on Dose Specification for 103 Pd and 125 I Interstitial Brachytherapy

In March 2004, the recommendations of the American Association of Physicists in Medicine (AAPM) on the interstitial brachytherapy dosimetry using 125I and 103Pd were reported in Medical Physics [TG-43 Update: Rivard et al., 31, 633-674 (2004)]. These recommendations include some minor changes in the dose-calculation formalism and a major update of the dosimetry parameters for eight widely used interstitial brachytherapy sources. A full implementation of these recommendations could result in unintended changes in delivered dose without corresponding revisions in the prescribed dose. Because most published clinical experience with permanent brachytherapy is based upon two widely used source models, the 125I Model 6711 and 103Pd Model 200 sources, in this report we present an analysis of the dosimetric impact of the 2004 TG-43 dosimetry parameters on the history of dose delivery for these two source models. Our analysis indicates that the currently recommended prescribed dose of 125 Gy for Model 200 103Pd implants planned using previously recommended dosimetry parameters [AAPM 103Pd dose prescription: Williamson et al., Med. Phys. 27, 634-642 (2000)] results in a delivered dose of 120 Gy according to dose calculations based on the 2004 TG-43 update. Further, delivered doses prior to October 1997 varied from 113 to 119 Gy for a prescribed dose of 115 Gy compared to 124 Gy estimated by the AAPM 2000 report. For 125I implants using Model 6711 seeds, there are no significant changes (less than 2%). Practicing physicians should take these results into account when selecting the clinically appropriate prescribed dose for 103Pd interstitial implant patients following implementation of the 2004 TG-43 update dose-calculation recommendations. The AAPM recommends that the radiation oncology community review this report and consider whether the currently recommended dose level (125 Gy) needs to be revised.


I. INTRODUCTION
In April 2000, 1 the American Association of Physicists in Medicine ͑AAPM͒ published recommended administered-toprescribed dose ratios, ͑D Tx / D Rx ͒ t , for 103 Pd permanent seed implants.These ratios, which are a function of time period t, describe the systematic impact of changes in source-strength standards and single-source dosimetry parameters on clinical dose specification.The originally published ͑D Tx / D Rx ͒ t ratios related prescribed doses, D t Rx , calculated in time periods t ranging from 1988 to 1999 using contemporaneous ͑ca.1999͒ source strength standards and dosimetry parameters, to administered doses, D 99 Tx , based upon an updated dose-rate constant and the National Institute of Standards and Technology ͑NIST͒ primary air-kerma strength standard, S K,N99 , using the wide-angle free-air chamber ͑WAFAC͒ 2 which had been implemented on 1 January, 1999.The updated dose-rate constant for the Model 200 103 Pd seed ͑TheraSeed®͒ was obtained by averaging a TLD measurement 3 with a value derived from Monte Carlo simulation. 4 The AAPM 2000 report concluded that for doses of 115 Gy prescribed in the periods 1988-1997 and 1997-1999, the corresponding administered doses were 124 and 135 Gy, respectively.Based on the AAPM 2000 recommendations, the American Brachytherapy Society 5 recommended that the standard prescribed dose of 115 Gy for definitive treatment of prostate cancer using 103 Pd brachytherapy alone be adjusted to 125 Gy.
This report presents updated guidance from the AAPM on the issue of 103 Pd and 125 I brachytherapy dose reconstruction, and was prepared by the AAPM Photon-Emitting Brachytherapy Dosimetry ͑PEBD͒ Subcommittee ͑Chair, J. Will-iamson͒ and approved by the AAPM Radiation Therapy Committee and Science Council.Because several unanticipated developments occurring after the publication of the 2000 recommendations 1 impacted its recommended dose ratios by more than 5%, PEBD believed that the issue of prescribed dose selection for 103 Pd brachytherapy needed to be revisited.These developments include: • Identifying and correcting a 5.3% error in NIST S K,N99 calibration measurements performed in 1999 for the Model 200 source.• Subsequent revisions of dosimetry parameters, most notably the one-dimensional ͑1D͒ anisotropy function.• Recent revisions in the 1D dose-calculation formalism recommended by AAPM, 6 resulting in replacement of the anisotropy constant by the 1D anisotropy function.• Publication 4,7 of reference-quality Monte Carlo single-source dosimetry parameters that distinguish between the "heavy" seed ͑low specific-activity reactor-produced radioactive palladium͒ and "light" seed ͑higher specific-activity accelerator-produced radioactive palladium͒ versions of the Model 200 source.These publications indicated a small change ͑1.2%͒ in the dose-rate constant and a 2.3% change in the anisotropy constant.
• An improved formalism for estimating ͑D Tx / D Rx ͒ t ratios.
In contrast to 103 Pd brachytherapy, no significant changes were anticipated for 125 I implant dosimetry.AAPM guidance last addressed the issue of dose prescription for 125 I implants in 1998. 8The AAPM recommended that clinics reduce the prescribed dose for 125 I implant monotherapy from 160 to 144 Gy upon simultaneously adopting dosimetric parameters recommended by the 1995 TG-43 report 9 and implementing the NIST 1999 S K primary standard.Since implementation of this standard in 1999, no significant shifts in source strength for this source model have occurred.In particular, the vendor's source strength calibration procedures for the Model 6711 source were not affected by the NIST measurement anomalies of 1999.The revised TG-43 dose-calculation formalism and Model 6711 dosimetry parameters published in 2004 6 did not significantly alter the single-seed dose-rate distribution for this source.However, because of the 2004 changes in 125 I recommended dose-calculation practice and the modified methodology for estimating ͑D Tx / D Rx ͒ t ratios presented in this report, PEBD believed it was necessary to reevaluate dose ratios for 125 I as well as 103 Pd brachytherapy.

