Monte Carlo dosimetry of the VariSource high dose rate 192 Ir sourceRuqing Wang and Ron S. Sloboda Citation: Medical Physics 25, 415 (1998); doi: 10.1118/1.598216 View online: http://dx.doi.org/10.1118/1.598216 View Table of Contents: http://scitation.aip.org/content/aapm/journal/medphys/25/4?ver=pdfcov Published by the American Association of Physicists in Medicine Articles you may be interested in Beta versus gamma dosimetry close to Ir-192 brachytherapy sources Med. Phys. 28, 1875 (2001); 10.1118/1.1395038 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-aided dosimetry of a new high dose-rate brachytherapy source Med. Phys. 25, 2200 (1998); 10.1118/1.598418 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 192Ir sourceRuqing Wang and Ron S. Slobodaa)

Department of Medical Physics, Cross Cancer Institute,11560 University Avenue, Edmonton, Alberta T6G 1Z2, Canada

~Received 28 March 1997; accepted for publication 27 January 1998!

The purpose of the work is to calculate basic dosimetry data for a VariSource high dose rate192Irsource in water. These basic dosimetry data, expressed in the dose calculation formalism endorsedby the Interstitial Collaborative Working Group and AAPM Task group 43, include the dose rateconstant, the radial dose function, and the anisotropy function. A modified version of the EGS4Monte Carlo code was used to calculate~1! the transverse-axis dose distribution at radial distancesfrom 0.1 to 14 cm,~2! the two-dimensional dose distribution for axial and radial distances from 0.1cm to 10 cm, and~3! the air-kerma strength, for the VariSource high dose rate192Ir source. Fromthese Monte Carlo results the basic dosimetry data were derived. The calculated dose rate constantfor the high dose rate source is 1.04460.2% cGy h21 per unit air-kerma strength. The anisotropyfunction exhibits 40%–60% deviations from isotropy at positions on the long axis. The radial dosefunction for the source is nearly identical to that for a microSelectron high dose rate192Ir source,except at radial distances smaller than 0.5 cm where values for VariSource are 1.7%–2.8% smaller.These basic dosimetry data were compared with corresponding results from other authors for highand low dose rate192Ir sources, as well as with Meisberger’s fitting formula. ©1998 AmericanAssociation of Physicists in Medicine.@S0094-2405~98!01404-7#

Key words: brachytherapy dosimetry, high dose rate,192Ir source, Monte Carlo calculations

I. INTRODUCTION

The VariSource™ high dose rate~HDR! brachytherapy re-mote afterloading system is a relatively new product avail-able from Varian Oncology Systems. In comparison with theNucletron microSelectron HDR192Ir source, the VariSourceHDR 192Ir source has a longer active core, and smaller coreradius and encapsulation thickness. Until now only two re-ports by Fessendenet al.1,2 describing the dosimetric proper-ties of the source have been available. The purpose of thiswork is to calculate basic dosimetry data for the VariSourceHDR source in a water medium, using a modified version3 ofthe EGS4 Monte Carlo code4 and its user code DOSRZ.5

These basic dosimetry data include the dose rate constant,radial dose function, and anisotropy function, which are con-stituents of the dose calculation formalism endorsed by theInterstitial Collaborative Working Group~ICWG!6 andAAPM Task group 43~TG-43!.7

The validity of the modified version of EGS4 for calcula-tion of brachytherapy dose distributions has been verified inRef. 3 for several common low dose rate~LDR! sources. In alater study8 the same computer code was used to calculatethe two-dimensional dose-rate distribution around a mi-croSelectron HDR192Ir source in water. The results obtainedare in good agreement with Monte Carlo calculations byWilliamson and Li.9

In this report we present calculated dose data for the Vari-Source HDR source, discuss dosimetric features of thesedata, and compare them with published results for the Vari-Source HDR192Ir source,1 for the microSelectron HDR192Irsource,9 and for the LDR steel-clad192Ir source,3,6,7,10as wellas with Meisberger’s fitting formula.11 Also, the influence of

different computational schemes on calculated results will beexplored.

II. MATERIALS AND METHODS

A. Radioactive source and phantoms

According to construction and material data provided byVarian Oncology Systems, the VariSource HDR source con-sists of a cylindrical active iridium core of 0.35-mm diameterand 10-mm length, encapsulated in a nickel/titanium alloywire of 0.61-mm outer diameter that extends 1 mm beyondthe distal end of the core. Although in a functional remoteafterloader the proximal end of the alloy wire extends morethan 1 m, in this study the extension was modeled as 3 mmlong, so that a pertinent comparison with the Monte Carloresults of Ref. 9 for a microSelectron HDR source could becarried out. In our calculations the192Ir was assumed to beuniformly distributed within the core, and the densities of theiridium metal core and the Ni/Ti alloy wire were taken as22.42 and 6.5 g/cm3.

To explore the effect of phantom dimension and shape, aspherical phantom with 30-cm diameter, a cylindrical phan-tom with 30-cm diameter and 30-cm length, and an un-bounded phantom were used. The VariSource HDR source islocated at the center of the phantom. For a cylindrical phan-tom the long axis of the source is assumed to be coincidentwith the phantom central axis. The long axis of the sourcewas specified as theZ axis in Cartesian coordinates, and asthe polar axis in polar coordinates, with positive values di-rected toward the proximal~drive wire! end of the source. Inall cases it was assumed that the phantom medium is water.

415 415Med. Phys. 25 „4…, April 1998 0094-2405/98/25 „4…/415/9/$10.00 © 1998 Am. Assoc. Phys. Med.

B. Dose calculation formalism

Dose rate in medium at distancer ~cm! from the sourcecenter and angleu relative to its long axis is expressed as:

D~r ,u!5Sk•LG~r ,u!

