Supplement to the 2004 update of the AAPM Task Group 43 Report

Implant Sciences model 3500, IBt model 1251L, IsoAid model IAI-125A, Mentor model SL-125/ SH-125, and SourceTech Medical model STM1251. The Best Medical model 2335 103 Pd source is also included. While the methodology used to determine these data sets is identical to that published in the AAPM TG-43U1 report, additional information and discussion are presented here on some questions that arose since the publication of the TG-43U1 report. Speciﬁcally, details of interpolation and extrapolation methods are described further, new methodologies are recommended, and example calculations are provided. Despite these changes, additions, and clariﬁcations, the overall methodology, the procedures for developing consensus data sets, and the dose calculation formalism largely remain the same as in the TG-43U1 report. Thus, the AAPM recommends that the consensus data sets and resultant source-speciﬁc dose-rate distributions included in this supplement be adopted by all end users for clinical treatment planning of low-energy photon-emitting brachytherapy sources. Adoption of these recommendations may result in changes to patient dose calculations, and these changes should be carefully evaluated and reviewed with the radiation oncologist prior to implementation of the current protocol. © 2007 American Association of Physicists in Medicine . (cid:3) DOI: 10.1118/1.2736790 (cid:4)


I. INTRODUCTION
The 1995 report from the American Association of Physicists in Medicine ͑AAPM͒ Task Group No. 43 ͑TG-43͒ 1 on the dosimetry of interstitial brachytherapy sources was updated in 2004, and was termed the AAPM TG-43U1 report. [2][3][4][5][6] The 1995 report contained recommended datasets for four interstitial brachytherapy sources: Amersham-Health models 6702 and 6711 sources of 125 I, the Theragenics Corporation model 200 source of 103 Pd and the Best Medical 192 Ir source ͑certain commercial equipment, instruments, and materials are identified in this work in order to specify adequately the experimental procedure. Such identification does not imply recommendation nor endorsement by either the AAPM or National Institute of Standards and Technology ͑NIST͒, nor does it imply that the material or equipment identified is necessarily the best available for these purposes͒. In the 2004 update, the AAPM updated the data on the 125 I and 103 Pd sources included in the original report and included data on six other interstitial brachytherapy sources. All of the following eight sources met the AAPM dosimetric prerequisites 7 and the AAPM Calibration Laboratory Accreditation ͑CLA͒ subcommittee requirements 8 as of July 15, 2001 and were presented in the AAPM TG-43U1 report: 1 Amersham-Health model 6702 125  Since July 15, 2001 several additional sources have been introduced in the market and have met the AAPM dosimetric prerequisites and the CLA subcommittee requirements. As planned during the writing of TG-43U1, a supplement was needed to present consensus datasets for these newer sources. This supplement is termed TG-43U1S1, and includes the following sources which met the criteria mentioned above as of January 10 Manufacturers, dosimetry investigators, and end users have generally adhered to AAPM recommendations given in the TG-43U1 and CLA subcommittee reports. The source models reviewed in this supplement ͑Fig. 1͒ satisfied AAPM recommendations ͑dosimetric parameters accepted for publication in a scientific, peer-reviewed journal and metrologically acceptable source calibration procedures͒ on or before January 10,2005. After review and approval, these data were posted on the online Joint AAPM/RPC Source Registry. 9 As stated in the AAPM TG-43U1 report, publications may re-port dosimetry parameters using Monte Carlo, experimental methods, or both techniques in the same publication. It is also worth stressing that special care is needed to address concerns for independence of various investigations included in the development of consensus datasets. The independence policy is described in detail in Sec. V F of the AAPM TG-43U1 report.

II. CONSENSUS DATASETS FOR CLINICAL IMPLEMENTATION
As presented in the TG-43U1 report, criteria used to evaluate dosimetry parameters for each source model included in this TG-43U1S1 report were: 1. Internal source geometry and a description of the source, 2. review of the pertinent literature for the source, 3. correction to ⌳ values due to the 1999 anomaly in NIST air-kerma strength measurements ͑if applicable͒, 4. solid water-to-liquid water corrections, 5. experimental method used: TLD or diode, 6. active length assumed for the geometry function linesource approximation, 7. name and version of the Monte Carlo transport code, 8. cross-section library used by the Monte Carlo simulation, 9. Monte Carlo estimator used to score kerma or dose, and 10. agreement between Monte Carlo calculations and experimental measurement.
AAPM-approved consensus datasets are provided in Tables I-X below with calculated dose rates using the onedimensional ͑1D͒ formalism in Table XI as similar to the 2004 AAPM TG-43U1 report. Descriptions of each source and details used for obtaining the consensus datasets are available in Appendix A. If essential items critical to the evaluation of a given source were omitted from the salient publications, then dosimetry investigators were contacted for additional information and/or clarification. Fortunately, in recent publications, analysis for some of these source models benefited from adherence by dosimetry investigators to recommendations provided in Secs. V D and V E of the AAPM TG-43U1 report. Data were italicized if they were not directly confirmed by other measurements or calculations; boldface values indicate that data were interpolated towards presenting data sets of all sources on a common mesh; extrapolated data are underlined. As in the 2004 report, data sets were thinned so as to minimize the amount of data while maintaining interpolation errors ഛ2% for the purposes of calculating dose rate distributions. Due to differences in source construction, appropriate angular resolution for F͑r , ͒ was used to keep bilinear interpolation errors ഛ2%.
Additionally, the AAPM TG-43U1 report recommended a mass density of 0.001 20 g cm −3 for both moist and dry air. Upon analyzing the impact of relative humidity from 0% to 100%, a value of 0.001 19 g cm −3 is more appropriate and should be used in conjunction with the recommended relative humidity of 40%.

III. CLARIFICATIONS ON RECOMMENDED INTERPOLATION AND EXTRAPOLATION METHODS
While a sampling space with uniform increments for g͑r͒ and either F͑r , ͒ or an ͑r͒ is desired, the published data indicate that authors have used a variety of spatial and angular increments and ranges. Therefore, interpolation or ex-trapolation may be required to determine dose rate distributions at spatial locations not explicitly included in published dosimetry-parameter tables. Methods for determining dose rates at positions not characterized by the available datasets or related publications were specified in the 2004 AAPM TG-43U1 report. Interpolation methods for 2D and 1D dosimetry parameters were provided in Sec. IV  AAPM TG-43U1 report, and extrapolation methods for these same parameters were provided in its Appendix C. Linearlinear interpolation was recommended for F͑r , ͒, and loglinear interpolation was recommended for g͑r͒. However, specific guidance on implementation of these recommendations by medical physicists or treatment planning software manufacturers was limited. The brachytherapy dosimetry formalism should minimize the contribution of interpolation and extrapolation errors to overall dose-calculation uncer-tainty. Therefore, we consider the physical effects that govern the two-dimensional ͑2D͒ and one-dimensional ͑1D͒ anisotropy functions and the radial dose function, and aim to clarify the recommended approaches towards ensuring improved interpolation or extrapolation accuracy. Below are presented the rationale and recommended methods for interpolation, r Ͻ r min extrapolation, and r Ͼ r max extrapolation of F͑r , ͒, an ͑r͒, and g L ͑r͒. Note that r min and r max are the smallest and largest radii for a set of reported dosimetry pa-