A. Brief history of 103 Pd brachytherapy dosimetry
The history of 103 Pd brachytherapy dosimetry is intimately related to that of the first 103 Pd interstitial source product, Theragenics Corporation's Model 200 TheraSeed®, introduced to the market in 1987.The early evaluated clinical experience, published by Prestidge et al. 10 in 1997, was based upon patients treated with the Model 200 source during the period 1988-1994.Later in 2000, Sharkey et al. 11 reported the clinical experience with 1048 patients with 103 Pd implants treated from 1991 to 1999.Thus for clinicians practicing today who wish to reproduce the doses prescribed by these investigators, knowing the equivalent dose to deliver, based upon currently recommended dose-computation and calibration practices, is essential, regardless of what commercial 103 Pd seed product they choose to use.Hence the dosimetric history of 103 Pd brachytherapy is equivalent to that of the Model 200 commercial product.
In the following sections, important events in the history of the Model 200 source dosimetry and development of airkerma strength ͑S K ͒ standard are reviewed.

Theragenics™ calibration standard "1988-1997…
Prior to the implementation of the 1999 NIST WAFAC standard, a primary S K standard was not available for 103 Pd or any other low-energy interstitial seed with the exceptions of the 3M ͑now Amersham Health͒ 125 I seeds, Models 6701, 6702, and 6711. 12Thus, Theragenics™ developed a method for measuring apparent activity using a NaI͑Tl͒ scintillation detector, which compared Model 200 103 Pd seed photon emission rate with the 22 keV emission line ͑the average energy of the 103 Pd seed emission spectrum͒ from a 109 Cd ⌳ 04D,N99S = 0.686 g L,04D ͑r͒ G L ͑r͒ an,04D ͑r͒ Equation ͑6͒ assumed calibration standard, which had a NIST-traceable activity calibration with an assigned uncertainty of Ϯ 5%.More details are given in the 2000 report. 1 The resultant apparent activity, A app,T88 , denotes the quantity measured by Theragen-ics™ assay, where the "T" of the subscript "Tnn" denotes Theragenics™ and "nn" denotes the year that the 109 Cd standard, to which the measurement is traceable, e.g., 1992 for the "T92" 109 Cd standard, was implemented.Note that A app,Tnn is fundamentally different from apparent activity as defined by the AAPM, 13 A app,N99 , which is a quantity derived from NIST's 1999 standard, S K,N99 .The vendor's apparent activity assay can be related to the vendor's air-kerma strength by where the exposure-rate constant for 103 Pd, ͑⌫ ␦ ͒ x , and mean energy expended per ion pair created, ͑W / e͒, take the numerical values recommended by the AAPM. 13ecause of the 463.3 day half life of 109 Cd, 14 four successive calibration sources were used during the period 1988-1997.used TLD dosimetry to measure the dose-rate constant and relative two dimensional ͑2D͒ dose distribution parameters.These investigators measured the absolute dose rate at 1 cm on the transverse axis, and normalized this measurement to the S K,T88 inferred from the vendor's A app,T88 value to obtain an estimate of the dose-rate constant.The dose-rate constant recommended by the 1995 AAPM TG-43 report 9 took the average of these two measurements and applied a multiplicative correction ͑1.048͒ to convert from Solid Water® measurement medium to a liquid water reference phantom,

͑2͒
The first subscript of ⌳ 95D,T88S , 95D, refers to the date of the publication documenting the measured dose rate at 1 cm, D 95D ͑r = 1 cm, = /2͒, ͑in this case, the 1995 TG-43 re-port͒, while the second subscript, terminating in an "S" for "strength," refers to the source calibration standard, to which the dose rate is assumed to be normalized.Thus, it is assumed that clinical investigators, whose subsequent reports define the clinical experience supporting 103 Pd prostate brachytherapy, utilized dose-calculation parameters equivalent to those tabulated in the 1995 TG-43 report.

Transition from "heavy" to "light" seed design
"1992-1993… The above-described TLD measurements were performed using seeds containing low specific activity reactor-produced 103 Pd.These seeds, called "heavy seeds," were gradually replaced with "light seeds," containing higher specific-activity, accelerator-produced 103 Pd, over a one-year period ending in early 1993.Each Model 200 seed contains two graphite pellets with palladium metal coatings within which the radioactivity is uniformly distributed.Monroe and Williamson 7 approximated the effect of the heavy-to-light seed manufacturing process modification on seed geometry by reducing the thickness of this metal coating from 10.5 µm ͑260 µg Pd/pellet͒ to 2.2 µm ͑57 µg Pd/pellet͒ in their simulations.Using Monte Carlo techniques, these authors found that the dose-rate constant ͑when normalized to the WAFAC stan-dard͒ and radial dose function were not significantly affected by this change.However, the anisotropy constant ¯an ͓based on an inverse-square law weighted average of an ͑r͒ over the 1 to 5 cm distance range͔ was found to be 0.884 and 0.862 for the "heavy" and "light" seed designs, respectively.Monroe and Williamson 7 provided a preliminary evaluation of this effect on ͑D Tx / D Rx ͒ t ratio using the results of their Monte Carlo analysis of the Model 200 seed.

Shift in vendor calibration "Fall 1997…
In contrast to previous 109 Cd standard replacements, the replacement implemented by Theragenics Corporation in fall, 1997 resulted in a 9.7% decrease in apparent activity assays relative to S K,T94 ͑column 4, rows 3 and 4 of Table IV͒, corresponding to the decrease in A app initially observed by several physicists in 1997.The apparent activities and nominal air-kerma strengths traceable to this standard are denoted by A app,T97 and S K,T97 , respectively.Relative to the time-weighted 1988-1997 average of the four prior S K,Tnn standards, S ¯K,T88-94 , S K,T97 calibration values are 9% smaller: S K,T97 / S ¯K,T88-94 = 0.911.These data indicate that the Ther-agenics™ assay was essentially constant from 1988 until Fall 1997.In 2000, Theragenics amended their calibration procedure to ensure that their A app calibration will be maintained within Ϯ 2% of its post-1997 level following future 109 Cd source standard replacements.

