1 Dose Calculation for Photon-Emitting Brachytherapy Sources with Average Energy Higher than 50 kev: Full Report of the AAPM and ESTRO Report of the High Energy Brachytherapy Source Dosimetry (HEBD) Working Group August 2012 DISCLAIMER: This publication is based on sources and information believed to be reliable, but the AAPM, the authors, and the editors disclaim any warranty or liability based on or relating to the contents of this publication. The AAPM does not endorse any products, manufacturers, or suppliers. Nothing in this publication should be interpreted as implying such endorsement by American Association of Physicists in Medicine
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3 Corrigenda Errata sheet listing chronologically the changes in the report. Please, check it often to verify that you have an updated version of the report. Date Change Comments September Data for the IPL Cs-137 source. Tables XLVIII and XLIX have been corrected. A typographical error was detected in the F(r,θ) table of the EPAPS Document No. E-MEDPHYSA in the EXCEL spreadsheet format. Table IV of the paper presents F(r,θ) values for r =, 1, 1.5, 2, 3, 4,.. (Correct ones) while the spreadsheet contains data for r =, 1, 1.25, 2, 2.5, 4,.. Consequently, the r values in the spreadsheet have been modified to match those given in Table IV of the original reference. The QA table calculated using the incorrect F(r,θ) has been updated. Authors of the original publication have submitted an erratum to the journal.
4 DISCLAIMER: This publication is based on sources and information believed to be reliable, but the AAPM, the authors, and the publisher disclaim any warranty or liability based on or relating to the contents of this publication. The AAPM does not endorse any products, manufacturers, or suppliers. Nothing in this publication should be interpreted as implying such endorsement. ISBN: ISSN: by American Association of Physicists in Medicine All rights reserved. Published by American Association of Physicists in Medicine One Physics Ellipse College Park, MD
5 HEBD Working Group Jose Perez-Calatayud (Chair) Radiotherapy Department, La Fe Polythecnic and University Hospital, Valencia 46026, Spain Facundo Ballester Department of Atomic, Molecular and Nuclear Physics, University of Valencia, Burjassot 46100, Spain Rupak K. Das Department of Human Oncology, University of Wisconsin, Madison, Wisconsin Larry A. DeWerd Department of Medical Physics and Accredited Dosimetry and Calibration Laboratory, University of Wisconsin, Madison, Wisconsin Geoffrey S. Ibbott Department of Radiation Physics, University of Texas M. D. Anderson Cancer Center, Houston, Texas Ali S. Meigooni Department of Radiation Oncology, Comprehensive Cancer Center of Nevada, Las Vegas, Nevada Zoubir Ouhib Radiation Oncology, Lynn Regional Cancer Center, Delray Beach, Florida Mark J. Rivard Department of Radiation Oncology, Tufts University School of Medicine, Boston, Massachusetts Ron S. Sloboda Department of Medical Physics, Cross Cancer Institute, Edmonton, Alberta T6G 1Z2 Canada Jeffrey F. Williamson Department of Radiation Oncology, Virginia Commonwealth University, Richmond, Virginia iii
6 ABSTRACT Purpose: Recommendations of the American Association of Physicists in Medicine (AAPM) and the European Society for Radiotherapy and Oncology (ESTRO) on dose calculations for high-energy (average energy higher than 50 kev) photon-emitting brachytherapy sources are presented, including the physical characteristics of specific 192 Ir, 137 Cs, and 60 Co source models. Methods: This report has been prepared by the High Energy Brachytherapy Source Dosimetry (HEBD) Working Group. This report includes considerations in the application of the TG-43U1 formalism to high-energy photon-emitting sources with particular attention to phantom size effects, interpolation accuracy dependence on dose calculation grid size, and dosimetry parameter dependence on source active length. Results: Consensus datasets for commercially available high-energy photon sources are provided, along with recommended methods for evaluating these datasets. Recommendations on dosimetry characterization methods, mainly using experimental procedures and Monte Carlo, are established and discussed. Also included are methodological recommendations on detector choice, detector energy response characterization and phantom materials, and measurement specification methodology. Uncertainty analyses are discussed and recommendations for high-energy sources without consensus datasets are given. Conclusions: Recommended consensus datasets for high-energy sources have been derived for sources that were commercially available as of January Data are presented according to the AAPM TG-43U1 formalism, with modified interpolation and extrapolation techniques of the AAPM TG-43U1S1 report for the 2D anisotropy function and radial dose function. Keywords: brachytherapy, TG-43 formalism, high-energy brachytherapy sources, Monte Carlo, experimental dosimetry, quality assurance. iv
7 CONTENTS I. INTRODUCTION... 1 II. III. PHYSICAL CHARACTERISTICS OF HIGH-ENERGY PHOTON-EMITTING BRACHYTHERAPY SOURCES... 4 II.A. 192 Ir... 5 II.B. 137 Cs... 6 II.C. 60 Co... 6 CONSIDERATIONS APPLYING THE TG-43U1 FORMALISM TO HIGH-ENERGY PHOTON-EMITTING BRACHYTHERAPY SOURCES... 7 III.A. Phantom size effects... 8 III.B. Dose calculation grid size and interpolation accuracy III.C. Dosimetry parameter dependence on active length IV. CONSENSUS DATASET METHODOLOGY IV.A. Dose rate constant IV.B. Radial dose function IV.C. 2D anisotropy function V. RECOMMENDATIONS ON DOSIMETRY CHARACTERIZATION METHODS FOR HIGH-ENERGY PHOTON-EMITTING BRACHYTHERAPY SOURCES V.A. Preparation of dosimetry parameters V.A.1. Air-kerma strength V.A.2. Dose rate constant V.A.3. Radial dose function V.A.4. 2D anisotropy function V.B. Reference data and conditions for brachytherapy dosimetry V.B.1. Radionuclide data V.B.2. Reference media v
8 V.C. Methodological recommendations for experimental dosimetry V.C.1. Detector choice V.C.2. Phantom material and energy response characterization V.C.3. Specification of measurement methods V.D. Methodological recommendations for Monte Carlo based dosimetry V.D.1. Specification of Monte Carlo calculation methods V.D.2. Good practice for Monte Carlo calculations V.E. Uncertainty analyses V.F. Publication of dosimetry results V.G. The role of non Monte Carlo computational tools in reference dosimetry VI. RECOMMENDED DOSIMETRY DATASETS FOR HIGH-ENERGY PHOTON-EMITTING BRACHYTHERAPY SOURCES VI.A. AAPM-RPC Source Registry VI.B. Consensus datasets VI.B.1. HDR 192 Ir sources VI.B.2. PDR 192 Ir sources VI.B.3. LDR 192 Ir sources VI.B.4. LDR 137 Cs sources VI.B.5. HDR 60 Co sources VI.C. Reference overview of sources without consensus datasets NOMENCLATURE APPENDIX A: Detailed Recommended Dosimetry Datasets for High-Energy Photon-Emitting Brachytherapy Sources A.1 High Dose Rate 192 Ir sources A.1.1 mhdr-v1 (Nucletron) A.1.2 mhdr-v2 (Nucletron) A.1.3 VS2000 (Varian Medical Systems) A.1.4. Buchler (E&Z BEBIG) A.1.5. GammaMed HDR 12i (Varian Medical Systems) A.1.6. GammaMed HDR Plus (Varian Medical Systems) vi
9 A.1.7. GI192M11 (E&Z BEBIG) A.1.8. Ir2.A85-2 (E&Z BEBIG) A.1.9. M-19 (Source Production and Equipment) A Flexisource (Isodose Control) A.2 Pulsed Dose Rate 192 Ir sources A.2.1. GammaMed PDR 12i (Varian Medical Systems) A.2.2. GammaMed PDR Plus (Varian Medical Systems) A.2.3. mpdr-v1 (Nucletron) A.2.4. Ir2.A85-1 (E&Z BEBIG) A.3. Low Dose Rate 192 Ir sources A.3.1. Steel clad 192 Ir seed (Best Industries) A.3.2. LDR 192 Ir wires (E&Z BEBIG) A Cs sources A.4.1. CSM3 (E&Z BEBIG) A.4.2. IPL (Radiation Products Design) A.4.3. CSM11 (E&Z BEBIG) A.5. High Dose Rate 60 Co sources A.5.1. GK60M21 (E&Z BEBIG) A.5.2. Co0.A86 (E&Z BEBIG) APPENDIX B: References for High-Energy Sources Not Commercially Available and Without Consensus Datasets B.1 LDR-HDR-PDR 192 Ir B.2 LDR 137 Cs B.3 HDR 60 Co REFERENCES vii
10 LIST OF FIGURES 1. Reference polar coordinate system for high-energy photon-emitting sources adapted from the 1995 TG-43 report Materials and dimensions (mm) of the Nucletron mhdr-v1 source.  Materials and dimensions (mm) of the Nucletron mhdr-v2 source.  Material and dimensions (mm) of the Varian Medical Systems VS2000 source.  Materials and dimensions (mm) of the E&Z BEBIG HDR 192 Ir Buchler model G0814 source.  Materials and dimensions (mm) of the Varian Medical Systems GammaMed HDR 12i source.  Materials and dimensions (mm) of the Varian Medical Systems GammaMed HDR Plus source.  Materials and dimensions (mm) of the E&Z BEBIG HDR model GI192M11 source.  Materials and dimensions (mm) of the E&Z BEBIG HDR model Ir2.A85-2 source.  Materials and dimensions (mm) of the Source Production and Equipment M-19 source.  Materials and dimensions (mm) of the Isodose Control Flexisource.  Materials and dimensions (mm) of the Varian Medical Systems GammaMed PDR 12i source.  Materials and dimensions (mm) of the Varian Medical Systems GammaMed PDR Plus source.  Materials and dimensions (mm) of the Nucletron mpdr-v1 source.  Materials and dimensions (mm) of the E&Z BEBIG Ir2.A85-1 source.  Materials and dimensions (mm) of the Best Medical model Ir seed.  Drawing is not to scale Materials and dimensions (mm) of the E&Z BEBIG LDR 192 Ir wire.  Plot is not to scale viii
11 18. Materials and dimensions (mm) of the E&Z BEBIG model CSM3 source.  Materials and dimensions (mm) of the Radiation Products Design model Cs source.  The source tip is on the side of the aluminum ring Materials and dimensions (mm) of the E&Z BEBIG CSM11 source.  Materials and dimensions (mm) of the E&Z BEBIG model GK60M21 source.  Materials and dimensions (mm) of the E&Z BEBIG model Co0.A86 source.  LIST OF TABLES I. Physical properties of radionuclides considered in this report. Data have been taken from the NNDC.  Mean photon energy values are calculated with a cutoff of = 10 kev. Data on Auger and internal conversion (IC) electrons are not included... 5 II. Polynomial coefficients of the correction factors (CF) used to quantitatively compare bounded to unbounded radial dose functions for common phantom shapes and sizes. CF was fitted as CF = C 0 + C 1 r + C 2 r 2 + C 3 r 3 + C 4 r 4.  These coefficients have been obtained by D. Granero (private communication) in a re-evaluation of their study which takes into account that with the coefficients in the original publication, g(r = 1 cm) was not exactly one III. Interpolation and extrapolation recommendations for high-energy (low-energy)  brachytherapy sources for the line-source approximation IV. Dose rate constant for HDR 192 Ir sources V. Radial dose function values for HDR sources. Interpolated/extrapolated data are boldface/underlined. Values inside the source are in italics. In [brackets] are the corrected values from bounded to unbounded geometry VI. VII. VIII. F(r, ) for the Nucletron mhdr-v1 source. Extrapolated data are underlined. Values inside the source are in italics QA away-along data [cgy h 1 U 1 ] for the Nucletron mhdr-v1 source. Values inside the source are in italics F(r, ) for the Nucletron mhdr-v2 source. Extrapolated data are underlined. Values inside the source are in italics ix
12 IX. QA away-along data [cgy h 1 U 1 ] for the Nucletron mhdr-v2 source. Values inside the source are in italics X. F(r, ) for the Varian Medical Systems VS2000 source. Extrapolated data are underlined. Values inside the source are in italics XI. XII. XIII. XIV. XV. XVI. XVII. XVIII. XIX. XX. XXI. XXII. XXIII. QA away-along data [cgy h 1 U 1 ] for the Varian Medical Systems VS2000 source. Values inside the source are in italics F(r, ) for the Buchler model G0814 source. Extrapolated data are underlined. Values inside the source are in italics QA away-along data [cgy h 1 U 1 ] for the Buchler model G0814 source. Values inside the source are in italics F(r, ) for the GammaMed HDR 12i source. Extrapolated data are underlined. Values inside the source are in italics QA away-along data [cgy h 1 U 1 ] for the GammaMed HDR 12i source. Values inside the source are in italics F(r, ) for the GammaMed HDR Plus source. Extrapolated data are underlined. Values inside the source are in italics QA away-along data [cgy h 1 U 1 ] for the GammaMed HDR Plus source. Values inside the source are in italics F(r, ) for the E&Z BEBIG model GI192M11 source. Extrapolated data are underlined. Values inside the source are in italics QA away-along data [cgy h 1 U 1 ] for the E&Z BEBIG model GI192M11 source. Values inside the source are in italics F(r, ) for the E&Z BEBIG model Ir2.A85-2 source. Extrapolated data are underlined. Values inside the source are in italics QA away-along data [cgy h 1 U 1 ] for the E&Z BEBIG model Ir2.A85-2 source. Values inside the source are in italics F(r, ) for the SPEC In. Co. model M-19 source. Extrapolated data are underlined. Values inside the source are in italics QA away-along data [cgy h 1 U 1 ] for the SPEC In. Co. model M-19 source. Values inside the source are in italics x
13 XXIV. XXV. F(r, ) for the Isodose Control model Flexisource. Extrapolated data are underlined. Values inside the source are in italics QA away-along data [cgy h 1 U 1 ] for the Isodose Control model Flexisource. Values inside the source are in italics XXVI. Dose rate constant for PDR sources XXVII. Radial dose function values for PDR sources. Extrapolated data are underlined. Values inside the source are in italics. In [brackets] are the corrected values from bounded to unbounded geometry XXVIII. F(r, ) for the GammaMed PDR 12i source. Extrapolated data are underlined. Values inside the source are in italics XXIX. XXX. XXXI. QA away-along data [cgy h 1 U 1 ] for the GammaMed PDR 12i source. Values inside the source are in italics F(r, ) for the GammaMed PDR Plus source. Extrapolated data are underlined. Values inside the source are in italics QA away-along data [cgy h 1 U 1 ] for the GammaMed PDR Plus source. Values inside the source are in italics XXXII. F(r, ) for the Nucletron mpdr-v1 source. Extrapolated data are underlined. Values inside the source are in italics XXXIII. QA away-along data [cgy h 1 U 1 ] for the Nucletron mpdr-v1 source. Values inside the source are in italics XXXIV. F(r, ) for the E&Z BEBIG PDR-Ir2.A85-1 model. Extrapolated data are underlined. Values inside the source are in italics XXXV. QA away-along data [cgy h 1 U 1 ] for the E&Z BEBIG PDR Ir2.A85-1 source. Values inside the source are in italics XXXVI. Dose rate constant for different LDR 192 Ir sources XXXVII. Radial dose function values for LDR 192 Ir sources. Extrapolated data are underlined. Values inside the source are in italics XXXVIII. F(r, ) for the Best Industries model Ir seed. Extrapolated data are underlined. Values inside the source are in italics XXXIX. QA away-along data [cgy h 1 U 1 ] for the Best Industries model Ir seed. Values inside the source are in italics xi
14 XL. XLI. XLII. XLIII. F(r, ) for the E&Z BEBIG L = 0.5 cm wire length. Extrapolated data are underlined. Values inside the source are in italics QA away-along data [cgy h 1 U 1 ] for the E&Z BEBIG L = 0.5 cm wire length. Extrapolated data are underlined. Values inside the source are in italics. 100 F(r, ) for the E&Z BEBIG L = 1 cm wire length. Extrapolated data are underlined. Values inside the source are in italics QA away-along data [cgy h 1 U 1 ] for the E&Z BEBIG L = 1 cm wire length. Values inside the source are in italics. Extrapolated data are underlined XLIV. Dose rate constant of 137 Cs sources XLV. XLVI. Radial dose function values for 137 Cs LDR sources. Interpolated/extrapolated data are boldface/underlined. Values inside the source are in italics F(r, ) for the E&Z BEBIG CSM3 source. Values inside the source are in italics. Extrapolated data are underlined XLVII. QA away-along data [cgy h 1 U 1 ] for the E&Z BEBIG CSM3 source. Values inside the source are in italics. Extrapolated values are underlined XLVIII. F(r, ) for the Radiation Products Design IPL source. Values inside the source are in italics. Extrapolated data are underlined XLIX. QA away-along data [cgy h 1 U 1 ] for the Radiation Products Design IPL source. Extrapolated data are underlined. Values inside the source are in italics. 109 L. F(r, ) for the E&Z BEBIG CSM11 source. Extrapolated data are underlined. Values inside the source are in italics LI. LII. QA away-along data [cgy h 1 U 1 ] for the E&Z BEBIG CSM11 source. Values inside the source are in italics Radial dose function values for 60 Co HDR sources. Values inside the source are in italics. Extrapolated data are underlined LIII. Dose rate constant for HDR 60 Co sources LIV. LV. F(r, ) for the E&Z BEBIG 60 Co HDR GK60M21 source. Values inside the source are in italics. Extrapolated data are underlined QA away-along data [cgy h 1 U 1 ] for the E&Z BEBIG 60 Co GK60M21 source. Values inside the source are in italics xii
15 LVI. LVII. F(r, ) for the E&Z BEBIG 60 Co HDR Co0.A86 source. Values inside the source are in italics. Extrapolated data are underlined QA away-along data [cgy h 1 U 1 ] for the E&Z BEBIG 60 Co Co0.A86 source. Values inside the source are in italics xiii
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17 High-energy photon-emitting brachytherapy dosimetry I. INTRODUCTION In 1995, the American Association of Physicists in Medicine (AAPM) Task Group No. 43 (TG-43) published a clinical protocol on dosimetry for interstitial brachytherapy sources,  colloquially known as the TG-43 formalism, and provided reference dosimetry datasets for several designs of 192 Ir, 125 I, and 103 Pd sources commercially available at the time. This report was instrumental in enhancing dose calculation accuracy and uniformity of clinical dosimetry practices for low-energy photon-emitting sources following general acceptance and implementation of the TG-43 dose calculation formalism by the brachytherapy vendor, treatment planning systems (TPS), and user communities. Development of the TG-43 methods in the area of low-energy brachytherapy source dosimetry, defined as sources emitting photons of average energy less than or equal to 50 kev, was carried out by the AAPM Low Energy Brachytherapy Source Dosimetry (LEBD) Working Group. In response to the vastly increasing use of low-energy interstitial brachytherapy sources, especially for permanent prostate implants, and the increasing number and variable design of commercially available low-energy sources, LEBD continued to develop the TG-43 formalism and to prepare referencequality AAPM consensus dosimetry datasets from published dosimetry papers. Most of the recent LEBD recommendations and advances in dosimetric characterization, recommended dose calculation methodologies, and data evaluation for low-energy interstitial brachytherapy, are summarized in two key reports: the 2004 update of the TG-43 report (TG-43U1)  and its 2007 supplement (TG- 43U1S1). [3,4] In the field of high-energy brachytherapy dosimetry, the TG-186 report will provide guidance for early adopters of model-based dose calculation algorithms. The Model-Based Dose Calculation Algorithms (MBDCA) Working Group will develop a limited number of well-defined test case plans and perform MBDCA dose calculations and comparisons. However, there will remain for the foreseeable future a need for reference dosimetry data obtained in liquid water phantoms to evaluate the uniform clinical implementation and robustness of these advanced dose calculation algorithms. Many publications propose various dose-estimation methods and dosimetric parameters for specific high-energy brachytherapy sources (defined as photon-emitting sources with average photon energies exceeding 50 kev) including 192 Ir, 137 Cs, 60 Co, and 198 Au sources. Many new source designs, especially high dose rate (HDR) and pulsed dose rate (PDR) sources, have been introduced for use in remote-afterloading machines, while traditional low dose rate (LDR) sources such as 192 Ir seeds in ribbons, 192 Ir wires, and 137 Cs tubes and spheres remain a mainstay for a number of brachytherapy applications. New brachytherapy radionuclides, such as 169 Yb [5,6] and 170 Tm, [7 9] are being actively investigated for application in HDR brachytherapy and should be discussed in the forthcoming TG-167 report. Also, new 60 Co sources have been designed to be used with HDR afterloaders. [10 12] HDR remote afterloading units are generally replacing traditional LDR 192 Ir and 137 Cs sources for intracavitary and interstitial brachytherapy applications. This trend will continue as other new highenergy brachytherapy sources are developed. It is paramount that the computational and experimental tools used in investigations to evaluate single-source dose distributions, consensus dataset formation processes, and calibration processes, are able to support the level of dosimetric accuracy and precision
18 2 HEBD report required to safely and efficiently deliver brachytherapy to patients. [13,14] To ensure that these criteria are met, reference dosimetry datasets obtained from these investigations must be independently verified for accuracy and be readily available in a format accepted by commonly used planning systems. The AAPM has made recommendations on dose calculation formalisms and the choice of dosimetry datasets for brachytherapy sources in its TG-43,  TG-56,  and TG-59  reports. Currently the number of source models in clinical use is very large, and medical physicists have few resources to turn to for selecting the best dosimetry parameters for a given source model. The availability in tabular form of critically evaluated and complete consensus dosimetry datasets for all commonly used sources, for use with the updated TG-43 formalism, would be of substantial benefit to clinical end users. The AAPM has reviewed and published reference-quality dosimetry datasets for low-energy brachytherapy sources in the LEBD reports (TG-43,  TG-43U1,  and TG-43U1S1 [3,4] ). No similar effort has been attempted by AAPM or the European Society for Radiotherapy and Oncology (ESTRO) for high-energy sources, nor have societal recommendations been made concerning appropriate methods for the acquisition and formation of such datasets. To fill this void, the AAPM Brachtherapy Subcommittee (BTSC) formed the High Energy Brachytherapy Source Dosimetry (HEBD) Working Group to focus on photon-emitting brachytherapy sources with average energy higher than 50 kev. This group has the following charges: 1. To compile a list of high-energy brachytherapy sources commonly used in North America and Europe, for which the dosimetry datasets and guidelines recommended by HEBD will apply. 2. To develop dosimetric prerequisites for routine clinical use of high-energy brachytherapy sources similar in scope to the low-energy brachytherapy dosimetry prerequisites.  3. To develop an extension of the TG-43 dose-calculation formalism that is applicable to elongated sources, i.e., with maximum linear dimensions that are large or comparable to typical calculation distances. 4. To provide consensus datasets for the sources defined in charge 1 above, using the currently acceptable dose calculation formalisms. 5. To perform a review of existing clinical source-strength calibration requirements and recommendations for high-energy (LDR/HDR/PDR) sources. 6. To provide a Brachytherapy Source Registry (BSR) for web-based access to high-energy brachytherapy source dosimetry data that satisfy the prerequisites defined in charge 2. The objective of this report is to fulfill charges 1 and 4. Charge 2 was addressed in the first publication of the group  developing a set of dosimetric prerequisites for routine clinical use of brachytherapy sources with average energy higher than 50 kev. These broad recommendations form the basis of the more detailed recommendations provided by this report. Charge 3 has been adopted as the principal charge by the joint AAPM/ESTRO Task Group No. 143 on Dosimetric Evaluation of Elongated Photon Emitting Brachytherapy Sources. Charge 5 on high-energy source calibrations is in
19 High-energy photon-emitting brachytherapy dosimetry 3 progress for inclusion in a complementary report. Charge 6, to expand the BSR in an analogous manner as done for low-energy sources, is an on-going collaborative project involving the Radiological Physics Center (RPC), the AAPM BTSC and BSR Working Group, and the ESTRO BRAchytherapy PHYsics Quality assurance System (BRAPHYQS) subcommittee analogous to the BTSC. Specifically, the current report addresses the following: 1. Review the construction and available published dosimetry data for high-energy 192 Ir, 137 Cs, and 60 Co sources that (i) continue in clinical use in North America or Europe and (ii) satisfy the AAPM s dosimetric prerequisites  (charge 1). 2. Perform a critical review of the existing TG-43U1 formalism  as used heretofore mainly for low-energy brachytherapy sources. Extension of the TG-43 dose-calculation formalism was not performed as considered in charge Critically review published dosimetric data for each of the prerequisite-compliant source models listed in 1., and develop a complete consensus dataset to support clinical planning for each source model (charge 4). 4. Develop guidelines for investigators on the use of computational and experimental dosimetry for determination of high-energy brachytherapy source dosimetry parameters. The recommendations included herein reflect the guidance of the AAPM and the ESTRO for brachytherapy users, and may also be used as guidance to vendors in developing good manufacturing practices for sources used in routine clinical treatments. Certain materials and commercial products are identified in this report in order to facilitate discussion and methodology description. Such identification does not imply recommendation nor endorsement by any of the professional organizations or the authors, nor does it imply that the materials or products identified are necessarily the best available for these purposes.