A. F"r , … 2D anisotropy function
The 2D anisotropy function is a function of polar angle for a specified radius and is normalized to unity at 0 ϵ 90°. For all angles except 0 , F͑r , ͒ values generally trend to asymptotically approach unity with increasing radial distance. The geometry function, G͑r , ͒, accounts for dose distribution variations attributed to distance-dependent changes in the solid angle and distribution of radioactivity, assuming a uniform radioactive distribution. Therefore, nonunity values of the 2D anisotropy function are due to nonuniform radionuclide distribution and to attenuation and scatter by the source encapsulation and internal components. As a function of polar angle, both of these effects generally change linearly over small changes in radius or angle. Dose distributions at 10°Ͻ Ͻ 170°for 0.5-cm-long capsules are primarily af-fected by attenuation as a function of polar angle through the cylindrical capsule wall. Dose distributions at other angles are primarily affected by attenuation through encapsulation end welds and radiation source carriers. Away from the source long axis, F͑r , ͒ behavior may be considered as a combination of primary dose and dose due to photons scattered in the surrounding medium where the proportion of scattered radiation generally increases with increasing r. For the sources included in this current report and the 2004 AAPM TG-43U1 report, 2 variations in F͑r , Ͻ 10°͒ or F͑r , Ͼ 170°͒ are largely due to photon attenuation by end welds and capsule internal components. While these variations may exceed 50%, points within these volumes, i.e., P͑r , Ͻ 10°͒ and P͑r , Ͼ 170°͒, subtend ϳ1% of the solidangle weighted dose rate distribution around a source. F͑r , ͒ may be accurately determined in general using linear interpolation. However, some sources have F͑r , ͒ that significantly exceed unity, e.g. the Draximage model LS-1 125 I source, due to the geometry function not readily approximating the particle streaming function ͑i.e., in vacuo photon energy fluence͒. 10 Thus, a linear-linear interpolation method for  F͑r , ͒ as a function of r and is appropriate, and should be based on the two data points for each variable located immediately adjacent to the interpolated point of interest. This approach is identical to that recommended by the 2004 AAPM TG-43U1 report. 2 When there is a need to extrapolate F͑r , ͒ data outside of the range of tabulated data, the 2004 AAPM TG-43U1 method ͑Appendix C 1͒ of using a nearest-neighbor or zeroth-order approach is still recommended since differing trends between different radionuclides do not warrant a different extrapolation methodology. Specifically, the nearestneighbor or zeroth-order approach presented in Appendix C of the 2004 AAPM TG-43U1 report is still recommended for F͑r , ͒ extrapolation for r Ͻ r min and also for r Ͼ r max . Regarding need for F͑r , ͒ extrapolation on polar angle, it appears that all sources have been characterized over the full angular range of 0°ഛ ഛ 90°. However, for example, if F͑7,45°͒ were sought and data were available at F͑6,40°͒ and F͑6,50°͒ data where r max = 6 cm, one should first perform linear interpolation to obtain F͑6,45°͒ then extrapolate ͑zeroth order͒ to obtain F͑7,45°͒.
We advise Monte Carlo dosimetry investigators to exploit continuously increasing computational and geometric modeling capabilities to estimate the dose rate distributions, including F͑r , ͒, as close to the source as possible and with fine angular resolution. For typical low-energy photon-emitting brachytherapy seeds which are 5 mm long and 0.8 mm in diameter capsule, it is reasonable to calculate F͑r , ͒ for r ഛ 2.5 mm for the limited range of theta values that place calculation voxels outside of the source capsule and in the range of dose calculation points relevant to specialized clinical applications such as eye plaques.

B. an "r… 1D anisotropy function
The recommended an ͑r͒ data sets were derived from solid-angle weighted dose rates based on F͑r , ͒ datasets, removing effects of the geometry function. These an ͑r͒ data sets demonstrated nearly constant or linear behavior for r ജ 1 cm, especially for quasi mono-energetic photon sources such as 125 I. For r Ͻ 1 cm, an ͑r͒ values significantly increased with decreasing r as illustrated by Rivard, Melhus, and Kirk for a general 103 Pd source. 11 This behavior is caused by volume averaging of larger dose rates near the source long-axis due to the increasing ellipsoidal shape of isodose distributions in comparison to the dose rate at the same r value along the transverse plane. Based on increased availability of high-resolution an ͑r͒ data determined over a wide range of distances, we recommend a log-linear approach to interpolating an ͑r͒ data. The interpolation should be based on the two data points located immediately adjacent to the interpolated point of interest. This log-linear approach differs from the 2004 AAPM TG-43U1 report which previously recommended that "linear interpolation may be used to match the grid spacing of g X ͑r͒ with the grid spacing of an ͑r͒." In light of the general behavior of an ͑r͒ observed in multiple high-resolution datasets, it is recommended that dosimetry investigators provide sufficient spatial sampling of an ͑r Ͻ 1 cm͒ and for suitably large r to minimize the need to extrapolate. This is especially convenient using Monte Carlo techniques. Additionally, having a common highresolution sampling space for both an ͑r͒ and g͑r͒ is crucial for implementation of the simple 1D formalism of Eq. ͑9͒ of TG-43U1. 2 Appendix C of the 2004 AAPM TG-43U1 report recommended using Eq. ͑1͒ below, Eq. ͑C3͒ of the 2004 TG-43U1 report, 2 for extrapolating an ͑r͒ for distances r Ͻ r min , where r min is the shortest distance for which an ͑r͒ data are provided In this report, we recommend replacing the aforementioned extrapolation procedure with a more accurate approach that approximates the short distance behavior of an ͑r͒ at r Ͻ r min by the solid-angle ͑⍀͒ weighted integral of the linesource geometry function correction   TABLE XI. Transverse plane dose rates ͑cGy· h −1 · U −1 ͒ as a function of distance for the 8 brachytherapy sources included in this report using g L ͑r͒ and an ͑r͒, and the 1-D formalism of Eq. ͑11͒ from the 2004 AAPM TG-43U1. Results using interpolated g L ͑r͒ or an ͑r͒ data are highlighted in boldface while extrapolated results based on g L ͑r͒ and/or an ͑r͒ data are underlined.
When using Eq. ͑2͒ instead of Eq. ͑1͒ for sources in this report and the TG-43U1 report, extrapolating from an ͑r min =1 cm͒ to an ͑0.25͒ and an ͑0.50͒ improved the average extrapolation accuracy by 8.8% and 0.2%, respectively, as shown comparing data at the bottom of the last two columns in Table XII. Extrapolated an ͑r͒ values are given in Table II as used in Table XI. Care should be taken when extrapolating an ͑r͒ to distances smaller than half the capsule length since dose rates at these distances for some polar angles are located within the source and are clinically irrelevant. For instance, for the 0.4 mm radius source capsules presented in this report, an ͑0.10͒ was integrated over 23.6°ഛ ഛ 156.4°and an ͑0.15͒ over 15.5°ഛ ഛ 164.5°, both with 0.1° increments.
There were no specific recommendations given in the 2004 AAPM TG-43U1 report on how to extrapolate an ͑r͒ at distances where r Ͼ r max . 2 While poly-energetic sources such as 103 Pd exhibit significantly diminished anisotropy at distances greater than 10 cm in liquid water due to contributions from the weakly abundant high-energy photon emissions ͑i.e., E␥ ജ 0.3 MeV͒, at this time a radionuclidespecific approach is not recommended. Conservatively, a nearest neighbor or zeroth-order extrapolation approach is recommended until more results at larger distances become available. Consequently, brachytherapy dosimetry investigators are advised to determine dose rate distributions and subsequently publish F͑r , ͒ and an ͑r͒ values at distances as large as reasonably achievable. For 125 I and 103 Pd, characterization out to distances exceeding 10 cm is possible with acceptable statistical precision using modern codes. However, the investigators should limit their published results to those data where contributions from scattered radiation approximate those of an infinitely large phantom. 12,13

C. Radial dose function
The physical effects that govern the behavior of g͑r͒ are based on attenuation and scatter in a recommended 15 cm radius liquid water medium, where broad beam attenuation is based on Ј/ and absorbed dose is based on en / . For points further than a few cm from the sphere surface yet beyond 1 cm for an 125 I or 103 Pd source, g͑r͒ should decrease approximately exponentially as a function of increasing r. Consequently, a log-linear function for g͑r͒ interpolation was recommended in the 2004 AAPM TG-43U1 report. 2 Upon additional examination, any logarithmic function such as log 10 or ln ͑i.e., log e ͒ will suffice to interpolate g L ͑r͒ data in a log-linear manner since differences are expressed as changes in slope and offset. Additionally, it is recommended that g L ͑r͒ data be interpolated instead of g P ͑r͒ since this latter function changes more rapidly for r Ͻ 1 cm due to improved approximation of the particle streaming function by G L ͑r , ͒. 10 The log-linear interpolation should be performed using data points immediately adjacent to the radius of interest. Equation ͑3͒ may be used to solve for g L ͑r 2 ͒ where r 1 Ͻ r 2 Ͻ r 3 given g L ͑r 1 ͒ and g L ͑r 3 ͒. XII. Extrapolation of an ͑r͒ from r = 1 cm to r = 0.25 cm and r = 0.50 cm. Equation ͑1͒ uses the ratio of point-and line-source geometry functions applied to an ͑r min ͒ to extrapolate to smaller distances. Equation ͑2͒ uses a solid-angle weighted line-source geometry function to extrapolate an ͑r min ͒ to smaller distances. These extrapolation approaches are tested on consensus an ͑0.25͒, an ͑0.50͒, and an ͑1.00͒ data for six brachytherapy sources. The percentage error relative to the consensus an ͑r͒ data when using Eq. ͑1͒ and Eq. ͑2͒ is indicated by an ͑r͒ error1 and an ͑r͒ error2 , respectively. From the summary in the lower right of this table, it is apparent that an ͑r͒ extrapolation for r Ͻ r min is significantly better using Eq. ͑2͒. g L ͑r 2 ͒ = g L ͑r 1 ͒e ͑r 2 −r 1 ͒/͑r 3 −r 1 ͒͑ln͓g L ͑r 3 ͔͒−ln͓g L ͑r 1 ͔͒͒ for r 1 Ͻ r 2 Ͻ r 3 . ͑3͒

