Dosimetric characterization of model Cs-1 Rev2 cesium-131 brachytherapy source in water phantoms and human tissues with MCNP5 Monte Carlo simulation Jianhua Wanga兲 Shanghai Institute of Applied Physics, CAS, Shanghai 201800, China
Hualin Zhang Department of Radiation Medicine, The Ohio State University, Columbus, Ohio 43210
共Received 16 October 2007; revised 15 January 2008; accepted for publication 15 January 2008; published 24 March 2008兲 A recently developed alternative brachytherapy seed, Cs-1 Rev2 cesium-131, has begun to be used in clinical practice. The dosimetric characteristics of this source in various media, particularly in human tissues, have not been fully evaluated. The aim of this study was to calculate the dosimetric parameters for the Cs-1 Rev2 cesium-131 seed following the recommendations of the AAPM TG-43U1 report 关Rivard et al., Med. Phys. 31, 633–674 共2004兲兴 for new sources in brachytherapy applications. Dose rate constants, radial dose functions, and anisotropy functions of the source in water, Virtual Water™, and relevant human soft tissues were calculated using MCNP5 Monte Carlo simulations following the TG-43U1 formalism. The results yielded dose rate constants of 1.048, 1.024, 1.041, and 1.044 cGy h−1 U−1 in water, Virtual Water™, muscle, and prostate tissue, respectively. The conversion factor for this new source between water and Virtual Water™ was 1.02, between muscle and water was 1.006, and between prostate and water was 1.004. The authors’ calculation of anisotropy functions in a Virtual Water™ phantom agreed closely with Murphy’s measurements 关Murphy et al., Med. Phys. 31, 1529–1538 共2004兲兴. Our calculations of the radial dose function in water and Virtual Water™ have good agreement with those in previous experimental and Monte Carlo studies. The TG-43U1 parameters for clinical applications in water, muscle, and prostate tissue are presented in this work. © 2008 American Association of Physicists in Medicine. 关DOI: 10.1118/1.2868754兴 Key words: brachytherapy, cesium-131, Monte Carlo, MCNP5, tissue water conversion factor I. INTRODUCTION Interstitial brachytherapy using low energy radioactive seeds for permanent implants is one of the most common means of treating low-risk prostate cancer.1 At present, sources containing 103Pd or 125I are most commonly used in permanent prostate brachytherapy.2 The primary difference between these two isotopes is their half-life, approximately 60 days for 125I and 17 days for 103Pd, though they also have difference spectra 共average energy 28.37 keV for 125I and 20.74 keV for 103Pd兲. The model Cs-1 cesium-131 source is a relatively new type of brachytherapy source that recently received FDA approval. First studied in the 1960s by Henschke and Lawrence3 and recently evaluated by Murphy et al.,4 Chen et al.,5 Witman et al.,6 and Rivard et al.,7 cesium131 is a low energy photon emitter with its most prominent peaks in the 29–34 keV region. In prostate brachytherapy, interest in the cesium-131 source and its potential radiobiologic effects has increased because its energy spectrum is similar to 125I, but it has a substantially shorter half-life 共9.7 days兲. In addition to its potential cell-killing advantages,8 a shorter acting isotope also reduces morbidity. With a half-life of 9.7 days and a presumed effective life of 4–5 half-lives, cesium-131 would deliver its effective dose in 40–50 days as opposed to 68–85 days for 103Pd, and 240–300 days for 125I. Theoretically then, any side effects which are dose or dose 1571
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rate related would be expected to dissipate much faster with cesium-131 than with long half-life isotopes, although it is also speculated that the initial acute reactions would presumably be more intense than with 125I and 103Pd. Therefore, cesium-131 sources may have both physical and radiobiological advantages in the brachytherapy treatment of prostate cancer. As previously mentioned, the cesium-131 brachytherapy seed is a relatively new source, so its dosimetric characteristics in media, particularly in human soft tissues, have not been well evaluated. Thus, the main objectives of this project were to use MCNP5 Monte Carlo simulation to carry out such an evaluation to determine the dosimetric characteristics of the cesium-131 brachytherapy source in water and in relevant human soft tissues, and to provide dosimetric conversion factors between soft tissues and water. Simulations in Virtual Water™ as well as in water were also used to validate our calculation technique and the results were compared with other authors’ measurements and calculations. II. MATERIALS AND METHODS II.A. Isoray™ Cs-1 Rev2 Cs-131 brachytherapy seed
The Isoray™ cesium-131 brachytherapy seed 共model Cs-1 Rev2兲 has a physical length of 4.5 with 0.1 mm thick
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Ceramic Core w/Cs-131 Attached
Y
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P(r,θ)
Gold X-Ray Marker (0.25mm Diameter) Titantium Case (0.05mm Wall)
Laser Weld Ends (0.1mm)
θ
0.8mm
FIG. 1. Schematic diagram of model Cs-1 Rev2 cesium-131 source.
