Monte Carlo calculation of dose rate distributions around 0.5 and 0.6 mm in diameter192 Ir wiresJ. Pérez-Calatayud, F. Lliso, V. Carmona, F. Ballester, and C. Hernández Citation: Medical Physics 26, 395 (1999); doi: 10.1118/1.598530 View online: http://dx.doi.org/10.1118/1.598530 View Table of Contents: http://scitation.aip.org/content/aapm/journal/medphys/26/3?ver=pdfcov Published by the American Association of Physicists in Medicine Articles you may be interested in Monte Carlo dosimetry of a new 192 Ir high dose rate brachytherapy source Med. Phys. 27, 2521 (2000); 10.1118/1.1315316 A Monte Carlo investigation of the dosimetric characteristics of the VariSource 192 Ir high dose ratebrachytherapy source Med. Phys. 26, 1498 (1999); 10.1118/1.598645 Monte Carlo and TLD dosimetry of an 192 Ir high dose-rate brachytherapy source Med. Phys. 25, 1975 (1998); 10.1118/1.598371 Monte Carlo dosimetry of the VariSource high dose rate 192 Ir source Med. Phys. 25, 415 (1998); 10.1118/1.598216 Monte Carlo calculation of dose rate distributions around Ir 192 wires Med. Phys. 24, 1221 (1997); 10.1118/1.598142

Monte Carlo calculation of dose rate distributions around 0.5 and 0.6 mmin diameter 192Ir wires

J. Perez-Calatayud, F. Lliso, and V. CarmonaPhysics Section, Radiation Oncology Department, ‘‘La Fe’’ University Hospital, Avda Campanar 21,46009 Valencia, Spain

F. Ballestera) and C. HernandezDepartment of Atomic, Molecular and Nuclear Physics, University of Valencia, Dr. Moliner 50,46100 Burjassot, Valencia, Spain

~Received 15 December 1997; accepted for publication 18 December 1998!

Monte Carlo simulations of absolute dose rate in liquid water are presented in the form of away-along tables for 1 and 5 cm192Ir wires of 0.5 and 0.6 mm diameter. Simulated absolute dose ratevalues can be used as benchmark data to verify the calculation results of treatment planning systemsor directly as input data for treatment planning. Best fit value of an attenuation coefficient suitablefor use in Sievert integral-type calculations has been derived based on Monte Carlo simulationresults. For the treatment planning systems that are based on the TG43 formalism we have alsocomputed the required dosimetry parameters. ©1999 American Association of Physicists inMedicine.@S0094-2405~99!00703-8#

Key words: iridium, dosimetry, brachytherapy, Monte Carlo, treatment planning systems

I. INTRODUCTION

Platinum-encapsulated192Ir wires are used as interstitialsources in low dose rate brachytherapy. There are severalmodels of192Ir wires provided either by Amersham~Amer-sham International p/c Little Chalfont, Buckinghamshire,England HP79NA! or CIS ~CIS bio International, B.P. 32-91/92 Gif-sur-Yvette, Cedex France!. All of them have thecentral core encased in a 0.1 mm Pt sheet. In a previouspaper1 we studied 0.3 mm external diameter192Ir wires. Thisone is focused on 0.5 and 0.6 mm external diameter sourcesthat are available as wires and as single or double leg hairpinshapes~Fig. 1!.

Amersham delivers 0.6 mm diameter wires which may besingle pin 7.3 cm in length~Models ICW.4040 to ICW.4300!or double leg hairpin 13.1 cm in length~Models ICW.3040to ICW.3300!. Different models cover a range of nominalair-kerma strength. CIS delivers 0.5 mm diameter wires~IRF-2, 14 cm long!, single pin~Models IREC.1, 3 cm long,and IREL.1, 5 cm long! or double leg hairpin~ModelsIREC.1, 7.2 cm long, and IREL.1, 11.2 cm long!.

In spite of the fact that192Ir wires are widely used, thereare few papers which present reference data of dose ratedistributions to be compared with calculations of commercialtreatment planning systems.

The only reference for these sources is by Dutreixet al.2

which presents calculated dose rates along a transverse axisfor 0.5 mm diameter sources for different lengths. In thispaper, we present Monte Carlo simulations of absolute doserate in water for192Ir wires or hairpins with 0.5 and 0.6 mmexternal diameters at distances up to 10 cm away and alongfrom the source center for two representative lengths: 1 and 5cm.

With this paper and the previous one,1 all available com-mercial iridium hairpins and wires have been studied.

Available treatment planning systems use different inputdata for their calculations. Most of them, using the Sievertintegral method, require a value of the attenuation coefficientof the encapsulation of the source. Others, very few, requirea tabular entry of two-dimensional dose distribution data.According to TG43 recommendation,3 it should be wishfulthat forthcoming treatment planning systems would followtheir formalism.