G~1,p/2!F~r ,u!g~r !, ~1!

where Sk is the air-kerma strength of the source,L is thedose-rate constant,G(r ,u) is the geometry factor,F(r ,u) isthe anisotropy function, andg(r ) is the radial dose function.With Sk andD(r ,u) calculated,L, g(r ), andF(r ,u) can beformulated as follows:

L5D~1,p/2!

Sk, ~2!

where D(1,p/2) is the dose rate at 1 cm from the sourcecenter on the transverse axis, and

g~r !5D~r ,p/2!•G~1,p/2!

D~1,p/2!•G~r ,p/2!, ~3!

whereD(r ,p/2) is the dose rate at distancer on the trans-verse axis, andG(1,p/2) andG(r ,p/2) are geometry factorsfor the source at 1 cm and at distancer on the transverseaxis. Finally

F~r ,u!5D~r ,u!•G~r ,p/2!

D~r ,p/2!•G~r ,u!. ~4!

To be consistent with the ICWG formalism, in our calcula-tions a line source approximation toG(r ,u) was used, whoseanalytical expression can be found in Ref. 6.

C. Monte Carlo calculations

Photon interactions simulated in the EGS4 Monte Carlocode include pair production, photoelectric absorption,Compton scattering, Rayleigh scattering and production ofK-edge characteristic x rays~for single-element materialonly!. The modified version of EGS4/DOSRZ3 includes thebinding correction for Compton scattering. In our EGS4simulations, photon fluence energy spectra used for evaluat-ing absorbed dose and air kerma were scored by the track-length estimator. The cutoff energy for photon transport inall calculations was 1 keV. When an electron is produced ina photon process the electron is immediately discarded. Theexponential transform technique12 was employed to reducestatistical errors at deep positions in the medium. The calcu-lations were carried out on a Sun Sparc-10 workstation.

The VariSource HDR source is a cylindrically symmetricobject that can be modeled accurately by the plane-cylindergeometry in the user code DOSRZ~cf. Ref. 3!. Source de-sign data and phantom geometries given in Sec. II A wereadopted in our Monte Carlo simulations. Modeling of thespherical phantom was implemented by adding a test of par-ticle position in the code for each simulated photon step. Intransport simulation, once the magnitude of the position vec-tor of a photon is larger than the radius of the sphericalphantom, the photon is immediately discarded. All Monte

Carlo simulations were carried out in a spherical water-phantom of 30-cm diameter, unless otherwise specified.

In our calculations a set of thin, short cylindrical shellsegments with various radiiR and axial positionsZ, concen-tric about the long axis of the source, were adopted as scor-ing zones of photon fluence. The photon fluence energyspectrum at a given point in medium, located at perpendicu-lar distanceR from the long axis and axial coordinateZ, wasaveraged over the volume of the cylindrical shell segmentcentred at that point. For a cylindrically symmetric sourcesuch a scoring scheme is a good approximation to point-fluence scoring when the thickness and length of each cylin-drical shell segment are reasonably small.3 In this study, toscore the fluence spectrum at position (R,Z) the radial thick-nessesDR of the cylindrical-shell segments were taken as0.01–0.03 cm forR,1 cm, 0.1 cm for 1 cm<R,5 cm, 0.2cm for 5 cm<R,7 cm, and 0.3 cm forR>7 cm; theirlengthsDZ were taken as 0.01–0.03 cm forZ,1 cm, 0.1 cmfor 1 cm<Z,2.5 cm, 0.2 cm for 2.5 cm<Z,6 cm, and 0.3cm for Z>6 cm. The suitability of these scoring-zone sizeswas tested in an additional Monte Carlo calculation of thegeometry factor for a VariSource HDR source. In this calcu-lation, source and surrounding materials were replaced byvacuum, keeping the spatial distribution of activity in thesource unchanged. Within Monte Carlo uncertainty(<0.5%), the scored water kerma was found to be equal tothat of a point192Ir source in vacuum at distancesr>4 cm,and when normalized by the point-source kerma, equal to thegeometry factor for the source at each position.

Absorbed dose and air-kerma at each position were ob-tained by multiplying the scored photon fluence energy spec-tra by corresponding energies and mass energy-absorptioncoefficients. The approximation of dose by collision-kermaassumes the existence of charged-particle equilibrium. As atest for this assumption, Monte Carlo dose rates for the Vari-Source HDR source in water on the transverse axis were alsocalculated by scoring electron energy deposition, in whichthe electron-energy loss fraction per electron step and thecutoff energy for electron transport were assumed as 0.01and 40 keV, and the scoring-zone sizes are just those adoptedin the evaluation of the photon fluence energy spectrum. Atthe transverse-axis positionsr 50.1, 0.2, 0.3, and 0.5 cm, thedifferences in dose rate scored by photon fluence energyspectrum from that by electron energy deposition are22.1%, 23.0%, 20.3%, and 0.5%, respectively, withabout 1% statistical errors for the electron deposition dosesat these positions. In comparison, atr 51 – 14 cm, agreementbetween dose rates scored by the two different schemes iswithin 1%, comparable with statistical errors for the electrondeposition doses. These differences indicate that only a smalldeviation from the assumption of charged-particle equilib-rium exists at the close positions.

The air-kerma strength~i.e., source strength! Sk wasevaluated in two schemes:

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~1! Simulation in vacuum: In an infinite vacuum space,the air-kerma rateK(d) at a distanced550 cm onthe transverse axis was evaluated. The sourcestrength is specified asSk5K(d)•d2.

~2! Simulation in air: In a dry air sphere of 5-m diam-eter, air-kerma ratesK(d) were evaluated at dis-tancesd55 – 100 cm on the transverse axis;Sk isobtained by fitting the productK(d)•d2 to a linearequationK(d)•d25Sk1b•d ~cf. Ref. 9!.