Z
0.62 mm
4.1 mm 4.5 mm
caps on each end and an outer dimension of 0.8 mm 共Fig. 1兲. The source was manufactured by encapsulating an inner core with a 0.05 mm thick titanium wall. The center x-ray marker is a 0.25 mm diameter gold wire. The wire is coated by a glass and ceramic material. The outside diameter of the source inner core is 0.65 mm. The active length of the source is 4.1 mm. Using this active length is based on the considerations that most experimental data were taken from the initial model Cs-1 with an active length of 4.2 mm, while more recent studies are for the revised model Cs-1 Rev2 with the claimed active length of 4.0 mm. In addition, the coating of active source may also add some thickness to both ends of inner x-ray marker. Therefore, an active length of 4.1 mm is supposed to be reasonable.
II.B. Monte Carlo simulation
Monte Carlo N-particle transport code 共MCNP5, version 5兲 共Refs. 9 and 10兲 was used to calculate the dose rate distribution in liquid water, Virtual Water™, muscle, and prostate tissue around the model Cs-1 Rev2 共revised model兲 source. The code is the latest version of MCNP. MCNP and its sister code MCNPX 共the extension for particle type and energy ranges of MCNP兲 have been used by many authors for brachytherapy seed studies,4,6,7,11–19 so their feasibility and appropriateness have been well verified. There are several tally types available in MCNP5 for scoring the dose rate. F6 directly scores the dose in tally cell per photon by determining the average energy deposition in MeV/g/photon; the *F5 calculates the average photon energy fluence at a point or ring detector in MeV/ cm2 / photon, which is then converted to the dose by incorporating the updated mass energy absorption20 coefficients 共cm2 / g兲. The *F4 is similar to *F5, which calculates the average photon energy fluence over the tally cell in MeV/ cm2 / photon, which is also then converted to the dose by incorporating the updated mass energy absorption coefficients 共cm2 / g兲. Several authors have reported13–15 that the previous DLC-200 cross section file might be problematic for low energy sources when the F6 tally was directly Medical Physics, Vol. 35, No. 4, April 2008
used in dose calculations. Wittman et al.6 and Melhus et al.19 recently investigated and reported that the available dose tally types of *F4 and F6 are equivalent and adequate in the updated cross section file P04, which is the default library file of the MCNP5 package and is based on release 8 of ENDF/B-VI,21 thus resolving the controversy over tally types. In this work, the F6 tally was used to directly calculate the dose at a given point. The photon interaction cross section file used in this study was the P04 library distributed by the Radiation Shielding Information Computing Center 共RSICC兲.10 The dose rate was also tallied in void space with dry air tally cells for air kerma strength. The spectrum of the cesium-131 consists of five energies22 in the following abundance: 29.461 keV 共0.211兲, 29.782 keV 共0.389兲, 33.562 keV 共0.0363兲, 33.624 keV 共0.0702兲, and 34.419 keV 共0.0213兲. It should be noted that the energy spectrum of the actual seed is influenced by the presence of the encapsulation and other internal materials, including attenuation and fluorescence effects.
TABLE I. Compositions of the different materials in percentage by mass and density 共g / cm3兲 of the different phantom materials used in this work. Water H C N O Ca Cl Na K P Mg Zn Ar Density a
11.2
88.8
1.0
Reference 3. Reference 24. c Reference 2. b
Virtual Water™ 7.69 68.74 2.27 18.86 2.31 0.13
1.03
a
Muscleb 10.2 14.3 3.4 71.0 0.1 0.1 0.1 0.2
1.05
Prostateb 9.76 9.11 2.47 78.10 0.023 0.10 0.21 0.20 0.10 0.019 0.008 1.045
Airc 0.0732 0.01237 75.0325 23.6077
1.2743 1.20e-3
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TABLE II. Dose rates constant of the cesium-131 and other sources calculated and measured by different authors in different media.
