Dose calculation for photonemitting brachytherapy sources with average energy higher than 50 keV: Report of the AAPM and ESTRO
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 highenergy (average energy higher than 50 keV) photonemitting 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 TG43U1 formalism to highenergy photonemitting 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 highenergy 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 highenergy sources without consensus datasets are given.
Conclusions:
Recommended consensus datasets for highenergy sources have been derived for sources that were commercially available as of January 2010. Data are presented according to the AAPM TG43U1 formalism, with modified interpolation and extrapolation techniques of the AAPM TG43U1S1 report for the 2D anisotropy function and radial dose function.
I. INTRODUCTION
In 1995, the American Association of Physicists in Medicine (AAPM) Task Group No. 43 published a clinical protocol on dosimetry for interstitial brachytherapy sources,^{1} colloquially known as the “TG43 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 lowenergy photonemitting sources following general acceptance and implementation of the TG43 dose calculation formalism by the brachytherapy vendor, treatment planning systems (TPS), and user communities. Development of the TG43 methods in the area of lowenergy 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 lowenergy interstitial brachytherapy sources, especially for permanent prostate implants, and the increasing number and variable design of commercially available lowenergy sources, LEBD continued to develop the TG43 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 lowenergy interstitial brachytherapy are summarized in two key reports: the 2004 update of the TG43 report (TG43U1)^{2} and its 2007 supplement (TG43U1S1).^{3,4} In the field of highenergy brachytherapy dosimetry, the TG186 report will provide guidance for early adopters of modelbased dose calculation algorithms. The modelbased dose calculation algorithms (MBDCA) Working Group will develop a limited number of welldefined 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 doseestimation methods and dosimetric parameters for specific highenergy brachytherapy sources (defined as photonemitting sources with average photon energies exceeding 50 keV) including ^{192}Ir,^{137}Cs, ^{60}Co, and ^{198} Au sources. Many new source designs, especially highdose rate (HDR) and pulseddose rate (PDR) sources, have been introduced for use in remoteafterloading machines, while traditional lowdose 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 (Refs. 5 and 6) and^{170 }Tm,^{7–9} are being actively investigated for application in HDR brachytherapy and should be discussed in the forthcoming TG167 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 singlesource dose distributions, consensus dataset formation processes, and calibration processes are able to support the level of dosimetric accuracy and precision 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 TG43,^{1} TG56,^{13} and TG59 (Ref. 15) 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 TG43 formalism, would be of substantial benefit to clinical end users.
 1.
To compile a list of highenergy 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 highenergy brachytherapy sources similar in scope to the lowenergy brachytherapy dosimetry prerequisites.^{16}
 3.
To develop an extension of the TG43 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 highenergy (LDR/HDR/PDR) sources.
 6.
To provide a Brachytherapy Source Registry (BSR) for webbased access to highenergy brachytherapy source dosimetry data that satisfy the prerequisites defined in charge 2.
 (a)
Review the construction and available published dosimetry data for highenergy ^{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^{17} (charge 1).
 (b)
Perform a critical review of the existing TG43U1 formalism^{2} as used heretofore mainly for lowenergy brachytherapy sources. Extension of the TG43 dose calculation formalism was not performed as considered in charge 3.
 (c)
Critically review published dosimetric data for each of the prerequisitecompliant source models listed in (a) and develop a complete consensus dataset to support clinical planning for each source model (charge 4).
 (d)
Develop guidelines for investigators on the use of computational and experimental dosimetry for determination of highenergy brachytherapy source dosimetry parameters.
The full report containing detailed descriptions on the sources included in this report, along with quantitative consensus datasets, is available on the AAPM website.
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.
II. PHYSICAL CHARACTERISTICS OF HIGHENERGY PHOTONEMITTING BRACHYTHERAPY SOURCES
The photonemitting 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 TG60 (Ref. 18) and TG149.^{19} Similarly, electronic brachytherapy sources will be addresed by the AAPM Task Groups TG167 and TG182. The limit of 50 keV was established by the AAPM to separate highenergy sources from those addressed by the LEBD.^{16}
This report addresses brachytherapy source models that were commercially available as of January 2010. For sources that were commercially available, the goal was to generate consensus datasets in a format acceptable to commercial treatment planning systems. 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)^{20} for a more complete description. Baltas et al.^{21} also provides a clear description of these radionuclides. Detailed information on recommended photon spectra is provided in Sec. ???.
^{192}Ir  ^{137}Cs  ^{60}Co  

