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Page 1: Assaying [sup 192]Ir line sources using a standard length well chamber

Assaying 192 Ir line sources using a standard length well chamberIvan A. Brezovich, Richard A. Popple, Jun Duan, Sui Shen, and Prem N. Pareek Citation: Medical Physics 29, 2692 (2002); doi: 10.1118/1.1517046 View online: http://dx.doi.org/10.1118/1.1517046 View Table of Contents: http://scitation.aip.org/content/aapm/journal/medphys/29/11?ver=pdfcov Published by the American Association of Physicists in Medicine Articles you may be interested in Air kerma standard for calibration of well-type chambers in Brazil using I 192 r HDR sources and its traceability Med. Phys. 36, 953 (2009); 10.1118/1.3056462 The design of a new insert for calibration of LDR and HDR 192 Ir sources in a well-type ionization chamber Med. Phys. 30, 1566 (2003); 10.1118/1.1578773 Experimental derivation of wall correction factors for ionization chambers used in high dose rate 192 Ir sourcecalibration Med. Phys. 29, 1 (2002); 10.1118/1.1427081 A parallel plate chamber for calibration of 192 Ir LDR and HDR sources Med. Phys. 26, 2438 (1999); 10.1118/1.598762 Evaluation of a new sealed reentrant well chamber for HDR and LDR brachytherapy calibrations Med. Phys. 25, 719 (1998); 10.1118/1.598242

Page 2: Assaying [sup 192]Ir line sources using a standard length well chamber

Assaying 192Ir line sources using a standard length well chamberIvan A. Brezovich,a) Richard A. Popple, Jun Duan, Sui Shen, and Prem N. PareekDepartment of Radiation Oncology, University of Alabama at Birmingham, Birmingham, Alabama 35233

~Received 25 February 2002; accepted for publication 5 September 2002; published 28 October 2002!

The strength of intravascular192Ir sources is typically measured by the manufacturer before ship-ment, and treatment planning is based on that assay. However, in-house verification of sourcestrength is required at some institutions by state law or internal policy, is recommended by theAAPM TG 60 report on intravascular brachytherapy, and is considered a necessity by many medicalphysicists. To accommodate the long sources used in intravascular therapy, special well chamberswith extended regions of constant response have been designed. To allow assays using a widelyavailable standard well chamber, we have measured its position dependent sensitivity and derivedfrom it a table of correction factors that account for the extended length of intravascular sources. Anexperimental verification shows that application of these correction factors yields assays with suf-ficient accuracy for routine quality assurance tests. ©2002 American Association of Physicists inMedicine. @DOI: 10.1118/1.1517046#

Key words: intravascular brachytherapy, well chambers, assays,192Ir

I. INTRODUCTION

Intravascular brachytherapy~IVB ! is an effective method forthe prevention of restenosis in coronary arteries and otherblood vessels, and is often administered with192Ir wire orstrings of closely spaced seeds.1,2 Although the sources areusually assayed by the vendors, medical physicists often feeluncomfortable without having done an independent verifica-tion. In addition, in-house activity verification is recom-mended by the AAPM Task Group Report No. 60~TG-60!on intravascular brachytherapy physics,3 and required insome institutions by state regulations and departmentalpolicy. Open air calibration methods applicable for mostgamma emitting isotopes and source configurations havebeen described in the literature.4,5 While such methods arevery accurate, they require special jigs for precise position-ing of sources and chamber and are not practical in the clinic.Well chambers, on the other hand, are well suited for routinequality assurance measurements.5 For the calibration of thelong sources typically used in IVB, special well chambershaving an extended region of near constant response havebeen developed. However, some institutions are reluctant tobear the cost of acquisition and periodic calibration of suchchambers, especially when source strength verification is notrequired by law. Furthermore, calibrations traceable to theNational Institute of Standards and Technology~NIST! maynot be available for some newly developed types of intravas-cular sources.