Cs-1 Cs-1 Cs-1 Cs-1 Rev2 Cs-1 Rev2 Cs-1 Rev2 Cs-1 Rev2 Cs-1 Rev2 Cs-1 Rev2 Pd-103 共model 200兲 I-125 共6711兲
Method
Medium
Dose rate constant 共cGy h−1 U−1兲
Reference
TLD TLD Gamma-ray spectroscopy MCNP5 共ring兲 MCNP5 共ring兲 MCNP5 共ring兲 MCNP5 共ring兲 MCNP5 共ring兲 MCNP5 共ring兲 TLD + MCNP4 TLD + MCNP4
Water Water Water Water Water Water Virtual Water™ Muscle Prostate Water Water
0.915⫾ 0.020 1.058⫾ 0.106 1.066⫾ 0.064 1.032⫾ 0.002 1.046⫾ 0.019 1.048⫾ 0.026 1.024⫾ 0.025 1.041⫾ 0.026 1.044⫾ 0.026 0.686⫾ 0.048 0.965⫾ 0.068
4 5 5 6 7 This work This work This work This work 2 2
The source was virtually placed at the center of a 30 cm in diameter spherical volume of water or Virtual Water™ or tissue phantom to ensure sufficient backscattering. Assuming a cylindrically symmetric source structure, circular torus cells 共1 mm in transverse diameter兲 around the source longitudinal axis were employed as the tally cells to score the eligible events. In the radial distance ranging from 0.5 to 10 cm, the anisotropy functions were tallied in torus tally cells from 0° to 90° in 5° intervals. The transverse diameters of toruses ranged from 0.5 to 1.0 mm, depending on the angles at which they were placed, in order to avoid overlapping each other and over-limiting the events in the toruses. The elapsed time for each simulation was approximately 52 h in water, 56 h in Virtual Water™ and human tissues, and 7 h in void space for air kerma simulations. The statistical uncertainties were found to be less than 2% for all anisotropy tally points when the distance was smaller than 5 cm and the angle was greater than 10°. However, the uncertainty increased for larger distances and smaller angles. When the distance was 7 cm and the angle was less than 10°, the statistical uncertainty was about 9%. This is understandable because when the distance is large and/or angle is at or close to 0°, the solid angle of this point to the source is very small, so very few photons and/or electrons will be able to enter this tally cell; thus the statistical uncertainty inevitably would be large. The statistical uncertainty for the dose rate constant was under 0.5%. The maximum statistical uncertainty for the
radial dose function tallies 共distance from 0.5 to 10 cm兲 was less than 3%. The statistical uncertainties from air kerma simulations were less than 0.3% at all tally points along the bisector axis. The air kerma strength, SK was calculated in the void space at distances ranging from 0.5 to 25 cm. The energy was deposited in the dry air tally cells. We simulated the air kerma exactly as the geometric condition in water and Virtual Water™, but replaced the phantom with void space and the tally cells with dry air. The variation of the air kerma strength 共air kerma rate multiplied by the distance squared兲 at distances greater than 10 cm was less than 0.5%. This is understandable because when the distance is fairly large, the effect of source structure on the air kerma rate would become very small. Therefore, the value of the air kerma rate at 10 cm could be used to uniquely determine the air kerma at 1 cm using the inverse square law. A ratio of the calculated dose rate in water, Virtual Water™, muscle, and prostate tissue at the reference point 共r0 = 1 cm, 0 = / 2兲 to the calculated air kerma strength was used to determine the dose rate constant of the model Cs-1 Rev2 cesium-131 brachytherapy source. These dose rates were also used to calculate phantom/water ratios at the reference point. The photon cutoff energy was set at 5.0 keV to comply with the AAPM TG-43U1 recommendations. Up to 2 ⫻ 108 source photon histories were processed for each set of inwater and in-air calculations.
TABLE III. The ratio of the dose rate in materials of dosimetric interest to that in liquid water 103 ˙ ˙ Pd, 125I, 192Ir, 169Yb, and cesium-131 xD共r0 , 0兲/waterD共r0 , 0兲. Cs-1 Rev2 is for the Isoray™ cesium-131 seed. were calculated by Melhus et al. 共Ref. 19兲 for unencapsulated point sources.
