.0367 0.0563 0.0947 0.1275 0.1766 0.2482 0.3429 0.3939 0.4381 0.4698 0.4812 0.4693 0.4386 0.3933 0.3433 0.2482 0.1767 0.1279 0.0947 0.0565 0.0366 0.0255 0.0140 0.0087 0.0040

0.0041 0.0088 0.0142 0.0253 0.0357 0.0530 0.0838 0.1078 0.1391 0.1791 0.2229 0.2442 0.2609 0.2725 0.2759 0.2722 0.2610 0.2439 0.2232 0.1790 0.1387 0.1076 0.0839 0.0533 0.0357 0.0253 0.0142 0.0088 0.0041

0.0042 0.0089 0.0141 0.0247 0.0338 0.0486 0.0723 0.0887 0.1090 0.1318 0.1544 0.1641 0.1719 0.1769 0.1807 0.1769 0.1719 0.1639 0.1546 0.1318 0.1089 0.0888 0.0722 0.0485 0.0338 0.0245 0.0140 0.0088 0.0042

0.0042 0.0088 0.0138 0.0233 0.0315 0.0436 0.0616 0.0731 0.0861 0.0997 0.1121 0.1175 0.1213 0.1238 0.1244 0.1236 0.1212 0.1172 0.1121 0.0995 0.0860 0.0730 0.0616 0.0437 0.0315 0.0234 0.0138 0.0088 0.0042

0.0041 0.0084 0.0128 0.0206 0.0264 0.0344 0.0446 0.0502 0.0560 0.0615 0.0661 0.0681 0.0693 0.0701 0.0704 0.0701 0.0695 0.0680 0.0662 0.0615 0.0560 0.0503 0.0445 0.0343 0.0265 0.0205 0.0128 0.0084 0.0041

0.0040 0.0079 0.0115 0.0175 0.0218 0.0269 0.0328 0.0358 0.0387 0.0412 0.0432 0.0441 0.0446 0.0450 0.0450 0.0455 0.0446 0.0441 0.0433 0.0413 0.0387 0.0357 0.0327 0.0269 0.0217 0.0176 0.0116 0.0078 0.0040

0.0038 0.0072 0.0103 0.0149 0.0178 0.0212 0.0247 0.0263 0.0279 0.0293 0.0304 0.0307 0.0310 0.0311 0.0311 0.0311 0.0309 0.0306 0.0303 0.0292 0.0279 0.0263 0.0246 0.0211 0.0178 0.0149 0.0103 0.0072 0.0038

0.0033 0.0059 0.0080 0.0105 0.0120 0.0135 0.0150 0.0155 0.0161 0.0166 0.0169 0.0170 0.0171 0.0172 0.0172 0.0172 0.0171 0.0170 0.0169 0.0165 0.0161 0.0155 0.0149 0.0135 0.0120 0.0106 0.0079 0.0059 0.0033

0.0029 0.0047 0.0060 0.0075 0.0083 0.0091 0.0097 0.0099 0.0102 0.0104 0.0105 0.0106 0.0106 0.0106 0.0107 0.0106 0.0106 0.0106 0.0105 0.0104 0.0102 0.0099 0.0096 0.0090 0.0083 0.0075 0.0060 0.0047 0.0028

0.0020 0.0029 0.0035 0.0040 0.0042 0.0045 0.0047 0.0047 0.0048 0.0049 0.0049 0.0049 0.0049 0.0049 0.0049 0.0049 0.0049 0.0049 0.0049 0.0049 0.0048 0.0048 0.0047 0.0045 0.0043 0.0040 0.0035 0.0029 0.0020

