Dosimetry characteristics of the Plus and 12i Gammamed PDR 192 Ir sourcesJ. Pérez-Calatayud, F. Ballester, M. A. Serrano-Andrés, V. Puchades, J. L. Lluch, Y. Limami, and F. Casal Citation: Medical Physics 28, 2576 (2001); doi: 10.1118/1.1418725 View online: http://dx.doi.org/10.1118/1.1418725 View Table of Contents: http://scitation.aip.org/content/aapm/journal/medphys/28/12?ver=pdfcov Published by the American Association of Physicists in Medicine Articles you may be interested in Dosimetry comparison of 192 Ir Sources Med. Phys. 29, 2239 (2002); 10.1118/1.1508378 Technical note: Monte-Carlo dosimetry of the HDR 12i and Plus 192 Ir sources Med. Phys. 28, 2586 (2001); 10.1118/1.1420398 Beta versus gamma dosimetry close to Ir-192 brachytherapy sources Med. Phys. 28, 1875 (2001); 10.1118/1.1395038 Dosimetry close to an 192 Ir HDR source using N-vinylpyrrolidone based polymer gels and magnetic resonanceimaging Med. Phys. 28, 1416 (2001); 10.1118/1.1382603 Monte Carlo dosimetry of a new 192 Ir high dose rate brachytherapy source Med. Phys. 27, 2521 (2000); 10.1118/1.1315316

Dosimetry characteristics of the Plus and 12i Gammamed PDR192Ir sources

J. Perez-CalatayudPhysics Section, Radiation Oncology Department, ‘‘La Fe’’ University Hospital, Avda. Campanar 21,E-46009 Valencia, Spain

F. Ballester,a) M. A. Serrano-Andres, V. Puchades, J. L. Lluch, and Y. LimamiDepartment of Atomic, Molecular and Nuclear Physics, University of Valencia, and Instituto de Fı´sicaCorpuscular (IFIC), C/ Dr. Moliner 50, E-46100 Burjassot, Spain

F. CasalDepartment of Atomic, Molecular and Nuclear Physics, University of Valencia,C/ Dr. Moliner 50,E-46100 Burjassot and Centro Nacional de Dosimetrı´a, Avda. Campanar 21, E-46009 Valencia, Spain

~Received 16 March 2000; accepted for publication 26 September 2001!

In this study a complete set of dosimetric data for the Plus and 12i Gammamed PDR~pulsed doserate! 192Ir sources is presented. These data have been calculated using the Monte Carlo simulationcodeGEANT3. Absolute dose rate distributions in water around these sources were calculated andare presented in form of conventional two dimensional~2D! Cartesian look-up tables. All dosim-etric quantities recommended by the AAPM Task Group 43 report have been also calculated. Thesequantities are dose rate constant, radial dose function, anisotropy function and anisotropy factor.The dose rate distribution of the 12i source was compared with the corresponding data for themicroselectron PDR source showing large differences between both sources. ©2001 AmericanAssociation of Physicists in Medicine.@DOI: 10.1118/1.1418725#

Key words: Ir-192, PDR sources, brachytherapy, dosimetry, Monte Carlo, treatment-planningsystems

I. INTRODUCTION

It is well known that the clinical use of brachytherapysources requires an extensive base of dosimetric data foreach source type. As it is indicated in the TG56 AAPMreport of brachytherapy1 accurate dose rate distributiontables based on realistic geometry and mechanical character-istic of each source type used in clinical practice areneeded to verify treatment planning system calculations, oras input data to them. Monte Carlo simulation technique is amethod chosen to estimate the dose rate distribution aroundbrachytherapy sources that can significantly reduce the ex-perimental uncertainties and provide the required accuratecalculations.

The motivation to present in this study a complete dosi-metric evaluation of the Plus and 12i Gammamed PDR192Irsources was the lack of data for these sources in the litera-ture. TheGEANT3 Monte Carlo particle transport code2 wasused to calculate the 2D absolute dose rate distributions inwater for distances up to 15 cm from the source. The data arepresented as conventional 2D look-up tables~‘‘away-and-along’’! and in terms of the dosimetric ratios recommendedby the AAPM Task Group 43.3 The two dimensional doserate distribution of the 12i source was compared with thecorresponding data of the microselectron PDR source4 thathas a similar design and dimensions.