Implementation of the NIST WAFAC 1999 standard
Based on measurements performed in 1998 and 1999, a new S K standard for Model 200 source air-kerma strength, S K,N99 , was established by NIST in 1999 based upon the WAFAC. 2 A difference of more than 23% between Theragenics' S K,T97 assay and the NIST WAFAC S K,N99 values was noted.The conversion factor relating the two definitions was determined to be: The ͑D Tx / D Rx ͒ t ratios recommended by the AAPM 2000 report were based upon this value.Theragenics began to issue calibration certificates traceable to S K,N99 on 20 March, 2000.

Revised dosimetry parameters and AAPM 2000 dose-specification guidance "1999-2000…
In preparation for implementing the S K,N99 standard, Theragenics commissioned two dose-rate constant determinations for the Model 200 source.Using TLD dosimeters in a solid water phantom, Nath et al. 3 reported a dose-rate constant, ⌳ 00D,N99S , value of 0.65± 0.05 cGy h −1 U −1 .Williamson 4 reported a value of 0.68± 0.02 cGy h −1 U −1 using Monte Carlo simulation techniques.Both values were traceable to the WAFAC standard as implemented in calendar year 1999.The AAPM 2000 guidance document recommended using an equally weighted average of these two values yielding ⌳ 00D,N99S = 0.665± 0.03 cGy h −1 U −1 .That report recommended that the relative dosimetry parameters, i.e., radial dose function and anisotropy constant, given in the 1995 TG-43 report continue to be used.These parameters are designated by the subscript "00D."

Discovery and correction of calendar year 1999 WAFAC measurement errors "March 2001…
Due to an unresolved anomaly, WAFAC calibrations performed at NIST in calendar year ͑CY͒ 1999 were systemati- As with other seed models, PEBD coordinated the transition to the corrected WAFAC standard with NIST, Theragenics, and the ADCLs on 5 March, 2001.Since each such transition was vendor-and model-specific, no AAPM report was published to advise the community and vendors were responsible for communicating the relevant action plan to their clients.For the Model 200 source, the corrected WAFAC standard was implemented simultaneously by the vendor, NIST, and ADCLs on 5 March, 2001 ͑Appendix A, Sec. 6 of the TG-43 2004 update 6 ͒.As part of this process, the measured dose-rate constant of Nath et al., 3 which was normalized to erroneous WAFAC measurements, was increased by 5.3% to compensate for the correction.This led to a new revised average dose-rate constant ⌳ 01D,N99S = 0.68 cGy h −1 • U −1 .At that time, AAPM advised the community to continue using the 2000 administered-to-prescribed dose ratios and guidance derived therefrom until further notice.It is assumed that these recommendations remain operative up to the present time.

Revised dosimetry parameters and the updated TG-43 protocol "March 2004…
Since implementation of the 2000 AAPM guidance report, 1 the Model 200 dosimetry parameters have been further refined.A comprehensive Monte Carlo-based study 7 was published by Monroe and Williamson, which contained TG-43 dosimetry parameters for both the "light" and "heavy" seed designs.In addition, Yue and Nath 17 published measured light-seed 2D anisotropy functions which were in excellent agreement with Monroe's calculations.Both studies confirmed that the 1995 TG-43 9 anisotropy functions, yielding a ¯an,95D = 0.90, significantly overestimated the source isotropy compared to more recent publications, which imply ¯an,04D = 0.862.
In March 2004, a major update of the TG-43 protocol was published. 6It contained revised data, designated by the subscript "04D," for the Model 200 seed.The recommended ⌳ 04D,N99S is nearly identical to ⌳ 01D,N99S .New radial dose functions, 1D anisotropy functions, and 2D anisotropy functions ͑based on Monroe's simulations 7 ͒ were recommended for clinical use.In addition, the dose-calculation formalism itself was modified.The revised formalism requires use of the 1D anisotropy function rather than the anisotropy constant, ¯an,04D and specifies a new method of calculating doses at small distances.It also advises users to adopt the linesource geometry function over the point-source function.Both the new relative "04D" dosimetry parameters and re-vised dose-calculation formalism are used in the analysis to follow as "reference dosimetry parameters," i.e., used to estimate "administered dose." The dose ratios recommended in the AAPM 2000 report 1 take into account the developments described in Secs.II A 1, II A 2, II A 4, II A 5, and II A 6 above.The revised analysis, presented in the following, takes into account the remaining phenomena: heavy-versus light-seed design ͑Sec.II A 3͒, 1999 WAFAC errors ͑Sec.II A 7͒, and dosimetry parameters and formalism revised as described by the new TG-43 protocol ͑Sec.II A 8͒.