The aim of this work is to obtain input data for treatmentplanning systems for the sources indicated above.

II. MATERIAL AND METHODS

A. Iridium sources description and design

The simulated sources are192Ir wires of 1 and 5 cm lengthwith 0.5 and 0.6 mm external diameters. The central coresare 0.3 and 0.4 mm in diameter, composed of about 25% Irand 75% Pt, encased in a 0.1 mm Pt sheath.

B. Monte Carlo code

The Monte Carlo method has been used to obtain absolutedose rate values in water around encapsulated192Ir sources.As stated by Williamson,4 Monte Carlo simulation is limited

FIG. 1. Diagram of the hairpins:~a! double hairpin and~b! single hairpin.

395 395Med. Phys. 26 „3…, March 1999 0094-2405/99/26 „3…/395/7/$15.00 © 1999 Am. Assoc. Phys. Med.

neither by the complexity of the underlying physics of radia-tion interactions nor by the geometric complexity of clinicalbrachytherapy sources and applicators, avoiding positioningerrors, averaging of dose over detector volume, variable en-ergy responses, etc., that are present in the experimentalmethods.

The simulations were performed using theGEANT code.5

The algorithm, methodology, and test for its use with brachy-therapy sources have been published elsewhere.1 It will bedescribed only briefly here.GEANT code is equipped with ageometric package that allows complex objects to be de-scribed. All physical processes for low-energy photons areimplemented inGEANT: photoelectric effect, Compton dis-persion, pair production, and Rayleigh scattering. X-rayemission is simulated assuming that an x-ray of energyEg

minus electron binding energy is emitted. The cutoff energy

for photons was taken at 10 keV. For electrons, multiplescattering and continuous energy loss were assumed. Thecutoff energy for electrons was taken at 10 keV.

The decay scheme for192Ir was taken fromNuclear DataSheets.6 The192Ir wires were modeled as cylinders with innercylindrical cores of 0.3 and 0.4 mm diameter encased in a0.1 mm Pt cylindrical sheath with the same height. The co-ordinate reference system has the longitudinal and transverseaxis of the source as thez and y axes, respectively. Theorigin is taken at the center of the source.

Absorbed dose is a nonstochastic quantity that is defined7

as a point function in a specific medium. In a Monte Carlosimulation we need to score the energy absorbed by the me-dium in a finite volume. A grid system is set up to scoreabsorbed dose in each cell, and the average absorbed dose inthe cell is assumed to be the absorbed dose in the center of

TABLE I. Dose rate~cGy/h! in water per unit air-kerma strength around a 1 cmlength of192I wire of 0.5 mm external diameter. The origin is taken at the centerof the source.

Away:y (cm)

Distances along the source:z (cm)

0.0 0.25 0.5 0.75 1 1.5 2 2.5 3 4 5 6 8 10

0.025 ¯ ¯ ¯ 3.950 1.919 0.900 0.573 0.381 0.278 0.182 0.125 0.107 0.067 0.0430.15 20.08 19.14 11.17 2.898 1.262 0.481 0.270 0.179 0.129 0.085 0.053 0.038 0.030 0.0150.3 7.697 6.968 4.686 2.288 1.191 0.465 0.254 0.161 0.110 0.064 0.041 0.030 0.018 0.0120.4 4.995 4.559 3.283 1.914 1.106 0.465 0.256 0.161 0.111 0.061 0.041 0.029 0.017 0.0110.5 3.509 3.234 2.456 1.602 1.004 0.458 0.255 0.159 0.112 0.063 0.039 0.028 0.017 0.0100.75 1.759 1.655 1.382 1.055 0.766 0.415 0.244 0.158 0.111 0.063 0.040 0.028 0.016 0.0101 1.044 1.002 0.883 0.731 0.581 0.356 0.226 0.154 0.110 0.063 0.040 0.028 0.015 0.0101.5 0.486 0.475 0.443 0.399 0.348 0.253 0.181 0.132 0.099 0.060 0.039 0.028 0.015 0.0102 0.279 0.274 0.263 0.246 0.225 0.181 0.141 0.110 0.086 0.055 0.037 0.027 0.015 0.0102.5 0.180 0.178 0.173 0.166 0.156 0.133 0.111 0.090 0.074 0.050 0.035 0.026 0.015 0.00953 0.126 0.125 0.122 0.118 0.113 0.101 0.087 0.074 0.063 0.044 0.032 0.024 0.014 0.00924 0.071 0.070 0.070 0.068 0.067 0.062 0.057 0.051 0.045 0.035 0.027 0.021 0.013 0.00875 0.045 0.045 0.045 0.044 0.043 0.041 0.039 0.036 0.033 0.027 0.022 0.018 0.012 0.00806 0.031 0.031 0.031 0.031 0.030 0.029 0.028 0.026 0.025 0.021 0.018 0.015 0.010 0.00738 0.017 0.017 0.017 0.017 0.017 0.016 0.016 0.015 0.015 0.013 0.012 0.010 0.0079 0.0059

10 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.0095 0.0088 0.0081 0.0073 0.0059 0.0046

TABLE II. Dose rate~cGy/h! in water per unit air-kerma strength around a 5 cmlength of192I wire of 0.5 mm external diameter. The origin is taken at thecenter of the source.