due to the use of different phantom material (polystyrene) and dosimeter (TLD) used by them. Further, it is also observed that the percentage difference in the values of dose rate constant is almost zero between old PDR and new PDR. There is only 0.27% difference in the dose rate constant between old MHDR and new MHDR. There is 5.89% difference in dose rate constant between old VHDR and new VHDR. The percentage differences in dose rate constant are minimal among between old PDR, new PDR, old MHDR, and new MHDR sources. However, a large percentage difference between old VHDR and new VHDR is observed due to the new VHDR source (0.5 cm). Further, these variations in the values may be due to variation in the filtration by the source core and encapsulation, in-water scattering, and spatial distribution of radioactivity within the source.21 Radial dose function The radial dose function values were computed using Eq. (3) and linear source model was considered. The computed radial dose function values for old PDR, new PDR, old MHDR, new MHDR, old VHDR, and new VHDR sources in unbounded spherical water phantom are presented in Table 2, and are graphically shown in Fig. 1(a) through 1(e). Results of this work for new PDR source design is in good agreement (⫾ 1.1%) with the

results of Karaiskos et al.10 calculated using Monte Carlo photon-transport (MCPT) simulation code under the same phantom condition. The computational values of radial dose function for old PDR and old MHDR source designs under unbounded water phantom condition were compared with the results of Williamson and Li20 using MCPT under bounded phantom conditions. A difference of 14.1% at r ⫽ 12 cm and 14.5% at r ⫽ 12 cm, respectively, was observed. The computed values of radial dose function values for old MHDR obtained in this study was compared with the reported values by Anctil et al.,22 who had performed TLD measurement in water equivalent phantom, observed a difference of 5.4% at r ⫽ 10 cm. Results of this work for new MHDR was compared with the results of Daskalov et al.23 calculated by MCPT calculations under bounded phantom conditions, observed a difference of 13.6% at r ⫽ 12 cm. Results of this work for old VHDR source design were compared with the results of Karaiskos et al.2 calculated by analytical MC simulation code for bounded phantom condition a difference of 13.8% at r ⫽ 12 cm was observed. Results of this work for new VHDR source design were compared with the results of Angelopoulos et al.,6 who calculated using MC particle-transport simulation code under bounded phantom condition and observed a difference of 7.9% at r ⫽ 12 cm. In all the cases, the differences in radial dose values between bounded

Evaluation of dosimetric parameters ● S. GANESAN et al.

313

Table 8. Dose rate in water per unit air-kerma strength (cGy/hU) around new VHDR source (origin taken at geometric center of source) Distance Along z (cm) 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