Halflife  73.81 days  30.07 yr  5.27 yr 
Type of disintegration  β^{−} (95.1%), EC (4.9%)  β^{−} (100%)  β^{−} (100%) 
Maximum xray energy (keV)  78.6  37.5  8.3 
Gamma energyrange (keV)  110.4–1378.2  661.6  1173.2–1332.5 
Mean xray and gamma energy (keV)  350.0  613.0  1252.9 
Maximum β^{−} ray energies (keV)  81.7 (0.103%)  514.0 (94.4%)  318.2 (99.88%) 
258.7 (5.6%)  1175.6 (5.6%)  1491.4 (0.12%)  
538.8 (41.43%)  
675.1 (48.0%)  
Mean β^{−} ray energy (keV)  180.7  188.4  96.5 
Airkerma rate constant, Γ_{δ}_{ = 10 keV} (μGy m^{2} h^{−1} MBq^{−1})  0.1091  0.0771  0.3059 
Specific activity (GBq mg^{−1})  341.0  3.202  41.91 
^{198} Au (halflife 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 soft tissue 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 xrays and gammarays 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 (halflife 59.4 days) and ^{103}Pd (halflife 17.0 days), both of which have longer halflives, 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.^{22} conducted a survey of 178 publications reporting on prostate brachytherapy between 1985 and 1998. 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^{23} 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.^{24} 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.
II.A. ^{192}Ir
The ^{192}Ir halflife of 73.81 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 β^{−} (95%) and ^{192}Os via electron capture (EC) (5%), emitting on average 2.3 gamma rays per disintegration with a range of energies between 0.061 and 1.378 MeV and a mean energy of 0.355 MeV. The β^{−} rays emitted have a maximum energy of 0.675 MeV and an average energy of 0.1807 MeV. ^{192}Ir is produced from enriched ^{191}Ir targets (37% natural abundance) in a reactor by the (n, γ) 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 β^{−}decay are absorbed by the core and the capsule.^{25–28}
II.B. ^{137}Cs
The ^{137}Cs halflife of 30.07 yr enables use over a long period of time. Its low specific activity makes it practical for LDR implants. ^{137}Cs decays purely via β^{−}, mainly (94.4%) to the second excited state of ^{137}Ba, where the deexcitation to the ground state (90%) with emission of a gamma ray of 0.662 MeV (absolute intensity 85.1%) is in competition with internal conversion (IC) (10%). The β^{−} rays emitted have a maximum energy of 0.514 MeV. A second β^{−} decay branch (5.6% probability) to the ^{137}Ba ground state occurs, with maximum β^{−} ray energy of 1.176 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 β^{−} decay are absorbed by the core and the capsule.^{28} 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 remoteafterloading intracavitary brachytherapy catheters.
II.C. ^{60}Co
The ^{60}Co halflife of 5.27 yr 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 β^{−} decay to the excited states of ^{60}Ni (94.4%). Deexcitation to the ground state occurs mainly via emission of γrays of 1.173 and 1.332 MeV, each with an absolute intensity of nearly 100%. The main β^{−} rays emitted (99.88%) have a maximum energy of 0.318 MeV and an average energy of 0.096 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 (Sec. II A). The lowenergy electrons emitted by ^{60}Co are easily absorbed by the cobalt source material or encapsulation layers, resulting in a “pure” photon source.^{10,28}
III. CONSIDERATIONS APPLYING THE TG43U1 FORMALISM TO HIGHENERGY PHOTONEMITTING BRACHYTHERAPY SOURCES
 (1)
Dosimetric modeling of seeds using the pointsource 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 discernable in clinical practice for nonstranded 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 θ 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 TG43 formalism^{1,2} assumes a water medium with superposition of single source dose distributions, no intersource attenuation (ISA) effects, and full scatter conditions (infinite or unbounded water medium) at dose calculation pointsofinterest (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 lowenergy and highenergy brachytherapy applications and is discussed in detail by Rivard et al.^{33,34}
Variable tissue composition has a larger influence on lowenergy brachytherapy source dosimetry than for highenergy sources due to the photoelectric effect and its high cross section at low energies. However, the effect of scatter conditions is more important for highenergy brachytherapy dosimetry. For lowenergy brachytherapy, mostly conducted as prostate implants, the surrounding tissue is adequate to provide full scatter conditions. In contrast, highenergy 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 TG43 formalism can account for partial radiation scatter conditions utilizing the current TG43 based TPS. Alternatively, new dose calculation algorithms that correct for partial radiation scatter conditions are emerging.
As for lowenergy brachytherapy sources, especially those used in multisource LDR implants, ISA effects are also present for highenergy LDR sources such as ^{192}Ir and ^{137}Cs. However, the clinical trend in the highenergy source domain is that HDR and PDR are more prevalent than the LDR procedures.
One important limitation of current TPS dose calculation tools is the nearuniversal 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.^{37} 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 MRIcompatible applicators, imaging artifacts due to highZ 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 is the subject of the active AAPM Task Group 186.
The TG43 formalism was originally applied to sources with active lengths ranging from 2 to 4 mm, while typical HDR/PDR sources have active lengths ranging from 0.5 to 5 mm, and some highenergy 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 TG43 formalism is presently being developed by the AAPM Task Group 143.
In Sec. III C of this report, the dependence of dosimetry parameters for highenergy 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–interpolation techniques presented in the AAPM TG43U1 and TG43U1S1 reports was performed for highenergy 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 source are addressed.
III.A. Phantom size effects
A limitation of the TG43 formalism when applied to high energy sources is the assumption of fixed scatter conditions at calculation points, without consideration of the tissue boundaries. The TG43 dose calculation formalism assumes an infinite scattering medium and can result in overestimation of absorbed dose at a lowdensity 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.^{38} showed a dose reduction at points close to lowdensity interfaces of up to 8% for HDR ^{192}Ir brachytherapy as typical for breast implants performed as a boost. Mangold et al.^{39} showed deviations of up to 14% with measurements close to the tissue–air interface, whereas Wallner and colleagues^{40} found the TPS to overestimate dose by no more than 5% at points close to the skin and lung for partial breast irradiation. However, Raffi et al. found TPS dose overestimations of up to 15%.^{41}
Lymperopoulou et al.^{42} 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.^{43} showed for breast implants at 2–5 cm depths with Monte Carlo (MC) radiation transport methods that the TPS overestimates by 5%–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, Rainaet al.^{44} 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 twodimensional (2D) water dose rate tables which assume cylindrically symmetric sources and applicators, a uniform waterequivalent medium, and negligible ISA effects. Usually, these dose rate tables consist of TG43 parameter values or awayalong 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 TG43U1 report^{2} recommended that the radial dose function g(r) extends 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 TG43U1 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 highenergy sources, the recommended range forg(r) is r ≤ 10 cm.
Another issue is whether the TG43 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 highenergy sources, an effectively unbounded spherical phantom radius R of 40 cm is recommended to promote uniformity of dose calculations forr < 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 Sec. V.
Phantom size is well known to be an important consideration in brachytherapy dosimetry. Ellet^{45} studied boundary effects for photon source energies ranging from 0.03 to 2.75 MeV by comparing the dose in water spheres of radiusR = 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 0.364 MeV, 11.7 cm for 0.662 MeV, and 17.3 cm for 1.46 MeV). Williamson^{46} 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 (20 × 20 × 20) cm^{3}. Agreement within 5% was observed up to 5 cm from the source, but differences of 5%–10% were noted forr > 5 cm. Williamson and Li^{47} 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.^{48} 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.^{49} performed MC and thermoluminescent dosimetry (TLD) studies of the microSelectron HDR^{192} Ir source using spherical water phantoms withR = 10–50 cm. They ascertained that phantom dimensions significantly affect nearphantom boundaries where deviations of up to 25% were observed. They did not observe significant differences in the anisotropy function F(r, θ) for the different values ofR. Other investigators have found a dose dependence onR due to the different scatter conditions.^{50–56}
PerezCalatayud et al.^{29} 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 forr ≤ 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.^{29} These results agree with the subsequent study by Melhus and Rivard,^{30} 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. PerezCalatayud et al.^{29} 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% forr < R − 2 cm if R < 17 cm and for r < 15 cm if . 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 forR = 40 cm the dose rate was equivalent to an unbounded phantom forr ≤ 20 cm. Some dosimetry investigators have used a 40cmhigh cylindrical phantom with a 20cm radius in their MC studies. It has been shown that this phantom is equivalent to a spherical phantom with a 21cm radius.^{29} The expression developed by PerezCalatayud et al.^{29} is not applicable to the outer 2 cm of this phantom.
To date, most published MC highenergy 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 withR = 40 cm.^{70–72} Granero et al.^{31} developed correction factors expressed as fourthdegree polynomials to transform g(r) data for ^{192}Ir and ^{137}Cs obtained using commonly published phantom sizes into approximateg(r) values for unbounded phantom conditions, with agreement within 1%.^{29–31} These correction factors are given in Table II.
Sphere 1 cm ≤ r ≤ 15 cm  Cylinder 1 cm ≤ r ≤ 20 cm  Cube 1 cm ≤ r ≤ 15 cm  