Source model
For example, if g L ͑r 1 ͒ = 1.000 and g L ͑r 3 ͒ = 0.800 where r 1 = 1 cm, r 2 = 1.5 cm, and r 3 = 2.0 cm, one may obtain g L ͑r 2 ͒ = 0.894 using Eq. ͑3͒. Appendix C 3 of the 2004 AAPM TG-43U1 report clearly specified an extrapolation method ͑nearest neighbor or zeroth order͒ for 1D dose rate distributions when r Ͻ r min for g͑r min ͒. 2 Due to the great variability in g͑r͒ based on choice of L and features of source construction, use of nearestneighbor or zeroth-order data is still recommended for extrapolation of g L ͑r͒ for r Ͻ r min . However, the g P ͑r͒ data should then be determined by applying the ratio of the pointand line-source geometry functions to g L ͑r͒ as previously explained.
The 2004 AAPM TG-43U1 report was not explicit for extrapolating beyond g͑r max ͒ where r Ͼ r max . 2 Consequently, we have revisited the g͑r͒ extrapolation methodology, and considered a variety of fitting functions such as the biexponential fit as suggested by Furhang and Anderson. 14 The AAPM now recommends adoption of a single exponential function based on fitting g L ͑r͒ data points for the largest two consensus r values in a similar vein as Eq. ͑3͒. Specifically, a log-linear extrapolation as illustrated in Eq. ͑4͒ may be used to solve for g L ͑r 3 ͒ where r 2 = r max , r 1 Ͻ r 2 Ͻ r 3 , and given g L ͑r 1 ͒ and g L ͑r 2 ͒.
For example, if g L ͑r 1 ͒ = 0.510 and g L ͑r 2 ͒ = 0.391 where r 1 = 4 cm, r 2 = 5 cm, and r 3 = 6 cm, one may obtain g L ͑r 3 ͒ = 0.300 using Eq. ͑4͒. Using g L ͑r max ͒ as a test for extrapolating g L ͑r͒ data for the sources included in this report, the single exponential function extrapolation technique reduces g L ͑r͒ extrapolation errors by over 40% as compared to zeroth-order extrapolation, with negligible differences in comparison to more complex fits such as a three-point linear regression. Therefore, the AAPM recommends that treatment planning software manufacturers no longer employ a zerothorder approach for determining g L ͑r͒ extrapolated values beyond g L ͑r max ͒, and that they immediately use a single exponential fit to extrapolate g L ͑r͒ values based on the furthest two consensus data points. Following this guidance, Table II includes g L ͑r͒ and g P ͑r͒ extrapolated beyond r max for the sources included in this report.
To provide practical data for treatment planning quality assurance that typically uses g P ͑r͒ instead of g L ͑r͒, values in Table XI include extrapolated an ͑r͒ or g P ͑r͒ data. These latter data were converted from extrapolated g L ͑r͒ data since g P ͑r͒ changes more rapidly and may be derived from g L ͑r͒ using the ratio of the point-and line-source geometry functions. It is also noteworthy to point out that these interpolation and extrapolation techniques may be extended to the dosimetry parameters in the 2004 AAPM TG-43U1 report or other brachytherapy sources in general.

IV. SUMMARY
As stated in the AAPM TG-43U1 report, the AAPM recommends that the revised dose-calculation protocol and revised source-specific dose-rate distributions be adopted by all end users for clinical treatment planning of low-energy brachytherapy using interstitial sources. Depending upon the dose-calculation protocol and parameters currently used by individual physicists, adoption of this protocol may result in changes to patient dose calculations. These changes should be carefully evaluated and reviewed with the radiation oncologist preceding implementation of the current protocol.

ACKNOWLEDGMENTS
The authors wish to thank Frank A. Ibbott for creation of the artwork in Fig. 1, which was supported by the AAPM Therapy Physics Committee ͑TPC͒. Also, we extend our appreciation to Sujat Suthankar of Rosses Medical Systems ͑now at Implant Sciences͒ for discussions on Sec. III. Furthermore, we thank Janelle A. Molloy for AAPM TPC review and Zuofeng Li, Ning J. Yue, and Bruce Thomadsen of the AAPM BTSC for their constructive comments and careful review of this report. We also wish to thank David W. O.  17 Experimental results were obtained using TLD-100 chip dosimeters ͑Harshaw/Bicron of Solon, OH͒ in a SolidWater™ phantom. The calibration of the TLD chips was performed using a 6 MV beam and an energy correction factor of 1.4 was used. Correction from SolidWater™ to water was done with a factor of 1.05 borrowed from Williamson. 18 The standard deviation from 16 chips was 5%. These measurements in SolidWater™ were compared with measurements by Meigooni et al. in SolidWater™. 16

6733 Λ
Values for the Monte Carlo dose rate constant were obtained at a point on the transverse plane in both liquid water and SolidWater™. Using the liquid water results, MC ⌳ = 0.99 cGy h −1 U −1 . The air-kerma strength was measured at NIST in Spring 2001 with EXP ⌳ measured in SolidWater™ using TLDs. After correction to liquid water, the value of EXP ⌳ was 0.97 cGy h −1 U −1 . Averaging these values gives a CON ⌳ = 0.98 cGy h −1 U −1 as in Table I.

6733 g"r…
The Monte Carlo and measured values for r ജ 1 cm for the radial dose function agree within 5%, which is within the experimental uncertainties. Therefore, Table II shows CON g͑r͒ as taken from the Monte Carlo data set in liquid water.