The HDR 1000 well chamber~Standard Imaging, Middle-ton, WI! is widely used for the calibration of192Ir sources forhigh dose rate~HDR! brachytherapy of cancer. This chamberhas been well characterized and is very stable.5,6 However,because it was designed for the calibration of HDR sourcestypically 5 mm in length, the chamber is short, having aregion of constant response~‘‘sweet spot’’! quoted by themanufacturer as1/20.5% over 25 mm at the center of theaxis. To use the HDR 1000 chamber for assaying strings ofmany 125I sources spaced 1 cm apart~Rapid Strand, Ny-

comed Amersham, Arlington Heights, IL!, it has been pro-posed to measure a chamber factor that takes into account thediminishing chamber sensitivity for the off-center seedpositions.7 In the present paper we present a similar correc-tion method that can be used for continuous intravascular192Ir source wires or closely packed seed strings of variouslengths. An experimental verification of the method is alsopresented.

II. METHODS AND MATERIALS

Well chambers for HDR therapy are commonly calibratedby accredited labs, using192Ir sources a few mm in lengths.An accurately assayed radiation source, having its strengthtraceable to NIST, is placed at a reference pointxref at theaxis of the chamber, and the ionization current is recorded.The reference point is chosen near the center of the well,where the ionization current is largest and relatively insensi-tive to the source position. The chamber response is thenexpressed by the calibration factorF, defined as the sourcestrength divided by the ionization current. In the case of openchambers, the dependence on atmospheric conditions is ac-counted for by referencing the calibration factor to standardconditions ~22 °C, 760 mm Hg!, using the temperature–pressure correction factorCTP.

The HDR 1000 well chamber is open to air, has a volumeof 245 cm3, and is 121 mm deep. The calibration factor ofour chamber was measured by an AAPM accredited calibra-tion laboratory~University of Wisconsin–Madison!, using a5 mm long, 0.34 mm diameter192Ir source, enclosed in a0.6 mm diameter nitinol wire.~Nitinol is an alloy of 55%nickel and 45% titanium by weight!. The calibration pointwas 50 mm from the bottom of the chamber insert, 52.5 mmfrom the bottom of the chamber. The Calibration Factor was5.1223105 Gy m2 h21 A21, with an uncertainty of 2.5%. Acalibration of the same ion chamber performed two yearsearlier by a different lab~K&S Associates, Nashville, TN!

2692 2692Med. Phys. 29 „11…, November 2002 0094-2405 Õ2002Õ29„11…Õ2692Õ6Õ$19.00 © 2002 Am. Assoc. Phys. Med.

Page 3: Assaying [sup 192]Ir line sources using a standard length well chamber

gave a calibration factor that was 0.3% higher (5.1383105

Gy m2 h21 A21!, and an uncertainty of 1.9%.Clinical HDR sources are assayed by placing them into

the well chamber at the pointxref , and multiplying the ion-ization currentI by the calibration factor and, if indicated,also byCTP. If the source is positioned above or below thereference point, the efficiency of ion production in the cham-ber gas decreases,4 resulting in an erroneous strength deter-mination. For long sources or source strings, positioningsome of the activity beyond the sweet spot is unavoidable. Touse the HDR 1000 for such sources, we have measured itsposition dependent sensitivity and used that sensitivity tocompute correction factors for sources of various lengths.The correction factor normalizes the ionization current read-ing as if the entire source were positioned at the sweet spot,so that the calibration factor supplied by the calibration labcan be used to find the strength of the clinical source.

The 3.5 mm long192Ir source of a Classic microSelectronremote afterloader~Nucletron Corporation, Columbia, MD!,together with its precise drive mechanism, provided a prac-tical instrument for measuring the position dependent sensi-tivity R(x) of our well chamber. We placed a plastic guidetube along the axis of the chamber, programmed the machineto move the source in 2.5 mm steps, and recorded the ion-ization currentI (x) at each of the steps as a function of thedistancex from the bottom of the well. From that, we com-puted the relative response using

R~x!5I ~x!/I ~xref!. ~1!

For a long source of uniform activity we can integrate Eq.~1! over the length of the source, to obtain the effective re-sponse of the chamber,

Reff~x1 ,x2!5@1/~x22x1!#Ex1

x2R~x!dx, ~2!

wherex1 andx2 are the respective distances of the proximaland the distal end of the source from the bottom of the well.Since (x22x1) is the lengthL of the source, Eq.~2! can bewritten as

Reff~x1 ,x11L !5@1/~L !#Ex1

x11L

R~x!dx. ~3!

For clinical use it is practical to define a correction factorCF(x1 ,L) as

CF~x1 ,L !51/Reff~x1 ,x11L !, ~4!

from which the air kerma strengthSk is calculated,

Sk5I •CTP•F•CF~x1 ,L !. ~5!