B. Generalized formalism for evaluation of administered-to-prescribed dose ratios
To evaluate the ratio of administered dose, D Tx , to prescribed dose, D Rx , the methodology described by Monroe and Williamson 7 has been adopted.Their analysis accounts for changes in the dose-rate constant used for treatment planning and time-dependent discrepancies between vendor and NIST source-strength specifications as does the original AAPM 2000 analysis.In addition, Monroe and Williamson 7 accounted for the dosimetric effect of Model 200 seed internal geometry changes caused by the transition from the heavy seed to the light seed production process, the NIST 1999 WAFAC anomaly, and the dose-parameter revisions published in the 2004 TG43 protocol, none of which were anticipated by the AAPM 2000 Report. 1 The influence of seed manufacturing process changes on the D Tx / D Rx ratio was incorporated into the analysis by introducing separate time-dependent reference dosimetry parameters for the light and heavy seeds.The current report adapts the Monroe-Williamson analysis with the addition of more sophisticated dose-averaging techniques.In addition, this report consistently uses the 1D dose-calculation formalism recommended by the 2004 AAPM report 6 in contrast to the Monroe-Williamson analysis which used the old TG43 dosecalculation formalism. 9he mean administered-to-prescribed dose ratio, ͑D t ͒ Rx Tx , is given by where t and tЈ refer to the past time in question and current time, respectively; ͑D t ͒ Rx Tx denotes the administered-toprescribed dose ratio for time t, and D͑r ៝͒ denotes the calcu- lated dose at position r ៝ in an implant.The bracketed quantity, ͗X͘, denotes the result of spatially averaging the indicated quantity over the appropriate region within the planning target volume ͑PTV͒ of a typical implant.Various approaches to spatial averaging are discussed in the following.The quantity D t ref ͑r ៝͒ denotes the administered dose at location r ៝, or dose actually delivered, during the period t as approximated by the selected reference dosimetry parameters.Reference parameters are those considered, based upon current knowledge, to provide the most accurate and physically rigorous method of retrospectively and prospectively calculating dose in an implant.The quantity D t Rx ͑r ៝͒ denotes the corresponding prescribed dose derived from the dosimetry parameters in use at time t.The last factor on the right of Eq. ͑3͒ is the ratio of "true" air-kerma strength ͑S K,N99 as implemented by Theragenics after March 2001 or as implemented in January 1999 for Model 6711 sources͒ to the source-strength standard, S K,t , accepted as definitive during the time period t for seeds of identical physical construction emitting identical quantities of radiation.Assuming that the new TG-43 report was implemented at time t TG43U1 Ͼ 3 / 04, Eq. ͑3͒ can be used to derive the prescribed dose, D t Ј Ͼt TG43U1

Rx
, for use with the reference dosimetry parameters and the current air-kerma strength standard that ensures that patients will continue to receive the same delivered dose ͑as estimated by retrospective application of reference dosimetry parameters͒ as otherwise identical patients planned with "t-era" dose distributions, source strength standards, and prescribed doses: Hence where D t Rx is the prescribed dose ͑in units of Gy͒ and the arguments to the right of the vertical line indicate the dosimetric data and S K standard used for treatment planning used at time t.Generally, the clinical goal is to reproduce the clinical outcomes of a previously treated group of patients in the face of significant dose-calculation and source-strength standard revisions.Obviously, it is necessary to carefully match the prescribed dose, dose-calculation formalism and parameters, and S K standardization procedures to the clinical experience one is trying to duplicate.In the sections to follow, each factor of Eq. ͑3͒, along with its method of evaluation, will be defined.

C. Air-kerma strength standard revisions
The air-kerma strength ratios, S K,t / S K,N99 , used in the analysis of 103

D. Reference dosimetry parameters
For the currently available "light" seed, the parameters recommended by the TG-43 2004 update 6 were used.The radial dose function, g L,04D ͑r͒, recommended therein was derived from the Monte Carlo study by Monroe and Williamson. 7The function g L,04D ͑r͒ was defined over the distance range 0.1-10 cm and the 1D anisotropy function, an,04D ͑r͒, over the distance range 0.25 to 10 cm.The recommended dose rate constant, ⌳ 04D,N99S , was obtained by averaging the measured value 3 ͑corrected for the 1999 anomaly in S K,N99 ͒ with the corresponding Monte Carlo estimate. 7These data are summarized in Table I.
For the "heavy" seed, the 2004 TG-43 report makes no recommendations regarding dosimetry parameters.The relative Monte Carlo data by Monroe and Williamson 7 are assumed, an approach consistent with the AAPM consensus data-formation methodology.This methodology offers two choices for estimating the consensus heavy seed dose-rate constant: ͑i͒ average the Monroe-Williamson Monte Carlo value ͑⌳ 02D,N99S MC = 0.694͒ with the average of the Chiu-Tsao 16 and Meigooni 15 measurements ͑⌳ ¯90D,N99S TLD = 0.650͒ or ͑ii͒ reject the experimental measurements as candidate data sets and use the Monte Carlo value without modification: ⌳ 04D,N99S = ⌳ 02D,N99S MC = 0.694.Because the Chiu-Tsao and Meigooni measurements were normalized to source-strength measurements that are not traceable to the current NIST S K standard and because these pioneering works do not adhere to modern standards of experimental dosimetry, 6 the AAPM believes that using the unmodified Monte Carlo dose-rate constant, i.e., option ͑ii͒, provides the least uncertain estimate of the heavy seed reference dose-rate constant consistent with the AAPM consensus-formation methodology.
Reference administered doses were calculated according to the 1D dose calculation formalism recommended by the 2004 TG-43 report ͑Eq.͑11͔͒͒. 6For a single seed, the reference dose rate, D ˙t ref ͑r ៝͒, is given by