CF parameter  ^{192}Ir  ^{137}Cs  ^{192}Ir  ^{137}Cs  ^{192}Ir  ^{137}Cs 
C_{0} (dimensionless)  1.002  1.001  1.001  1.001  1.002  1.001 
C_{1} (cm^{−1})  −3.52 × 10^{−3}  −2.28 × 10^{−3}  −1.23 × 10^{−3}  −1.09 × 10^{−3}  −3.27 × 10^{−3}  −1.85 × 10^{−3} 
C_{2} (cm^{−2})  2.06 × 10^{−3}  1.24 × 10^{−3}  3.00 × 10^{−4}  4.02 × 10^{−4}  1.31 × 10^{−3}  8.89 × 10^{−4} 
C_{3} (cm^{−3})  −2.39 × 10^{−4}  −1.35 × 10^{−4}  −2.40 × 10^{−5}  −3.93 × 10^{−5}  −2.46 × 10^{−4}  −9.45 × 10^{−5} 
C_{4} (cm^{−4})  1.38 × 10^{−5}  7.78 × 10^{−6}  1.90 × 10^{−6}  2.08 × 10^{−6}  8.50 × 10^{−6}  5.23 × 10^{−6} 
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 forr ≤ 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 Λ is directly comparable in all cases. As noted in the literature,^{49}F(r, θ) has been shown to be nearly independent of phantom size. Consequently, research has focused ong(r). Anagnostopoulos et al.^{54} proposed a calculation algorithm based on the scattertoprimary ratio to relate g(r) for one spherical phantom size to g(r) for otherR values. Russell et al.^{73} 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.^{74} developed a novel approach inspired by field theory to calculating the dose decrease in a finite phantom for ^{192}Ir point source(s).
III.B. Dose calculation grid size and interpolation accuracy
Traditionally, brachytherapy TPS utilized analytical methods such as the Sievert integral^{75} 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 TG43 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 highenergy 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 TG43U1 report^{2} provided guidelines for interpolation and extrapolation of onedimensional (1D) and 2D dosimetry parameters. The 2007 supplement (i.e., TG43U1S1)^{3,4} included further clarification and modifications of the interpolation and extrapolation techniques in order to make these procedures more accurate. Unlike for lowenergy sources, the 1D approximation for highenergy 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 AAPM TG43U1S1 recommendations for interpolation and extrapolation of 2D dosimetry are summarized in Table III.
r < r_{min}  r_{min} < r ≤ r_{max}  r > r_{max}  