20 4 HEBD report II. PHYSICAL CHARACTERISTICS OF HIGH-ENERGY PHOTON- EMITTING BRACHYTHERAPY SOURCES The photon-emitting brachytherapy sources included in this report have average energies exceeding 50 kev. Only sources intended for conventional clinical interstitial and intracavitary use were included; sources intended for intravascular brachytherapy are covered by AAPM task groups TG-60  and TG-149.  Similarly, electronic brachytherapy sources will be addressed by the AAPM task groups TG-167 and TG-182. The limit of 50 kev was established by the AAPM to separate high-energy sources from those addressed by the LEBD.  This report addresses brachytherapy source models that were commercially available as of January For sources that were commercially available, the goal was to generate consensus datasets in a format acceptable to commercial TPS. For sources that are in current clinical use but no longer manufactured, the scientific literature was reviewed and acceptable published datasets were identified. In a few cases, datasets were included for sources that are no longer in clinical use to assist in the retrospective calculation of dose distributions. The radionuclides considered in this report and described in this section are 192 Ir, 137 Cs, and 60 Co. Their most important physical properties are presented in Table I; see the National Nuclear Data Center (NNDC)  for a more complete description. Baltas et al.  also provides a clear description of these radionuclides. Detailed information on recommended photon spectra is provided in section V.D Au (half-life 2.7 days) brachytherapy sources have been used extensively in the past for treatment of various tumors including gynecological, breast, prostate, head and neck, and other softtissue cancers. These sources were generally of low activity (typically mci) and were in the form of seeds or grains. 198 Au emits a wide spectrum of x-rays and gamma rays with an average energy of approximately 400 kev. The use of this radionuclide has decreased in recent years, perhaps because of the availability of competing radionuclides. These include 125 I (half-life 59.4 days) and 103 Pd (halflife 17.0 days), both of which have longer half-lives, making shipment and scheduling of treatments more convenient, and lower photon energies, leading to more acceptable radiation safety characteristics than 198 Au. Vicini et al.  conducted a survey of 178 publications reporting on prostate brachytherapy between 1985 and They found that 198 Au had not been used for monotherapy according to these studies, and had been used in combined modality therapy only in 11% of cases. Correspondingly, they found that 125 I and 103 Pd were used far more frequently. Yaes  showed that, regardless of treatment site, the heterogeneity of the dose distributions from 198 Au could be greater than those from 125 I and 103 Pd. Similarly, Marsiglia et al.  reported that 198 Au implants more often showed significant cold spots, and generally inferior dosimetric coverage, than did implants with other radionuclides. These reports, together with others reporting on comparisons with other radionuclides, have resulted in relatively infrequent use of 198 Au. As a result, this report will not address 198 Au brachytherapy sources.
21 High-energy photon-emitting brachytherapy dosimetry 5 Table I. Physical properties of radionuclides considered in this report. Data have been taken from the NNDC.  Mean photon energy values are calculated with a cutoff of = 10 kev. Data on Auger and internal conversion (IC) electrons are not included. 192 Ir 137 Cs 60 Co Half-life days years 5.27 years Type of disintegration (95.1%), EC (100%) (100%) (4.9%) Maximum x-ray energy (kev) Gamma energy-range (kev) to to Mean x-ray and gamma energy (kev) Maximum ray energies (kev) 81.7 (0.103%) (5.6%) (41.43%) (48.0%) (94.4%) (5.6%) (99.88%) (0.12%) Mean ray energy (kev) Air kerma rate constant, =10 kev (μgy m 2 h 1 MBq 1 ) Specific activity (GBq mg -1 ) II.A. 192 Ir The 192 Ir half-life of days allows it to be easily used for temporary implants. Its high specific activity makes it practical to deliver sources of activities of as much as hundreds of GBq. 192 Ir decays to several excited states of 192 Pt via (95%) and 192 Os via electron capture (EC) (5%), emitting on average 2.3 gamma rays per disintegration with a range of energies between and MeV and a mean energy of MeV. The rays emitted have a maximum energy of MeV and an average energy of MeV. 192 Ir is produced from enriched 191 Ir targets (37% natural abundance) in a reactor by the (n, ) reaction, creating HDR 192 Ir sources (typically 1 mm diameter by 3.5 mm length cylinders) with activities exceeding 4.4 TBq. HDR 192 Ir sources are encapsulated in a thin titanium or stainless steel capsule and laser welded to the end of a flexible wire. Electrons from decay are absorbed by the core and the capsule. [25 28]
22 6 HEBD report II.B. 137 Cs The 137 Cs half-life of years enables use over a long period of time. Its low specific activity makes it practical for LDR implants. 137 Cs decays purely via, mainly (94.4%) to the second excited state of 137 Ba, where the de-excitation to the ground state (90%) with emission of a gamma ray of MeV (absolute intensity 85.1%) is in competition with IC (10%). The rays emitted have a maximum energy of MeV. A second decay branch (5.6% probability) to the 137 Ba ground state occurs, with maximum ray energy of MeV. 137 Cs is extracted from 235 U fission products, with the 137 Cs trapped in an inert matrix material such as gold, ceramic, or borosilicate glass. The sources are doubly encapsulated with a total of 0.5 mm thick stainless steel. Electrons from decay are mainly absorbed by the core and the capsule.  Cylindrical source models commercially available are manufactured with 3 mm diameter and external lengths up to 21 mm. Spherical sources are made for use in remote-afterloading intracavitary brachytherapy devices. II.C. 60 Co The 60 Co half-life of 5.27 years and its high specific activity make it practical for HDR brachytherapy implants. Newly designed HDR sources have been introduced in the market. 60 Co undergoes decay to the excited states of 60 Ni (94.4%). De-excitation to the ground state occurs mainly via emission of -rays of MeV and MeV, each with an absolute intensity of nearly 100%. The main rays emitted (99.88%) have a maximum energy of MeV and an average energy of MeV. 60 Co is produced through neutron capture by 59 Co, but its long halflife requires long irradiation times for sufficient source strength. HDR 60 Co sources have dimensions similar to those of 192 Ir (section II.A). The low-energy electrons emitted by 60 Co are easily absorbed by the cobalt source material or encapsulation layers, resulting in a pure photon source. [10,28]
23 High-energy photon-emitting brachytherapy dosimetry 7 III. CONSIDERATIONS APPLYING THE TG-43U1 FORMALISM TO HIGH-ENERGY PHOTON-EMITTING BRACHYTHERAPY SOURCES The TG-43 formalism  was initially developed for use in interstitial brachytherapy including low-energy 125 I and 103 Pd seeds and high-energy 192 Ir seeds in ribbons. In 2004, the AAPM TG-43U1 report  updated the formalism and provided data for several new models of low-energy seeds. The application of this formalism has subsequently been extended significantly by the brachytherapy physics community, making it the international benchmark for nearly all brachytherapy sources in brachytherapy dosimetry publications and brachytherapy TPS. The TG-43 formalism applied to lowenergy sources has the following advantages: 1. Dosimetric modeling of seeds using the point-source approximation is facilitated by averaging dose anisotropy over all solid angles. This method of calculation is used primarily for permanent prostate brachytherapy where seed orientation is not discernible in clinical practice for non-stranded applications and due to the large number of seed orientations. 2. Accurate interpolation of the dose distribution is readily achieved because the geometric dependence of dose falloff as a function of radial distance r and polar angle is accounted for. This allows the use of a limited dataset while providing for robust dose calculation. 3. An analytic, uniform approach to brachytherapy dose calculation is readily available, thereby promoting consistent clinical practice worldwide. The TG-43 formalism [1,2] assumes a water medium with superposition of single source dose distributions, no inter-source attenuation (ISA) effects, and full scatter conditions (infinite or unbounded water medium) at dose calculation points-of-interest (POIs). Partial scatter conditions can potentially be accommodated through the use of appropriate correction factors. [29 32] This approximation of realistic clinical conditions is pertinent for both low-energy and high-energy brachytherapy applications, and is discussed in detail by Rivard et al. [33,34] Variable tissue composition has a greater influence on low-energy brachytherapy source dosimetry than for high-energy sources due to the photoelectric effect and its high cross section at low energies. However, the effect of scatter conditions is more important for high-energy brachytherapy dosimetry. For low-energy brachytherapy, mostly conducted as prostate implants, the surrounding tissue is adequate to provide full scatter conditions. In contrast, high-energy brachytherapy implants vary from those deeply positioned (e.g., gynecological) to surface applications (e.g., skin), with scatter significantly influencing dose calculations at clinically relevant POIs. It is not clear whether a simple modification of the current TG-43 formalism can account for partial radiation scatter conditions utilizing the current TG-43 based TPS. Alternatively, new dose calculation algorithms that correct for partial radiation scatter conditions are emerging. As for low-energy brachytherapy sources, especially those used in multi-source LDR implants, ISA effects are also present for high-energy LDR sources such as 192 Ir and 137 Cs. However, the clinical trend in the high-energy source domain is that HDR and PDR are more prevalent than the LDR procedures.
24 8 HEBD report One important limitation of current TPS dose calculation tools is the near-universal neglect of applicator shielding. For example, doses to the rectal and bladder walls are generally not accurately calculated for gynecological implants, and subsequently the reported doses associated with toxicities are incorrect. Correction methods [35,36] were developed based on attenuation values that were experimentally obtained, giving reasonable values in specific clinical applications such as shielded cylinders.  Shielding is also present on some vaginal applicators to protect the healthy vagina at variable applicator angles. Fortunately, the use of magnetic resonance imaging (MRI) is increasing relative to computed tomography (CT) for cervical brachytherapy. With the use of MRI-compatible applicators, imaging artifacts due to high-z shields are mitigated. New algorithms that account for these effects are now appearing in commercial TPS as reviewed by Rivard et al. [33,34] and are the subject of the active AAPM Task Group 186. The TG-43 formalism was originally applied to sources with active lengths ranging from 2 mm to 4 mm, while typical HDR/PDR sources have active lengths ranging from 0.5 mm to 5 mm, and some high-energy LDR sources such as 137 Cs tubes have active lengths >15 mm. Other LDR sources have a variable active length and/or curved active components like 192 Ir wires. An approach to dose calculation for these sources that falls within the framework of the TG-43 formalism is presently being developed by the AAPM Task Group 143. In section III.C of this report the dependence of dosimetry parameters for high-energy sources on source active length is discussed, as is the effect of phantom size used in dose calculations and/or measurements. The latter discussion includes a methodology to convert datasets from bounded to unbounded (full scatter) conditions to compare data from different publications. The procedure used in this report for developing consensus datasets is based on this conversion methodology in some cases. Adaptation of extrapolation and interpolation techniques presented in the AAPM TG-43U1  and TG-43U1S1 [3,4] reports was performed for high-energy sources. Finally, aspects specific to highenergy sources such as the electronic equilibrium region close to the source and the need for higher spatial resolution of the dose distribution close to the source are addressed. III.A. Phantom size effects A limitation of the TG-43 formalism when applied to high-energy sources is the assumption of fixed scatter conditions at calculation points, without consideration of the tissue boundaries. The TG- 43 dose calculation formalism assumes an infinite scattering medium and can result in overestimation of absorbed dose at a low-density interface. In many clinical settings, the actual scatter conditions may significantly deviate from these reference conditions, leading to significant dose overestimates, e.g., when the source is near the surface of the patient. This is often the case for breast implants. For example, some breast protocols [e.g., Radiation Therapy Oncology Group (RTOG) protocol 0413] require that the dose homogeneity index include the skin dose calculations. Errors/limitations in calculating dose at shallow depths affect the dose calculation. Serago et al.  showed a dose reduction at points close to low-density interfaces of up to 8% for HDR 192 Ir brachytherapy as typical for breast implants performed as a boost. Mangold et al.  showed deviations of up to 14% with measurements close to the tissue-air interface, whereas Wallner and colleagues  found the TPS to overestimate dose by no more than 5% at points close to the skin
25 High-energy photon-emitting brachytherapy dosimetry 9 and lung for partial breast irradiation. However, Raffi et al.  found TPS dose overestimations of up to 15%. Lymperopoulou et al.  reported that the skin dose overestimation can increase from 15% to 25% when 169 Yb is used in place of 192 Ir. Pantelis et al.  showed for breast implants at 2 to 5 cm depths with Monte Carlo (MC) radiation transport methods that the TPS overestimates by 5% to 10% the isodose contours lower than 60% of the prescribed dose. Other extreme clinical situations are superficial implants involving shallow clinical target volume (CTV) irradiations, or intraoperative brachytherapy for which specialized applicators have been designed. In the latter situation Raina et al.  showed differences of up to 13% between the dose calculated for actual and full scatter conditions in the surface tissue layer. In practice, this difference can be minimized by adding bolus, but this may not be clinically beneficial. TPS calculations are based on interpolation over stored two-dimensional (2D) water dose rate tables which assume cylindrically symmetric sources and applicators, a uniform water-equivalent medium, and negligible ISA effects. Usually, these dose rate tables consist of TG-43 parameter values or away-along dose rate tables. In principle, it seems logical that the tables include larger distances to avoid extrapolation. Although these larger distance values are not often clinically significant, accurate data are useful for dose calculations to radiosensitive anatomical structures outside the CTV, especially when the patient has undergone external beam radiotherapy. For lowenergy brachytherapy dosimetry, the TG-43U1 report  recommended that the radial dose function g(r) extend to 7 cm for 125 I and to 5 cm for 103 Pd, which correspond to values of approximately 0.5% and 0.3% of the dose rate at 1 cm, respectively. Also in the TG-43U1 report, recommendations for good practice for MC dosimetry included determination of the dose distribution for r 10 cm, with at least 5 cm of backscatter material for 125 I and 103 Pd. As will be justified below for high-energy sources, the recommended range for g(r) is r 10 cm. Another issue is whether the TG-43 dosimetry parameters and the dose rate tables used by the TPS should be obtained with full scatter conditions for the complete range of distances. This issue is related to the appropriate phantom size to be used in MC calculations (henceforth labeled with MC subscript) or experimental purposes (henceforth labeled with EXP subscript), in order to establish the reference dose rate distributions used as input and benchmark data for TPS clinical dosimetry. For high-energy sources, an effectively unbounded spherical phantom radius R of 40 cm is recommended to promote uniformity of dose calculations for r < 20 cm, since it is not possible to cover all applications that move from superficial to deeper implants by selecting a smaller phantom size. Another issue to consider is the promise of new TPS algorithms to solve traditional calculation limitations such as tissue heterogeneities, patient and applicator scatter of radiation, intersource effects, and shielding corrections. These new algorithms will be discussed in section V. Phantom size is well known to be an important consideration in brachytherapy dosimetry. Ellet  studied boundary effects for photon source energies ranging from 0.03 to 2.75 MeV by comparing the dose in water spheres of radius R = 10, 20, 30, and 40 cm with the dose in an unbounded medium. Doses were observed to be within 5% of the values in an unbounded medium at distances of more than one mean free path from the interface (citing a mean free path of 2.19 cm for an energy of 0.03 MeV, 9.10 cm for MeV, 11.7 cm for MeV, and 17.3 cm for 1.46
26 10 HEBD report MeV). Williamson  compared MC calculations for 192 Ir assuming an unbounded water phantom and a R = 15 cm spherical phantom with measured data from the Interstitial Collaborative Working Group for a cubic phantom of approximate size ( ) cm 3. Agreement within 5% was observed up to 5 cm from the source, but differences of 5% to 10% were noted for r > 5 cm. Williamson and Li  found a difference of 12% at r = 12 cm from a microselectron PDR 192 Ir source between the dose calculated in an unbounded water phantom and that obtained with a spherical phantom (R = 15 cm). Venselaar et al.  measured the influence of phantom size on dose by changing the water level in a cubic water tank for 192 Ir, 137 Cs, and 60 Co sources. Significant dose differences were observed between experiments with different phantom sizes. Karaiskos et al.  performed MC and thermoluminescent dosimetry (TLD) studies of the microselectron HDR 192 Ir source using spherical water phantoms with R = cm. They ascertained that phantom dimensions significantly affect g(r) near-phantom boundaries where deviations of up to 25% were observed. They did not observe significant differences in the anisotropy function F(r, ) for the different values of R. Other investigators have found a dose dependence on R due to the different scatter conditions. [50 56] Pérez-Calatayud et al.  presented a study where MC g(r) was obtained for water phantoms with 5 cm R 30 cm ( 125 I and 103 Pd) and 10 cm R 50 cm ( 192 Ir and 137 Cs). They showed that dose differences with respect to full scatter conditions for 192 Ir and 137 Cs sources, in the case of the most popular phantom size cited in the literature (R = 15 cm), reached 7% ( 192 Ir) and 4.5% ( 137 Cs) at r = 10 cm, but were only 1.5% ( 192 Ir) and 1% ( 137 Cs) at r = 5 cm. For R = 40 cm and 192 Ir or 137 Cs, the dose rate was equivalent to an unbounded phantom for r 20 cm, since this size ensured full scatter conditions. For 125 I and 103 Pd, R = 15 cm was necessary to ensure full scatter conditions within 1% for r 10 cm.  These results agree with the subsequent study by Melhus and Rivard,  who in addition showed that for 169 Yb a radius of R 40 cm is required to obtain data in full scatter conditions for r 20 cm. Pérez-Calatayud et al.  developed a simple expression relating values of g(r) for various phantom sizes based on fits to the dose distributions for 192 Ir and 137 Cs. This expression is useful to compare published dose rate distributions for different phantom sizes, and to correct g(r) values for bounded media of radius 10 cm R 40 cm to unbounded phantom values. Differences between corrected dose rate distributions and the corresponding MC results for a given phantom size were less than 1% for r < R 2 cm if R < 17 cm, and for r < 15 cm if R 17 cm. At larger distances r, the fitted dose rate distribution values did not lie within the 1% tolerance. These relations were based on the previous result that for R = 40 cm the dose rate was equivalent to an unbounded phantom for r 20 cm. Some dosimetry investigators have used a 40-cm-high cylindrical phantom with a 20-cm radius in their MC studies. It has been shown that this phantom is equivalent to a spherical phantom with a 21-cm radius.  The expression developed by Pérez-Calatayud et al.  is not applicable to the outer 2 cm of this phantom. To date, most published MC high-energy brachytherapy dosimetry studies have been performed in a water sphere with R = 15 cm, [10,46,55,57 61] a cylindrical phantom of size 40 cm 40 cm, [62 69] or a sphere with R = 40 cm. [70 72] Granero et al. 
27 High-energy photon-emitting brachytherapy dosimetry 11 developed correction factors expressed as fourth-degree polynomials to transform g(r) data for 192 Ir and 137 Cs obtained using commonly published phantom sizes into approximate g(r) values for unbounded phantom conditions, with agreement within 1%. [29 31] These correction factors are given in Table II. Table II. Polynomial coefficients of the correction factors (CF) used to quantitatively compare bounded to unbounded radial dose functions for common phantom shapes and sizes. CF was fitted as CF = C 0 + C 1 r + C 2 r 2 + C 3 r 3 + C 4 r 4.  These coefficients have been obtained by D. Granero (private communication) in a re-evaluation of their study which takes into account that with the coefficients in the original publication, g(r = 1 cm) was not exactly one. Sphere ( ) ( ) CF = g R sph = 40 cm, r g R sph = 15cm, r 1 cm r 15 cm Cylinder ( ) ( ) CF = g R sph = 40 cm, r g R cyl = 20 cm, r 1 cm r 20 cm Cube ( ) CF = g R sph = 40 cm, r g R cube = 15cm, r ( ) 1 cm r 15 cm CF parameter 192 Ir 137 Cs 192 Ir 137 Cs 192 Ir 137 Cs C 0 [dimensionless] C 1 [cm 1 ] C 2 [cm 2 ] C 3 [cm 3 ] C 4 [cm 4 ] In this joint AAPM/ESTRO report, g(r) values from published studies obtained under bounded conditions have been transformed to full scatter conditions with the correction factors in Table II. So, with these relationships, TPS users can transform data from the literature obtained in a bounded medium to input data in full scatter conditions for r 15 cm. When different datasets obtained with different phantom sizes are compared, the boundary scatter defect must be taken into account. At r = 1 cm, full scatter exists within 0.5% for all studies, hence the dose rate constant is directly comparable in all cases. As noted in the literature,  F(r, ) has been shown to be nearly independent of phantom size. Consequently, research has focused on g(r). Anagnostopoulos et al.  proposed a calculation algorithm based on the scatter-to-primary ratio to relate g(r) for one spherical phantom size to g(r) for other R values. Russell et al.  proposed another dose calculation algorithm based on primary and scatter dose separation involving parameterization functions which could also be used to correct the scatter defect. Melchert et al.  developed a novel approach inspired by field theory to calculating the dose decrease in a finite phantom for 192 Ir point source(s).