͑6͒
Equation ͑6͒ was implemented on a commercial treatment planning system ͑VariSeed Planning Workstaion, Version 7.1, Varian Medical Corporation, Inc., Palo Alto, CA͒ for permanent seed implants.However, this treatment planning system, like many others, does not support the implementation of Eq. ͑6͒ since it allows only the point-source geometry function to be used in its implementation of the 1D TG43 formalism.PEBD notes that this planning system, as well as many other commercial systems, would have supported implementation of the allowed but not recommended 1D formalism ͓Eq.͑10͒ of the 2004 TG-43 protocol, using G P ͑r͒ rather than G L ͑r , 0 ͔͒.This option closely approximates Eq. ͑6͒ although it is less accurate at small distances, e.g., r Ͻ 1 cm.To implement Eq. ͑6͒, it was necessary to "fool" the planning system's algorithm into performing the new calculations using the older point-source approximation by using dummy parameters.Essentially, the anisotropy constant can be folded into the radial dose function, creating a dummy radial dose function, gЈ͑r͒.This was accomplished as follows: where the primed quantities denote dummy parameters, listed in Table II, designed to reproduce the dose rates predicted by Eq. ͑6͒ down to distances of 0.1 cm using the point-source geometry function and the now-forbidden anisotropy constant.Letting r min be the smallest distance for which an,04D ͑r͒ is tabulated, these ratios are selected so as to force Eq. ͑7͒ to agree with the currently recommended model, Eq. ͑6͒, for each of the tabulated data entries.
For the case r ജ r min , this leads to the following equivalences: In the case of r Ͻ r min , we set Eq. ͑6͒ to the short-distance extrapolation formula found in Appendix C of the 2004 TG-43 report:

͑9͒
This leads to the following dummy parameter definition for r Ͻ r min :

͑10͒
To evaluate the dummy quantities defined by Eqs.͑8͒ and ͑10͒, the tabulated 1D anisotropy functions 6,7 were interpolated onto the finer radial dose function grid by applying linear interpolation to the quantity r 2 • G L ͑r , 0 ͒ • an,04D ͑r͒ and then converting the result back to an,04D ͑r͒.This procedure is based upon Williamson's approximation 18 ¯an Ϸ r 2 • G L ͑r , 0 ͒ • an,04D ͑r͒.The resultant values of gЈ͑r͒ and ¯an Ј are given in Table II.

E. Prescription dosimetry parameters
The prescribed dose-rate distribution, D ˙t Rx ͑r ៝͒, for all times other than t ജ t TG43U1 , was assumed to have been derived from the original TG43 point-source dose-calculation formalism: • g tD ͑r͒ • ¯an,tD Ј .

͑11͒
In the case of the future era t ജ t TG43U1 , D ˙t Rx ͑r͒ was evaluated using Eq.͑7͒, using both the dummy parameters given by Eqs.͑8͒ and ͑10͒, ͓the equivalent 1D dose calculation formula, Eq. ͑6͒, preferred by the 2004 TG-43 report͔, and the following parameters: ⌳ tD,XtS = ⌳ 04D,N99S , g tD ͑r͒ = g L,04D ͑r͒ and ¯an,tD Ј = ¯an,04D , where ¯an,04D Ј = 0.862. 7The latter option is equivalent to using the anisotropy constant-based 1D formalism given by Eq.D1 of the 2004 TG-43 report, a formalism widely used in the past but no longer endorsed by the AAPM.The dosimetric parameters assumed for various eras are summarized in Table I.This report assumes that 1995 TG-43 compatible parameters were used throughout the era 1988-2000 even though the TG-43 report was published in 1995, the same assumption made by the AAPM 2000 report. 1 The 1995 TG-43 report recommendations were based upon averaging the two measured dose-rate constants published at that time. 15,16Those readers who wish to duplicate a particular institutional implant experience based on pre-1995 implants should confirm that the prescription parameters assumed by this report are reasonable approximations to the institution's dose-calculation procedures.

F. Dose-averaging procedures
Three different approaches to evaluating ͗D t Rx ͑r ៝͒͘ and ͗D t ref ͑r ៝͒͘ were investigated by this report.In ascending order of complexity, these approaches are called "radial dose function equivalence approximation ͑RDA͒," "geometry function-weighted single-seed approximation ͑GFSA͒," and "clinical implant averaging ͑CIA͒."Each of these approaches will be described in turn.

"RDA…
The RDA approach has been used by most administeredto-prescribed dose ratio analyses published to date, including the AAPM 2000 Report 1 and the Monroe-Williamson article. 7RDA assumes that Eqs.͑6͒ and ͑11͒ yield equivalent dose-rate predictions and that g t ͑r͒Ϸg 95D ͑r͒.In addition, it ignores other subtleties such as errors arising from mixing G P ͑r͒ and g L ͑r͒ data in the same equation.Given these assumptions, mean dose ratio assumes a very simple form: For the Model 200 seed, using the data from

Geometry-function weighted single-seed approximation "GFSA…
The simple RDA approximation is not consistent with the 2004 TG-43 report guidance, which recommends using the 1D anisotropy function over the anisotropy constant.Nor does it account for the differences between g 95D ͑r͒ and g 04D ͑r͒ data recommended by the new report.To accommodate these changes, a generalized single-seed averaging procedure was explored, defined by where ͕r i ͖ i=1 N denotes the set of radial distances ജ1 cm for which g͑r͒ and an ͑r͒ are specified; G͑r i ͒ is the inverse square-law weighting factor; and f͑r͒ is the function to be averaged.The mean-dose ratio is then given by .

͑15͒
This approach is identical to that recommended in 2004 TG-43 report for estimating the now-forbidden anisotropy constant.It was found that ͗f͘ G͑r͒ was quite sensitive to the ͕r i ͖ i=1 N grid assumed.Hence all averages, both for planned and reference doses, were based on the choice ͕r i ͖ i=1 N = ͕1,1.5,2,2.5,3,3.5,4,5cm͖.
For the reference dose calculations, GFSA yields the following:

͑17͒
where t TG43U1 ജ 3 / 04 denotes the date on which the 2004 TG43 recommendations were implemented.