6733 F"r , …
Experimental and Monte Carlo results agree within 5% for angles greater than 20°. The experimental and Monte Carlo results agree within 5% for distances 5 cm or greater, but have greater differences at 0°for a distance of 2 cm because of uncertainties in the TLD measurement. Table III  presents  The model LS-1 features a two-bead geometry and unique laser weld about the center of the 4.4-mm-long and 0.8-mm-diam seed. 125 I is uniformly impregnated in 0.5 mm diameter ceramic ͑alumina-silicate͒ beads, separated by a 2.97-mm-long Pt/ Ir radio-opaque marker ͑Fig. 1͒. A medial Ti spacer is included to center the x-ray marker and provide a surface for the central weld of the two end capsules, which have a wall thickness of 0.05 mm. There are four peerreviewed papers that assess the 2D dosimetry parameters of the BrachySeed™ model LS-1, and a fifth publication describes a consensus dataset methodology using the Brachy-Seed™ publications as examples.
Nath and Yue measured 2D brachytherapy dosimetry parameters in a water-equivalent phantom using 1 mm 3 TLD rods and TLD-specific calibration factors. 19 A SolidWater™ to liquid water correction factor of 1.043 obtained by Williamson 18 and a TLD energy dependence correction of 1.41 published by Meigooni et al. 20 were used to calculate ⌳. On the transverse plane, radial distances are listed for a range of 0.5-7 cm, and 2D measurements are reported between 1 and 6 cm. A correction was made to account for the 1999 NIST WAFAC anomaly, which impacted measurements of ⌳ by +6.8%. Towards the calculation of 2D dose distributions, results were presented for both a line source model ͑L eff = 4.1 mm͒ and a two-point source model ͑separation = 3.6 mm͒.
Chan and Prestwich measured and calculated dosimetry parameters for the model LS-1 source. 21 Measurements were performed using GafChromic MD-55-2 film, which is currently not a well-established method for determining singleseed brachytherapy dose distributions, and the data were not included in the consensus. Chan and Prestwich used the Integrated Tiger Series CYLTRAN ͑version 3.0͒ with photon cross sections published by NIST 17 to perform Monte Carlo photon transport simulations. The CYLTRAN code has been benchmarked using the MED3631-A/M 125 I source. The authors state that the source geometry was modeled exactly with the exception of the capsule ends, which were given a flat thickness of 60 m instead of modeling a spherical shell with thickness 65 m. s K was estimated using a cylindrical volume of air and a 5 keV photon energy cutoff to simulate the NIST WAFAC. Material densities and compositions were not explicitly stated, and the calculation geometry was described as a series of concentric cylinders. A two-point source model with 3.6 mm separation was employed for reconstructing 2D brachytherapy dose distributions. The number of particle histories was chosen to ensure that 1 standard uncertainty about the mean was less than 1%.
Williamson 22 published calculated single-seed brachytherapy dosimetry parameters for the model LS-1 125 I seed using the PTRAN code ͑PTRANគCCG, version 7.43͒, the DLC-146 photon cross-section library, and the mass-energy absorption coefficients of Hubbell and Seltzer. 17 The collision kerma rate at a given geometric location was calculated using the bounded next flight estimator, and for distances less than 3 mm, a once-more collided flux point-estimator was employed. Results for g͑r͒ were evaluated over 0.1-14 cm in radial distance. F͑r , ͒ was evaluated from 0.25 to 10 cm in distance range and over 0°ഛ ഛ 180°at 34 angular increments with a maximum 5°spacing, although, data were presented graphically. Towards calculation of ⌳, S K was estimated by simulating the measurement geometry of the NIST WAFAC. Ti characteristic x-ray production was suppressed in the PTRAN code to simulate the function of the aluminum filter in the NIST WAFAC. Three geometry functions were included in the 2D dosimetry calculations: a point source model, a two-point source model ͑separation = 3.6 mm͒, and a line source model of length 7.2 mm. Additional simulations were performed to assess the variation of g͑r͒ with respect to internal motion of the active beads. The number of starting particles was chosen to provide statistical standard errors of the mean between 0.2% and 2%.
For the BrachySeed™ model LS-1 125 I source, Wang and Sloboda 23 calculated the 2D dosimetry parameters using EGS4 and an associated user code, DOSCGC. A track-length estimator was used to score photon energy fluence and then combined with appropriate mass-energy absorption coefficients from Hubbell and Seltzer to estimate absorbed dose. Furthermore, the EGS4/DOSCGC code was verified by the authors using the model 6702 and 6711 125 I brachytherapy seeds, among other radiation sources. As EGS4 does not simulate the production of characteristic x rays, three methods were used to model characteristic x-ray production from the Ag doped into the ceramic beads. Published results of Wang and Sloboda include the method that simulates characteristic x-ray production by determining the probability of interaction between the principal 125 I photons and Ag. 23 Results were evaluated between 0.1 and 14 cm of radial distance for g͑r͒ and over 0.25-10 cm for F͑r , ͒ using a spherical coordinate geometry. Ti characteristic x-ray contributions were removed to simulate NIST WAFAC measurement. Assuming a source separation of 3.6 mm, a doublepoint model was used in the reconstruction of the 2D dose distributions.
Chan, Nath, and Williamson 24 published a methodology for constructing consensus reference dosimetry parameters for a single brachytherapy source, and used the four aforementioned BrachySeed™ publications as an example. Additionally, Chan, Nath, and Williamson included minor corrections or clarifications of results published by Chan and Prestwich and by Williamson, 22 and a detailed table of Williamson's F͑r , ͒ data is included, which was not present in the original publication. The recommended consensus values in Chan and co-workers 24 are similar to those published here, with specific differences listed below. However, the 1D dose rate per unit air-kerma strength values published in Table IV of Chan et al. are not in agreement with the recommended dosimetry data of Chan et al. 24 For example, a value of 0.9673 cGy h −1 · U −1 is published for 1 cm, while a value of 0.9594 cGy h −1 · U −1 is expected ͑ CON ⌳ = 0.972 cGy h −1 · U −1 ; an ͑r͒ = 0.987; and, g P ͑r͒ =1͒. Because of this discrepancy and because Chan et al. do not describe how the values were generated, use of the 1D dose rate per unit air-kerma strength values in Table IV of Chan et al. 24 to validate the entry of consensus dosimetry data into a given treatment planning system is not recommended.

LS-1 g"r…
The Monte Carlo results of Williamson 22 and of Wang and Sloboda 23 covered the largest radial distance range and came closest to the source. After both datasets were converted to a common effective length of 4.1 mm, agreement in g L ͑r͒ between the two reports was Ͻ2% within 5 cm, increases to 6% at 10 cm, and is 10% at 14 cm. Because the Williamson 22 result included greater sampling at large radial distances, the g͑r͒ results generated using PTRAN are recommended for CON g͑r͒ data ͑Table II͒. Note that the experimental data of Nath and Yue 19 and the Monte Carlo result of Chan and Prestwich, 21 corrected to L eff = 4.1 mm, were also in good agreement, often within 5%. The publication by Williamson 22 contains a rounding error in its Table III, where the g͑r͒ values listed at 0.8 cm were actually calculated for a radial distance of 0.75 cm. 25 This error was corrected in Chan, Nath, and Williamson 24 by publishing data at a radial distance of 0.8 cm, although, Chan et al. do not acknowledge the error or publication of new data. The corrected value for 0.75 cm is included in CON g͑r͒.

LS-1 F"r , …
Monte Carlo results of Williamson, 22 published in Chan, Nath, and Williamson 24 were chosen to be the consensus F͑r , ͒ dataset because they featured finer radial distance range resolution below 2 cm and higher angular resolution near = 0°and = 90°compared to that of Wang and Sloboda. 23 The data were compared with Monte Carlo results by Chan and Prestwich, 21 and with TLD results by Nath and Yue 19 at common radial distances of 1, 2, and 5 cm. Over these radii, the Chan and Prestwich 21 results agreed with Williamson's 22 data within ±2% ͓maximum was −8.5% at F͑5,0°͔͒. Nath and Yue results were generally +6% in comparison to those by Williamson, 22 with a maximum difference of +11.5% at ͑5,50°͒.
Towards derivation of CON F͑r , ͒, Williamson's 22 highangular resolution data were condensed using the recommendations of TG-43U1 ͑Sec. V Part B.4͒ to simplify entry into treatment planning systems, and results taken directly from Chan, Nath, and Williamson 24 in Table IV are presented us-ing a 10°sampling space. Calculation of an ͑r͒ using the condensed CON F͑r , ͒ data yields results within 0.1% of Williamson's, 22 except at 0.25 cm where the discrepancy is −1.3%; thus the an ͑r͒ data from Williamson in Chan and co-workers 24 are used herein.