Away:y (cm)

Distances along the source:z (cm)

0.0 0.25 0.5 0.75 1 1.5 2 2.5 3 4 5 6 8 10

0.025 ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ 0.421 0.169 0.099 0.066 0.041 0.0240.15 4.458 4.443 4.437 4.445 4.429 4.347 4.221 2.266 0.280 0.083 0.041 0.029 0.017 0.0100.3 2.027 2.019 2.005 2.007 1.982 1.942 1.788 1.047 0.293 0.077 0.042 0.028 0.015 0.00950.4 1.491 1.490 1.485 1.476 1.461 1.411 1.268 0.775 0.283 0.081 0.042 0.028 0.014 0.00890.5 1.171 1.170 1.159 1.153 1.142 1.093 0.960 0.612 0.271 0.084 0.043 0.028 0.014 0.00890.75 0.738 0.736 0.732 0.721 0.710 0.668 0.573 0.402 0.230 0.086 0.045 0.028 0.014 0.00891 0.521 0.519 0.514 0.510 0.499 0.463 0.396 0.296 0.195 0.086 0.046 0.029 0.015 0.00891.5 0.304 0.304 0.300 0.296 0.289 0.266 0.231 0.186 0.140 0.076 0.045 0.029 0.015 0.00912 0.200 0.200 0.198 0.194 0.189 0.175 0.155 0.131 0.106 0.066 0.042 0.029 0.015 0.00922.5 0.141 0.141 0.139 0.137 0.134 0.125 0.112 0.098 0.083 0.057 0.039 0.027 0.015 0.00913 0.104 0.104 0.103 0.102 0.100 0.093 0.086 0.076 0.067 0.049 0.035 0.025 0.015 0.00904 0.063 0.063 0.062 0.062 0.061 0.058 0.054 0.050 0.045 0.036 0.028 0.022 0.013 0.00855 0.042 0.042 0.041 0.041 0.040 0.039 0.037 0.035 0.032 0.027 0.022 0.018 0.012 0.00796 0.029 0.029 0.029 0.029 0.029 0.028 0.027 0.025 0.024 0.021 0.018 0.015 0.010 0.00728 0.016 0.016 0.016 0.016 0.016 0.016 0.015 0.015 0.014 0.013 0.012 0.010 0.0078 0.0058

10 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.0093 0.0086 0.0080 0.0072 0.0058 0.0045

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the cell. For nonlinear varying functions this is not correctand the effective point to assign the scored dose to deviatesfrom the geometrical center of the cell. Consequently, wehave chosen a score volume ofDz5Dy50.5 mm such thatthe systematic error~for points alongy axis! is lower than1% at a distance ofy51.5 mm. This error goes down to0.1% at y55 mm for points in the transverse axis of thesource.1 This estimation can be extended to points off thetransverse axis of the source, but could be critical at largeoblique angle. In any case, for these cells the geometricalaccuracy when the dose is assigned to the geometrical centerof the cell will be better than 0.25 mm.

C. Monte Carlo simulations

In order to estimate the air-kerma strength each sourcewas located in a 63636 m3 dry air cube and air-kerma wasscored on a grid with cells of sizeDz5Dy55 mm ~alongtransverse axis atz50! from y510 cm to y5100 cm and23109 histories were performed for each source.

In order to reach full scatter conditions, a 40 cm heightcylinder of water and 40 cm in diameter was assumed. Toexploit cylindrical symmetry, the cells in which energy depo-sition was accumulated were rings of 0.5 mm square sectionwith its center on thez axis. Then, the dose was scored in a

TABLE III. Dose rate~cGy/h! in water per unit air-kerma strength around a 1 cmlength of192I wire of 0.6 mm external diameter. The origin is taken at thecenter of the source.