28 12 HEBD report III.B. Dose calculation grid size and interpolation accuracy Traditionally, brachytherapy TPS utilized analytical methods such as the Sievert integral  to generate dose rate tables for conventional LDR brachytherapy sources such as 137 Cs tubes and 192 Ir wires. These systems then utilized the same method for data interpolation to calculate dose for clinical implants. However, current TPS used for HDR, PDR, and LDR brachytherapy allow direct introduction of tabulated dosimetry parameters from the literature. Some of this information is included in the TPS default dosimetric data supplied by the TPS manufacturer. In some systems, values of the dosimetry parameters are manipulated from one format to another in order to match the dose calculation algorithm used by the system. Examples include changing from rectangular to polar coordinates, using different mathematical functions to fit and smooth tabulated data, and extrapolating data outside of the available data range. Therefore, it is desirable that TG-43 consensus data be presented with adequate range and spatial resolution in order to facilitate input and verification of the accuracy of the TPS dose calculation algorithm. A review of the published data on dosimetry parameters for various high-energy brachytherapy sources indicates that different authors have used a variety of spatial and angular increments and ranges in their dosimetric procedures. Therefore, a clear methodology for interpolation or extrapolation of the published data may be required to determine dose rate distributions at spatial locations not explicitly included in the published data. The AAPM TG-43U1 report  provided guidelines for interpolation and extrapolation of one-dimensional (1D) and 2D dosimetry parameters. The 2007 supplement (i.e., TG-43U1S1) [3,4] included further clarification and modifications of the interpolation and extrapolation techniques in order to make these procedures more accurate. Unlike for low-energy sources, the 1D approximation for high-energy brachytherapy source dosimetry is not recommended, based on the smaller number of sources generally used, known source orientation(s), and the method used for source localization. In this section, the parameter range and spatial resolution, as well as interpolation and extrapolation recommendations are provided. The interpolation and extrapolation recommendations for high-energy (and low-energy from TG-43U1S1) brachytherapy sources of 2D dosimetry are summarized in Table III. Table III. Interpolation and extrapolation recommendations for high-energy (low-energy)  brachytherapy sources for the line-source approximation. Parameter g L (r) F(r, ) r < r min Extrapolation Nearest neighbor or zeroth-order extrapolation (Ditto) Nearest neighbor or zeroth-order extrapolation (Ditto) r min < r r max Interpolation Linear (log-linear) using datapoints immediately adjacent to the radius of interest Bilinear (bilinear) interpolation method for F(r, ) r > r max Extrapolation Linear using data of last two tabulated radii (single exponential function based on fitting g L (r) datapoints for the furthest three r values). Nearest neighbor or zeroth-order r- extrapolation (Ditto)
29 High-energy photon-emitting brachytherapy dosimetry 13 With respect to the angular resolution for F(r, ), 10 steps were generally recommended by the TG-43U1 report, although 1 steps near the source long axes may be needed to have 2% interpolation accuracy over the range of angles. For radial resolution, TG-43U1 recommended F(r, ) be tabulated at 0.5, 1, 2, 3, and 5 cm for 103 Pd and also at 7 cm for 125 I. For g L (r), the recommended range was the same as the F(r, ) radial range, but no specifics were provided concerning radial resolution. However, both the TG-43U1 and TG-43U1S1[3,4] reports required that the g L (r) radial resolution permit log-linear interpolation and fitting with ±2% accuracy. The radial coordinate mesh recommended by HEBD is similar to that recommended by LEBD for low-energy sources. However, a maximum range of 10 cm is indicated since the dose rate here is about 1% of the value at r 0 due to the more uniform g(r) behavior for high-energy sources. The minimum r value for the high-energy consensus datasets will also differ based on consideration of radiological interactions. Some differences between low-energy and high-energy source dosimetry include the following: 1. From a clinical perspective, there is more concern with dose accuracy along the longitudinal axis region of the source for high-energy sources as there is a larger proportion of treatments in which the dose along this axis is included in the prescription (e.g., dome applicators for hysterectomyzed patients, endometrial applicators) than for low-energy brachytherapy. In contrast, permanent prostate implants use many seeds, and the longitudinal axis region is less relevant because of volume averaging and the contribution of many seeds with variable axis orientation. [76 78] 2. For high-energy sources, MC-based dosimetry is the predominant method in part due to its robustness at these energies. When measurement conditions are subject to challenges (associated with detector energy response, detector radiation sensitivity, positioning uncertainty, detector volume averaging, influence of radiation scatter conditions on results, etc.), the role of experimental dosimetry for high-energy brachytherapy may be more limited than MC-based dosimetry. Experiment may primarily serve to validate MC, and to obtain for averaging with MC-derived values since MC is primarily used to determine F(r, ) and g L (r) for high-energy sources. Consequently, range and spatial resolution limitations are not of concern for MC methods and high-energy brachytherapy source dosimetry. However, caution must be taken at close distances if electron transport and electron emissions are not considered. A study by Pujades-Claumarchirant et al.  has been performed for high-energy sources to check methods of interpolation/extrapolation that allow accurate reproduction of g L (r) and F(r, ) from tabulated values, including the minimum number of entries for g L (r) and F(r, ) that allow accurate reproduction of dose distributions. Four sources were studied: 192 Ir, 137 Cs, 60 Co, and a hypothetical 169 Yb source. The r mesh was that typically used in the literature: 0.25, 0.5, 0.75, 1, and 1.5 cm, and for 2 to 10 cm in 1 cm steps, adding the point r gmax = 0.33 cm for 60 Co and r gmax = 0.35 cm for 137 Cs near the maximum value g(r gmax ). For F(r, ), the entries for polar angles close to the source
30 14 HEBD report long axis were evaluated at four different step sizes: 1, 2, 5, and 10. For g L (r), linear interpolations agreed within 0.5% compared with MC results. The same agreement was observed for F(r, ) bilinear interpolations using 1 and 2 step sizes. Based on the Pujades-Claumarchirant et al. study,  minimum polar angle resolutions of 2 (0 to 10 interval), 5 (10 to 30 interval), and 10 (30 to 90 interval) with the addition of corresponding supplementary angles as applicable if dosimetric asymmetry about the transverse plane is >2% are recommended. Further, use of bilinear and linear interpolation for F(r, ) and g L (r), respectively, is recommended since log-linear interpolation is not a significant improvement over linear g(r) interpolation for high-energy sources.  F(r, ) and g L (r) extrapolation for r > 10 cm could be performed by linear extrapolation from the last two tabulated values. However, because of the inverse square law, the dose rate is very low and not clinically relevant. If dosimetric accuracy is required for r > 10 cm, for example to calculate organ-at-risk dose, users must refer to the original MC publication. In contrast with low-energy brachytherapy dosimetry, extrapolation for high-energy sources for r r min is complicated. Electronic equilibrium is reached within a distance of 0.1 mm from the capsule for a low-energy source due to the short electron range. Thus, it can be assumed that collisional kerma is equal to absorbed dose everywhere. For high-energy brachytherapy dosimetry, the region of electronic disequilibrium near the source and the contribution from emitted electrons can be important issues, and are not considered in most MC publications. In a recent study of Ballester et al.  MC calculations scoring dose and taking into account electronic emission are compared with MC calculations scoring collisional kerma at short distances for spherical sources with active and capsule materials mimicking those of actual sources. Electronic equilibrium is reached to within 1% for 192 Ir, 137 Cs, 60 Co, and 169 Yb at distances greater than 2, 3.5, 7, and 1 mm from the source center, respectively. Electron emissions are important (i.e., >0.5% of the total dose) within 3.3 mm of 60 Co and 1.7 mm of 192 Ir source centers but are negligible over all distances for 137 Cs and 169 Yb. Ballester et al.  concluded that electronic equilibrium conditions obtained for spherical sources could be generalized to actual sources, while electron contributions to total dose depend strongly on source dimensions, material composition, and electron spectra. Consequently, no extrapolation method can accurately predict near-source dose rate distributions because they depend on both the extent of electronic disequilibrium and the electron dose at distances closer than the minimum tabulated results. However, tabular data containing voids close to and inside the source should not be presented, and adoption of the TG-43U1S1 extrapolation method for r < r min using the nearest neighbor data for g L (r) is recommended until such time as future studies generate data for this region. For F(r, ), HEBD decided to take advantage of partial data and proposed the following approach as a compromise to maintain consistency with the TG-43U1S1 report: fill in missing data for partially complete F(r, ) tables using linear extrapolation in polar angle for fixed r based on the last two tabulated values, and use zeroth order (nearest neighbor) extrapolation for r < r min as recommended in the AAPM TG-43U1S1 report. It is emphasized that extrapolated values are only included for the purpose of providing complete data tables as required by some TPS. Dose data outside the source
31 High-energy photon-emitting brachytherapy dosimetry 15 obtained from these extrapolated values could be subject to large errors due to beta (electron) contribution, kerma versus dose differences, and linear extrapolation limitations. Data inside the source are only provided for TPS requirements and they do not have any physical meaning. These extrapolated values should be used with caution in clinical dosimetry because potentially large errors exist; this scenario is different from the low-energy case of TG-43U1S1 where differences between MC calculated and extrapolated doses are generally minimal. The formalisms of the 1995  and 2004  TG-43 reports were based on dosimetric characteristics of seed models for brachytherapy sources containing 125 I, 103 Pd, and 192 Ir having nearly spherical dose distributions, given their relatively large ratios of radial distance to active source length. Therefore, it is appropriate to use the polar coordinate system to describe dosimetric parameters around these sources. However, several investigators have shown that this approach fails when the active length is greater than the distance to the POI. [80 83] Alternatively, the advantage of using the cylindrical coordinate system (Y, Z) based TG-43 formalism has been demonstrated for dose calculations around elongated brachytherapy sources by Patel et al.  and Awan et al.  Detailed comparisons between the polar and cylindrical coordinate based formalisms are given by Awan et al.  and the forthcoming AAPM TG-143 report. In these comparisons, it has been demonstrated that the basic dosimetry parameters in the two coordinate systems are very similar. The main difference is in the F(r, ) definition: F pol ( r, )= F cyl Y, Z ( ) gy ( ) gr ( ). (1) However, the cylindrical coordinate system based formalism provides a more accurate tool for interpolation and extrapolation of dosimetry parameters for a given source, since the spatial sampling better approximates the cylindrical radiation dose distribution. For the high-energy sources considered in this report, the active length up to 1.5 cm, the TG-43 approach using polar coordinates also applies well if adequate mesh resolution is utilized, and then it is recommended here. Dosimetric considerations (source calibration, TG-43 parameter derivation, TPS implementation, etc.) for sources with larger active lengths and curved lengths are being evaluated by AAPM TG-143. III.C. Dosimetry parameter dependence on active length The dosimetric properties of a brachytherapy source depend upon the geometry and material composition of the source core and its encapsulation. For high-energy photon emitters such as 192 Ir, the material composition dependence is much less pronounced than that for low-energy emitters such as 125 I. [1,2] This leads to a greater similarity of TG-43 dosimetry parameters for high-energy sources containing the same radionuclide and having comparable dimensions than for low-energy sources. For example, a study by Williamson and Li  comparing the original microselectron Classic HDR 192 Ir source (Nucletron B.V., The Netherlands) with the PDR source and the old VariSource HDR 192 Ir source revealed that they have nearly identical values, and their g L (r) data agreed within ~1%
32 16 HEBD report for r > 0.5 cm. Selected reports from the literature describing such similarities for 192 Ir, 137 Cs, and 60 Co brachytherapy sources are summarized below. Wang and Sloboda  compared the transverse plane dose distributions for four 192 Ir brachytherapy sources (Best Medical model 81-01, Nucletron microselectron HDR and PDR 192 Ir sources, Varian VariSource HDR) and five hypothetical 192 Ir cylindrical source designs using the EGS4 MC code. The transverse-plane dose rate and air-kerma strength s K per unit contained activity were calculated in a spherical water phantom of R = 15 cm and a dry air sphere of 5 m diameter, respectively, to study the influence of the active length L and R on these quantities. For r 4L, the transverse-plane dose rate and s K depended on R but not on L, and were proportional to the corresponding quantities for an unencapsulated point source to within 1%. When the transverseplane dose rate was normalized to s K, differences in the dose rate profiles between the various sources disappeared for r 4L. For r < 4L, the transverse-plane dose rate and s K were dependent on both R and L, and the geometry function G(r, ) was the principal determinant of the shape of the normalized dose rate profile. Photon absorption and scattering in the source had a considerably smaller influence and partly compensated one another, whereas differences in the photon energy fluence exiting the source were not of sufficient magnitude to influence absorption and scattering fractions for the dose rate in water. Upon calculating and g L (r) for the four real sources using G L (r, ) (except for the microselectron PDR source for which the particle streaming function S L (r, ) was used),  observed differences in were explained on the basis of differences in G L (r, ) and source core diameter d. For r 1 cm, g L (r) were similarly identical within 1%, and small differences for r < 1 cm were caused by varying degrees of photon absorption and scattering in the sources. Karaiskos and colleagues  obtained TG-43 dosimetry parameters for 192 Ir wire of active lengths 0.5 cm L 12 cm and internal diameters d = 0.1, 0.3, and 0.4 cm using an in-house MC code and a modified Sievert-integral method. They employed G L (r, ), as they had previously shown it to introduce differences of <1% compared with S L (r, ) for r > L/2 and similarly small differences for clinically relevant wire lengths of 4 to 6 cm for r L/2.  With the line source approximation, a scaling relation holds between geometry functions for sources of different active lengths L and L G L G L ( r, ) ( r, ) = Lrsin ( ) L r sin ( ) = L r Lr = L L, (2) where is the angle subtended by the active length with respect to the calculation point P(r, ) and r r = L due to similar triangles. Karaiskos et al. subsequently determined that for wires of equal L length was only weakly dependent on d, differences being <3%. Based on this observation, they
33 High-energy photon-emitting brachytherapy dosimetry 17 showed that for any 192 Ir source of active length L can be related to that of a reference source of active length L REF using: L ( ) = LREF ( ). (3) G L r 0, 0 G LREF r 0, 0 This relation was found to hold to within 2% for L REF 5 cm, and to <3% when realistic HDR 192 Ir brachytherapy sources were considered. Thus, this relation can be used to calculate for 192 Ir wires of arbitrary length, and may also be useful to check the consistency of EXP- or MC-derived values for other source models. The investigators also determined that g L (r) for 0.2 cm r 10 cm was independent of L to <2% and of d to <3%. They concluded that MC-calculated values of g L (r) for L set to 5 cm were adequate for most any length. Sievert-integral  calculated F(r, ) values decreased as d increased, but by no more than 3% over all radial distances examined. MC-calculated F(r, ) values were nearly unity for polar angles for all r and L. However, a strong dependence on both r and L was observed for < 30. This was due in part to the fact that the main dose contributor to a point close to the source is the source segment closest to that point; whereas for points further away from the source, the entire source length contributes and F(r, ) decreases for polar angles close to the long axis due to oblique filtration within the source structure. Then, van der Laarse et al.  developed these ideas to create a new method, named the Two Length Segmented (TLS) method, which models brachytherapy dose parameters for 192 Ir wires of any length and shape using dose parameters for straight wire segments 0.5 and 1.0 cm in length. The resultant dose rate distributions around straight and U-shaped wires agreed better with MC calculations than those obtained with the Point Segmented Source method, Line Segmented Source method, or Karaiskos et al.  dose calculation models. Papagiannis et al.  performed a dosimetry comparison of five HDR 192 Ir sources (old and new Nucletron microselectron, old and new Varian VariSource, and the Buchler source), the LDR 192 Ir seed (Best Medical model 81-01), and the LDR 192 Ir wire source (Eckert & Ziegler BEBIG GmbH) in an R = 15 cm liquid water sphere using their own MC code. They tested the validity of equation (3) relating using the reference geometry function G L (r 0, 0 ), with a point 192 Ir source serving as the reference, and found that the ensuing expression, = 1.12 G L ( r 0, 0 ) cgy h 1 U 1 (4) yielded with differences <2% at reference radial distances of 1 and 2 cm for any of the 192 Ir source designs. The value 1.12 cgy cm 2 h 1 U 1 corresponds to for an 192 Ir point source.  These investigators also found that g(r) for all sources except the Buchler source were in close agreement for distances 0.1 cm r 5 cm, and lay within 2% of g(r) for a point 192 Ir source. The Buchler
34 18 HEBD report source presented a slight increase at radial distances r < 0.5 cm, possibly arising from hardening of the emerging photon spectrum due to its larger source core diameter. All sources were observed to exhibit non-negligible anisotropy, with F(r, ) values being strongly dependent on source geometry. F(r = 0.2 cm, ) did not significantly differ from unity over all polar angles for all sources since the main contributor to the dose rate at P(r, ) is the source segment closest to that point. Using their established MC code, Karaiskos et al.  compared the dosimetry of the old and new Nucletron microselectron PDR 192 Ir source designs in an R = 15 cm liquid water sphere. They found the to be identical to each other and to that for a point source to within statistical uncertainties of ~0.5% and explained the result in terms of equation (3) on the basis of the short L of 0.6 and 1.0 mm for the sources. Using S L (r, ), [87,89] the g L (r) values were found to be identical within 1% to those obtained using the linear source approximation G L (r, ) over the distance interval 0.1 cm r 14 cm. When the point source geometry function r 2 was used, differences >1% were observed only for r < 0.3 mm. The F(r, ) for both source designs was found to be significant only at polar angles close to the longitudinal source axis ( < 30 and > 150 ) and to be greatest within these angular intervals at intermediate radial distances for reasons discussed previously.  The new design presented increased F(r, ) up to 10% at polar angles near = 0 (distal end of the source) as a result of its longer active core. Casal et al. [63,67] and Pérez-Calatayud et al. [63,67] calculated the dose rate distributions around three different LDR 137 Cs sources (Amersham models CDCS-M, CDC-1, and CDC-3) in a 40 cm high, 40 cm diameter water cylinder using the GEANT3 MC code. TG-43 dosimetry parameters were obtained using G L (r, ). For the model CDCS-M source they found /G L (r 0, 0 ) constancy, 1.05 cgy cm 2 /(h U), within 0.9% for the corresponding ratio of the model CDC-J source, which had the same encapsulation but a 1.5 mm shorter active length. The latter ratio was determined from MC data published by Williamson.  For the CDC-1 and CDC-3 sources, the values of /G L (r 0, 0 ) differed by only 0.1%. For all three sources, g L (r) was no more than 1% different from the normalized Meisberger polynomial for 0.5 cm r 10 cm.  The F(r, ) results corresponded to the varying self-attenuation associated with the different source designs. Papagiannis et al.  compared the dosimetry of three HDR 60 Co sources containing two active pellets in contact or spaced 9 or 11 mm apart, used in the Ralstron remote afterloader. MC calculations for an R = 15 cm water sphere were done with the group s own simulation code and included electron transport for r < 0.5 cm. The dose rate distribution around the source having the pellets in contact closely resembled that for an unencapsulated 60 Co point source. As r increased sufficiently for the point-source approximation to apply, the dose rate distributions for the other two designs also conformed to that of a point source, presenting only minor spatial dose anisotropy close to the source long axis. The main influence on once again proved to be the spatial distribution of activity, represented by G L (r, ), for reasons similar to those cited for commercial 192 Ir source designs. Consequently, the relation
35 High-energy photon-emitting brachytherapy dosimetry 19 = G L ( r 0, 0 ) cgy h 1 U 1, (5) where = cgy cm 2 h 1 U 1 for a 60 Co point source,  was used to obtain values for realistic 60 Co sources within ±2%. Using the G L (r, ), g L (r) also agreed within 2% for 0.5 cm r 15 cm. However, using G P (r), differences of up to 28% were noted. F(r, ) for all three source designs calculated using G L (r, ) indicated that dose anisotropy was negligible for r 1 cm, and was only evident for r > 1 cm at points close to the source drive wire ( ~ 180 ). In summary, the dosimetry for r < 2 cm is primarily determined by the contained activity distribution for high-energy photon-emitting brachytherapy sources. The influence of photon attenuation and scattering in the source core and capsule is comparatively smaller in magnitude, and is further diminished when Dr, ( ) S K is calculated. As a consequence, for commercially available 192 Ir, 137 Cs, and 60 Co brachytherapy sources containing the same radionuclide are equal (within a few percent) to the product of for an unencapsulated point source and G L (r, ). Corresponding g L (r) values for sources containing the same radionuclide that have been extracted from dose distribution data using G L (r, ) also agree to within a few percent over the radial interval 0.3 cm r 10 cm. Self-attenuation in the active core and surrounding encapsulation characterizing each source design influences F(r, ).
36 20 HEBD report IV. CONSENSUS DATASET METHODOLOGY The source models reviewed in this report satisfy the AAPM/ESTRO recommendations published by the HEBD in Li et al.  The consensus methodology for these high-energy sources is similar to that recommended for low-energy sources by LEBD  but has been adapted for highenergy sources. According to these HEBD recommendations,  there are two source categories: 1. For conventional encapsulated sources similar in design to existing or previously existing ones, a single dosimetric study published in a peer-reviewed journal is sufficient. MC or EXP dosimetry (or both) methods may be used. 2. For all other high-energy sources, at least two dosimetric studies published in peer-reviewed journals by researchers independent of the vendor, one theoretical (i.e., MC-based) and one experimental, are required. In the present report, all 192 Ir and 137 Cs sources are categorized as conventional encapsulated sources. While not commercially available at the time of publication of the current recommendations, HDR 60 Co sources are also included in this first category. The remaining radionuclides, 169 Yb and 170 Tm, fall into the second category. Similarly to the AAPM TG-43U1 report, appropriate publications reporting single source dosimetry were evaluated. For each source model, a single TG-43U1 consensus dataset ( CON L, CON, CONg L (r), CON F(r, ) including data up to r = 10 cm) was derived from multiple published datasets as detailed below. If items essential to critical evaluation were omitted from a publication, the authors were contacted for information or clarification. The methodology followed to derive a consensus dataset was as follows: 1. The peer-reviewed literature was examined to identify candidate datasets for each source model that were derived either from measurements or MC studies and that followed the guidelines of the TG-43U1  and HEBD report.  The quality of each dataset was then examined, taking into consideration salient factors such as data consistency, MC code benchmarking, etc. 2. The value of CON was obtained from MC data for the following reasons: MC results uncertainties were always less than the measured uncertainties. Frequently, only MC results were available without measured results, and the variations of MC were typically less than the MC uncertainties for high-energy sources. The EXP have been in good agreement with MC. For example, Daskalov et al.  showed that EXP for the mhdr-v2 source agreed with MC to within 2%. The value from Meisberger et al.  agreed to within 0.3%. 3. In most cases, CON g L (r) and CON F(r, ) were taken from a single MC study. When available, experimental studies were used to validate MC g L (r) and MC F(r, ). Data selection was based on
37 High-energy photon-emitting brachytherapy dosimetry 21 highest spatial resolution (r and ), largest radial range, and highest degree of smoothness. Even though some selected published data used the point-source approximation or the particle streaming function, [87,89] those data were transformed for use with the linear geometry function. 4. Values of CON g L (r) were determined for full scatter conditions as described in section III.A and for values of r 10 cm. 5. As described in section III.B, a candidate publication s g L (r) and F(r, ) data were examined to determine whether the values at short distances took into account a possible lack of electronic equilibrium (if collisional kerma was simulated instead of absorbed dose) and included any non-negligible beta component. This issue should be addressed in the publication because of the dependence of g L (r) at short distances on capsule material and thickness. If it was not, data at affected small r were removed. Future publications need to explicitly consider these electronic dose effects. 6. If the liquid water phantom used in a selected MC calculation did not generate g L (r) under full scatter conditions for r 10 cm, the data were corrected to unbounded conditions as justified in section III.A according to the polynomial corrections in Table II. These modified values are indicated using [brackets] in the consensus dataset tables. 7. Data inside the source are only provided for TPS requirements and they do not have any physical meaning. These data are italicized. 8. For sources included in this report, AAPM/ESTRO recommends the 2D brachytherapy dosimetry formalism and 2D tables: F(r, ), G L (r, ), and g L (r). Source orientation is considered in all currently available TPS for nonpermanent implants. From the clinical point of view, source orientation is more relevant along and near the source long axis for high-energy dosimetry. There are a significant number of treatments in which the long-axis dose close to the first source position is included in the target prescription (i.e., gynecological applications). In contrast, it is less relevant for low-energy permanent implants with many seeds, where source orientation averaging is adequate. 9. Data interpolation of g L (r) and F(r, ) is needed for dataset comparison and within consensus tables. In the TG-43U1 report,  interpolations were required to yield 2% error. For the highenergy regime, this should be reduced to 1%. Interpolated data are indicated by boldface and follow the methodology described in section III.B. 10. Similar to TG-43U1S1, CON g L (r) values were tabulated on a common mesh for all source models of the same radionuclide. In contrast, the mesh used for CON F(r, ) follows the one(s) included in the selected publication(s). CON g L (r) starts from the minimum available distance, and continues with the common mesh [0.25, 0.5, 0.75, 1, 1.5, 2, 3, 4, 5, 6, 8, 10] cm, according to section III.B, to ensure linear-linear interpolation accuracy within 1%. Further, for the case of 60 Co, high-resolution radial distance data are required in the vicinity of the source. The minimum r-value in the consensus dataset may be different as a function of the source model
38 22 HEBD report considered, physical processes in play based on photon energy, and the method used to simulate or measure dose in this region. 11. According to section III.B, the recommended angular mesh for CON F(r, ) is: 0 to 10 (1 increments), 10 to 20 (5 increments), 20 to 160 (10 increments), 160 to 170 (5 increments), 170 to 180 (1 increments). Consensus data were selected based on having an angular mesh closest to the recommended one. 12. Extrapolation of consensus datasets was performed following the methodology described in section III.B. Extrapolated values are underlined in dataset tables. 13. Upon derivation of the consensus TG-43 dataset, an away-along dose rate table was obtained (cgy h 1 U 1 ) for TPS quality assurance purposes. Range and resolution of this table are: away [0, 0.25, 0.5, 0.75, 1, 1.5, 2 7 (1 cm increment)] cm and along [0, 0.5, 1, 1.5, 2 7 (1 cm increments)] cm. 14. To provide a consistent convention for all brachytherapy sources, the angle origin is selected to be the source tip, i.e., is defined such that 0 is in the direction of the source tip. For the case of asymmetric LDR sources (without driven cable) the angle origin will be clearly identified for each source model. The origin of coodinates is selected to be the center of the active volume for all sources. Published data with a different angle/coordinate origin were transformed accordingly. This convention is recommended for future studies. The criteria used to evaluate dosimetry parameters for each source were similar to those of the TG-43U1 report and are as follows: 1. Internal geometry and description of the source. 2. Review of pertinent literature for the source. 3. Measurement medium to liquid water medium corrections (if applicable). 4. Experimental method used. 5. Geometry function used; active length assumed for the line source approximation. 6. Name and version of MC code. 7. MC cross-section library. 8. Variance reduction techniques used (for s K and dose in water). 9. Electron emission inclusion. 10. Photon emission spectrum. 11. MC benchmarking according to the HEBD prerequisites.  12. Phantom shape and size used in MC and EXP. 13. Agreement between MC and experimental dosimetry (if applicable, according to the HEBD prerequisites). 
39 High-energy photon-emitting brachytherapy dosimetry 23 IV.A. Dose rate constant As pointed out in TG-43U1,  MC and experimental studies complement one another, and when combined can average out possible biases of each individual methodology. In contrast to the low-energy case, the high-energy CON is obtained from the average of MC values alone, while available EXP are used to validate MC. For the sources considered in this report, the EXP agrees with MC to within 2%.  This approach is justified because unlike for lower energy sources, the influence of source geometry on the dose distribution is less important at higher energies. It also has the advantage of utilizing the smaller uncertainties of the MC method, thus providing reduced uncertainty in the value of CON. In the case of sources within the category of conventional encapsulated, similar to existing ones for which just one study was available, the value was compared with those for sources of similar design, first removing the geometrical dependence by forming the ratio /G L (r 0, 0 ), as discussed in section III.C. Based on trends observed during the compilation of this report, the agreement between MC- and EXP-derived values should be 1%. IV.B. Radial dose function For each source, MC and experimental g L (r) results were graphically compared. When a published study used a geometry function that was different from the simple linear geometry function, g L (r) was recomputed. Based on trends observed during the compilation of this report, the agreement between MC and EXP g L (r) values should be 3%. The most complete and smooth MC dataset was selected that also considered electronic disequilibrium and the dose from electron emissions. IV.C. 2D anisotropy function For each source, published F(r, ) values from MC and EXP results were graphically compared. If a geometry function different from the simple linear geometry function was used, F(r, ) was recomputed. Based on trends observed during the compilation of this report, the agreement between MC and EXP F(r, ) values, when available, should be 5%.