The EGS4 version used in our study is unable to simulatecharacteristic x-ray production for multiple-element material.Therefore, this interaction process was not taken into accountfor Ni/Ti encapsulation in calculations of air-kerma strengthand dose rate. To assess the influence of characteristic x-raysfrom Ti ~or Ni! atoms on our Monte Carlo results, air kermaof the VariSource HDR source in vacuum was calculated atdistances of 5–100 cm on the transverse axis for character-istic x-ray production solely from either Ni or Ti atoms in thecapsule. Within Monte Carlo uncertainties (<0.5%), thetwo sets of results for air kerma are identical, at each posi-tion, to that obtained by excluding all characteristic x-rayproduction. The absence of characteristic x-rays from Ni/Tiis due to the relatively high photon energies~average energy370 keV! of 192Ir source, leading to minimal photoelectricalabsorption. In fact, the photoelectrical absorption coefficientin Ni/Ti at 370 keV is 3.9331023 cm2/g, whereas the coef-ficient in Ti at 30 keV~125I source! is 4.62 cm2/g.

Monte Carlo outputs of the absorbed doses and air-kermastrengths were normalized to one simulated photon. The en-ergy spectrum of source photons was that of Glasgow andDillman13 for 192Ir. Mass energy-absorption coefficientswere adopted from the compilation of Hubbell.14 Using Eqs.~2!, ~3!, and ~4!, the calculated dose rates and air-kermastrengths were transformed to dose-rate constants, radialdose functions, and anisotropy functions. The statistical un-certainties of the Monte Carlo calculations are within 0.5%for the dose-rate constant and radial dose function. For theanisotropy function the uncertainties are within 1% for mostpositions, but are 1%–5% for those on or close to the longaxis.

III. RESULTS AND DISCUSSION

In this section the calculated dosimetry data are comparedwith Monte Carlo calculations and measurements by otherauthors for various192Ir sources. The following works werereferenced for the comparisons:~1! Monte Carlo calculationsby Fessendenet al.1 for a VariSource HDR source in aspherical water phantom of 30 cm diameter;~2! Monte Carlocalculations by Williamson and Li9 for a microSelectronHDR source in a spherical water phantom of 30 cm diam-eter; ~3! ICWG/TG-43 recommended dosimetry data for aLDR steel-clad source,6,7 which are based on measurementsin a bounded solid water phantom@20320320 cm3 for theg(r ) measurements, and 20328328 cm3 for the F(r ,u)measurements#; ~4! Monte Carlo calculations byWilliamson10 for a LDR steel-clad source in an unbounded

water medium;~5! Monte Carlo calculations by Wang andSloboda3 for a LDR steel-clad source in an unbounded watermedium~The calculated radial dose function is in excellentagreement with that of Ref. 10. Therefore, in the compari-sons this will not be presented, only the result for the dose-rate constant is given!; ~6! Meisberger’s fitting for a~point!192Ir source in a bounded water phantom11 ~averaged overthe measurements in a water phantom of size 21325330 cm3 and the calculations in unbounded water!.

A. One- and two-dimensional dose-rate distributions

In this subsection all dose rates were normalized to unitair-kerma strength calculated in a dry air sphere. Figure 1illustrates the transverse-axis dose-rate distributions for theVariSource HDR source calculated in spherical and cylindri-cal water phantoms, whose dimensions are defined in Sec.II A, as well as in an unbounded water phantom. It is foundfrom Fig. 1 that the shape and dimension of a phantom onlyinfluence the dose rates at distances larger than 5 cm. Thisobservation is consistent with the finding of Williamson for aLDR steel-clad source.10 In comparison to the sphericalphantom, the cylindrical and unbounded phantoms give alarger dose rate with increasing distance; atr 514 cm thedose rate is 2.6% larger for the cylindrical phantom, and23% larger for the unbounded phantom. Hence, the effect ofphantom geometry in determining scatter conditions must betaken into account when comparing calculated or measuredresults.

Figure 1 also compares dose rates on the transverse axisfor the VariSource HDR source with those for a microSelec-tron HDR source, calculated using the modified EGS4 codein a spherical water phantom. Distinguishable differences~1% or larger! in dose rates appear at distances smaller thanr 52 cm; atr 51 cm the ratio of dose rate for the microSe-lectron HDR source to that for VariSource is 1.065, whilethe ratio is as large as 2.2 atr 50.1 cm. Forr .2 cm, thedifferences in dose rates are quite small and are comparablewith the statistical uncertainties of the Monte Carlo calcula-tions. These features are quite similar to those shown in Fig.

FIG. 1. Dose-rate distributions on the transverse axis for the VariSourceHDR 192Ir source and microSelectron HDR192Ir source in various waterphantoms. All results were calculated by the EGS4 Monte Carlo code in thisstudy.

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3 of Ref. 1. The dose-rate differences between the Vari-Source and microSelectron HDR sources at short distancesindicate that the point source approximation described in theTG-43 report7 is inadequate at distances nearer thanr52 cm from the VariSource HDR source. A similar obser-vation has been made for the microSelectron HDR source,9,15

although in this case the point source approximation breaksdown closer to the source due to its shorter length,15 at dis-tancesr ,1 cm.

Since the cylinder-plane geometry in DOSRZ only allowsthe two-dimensional dose distribution to be scored on a Car-tesian plane (R,Z) rather than on a polar plane (r ,u), ourdose-rate data were obtained onR-Z grids ~i.e., along-awaydistribution,9 Z is in the direction along the long axis andRis along the transverse axis!. The two-dimensional dose-ratedistributionD(R,Z) is listed in Table I, which covers a dis-tance range ofR,Z50.1– 10 cm.