Parameter  Extrapolation  Interpolation  Extrapolation 
g_{L}(r)  Nearest neighbor or zerothorder extrapolation(Ditto)  Linear (loglinear) using datapoints immediately adjacent to the radius of interest  Linear using data of last two tabulated radii (single exponential function based on fitting g_{L}(r) datapoints for the furthest three r values) 
F(r, θ)  Nearest neighbor or zerothorder extrapolation(Ditto)  Bilinear (bilinear) interpolation method for F(r, θ)(Ditto)  Nearest neighbor or zerothorderrextrapolation (Ditto) 
 (1)
From a clinical perspective, there is more concern with dose accuracy along the longitudinal axis region of the source for highenergy 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 lowenergy 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 highenergy sources, MCbased 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 highenergy brachytherapy may be more limited than MCbased dosimetry. Experiment may primarily serve to validate MC and to obtain Λ for averaging with MCderived values since MC is primarily used to determine F(r, θ) andg_{L}(r) for highenergy sources. Consequently, range and spatial resolution limitations are not of concern for MC methods and highenergy brachytherapy source dosimetry. However, caution must be taken at close distances if electron transport and electron emissions are not considered.
A study by PujadesClaumarchirant et al.^{79} has been performed for highenergy sources to check methods of interpolation/extrapolation that allow accurate reproduction ofg_{L}(r) andF(r, θ) from tabulated values, including the minimum number of entries forg_{L}(r) andF(r, θ) that allow accurate reproduction of dose distributions. Four sources were studied: ^{192}Ir,^{137}Cs, ^{60}Co, and a hypothetical ^{169}Yb source. Ther mesh was that typically used in the literature: 0.25, 0.5, 0.75, 1, and 1.5 cm, and for 2–10 cm in 1 cm steps, adding the pointr_{gmax} = 0.33 cm for ^{60}Co andr_{gmax} = 0.35 cm for ^{137}Cs near the maximum valueg(r_{g}_{max}). ForF(r, θ), the entries for polar angles close to the source long axis were evaluated at four different step sizes: 1°, 2°, 5°, and 10°. Forg_{L}(r), linear interpolations agreed within 0.5% compared with MC results. The same agreement was observed forF(r, θ) bilinear interpolations using 1° and 2° step sizes.
Based on the PujadesClaumarchirant et al. study,^{79} 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, θ) andg_{L}(r), respectively, is recommended since loglinear interpolation is not a significant improvement over linearg(r) interpolation for highenergy sources.^{79}
F(r, θ) andg_{L}(r) extrapolation forr > 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 organatrisk dose, users must refer to the original MC publication.
In contrast with lowenergy brachytherapy dosimetry, extrapolation for highenergy sources forr ≤ r_{min} is complicated. Electronic equilibrium is reached within a distance of 0.1 mm from the capsule for a lowenergy source due to the short electron range. Thus, it can be assumed that collisional kerma is equal to absorbed dose everywhere. For highenergy 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.,^{28} 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.^{28} 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 nearsource 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 TG43U1S1 extrapolation method forr < r_{min} using the nearest neighbor data for g_{L}(r) is recommended until such time as future studies generate data for this region. ForF(r, θ), HEBD decided to take advantage of partial data and proposed the following approach as a compromise to maintain consistency with the TG43U1S1 report: fill in missing data for partially completeF(r, θ) tables using linear extrapolation in polar angle for fixed r based on the last two tabulated values and use zeroth order (nearest neighbor) extrapolation forr < r_{min} as recommended in the AAPM TG43U1S1 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 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 lowenergy case of TG43U1S1 where differences between MC calculated and extrapolated doses are generally minimal.
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 highenergy sources considered in this report, the active length up to 1.5 cm, the TG43 approach using polar coordinates also applies well if adequate mesh resolution is utilized, and then it is recommended here. Dosimetric considerations (source calibration, TG43 parameter derivation, TPS implementation, etc.) for sources with larger active lengths and curved lengths are being evaluated by AAPM TG143.
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 highenergy photon emitters such as ^{192}Ir, the material composition dependence is much less pronounced than that for lowenergy emitters such as^{125}I.^{1,2} This leads to a greater similarity of TG43 dosimetry parameters for highenergy sources containing the same radionuclide and having comparable dimensions than for lowenergy sources. For example, a study by Williamson and Li comparing the original Nucletron microSelectron Classic HDR^{192} Ir source with the PDR source and the old VariSource HDR^{192} Ir source revealed that they have nearly identical Λ values, and theirg_{L}(r) data agreed within ∼1% forr > 0.5 cm.^{47} 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 8101, Nucletron microSelectron HDR and PDR^{192} Ir sources, Varian VariSource HDR) and five hypothetical ^{192}Ir cylindrical source designs using the EGS4 MC code.^{86} The transverseplane dose rate and airkerma 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 andR on these quantities. For r ≥ 4 L, the transverseplane dose rate and s_{K} depended onR 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 forr ≥ 4 L. Forr < 4 L, the transverseplane dose rate ands_{K} were dependent on both R andL, and the geometry function G(r, θ) 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 Λ and g_{L}(r) for the four real sources using G_{L}(r, θ) (except for the microSelectron PDR source for which the particle streaming functionS_{L}(r, θ) was used),^{87} observed differences in Λ were explained on the basis of differences in G_{L}(r, θ) 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.
Using their established MC code, Karaiskos et al.^{55} compared the dosimetry of the old and new Nucletron microSelectron PDR^{192} Ir source designs in a R = 15 cm liquid water sphere. They found the Λ 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 Eq. (3) on the basis of the short L of 0.6 and 1.0 mm for the sources. UsingS_{L}(r, θ),^{87,89} theg_{L}(r) values were found to be identical within 1% to those obtained using the linear source approximationG_{L}(r, θ) 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, θ) for both source designs was found to be significant only at polar angles close to the longitudinal source axis (θ < 30° and θ > 150°) and to be greatest within these angular intervals at intermediate radial distances for reasons discussed previously.^{90} The new design presented increased F(r, θ) up to 10% at polar angles nearθ = 0° (distal end of the source) as a result of its longer active core.
Casal et al.^{63} and PerezCalatayud et al.^{67} calculated the dose rate distributions around three different LDR^{137}Cs sources (Amersham models CDCSM, CDC1, and CDC3) in a 40 cm high, 40 cm diameter water cylinder using the GEANT3 MC code.^{63,67} TG43 dosimetry parameters were obtained usingG_{L}(r, θ). For the model CDCSM source, they found Λ/G_{L}(r_{0}, θ_{0}) constancy, 1.05 cGy cm^{2}/(h U), within 0.9% for the corresponding ratio of the model CDCJ 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.^{57} For the CDC1 and CDC3 sources, the values of Λ/G_{L}(r_{0}, θ_{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.^{92} TheF(r, θ) results corresponded to the varying selfattenuation associated with the different source designs.
In summary, the dosimetry for r < 2 cm is primarily determined by the contained activity distribution for highenergy photonemitting 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 is calculated. As a consequence, Λ 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 Λ for an unencapsulated point source and G_{L}(r, θ). Corresponding g_{L}(r) values for sources containing the same radionuclide that have been extracted from dose distribution data usingG_{L}(r, θ) also agree to within a few percent over the radial interval 0.3 cm ≤ r ≤ 10 cm. Selfattenuation in the active core and surrounding encapsulation characterizing each source design influences F(r, θ).
IV. CONSENSUS DATASET METHODOLOGY
 (1)
For conventional encapsulated sources similar in design to existing or previously existing ones, a single dosimetric study published in a peerreviewed journal is sufficient. MC or experimental dosimetry (or both) methods may be used.
 (2)
For all other highenergy sources, at least two dosimetric studies published in peerreviewed journals by researchers independent of the vendor, one theoretical (i.e., MCbased) 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 TG43U1 report, appropriate publications reporting single source dosimetry were evaluated. For each source model, a single TG43U1 consensus dataset (_{CONL},_{CON}Λ,_{CON}g_{L}(r),CONF(r, θ) including data up tor = 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.
 (a)
The peerreviewed 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 TG43U1 (Ref. 2) and HEBD report.^{17} The quality of each dataset was then examined, taking into consideration salient factors such as data consistency, MC code benchmarking, etc.
 (b)