Away:y (cm)

Distances along the source:z (cm)

0.0 0.25 0.5 0.75 1 1.5 2 2.5 3 4 5 6 8 10

0.025 ¯ ¯ ¯ 3.561 1.916 1.039 0.695 0.501 0.424 0.288 0.223 0.164 0.112 0.0670.15 19.82 18.42 10.84 2.588 1.056 0.390 0.217 0.153 0.111 0.073 0.050 0.037 0.023 0.0150.3 7.545 7.014 4.625 2.163 1.084 0.411 0.213 0.135 0.093 0.058 0.038 0.028 0.017 0.0110.4 5.027 4.543 3.264 1.841 1.032 0.415 0.220 0.135 0.092 0.054 0.036 0.025 0.015 0.0100.5 3.536 3.249 2.447 1.555 0.957 0.412 0.226 0.137 0.094 0.054 0.034 0.024 0.015 0.0100.75 1.783 1.676 1.382 1.038 0.744 0.385 0.223 0.143 0.097 0.054 0.034 0.024 0.014 0.00901 1.050 1.010 0.886 0.728 0.573 0.345 0.215 0.142 0.099 0.055 0.035 0.024 0.014 0.00861.5 0.490 0.478 0.446 0.399 0.347 0.248 0.175 0.126 0.092 0.055 0.036 0.025 0.014 0.00872 0.281 0.276 0.265 0.247 0.226 0.179 0.139 0.107 0.082 0.052 0.035 0.024 0.014 0.00872.5 0.181 0.179 0.174 0.166 0.156 0.133 0.109 0.089 0.072 0.048 0.033 0.024 0.014 0.00863 0.126 0.125 0.123 0.119 0.114 0.101 0.087 0.073 0.061 0.043 0.031 0.023 0.013 0.00854 0.071 0.071 0.070 0.069 0.067 0.062 0.057 0.051 0.045 0.034 0.026 0.020 0.012 0.00815 0.045 0.045 0.045 0.044 0.044 0.041 0.039 0.036 0.033 0.027 0.022 0.017 0.011 0.00766 0.031 0.031 0.031 0.031 0.030 0.029 0.028 0.026 0.025 0.021 0.018 0.015 0.010 0.00708 0.017 0.017 0.017 0.017 0.017 0.016 0.016 0.015 0.015 0.013 0.012 0.010 0.0077 0.0057

10 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.0095 0.0088 0.0081 0.0073 0.0058 0.0045

TABLE IV. Dose rate~cGy/h! in water per unit air-kerma strength around a 5 cmlength of192I wire of 0.6 mm external diameter. The origin is taken at thecenter of the source.

Away:y (cm)

Distances along the source:z (cm)

0.0 0.25 0.5 0.75 1 1.5 2 2.5 3 4 5 6 8 10

0.025 ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ 0.425 0.163 0.108 0.071 0.044 0.0320.15 4.401 4.386 4.429 4.375 4.381 4.299 4.172 2.282 0.275 0.078 0.044 0.029 0.015 0.0120.3 2.000 1.996 1.993 1.984 1.969 1.930 1.768 1.041 0.281 0.077 0.041 0.027 0.014 0.00940.4 1.472 1.467 1.476 1.462 1.445 1.403 1.253 0.774 0.277 0.080 0.041 0.027 0.014 0.00890.5 1.157 1.157 1.156 1.143 1.129 1.083 0.957 0.615 0.263 0.081 0.041 0.027 0.014 0.00880.75 0.732 0.732 0.729 0.719 0.707 0.664 0.574 0.398 0.225 0.084 0.043 0.027 0.014 0.00861 0.519 0.518 0.514 0.507 0.498 0.460 0.393 0.293 0.193 0.084 0.045 0.028 0.014 0.00871.5 0.304 0.303 0.300 0.295 0.288 0.264 0.229 0.185 0.139 0.075 0.044 0.028 0.015 0.00892 0.200 0.199 0.197 0.194 0.189 0.174 0.154 0.130 0.106 0.065 0.042 0.028 0.015 0.00902.5 0.141 0.140 0.139 0.137 0.134 0.124 0.112 0.098 0.083 0.056 0.038 0.027 0.015 0.00893 0.104 0.104 0.103 0.101 0.099 0.093 0.085 0.076 0.066 0.048 0.035 0.025 0.014 0.00884 0.063 0.063 0.062 0.062 0.061 0.058 0.054 0.050 0.045 0.036 0.028 0.021 0.013 0.00845 0.042 0.042 0.041 0.041 0.040 0.039 0.037 0.035 0.032 0.027 0.022 0.018 0.012 0.00786 0.029 0.029 0.029 0.029 0.029 0.028 0.027 0.025 0.024 0.021 0.018 0.015 0.010 0.00718 0.016 0.016 0.016 0.016 0.016 0.016 0.015 0.015 0.014 0.013 0.012 0.010 0.0078 0.0057

10 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.009 0.0093 0.0086 0.0080 0.0072 0.0058 0.0045

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4003400 matrix in ay2z plane fromz5y50 mm toz5y5200 mm. Note that all energy deposition in water volumewas taken into account.

Up to 109 histories were simulated for each wire. Statis-tical errors of the absorbed dose in each cell at distanceslower than 5 cm from the origin ranged from 0.1% to 1.5%,rising to 5% at 10 cm.