By providing a table of correction factors, the HDR 1000chamber becomes usable for a wide range of lengths andinsertion depths. To allow comparisons when the sourcestrength was given in the traditional units of mCi, we used

the AAPM TG-43 recommended factor of 4.030 U/mCi~1U51 mGy m2 h21! to convert the apparent activity to AirKerma strength.8

To test the accuracy of the correction method, we carriedout two sets of experiments. In the first set, we used ourHDR 1000 chamber in conjunction with the correction fac-tors to measure the strength of a 45 mm long endovascularline source that was inserted to various depths~Fig. 1!. Thevertical drive mechanism of a water phantom provided forremotely controlled source positioning along the chamberaxis with an accuracy better than 1 mm. The source strengthsmeasured at the various insertion depths were compared toone another for consistency, as well as to the activity speci-fied by the manufacturer of the source~Rads S.S. Inc., LakeCharles, LA!. The strength of a second source that was pro-vided by the same manufacturer as replacement for the de-caying original source was measured at only one insertiondepth, and compared to the manufacturer’s specifications.

The endovascular source was provided to our institutionfor a clinical trial that was sponsored by InterventionalTherapies, LLC~Westport, CT!, and authorized by the Foodand Drug Administration~FDA! under an Investigational De-vice Exemption~IDE!. The source consisted of two sectionsof 0.13 1/20.01 mm ~0.005 in. 1/20.0005 in.! diameter192Ir wire, one 30 mm and the second one 15 mm long. Thelength uncertainty for each section was quoted as1/20.2mm. The two sections of the192Ir wire were abutted andsealed inside a 0.361/20.01 mm~0.014 in.1/20.0005 in.!outer diameter nitinol tube, 1 mm from the distal end, toform a single 45 mm long radioactive source. The wall thick-ness of the nitinol tube was 0.071/20.01 mm ~0.0028 in.

FIG. 1. Experimental setup for a verification of the correction method.

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Page 4: Assaying [sup 192]Ir line sources using a standard length well chamber

1/20.0005 in.!. For a calibration, the manufacturer sent offone such source to a calibration lab~Battelle Pacific North-west National Laboratory!, and used it to calibrate a wellchamber~Model WC-2, Precision Radiation Measurements,Nashville, TN!, having a region of near constant response~1/20.5%! over a length of more than 100 mm. That cham-ber was used to measure the strength of each intravascularsource before it was shipped to the customer. A record of themeasured strength, decay corrected to noon of the assay day,accompanied the shipments. The manufacturer quoted a1/25% calibration error.

The second set of verification experiments was done withthe aid of two radioactive ribbons~Best Medical, Springfield,VA ! that were used for clinical IVB as part of the CordisCheckmate Delivery System~Cordis Corporation, Miami,FL!. The Checkmate System had Premarket Approval~PMA!from the FDA. The ribbons consisted of 3 mm long, 0.5 mmdiameter seeds contained in a 0.78 mm outer diameter plastictube. The individual seeds were made of a 0.1 mm diameter192Ir wire encased in a 0.2 mm thick cylindrical stainlesssteel shell. The radioactive wire was kept inside the jacket bythe press fit resulting from the manufacturing method~swag-ging!, and there were no end caps. The end-to-end distancebetween neighboring seeds was 1 mm. The two ribbons con-tained 10 and 14 seeds, respectively. Neglecting dosimetriceffects of the air gaps, we considered the 10-source ribbon asa 39 mm long line source~30 mm total source length plus 9air gaps of 1 mm each!. For similar reasons, the 14-seedstring was considered a 55 mm long line source. The manu-facturer obtained the strength of each ribbon by multiplyingthe number of seeds contained in it by the average seedstrength of the batch from which the ribbon was assembled.According to the manufacturer, the strength of individualseeds within the batch varied by less than1/25% from thebatch average. Before shipment, each ribbon was assayed toreassure that its strength was within1/25% of its nominalvalue.