40 24 HEBD report V. RECOMMENDATIONS ON DOSIMETRY CHARACTERIZATION METHODS FOR HIGH-ENERGY PHOTON-EMITTING BRACHYTHERAPY SOURCES The TG-43U1 report  on low-energy brachytherapy contains many methodological recommendations and suggestions that should be followed by investigators who would like their published work, whether based upon experimental or computational methods, to be considered as a reference-quality dataset for inclusion in the consensus dose-distribution formation process. In general, all TG-43U1 guidelines and recommendations are also applicable to high-energy source dosimetry, unless otherwise specified in the sections below. Thus, the present recommendations emphasize mainly variances from the TG-43U1 LEBD-recommended methodology for obtaining brachytherapy dosimetry parameters. In 2007, AAPM/ESTRO recommendations on dosimetric prerequisites for routine clinical use of photon-emitting brachytherapy sources with average energies higher than 50 kev were published.  These recommendations, similar to the AAPM LEBD recommendations  apply to brachytherapy sources that are intended for routine clinical use, and were intended to define minimum requirements for future source dosimetry studies so that the accuracy and consistency of the consensus datasets may be improved. In the current report, only the deviations from the TG-43U1 recommendations  (section V, p. 650) necessitated by the higher photon energies or different physical configurations of the sources are noted. These are categorized as (A) preparation of dosimetry parameters, (B) reference data and conditions for brachytherapy dosimetry, (C) and (D) methodological recommendations, (E) uncertainty analyses, (F) publication of dosimetry results, and (G) non-mc computational methods. V.A. Preparation of dosimetry parameters For the high-energy sources, e.g., HDR 192 Ir sources, dosimetric parameters should be tabulated for 2D formalisms. Exceptions include spherical pellets (e.g., 137 Cs Selectron from Nucletron) where a 2D model cannot be formulated. Regardless of the dimensionality of the formalism adopted, the line-source approximation should always be used for computing the geometry function (with the obvious exception of spherically symmetric sources), G L (r, ), and g L (r). For reader convenience, we include the following alternative expression for G L (r, ): G L r cos L r cos + L cos 1 2 cos 1 2 r 2 + L 2 2 Lr cos r 2 + L Lr cos ( r, )=. (6) Lrsin
41 High-energy photon-emitting brachytherapy dosimetry 25 This expression of G L (r, ) has been included in which cos and cos 1 are used as alternatives to tan and tan 1. The practical reason is that a negative argument of tan 1 results in a negative angle, instead of an angle between 90 and 180 as required by the TG-43 formalism polar coordinate system. For F(r, ) and g L (r), the minimum-maximum range for r and, and the resolution within this range where dose rate shall be calculated or measured, has been discussed in section IV. If polynomial fits are presented, care should be taken to assure agreement within 0.5% between the polynomial fit prediction and the original tabulated data over the whole range. Special care must be taken rounding-off parameters from the fit. To assure that g(r 0 = 1 cm) = 1 with enough precision, the summation of all the parameters must be Further, the range over which the fit is applicable should be stated. In addition to the TG-43 dosimetry parameters, a derived away-along table should be included for TPS QA testing purposes as described in section IV. V.A.1. Air-kerma strength As similarly recommended in the TG-43U1 report,  source strength for high-energy sources should be expressed in terms of air-kerma strength or reference air-kerma rate (RAKR), not apparent activity, mg-ra-eq, or other antiquated units. Exceptions may result in patient harm. V.A.2. Dose rate constant All TG-43U1 recommendations are applicable to high-energy sources, with the exception that for conventionally encapsulated 192 Ir, 137 Cs, and 60 Co sources, only a single source is required for experimental purposes. To ensure validity of the source model used by MC simulations, pinhole autoradiography,  multi-slit techniques,  and transmission radiography should be utilized to confirm the manufacturer s specifications for active length, uniform activity distribution, and physical-to-active source-tip offset. Experimental determinations of absolute dose rates to water from high-energy sources should have direct traceability of S K to a primary or secondary standard dosimetry laboratory such as the National Institute of Standards and Technology (NIST) or an Accredited Dosimetry Calibration Laboratory (ADCL). Experimentally, is evaluated by taking the ratio Dr ( 0, 0 ) S K. V.A.3. Radial dose function In addition to the TG-43U1 recommendations, investigators must consider using coupled photon-electron MC codes for short distances where secondary charged particle equilibrium failures imply a deviation of dose from collisional kerma in excess of 2%. As discussed in section III.B, deviations greater than 1% may occur at distances less than 7, 3.5, 2, and 1 mm from the center of 60 Co, 137 Cs, 192 Ir, and 169 Yb sources, respectively. Similarly, -ray transport must be simulated at distances where dose-to-kerma ratio deviations exceeding 1% are possible.
42 26 HEBD report V.A.4. 2D Anisotropy function The recommendations of the AAPM TG-43U1 report  are to be followed. V.B. Reference data and conditions for brachytherapy dosimetry V.B.1. Radionuclide data The influence of photon spectrum choice on brachytherapy dosimetry parameters such as and g(r) has been studied by Rivard et al.  For 192 Ir sources, they found that the uncertainties propagated to these parameters by photon-spectrum uncertainties were much less than 1% (k = 1). Given the standardization of radionuclide data available from the NNDC and the rigorous infrastructure for performing and maintaining the dataset evaluations, the AAPM and ESTRO recommend that NNDC data be used for clinically related applications of all brachytherapy.  V.B.2. Reference media As recommended by TG-43U1, pure degassed liquid water (H 2 O) with a mass density of g/cm 3 at 22.0 C should be used for MC as the medium for both specification of absorbed dose and dose distributions. As clarified in the TG-43U1S1 report,  dry air (0% humidity) is recommended for S K in contrast to the TG-43U1 report, which recommended air at 40% relative humidity. The composition of dry air is given in Table XIV of the TG-43U1 report. V.C. Methodological recommendations for experimental dosimetry Historical reviews of experimental dosimetry for interstitial brachytherapy sources, including high-energy sources, appear in Williamson  and, for 192 Ir only, in the original TG-43 report.  Starting from the earliest work of Meredith et al.,  who used a cylindrical perspex ion chamber to measure exposure in air and water for 192 Ir interstitial sources, and progressing to dose measurements using lithium fluoride (LiF) TLDs in solid phantoms, these papers and their associated references give an excellent perspective on experimental dosimetry methodologies in this field. A more detailed and contemporary review of experimental brachytherapy dosimetry methods, including emerging detector technologies such as radiochromic film, gels, and liquid-filled ionization chambers, has been given by Williamson and Rivard.  V.C.1. Detector choice Experimental determination of dose distributions around high-energy brachytherapy sources face the same challenges as their low-energy counterparts: high-dose gradients near the source and low-dose rates further away. Moreover, at close distances to the brachytherapy source, detector size can significantly influence dose measurement accuracy due to averaging in the presence of high dose
43 High-energy photon-emitting brachytherapy dosimetry 27 gradients and source self-attenuation. Thus, a suitable detector should possess a wide dynamic range, high sensitivity, flat energy response, and small geometric dimensions. A number of detectors (e.g., diodes, radiochromic films, and TLDs) satisfy the above criteria and therefore have commonly been used. Dosimeters used for reference data should satisfy the following criteria: 1. A relatively small active volume such that effects resulting from averaging of high-gradient dose fields over this volume are negligible or are accurately accounted for by correction factors. 2. A well-characterized energy-response function such that differences between the calibration energy and experimentally measured energy are either negligible or may be quantitatively accounted for. 3. Sufficient precision and reproducibility to permit estimation of dose rate in medium with k = 1 Type A (statistical) uncertainties 3% and k = 1 Type B uncertainties 6%. While no practical detector system perfectly fulfills the three requirements above, among the established dosimetry techniques, LiF TLD-100 detectors provide a good trade-off between flat energy dependence, small size, and detector dynamic range for both high- and low-energy brachytherapy sources and thus has been used most frequently. [99,100] For example, silicon diodes, which have smaller active detector volumes and larger sensitivities (reading per unit dose in water), violate requirement 2 above. They have sensitivities that vary by as much as 60% with respect to source-detector distance [101,102] for 169 Yb and 192 Ir sources due to the variation in photon spectra. Thus, the AAPM and ESTRO currently do not recommend silicon diode detectors for reference-quality dose measurement for sources with mean energies exceeding 50 kev. Among validated and fully developed dosimeter technologies, TLD dosimetry has the least position-dependent sensitivity for high-energy sources. TLD energy response has been reported to vary 10% to 15% over the 1 to 10 cm distance range for 192 Ir sources.  Similar magnitude but opposite direction variations have been reported for older (MD-55-2 and earlier) radiochromic film models. [104,105] Newer models of radiochromic film [EBT [ ] and EBT2 [ ] include small concentrations of a medium atomic number loading compound designed to compensate for the absorbed dose under-response of the diacetylene monomer active sensor medium. EBT film type has a nearly energy-independent dose response. [113,114] MD-55-2 radiochromic film has been used successfully to measure high-resolution (<0.25 mm) absolute dose distributions around HDR 192 Ir sources  and LDR 137 Cs sources  with k = 1 total uncertainties of 4% to 4.6%, among the lowest ever reported for such measurements around a brachytherapy source using a secondary detector. However, these detectors must be considered under development at this time because of numerous artifacts (non-uniformity, dose rate dependence, film darkening kinetics, scanner artifacts) which require rigorous correction. TLD dosimetry techniques for both general radiotherapy applications [100,117] and reference-quality brachytherapy dosimetry [99,100] have been reviewed extensively.
44 28 HEBD report V.C.2. Phantom material and energy response characterization For low-energy brachytherapy dosimetry, accurate knowledge of the atomic composition of the phantom is critical for proper results.  The TG-43U1 report allows use of either singlecomponent high-purity industrial plastics or polyamine-based epoxy resin mixtures (e.g., commercial solid water), which can have somewhat variable atomic compositions in their makeup. Therefore, it is suggested that the composition be independently determined by elemental composition assays of representative samples. In all cases, phantom-to-liquid-water corrections (based upon MC calculations) must be applied to the measurements. For 192 Ir and other high-energy sources, absorbed-dose water equivalence is less dependent on phantom composition,  so that commercial plastics such as polymethylmethacrylate (PMMA) as well as single-component resin mixtures can be used with lower correction uncertainties due to knowledge of their composition. Experimentally, Meli et al.  found that PMMA, polystyrene, and Solid Water TM introduced corrections ranging from 4% to +2% relative to liquid water at distances of 3 to 6 cm. MC calculations, simulating mono-energetic point sources embedded in 1 m radius phantoms composed of liquid or Solid Water, demonstrated that the latter introduced corrections of less than 5% at 10 cm distance for photon energies greater than 100 kev. A more recent MC study  of 192 Ir phantom correction factors for cylindrical phantoms of PMMA, polystyrene, and Solid Water found that corrections depended on phantom dimensions as well as phantom media. For a phantom size of 20 cm diameter and height (typical for experimental purposes), correction factors were <4% at distances for r 10 cm. For larger 40 cm phantoms, larger corrections (up to 6% at 10 cm for PMMA) were noted. Industrial plastic phantoms (PMMA, polystyrene, or polycarbonate) for high-energy brachytherapy dosimetry are recommended. Single-component resin phantoms are recommended and should be accompanied by the appropriate phantom to water correction factors or should include an estimate of the uncertainties associated with the non-water equivalence of the phantom for sources with average photon energies greater than 0.2 MeV, but should be avoided for average energies between 0.05 and 0.2 MeV unless validated by elemental composition assays. While atomic composition measurements are mostly unnecessary in this energy range, density measurements should be performed. MC-based medium corrections (phantom to liquid water conversion factors based upon the assumed composition and actual geometry and density of the experimental phantom) should be used. However, the dosimetry investigator should also consider the dependence of detector response as a function of source distance within the phantom due to differences in response between the phantom and reference medium, i.e., liquid water. The TG-43U1 report recommended the experimental dosimetry formalism introduced by Williamson and Meigooni,  which has been updated  and whose notation is used below. An important correction factor is the relative energy response correction, E(Q 0, G 0 Q ref, G ref, r;g exp ), which accounts for the difference in detector sensitivity between the megavoltage photon beam used to calibrate the detector and the brachytherapy source irradiation geometry. G 0, G ref, and G exp are vectors corresponding to the energy-response correction factors associated with measurements taken during the calibration setup, the reference geometry (G ref = unbounded water phantom with point
45 High-energy photon-emitting brachytherapy dosimetry 29 detectors) and the source irradiation setup (e.g., G exp = (25 cm) 3 PMMA phantom, (1 1 1) mm 3 TLD-100 detectors), respectively. Q 0, Q exp, and Q ref denote the corresponding spectra in these irradiation geometries. The relative energy response correction can be factored into three separate corrections:  EQ ( 0,G 0 Q ref,g ref,r;g exp )= k rel bq ( Q 0 Q exp ; M 0 ) f rel Q 0,G 0 Q exp,g exp,r ( ) ( ) p phant,wat Q exp,g exp Q ref,g ref ;r where the intrinsic relative energy response correction is given by: rel k bq ( ) ( Q 0 Q exp ; M) k bq M,Q 0 k bq ( M,Q exp ) = M 0 D det M 0 D det ( )( r,q exp,g exp ) ( )( Q 0,G 0 ), (7), (8) where M is the detector reading and D det is the mean absorbed dose to the active detector volume. rel k bq ( Q 0 Q exp ; M) describes the efficiency with which the detector-response mechanism transforms energy imparted to its active collection volume by the brachytherapy radiation field into an observable response, relative to its efficiency in the calibration beam. The relative absorbed-dose energy dependence is given by f rel ( Q 0,G 0 Q exp,g exp,r) f r,q 0,G 0 f r,q exp,g exp ( ) ( ( ) = D det D wat )( r,q exp,g exp ) ( D det D med0 )( Q 0,G 0 ). (9) f rel is that component of relative detector response which is due only to the efficiency with which the brachytherapy spectrum imparts energy to the active detector volume relative to the corresponding efficiency in the calibration beam, when both efficiencies are normalized to dose in medium in the absence of the detector. f rel includes the displacement and volume-averaging corrections. The dosemeasurement phantom correction factor, p phant,wat (Q exp, G exp Q ref, G ref ;r), corrects for differences between the irradiation geometry used to perform the measurements and the reference geometry in which the final dose distribution is to be specified. As a ratio of geometric point doses in homogeneous media, it is independent of the detector geometry, composition, and underlying mechanism, and depends only on the reference and experimental phantom dimensions, composition, and positioning relative to other sources of scattered radiation near the measurement phantom. rel The controversies surrounding the choice of k bq ( Q 0 Q exp ; M) corrections for TLD dosimetry of low-energy brachytherapy sources, where recent experiments suggest energy response correction factors ranging from 1.05 to 1.10, have been reviewed by Williamson and Rivard.  rel While k bq values are closer to unity for high-energy brachytherapy sources, two recent publications
46 30 HEBD report found anomalously high values of k rel bq = for 137 Cs relative to 60 Co. [120,121] Overall energyresponse corrections for HDR 192 Ir brachytherapy sources have been measured, but without result comparisons to MC calculated absorbed-dose energy-dependent factors. Because definitive factors rel are not yet available, it is recommended that k bq be taken as unity for high-energy photon dosimetry, while p phant,wat and f rel should be carefully calculated for the experimental geometry used. Without additional information, a k = 1 uncertainty of 3% may be assigned to the overall energy response correction factor. For radiochromic film, it is not clear whether or not dosimetrically significant energy response corrections exist. Based on a study of Model MD-55-2, Bohm et al.  concluded that f rel MC accounted for measured E(Q 0 Q ref ) values within 5%. On the other hand, Sutherland and Rogers  found relatively poor agreement between their MC calculations and previously reported measurements. [123,124] Since radiochromic film response is highly dependent upon film composition, and depends on a host of other factors, including temporal history and temperature, [125,126] it is recommended that this detector be used cautiously. V.C.3. Specification of measurement methods Recommended methodologies for using TLD dosimetry in brachytherapy have been reviewed elsewhere. [99,100] All recommendations in section V.D.3 of the 2004 AAPM TG-43U1 report  should be followed for high-energy brachytherapy dosimetry. Careful correction for volume averaging, source and/or detector displacements, and phantom composition/size should be applied so that the final dose rates represent absorbed dose rates to water per unit S K at geometric points in an unbounded liquid water medium. The location of dose measurement points should be referenced to the geometric center of the active source core. V.D. Methodological recommendations for Monte Carlo based dosimetry Codes that have been widely used for high-energy source dosimetry include PTRAN, MCNP, GEANT4, PENELOPE, and EGSnrc. At the time of publication of this report, all these codes are based upon modern cross-section libraries and complex and accurate physics models to simulate transport of electrons and photons through complex media. All these codes have been benchmarked against experimental measurements or by code intercomparisons. For high-energy sources, collisional kerma approximates dose at distances from the source surface where electronic equilibrium is reached. However, electronic equilibrium at close distances from 192 Ir, 137 Cs, and 60 Co sources is not reached, and beta and internal conversion electrons emerging from the source capsule require detailed electron transport if accurate dose rate estimates near the sources are required (section III.B). Errors exceeding 2% will occur if photon-only MC transport simulation is used to estimate dose for distances at or below 1.6, 3, and 7 mm for 192 Ir, 137 Cs, and 60 Co sources, respectively. 
47 High-energy photon-emitting brachytherapy dosimetry 31 In general, the AAPM and ESTRO recommend that MC investigators utilize wellbenchmarked codes for brachytherapy dosimetry studies intended to produce reference-quality dose rate distributions for clinical use. A benchmarked code is able to reproduce MC simulations comparable to those obtained by other codes validated experimentally or a code whose results have been validated experimentally. However, all investigators should assure themselves that they are able to reproduce previously published dose distributions for at least one widely used brachytherapy source model. The 2007 HEBD prerequisites  stated that MC transport codes should be able to support dose rate estimation with expanded uncertainties (k = 2) no greater than the 3% to 5% characteristic of the MC transport codes currently used for low-energy source dosimetry. Also, the 2007 report included methods to benchmark the MC calculation method. Agreement between the MC results and the benchmark data should be within 2% for, 5% for g L (r), and 10% for F(r, ) within 5 from the source long axis.  Unlike for low-energy sources, the range of secondary electrons from high-energy sources will require electron transport at short distances.  V.D.1. Specification of Monte Carlo calculation methods The nine points in the list in section V.E.1 of the TG-43U1 report  are applicable to highenergy sources with the following changes: 1. Limit consideration to emitted photon energies above 10 kev (for simulations in both water and in-air or in vacuo). Based on typical PDR/HDR source encapsulations, 10 kev should be an adequate cutoff and is commonly used in publications. A lower energy cutoff does not produce more accurate results for most dosimetry applications, but prolongs the calculation time required to achieve a fixed Type A uncertainty level (or prevents finer spatial resolution with associated volume averaging). 2. All photons emitted with an energy above the 10 kev cutoff must be included in dosimetry calculations. At least one publication has reported that high-energy photons with low emission probabilities can influence results significantly.  Therefore, reference spectra must be used in their entirety in MC simulations, i.e., NNDC reference spectra  must not have low-intensity lines removed. 3. If charged particle transport is simulated, the underlying transport algorithm should be described clearly, if only by reference. The quantity used to approximate dose (e.g., collisional kerma) or any variance reduction techniques should be clearly specified. Whether beta-ray and internal conversion electron transport is included, along with the initial beta spectrum used, should be specified. V.D.2. Good practice for Monte Carlo calculations 1. Reference-quality absorbed dose rate to water distributions should be computed in liquid water in a phantom which approximates full scatter conditions characteristic of an unbounded phantom. For 192 Ir, 137 Cs, and 169 Yb sources, a spherical phantom with radius R = 40 cm (or the
48 32 HEBD report equivalent cylindrical phantom dimensions) should be used, while R = 80 cm is required for 60 Co [29 31] sources. 2. A sufficient number of histories should be calculated to ensure that the dose rate per simulated history d ( r 0, 0 ) and k air ( d, 0 ) calculations for derivation of s K have Type A uncertainties (k = 1) < 0.1% for distances 5 cm and Type A uncertainties (k = 1) < 0.2% for distances 10 cm. In evaluating s K, the confounding influence of contaminant low-energy photons below 10 kev (and contaminant electrons as well if charged-particle transport is simulated) should be assessed and corrected for if necessary. By convention, k air ( d, 0 ) and s K must be specified in dry air. 3. The influence of photon cross-section uncertainties on dose estimation accuracy has not been comprehensively studied in the high-energy brachytherapy regime. Until careful studies demonstrate otherwise, TG-43U1 recommendations should be followed. This includes use of post-1980 cross-section libraries, preferably those equivalent to the current NIST XCOM database such as DLC-146 or EPDL97. Older cross-section libraries based on Storm and Israel data [127,128] must be avoided. Electron binding effects on coherent and incoherent scattering should be simulated using the form factor approximation. In the presence of high atomic number absorbers, atomic relaxation processes resulting in characteristic x-rays exceeding 10 kev should be simulated. Mass-energy absorption coefficients used to convert energy fluence into collisional kerma must be consistent with the interaction physics models and photon cross sections used for transport. 4. Collisional kerma and dose estimators (scoring tally)  and detector volumes should be chosen to limit volume-averaging artifacts to <0.1%. To minimize the impact of voxel size effects [ ] while maintaining reasonable efficiency for track-length and analog estimators, maximum voxel sizes in Cartesian coordinates could be chosen in the following way: (0.1 mm) 3 voxels for distances in the range of r source < r 1 cm, ( ) mm 3 voxels for 1 cm < r 5 cm, (1 1 1) mm 3 voxels for 5 cm < r 10 cm, and (2 2 2) mm 3 voxels for 10 cm < r 20 cm, where r is defined as the distance from the center of the source. Rectilinear or toroidal voxels of similar radial dimensions should have similar volume-averaging effects. 5. Especially for photon sources in the 50 to 300 kev energy range, the manufacturer-reported dimensions of encapsulation and internal components should be verified through the use of physical measurements, transmission radiography, and autoradiography. For all sources, transmission radiography and pinhole radiography should be used to verify the active source dimensions and location relative to the physical source dimensions, and that the radioactivity is approximately uniformly distributed. The impact of internal source component mobility  on the dose distribution should be assessed. 6. Some MC studies consider the effect of electronic non-equilibrium conditions near a brachytherapy source, or the beta-ray contribution to the dose distribution near the source. In these cases, secondary electron transport should be simulated. To avoid inconsistencies and systematic errors in the results, the following precautions should be heeded. Because
49 High-energy photon-emitting brachytherapy dosimetry 33 brachytherapy simulations involve rather extreme conditions (very small detector thicknesses, low energies, etc.) that may invalidate the approximations upon which the charged particle transport algorithms are based, they may produce artifacts that are evident only in extreme cases but that are masked in other situations. The following precautions cover different aspects including physics models implemented in the codes and electron tracking techniques, among others: a. Usually, the simplest strategy is to perform test simulations starting with standard simulation parameters recommended for the code under consideration, followed by other test runs that vary these parameters to study their influence on the final results. b. Electron step size is a critical parameter that influences deposited doses in small geometry regions. It should be handled with care in each simulation and, if adjustable, parametric studies should be performed to demonstrate that the dosimetric results are not sensitive to this parameter choice. c. Some multiple scattering (MS) theories place limits on the minimum number of mean collisions that must occur in each condensed history step for validity to be maintained. The existence of steep dose gradients at the distances of interest necessitates high spatial resolution for dose computation. Consequently, shells to score dose are very thin close to the source. The Molière MS minimum step size imposes a restriction on the spatial resolution of MC simulation. Care must be taken to maintain the dimension of the scoring region above this limit.  This limitation affects mainly codes derived from EGS4. d. The user must be sure that the number of interactions in a voxel is large enough (a minimum of 10) for the result to be statistically well behaved. e. Some codes handle boundary crossing algorithm corrections poorly while others generate artifact-free corrections. Switching to single-scattering mode near boundaries is the preferred solution. For example, Type-1 transport algorithms (MCNP, ITS, ETRAN), which use Goudsmit-Saunderson multiple-scattering formalism parameters, stopping powers, and energy-straggling corrections precalculated on a fixed logarithmically spaced energy-loss grid, are particularly subject to boundary crossing algorithm artifacts as media and detector interfaces truncate condensed history steps at arbitrary intermediate values. The influence of such partial steps cannot be recovered by interpolation of precalculated data. Chibani and Li  demonstrate that pre-2000 versions of MCNP-determined lowenergy electron dose distributions were sensitive to choice of energy-indexing (boundary crossing algorithm interpolation scheme). f. Variance reduction techniques are often implemented in the codes and although they are generally robust they should be used with care. In particular, the user is advised to check that results are unbiased. V.E. Uncertainty analyses Both experimental and MC determinations of reference-quality single-source dose rate distributions should include formal uncertainty analyses that adhere to the methodology of NIST Technical Note  While a number of publications, [100,137] including the TG-43U1  and TG-
50 34 HEBD report 138  reports give detailed guidance on applying this methodology to low-energy brachytherapy, complete and rigorous uncertainty analyses for high-energy brachytherapy are generally lacking. However, extensive uncertainty analyses are given by Raffi et al.  for HDR 192 Ir experimental and MC and Granero et al.  for HDR 192 Ir MC simulations. These papers include both Type A and Type B uncertainties. These uncertainties are in agreement with those in the AAPM TG-138 report, and are over a factor of two lower than those in Table XII of the TG-43U1 report for low- and highenergy sources. While 169 Yb has been considered by some manufacturers, the S K calibration uncertainties are still a matter of study and are of the order of 3% (k = 1). As similarly recommended in section V.D.3(10) and section V.E.1(9) of the AAPM TG-43U1 report for measurements and simulations of low-energy photon-emitting brachytherapy dosimetry studies, respectively, the AAPM recommends that high-energy brachytherapy source dosimetry investigators perform detailed uncertainty analyses in a manner similar to Raffi et al., and Granero et al., yet specific to the source model and conditions examined in their investigation. V.F. Publication of dosimetry results As recommended by TG-43U1  and the HEBD prerequisites,  commercially distributed high-energy sources used in routine clinical practice should be supported by two independent dosimetry studies that adhere to the methodological recommendations of this report. As defined by TG-43U1, independence requires (a) that dosimetry investigators be free of affiliations or other conflicts of interest with the source vendor and (b) the two studies be scientifically independent of one another. The Li et al.  recommendations require that one study be experimental (usually TLDbased) and that the other be theoretical (MC). The studies must be published in the peer-reviewed literature. A technical note format is acceptable as is publishing the two independent studies in the same publication. Given publication length limitations, AAPM committees do not require that all expected or needed documentation and method description be included in the published paper. However, it must be either posted electronically with the online version of the paper or made available by the authors via a personal communication upon request. Conventionally encapsulated 192 Ir, 137 Cs, and 60 Co sources require only a single MC-based study for comprehensive dose characterization. Some TPS algorithms correct the dose from full scatter to the clinical specific conditions, and require dosimetry parameter data based on full scatter conditions. For some of these TPS algorithms, it has been proposed that the primary- and scatter-component functions be obtained from TG-43 based dose rate tables and will need to be handled independently by the TPS dose calculation algorithm.  V.G. The role of non Monte Carlo computational tools in reference dosimetry Over the years, a variety of computational tools, in addition to MC simulation, have been proposed or even widely used for the determination of single-source dose distributions in the highenergy photon regime.