D. Analysis of simulated data

As pointed out by Williamson,8 air-kerma estimation wasfound to be well described by the linear equationkair(y,z50)/G(y,z50)5Sk1by. The slopeb describes the in-crease inkair(y,0)/G(y,0) due to buildup of scatter in the airand the intercept is an estimate of the ratio of the air-kermarate in free space and the geometry factor.

The absolute dose rate data for points 1 cm away from thesource were grouped as curves~z constant andy variable!and these curves were fitted to a function given by the prod-uct of the geometry factor for linear sources3 G(y,z) and afourth degree polynomy iny with adjustable parameters. Inorder to avoid statistical fluctuations of dose in the cells, thedose assigned to each point was that obtained from the fitinstead of the individual value obtained from the simulations.For those points whose dose rate is not well described by thefit we took the simulated dose value in the cell.

III. RESULTS AND DISCUSSION

A. Results for 192Ir wires

Simulations with 1 and 5 cm long192Ir wires were per-formed as described above for both kinds of sources. Ab-sorbed dose rates in water have been normalized to a valueof air-kerma strength of 1mGym2h21 and are presented inTables I–IV. Distances are taken along the source axis andtransverse away from the source center.

For the 0.5 mm sources~both lengths! Dutreix values2 andour simulations agree within 1%.

Dose rate differences for equal length sources are signifi-cant at short distances from the source and for points inside a25° cone with its vertex in the edge of the source and its axisalong thez axis forL51 cm~'45° forL55 cm!. Otherwise,differences are lower than 2%.

B. Application to treatment planning systems

Frequently, currently available treatment planning sys-tems make use of the Sievert9 model to generate two-

TABLE V. Dose rate constants in water medium for192Ir wires.

Wire L ~cGy h21 U21!

192Ir (L51 cm) 1.047192Ir (L55 cm) 0.521

TABLE VI. Radial dose functiong(r ).

Distance alongtransverse axis

~cm!

Radial dose functiong(r )

0.5 mm external diameter 0.6 mm external diameter

192Ir (L51 cm) 192Ir (L55 cm) 192Ir (L51 cm) 192Ir (L55 cm)

0.15 1.046 1.002 1.011 1.0020.3 0.986 0.958 0.972 0.9540.4 0.989 0.967 0.979 0.9600.5 0.994 0.978 0.984 0.9710.75 0.997 0.991 0.994 0.9871 1.000 1.000 1.000 1.0001.5 1.005 1.012 1.005 1.0142 1.008 1.021 1.008 1.0242.5 1.011 1.027 1.009 1.0313 1.012 1.031 1.010 1.0354 1.010 1.033 1.007 1.0385 1.005 1.028 1.001 1.0336 0.996 1.019 0.990 1.0237 0.984 1.005 0.977 1.0088 0.969 0.989 0.961 0.9919 0.950 0.970 0.942 0.972

10 0.929 0.949 0.920 0.950

Radial dose function are fit to a fourth-order polynomialg(r )5a01a1r 1a2r 21a3r 31a4r 4 between 0.5 and10.0 cm. Coefficients are:

a0 a1 a2 a3 a4

L51 cm, f50.5 mm 0.985675 1.7522731022 23.337331023 1.4399131024 24.254031026

L55 cm, f50.5 mm 0.966380 4.1017931022 27.886531023 5.0306131024 21.420931025

L51 cm, f50.6 mm 0.986034 1.4538531022 23.656531023 1.7339731024 24.850031026

L55 cm, f50.6 mm 0.961317 4.7303131022 29.209931023 6.0674531024 21.701431025

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dimensional dose rate arrays for filtered linear sources. Theself-absorption and absorption in the filter material are takeninto account using exponential corrections by means of ef-fective attenuation coefficients. These corrections are appliedto the crossed thickness of the source and its filter, to eachray going from the elementary source to the calculationpoint. TG43 recommends3 to treating the attenuation coeffi-cients as free parameters of best fit chosen to minimize thedeviations from the Sievert model against the results ob-tained by the most adequate method.

We have carried out a program based on the Cassell10

algorithm which uses the quantization method based on thedecomposition of the source in small cells. This algorithm issimilar to the Sievert integral model described byWilliamson.4 The program uses Meisberger scattering andattenuation corrections. The self-absorption and the attenua-tion in the filter are taken into account by means of an ex-ponential correction for each ray going from the elementary

source to the calculation point. Due to the small diameter ofthe 192Ir sources, an accurate determination ofm is not criti-cal.

We have found that calculations with this program for 5and 1 cm192Ir lengths for both kinds of sources with the useof the m54.45 cm21 value reproduce Monte Carlo resultswithin 2% for both wires except for points inside a 50° conewith its vertex in the edge of the source and its simmetry axisalong thez axis for which differences ranges from 5% to70%. It is well known that this algorithm does not properlywork for these regions.3

TG43 formalism3 establishes that the absorbed doseshould be expressed as:

D~r ,u!5SkLtG~r ,u!