II. MATERIAL AND METHODS

A. The radioactive sources

The Plus and 12i Gammamed PDR192Ir sources, accord-ing to the material composition and the construction designprovided by Gammamed,5 consist of a cylindrical active iri-dium core~70% Ir and 30% Pt,r521.76 g/cm3! of 0.6-mmdiameter and 0.5-mm length~Fig. 1!. The active iridium isuniformly distributed in this core, which is encapsulated in astainless steel wire~No 1.4404!. The active core in bothsources is filtered in the extreme end by a cylindrical piece ofaluminum ~No 3.1645! and a cap of stainless steel~No.1.4404!. The extreme end of this cap was approximated inthe Monte Carlo geometry by a cone 0.2-mm length for the12i source and 0.12-mm length for the Plus source. In thelower part of the source, the radiation is filtered by 0.5-mmstainless steel in the 12i source and by 0.3-mm stainless steelin the Plus source. Dimensions of the different parts of bothsources are included in the diagram shown in Fig. 1.

These PDR sources are used in single-stepping source re-mote afterloaders. The source welded to the end of cableadvances through one catheter after another, sequentiallytreating each programmed dwell position. The dose rate dis-tribution delivered to the patient is then calculated by addingthe dose rate distribution delivered in each dwell position. Ineach dwell position the source and the cable orientation

2576 2576Med. Phys. 28 „12…, December 2001 0094-2405 Õ2001Õ28„12…Õ2576Õ10Õ$18.00 © 2001 Am. Assoc. Phys. Med.

changes and the calculation of the total dose rate distributiondelivered must take into account the presence of the cable. Inorder to provide realistic dose rate distributions data of thePDR sources, in this study the extension of the proximal endof the cable was modeled as 6 cm long and an effectivedensity5 of r55.6 g/cm3.

B. Monte Carlo simulation code

The Monte Carlo method has been used to calculate air-kerma strength and absolute dose rate values to water inwater around the Plus and 12i Gammamed PDR192Irsources. The calculations have been performed by means ofthe GEANT3 Monte Carlo code.2 Methods, approximationsand restrictions about the physical processes can be found inthe GEANT3 user manual.6

All physical processes for low energy photons are imple-mented inGEANT3: photoelectric effect, Rayleigh and Comp-ton scattering and pair production. The total cross-section ofe2e1 pair production has been parametrized from a least-square fit to the data of Hubbellet al.7 and the Bethe–Heitlerdifferential cross-section with the Coulomb correction hasbeen assumed.8 For the total cross-section for Compton scat-tering an empirical cross-section formula is used which re-produces the cross-section data fairly accurately well downto 10 keV. Electron binding energy is ignored. The totalcross-section for photoelectric effect was fitted as SANDIAparametrization.9 After photoelectric emission a fluorescentphoton or Auger electron is emitted. The decay scheme for

192Ir was taken from nuclear data sheets.10 The cut-off energyfor photons was taken at 10 keV. The validation of the codefor Ir-192 energies have been described in previous publica-tions by our group.11–13

For electrons, Gaussian multiple scattering, bremsstrah-lung production~in the source materials! and continuous en-ergy loss were assumed.6 The cut-off energy for electronswas taken at 10 keV. For the Ir-192 energies electronic equi-librium exists for radial distancesr .1 cm from the source,and then dose and water kerma are equal.

C. Monte Carlo calculations and data analysis

The coordinate systems used in this study are shown inFig. 1. The origin was taken at the center of the active coreof the source, the long axis of the source has been chosen asthe z-axis ~which coincides with the polar axis! and they-axis along the transverse bisector. The cylindrical symme-try of the sources allows us to present the data as a twodimensional dose rate distributions although Monte Carlocalculations have been done in three dimensions.

1. Air-kerma strength simulation

The air-kerma strength of a source,Sk , is specified interms of air-kerma rate at a point along the transverse axis ofthe source in free space. It is defined14 as the product ofair-kerma rate at a calibration distance,d, in free space,kair(d), measured along the transverse bisector of the source(y-axis!, and the square of the distance, that is,Sk5 kaird

2 inU units ~1 U 5 1 mGy m2 h21!. To evaluateSk , the sourceswere positioned in a 63636 m3 dry air cube and cells toscore air-kerma were defined for transverse axis distancesranging from 2 cm to 150 cm. The air-kerma has been scoredat distances from the source large enough so as to treat thesource as a mathematical point. Cell sizes were taken asrings of cross-sectional area withDy5Dz51 cm, and 23109 photon histories were simulated in four calculations toestimate statistical fluctuations. The approach to point esti-mation of the collision air-kerma was the analog estimatormethod.