51 High-energy photon-emitting brachytherapy dosimetry 35 Heuristic analytical model algorithms were not introduced as dosimetry or dose-estimation tools, but as treatment-planning tools for computing more realistic and accurate dose distributions for clinical multi-source implants in the presence of tissue-composition and density heterogeneities, applicator shielding and attenuation, and inter-seed attenuation. Accelerated MC simulation codes  have also been adapted for clinical dose computation. The potential for these innovations in clinical dose computation has been reviewed by Rivard et al.  and is the subject of the active AAPM Task Group 186. Prior to community-wide acceptance of the 1995 AAPM TG-43 report, nearly every generalpurpose brachytherapy planning system utilized the 1D path-length or Sievert model to generate single-source dose distributions around encapsulated line sources such as intracavitary brachytherapy tubes. Comparisons with MC simulation demonstrate that with properly selected input parameters and realistic modeling of the source geometry, accurate results (2% transverse axis and 5% longitudinal axis differences) can be achieved for 137 Cs tubes and needles. [57,141] However, for lower energy sources, including LDR 192 Ir seed and HDR 192 Ir sources, accurate modeling of 2D anisotropy corrections cannot be achieved.  Simple extensions of the Sievert model can restore accuracy in many cases, such as by separating primary and scatter components and modeling the latter as an isotropic distribution. [142,143] However, comparisons between benchmark calculations from MC or analytical methods such as the Sievert integral are required to ensure dose prediction accuracy for new source designs. Hence, 1D path-length models are not endorsed by this report for estimation of reference-quality dose distributions for any category of high-energy sources. A number of more sophisticated scatter separation algorithms, which involve one-, two-, or even three-dimensional integration of the scatter dose distribution over the implant geometry have been proposed. [73, ] Closely related are superposition/convolution algorithms  of which the most fully developed is Carlsson-Tedgren s [149,150] brachytherapy adaptation of the external-beam collapsed cone approach. As with the simpler Sievert-style algorithms, these approaches require significant fine tuning and validation against more definitive MC simulations to avoid excessive systematic dose computation errors, and thus are not acceptable as substitutes for MC simulation for estimation of reference-quality single-source dose distributions. A more empirical scatter-separation method was introduced  for CT-based planning for HDR 192 Ir brachytherapy; the primary and scatter dose distributions for each dwell position are calculated first as if the patient is an infinite water phantom. Corrections for photon attenuation, scatter, and spectral variations along medium- or low-z heterogeneities are made according to the radiological paths determined by ray tracing. The scatter dose is then scaled by a correction factor that depends on the distances between the points of interest, the body contour, and the source position. Dose calculations were evaluated for phantoms with tissue and lead (Pb) inserts, as well as patient plans for head-and-neck, esophagus, and balloon breast brachytherapy treatments. PTRAN_CT-based MC calculations were used as the reference dose distributions. For the breast patient plan, the TG-43 formalism overestimated the target volume receiving the prescribed dose by about 4% and skin D 0.1cc by 9%, whereas the analytical and MC results agreed within 0.4%.
52 36 HEBD report Deterministic transport equation solvers, most commonly discrete ordinates methods simulations, have also been investigated for their potential use in brachytherapy planning applications. [152,153] A Grid-Based Boltzmann Solver (GBBS) was introduced as a supported option in a commercially available brachytherapy planning system. [154,155] In contrast to the more sophisticated heuristic algorithms [class 1(b) above], GBBS directly solves the underlying Boltzmann transport equation on a systematically discretized seven-dimensional phase-space mesh. Because GBBS algorithms use random sampling on a very limited basis if at all, GBBS results do not suffer from statistical noise and very slow convergence rates. However, many application-specific parameters need to be optimized, including density of the angular mesh, energy group structure and weighting functions, as well as spatial mesh geometry and angular-flux interpolation technique. Inadequate optimization can lead to substantial systematic errors and artifacts, e.g., ray effects. While very promising tools for radiotherapy planning purposes, inherently more accurate MC benchmarks are required for GBBS tuning and validation. Hence, GBBS and related techniques  are not suitable reference-quality dosimetry tools. In summary, of the computational tools developed to date, only MC simulation is an acceptable method for estimating reference-quality dosimetry parameters. This is a consequence of the fundamental mathematical nature of MC simulation, which yields a statistically imprecise, but exact first-principles solution of the transport equation. While statistical noise in some settings can be a limiting problem, in the context of brachytherapy reference dosimetry it can be eliminated as a practical issue through long run times, efficient sampling techniques, or proper selection of variancereduction strategies.  Although approximations are often used within MC codes, the ideal of convergence to an unbiased solution of the Boltzmann equation is approximated to a high degree of accuracy in practice. Residual errors, e.g., volume averaging, are straightforward to correct or eliminate using modern codes. In contrast, both deterministic heuristic and transport-solution algorithms, while free of statistical uncertainty, are always subject to complex, geometry-dependent patterns of systematic error.
53 High-energy photon-emitting brachytherapy dosimetry 37 VI. RECOMMENDED DOSIMETRY DATASETS FOR HIGH-ENERGY PHOTON-EMITTING BRACHYTHERAPY SOURCES Recommended consensus datasets for high-energy sources have been obtained for sources that were commercially available as of January Data are presented according to the AAPM TG- 43U1 formalism, with upgraded interpolation and extrapolation techniques in Table III for F(r, ) and g(r). Additionally, the radial and angular ranges of the datasets are chosen to accurately represent the dosimetric characteristics given linear interpolation by TPS. A common mesh was introduced for g L (r), and the mesh of the selected publication has been kept for F(r, ). For each source model the source is described and consensus datasets are presented (Appendix A). For TPS that use the TG-43 dose-calculation formalism and permit user input of dosimetry parameters, the medical physicist should enter the dosimetry parameters and check the accuracy of the dose calculation.  These tasks should be well documented. For some TPS, dosimetry parameters are entered by the manufacturer, without the possibility of user modification. In these cases, users should verify the correct entry and document these commissioning findings before releasing the TPS for clinical use. Clinical implementation of these datasets should follow the recommendations included in section VI of the TG-43U1 report.  A medical physicist should implement the dose calculation data and techniques recommended by this report on the TPS and quantitatively assess the influence of this action on dose delivery. In cases where data are introduced as coefficients in an equation, [e.g., a polynomial function for g L (r)], it is necessary to evaluate the quality of the fit over the intended calculation range. Users must verify that the TPS follows the TG-43U1 formalism, and should also document the TPS methods for interpolation and extrapolation (applying the recommendations introduced in TG-43U1S1  and also more specifically in this report) of dose calculations within and beyond the range provided dosimetry. The dose rates calculated by the TPS from a single source should be compared with the dose rate distribution derived from the tabulated consensus values presented in this report. To facilitate this comparison, dose rate tables in a Cartesian coordinate system have been included as has been recommended previously by the AAPM (TG-40,  TG- 53,  TG-56,  and TG-43U1.  ) This comparison should yield agreement within ±2% over all angles and over the range of radial distances commissioned. Discrepancies exceeding 2% should be documented and critically examined since better agreement is expected. VI.A. AAPM-RPC Source Registry In 2001, the RTOG approached the RPC with the request to make available a list of brachytherapy sources that met appropriate criteria and could be considered usable for clinical trials. The RPC collaborated with the AAPM, which had issued a report entitled Dosimetric prerequisites for routine clinical use of new low-energy photon interstitial brachytherapy sources by Williamson et al.  Sources that met these dosimetric prerequisites were judged to be sufficiently well characterized, have adequate traceability to national standards, and be manufactured under processes
54 38 HEBD report subjected to appropriate quality control standards. Shortly afterwards, the joint AAPM/RPC Source Registry was established on the RPC web page and has been maintained ever since. Institutions considering enrolling patients in clinical trials sponsored by the U.S. National Cancer Institute (NCI) that involve low-energy seeds must use sources that are listed on the Registry. The Registry includes tables of dosimetry parameters that have been compiled from peer-reviewed publications and issued as consensus data deemed suitable by the AAPM for clinical use. Development of a new RTOG protocol requiring use of high-energy photon-emitting brachytherapy sources prompted expansion of the Registry in 2009 to include such sources. For high-energy sources to be included in the Registry, there must be compliance with the HEBD prerequisites.  The BTSC and BSR have identified a number of high-energy sources that meet these prerequisites. In response, the RPC has added these sources to the Registry. The differences in radionuclide characteristics stimulated some changes in the requirements between low- and high-energy photon-emitting brachytherapy sources. Whereas source manufacturers must submit low-energy sources at least annually to NIST or other primary standards labs for S K calibration consistency, a calibration comparison frequency of 2 years for 60 Co, 137 Cs, and 192 Ir sources is recommended. Vendors of sources containing these high-energy radionuclides should comply with this comparison frequency, and are monitored for compliance by the AAPM and ESTRO. For 192 Ir, 137 Cs, and 60 Co sources of conventional design, the Registry only requires a single published dataset. This must be a MC study of dose to water in water medium as stated in section IV. A special case exists for orphaned sources: those no longer commercially available, but still in regular use in hospitals. These must be sources with long half-lives and suitable dose rates that consequently comprise only certain models of 137 Cs and 60 Co sources. In the case of these sources, there is no manufacturer available to submit the Registry application forms. For these orphaned sources, the AAPM and RPC have developed an approved alternative procedure for Registry application: a hospital that wishes to participate in a clinical trial that involves brachytherapy sources not currently posted on the Registry may submit the application, listing the dosimetric studies available and the dosimetry parameters to be used for treatment planning. The hospital must also describe their method of source strength traceability for review by the RPC to assure the correct calibration of the sources. In the special case of source trains, in which individual sources cannot be removed for calibration with a well chamber, the hospital may describe a method of calibration at a distance in a phantom, in accordance with calibration procedures described in the peer-reviewed literature. As extensively described by Rivard et al.,  while posting of a source model on the Registry does not imply existence of an AAPM-endorsed consensus dataset, clinical use of Registry-posted data represents a reasonable choice for medical physicists, the source vendor, and clinical trial investigators for implementing newly marketed seed products. AAPM consensus datasets are typically issued within 3 years after posting on the Registry, and then included on the RPC website. In the absence of AAPM-issued consensus datasets, ESTRO manages a database for brachytherapy dosimetry parameters and other related data BRACHYTHERAPYCOMMITTEEACTIVITY.aspx. For low-energy LDR brachytherapy sources for which AAPM-endorsed consensus datasets are available, ESTRO recommends adopting these
55 High-energy photon-emitting brachytherapy dosimetry 39 datasets and the ESTRO website includes a link to the Registry website. A similar policy is implemented for high-energy sources once consensus data are published. Another online venue for brachytherapy dosimetry parameter data is the Carleton University file://localhost/website http/::www.physics.carleton.ca:clrp:seed_database. Data for this website includes results of MC simulations for 125 I, 103 Pd, 192 Ir, and 169 Yb sources. A key difference between this site and the other three venues is that the data were derived from a common MC radiation transport code, BrachyDose.  In addition to the TG-43 dosimetry parameters, dose rate tables for high-energy sources are also presented separately for primary, single-scattered, and multiplescattered photons. For the 192 Ir sources, these datasets have been evaluated in this report. VI.B. Consensus datasets Sources meeting the 2007 AAPM prerequisites  are considered in this section. The publications pertaining to each source have been evaluated following the guidelines described in section IV. Details about source characteristics including source schematic diagram, criteria for selecting consensus data among those published, and a brief discussion about the publications related to each source are available in Appendix A. This section presents a list of sources. VI.B.1. HDR 192 Ir sources The HDR 192 Ir brachytherapy sources for which consensus datasets have been obtained are as follows: a. Nucletron model mhdr-v1 (classic) source b. Nucletron model mhdr-v2 source c. Varian Medical Systems model VS2000 source d. Eckert & Ziegler BEBIG GmbH model Buchler source e. Varian Medical Systems model GammaMed HDR 12i source f. Varian Medical Systems GammaMed HDR Plus source g. Eckert & Ziegler BEBIG GmbH model GI192M11 source h. Eckert & Ziegler BEBIG GmbH model Ir2.A85-2 source i. SPEC Inc. model M-19 source j. Isodose Control model Flexisource. VI.B.2. PDR 192 Ir sources The PDR 192 Ir brachytherapy sources for which consensus datasets have been obtained are as follows: a. Varian Medical Systems model GammaMed PDR 12i source b. Varian Medical Systems model GammaMed PDR Plus source c. Nucletron model mpdr-v1 source
56 40 HEBD report d. Eckert & Ziegler BEBIG GmbH model Ir2.A85-1 source. VI.B.3. LDR 192 Ir sources The LDR 192 Ir brachytherapy sources for which consensus datasets have been obtained are as follows: a. Best Industries model seed b. Eckert & Ziegler BEBIG GmbH 0.5 and 1.0 cm long wires. VI.B.4. LDR 137 Cs sources The LDR 137 Cs brachytherapy sources for which consensus datasets have been obtained are as follows: a. Eckert & Ziegler BEBIG GmbH model CSM3 source b. Isotope Product Laboratories model IPL source c. Eckert & Ziegler BEBIG GmbH model CSM11 source. VI.B.5. HDR 60 Co sources The HDR 60 Co brachytherapy sources for which consensus datasets have been obtained are as follows: a. Eckert & Ziegler BEBIG GmbH model GK60M21 source b. Eckert & Ziegler BEBIG GmbH model Co0.a86 source. VI.C. Reference overview of sources without consensus datasets In addition to the sources enumerated in section VI.B for which consensus data have been produced, there are other sources that have been used in the past in clinical practice or are even still being used at the time of publication of this report. However, these sources were no longer commercially available as of January 2010, and consensus datasets are not issued. However, since there may be retrospective dosimetry trials involving these sources, and also to guide medical physicists still using them clinically, references are provided from which dosimetry data can be obtained (these are justified in Appendix B of the online report). Any manipulation of these datasets is the responsibility of the individual user or company. These sources are as follows: a. LDR 137 Cs: pellet, CSM2, CSM3-a, CDCS-J, 6500/6D6C, Gold-matrix series , CSM1, CDCS-M, CDC.K1-K3, CDC.K4, CDC to CDC 12035, and CDC.G and CDC.H b. LDR 192 Ir: Platinum-clad seed c. HDR 192 Ir: Varian classic d. PDR 192 Ir: Nucletron e. HDR 60 Co: Ralstron Type-1, Type-2, and Type-3.
57 High-energy photon-emitting brachytherapy dosimetry 41 NOMENCLATURE 1D 2D AAPM ADCL BRAPHYQS BSR BTSC CF CSDA CT CTV EC ESTRO EXP GBBS GBq HDR HEBD IC ICWG ISA kev LDR LEBD LiF MBDCA one-dimensional two-dimensional American Association of Physicists in Medicine Accredited Dosimetry Calibration Laboratory ESTRO BRAchytherapy PHYsics Quality assurance System Brachytherapy Source Registry (AAPM Working Group) Brachytherapy Subcommittee (AAPM) correction factor continuous slowing down approximation computed tomography clinical target volume electron capture European Society for Radiotherapy and Oncology experimental measurement Grid-Based Boltzmann Solver gigabecquerel high dose rate AAPM High Energy Brachytherapy Source Dosimetry Working Group internal conversion Interstitial Collaborative Working Group inter-source attenuation kiloelectron volt low dose rate AAPM Low Energy Brachytherapy Source Dosimetry Working Group lithium fluoride Model-Based Dose Calculation Algorithms (working group)
58 42 HEBD report MC mci MCPT MeV MRI MS NCI NIST NNDC PDR PMMA POI PSS RAKR RPC RTOG STP TG-43 TG-43U1 TG-43U1S1 TLD TLS TPS QA Monte Carlo millicurie Monte Carlo Photon Transport megaelectronvolt magnetic resonance imaging multiple scattering Natonal Cancer Institute U.S. National Institute of Standards and Technology National Nuclear Data Center pulsed dose rate polymethyl methacrylate points-of-interest primary and scatter dose separation reference air-kerma rate Radiological Physics Center Radiation Therapy Oncology Group (U.S.) standard temperature pressure AAPM Task Group No. 43 brachytherapy dose calculation formalism 2004 update to the TG-43 report 2007 supplement to the 2004 AAPM TG-43U1 report thermoluminescent dosimeter, generally composed of LiF (TLD-100) two length segmented method treatment planning system(s) quality assurance U The unit of air-kerma strength, equivalent to μgy m 2 h 1 or cgy cm 2 h 1. Angle subtended by P(r, ) and the two ends of the brachytherapy source active length. As used in the line-source approximation, has units of radians.
59 High-energy photon-emitting brachytherapy dosimetry 43 d d r 0, 0 Distance to the point of measurement from the source center in its transverseplane. Typically measured in air or in vacuo. Units of cm. ( ) The dose rate per history estimated using Monte Carlo methods at the reference position. ( ) Dose rate in water at P(r, ). The dose rate is generally specified with units cgy h 1 and the reference dose rate, Dr ( 0, 0 ), is specified at P(r 0, 0 ) with units D r, of cgy h 1. F(r, ) G X (r, ) g(r) g L (r) g P (r) CONg(r) Energy cutoff parameter used for air-kerma rate evaluation, with units of kev. 2D anisotropy function describing the ratio of dose rate at radius r and angle around the source, relative to the dose rate at r 0 = 1 cm and 0 = 90 when removing geometry function effects. Dimensionless units. Geometry function approximating the influence of the radionuclide physical distribution on the dose distribution. G X (r, ) is calculated by the following: r, G P G L ( ) = r 2 point-source approximation ( r, )= Lr sin r 2 L 2 4 with units of cm 2. if 0 ( ) 1 if = 0 line-source approximation Radial dose function describing the dose rate at distance r from the source in the transverse plane relative to the dose rate at r 0 = 1 cm. Dimensionless units. Radial dose function, determined under the assumption that the source can be represented as a line segment. Dimensionless units. Radial dose function, determined under the assumption that the source can be represented as a point. Dimensionless units. radial dose function derived from consensus dataset. Dimensionless units. k ( d) Air-kerma rate in vacuo, per history as estimated using Monte Carlo methods, due to photons of energy greater than. K ( d) Air-kerma rate in vacuo on the source transverse plane due to photons of energy greater than, with units of cgy h 1.
60 44 HEBD report CON EXP MC L Dose rate constant in water, with units of μgy h 1 U 1. is defined as the dose rate at P(r 0, 0 ) per unit S K. Notation indicating that the reported value of is the consensus value determined by the AAPM from published data, with units of cgy h -1 U -1. Notation indicating that the reported value of was determined by experimental measurement. Notation indicating that the reported value of was determined using Monte Carlo calculations. Active length of the source (length of the radioactive portion of the source) with units of cm. L eff P(r, ) r r 0 s K S K 0 The effective active length of the source. L eff is used for brachytherapy sources containing uniformly spaced multiple radioactive components. L eff = S N, where N represents the number of discrete pellets contained in the source with center-to-center spacing S. Point-of-interest, positioned at distance r and angle from the geometric center of the radionuclide distribution. The distance from the source center to P(r, ), with units of cm. The reference distance, generally 1 cm. The air-kerma strength per history estimated using Monte Carlo methods. Air-kerma strength: the product of the air-kerma rate and the square of the distance d to the point of specification from the center of the source in its transverse-plane. S K is expressed in units of μgy m 2 h 1, a unit also identified by U. The polar angle between the longitudinal axis of the source and the ray from the active source center to the calculation point, P(r, ). The reference polar angle, generally 90 or /2 radians.