C. Implant Sciences model 3500 125 I source
The model 3500 I-Plant™ source was first marketed in August 2000 and is notable for a novel manufacturing process involving ion implantation with 124 Xe. The outer surface of a 0.64-mm-diam quartz tube is coated with a 16 m layer of silicon into which approximately 10 17 124 Xe ions are implanted. A 5-m-thick layer of SiO 2 is then applied as an overcoat to contain the xenon and later the radioactive 125 I. These nonradioactive-doped quartz tubes are then stored until 125 I seeds are needed. At that time, the 125 Xe is neutron activated to 125 I, and the assembly, consisting of the quartz tube and a conical ended silver radiographic marker inside the tube, is sealed in a laser-welded titanium capsule. Fig. 1 illustrates the assembled source. The wall thickness of the 0.8-mm-diam titanium capsule is 0.05 mm, and the end welds are 0.25 mm thick. The overall seed length is 4.5 mm, and the effective active source length, L eff , is taken as the length of the glass tube, 3.76 mm.
Four published papers were reviewed to determine the full consensus dataset for the model 3500 I-Plant™ source. Duggan and Johnson 26 measured dosimetry parameters using LiF TLD rods in SolidWater™ for dose rate constant measurements and in PlasticWater™ ͑CIRS PW2030͒ for radial dose function and anisotropy measurements. The TLDs were calibrated against 60 Co, and the distance-dependent phantom to water correction was calculated from the MCNP4B Monte Carlo code based on the NIST measured photon spectrum of the model 3500 source. The PlasticWater™ to liquid water correction varied from 0.99 at 0.5 cm to 1.07 at 7 cm. Three separate measurements of the dose rate constant, each measurement based on six TLD rods, were made, but the actual determination was by cross calibration relative to Accredited Dosimetry Calibration Laboratory ͑ADCL͒ calibrated Amersham model 6711 seeds. Radial dose function measurements were made at 0.5 cm increments from 0.5 to 5.0 cm and at 6.0 and 7.0 cm. Anisotropy was measured at 9 or 10 angles in a given quadrant at distances from 1 -4 cm in 0.5 cm increments and at 5, 6, and 7 cm. Wallace 27 also determined dosimetry parameters, and used LiF TLD rods in plastic water phantoms ͑CIRS PW2030͒ measuring 30ϫ 30ϫ 7 cm 3 . The TLDs were calibrated against 60 Co, and corrections for the plastic phantom, finite TLD volume, and energy response were applied to the TLD readings. Twelve evaluations of the dose rate constant, each based on ten TLD rods at 1 cm from one of two seeds with NIST traceable calibrations, were made with an estimated net uncertainty of 6% ͑k =2͒. Wallace measured the radial dose function at 0.5 cm increments from 0.5 to 6.0 cm and at 1.0 cm increments from 7.0 to 10.0 cm plus some intermediate distances. 27 Two-dimensional anisotropy was measured in 10°increments from 0°to 90°at distances from 1 to 6 cm in 1.0 cm increments and at 0.5, 0.75, and 1.5 cm. With at most 3.5 cm of top/bottom scattering material, these results may be lower than expected values by at least a few percent due to differences from an infinite scattering environment. Therefore, these data are not recommended.
Two papers reported Monte Carlo calculated dosimetry parameters for this source. Rivard 28 also used the MCNP4B software and photon and electron cross sections from the supplied DLC-189 library with the source in a 30-cm-diam phantom. Dose rates were calculated from the MCNP pulse height tally, and the dose rates extrapolated to zero distance ͑to remove effects of air attenuation͒ after subtraction of titanium fluorescent x-ray contributions to calculate the dose rate constant. Each calculation of ⌳, g͑r͒, and F͑r , ͒ involved 2 ϫ 10 9 photon histories. The radial dose function was calculated at distances from 0.05 to 10 cm with a standard deviation typically less than 0.3%. Two-dimensional anisotropy function was reported in 5°increments from 0°to 90°a t distances from 0.05 to 10 cm. The statistical uncertainty in these calculations was angle dependent, ranging from Ͻ0.3% at 90°to 3% at 0°.
While the Monte Carlo calculations by Duggan 29 also used MCNP to calculate the radial dose function of the model 3500 source, the impact of using versions 4C2 and 5 was examined. The latter version includes completely revised low-energy photon cross-section data. Each simulation consisted of four-batches of 3 ϫ 10 8 histories. Using an effective source length, L = 4 mm, the radial dose function was calculated at distances from 0.25 to 10 cm with a standard deviation ഛ0.3% in the range 0.5-8 cm.

3500 Λ
Because Duggan and Johnson 26 used a relative methodology comparing the air-kerma strength adjusted dose rates of the model 3500 with that of a measured Amersham model 6711 source, their value of ⌳ was not included in the average of EXP ⌳. The Wallace 27 value of the dose rate constant in water, 1.01± 0.005 cGy h −1 U −1 , was taken as EXP ⌳. The MCNP derived value of the dose rate constant from Rivard 28 of 1.017± 0.04 cGy h −1 U −1 , obtained by extrapolating to zero distance on the transverse plane, was taken as MC ⌳. Averaging these two values gives a CON ⌳ of 1.014 cGy h −1 U −1 as in Table I.

3500 g"r…
The Monte Carlo values of g͑r͒ from Duggan 29 in the range 0.5-10 cm were converted to L eff = 3.76 mm and are listed as CON ⌳g͑r͒ in Table II. These values were chosen because the updated low-energy photon cross sections used by Duggan 29 are considered more accurate than those used by Rivard, 28 particularly at greater distances. Values at r Ͻ 0.5 cm from the source, where differences in the photoelectric interaction cross sections are less important, are taken from Rivard. 28

3500 F"r , …
Comparing F͑r , ͒ at the common radial distances of 1, 2, and 5 cm, the average pair wise difference between the three published values is less than 6%. The maximum difference is 24.8% between the Monte Carlo results and Wallace's 27 values at F͑1,10°͒. The maximum difference between the two TLD studies is 14.5% at F͑5,20°͒. Because the MCNPderived values of F͑r , ͒ from Rivard 28 are of finer angular resolution and finer distance resolution less than 2 cm from the source than those of the TLD based measurements, 26,27 these are chosen as CON F͑r , ͒ in Table V.

D. IBt model 1251L 125 I source
A double walled encapsulated source of radioactive 125 I was developed in 2000 for interstitial brachytherapy by International Brachytherapy ͑IBt, SA Zone Industrielle C, Seneffe, Belgium 7180͒. The source is marketed as InterSource 125 model 1251L and is composed of two concentric titanium tubes of 0.04 mm wall thickness, laser welded at the edges ͑Fig. 1͒. The capsule diameter is 0.8 mm, and capsule length is 4.5 mm. An x-ray marker composed of 0.045-mm-thick 90% platinum/10% iridium alloy is attached to the inner tube. The radioactive iodine is deposited on the inner tube in three printed bands. The distance between the outermost edges of the bands of activity is 3.7 mm. The sources are available with air-kerma strengths between 0.254 U and 1.27 U. The source strength is determined by comparison to the NIST WAFAC standard, developed in 1999 and revised in 2000. The lack of silver in this design results in dosimetric characteristics that are very different from those of the Amersham model 6711 seed, and similar designs that incorporate silver. Instead, the dosimetry data are more consistent with those of the Amersham model 6702 seed, which likewise did not incorporate silver. 2 Dosimetry characteristics have been reported for this source model by Reniers, Vynckier, and Scalliet 30,31 and by Meigooni et al. 32 Both reports were based on the revised 1999 NIST standard. Both authors performed measurements in a solid water-equivalent phantom with 1 mm 3 LiF thermoluminescent dosimeters. Reniers et al. used material identified as "WT1" without further description. Meigooni used SolidWater™. The TLDs were calibrated in a 6 MV accelerator beam by both authors. Reniers used an energy correction factor of 1.41 while Meigooni et al. reported using a value of 1.4. Neither author adjusted the energy conversion factor with distance from the source. Reniers, Vynckier, and Scalliet 30 performed Monte Carlo calculations using the MCNP4B code, with antiquated photoelectric cross-section libraries. Those calculations were later updated by Reniers, Vynckier, and Scalliet 31 using the more recent cross-section data from EPDL97 and from XCOM. Meigooni used PTRAN v.6.3 Monte Carlo code with the DLC-99 crosssection libraries. 32 Both authors performed calculations to estimate the dose in water-equivalent plastic for comparison with measurements. Additional calculations were performed with liquid water as the medium.

1251L Λ
Reniers, Vynckier, and Scalliet 30 measured a dose rate constant in WT1 of 1.03± 0.07 cGy h −1 U −1 , and calculated a corresponding value of 0.98± 0.01 cGy h −1 U −1 ͑where the uncertainty of the Monte Carlo calculations is a reflection of the statistical uncertainty only͒. They then calculated the dose rate constant in water to be 1.02± 0.01 cGy h −1 U −1 , obtained at a distance of 5 cm on the transverse plane. Reniers and co-workers used the ratio of calculated values to determine a correction factor for WT1. 30 They reported a value of 1.031, although the ratio is in fact 1.041. The plastic-to-water correction factor was then applied to the TLD measurements to estimate a measured value of dose rate constant in water of 1.072 cGy h −1 U −1 , although Reniers and co-workers reported this value to be 1.05± 0.07 cGy h −1 U −1 . 30 Meigooni et al. reported a measured dose rate constant in SolidWater™ of 1.014± 0.08 cGy h −1 U −1 . 32 They also calculated a value of 0.981± 0.03 cGy h −1 U −1 , obtained at 5 cm by extrapolating to 1 cm on the transverse-plane. The calculated dose rate constant in water medium was 1.013± 0.03 cGy h −1 U −1 . Calculated dose rate constants from Meigooni et al. can be used to determine a correction factor for SolidWater™ of 1.033, leading to an estimated measured value in liquid water of 1.047 cGy h −1 U −1 , although Meigooni et al. did not report this value. 32 Measured and calculated values from both publications have been averaged to yield CON ⌳ = 1.038 cGy h −1 U −1 .