Cs-1 Rev2 Cs-1 Rev2 Pd-103 I-125 Ir-192 Yb-169 Cs-137
Muscle
Prostate tissue
Virtual Water™
Solid Water™
0.996
0.994
0.977 1.063
0.945
0.981 1.016 0.992 1.014 0.991
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Reference This study 7 19 19 19 19 19
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0.8
1.0
0.6 0.4
water
0.2 0.0 1.2
Riadil dose function, g(r)
MC Wang et al. MC Murphy et al. MC Rivard
1.0
Radial dose function, g(r)
Radial dose function, g(r)
1.2
0
2
4
6
8
1.0
10
12
14
0.8
0.6
0.4
0.2
16 0.0
MC, Wang et al. TLD Murphy et al. MC Rivard
0.8
MC in water MC in muscle MC in prostate tissue
0
2
4
6
8
10
12
14
16
Radial distance, r (cm)
0.6
FIG. 3. Comparison between the Monte Carlo simulated radial dose functions in water and human tissues of the Isoray™ Cs-1 Rev2 source at distances ranging from 0.2 to 15 cm.
0.4 0.2
virtual water
0.0 0
2
4
6
8
10
12
14
16
Radial distance, r (cm) FIG. 2. Comparison between the measured and Monte Carlo simulated radial dose functions of the cesium-131 seed, evaluated by Murphy et al. 共model Cs-1兲 共Ref. 4兲, Rivard et al. 共model Cs-1 Rev2兲 共Ref. 7兲, and this work 共model Cs-1 Rev2兲, in Virtual Water™ and water at distances ranging from 0.2 to 15 cm.
II.C. TG-43U1 parameters calculation
Dosimetric characteristics of the cesium-131 source were determined following AAPM recommendations published in the TG-43U1 report2 and the AAPM recommendation on source calibration.23 An active length 共L兲 of 0.41 cm was used in calculating the geometry functions. Because in clinical applications the radioactive sources are often considered as point sources for dosimetry calculation, the one-dimensional 共1D兲 anisotropy function is usually used in place of the two-dimensional 共2D兲 anisotropy function to simplify dose calculation. The 1D anisotropy function is the ratio of the dose rate at distance r 共averaged with respect to the solid angle兲 to the dose rate on the transverse axis at the same distance. It usually changes slightly with radial distance and can be calculated as
an共r兲 =
˙ 共r, 兲sin d 兰0D . ˙ 共r, /2兲 2D
共5兲
The 1D anisotropy functions, an共r兲, at each radial distance were calculated from the simulated dose rate distributions as a function of the angle. Medical Physics, Vol. 35, No. 4, April 2008
II.D. Medium materials
Table I lists the compositions of four media used in this study. The composition and densities of human tissues are taken from ICRU 44.24 Muscle and prostate tissue are the most relevant tissues for brachytherapy seeds and experimental measurements performed in Virtual Water™ and Solid Water™ provided the most reliable basis for any theoretical calculations, including Monte Carlo simulations. Thus, far the thermoluminescent dosimetry 共TLD兲 measurements have proven to be most useful and reliable in the determination of the dosimetric characteristics of brachytherapy seeds.2 TLD measurements are usually carried out either in Solid Water™ or Virtual Water™ phantom, but are less suitable for directly measuring doses in water and human tissues. Therefore, we first compared our results in a water phantom with other authors’ TLD experimental data to verify our seed modeling. TG-43U1 parameters in water and human tissues were then calculated using the validated technique.