61 High-energy photon-emitting brachytherapy dosimetry 45 APPENDIX A DETAILED DOSIMETRY DATASETS FOR HIGH-ENERGY PHOTON-EMITTING BRACHYTHERAPY SOURCES The general 2D dose rate equation from the 1995 TG-43 formalism is retained: D ( r, )= S K G r, L G L r 0, 0 ( ) ( ) g r L ( )Fr, ( ), (10) where r denotes the distance from the center of the active source to the point of interest, r 0 denotes the reference distance which is specified to be r 0 = 1 cm in that protocol, and denotes the polar angle specifying the point of interest, P(r, ), relative to the source longitudinal axis. The reference angle, 0, defines the source transverse plane, and is specified to be 0 = 90 (Figure 1). In clinical practice, an HDR-PDR source is fixed to a cable, such that its position and orientation are easily identified. So, we have chosen as Z- and Y-axis the longitudinal and transverse axes, respectively. The origin is taken as the center of the active part, with the positive Z-axis directed through the source tip. In the case of LDR 137 Cs sources, the source tip must be defined for each source model. Figure 1. Reference polar coordinate system for high-energy photon-emitting sources adapted from the 1995 TG-43 report.  The TG-43 formalism applies to sources with cylindrically symmetric dose distributions with respect to the source longitudinal axis. HDR-PDR sources discussed in this report can be accurately represented by a capsule and a cable, and consequently are asymmetric with respect to the transverse plane. In the case of LDR sources, 137 Cs sources are asymmetric while 192 Ir seeds and wires are symmetric with respect to the transverse axis. In the latter case, consensus datasets presented in this section assume that dose distributions are symmetric with respect to the transverse plane, i.e., that radioactivity distributions to either side of the transverse plane are mirror images of one another. For
62 46 HEBD report the sources included in this report, only the line-source approximation used for the geometry function applies. Before using data in this section, please read section III.B to be aware of extrapolation methods used for some datapoints in the tables. A.1. High Dose Rate 192 Ir sources A.1.1. mhdr-v1 (Nucletron) Source Description This microselectron HDR source was introduced in 1991 by Nucletron (Veenendaal, The Netherlands). The radioactive source (10 Ci or U) consists of a 0.60 mm diameter by 3.5 mm long cylinder of pure iridium, which is encapsulated in an AISI 316L stainless steel capsule with an outer diameter of 1.1 mm and a spherical distal end with a 0.55 mm radius of curvature. The distance from the physical source tip to the distal face of the active core tip is 0.35 mm. A schematic of the source is shown in Figure 2. Publications Figure 2. Materials and dimensions (mm) of the Nucletron mhdr-v1 source.  Muller-Runkel and Cho  performed anisotropy measurements in polystyrene and air using TLDs at radial distances r = 1 cm to 10 cm at polar angles restricted, however, to ±45 with respect to the long axis of the source. Williamson and Li  used the Monte Carlo Photon-Transport (MCPT) code to calculate 2D dose rate distributions and also tabulated their published data in the Interstitial Collaborative Working Group (ICWG) and TG-43 formalism formats. This code simulates photoelectric absorption, followed by K-shell and L-shell characteristic x-ray emission, pair production, and coherent and incoherent scattering. The photon cross-section library DLC-99 (HUGO)  was used. The primary photon spectrum for 192 Ir was that of Glasgow and Dillman.  The photon cutoff energy was not indicated. Since their code did not model transport and scattering of secondary electrons, they calculated the collisional kerma rate (using either the next-flight or exponential track-
63 High-energy photon-emitting brachytherapy dosimetry 47 length estimator) and converted to dose rate by normalizing the data to air-kerma strength per unit contained activity. Air-kerma rates were calculated for distances ranging from 5 to 100 cm along the transverse source bisector with the source inmersed in a 5 m sphere of dry air. The 2D dose rate was calculated at approximately 500 points in a 30 cm water sphere. For transverse axis data, dose rates were calculated at distances ranging from 0.1 cm to 14 cm. To obtain the 2D anisotropy function, they used a variable grid of 70 polar angles at 6 distances from 0.25 cm up to 5 cm. The standard deviation of the mean (k = 1) for total dose ranged from 0.5% (near the source) to 2% (far from the source). They deduced a MC estimate of cgy h l U l ± 0.5%. Observe that in this paper polar angle is defined as 180 (Fig. 1). TLD, diode, and MC dosimetry of this source was published by Kirov et al.  They measured the 2D dose rate distribution around the source and used the results to validate MC simulations by Williamson and Li.  TLDs in a solid-water phantom were used to measure the transverse-axis dose rates for 0.5 r 10 cm and the polar dose rate profiles at 1.5 cm, 3 cm, and 5 cm distances from the source. At close distances, 7 mm to 40 mm from the HDR source, they performed transverse axis dose rate measurements with an Si diode in water. Agreement between MC photon transport absolute dose rate calculations  and measurements was, on average, within 5%. From the transverse-axis experimental data, they deduced a value for the dose rate constant of 1.14 cgy h l U 1 ± 5%. Anctil et al.  made TLD measurements in a polystyrene phantom of size ( ) cm 3 using 1.0 mm 6 mm LiF rods calibrated in a 6 MV linac beam and having a measurement precision of 3%. Approximately 7 cgy was delivered to each TLD position in the phantom. Measurements were repeated 5 times except at the reference position, where they were repeated 24 times using bilateral TLD placement to minimize source positioning error in the transverse direction. A distance-dependent photon energy response correction was made using factors taken from Meigooni et al.  TG-43 parameters were obtained using a line source approximation for the geometry function, with L = 0.35 cm. was (1.13 ± 0.03) cgy h 1 U 1. The radial dose function was obtained over the distance range 1.0 cm to 10.0 cm in 1.0 cm steps, and the 2D anisotropy function was obtained on a polar grid sampling the same radial points and an angular range from 0 to 170 in 10 steps. Karaiskos et al.  performed MC and TLD studies of the source using spherical water phantoms with R = 10 cm to 50 cm. Analytical tracking was performed for every primary photon initiated in a random position and emitted in a random direction within the source. Primary and secondary photons were sampled individually in direct analogy to the main processes, namely photoabsorption and coherent and incoherent scattering. The tracking and interactions of photons were based on up-to-date and self-consistent total, partial, and differential cross sections and the procedure outlined by Chan and Doi  for the sampling of coherent and incoherent scattering. The photon spectrum and cutoff energies used were not indicated. The electron binding energy of the scattering atom was taken into account in the incoherent scattering process. For electrons, the continuous slowing down approximation (CSDA) was followed. The calculation of energy
64 48 HEBD report deposition was performed either directly from the electron energy deposition within the voxel volume or from the photon energy fluence. For the energies considered, both methods gave results within statistical uncertainties. The results presented were generated using the second method yielding statistical uncertainties <1%. The 30 cm diameter phantom was divided into discrete concentric spherical shells of 1 mm thickness, each split into angular intervals of up to 2. In these voxels, quantities such as the number and kind of interactions, the energy transferred to electrons by primary and/or secondary interactions, photon spectra, as well as the primary, scattered and total energy deposition were scored. Using these quantities, absorbed dose, air kerma, water kerma, dose anisotropy function, and radial dose function can be calculated for all voxels in a single run. They ascertained that phantom dimensions significantly affected g(r) near phantom boundaries where deviations of up to 25% were observed. They also did not observe significant differences in the 2D anisotropy function F(r, ) for the different values of R. Radial dose functions, dose rate constant, and 2D anisotropy functions, utilized in the TG-43 dose estimation formalism, were calculated. In addition, measurements of anisotropy functions using LiF TLD-100 rods were performed in a polystyrene ( ) cm 3 phantom to support their MC calculations using the same phantom size. The energy dependence of LiF TLD response was investigated over the whole range of measurement distances and angles. TLD measurements and MC calculations are in agreement with each other and agree with published data. They deduced a value of = (1.116 ± 0.006) cgy h 1 U 1. They provided g L (r) (L = 0.35 cm) and F(r, ) for a spherical phantom with R = 15 cm. Observe that in this paper polar angle is defined as 180 (Fig. 1) Papagiannis et al.  used their own MC simulation (the same code used by Karaiskos et al.  ) to calculate the gamma dose rate distribution in water around this source. The 192 Ir source photon spectrum from Glasgow and Dillman  was used. The dose component due to the beta spectrum of 192 Ir was evaluated. The water kerma approximation was utilized and results were presented for points at transverse distances greater than 1 mm from the source. The source was centrally positioned in a 30 cm diameter spherical water phantom. The phantom sphere was divided into discrete concentric spherical shells of cm thickness up to r = 0.5 cm and 0.1 cm thickness thereafter, each split into angular intervals of 1 with respect only to. The particle streaming function as described in Karaiskos et al.  was used. They reported = cgy h 1 U 1 ±0.13%. Numerical values of the radial dose function and anisotropy functions were not provided. Taylor and Rogers  used BrachyDose,  a brachytherapy user code for EGSnrc,  to perform an exhaustive dosimetric study of all HDR and PDR 192 Ir and 169 Yb sources available at the time of publication. For the transport of photons, Rayleigh scattering, bound Compton scattering, photoelectric absorption, and fluorescent emission of characteristic x-rays were all simulated. Photon cross sections from the XCOM database were used and mass-energy absorption coefficients were calculated using the EGSnrc user-code g. The incident 192 Ir spectrum used was taken from work by Duchemin and Coursol,  while the 169 Yb spectrum was the simplified spectrum presented by Medich et al.  The photon cutoff energy was set to 1 kev for all dose-to-water calculations. Dose calculations were performed scoring kerma using a track-length estimator in a water cube of side
65 High-energy photon-emitting brachytherapy dosimetry cm surrounding the source and considering a length of cable equal to those used previously by other authors for the same source. To minimize the impact of voxel size effects while maintaining reasonable efficiency, voxel sizes were chosen in the following way: ( ) mm 3 voxels for distances in the range of r source < r 1 cm, ( ) mm 3 voxels for 1 cm < r 5 cm, (1 1 1) mm 3 voxels for 5 cm < r 10 cm, and (2 2 2) mm 3 voxels for 10 cm < r 20 cm, where r is defined as the distance from the center of the source. The magnitude of uncertainty introduced by voxel size effects is typically less than 0.25%.  Calculations of the air kerma per history were made in vacuo, thereby avoiding the need to correct for attenuation by air. The mass energy absorption coefficients for air used in this calculation were calculated with the composition recommended by TG-43U1. Air kerma times d 2 per history was calculated in a ( ) cm 3 voxel located 100 cm from the source along the transverse axis and then corrected to give the air kerma times d 2 per history at a point (assuming an isotropic point source).  Low-energy photons emitted from the source encapsulation were suppressed in the air-kerma calculations by discarding all photons with energies less than 10 kev. The radial dose function was obtained using a line source geometry function over a radial range r = [0.2 to 1(0.1), 1 to 2 (0.25), 2 to 5(0.5), 5 to 20(1)] cm. It was fit with a 5 th order polynomial, and alternatively with a modified polynomial, over the full range. The 2D anisotropy function was obtained over the same radial range and an angular range = 0 to 3 (1 ), 3 to 7 (2 ), 10, 12, 15 to 165 (5 ), 168, 170, 173, 177 to 180 (1 ). Datasets for all sources studied are avalaible online (http://www.physics.carleton.ca/clrp/seed_database/). For the mhdr-v2 source they provided = (1.117 ± 0.002) cgy h 1 U 1. Consensus Data The four MC studies mentioned above [47,49,90,168] derived very close values of and their average value was taken as the consensus value: CON = cgy h 1 U 1 (Table IV). The TLD measurements  and the MC results [47,49] for the 30 cm diameter phantom agreed within uncertainites. The MC radial dose function data from Karaiskos et al.  and Williamson and Li  were converted to unbounded ones as explained in section III.A to be compared with the corresponding data of Taylor and Rogers.  Unbounded radial dose data by Williamson and Li and Taylor and Rogers are very close to each other, while the correponding data from Karaiskos et al., are slightly higher. Because the Taylor and Rogers data present a step at r = 1 cm, the data from Williamson and Li (unbounded) are selected as CON g L (r) (Table V), removing the published data at r = 0.1 cm because electronic disequilibrium exists and kerma was scored instead of absorbed dose. The comparison of the anisotropy results from the three MC studies [47,49,168] shows good agreement (differences of less than 1% except at r = 0.25 cm and at small angles where differences are up to 6%). Moreover, they agree within uncertainities with the TLD data of Anctil et al.  Because the data of Taylor and Rogers present the best mesh in both r and, these data are recommended as CONF(r, ) (TableVI).
66 50 HEBD report Derived from the consensus TG-43 dataset, an away-along dose rate table is presented (cgy h 1 U 1 ) for TPS quality assurance purposes (Table VII). Source Name (Manufacturer) Table IV. Dose rate constant for HDR 192 Ir sources. CON [cgy h 1 U 1 ] Statistical uncertainty (k = 1) CON /G L (r, ) [cgy cm 2 h 1 U 1 ] mhdr-v1 (Nucletron) % mhdr-v2 (Nucletron) % VS2000 (Varian) % Buchler (E&Z BEBIG) % GammaMed HDR 12i (Varian) % GammaMed HDR Plus (Varian) % GI192M11 (E&Z BEBIG) % Ir2.A85-2 (E&Z BEBIG) % M-19 (SPEC) % Flexisource (Isodose Control) % Table V. Radial dose function values for HDR sources. Interpolated/extrapolated data are boldface/underlined. Values inside the source are in italics. In [brackets] are the corrected values from bounded to unbounded geometry. g L (r) Nucletron Nucletron Varian E&Z BEBIG Varian Varian E&Z BEBIG E&Z BEBIG SPEC Isodore Control mhdr-v1 mhdr-v2 VS2000 Buchler GammaMed HDR 12i GammaMed HDR Plus GI192M11 Ir2.A85-2 M-19 Flexisource r [cm] L = 0.35 cm L = 0.35 cm L = 0.5 cm L = 0.13 cm L = 0.35 cm L = 0.35 cm L = 0.35 cm L = 0.35 cm L = 0.35 cm L = 0.35 cm 0.00 [0.991] , , , , [0.991] 1, [0.992] [0.997] [0.999] [1.002] 1, [1.004] 1, [1.006] 1, [1.006] 1, [1.001] 1, [0.993] [0.970] [0.934]
67 High-energy photon-emitting brachytherapy dosimetry 51 Table VI. F(r, ) for the Nucletron mhdr-v1 source. Extrapolated data are underlined. Values inside the source are in italics. r (cm) (deg)
68 52 HEBD report Table VII. QA away-along data [cgy h 1 U 1 ] for the Nucletron mhdr-v1 source. Values inside the source are in italics. z (cm) y (cm) A.1.2. mhdr-v2 (Nucletron) Source Description This microselectron HDR source from Nucletron (up to 12 Ci or U), also known as the mhdr-v2, consists of a pure iridium metal cylinder which is 3.6 mm long with a diameter of 0.65 mm. The outer capsule diameter and the capsule length are 0.90 mm and 4.5 mm, respectively. It is welded to a 200 mm long and 0.70 mm diameter woven steel cable. It was developed to allow the source to pass through smaller diameter (and curved) catheters than the v1 model. The mechanical design of this source is shown in Figure 3. Publications The MC study data published by Daskalov et al. [93,169] have been distributed by Nucletron in its TPS. As in the mhdr-v1 model (Appendix A.1.1), these data were generated by the MCPT code with the DLC-99 (HUGO)  photon cross-sections library; 192 Ir source photon spectrum from Glasgow and Dillman  with no electron emissions; photon-only transport (no electron transport was performed) with kerma rate at a geometric point calculated using either exponential track-length estimator or once-more collided flux estimator; air-kerma rate per unit contained activity was calculated in a dry air sphere 5 m in diameter, and linear corrections were used due to the buildup of scattered photons in air; the source was centrally positioned in a 30 cm diameter spherical water
69 High-energy photon-emitting brachytherapy dosimetry 53 phantom. Water-kerma rate was estimated at 600 positions from 0.1 cm r 14 cm; radial dose function was generated from 1 mm to 14 cm from the source; anisotropy functions were generated with 67 polar angles at distances of r = 0.25 cm, 0.5 cm, 1.0 cm, 2.0 cm, 3.0 cm, and 5.0 cm.they reported = cgy h 1 U 1 ± 0.13%. Figure 3. Materials and dimensions (mm) of the Nucletron mhdr-v2 source.  Papagiannis et al.  (Appendix A.1.1) reported = (1.109 ± 0.005) cgy h 1 U 1. Wang and Li  studied the dose rate distribution with MC methods up to radial distances of 1 cm, accounting for the charged particle nonequilibrium and beta particle contribution, for intravascular treatment planning applications. They deduced = (1.108 ± 0.002) cgy h 1 U 1. Taylor and Rogers  (Appendix A.1.1) obtained = (1.109 ± 0.002) cgy h 1 U 1. Granero et al.  studied again this source because Nucletron reported some minor changes that are within the manufacturing tolerances: the source core diameter has been reduced to 0.60 mm, the length has been reduced to 3.5 mm, and 0.4 mm of the cable attached to the source capsule has been replaced with stainless steel. Encapsulation thicknesses and the materials and composition by weight remain unchanged. Granero et al., have used three different MC codes: MCNP5, Penelope2008, and GEANT4 (version 9.3). They have reproduced the calculation as in Daskalov et al. (including the same geometry) using the three codes. Comparisons of the Daskalov et al. results with their results indicate that the TG-43 dosimetry parameters agree within k = 1 statistical uncertainties (<0.2%). Therefore, they concluded that any statistically significant dosimetric differences between the mhdr-v2 before and after the changes reported by the manufacturer can be attributed to source design differences and are not due to choice of MC code and related differences in radiological physics modeling. They repeated the MC simulations introducing the changes in the source geometry and adhered to the HEBD prerequisites. Moreover, they have considered contribution to the dose distribution and the lake of electronic equilibrium was taken into account. They have calculated dose to water using cells 0.01 cm in thickness for r 1 cm from the source, and factors of five and ten thicker for 1 cm < r 3 cm and 3 cm < r 20 cm, respectively. Angular
70 54 HEBD report sampling was taken every 2. Energy cutoff for both electrons and photons was taken as 10 kev. The source was located at the geometric center of a spherical liquid water phantom with 40 cm in radius to estimate dose to water and simulate unbounded phantom conditions for r 20 cm. Air-kerma strength was simulated in vacuo. Upon averaging results from the three MC codes, = ( ± ) cgy h 1 U 1 was obtained. This value is comparable with the results of Daskalov et al., Papagiannis et al., Wang and Li, and Taylor and Rogers for this source. For r 0.25 cm, g L (r) was obtained using kerma estimation, while absorbed dose due to photons and source electrons was used for smaller distances. The g L (r) they obtained agree well (typically < 0.2% differences) with Taylor and Rogers data for r 0.25 cm as well as with their own study of the unmodified mhdr-v2 source. F(r, ) is provided with high resolution for radial distances r < 0.4 cm in 2 increments. In general, F(r, ) agreement with published data on the unchanged mhdr-v2 source is within a few percent except for r < 0.25 cm, where electron dose contributions and the lack of electronic equilibrium become significant. Consensus Data The MC studies [27,90,93,138,139,169] derived very close values of and their average value was taken as the consensus value: CON = (1.109±0.012) cgy h 1 U 1 (Table IV). The radial dose function and anisotropy function from Granero et al.  were selected as CON g L (r) (Table V) and CON F(r, ) (Table VIII and Table VIII (cont.)) because they provide data at short distances from the source capsule. Derived from the consensus TG-43 dataset, an away-along dose rate table is presented (cgy h 1 U 1 ) for TPS quality assurance purposes (Table IX).
71 High-energy photon-emitting brachytherapy dosimetry 55 Table VIII. F(r, ) for the Nucletron mhdr-v2 source. Extrapolated data are underlined. Values inside the source are in italics. r (cm) (deg)
72 56 HEBD report Table VIII (cont). F(r, ) for the Nucletron mhdr-v2 source. Extrapolated data are underlined. Values inside the source are in italics. r (cm) (deg)
73 High-energy photon-emitting brachytherapy dosimetry 57 Table IX. QA away-along data [cgy h 1 U 1 ] for the Nucletron mhdr-v2 source. Values inside the source are in italics. z (cm) y (cm) A.1.3. VS2000 (Varian Medical Systems) Source Description The VS2000 is an HDR 192 Ir source model brought to the market in the year 2000 by Varian Medical Systems (Palo Alto, CA) designed to be used in their remote afterloading system. The active core length (5.0 mm), in comparison to their previous VariSource source (10.0 mm), was reduced in length to provide better flexibility for clinical cases. The source design and encapsulation details remained similar. A schematic diagram is provided in Figure 4. The active source consists of two, 0.34 mm diameter, 2.5 mm long cylinders with semispherical ends. The radioactive material, pure iridium metal (22.42 g/cm³), is uniformly distributed in these two pellets. The source is encapsulated at the end of a 0.59 mm outer diameter nitinol cable consisting of two parts: one flexible part close to the source and a stiffer one in the proximal part of the cable. The composition is 44.4% Ti and 55.6% Ni by weight (density 6.5 g/cm³). The encapsulation extends 1 mm beyond the distal end of the active core and can be approximated by a 0.59 mm diameter, mm long cylinder with a hemispherical end of mm radius.
74 58 HEBD report Figure 4. Material and dimensions (mm) of the Varian Medical Systems VS2000 source.  Publications The VS2000 model has been evaluated by Angelopoulos et al.  using a custom yet wellbenchmarked MC simulation code (Karaiskos et al.  in Appendix A.1.1). The MC code used the detailed active core, encapsulation geometry and materials of the source design. Water-kerma approximation was utilized and results were presented for points at transverse distances greater than 1 mm from the source. 192 Ir source photon spectrum from Glasgow and Dillman  was considered. The source was centrally positioned in a 30 cm diameter spherical water phantom. The phantom sphere was divided into discrete concentric spherical shells of 0.1 cm thickness up to 15 cm, each split into angular intervals of 1 with respect only to. Air-kerma strength was derived using both simulation in free space and dry air. The data from Angelopoulos et al.  were cross-checked by the same authors against other sources such as the VariSource and the microselectron and to a point source to validate their findings. Percentage differences between the values of these three sources follow the percentage differences detected between their geometry functions, G L (r = 1 cm, /2), where is defined. When compared to the point source and using the same phantom dimensions, g L (r) was not significantly affected by the source and the encapsulation geometry (3% at distance close to the source 2 mm and less than 1% for all other radial distances). They reported = (1.101 ± 0.006) cgy h 1 U 1. Observe that in this paper polar angle is defined as 180 (Fig. 1). Taylor and Rogers  (see Appendix A.1.1) obtained = (1.099 ± 0.002) cgy h 1 U 1. Consensus Data The average value of the MC studies  was taken as the consensus value: CON = (1.100 ± 0.006) cgy h 1 U 1 (Table IV). The radial dose function and anisotropy function from Taylor and Rogers were selected as CON g L (r) (Table V) and CON F(r, ) (Table X) because these were obtained in an unbounded phantom, although both studies provided close results for the anisotropy function. Derived from the consensus TG-43 dataset, an away-along dose rate table is presented (cgy h 1 U 1 ) for TPS quality assurance purposes (Table XI).
75 High-energy photon-emitting brachytherapy dosimetry 59 Table X. F(r, ) for the Varian Medical Systems VS2000 source. Extrapolated data are underlined. Values inside the source are in italics. r (cm) (deg)
76 60 HEBD report Table XI. QA away-along data [cgy h 1 U 1 ] for the Varian Medical Systems VS2000 source. Values inside the source are in italics. z (cm) y (cm) A.1.4. Buchler (E&Z BEBIG) Source Description This source is the HDR 192 Ir source from Amersham (Product code ICCB2113, Source G0814, described in the Technical Information and Operation Instructions of the Unit). The 192 Ir Buchler HDR source consists of a cylindrical active iridium core ( = g/cm 3 ) of 1 mm diameter and 1.3 mm length (Figure 5). The active iridium is assumed to be uniformly distributed in this core, which is encapsulated in a stainless steel wire (No ) of 1.6 mm outer diameter and 1.2 mm inner diameter. The upper rounded end of the source is a stainless steel hemisphere of radius 0.8 mm. Publications This source has been studied by Ballester et al.  using the GEANT3 code.  Photon interactions simulated in this code include photoelectric effect (followed by characteristics x-rays), Compton scattering, pair production, and Rayleigh scattering. They used the spectrum from Shirley.  The cutoff energy for photons was taken as 10 kev. The electron transport was done in order to account for the small differences between kerma and absorbed dose at positions close to the
77 High-energy photon-emitting brachytherapy dosimetry 61 Figure 5. Materials and dimensions (mm) of the E&Z BEBIG HDR 192 Ir Buchler model G0814 source.  source due to the lack of charged-particle equilibrium near the source (r < 1 cm). A cutoff energy of 10 kev was taken for electrons. A cylinder of water of 80 cm height and 40 cm in radius was assumed with the source in its center. Ballester et al. [private communication] have reported a misprint in ref.  where the phantom dimensions given (40 cm height and 40 cm diameter) are incorrect. The extension of the proximal end of the wire was modeled as 6 cm long with effective density of = 5.6 g/cm 3 in both cases. The dose analog estimator was used to calculate absorbed dose. The dose was calculated up to 20 cm away from the source in 0.5 mm steps and for angles from 0 to 180 in 1 steps. Next, the dose was stored in Cartesian coordinates as a matrix from y = 0 to y = 20 cm and from z = 20 cm to z = +20 cm, and in polar coordinates as a matrix from r = 0 to r = 20 cm and from = 0 to = 180. The standard deviation (k = 1) of the absorbed dose in cells at distances less than 5 cm from the origin ranged from 0.1% to 1.5%, increasing to 5% at 20 cm. To evaluate S K, the source was positioned in a (6 6 6) m 3 dry air cube and cells to score air kerma were defined for transverse axis distances ranging from 5 cm to 150 cm. The air kerma has been scored at distances from the source large enough to treat the source as a mathematical point. y = z =1 cm cell sizes were taken. The active length L = 0.15 cm was used to calculate g L (r) and F(r, ) from 0.2 cm up to 20 cm. They reported a = (1.115 ± 0.003) cgy h 1 U 1. Taylor and Rogers  (Appendix A.1.1) studied this source with the same geometry and source cable as in Ballester et al., obtaining = (1.119 ± 0.003) cgy h 1 U 1. Consensus Data The average of the two published values was used for CON = (1.117 ± 0.004) cgy h 1 U 1 and is recommended (Table IV). For CON g L (r), data from Ballester et al.  reproduced in Table V are recommended, because electron transport was included and Taylors and Rogers data present a step at
78 62 HEBD report r = 1 cm. For CON F(r, ), data from Ballester et al.  reproduced in Table XII are recommended, because of the step at 1 cm in Taylor and Rogers data and the dose was reported close to the source by Ballester et al. Derived from the consensus TG-43 dataset, an away-along dose rate table is presented (cgy h 1 U 1 ) for TPS quality assurance purposes (Table XIII). Table XII. F(r, ) for the Buchler model G0814 source. Extrapolated data are underlined. Values inside the source are in italics. r (cm) (deg)
79 High-energy photon-emitting brachytherapy dosimetry 63 Table XII (continued). r (cm) (deg) Table XIII. QA away-along data [cgy h 1 U 1 ] for the Buchler model G0814 source. Values inside the source are in italics. y (cm) z (cm) A.1.5. GammaMed HDR 12i (Varian Medical Systems) Source Description The model GammaMed HDR 12i source consists of an iridium core of 3.5 mm in length and 0.7 mm in diameter, encapsulated in a stainless steel wire as shown in Figure 6, which is nearly identical to the mhdr-v1 source. The distance from the physical tip of the source to the distal face of the active source core is 0.86 mm.
80 64 HEBD report Figure 6. Materials and dimensions (mm) of the Varian Medical Systems GammaMed HDR 12i source.  Publications Ballester et al.  published the absolute dose distributions in water as 2D Cartesian look-up tables for the source using the GEANT3 MC code.  The methodology is the same described in Appendix A.1.4 for the Buchler source from the same group. Ballester et al. [private communication] have reported a misprint in ref.  where the phantom dimensions given (40 cm height and 40 cm diameter) are incorrect. They also used this absolute dose distribution data to derive TG-43 parameters for this source. They derived, using L = 3.5 mm, = (1.118 ± 0.003) cgy h 1 U 1. A second study was done by Taylor and Rogers  that obtained = (1.117 ± 0.003) cgy h 1 U 1. Consensus Data The g L (r) data from both studies are in good agreement, but the Taylor and Rogers results present a step at 1 cm. F(r, ) data from both studies are indistinguishable. An averaged CON = (1.118 ± 0.004) cgy h 1 U 1 is taken as the consensus value (Table IV). Due to the g L (r) data step at 1 cm in the Taylor and Rogers data and taking into account the electron transport inclusion and angular mesh, datasets from Ballester et al.  have been taken as CON g L (r) and CON F(r, ) (Table V and Table XIV). Derived from the consensus TG-43 dataset, an away-along dose rate table is presented (cgy h 1 U 1 ) for TPS quality assurance purposes (Table XV).
81 High-energy photon-emitting brachytherapy dosimetry 65 Table XIV. F(r, ) for the GammaMed HDR 12i source. Extrapolated data are underlined. Values inside the source are in italics. r (cm) (deg)
82 66 HEBD report Table XV. QA away-along data [cgy h 1 U 1 ] for the GammaMed HDR 12i source. Values inside the source are in italics. y (cm) z (cm) A.1.6. GammaMed HDR Plus (Varian Medical Systems) Source Description The model GammaMed HDR Plus source, shown in Figure 7, is almost identical to the HDR model 12i. With an active core of 3.5 mm in length and 0.7 mm in diameter, the physical source is 4.52 mm in length and 0.9 mm in diameter. The distance from the physical tip of the source to the distal face of the active source core is 0.62 mm, which is smaller than the model HDR 12i. Publications In the same publication with the Model 12i data (Appendix A.1.5), Ballester et al.  published the absolute dose distributions in water as 2D Cartesian look-up tables for the Model Plus. They also used this absolute dose distribution data to derive TG-43 parameters for this source. Using L = 3.5 mm, they reported = (1.118 ± 0.003) cgy h 1 U 1. A second study by Taylor and Rogers  (Appendex A.1.1) derived = (1.115 ± 0.003) cgy h 1 U 1.