1251L g"r…
All three publications 30-32 considered the active length of the source to be the distance between the outermost edges of the bands of activity, or 3.7 mm. Recently, the AAPM recommended a value of 4.35 mm, 6 which has been used here to assure consistency among data sets. The data from Meigooni et al. 32 Table II.

1251L F"r , …
Reniers and co-workers 30 and Meigooni et al. 32 performed measurements and calculations of anisotropy function. Measurements by Reniers and co-workers 30 were made in WT1 at 2, 3, and 5 cm, at increments of 10°around the source, and corresponding calculations were performed for comparison. Calculations were performed in liquid water medium at 0.5, 1, 2, 3, and 5 cm from the source, at increments of 5°. TLD measurements of anisotropy by Meigooni et al. 32 were made in SolidWater™ at 2, 3, 5, and 7 cm, with 10°increments, and calculations were made at 2, 3, and 5 cm for comparison. Meigooni et al. also performed calculations in liquid water medium from 1 to 7 cm from the source in 1 cm increments and from 0°to 90°and with 10°increments. Monte Carlo calculations from Reniers and co-workers, 30 reprocessed using L eff = 4.35 mm, were chosen for CON F͑r , ͒ ͑Table VI͒ because of their consistency with measurements from Meigooni et al. 32 and Reniers and co-workers. 30 Monte Carlo calculations by Meigooni et al. 32 show nonphysical excursions at = 0°, and values considerably greater than unity at angles close to 90°.

E. IsoAid model IAI-125A 125 I source
The IsoAid ADVANTAGE™ 125 I model IAI-125A source was introduced in the North American market in 2002. The model consists of a cylindrical silver core, 3 mm long and 0.5 mm in diameter, onto which 125 I has been uniformly adsorbed as a 1-m-thick coating of silver halide. The silver core is sealed within cylindrical titanium housing with a physical length of 4.5 mm and outer diameter of 0.8 mm ͑Fig. 1͒. The cylindrical portion of the titanium housing is 0.05 mm thick, with rounded titanium welds at each end. There are two published papers for this model; both of these papers report values for all the TG-43 parameters. [34][35][36] In 2002, Meigooni et al. published the results of both TLD measurements and Monte Carlo simulations of the dosimetric characteristics of the model IAI-125A source. 34,35 The measurements were performed in a SolidWater™ phantom of dimension ͑25ϫ 25ϫ 20 cm 3 ͒, machined precisely to accept LiF TLD-100 chips of dimensions ͑3.1ϫ 3.1 ϫ 0.8 mm 3 ͒ and ͑1.0ϫ 1.0ϫ 1.0mm 3 ͒. An energy response correction factor between the 6 MV calibration energy and 125 I of 1.4 was used. 37 Nonlinearity correction of the TLD response for the given dose was included. Monte Carlo simulations utilized the PTRAN code in both SolidWater™ and water. Although unspecified, it was learned that the DLC-99 photon cross section library was employed. Simulation data from 1.375ϫ 10 6 histories ͑divided into 55 batches͒ were combined using a distance and attenuation-average bounded next flight point kerma estimator. 38 This resulted in standard errors about the mean ranging from 1.5% ͑near the source: r Ͻ 3 cm͒ to 5-6% ͑far from the source: r Ͼ 5 cm͒. s K was determined by calculating the air-kerma rate at a distance of 5 cm and subsequently correcting for inverse square law to 1 cm. The titanium characteristic x-ray production was suppressed for the simulations of air-kerma rate in air.
Solberg et al. 36 published the results of Monte Carlo calculations and TLD measurements on the model IAI-125A source in 2002. The measurements were performed in a Plastic Water® phantom ͑model PW2030, Computerized Imaging References Systems of Norfolk, Virginia͒ of dimensions ͑30ϫ 30ϫ 7 cm 3 ͒, machined precisely to accept LiF TLD-100 rods of dimensions 6 mm long and 1 mm diameter. A correction factor of 0.995, calculated for the phantom mate-rial at 1 cm, was applied to TLD responses to arrive at the dose rate constant in water. The IAI-125A source, used for measurements, had a direct traceability to NIST ͑1999 stan-dard͒. Total combined uncertainty of dose rate constant measurement was estimated at 4.8%. The component uncertainties that contribute to the combined uncertainty are an assumed uncertainty of 0.5% for the air-kerma strength S K , statistical uncertainty in the TLD responses of 4-5%, uncertainty in the TLD energy correction factor of 1-2%, and a phantom correction of 2%. These uncertainties were added in quadrature to arrive at the combined estimated uncertainty of 4.8%. The radial dose function had a quoted uncertainty of 7-8% at the 95% confidence level and the net uncertainty of the anisotropy data was quoted at 10% which results from statistical uncertainty of the measurements of TLD responses. As above for the model 3500 125 I source for consistency, these data were excluded due to lack of sufficient backscattering material and these data are not recommended. Monte Carlo simulations utilized the MCNP4C in liquid water. The photoelectric cross section data were taken from XCOM tabulations of Berger and Hubbell. 39 The 125 I spectrum used for all calculations consisted of five energies which were similar to those recommended in AAPM TG-43U1. 2 Dose rate was determined at 1 cm in a cylindrical annulus 0.05 cm thickϫ 0.05 cm deep. The MCNP * F4 tally was used to score the energy fluence in the cylindrical annulus; the energy fluence was converted to dose rate using mass-energy absorption coefficients obtained from Seltzer. 40 Air-kerma strength was scored in vacuum in a similar cylindrical geometry 0.2 cm thickϫ 0.2 cm deep at a radial distance of 50 cm from the center of the source. For TLD measurements, the geometry function was calculated using the AAPM TG-43 approximation for a line source; for Monte Carlo calculations, MCNP was used to determine the particle streaming function. 10 36 Here, air-kerma strength was determined at 50 cm on the transverse plane with vacuum between the source and tally region. Consequently, MC ⌳ = 0.971 cGy h −1 · U −1 was obtained as an average of these two results, and CON ⌳ = 0.981 cGy h −1 · U −1 as shown in Table I.

IsoAid IAI-125A g"r…
Both Meigooni et al. 34 and Solberg et al. 36 obtained g L ͑r͒ data using measurements and calculations. The ratio of Mei-gooni et al. corrected measurements and calculations for liquid water from r = 0.5 to 6.0 cm was typically 0.95, and ranged from 0.99 at 0.5 cm to 0.87 at 5.0 cm. Over the same radial range, the ratios were typically 0.98 for Solberg et al., 36 and ranged from 0.96 at 3.0 cm and 1.02 at 6.0 cm. Comparisons of Monte Carlo results by Meigooni et al. 34 and Solberg et al. 36 gave an average ratio of 1.06 from 0.5 to 6.0 cm, ranging from 0.97 at 0.5 cm and 1.12 at 4.0 cm. Comparisons of TLD results by Meigooni et al. 34 and Solberg et al. 36 gave an average ratio of 0.98 over the same radial range, and ranged from 1.03 at 1.5 and 0.93 at 5.0 cm. Based on this analysis, there was good agreement among the calculations of Solberg et al., 36 measurements by Solberg et al., 36 and measurements by Meigooni et al. 34 Thus, the Monte Carlo results of g L ͑r͒ directly from the publication by Solberg et al. 36 were chosen as the consensus data set and listed in Table II, with italicized data indicating data from Meigooni et al. 34 to expand the radial range.

IsoAid IAI-125A F"r , …
Meigooni et al. 34 calculated results using an end weld thickness of 0.1 mm, while Solberg et al. 36 calculated using 0.25 mm. Thus, it was expected that the anisotropy along the long axis would be larger as calculated by Solberg et al. 36 in comparison to Meigooni et al. 34 Solberg et al. 36 also explicitly mentioned that the source geometry was per manufacturer provided specifications. Finally, results of Meigooni et al. 34 exhibited nonphysical behavior of anisotropy along the long axis to generally decrease with increasing distance. This should not be expected due to increased scatter for increasing distances that would tend to reduce the effects of anisotropy. Thus, the Monte Carlo results of Solberg et al. 36 are recommended as the CON F͑r , ͒ as in Table VII.