The value of_{CON}Λ 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}Λ were typically less than the MC uncertainties for highenergy sources. The _{EXP}Λ values have been in good agreement with MC. For example, Daskalov et al.^{93} showed that_{EXP}Λ for the mHDRv2 source agreed with_{MC}Λ to within 2%. The value from Meisbergeret al.^{92} agreed to within 0.3%.
 (c)
In most cases,_{CON}g_{L}(r) and_{CONF}(r, θ) were taken from a single MC study. When available, experimental studies were used to validate _{MC}g_{L}(r) and _{MC}F(r, θ). Data selection was based on highest spatial resolution (r andθ), largest radial range, and highest degree of smoothness. Even though some selected published data used the pointsource approximation or the particle streaming function,^{87,89} that data were transformed for use with the linear geometry function.
 (d)
Values of_{CON}g_{L}(r) were determined for full scatter conditions as described in Sec. III A and for values ofr ≤ 10 cm.
 (e)
As described in Sec. III B, a candidate publication's g_{L}(r) andF(r, θ) 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 nonnegligible 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.
 (f)
If the liquid water phantom used in a selected MC calculation did not generateg_{L}(r) under full scatter conditions forr ≤ 10 cm, the data were corrected to unbounded conditions as justified in Sec. III according to the polynomial corrections in Table II. These modified values are indicated using [brackets] in the consensus dataset tables.
 (g)
If some consensus dataset values were selected for inclusion from a nonideal candidate dataset in order to cover a larger range of distances and angles, these data are italicized as was done in the TG43U1 report.
 (h)
For sources included in this report, AAPM/ESTRO recommends the 2D brachytherapy dosimetry formalism and 2D tables: F(r, θ),G_{L}(r, θ), andg_{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 highenergy dosimetry. There are a significant number of treatments in which the longaxis dose close to the first source position is included in the target prescription (i.e., gynecological applications). In contrast, it is less relevant for lowenergy permanent implants with many seeds, where source orientation averaging is adequate.
 (i)
Data interpolation ofg_{L}(r) andF(r, θ) is needed for dataset comparison and within consensus tables. In the TG43U1 report,^{2} 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 Sec. III B.
 (j)
Similar to TG43U1S1,_{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_{C}ON_{F}(r, θ) 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 Sec. III B, to ensure linearlinear interpolation accuracy within 1%. Further, for the case of ^{60}Co, highresolution radial distance data are required in the vicinity of the source. The minimum rvalue in the consensus dataset may be different as a function of the source model considered, physical processes in play based on photon energy, and the method used to simulate or measure dose in this region.
 (k)
According to Sec. III B, the recommended angular mesh for _{CON}F(r, θ) is 0° to 10° (1° increments), 10° to 20° (5° increment), 20° to 160° (10° increment), 160° to 170° (5° increment), 170° to 180° (1° increments). Consensus data were selected based on having an angular mesh closest to the recommended one.
 (l)
Extrapolation of consensus datasets was performed following the methodology described in Sec. III B. Extrapolated values are underlined in dataset tables.
 (m)
Upon derivation of the consensus TG43 dataset, an awayalong 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 increment)] cm.
 (n)
To provide a consistent convention for all brachytherapy sources, the angle origin is selected to be the source tip, i.e.,θ 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.
 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 crosssection 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^{17}
 12.
Phantom shape and size used in MC and EXP
 13.
Agreement between MC and experimental dosimetry (if applicable, according to the HEBD prerequisites)^{17}
IV.A. Dose rate constant
As pointed out in TG43U1,^{2} MC and experimental studies complement one another and when combined can average out possible biases of each individual methodology. In contrast to the lowenergy case, the highenergy_{CON}Λ is obtained from the average of MC values alone, while available _{EXP}Λ are used to validate MC. For the sources considered in this report, the _{EXP}Λ agrees with the_{MC}Λ 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}Λ. In the case of sources within the category of “conventional encapsulated, similar to existing ones” for which just one study was available, the Λ value was compared with those for sources of similar design, first removing the geometrical dependence by forming the ratio Λ/G_{L}(r_{0}, θ_{0}), as discussed in Sec. III. Based on trends observed during the compilation of this report, the agreement between MC and EXPderived Λ 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 which was different than 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 EXPg_{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, θ) values from MC and EXP results were graphically compared. If a geometry function different than the simple linear geometry function was used, F(r, θ) was recomputed. Based on trends observed during the compilation of this report, the agreement between MC and EXPF(r, θ) values, when available, should be ≤5%.
V. RECOMMENDATIONS ON DOSIMETRY CHARACTERIZATION METHODS FOR HIGHENERGY PHOTONEMITTING BRACHYTHERAPY SOURCES
The TG43U1 report^{2} on lowenergy 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 referencequality dataset for inclusion in the consensus dosedistribution formation process. In general, all TG43U1 guidelines and recommendations are also applicable to highenergy source dosimetry, unless otherwise specified in the sections below. Thus, the present recommendations emphasize mainly variances from the TG43U1 LEBD recommended methodology for obtaining brachytherapy dosimetry parameters.
In 2007, AAPM/ESTRO recommendations on dosimetric prerequisites for routine clinical use of photonemitting brachytherapy sources with average energies higher than 50 keV were published.^{17} These recommendations similar to the AAPM LEBD recommendations^{16} 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 TG43U1 recommendations^{2} (Sec. 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) nonMC computational methods.
V.A. Preparation of dosimetry parameters
For F(r, θ) andg_{L}(r), the minimum–maximum range forr and θ, and the resolution within this range where dose rate shall be calculated or measured, has been discussed in Sec. 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 roundingoff parameters from the fit. To assure that g(r_{0}) = 1 with enough precision, the sumation of all the parameters must be “1.0000.” Further, the range over which the fit is applicable should be stated. In addition to the TG43 dosimetry parameters, a derived awayalong table should be included for TPS QA testing purposes as described in Sec. IV.
V.A.1. Airkerma strength
As similarly recommended in the TG43U1 report,^{2} source strength for highenergy sources should be expressed in terms of airkerma strength or RAKR, not apparent activity, mgRaeq, or other antiquated units. Exceptions may result in patient harm.
V.A.2. Dose rate constant
All TG43U1 recommendations are applicable to highenergy 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,^{94} multislit techniques^{95} and transmission radiography should be utilized to confirm the manufacturer's specifications for active length, uniform activity distribution, and physicaltoactive sourcetip offset. Experimental determinations of absolute dose rates to water from highenergy sources should have direct traceability ofS_{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, Λ is evaluated by taking the ratio /S_{K}.
V.A.3. Radial dose function
In addition to the TG43U1 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 Sec. III, 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, βray transport must be simulated at distances where dosetokerma ratio deviations exceeding 1% are possible.
V.A.4. 2D Anisotropy function
The recommendations of the AAPM TG43U1 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 Λ and g(r) has been studied by Rivard et al.^{96} For^{192} Ir sources, they found that the uncertainties propagated to these parameters by photonspectrum 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 sources.^{20}
V.B.2. Reference media
As recommended by TG43U1, pure degassed liquid water (H_{2}O) with a mass density of 0.998 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 TG43U1S1 report,^{3} dry air (0% humidity) is recommended forS_{K} in contrast to the TG43U1 report which recommended air at 40% relative humidity. The composition of dry air is given in Table XIV of the TG43U1 report.
V.C. Methodological recommendations for experimental dosimetry
Historical reviews of experimental dosimetry for interstitial brachytherapy sources, including highenergy sources, appear in Williamson^{97} and, for ^{192}Ir only, in the original TG43 report.^{1} Starting from the earliest work of Meredith et al.,^{98} 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 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 liquidfilled ionization chambers, has been given by Williamson and Rivard.^{99}
V.C.1. Detector choice
 1.
A relatively small active volume such that effects resulting from averaging of highgradient dose fields over this volume are negligible or are accurately accounted for by correction factors.