83 High-energy photon-emitting brachytherapy dosimetry 67 Figure 7. Materials and dimensions (mm) of the Varian Medical Systems GammaMed HDR Plus source.  Consensus Data Both studies provide similar TG-43 parameters, but the g L (r) data from Taylor and Rogers are noisy. F(r, ) data from both studies are indistinguishable. Averaged CON = (1.117 ± 0.004) cgy h 1 U 1 is taken as consensus value (Table IV). Due to the g L (r) data fluctuations in Taylor and Rogers, the data from Ballester et al., have been taken as CON g L (r) and CON F(r, ) for Table V and Table XVI. In Ballester et al., dose was scored instead kerma giving more accuracy in values close to the source and it presented higher angular resolution close to the source longitudinal axis. Derived from the consensus TG-43 dataset, an away-along dose rate table is presented (cgy h 1 U 1 ) for TPS quality assurance purposes (Table XVII). Table XVI. F(r, ) for the GammaMed HDR Plus source. Extrapolated data are underlined. Values inside the source are in italics. r (cm) (deg)
84 68 HEBD report Table XVI (continued). r (cm) (deg)
85 High-energy photon-emitting brachytherapy dosimetry 69 Table XVII. QA away-along data [cgy h 1 U 1 ] for the GammaMed HDR Plus source. Values inside the source are in italics. z (cm) y (cm) A.1.7. GI192M11 (E&Z BEBIG) Source Description This source is composed of a cylindrical 192 Ir active core with 3.5 mm active length and an active diameter of 0.6 mm covered by a 316L stainless steel capsule. A schematic view of this source is shown in Figure 8. Figure 8. Materials and dimensions (mm) of the E&Z BEBIG HDR model GI192M11 source. 
86 70 HEBD report Publications The MC code GEANT4 (version 6.1) was used by Granero et al.  to estimate dose rate in water and air-kerma strength around the source. The code was benchmarked for HDR 192 Ir sources by comparison of the dose rate distributions obtained with published data of Williamson et al.  and Daskalov et al. [93,169] for the mhdr-v1 and mhdr-v2, respectively. In the calculations, Compton scattering, photoelectric effect and Rayleigh scattering processes were used from the low-energy package of GEANT4. This low energy package uses the EPDL97 cross sections tabulation.  The 192 Ir photon spectrum was taken from the NuDat database neglecting the -spectrum.  A cutoff energy of 10 kev for photons was used. Only collision kerma was scored using the linear track-length kerma estimator to estimate dose. The source was located in the center of a spherical 40 cm radius water phantom. The density of the water used in the simulation was g/cm 3 at 22 C, as is recommended in the TG-43U1 report. Two different grid systems were used in order to obtain the dose rate in the form of away-along tables and in the form given by the TG-43 formalism. The first one was composed of cm thick and 0.05 cm high cylindrical rings concentric to the longitudinal source axis, and has been used to obtain the dose rate in Cartesian coordinates. To obtain the dose rate in polar coordinates following the TG-43 formalism, a grid system composed of 0.05 cm thick, concentric spherical sections and an angular width of 1 in the polar angle was used. The source was along the z-axis with positive z towards the source tip. The origin of the coordinates was located at the geometric center of the active core. The origin of the polar angle is at the tip side of the source. Standard deviations of the mean (k = 1) dose rate values of less than 0.5% were obtained, except along the longitudinal axis where 1% is reached. To estimate the air-kerma strength, the source was located in a (4 4 4) m 3 air volume. The composition and density used for the air in the simulation are the ones recommended in Table XIV of the TG-43U1 report  for air with relative humidity of 40%. Cylindrical cells 1 cm thick and 1 cm high located in the plane z = 0 were used to score air-kerma along the transverse axis of the source from y = 5 cm to y = 150 cm. Air-kerma strength values were found to be well described by a linear equation k air ( y)y 2 = S K + by where the slope b describes the deviation in k air ( y)y 2 due to a buildup of scattered photons in air. The air-kerma strength was derived with a statistical uncertainty (k = 1) in air-kerma values of less than 0.5%. They derived = (1.108 ± 0.003) cgy h 1 U 1. Taylor and Rogers  (Appendix A.1.1) studied this source with the same geometry and source cable as in Granero et al.  obtaining = (1.112 ± 0.003) cgy h 1 U 1. Consensus Data Both studies provide similar TG-43 parameters. The values are only 0.36% different from each other and the F(r, ) data are indistinguishable. The g L (r) data are also similar but the Taylor and Rogers results are noisy. The average of values from both studies is taken as the consensus value CON = (1.110 ± 0.004) cgy h 1 U 1 (Table IV). Due to the g L (r) data fluctuations in Taylor and
87 High-energy photon-emitting brachytherapy dosimetry 71 Rogers, the data from Granero et al. have been taken as CON g L (r), while the data from Taylor and Rogers is selected for CON F(r, ) for Table V and Table XVIII. Derived from the consensus TG-43 dataset, an away-along dose rate table is presented (cgy h 1 U 1 ) for TPS quality assurance purposes (Table XIX). Table XVIII. F(r, ) for the E&Z BEBIG model GI192M11 source. Extrapolated data are underlined. Values inside the source are in italics. (deg) r (cm)
88 72 HEBD report Table XVIII (continued). r (cm) (deg) Table XIX. QA away-along data [cgy h 1 U 1 ] for the E&Z BEBIG model GI192M11 source. Values inside the source are in italics. z (cm) y (cm)
89 High-energy photon-emitting brachytherapy dosimetry 73 A.1.8. Ir2.A85-2 (E&Z BEBIG) Source Description This HDR source is shown in Figure 9 together with the coordinate axes used to give the dose rate tables and the TG-43 parameters for the sources. The HDR source is composed of a cylindrical pure iridium core (density g/cm 3 ) with 3.5 mm active length and with a diameter of 0.6 mm. The source is covered by a capsule made of 316L stainless steel. This design is very similar to the old E&Z BEBIG HDR source model GI192M11 with the main difference being that the external diameter of the outer capsule is 0.9 mm in this new source and 1 mm in the old one. Figure 9. Materials and dimensions (mm) of the E&Z BEBIG HDR model Ir2.A85-2 source.  Publications There is only one study of this source by Granero et al.  that accomplishes the prerequisites of Li et al.  This study used the GEANT4 code following the methodology outlined in Appendix A.1.7 for the GI192M11 source model and is validated for this very similar source. Consensus Data Consensus data have been taken from the only publication available (Tables IV, V, and XX). Derived from the consensus TG-43 dataset, an away-along dose rate table is presented (cgy h 1 U 1 ) for TPS quality assurance purposes (Table XXI).
90 74 HEBD report Table XX. F(r, ) for the E&Z BEBIG model Ir2.A85-2 source. Extrapolated data are underlined. Values inside the source are in italics. (deg) r (cm)
91 High-energy photon-emitting brachytherapy dosimetry 75 Table XXI. QA away-along data [cgy h 1 U 1 ] for the E&Z BEBIG model Ir2.A85-2 source. Values inside the source are in italics. z (cm) y (cm) A.1.9. M-19 (Source Production and Equipment) Source Description The M-19 source was produced by the Source Production and Equipment Co., Inc. (Rose, LA) for use with the AccuSource HDR remote afterloader. The active core of this source is 3.5 mm in length with 0.65 mm diameter, while the physical source is 5.1 mm in length with an outer diameter of 1.17 mm, as shown in Figure 10. The distance from the physical tip of the source to the distal face is 0.65 mm. Figure 10. Materials and dimensions (mm) of the Source Production and Equipment M-19 source. 
92 76 HEBD report Publications Version of the MCNP5 Monte Carlo computer code was used by Medich et al.  to study this source. 192 Ir photons were generated uniformly inside the iridium core with photon and secondary electron transport replicated, using default MCPLIB04 photo atomic cross-section tables. Simulations were performed for both water and air/vacuum computer models with a sufficient number of photon histories generated to obtain a Monte Carlo tally precision of approximately 1% or lower within each tally cell. All simulations were operated in the photon and electron transport mode (Mode: p,e in the MCNP code) so that both primary photons and resulting secondary electrons were properly transported. The 192 Ir photon spectrum was simplified by disregarding photons with intensities below 0.1% and by omitting 192 Ir source x-rays lower than 15 kev since transmission of these photons through the encapsulating steel shell is dosimetrically negligible. The resulting 192 Ir spectrum uncertainty (0.5%) was calculated as the intensity weighted average of the uncertainty in each spectral line. The M-19 source was placed at the center of a spherical water phantom of 40 cm radius. Dosimetric data were determined at radial distances ranging from 0.5 cm to 10 cm (0.5 cm increments) and over angles ranging from 0 to 180 (10 increments) using the MCNP5 F6 energy deposition tally. Dosimetric data in a water phantom, suitable for use as an away-along table, were also generated for 1 mm 3 tally volumes between ±10 cm along the source axis and out +10 cm away from the source axis using the MCNP5 *F4 Mesh track-length tally. Here, the phantom radius was adjusted to 50 cm to accommodate the outlying edges of the tally, roughly 14 cm from source center, to allow for full scattering conditions within the phantom. The air-kerma strength in free space, s K, was calculated centering the M-19 source at the origin of an evacuated phantom in which a critical volume containing air at STP (standard temperature pressure) was added 100 cm from source center; dimensions of the critical volume were chosen to limit volumetric averaging errors to below 1%. The x-ray cutoff energy was chosen to be 10 kev; photons within the critical target with energies less than or equal to 10 kev were removed from the final air-kerma rate calculation. Medich et al., report = (1.13 ± 0.03) cgy h 1 U 1. Taylor and Rogers  (Appendix A.1.1) report = (1.114 ± 0.001) cgy h 1 U 1. Consensus Data The calculated by Medich et al.  is significantly higher than the rest of the HDR 192 Ir source models studied in this report. The average value of /G L (r 0, 0 ) calculated for all sources in this report is cgy cm 2 h 1 U 1 (maximum and minimum values and 1.119, respectively) with a standard deviation of cgy cm 2 h 1 U 1, i.e., all values lie in the interval of 1.5 standard deviations. Nevertheless, the corresponding value of Medich et al., at 4.3 standard deviations is extremely unlikely. Because the M-19 does not present any characteristic (source core dimensions or encapsulation thickness) different from those of the rest of the HDR 192 Ir sources, we adopt as consensus data the value given by Taylor and Rogers that fulfills the mentioned condition: CON = (1.114 ± 0.001) cgy h 1 U 1 (Table IV). g L (r) data in both studies are noisy and contain steps at various r-values. F(r, ) data present differences at small and large angles. Because the g L (r) and
93 High-energy photon-emitting brachytherapy dosimetry 77 F(r, ) reported by Taylor and Rogers have better radial and angular mesh, a lower statistical uncertainty, and use a more modern cross-section library, these are taken as consenus datasets (Table V and Table XXII). Derived from the consensus TG-43 dataset, an away-along dose rate table is presented (cgy h 1 U 1 ) for TPS quality assurance purposes (Table XXIII). Table XXII. F(r, ) for the SPEC In. Co. model M-19 source. Extrapolated data are underlined. Values inside the source are in italics. r (cm) (deg)
94 78 HEBD report Table XXII (continued). r (cm) (deg) Table XXIII. QA away-along data [cgy h 1 U 1 ] for the SPEC In. Co. model M-19 source. Values inside the source are in italics. y (cm) z (cm)
95 High-energy photon-emitting brachytherapy dosimetry 79 A Flexisource (Isodose Control) Source Description The active core of the Isodose Control (Veenendaal, The Netherlands) source is a pure iridium cylinder (density g/cm 3 ) with an active length of 3.5 mm and a diameter of 0.6 mm. The stainless-steel-304 capsule (composition by weight: Fe 67.92%, Cr 19%, Ni 10%, Mn 2%, Si 1%, and C 0.08%, density 8 g/cm 3 ) leads to outer dimensions of the source of 0.85 mm in diameter and 4.6 mm of total length. The 304 stainless steel cable is a cylinder of 5 mm length and 0.5 mm in diameter (Figure 11). Figure 11. Materials and dimensions (mm) of the Isodose Control Flexisource.  Publications There are two studies about this source: the first one uses the GEANT4 code  as described by Granero et al.  in the study of the HDR source GI192M11 model (Appendix A.1.7); the second one by Taylor and Rogers  (Appendix A.1.1). Consensus Data Both studies provide similar TG-43 parameters. values from both studies are only 0.6% different from each other and the F(r, ) data are indistinguishable. The g L (r) data are also similar but the Taylor and Rogers results are noisy. The average of values is taken as the consensus value CON = (1.113 ± 0.011) cgy h 1 U 1 (Table IV). Due to the g L (r) data fluctuations in Taylor and Rogers, the data from Granero et al., have been taken as CON g L (r), while the data from Taylor and Rogers is selected for CON F(r, ) in Table V and Table XXIV. Derived from the consensus TG-43 dataset, an away-along dose rate table is presented (cgy h 1 U 1 ) for TPS quality assurance purposes (Table XXV).
96 80 HEBD report Table XXIV. F(r, ) for the Isodose Control model Flexisource. Extrapolated data are underlined. Values inside the source are in italics. r (cm) (deg)
97 High-energy photon-emitting brachytherapy dosimetry 81 Table XXIV (continued). r (cm) (deg) Table XXV. QA away-along data [cgy h 1 U 1 ] for the Isodose Control model Flexisource. Values inside the source are in italics. z (cm) y (cm) A.2. Pulsed Dose Rate 192 Ir sources A.2.1. GammaMed PDR 12i (Varian Medical Systems) Source Description A 1.1 mm external diameter, 3.36 mm long 192 Ir source is used in the GammaMed 12i PDR system. The source design (Figure 12) incorporates an active core of length 0.5 mm and diameter 0.6 mm, whose center is located 2.61 mm from the source tip. A 1.4 mm long, 0.6 mm diameter aluminum plug is also located within the source capsule, distal to the active core. The encapsulating
98 82 HEBD report material is stainless steel having a sidewall thickness of 0.2 mm. The active core and plug are the same as those in the GammaMed Plus source. Figure 12. Materials and dimensions (mm) of the Varian Medical Systems GammaMed PDR 12i source.  Publications Pérez-Calatayud et al.  used the GEANT3 MC code  as previously described in Appendix A.1.4 with the same methodology in the study of the Buchler source.  Taylor and Rogers  also studied this source using previously described methods (Appendix A.1.1). Consensus Data Both studies adhere to recommendations for MC dosimetry given in Li et al.  and the TG- 43U1 report.  Reported values differ by 0.6%. g L (r) agree to within 1% (and mostly to within 0.5%) over the range r = 0.2 cm to 10 cm after correction of the Pérez-Calatayud et al.  data to reflect unbounded scattering conditions. F(r, ) agree everywhere to within 2% (and mostly to within 1%). L = 0.5 mm was used to calculate G L (r, ) in both studies. The average of the published values, CON = (1.126 ± 0.003) cgy h 1 U 1 (Table XXVI) is recommended. For CON g L (r), data from Pérez- Calatayud et al.  corrected to unbounded scattering conditions and presented in Table XXVII are recommended, as it was obtained scoring dose and exhibits fewer fluctuations than the Taylor and Rogers  data, especially near the reference distance r = 1 cm. For the CON F(r, ), data from Pérez- Calatayud et al.  reproduced in Table XXVIII are recommended, as they were obtained with more complete angular sampling near the longitudinal axis of the source. Derived from the consensus TG-43 dataset, an away-along dose rate table is presented (cgy h 1 U 1 ) for TPS quality assurance purposes (Table XXIX).
99 High-energy photon-emitting brachytherapy dosimetry 83 Table XXVI. Dose rate constant for PDR sources. CON Statistical uncertainty CON /G L (r, ) Source Name (Manufacturer) [cgy h 1 U 1 ] (k = 1) [cgy cm 2 h 1 U 1 ] GammaMed PDR 12i (Varian) % GammaMed PDR Plus (Varian) % mpdr-v1 (Nucletron) % Ir2.A85-1 (E&Z BEBIG) % Table XXVII. Radial dose function values for PDR sources. Extrapolated data are underlined. Values inside the source are in italics. In [brackets] are the corrected values from bounded to unbounded geometry. Varian GammaMed PDR 12i g L (r) Varian GammaMed PDR Plus Nucletron mpdr-v1 E&Z BEBIG Ir2.A85-1 r [cm] L = 0.05 cm L = 0.05 cm L = 0.12 cm L = 0.05 cm [1.009] [1.007] [0.999] [1.000] [1.002] [1.006] [1.008] [1.008] [1.007] [1.002] [0.985] [0.960]
100 84 HEBD report Table XXVIII. F(r, ) for the GammaMed PDR 12i source. Extrapolated data are underlined. Values inside the source are in italics. r (cm) (deg)
101 High-energy photon-emitting brachytherapy dosimetry 85 Table XXIX. QA away-along data [cgy h 1 U 1 ] for the GammaMed PDR 12i source. Values inside the source are in italics. z (cm) y (cm) A.2.2. GammaMed PDR Plus (Varian Medical Systems) Source Description A 0.9 mm external diameter, 2.92 mm long 192 Ir source is used in the GammaMed Plus PDR system. The source design (Figure 13) incorporates an active core of length 0.5 mm and diameter 0.6 mm, whose center is located 2.37 mm from the source tip. A 1.4 mm long, 0.6 mm diameter aluminum plug is also located within the source capsule, distal to the active core. The encapsulating material is stainless steel having a sidewall thickness of 0.1 mm. Figure 13. Materials and dimensions (mm) of the Varian Medical Systems GammaMed PDR Plus source. 
102 86 HEBD report Publications Pérez-Calatayud et al.  used the MC code GEANT3  to score dose in a water cylinder 40 cm in length and 40 cm in diameter surrounding the source and 6 cm of stainless steel cable. Additional details are in Appendix A.1.4 about the methodology followed by the same research group in the study of the Buchler source.  Taylor and Rogers  used BrachyDose  to score kerma using a track-length estimator in a water cube of side 80 cm surrounding the source and 6 cm of cable. See Appendix A.1.1 for additional details about this study. Consensus Data Both studies adhere to recommendations for MC dosimetry given in Li et al.  and TG- 43U1.  Reported values agree to within 0.4%. g L (r) agree to within 1% over the range r = 0.2 cm to 10 cm after correction of the Pérez-Calatayud et al. data to reflect unbounded scattering conditions.  F(r, ) agree everywhere to within 1% except near = 0, where agreement is within 2%. An active length L = 0.5 mm was used to calculate the geometry function in both studies. The reported dosimetric data is of high quality. The average of the published values was used for CON = (1.123 ± 0.003) cgy h 1 U 1 and is recommended (see Table XXVI). For CON g L (r), data from Taylor and Rogers  reproduced in Table XXVII are recommended, as they were calculated in a large phantom that closely approximates unbounded scattering conditions. For CON F(r, ), data from Pérez- Calatayud et al.  reproduced in Table XXX are recommended, as they were obtained with more complete angular sampling near the longitudinal axis of the source. Derived from the consensus TG-43 dataset, an away-along dose rate table is presented (cgy h 1 U 1 ) for TPS quality assurance purposes (Table XXXI).
103 High-energy photon-emitting brachytherapy dosimetry 87 Table XXX. F(r, ) for the GammaMed PDR Plus source. Extrapolated data are underlined. Values inside the source are in italics. r (cm) (deg)
104 88 HEBD report Table XXXI. QA away-along data [cgy h 1 U 1 ] for the GammaMed PDR Plus source. Values inside the source are in italics. y (cm) z (cm) A.2.3. mpdr-v1 (Nucletron) Source Description The microselectron PDR is a single 1 Ci ( U) source of 192 Ir with active core 1.2 mm long and 0.6 mm in diameter (Figure 14). Like the HDR 192 Ir sources of this vendor, the source is encapsulated in a 316L stainless steel capsule with an outer diameter of 1.1 mm. The distance from the physical tip of the source to the distal face is 0.5 mm. Figure 14. Materials and dimensions (mm) of the Nucletron mpdr-v1 source. 
105 High-energy photon-emitting brachytherapy dosimetry 89 Publications This source model has been evaluated by Karaiskos et al.  using a custom, yet wellbenchmarked MC simulation code (see Karaiskos et al.  in Appendix A.1.1). The MC code used the detailed active core, encapsulation geometry, and materials of the source design. Water kerma approximation was utilized and results were calculated using the mass energy absorption coefficients from Hubbell and Seltzer (version 1.03).  192 Ir source photon spectrum from Glasgow and Dillman  was considered. The photon cutoff was 2 kev. The source was centrally positioned in a 30 cm diameter spherical water phantom as well as in an unbounded water phantom. The phantom spheres were divided into discrete concentric spherical shells of 0.05 cm intervals up to 0.5 cm, 0.1 cm intervals between 0.5 cm and 3 cm, and 0.5 cm intervals at larger r values. All shells were split in 1 intervals with respect to. Air-kerma strength was derived using both simulations in free space and dry air. A point source geometry factor was used to derive radial dose and anisotropy functions. They reported = (1.121 ± 0.006) cgy h 1 U 1. The anisotropy function was tabulated up to 5 cm. Taylor and Rogers,  see Appendix A.1.1, obtained = (1.119 ± 0.003) cgy h 1 U 1. Consensus Data The average of two MC study values is recommended as CON. [55,139] CON = (1.120 ± 0.006) cgy h 1 U 1 (see Table XXVI). The data of Karaiskos et al., corrected to unbounded phantom and also corrected by the linear geometry function, with L = 0.12 cm, were selected for CON g L (r) (Table XXVII) because of fluctuations in the Taylor and Rogers  data at 1 cm, which clearly affects their normalization. For CON F(r, ), the data by Taylor and Rogers are taken because of the higher resolution. For r = 0.25 cm, the values of Karaiskos et al.  are proposed as consensus data because it presents a wider angular range. See Table XXXII. Derived from the consensus TG-43 dataset, an away-along dose rate table is presented (cgy h 1 U 1 ) for TPS quality assurance purposes (Table XXXIII).
106 90 HEBD report Table XXXII. F(r, ) for the Nucletron mpdr-v1 source. Extrapolated data are underlined. Values inside the source are in italics. r (cm) (deg)
107 High-energy photon-emitting brachytherapy dosimetry 91 Table XXXII (continued). r (cm) (deg) Table XXXIII. QA away-along data [cgy h 1 U 1 ] for the Nucletron mpdr-v1 source. Values inside the source are in italics. y (cm) z (cm) A.2.4. Ir2.A85-1 (E&Z BEBIG) Source Description The model Ir2.A85-1 source (E&Z BEBIG) is composed of two iridium (density g/cm 3 ) cylindrical pellets 0.5 mm in length and 0.5 mm in diameter. The distal pellet represents the active 192 Ir source. The external capsule has the same inner and outer diameter (0.9 mm) as the HDR source type Ir2.A85-2 and is also made of 316L stainless steel. See Figure 15.
108 92 HEBD report Figure 15. Materials and dimensions (mm) of the E&Z BEBIG Ir2.A85-1 source.  Publications The only study of this source model was done by Granero et al.  using the GEANT4 code and following the prerequisites in Li et al.  This source is very close in materials/geometry to the already discussed model GammaMed PDR Plus source. The most significant difference is the distance from active edge to tip (1.8 mm vs. 1.2 mm). values for both source models are in very good agreement. In the simulations, 5 mm of guiding cable was considered. They provided dosimetric data in the TG-43 U1 formalism and as an away-along table. This study follows the methodology outlined in Appendix A.1.7 for the GI192M11 source model. Consensus Data The data from Granero et al.  are taken as the consensus dataset. They reported CON = (1.124 ± 0.011) cgy h 1 U 1 (see Table XXVI), with CON g L (r) and CON F(r, ) reproduced in Tables XXVII and XXXIV. Derived from the consensus TG-43 dataset, an away-along dose rate table is presented (cgy h 1 U 1 ) for TPS quality assurance purposes (Table XXXV).