The source strengthSk was estimated by fitting the air-kerma data4 to the linear equationkair(r ,u590°)r 25Sk

1br. The slope b describes the deviation inkair(r ,u590°)r 2 due to the build-up of scatter in the air and theintercept is an estimate of the product of the air-kerma rate infree space and the square of the distance.

2. Dose rate simulations in water

In order to reach full scatter conditions, a cylinder of wa-ter of 40 cm height and 40 cm in diameter was assumed. Twogrid systems were set up to score the absorbed dose rate: onein Cartesian coordinates,D(y,z), and the other in polar co-ordinates, D(r ,u). The purpose of this double scoringmethod was to avoid interpolation problems because the cal-culation of the anisotropy functionF(r ,u) from the Carte-sian dose rate distributionD(y,z) do not provide anF(r ,u)function for uniformly distributedr andu values. For Carte-

FIG. 1. Mechanical design of the 12i and Plus Gammamed PDR192Irsources. Dimensions are in mm.

2577 Perez-Calatayud et al. : Plus and 12i Gammamed PDR 192Ir sources 2577

Medical Physics, Vol. 28, No. 12, December 2001

TAB

LEI.

Dos

era

teD

(y,z

)~c

Gyh

21

U2

1 !in

wat

erar

ound

the

12is

ourc

e.T

heor

igin

ista

ken

atth

ece

nter

ofth

eac

tive

leng

th.

y~c

m!

z~c

m!

00.

20.

40.

60.

81

1.25

1.5

1.75

22.

53

3.5

45

68

10

100.

0103

0.01

030.

0103

0.01

030.

0102

0.01

020.

0102

0.01

010.

0100

0.00

993

0.00

974

0.00

951

0.00

924

0.00

893

0.00

824

0.00

751

0.00

608

0.00

481

80.

0165

0.01

650.

0165

0.01

650.

0164

0.01

630.

0162

0.01

610.

0159

0.01

570.

0153

0.01

470.

0141

0.01

340.

0120

0.01

060.

0080

90.

0060

96

0.02

990.

0299

0.02

990.

0298

0.02

950.

0293

0.02

900.

0286

0.02

810.

0275

0.02

610.

0246

0.02

290.

0213

0.01

810.

0152

0.01

070.

0075

65

0.04

330.

0434

0.04

310.

0428

0.04

250.

0421

0.04

140.

0405

0.03

950.

0383

0.03

570.

0329

0.03

000.

0272

0.02

230.

0181

0.01

210.

0083

24

0.06

800.

0678

0.06

740.

0667

0.06

580.

0648

0.06

310.

0611

0.05

870.

0561

0.05

060.

0451

0.03

990.

0352

0.02

740.

0214

0.01

360.

0090

53.

50.

0880

0.08

810.

0874

0.08

630.

0851

0.08

320.

0804

0.07

700.

0733

0.06

920.

0611

0.05

320.

0462

0.04

000.

0302

0.02

310.

0143

0.00

938

30.

120

0.12

00.

118

0.11

70.

114

0.11

10.

106

0.09

970.

0933

0.08

680.

0743

0.06

300.

0534

0.04

530.

0332

0.02

490.

0150

0.00

970

2.5

0.17

20.

171

0.16

90.

165

0.16

00.

153

0.14

30.

133

0.12

10.

110

0.09

090.

0745

0.06

140.

0510

0.03

610.

0265

0.01

560.

0100

20.

268

0.26

60.

261

0.25

20.

239

0.22

40.

202

0.18

10.

160

0.14

20.

111

0.08

750.

0700

0.05

680.

0390

0.02

810.

0161

0.01

021.

750.

348

0.34

60.

337

0.32

20.

301

0.27

60.

244

0.21

30.

185

0.16

10.

122

0.09

430.

0743

0.05

960.

0403

0.02

880.

0164

0.01

031.

50.

474

0.46

80.

452

0.42

50.

387

0.34

60.