Distance Away y (cm) 0

0.25

0.5

0.75

1

1.5

2

2.5

3

4

5

6

8

10

14

0.0038 0.0039 0.0040 0.0040 0.0041 0.0042 0.0042 0.0042 0.0042 0.0042 0.0040 0.0038 0.0034 0.0029 0.0020 0.0078 0.0080 0.0083 0.0084 0.0086 0.0089 0.0089 0.0090 0.0089 0.0084 0.0079 0.0073 0.0059 0.0047 0.0029 0.0118 0.0124 0.0128 0.0134 0.0138 0.0141 0.0143 0.0142 0.0138 0.0128 0.0116 0.0103 0.0079 0.0060 0.0035 0.0203 0.0215 0.0229 0.0241 0.0250 0.0256 0.0253 0.0245 0.0233 0.0205 0.0175 0.0148 0.0106 0.0075 0.0040 0.0276 0.0306 0.0335 0.0356 0.0365 0.0368 0.0356 0.0339 0.0315 0.0264 0.0217 0.0178 0.0120 0.0083 0.0043 0.0420 0.0474 0.0528 0.0557 0.0571 0.0563 0.0528 0.0486 0.0436 0.0344 0.0269 0.0211 0.0135 0.0090 0.0045 0.0707 0.0853 0.0966 0.1005 0.1005 0.0938 0.0832 0.0720 0.0615 0.0446 0.0327 0.0246 0.0149 0.0097 0.0047 0.0984 0.1254 0.1416 0.1456 0.1415 0.1259 0.1069 0.0885 0.0729 0.0503 0.0358 0.0264 0.0156 0.0100 0.0048 0.1502 0.2028 0.2245 0.2245 0.2105 0.1742 0.1382 0.1083 0.0858 0.0563 0.0388 0.0280 0.0161 0.0102 0.0048 0.2652 0.3808 0.4013 0.3757 0.3325 0.2448 0.1781 0.1317 0.0997 0.0619 0.0414 0.0293 0.0166 0.0104 0.0049 0.6139 0.9262 0.8569 0.7007 0.5511 0.3415 0.2234 0.1552 0.1127 0.0664 0.0435 0.0304 0.0169 0.0105 0.0049 1.1809 1.7115 1.3644 0.9844 0.7107 0.3959 0.2453 0.1652 0.1180 0.0684 0.0443 0.0308 0.0171 0.0106 0.0049 3.4401 3.8528 2.2531 1.3627 0.8867 0.4455 0.2640 0.1734 0.1222 0.0695 0.0449 0.0310 0.0171 0.0106 0.0049 —– 9.6551 3.4756 1.7433 1.0346 0.4814 0.2763 0.1787 0.1246 0.0708 0.0452 0.0311 0.0172 0.0107 0.0050 —– 13.8800 4.1242 1.9168 1.0962 0.4951 0.2807 0.1807 0.1254 0.0708 0.0455 0.0312 0.0173 0.0107 0.0050 —– 9.6593 3.4744 1.7443 1.0373 0.4814 0.2764 0.1782 0.1244 0.0706 0.0453 0.0312 0.0172 0.0107 0.0049 —– 3.8633 2.2578 1.3697 0.8858 0.4462 0.2638 0.1733 0.1223 0.0698 0.0449 0.0310 0.0171 0.0106 0.0049 —– 1.7175 1.3660 0.9890 0.7103 0.3965 0.2455 0.1651 0.1179 0.0685 0.0445 0.0307 0.0170 0.0106 0.0049 —– 0.9254 0.8598 0.7012 0.5523 0.3429 0.2238 0.1549 0.1126 0.0664 0.0434 0.0304 0.0170 0.0106 0.0049 —– 0.3770 0.4013 0.3761 0.3332 0.2453 0.1783 0.1318 0.0999 0.0619 0.0414 0.0293 0.0166 0.0105 0.0049 —– 0.1989 0.2241 0.2250 0.2115 0.1739 0.1382 0.1087 0.0864 0.0562 0.0388 0.0280 0.0161 0.0102 0.0048 —– 0.1222 0.1406 0.1455 0.1420 0.1259 0.1069 0.0885 0.0731 0.0503 0.0359 0.0264 0.0156 0.0100 0.0048 —– 0.0823 0.0955 0.1007 0.1002 0.0937 0.0833 0.0718 0.0615 0.0445 0.0327 0.0246 0.0150 0.0097 0.0047 —– 0.0452 0.0524 0.0557 0.0573 0.0562 0.0528 0.0483 0.0435 0.0344 0.0269 0.0212 0.0135 0.0090 0.0045 —– 0.0286 0.0330 0.0353 0.0363 0.0367 0.0361 0.0338 0.0315 0.0265 0.0218 0.0178 0.0120 0.0083 0.0043 —– 0.0203 0.0225 0.0239 0.0249 0.0257 0.0253 0.0244 0.0233 0.0204 0.0176 0.0148 0.0105 0.0075 0.0040 —– 0.0112 0.0124 0.0131 0.0136 0.0143 0.0143 0.0142 0.0138 0.0128 0.0116 0.0103 0.0079 0.0060 0.0035 —– 0.0073 0.0081 0.0082 0.0085 0.0088 0.0090 0.0089 0.0088 0.0084 0.0079 0.0073 0.0059 0.0047 0.0029 —– 0.0037 0.0038 0.0039 0.0040 0.0041 0.0042 0.0042 0.0042 0.0041 0.0040 0.0038 0.0033 0.0028 0.0020