B. Dose-rate constant

Based on the transverse-axis dose-rate distribution pre-sented in Sec. III A and the calculated source strength evalu-

ated in a dry air sphere of 5 m diameter, we obtained a doserate constant for the source ofL51.04460.2%.

As L is a parameter of fundamental importance, we ex-amined the influence of both scoring-zone dimensions andsource strength evaluation schemes on our result. A one-dimensional dose distribution on the transverse axis in waterwas recalculated in which radial and axial thicknesses,DRandDZ, of all scoring zones were decreased to one-half ofthe standard setup mentioned in Sec. II C. It was found thatat all distances the decrease in zone dimensions changedscored doses by less than 0.5%, which is comparable withthe statistical uncertainty of the calculation (,0.5%). Thisshows that in our calculation ofL, volume averaging of dosein scoring zones has not given rise to any significant error.The source strength evaluated in vacuum is 1.005 timeslarger than that simulated in an air sphere, with a statisticaluncertainty of 0.3%. Using this latter value of sourcestrength the dose-rate constant isL51.03960.3%. In fact,the two schemes for source strength evaluation have not ledto a statistically significant difference.

Table II compares our dose rate constant for the Vari-Source HDR source with that of Fessendenet al.1 for the

TABLE I. Dose-rate distributionD(R,Z) per unit source strength for VariSource HDR192Ir source (cGy h21 U21).

Z ~cm!a

R ~cm!

0.0 0.10 0.25 0.50 0.75 1.00 1.50 2.00 2.50 3.00 4.00 5.00 6.00 7.00 10.00

210.00 0.0057 0.0065 0.0066 0.0071 0.0074 0.0077 0.0080 0.0082 0.0082 0.0081 0.0077 0.0071 0.0065 0.0058 0.003827.00 0.0129 0.0136 0.0142 0.0155 0.0166 0.0173 0.0180 0.0181 0.0177 0.0172 0.0155 0.0136 0.0116 0.0101 0.005926.00 0.0175 0.0180 0.0193 0.0217 0.0234 0.0243 0.0250 0.0248 0.0240 0.0228 0.0199 0.0170 0.0142 0.0118 0.006725.00 0.0241 0.0253 0.0282 0.0320 0.0343 0.0358 0.0364 0.0353 0.0334 0.0310 0.0260 0.0212 0.0172 0.0139 0.007524.00 0.0347 0.0372 0.0440 0.0522 0.0557 0.0570 0.0563 0.0528 0.0482 0.0433 0.0340 0.0264 0.0206 0.0162 0.0083

23.00 0.0558 0.0647 0.0825 0.0967 0.1018 0.1021 0.0949 0.0837 0.0720 0.0614 0.0441 0.0323 0.0241 0.0184 0.008922.50 0.0780 0.0969 0.1237 0.1444 0.1489 0.1452 0.1280 0.1076 0.0888 0.0730 0.0499 0.0354 0.0258 0.0194 0.009222.00 0.1238 0.1614 0.2073 0.2340 0.2321 0.2175 0.1770 0.1393 0.1091 0.0860 0.0559 0.0383 0.0274 0.0203 0.009521.50 0.2292 0.3173 0.4144 0.4337 0.3976 0.3463 0.2495 0.1794 0.1319 0.0998 0.0614 0.0409 0.0287 0.0211 0.009721.00 0.6676 0.9841 1.1420 0.9742 0.7502 0.5706 0.3449 0.2239 0.1547 0.1123 0.0661 0.0429 0.0298 0.0217 0.0098

20.75 1.8060 2.5951 2.3897 1.5627 1.0378 0.7225 0.3962 0.2449 0.1646 0.1175 0.0679 0.0437 0.0302 0.0219 0.009920.50 ¯ 15.435 5.7097 2.4301 1.3746 0.8779 0.4418 0.2622 0.1724 0.1216 0.0692 0.0443 0.0304 0.0220 0.009920.25 ¯ 28.207 8.9179 3.2147 1.6503 0.9981 0.4733 0.2735 0.1774 0.1242 0.0701 0.0446 0.0306 0.0222 0.009920.10 ¯ 29.225 9.5971 3.4506 1.7406 1.0347 0.4827 0.2768 0.1787 0.1251 0.0700 0.0448 0.0307 0.0221 0.0100

0.00 ¯ 29.418 9.7037 3.4958 1.7563 1.0432 0.4842 0.2777 0.1793 0.1247 0.0705 0.0447 0.0307 0.0221 0.0100

0.10 ¯ 29.268 9.5966 3.4502 1.7394 1.0342 0.4833 0.2768 0.1788 0.1245 0.0701 0.0448 0.0307 0.0222 0.01000.25 ¯ 28.252 8.9090 3.2076 1.6511 0.9978 0.4725 0.2734 0.1770 0.1239 0.0701 0.0445 0.0306 0.0220 0.00990.50 ¯ 15.424 5.7044 2.4362 1.3730 0.8778 0.4411 0.2619 0.1721 0.1214 0.0692 0.0443 0.0304 0.0220 0.00990.75 ¯ 2.6069 2.3937 1.5630 1.0377 0.7228 0.3960 0.2446 0.1644 0.1175 0.0677 0.0437 0.0302 0.0219 0.00991.00 0.6072 0.9784 1.1398 0.9753 0.7501 0.5711 0.3452 0.2240 0.1549 0.1124 0.0660 0.0429 0.0300 0.0217 0.0098