Clinical implant averaging
The most accurate and appropriate approach to dose averaging is to implement reference and prescription dosecalculation models on a brachytherapy treatment planning system using the geometry from typical clinical implants to assess the change in typical prescription parameters. 19This method is referred to as clinical implant averaging ͑CIA͒.To implement CIA, the seed geometry from four typical clinical 103 Pd implants was used.The implants consisted of prostate target volumes ranging from 22 to 46 cm 3 , prescribed D 90 doses ranging from 76 to 130 Gy, and 40-72 Model 200 103 Pd seeds implanted with a modified peripheral loading. 20urce positions and the prostate CTV contours were derived from x-ray CT examinations obtained 30 days following the implant.The planning system ͑VariSeed Planning Workstation, Version 7.1, Varian Medical Corporation, Inc., Palo Alto, CA͒ calculated dose on a ͑2 ϫ 2 ϫ 3͒ mm 3 grid using the "constant ͑point model͒" with the option "anisotropic correction" selected.The dose calculation was repeated using different dosimetric parameters for the various prescription and reference dose eras specified above.The source strength per seed was held constant for each simulation, using the S k,N99 /seed value assumed for the clinical treatment plan.Dose calculations were performed using the vendor's dosecalculation algorithm described by Eqs.͑7͒ and ͑11͒.In the case of the reference dosimetry calculations, the dummy parameters summarized in Table II were used, which yields doses equivalent to Eq. ͑6͒.
As our results ͑see Sec.III below͒ show that the mean dose ratio is constant within 1% for doses ranging from 0.25D 90 to 1.8D 90 , D 90 and D 60 were extracted from the resultant prostate DVHs for the four patients to derive the mean dose ratios recommended by this report: where XX denotes either 90% or 60% of the prostate volume, and D XX,i represents the corresponding DVH statistic from the ith sample implant.

A. Reference-to-prescription dose ratios for 103 Pd brachytherapy
Figure 1 illustrates the dependence of mean dose ratio, as evaluated by CIA, on the dose in multiples of D 90 for the implant having the largest volume.For all three primary comparisons of reference and prescription dosimetry parameters ͑the others can be obtained by scaling the graphs by the appropriate dose-rate constant ratio͒, the mean dose ratio is virtually constant between 0.5D 90 and 2D 90 , which includes the peripheral layers of the target most relevant to clinical dose prescription.Figure 2 shows the dependence of the dose ratio on spatial position in the transverse bisecting plane of the implant.As illustrated by Figs. 1 and 2, at doses below 0.25D 90 , the mean dose ratio increases.As the commercial planning system exports dose values as 16 bit integers scaled from zero to the maximum dose, this behavior arises from integer truncation.The uncertainty introduced by discretization of doses is less than 0.2% in the therapeutic dose range.Very near the seeds, Figs. 1 and 2 indicate that the dose ratios are much larger and more variable.The ͑D XX,i ͒ ref,t / ͑D XX,i ͒ Rx,t ratios were found to be nearly independent of the implant geometry, i, showing a maximum range of 0.001 over the four implants for both D 60 and D 90 .Table III compares the mean reference-to-prescribed dose ratios for the RDA, GFSA, and CIA averaging methods.With the exception of one case ͑comparison of ¯an -and an ͑r͒-based formalisms using 04D data͒, all estimates agree within 1.5%.Generally, the RDF approximation overestimates the CIA ͗D t ref ͑r ៝͒ / D t Rx ͑r ៝͒͘ value by about 1% while GFSA results in a 0.5% underestimate.For all cases, the D 90 and D 60 specification parameters produce virtually identical CIA estimates.However, in the ¯an vs an ͑r͒ formalism comparison case, the CIA dose-ratio estimate is 1.6% and 2% smaller than the RDA and GFSA estimates, respectively.Since the same dosimetry data are used by all three methods, the difference between GFSA and CIA must arise from the different formalisms, Eqs.͑6͒ and ͑11͒, used in the denominator and numerator, respectively, of these two methods.The discrepancy suggests that the r −2 weighting scheme for r ജ 1 cm gives a biased estimate of the average single-seed calculation distance characteristic of clinical implants.In the 1988-present comparisons, this effect could have been masked by differences in radial dose function in the prescription versus reference eras.While the discrepancies among these three methods are small in relation to the overall un-certainty of clinical dose calculation, it is prudent to recommend the clinical implant averaging technique for performing future assessments of this type.

B. Administered-to-prescribed dose ratios
The final ͑D t ͒ Rx Tx ratios recommended in this report, as estimated by the CIA technique, are listed in Table IV and plotted in Fig. 3, along with the corresponding values from the 2000 AAPM report 1 and the Monroe paper. 7In addition, the time-weighted average ͑D t ͒ Rx Tx ratios for the heavy seed ͑1988-1993͒ and pre-9/97 light seed ͑1993-1997͒ eras are tabulated.Compared to the 2000 AAPM report, the revised ratios for the heavy seed and pre-9/97 light seed eras are 3.8% and 7.1% smaller, respectively.Thus, a dose of 115 Gy prescribed in the periods 1988-1993 and 1993-1997 yields administered doses of 118 and 114 Gy, respectively, in contrast to the average administered dose of 124 Gy estimated by AAPM in 2000. 1 The revised 9 / 97 to 3 / 00 dose ratio is 7% smaller than that recommended by the 2000 Report, resulting in an administered dose of 124 Gy compared to 135 Gy.Using the revised dose ratios recommended by this re- port, a prescribed dose of 125 Gy 5 delivered during the 3 / 00 to 3 / 01 era ͑following WAFAC implementation by Theragenics but preceding correction for the 1999 NIST measurement anomalies͒, corresponds to a delivered dose of 116 Gy, which is 7% lower than the 2000 Report estimate.Following Theragenics' implementation of the corrected S K,N99 standard and the associated dose-rate constant adjustment in 3 / 01, this difference was reduced to a 4% underdose, i.e., 125 Gy prescribed corresponds to a delivery of 120 Gy.The major causes of these revised ratios are the 5.3% error caused by the 1999 NIST WAFAC anomaly for the Model 200 source ͑which was partially mitigated by the revision of the doserate constant from 0.665 to 0.68͒ and the adoption of revised 2D anisotropy functions, which resulted in a change in anisotropy constant from 0.90 to 0.862.These two changes were first evaluated by Monroe and Williamson 7 in 2002, but neither was anticipated by the 2000 report.For institutions that implement the revised TG43 formalism, Eq. ͑6͒, and associated dosimetry parameters 6 ͑next-to-last line, Table IV͒ without adjusting the prescribed dose, the delivered dose will increase by 4%, from 120 to 125 Gy.For those who implement the revised dosimetry parameters using the old TG43 1-D formalism, Eq. ͑11͒, the administered dose will increase by 1.7%, from 120 to 122 Gy ͑last line, Table IV͒.