296

0.25

20.

213

0.18

10.

134

0.10

10.

0785

0.06

230.

0416

0.02

940.

0166

0.01

041.

250.

682

0.66

80.

636

0.57

80.

509

0.44

00.

361

0.29

70.

245

0.20

40.

146

0.10

80.

0824

0.06

480.

0426

0.02

990.

0168

0.01

051

1.06

1.03

0.95

10.

821

0.68

50.

564

0.44

10.

349

0.27

90.

227

0.15

70.

114

0.08

590.

0668

0.04

350.

0304

0.01

690.

0105

0.8

1.66

1.59

1.39

1.12

0.87

90.

688

0.51

30.

392

0.30

60.

244

0.16

50.

118

0.08

820.

0683

0.04

410.

0307

0.01

700.

0106

0.6

2.95

2.73

2.15

1.56

1.12

0.83

00.

588

0.43

40.

331

0.26

00.

172

0.12

10.

0901

0.06

940.

0446

0.03

090.

0171

0.01

060.

46.

665.

533.

502.

161.

410.

973

0.65

60.

469

0.35

10.

272

0.17

70.

124

0.09

140.

0701

0.04

490.

0311

0.01

710.

0106

0.2

Sou

rce

14.0

5.61

2.81

1.66

1.08

0.70

30.

492

0.36

40.

280

0.18

00.

125

0.09

220.

0706

0.04

510.

0312

0.01

720.

0106

028

.27.

003.

111.

751.

120.

719

0.50

00.

368

0.28

30.

181

0.12

60.

0924

0.07

080.

0452

0.03

120.

0172

0.01

062

0.2

13.9

5.60

2.81

1.65

1.08

0.70

20.

492

0.36

40.

280

0.18

00.

125

0.09

220.

0706

0.04

510.

0312

0.01

720.

0106

20.

45.

483.

492.

161.

410.

971

0.65

50.

469

0.35

10.

272

0.17

70.

124

0.09

140.

0701

0.04

490.

0311

0.01

710.

0106

20.

62.

702.

131.

551.

120.

828

0.58

70.

433

0.33

10.

260

0.17

20.

121

0.09

000.

0693

0.04

460.

0309

0.01

710.

0106

20.

81.

561.

381.

110.

875

0.68

50.

512

0.39

10.

306

0.24

40.

165

0.11

80.

0882

0.06

820.

0441

0.03

070.

0170

0.01

062

10.

998

0.94

20.

816

0.68

10.

561

0.43

90.

347

0.27

80.

226

0.15

70.

114

0.08

580.

0668

0.04

350.

0304

0.01

690.

0105

21.

250.

638

0.62

80.

574

0.50

60.

437

0.36

00.

296

0.24

40.

203

0.14

50.

108

0.08

230.

0647

0.04

260.

0299

0.01

680.

0105

21.

50.

437

0.44

50.

420

0.38

40.

343

0.29

40.

250

0.21

20.

181

0.13

30.

101

0.07

840.

0622

0.04

150.

0294

0.01

660.

0104

21.

750.

317

0.32

90.

319

0.29

80.

274

0.24

20.

212

0.18

40.

160

0.12

20.

0941

0.07

420.

0596

0.04

030.

0287

0.01

640.

0103

22

Cab

le0.

237

0.25

20.

249

0.23

70.

222

0.20

10.

179

0.15

90.

141

0.11

00.

0873

0.06

990.

0567

0.03

900.

0281

0.01

610.

0102

22.

50.

148

0.16

10.

162

0.15

80.

152

0.14

20.

132

0.12

10.

110

0.09

030.

0742

0.06

120.

0509

0.03

610.

0265

0.01

560.

0099

62

30.

101

0.11

10.

113

0.11

20.

109

0.10

50.

0989

0.09

260.

0862

0.07

380.

0627

0.05

320.

0452

0.03

310.

0248

0.01

500.

0096

92

3.5

0.07

250.

0803

0.08

280.

0830

0.08

180.

0794

0.07

630.

0726

0.06

870.

0606

0.05

290.

0460

0.03

990.

0301

0.02

310.

0143

0.00

938

24

0.05

480.

0608

0.06

320.

0637

0.06

340.

0622

0.06

040.

0581

0.05

560.

0502

0.04

490.