 2.
A wellcharacterized energyresponse 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% andk = 1 Type B uncertainties ≤6%.
While no practical detector system perfectly fulfils the three requirements above, among the established dosimetry techniques, LiF TLD100 detectors provide a good tradeoff between flat energy dependence, small size, and detector dynamic range for both highand lowenergy 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 sourcedetector distance^{101,102} for ^{169}Yb and ^{192} Ir sources due to variations in photon spectra. Thus, the AAPM and ESTRO currently do not recommend silicon diode detectors for referencequality dose measurement for sources with mean energies exceeding 50 keV. Among validated and fully developed dosimeter technologies, TLD dosimetry has the least positiondependent sensitivity for highenergy sources. TLD energy response has been reported to vary 10%–15% over the 1 to 10 cm distance range for^{192} Ir sources.^{103} Similar magnitude but opposite direction variations have been reported for older (MD552 and earlier) radiochromic film models.^{104,105} Newer models of radiochromic film [EBT (Refs. 106–108) and EBT2 (Refs. 109–112)] include small concentrations of a medium atomic number loading compound designed to compensate for the absorbed dose underresponse of the diacetylene monomer active sensor medium. EBT film type has a nearly energyindependent dose response.^{113,114} MD552 radiochromic film has been used successfully to measure high resolution (<0.25 mm) absolute dose distributions around HDR^{192} Ir sources^{115} and LDR^{137}Cs sources^{116} withk = 1 total uncertainties of 4%–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 (nonuniformity, dose rate dependence, film darkening kinetics, scanner artifacts) which require rigorous correction. TLD dosimetry techniques for both general radiotherapy applications^{100,117} and referencequality brachytherapy dosimetry have been reviewed extensively.^{99,100}
V.C.2. Phantom material and energy response characterization
For lowenergy brachytherapy dosimetry, accurate knowledge of the atomic composition of the phantom is critical for proper results.^{100} The TG43U1 report allows use of either singlecomponent highpurity industrial plastics or polyaminebased 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, phantomtoliquidwater corrections (based upon MC calculations) must be applied to the measurements.
For ^{192}Ir and other highenergy sources, absorbeddose water equivalence is less dependent on phantom composition,^{103} so that commercial plastics such as polymethylmethacrylate (PMMA) as well as singlecomponent resin mixtures can be used with lower correction uncertainties due to knowledge of their composition. Experimentally, Meli et al.^{103} found that PMMA, polystyrene, and Solid Water™ introduced corrections ranging from −4% to +2% relative to liquid water at distances of 3–6 cm. MC calculations, simulating monoenergetic 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^{118} 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% 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 highenergy brachytherapy dosimetry are recommended. Singlecomponent 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 nonwater 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. MCbased medium corrections (phantomtoliquid 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 controversies surrounding the choice of corrections for TLD dosimetry of lowenergy brachytherapy sources, where recent experiments suggest energy response correction factors ranging from 1.05 to 1.10, have been reviewed by Williamson and Rivard.^{100} While values are closer to unity for highenergy brachytherapy sources, two recent publications found anomalously high values of 1.018–1.038 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 absorbeddose energydependent factors. Because definitive factors are not yet available, it is recommended that be taken as unity for highenergy photon dosimetry, while and 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 if dosimetrically significant energy response corrections exist or not. Based on a study of Model MD552, Bohm et al.^{104} concluded that MC accounted for measured values within 5%. On the other hand, Sutherland et al.^{122} 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 Sec.V D 3 of the 2004 AAPM TG43U1 report^{2} should be followed for highenergy 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 highenergy source dosimetry include ptran, mcnp, geant4, penelope, and egsnrc. At the time of publication of this report, all these codes are based upon modern crosssection 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 highenergy 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 (Sec. III B). Errors exceeding 2% will occur if photononly 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.^{28}
In general, the AAPM and ESTRO recommend that MC investigators utilize wellbenchmarked codes for brachytherapy dosimetry studies intended to produce referencequality 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^{17} stated that MC transport codes should be able to support dose rate estimation with expanded uncertainties (k = 2) no greater than the 3%–5% characteristic of the MC transport codes currently used for lowenergy 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 Λ, 5% forg_{L}(r), and 10% forF(r, θ) within 5° from the source long axis.^{17} Unlike for lowenergy sources, the range of secondary electrons from highenergy sources will require electron transport at short distances.^{28}
V.D.1. Specification of Monte Carlo calculation methods
 1.
Limit consideration to emitted photon energies above 10 keV (for simulations in both water and inair or in vaccuo). 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 highenergy photons with low emission probabilities can influence results significantly.^{96} Therefore, reference spectra must be used in their entirety in MC simulations, i.e., NNDC reference spectra^{20} 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 betaray 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.
Referencequality 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 radiusR = 40 cm (or the equivalent cylindrical phantom dimensions) should be used, while R = 80 cm is required for ^{60}Co (Refs. 29–31) sources.
 2.
A suficient number of histories should be calculated to ensure that the dose rate per simulated history and 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 lowenergy photons below 10 keV (and contaminant electrons as well if chargedparticle transport is simulated) should be assessed and corrected for if necessary. By convention, ands_{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 highenergy brachytherapy regime. Until careful studies demonstrate otherwise, TG43U1 recommendations should be followed. This includes use of post1980 crosssection libraries, preferably those equivalent to the current NIST XCOM database such as DLC146 or EPDL97. Older crosssection 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 xrays 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)^{129} and detector volumes should be chosen to limit volumeaveraging artifacts to <0.1%. To minimize the impact of voxel size effects^{130–132} while maintaining reasonable efficiency for tracklength 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 ofr_{source} < r ≤ 1 cm, (0.5 × 0.5 × 0.5) 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, wherer is defined as the distance from the center of the source. Rectilinear or toroidal voxels of similar radial dimensions should have similar volumeaveraging effects.
 5.
Especially for photon sources in the 50 to 300 keV energy range, the manufacturerreported 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^{133} on the dose distribution should be assessed.
 6.
Some MC studies consider the effect of electronic nonequilibrium conditions near a brachytherapy source, or the betaray 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 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.^{134} 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 artifactfree corrections. Switching to singlescattering mode near boundaries is the preferred solution. For example, Type1 transport algorithms (MCNP, ITS, ETRAN), which use Goudsmit–Saunderson multiplescattering formalism parameters, stopping powers, and energystraggling corrections precalculated on a fixed logarithmically spaced energyloss 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^{135} demonstrate that pre2000 versions of MCNPdetermined lowenergy electron dose distributions were sensitive to choice of energyindexing (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.
 (a)
V.E. Uncertainty analyses