C. 125 I Model 6711 source
As is the case with palladium, the history of iodine seed dosimetry is closely related to the history of a single seed model, the Amersham Model 6711 seed.It is well understood that the original prescribed dose of 160 Gy, used from 1985 until 1995, was based on dosimetry parameters 21 that were changed by the publication of the 1995 TG-43 report.The result was to change the prescribed dose to 144 Gy, 8 and from 1995 to the present, most institutions have followed this change.
The manufacturer of the 6711 seed did not adopt the NIST 1999 air-kerma standard through the transfer of a calibrated source, but instead mathematically implemented an adjustment of 0.897.Consequently, the NIST measurement anomaly ͑ϩ5.1% for the Model 6711 seed͒ of 1999 that affected the vendor calibrations of the Model 200 and many other source types did not influence Amersham calibrations of the Model 6711 seed.Therefore, only one transition was made in the determination of air-kerma strength of this seed; that of the introduction of the NIST 1999 standard.
It is recognized that the incorrect NIST 1999 standard was disseminated to the ADCLs, who may have passed it along to customers, who may then have adjusted the strengths of seeds delivered to them by the manufacturer, but this is not known with any certainty.Thus, this possibility is ignored for this analysis.
For the 6711 seed, an,04D ͑r͒ is almost constant from 1 to 5 cm, so that the anisotropy constant, ¯an,04D , 0.943, was used in a comparison of delivered doses via the RDA method.This value is slightly different from the value of 0.93 recommended by the 1995 TG-43 report. 9The differences among the 83D, 95D, and 04D radial dose functions are not large.The comparison of the RDA and GFSA doserate analyses in Table V shows that these errors influence the administered-to-prescribed dose ratios by at most 1%.
The 1995 TG-43 report recommended a dose rate constant of 0.88, which was mathematically modified to 0.98 in 1999, to accommodate implementation of the 1999 NIST standard. 8The 2004 TG-43 report further revises this value to 0.965, which almost exactly compensates for the changes in ¯an from 1995 to 2004.As a result, the changes in delivered dose from the introduction of the Model 6711 seed to the present have been less than 0.5% and can safely be ignored.These data are summarized in Table V.