F. Mills Biopharmaceuticals Corporation model SL-125/SH-125 125 I source
Mills Biopharmaceuticals originally introduced the model SL-125 ͑ProstaSeed®͒ 125 I source in 1999 and was acquired by Mentor Corporation in early 2003. The source is encapsulated in a 0.05-mm-thick Ti tube with a measured external length of 4.5 mm, an average measured outer diameter of 0.8 mm, and an end-weld thickness of 0.3 mm ͑Fig. 1͒. Internal source components include five 0.50-mm-diam silver spheres upon which a mixture containing radioactive iodine is adsorbed, similar to the process employed in production of the Amersham model 6711 seed. The deposition of radioactive iodine is nominally within several micrometers of the surface of the Ag sphere. Two published papers were reviewed to determine the full consensus dataset for the Pros-taSeed®. Wallace presents comprehensive experimental measurements using lithium fluoride TLD 100 rods in PW2030 plastic water. 44 Li has published Monte Carlo calculations using version 7.3 of the PTRAN Monte Carlo code and the DLC-99 photon cross-section library for a 30ϫ 30 ϫ 30 cm 3 liquid water phantom. 45

SL-125/SH-125 Λ
Wallace determined EXP ⌳ using two calibration methods: 44 a 60 Co standard with corrections for photon energy response 46 and a cross calibration using NIST-traceable Amersham model 6711 and 6702 125 I seeds. Due to the relative methodology employed, the cross-calibration results were not included in EXP ⌳. In addition, TLD measurements of ⌳ utilized S K,N99 and were subject to the 1999 WAFAC anomaly. Thus, a +3.1% correction was applied to give EXP ⌳ = 0.9805 cGy h −1 U −1 . Phantom correction factors were taken from an unpublished manuscript by Wallace. However, Wallace specified that correction factors varied between 1.002 at 0.5 cm and 0.99 at 10 cm and were 0.995 at 1 cm. Li's calculation of MC ⌳ employed the once more collided flux estimator for points adjacent to the seed ͑Ͻ5 mm͒ and the bounded next flight dose estimator for points beyond 5 mm. 45 In combination with the number of photon histories simulated, these estimators resulted in statistical uncertainties ͑1 ͒ within 1.3% for all calculation points and distances. For CON ⌳, Wallace's 44 measured value ͑multiplied by 1.031 to reflect the 1999 WAFAC measurement anomaly͒ was averaged with Li's 45 Monte Carlo estimate, yielding the 0.953 cGy h −1 U −1 value given in Table I. These two values agreed within 6%.

SL-125/SH-125 g"r…
Because Wallace 44 used a five-point geometry function and Li 45 employed the maximum extent of the radioactivity ͑0.29 cm͒ assuming 0.1 cm spacing between the pellets, g L ͑r͒ results for both studies were recalculated using L eff = 3.0 mm according to Eq. ͑5͒ of the AAPM TG-43U1 report. Except for r Ͻ 0.5 cm, good agreement with measured results by Wallace 44 is achieved between 0.5 and 7 cm, yielding maximum and minimum ratios of 1.13 and 0.90 at 4.0 and 7.0 cm, respectively. Due to the influence of volumeaveraging effects at short distances, the g͑r͒ Monte Carlo data of Li 45 are recommended as consensus data ͑Table II͒.

SL-125/SH-125 F"r , …
After conversion to a common L eff , the Li F͑r , ͒ Monte Carlo data 45 were compared to the Wallace measured data. 44 Good agreement of F͑r , ͒ between Monte Carlo results and measured results for radial distances of 1, 2, 3, 4, and 5 cm is observed, often within 6%. The Li 45 data covered the distance range from 1 to 5.0 cm and were smooth and continuous in comparison to the measured result. Furthermore, the measured F͑r , ͒ data exhibited a different trend near the transverse plane in comparison to the calculated result, e.g., average differences of 6%, 8%, and 7% at 60°, 70°, and 80°, respectively. Thus, the Monte Carlo data of Li 45 are recommended as the consensus data set ͑Table VIII͒.

G. Source Tech Medical model STM1251 125 I source
The Model STM1251 125 I interstitial source was introduced to the market in 2002 by Source Tech Medical, who manufactured and marketed the source under the trade name " 125 Implant Seed." In 2003, C.R. Bard acquired the assets of Source Tech Medical and now markets the source. The model STM1251 source core ͑see Fig. 1͒ consists of a right circular cylinder of aluminum ͑0.51 mm diameter by 3.81 mm long͒ in which a 0.36-mm-diam gold radiographic marker is embedded. The aluminum cylinder is coated with 2-m-thick inner and outer layers of nickel and copper, respectively, upon which a very thin ͑17 nm͒ layer of radioactive and cold iodine is deposited. The core is encapsulated in a titanium shell that is somewhat thicker than usual ͑0.08 mm radial thickness͒ but with very thin 0.13-mm-thick end caps. The external dimensions of the source are similar to those of other seeds.
The first published paper on model STM1251 dosimetry is a complete Monte Carlo study by Kirov and Williamson 47,48 in 2001 based upon the photon-transport code, PTRANគCCG ͑version 7.44͒ using the DLC146 photon cross-section library and the corresponding mass-energy absorption coefficients. 17 The model was placed at the center of a 30-cm-diam liquid-water sphere and the radial dose function calculated over the 0.1-14 cm distance range. The 2D anisotropy functions were calculated over the 0.25-7 cm distance at 1°-5°angular intervals. The dose-rate constant was calculated using both extrapolation from transverseplane point kerma-rate estimates ͑⌳ extr ͒ and explicit simulation of the WAFAC standard ͑⌳ WFC ͒ to estimate the airkerma strength/contained activity ratio. Two experimental dosimetry studies, utilizing TLD-100 dosimeters in SolidWa-ter™ phantom material, were subsequently published. 49,50 The Li and Williamson study 49 was based upon three seeds calibrated against the S K,N99 standard ͑as revised in 2000͒ by an ADCL. The study was limited to the transverse plane, and the PTRAN calculational model used by Kirov and Williamson 47 was used to derive SolidWater™-to-liquid water corrections based upon the vendor's estimate of SolidWa-ter™ composition. A standard distance-independent relative energy response correction of 1.41 was used. The TLD investigation of Chiu-Tsao et al. 50 included 2D anisotropy function measurements at 1, 2, 3, and 5 cm distances as well as partial measurements at 0.5 and 1.5 cm. Using the same Monte Carlo simulation approach as Kirov and Williamson, 47 the relative energy response function, E͑r͒, was calculated for the transverse axis measurement positions based upon the measured chemical composition of their SolidWater™ phantom ͑which had a calcium content about 10% lower than the vendor's specified concentration͒. The dependence of E͑r͒ on polar angle was not investigated. Eight seeds, calibrated against the S K,N99 standard ͑as revised in 2000͒, were used to measure the dose-rate constant. For r = 1 cm detector locations, 28 TLD readings from eight seeds were obtained while 18 readings from three seeds were obtained at other distances.

STM1251 Λ
Li and Williamson reported a measured ⌳ in water of 1.039± 0.075 cGy h −1 U −1 excluding uncertainties associated with SolidWater™ composition. 49 Chiu-Tsao et al. reported a somewhat higher value of 1.07± 0.06 cGy h −1 U -1 although their uncertainty analysis did not appear to include uncertainties associated with E͑r͒. 50 Based on the PTRAN calculations, described above, Kirov and Williamson reported ⌳ extr and ⌳ WFC values of 1.041± 0.026 and 0.982± 0.025 cGy h −1 U −1 , respectively. 47,48 The discrepancy between the point-detector extrapolation and WAFAC simulation methods was attributed to the fact that the right cylindrically shaped core is coated with a radio-opaque layer upon which the radioactive material is deposited. Similar to the model 200 103 Pd and model 6711 125 I seeds, 2,51 this induces polar anisotropy near the transverse axis at typical calibration distances due to selfabsorption of radiation emitted by the radioactivity on the circular end surfaces of the core. Because the high atomic number Cu and Ni layers are so thin, they do not significantly attenuate 125 I x rays at short distances of 1 -3 cm. In support of this explanation, the authors demonstrate that inair profiles at 30 cm reveal "anisotropy overshoot" of 5% near the transverse axis. Polar dose profiles in medium also revealed subtle discontinuities that could be explained by screening of radioactivity on the core end surfaces. The error analysis by Kirov and Williamson included the influence of underlying cross-section uncertainties. To estimate a consensus dose-rate constant, CON ⌳, the two TLD measurements were averaged to yield EXP ⌳ = 1.055 cGy h −1 U −1 . This was averaged with the Monte Carlo estimate of ⌳ WFC , yielding CON ⌳ = 1.018 cGy h −1 U −1 .