and unbounded phantoms were small at short radial distances and the percentage difference increased as the radial distance increased. This may be due to lack of backscatter at points lying close to the boundary of the 15-cm radius water phantom. Comparison of the computed values of radial dose function values for old PDR with new PDR, old MHDR with new MHDR, and old VHDR with new VHDR source design shows a difference of 0.5%, 0.3%, and 0.6%, respectively. This minimal difference between the sources confirms the results of previous studies, that the source dimensions and encapsulations do not contribute significantly in the values of radial dose function.2,10 “Along-and-away” dose rate look-up tables The derived single-source dose rate per unit air kerma strength values D(z, y)/Sk, are presented Tables 3 through 8 as the function of distance “along” z and distance “away” y, from the longitudinal axes of the old PDR, new PDR, old MHDR, new MHDR, old VHDR, and new VHDR source designs, respectively. The transverse axis dose comparison between the sources is graphically shown in Fig. 2. Comparison of our transverse axis (z ⫽ 0) dose rate distribution data for old PDR and new PDR source designs shows a difference of 0.4% at y ⫽ 0.25 cm and 0.5% at y ⫽ 2.5 cm. Comparison of our transverse axis

(z ⫽ 0) dose rate distribution data for old MHDR and new MHDR source designs shows a difference of 0.7% at y ⫽ 0.25 cm and 0.4% at y ⫽ 2 cm. Comparison of our transverse axis (z ⫽ 0) dose rate distribution data for old VHDR and new VHDR source designs shows a difference of 43.8% at y ⫽ 0.25 cm and 1.8% at y ⫽ 2 cm. The differences are small for old PDR, new PDR, old MHDR, and new MHDR sources, because they possess minimal dimensional differences. However, the difference is large between old VHDR source (L ⫽ 1 cm) and new VHDR (L ⫽ 0.5 cm) source, because the dimensional differences between them is around 50%. In gen-

Fig. 2. Transverse axis dose comparison of various sources in unbounded water phantom.

192

Ir

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Medical Dosimetry

Volume 32, Number 4, 2007

Table 9. Computed anisotropy function F(1 cm, ␪) values for various

192

Ir sources

Anisotropy Function F(1 cm, ␪) Polar Angle (␪ Degrees)

Old PDR

New PDR

Old MHDR

New MDHR

Old VHDR

New VHDR

0.5 1.5 2.5 3.5 4.5 5.5 9.5 19.5 27.5 37.5 47.5 67.5 90 112.5 132.5 142.5 152.5 160.5 170.5 175.5 176.5 177.5 178.5 179.5

1.0233 1.0247 1.0247 1.0260 1.0255 1.0271 1.0304 1.0336 1.0354 1.0331 1.0339 1.0225 1.0000 0.9635 0.9168 0.8791 0.8240 0.7669 0.6654 0.6170 0.6133 0.6099 0.6081 0.6083

0.8785 0.8814 0.8842 0.8852 0.8854 0.8893 0.8979 0.9242 0.9423 0.9693 0.9794 0.9982 1.0000 0.9959 0.9796 0.9631 0.9328 0.8945 0.7982 0.7639 0.7576 0.7556 0.7533 0.7530

0.6321 0.6349 0.6404 0.6494 0.6597 0.6731 0.7239 0.8343 0.8897 0.9327 0.9594 0.9892 1.0000 0.9876 0.9622 0.9358 0.8873 0.8249 0.6740 0.5735 0.5651 0.5597 0.5561 0.5512

0.6317 0.6336 0.6358 0.6459 0.6540 0.6691 0.7164 0.8279 0.8854 0.9296 0.9593 0.9904 1.0000 0.9877 0.9620 0.9325 0.8834 0.8185 0.6679 0.5719 0.5636 0.5587 0.5541 0.5509

0.4416 0.4608 0.5034 0.5598 0.6119 0.6567 0.7735 0.8977 0.9397 0.9658 0.9787 0.9966 1.0000 0.9976 0.9827 0.9678 0.9392 0.8993 0.7765 0.6059 0.5496 0.4713 0.3830 0.3688