1.50 0.2218 0.3094 0.4123 0.4345 0.3979 0.3458 0.2494 0.1794 0.1320 0.0998 0.0614 0.0407 0.0288 0.0211 0.00972.00 0.1227 0.1524 0.2059 0.2346 0.2321 0.2176 0.1774 0.1394 0.1091 0.0861 0.0559 0.0382 0.0274 0.0203 0.00952.50 0.0789 0.0926 0.1232 0.1442 0.1487 0.1450 0.1281 0.1077 0.0889 0.0730 0.0500 0.0353 0.0258 0.0194 0.00923.00 0.0570 0.0633 0.0815 0.0969 0.1021 0.1021 0.0950 0.0838 0.0721 0.0614 0.0443 0.0323 0.0241 0.0184 0.00894.00 0.0338 0.0349 0.0434 0.0514 0.0554 0.0569 0.0563 0.0529 0.0482 0.0433 0.0340 0.0264 0.0206 0.0162 0.0083

5.00 0.0239 0.0245 0.0274 0.0317 0.0343 0.0357 0.0364 0.0353 0.0334 0.0311 0.0259 0.0212 0.0172 0.0139 0.00756.00 0.0162 0.0172 0.0192 0.0215 0.0231 0.0242 0.0250 0.0247 0.0239 0.0228 0.0200 0.0169 0.0142 0.0118 0.00677.00 0.0130 0.0129 0.0138 0.0154 0.0165 0.0173 0.0180 0.0180 0.0178 0.0172 0.0155 0.0136 0.0117 0.0100 0.0059

10.00 0.0061 0.0063 0.0066 0.0071 0.0074 0.0076 0.0080 0.0081 0.0081 0.0081 0.0077 0.0071 0.0065 0.0058 0.0038

aNote: Z is along the long axis of the source, andR away from the long axis.

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same source, with those of Wang and Sloboda8 and William-son and Li9 for the microSelectron HDR source, and withthree published results3,6,7,10 for a LDR steel-clad192Irsource. OurL values are in good agreement with that in Ref.1, with deviations of 0.4%~vacuum! and 0.9%~air!, and areabout 6.0%–7.0% smaller than those for microSelectronHDR and LDR steel-clad192Ir sources. The greater corelength of 1 cm and corresponding smaller geometry factorG(1 cm,p/2)50.927 of the VariSource HDR source, ascompared with values of 0.35 cm and 0.990 for a microSe-lectron HDR source, is responsible for the smallerL value.

C. Radial dose function

As a benchmark test of our EGS4 calculation for the ra-dial dose function, we derived theg(r ) values for a microSe-lectron HDR source using the transverse-axis dose rates pre-sented in Sec. III A and geometry factor for the source, andcompared them with those provided by Williamson and Li9

for the same source. It was found that the deviations of ourresults from those in Ref. 9 are within10.4% at positionsr<7 cm, and are less than10.8% for 8<r<13 cm. Only atr 514 cm is a larger deviation of11.2% observed. These

differences at greater distances, which in fact are onlyslightly larger than the statistical uncertainties of both calcu-lations ~,0.5% in this study, 0.5%–2% in Ref. 9!, demon-strate very small (,1%) systematic deviations between themodified EGS4 code and the MCPT code used in Ref. 9.

Table III and Fig. 2 compare the radial dose functiong(r )calculated in this study for the VariSource HDR source withthat for the microSelectron HDR source,9 that for the LDRsteel-clad seed,6,7,10and with normalized values of Meisberg-er’s tissue attenuation and scatter buildup factors,11

T(r )/T(1 cm). Theg(r ) function calculated by Fessendenet al.1 for the VariSource HDR source was not presentedhere since numerical results are not available.

The largest differences~21.7% to 22.8%! in g(r ) be-tween the VariSource HDR and microSelectron HDRsources9 are found at radial distancesr ,0.5 cm, while theyare much smaller~within 0.8%! for 0.5 cm<r<4 cm. Withincreasing distance the differences ing(r ) become11.1%to 11.8% for 5 cm<r<13 cm and, particularly,12.5% atr 514 cm. To further assess the accuracy of our calculations,we also comparedg(r ) for the VariSource HDR source withthat for the microSelectron HDR source calculated by EGS4

TABLE II. Comparison of dose-rate constantsL (cGy h21 U21).

Source Our calculations Fessenden Williamson TG-43/ICWG

VariSource HDR 1.04460.2%a 1.03560.5% ~Ref. 1!1.03960.3%b

microSelectron HDR 1.11260.2% ~Ref. 8! 1.11861.3% ~Ref. 1! 1.11560.5% ~Ref. 9!Steel-clad LDR 1.11360.3% ~Ref. 3! 1.11060.2% ~Ref. 10! 1.12 ~Refs. 6, 7!

aEvaluated by source strength in air.bEvaluated by source strength in vacuum.

TABLE III. Comparison of radial dose functionsg(r ).

r~cm!

VariSourceHDRa

microSelectronHDR ~Ref. 9!

Steel-clad LDR~ICWG/TG-43! ~Ref. 7!

Steel-clad LDR~Monte Carlo!~Ref. 10!

Meisberger~Ref. 11!b

0.1 0.952 0.979 0.9880.2 0.967 0.9900.3 0.976 0.9930.5 0.989 0.997 0.994 0.9971.0 1.0 1.0 1.0 1.0 1.01.5 1.005 1.002 1.006 1.0012.0 1.007 1.003 1.011 1.013 1.0012.5 1.006 1.002 1.014 1.0013.0 1.006 1.002 1.015 1.019 1.04.0 1.003 0.997 1.010 1.019 0.9965.0 0.998 0.987 0.996 1.014 0.9906.0 0.984 0.973 0.972 1.005 0.9807.0 0.967 0.956 0.942 0.9678.0 0.947 0.933 0.913 1.003 0.9529.0 0.920 0.904 0.891 0.932

10.0 0.885 0.871 0.887 0.960 0.91011.0 0.850 0.83612.0 0.807 0.79513.0 0.757 0.74914.0 0.699 0.682

aPresent calculation.bNormalized values of Meisberger’s tissue attenuation and scatter buildup factors~Ref. 11!, T(r )/T(1 cm).