Both experimental and MC determinations of referencequality singlesource dose rate distributions should include formal uncertainty analyses that adhere to the methodology of NIST Technical Note 1297.^{136} While a number of publications^{100,137} including the TG43U1 and TG138 (Ref. 14) reports give detailed guidance on applying this methodology to lowenergy brachytherapy, complete and rigorous uncertainty analyses for highenergy brachytherapy are generally lacking. However, extensive uncertainty analyses are given by Raffi et al.^{41} for HDR ^{192}Ir experimental and MC and Granero et al.^{138} 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 TG138 report and are over a factor of two lower than those in Table XII of the TG43U1 report for low and highenergy sources. While ^{169}Yb has been considered by some manufacturers, theS_{K} calibration uncertainties are still a matter of study and are of the order of 3% (k = 1). As similarly recommended in Sec. V D 3(10) and Sec. V E 1(9) of the AAPM TG43U1 report for measurements and simulations of lowenergy photonemitting brachytherapy dosimetry studies, respectively, the AAPM recommends that highenergy brachytherapy source dosimetry investigators perform detailed uncertainty analyses in a manner similar to Raffiet 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 TG43U1 (Ref. 2) and the HEBD prerequisites,^{17} commercially distributed highenergy 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 TG43U1, “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^{17} require that one study be experimental (usually TLDbased) and that the other be theoretical (MC). The studies must be published in the peerreviewed 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 MCbased 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 scattercomponent functions be obtained from TG43based dose rate tables and will need to be handled independently by the TPS dose calculation algorithm.^{139}
V.G. The role of nonMonte 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 singlesource dose distributions in the highenergy photon regime.
Heuristic analytical model algorithms were not introduced as dosimetry or doseestimation tools, but as treatmentplanning tools for computing more realistic and accurate dose distributions for clinical multisource implants in the presence of tissuecomposition and density heterogeneities, applicator shielding and attenuation, and interseed attenuation. Accelerated MC simulation codes^{140} have also been adapted for clinical dose computation. The potential for these innovations in clinical dose computation has been reviewed by Rivard et al.^{33} and is the subject of the active AAPM Task Group 186.
Prior to communitywide acceptance of the 1995 AAPM TG43 report, nearly every generalpurpose brachytherapy planning system utilized the 1D pathlength or Sievert model to generate singlesource 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.^{142} 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 pathlength models are not endorsed by this report for estimation of referencequality dose distributions for any category of highenergy sources.
A number of more sophisticated scatter separation algorithms, which involve 1 , 2 , or even 3dimensional integration of the scatter dose distribution over the implant geometry have been proposed.^{73,144–147} Closely related are superposition/convolution algorithms^{148} of which the most fully developed is Carlsson–Tedgren's^{149,150} brachytherapy adaptation of the externalbeam 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 referencequality singlesource dose distributions.
A more empirical scatterseparation method was introduced^{151} for CTbased 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 lowZ 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 headandneck, esophagus, and balloon breast brachytherapy treatments. PTRAN_CTbased MC calculations were used as the reference dose distributions. For the breast patient plan, the TG43 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%.
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 gridbased 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 sevendimensional phasespace 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 applicationspecific parameters need to be optimized including density of the angular mesh, energy group structure and weighting functions, as well as spatial mesh geometry and angularflux 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^{156} are not suitable referencequality dosimetry tools.
In summary, of the computational tools developed to date, only MC simulation is an acceptable method for estimating referencequality dosimetry parameters. This is a consequence of the fundamental mathematical nature of MC simulation, which yields a statistically imprecise, but exact firstprinciples 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.^{100} 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 transportsolution algorithms, while free of statistical uncertainty, are always subject to complex, geometrydependent patterns of systematic error.
VI. RECOMMENDED DOSIMETRY DATASETS FOR HIGHENERGY PHOTONEMITTING BRACHYTHERAPY SOURCES
Recommended consensus datasets for highenergy sources have been obtained for sources that were commercially available as of January 2010. Data are presented according to the AAPM TG43U1 formalism, with upgraded interpolation and extrapolation techniques in Table III for F(r, θ) andg(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, θ). For each source model, and the selection procedure is explained with additional discussion included (Appendix A).
For TPS that use the TG43 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.^{13} 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 Sec. VI of the TG43U1 report.^{2} 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 TG43U1 formalism and should also document the TPS methods for interpolation and extrapolation (applying the recommendations introduced in TG43U1S1 and also more specifically in this report) of dose calculations within and beyond the range of provided dosimetry parameters. 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 (TG40,^{157} TG53,^{158} TG56,^{13} and TG43U1.^{2}) 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. AAPMRPC 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.^{16} Sources that met these dosimetric prerequisites were judged to be sufficiently well characterized, have adequate traceability to national standards, and be manufactured under processes subjected to appropriate quality control standards. Shortly afterward, 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 lowenergy seeds must use sources that are listed on the Registry. The Registry includes tables of dosimetry parameters that have been compiled from peerreviewed publications and issued as consensus data deemed suitable for clinical use by the AAPM.
Development of a new RTOG protocol requiring use of highenergy photonemitting brachytherapy sources prompted expansion of the Registry in 2009 to include such sources. For highenergy sources to be included in the Registry, there must be compliance with the HEBD prerequisites.^{17} The BTSC and BSR have identified a number of highenergy 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 highenergy photonemitting brachytherapy sources. Whereas source manufacturers must submit lowenergy sources at least annually to NIST or other primary standards labs for S_{K} calibration consistency, a calibration comparison frequency of 2 yr for ^{60}Co,^{137}Cs, and ^{192} Ir sources is recommended. Vendors of sources containing these highenergy 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 Sec. 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 halflives 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 peerreviewed literature.
As extensively described by Rivard et al.,^{159} while posting of a source model on the Registry does not imply existence of an AAPMendorsed consensus dataset, clinical use of Registryposted 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 yr after posting on the Registry and then included on the RPC website.
In the absence of AAPMissued consensus datasets, ESTRO manages a database for brachytherapy dosimetry parameters and other related data.^{160} For lowenergy LDR brachytherapy sources for which AAPMendorsed consensus datasets are available, ESTRO recommends adopting these datasets and the ESTRO website includes a link to the Registry website. A similar policy is implemented for highenergy sources once consensus data are published.
Another online venue for brachytherapy dosimetry parameter data is the Carleton University website.^{161} 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.^{132} In addition to the TG43 dosimetry parameters, dose rate tables for highenergy sources are also presented separately for primary, singlescattered, and multiplescattered photons. For^{192} Ir sources, these datasets have been evaluated in this report.
VI.B. Consensus datasets
Sources meeting the 2007 AAPM prerequisites^{17} are considered in this section. The publications pertaining to each source have been evaluated following the guidelines described in Sec. 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 of the full report available online on the AAPM website. In the following section, a brief summary for each source is presented.
VI.B.1. HDR ^{192}Ir sources
 (a)
Nucletron model mHDRv1 (classic) source
 (b)
Nucletron model mHDRv2 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.A852 source
 (i)
SPEC, Inc. model M19 source
 (j)
Isodose Control model Flexisource
VI.B.2. PDR ^{192}Ir sources
 (a)
Varian Medical Systems GammaMed PDR 12i source
 (b)
Varian Medical Systems GammaMed PDR Plus source
 (c)
Nucletron model mPDRv1 source
 (d)
Eckert & Ziegler BEBIG GmbH model Ir2.A851 source
VI.B.3. LDR ^{192}Ir sources
 (a)
Best Industries model 8101 seed
 (b)
Eckert & Ziegler BEBIG GmbH 0.5 and 1.0 cm long wires
VI.B.4. LDR ^{137}Cs sources
 (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
 (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 Sec. 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.
 (a)
LDR ^{137}Cs: pellet, CSM2, CSM3a, CDCSJ, 6500/6D6C, Goldmatrix series 67800, CSM1, CDCSM, CDC.K1K3, CDC.K4, CDC 12015 to CDC 12035, and CDC.G and CDC.HLDR ^{192}Ir: Platinumclad seed
 (b)
HDR ^{192}Ir: Varian classic
 (c)
PDR ^{192}Ir: Nucletron
 (d)
HDR ^{60}Co: Ralstron Type1, Type2, and Type3
NOMENCLATURE