STM1251 g"r…
All three studies 47-50 used a simple line source model with L = 3.81 mm to evaluate the geometry function, G L ͑r , ͒. Both Li and Williamson 49 and Chiu-Tsao et al. 50 corrected their TLD readings for the line-source geometry function and applied SolidWater™-to-liquid water corrections derived from PTRAN Monte Carlo calculations using the same geometric model of the seed. Li and Williamson 49 estimated g L ͑r͒ uncertainties to range from 3% to 10% while Chiu-Tsao et al. 50 claimed that g͑r͒ and F͑r , ͒ functions derived from TLD measurements had uncertainties of 2% at all distances. The Chiu-Tsao et al. 50 article also states that overall measurement uncertainty was 8% or less at all detector locations. Both reports 49,50 provided g L ͑r͒ at distances of 0.5-5 cm. A comparison of the three datasets reveals moderately good agreement between TLD measurements and the Monte Carlo calculations. At distances greater than 2 cm, Li and Williamson's 49 radial dose function is systematically more penetrating than that derived from the Monte Carlo calculations, by 5% at 2 cm to 13% at 5 cm. Li and Williamson 49 hypothesized that this discrepancy was due to errors in the solid-to-liquid correction function, which was based upon the vendor's specified composition which others have shown overestimates SolidWater™ calcium content. 52,53 Results by Chiu-Tsao et al. 50 for g L ͑r͒ are also larger than the Monte Carlo counterpart by 5%-6% in the 3 -5 cm distance range. However, Kirov and Williamson's 47,48 g L ͑r͒ function agrees with the consensus radial dose function for the model 6702 seed, 2 also based upon PTRAN Monte Carlo calculations, within 2%. This was an expected finding since there is no reason to believe that the STM1251 photon spectrum should significantly differ from that of the model 6702 seed. Thus Kirov and Williamson's Monte Carlo data are recommended for CON g͑r͒. 47

STM1251 F"r , …
A comparison of F͑r , ͒ data from Chiu-Tsao et al. 50 with the corrected Monte Carlo data published by Kirov and Williamson 48 shows excellent agreement ͑2%-5%͒ at all angles and distances except the longitudinal axis ͑ =0͒. The agreement is especially good at 1 cm, which is Chiu-Tsao et al.'s highest precision dataset. 50 The poor agreement ͑19%-46% differences͒ on the longitudinal axis may be due to the very large dose gradients in this region ͑30%-40% dose reduction in a 1°interval, corresponding to a 0.2-1 mm spatial increment depending on distance͒, which are caused by self-absorption of the primary photons emitted from the cylindrical surface of the core. The Monte Carlo simulation used a point-kerma estimator to score dose and is able to accurately resolve rapidly changing dose distributions. 38 However, TLD measurements from Chiu-Tsao et al. 50 were corrected for volume averaging only on the transverse axis, where gradients are much smaller. The TLD and Monte Carlo 1D anisotropy functions agree within experimental uncertainties. Thus the Monte Carlo data of Kirov and Williamson,48 were selected for CON F͑r , ͒.

H. Best Medical model 2335 103 Pd source
The model 2335 consists of 6 103 Pd-coated spherical polymer ͑composition by weight percent: C: 89.73%, H: 7.85%, O: 1.68%, and N: 0.74%͒ beads 0.56 mm in diameter, three on each side of a 1.2-mm-long tungsten x-ray marker, all contained within a double-wall titanium capsule of total thickness 0.08 mm. As shown in Fig. 1, the outside dimensions of the cylindrical capsule are 5 mm in length and 0.8 mm in diameter, where the rim of the outer capsule is laser welded to the wall of the inner capsule.
In 2001, Meigooni et al. published the results of both TLD measurements and Monte Carlo simulations of the dosimetric characteristics of the model 2335 source. 54 For the measurements, a total of 12 seeds from three-different batches were used to irradiate TLD chips ͑1.0ϫ 1.0 ϫ 1.0 mm 3 and 3.1ϫ 3.1ϫ 0.8 mm 3 ͒ placed in holes machined in SolidWater™ blocks 25ϫ 25ϫ 20 cm 3 . An energy response correction factor between the 6 MV calibration energy and 103 Pd of 1.4 was used. Monte Carlo simulations utilized the PTRAN v.6.3 code in both SolidWater™ and water. The DLC-99 photon cross section library, Hubbell and Seltzer mass-energy absorption coefficients, 17 and NCRP Report 58 primary photon spectrum ͑1985͒ were employed. Simulation data from 3 ϫ 10 6 histories ͑divided into 75 batches͒ were combined using a distance and attenuationaverage bounded next flight point kerma estimator. The airkerma rate, s K , was calculated at a distance of 5 cm and subsequently corrected for inverse square law to 1 cm.
In 2002, Peterson and Thomadsen published the results of TLD measurements on the model 2335 source. 53 The 103 Pd source was mounted in the center of a Virtual Water™ ͑MED-CAL, Inc.͒ phantom on a rotating insert, allowing the source to be positioned at any angle with respect to the TLDs. Six phantoms were constructed from pairs of 15.2 ϫ 15.2ϫ 5.0 cm 3 blocks ͑28 TLD holes per block͒ which could accommodate 12 TLD cubes 1.0ϫ 1.0ϫ 1.0 mm 3 ͑r ഛ 1 cm͒ and 16 TLD rods 1.0ϫ 1.0ϫ 3.0 mm 3 ͑r Ͼ 1 cm͒. Twenty three sources were used in 34 independent experiments, with a total of 28 TLDs for each run ͑two for each data point͒. Conversion factors from dose rate in SolidWater™-to-liquid water were obtained from Williamson. 55 One factor was used for each source-to-TLD distance, assumed to apply to Virtual Water due to the essentially identical chemical formulas of SolidWater™ and Virtual Water™. An energy response correction factor between the 60 Co ͑used for TLD calibration͒ and 103 Pd of 1.41 was used.

2335 Λ
Meigooni et al. 54 reported a TLD-measured value of ⌳ in SolidWater™ of 0.67± 0.054 cGy h −1 U −1 , as well as an estimated TLD value of ⌳ in water of 0.69± 0.055 cGy h −1 U −1 . The latter was obtained by multiplying the measured value of ⌳ in SolidWater™ by 1.031, the ratio of the calculated value of ⌳ in water, 0.67± 0.02 cGy h −1 U −1 , to the calculated value of ⌳ in SolidWater™, 0.65± 0.02 cGy h −1 U −1 . Uncertainties in the TLD determination of ⌳ were quoted as having a Type A component of 4.0%, a Type B component of 5.5%, and a 2.5% uncertainty in S K for a combined standard uncertainty of 7.2%. Uncertainty in the calculated values of ⌳ given above was estimated to be 1.5%, not including the component of uncertainty due to use of the DLC-99 cross section library.
Peterson and Thomadsen reported a TLD-measured value of 0.71± 0.07 cGy h −1 U −1 which was not impacted by the NIST WAFAC anomaly. 53 Uncertainties in ⌳ were quoted as having a Type A component of 10.0% ͑n =10͒ and a Type B component of 6.0% for a combined standard uncertainty of 11.7%. TLD measurements by Meigooni et al. were performed in SolidWater™, and produced in-phantom and inwater ⌳ values of 0.67 cGy h −1 U −1 and 0.69 cGy h −1 U −1 , respectively. As the calcium content ͑1.7% by mass͒ used for the in-phantom correction was only 0.6% less than the expected value, no significant change in the Meigooni et al. measured ⌳ values is expected beyond the experimental uncertainties ͑8%͒. 56 Therefore, EXP ⌳ = 0.700 cGy h −1 U −1 is based on the equally weighted average of Peterson and Thomadsen 53 and Meigooni et al. 56