III. RESULTS AND DISCUSSION III.A. Dose rate constant ⌳
Table II presents the ⌳ results for all types of materials used in this study. Those values were determined following the updated AAPM TG-43 recommendations for low-energy brachytherapy sources. The simulated dose rate constant ⌳ in water was 1.048⫾ 0.02 cGy h−1 U−1, which is within 0.2% agreement with Rivard’s calculation for the Cs-1 Rev2 source.7 However, this ⌳ in water is 14% greater than that with TLDs, measured by Murphy et al.4 −1 −1 共0.915⫾ 0.020 cGy h U 兲, and only 1% smaller than that
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TABLE IV. Radial dose function g共r兲 of cesium-131 source in different media, evaluated by Murphy et al. 共model Cs-1兲 共Ref. 4兲, Rivard et al. 共model Cs-1 Rev2兲 共Ref. 7兲, and this work 共model Cs-1 Rev2兲. Distance r共cm兲
Liquid Water™ This work 共MC兲
0.2 0.25 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.5 2 2.5 3 4 5 6 7 8 10 12 15
0.981 0.988 0.998 1.003 1.007 1.006 1.008 1.007 1.004 1.000 0.963 0.909 0.846 0.778 0.641 0.516 0.410 0.321 0.250 0.147 0.0850 0.0362
Rivard 共MC兲a
Virtual Water™ Murphy 共MC兲b
Muscle
Prostate tissue
This work 共MC兲
This work 共MC兲
0.999
0.986
0.984
1.010 1.015 1.017 1.018 1.015 1.012 1.007 1.000 0.948 0.879 0.811 0.737 0.590 0.464 0.359 0.274 0.207 0.118 0.0649 0.0260
1.003 1.008 1.011 1.010 1.011 1.009 1.005 1.000 0.953 0.891 0.822 0.749 0.604 0.477 0.371 0.285 0.215 0.122 0.0673 0.0272
1.001 1.007 1.010 1.008 1.010 1.008 1.005 1.000 0.956 0.896 0.829 0.757 0.615 0.488 0.382 0.295 0.224 0.129 0.0722 0.0291
This work 共MC兲
Rivard 共MC兲a
Murphy 共MC兲b
0.986
1.006
1.003
1.000 0.962 0.908
1.000
0.777 0.642 0.518 0.411 0.323 0.251 0.147
0.806 0.679 0.558 0.454 0.361 0.286
0.923
0.0368
1.023
1.024
1.000
1.000
0.864
0.879
0.736 0.586 0.462 0.361 0.274
0.731 0.586 0.460 0.356 0.272 0.206 0.116 0.0260
a
Reference 7. Reference 4.
b
measured by Chen et al.5 with TLDs −1 −1 共1.058⫾ 0.106 cGy h U 兲, and 1.7% smaller than that measured by the same author using gamma-ray spectroscopy 共1.066⫾ 0.064 cGy h−1 U−1兲 for the Cs-1 model. A possible explanation for the difference is that the model Cs-1 Rev2 is slightly different from the Cs-1 in source structure. Considering that a TLD measurement has at least 7% uncertainty,2 our data are in good agreement with these other experimental measurements. The dose rate constants in muscle and prosand tate tissue are 1.041⫾ 0.026 cGy h−1 U−1 −1 −1 1.044⫾ 0.026 cGy h U , respectively. Thus, conversion factors of 0.993 and 0.996 are needed to convert water data into muscle and prostate tissue, respectively, at the reference point. The conversion factor between water and solid water is 0.997, which is similar to that reported by Meigooni et al.25 for 125I seeds. Table II also lists the dose rate constants for other types of brachytherapy seeds.2 The dose rate constant of the Cs-1
Rev2 source is 35% greater than that of the model 200 103Pd source and 5% greater than that of the 6711 125I seed. Table III shows the dose rate conversion factors for comparison of muscle, prostate tissue, Virtual Water™ and Solid Water™ to water at the reference point as compared with the results from Rivard,7 as well as for other types of seeds reported by Melhus et al.19 The dose rate conversion factor of Virtual Water™ to water reported by Rivard7 is 9% higher than ours. In general, these dose rate conversion factors are very close to those of 103Pd and 125I seeds. III.B. Radial dose function, g„r…
The calculated radial dose function, g共r兲, for the model Cs-1 Rev2 brachytherapy seed in water and Virtual Water™ was compared with TLD measurements by Murphy et al.4 and Rivard’s Monte Carlo calculations7 共Fig. 2兲. The g共r兲 values in water and human tissues are graphed in Fig. 3 for
TABLE V. Fifth order polynomial fitting coefficients of radial dose functions of Cs-1 Rev2 source in water and human tissue phantoms studied in this work. Medium Water Muscle Prostate tissue
a0
a1
0.9798 0.99276 0.98953
0.0831 0.06815 0.07148
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a2 −0.08036 −0.0813 −0.08055
a3
a4
a5
0.01262 0.01321 0.01294
−8.15322e-4 −8.68888e-4 −8.45485e-4
1.92152e-5 2.06887e-5 2.00381e-5
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1.1
1.00
2 cm
0.9
MC Wang et al. TLD Murphy et al. MC Murphy et al.
0.8
0.90
Water Muscle Prostate tissue
0.85 0.80 0.75 0.70
0.7 1.1
1.00
3 cm
3 cm
0.95
0.9
F(r,θ)
1.0
F(r,θ)
2 cm
0.95
F(r,θ)
F(r,θ)
1.0
MC, Wang et al. TLD Murphy et al. MC Murphy et al.
0.8
0.90
Water Muscle Prostate tissue
0.85 0.80 0.75 0.70
0.7 1.1
1.00
F(r,θ)
0.9
MC Wang et al. TLD Murphy et al. MC Murphy et al.