0.5215 0.5302 0.5549 0.5854 0.6201 0.6532 0.7574 0.8847 0.9280 0.9607 0.9755 0.9943 1.0000 0.9962 0.9783 0.9607 0.9291 0.8853 0.7567 0.6004 0.5467 0.4769 0.3907 0.3828

eral, in all the cases, an increased dose rate at points closer to the distal end (positive z values) relative to the drive cable wire (negative z values) exists. This may be due to the fact that the cable in all source designs may attenuate the radiation, significantly. Anisotropy function The anisotropy function values were calculated by linear source approximation using Eq. (4). The results of the anisotropy function F(1 cm, ␪) for all sources for polar angles ranging from 0.5° to 179.5° relative to the longitudinal axis of the source are presented in Table 9. The angle 0° is defined at the distal end of the source, while the angle 180° is defined at the side of the drive wire. The comparison between the anisotropy data of all the sources show an increased value at ␪ ⫽ 0° and decreased value at ␪ ⫽ 179.5°. Comparison of the anisotropy function values between old PDR and new PDR source design shows a percentage difference of 14.1% at ␪ ⫽ 0.5° (distal end) and ⫺23.8% at ␪ ⫽ 179.5° (drive wire end). Comparison of the anisotropy function values between old MHDR and new MHDR source design shows a percentage difference of 0.1% at ␪ ⫽ 0.5° (distal end) and 0.4% at ␪ ⫽ 178.5° (drive wire end). Comparison of the anisotropy function values between old VHDR with new VHDR source design shows a percentage difference of ⫺18.1% at ␪ ⫽ 0.5° (distal end) and ⫺3.8% at ␪ ⫽ 179.5° (drive wire end). This comparison shows that the percentage difference is considerable in the case of old and new PDR, and old and new VHDR when compared with old and new

MDHR, for which the difference is very much less. This is due to the difference in geometry of the sources. The geometry of the old and new MDHR is almost similar, whereas there is a considerable difference in geometry between the other types of brachytherapy sources. From this study, it is clearly observed that all of the sources are exhibiting significant anisotropy, with anisotropy function values being strongly dependant on source geometry. CONCLUSIONS In this study, a complete dosimetric data set for various brachytherapy 192Ir sources (old PDR, new PDR, old MHDR, new MHDR, old VHDR, and new VHDR source designs) were obtained under unbounded liquid water phantom using Monte Carlo MCNP4B code. Functions and parameters following TG-43 formalism such as dose rate constant, radial dose function, and anisotropy function were presented. To aid quality control on TPS, 2D rectangular dose rate tables (“along-and-away” tables) that are consistent with TG-43 dose calculation formalism are also given for all of the source designs, as listed above. It is observed that that the geometric characteristics of the examined sources (including their encapsulations) do not significantly affect the radial dose function calculations. Further, a decreased anisotropy characteristic is observed for new VHDR source than old VHDR source design, due to its decreased length. This significant difference between the dose rate distributions computed around the investigated sources, which are observed at short radial distances and/or along their

Evaluation of dosimetric parameters ● S. GANESAN et al.

longitudinal axes, are due to the different geometric characteristics of the sources. This implies that specific data set must be used in clinical dosimetry for each source design.

Acknowledgment—The authors thank the Board of Research in Nuclear Sciences (BRNS), Department of Atomic Energy (DAE), and Government of India for financial support (Ref. No. 2001/34/11-BRNS/527).