0397

0.03

510.

0273

0.02

130.

0136

0.00

904

25

0.03

380.

0381

0.03

990.

0407

0.04

080.

0405

0.03

990.

0390

0.03

780.

0354

0.03

270.

0299

0.02

710.

0221

0.01

800.

0121

0.00

831

26

0.02

300.

0258

0.02

720.

0279

0.02

820.

0283

0.02

800.

0276

0.02

710.

0258

0.02

430.

0228

0.02

110.

0179

0.01

510.

0106

0.00

755

28

0.01

260.

0141

0.01

480.

0153

0.01

550.

0157

0.01

560.

0156

0.01

550.

0151

0.01

460.

0140

0.01

330.

0119

0.01

050.

0080

30.

0060

72

100.

0080

60.

0087

10.

0091

60.

0094

10.

0095

90.

0096

80.

0097

30.

0097

10.

0097

10.

0095

80.

0093

80.

0091

30.

0088

40.

0081

80.

0074

60.

0060

30.

0047

8

2578 Perez-Calatayud et al. : Plus and 12i Gammamed PDR 192Ir sources 2578

Medical Physics, Vol. 28, No. 12, December 2001

TAB

LEII.

Dos

era

teD

(y,z

)~c

Gyh

21

U2

1 !in

wat

erar

ound

the

Plu

sso

urce

.T

heor

igin

ista

ken

atth

ece

nter

ofth

eac

tive

leng

th.

y~c

m!

z~c

m!

00.

200.

400.

60.

81

1.25

1.5

1.75

22.

53

3.5

45

68

10

100.

0103

0.01

040.

0104

0.01

030.

0103

0.01

030.

0102

0.01

020.

0101

0.01

000.

0098

30.

0095

70.

0093

00.

0089

80.

0082

80.

0075

40.

0060

90.

0048

28

0.01

660.

0166

0.01

670.

0166

0.01

650.

0165

0.01

630.

0162

0.01

610.

0159

0.01

540.

0148

0.01

420.

0135

0.01

210.

0107

0.00

810

0.00

610

60.

0298

0.03

020.

0301

0.03

000.

0298

0.02

960.

0292

0.02

880.

0283

0.02

770.

0263

0.02

470.

0230

0.02

130.

0181

0.01

520.

0107

0.00

757

50.

0432

0.04

350.

0434

0.04

330.

0429

0.04

250.

0417

0.04

080.

0398

0.03

860.

0359

0.03

300.

0301

0.02

730.

0223

0.01

810.

0121

0.00

832

40.

0675

0.06

800.

0676

0.06

700.

0664

0.06

540.

0636

0.06

140.

0591

0.05

630.

0508

0.04

530.

0401

0.03

530.

0274

0.02

140.

0136

0.00

905

3.5

0.08

790.

0889

0.08

820.

0873

0.08

600.

0841

0.08

110.

0775

0.07

370.

0696

0.06

120.

0534

0.04

630.

0401

0.03

020.

0231

0.01

430.

0093

93

0.12

00.

121

0.12

00.

118

0.11

50.

112

0.10

60.

100

0.09

380.

0871

0.07

440.

0631

0.05

350.

0453

0.03

320.

0249

0.01

500.

0097

02.

50.

172

0.17

30.

171

0.16

80.

162

0.15

50.

144

0.13

30.

122

0.11

10.

0910

0.07

460.

0615

0.05

100.

0361

0.02

650.

0156

0.01

002

0.26

80.

268

0.26

40.

255

0.24

20.

225

0.20

30.

181

0.16

10.

142

0.11

10.

0876

0.07

010.

0568

0.03

900.

0280

0.01

610.

0102

1.75

0.35

10.

349

0.34

10.

325

0.30

30.

277

0.24

50.

213

0.18

50.

161

0.12

20.

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582

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121

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5.57

3.51

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9

2579 Perez-Calatayud et al. : Plus and 12i Gammamed PDR 192Ir sources 2579

Medical Physics, Vol. 28, No. 12, December 2001

sian coordinates, the cells were defined as rings with theirsymmetry axis along thez-axis and a rectangular cross-sectionDy Dz (Dy5Dz50.5 mm! in the y2z plane. Forpolar coordinates the rings have a cross sectionr Dr Du. Thedose rate was calculated up to 20 cm away from the source in0.5 mm steps and for angles from 0° to 180° in 1° steps. Thesource asymmetry was taken into account scoring indepen-dently the dose rate for positive and negativez-values~or foru and p2u). Then, the dose rate was stored in Cartesiancoordinates as a 4003800 matrix fromy50 cm toy520 cmand fromz5220 cm toz5120 cm, and in polar coordi-nates as a 4003180 matrix fromr 50 cm to r 520 cm andfrom u50° to u5180°.