109 High-energy photon-emitting brachytherapy dosimetry 93 Table XXXIV. F(r, ) for the E&Z BEBIG PDR-Ir2.A85-1 model. Extrapolated data are underlined. Values inside the source are in italics. (deg) r (cm)
110 94 HEBD report Table XXXV. QA away-along data [cgy h 1 U 1 ] for the E&Z BEBIG PDR Ir2.A85-1 source. Values inside the source are in italics. y (cm) z (cm) A.3. Low Dose Rate 192 Ir sources A.3.1. Steel clad 192 Ir seed (Best Industries) Source Description The source, designated model (Best Industries, Springfield, VA), is cylindrical in shape with an overall length of 3.0 mm and an external diameter of 0.5 mm (Figure 16). The active core element is 70% mass Pt and 30% mass Ir with a 3.0 mm length and 0.1 mm diameter. This core is encapsulated in a 0.2 mm thick 304 stainless steel shell for a total diameter of 0.5 mm. According to product literature, sources are available in activities of up to 15 mci. Publications The dosimetry of the Best Medical 192 Ir seed has been studied extensively using MC simulation [27,46,72,86, ] and experimental measurement. [1,163, ]
111 High-energy photon-emitting brachytherapy dosimetry 95 Figure 16. Materials and dimensions (mm) of the Best Medical model Ir seed.  Drawing is not to scale. Anctil et al.  made TLD measurements in a polystyrene phantom of size ( ) cm 3 using 1.0 mm 6 mm LiF rods calibrated in a 6 MV linac beam and having a measurement precision of 3%. Approximately 7 cgy was delivered to each TLD position in the phantom. Measurements were repeated 5 except at the reference position, where they were repeated 24 using bilateral TLD placement to minimize source positioning uncertainties in the transverse direction. A distance-dependent photon energy response correction was made using factors taken from Meigooni et al.  TG-43 parameters were obtained using a line source approximation for the geometry function, with L = 3 mm. was (1.110 ± 0.032) cgy h 1 U 1. The radial dose function was obtained over the distance range 1.0 cm to 10.0 cm in 1.0 cm steps, and the anisotropy function was obtained on a polar grid sampling of the same radial points and an angular range from 0 to 170 in 10 steps. Ballester et al.  used the GEANT4 code  to calculate dosimetry parameters for the Best Medical 192 Ir seed. The air-kerma strength was calculated with a statistical uncertainty of <0.5% in a (4 4 4) m 3 dry air volume using the 192 Ir emission spectrum from the NuDat database (NNDC), excluding emissions <10 kev. Kerma rate was scored in 1 cm 3 detectors located on the transverse axis at distances r = 5 cm to 150 cm from the source, the values fitted to the expression K air ( r)r 2 = S K + br. Collisional kerma, approximating absorbed dose, was scored within an 80 cm diameter water sphere in a set of concentric spherical shell segments 0.5 mm thick and 1 wide in polar angle. Statistical uncertainty was <0.5% except along the source longitudinal axis, where it was <2%. TG-43 parameters were derived using a line source approximation for the geometry function with L = 3 mm. was (1.112 ± 0.003) cgy h 1 U 1. g L (r) was calculated for variable-length steps within the range 0.25 cm to 20.0 cm. F(r, ) was obtained on a polar grid spanning the same radial interval and an angular interval from 0 to 90 in variable-angle steps.
112 96 HEBD report Wang et al.  used a modified version of the EGS4 MC code [134,184] to calculate dosimetry parameters for the Best Medical 192 Ir seed over a limited radial range 0.05 cm < r < 1.0 cm, of interest in intravascular brachytherapy. The 192 Ir emission spectrum used was that of Glasgow and Dillman.  Both photons and electrons were transported, and dose was scored in a water phantom with dimensions large compared to the most energetic secondary particles, using an analog estimator and a cylindrical coordinate system. The statistical accuracy of dose estimates was <0.5% for all radial positions r > 0.4 mm and all axial positions z < 10 mm. Doses were normalized to the source strength, and TG-43 parameters were derived using a line source approximation for the geometry function with L = 3 mm. was (1.109 ± 0.004) cgy h 1 U 1. The radial dose function calculated within an extended range 5 mm < r < 30 mm was found to be in excellent agreement with the published data of Williamson  and Wang and Sloboda.  Consensus Data Previously recommended dosimetry parameters for this source provided in the original TG-43 report  were derived from a combination of measured and MC data. Since the publication of TG-43, additional high-quality data have become available in the form of TLD measurements  and MC calculations. [72,86, ,185] The quality of the MC data as evaluated by guidelines described in Li et al.  and TG-43U1 report  is generally superior to that of the experimental data, with few exceptions. Hence for, the average of five MC values, [46,72,86,179,185] CON = (1.110 ± 0.015) cgy h 1 U 1 (see Table XXXVI) is recommended. Table XXXVI. Dose rate constant for different LDR 192 Ir sources. Seed Name (Manufacturer) CON [cgy h 1 U 1 ] Statistical uncertainty (k = 1) CON /G L (r, ) [cgy cm 2 h 1 U 1 ] Model (Best Industries) % Wire 0.5 cm (E&Z BEBIG) % Wire 1.0 cm (E&Z BEBIG) % To calculate G L (r, ), L = 0.3 cm was used. For CON g L (r), a combination of data from two studies is recommended: for 0.05 cm r 0.5 cm, the data of Wang and Li  are recommended because electron transport was explicitly taken into account and dose was scored directly; for 0.75 cm r 10 cm, the data of Ballester et al.  are recommended because they were obtained with recommended unbounded scatter conditions. These data are reproduced in Table XXXVII. For CONF(r, ), the Ballester et al.  data reproduced in Table XXXVIII are recommended, as they were obtained with denser angular sampling near the source long axis. Derived from the consensus TG-43 dataset, an away-along dose rate table is presented (cgy h 1 U 1 ) for TPS quality assurance purposes (Table XXXIX).
113 High-energy photon-emitting brachytherapy dosimetry 97 Table XXXVII. Radial dose function values for LDR 192 Ir sources. Extrapolated data are underlined. Values inside the source are in italics. r [cm] seed Best Industries L = 0.3 cm g L (r) Wire 0.5 cm E&Z BEBIG L = 0.5 cm Wire 1.0 cm E&Z BEBIG L = 1 cm Table XXXVIII. F(r, ) for the Best Industries model Ir seed. Extrapolated data are underlined. Values inside the source are in italics. r (cm) (deg)
114 98 HEBD report Table XXXIX. QA away-along data [cgy h 1 U 1 ] for the Best Industries model Ir seed. Values inside the source are in italics. y (cm) z (cm) A.3.2. LDR 192 Ir wires (E&Z BEBIG) Source Description Platinum encapsulated 192 Ir wires are used as interstitial sources in LDR brachytherapy in manual and remote afterloading systems in Europe. There are several different models of 192 Ir wires that are commercially available.  192 Ir wires of 0.3 mm and 0.5 mm in total diameter, encapsulated with 0.1 mm Pt are the most clinically used source models (Figure 17). Currently there is only one manufacturer: E&Z BEBIG. The total length of the source wires as supplied by the manufacturer is 14 cm. The wire is flexible and is designed to be cut to the desired length in clinical practice, so one can obtain wires of any length and curvature. TPSs calculate dose distributions around the wires with different algorithms using stored data for elemental wires: punctual source, 0.5 cm long wire, 1 cm long, etc. Figure 17. Materials and dimensions (mm) of the E&Z BEBIG LDR 192 Ir wire.  Plot is not to scale.
115 High-energy photon-emitting brachytherapy dosimetry 99 Publications Elongated source dosimetry, most appropriate for 192 Ir wires, will be covered by TG-143. The current report focused only on data for the fundamental lengths used by TPS. So, consensus datasets only for 0.5 cm and 1 cm wire lengths will be produced. For the 0.5 cm and 1 cm wires there is only one publication  using GEANT4, scoring kerma in an unbounded phantom. However, several MC and EXP studies have been done for the 5 cm Ir wire: Karaiskos et al.,  van der Laarse et al.,  Ballester et al.,  and Pérez-Calatayud et al.  The studies of Ballester et al., and Perez-Calatayud et al., were not considered because a bug was discovered in GEANT3 that affected the dose calculated along the source. There are two EXP studies: Bahar-Gogani et al.  that used a liquid ionization chamber and Gillin et al.  that used TLD. In the comparison, the MC study of Karaiskos et al.  data has been corrected from the particle streaming function to the geometry function G L (r, ) and unbounded scattering conditions.  A comparison has been done between the previously commented MC and EXP studies using away-along dose rate tables corrected by r 2, showing very good agreement within uncertainties except at points where the different phantoms used introduced dose differences. Consensus Data The previous comparison done for the same source but with L = 5 cm supports the GEANT4 code on the van der Laarse et al.  study as the only study for the 0.5 cm and 1 cm wire lengths. So, CON (see Table XXXVI), CON g L (r) (see Table XXXVII), and CON F(r, ) (Tables XL and XLIII) consensus for the 0.5 cm and 1 cm length wires are taken from van der Laarse et al.  study. Derived from the consensus TG-43 dataset, an away-along dose rate table is presented (cgy h 1 U 1 ) for TPS quality assurance purposes (Tables XLI and XLII). Table XL. F(r, ) for the E&Z BEBIG L = 0.5 cm wire length. Extrapolated data are underlined. Values inside the source are in italics. r (cm) (deg)
116 100 HEBD report Table XL (continued). r (cm) (deg) Table XLI. QA away-along data [cgy h 1 U 1 ] for the E&Z BEBIG L = 0.5 cm wire length. Extrapolated data are underlined. Values inside the source are in italics. z (cm) y (cm)
117 High-energy photon-emitting brachytherapy dosimetry 101 Table XLII. F(r, ) for the E&Z BEBIG L = 1 cm wire length. Extrapolated data are underlined. Values inside the source are in italics. r (cm) (deg) Table XLIII. QA away-along data [cgy h 1 U 1 ] for the E&Z BEBIG L = 1 cm wire length. Values inside the source are in italics. Extrapolated data are underlined. z (cm) y (cm)
118 102 HEBD report A Cs sources A.4.1. CSM3 (E&Z BEBIG) Source Description This 137 Cs source manufactured by E&Z BEBIG is used in manual and remote-controlled LDR afterloading systems. The source (Figure 18) is composed of three cylindrical pollucite pellets, 0.08 cm in diameter and 0.36 cm long contained in a 2.03 cm long outer stainless-steel cylinder with an outer diameter of cm. The 137 Cs radionuclide is uniformly distributed in the active pellets. The source is asymmetric due to the presence of the eyelet and the upper wedge-shaped end. Figure 18. Materials and dimensions (mm) of the E&Z BEBIG model CSM3 source.  Publications The CSM3 source has been studied by Williamson  and Liu et al.  using analytical methods, and by Pérez-Calatayud et al.  using MC. Only calculated data have been published for this source, although in Pérez-Calatayud et al.  the MC results were validated using TLD dosimetry for a very similar source model, CSM2 (the CSM2 has the same design as the CSM3 but with the central pollucite pellet made inactive). The CSM3 source belongs in the category of conventionally encapsulated 137 Cs and 192 Ir, similar in design to existing ones where a single dosimetric study is sufficient as recommended.  Because this is a segmented active volume source, to obtain the parameters and functions of the TG-43 formalism, an effective active length L eff of 1.8 cm was used (L eff = N S, where N is the number of active pellets and S the separation between the centers of two consecutive active pellets) as proposed by Williamson  and recommended in the TG-43U1 report.  The origin for dose calculations in Williamson  and Liu et al.  is the geometrical center of the three active source pellets, while in Perez-Calatayud et al.  it is the center of the capsule. So, the origins are 0.15 mm apart. For the purposes of this report, the data in Pérez-
119 High-energy photon-emitting brachytherapy dosimetry 103 Calatayud et al.  were interpolated to effectively shift the origin to the geometrical center of the three active pellets. Williamson  studied the dosimetric proprieties of this source. The source was considered symmetrical, neglecting the asymmetry between the two source ends. MC was used to fit the parameters for a Sievert-based algorithm that was later used to give the away-along dose rate tables for this source. No TG-43 formatted data were presented. Williamson  used a tissue attenuation and scatter factor calculated by himself.  Liu et al.  produced a dosimetric report with the TG-43 formalism for these sources using the same Sievert-derived algorithm as Williamson with identical fitted parameters (attenuation coefficients) but considering the sources as linear sources with the radioactivity uniformly distributed on the central source axis. In contrast with Williamson s study, the authors used the Meisberger polynomial  for tissue attenuation. Pérez Calatayud et al.  used the GEANT4 MC code.  The application of this calculation method was experimentally validated with TLD. Absorbed dose was approximated by kerma with a cutoff of 10 kev. Kerma was scored in an R = 20 cm water sphere surrounding the source. Source s K was determined in dry air, using a linear fitting function to correct for air attenuation and scattering. For both simulations, in water and dry air, the linear track-length kerma estimator  was used. g L (r) was obtained using the line-source approximation with L = 1.8 cm over a radial range r = 0.25 cm to 15 cm. It was fit with 5 th order polynomials in two domains, 0.25 cm < r < 0.8 cm and 0.8 cm r < 15 cm, respectively. The anisotropy function was obtained over the same radial range and an angular range = 0 to 180, with 1 angular sampling close to the source long axis. Consensus Data The Pérez-Calatayud et al.  study adhered to recommendations for MC dosimetry given in Li et al.  and TG-43U1 report  with the exception that it did not provide experimental verification of source geometry or address source geometry uncertainty. Reported values differ by 0.2%. Radial dose functions from the studies of Liu et al.  and Pérez-Calatayud et al.  agree to within 0.5%. Anisotropy functions show significant disagreement due to the simplifications of the Liu et al.  study: symmetrical source and radioactivity uniformly distributed along the source axis. The average published values were used for CON = (0.902 ± 0.003) cgy h 1 U 1 (see Table XLIV). Due to the data range and resolution, both CON g L (r) and CON F(r, ) were taken from Pérez-Calatayud et al.  as presented in Tables XLV and XLVI. These data are provided for full scatter conditions. An awayalong table (Table XLVII) derived from the recommended consensus datasets is presented for TPS quality assurance purposes.
120 104 HEBD report Seed Name (Manufacturer) Table XLIV. Dose rate constant of 137 Cs sources. CON [cgy h 1 U 1 ] Statistical uncertainty (k = 1) CON /G L (r, ) [cgy cm 2 h 1 U 1 ] CSM-3 (E&Z BEBIG) % IPL (RPD) % CSM11 (E&Z BEBIG) % The value g L (r = 0.25 cm) = presents a step with respect to its neighbor g L (y= 0.5 cm) = A possible reason could be an artifact of G L (r, ) due to choice of L eff = 1.8 cm and the three source segments. A study was done by HEBD comparing: (a) g L (r) obtained using G L (r, ) and L eff = 1.8 cm, and (b) g L (r) obtained using the particle streaming function as used by Rivard  and Karaiskos et al.  This study demonstrated that the g L (r) step was attributed to G L (r, ) due to choice of L eff = 1.8 cm. Table XLV. Radial dose function values for 137 Cs LDR sources. Interpolated/extrapolated data are boldface/underlined. Values inside the source are in italics. r [cm] E&Z BEBIG CSM3 L = 1.8 cm g L (r) RPD IPL L = 1.48 cm E&Z BEBIG CSM11 L = 0.32 cm
121 High-energy photon-emitting brachytherapy dosimetry 105 Table XLVI. F(r, ) for the E&Z BEBIG CSM3 source. Values inside the source are in italics. Extrapolated data are underlined. r (cm) (deg)
122 106 HEBD report Table XLVII. QA away-along data [cgy h 1 U 1 ] for the E&Z BEBIG CSM3 source. Values inside the source are in italics. Extrapolated values are underlined. y (cm) z (cm) A.4.2. IPL (Radiation Products Design) Source Description The IPL 137 Cs, Model , sources are 3.05 mm in diameter and 20 mm in length. These sources are manufactured by Isotope Product Laboratories (IPL, Valencia, CA) and distributed by Radiation Products Design, Inc. (Albertville, MN). See Figure 19. Figure 19. Materials and dimensions (mm) of the Radiation Products Design model Cs source.  The source tip is on the side of the aluminum ring.
123 High-energy photon-emitting brachytherapy dosimetry 107 Figure 19 shows a schematic diagram of this source model. The capsules of these sources are composed of two layers of 304 stainless steel with a total wall thickness of mm. There are two end caps (one for each capsule layer) on each end of the source. The total thickness of the end cap on one side is 2 mm and on the opposite side it is 3 mm. The active portion of the source is 1.52 mm in diameter and 14.8 mm in length. The 137 Cs radionuclide is uniformly distributed in a core of cesium oxide ceramic, assuming approximately 5.29 mg Cs 2 O in a 50 mci source. The mass density of the active ceramic material is 1.47 g/cm 3, while the density of the ceramic itself is 1.27 g/cm 3. A colorcoded aluminum ring easily identifies the source activity and defines the source tip. The S K calibration is traceable to NIST through the University of Wisconsin ADCL in Madison. Publications The GEANT4 (version 8.0) MC code was used by Meigooni et al.  to calculate the airkerma and the dose rate distributions around an IPL 137 Cs source in liquid water and in Solid Water TM phantom materials. TLD measurements were done to validate MC calculations. The track-length estimator was used to derive kerma. In order to validate the accuracy of the source design, dimensions, and composition materials used in the MC studies, simulations were performed in a ( ) cm 3 Solid Water TM phantom, which is identical to that used in the experimental setup for TLD measurements. They followed AAPM TG-43U1 recommendations  in both MC calculations and TLD measurements. In their data analysis, an active length L = 1.48 cm was used to calculate G L (r, ) in both dosimetric investigations. In this study, the MC-calculated values were validated by comparison of the simulated data with the TLD measured values in the same phantom material. Consensus Data The data from Meigooni et al.  are the only published data about this source. Their MC results were validated against TLD measurement. In general, the agreement was good. Moreover, the MC value they obtained, once corrected by the geometry factor, is close to that for the CSM3 source, as expected. Subsequently, MC = cgy h 1 U 1 ± 2.6% (see Table XLIV), MC g L (r), and MC F(r, ) were introduced for their clinical applications (Table XLV and Table XLVIII, respectively). Because there is only the one study for this source, the derived MC TG-43 data from Meigooni et al.  are recommended as consensus data. In addition, Meigooni et al.  provided the tabulated data that was required in source characterization with the primary and scatter dose separation (PSS) formalism. [73,148] Derived from the consensus TG-43 dataset, an away-along dose rate table is presented (cgy h 1 U 1 ) for TPS quality assurance purposes (Table XLIX).
124 108 HEBD report Table XLVIII. F(r,θ) for the Radiation Products Design IPL source. Values inside the source are in italics. Extrapolated data are underlined. r (cm) θ (deg)
125 High-energy photon-emitting brachytherapy dosimetry 109 Table XLIX. QA away-along data [cgy h 1 U 1 ] for the Radiation Products Design IPL source. Extrapolated data are underlined. Values inside the source are in italics. z (cm) y (cm) A.4.3. CSM11 (E&Z BEBIG) Source Description This 137 Cs source manufactured by E&Z BEBIG is used in manual and remote-controlled LDR afterloading systems. The source (Figure 20) is composed of a cylindrical pollucite pellet, 0.85 mm in diameter and 3.6 mm long. The pellet is encapsulated in stainless steel with total length of 5.2 mm and with an outer diameter of 1.65 mm. The 137 Cs radionuclide is uniformly distributed in the active pellets. The source is asymmetric due to the hemispherical end. Figure 20. Materials and dimensions (mm) of the E&Z BEBIG CSM11 source. 
126 110 HEBD report Publications The CSM11 source has been studied by Ballester et al.  and by Otal et al.  using both Monte Carlo methods. Calculation guidelines described in Li et al.  and TG-43U1  have been closely adhered to in both studies. Only calculated data have been published for this source, which belongs in the category of conventionally encapsulated 137 Cs and 192 Ir similar in design to existing ones where a single dosimetric study is sufficient.  Ballester et al.  used GEANT3 MC code to generate an away-along table and TG-43 parameters. Electron transport was performed and a cutoff energy of 10 kev was taken for both electron and photons. The origin of coordinates is the geometrical center of the source instead of the center of the active part as recommended in this report. The reported dosimetric data are of poor quality because they are too noisy. They obtained a = ± cgy h 1 U 1. Otal et al.  studied this source considering the same dimensions and composition materials as Ballester et al.  but using the GEANT4 code and using track-length kerma estimator. In this case authors considered the origin of coordinates at the center of the active part, as it is recommended in this report. Parameters and simulation conditions were the same that in Ballester et al.  They obtained a = ± cgy h 1 U 1 and derived g L (r) and F(r, ) along with an away-along table. The data presented are of low noise. Consensus Dataset Because Ballester et al.  considered the origin of coordinates at the capsule center and the their data have larger statistical uncertainties, CON = ± cgy h 1 U 1 (see Table XLIV), CONg L (r) (see Table XLV), and CON F(r, ) (see Table L) were taken from the study of Otal et al.  An away-along table derived from the recommended consensus datasets is presented for TPS quality assurance purposes (see Table LI). Table L. F(r, ) for the E&Z BEBIG CSM11 source. Extrapolated data are underlined. Values inside the source are in italics. (deg) r (cm)
127 High-energy photon-emitting brachytherapy dosimetry 111 Table L (continued). r (cm) (deg) Table LI. QA away-along data [cgy h 1 U 1 ] for the E&Z BEBIG CSM11 source. Values inside the source are in italics. y (cm) z (cm)
128 112 HEBD report A.5. High Dose Rate 60 Co sources A.5.1. GK60M21 (E&Z BEBIG) Source Description This 60 Co HDR source (E&Z BEBIG) is similar in shape and materials to other commercially available 192 Ir HDR sources. This source model is composed of a central cylindrical active core made of metallic 60 Co, 3.5 mm in length and with a diameter of 0.6 mm. This active core is covered by a cylindrical 316L stainless steel cover of 1 mm external diameter. This 60 Co HDR source is shown schematically in Figure 21. Figure 21. Materials and dimensions (mm) of the E&Z BEBIG model GK60M21 source.  Publications The MC GEANT4 code was used by Ballester et al.  to obtain the dose rate distribution following the Li et al.  prerequisites. Only the gamma part of the 60 Co spectrum was considered. The beta spectrum contribution to the dose was assumed to be negligible.  A cutoff energy of 10 kev was used for both photons and electrons. Ballester et al., scored kerma and dose separately to account for the electronic disequilibrium near the source due to the high energy of the photons emitted. For points located at distances of less than 1 cm from the source they scored dose, while for distances where electronic equilibrium is achieved they scored kerma. They derived TG-43U1 parameters  and an away-along table. Selvam and Bhola  reproduced the Ballester et al.  study but using the EGSnrc code. They derived only an away-along table. The comparison of away-along tables from both studies reveals consistency between both studies except at y = 0.25 cm and z = 0.25, z = 0, and z = 0.25 cm where the Ballester et al.  data had an error.
129 High-energy photon-emitting brachytherapy dosimetry 113 Consensus Dataset An average CON = (1.089 ± 0.055) cgy h 1 U 1 was taken (see Table LIII). Selvam and Bhola  data are taken as consensus for CON g L (r) (Table LII) because of higher resolution close to the source and the previously noted error at r = 0.25 cm in the other published study. Ballester et al.  data for F(r, ) (Table LIV) is taken as consensus data because of the previous demonstration of away-along table agreement. Derived from the consensus TG-43 dataset, an away-along dose rate table is presented (cgy h 1 U 1 ) for TPS quality assurance purposes (Table LV). Table LII. Consensus radial dose function values for 60 Co HDR sources. Values inside the source are in italics. Extrapolated data are underlined. r [cm] E&Z BEBIG GK60M21 L = 0.35 cm g L (r) E&Z BEBIG Co0.A86 L = 0.35 cm Seed Name (Manufacturer) Table LIII. Dose rate constant for HDR 60 Co sources. CON [cgy h -1 U -1 ] Statistical uncertainty (k = 1) CON /G L (r, ) [cgy cm 2 h 1 U 1 ] GK60M21 (E&Z BEBIG) % Co0.A86 (E&Z BEBIG) % 1.103
130 114 HEBD report Table LIV. F(r, ) for the E&Z BEBIG 60 Co HDR GK60M21 source. Values inside the source are in italics. Extrapolated data are underlined. r (cm) (deg)
131 High-energy photon-emitting brachytherapy dosimetry 115 Table LV. QA away-along data[cgy h 1 U 1 ] for the E&Z BEBIG 60 Co GK60M21 source. Values inside the source are in italics. z (cm) y (cm) A.5.2. Co0.A86 (E&Z BEBIG) Source Description The geometric design and materials of the E&Z BEBIG 60 Co model Co0.A86 source are shown schematically in Figure 22. It is very similar to the E&Z BEBIG model GK60M21 source (Appendix A.5.1), both in design and materials. The model Co0.A86 source differs from the model GK60M21 in that it has a smaller active core (0.5 mm in diameter for this source vs. 0.6 mm in diameter for the GK60M21) and a more rounded capsule tip. The model Co0.A86 source is composed of a central cylindrical active core made of metallic 60 Co, 3.5 mm in length and with a diameter of 0.5 mm. The active core is covered by a cylindrical stainless steel capsule 0.15 mm thick with an external diameter of 1 mm. Publications Granero et al.  used GEANT4 MC code to obtain the dose rate distribution adhering to the Li et al.  prerequisites. The same type of study described in Appendix A.5.1 for the GK60M21 source model was done for the present source. Selvam and Bhola  also reproduced the Granero et al.  study but using the EGSnrc code, obtaining only an away-along table. The comparison of awayalong tables from both studies reveals that at y = 0.25 cm and z = 0.25, z = 0, and z = 0.25 cm the Granero et al.  data are underestimated. This is the same typo as in Ballester et al.  data for the
132 116 HEBD report model GK60M21 source. However, some inconsistencies are observed in the Selvam and Bhola  data because at large distances from the source their data are not symmetric. Figure 22. Materials and dimensions (mm) of the E&Z BEBIG model Co0.A86 source.  Consensus Dataset An average CON = ± cgy h 1 U 1 was taken. Because of the error in Granero et al.  data, Selvam and Bhola  data for CON g L (r) (Table LII) and Granero et al.  data for F(r, ) (Table LVI) were taken as consensus data. Derived from the consensus TG-43 dataset, an awayalong dose rate table is presented (cgy h 1 U 1 ) for TPS quality assurance purposes (Table LVII).
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