0.8
20
40
60
80
Water Muscle Prostate tissue
0.85 0.80 0.70
100
0
20
40
60
80
100
Angle, θ (degrees)
Angle, θ (degrees) FIG. 4. Comparison between the measured and Monte Carlo simulated anisotropy functions of the cesium-131 seed, evaluated by Murphy et al. 共model Cs-1兲 共Ref. 4兲, Rivard et al. 共model Cs-1 Rev2兲 共Ref. 7兲, and this work 共model Cs-1 Rev2兲, in Virtual Water™ at the radial distances of 2, 3, and 5 cm.
visual comparison and tabulated in Table IV for clinical application. Our results were in excellent agreement with those measured and calculated by other authors 共less than 3% difference兲 共Fig. 2兲. Figure 3 and Table IV show that the radial dose functions in muscle and prostate tissue are very close to each other. The g共r兲 in water is over 2% higher than that in the human tissues studied at distances greater than 2 cm, but they are very close to each other when the distance is less than 2 cm. For easy clinical application of the Cs-1 Rev2 source, the Monte Carlo calculated g共r兲 in water and human tissues in the range of 0.6–10 cm were fitted using a fifth order polynomial curve, namely, g共r兲 = a0 + a1*r + a2*r2 + a3*r3 + a4*r4 + a5*r5 .
0.90
0.75
0.7 0
5 cm
0.95
5 cm
1.0 F(r,θ)
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FIG. 5. Comparison of the Monte Carlo simulated anisotropy functions in water and human tissues of the Isoray™ Cs-1 Rev2 source at the radial distances of 2, 3, and 5 cm.
Water™. Our calculations agree closely 共less than 4% difference兲 with Murphy’s TLD measurements, in which a 7% error bar was added. 关The error bar of 7% is based on the suggestions by Meigooni et al.12 and TG-43 U1 共Ref. 2兲 that TLD measurements would have an uncertainty of at least
共4兲
The polynomial term coefficients of this function for each medium are listed in Table V.
III.C. Anisotropy function, F„r , …
As with the radial dose functions, two kinds of water and two types of human tissue were used in the study of anisotropy functions. In Fig. 4 our calculated results are compared with Murphy’s4 measurements at 2, 3, and 5 cm in Virtual Medical Physics, Vol. 35, No. 4, April 2008
FIG. 6. The 1D anisotropy functions of the Cs-1 Rev2 source as a function of radial distance.
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TABLE VI. Anisotropy function F共r , 兲 of Cs-1 Rev2 source in water. Radius 共cm兲 共°兲
0.5
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 an共r兲
0.821 0.788 0.688 0.718 0.776 0.822 0.862 0.893 0.923 0.937 0.955 0.966 0.976 0.985 0.990 0.993 0.998 0.997 1.000 1.010 ¯ an Anisotropy constant
1
1.5
2
3
4
5
7
10
0.836 0.784 0.727 0.759 0.808 0.848 0.878 0.909 0.926 0.947 0.957 0.972 0.980 0.986 0.992 0.994 0.998 0.999 1.000 0.968
0.832 0.788 0.745 0.782 0.820 0.861 0.891 0.917 0.933 0.947 0.964 0.968 0.982 0.987 0.993 0.996 0.997 0.998 1.000 0.963
0.838 0.791 0.766 0.797 0.833 0.865 0.898 0.926 0.938 0.954 0.965 0.973 0.979 0.984 0.990 0.996 0.997 0.998 1.000 0.962
0.840 0.786 0.774 0.817 0.848 0.877 0.906 0.924 0.940 0.953 0.966 0.974 0.977 0.986 0.992 0.994 0.995 0.996 1.000 0.961 0.995
0.854 0.818 0.796 0.828 0.864 0.879 0.908 0.927 0.943 0.960 0.967 0.971 0.981 0.993 0.995 0.997 1.001 0.998 1.000 0.964
0.852 0.817 0.807 0.840 0.866 0.887 0.911 0.924 0.947 0.960 0.967 0.974 0.987 0.991 0.996 1.000 1.001 1.002 1.000 0.965
0.866 0.825 0.827 0.843 0.860 0.900 0.910 0.933 0.951 0.945 0.972 0.972 0.979 0.990 0.991 0.998 1.000 0.997 1.000 0.964
0.886 0.826 0.835 0.843 0.860 0.911 0.914 0.948 0.935 0.952 0.964 0.970 0.982 0.989 0.992 0.998 1.010 1.000 1.000 0.965