G~r 0 ,u0!g~r !F~r ,u!, ~1!

wherer is the radial distance from the source center in the

TABLE VII. Anisotropy functionF(r ,u) for 192Ir of length L51 cm and 0.5 mm external diameter.

u~deg!

r (cm)

0.15 0.25 0.5 0.75 1 2 3 4 5 6 7 8 9 10

0 ¯ ¯ ¯ 2.235 2.798 2.871 2.946 3.211 3.324 4.087 4.305 4.362 4.523 4.5401 ¯ ¯ ¯ 2.150 1.529 1.491 1.250 1.300 1.315 1.324 1.567 1.784 1.432 1.0852 ¯ ¯ ¯ 1.000 0.991 1.100 1.191 1.192 1.091 1.092 1.273 1.070 1.076 1.0853 ¯ ¯ ¯ 0.990 0.950 0.928 0.967 1.080 0.915 0.947 1.000 1.000 1.000 0.9854 ¯ ¯ ¯ 0.981 0.931 0.925 0.920 0.910 0.910 0.920 0.932 0.982 0.983 0.9835 ¯ ¯ 1.083 0.970 0.894 0.849 0.854 0.858 0.869 0.898 0.902 0.933 0.938 0.940

10 ¯ ¯ 1.071 0.911 0.857 0.867 0.880 0.905 0.910 0.910 0.910 0.926 0.927 0.94720 ¯ ¯ 1.058 0.964 0.949 0.925 0.960 0.960 0.960 0.960 0.960 0.960 0.970 0.98230 ¯ 1.095 1 0.969 0.968 0.965 0.965 0.961 0.961 0.961 0.961 0.961 0.977 0.98540 ¯ 1.053 1 0.996 0.993 0.993 0.992 0.992 0.992 0.991 0.991 0.991 0.990 0.99050 ¯ 1.014 1 0.997 0.995 0.994 0.993 0.993 0.993 0.992 0.992 0.990 0.990 0.99060 1 1 1 0.999 0.998 0.997 0.996 0.996 0.995 0.995 0.992 0.991 0.991 0.99170 1 1 1 0.999 0.999 0.999 0.998 0.997 0.997 0.997 0.997 0.991 0.991 0.99180 1 1 1 1 1 1 0.999 0.999 0.998 0.998 0.998 0.996 0.996 0.99690 1 1 1 1 1 1 1 1 1 1 1 1 1 1

TABLE VIII. Anisotropy functionF(r ,u) for 192Ir of length L55 cm and 0.5 mm external diameter.

u~deg!

r (cm)

0.15 0.25 0.5 0.75 1 2 3 4 5 6 7 8 9 10

0 ¯ ¯ ¯ ¯ ¯ ¯ 1.100 1.620 2.050 2.030 2.200 2.450 2.400 2.4001 ¯ ¯ ¯ ¯ ¯ ¯ 0.950 1.200 0.670 0.790 0.900 0.920 0.800 0.7502 ¯ ¯ ¯ ¯ ¯ 1.600 0.720 0.710 0.690 0.780 0.785 0.800 0.800 0.8303 ¯ ¯ ¯ ¯ 1.070 1.320 0.710 0.680 0.700 0.740 0.760 0.775 0.790 0.8004 ¯ ¯ ¯ 1.000 1.050 1.050 0.790 0.670 0.710 0.745 0.755 0.760 0.775 0.7955 ¯ ¯ ¯ 1.010 1.045 0.990 0.810 0.690 0.720 0.745 0.755 0.763 0.780 0.790

10 ¯ ¯ 1.025 1.020 0.975 0.965 0.880 0.820 0.810 0.820 0.830 0.835 0.840 0.85020 ¯ ¯ 1.035 0.975 0.960 0.950 0.940 0.930 0.920 0.923 0.925 0.928 0.930 0.93530 ¯ 1.045 0.985 0.981 0.980 0.975 0.965 0.960 0.940 0.945 0.955 0.960 0.965 0.97040 ¯ 1.020 0.991 0.989 0.990 0.987 0.975 0.975 0.965 0.960 0.970 0.970 0.980 0.98050 1.010 1.007 0.993 0.997 1 0.988 0.980 0.981 0.977 0.980 0.980 0.980 0.990 0.99060 1 1.003 0.995 0.998 1 0.990 0.985 0.987 0.989 0.990 0.995 0.992 0.995 0.99570 1 1 0.999 0.999 1 0.994 0.991 0.995 0.995 0.999 0.999 0.993 0.998 0.99880 1 0.999 1 1 1 1 1 1 1 1 0.999 1.000 1.000 0.99990 1 1 1 1 1 1 1 1 1 1 1 1 1 1

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plane containing the source axis,u denotes the polar angle,Sk stands for the air-kerma strength,L is the dose rate con-stant,t is the exposure time,G(r ,u) is the geometry factorthat accounts for the distribution of the radioactive material,F(r ,u) is the anisotropy function that accounts for the angu-lar dependence of photon absorption and scatter, andg(r )represents the radial dose function that accounts for radialdependence of photon absorption and scatter in the mediumalong the transverse axis~u5p/2!. The reference point(r 0 ,u0) is r 051 cm andu05p/2.