To evaluate statistical fluctuations of the data five differ-ent calculations were performed~each one with different ran-dom number seeds! and a total of 23109 histories weresimulated for each source. For each cell, the mean value ofthe dose rate and its standard deviation were calculated. Asrepresentative values, statistical fluctuations of the absorbeddose rate in cells are less than 0.5% for polar angles 30°,u,150°, less than 1% for polar angles 10°,u,30° and 150°,u,170° and 3–6% for polar anglesu,10° and u.170°.

The air kerma strengthSk converts the data obtained todose rate per unit air-kerma strength normalizing it. In thisway, D(y,z) and D(r ,u) were obtained in units ofcGyh21 U21. From theD(r ,u) dose rate matrix we derivedthe dose rate constant,L, the anisotropy function,F(r ,u),

and the radial dose function,g(r ). These calculated datawere binned in slices~on thez-axis,y-axis,r-axis andu-axis,in each case! and were analyzed as described in detail in aprevious paper.15 These analysis effectively show the trendof the data in all cases, and the final errors assigned to thedose rate data obtained from these analysis are much lowerthan the statistical errors of the dose rate data obtained di-rectly from simulations. To estimate the uncertainties ofthese fitted data, we studied the difference of the dose ratevalue in a point by fitting the two perpendicular slices thatcross in this point. The study of this difference for manypoints indicates that the accuracy of the final data are of theorder of'0.2%.

III. RESULTS AND DISCUSSION

A. 2D Cartesian look-up table

The Cartesian dose rate distribution data,D(y,z), for thePlus and 12i Gammamed PDR192Ir sources have been ob-tained and are presented in Tables I and II. Distances aretaken along the source axis and transverse away from theactive center. An inspection of Tables I and II shows that thedose rate distribution for both sources is very similar. Thedifferences in the dose rate for both sources are,1.5% (u,35°); ,0.5% (35°,u,150°); 0.5–5% (u.150°). Dif-ferences in filtering produce differences in dose rate at largepolar angles big enough so as to justify to present separatelythe dose rate distributions for each source.

FIG. 2. A comparison of the dose ratedistribution~without the geometry fac-tor! of the microselectron PDR source4

~crosses! and the 12i PDR source~dots! for some selectedy-values. Theline through the dose rate data for the12i source is to guide the eyes.

2580 Perez-Calatayud et al. : Plus and 12i Gammamed PDR 192Ir sources 2580

Medical Physics, Vol. 28, No. 12, December 2001

TAB

LEIII

.C

alcu

late

dan

isot

ropy

func

tionF

(r,u

)fo

rth

eP

DR

12is

ourc

e.

2581 Perez-Calatayud et al. : Plus and 12i Gammamed PDR 192Ir sources 2581

Medical Physics, Vol. 28, No. 12, December 2001

TAB

LEIV

.C

alcu

late

dan

isot

ropy

func

tionF

(r,u

)fo

rth

eP

lus

sour

ce.

2582 Perez-Calatayud et al. : Plus and 12i Gammamed PDR 192Ir sources 2582

Medical Physics, Vol. 28, No. 12, December 2001

There is in the market another PDR source, the microse-lectron PDR source that has been studied by Williamson andLi.4 The active core of this source consists of two 0.6 mmlong by 0.6 mm diameter iridium pellets, of which only thedistal most is radioactive. The distance from the distal faceof the active source core to the physical spherical tip of thesource is 0.55 mm. This source is encapsulated by 0.275 mmstainless steel. The dose rate distribution data for this sourcewere compared with the corresponding data for the 12isource~Fig. 2!. The differences in dose rate are higher in thearea of negativez-values near the transverse axis and theyare due to the presence of the inactive iridium pellet in themicroselectron PDR source. There are also differences in thearea of positivez-values, close to the transverse axis, that aredue to the higher filtration that the 12i sources present in thisdirection with respect to the filtration in the microselectronPDR source. At distances greater than 5 cm from the sourcethe differences are due to both the design of the sources andthe shape and dimension of the phantom considered:16 Will-iamson and Li use a 30 cm diameter spherical phantom whilein this paper a cylindrical phantom 40 cm diameter and 40cm long was considered. At 7 cm in the transverse axis thedifference is about 2%.