We first measured the strengths of the two ribbons sepa-rately by placing each ribbon at a well defined distance fromthe bottom of the chamber, and using the proper correctionfactor CF for the respective source position and sourcelength. In the next measurement, both ribbons were insertedat the same time. A special adapter mounted on top of thechamber insert made it possible to remotely load bothsources simultaneously into the 2 mm diameter bore of thechamber insert. The 10-seed ribbon was placed so that thedistal end was located 12.5 mm from the bottom of the well,whereas the 14-seed ribbon was inserted so that the tip of itsfirst seed was 52.5 mm from the bottom. This arrangementsimulated a 95 mm long line source centered in the well.Using the correction factor for a 95 mm long source insertedto a depth of 12.5 mm, the strength was computed and com-pared to the sum of the measured activities of the individualstrings. The strength of a second set of ribbons that replacedthe decaying original ribbons was measured at only one in-sertion depth. All measurements were compared to the manu-facturer’s data.

The merit of our correction method was judged primarily

by the consistency of strength it provided for sources ofsimilar construction but different lengths and insertiondepths~relative accuracy!. The method was also evaluatedaccording to the agreement between our measurements andthe strengths quoted by the source manufacturers~absoluteaccuracy!.

III. RESULTS

Figure 2 shows the relative sensitivity of our well cham-ber, normalized to the sensitivity at the calibration depth of52.5 mm from the bottom of the well. The region of constantresponse~less than 0.05% variation! is about 7 mm long, andincludes that depth. Table I shows correction factors calcu-lated using Eq.~4! for 192Ir sources of various lengths in-serted into the well chamber to a given depth.

The results of our first experimental verification are sum-marized in Table II. The first column lists the insertion depthx1 of the 45 mm long intravascular source. The second col-umn shows the strength that would be obtained by ignoringthe position and source length dependence of the chamber.The third column shows the correction factor CF obtainedfrom Table I at each insertion depth. The next column indi-cates the strength obtained by applying the correction factor,whereas the last column shows the percent difference be-tween our assay and the air kerma source strength quoted bythe manufacturer~1808.9 U1/25%! when projected to thedate and time of our assay. The discrepancy was within 1%for all insertion depths, and consistent within 0.3% for inser-tion depths<70 mm. At the depth of 75 mm the proximalend of the source was very close to the opening of the cham-ber, and the strong position sensitivity in that region mayhave caused the slight change in measured strength.

An additional check of the correction method was doneone month later when the original source was replaced toavoid excessive treatment times due to radioactive decay. Wechose an insertion depth of 30 mm from the well bottom to

FIG. 2. Normalized ionization current of the HDR 1000 well chamber, as afunction of the source position along the chamber axis. Measurements weredone using a 0.35 mm diameter, 3.5 mm long192Ir source.

2694 Brezovich et al. : Assaying 192Ir line sources 2694

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Page 5: Assaying [sup 192]Ir line sources using a standard length well chamber

minimize measurement sensitivity to small position errors.Our assay yielded an activity that was 0.2% lower than thatquoted by the manufacturer.

The results of our second set of experiments are shown inTable III. The ten-seed ribbon was inserted to 33 mm,whereas the 14-seed string was placed 25 mm from thechamber bottom. As before, we chose these depths to mini-mize the effect of small positioning errors. When both stringswere inserted at the same time the correction factor CF51.066 was used, applicable to a 95 mm long 24-seed rib-bon inserted to 12.5 mm. The sum of the two individual

ribbon strengths agreed within 0.6% with the measurement atsimultaneous insertion, but our assays were 4.2 % and 3.4%higher than quoted by the manufacturer for the 10-seed andthe 14 seed ribbon, respectively. Our assays of similar rib-bons from a subsequent shipment were, respectively, 2.0%and 1.5% higher than quoted.

IV. DISCUSSION AND CONCLUSIONS

A correction method has been presented that allows theHDR 1000 chamber, designed and calibrated for typically

TABLE I. Calculated Correction Factors CF for sources of various lengths.

Distance from

source tip to

bottom of

chamber~mm!

Length of source~mm!