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in this study. At distances ofr ,5 cm the differences be-tween the two calculations are identical to those of the pre-ceding comparison. At distances 5 cm<r<14 cm, however,the differences are only10.59% to 10.98%, which arecomparable to statistical uncertainties. Similar differenceswere found by Fessendenet al.1 in comparing their resultsfor the two HDR sources. Thus it may be said that in thepreceding comparison the somewhat larger deviations, atgreater distances, between theg(r ) values for the Vari-Source HDR source and those calculated in Ref. 9 for themicroSelectron HDR source were caused partly by small sys-tematic deviations between the EGS4 and MCPT codes, asshown by the benchmark test described at the beginning ofthis subsection.

Normalized values of Meisberger’s tissue attenuation andscatter buildup factors,11 T(r )/T(1 cm), were derived fromthe polynomial fit of the tissue attenuation factorT(r ) for an192Ir source over a distance range ofr 51 – 10 cm.11 OurMonte Carlo result forg(r ) for the VariSource HDR sourceis in excellent agreement with the values of Meisberger, withdifferences of less than 1% forr<8 cm, and of21.4% and22.8% for r 59 and 10 cm. It demonstrates that attransverse-axis distances of 1–8 cm,g(r ) for the VariSourceHDR source can be approximated by the renormalized Meis-berger polynomial. Our values ofg(r ) for the HDR sourceare also in reasonably good agreement with those recom-mended by ICWG/TG-43 for a LDR steel-clad seed.6,7 Thedeviations between the latter two are within 1% for distancesr<5 cm, but are11.3% to13.2% for distancesr .5 cm.One reason for these differences may be the different vol-umes of the phantoms: the phantom volume used in thisstudy is smaller than that in Ref. 11, and larger than that inRefs. 6 and 7.

In contrast, only at distances of 0.5 cm<r<2 cm are ourresults forg(r ) for the HDR source in excellent agreement~within 1%! with Monte Carlo calculations by Williamsonfor a LDR steel-clad seed.10 The differences are21.3% to

21.6% at distances of 3–5 cm, and22% to 29% at 6–10cm. Apparently the larger differences at the greater distancesare caused mainly by the use of an unbounded phantom inRef. 10.

D. Anisotropy function

Based on the Cartesian two-dimensional dose-rate distri-bution D(R,Z) for the VariSource HDR source, the anisot-ropy function at each grid point (R,Z) was evaluated. Then abicubic spline interpolation was used to calculate the anisot-ropy function F(r ,u) at a set of given coordinates (r ,u),tabulated in Table IV. It should be noted that for the purposeof making the interpolation smooth enough, additional datasets forD(R,Z) were calculated at six extra radial distancesless thanR51 cm for allZ, and added to the data of Table I.

In the following comparisons we will use the deviationfrom isotropy at positions on the long axis to describe thefeature of anisotropy for a given source, which is defined asthe difference between values of the anisotropy function atthe transverse and the long axis for each radial distancer ,i.e.,F(r ,p/2)2F(r ,u), u50 andp, and expressed as a per-centage. Since for a given value ofr the F(r ,u) function issmallest on the long axis, the largest deviation from isotropyis determined.

Comparing with the anisotropy function calculated byFessendenet al. for the VariSource HDR source~Figs. 5 and6 in Ref. 1!, we find that our results are in good agreementexcept at the positions of proximal-end extension (u50) onthe long axis, where our calculatedF(r ,u) values are larger.This results from the fact that in the simulation of Ref. 1 alarger alloy-wire length of 15 mm was taken. As there are nonumerical values ofF(r ,u) available from Ref. 1, exact nu-merical comparison of the two calculations is not possible.

Figure 3 comparesF(r ,u) values for the VariSourceHDR source calculated in this study with those of William-son and Li9 for a microSelectron HDR source. The followingfeatures are observed:

~1! In the angular range 60°<u<120° and for all radialdistancesr , the anisotropy functions are nearly identicalwith differences of less than 1%, which are comparablewith statistical uncertainties.

~2! For 5°<u,60°, or 120°,u<170° and for allr , theanisotropy function for the VariSource HDR source islarger than that for the microSelectron source. The dif-ferences can be as much as 54% atr 50.5 cm, and are1%–25% for the other radial distances.

~3! For u,5°, or u.170° and forr>1 cm, F(r ,u) for theVariSource HDR source is 1%–37% smaller than thatfor the microSelectron source. These features are similarto those observed by the authors of Ref. 1. Evaluateddeviations from isotropy at positions on the long axis are40%–60% for the VariSource HDR source, as comparedwith 33%–55% for the same source obtained in Ref. 1,and 35%–45% for the microSelectron HDR source.9

Figure 4 compares theF(r ,u) function for the VariSourceHDR source to that for a LDR steel-clad source.7 At all

FIG. 2. Comparison of the radial dose function for the VariSource HDR192Irsource with those for the microSelectron HDR192Ir source and LDR steel-clad source. Data sources: VariSource HDR—this study; microSelectronHDR—Monte Carlo results by Williamson and Li~Ref. 9!; LDR steel-clad—TG-43 recommendation based on measurements~Ref. 7!, and MonteCarlo calculations by Williamson~Ref. 10!; Meisberger fitting—Ref. 11.