B. TG43 dose calculation formalism

The dosimetry parameters based on the TG43 formalismhave been extracted from the simulation results ofD(r ,u).

The value of the dose-rate constant has been found to be thesame for both the 12i and Plus sources:L51.12260.003cGy h21 U21. This value is very close to the dose-rate con-stant for the PDR microselectron source4 that is L51.12860.006 cGy h21 U21.

The results for the anisotropy function,F(r ,u), for the12i and Plus sources are presented in Tables III and IV, re-spectively, for radial distancesr 50.2– 15 cm and polaranglesu50° – 180°. The line source approximation has beenused as geometry factor withL50.05 cm. In Fig. 3 the an-isotropy function for the Plus source at radial distancesr50.4, 0.8, 1, 2, 5 and 10 cm is plotted showing the biganisotropy of the source between forward and backwardangles.

The anisotropy factor for both sources have been fitted toa linear equation, being the result for the 12i sourcefan(r )50.996715.3731025r , and for the Plus sourcefan(r )50.999113.3031025r . The anisotropy constant can beeasily calculated as the average of the anisotropy factor. Theuse of fan(r ) instead ofF(r ,u) in deriving the dose ratedistribution for these sources introduces errors that are1.5%–5% atu,20°, and 1.5%–25% atu.150°.

The radial dose functiong(r ) for each source was fitted intwo parts due to the fact that atr ,0.5 cm this functionincreases abruptly for both sources. For the 12i source, in theinterval 0.2 cm,r ,1.0 cm the radial dose function wasfitted to a fifth order polynomial, and for the interval 1 cm

FIG. 3. Anisotropy function,F(r ,u),for the PDR Plus source for some se-lectedr-values~in cm!.

2583 Perez-Calatayud et al. : Plus and 12i Gammamed PDR 192Ir sources 2583

Medical Physics, Vol. 28, No. 12, December 2001

,r , 15 cm g(r ) was fitted to a sixth order polynomial,while for the Plus source the radial dose function was fittedto a sixth order polynomial in both intervals. Although theradial dose functions for both sources are very similar~thelargest difference is 0.5% atr 56 cm!, a different radial dosefunction is maintained for each source because these differ-ences are translated to the final value of dose rate data cal-culated in the TG43 formalism. The values of the radial dosefunctions and the coefficients of these polynomial fits arepresented in Table V. As an example, the plot of the raw dataand adjusted radial dose function data are shown in Fig. 4 forthe 12i source.

IV. CONCLUSION

Dosimetric characteristics of the Plus and 12i GammamedPDR 192Ir stainless-steel encapsulated sources have beenstudied using the Monte Carlo codeGEANT3. The internalsource geometry of each source and its composition materi-als were accurately simulated. The results of this study arepresented as away-and-along dose rate tables. Also dosimet-ric characteristics of the source using the TG43 formalismhave been derived~i.e., dose rate constant, radial dose func-

FIG. 4. Radial dose function,g(r ), for the 12i PDR source. Points representMonte Carlo raw data and the solid line is the result of the fit~see alsoTable V!.

TABLE V. Radial dose functiong(r ) for the 12i and Plus PDR192Ir sources obtained with the results of the fitsto the Monte Carlo data as explained in the text.

12i Plus

r ~cm! g(r )

0,2 1,0074 1,01000,4 0,9998 1,00440,6 0,9974 1,00090,8 0,9981 0,99951 1,0000 1,0000

1,25 1,0018 1,00231,5 1,0034 1,00441,75 1,0048 1,0062

2 1,0060 1,00792,5 1,0079 1,01053 1,0090 1,0123

3,5 1,0094 1,01314 1,0090 1,01325 1,0059 1,01066 0,9999 1,00478 0,9791 0,983410 0,9478 0,951112 0,9075 0,910015 0,8348 0,8376