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110

7.5 1.140 1.124 1.108 1.095 1.083 1.072 1.063 1.056 1.050 1.045 1.041 1.039 1.037 1.037 1.039 1.041 1.045 1.051 1.059 1.069 1.081 1.096

10 1.124 1.108 1.094 1.081 1.071 1.062 1.054 1.047 1.042 1.038 1.035 1.034 1.033 1.034 1.036 1.040 1.045 1.052 1.062 1.073 1.087 1.104

15 1.093 1.079 1.068 1.058 1.050 1.043 1.037 1.032 1.029 1.027 1.026 1.026 1.028 1.030 1.035 1.041 1.048 1.058 1.070 1.085 1.103

20 1.066 1.056 1.047 1.039 1.033 1.028 1.024 1.021 1.020 1.019 1.020 1.022 1.026 1.030 1.037 1.045 1.056 1.069 1.084 1.103

25 1.045 1.037 1.030 1.025 1.020 1.017 1.015 1.014 1.014 1.016 1.018 1.022 1.027 1.035 1.044 1.055 1.068 1.085 1.105

30 1.029 1.022 1.018 1.014 1.011 1.010 1.009 1.010 1.012 1.015 1.020 1.026 1.033 1.043 1.055 1.070 1.087 1.108

35 1.016 1.012 1.009 1.007 1.006 1.006 1.007 1.010 1.014 1.019 1.025 1.034 1.044 1.057 1.072 1.090 1.112

40 1.007 1.005 1.003 1.003 1.004 1.006 1.009 1.013 1.019 1.026 1.035 1.046 1.060 1.076 1.095 1.119

45 1.002 1.001 1.001 1.003 1.005 1.009 1.013 1.020 1.028 1.037 1.049 1.064 1.081 1.102 1.127

50 1.000 1.001 1.003 1.006 1.010 1.015 1.022 1.031 1.041 1.054 1.070 1.088 1.110 1.136

55 1.001 1.004 1.007 1.012 1.018 1.025 1.035 1.046 1.060 1.077 1.096 1.119 1.148

60 1.006 1.010 1.015 1.022 1.030 1.040 1.053 1.068 1.085 1.107 1.131 1.161

65 1.014 1.019 1.027 1.036 1.047 1.061 1.077 1.096 1.119 1.145 1.177

70 1.025 1.033 1.043 1.056 1.070 1.088 1.108 1.133 1.161 1.196

75 1.041 1.052 1.066 1.081 1.100 1.123 1.149 1.180 1.218

80 1.063 1.078 1.095 1.116 1.140 1.169 1.202 1.244

85 1.092 1.111 1.134 1.160 1.192 1.228 1.274

90 1.130 1.155 1.184 1.219 1.259 1.309

95 1.181 1.213 1.251 1.295 1.351

100 1.246 1.288 1.337 1.400

105 1.333 1.386 1.459

110 1.444 1.529

115 1.617

TABLE II. Measurement of source strength at various insertion depths and a comparison with manufacturer’sstated strength~1809 U!.

Distance fromsource tip tobottom of chamber~mm!

Uncorrectedstrength

~U!Correction

factor

Measuredstrength

~U!

Difference betweenmeasured strengthand stated strength

7.5 1708 1.050 1793 20.9%10 1720 1.042 1793 20.9%15 1741 1.029 1792 20.9%20 1756 1.020 1791 21.0%25 1766 1.014 1791 21.0%30 1769 1.012 1791 21.0%35 1766 1.014 1790 21.0%40 1758 1.019 1790 21.0%45 1742 1.028 1791 21.0%50 1719 1.041 1790 21.0%55 1690 1.060 1792 20.9%60 1652 1.085 1793 20.9%65 1605 1.119 1795 20.8%70 1547 1.161 1797 20.7%75 1480 1.218 1803 20.3%

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Page 6: Assaying [sup 192]Ir line sources using a standard length well chamber

5 mm long HDR sources, to be used for surveys of IVB192Irsources. The validity of the method has been verified forsources up to 95 mm in length, but should be applicable forup to 110 mm length. The relative accuracy of the method,i.e., the ability to yield consistent strength measurements forsources of similar design but different lengths and positionswithin the chamber, is better than 1%. Sources having physi-cal characteristics different from the source used for the cali-bration of the HDR 1000 chamber can be assayed with anabsolute accuracy of about 3%.

We base our conclusion concerning the relative accuracyon the observation that the measured strength of the 45 mmlong line source remained constant within 0.3% for positionsspanning almost the entire depth of the well. Only when theproximal end of the source was located within 1 mm fromthe open end of the ion chamber, a 0.7% discrepancy re-sulted. To occupy that location, a source placed with its tip atthe bottom of the chamber insert would have to be longerthan 110 mm. The experiments involving combinations ofribbons to simulate a 95 mm long source provided furtherevidence for the validity of the method. The 0.6% lowermeasurement in the simultaneous insertion of the two rib-bons may have been due to the absorption of some of theradiation emerging from the proximal sources by the shaft ofthe distally placed ribbon. Differences in construction be-tween the Nucletron source that was used to measure theposition dependent response of the HDR 1000 chamber andthe IVB sources may have also contributed to the discrep-ancy. When a radiation source is placed at different positionsalong the chamber axis, the angular range of rays emittedfrom the source that pass through the active chamber volumechanges. Hence, the chamber response is affected by sourceanisotropy and thereby depends on the construction of thesource used to measure it.