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radial distancesr it is observed that in the angular rangeu<20°, or u>160°, F(r ,u) values for the HDR source aresmaller than those for the LDR source. The differences atmost positions are larger than 10%, with the maximum aslarge as 50%. For the rest of the angles the differences arejust about a few percent. The LDR steel-clad source has lessanisotropy, with 19%–23% deviation from isotropy on thelong axis, as compared with about 40%–60% for Vari-Source. This diminished anisotropy is because the LDRsource has a shorter core length and no encapsulation on itstwo ends.

Since the statistical uncertainties of theF(r ,u) values are1%–5% for our Monte Carlo results for the VariSource HDRsource, 5% for the measurements of Ref. 7 for the LDRsteel-clad seed, and 3% at most for the Monte Carlo calcu-lations of Ref. 9 for the microSelectron HDR source~de-duced from the statistical uncertainties of their dose-rate cal-culations!, it was concluded that the VariSource HDR source

has greater anisotropy as compared with the other two192Irsources. Clearly, this is caused by the longer active core ofthe former, leading to increased oblique filtration. As men-tioned earlier in Sec. III A, calculations by Williamson andLi9 have indicated the inaccuracy of using a point sourceapproximation~cf. Ref. 7! to describe the dose distributionclose to a microSelectron HDR source, due to its finitelength. Consequently the same point-source model will alsobe inaccurate for the VariSource HDR source at small dis-tances because its relatively greater length.

IV. CONCLUSIONS

Using a modified version of the EGS4 Monte Carlo codewhich has been validated in Ref. 3, basic dose data for theVariSource HDR192Ir source have been calculated. Thesebasic data include the dose rate constant, radial dose functionand anisotropy function. Statistical uncertainties of these

TABLE IV. Anisotropy functionF(r ,u) for the VariSource HDR Ir-192 source.

u ~degree!

r ~cm!

0.25 0.50 1.00 2.00 3.00 4.00 5.00 6.00 7.00 10.00

0.0 ¯ ¯ 0.405 0.406 0.441 0.469 0.528 0.524 0.582 0.6061.0 ¯ ¯ 0.407 0.405 0.454 0.481 0.525 0.555 0.575 0.6332.0 ¯ ¯ 0.444 0.456 0.494 0.516 0.558 0.594 0.620 0.6773.0 ¯ ¯ 0.510 0.512 0.544 0.581 0.614 0.645 0.669 0.7095.0 ¯ 0.942 0.635 0.617 0.645 0.657 0.681 0.709 0.720 0.764

7.0 ¯ 0.943 0.712 0.690 0.713 0.722 0.742 0.755 0.771 0.79310.0 0.973 0.943 0.789 0.765 0.780 0.785 0.800 0.812 0.822 0.84212.0 0.975 0.948 0.824 0.803 0.812 0.819 0.828 0.840 0.847 0.86015.0 0.974 0.954 0.861 0.843 0.851 0.852 0.862 0.869 0.874 0.88520.0 0.976 0.959 0.905 0.887 0.892 0.892 0.899 0.902 0.908 0.914

25.0 0.981 0.964 0.930 0.917 0.920 0.920 0.923 0.927 0.931 0.93630.0 0.985 0.973 0.946 0.938 0.940 0.939 0.942 0.944 0.949 0.95235.0 0.989 0.981 0.960 0.952 0.955 0.952 0.955 0.957 0.961 0.96045.0 0.994 0.990 0.975 0.973 0.975 0.971 0.974 0.975 0.977 0.97450.0 0.996 0.992 0.983 0.980 0.981 0.978 0.981 0.982 0.983 0.981

60.0 0.998 0.995 0.991 0.989 0.991 0.988 0.989 0.990 0.992 0.99575.0 1.000 0.999 0.998 0.994 0.999 0.994 0.994 0.997 1.000 0.99890.0 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

105.0 1.000 0.999 0.998 0.995 0.999 0.995 0.997 0.997 0.999 0.998120.0 0.998 0.995 0.991 0.988 0.990 0.987 0.988 0.990 0.993 0.994

130.0 0.995 0.988 0.983 0.980 0.981 0.977 0.979 0.981 0.983 0.988135.0 0.993 0.985 0.977 0.973 0.974 0.971 0.974 0.975 0.977 0.986145.0 0.988 0.984 0.961 0.954 0.954 0.951 0.956 0.957 0.960 0.954150.0 0.984 0.980 0.947 0.938 0.940 0.938 0.941 0.943 0.947 0.950155.0 0.979 0.973 0.929 0.917 0.920 0.921 0.922 0.927 0.931 0.936

160.0 0.974 0.963 0.904 0.887 0.893 0.892 0.898 0.903 0.908 0.917165.0 0.973 0.953 0.863 0.841 0.849 0.851 0.864 0.868 0.875 0.887168.0 0.974 0.948 0.822 0.804 0.813 0.822 0.831 0.836 0.847 0.863170.0 0.974 0.943 0.787 0.771 0.779 0.788 0.798 0.812 0.822 0.837173.0 ¯ 0.944 0.716 0.694 0.714 0.733 0.749 0.765 0.774 0.796

175.0 ¯ 0.943 0.637 0.624 0.651 0.671 0.688 0.710 0.724 0.758177.0 ¯ ¯ 0.540 0.545 0.558 0.588 0.628 0.651 0.670 0.719178.0 ¯ ¯ 0.469 0.472 0.503 0.551 0.583 0.603 0.637 0.669179.0 ¯ ¯ 0.448 0.439 0.474 0.488 0.562 0.586 0.622 0.659180.0 ¯ ¯ 0.445 0.410 0.431 0.482 0.531 0.566 0.577 0.571

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Monte Carlo estimates are within 0.5% for the dose-rate con-stant and radial dose function. For the anisotropy functionthe uncertainties are within 1% for most positions in thepolar plane, but are 1%–5% for those on or close to the longaxis.