 1D

Onedimensional

 2D

Twodimensional

 AAPM

American Association of Physicists in Medicine

 ADCL

Accredited Dosimetry Calibration Laboratory

 BRAPHYQS

ESTRO Brachytherapy Physics Quality assurance System

 BSR

AAPM Brachytherapy Source Registry Working Group

 BTSC

AAPM Brachytherapy Subcommittee

 CTV

Clinical target volume

 EC

Electron capture

 ESTRO

European Society for Radiotherapy and Oncology

 EXP

Experimental measurement

 GBBS

Gridbased Boltzmann solver

 HDR

Highdose rate

 HEBD

AAPM High Energy Brachytherapy Source Dosimetry Working Group

 IC

Internal conversion

 ISA

Intersource attenuation

 LDR

Lowdose rate

 LEBD

AAPM Low Energy Brachytherapy Source Dosimetry Working Group

 MC

Monte Carlo

 MRI

Magnetic resonance imaging

 NIST

U.S. National Institute of Standards and Technology

 NNDC

National Nuclear Data Center

 PDR

Pulseddose rate

 POI

Pointsofinterest

 RPC

Radiological Physics Center

 RTOG

U.S. Radiation Therapy Oncology Group

 TG43

AAPM Task Group No. 43 brachytherapy dose calculation formalism

 TG43U1

2004 update to the TG43 report

 TG43U1S1

2007 supplement to the 2004 AAPM TG43U1 report

 TLD

Thermoluminescent dosimeter generally composed of LiF (TLD100)

 TLS

Two length segmented method

 TPS

Treatment planning system(s)

 U

The unit of airkerma strength equivalent to μGy m^{2} h^{−1} or cGy·cm^{2}·h^{−1}.

 β

Angle subtended by P(r, θ) and the two ends of the brachytherapy source active length; as used in the linesource approximation, β has units of radians

 d

Distance to the point of measurement from the source center in its transverseplane, typically measured inair orinvacuo; units of cm

The dose rate per history estimated using Monte Carlo methods at the reference position

Dose rate in water at P(r,θ); the dose rate is generally specified with units cGyh^{−1} and the reference dose rate, , is specified at P(r_{0},θ_{0}) with units of cGyh^{−1}

 δ

Energy cutoff parameter used for airkerma rate evaluation, with units of keV

 F(r, θ)

2D anisotropy function describing the ratio of dose rate at radiusr and angle θ around the source, relative to the dose rate at r_{0} = 1 cm andθ_{0} = 90° when removing geometry function effects; dimensionless units

 G_{X}(r, θ)

Geometry function approximating the influence of the radionuclide physical distribution on the dose distribution;G_{X}(r, θ) is calculated by the following:
with units of cm^{−2} 
 g(r)

Radial dose function describing the dose rate at distance r from the source in the transverse plane relative to the dose rate atr_{0} = 1 cm; dimensionless units

 g_{L}(r)

Radial dose function determined under the assumption that the source can be represented as a line segment; dimensionless units

 g_{P}(r)

Radial dose function determined under the assumption that the source can be represented as a point; dimensionless units

 _{CONg}(r)

Radial dose function derived from consensus dataset; dimensionless units

Airkerma rate in vacuo, per history as estimated using Monte Carlo methods, due to photons of energy greater than

Airkerma rate in vacuo on the source transverse plane due to photons of energy greater than δ, with units of cGy·h^{−1}

 Λ

Dose rate constant in water, with units ofμGy·h^{−1}·U^{−1}; Λ is defined as the dose rate atP(r_{0}, θ_{0}) per unit S_{K}

 _{CON}Λ

Notation indicating that the reported value of Λ is the consensus value determined by the AAPM from published data, with units of cGy·h^{−1}·U^{−1}

 _{EXP}Λ

Notation indicating that the reported value of Λ was determined by experimental measurement

 _{MC}Λ

Notation indicating that the reported value of Λ was determined using Monte Carlo calculations

 L

Active length of the source (length of the radioactive portion of the source) with units of cm

 L_{eff}

The effective active length of the source; L_{eff} is used for brachytherapy sources containing uniformly spaced multiple radioactive components; L_{eff} = ΔS × N, whereN represents the number of discrete pellets contained in the source with centertocenter spacing ΔS

 P(r, θ)

Pointofinterest, positioned at distance r and angleθ from the geometric center of the radionuclide distribution

 φ_{an}(r)

1D anisotropy function; at any radial distance r,φ_{an}(r) is the ratio of dose rate averaged over 4π steradian integrated solidangle to the dose rate at the same distance r on the transverseplane; dimensionless units

 r

The distance from the source center toP(r, θ), with units of centimeter

 r_{0}

The reference distance, generally 1 cm

 s_{K}

The airkerma strength per history estimated using Monte Carlo methods

 S_{K}

Airkerma strength: the product of the airkerma rate and the square of the distance d to the point of specification from the center of the source in its transverseplane; S_{K} is expressed in units of μGy m^{2} h^{−1}, a unit also identified by U

 θ

The polar angle between the longitudinalaxis of the source and the ray from the active source center to the calculation point,P(r, θ)

 θ_{0}

The reference polar angle, generally 90° or π/2 radians