7%, although the particular measurements at different distances may have different uncertainties.兴 The maximum difference occurs on the axis of the source or at the angle closest to 0° where the uncertainties of the calculations are high. Figure 5 gives a visual comparison of anisotropy functions in
water, muscle, and prostate tissue and indicates that the anisotropy functions in muscle and prostate tissue are almost identical to those in water. The 1D anisotropy functions, an共r兲, of Cs-1 Rev2 were extracted from the calculated dose rate D共r˙ , 兲 in water, Vir-
TABLE VII. Anisotropy function F共r , 兲 of Cs-1 Rev2 source in Virtual Water™. Radius 共cm兲 共°兲 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 an共r兲
0.5
0.808 0.780 0.688 0.719 0.777 0.822 0.863 0.893 0.922 0.938 0.955 0.967 0.976 0.985 0.990 0.990 0.998 0.998 1.000 1.010 ¯ an Anisotropy constant
1
1.5
2
3
4
5
7
10
0.806 0.774 0.723 0.756 0.805 0.849 0.877 0.909 0.926 0.946 0.958 0.970 0.982 0.986 0.991 0.996 0.997 1.000 1.000 0.968
0.812 0.787 0.738 0.779 0.824 0.861 0.890 0.915 0.930 0.950 0.965 0.968 0.985 0.985 0.994 0.995 0.996 1.001 1.000 0.963
0.818 0.778 0.761 0.790 0.832 0.865 0.898 0.918 0.938 0.951 0.962 0.974 0.981 0.986 0.989 0.995 0.998 0.999 1.000 0.961
0.838 0.802 0.773 0.815 0.846 0.872 0.906 0.922 0.942 0.953 0.966 0.971 0.980 0.988 0.994 0.998 0.996 1.000 1.000 0.962 0.995
0.846 0.804 0.793 0.814 0.868 0.868 0.906 0.926 0.936 0.954 0.958 0.977 0.991 0.994 0.989 0.988 0.992 1.000 1.000 0.961
0.829 0.806 0.799 0.813 0.847 0.886 0.909 0.919 0.950 0.952 0.961 0.964 0.982 0.983 0.994 0.996 0.989 0.993 1.000 0.962
0.859 0.801 0.817 0.827 0.860 0.877 0.899 0.920 0.945 0.942 0.954 0.964 0.967 0.976 0.973 0.978 0.984 0.981 1.000 0.963
0.902 0.835 0.839 0.855 0.878 0.917 0.943 0.946 0.964 0.961 0.977 0.985 0.993 1.005 0.997 1.014 1.007 1.019 1.000 0.977
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TABLE VIII. Anisotropy function F共r , 兲 of Cs-1 Rev2 source in prostate tissue. Radius 共cm兲 共°兲
0.5
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 an共r兲
0.824 0.789 0.689 0.722 0.777 0.823 0.863 0.894 0.923 0.937 0.955 0.966 0.975 0.985 0.990 0.992 0.997 0.998 1.000 1.010 ¯ an Anisotropy constant
1
1.5
2
3
4
5
7
10
0.837 0.786 0.728 0.759 0.807 0.849 0.878 0.908 0.925 0.946 0.957 0.969 0.980 0.985 0.991 0.995 0.998 1.000 1.000 0.968
0.815 0.791 0.748 0.786 0.826 0.862 0.892 0.917 0.934 0.951 0.964 0.969 0.983 0.986 0.993 0.995 0.998 1.000 1.000 0.964
0.825 0.792 0.765 0.797 0.834 0.863 0.898 0.920 0.939 0.952 0.963 0.975 0.982 0.987 0.990 0.997 0.997 1.000 1.000 0.962
0.852 0.800 0.782 0.821 0.846 0.876 0.906 0.924 0.942 0.956 0.966 0.973 0.979 0.984 0.993 0.999 0.997 1.001 1.000 0.962 0.996
0.868 0.811 0.800 0.838 0.866 0.884 0.915 0.929 0.953 0.961 0.978 0.980 0.991 0.993 0.998 0.991 0.996 1.004 1.000 0.967
0.873 0.818 0.809 0.831 0.866 0.888 0.912 0.928 0.952 0.963 0.969 0.971 0.986 0.992 0.997 1.001 0.998 1.000 1.000 0.966
0.869 0.825 0.824 0.838 0.873 0.890 0.907 0.927 0.941 0.953 0.966 0.971 0.982 0.988 0.980 0.991 0.998 0.995 1.000 0.961
0.904 0.841 0.842 0.849 0.869 0.912 0.933 0.961 0.957 0.949 0.963 0.975 0.980 0.997 0.994 0.984 0.995 0.996 1.000 0.967
tual Water™, prostate tissue, and muscle. Although the an¯ an, is not recommended by TG-43U1, we isotropy constant, still calculated it using the weighted 共inverse-square of the distance兲 mean of the 1D anisotropy functions an共r兲 because some older treatment planning systems still rely on it.