Polynomial coefficients:12i Plus

Coefficient r ,1 cm r .1 cm r ,1 cm r .1 cm

a0 1.0220 0.9910 1.0176 0.9888a1 29.270431022 1.050631022 24.279131022 1.288431022

a2 1.043231021 21.479131023 2.299431022 21.625731023

a3 22.068931022 25.506631026 4.775331023 22.527531025

a4 22.068931022 23.672731027 21.509331023 1.657231026

a5 7.751431023 1.176631027 21.214431023 8.182431028

a6 22.912831029 1.637931024 23.457231029

2584 Perez-Calatayud et al. : Plus and 12i Gammamed PDR 192Ir sources 2584

Medical Physics, Vol. 28, No. 12, December 2001

tion, anisotropy function and anisotropy factor!. Differenceswith respect to the microselectron PDR source has been stud-ied. There, the Monte Carlo simulation data in water can beused for clinical applications as input data or as benchmarkdata to verify the results of the treatment planning systems.

ACKNOWLEDGMENTS

This work has been supported in part by ‘‘Generalitat Va-lenciana’’ ~under Project No. GV98-12-122!, by Ministeriode Educacio´n y Cultura ~Spain! under Project No. FEDER1FD97-0609, and by Schering Espan˜a S.A.

a!Electronic mail: facundo.ballester@uv.es1R. Nath, L. L. Anderson, K. J. A. Meli, A. J. Olch, J. A. Stitt, and J. F.Williamson, ‘‘Code of practice for brachytherapy physics: Report of theAAPM Radiation Therapy Committee Task Group No. 56,’’ Med. Phys.24, 1557–1598~1997!.

2R. Brun, F. Bruyant, M. Maire, A. C. McPherson, and P. Zanarini,GEANT3, CERN DD/EE/84-1, 1987.

3R. 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!.

4J. Williamson and Z. Li, ‘‘Monte Carlo aided dosimetry of the microse-lectron pulsed and high dose-rate192Ir sources,’’ Med. Phys.22, 809–819~1995!.

5A. Butzer, Sauerwein Isotopen Technik. MDS Nordion~private commu-nication!.

6GEANT-Detector Description and Simulation Tool, Application SoftwareGroup, Computing and Software Division, CERN Geneva, Switzerland,Edition March 1995.

7J. H. Hubbell, H. A. Gimm, and I. Overbo, J. Phys. Chem. Ref. Data9,1023 ~1980!.

8R. L. Ford and W. R. Nelson, ‘‘TheEGS code systems: Computer pro-grams for the Monte Carlo simulations of electromagnetic cascade show-ers ~Version 3!,’’ Stanford Linear Accelerator Center Report No.SLAC210, UCX32, SLAC, June 1978.

9F. Biggs and R. Lighthill, ‘‘Analytical approximations for x-ray crosssections,’’ Sandia National Laboratory, SAND87-0070 UC-34, 1987.

10V. S. Shirley, ‘‘Revised A-chains A5192,’’ Nucl. Data Sheets64, 395–401 ~1991!.

11F. 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!.

12J. Perez-Calatayud, F. Lliso, V. Camona, F. Ballester, and C. Herna´ndez,‘‘Monte Carlo calculations of dose rate distributions around 0.5 and 0.6mm in diamter192Ir wires,’’ Med. Phys.26, 395–401~1999!.

13F. Ballester, V. Puchades, J. L. Lluch, Y. Limami, M. A. Serrano, J.Perez-Calatayud, F. Lliso, and E. Casal, ‘‘Monte Carlo dosimetry of theBuchler high dose rate192Ir source from Amersham,’’ Phys. Med. Biol.46, N79–N90~2001!.

14AAPM Report No. 21,Recommendations of AAPM Task Group 32:Specifications of Brachytherapy Source Strength~American Institute ofPhysics, New York, 1987!.

15F. Ballester, J. L. Lluch, Y. Limami, M. A. Serrano, E. Casal, J. Pe´rez-Calatayud, and F. Lliso, ‘‘A Monte-Carlo investigation of dosimetriccharacteristics of the CSM11137Cs source from CIS,’’ Med. Phys.27,2182–2189~2000!.

16R. Wang and R. Sloboda, ‘‘Monte Carlo dosimetry of the Varisource highdose rate Ir-192 source,’’ Med. Phys.25, 415–423~1998!.

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