The dose-rate constant obtained for the source is 1.04460.2%, which is in good agreement with the Monte Carloresult of Fessendenet al.1 for the same source, and is 6.0%–7.0% smaller than that of Williamson and Li9 for a microSe-lectron HDR192Ir source and that of Williamson10 and Wangand Sloboda3 for a LDR steel-clad192Ir source.

The radial dose functiong(r ) calculated for VariSource isnearly identical with that for a microSelectron HDR source,9

except at small distances less than 0.5 cm from the sourcecenter where differences of 1.7%–2.8% were found. At ra-dial distancesr 51 – 10 cm, theg(r ) values for VariSourceclosely approximate the renormalized Meisbergerpolynomial11 and those of ICWG/TG-436,7 for a LDR steel-clad 192Ir source, but at deeper positions they are noticeablysmaller than those calculated by Williamson10 in a un-bounded phantom for a LDR steel-clad source.

The VariSource HDR source has a larger anisotropy thanthe microSelectron HDR and LDR steel-clad sources. Thedeviations from isotropy on the long axis are 40%–60%, ascompared with 35%–45% for the microSelectron source and19%–23% for the LDR steel-clad source.

ACKNOWLEDGMENTS

This work was funded by the Alberta Cancer Board Re-search Initiative Program under Grant No. RI-5~5! and wassupported partly by a contract awarded by Varian Oncologysystems.

a!Electronic mail: sloboda@cancerboard.ab.ca1K. K. Fessenden, J. J. DeMarco, J. B. Smathers, J. Kleck, and A. Wright,‘‘Dosimetry of the VariSource high dose rate Ir-192 source using MonteCarlo calculations,’’ presented at American Association of Physicists inMedicine 37th Annual Meeting, Boston, MA, July 23–27, 1995.

2K. K. Fessenden, J. J. DeMarco, T. D. Solberg, J. B. Smathers, A. Wright,and J. Kleck, ‘‘Measured and calculated dosimetry for an Ir-192 HDRsource,’’ American Association of Physicists in Medicine 38th AnnualMeeting, Philadelphia, PA, July 21–25, 1996. Also see: Med. Phys.23,1149 ~1996!.

3Ruqing Wang and R. S. Sloboda, ‘‘EGS4 dosimetry calculations for cy-lindrically symmetric brachytherapy sources,’’ Med. Phys.23, 1459–1465 ~1996!.

4W. R. Nelson, H. Hirayama, and D. W. O. Rogers, ‘‘The EGS4 codesystem,’’ SLAC-265, Stanford Linear Accelerator Center, Stanford, CA~1985!.

5A. F. Bielajew, ‘‘How to Manage the EGS4 System,’’ NRCC report,PIRS-0391, National Research Council of Canada, Ottawa, 1993.

6L. L. Anderson, R. Nath, K. A. Weaver, D. Nori, T. L. Phillips, Y. H.Son, S. T. Chiu-Tsao, A. S. Meigooni, J. A. Meli, and V. Smith~Inter-stitial Collaborative Working Group!, Interstitial Brachytherapy, Physi-cal, Biological and Clinical Considerations~Raven, New York, 1990!.

7R. Nath, L. L. Anderson, G. Luxton, K. A. Weaver, J. F. Williamson, andA. S. Meigooni, ‘‘Dosimetry of interstitial brachytherapy sources: Rec-ommendations of the AAPM Radiation Therapy Committee Task GroupNo. 43,’’ Med. Phys.22, 209–234~1995!.

FIG. 3. Comparison of the anisotropy function for the VariSource HDR192Irsource with that for the microSelectron HDR192Ir source at different radialdistancesr . Filled circle—VariSource HDR192Ir source, calculations of thisstudy; open square—microSelectron HDR192Ir source, Monte Carlo resultsby Williamson and Li~Ref. 9!.

FIG. 4. Comparison of the anisotropy function for the VariSource HDR192Irsource with that for the LDR steel-clad192Ir source at different radial dis-tancesr . Filled circle—VariSource HDR192Ir source, calculations of thisstudy; open triangle—LDR steel-clad192Ir source, TG-43 recommendationbased on measurements~Ref. 7!.

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8R. Wang and R. S. Sloboda, ‘‘Accuracy of NPS calculated HDR Ir-192source dosimetry for endobronchial brachytherapy,’’ Med. Phys.23, 804~1996! ~abstract!.

9J. 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!.

10J. F. Williamson, ‘‘Comparison of measured and calculated dose rates inwater near125I and 192Ir sources,’’ Med. Phys.18, 776–786~1991!.

11L. L. Meisberger, R. J. Keller, and R. J. Shalek, ‘‘The effective attenua-tion in water of the gamma rays of gold-198, iridium-192, cesium-137,radium-226 and cobalt-60,’’ Radiology90, 953–957~1968!.

12A. F. Bielajew and D. W. O. Rogers, ‘‘Lecture notes: Variance reductiontechniques,’’ NRCC report, PIRS-0396, National Research Council ofCanada, Ottawa, 1994.

13G. P. Glasgow and L. T. Dillman, ‘‘Specificg-ray constant and exposurerate constant of192I, ’’ Med. Phys.6, 49–52~1979!.

14J. H. Hubbell, ‘‘Photon mass attenuation and energy absorption coeffi-cients from 1 keV to 20 MeV,’’ Int. J. Appl. Radiat. Isot.33, 1269–1290~1982!.

15M. B. Podgorsak, L. A. DeWerd, B. R. Paliwal, A. K. Ho, and C. H.Sibata, ‘‘Accuracy of the point source approximation to high dose-rateIr-192 source,’’ Med. Dosim.20, 177–181~1995!.

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