IV. CONCLUSIONS The dosimetric characteristics of the model Cs-1 Rev2 cesium-131 source in water, Virtual Water™, muscle, and prostate tissue were determined using MCNP5 Monte Carlo
TABLE IX. Anisotropy function F共r , 兲 of Cs-1 Rev2 source in muscle. Radius 共cm兲 共°兲 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 an共r兲
0.5
0.823 0.790 0.690 0.722 0.778 0.822 0.863 0.893 0.923 0.937 0.955 0.967 0.975 0.986 0.990 0.992 0.997 0.998 1.000 1.010 ¯ an Anisotropy constant
1
1.5
2
3
4
5
7
10
0.838 0.787 0.730 0.758 0.808 0.849 0.879 0.909 0.924 0.946 0.957 0.970 0.982 0.986 0.991 0.995 0.999 0.999 1.000 0.968
0.815 0.791 0.749 0.787 0.828 0.864 0.893 0.918 0.935 0.951 0.967 0.969 0.984 0.988 0.994 0.997 0.999 1.002 1.000 0.965
0.824 0.795 0.769 0.801 0.835 0.865 0.897 0.920 0.941 0.949 0.963 0.974 0.979 0.984 0.988 0.994 0.999 0.999 1.000 0.961
0.855 0.801 0.785 0.818 0.846 0.877 0.904 0.921 0.943 0.956 0.967 0.972 0.978 0.986 0.994 0.997 0.999 1.000 1.000 0.962 0.995
0.868 0.816 0.799 0.830 0.862 0.884 0.909 0.924 0.945 0.955 0.970 0.976 0.983 0.991 0.991 0.994 0.998 0.998 1.000 0.964
0.881 0.821 0.802 0.830 0.865 0.890 0.917 0.921 0.947 0.959 0.967 0.971 0.982 0.993 0.993 0.998 0.998 0.997 1.000 0.964
0.868 0.831 0.828 0.826 0.873 0.882 0.908 0.921 0.944 0.961 0.970 0.973 0.987 0.984 0.983 0.993 0.996 1.003 1.000 0.963
0.897 0.835 0.831 0.848 0.873 0.896 0.916 0.926 0.944 0.936 0.959 0.976 0.979 1.001 0.999 0.992 0.988 1.001 1.000 0.964
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simulations. The results were compared with those of previous experimental studies4,5 and Monte Carlo calculations.6,7 The differences in the Monte Carlo simulations are quite small, verifying the seed modeling consistency of the two independent Monte Carlo studies. The minor differences can be attributed to the different source geometry designs in the simulations, different source physics definitions such as energy spectrum, different history numbers, as well as the minor differences introduced by tally types. The dosimetric characteristics of the Cs-1 Rev2 seed in muscle and prostate tissue were found to be very close to that of water. The radial dose function in water is slightly greater than that in the human tissues studied. The anisotropy functions of Cs-1 Rev2 in muscle and prostate tissue were almost identical to those in water; therefore, anisotropy functions in water may be safely substituted for those in muscle and prostate tissue for clinical applications. The Cs-1 Rev2 brachytherapy source was found to be equivalent to well known 125I and 103Pd sources in terms of dose rate conversion factors at the reference point for water and the human tissues studied. The dose rate constant of the Cs-1 Rev2 source was 9% larger than that of 125I 共model 6711兲 and 53% larger than that of 103Pd 共model 200兲 seeds. Figure 6 shows the variation of the 1D anisotropy functions of the model Cs-1 Rev2 source as a function of distance. The 1D anisotropy functions was nearly constant at radial distances greater than 2 cm. The values of 2D anisotropy functions F共r , 兲, 1D anisotropy functions an共r兲, and ¯ an, in water, Virtual Water™, prosthe anisotropy constant tate tissue, and muscle, are provided in Tables VI–IX, respectively. a兲
Author to whom correspondence should be addressed. Electronic mail:
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