For the use of our simulated data in treatment planningprograms based on TG43 formalism we have extracted fromour simulation the necessary dosimetry parameters for bothlengths and for both kind of sources:

L5D~r 0 ,u0!

Sk,

g~r !5D~r ,u0!

D~r 0 ,u0!

G~r 0 ,u0!

G~r ,u0!, ~2!

F~r ,u!5D~r ,u!

D~r ,u0!

G~r ,u0!

G~r ,u!.

See Tables V–X.From our simulations we have found that dose rate con-

stant valuesL for wires with the same length are almostequal ~for example, forL51 cm differences inL for 0.3,0.5, and 0.6 mm diameter wires are lower than 0.5%! be-cause all wires have the same filtration and the internal di-

TABLE IX. Anisotropy functionF(r ,u) for 192Ir of length L51 cm and 0.6 mm external diameter.

u~deg!

r (cm)

0.15 0.25 0.5 0.75 1 2 3 4 5 6 7 8 9 10

0 ¯ ¯ ¯ 1.512 2.008 2.438 4.489 4.501 6.203 6.409 7.124 7.702 8.578 7.2001 ¯ ¯ ¯ 1.000 1.394 2.213 1.841 2.987 1.462 1.384 1.160 1.380 1.513 0.9002 ¯ ¯ ¯ 0.990 1.100 1.300 1.200 1.030 0.940 0.870 0.870 1.010 1.000 1.0003 ¯ ¯ ¯ 0.910 0.900 0.845 0.795 0.900 0.842 0.905 0.891 0.890 0.921 0.9204 ¯ ¯ ¯ 0.890 0.800 0.727 0.840 0.829 0.827 0.769 0.858 0.868 0.882 0.8875 ¯ ¯ 1.063 0.750 0.664 0.688 0.706 0.745 0.745 0.765 0.765 0.815 0.700 0.821

10 ¯ ¯ 1.051 0.810 0.761 0.736 0.734 0.770 0.780 0.791 0.794 0.819 0.835 0.86020 ¯ ¯ 1.032 0.885 0.857 0.849 0.862 0.864 0.872 0.881 0.891 0.904 0.905 0.91430 ¯ 1.053 0.974 0.952 0.924 0.920 0.915 0.926 0.932 0.937 0.938 0.939 0.940 0.94240 ¯ 1.027 0.991 0.966 0.955 0.953 0.951 0.950 0.952 0.954 0.955 0.957 0.958 0.96150 1 1 1 0.984 0.979 0.978 0.977 0.978 0.980 0.981 0.982 0.983 0.984 0.98960 1 1 1 0.999 0.996 0.994 0.992 0.991 0.991 0.991 0.991 0.994 0.996 0.99770 1 1 1 1 1 1 1 1 1 0.999 0.999 0.999 0.999 0.99980 1 1 1 1 1 1 1 1 1 1 1 1 1 190 1 1 1 1 1 1 1 1 1 1 1 1 1 1

TABLE X. Anisotropy functionF(r ,u) for 192Ir of length L55 cm and 0.6 mm external diameter.

u~deg!

r (cm)

0.15 0.25 0.5 0.75 1 2 3 4 5 6 7 8 9 10

0 ¯ ¯ ¯ ¯ ¯ ¯ 1.100 1.650 2.200 2.300 2.500 2.700 2.900 3.1801 ¯ ¯ ¯ ¯ ¯ ¯ 0.960 0.900 0.825 0.780 0.740 0.805 0.860 0.7892 ¯ ¯ ¯ ¯ ¯ 0.800 0.750 0.682 0.710 0.730 0.737 0.760 0.780 0.8103 ¯ ¯ ¯ ¯ 0.900 1.400 0.690 0.670 0.698 0.715 0.732 0.740 0.760 0.7834 ¯ ¯ ¯ 0.990 0.990 1.010 0.740 0.660 0.683 0.720 0.740 0.750 0.765 0.7895 ¯ ¯ ¯ 0.992 0.986 1.000 0.770 0.680 0.687 0.710 0.740 0.752 0.770 0.795