IV. DISCUSSION AND CONCLUSIONS
The methodology for analyzing the impact of the implementation of new dose calculation parameters, formalism, and changes in source strength calibration standards, presented here, was developed originally by Dr. Williamson and Dr. Todor at Virginia Commonwealth University.Later, it was reviewed, reformulated, and incorporated into this report by the AAPM PEBD subcommittee.This document was reviewed and approved by the AAPM PEBD Subcommittee, Radiation Therapy Committee, and Science Council.Hence this report represents the official position of the AAPM on the recommendations for the impact of the implementation of 2004 TG-43 update on the dose delivered by interstitial brachytherapy sources.
For this analysis, we selected four typical prostate implants because the most popular application of interstitial brachytherapy continues to be organ-confined early stage prostate cancer.That the doses used in the actual treatment of the four patients differ from the commonly prescribed monotherapy dose of 125 Gy for 103 Pd prostate implants does not impact this analysis, since absolute source strength and dose do not influence the estimated dose ratios.Of the eight sources presented in the 2004 TG-43 update, our analysis considered only the 125 I Model 6711 source and 103 Pd Model 200 source because the vast majority of papers documenting the clinical efficacy of permanent prostate brachytherapy, representing decades of clinical experience, are based upon these sources.Brachytherapy of prostate cancer has become the treatment of choice for selected patients because of excellent rates of local control with minimal treatment related toxicity.With such a successful therapeutic option, it is critical that any changes in dose delivery techniques, including changes in dose calculation parameters and formalism, as well as procedures used in establishing source strength, should be analyzed critically in order not to compromise the therapeutic implant in potentially curable patient populations.This is the motivation behind this rather densely written and complex analysis.
As mentioned earlier, the 1999 NIST anomaly affected many interstitial brachytherapy sources, some by up to 7%.Although dose calculations for several source models were affected by 1999 WAFAC measurement anomalies comparable to or greater than those affecting the Model 200 seed, these sources are not considered by our analysis.Because these source models were relatively new products, any dosedelivery errors associated with their use are irrelevant to the interpretation and duplication of the published and evaluated clinical experience.As discussed in more detail in Sec.III C Model 6711 125 I vendor calibrations were not affected by the 1999 S K,N99 measurement anomaly.
Three different methods for evaluating the impact of dosimetry changes on prostate implants were employed.The RDA method is the simplest and the most clear intuitively in that the delivered doses will scale proportionally with the product of dose rate constant and the anisotropy constant provided the radial dose function is unchanged.Like the RDA method, the GFSA is also a single source method and uses inverse square-law ͑approximately͒ to weight the dose contributions at different distances.The most comprehensive method is the CIA method, which uses typical implant geometries for averaging the dose contributions from different distances and from many different sources.The next level calculational techniques, which can further enhance the evaluation of dosimetric impact, would be to use theoretical models of radiation induced cell killing ͑for example, Yue et al. 17 ͒.At this stage we feel that the CIA model is quite adequate for the analysis presented considering the lack of sensitivity of these calculation results to the method used.Even the simplest RDA method using the product of dose rate constant and anisotropy constant gives results within 2% of the results from CIA method.Thus, the analysis presented here is relatively insensitive to the choice of calculational technique.
Our analysis indicates that the full implementation of 2004 TG-43 report recommendations will have no significant impact on the 125 I dose prescriptions and dose delivered ͑less than 2%͒.However, for 103 Pd sources, there will be a systematic escalation of dose delivered by about 4.2% compared to current practice unless the prescribed doses are revised downward from 125 Gy.The radiation oncologist has three choices: ͑1͒ stay with the current dose prescription of 125 Gy and accept a 4% dose escalation; ͑2͒ decrease the prescribed dose to a round number of 120 Gy which will deliver doses very close to the current practice; or ͑3͒ decrease the prescribed dose to 115 Gy, which will restore future delivered doses to levels characteristic of pre-1997 delivery practices.Of course, radiation oncologists should also consider their own clinical techniques and experiences in terms of disease control and toxicity, which depend upon many procedural and technical details such as the choice of margins around the tumor volume, the loading pattern, number of needles used and patient selection for brachytherapy.For the sake of consistency at the national level, the AAPM recommends that the radiation oncology physician community review this report and make recommendations regarding the need for prescribed dose revision, if any, similar to the American Brachytherapy Society recommendations 5 published in response to the AAPM 2000 guidance. 1lthough we have focused on the dose prescription for prostate cancer only, the methods described here are applicable for implants at any other site.However, caution should be exercised in extrapolating the ͗D t   implants that differ significantly from the geometry of typical prostate volume implants, e.g., planar implants or eye plaques.In such cases, it may be prudent to re-evaluate the ͗D t ref ͑r ជ͒ / D t Rx ͑r ជ͒͘ ratio for the specific implant geometry in question.
Finally, it should be emphasized that the impact of the adoption of the 2004 AAPM TG-43 report recommendations is a systematic change that would affect all patients under treatment if adopted uniformly.Therefore, such systematic changes, even though they may appear small for an individual patient, especially considering the dose inhomogeneity within a tumor volume, can have a profound effect on the efficacy of a treatment regimen.Thus, a careful consideration of all clinical factors is necessary before making systematic changes in dose prescription and dose delivered by a thoughtless adoption of a new dosimetry protocol.

WHOM TO CONTACT FOR FURTHER ASSISTANCE
If you have questions regarding the recommendations of this report or implementing them in your clinic, please contact the Radiological Physics Center ͑RPC͒ at MD Anderson Cancer Center, Houston, TX at ͑713͒ 792-3226.

FIG. 1 .
FIG. 1. Plots of mean dose ratios, ͗D t ref ͑r ៝͒ / D t Rx ͑r ៝͒͘ and corresponding standard deviation as a function of reference dose in units of D 90 for sample clinical implant No. 1.The means and standard deviations are averages of the calculation-point dose ratios falling in dose bins with widths of approximately 12 Gy.The right upper and lower left graphs compare the 95D prescription dose parameters and formalism ͓Eq.͑11͔͒ to the heavy and light seed reference ͑04D͒ dose parameters, respectively.The upper left graph compares the anisotropy constant prescription formalism ͑D1 of 2004 TG-43͒ to the Eq.͑11͒ reference dose formalism using 04D parameters in both cases.

FIG. 3 .
FIG. 3. Plot illustrating the variation of the delivered dose for prescribed doses of 115 and 125 Gy as a function of time for the Model 200 103 Pd source.After 2000, delivered doses are plotted for prescribed doses of 115 Gy ͑solid line͒ and 125 Gy ͑broken line͒.For illustration only, we have assumed t TG43U1 = 7 / 05.For post-t TG43U1 implants, the plot assumes that the AAPM preferred 1D dose-calculation model is used ͓Eq.͑6͔͒.

a
Current analysis, using RDA method.

TABLE I .
Prescription and reference dose calculation parameters for the model 200 103 Pd Source.t TG43U1 Ͼ March 2004 denotes the date on which the revised TG-43 recommendations were implemented.

TABLE II .
Dummy TG-43 dose calculation parameters for the Model 200 Pd-103 source.

TABLE IV .
Ratios of administered-to-prescribed dose, ͑D t ͒ Rx Tx , as a function of year t and dosimetry data tD for 103 Pd Implants.Bold indicates current analysis, using CIA D 90 values.t TG43U1 Ͼ March 2004 denotes the date on which the revised TG-43 recommendations were implemented.S K,N99 ͗D͑r ៝͒͘ x ref ր ͗D͑r ៝͒͘ x Rx elevated by seed model-dependent factors of up to 7%, relative to measurements performed before and after this period.Many models of 125 I and 103 Pd sources were unfortunately affected by this anomaly.For the Model 200 source, the S K,N99 measurements were elevated by 5.3% during this period ͑see Appendix A, Sec. 6, and Appendix B, Sec.2.3 of the TG-43 2004 update 6 ͒.Unfortunately, the AAPM 2000 1 recommendations were based upon these erroneous measurements.This measurement error was corrected by NIST in the first quarter of 2000.

TABLE V .
Ratios of administered-to-prescribed dose,Rx Tx, as a function of year t and dosimetry data tD for 125 I implants.Bold indicates current analysis, using GFSA method.