REFERENCES 1. Nath, R.; Anderson, L.L.; Luxton, G.; et al. Dosimetry of interstitial brachytherapy sources: Recommendations of the AAPM Radiation Therapy Committee Task Group No. 43. Med. Phys. 22: 209 –34; 1995. 2. Karaiskos, P.; Angelopoulos, A.; Baras, P.; et al. A Monte Carlo investigation of the dosimetric characteristics of the Varisource 192 Ir high dose rate brachytherapy source. Med. Phys. 26:1498 – 502; 1999. 3. Rustgi, S.N. Application of a diamond detector to brachytherapy dosimetry. Phys. Med. Biol. 43:2085–94; 1998. 4. Baltas, D.; Karaiskos, P.; Papagiannis, P.; et al. Beta versus gamma dosimetry close to Ir-192 brachytherapy sources. Med. Phys. 28:1875– 82; 2001. 5. Cho, S.H.; Muller-Runkel, R.; Hanson, W.F. Determination of the tissue attenuation factor along two major axes of a high dose rate (HDR) 192Ir source. Med. Phys. 26:1492–7; 1999. 6. Angelopoulos, A.; Baras, P.; Sakelliou, L. Monte Carlo dosimetry of a new 192Ir high dose rate brachytherapy source. Med. Phys. 27:2521–7; 2000. 7. Ye, S.J.; Brezovich, I.A.; Pareek, P.; et al. Benchmark of PENELOPE code for low-energy photon transport: Dose comparisons with MCNP4 and EGS4. Phys. Med. Biol. 49:387–97; 2004. 8. Ballester, F.; Hernandez, C. Monte Carlo calculation of dose rate distributions around 192Ir wires. Med. Phys. 24:1221– 8; 1997. 9. Williamson, J.F. Comparison of measured and calculated dose rates in water near I-125 and Ir-192 seeds. Med. Phys. 18:776 – 86; 1991. 10. Karaiskos, P.; Angelopoulos, A.; Pantelis, E.; et al. Monte Carlo dosimetry of a new 192Ir pulsed dose rate brachytherapy sources. Med. Phys. 30:9 –16; 2003.

315

11. Ballester, F.; Granero, D.; Perez-Calatayud, J.; et al. Monte Carlo dosimetric study of Best Industries and Alpha Omega Ir-192 brachytherapy seeds. Med. Phys. 31:3298 –305; 2004. 12. Nath, R.; Meigooni, A.S.; Meli, J.A. Dosimetry on the transverse axes of 125I and 192Ir interstitial brachytherapy sources. Med. Phys. 17:1032– 40; 1990. 13. Daskalov, G.M.; Baker, R.S.; Rogers, D.W.O.; et al. Dosimetric modeling of the microselectron high-dose rate 192Ir source by the multigroup discrete ordinates method. Med. Phys. 27:2307–19; 2000. 14. MCNP - A General Monte Carlo N-Particle Transport Code, Version 4B, Transport Methods Group. Los Alamos National Laboratory Report; 1997. 15. Selvam, T.P.; Govinda Rajan K.N.; Sethulakshmi, P.; et al. Monte Carlo-aided room scatter studies in the primary air kerma strength standardization of a remote afterloading 192Ir HDR source. Phys. Med. Biol. 46:2299 –315; 2001. 16. DeMarco, J.J.; Wallance, R.E.; Boedeker, K. Analysis of MCNP cross sections and tally methods for low-energy photon emitters. Phys. Med. Biol. 47:1321–32; 2002. 17. Reniers, B.; Verhaegen, F.; Vynckier, S. The radial dose function of low-energy brachytherapy seeds in different solid phantoms: Comparison between calculations with the EGSnrc and MCNP4C Monte Carlo codes and measurements. Phys. Med. Biol. 49:1569 – 82; 2004. 18. Hubbell, J.H.; Seltzer, S.M. Tables of x-ray mass attenuation coefficients and mass energy-absorption coefficients 1 keV to 20 MeV for elements z ⫽ 1 to 92 and 48 additional substances of dosimetric interest. NISTIR 5632; 1995. 19. Watanabe, Y.; Roy, J.; Harrington, P.J.; et al. Experimental and Monte Carlo dosimetry of the Henschke applicator for high doserate 192Ir remote afterloading. Med. Phys. 25:736 – 45; 1998. 20. Williamson, J.F.; Li, Z. Monte Carlo aided dosimetry of the microselectron pulsed and high dose-rate 192Ir sources. Med. Phys. 22:809 –18; 1995. 21. Papagiannis, P.; Angelopoulos, A.; Pantelis, E.; et al. Dosimetry comparison of 192Ir sources. Med. Phys. 29:2239 – 46; 2002. 22. Anctil, J.C.; Clark, B.G.; Arsenault, C.J. Experimental determination of dosimetry functions of Ir-192 sources. Med. Phys. 25: 2279 – 87; 1998. 23. Daskalov, G.M.; Loffler, E.; Williamson, J.F. Monte Carlo-aided dosimetry of a new high-dose-rate brachytherapy source. Med. Phys. 25:2200 – 8; 1998.