10 ¯ ¯ 1.040 1.000 0.983 0.935 0.863 0.804 0.783 0.798 0.819 0.830 0.850 0.86020 ¯ ¯ 1.020 0.980 0.950 0.960 0.915 0.890 0.881 0.882 0.890 0.900 0.910 0.91530 ¯ 1.040 0.980 0.975 0.955 0.960 0.950 0.940 0.930 0.938 0.940 0.950 0.950 0.95140 ¯ 1.020 0.985 0.996 0.970 0.980 0.984 0.972 0.961 0.964 0.970 0.980 0.988 0.99050 1 1.007 0.990 0.997 0.990 0.990 0.984 0.975 0.968 0.975 0.975 0.990 0.995 0.99960 1 0.999 0.998 0.998 0.996 0.993 0.985 0.997 0.983 0.990 0.990 0.990 0.999 0.99970 1 1 1 0.999 0.998 0.995 0.993 0.992 0.991 0.991 0.991 0.991 0.999 0.99980 1 1 1 1 1 1 1 0.999 0.999 0.999 0.999 0.999 0.999 0.99990 1 1 1 1 1 1 1 1 1 1 1 1 1 1

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ameters are small. Then we have adopted forL the values inTable V that were calculated in a previous work.1 Ratiosbetween the dose rate constant values for both lengths andbetween the respective geometry factors are slightly differ-ent, about 3%. Radial dose functions,g(r ), agree within 1%for the same length sources. The anisotropy function forsources with the same length shows also a similar trend ex-cept for small angles at close distances from the source.

A specific problem of linear192Ir sources is that they areemployed with different lengths in each specific implant oras the result from reconstruction processes when the wire isnot straight, for example, in the form of hairpin. Unfortu-nately there is not a simple method to obtain a dosimetryparameters set for all the lengths. The radial dose functiong(r ) and the anisotropy functionF(r ,u) are not easily cor-related with the active source lengthL for small distances.

Treatment planning systems try to overcome this problemtwofold. In the geometric reconstruction the wires are ap-proximated by the sum of small line sources. On the otherhand, the reduced coordinates method~Batho and Young11!that uses only one or a few dosimetry tables to obtain datafor all the lengths is included in the treatment planning sys-tems. This method consists of expressing the coordinates asmultiples of the active length of the source. So, reduced co-ordinate system application can be tested with our simula-tions of absorbed dose rates for the two representativelengths, 1 and 5 cm192Ir wires.

IV. CONCLUSION

Dose-rate tables for 1 and 5 cm length192Ir sources 0.5and 0.6 mm in diameter have been obtained using a MonteCarlo code. These tables with simulated absolute dose ratevalues can be used as benchmark data to verify the calcula-tion results of treatment planning systems or directly as inputdata for treatment planning.

Moreover, the Monte Carlo simulations for 1 and 5 cm192Ir wires presented in this paper allow us to test the reduced

coordinate system application assumed by most of the com-mercial treatment planning systems.

For the treatment planning systems that make use of theSievert model to generate two-dimensional dose rate arraysfor filtered linear sources, we have shown that the use of anattenuation coefficient value ofm54.45 cm21 reproducesMonte Carlo simulations for both lengths and sources in themain clinically relevant zones. In any case, the limitations ofeach treatment planning algorithm should be tested before itsuse in clinical dosimetry.

Dosimetry parameters in the TG43 formalism have beenobtained suitable for use in treatment planning systems pro-grams.

We present in this paper all the input data required by thedifferent treatment planning systems for these sources.

a!Electronic mail: Facundo.Ballester@uv.es1F. Ballester, C. Herna´ndez, J. Pe´rez-Calatayud, and F. Lliso, ‘‘MonteCarlo calculation of dose rate distributions around192Ir wires,’’ Med.Phys.24, 1221–1228~1997!.

2A. Dutreix, G. Marinello, and A. Wambersie,Dosimetrie en Curiethera-pie ~Masson, Paris, 1982!.

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4J. F. Williamson, ‘‘Monte Carlo and analytic calculation of absorbed dosenear137Cs intracavitary sources,’’ Int. J. Radiat. Oncol., Biol., Phys.15,227–237~1988!.

5GEANT code version 3.21. CERN Program Library.6V. S. Shirley, Nucl. Data Sheets64, 205 ~1991!.7International Commission on Radiation Units and Measurements,Radia-tion Quantities and Units, ICRU Report 33~1980!.

8J. F. Williamson and Z. Li, ‘‘Monte Carlo aided dosimetry of the mi-croselectron pulsed and high dose-rate192Ir sources,’’ Med. Phys.22,809–819~1995!.

9R. M. Sievert, Acta Radiol.11, 249 ~1930!.10K. J. Cassell, ‘‘A fundamental approach to the design of a dose rate

calculation for use in brachytherapy planning,’’ Br. J. Radiol.56, 113–119 ~1983!.

11H. F. Batho and M. E. J. Young, ‘‘Tissue absorption corrections for linearradium sources,’’ Br. J. Radiol.37, 689–692~1964!.

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