The effect of source construction and encapsulation onresponse of the HDR 1000 chamber has been investigated forspherical and cylindrical137Cs sources, theoretically as wellas experimentally.9 Despite the significant differences in con-struction, the activity as detected by the well chamber wasonly 4% lower for the cylindrical source than for the spheri-cal one. Considering that HDR brachytherapy and intravas-cular sources are cylindrical, have radii that are typicallyone-third or smaller than those of the investigated137Cssources, differences in construction should affect the de-tected strength by not more than about 1%. Hence the ob-

served consistency in our measurements is not just coinci-dental. For low energy emitters, on the other hand,differences in source construction and encapsulation stronglyaffect chamber response. The method used by Butleret al.7

for the assay of125I seed strings was successful because theseeds used to obtain the correction factors were of the sameconstruction as the seeds comprising the string to be assayed.

The estimation of 3% absolute accuracy of our method isbased on the agreement of our assays with those of the twosource manufacturers. The<1% discrepancies in the sourcesfrom Rads S.S. Inc. were within experimental error. By pro-viding assays of individual sources the company greatly re-duced uncertainties arising from the manufacturing process.The 1.5% to 4.2% disparities between our and the Best In-dustries calibrations are indicative of additional errors, sinceit is statistically unlikely that the average seed strength in allfour strings was lower than the batch average, especially bysuch a high percentage. The fact that Best Industries did notreport the assay results of individual ribbons indicates thatthe company considers1/25% accuracy as sufficient, andmost of the error may be on their side.

To improve absolute accuracy, one could obtain a NISTtraceable calibration of the chamber for the types of source tobe measured. One could then use our correction factors forassaying sources shorter or longer than the ones used for thechamber calibration. To reduce potential errors in relativeaccuracy, one could measure the position dependent chamberresponse using sources of various construction and obtainsource specific correction factors that would account for dif-ferences in anisotropy. However, clinical IVB is usually ad-ministered with carefully tested and FDA cleared sourceswhich have tolerances of typically1/25%. In-house calibra-tions are performed only to assure that the sources meetthose specifications. We have demonstrated that such accu-racy is provided by the presented method.

a!Corresponding author: Ivan A. Brezovich, Ph.D., 1824 6th Avenue South,Birmingham, Alabama 35233. Telephone:~205! 934-1758; Fax:~205!975-2546; electronic mail: [email protected]. Schopohl, D. Leirmann, L. J. Pohlit, R. Heyd, G. Strassmann, R.Bauersachs, D. Schulte-Huermann, C. G. Rahl, K. H. Manegold, J. Kol-lath, and H. D. Bottcher, ‘‘192Ir endovascular brachytherapy for avoidanceof intimal hyperplasia after percutaneous transluminal angioplasty andstent implantation in peripheral vessels: 6 years of experience,’’ Int. J.Radiat. Oncol., Biol., Phys.36, 835–840~1996!.

TABLE III. A comparison of individual strength measurements with combined strength measurements.

Ribbon

Manufacturer’s statedstrength

~U!

Ribbonlength~mm!

Insertiondepth~mm!

CorrectionfactorCF

Measuredstrength

~U!

10-seed 1047 39 33.0 1.010 109114-seed 1466 55 25.0 1.018 1516Sum 2513 2607

10-seed114-seed N/A 95 12.5 1.066 2591Ratio of sum of individual strength measurementsto combined strength measurement

1.006

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re-entrant ionization chamber for the calibration of iridium-192 high doserate sources,’’ Int. J. Radiat. Oncol., Biol., Phys.24, 167–170~1992!.

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8R. 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!.

9R. J. Meiler, C. H. Sibata, A. K. Ho, C. de Souza, and K. H. Shin, ‘‘Awell-type ionization chamber correction factor,’’ Phys. Med. Biol.41,1141–1148~1996!.

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